Copyright, i Besa Xhaferi 2013

Copyright,
i
Besa Xhaferi
2013
1
Udhёheqёsi i Besa Xhaferi, vёrteton se ky ёshtё version i miratuar i disertacionit tё
mёposhtёm:
PRODUCTION FUNCTION OF FIRMS IN TRANSITION:
EMPIRICAL EVIDENCE FROM ALBANIA AND
MACEDONIA
Prof.Dr. Mit‟hat Mema
2
PRODUCTION FUNCTION OF FIRMS IN TRANSITION:
EMPIRICAL EVIDENCE FROM ALBANIA AND
MACEDONIA
Pёrgatitur nga: MSc. Besa Xhaferi
“Disertacioni i paraqitur nё
Fakultetin e Biznesit
Universiteti “Aleksandёr Moisu” Durrёs
Nё pёrputhje tё plotё
Me kёrkesat
Pёr gradёn “Doktor”
Universiti “Aleksandёr Moisu” Durrёs
Tetor, 2013
3
ACKNOWLEDGMENTS
This thesis has benefited from the supportive attitude and insights of several people on
different grounds. First of all I would like to show my gratitude to Prof. Mit‟hat Mema
for the ongoing timely and critical comments. Then I wish to thank all professors who
taught on the Doctoral Studies in Economics who challenged my critical thinking and
significantly improved my knowledge of economics. Next, I wish to thank my parents
who showed unreserved support which enabled me to complete my degree. Finally I want
to thank to all my colleagues on the doctoral program from whom despite our differences,
I learnt a lot about our common language- the language of economics.
4
Deklaratё mbi origjinalitetin
Besa Xhaferi
Deklaroj se kjo tezë përfaqëson punën time origjinale dhe nuk kam përdorur burime të
tjera, përveç atyre të shkruajtura nëpërmjet citimeve.
Të gjitha të dhënat. Tabelat, figurat dhe citimet në tekst, të cilat janë riprodhuar prej
ndonjë burimi tjetër, duke përfshire edhe internetin, janë pranuar në mënyre eksplicide si
të tilla.
Jam i/ e vetëdijshme/shme se në rast të mospërputhjeve, Këshilli i Profesorëve të UAMDsë është i ngarkuar të më revokojë gradën “Doktor”, që më është dhënë mbi bazën e kësaj
teze, në përputhje me “Rregulloren e programeve të studimit të ciklit të tretë (Doktoratë)
të UAMD-së, neni 33, miratuar prej Senatit Akademik të UAMD-së me Vendimin nr. ,
datë ________
Durrës, më _________________
Firma
5
PЁRMBLEDHJE
Palёt kryesore tё interesuara nё produktivitetin dhe profitabilitetin e firmёs janё
punёtorёt, pronarёt dhe qeveria. Debati konsiston nё mёnyrёn si matet produktiviteti nё
kuptimin e varibalve dhe metodologjisё qё zbatohet nё vlerёsim. Qёllimi i kёtij studimi
ёshtё tё ofrojё prova mbi funksionin e prodhimit dhe produktivitetit pёr kompanitё nё
Shqipёri dhe Maqedoni.
Tё dhёnat e pёrdorura janё ato tё ofruara nga BEEPS pёr njё kampionё tё firmave nё
Shqipёri dhe Maqedoni, ndёrsa modelet e pёrdorura pёr vlerёsimn si
metoda e
katrorёve tё vegjёl dhe metoda e pёrgjasёsisё maksimale janё modele qё pёrshkruajnё
produktivitetin dhe funksionin e prodhimit Cobb-Douglas.
Studimet e produktivitetit mund ti ndajmё nё tre grupe: studime lidhur me pёrkufizimin e
produktivitetit, studime lidhur me faktorёt qё ndikojnё nё produktivitet dhe studime pёr
krahasimin e produktivitetit. Sugjerojmё se pёrkufizimi i inputeve dhe outputeve sё
bashku me metodologjinё e studimit janё thelbёsore nё interpretimin e rezultatteve si dhe
rekomandimit tё politikave pёrkatёse. Natyra e firmёs, struktura e tregut dhe financimi
janё pёrcaktues tё mundshёm tё inovacionit. Prurje tjetёr ёshtё se zgjerimi i mumdёsive
nё pёrdorimin e internetit rrit probabilitetin pёr tё pasur investime nё R&D. Sё fundi
arrijmё nё pёrfundimin se kompanitё nё kampionin e pёrdorur operojnё me tё ardhura
rritёse tё shkallёs.
Studimi paraqet kornizёn teorike pёr objektin e studimit dhe mbi metodologjinё e zbatuar
pёr provat e prezantuara. Kontribut themelor i studimit ёshtё paraqitja e provave pёr
pёrshkrimin e produktivitetit si dhe faktorёve qё influencojnё produktivitetin pёr vendet
nё tranzicion.
FJALЁ KYCE: elasticiteti i çmimit i faktorёve, funksioni i prodhimit, produktiviteti i
punёs, R&D
6
ABSTRACT
The main stakeholders in the productivity and profitability of the firm are the employees,
the owners and the government. Disputable is how to measure productivity in the sense
of variables used as proxies and the methodology used for estimation. The purpose of this
study is to provide evidence on production function and productivity for companies in
Albania and Macedonia
BEEPS data are used, and estimation methods are: OLS and MLE for models describing
productivity and a Cobb-Douglass production function for a sample data in Albania and
Macedonia.
Studies on productivity may be divided into three strands: Studies exploring the definition
of productivity, studies measuring factors that may influence productivity and
comparative studies on productivity. We suggest that definition of inputs and outputs as
well as the methodology we apply are crucial for interpretation and policy
recommendation. The nature of the firm, the structure of the market and financing are
possible determinants of innovation. Another finding is that having internet broadband
increases the probability to have an R&D investment. Last we find that companies in our
sample data operate with increasing returns to scale.
The study provides the theoretical background framework both for the issue discussed
and the estimation methodology used for the evidence provided. The main contribution to
the literature is providing evidence for describing productivity and also factors that
influence productivity for transition countries.
Key Words: Factor Price Elasticity, Production Function, Labor Productivity, R&D
7
TABLE OF CONTENTS:
List of figures: ................................................................................................................. 11
Table of tables: ................................................................................................................ 12
1.
INTRODUCTION ................................................................................................... 13
2. THEORETICAL FRAMEWORK ON RESEARCH AND MEASURMENT OF
PRODUCTIVITY ........................................................................................................... 17
2.1 INTRODUCTION..................................................................................................... 17
2.2. DEFINITION OF PRODUCTIVITY .................................................................... 18
2.2.1 MICRO AND MACRO PRODUCTIVITY ..................................................... 22
2.3. MEASURING PRODUCTIVITY, PROFITABILITY, PERFORMANCE,
INPUT, OUTPUT ........................................................................................................... 25
2.3.1 PRODUCTIVITY AS PERFORMANCE MEASURE ................................... 29
2.4 INDEX NUMBER STUDIES ............................................................................... 31
2.4.1 MALMQUIST INDEX ...................................................................................... 32
2.4.2. TORNQVIST INDEX ....................................................................................... 34
2.5
COBB DOUGLAS PRODUCTION FUNCTION ............................................. 36
2.6.
DISTANCE FUNCTION..................................................................................... 41
2.7.
DEA ANALYSIS .................................................................................................. 42
2.8. PRODUCTIVITY RELATIONSHIP WITH OTHER VARIABLES
(INNOVATION, R&D, IT, INSTITUTIONAL CHANGE) ....................................... 43
2.9.
COMPARATIVE STUDIES ............................................................................... 47
2.10.
2.11.
MORE ON PRODUCTIVITY .................................................................... 48
CONCLUSION ................................................................................................. 49
3. A DISCUSSION ON DATA AND METHODOLOGY: MLE AND COBBDOUGLAS MODEL SPECIFICATION ...................................................................... 50
3.1. INTRODUCTION.................................................................................................... 50
3.2. THE QUESTIONARE............................................................................................. 51
3.3. PANEL DATA .......................................................................................................... 51
3.4. VARIABLE DEFINITION ..................................................................................... 54
3.5. MODEL AND ESTIMATION DISCUSSION ...................................................... 58
3.5.1. LOGIT ESTIMATION ........................................................................................ 60
3.6. COBB- DOUGLAS PRODUCTION FUNCTION ............................................... 67
8
3.7. BUSSINESS CONSTRAINTS ............................................................................ 69
3.8. MAIN CHARACTERISITICS OF FIRMS........................................................... 71
3.9. CONCLUSION ........................................................................................................ 73
4. EVIDENCE ON FACTORS DESCRIBING PRODUCTIVITY AND
PRODUCTION FUNCTION ......................................................................................... 74
4.1.
INTRODUCTION................................................................................................ 74
4.2.
MODEL INTRODUCTION ............................................................................... 74
4.2. INNOVATION MODEL ......................................................................................... 76
4.3.
DEFINITION AND IMPROTANCE OF INNOVATION ............................... 76
4.4.
PREDICTORS OF INNOVATION ................................................................... 78
4.5.
R&D PREDICTORS ........................................................................................... 83
4.6.
THE R&D MODEL ............................................................................................. 85
4.7.
EVIDENCE ON PREDICTORS OF R&D........................................................ 85
4.8.
COBB- DOUGLAS ESTIMATION .................................................................. 87
4.9.
CONCLUSIONS .................................................................................................. 93
5. CONCLUSION, POLICY RECOMANDATION, LIMITATIONS AND
FUTURE RESEARCH ................................................................................................... 95
5.1 SUMMARY ON THE LITERATURE REVIEW .................................................. 95
5.2 POLICY RECOMANDATION ............................................................................... 96
5.3 MAIN CONCLUSIONS ........................................................................................... 97
5.4LIMITATIONS OF THE STUDY AND RECOMANDATIONS FOR FUTURE
RESEARCH .................................................................................................................... 99
APPENDIX .................................................................................................................... 101
A.1 LIST OF ABREVIATIONS .................................................................................. 101
A.2 SUMMARY OF LITERATURE REVIEW ......................................................... 102
A.3 DATASET QUESTIONS OF INTEREST/QUESTIONARE ............................ 107
A.4 SUMMARY STATISTICS OF THE QUESTIONARE: AFTER
CORRECTIONS ........................................................................................................... 110
A.5 SUMMARY STATISTICS OF VARIABLES ..................................................... 115
A.6 SUMMARY TABLE OF SUMMARY STATISTICS..................................... 117
A.7 NATURE OF DATA .............................................................................................. 118
A.8 ESTIMATION OUTPUTS .................................................................................... 119
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A.8.1 INNOVATION MODEL .................................................................................... 119
A.8.2 R&D MODEL ..................................................................................................... 122
A.8.3 COBB DOUGLAS ESTIMATION ................................................................... 125
A.8.4 ELASTICITY OF SUBSTITUTION OUTPUT ............................................... 129
REFERENCES .............................................................................................................. 130
10
List of figures:
Figure 1 Model of low productivity growth ................................................................................. 19
Figure 2 Productivity studies ......................................................................................................... 21
Figure 3 Overview of main productivity measures ....................................................................... 25
Figure 4 Performance measurement system .................................................................................. 26
Figure 5 Goal alignment model ..................................................................................................... 28
Figure 6 A framework for performance measurement system design .......................................... 30
Figure 7 Analytical framework of sources of growth.................................................................... 37
Figure 8 Knowledge production function...................................................................................... 39
Figure 9 Innovation and productivity ............................................................................................ 44
Figure 10 Superior performance principles ................................................................................... 45
Figure 11 Business constraints ...................................................................................................... 70
Figure 12 Business constraints ...................................................................................................... 70
Figure 13 Comparison of firm characteristic ................................................................................. 72
11
Table of tables:
Table 1 Variable Description......................................................................................................... 56
Table 2 Comparison of business constraints in descending order ................................................. 71
Table 3 Summary statistics............................................................................................................ 75
Table 4 Logit estimate ................................................................................................................... 80
Table 5 The marginal effect of logit estimate................................................................................ 81
Table 6 Estimation results- Macedonia and Albania (1) ............................................................... 82
Table 7 Estimation results- Macedonia and Albania (2) ............................................................... 83
Table 8 Logit estimate ................................................................................................................... 86
Table 9 Marginal effects................................................................................................................ 86
Table 10 Cobb-Douglas estimation ............................................................................................... 89
Table 11 Model estimation ............................................................................................................ 91
Table 12 Heteroscedascity corrected estimation, robust ............................................................... 91
Table 13 Estimating elasticity of substitution ............................................................................... 92
12
“All theory depends on assumptions which are not quite true. That is
what makes it theory. The art of successful theorizing is to make the
inevitable simplifying assumptions in such a way that the final results
are not very sensitive.” Solow (1956), p. 65.
1. INTRODUCTION
The interest of researchers in studying productivity and production functions dates from
the XIX century and is rising because of the acknowledged gains from working with
higher productivity both theoretically and empirically. Albeit the benefits, difficulties on
different grounds arise when measuring productivity. The long history of productivity
studies and the transition since the beginning till nowadays resulted with offering a menu
of alternatives of measurements. While measurement alternatives were proposed on the
other hand critics and remedial measures were developed in order to have a better
understanding on productivity. The rising interest hand in hand with the long history
contributed the fact that nowadays the scope of productivity studies widen ( in different
fields of economics) and deepen ( development of a range of models for estimation
purposes) in order to provide more reliable and accurate measures. Productivity itself can
take several meanings but the thesis attempts to analyze it in the production function
context in microeconomics level.
The focus of the thesis is to provide conceptual and methodological issues regarding
productivity measurement, identifying and providing evidence for factors contributing to
productivity growth. The thesis aims at estimating marginal labor productivity and
marginal capital productivity. The main focus of this thesis is to look at firm, industry
and market factors that drive productivity growth and estimation of elasticity‟s of
corresponding inputs.
The economies we are looking at have been centralized economies. Having a planned
economy and being centralized does not really help productivity. The literature on
productivity is not sparse but is limited for the scope of transition countries. Also there is
no general remedy how to employ unproductive inputs in productive or how to make
unproductive firms to turn in productive ones. In order to reach desirable productivity
results there should rather be multilevel changes in considerable aspect that will be
tangible to employees and employers. Academicians and researcher provide theories on
productivity, but in order to suggest policy recommendations these theories we need
measurement techniques and empirical evidence.
Since Smiths classification of labor in productive and unproductive in The Wealth of
Nations the insight of productivity in economics evolved and nowadays is extensively
used. Productivity assessments provide reflections regarding the performance of
individuals or business entities; utilization of resources and sustainability of business in
the long-run. We acknowledge that the literature on productivity is diverse and looking at
different aspects of productivity. Productivity may be discussed in the production
functions using inputs such as labour and capital. An alternative way of studying
productivity is looking at the cost function- the minimum cost to produce. And there is
duality between approaches.
13
Economists relate input and output since 1800 ( Levinsohn and Petrin, (2000)). Sandelin
(1976) notes that there are different dates regarding to the origins of Cobb-Douglas
production function and suggest that the origins go back in Wicksteed (1984) while it is
often stated that the origins date in Wicksell (1901). The very first estimation relating
input with outputs using least squares is in the study of Cobb (mathematician) and
Douglas (economist) and presented in the paper A theory of production in 1928.The
Cobb- Douglas production function is discussed widely on economic and econometric
grounds and yet is widely used for estimation purposes.
Since the Cobb-Douglas estimation till nowadays various studies empirically test
productivity. What they try to answer is what determines productivity and how to develop
more accurate techniques for measurement. But yet the researchers do not develop a
general road map of how productivity may be increased or incentivized because of the
complexity of the matter beginning from the numerous available definition of
productivity and followed by different estimation techniques. Consequently a large
importance on productivity studies is addressed to issues of measurement such as: how to
measure our variables of interest, check for the availability of the data, select the country
and firms of our interest and then use the quantitative methods for estimating our sample
of data. The purpose of the study is to asses relationships between factors driving
productivity and firm specific characteristics, market structure and business environment.
Transition countries are characterized with large number of small and medium size
companies because of their flexibility to change accordingly to changes in the market or
economy which on the other hand is typical for such countries. In this study the focus of
interest is for companies in two countries: Albania and Macedonia. The focus group of
companies are only SME for transition countries. Emerging market based countries such
as the case of Macedonia and Albania are looking at the development of SME‟s as one of
the key features for encacing the economic development of the country.
In order to provide empirical evidence we employ a sample generated from BEEPS (The
Business Environment and Enterprise Performance Survey) dataset and estimate with
regression analysis. The sample structure was selected using stratified random sampling
for the countries covered in the questionnaire except for Albania where frame blocks
enumeration was used. The questionnaire was accomplished by EBRD( European Bank
for Research and Development), World Bank and official sources in respective countries
and data collection was organized in two phases : in the first one eligible enterprises were
contacted , and after successfully contacted in the second phase face to face interviews
were conducted..The underlying model estimated in the thesis is Cobb-Douglas
production function in order to obtain input elasticity and estimate economies of scale.
Maximum likelihood estimation (MLE) is applied in the models for determining
predictors of factors that describe productivity.
This research contributes to the literature responding to the challenge of providing
evidence on two Candidate Countries for European Union, namely Albania and this study
is referred both to factors that may possibly determine productivity and to describing
productivity. The study aims to provide evidence for the hypothesis stated as follows:
 H1: companies in respective countries possibly do not operate at their minimum
cost
14
 H2:Labour market may be crucial for well-being of companies
 H3: structure of the market may influence determinants of productivity
 H4 : IT investment may describe factors determining productivity
The research on this study has some underlying assumptions:
 Assumption1: according to the fact that the targeted number of questionnaire has
been reached in the respective countries we assume that our sample data is a fair
representation;
 Assumption 2: taking under consideration that companies in both countries tend
to show similar characteristics and that countries share similarities we assume that
companies have identical production function;
 Assumption 3: following we assume that Cobb-Douglas production may describe
the company‟s‟ production function and its underlying assumptions hold ;
 Assumption 4: we assume that innovation and R&D are factors describing
productivity;
 Assumption 5: we assume that increasing labor productivity does not cause
Principle-Agent problem;
 Assumption 6: we assume that increasing labor productivity may increase the
company‟s productivity respectively a paradox of vanishing productivity from
individual level to firm level do not happen.
The structure of the thesis is as follows: the study begins with this introductory part and it
is followed by three chapters and finalized with a concluding chapter. Additionally
contains an appendix with more details about interested reader and the literature which
was helpful for the successful finishing of the study.
Productivity enhances growth in the macro level. The hypothesis is that the channel to
this are form a micro level: employee productivity lead to company productivity which
lead to better macroeconomic indicators – growth of the production frontier. Issues such
as theoretical grounds, micro foundations and literature review on the area of interest are
the focus of the first chapter: THEORETICAL FRAMEWORK ON RESEARCH AND
MEASURMENT OF PRODUCTIVITY. Thus the aim of this chapter is to review the
range of available studies regarding productivity measurement.
Chapter two concludes that the definition of variables and estimation methodology is
important. Analyzing the available datasets there are resulting difficulties in data that are
comparable to larger number of countries, measurement problems, defining problems.
Therefore a detailed overview of data, variables, characteristics of firms and estimation
methodology is discussed in the third chapter: A DISCUSSION ON DATA AND
METHODOLOGY: MLE AND COBB-DOUGLAS MODEL SPECIFICATION.
The results of the empirical evidence are estimated using regression analysis respectively
OLS and MLE for sample companies in Albania and Macedonia. The detailed evidence
and economic interpretation of results is the object of analysis in chapter four:
EVIDENCE ON FACTORS DESCRIBING PRODUCTIVITY AND PRODUCTION
FUNCTION. The main purpose of this chapter is to estimate the model in order to
provide empirical evidence for the conclusions of the study which will be presented in the
last chapter.
15
Summarizing the study contains three main chapters respectively, the second one is about
the literature review, the third one discusses data and methodology and the fourth chapter
provides estimation results. In the final chapter we summarize main findings and
conclusions of the study. Additionally we provide ideas and scope for future research that
may contribute to this field of interest and we offer some policy recommendations. The
limitations of the study are discussed in this last chapter: CONCLUSION, POLICY
RECOMANDATION, LIMITATIONS AND FUTURE RESEARCH.
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2. THEORETICAL FRAMEWORK ON RESEARCH AND
MEASURMENT OF PRODUCTIVITY
2.1 INTRODUCTION
Productivity studies are an important area for the employees, the owners and the
government. Productivity is a performance measure for any state of development since
productivity may enhance growth. Micro data in studying productivity are important in
different fields of economics: microeconomics, macroeconomics, labor economics,
international trade and industrial organization. We identify several approaches for
studying productivity: index number studies, production function, distance function and
DEA analysis. Besides different approaches for studying productivity we identify
different empirical approaches for estimation in the empirical evidence of productivity
studies and we notice that studies that use panel data are sparse. Concluding we suggest
that identification of drawbacks of the empirical estimation is crucial for deciding the
choice of empirical estimation.
The theoretical framework of the literature review on studies on productivity finds
different measures of productivity, input, and output used to study the nature and the
determinants of productivity. Therefore arrives the note that researches should be
cautious when proposing policies depending on the measurement of individual variables
used in the estimation process. Concluding the definition of variables used in the model
and the estimation methodology are crucial for the results we will obtain. There is a large
“menu” of methodologies used in productivity studies but this chapter aims looking at the
most common used methodologies such as: Index Numbers, Production Function,
Distance Function and DEA analysis. The problem of availability of data for large
samples and longer time periods is a limitation for conducting studies on productivity. In
order to address in detail to the question of interest the chapter suggests that micro- panel
dataset may be helpful in solving estimation and comparison problems resulting in
productivity studies.
The chapter tempts to answer how to define productivity, how it can be measured and
how can it be practiced. Looking at the literature review was crucial for finding that most
of definitions of productivity use input and output or simply define productivity as a
measure of translating inputs to output. This leads to another question how inputs and
outputs can be defined and are they always measurable? “Translating” inputs in outputs is
a process so there may not be straightforward answers. Productivity is not a matter of
only developing countries is a matter of any state of development.
The theoretical framework chapter is structured as follows: begins with the definition of
productivity in section 2.2; then follows with measurement issues in section 2.3. After
defining notions and identifying the measurement problems develops with specific
measures used in productivity studies such as: index number studies in 2.4; production
function studies in 2.5; distance function in 2.6; DEA analysis in 2.7. On the next section
the focus is on studies that correlate productivity with other variables in 2.8 and further
identifies comparative studies in 1.9. We end this chapter with our main conclusions.
17
2.2. DEFINITION OF PRODUCTIVITY
First we want to point out difference between physical and economical productivity. The
first one is about the quantity obtained by a unit of input whereas the latter is the value
obtained by a unit of input. If we are only interested in just one input ( being that labor or
capital) than we have to do with partial productivity for example labor productivity1 or
capital productivity, whereas if we are interested in aggregation of all the inputs used in
the production function than we are dealing with total factor productivity2. Thus, in the
process of productive translating of inputs in outputs, we may be interested in technology
that the company uses, the demand and the elasticity of the demand for the goods
produced the skills of the labor input and their respective learning curve. Thus in the firm
level being productive may be understood as incentivizing employees to work efficiently.
In the macro level studies on productivity we may be interested in GDP and employment.
While firms increase productivity there are three scenario possibilities:
 Increasing technological unemployment because of investment in technology;
 Increasing the employment because of more qualitative and more costly products;
 Ensure stability of employment by reacting with proportional changes.
This suggest us that just being productive itself does not mean that we will be able to
have straightforward benefits so any institutional change should be looked with caution.
While defining productivity as a ratio of output and inputs sounds simple the
measurement is complex.
The most common definition used for productivity is output per unit of input used. On the
basic principles of economics we are aware of the fact that input resources are scarce thus
it is very important to know how to utilize them efficiently.
According to Smith in “The wealth of nations‟‟ productivity is related to outcomes that
are fixed to tangible assets what is invested, while the outcome (the value) that is
consumed than that is unproductive. He explains this difference by dividing the labor in
two broad categories: productive and unproductive.
Sink and Smith (p. 136) use the following definition “Productivity is the relationship
between what comes out of the organizational system and what is consumed to create
those outputs”, while “profitability measures the relationship between revenues and
costs” (p.137).
Buccola and Steve (2008) review three frameworks to study productivity : Dynamic
framework, Distance function framework and Price-induced innovation framework and
conclude that since three approaches have different motives it is difficult to make
comparisons between them and suggest that the three approaches can bridge the gaps that
makes them have dissimilarities.
Oyeranti note that misconception about productivity are made
 when productivity is related only to labor productivity
 Productivity is not same with increase in performance.
 Cutting cost does not mean increasing productivity
1
2
We will abbreviate it as LP in the rest of the text
We will abbreviate it as TFP in the rest of the text
18
Accordingly productivity simultaneously considers effectiveness and efficiency.
Scot (1985) model low productivity traps as shown in the figure below:
Low productivity growth
(compared with input
prices especially labour and
energy
Lagging capital
formation ( and
insufficient capitallabor ratio
Rising prices
domestic and
export goods
Rising unit (labour
and energy) cost
Lower utilization of
domestic plant
capacity
Sluggish sales (in
domestic and forign
markets)
Figure 1 Model of low productivity growth
Source: Scott, 1985, p.8
The importance of research on productivity is outlined in Mawson et al. (2003). They
refer to productivity as the economy‟s ability to translate inputs in outputs and different
types of inputs give various measures of productivity. They point the difference between
partial productivity and total factor productivity. When productivity is measured, usually
growth and not levels are measured. They summarize approaches to measuring
productivity:
19
1.
The growth accounting approach ( assumes that technology is separable; constant
returns to scale; producers behave efficiently; perfect competition) The TFP is
the residual of Cobb Douglas production function;
2.
The index number approach (TFP index is calculated straightforward as a ratio of
output index and input index. The issue here is which index to choose:
Laspeyres, Paasche, Fisher, Tornqvist index);
3.
Distance function approach (how close the output vector is to the production
function given the input vector. If the economy is in the production frontier the
distance will take value of 1, when it is below the frontier the value will be below
1. To construct Malmquist productivity index we need the production frontiers
with constant returns to scale that show the technology available in two periods
and information on input/output combinations in the two periods. We calculate
two distance functions which will take values between 0 and 1 and describe the
relative efficiency, how close was output to the production frontier;
4.
Econometric approach (incorporates estimating parameters of a specified
production function and gains information on full representation.
Researchers have used different techniques to measure productivity in New Zeeland such
as OLS (Razzak, 2002); growth accounting approach and peak-to peak- approach (Mc
Lellan, 2001); chained Fisher index (Diewert and Lawrence 1999) and they provide
different productivity measures as outlined in Mawson et al. (2003) in their literature
review. Thus there is a large “menu” of alternatives in the research of productivity but
this has the problem of choosing which alternative is most appropriate since they provide
different measures. They explain that differences in measures may be due to different
measures of inputs and output. For example capital may be measured as gross capital
stock or net capital stock. Usually researches use own estimates of capital even when data
are available. As considered to labor input it may be measured as total number of
employees, full time equivalent or number of hours worked. While measures of output
may be gross output or value added measures. They conclude that differences in
productivity measures in New Zealand are due to different methodologies, different time
and different industries used in the studies. Looking at the conclusions of this study, we
are aware that we should be careful with the interpretation of the data, and add to our
results detailed explanation of the sample selection, time, measures of variables used and
the methodology used.
Despite the variety of research and the methodology used in productivity research, still
remains a field of interest. The micro data used in productivity studies are important for
different fields of economics such as microeconomics, macroeconomics, labor
economics, international trade, industrial organization.
Another study that reviews the literature on productivity in industrialized countries can be
found in Barteslamn and Doms (2000). They discuss two groups of studies: studies
describing productivity and studies describing factors that influence productivity growth.
They illustrate the story behind the group of studies as shown below:
20
Firm choices



Market interaction
Innovative
activity
Input choices
Product output


Competition
type
Market share
Aggregate
Productivity
Figure 2 Productivity studies
Source: Barteslamn and Doms (2000), p.3
They underline four reasons why productivity studies are important:
1.
2.
3.
4.
The dispersion of productivity is large;
Productive firms today are more prone to be productive tomorrow;
Resource reallocation attributes to aggregate productivity;
Quantifying Schumpeterian idea of creative destruction.
The micro longitudinal data have helped to improve empirical problems. Barteslamn and
Doms (2000) discuss the aggregation problem for input and input in longitudinal data and
simple measures cannot be used. The data on output use deflators which when do not
capture quality may result in downward bias for productivity. Researches use as measure
of output: physical output or gross production. Vector of outputs and inputs may be used
to measure TFP. Estimating a cost function and factor demand is another method of
computing productivity index. They review Oley and Pakes (1996) method: “by inverting
the investment function, one can estimate the unobserved productivity component semiparametrically as a function of investment” p.10. They mention problems of no ideal
dataset, problems of measuring inputs and outputs and the quality of data obtained is
unknown. In their literature review they note some stylized facts on productivity:
1. There is heterogeneity between firms and establishments in productivity.
Measuring the degree of dispersion in productivity: how much reflects differences
among firms and how much is measurement error;
2. Theoretical models and assumptions underlying them vary;
3. Changes in distribution over time have been estimated using parametric and
nonparametric methods;
4. The variance of productivity increases once they allow entry and exit;
5. Whether productivity moves procyclically with output.
Incentive theory as a source of productivity is discussed in Lazear (2000).; “Hourly
wages that are coupled with some minimum standard could be called performance pay
because an output based performance standard must be met to retain
employment”(Lazear, 2000, p. 1347). He analyses the effects of shifting from hourly
wage to performance wage. Performance pay plan does not work equally for all workers
because of different preferences they face. Some workers will be incentivized to work
more and get paid more than the guaranteed wage. The performance indicator they use is
units-per worker- per day, which results to be 20% higher under the performance pay
21
than hourly wage and the variance in output also goes up. Thus this may indicate also that
profitability may increase as a result of the switch. Their result suggests productivity is as
a result of incentive effect. Also the results do not show a Hawthorne effect since the
initial effect of log productivity as a result of the change in payment increases after 1
year. As a result of the switch in the pay the turnover is higher; which may indicate that
the less productive workers leave. But the increase in the ability is not as a consequence
of the switch but as a result of selection of workers- high ability workers tend to choose
performance paid jobs. Their results suggest that as a result of the switch the productivity
rose by 44% and the wages increased for 7% which may also result with higher firm
earnings. They discuss what happens to quality of work. Because of peer control and
easily identifiable defective work (employee), and since the employee who was
responsible for the work had to do the re-work, it has shown that quality of work has
improved after the switch of the pay. Also the customer satisfaction index rose. Their
conclusion is that in this case of this specific firm the switch results with higher
productivity but this does not mean that the conclusions should be general for all the
forms. Just is an evidence that workers react according to incentivize theory.
Pritchard et al. (2008) use meta-analysis for the impact of the productivity system. Their
conclusion is that PROMES have induced productivity improvements reflecting that
potential is underutilized. According to their analysis the result is that this improvement
does last over time, and in different settings. They use 83 studies from PROMES
database with dependent variable productivity improvement. They conduct WLS
regression and bivariate correlation to examine the relationship between moderators and
continuous variables and find quite similar results with both of them. Referring to their
results overall effectiveness scores improved and the effect size were large, the
improvement lasts over time, in different categorical settings (different countries,
organization type, job types, and organization with different functions) with variability in
each subgroup. Factors that may influence effectiveness of intervention are:
 Positively related: quality of feedback meeting was positively strongly related to
effect size,
 Negatively related: level of changes in the feedback system was negatively
related, amount of price feedback, interdependence.
2.2.1 MICRO AND MACRO PRODUCTIVITY
In the literature review we find studies that look at the productivity issue in micro and
macro level. The difference is that micro studies look at the micro level firm data; while
macro studies look at the macroeconomic indicators such as GDP, employment, capital,
investments. The main point is that the macro level studies reference that further studies
should be done using micro level data and disaggregating productivity. The general
conclusion that we may draw from the literature review is that productivity is likely to
generate desired results for the stakeholders and therefore should be a goal for firms and
countries. What we want to point out that we still do not know what the optimal
productivity ratio will be and how that can be measures? The issue we want to raise is
based on the main definition on productivity which we mentioned on the first part. So if
increasing productivity is desirable we may just increase it by increasing the quantity of
22
inputs. But is that optimal? Or, maybe we want an increase in productivity that will be
conditional on the quality improvement of inputs and not the quantity.
Growth and determinants of growth are focus of policymakers. Since the Solow model
and the results suggesting that investment leads to growth researches have focused of
analyzing the role of investment and capital accumulation and how it can enhance
growth.
According to Solow, growth is attributed to technological change. Also
according to him the effect of investment is transitory.
Solow (1957) represents the production function: the output as a function of labor and
capital inputs and time that allows technical change. He aggregates all the changes in the
production function in the notion technical change. He assumes that inputs are rewarded
the marginal products. As a measure of output he uses GNP. He uses Glodsmith
calculation of capital but notes that the measurement of capital is arguable since what
matters in the production function is the capital in use not the capital in place. Their result
show that there is increase in GNP and only 1/7 part is attributable to increased capital
intensity while the other part to technical efficiency. He refers to the major part of
increased GNP as a result of increased productivity. He assumes a linear production
function and constant returns to scale. They try to fit their data and find that the CobbDouglas and semi logarithmic form are a bit better than others. He segregates the shifts in
the production function and movements along the production function. For their
estimation on data on American economy, he concludes that technical change was neutral
on average, there was an upward shift in the production function and the increase was
attributable to technical change (87.5%) and increase in capital input (12.5%).
Arnold, Bassanini and Scarpetta (2007) use a sample of OECD countries for the time
period 1971-2004 and test the Solow and Lucas model. They use pooled mean approach.
According to their estimates they do not reject the hypothesis that Lucas model is better
representation for CRS, also the convergence parameter is inconsistent with Solow
model. They perform Wald test and the result is that Solow model is rejected by the data
whereas Lucas model is never rejected. They also estimate excluding countries one by
one, and again even in their restricted sample the results are not inconsistent with Lucas
CRS. Even when they check for endogeneity problem still the results are in favor of
Uzawa-Lucas model. They give evidence in favor of Lucas model i.e. human capital has
persistent impact on GDP growth or with the model of endogenous growth. Moreover
their results are consistent and robust to different robustness tests and suggesting that the
growth in OECD countries for the time period 1971-2004 is endogenous.
Contrarily to Solow, Temple (1998) using three sample OECD countries (than divides it
in developing and industrialized countries), find that share of equipment is higher than
Solow prediction and share of structures lower. His results suggest that equipment
investment is important in developing countries and also test and suggest that their result
is not due to simultaneity bias, nor by measurement error bias. The estimation is robust
and not driven by outliers.
Douglas (1992) test the Solow model for the states for the time period 1973-1986 using a
single cross section data, and they use non-linear least square for their estimates. Their
estimate is evidence in favor of Solow model; therefore suggesting that investment,
human capital, labor, technological progress is important for growth.
23
Bernard and Jones (1996) measure labor productivity3 and total factor productivity and
suggest that less productive countries catch up more productive countries i.e. countries in
the 70s and 80s converge. They suggest that lagged gaps measure the degree of catch up.
They use ISDB dataset for 14 OECD countries and six sectors. Their measure of
productivity is value added per worker and a Divisa-Tornquist multifactor productivity
growth rates. The dataset provides with data on GDP, employment and capital. The
standard total factor productivity is measured using a Cobb –Douglass production
function. Their data show productivity is heterogenic across countries and industries.
Their results underline the role of capital accumulation in changes in labor productivity.
They test for β convergence for labor productivity and find that some industries converge
(services, construction and EGW) and other industries do not converge (manufacturing,
mining and agriculture). As regarded to total factor productivity they find convergence in
services, agriculture, EGW while mining, construction and manufacturing do not show
evidence of convergence. They also measure σ convergence where services and EGW
show catch up while evidence for other industries related to labor productivity is less
clear cut and the results do not change even when they try to remove USA form the
sample. While the convergence for total factor productivity result again in services,
agriculture and EGW and there is no convergence in manufacturing. These results
suggest convergence at aggregate level while the manufacturing sector shows divergence
which is contrary to the evidence from Dollar and Wolf (1993). They show that, in the
Cobb- Douglas model, the measure of technology (Hicks neutral measure of TFP) is
incomplete and comparisons between countries may be misleading. Since productivity
varies both from the measure of technology and input exponents in order to capture this
they introduce the total technological progress (TTP) measure- the output produced by
countries using same inputs. The problem with this measure is that it assumes same
capital /labor ratio among countries- if this changes the measure may change rank. The
TFP measure ignores that technology may change across country which is not the case
with TTP. They suggest that answering which country is more productive depends on the
capital/labor ratio we use. They check for robustness and estimate β convergence for TTP
but the conclusions do not change from TFP measures. They use different measures of
multifactor productivity and still they find aggregate convergence in productivity in
countries in their sample but no evidence for convergence in manufacturing sector. They
also check whether this results in manufacturing are due to labor measure as workers and
not as hours worked but even than there is little or no evidence that manufacturing sector
converges. They test whether their results may be due to PPP deflator used so they
estimate again using 1970, 1975 and 1985 PPP and again they find robust results with the
previous ones.
Authors and researchers address productivity in micro and macro aspect. Mainly they use
a production function which combines inputs such as labor and capital in producing
outputs. Most of macroeconomic studies finish noting the limitations on macroeconomic
studies and suggesting micro studies to capture the channels to which business climate
enhances growth (Durlauf et al., 2008; Straub (2008); Pande and Udry (2005)).
3
Output per worker measure
24
2.3.
MEASURING PRODUCTIVITY, PROFITABILITY,
PERFORMANCE, INPUT, OUTPUT
Measurement issues are very important generally and in measuring productivity
specifically. Is what we call the increase in productivity the increase in the quantity of
inputs or the quality of inputs? If we are measuring the ratio of output and only one
particular input we are measuring partial productivity while if we are measuring the ratio
of output and all inputs than we are measuring total factor productivity. While if we use
TFP we are sure that every input is included we cannot answer to what factor the change
in productivity may be addressed to. All of them are measures of productivity but we
should be careful when choosing the measure according to the question we are interested
in to answer. Another measurement issue that needs to be clarified is whether we are
using level productivity or growth of productivity. If we are measuring growth
accounting we are decomposing the growth of output in its potential components. Going
back again at the productivity definition we know that the first thing for measurement
issue is how to measure output and input. The problem that may arise with output is when
output is not homogenous, and this brings the question of how to aggregate the data.
Regarded to input most commonly inputs used are labor and capital, the latter may be
more problematic to measure. Even after we solve all these issues still remains the
problem of choosing the econometric method for modeling and estimating an issue which
is not the focus of this part, but will be discussed in the next sections.
„‟ Broadly, productivity measures can be classified as single factor productivity measures
(relating a measure of output to a single measure of input) or multi-factor productivity
measures (relating a measure of output to a bundle of inputs)‟‟ Schreyer (2001, OECD
p.38.). He overviews the productivity measures in the following table:
Type of input measure
Type of
output
measure
Capital&labor
Labour
Capital
Gross
output
Labour
productivity
(based on gross
output)
Capital
productivity (based
on gross output)
Capital-labour
MFP (based on
gross output)
Value
added
Labour
productivity
(based on value
added)
Capital
productivity (based
on value added)
Capital-labour
MFP (based on
value added)
Single factor productivity measures
Capital, labor&
intermediate inputs
(energy, materials,
services)
KLEMS multifactor productivity
Multi-factor productivity (MFP)
measures
Figure 3 Overview of main productivity measures
Source: Schreyer (2001), p.39
25
He suggests that labor input is better measured with working hours and capital by total
machine hours and adds that “Multi-factor productivity measurement and growth
accounting helps disentangle the direct growth contributions of labour, capital,
intermediate inputs and technology” p. 48 .
De Toni and Tonchia (2001) use a sample of medium and large sized Italian
manufacturing firms. They use test-retest method and Cronbachs α. They outline the
interest in studying Performance measurement system. They indicate three structures of
models: vertical, horizontal and balanced. The firms that they analyze seem to have the
structure of frustum model. They outline cost performance dimension (cost /productivity)
and non –cost indicators (time, flexibility and quality). Illustratively they show the
framework for Performance measurement system:
Matrials &
Labour
PRODUCTION
COSTS
Machinery
COST
CAPITAL ( fixed and
working)
TOTAL
PRODUCTIVITY
SPECIFIC
INTERNAL
PERFORMANC
E MEASURES
PRODUCTION ( Labor
productivity, machinery
saturation, inventory&WIP
levy)
Run&setup times
Wait&Moves
time
System
timer
TIME
Supplying lead
times
Manufacturing lead
times
Distributionn lead
times
EXTERNAL
"NONCOST
"
Delivery
speed&Reliability
Produced
quality
FLEXIBILITY
Perceived
quality
QUALITY
In-bound
quality
Quality
costs
Figure 4 Performance measurement system
Source: De Toni and Tonchia (2001), fig.3. Framework for PMS measures
26
Time to
market
As shown in the figure they classify productivity as performance measure in the cost
group same as production cost while non-cost performance measures are time, flexibility
and quality.
Dean (1999) reviews the literature that deals with output measurement in service sector
data. According to the problems statistical agencies have answered improving the
Producer Price Index, increased the coverage of the service industries, introduced
geometric means indexes, and improved data on annual capital investment by asset
category, improved methods for measuring prices of computers. He suggests that despite
improvements there is still more to do for the data. Definition of output in the banking
sector may need improvement for example.
Crespi et al. (2006) discuss that output data are important for productivity but the
problem is their adjustment. Mainly industries use turnover as a measure of productivity.
They review the problems of productivity measurement in the service sector. They think
of services as intermediation activities for time and space. Their message is that service
sector data are problematic for productivity studies and suggest that better deflators
should be used.
Nordhaus (2000) provide data for measuring productivity using the income side instead
of using output side. They introduce the well measured output instead of GDP.
Comparing the BEA-output side and BLS- income side they both show increase in labor
productivity.
Chambers (1998) review mathematically input, output indicators. His indicators are
translation invariant and not homogenous of degree zero as Malmquist indexes. On the
other hand Dethier et al. (2008) propose a mathematical model for estimating TFP which
results in line with Schumpeterian view on productivity dispersion.
“Only by understanding the individual level of productivity, however, can practitioners
and researchers begin to build the theories and models that deal with the dysfunctions and
synergies that occur when individuals are grouped into work teams, departments,
organizational systems, and economies” (Measuring and managing individual
productivity- William Ruch p. 105). Ruch identifies couple of productivity linkages:







Direct
Indirect
Proportional
Unidirectional
Temporal
Stochastic
Nominal
He also identifies problems such as determining the unit of output and input whereas the
problem of determining inputs is in determining labor. Rusch builds a goal alignment
model when he suggests that business units are not goal driven but management drive.
27
Business Unit
Goals
Higher Level
Goals
Organizational
Goals
Individual
Measures
Business Unit
Measures
Organizational
Measures
Business Unit
Performance
Organizational
Performance
Gorup
Measures
Individual
Behaviour
Group
Behaviour
Figure 5 Goal alignment model
Source: Rusch, Goal Alignment model 5-2., p110
Five functions of productivity analysis identified by Rusch are:
1.
2.
3.
4.
5.
Define productivity and direct behavior;
Monitor performance and provide feedback;
Diagnose problems;
Facilitate planning and control;
Support innovation.
We add to these regulating industrial relations and suggesting government policies to
reach their targets. The measurement issue is very important because different
measurement definitions may lead us to different conclusions. In a company is very
important if the productivity measures align with respect to employees and the company
since if this does not hold may lead to Principle –agent problems.
Holzer (1988) uses data from EOPP of 3400 firms in the 80s. They estimate wage and
productivity equation using levels and changes as a function of variety of determinants.
They measure productivity in their questionnaire scoring it from 1 to 100. They use the
same independent variables for both productivity and wage and their corresponding
coefficients show which of the determinants are comparable. Their result shows that
positive effect of experience and tenure on productivity. Their results give evidence that
productivity scores are meaningful as measure of worker performance. Using
differentials in their equations they find that tenure and training have positive effects on
28
wage growth. Even in the wage change and productivity change they confirm that tenure
is positively linked with productivity and earnings, training also contribute to wage
growth and productivity growth.
Diewert (2008) revise measurement problems. In the input output model they note that
we need information on the outputs produced, but revenues should not include any
commodity taxes imposed on the industry whereas input costs should include taxes
imposed. Reasoning is since tax on revenues is not received from the firm as well taxes
on inputs are paid by companies. They note that this system misses information on
contracted labor and rented capital. They also note the problem of labor inputs since
hours worked differ, also workers skills differ therefore using the number of employees
it‟s not accurate. They claim that there are difficulties in measuring productivity.
2.3.1 PRODUCTIVITY AS PERFORMANCE MEASURE
We have seen the diversity in measurement and still we are questioning the causes for
heterogeneity of the firms. What are the impediments and what sources are opportunities
for firms? Maybe the answer will depend of the measures we are using and the
measurement methodology we are using. In the following section we will look at
different methodologies. Therefore we are questioning the causes for heterogeneity of
the firms. What are the impediments and what sources are opportunities for firms.
Dethier, Hirn and Straub in their paper provide a summary of empirical evidence on
performance. They claim that the literature review shows that most papers find
significant relationship between infrastructure indicators and firm performance. On the
other hand, Aaker and Jakobson (1987) demonstrated that systematic risk can impact the
profitability of the firm.
Stierwald (2009) aims to look at determinants of firm profitability. Their dependent
variable is the current profit rate and the data are for 961 Australian firms using IRESS
dataset. They use GLS random and fixed effects in their estimates. They apply first
differencing to correct for dynamic panel bias since GLS generates inconsistent
estimates. They use a productivity estimate using log-difference between predicted and
empirical cost and also control for firm level variables. Their GLS estimates with random
and fixed effect and corrected for bias result with similar results. Determinants of
profitability in their estimates are lagged profit rates, lagged productivity level and
persistence of high productivity. Therefore their results suggest that firms with higher
productivity and more profitable. Related to firm characteristics their results show that
size matter i.e. larger firms are more profitable, higher leveraged firms are more
profitable. Their analysis therefore e is in favor of firm effect model. The limitations of
the study are that they do not answer for how long is the effect of productivity on
profitability.
Neelu et al. (2005) reviews the literature in order to draw the importance of performance
measurement. They note the importance of quantifying efficiency and effectiveness of
action in this process. They reviewed performance measurement system in three levels:
(1) The individual performance measures;
29
(2) The set of performance measures – the performance measurement system as
an Entity; and
(3) The relationship between the performance measurement system and the
environment within which it operates.
Their framework is illustrated in the figure below:
Figure 6 A framework for performance measurement system design
Source: Neelu et al. (2005), p.1229
They specify that the literature is diverse and identify the need that performance
measures to be positioned in strategic context. They review a large body of literature. The
multiple dimensions of performance measurements that they revise are:
1)
2)
3)
4)
Related to quality;
Related to time;
Related to cost;
To flexibility.
They identify the ABC sorting system for generating more accurate product costs.
Productivity is also a performance measure. They suggest that companies should explore
the rationale of measures of performance. They suggest that an individual performance
measurement is included in the performance measurement system. Finally they identify:
1) Issues associated with individual measures of performance;
2) Issues associated with the performance measurement system as an entity;
3) Issues associated with the system and its environment.
30
Steindel and Stiroh (2001) review measures of labor productivity and total factor
productivity or the overall efficiency of transforming inputs in outputs. They draw the
difference between two concepts of output: value added (Gross- inputs (sales and input
should be deflated by price index) and gross output (Total value of sales; productivity
measured as sales per worker). Traditional source of productivity analysis is a production
function that relates labor productivity to capital, labor quality and total factor
productivity.
2.4 INDEX NUMBER STUDIES
We start this section first with mathematical definitions of some of the indexes that we
will use in the following parts.
Paasche‟s index number mathematically is expressed as:
𝑷𝟎𝟏 =
Equation 1
𝒑𝟏 𝒒𝟏
𝒑𝟎 𝒒𝟏
𝒙𝟏𝟎𝟎
Laspyre‟s price index number mathematically is expressed as:
𝑃01 =
Equation 2
𝑝1 𝑞0
𝑝0 𝑞0
𝑥100
While Fischer index is Pashces index and Laspyres index geometric mean or
mathematically expressed:
𝑷𝟎𝟏 = 𝑳 𝒙 𝑷
Equation 3
Substituting equation 1 and equation 2 in equation three we have the following:
Equation 4
𝑷𝟎𝟏 =
𝒑𝟏 𝒒𝟎
𝒑𝟎 𝒒𝟎
𝒙
𝒑𝟏 𝒒𝟏
𝒑𝟎 𝒒𝟏
𝒙 𝟏𝟎𝟎
“An index number represents the development of certain economic aggregates (such as
the total production of industry or turnover) over time. The index number abstracts from
the real values (e.g. the production of steel measured in tons) or the monetary values (e.g.
the turnover in a certain sector) and only reflects the change of such figures in
comparison with the value of the aggregate in a reference period.‟‟4 An index number is a
number which is used to measure the level of a certain phenomenon as compared to the
4
http://stats.oecd.org/glossary/detail.asp?ID=3750
31
level of the same phenomenon at some standard period.5“Index numbers are used to
measure the changes in some quantity which we cannot observe directly” (Bowly) Index
number measure changing effects that cannot be measured directly. Index numbers are
used for showing average changes.
For testing the adequacy of index numbers we may use different tests (unit test, time
reversal test, factor reversal test, circular test). We should be cautious with calculation
and interpretation of index numbers before drawing conclusions. When constructing
index numbers the best average that we can use is geometric average.
Diewert (1995) note that the competing approaches to index number are the test approach
and the economic approach. They show mathematically whether Selvanathan and Prasada
Rao new stochastic approach yield estimator of variance of Paasche and Laspeyeres
index. This would tell us how precise these indexes are. He criticize the test and
economic approach and concludes that they „‟ give a false sense of precision” p. 29.
Balk (2008) concludes that Fisher index, though is ideal, is not perfect and is inconsistent
in aggregation. „‟ The Fisher quantity index is an average of a Laspeyres index, which
values the quantity change for the ith item at pi0, and a Paasche index, which values its
quantity change at price pi1.‟‟ P.4 (Marshall B. Reinsdorf, W. Erwin Diewert & Christian
Ehemann, 2000)
Chambers (2008) note that measuring productivity requires stochastic measures. The
paper underlines 3 premises: 1. Accountability for the stochastic world; 2. no stochastic
productivity measurement should be a special case of stochastic productivity
measurement and 3 productivity measures should be computable from the available
market data. The stochastic Luenberger productivity indicator generalizes nostochoastic
indicators to stochastic. They note that in stochastic case we cannot compute the
productivity index even when we have information about the technology because this
indicator depends on output data which are not available ex ante. He suggests that the no
stochastic productivity indicators may be decomposed in two components: 1: true
productivity change and 2. Luck. Their measure of luck is the difference of nonstochatic
productivity indicator and productivity change:
𝛅
Equation 5 L𝐁𝐁 𝐭 + 𝟏, 𝐭 ≡ 𝟐
𝜹
𝒑𝒕+𝟏
𝒑𝒕
𝑬
+
𝟐
𝒘𝒕+𝟏 𝒈 𝒘𝒕 𝒈
𝐩𝐭+𝟏
𝐩𝐭
+ 𝐰𝐭 𝐠
𝐰 𝐭+𝟏 𝐠
𝐳 𝐭+𝟏 − 𝐳 𝐭 −
𝒛𝒕+𝟏 − 𝒛𝒕
He specifies stochastic productivity indicators and uses data to decompose the no
stochastic productivity indicator.
2.4.1 MALMQUIST INDEX
The theoretical grounds of the Malmquist index originate from 1953 from Sten
Malmquist who introduced this productivity index after whom is also named. The
5
Statistics For Management, p. 234
32
Malmquist index is often referred as productivity index has to do with the production
function or a function of maximum possible production using inputs (labour and capital).
The Malmquist index was introduced by Caveset et al. (1982). They assume that each
firm operates in the production function. They want to introduce a productivity index that
will allow us to compare two different firms either operating at the same year or in
different time periods. Their Malmquist input index is expressed as:
Equation 6 𝐐𝐤 (𝐱 𝐥 , 𝐱 𝐤 ) ≡
𝐃𝐤 (𝐲 𝐤 ,𝐱 𝐥 )
𝐃𝐤 (𝐲 𝐤 ,𝐱 𝐤 )
Their Malmquist input index is defined with respect to technology and output. They show
that the geometric averages of the Malmquist index result in Tornqvist index. The
translog distance function for the two firms is:
Equation 7 𝐥𝐧𝐡𝐬 𝐲, 𝐱 ≡ 𝛂𝐒𝟎 +
𝐈
𝐢=𝟏
𝛂𝐒𝐢 𝐥𝐧𝐲𝐢 +
𝟏
𝟐
𝐈
𝐢=𝟏
𝐍
𝐧=𝟏
𝐈
𝐣=𝟏
𝛃𝐒𝐧 𝐥𝐧𝐱 𝐧 +
𝛂𝐒𝐢𝐣 𝐥𝐧𝐲𝐣 𝐥𝐧𝐲𝐣 +
𝟏
𝟐
𝐍
𝐧=𝟏
𝐈
𝐢=𝟏
𝐍
𝐦=𝟏
𝐍
𝐧=𝟏
𝛃𝐒𝐧𝐦 𝐥𝐧𝐱 𝐧 𝐥𝐧𝐱 𝐦 +
𝛄𝟐𝐢𝐧 𝐥𝐧𝐲𝐢 𝐥𝐧𝐱 𝐧𝐣
They also assume cost minimizing behaviour of firms and that firms use positive amounts
of inputs. The Malmquist output index is expressed as:
Equation 8 𝐪𝐤 (𝐲 𝐥 , 𝐲 𝐤 ) ≡
𝐝𝐤 (𝐲 𝐥 ,𝐱 𝐤 )
𝐝𝐤 (𝐲 𝐤 ,𝐱 𝐤 )
The output index can be calculated as geometric mean without knowing technology
parameter if we assume profit maximizing behaviour. They identify two ways of
productivity index: the first if we are looking at the maximization of output – output
productivity index and another approach is minimizing the inputs- input productivity.
Their definition of output productivity index is:
Equation 9 𝐦𝐤 (𝐱 𝐥 , 𝐱 𝐤 , 𝐲 𝐥 , 𝐲 𝐤 ) ≡
𝐝𝐤 (𝐲 𝐥 ,𝐱 𝐥 )
𝐝𝐤 (𝐲 𝐤 ,𝐱 𝐤 )
While the input productivity index is defined as:
Equation 10 𝐌 𝐤 (𝐱 𝐥 , 𝐱 𝐤 , 𝐲 𝐥 , 𝐲 𝐤 ) ≡
𝐃𝐤 (𝐲 𝐤 ,𝐱 𝐤 )
𝐃𝐤 (𝐲 𝐥 ,𝐱 𝐥 )
Their conclusion is that the Tornqvist index is superlative to other indexes.
Fare et al. (1994) applied the theory of Malmquist index and they decomposed it in
efficiency change and technological change. The Malmquist index assumes CRS.
Grosskopf (2002) propose that decomposition of Malmquist index depends on the
question we are asking.
Ball et al. (2004) propose a measure of total factor productivity the Malmquist cost
productivity measure (MCP) within the cost framework. Their cost index is calculated
33
using an environmental activity analysis model for the farm sector. They are measuring
productivity in the presence of externalities.
Fare, Grosskopf and Margaritis (2008) employ Bennet–Bowley productivity index on US
agricultural sector using technology and distance production function. They show that
Luenberger indicator is a difference between directional distance functions and since find
a relationship between this indicator and Malmquist index.6 They use Bennet–Bowley
„approximation‟ of the Luenberger indicator in their time series data. They construct
Bennet–Bowley productivity indicator for the time period 1910-1990. R&D growth and
the Bennet–Bowley productivity indicator track each other in the most time period. They
use two outputs and for input data and the series result no stationary and also they cannot
reject the presence of a cointegrating relationship between the two series. According to
their result we cannot reject the hypothesis that productivity does not Granger cause
R&D while we reject the hypothesis that R&D does not Granger cause productivity
change. Summing up their results show that productivity growth may be addressed to
R&D expenditures.
Camanho and Dyson (2006) compare branches of Portuguese banks using the Malmquist
index while Dong-hyun Oh(2010) note that Malmquist-Luenberger is used for measuring
evaluation environment sensitive productivity growth at micro and macro level and
propose another index called global Malmquist-Luenberger index for measuring
productivity in 26 OECD countries for the time period 1990-2003. They use GDP as a
proxy for output, CO2 and SOx emissions as the proxies of the undesirable outputs while
labour force, capital and energy consumption as input. They obtain the data from Penn
World Table, the World Development Indicators website. They employ to tests: the
Wilcoxon test to test the null that measures are the same between indices and Kernel
density plots and the results are robust for the null test. They suggest that using GM and
GML generated different results. They suggest that productivity growth is mainly
addressed to technology change and not efficiency change.
2.4.2. TORNQVIST INDEX
The Tornqvist index is used for calculating multifactor productivity and is measures as
the geometric mean of growth of rates of inputs used. When calculating the Tornqvist
index the assumptions are that the firm operates under constant returns to scale and the
input factor are paid their marginal product. The geometric mean of Laspayers and
Pasches index is Fischer index.
Grifell-tatjé and Lovell (1998) introduce a generalized Malmquist productivity index
and express it as a ratio of Malmquist quantity index and Malmquist input quantity index
(it is defined relative to a reference technology satisfying constant returns to scale). They
note that: “It is the difference between the scale properties of these two quantity indexes
which permits the measurement of the contribution of scale economies to productivity
change” p7. They show that the Malmquist productivity index can be expressed as
34
Malmquist productivity index and a Malmquist scale index. They decompose the
Malmquist index in three parts technical change, technical efficiency and returns to scale.
Equation 11
Is the expression of their generalized Malmquist index where technical change and
technical efficiency are measured relative to variable returns to scale and there is a scale
effect that measures the change in scale efficiency relative to the period technology. They
use experimental data to test the accuracy of measuring productivity change and
productivity decomposition of five index : CCD Malmquist productivity index, Färe et al.
(1994)(FGNZ) productivity index, Ray and Desli (1997) (RD) productivity index, The
generalized Malmquist productivity index, Bjurek‟s Malmquist index and conclude that
RD and generalized index give accurate results for measurement and decomposition.
Some indexes are not accurate in measurement (CCD) while another index does not
decompose accurately (FGNZ). So if the purpose is only measuring or only decomposing
we can use more indexes. They demonstrate that the generalized Malmquist productivity
index is equal to the Törnqvist productivity index and therefore suggesting that we can
measure productivity index indirectly. They present a generalized productivity index
which is accurate measure of productivity growth even in scale economies and also
provides an accurate decomposition of productivity.
Resendorf et al. provide formulas for decomposition of the contribution of individual
changes to the Fishcer index and Tornqvist index. ”The Törnqvist index is a kind of
geometric mean (or “log change”) index.‟‟p.7 (Reinsdorf, Diewert and Ehemann,
(2000)).
Lawrence et al. (2006) outline that the value of a firm‟s gross return to capital may be
caused by growth in the size of the enterprise, improvements in productivity and price
changes. They note the Törnqvist index formula has the form of a (weighted) geometric
mean. They use the Törnqvist index formula in the form of a (weighted) geometric mean
price and quantity index because it is easily to decompose it as a product of sub-indexes,
because it can be justified by the axiomatic (or “test”) approach and because closely
approximates the Fisher Ideal index. They underline how the high productivity growth of
a telecommunication service was passed as a benefit to employees in form of higher real
wages (30 % of benefits from productivity), to consumers in form of lower prices (50%
of the benefits) and benefits for the owners (30 % of benefits from productivity). The gap
showing productivity growth was positive for all 11 years in their study except for 1985.
They are researching for Australian Telestra largest communication company. They
suggest that there are different groups of stakeholders that do benefit from productivity
growth and that are consumers, employees and owners.
35
2.5 COBB DOUGLAS PRODUCTION FUNCTION
The production function relates the amount of the output to the amount of input used – a
function that describes the technology. Following the literature we find that input-output
models may use deflated revenue as output or nominal sales as output.
Macroeconomic studies look at per capita income as a proxy for productivity, while labor
productivity is important both at micro and macro level studies. Productivity in the
research is discussed through production function through the relationship inputs-outputs.
Banda and Verdugo (2011) calculate MFP on manufacturing data in Mexico. They use
AIS data for the period 1993-2006. They use value added as a proxy for productivity and
use a Cobb Douglas production function. Their results suggest: „‟ the output elasticity of
capital is between 0.28 (with KLET) and 0.34 (with KL), whilst the elasticity of labour is
between 0.56 (with KLET) and 0.66 (with KL). These parameters are in line with those
used by others studies on MFP in the Mexican economy, assigning elasticity between
0.30 and 0.33 to capital, and for labour between 0.67 and 0.70 (see for instance, Faal
2005 and Bergoeing et al. 2002). Regarding the other factors, electricity‟s values are
between 0.06 and 0.07 and for transport between 0.10 and 0.11. „‟MFP explains output
growth between 58 and 69% and LP growth is explained by MFP 61.8%. Electricity is
contributing negatively while transport positively to the Solow residual and this is true
for different estimations and econometrical methods. They have the same effect even in
the group level. When they decompose the LP growth they find that the LP growth is
explained 61.8% by MFP, capital accumulation 32.4%, electricity contributes negatively
by 3%, and the increase in transport explains the remaining 8.8%. They estimate using
the system GMM and assume CRS. Using dynamic panel data they have TFP and LP as
dependent variables and explanatory variables factor intensities, concentration,
technology adoption, human capital intensity, exports using the method of system GMM.
Regarded MFP they find positive relationship with: technology, human capital intensity
and negative relationship with concentration, capital intensity. While as considered to LP
they find positive relationship with technology adoption, human capital. Since technology
is important in both cases they estimate a model with technology as a dependent variable
and find positive relationship with concentration which on the other hand is in line with
Schumpeterian idea: to innovate more and to use more technology a degree of
concentration is needed. Additionally they find that concentration contributes to
innovation but the net effect of concentration to MFP is negative.
“Productivity measures the effectiveness with which inputs (materials, capital and labor)
are transformed into output.” (Bart van Ark, 2002, p 69). They look at the productivity
level and per capita income in USA, Canada and Europe (OECD countries) and find
differences in their respective growth in the 90s. They conclude that source of slower
income growth in Europe and Canada relative to USA may be underutilization of labor
potential and another reason may be slower productivity growth. While the US
productivity growth is explained by ICT investment. Total factor productivity is the
residual of any growth model. They also look at the contribution of intangible asset to
growth. They illustrate the difficulties in measuring intangible assets and its contribution
to growth. They look at ICT investment and the impact of creation of intangible asset and
find that different levels of ICT contribute to the differential economic growth among
OECD countries.
36
GDP PER CAPITA
LABOR
PRODUCTIVITY
Sectoral
growth
Efficiency
of factor
(TFP)
LABOR SUPPLY
Within industry
labor
productivity
Investment
in physical
capital
Non
ICT
capital
ICT
capital
Hours
worked per
person
employed
Investment in
intangiable
capital
Capital
markets
Share of
working
age
populatio
n in total
populatio
n
Human capital
Knowledge
capital
Organizational
capital
Product
markets
Share of
employmen
t in
working
age
population
Labor
markets
Figure 7 Analytical framework of sources of growth
Source: (Bart van Ark, 2002) p.71
37
Active
demand
side
policies
Active
supply
side
policies
Structural reforms
Songqing et al. (2010) uses a translog production function:
Equation 12 𝐥𝐧𝐲𝐢𝐭 = 𝛂𝟎 +
𝐣 𝛃𝐣 𝐥𝐧𝐱 𝐣𝐢𝐭
𝟏
+ 𝛃𝐭 𝐭 +
𝟐 𝐣
𝟏𝟐𝛃𝐭𝐭𝐭𝟐+𝐣𝛃𝐣𝐭𝐥𝐧𝐱𝐣𝐢𝐭𝐭+𝐯𝐢𝐭−𝐮𝐢𝐭
𝐤 𝛃𝐣𝐤 𝐥𝐧𝐱 𝐣𝐢𝐭 𝐥𝐧𝐱 𝐤𝐢𝐭
+
They add a trend variable for observing the unobserved factors in their panel data. They
are using stochastic production function. They use the data from State Price Bureau in
China. Their stochastic production function estimates for 23 commodities suggest that the
TFP growth in the time period 1995-2004 was positive. They suggest that technical
change is driving China‟s productivity and the notice a fall in the efficiency.
Legros and Galia (2011) acknowledge that many studies use R&D expenditure as a proxy
for knowledge mainly in Cobb Douglas production function. In their work they add
training and knowledge capitalization as measured by ISO 9000 certification as sources
of knowledge. They note that training is an investment as R&D is. Their sample consists
of French manufacturing companies. They use simultaneous equations consisted of six
equations where productivity equation consists Innovation, training and ISO 9000
certification simultaneously. So in their analysis they once check if the firm is involved in
knowledge investment and then they put in the productivity equation. They estimate
using the asymptotic least square (ALS) method.
They do explain each equation separately cause they are of different types: in the R&D
expenditure equation the dependent variable is censored and they use Type II tobit with
two equations; they use a probit model for the innovation equation. And for the second
measure of innovation share of innovation sale they use type 2 Tobit with two equations
where the first equation is a probit model explaining product innovation and the second
equation is an OLS model explaining share of innovative sales; they use OLS for the
training equation while the productivity equation is a Cob –Douglass production function.
They use six data sources: 1997 French Community Innovation Survey (CIS2); the
French annual survey of firms‟ research expenditure, the „„ Competences pour Innover
1997‟‟ survey (Competencies for Innovation Survey), the „„ Enqueˆte Annuelle
d‟Entreprises‟‟ 1996 (EAE), the French 24–83 tax returns for firms‟ annual training
expenditure, and the 1996 „„ Enqueˆte sur la Structure des Emplois‟‟ (ESE). They find
that that the probability to be engaged in R&D increases with the Lerner index, also
market share are positively related to R&D. Innovation is a crucial issue for productivity.
Training intensity has a positive and significant impact on firms‟ productivity in France.
Their results show a positive effect of all employees‟ categories on labour productivity.
38
Market share
New equipments
Analysis new
consumption components
New supplies
Analysis consumers‟ moods
Evaluation of
training needs
Cooperation agrrements
Analysis consumers‟
needs public financing
Imitation
Lerner index
Size
Sectoral
effects
Research and
development
Belongin
g to a
grouop
Cooperation agreements
Analyzing competing
products
Innovation
Training
ISO 9100
certification
Analyzing competing
patents
imitation
Qualification
Productivity
Physical
capital
Figure 8 Knowledge production function
Source: Legros and Galia (2011), Knowledge production function, p. 4.
7
Authors‟ reproduction
39
7
Grimes, Arthur Ren, Cleo Stevens, Philip (2011) in their literature review note that
previous research does not treat micro data and looking at internet connection as a boast
for productivity. They are testing whether firms with faster internet connection are more
productive relative to firms with slower internet connection. They use a production
function and their dependent variable is (log of) firm i‟s labor productivity relative to the
industry average. They note that there are observable and no observable factors
influencing the choice of access and productivity and in order to address this they use
propensity score matching. They use a probit equation for internet and then use the
results with a set of control firms and they find similar likelihoods. They also use the IV
approach, as an alternative approach. They hypothesize that a firms choice for broadband
is determined by: firm size, firm age, industry structure, the quality of ICT infrastructure in the firm‟s locality (positive);the capability of the firm‟s management with
respect to ICT issues application of „modern‟ general management approaches within the
firm especially with respect to high-performance HR systems, knowledge intensity of the
firm‟s sector and whether the firm conducts R&D , being foreign-owned or having a
foreign subsidiary, location in a city or high-density area. They use Statistics New
Zealand‟s Business Operations Survey 2006 (BOS06) and Statistics NZ‟s prototype
Longitudinal Business Database (LBD) as sources for the data. They estimate a probit
model for firm broadband adoption and their results suggest that positively related with
uptake are variables associated with the quality of management, knowledge intensity of
the sector, foreign ownership, and ICT knowledge within the firm; older firms and firms
with bad local ICT infrastructure have lower uptake and they find no evidence of reverse
causality that highly productive firms are more or less likely to have a broadband. They
statistically find that firms having a broadband are 7-10% more productive relative to the
ones with no broadband, still this is not a final word that having a broadband means that
firms will perform better. Their estimates are consistent across firm type.
Fernandes (2008) use a sample of 575 firms in Bangladesh. They estimate a Cobb
Douglass production function using OLS which may result with simultaneity bias. They
measure output as ration of nominal sales or material costs and corresponding firm
specific deflators, capital stock is calculated using the perpetual inventory method
formula, labor is measured by the number of workers while workforce human capital by
share of skilled workers. They follow Ackerberg, Caves and Frazer (2007) ACF.
According to their estimates they find:
1. Firms of smaller size have higher TFP and medium sized firms are the most
productive and the results are robust even whet total employment is included as
continuous variable although their sample is skewed to the large firms so the
results should be taken with cautious;
2. The relationship between firm age and TFP is inverse U shaped- 10-20 years old
firms are the most productive- TFP increases with firm age but at a decreasing
rate;
3. Firms with more educated managers are more productive;
4. Foreign owned firms are more productive;
5. Exporters are more productive;
6. Firms with quality certifications are more productive;
7. R&D is not a TFP advantage for firms in Bangladesh;
40
8. More computerized machinery is associated with higher productivity;
9. Negative correlation between advanced technology and TFP;
10. Overdraft is positively related to TFP while firms while access to loan is
negatively related to TFP but the effect is insignificant;
11. Firms facing poor electricity show lower TFP;
12. Crime and TFP are negatively correlated;
13. Heavier bureaucracy is negatively correlated with TFP;
14. Positive correlation between corruption and productivity (reverse causality).
Griliches and Mairesse (1995) note the critics of Cobb Douglas production function is
that input variables cannot be treated as independent and the model cannot be run by OLS
since they will be biased. The critics say that there may be correlation between inputs and
error term. They introduce that in the anatomy of the error there is a part known by the
producer but not by the econometrician and a part that is only econometrician‟s problem
(error of measurement, data collection and computational procedures). Thus this anatomy
leads to simultaneity problem. As a result of the critics there are used panel industrial
micro-data. They discuss simultaneity, selectivity, lack of information on quality
problems. These problems made researcher to use thinner slices of data to solve for
simultaneity but that lead to other problems such as misspecifications.
Bartel et al. (2003) state that there are two types of insider econometric
studies:
 Cross organization studies ( plant visit)
 Single firm studies (interviews)
The first type is very costly and time consuming process while the second type cannot
examine organization specific characteristics.
Another type may be using informed surveys for industry specific survey which they
employ in their study in valve making industry. The matching process involves setup
time, run time and inspection time. They use a production function where output8 is
function of labor hours, capital and materials. The capital in preliminary estimations
results insignificant but this may be because the industry has fixed factor production
characteristics; capital may be measured with error or is endogenous. The results are: new
technologies reduce production time, fewer machines reduce setup time, FMS technology
reduces run time, and there are efficiency gains from introducing newer technologies. A
related to human resource management variable training for new technologies improves
efficiency in setup times and run times. The problem with their approach may be omitted
variable bias and selectivity bias. They conclude that “getting the “right data” matter a
great deal, but so does getting insiders‟ insight about what the right data really is” p. 10”.
2.6.
DISTANCE FUNCTION
Conceição, Portela and Thanassoulis (2006) use a geometric distance function where they
put input and output vectors while assuming that they know the efficient input and output
8
Shipments minus change in inventories
41
levels according to the efficient Pareto-frontier. So they use target outputs. They calculate
the ratio of geometric average of inputs towards geometric average to outputs which will
tend to show the inefficiencies in the production under the assumption that the target is
Pareto efficient. Their GDF measure is used for calculating TFP measure and finding the
sources of inefficiencies. What TFP measures is the ration of ratios of input and outputs
in different time periods. In multiple input- output case there is a need for aggregation
and use of index numbers (Laspeyres, Paasche and Fisher). They suggest that GDF
measure has advantages since is does not impose any assumptions on technology.
Equation 13 𝑻𝑭𝑷 − 𝑮𝑫𝑭 𝒚𝒕, 𝒙𝒕 , 𝒚𝒕+𝟏, 𝒙𝒕+𝟏 =
𝒀𝒓𝒕+𝟏 𝟏
) 𝒔
𝒀𝒓𝒕
𝑿𝒊
𝟏
(𝚷𝒊 𝒕+𝟏 ) 𝒎
𝑿𝒊𝒕
(𝚷𝒓
They suggest that gdf can be used for malmquist index
Equation 14 𝐌𝐆𝐃𝐅 =
𝐆𝐃𝐅 𝐭+𝟏 (𝐲𝐭+𝟏, 𝐱𝐭+𝟏 )
𝐆𝐃𝐅 𝐭 (𝐲𝐭,𝐱𝐭 )
𝐱
𝐆𝐃𝐅 𝐭 (𝐲𝐭+𝟏, 𝐱𝐭+𝟏 )
𝐆𝐃𝐅 𝐭+𝟏 (𝐲𝐭+𝟏, 𝐱𝐭+𝟏 )
𝐱
𝐆𝐃𝐅 𝐭 (𝐲𝐭, 𝐱𝐭 )
𝟏
𝟐
𝐆𝐃𝐅 𝐭+𝟏 (𝐲𝐭, 𝐱𝐭 )
They use the GDF Malmquist procedure on monthly data on 57 Portuguese bank
branches. Than they use a base month and their results still show that banks are not
catching up with frontier movements. Looking at both approaches they conclude that the
best month is August while the worst month is November. They also provide calculation
on classical approaches and compare it with the GDF approach and the conclusion is that
in general the results are the same with differences in unit level. However they note that
GDF is still reflecting better the changes in productivity. Saal, Parker and Weyman-Jones
(2007) also use an input distance function.
2.7.
DEA ANALYSIS
Feng-Cheng Fu , Chu-Ping C. Vijverberg and Yong-Sheng Chen (2007) use data for state
owned enterprise to measures for productivity. They use the DEA method and linear
programming model in an output oriented model with the assumption of CRS for China
enterprises. They also use the Malmquist productivity indicator (MPI) and decompose it
in technological change and efficiency change. With DEA they calculate production
frontiers. They use value added as a proxy for output and in a separate model they use
taxable profits as a proxy for output. The definition of taxable profits is total sales minus
cost of goods sold. Their research is on the industrial sector for financially independent
companies for the time period 1986-2003. They calculate DEA efficiency for Panel data
and Cross section data. According to their results efficiency in state owned enterprises in
china grew in the 80; s, declined‟ in the 90‟s and then steadily progressed from 2000.
They suggest that favourable reform contributed to the increased efficiency. Thus they
classify the economy in three stages: the first one is reforms on the 80s, the market
oriented on the 90s and after 2000 the period of privatization. They find that a favourable
macroeconomic indicator may lead to productivity though they admit it is a long term
determinant of productivity.
42
Andries suggest that studying banking productivity is important because increased
productivity may lead to better performance. He provides comparative analysis of CEE
countries for efficiency in banks. He uses Stochastic Frontier Analysis which allows the
error term and Data Envelopment Analysis (DEA) which assumes that all deviation in
efficiency are caused by firm characteristics and does not account elements that also
affects the performance. He calculates Malmquist productivity index. With the DEA
method you can identify the inefficiency and what should be done to improve it. Whether
DEA is input oriented or output oriented will lead to different efficiency scores. The
general form of production function is:
Equation 15
𝐲𝐢𝐭 = 𝐱 𝐢𝐭 𝛃 + 𝐯𝐢𝐭 − 𝐮𝐢
Where v is random error, u truncated error variable, y output vector, x input vector and it
can be estimated using Maximum likelihood estimation, least squares dummy variable
approach and the generalized least square. They calculate Malmquist index using DEAlinear programming method. According to the studies the efficiency in banks differs in
time and among banks and this is due to internal and external factors that banks face.
They use two stage estimation, first they estimate the level of efficiency and then they use
the estimation as a dependent variable. When the dependent variable is DEAS efficiency
scores OLS cannot be used but the two tails TOBIT to analyze efficiency with other
variables. Their dataset consist of 112 banks in 8 CEE countries in the period 2004-2008.
They find that the average efficiency increased. The analysis uses the hypothesis of
constant returns to scale. According to them private banks are more efficient while in
terms of productivity state owned banks show a larger increase. When size is controlled
they find that medium sized banks seem to be more productive and small banks are more
efficient. They apply OLS with efficiency as a dependent variable and find that it is
influenced by variables such as: bank capital structure, size of the bank, total asset of
banking system, annual inflation rate, asset share of state owned banks, asset share of
foreign owned banks, ownership form of the bank, the level of concentration in the banks
in system; percentage of the asset owned by the 5 largest banks in the system, the
banking reform and interest rate liberalization level, deposit rate and lending rate.
2.8. PRODUCTIVITY RELATIONSHIP WITH OTHER VARIABLES
(INNOVATION, R&D, IT, INSTITUTIONAL CHANGE)
The expectation is that innovation will lead to higher productivity growth. In order to
give evidence that there is a large body of literature and diverse related to productivity
and profitability we bring some studies that have to do with profitability and productivity
from different sector industries, different countries and looking at different variables. We
are reviewing studies on : the analysis that size and growth of German companies as a
result of the institutional change; the relationship between TFP and technological
progress in the electricity industry; innovation and productivity in manufacturing
industry; evidence of practice principles of productive firms; evidence that
computerization increases productivity, innovation and productivity; infrastructure and
firm performance; IT and performance and a study on determinants of profitability.
43
Audretsch, Elston and Ann (2006) check the relationship between size and growth for
German companies. They use three dataset the Hoppenstedt database, Deutsche
Bundesbank data sources, and publicly available data from the web. Their estimates
classify between Neuer Markt firm and traditional manufacturing firms. Their estimates
suggest that Neuer Markt small firms grow faster whereas in the traditional firms big
firms grow faster. They present parsimonious model but still the size variable is
significant unless cash flow is included when it turns to insignificant. They check for
robustness dividing the sample in 3 using different criteria for small firms but the
conclusions remain the same- small firms grow faster. They conclude that the
institutional change of Neuer Markt has enabled new technology sectors driven by small
firm growth.
Rungsuriyawiboon, Supawat Stefanou, Spiro E. (2008) employ dynamic efficiency model
and use two step estimation: first maximum likelihood estimation and in the second step
generalized method of moment. They use electricity industry data. The time period they
analyze is 1986-1999 and data are obtained from the Energy Information Administration
(EIA), the Federal Energy Regulatory Commission (FERC) and the Bureau of Labor
Statistics (BLS). “The empirical findings show that the alocative efficiency gain effect
from the change of variable input is the most attributed factor to TFP growth, while that
from the change of marginal value of capital is nearly negligible.” p.186 Their study
suggests that TFP growth was mainly driven by technological progress.
Figure 9 Innovation and productivity
Source: Baily and Chakrabarti (1985). P631
44
Baily and Chakrabarti (Innovation and productivity in US industry, 1985) study two
manufacturing industries which vary in the capital intensity they use to look for the
relationship between innovation and productivity. “It is at the point of commercial
introduction that the new product or process is described as an innovation” (Baily and
Chakrabarti , 1985)p. 610. Technology does not provide direct productivity enhancement
but it provides the means for it. New processes and new product development improve
productivity in manufacturing industry. They collected data on innovation. They have
found that slowdown of innovation caused a slowdown in productivity in manufacturing
industry in US. They suggest the link between innovation and productivity and also
suggest that output slowdown may be as a consequence of business cycle and structural
shocks.
Cooper and Edgett outline how new product development productivity is measured:
NPD productivity= Sales or profit from NPD (output)/ R&D spending (input)
According to them studies show that there is a decrease in profitability but R&D remains
constant. “The one factor that does show a dramatic change, however, and that explains
the decrease in profitability, is the balance in the portfolio of projects undertaken today
versus in 1990.” P.3. APQC study has developed seven principles that when employed in
business will result with superior performance. These principles are outlined in the
figure:
Figure 10 Superior performance principles
Source: Copper and Edget, fig 2.
In the same study in order to have Customer focused- differentiated superior product six
methods were introduced:
1. customer visit with in-depth interviews;
45
2.
3.
4.
5.
6.
camping out or ethnography;
lead user analysis;
focus group problem detection sessions;
brainstorming group events with customers;
crowd sourcing using online or IT based approaches.
According to them (APQC) high productivity firms compared to less productivity firms
are front end loaded with assessments such as: preliminary market assessment, technical
assessment, source of supply assessment, market research, concept testing, value to
customer assessment, product definition, business and financial analysis. They underline
the importance of metrics for successful projects and successful new products. They find
that high productivity firms practice the principles of lean, rapid and profitable NPD:
1.
2.
3.
4.
5.
6.
customer focused;
heavy front-end;
spiral development –loops;
holistic-effective teams;
metrics, accountability and continuous improvement;
focus and portfolio management.
Brynjolfson and Hitt (1998) note that while you can easily define productivity as output
per unit of input the measurement is not that easy. They mention that it is even harder to
measure in the information economy. ”Productivity growth comes from working smarter”
p.50. They state that the conventional wisdom does not find relationship between
computers and productivity but level studies contradict the productivity paradox and find
that IT investments are positively correlated with firm output. When they look at
variation in productivity and investment they find positive relationship but there is
difference between firms on the size of the relationship. They use a firm effect model and
the benefits from IT were reduced which they interpret that half of the value of the
benefit is due to firm characteristics and the other part is general for all firms. When they
look at the relationship in different time periods they find that the long term benefits are
larger which they explain by the fact that it investments are time consuming and costly.
They conclude that computerization itself does not induce productivity but it‟s a
component of the system which increases productivity.
“It is at the point of commercial introduction that the new product or process is described
as an innovation” p. 610 (Innovation and productivity in US industry Baily and
Chakabakri (1985), Broking papers on economic activity.) On their case study for two
industries (chemical and textile) the management interviews answer that the slowdown of
innovation contributes to the slowdown in the productivity growth (Baily and Chakabakri
(1985)).
Stratapoulos and Dehning (2000) are looking at the productivity paradox (the link
between IT investment and performance. They note that IT investments have an upward
trend and they are not expected to slow down in the near future. In their literature review
they find that the evidence is that either there is no proved relationship between IT and
performance or the relationship is positive. They claim that this may be due to not
distinguishing successful users and not successful ones and suggest that their study is
based on the fact that IT can use effectively or ineffectively. They test the hypothesis that
46
financial performance is the same between successful and les successful users of IT. They
state that the IT investment would rather be short time improvement than long-term
performance advantage. Their selection of the sample is from CWP100 list. They use a
match paired design with matching variables controls for industry, size and capital
intensity. Financial performance variables used are profitability (growth in net sales,
gross profit margin, operating profit margin, net profit margin, ROA, ROE and ROI) and
efficiency(fixed asset turnover, total asset turnover and inventory turnover) measures. To
test their hypothesis they use nonparametric statistics the Wilkoxon signed rank test for
matched pairs. Their results demonstrate in favor of rejecting their hypothesis. Therefore
successful users of IT outperform in profitability measures such as ROA, ROE, ROI
while as considered to efficiency measures only total asset turnover supports their
hypothesis. Their study attributes explanation to the productivity paradox to the
mismanagement. Their work is evidence that successful IT investment may lead to better
performance. We can draw the conclusion that their study notes the importance of
efficiently using IT investment rather than on costs of IT investments that make firms
outperform.
2.9. COMPARATIVE STUDIES
Fox (2011) notes that aggregating productivity and comparing productivity among
countries arises many problems.
Laurent Weill (2008) suggests that in centralized economies they could not get neither
the stick (guaranteed employment), nor the carrot (increased wages). They note six
characteristic of socialist economies that do not help enhancing productivity:
 Failure in innovation and incentive to reduce costs;
managers online wanted to hit the target planned by employing more labor
because of the risk of ratchet effect;
 guaranteed employment;
 prevalence of seller‟s markets;
 national self-sufficiency and independency from market economies;
 poor quality of institutions, with notably the lack of political freedom, a weak
quality of the administration, and corruption.
What these facts suggest as that is hazardous to compare west developed countries with
developing countries or otherwise stated we are expecting a productivity gap between
these country groups. He measures technical efficiency in the 70s and 80s using a Cobb
Douglas production function of the form:
Equation 16 𝒍𝒏
𝒀
𝑳 𝒊𝒕
= 𝜶𝒕 + 𝜷𝟏𝒕 𝒍𝒏
𝑲
𝑳 𝒊𝒕
+ 𝜷𝟐𝒕 𝒍𝒏
𝑯
𝑳 𝒊𝒕
+ 𝒗𝒊𝒕 − 𝒖𝒊𝒕
Where dependent variable is output per worker and input variables are capital per worker
and human capital per worker, while the error term is compose of statistical noise and
inefficiency term. They use two model for their panel WITHIN model proposed by
Cornwell et al. (1990) and firm effects model proposed by Battese and Coelli (1992).
They use Penn World Tables as a dataset for 89 countries for the time 1971–1987. Their
47
result shows that socialist countries were underperforming in the meaning they were
producing only 32.36% of what could be produced optimally. The gap between socialist
and developed countries increased in the beginning and end of the period showing that
there was a productivity slowdown in socialist countries in the 80s. They suggest that
market oriented reforms favoured efficiency especially in Yugoslavia. The country (from
socialist countries) with lower level of efficiency had the lower increase in efficiencyPoland. They obtain similar efficiency coefficient and similar variations with the BC
model. The difference is that with BC model the developed countries show higher
efficiency coefficient (65.62%) whereas in the WITHIN model middle income countries
have higher efficiency, and with BC model lower income countries are less efficient
(with a mean of 36.11%) not as in WITHIN model where socialist countries are. They
compute Sperman correlation coefficient and the results are robust for the frontier
analysis techniques. Their result show that the mean efficiency coefficient for socialist
countries varies a little from lower income countries but varies a lot from middle income
and developed countries. They also compute weighted means of efficiency scores and the
results remain robust to the previous stated findings. Their findings suggest that socialist
countries have low efficiency indicators, market oriented reforms improve efficiency and
their data estimates suggest that there is a gap between socialist countries and developed
countries.
Van Ark (1996) note that studying productivity is important because of its relation to
accumulation of physical and human capital, technological progress, resource allocation
and efficiency and competitiveness. He suggests that aggregate production function
assumes assumption which cannot be fulfilled in practice -this is in favor of research that
disaggregates production. He discusses issues in measuring output, labor inputs, and
capital inputs. He outlines the international productivity datasets available: US Bureau of
Labor Statistics, The International Sectoral Database, STAN, and Eurostat. Studies that
make international comparisons mainly use Tornqvist indices. They admit that the lack of
comparable data makes it difficult to make international comparison studies, besides the
measurement problem and linking it with economic theory. They suggest that inputoutput tables may be helpful in international comparison by sector and industry.
Johannes Van Biesebroeck (2009) constructs sectorial PPP to make country comparisons.
They use that data form OECD‟s Statistics Department and the STAN database. They use
value added price deflators because fewer countries report gross output and because the
dependent variable is value added per worker. They conclude that there is convergence
independently of the base year chosen for PPP.
2.10. MORE ON PRODUCTIVITY
Productivity is a profit incentive or reward according to Marshall while the idea of
innovative businessman is developed by Schumpeter.
“Although there were many challenges facing the agricultural economy as China entered
the end of the 1990s, it was shown that the investment into R&D (which because of time
lags between investment and production of new varieties had taken place in the late
1970s and 1980s) was producing the technology that was driving TFP.” P 192, Jin et al.
48
(2010). The production technology that they employ is translog production and use panel
data.
Productivity can arise as growth of technology progress one strand but this has the
assumption that firms are efficient. Innovation is a factor to firms‟ performance. R&D
and productivity are expected to have positive relationship. R&D is used to measure
knowledge in studies using a Cobb Douglas production function.
Legros, Diégo Galia, Fabrice (2011) introduce besides R&D, training expenditure and
knowledge capitalization as measures of knowledge. They note that training is an
investment for firms.
2.11. CONCLUSION
The main stakeholders in the productivity and profitability of the firm are the employees,
the owners and the government. The importance of research on productivity is outlined in
Mawson et al (2003). With further reviews of the literature on productivity found in:
Barteslamn and Doms (2000); Mawson et al (2003). We can divide studies on
productivity into three strands: Studies exploring the definition of productivity, studies
measuring factors that may influence productivity and comparative studies on
productivity. We conclude that the definition of productivity is crucial for the results on
productivity research. There is a “menu” of alternatives in the empirical research on
productivity and the lack of micropanel datasets makes the comparative studies difficult.
We identify these approaches for studying productivity: index number studies, production
function, distance function and DEA analysis. Malmquist index and Törnqvist index are
the most common used indexes on productivity studies. For example they are used in
studies such as: Fare et al (1994), Ball et al (2004); Camanho and Dyson (2006);
Grifell-tatjé and Lovell (1998).The production function relates the amount of the output
to the amount of input used – a function that describes the technology. For example they
are used in studies such as: Solow (1957); Banda and Verdugo (2011); Grimes, Arthur
Ren, Cleo Stevens, Philip (2011); Fernandes (2008).Distance function studies: Saal et al.
(2007); Conceição et al. (2006) while Dea analyzis studies: Feng-Cheng Fu and ChuPing C. Vijverberg and Yong-Sheng Chen (2007). According to empirical research we
find that variables correlated with productivity are: institutional change, technological
progress, IT investment, innovation and R&D.
Micro data in studying productivity are important in different fields of economics:
microeconomics, macroeconomics, labor economics, international trade and industrial
organization. Besides different approaches for studying productivity we identify different
empirical approaches for estimation in productivity studies and we notice that studies
that use panel data are sparse. Concluding we suggest that identification of drawbacks of
each empirical estimation is crucial for deciding the choice of empirical estimation.
49
3. A DISCUSSION ON DATA AND METHODOLOGY: MLE
AND COBB-DOUGLAS MODEL SPECIFICATION
3.1. INTRODUCTION
Science and research provides us with information and conclusion about certain topics of
interest. Theoretical framework often may open discussion and contradictions among
researchers. Thus overview of the theory (historical method) itself may not always
provide sufficient evidence for advocating or rejecting certain theories, instead it should
be complemented with empirical evidence from the recent datasets. The dynamic of
society and technology may be considered as potential reason why theory often does not
draw indisputable conclusions. Business activities and economy are dynamic subjects
and as a consequence there is a continuous interest of researches for testing the theory,
providing supporting or contradicting evidence and proposing new policies. Nowadays
research on social sciences especially economics extensively use estimation methods and
modeling. Thus theory is complemented with data estimation before coming up with
conclusion.
The follow up of the theoretical framework is identifying available datasets that will
enable testing models on productivity and provide empirical evidence. Looking at
datasets that contain information for conducting production function estimation for
enterprises in Albania and Macedonia we choose to employ the questionnaire of The
Business Environment and Enterprise Performance Survey (BEEPS) because of the
reliability of data collection, geographic coverage and because of the high response rate.
The main focus of the chapter is to identify variables of interest, their definition and
discuss summary statistics of the sample employed. Additionally the estimation
methodology for the underlying models estimated in the following chapter is discussed in
detail.
The object of this part is to analyze and draw conclusions about:
1.
2.
3.
4.
Questionnaire;
Type of data;
Variables and model;
Estimation methodology.
The chapter begins with the discussion about the nature of the questionnaire and dataset
on section 3.2 and on section 3.3 the type of data we have available are discussed in
detail. On the next section (3.4) the variables of interest and their nature are introduced
and also the methodology of estimation is discussed on section 3.5 and 3.6. Next section
3.7 introduces the main business constrains that companies face. Follows a discussion on
main characteristics of firms in section 3.8.The chapter finalizes with some concluding
notes and technical information necessary for understanding the estimation results in the
next chapter.
50
3.2. THE QUESTIONARE
The Business Environment and Enterprise Performance Survey (BEEPS) collects and
assess data on private enterprise and business development. There have been four rounds
of the survey starting from:
-
the first round ( 1999-2000) which covered 4000 enterprises in 26 countries;
the second round (2002) which covered 6500 enterprises in 27 countries;
the third round (2005) which covered 9500 enterprises in 28 countries;
the fourth round (2008-2009) which covered 11 800 enterprises in 29 countries.
All these rounds make possible to construct a panel data on enterprises in EBRD
countries which can be used for analysis and provide suggestions to the private sector and
the government. As we can see the geographic coverage and sample size increases from
the first round to the last round. The data provided from BEEPS are comparable and may
be used to assess how the business environment has changed through time.
Countries that are cover in BEEPS (round four) are: Albania, Armenia, Azerbaijan,
Belarus, Bosnia and Herzegovina, Bulgaria, Croatia, Czech Republic, Estonia, Former
Yugoslav Republic of Macedonia, Georgia, Hungary, Kazakhstan, Kyrgyz Republic,
Latvia, Lithuania, Moldova, Mongolia, Montenegro, Poland, Romania, Russia, Serbia
(including Kosovo under UNSCR 1244), Slovak Republic, Slovenia, Tajikistan, Turkey,
Ukraine and Uzbekistan. The sample is reliable according to sample selection criteria for
all countries while in Albania stratified random sampling was used. The sample frame
was obtained from official sources in each specific country and enterprises in BEEPS
2005. The target number of interviews was reached in most of the countries ( Belarus,
Kyrgys and Croatia had larger discrepancies between the target and realized interviews).
We are inspecting the panel data and we expect that we might have a problem of missing
data in the panel dataset. Therefore we are going to seek the variables of interest in the
panel dataset to get the general picture for the whole sample of countries and years of the
questionnaire and then look at specific years and specific countries of interest for a more
detailed picture. The missing data may arise because of the differences in the
questionnaire through time and another reason is because the questionnaire is constructed
so that in most of the questions it allows the respondent to respond with I don‟t know.
These reasons will result with missing data for our questions of interest. We can use time
series or cross section analyzes as subsamples of the main panel data.
3.3. PANEL DATA
The simple general definition for the panel data is N sample units (i) observed over time
(t). Our panel data is firms in 29 different countries for a time of 5 year. The main
conclusion when looking at the summary statistics of our data is that we are having an
unbalanced panel. Panel data offer hetereoiginity among units across time. Gujarati
suggest that panel data enriched empirical analysis though the mathematics and statistics
are high leveled, but the availability of econometric software allows us easy of
computation and practice of these types of data. A simple linear model that uses panel
data mathematically may be expressed as:
51
Equation 17 𝐘𝐢𝐭 = 𝛃𝟎 + 𝛃𝟏 𝐗 𝟏𝐢𝐭 + 𝛃𝟐 𝐗 𝟐𝐢𝐭 + 𝐮𝐢𝐭
Where i stand for units of analysis (individuals, firms, states) or the cross section and t for
the time of analysis (the time of available data). The panel data may be balanced and
unbalanced. We have balanced data if we have the information for the cross section for
all the time period whereas if the number of observations differs than we have
unbalanced panel. In our sample data, accordingly we have unbalanced panel because we
do not have information for all of the firms for the time series. We explain this that some
firms may have gone bankrupt, changed legal status or merged with other companies.
Therefore not all the firms covered on the first BEEPS questionnaire appear in the
second, third or fourth questionnaire. When estimating these types of data we have to
make assumptions on constant, slope coefficients and error term whether they are
constant or vary over individual and time. These assumptions will show the complexity
that we have to deal with. Thus is the coefficients and intercept varies over time and
individuals we have more complexity involved but on the same time we may have more
information. More simple assumptions may mean easy of computation but may distort
the true picture. Fixed effect regression means that intercept varies between units but is
time invariant ore often expressed as FEM.
We can use differential intercept dummies for estimating the fixed effect and the model is
least –square dummy variable model (LSDV) or as a covariance model. We can account
for time varying using time dummies for each year9. Gujarati lists the problem from using
panel data: introducing to many dummies may lead to losing the degrees of freedom;
having to many variables may lead to multicolinearity problem; the impact of time
invariant variables may not be captured; classical assumptions for the error term may
have to be modified.
Another approach for the panel data is the error components model (ECM) or random
effects model (REM). The main point of this model is the error term which is expressed
as:
Equation 18 𝐰𝐢𝐭 = 𝛆𝐢 + 𝐮𝐢𝐭
And consists of two parts: the individual effect error and the combined time series and
cross section error. Thus the intercept represent the mean value of all the individuals
while the individual error component is the deviation from the mean which is a latent
variable. Gujarati suggests that the decision which model to choose should be based on
the following: „‟If it is assumed that εi and the X‟s are uncorrelated, ECM may be
appropriate, whereas if εi and the X‟s are correlated, FEM may be appropriate (p. 650).
Our sample is random drawing so according to Judge et al. we should use ECM taking
under consideration the big number of cross section and the small time; if the error and
estimators are correlated ECM gives biased estimators while from FEM unbiased. We
can also do the Hausman test when choosing between models.
9
Interactive or differential slope dummies
52
Greene (2005) describe the stochastic frontier model
Equation 19 𝐲𝐢𝐭 = 𝐟 𝐱 𝐢𝐭 , 𝐳𝐢 + 𝐯𝐢𝐭 − 𝐒𝐮𝐢𝐭 = 𝛃′ 𝐱𝐢𝐭 + 𝐮′𝐳𝐢 + 𝐯𝐢𝐭 − 𝐒𝐮𝐢𝐭 ,
𝐢 = 𝟏, … , 𝐍; 𝐭 = 𝟏, … , 𝐓.
And the sign of S is positive if it is a production function or profit function while minus if
it is a cost function and the meaning is the inefficiency term. Greene reviewing the
literature notes that there are both shortcoming and virtues for both approaches fixed and
random effects. The virtues of fixed effect is that is distribution free but the shortcoming
is that it only draws the general picture and loses individuality of estimating inefficiency.
On the other hand the random effect has tighter parameterization but allows looking at
the individuality of the inefficiency term but assumes that effects are time invariant and
uncorrelated with the variables in the model. The time invariant assumption is a
shortcoming for both fixed and random effect model. The time invariant term in his
formulations is reinterpreted as firm specific heteregoinity and not as inefficiency.
Huberler (2006) notes that because of unavailability to do the cross section data in all the
years of interest we result with missing data which is referred to as unbalanced panel. If
the time invariant error term is uncorrelated with the error term than we have the random
effect model. On the other hand fixed effect model wipe out time invariant regros and
individual effects. They suggest that when estimating nonlinear panel data we can use
conditional maximum likelihood estimation. They conclude that there is no uniform
method for estimation of nonlinear models but there are specific forms that when we
estimate the results will vary on the assumptions.
Patriota et al. (2011) suggest that biased problem with heteroscadastic errors is usually a
problem with the small sample with MLE estimators. They introduce bias correction
estimation and show that these corrected estimators prove to be effective for the
maximum likelihood estimators. They suggest that biased in small sample size may be
nonnegligable. They use the epidemiological data set from the WHO MONICA and
compare estimators from ML and bias corrected estimator and conclude that the biases
are larger in ML estimators. They conclude that using the correction scheme the
estimators are nearly unbiased even for large sample.
Huwang et al. (2009) provide uniformly robust tests for the vector coefficient and vector
slope parameter using testing with confidence intervals and the estimated results are close
to the nominal ones.10
Semykina, and Wooldridge (2010) propose a test for selection bias FE-2SLS where
endogeneity is conditional on the unobserved effect. Their test is robust even with
endogenous repressors. Gerd Ronning, Hans Schneeweiss (2011) analyze panel
regressions with fixed effect estimators.
First we try to check the nature of our data and what the figures tell us is that 2009 and
2005 have larger number of firms interviewed while 2007 have the lowest number of
interviewed firms. If we want to look at two years than we have larger sample if we
choose 2005 and 2009 (refer to Appendix for details). We should avoid having the year
10
For more technical issues refer to the original paper
53
2007 because it results with very little number of firms‟ interviews that are also provided
in other years. The conclusion from this is that we are far away from having balanced
panel. Also we review our primary idea of using the panel for all the years because from
the overall 26 911 total sample shrinks almost by 10 times, but however the object of our
analysis are two countries. After data examination we choose to work with a cross section
data for Albania and Macedonia for the sample of 2009 (which is the most recent data
sample available at the time we obtained and examined the data). Another reason why we
choose not to work with the panel data is because our focus is to estimate a production
function and we are not sure that the production function is the same for all the time
period. Therefore we assume Porters effect holds and continue our analysis for a sample
data for Albania and Macedonia. The data collection in Albania was obtained in five
regions: Tirana, Durres, Elbasan, Fier and Vlora. In Macedonia there were 4 regions
defined: Eastern, North-west &West, Skopje and South.
3.4. VARIABLE DEFINITION
We want to look at the nature of data than the nature of the enterprises included in the
questionnaire. We introduce the definition and summary statistics (in appendix) of the
variables of interest.
YEAR
The questionnaire has 4 years of data where:
-
year 1 stands for 2000
year 2 stands for 2005
year 3 stands for 2007
year 4 stands for 2009
SALES
Sales- is continues variable and provides the amount of sales in the last year. We expect
that the higher the sales the higher the probability that company will spend on R&D. Also
a sale is proxy for the gross output.
POWER OUTAGES
Power outages- is a dummy variable showing whether the company faces the problem of
power outages or not. Power outage is reported as an obstacle for the business
environment so we want to check whether it will represent an obstacle for R&D as well.
We want to check this variable because is reported as an obstacle of business in transition
countries.
SIZE
The dataset contains data from small, medium and large companies where small are
companies that have 5-19 employees, medium 20-99 and large more than 100. We use a
dummy variable and make a new classification of two groups: the first one is small and
medium companies and the second group is of large companies.
54
SME is controlling for the size of the enterprises using a dummy. We used the
conventional classification of small, medium and large enterprises and compare small and
medium with large enterprises. We expect that smaller companies innovate less compared
to large companies. The size variable is based on the number of employees and the
categories are the standard one: small, medium, large.
INNOVATION
Innovation – has the establishment introduced new product or service? Innovation – in
the model is a dummy variable showing whether the company has spent on innovation
(introduction of a new product). The expectation is that companies that innovate also
spend on R&D.
The definition of innovation used in our analysis is the introduction of a new product. We
will use it both as dependent and independent variable. This dependent variable is a
dummy variable indicating whether the company has introduced a new product or not.
INTERNET BROADBAND
We have created a variable internet from the question does the company have a high
speed broadband connection. Internet- is a dummy variable whether the company has an
internet broadband or not. We expect that companies that have internet broadband will be
more prone to R&D spending because of the speed of information that internet provides.
Having internet broadband means more access to the new technology to new
developments in the competition world. So we are expecting that companies that have
high speed broadband have higher probability to innovate. We do not have information
on our dataset whether they are using efficiently the internet broadband. The information
that we have is just whether they have internet broadband or not.
RESEARCH AND DEVELOPMENT(R&D)
One question in the questionnaire addresses whether the company has an R&D
investment or not. We have two questions that provide us information about R&D
investment: the first one is whether the enterprises invest in R&D and the second one is
the amount spent on R&D.
R&D investment means that the company is incentivizing development and research
which is core for innovation. Therefore we expect that the probability to innovate will
increase as a result of R&D investment. The dataset as mentioned provides two sources
of information on R&D. When looking at summary statistics we chose to use the question
whether they engage in R&D or not since it is answered for more observations while on
the other hand the question on the amount of R&D results with relatively large number of
missing data.
R&D- in the model is a dichotomy variable telling whether the firm is engaged in R&D
spending or not; since this is our variable of interest and because of its nature we have to
choose from the choice of binary models for estimating. There are a lot of studies that
correlate R&D with higher growth; therefore we want to estimate what may determine
the probability for R&D.
55
ACCESS TO FINANCE
The scale for obstacles is: no obstacle, minor, moderate, major or very severe obstacle.
The dummy we created is grouped moderate, major and severe obstacle in one group and
minor or no obstacle in another group.
Access to finance- we expect that firms that find access to finance as a major obstacle
will probably innovate less than companies that do not have obstacle in access to finance.
Innovating is a costly process in the first stages until the product is introduced to the
market. Innovation may be explained by the availability of financial resources.
We also check whether financing is an impediment and control how access to finance
being an obstacle impacts the probability to innovate compared to not facing obstacles on
access to finance.
EMPLOYEES
Employees- we expect that the probability to innovate will increase if we have more
skilled labor. We have chosen to check for the labor since in our observation regarding
obstacles of businesses indicate that inadequate labor force is one of the major problems
for Macedonia and Albania and therefore we include this variable on the estimation for
these countries.
LABOR PRODUCTIVITY
We have defined labor productivity as sales per labor and generated this variable for the
sample data used in the estimation.
INFORMAL COMPETITION
The variable is generated from the question does the company compete against informal
sector. We use this variable to check the Schumpeterian view respectively to check how
competitiveness responds to innovation.
QUALITY CERTIFICATION
The question is whether the company has international quality certification. Quality
certification is a source of knowledge. We expect that companies that have quality
certification are more prone to innovate. Where quality certificate=1 if the enterprise has
a quality certification and equals 0 if otherwise. As a source of knowledge quality
certification is important for enterprises.
We summarize the variables in the following table:
Table 1 Variable Description
VARIABLE
SALES
LN_SALES
EMPLOYEES
LN_EMPLOYEES
DESCRIPTION
the establishment total annual
sales
The logarithm of sales
Number of permanent full time
employees in the firm
The logarithm of employees
56
EXPLANATION
Gross output
Logarithmic growth
Gross labor input
Logarithmic growth
RESEARCH AND
DEVELOPMENT
(R&D)
Whether the company
invested in R&D or not
CAPITAL
Net capital of the company
LN_CAPITAL
INTERMEDIATE
The logarithm of capital
Logarithmic growth
Intermediate goods employed in Cost of raw materials
the production
and intermediate goods
used in production
LN_INTERMEDIATE
ELECTRICITY
The logarithm of intermediate
SME
INNOVATION
INTERNET
BROADBAND
ACCESS TO FINANCE
has 1 if the firm is engaged
in R&D spending; 0
otherwise
net book value of
machinery and
equipment +net book
value of land and
buildings
Logarithmic growth
Total annual cost of
Electricity cost
electricity
Size of the company ( number of <100 equals to 1 and 0
employees)
for >100
The definition of innovation is
the introduction of a new
product.
Whether the company has an
internet broadband or not.
1 if the company
introduced
a
new
product; 0 otherwise
1 if the company has
internet broadband; 0
otherwise
Whether the company finds 1 if
they find
access to finance as an obstacle
moderate, major and
severe obstacle and 0 if
minor or no obstacle
LABOR
PRODUCTIVITY
We
have
defined
labor Sales/employee
productivity as sales per labor
INFORMAL
COMPETITION
Does the company compete 1 if yes and 0 otherwise
against informal sector.
QUALITY
CERTIFICATION
The question is whether the
company
has
international
quality certification.
Whether the company faces the
problem of power outages or
not.
POWER OUTAGES
Source: BEEPS Questionnaire
57
1 if the enterprise has a
quality certification and
equals 0 if otherwise.
1 if yes and 0 otherwise
3.5. MODEL AND ESTIMATION DISCUSSION
On the literature review we find that possible determinants of productivity are R&D and
innovation. Also we identified that among other methods Cobb-Douglas production
function is applied in productivity studies. Therefore we are suggesting the estimation of
three regressions.
Two of them are nonlinear regressions: the first one where the dependent variable is new
product and the second investment in R&D. With the first two models we want to check
the nature of the firms respectively what influences the enterprises to innovate and to
have R&D investment. Our dependent variables are two of the main factors for which the
research provides evidence as determinants of productivity.
The model for the logit is as follows:
Innovation= f (sales, SME, compete with unregistered, credit)
Whenever our dependent variable is a binary choice variable the model we chose to
estimate is from the probability models. Most commonly used for this type of models are
probit and logit.
The general mathematical expression for this model is as follows:
1) probit: 𝐏𝐫 𝒀 = 𝟏𝚰𝑿 = 𝝓 (𝑿′ 𝜷)
The model for the probit is as follows:
Equation 20 Yit= β0it +β1it+uit
Where Yit= 1 if Yit>0 and Yit=0 if otherwise
2) Logit 𝑙𝑜𝑔𝑖𝑡 (𝔼 𝑌𝑖 𝔩𝑋𝑖 = 𝑙𝑜𝑔𝑖𝑡 𝑝𝑖 = ln
𝑝𝑖
1− 𝑝 𝑖
= 𝛽𝑋𝑖 or respectively as a latent
variable model
y*=  0  x  e , where
y = 1[y*>0]
y = 0[y*≤0]
The link function in probit models is the inverse normal cumulative distribution while in
the logit model is the logit transformation. Logistic distribution is leptokurtic relative to
the normal distribution. Binary response models are widely used in economics.
Hahn and Soyer examine how the links in multivariate binary response models can be
distinguished respectively the multivariate link function and random effects model. They
note that when there are extreme independent variable levels than the ability to
distinguish between probit and logit is maximized. They try to find differences and
compare logit and probit models using 4 conditions:
1) Nonextreme independent variable level; moderate dependent variable correlation;
58
2) Nonextreme independent variable level; high dependent variable correlation;
3) Extreme independent variable level; moderate dependent variable correlation;
4) Extreme independent variable level; high dependent variable correlation.
They also compare the differences once the sample size is small and larger. They find
that in small sample the probit model may slightly perform better. When the sample is
larger they find superiority in the logit model.
Considering that the nature dataset provides information about innovation from YES or
NO answer, in the model that will be estimated it will take a binary form, therefore we
will apply the logit model. We will use the logit model in order to see what are the
possible effects of dependent variables in case that the binary dependent variable
(innovation) takes a value of 1 in cases that the company introduces new product and
zero otherwise. We may conclude that our dependent variable is dichotomous therefore
the model that we will use is a logit model. In the following part we will describe the
variables that we consider to have an impact on the outcome of our binary dependent
variable and our expectations.
Being a binary dependent variable innovation is analyzed using maximum likelihood
estimation; explicitly in our model we will use logit11 regression. Wooldridge (2006)
suggests that we cannot express the logit model with formulas because of the nonlinear
nature, thus we express our dependent variable as a function of independent variables.
“Innovative activity has a positive spillover in that all firms innovate on the same quality
frontier and innovations push the frontier forward”p.1319, Lentz and Mortensen (2008).
“Most firms in emerging markets are engaged in activities far from the technological
frontier and entrepreneurs innovate not just through original inventions but also by
adopting new means of production, new products and new forms of organization.” p.2,
Ayyagari et al. (2007). They test whether innovation is the channel through which initial
development affects growth. Their results find positive relationship between external
finance and innovation also that foreign financing is associated with more innovation.
They find that state owned firms are less likely to innovate. Also that firms owned by
individuals are more prone to innovating than firms owned by financial institutions.
Foreign competition is positively related to innovation. Firms that are run by experienced
managers tend to innovate more. They note that human capital investment is important
for innovation and conclude that higher competition and good governance may lead to
greater innovation. The questions we want to answer are what determines firm to
innovate?
Heshmati and Pietola (2004) use CIS Swedish DATA for time period 1996-98. Their
definition of innovation is positive innovation input and positive innovation sales. They
use one step generalized tobit model for innovation and 3SLS. They find negative
relationship between size and inefficiency. Industries with intensive production factors
are less efficient than industries with average production factors. Also innovation,
productivity and temporarily hired labor are enhancing efficiency. Their estimates show
that larger firms and firms that innovate are more efficient. They also find differences in
11
We can also apply the probit model but since we get similar results we estimate only using logit. These
models allow predicting the probability that an employee is part of a particular scheme as a nonlinear
function of the independent variables.
59
efficiency of sectors. They find evidence on positive link between innovation and
productivity growth at firm level. According to their results positively influence the
decision to invest in innovation: profitability, knowledge intensity, size, investment
intensity, and export share and labor and capital intensive production technologies. They
note that innovation on input and the process of innovation impacts the innovation output.
Their results suggest two-way positive causal relationship between the innovation output
and productivity growth among the innovative firms. “The relationship between
corporate competitiveness strategy, innovation, increased efficiency, productivity growth
and outsourcing” Almas Heshmati and Kyösti Pietola (2004)
Buddelmeyer et al. (2006) note that since is difficult to measure the success of innovation
the relationship between innovation and firm survival is ambiguous. Their data consist of
Australian firms for the time period 1997-2003.
Aghion et al. (2002) provide evidence that in transition countries old firms innovate
because of agency problem while new firms innovate because of competitive pressure.
They suggest that hard budget constraint, competition and access to external finance may
lead to more innovation and growth in companies in transition countries.
Harrison et al. (2008) assess the relationship between innovation and employment. Their
evidence suggests that innovators have higher employment growth than noninovators,
also sales growth and productivity is higher for innovators. Their evidence is on
manufacturing and service and they make a distinction between process innovation and
product innovation. The evidence they provide may suggest that transition countries
should boost innovation because of the expectation that it may lead to higher
employment.
According to the Central Limit theorem if the sample is large enough than every
distribution follows the normal distribution. Biernes (2008) discuss how the logit model
is interpreted.
The hypothesis we are testing is whether sales, internet, power outages and innovation
are determinants for R&D. Thus the second estimated model is also a logit model:
R&D= f (SME, internet, power outages, compete with unregistered and innovation).
3.5.1. LOGIT ESTIMATION
Probabilistic models originate from Luce 1959 and now are extensively used in social
sciences. Probability models are models of choice between mutually exclusive events.
The difference between probit and logit is in the cumulative distribution function where
the first is specified for the normal distribution while the latter for the logisitic
distribution. Whenever we have discrete choice variables we have to respond them with
binary choice models respectively the basic models of this kind are probit and logit.
Despite the extensive use the interpretation of these models is not straightforward task.
The difficulty arises because these types of models are not linear and therefore they can
no longer be estimated using OLS but rather with MLE. The idea behind MLE is
choosing the maximum likelihood function contrarily to OLS where we seek for the least
60
square. Koppelman, (2000) note that likelihood is an estimation of a function of
maximum utility estimation.
The OLS cannot be used since the Gauss- Markov assumptions are violated respectively
the error term has a logistic distribution. Therefore the OLS will produce biased,
inefficient and non-reliable results. We can find that these types of model are interpreted
as probabilities, odds and marginal effects.
In the binary choice model log of odds ratio is the dependent variable where independent
variables may be quantitative and/or qualitative variable and the difficulty in
interpretation arises especially with the qualitative independent variables. The slope of
coefficients in a logit model are not constant so the information that we reach from the
estimation is only for the direction of the impact and it does not tell much about the
magnitude of the impact. Thus before concluding the research should follow more
estimation. Noteworthy “effective interpretation of the binary logit/probit models calls
for more than model estimation” p.1 (Park, 2004).
Logit and probit model is most common used model for a binary response dependent
variable and the probability that the event will occur has a Bermuoli distribution. The
difference is that the logit model follows a logistic cumulative distribution while the
probit follows normal cumulative function. The formal preposition of the logit model
assumes that the probability of the dependent variable is a function of independent
variables. The slope of logit curve is the marginal effect of the independent variable on
the probability of the dependent variable and it can be estimated as a derivative. The
marginal effect in the probability of the dependent variable in the logit model depends on
the value of all independent variables in the model.
The logit model is formulated:
Equation 21 𝐏 𝐘 = 𝟏 𝐗 =
𝟏
𝟏+𝐞𝐱𝐩⁡
(−𝛂−𝛃𝐗)
Or alternatively:
Equation 22 𝑷 𝒀 = 𝟎 𝑿 =
𝐞𝐱𝐩⁡
(−𝜶−𝜷𝑿)
𝟏+𝐞𝐱𝐩⁡
(−𝜶−𝜷𝑿)
Probit and logit models produce similar results even though they use different
distribution: the probit uses normal distribution where the logit the logistic distribution.
Thus for logit the function of the cumulative distribution of the error is expressed as:
Equation 23 𝐟 𝐮 =
𝟏
𝟏+𝐞−𝐮
And for the probit:
Equation 24 𝐟 𝐮 =
61
𝟐
−𝐭
𝐮
𝟐𝛔𝟐
𝐞
𝟐𝛑𝛔𝟐 −∞
𝟏
𝐝𝐭
The MLE is sensitive to size. In an OLS model some of the main figures for the
significance of the variables and the model that we look are t-statistic‟s and/or probability
values, F values and R2 and the interpretation of the coefficients is straightforward
respectively the parameter of the variables tell us about the magnitude of the impact when
other variables are hold constant. In a logit model we no longer look at the F value or R2
(instead of there are other fit values which will be discussed in the following parts) and
the parameter does not directly tell the magnitude of the impact alternatively researches
may look at:
 Predicted probability
 Marginal effects
 Changes in odds
Estimation of predicted probability results:
Equation 25 𝐥𝐨𝐠𝐢𝐭 (𝔼 𝐘𝐢 𝖑𝐗 𝐢 = 𝐥𝐨𝐠𝐢𝐭 𝐩𝐢 = 𝐥𝐧
𝐩𝐢
𝟏− 𝐩𝐢
= 𝛃𝐗 𝐢
The formulation was named logistic by Verhulst.
Equation 26 𝑷 𝒀 = 𝟏 𝑿 =
𝟏
𝟏+𝐞𝐱𝐩⁡(−𝒀)
=
𝟏
𝟏+𝐞𝐱𝐩⁡(−𝜷𝟎 −𝜷𝟏 𝑿)
Or alternatively:
Equation 27 𝑷 =
𝟏
𝟏+ 𝒆−𝑿𝜷
while the odds ratio is:
Equation 28 odds=
𝟏
𝒆−𝑿𝜷
The marginal effects are not constant but vary from the independent variables therefore
they can be interpreted as the magnitude changes in the probability of the dependent
variable for a unit change, holding other factors constant. Marginal effect is relative
changes in odds.
The marginal effect tells the probability that our dependent variable takes value of 1,
holding other factors constant and is estimated using partial derivatives with respect to
independent variables:
Equation 29
𝛛(𝐗𝛃)
𝛛𝐗 𝐤
=
𝐞𝐗𝛃
(𝟏+𝐞𝐗𝛃 )𝟐
𝛃𝐤
When we take the exponential of logit we have calculated the odds ratio. The odds ratio
give information about the magnitude change of the dependent variable for an increase of
a standard deviation, holding other factors constant.
62
A formal knowledge for the general logit formulation and the interpretation of marginal
effects, odds and odds ratio is provided by Bierens, (2008).
The latent logit model may be expressed as:
y*=  0  x  u , where
y = 1[y*>0]
y = 0[y*≤0]
In the model X is a vector of random variables and u is the error term. The vector
variables are variables that are expected to influence the occurrence of Y. Thus logit is
often used based on utility choice and utility is determined by stochastic and no stochastic
term. We have the information about the choice between alternatives. The nosntohastic
term follows a logistic distribution. In case of dummy variables included we check
whether there are significant differences between groups. Following we discuss
estimation problems that are identified by researchers when estimating probabilistic
models.
The logit model is based on the assumption Independence of Irrelevant Alternatives and
testing this assumption tells how well the logit fits the data i.e. if the assumption (H0) is
not rejected. The underlying test was developed by Hausman and McFaden (1984).
MLE can be estimated using different software‟s which provide us with information
about the pseudo t statistics (testing the significance of independent variables), pseudo R2
which
is
similar
to
the
R2
in
the
OLS. In order to check for the significance of variables or joint significance of variables
2
we can follow Wald test and has 𝜒𝑚
distribution.
Andrews et al. (2002) assess the fit of logit models using log likelihood and BIC as
approximation of marginal likelihood. They use prediction accuracy, parameter recovery
error and fit as measure of performance of the logit model.
Nagler, (1994) propose a scobit estimation which follows Burr 10 distribution as an
alternative to probit and logit models which allows skewed disturbance term. They
compare scobit to logit not probit and note that logit is a constrained version of scobit.
They sum that scobit is preferable to logit when α=1 while if α≠1 there is no much gain
of estimating with scobit and that scobit may perform well for small samples. He notes
that in the voting model scobit outperforms logit and the prediction between two models
differ. They propose the scobit estimation as a result of the limitations that logit and
probit face due to the assumption that individuals with probability 0.5 are more sensitive
to changes. Logit and probit underestimate low probabilities- in the corner of distribution.
Pradeep, (1994) note that when reporting probit and logit estimates usually researches use
wrong formula and interpret them as probabilities and they also note that quantitative
independent variables are interpreted straightforward but for dummy variables is the
slope evaluation of infinitesimal of a change in the categorical variable.
63
Berry et al. (2010) note that in recent year‟s logit and probit model are used in political
sciences with two independent variables that interact in influencing the probability of the
dependent variable. A product term is introduced in the model and the estimation
determines whether is significant or insignificant. According to them the presence of a
product term does not necessarily mean that there is interaction and therefore should not
be used to test and conclude interaction but should be used on theory grounds. They
outline the meaning of a compression effect i.e. the marginal effect of a variable in probit
and logit model in the probability of Y is strongest when probability of Y equals 0.5 and
it gets smaller when the probability gets closer to 0 or 1. Thus they note that due to
compression there will be interaction between independent variable nevertheless if there
is a product term or not. On the other hand the introduction of a product term brings a
second source of variation of the marginal effect on the probability. They specify that
after Nagler (1991) paper researches were cautious to not identify compression with
interaction but rather use product term to specify variable-specific interaction. Contrarily
to Nagler their suggestion is that sometimes but not always a product term is necessary to
capture interaction in logit and probit models. Thus they point that interaction may be
caused by compression (in model with not product term) or by compression and variablespecific interaction (in models with product term). They also discuss that in a logit model
if independent variables also take finite range values than their effect on the probability
of Y is linear and additive and that nearly no compression is present. They note that large
sample will result with consistent marginal effect on probability estimate and on average
will be on target. They show that a statistical significant product term is not necessarily a
confirmation for interaction and contrarily that an insignificant product term does not
necessarily imply that there is no interaction. Since product term is neither necessary nor
sufficient for finding interaction than the theory the answer whether or not to include a
product term. They identify differences between product term, interaction term and
compression and the application of logit in political sciences.
Borooah, (2003) note that Oaxaca-Blinder decomposition method may be applied if there
are two mutually exclusive groups. Contrarily to Oaxaca-Blinder he proposes a
decomposition method when there are more than two groups. He introduces a
decomposition method to capture inter group differences in a logit formulation.
Norton and Wang, (2004) note that interaction variables should not be treated same in
linear and nonlinear models. In nonlinear models the marginal effect of the interaction
variable is dependent on independent variables, the significance cannot be tested using z
test and the sign of the interaction term may not indicate the sign of the interaction. Thus
interaction variables should not be interpreted straightforward. They summarize that
interacted variables are difficult to estimate and interpret in nonlinear models.
Contrarily Allison, (1999) note that variation in the error makes comparison between
groups in logit and probit invalidated. The model that they estimate is the probability a
professor to get promoted and find that publishing a paper has significant different effect
in male and female professors. They propose that if we want to make comparisons
between groups in the legit model two things should be taken account of: sampling error
and over identification.
In the binary models is an important variable that may impact the dependent variable to
be included no matter if they are correlated with other independent variables. Colinearity
64
may cause instability in estimation of parameters in a logit model. The problem of
missing data applies also to nonlinear model and if missing data is relatively large as a
consequence the research may not be conducted because no sample is left. In such
situations the solution may be same suggestion as in linear models. Stepwise selection
procedure should be applied in a logit model in order to check the independent variables
that will be used in estimation.
Lennox, (1999) note that nonlinear models should be tested for variable bias and
homoscedascity in order to check if they are correctly specifies. He adds than when
correctly specified nonlinear model such as probit and logit are better than DA in
predicting bankruptcy models. They recognized superiority of nonlinear models over DA
when they are well specified.
Dubin and Rivers, (1989) note that despite the extensive use of logit model, very little
focus has been on the issue of missing data for this type of models. They suggest that a
Hackman extended framework can be applied to logit and probit models in order to
overcome missing data problem.
Allison, (1987) underline that, the logit model does not account for heterogeneity and
they propose a remedy- introducing a disturbance term. The introduction of the
disturbance term does not change the likelihood function.
Al, (2007) note that the logit response model are restricted to well behaved classes of
games. The generalization of the logit response model is on the basis of mistake model
and the convergence to the Nash equilibrium in the general classes of games.
Werden,Froeb and Tardiff, (2001) review the use of logit model in antitrust of mergers
and advocate the use of logit in industrial organization. They note that in demand choice
models endogeneity may arise as a problem. In their review they find that the application
of logit is in estimating demand of hospitals, demand for telecommunication services,
antitrust policy.
Boskin, (1974) apply conditional logit model in the choice of occupation model and
conclude that the choice is based on the maximization of the discounted present value of
potential future earnings.
Anderson and Holt, (2001) prove that there is a logit equilibrium in minimum and median
effort coordination game and is a stochastic version of Nash equilibrium. They sum that
by incorporating noise in the game an alternative of Nash analyses empirically grounded
is provided.
Werden and Froeb, (1994) use the logit model for the demand in differentiated product
industry and the effect of mergers in this industries. They note that sometimes probit and
nested logit may be preferable to logit.
Schmidt ans Strauss, (1975) analyze employment using multiple logit. This model
emphasizes differences due to preferences and differences due to labor market
discrimination. They estimate whether there is gender and race discrimination in the
employment.
Consumer choice modeling literature applies logit model (Waerden, 1991). He proposes
mother logit as an alternative to the consumer choice theory which is a generalization of
65
multinomial logit model. In the model for consumer choice of shopping center they apply
mother logit which avoids the IIA property and it performed slightly better than
multinomial logit and the difference between two models is statistically significant but
relatively small. He identifies three class of study models that avoid IIA: the class that
allows variances and covariance among the error term, the second class includes measure
of (DIS) similarity in the utility function and the third class assumes a hierarchical
decision making process.
Independence from Irrelevant Alternative preposition holds in the simple logit model but
does not hold in the mixed logit (Brownstone, Bunch, & Train, 2000). Mixed logit vary
on the structure that they use. They estimate multinomial logit and mixed logit and
capture the unobserved error correlation. They apply mixed logit in transportation
analysis and conclude that using probability models in alternative fuel vehicle choice is
difficult because of the large availability of choice.
Nevo, (2000) note the extensive research on demand use mixed logit. Logit model is an
improvement in estimating demand since it counts for heterogeneity of taste in
differentiated product industries i.e. it counts for dimensionality of products. They note
that in logit the substitution is estimated by the market share of the product. Utility
shocks correlated across brand according to them may fix this problem of logit which on
the other hand comes because of iid preposition. They propose the nested logit for
modeling demand.
Salas and Velasco, (2000) note that a lot focus has been attached to the economics of
education. In models where individuals are choosing whether a certain level will be
followed (having a dichotomous dependent variable whether or whether not) a logit
model may be applied. With such models we can predict the determinant of choosing an
investment in education by individuals. They estimate educational choice model using a
logit model.
Pradeep, (1994) underline using log likelihood tests the importance of demographic
information on household segment membership. They use BIC for the choice of number
of segments and their model is an extension of logit mixture model.
Finnie, (2000) use a panel logit model to estimate the probability of migration. In the
model they use both qualitative and quantitative independent variables and report the
results as probabilities focusing only on the direction of the effect not size.
Vanhoof, Ooghe and Siernes, (1998) compare logit model and decision trees in analysis
of the choice of banks to give or cancel a credit. They note that logit provides with the
direct link of variables and output and that in the first sight logit estimates are abstract
compared to decision tree but in the logit model we can test for the “true” model, “true”
variables and obtain coefficients while contrarily in decision tree only ad hoc methods
can be applied in the decision to use the variables. Another feature of comparison is that
particular variable can be tested in logit while in decision tree only nodes not variables
can be tested and in decision trees there is no direct link between variables and output ( a
variable may be used several times).
66
The literature on theoretical and empirical estimation of binary models provides evidence
on difficulties in interpretation of such models and yet we find extensive use of them in
different fields of economics and other social sciences.
3.6. COBB- DOUGLAS PRODUCTION FUNCTION
In order to observe input elasticity‟s and returns to scale, in this thesis we rely on the
Cobb-Douglas production function. Beginning with the work of Cobb and Douglas
(1928) production function estimation studies originate since 1928 with tendency to
prove that production functions are linear homogenous functions. The Cobb- Douglas
production function is discussed widely on economic and econometric grounds and yet is
widely used for estimation purposes. The regression to be estimated in this section is
based on a Cobb Douglas production function, with the dependent variable growth of
sales. The purpose is to observe only behavior of labor input and capital. A second
regression is log of sales, where more variables are included. Mathematically we can
express the Cobb Douglas production function as:
Equation 30 Y = A * La K(1-a)
Since the exponents on labor and capital sum up to 1, the production displays constant
returns to scale. Rewriting equation 30 we get:
Equation 31 A = Y / La * K(1-a)
Where A is the total product output per unit of each of the inputs. In linear form we can
express the general production function as:
Equation 32 ln Y = ln A + a * ln L + (1-a) * ln K
While if we want to look at growth instead of levels of output we take the derivatives and
get the form:
Equation 33 dY / Y = dA / A + a * dL / L + (1-a) * dK / K
So that we can account for the percentage changes of output caused by percentage
changes of each input, when knowing that A can be calculated as “residual”.
The underlying econometric Cobb-Douglas production function that describes output by
two inputs: respectively labor and capital, can be written as:
Equation 34 𝒍𝒏𝒀 = 𝜷𝟎 + 𝜷𝑳 𝒍𝒏𝑳 + 𝜷𝑲 𝒍𝒏𝑲 + 𝒖12
The β parameters describe respective input elasticity‟s of output and the sum of
parameters represent returns to scale which we denote with R.
12
𝑌 = 𝐴𝐿𝛽𝐿 𝐾𝛽𝐾 where L denotes Labor input and K denotes capital input
67
Additionally to Ark‟s (2002) definition that productivity is a measure of effectiveness, we
note that productivity is a measure of both effectiveness and efficiency and that is how it
defers from profitability. Schools of firm profitability are identified in Stierwald (2009).
Grosskopf (2002) reviews productivity measurement and decomposition and suggest that
productivity should be directed to economic growth literature from frontier productivity
measurement. TFP growth estimation assumes that the units are efficient otherwise the
estimation is biased also human capital is important for accuracy of measurement
(Maudos et al. ,1999). Moreover they note the importance of human capital in measuring
productivity growth in macro level in OECD countries using dataset of World Penn
Tables. Bhanumurthy (2002) note that Cobb-Douglas production function may be used
not just because of ease of computing but also because to the problems that may arise
with its estimation may be addressed with corresponding remedies.
Felipe and Adams (2005) note that the aim of aggregate production function is producing
distribution income accounting identity. They discuss aggregation problems of
production function and note that Cobb-Douglas production is the most ubiquitous form
of theoretical and empirical analysis. Chambers (1998) discusses input, output and
productivity measures and develop Benet Bowley measures transformation which are
translation invariant. Douglas (1967) in his Comments on the Cobb-Douglas production
function answers to the critics and explains how their production function started from
the intuition of Euler theorem but faced most caustic criticism from neoclassicists,
institutionalists, econometricians and statisticians. He ends the comments challenging
researchers with the question: “There is law and relative regularity everywhere else- why
not in production and distribution?” (Douglas, 1967, p.22). Without taking sides
advocating Douglas or the critics and trying to answer who is right and who is wrong,
one thing is sure their paper raised the voice for consistent and better data collection
especially for capital which on the other hand made possible further research in different
fields.
Douglas (1948) accepted two critics: one of independently determining exponentials in
the production function (Durand, 1937) and broadening the field of investigation
(Hitherto) and they find agreement in exponential values between the results for US,
Australia and South Africa. He concludes that this is not the final say and yet there is
much to be done in the road ahead regarding production function.
In order to check the benefits from productivity in international trade gains Harrison
(1994) discuss productivity competition and trade reform. He underline that previous
research found that free-trade can increase growth, though the relationship between trade
reform and productivity growth is inconclusive due to that how productivity is measured.
He finds strong positive correlation between trade reform and productivity for the panel
sample of manufacturing firms undertaken in their study. Bernard and Jones (1996) do
not find evidence of productivity convergence in OECD countries but they raise the
question of comparison between countries and over time.
Diewert (1991) discuses measurement issues on productivity Productivity measurement
is discussed in Dean (1999). Diwert (2008) makes suggestions to agencies for data
improving in relation to productivity measurement and also suggest that balance sheet
information should be public.
68
It is argued by Diwert and Fox (1997) that measurement errors (adjustment error, error
because of failing to deal with cost allocation and error of measuring input and output)
may contribute to explaining the productivity paradox. A discussion on index numbers
can be found in Caves et al. (1982) where they introduce indexes for general comparisons
but note this index needs to be developed for econometric estimation. Ball et al. (2005)
introduce a Malmquist cost productivity measure.
The geometric mean of Malmquist index may be decomposed in catching up effect and
technical change (Fare et al.1994). Stratopoulos and Dehning (2000) note that statistically
is proven that using successfully Information Technologies (IT) leads to better
performance to profitability and efficiency. They outline that IT investments have an
increasing trend which is not expected to slow down.
Regarding above theoretical considerations we suggest the estimation of the following
function models:
 Innovation= f (sales, SME, compete with unregistered, credit)
 R&D= f (SME, internet, power outages, compete with unregistered and
innovation).
 Log sales= β0+ βLLnLAB+ βKlncapital + u
 Log sales= β0+ βLLnLAB+ βKlncapital + βIlnintermediate +βElnelectricity+u
The following section will focused on analyzing the dataset, the variables and the model
methodology while the estimation and result interpretation will follow on the next
chapter.
3.7. BUSSINESS CONSTRAINTS
Emerging market based countries such as the case of Macedonia are looking at the
development of SME‟s as one of the key features for enhacing the economic
development of the country. The begining of the transition is characterized with a large
number of new SME, and in later periods of transition the number of new SME is not
growing rapidly but their capital is. Financing of SME in trasition countries strongly rely
on credits, therefore restrictive credit policies may be considered as an obstacle for the
development of SME. High interest rates as well as crediting based on conections reduces
the acces to credits. SME find the credit difficult and expensive to obtain and as a result
the bussines will suffer. Small enterprises compared to big enterrprises have smaller
levereage coeffiecients.
On the following figures we will list the business constraints that companies in
Macedonia and Albania face compared to Eastern Europe& Central Asia.
69
Figure 11 Business constraints for Macedonia
Source: Enterprise survey (www.enterprisesurvey.org)
As the figure shows the major constraints in descending order that firms in Macedonia
face are: practices in informal sector, access to finance, political instability.
Figure 12 Business constraints for Albania
Source: Enterprise Surveys (http://www.enterprisesurveys.org), The World Bank
As the figure shows the major constraints in descending order that firm in Albania (2007)
face are: electricity, practices informal sector, corruption. On the following table we will
illustrate the differences of bussines constraints between : Albania, Macedonia and
Eastern Europe and Central Asia.
70
Table 2 Comparison of business constraints in descending order
MACEDONIA
EASTERN EUROPE
AND CENTRAL ASIA
ALBANIA
practices in informal
sector,
tax rates
Electricity
access to finance,
access to finance,
practices informal sector
political instability,
practices in informal
sector
Corruption
courts,
political instability,
Inadequately educated
workforce
licenses and permits,
Inadequately educated
workforce
access to finance,
crime, theft and
disorder,
Electricity
political instability,
tax rates
licenses and permits,
Customs and trade regulations
Electricity
Customs and trade
regulations
Access to land
Inadequately educated
workforce
crime, theft and disorder
tax rates
Customs and trade
regulations
courts,
crime, theft and disorder
Source: According to Bussines Enterprise listing, authors comparison
71
3.8. MAIN CHARACTERISITICS OF FIRMS
Accordingly in Macedonia in the 2009 questionnaire approximately 75% of sample
enterprises are small and medium and the others are large. While for Albania only
approximately 2% of the sample enterprises in 2009 are large the others are small and/or
medium. Approximately 78% of the sample enterprises are small and/or medium the
others are large. Around 60% of enterpsisess in the Macedonia sample for 2009 introduce
a new product. In Albania only around 37% of firms introduce a new product. Overall in
our sample data approximately 57% of firms introduce a new product. Around 41% of
firms in the Macedonia sample for 2009 invest in R&D . In Albania same around 41% of
firms invest in R&D. Overall in our sample data approximately 41% of firms invest in
R&D. Around 74% of firms in the Macedonia sample for 2009 have internet broadband.
In Albania around 72% of firms have internet broadband. Overall in our sample data
approximately 73% of enterprises have internet broadband. Around 54% of firms in
Macedonia in 2009 reported that access to finance is an obstacle. And, for Albania only
37% of the firms in 2009 reported that, they face obstacles in access to finance. The
average number of employees in the sample firms in Macedonia is 91 with a standard
deviation of 220 where the smallest number of employees is 1 and the largest 2146. The
average number of employees in the sample firms in Albania is 23 with a standard
deviation of 45 where the smallest number of employees is 2 and the largest 320. The
average number of skilled labor in the sample firms in Macedonia is 74. The average
number of skilled labor in Albania is 28. According to statistics only 36% of firms in
Macedonia have an internationally recognized quality certification. In Albania the
percentage of firms having internationally recognized quality certification is even
smaller- is 20%.
In sum both countries have a line of similarities and the main difference is in their
attitude to innovation (Macedonia companies tend to introduce new products more
compared to Albania companies) and the substantial difference is in the skilled
employees in companies which may be an indicator for labor market distortions in the
countries. We illustrate these differences in the figure below:
Comparison of firm characteristics
80
70
60
50
40
30
20
10
0
74.4
73.94
59.56
41.26
54.1
35.79
ALBANIA
MACEDONIA
Figure 13 Comparison of firm characteristic
Source: BEEPS data, authors estimation
72
3.9. CONCLUSION
In this chapter we analyzed the dataset. We provide more details about the selected
question of interest in the appendix respectively their summary statistics. After inspecting
the data we chose to follow the estimation for 2009 sample of data for two countries of
our interest: Albania and Macedonia because of limitations of availability of data. The
methodology we will be using for estimation is MLE and OLS. The sample representation
and data collection is fair and we suggest following with the estimation.
We are inspecting the panel data and we expect that we might have a problem of missing
data in the panel dataset ( for our questions of interest) that may have resulted because of
item no-response and not as a result of survey no-response. The missing data may arise
because of the differences in the questionnaire through time and another reason is
because the questionnaire is constructed so that in most of the questions it allows the
respondent to respond with I don’t know. Consequently because of high rates of missing
data and since data imputation may produce biased results we can follow using time
series or cross section analyzes as subsamples of the main panel data. The conclusion
after inspecting dataset is that the most appropriate way regarded our question of
interest is to use the subsample from the fourth round of BEEPS.
We presented the formal formulation of nonlinear models with specific reference to logit
model, the method used to estimate and how they are interpreted. We sum that the
interpretation of nonlinear models is not straightforward and the difficulty arises
especially with dummy variables. We also noted the confusion that is usually about
product term and interaction variables in logit models. The problems with logit model
may be problems of the nature of sampling, missing data, variable bias and
heteroscedascity. Despite the above mentioned logit model is applied in different fields of
economics such as: industrial relations, game theory, labor market, mergers, transport,
consumer choice and demand, economics of education, emigration, banking, mergers.
The extensive use of nonlinear models in different fields of economics suggest us that we
should acknowledge more understating and research in the nature, scope, advantages
and disadvantages of these models in economics analysis.
73
5. EVIDENCE ON FACTORS DESCRIBING
PRODUCTIVITY AND PRODUCTION FUNCTION
4.1.
INTRODUCTION
It is usually tempting to do research on transition a country especially is the aim is to
provide empirical evidence. Often research on these countries may not answer all the
needs because of the lack of availability of data and relatively large missing data in the
available dataset. The refusal of answering questionnaire is even larger when companies
are asked for questions regarding finances. However as we already introduced in the
previous chapter we have a reliable dataset involving companies from both countries of
interest. The aim of this chapter is to provide empirical evidence on the subject. We
begin the chapter with explaining why SME studies are important and introduce the
models that are estimated in section 4.2. Following sections 4.3 and 4.4 discuss the logit
model for innovation and offers interpretation of the determinants of innovation- which
on the other hand is expected to increase productivity. Than sections 4.5; 4.6 and 4.7
discuss the model for R&D predictors and also provide estimation results. Section 4.8 is
dedicated to Cobb-Douglas production estimation and section 4.9 summarizes brief
conclusions of the underlying chapter.
4.2.
MODEL INTRODUCTION
The SME are important for inducing competitiveness and competitive business
environment. The number of SME is large in developed European countries especially in
transition countries. To illustrate why the study of SME and SME policy is of great
interest for researches and policymakers lets illustrate with numbers. SME in Macedonia
employ 80% of the employees and represent over 50% of the GDP of the foreign trade in
the country. European SMEs employ 68 million people - 72 percent of the workforce of
the non-primary private sector (ENSI 1994). Thus SME are important for job creation.
We propose that government policies should be simulative to SME with respect to the
legislation for ease of entering the market and soften the financing obstacles that they
face. Macedonia as an EU Candidate country should also change the legislation in
accordance with EU regulations. The European Council in Lisbon 2000 induces EU –
Member States to be focused and responsive to SME and their needs. Stiervald (2010)
find empirical evidence that more productive firms are more profitable therefore we want
to address factors that contribute to productivity.
Despite Gibrats Law for the independence between size of the firm and firm growth; this
hypothesis has been rejected from scholars‟ empirical work. Scholars provide evidence
that SMEs are positively responding to Lisbon Strategies. Governments consider SME
policy as a strategy for economic growth, employment generation, and source of
innovation. Schumpeter (1942) called the large companies as the engine of progress;
nowadays we say that this critical role may be addressed to SMEs. Piore and Sabel
(1984) recognized SME as a new trend to the industrial organization. In transition
74
countries SME resulted as a consequence of the privatization process during the transition
to market oriented economies.
The evidence suggests that SME have positive impact on growth of the economy is large
(Carree, van Stel, Thurik and Wennekers (2002), Carree and Thurik, 2006, Schimitz
(1989), Acs (1992), Calderon and Nickel (1998) and Audretsch and Thurik (2000)) and
that SME induce employment (Thurik et al. (2008), Tambunam (2006)). Despite the
recognized opportunities of SME for the economy they face obstacles of legislation
nature and difficulties in access of financing.
In the following table we introduce the summary statistics of variables:
Table 3 Summary statistics
VARIABLE
LN_SALES
EMPLOYEES
(LABOR)
LN_EMPLOYEES
R&D
LN_CAPITAL
LN_INTERMEDIATE
LN_ELECTRICITY
SME
INNOVATION
INTERNET
BROADBAND
ACCESS TO
FINANCE
LN_LABOR
PRODUCTIVITY
INFORMAL
COMPETITION
QUALITY
CERTIFICATION
POWER OUTAGES
MEAN
STANDARD
DEVIATION
5.55
207.79
11.13
82.8
3.27
.409
16.83
8.58
8.13
0.78
.56
.715
7.67
.492
10.69
5.95
3.30
0.41
.49
.452
.519
.50
7.8
5.3
.657
.475
.338
.473
.435
.496
We follow with the introduction of models to be estimated:
 Innovation= f (sales, SME, compete with unregistered, credit)
 R&D= f (SME, internet, power outages, compete with unregistered and
innovation).
 Log sales= β0+ βLLnLAB+ βKlncapital + u
 Log sales= β0+ βLLnLAB+ βKlncapital + βIlnintermediate+βElnelectricity+u
75
This part is dedicated to estimation and interpretation of results. First we estimate two
models that describe factors that influence productivity, respectively innovation and
R&D and then a model describing marginal productivity.
4.2. INNOVATION MODEL
In this part we estimate a model for predictors of innovation. We expect that both firm
and market specific characteristics are possible predictors of innovation. Following the
literature on the field and the nature of our data we incorporate standard variables to test
the Schumpeterian view and also we control how financing access responds to innovation
as a result that is often used in recent papers related to innovation respectively whether
financing is an impediment for innovation. In the first part we give an outline of the
literature review on innovation, than follow with the model and results of estimation and
in the final part we conclude. Information asymmetry, moral hazard and principle-agent
problems are helpful starting points in explaining financing of innovation investment.
4.3. DEFINITION AND IMPROTANCE OF INNOVATION
The dynamics of market has posed innovation as condition rather than a choice for
companies that want to sustain and grow. Thomson (1965) outlines the broad definition
of innovation as the introduction of new product, process or idea. Increasing productivity
and performance are key expected benefits from innovation. Innovation may also be
defined as knowledge.
Emphasizing the role of innovation is crucial for market orientation companies which on
the other hand mean new ideas and not necessarily new entry Hurley and Hult (1998).
They note that innovation definition miss the learning orientation element. According to
them the innovation process is affected by market and learning orientation,
innovativeness and innovativeness capacity. Therefore firms that innovate may have
competitive advantage and perform better than the ones that don‟t. On empirical grounds
they find positive correlation between innovativeness and innovation capacity.
Innovation implementation is a process where employees adopt the innovation in their
work (Klein and Sorra (1996)). If the potential benefits are not achieved than the
innovation has failed. Thus the object of their study is implementation effectiveness at
organizational level which they define as consistency and quality use of innovation by
employees. They note that implementation effectiveness is not a guarantee for the
innovation benefits. Innovation value fit (they classify them in good fit, poor fit or
neutral) and implementation climate (it may be weak or strong) are factors that they
check how can influence innovation use. Summarizing their result: if the implementation
climate is weak it is companies‟ responsibility for innovation implementation while if the
values fit is poor (even in the case of strong implementation climate) than the employees
may not be willing to implement the innovation or resist the implementation. Taking
under consideration implementation effectiveness three scenarios may appear:
implementation is effective and yields benefits to the company, implementation is
effective and does not yield benefits to the company or the implementation fails. Thus
76
they make a distinction between implementation effectiveness and innovation
effectiveness.
Cohen and Levinthal (1989) model a symmetric Nash equilibrium of R&D investments
where the level of R&D is chosen from firm i in order to maximize the profit given the
level of R&D in the other firm. Thus the company anticipates R&D based on the
information about the other firm and the change in R&D has impact on firms‟ profit.
They find that the effect of ease of learning leads to higher return from R&D and
therefore more R&D. The firm has incentive to invest in R&D since its own investment
in R&D will make the firm to assimilate other firms and industry knowledge and at the
same time the other firms will be less able to absorb the firms‟ spillovers. Ambiguous
results are found about whether the increase in R&D investment will increase or decrease
the investment incentive for R&D which is not the same as the traditional view. Also they
model a cost reducing technological change which is again Nash equilibrium in order to
find how demand function and market structure respond to R&D. According to them
spillovers will encourage R&D if the environment is competitive and less concentrated.
The result of the question how new technology improves technology performance is
ambiguous. Their analysis suggests that the ease of learning had direct impact on R&D
level. The sample in their analysis consists of two kinds of data: the first one is 1719
business units (both R&D performing and non performing) and the second sample is
1302 business units (only R&D performing). They used Breusch Pagan test for
heteroscedascity in order to obtain efficient GLS estimates and because of the possibility
to have biased result (for the sample data they have business units that perform R&D),
they prefer OLS to Tobit and for the 1719 sample data the Tobit model. Another
estimation problem may be the endogeneity of market concentration which they address
using two stage OLS. Hence they estimate using OLS, GLS and Tobit. It results that
external applied research is a substitute for internal R&D while basic research is a
complement and determinants of ease of knowledge have impact on R&D investments.
They conclude that the greater the variability in the knowledge inputs the more the
investment in R&D basic research, also R&D investment have dual role in pursuing
innovation and learning from external information.
Breschi and Lissoni (2001) review the literature on localized knowledge spillover
(production function approach and Jaffe‟s approach for knowledge spillovers) and note
that a group of studies have acknowledged that knowledge spillovers are geographically
concentrated. A source of knowledge spillover is labor mobility. Studies that suggest that
innovation activities are localized can be found in: Kelly and Hagemann (1999), Jaffe et
al. (1993). The empirical literature misses the point how the knowledge is transferred to
people in same area or between firms. Firms or individual may wish to keep the
knowledge as their private good; they note and also discuss the role of University and
University R&D in innovation activities for firms. First the research results may be
helpful for the innovation of firms, than training program that Universities offer also
transfer knowledge and last but not least Universities can prepare skilled labor which
may persuade firms a competitive advantage. Even the University is a sample of localized
knowledge spillover. They conclude that knowledge spillovers are pecuniary and when
the black box of knowledge spillover is opened we find that there is space for further
research on the field.
77
Ahm (2002) note that, empirical studies on competition are based on Schumpeterian
idea13 and, they find arguments and counter-arguments on his view. They outline that
measuring the benefits in welfare from innovation is empirically challenging.
4.4.
PREDICTORS OF INNOVATION
For the model we take a sample from the BEEPS dataset and model innovation as:
Innovation= f (sales, SME, compete with unregistered, credit)
The definition of innovation that we use is the introduction of a new product respectively
whether the company introduced a new product or not and in the model that is the
variable of interest. The predictors we consider are sales (the size of sales in the last
year), SME (whether the company has up to 99 employees or more), compete with
unregistered firms (whether the company has unregistered firms as competitors) credit
(whether the company has a credit or a loan from a financial institution).
Kim and Mauborgne (1997) note that the answer why some firms grow faster than others
is in the value of innovation. According to them what mattered in the question why some
firms grow faster was how mangers thought about strategy- and it was the strategy of
value of innovation that distinguished fast growth firms. In a sample of 100 firms they
find that value innovation increase profits and revenues. According to them the specific
of the value of innovation is dominating the market not competing with others in
industry. Therefore they should produce some unique products that will be demanded.
They conclude that a strategy of value innovation may induce growth. In order to check
the hypothesis that the increase in sales will make companies to innovate more we have
included the independent variable sales in our model. We expect that firms that are larger
in sales will tend to innovate more.
Mansfield (1962) suggests that entry is the n number of firms that entered the industry as
proportion of the number of firms already in the industry. In their OLS estimates despite
the small number of observations, large errors we may have biased results but the
direction is correct and thus their result suggest that entry is positively correlated with
profit (entry increases 60% if profits double)
and negatively with the capital
requirement( entry decreases by 7% if capital requirements double). Also their estimates
for exit of the firms suggest that firms will exit if they are small relative to the industry
and if the profits are lower (exit decreases by 15% if profits or average size doubles). In
this work Gibrats Law14 it‟s tested for three industries (steel, petroleum and rubber ties)
and it fails to hold. The reasoning for this may be that the exit of firms from the industry
is not independent of the size respectively small firms are more prone to leave the
industry that large ones. Their results when testing Gibrats Law suggest that small firms
that stayed in the market have higher and more variable growth than large ones.
Accordingly Gibrats‟ Law does not hold empirically. Another noteworthy feature in their
estimates is that successful innovator firms had larger growth compared to similar firms
13
Studying the relationship between size and innovation
A proportionate change in size for a period of time is the same for firms in the same industry
independently of the size they begin with
14
78
that did not innovate successfully and the growth effect of innovation was larger in small
firms compared to large ones. This suggests again that size does matter. The market
structure and age according to their results has impact on the mobility in an industry. In
this line we control if size matters in our sample data respectively are there statistically
differences between SMEs‟ and large firms in their probability to innovate.
Competition according to principal-agent models tend to explain is beneficiary for the
firms since induces employees to work more effectively. The positive correlation
between competition and innovation can be found in Schumpeter (1934). Thus there are
expected gains if there is competition in the market. What about if the competition is
informal? In our model we want to control how facing informal competitors affects the
odds to innovate. We add the informal competition variable since enterprises in the
countries involved in the data may have significant informal economy. Approximately
40% of the enterprises answered that they do face informal competition.
Innovation is a process that requires highly qualified employees which on the other hand
means high financing requirements. Due to information asymmetries innovation activities
may face financing difficulties. The more recent papers on innovation control whether
financing is an impediment (usually proxy by the cash flow) for innovation process but
still they are inconclusive. We take an alternative approach and control whether access to
finances, proxy with the variable whether the company has a credit or loan or not, is a
predictor for innovation. The main problem of financing investments in innovation is the
uncertainty involved regarded to the fact that whether it will be successful and whether it
will provide returns.
Savignac (2007) contrarily to other studies that look at financial constraints for
innovation, use a direct measure of financial constraint for innovation activities stated by
firms themselves and how does it impact the likelihood to innovate. Financial constrains
delayed or made the process of innovation not to start at all. They estimate the propensity
to innovate using a probit model and as independent variables they use conventional
determinants of innovation and the financial constraint qualitative variable. They find
positive correlation between financing obstacles and propensity to innovate and note that
this striking result may be because of endogeneity problems. When endogeneity problem
is taken account for the results suggest that the likelihood to innovate reduces 20% with
the presence of financial constraints, c.p.
Bronwyn (2009), note that the knowledge of the specific human capital in an innovation
process may be lost if the employee leaves the firm. According to him we should not treat
investment in innovation as an ordinary investment and also because of the degree of
uncertainty this kind of specific investments are riskier. Thus financing innovation is
more expensive than an ordinary investment. Another fact, pointed in the paper is that,
innovative firms as a result of high external financing cost should rely on retained
earnings and also that young and/or small firms are more prone to have financing
difficulties.
The nature of our dependent variable is dichotomous and since OLS produces biased and
inefficient estimates for dichotomous dependent variable we use MLE. We want to
determine factors for the occurrence of innovation. The model that we estimate is a logit.
The results of the estimates suggest that the model fits well the data (according to log
79
likelihood) and the independent variables result significant. Hosmer-Lemeshow‟s test
suggests that we may not reject the hypothesis that the distribution fits the data.
Crostabulation of observed and predicted outcomes, where one predicts a positive
outcome if the probability is 0.5 or more and a negative outcome otherwise suggests that
we predict correctly approximately 58% of cases. Accordingly we suggest that sales,
having a credit, having an unregistered firm as competitor increase the odds to innovate
while being a SME company decreases the odds to innovate compared to being large
company.
The MLE estimation of our logit model results as shown below:
Table 4 Logit estimate
Innovation
Coefficient Stan.
Error
Z
P>|z|
95%
95%
confidence confidence
intervals
intervals
Sales
2.38*
1.38
1.72
.085
-3.32
5.09
SME
.466*
.26
1.78
.075
-.047
.978
Compete.unreg .42**
.21
1.98
.048
.004
.836
Credit
.556***
.206
2.69
.007
.152
.960
Cons
-.765**
.299
-2.56
.011
-1.35
-.179
Note: level by significance *** for 1%; ** for 5% and * for 10% statistical significance
Source: authors‟ estimation
The theory of the choice between Wald and LR test is unclear, in our estimation we chose
the LR test. We computed LR test and it resulted that the variable credit is significant
(LRχ2=7.26, df=1, p <.007). The LR test suggests also that sales are significant
(LRχ2=2.96, df=1, p <.085). The LR test for SME also suggests that is significant
(LRχ2=3.17, df=1, p <.0). The LR test for compete with unregistered also suggest that is
significant (LRχ2=3.92, df=1, p <.047). The estimated sign of dependent variables results
positive.
We also conducted multiple test of coefficient and the results suggest that the hypothesis
that SME and credit are simultaneously equal to zero can be rejected (LRχ2=9.59, df=2, p
<.008). We also tested the hypothesis that the effect of all independent variable are
simultaneously equal zero and the results suggest that we reject the hypothesis at 1%
80
level of significance (LRχ2=16.99, df=4, p <.001). Even in the case of multicolinearity
the results will not be biased but the standard errors will be inflated. Additionally the
correlation matrix suggests that we do not have correlation problems since the value of
correlation matrix is relatively small.
According to the results enterprises that compete with informal competition and have a
line of credit or loan are more likely to innovate as well as enterprises with larger sales.
We also calculated confidence intervals for discrete changes for binary variables with
marginal effects which uses numerical methods for computing confidence intervals. The
predicted probability to innovate at means of independent variables is 0.61. The estimates
of marginal effect of our model are presented in the table below:
Table 5 The marginal effect of logit estimate
Innovation
dy/dx
Sales
Stan.
Error
Z
P>|z|
95%
95%
X
confidenc confidenc
e intervals e intervals
5.83** .00
1.72
.085
-8.0
1.2
3.4
SME
.115** .06
1.78
.075
-.01
.24
.78
Compete.unreg
.103** .05
1.98
.048
.001
.20
.65
Credit
.136** .05
*
2.71
.007
.03
.23
.58
Note: level by significance *** for 1%; ** for 5% and * for 10% statistical significance
Source: authors‟ estimation with details in appendix
SME, Credit and compete with unregistered are discrete variables and therefore
magnitude of change is measured for a discrete change.
the
The predicted probabilities of positive outcome of dependent variable range from 0.52 to
0.61 with a mean of predicted value of innovation 0.57. For prediction purpose the choice
between probit and logit (two most common models for binary choice outcomes) is
irrelevant but choosing between linear probability models and logit and/or probit is
crucial.
We are 95% confident that the probability to innovate is between 0.58 and 0.71 if we set
the independent variable credit equal 1 and if the company belongs to SME.
81
For a standard deviation increase in sales the odds of innovating increase by 27.6%
holding other things constant. Odds for innovation are: 74.4% greater to firms that have
credit than those who don‟t, holding all other covariates constant; 52.2% greater for
enterprises that compete with informal competition than those who don‟t, holding all
other covariates constant; 59.3% higher for SME than for large companies, holding all
other covariates constant. Thus our results are in line with Schumpeterian view.
In sum our estimates suggest that for our sample data the size of sales has increased the
probability to innovate, also companies that face informal competition and have a line of
credit or loan have higher probability to innovate compared to companies that do not face
informal competition respectively companies that do not have a credit. Thus the nature of
the firm, the structure of the market and financing are possible determinants of
innovation.
In order to check whether historically internet is a determinant of innovation we
performed additional estimation where the scope of interest is only the statistical
significance. We estimate for two countries Albania and Macedonia again using BEEPS
dataset but for 200215:
Table 6 Estimation results- Macedonia and Albania (1)
Dependent variable: innovation
Sample n=226
Albania& Macedonia
BEEPS 2
Independent variables
Amount R&D
Sales
Power outages
Access to finance
Statistically significant
Internet
Skilled labor
As we can see from for BEEPS (2002) data only internet is statistically significant
variable. We add another independent variable: quality certification and get the following
results:
15
Remember that in the data inspection there are no observations for these countries for 2005
82
Table 7 Estimation results- Macedonia and Albania (2)
Dependent variable: innovation
Sample n=226
Albania& Macedonia
Independent variables
BEEPS (2002)
Amount R&D
Sales
Power outages
Access to finance
Statistically significant
Internet
Skilled labor
Statistically significant
Quality certification
The results suggest that internet broadband and quality certification are statistically
significant and the sign is positive. Thus even in the case of Albania and Macedonia
having internet broadband will increase the probability to innovate. Also firms that have
quality certification tend to innovate more.
4.5.
R&D PREDICTORS
One of the objective of the firm is to be competitive in the market therefore firms seek
how to attain this through different channels. Investment in technology, know-how,
quality may empower firms to be competitive.
The hypothesis we are testing is whether sales, internet, power outages and innovation
are determinants for R&D. Hosmer & Lemeshow are among those who argue that we
shouldn't report 'pseudo R2' in published results because its metric is not comparable to
that of OLS R2. With probit and logit we get ML estimators.
Researches find that R&D investment is translated in growth. The government
encourages business for R&D investment through tax reduction or subsidies. Enkel et al.
(2009) differentiate three processes in open innovation: inside-out, outside- in and
coupled process. They note that researcher lack at looking the inside out process.
David et al. (1999) note that the econometric results are in favor of complementarity
between private and public R&D although this is not based on scientific observation such
as Meta regression. They also underline complexities in the econometric research of
R&D. They note that typically private R&D is regressed on public R&D and some
control variables and then we look at the sign not the magnitude i.e. a positive sign
suggest for complementarity, whereas a negative sign suggest for substitution between
public and private investment. In order to make comparisons based on the study unit they
83
classify four types of studies: cross section- micro level studies, panel studies,
macroeconomic studies and studies controlling for simultaneity between private and
public investments. Another feature is that studies have different unit of analyzes such as
firm, industry, government. The laboratory studies suggest complementary. Firm studies
suggest that complementarity depends on the industry. Macroeconomic studies reviewed
by them also suggest complementarities between public and private investment.
Studies on R&D are not easily comparable since they have different scope on the issue.
Aboody and Lev (2000) note that proxies for information asymmetry are reflecting also
firm and market attributions and address to information asymmetry looking at the
investment in R&D. Investment in R&D is unique, there are no organized markets for
R&D, accounting measurement (R&D is immediately expensed). They suggest that R&D
contributes to information asymmetry. Their dataset consist of 253 038 transactions for
10 013 firms for the time January 1985- December 1997. Their result suggest that insider
gain are larger in R&D companies than in those with no R&D, therefore they proxy
information asymmetry with firms R&D intensity. They classify portfolios taking under
consideration where firms have R&D investment or not and whether insiders are “net
sellers” or “net buyers” and obtain 4 types of portfolios. Their dependent variable is the
difference between portfolio returns of firms with R&D and firms with no R&D and the
regression is run for 155 observations with independent variables: market return, size and
book to market employing the three factor model. Their results suggest that the returns
are higher when insider purchased shares in R&D firms compared to no R&D firms,
while lower when they sold shares. Insider gain is monotonic in R&D intensities for
insider sales while the purchase gain of insiders is attributed to higher R&D intensities.
These results suggest that R&D contributes to information asymmetry. They also
document that shares trade increases in R&D firms compared to no R&D firms when
insider purchase is disclosed. This finding is again consistent with the note that R&D
contributes to information asymmetry. They also find that insider trade is greater and
more intensive in firms with R&D than in firms with no R&D.
Goyal and Moraga (2000) model collaboration in R&D activity and its impact on cost
reduction, market structure and industry profits. Pissano (1990) note that the choice
betwean internal R&D investment or from outside sources may imact the long term
viability in the technological envierment. If this is important than we may say that this
choice leads firms to cooperate and collaborate betwean each other. Competing in the
technological envirement is what Schumpeter called “ creative destruction”. Pissano note
that it might be the case that technological envierement (change) may lead to beneficial
trade rather than competition betwean new entrants and established firms. He outlines
that established firms remain competitive in marketing but not competitive regarded new
technologies introduced. This may suggest as that the most productive alternative is
integration betwean firms and, this is attractive for both established and new firms
because of their different competitive advantages. He suggest that trasaction costs may
explain why R&D may lead to vertical integration in pharmaceutical industry because of
the small number barganinig and because of appropriability problems. R&D is a
transaction specific investment in projects in pharmaceutical industry therefore its not
ecconomicaly efficient if the project is not finished by the original contractor. This leads
to small bargaining problem and less favourable situation for the R&D investor (sponsor)
because of the specific nature of the investment and the difficulties in switching suppliers
84
of projects. In the case that there is competition in supplieres as well as expertise and
experiece this will favour the R&D investor situation.
Dasgupta and Stiglitz (1979) show that competition leads to more research. Cassiman and
Veugelers (2004) note that studies find complementarity between innovation activities.
They test complementarities between firm activities. They look at complementarity of
innovation activities and also sources of complementarities. They estimate a bivariate
probit and multinomial logit model for joint adoption on innovation activities and find
evidence for complementarities. They apply performance and adoption approach. They
employ sample of Belgian manufacturing firms. They find positive correlation between
internal and external innovation activities.
4.6.
THE R&D MODEL
Our research is focused on determinant of R&D in a sample of transition country. The
data are from BEEPS -2009. On this part we are going to describe the variables used for
estimation:
R&D- in the model is a dichotomy variable telling whether the firm is engaged in R&D
spending or not; since this is our variable of interest and because of its nature we have to
choose from the choice of binary models for estimating. There are a lot of studies that
correlate R&D with higher growth; therefore we want to estimate what may determine
the probability for R&D.
Innovation – in the model is a dummy variable showing whether the company has spent
on innovation (introduction of a new product). The expectation is that companies that
innovate also spend on R&D.
Power outages- is a dummy variable showing whether the company faces the problem of
power outages or not. Power outage is reported as an obstacle for the business
environment so we want to check whether it will represent an obstacle for R&D as well.
Internet- is a dummy variable whether the company has an internet broadband or not. We
expect that companies that have internet broadband will be more prone to R&D spending
because of the speed of information that internet provides.
4.7.
EVIDENCE ON PREDICTORS OF R&D
Again since OLS produces biased and inefficient estimates for dichotomous dependent
variable so we use maximum likelihood estimation. According to results variables
innovation, internet, competer with unregistered and SME are significant with
corresponding χ2 (in APPENDIX) while power outages results insignificant at
conventional levels of significance.
85
Table 8 Logit estimate
R&D
Coefficient
Stan.
Error
Z
P>|z|
95%
confidence
intervals
95%
confidence
intervals
Innovation
1.41***
.406
3.48
.001
.617
2.21
Power out
.284
.375
0.76
.449
-.451
1.02
Internet
1.161***
.444
2.61
.009
.290
2.03
Compete
unreg.
SME
.984**
.448
2.19
.028
.104
1.86
-1.35**
.681
-1.98
.047
-2.68
-.01
Cons
-1.84**
.825
-2.24
.025
-3.466
-.23
Source: authors‟ estimation with details in appendix
Note: level by significance *** for 1%; ** for 5% and * for 10% statistical significance
Hosmer- Lesmenhiv goodness of fit test suggests that the model is fitted well. The
probability to have an R&D investment increases at sample means if the companies do
innovate also if the company has an internet broadband. We estimated the correlation
matrix and it suggests there is only weak and no strong correlation between variables.
We also calculated confidence intervals for discrete changes for binary variables with
marginal effects which use numerical methods for computing confidence intervals and
the results are shown below while more details are provided in appendix.
Table 9 Marginal effects
dy/dx
Stan.
Error
Z
P>|z|
95%
confidence
intervals
95%
confidence
intervals
X
Innovation
.304***
.077
3.95
.000
.153
.4559
.613
Power out
.066
.088
.75
.451
-.106
.239
.398
Internet
.244***
.081
3.01
.003
.085
.404
.715
Compete
unreg.
.209**
.085
2.47
.014
.043
.376
.734
SME
-.325**
.151
-2.15
.032
-.623
-.028
.911
R&D
Source: authors‟ estimation with details in appendix
Note: level by significance *** for 1%; ** for 5% and * for 10% statistical significance
86
The results suggest that enterprises that innovate, have an internet broadband, face
informal competition and large enterprises compared to small and medium have higher
probability to be engaged in R&D investments. According to descriptive statistics 40, 9%
of enterprises from our sample data are engaged in R&D. The predicted probabilities
range from 0.03 to 0.88 with a mean of predicted value of having spent on R&D of 0.39.
For prediction purpose the choice between probit and logit is irrelevant. Enterprises that
innovate have 30.4% higher probability to be engaged in R&D than enterprises that do
not innovate, holding other covariates constant.
We are 95% confident that the probability to have R&D is between 0.3 and 0.6 given that
it innovates. The estimates suggest that predictors of R&D are innovation, internet
broadband, competition and size. According to our estimation results it is suggested that
firms that do innovate are more likely for 0.3 to have invested in R&D than the ones who
don‟t, holding other things constant. The estimated results also suggest that having
comepetition (in our case informal one) and having internet broadband increases
probability to invest in R&D at sample means by 0.2 respectively by 0.244 holding other
covariates constant.
4.8.
COBB- DOUGLAS ESTIMATION
The very first estimated micro production function is in agricultural studies. A
production function is an empirical relationship between inputs employed and outputs
produced. Economists relate input and output since 1800 ( Levinsohn and Petrin, (2000)).
Sandelin (1976) notes that there are different dates regarding to the origins of CobbDouglas production function and suggest that the origins go back in Wicksteed (1984)
while it is often stated that the origins date in Wicksell (1901). The very first estimation
of input-output relationship was in Cobb and Douglas (1928). Their work was object of
discussions among researchers criticizing and giving credit to the same. Despite the
critics Douglas continued working on the theory of production for two decades and
estimating both time series and cross section. Later it was generalized and extensively
used especcialy after Solow (1957) for estimating economic growth both in
microeconomics and macroeconomics. Theoretically a less restrictive estimation than
Cobb-Douglas is a translog production function. We estimate an equivalent linear
function of logarithms of Cobb-Douglas production function. Cobb-Douglas production
function may be estimated in the state level, industry level, firm or plant level. In this
study we are estimating Cobb-Douglas for manufacturing industries. Allocation of
resources in the production process is important because they address productivity and
are a response to market demand.
We estimated a two-input model:
Equation 35
Sales=f (labor, capital)
The above equation expresses that the production of outputs a function of labor (LAB)
and capital. The definition of output in our case is the value of sales, the definition of
labor is only the number of full time employees and we aggregate the capital measure
87
form the net book value of machinery &equipment and as well as land&buildings.
Capital is usually the most problematic measure in production function studies since data
for it are usually not readily available and researchers use their own measures of diverse
aggregation components. The properties that such production functions follow are that we
include the inputs required for the production and an increase in an input translates with
an increase in the output and they can exhibit increasing16, constant17 or decreasing18
returns to scale.
A Cobb-Douglas representation of the production function, given our variables of interest
is stated as in equation 36:
Equation 36
𝐒𝐚𝐥𝐞𝐬 = 𝛃𝟎 𝐋𝐀𝐁 𝛃𝟏 𝐂𝐀𝐏𝐈𝐓𝐀𝐋𝛃𝟐
An equivalent linear function as a logarithmic representation of Cobb-Douglas
production function can be stated as follows:
Equation 37
 Log sales19= β0+ βLLnLAB20+ βKlncapital21 + u
The allocation problem of inputs for the production process is mainly management
decision but it should be based on optimization. The residual of this equation is the
logarithm of total factor productivity
We have estimated Cobb-Douglass production function for a sample industry data in
Albania and Macedonia22. We recall the definition of variables in the underlying model:
the dependent variable is the logarithm of sales, labor is the number of full time
employees in the company and capital is the net book value of machinery and equipment
as well as land and buildings. The elasticity coefficients obtained from the estimates are
approximately 0, 7 for labor and 0, 4 for capital (estimation details are provided in
appendix) and they are both significant at conventional levels of significance.
We performed the diagnostic testing (see Appendix) for multicolinarity and
heteroscedscity and results that the model does not suffer from multicolinearity but it has
the heteroscedascity problem. Heteroscedascity problem is usually present in crosssection data but it does affect only estimator‟s efficacy and does not affect the bias of
estimators. We performed different types of hetersoscedascity tests such as: BreuschPagan; Cameron-Trivedi and White test and they all suggest that out model is
heteroscedastic. As a result we performed White corrected standard errors and interpret
these coefficients.
16
If an increase in inputs results with greater increase in output
If an increase in inputs results with exactly equal increase in output
18
If an increase in inputs results with smaller increase in output
19
What were the establishment total annual sales?
20
The number of permanent full time employees in the firm
21
Where capital= net book value of machinery and equipment +net book value of land and buildings
22
Details on sampling issues are provided in the previous chapter
17
88
Table 10 Cobb-Douglas estimation
O.L.S. Estimation
Regressor
Coefficient
tratio
p
value
S.E.
t-ratio
.072
6.39
.000
.250
3.12
.002
.27
2.89
.005
.103
4.43
.000
1.24
3.09
.002
1.23
4.11
.002
S.E.
LN_CAP
0.46***
LN_LABOUR 0.78***
CONS
3.85***
O.L.S. Results based on
White’s Heteroscedasticity
adjusted S.E.’s
p value
Source: authors‟ calculation
Note: level by significance *** for 1%; ** for 5% and * for 10% statistical significance
From the results we can write the estimated equation in the log-linear form:
lnSales= 3.85+0.78LAB+0.46 capital
The estimated equation in its multiplicative form is:
Sales=46.99LAB0.78CAPITAL0.46
This production shows that the output elasticitie‟s of labor and capital in the
manufacturing sector and is interpreted as follows: holding the labor constant, a 1
percent increase in the capital input leads on the average to a 0.46 percent increase in the
output; Similarly, holding the capital and constant, a 1 percent increase in the labor
input leads on the average to a 0.78 percent increase in the output. Alternatively we can
interpret the estimate that a 10% increase in capital will increase the output by 4, 6%
which implies that there are decreasing returns to capital. Similarly a 10% increase in
labor will lead to 7.8% increase in output and again implies that there are diminishing
returns to labor as well. The resulting estimated coefficients are output elasticity‟s of
respective inputs. In our estimation output elasticity of capital is 0.46 and output
elasticity of labor is 0.78. Thus, our results are in accordance with the economic theory
which tells us that marginal products of capital and labor are both positive, and both
these inputs individually exhibit diminishing returns. The results suggest that labor
contributes more than capital in the output i.e. in order to add output the distribution of
input goods should be toward labor in order to have higher increase in the output level.
Thus our estimates are evidence of applied Cobb-Douglas production function with
statistically valid results.
89
The mathematics for proving that Cobb-Douglas production function is homogenous is
simple:
We introduced sales= f( labor, capital) and than we have the general form of the
production function:
𝑆𝑎𝑙𝑒𝑠 = 𝐴𝐿𝛽𝐿 𝐾𝛽𝐾
and after estimation we obtained the following result:
Sales=46.99LAB0.78CAPITAL0.46
If we increase both inputs with o constant let‟s say 10 the resulting increase in output
will be: A times 101.24 respectively 17.378.
Returns to scale in the industry are obtained summing up the elasticitie‟s in coefficients
in equation above. The obtained value of 1.24 suggests that firms are experiencing
positive economies of scale of 0.24, on average. This implies that increasing all the inputs
(labor and capital) will lead to a more than proportional increase in sales. Increasing
returns to scale at the coefficient level of 1.24 indicates that if the inputs are increased by
100 percent the output will increase by 124 percent. Capital labor ratio may be one of the
explanations for these increasing returns to scale. Another explanation may be the costs
of production. Some studies report that countries with high capital labor ratio are more
efficient than the ones with lower ratio. The drawback of this consideration is that they do
not capture factor prices and factor endowment which may be crucial for facto allocation.
The positive economies of scale suggest that industries can produce and export at
competing prices and may grow employing more inputs. If this is the case these firms
may generate revenues for the economy. Decreasing returns to scale means that the
industry is inefficient.
Bhanymurthy (2002) discusses that Cobb- Douglas production function should be used
not just because it is a simple tool as critics suggest but because of advantages it
possesses in handling multiple inputs in its generalized form. For these purpose we will
have a closer look to the 4-input model estimation.
We construct again a Cobb-Douglas production function but beside two inputs that we
had in the previous model respectively labor and capital we add cost of materials and
intermediate goods ( intermedite) and the electiricity input ( cost of electiricity) and have
the following equation:
 Log sales= β0+ βLLnLAB23+ βKlncapital24 +βIlnintermediate25+βElnelectricity26+u
Estimation results of the above equation are presented in Table 11:
23
24
25
26
The number of permanent full time employees in the firm
capital= net book value of machinery and equipment +net book value of land and buildings
Cost of raw materials and intermediate goods used in production
Total annual cost of electricity
90
Table 11 Model estimation
P>│t│ 95%
INTERV
CONF. AL
LN_SALES
COEF
STD.ERR T
LN_labour
.529**
.247
2.14 .034
.041
1.01
LN-CAPITAL
.272*** .074
3.68 .000
.126
.419
.064
1.09 .278
-.057
.196
LN_ELECTRICITY
.669*** .126
5.31 .000
.420
.919
_CONS
.313
.25
-2.20
2.82
LN_INTERMEDIATE .069
1.27
.806
Source: authors estimation
Note: level by significance *** for 1%; ** for 5% and * for 10% statistical significance
Before starting with inference we performed diagnostic testing for the assumptions of
classical linear regression model (provided in detail in appendix). The variable inflation
factor suggests that the model does not suffer of any multicolinearity problems. Felipe
and Adams (2005) suggest that Cobb-Douglas production function may suffer from
multicolinearity so we have tested for it. We performed different types of
hetersoscedascity tests such as: Breusch- Pagan; Cameron-Trivedi and White test and
they all suggest that out model is heteroscedastic. The econometric literature related to
this type of problem offers remedial measures such as white heteroscedastic corrected
standard errors or estimation with GLS. We performed white heteroscedastic corrected
standard errors for our model and noticed that the sign and significance of parameter
coefficients do not change and the differences in the model with no corrections and the
model with correction are relatively small. As a consequence we choose to interpret the
heteroscedascity corrected model at robust parameters estimation as shown in Table 12.
Because of the consequences and drawbacks of GLS (which we do not intend to discuss
in this work) we do not use GLS which is usually suggested only when the significance
of variables changes when corrected with white heteroscedatic corrected standard errors.
Table 12 Heteroscedascity corrected estimation, robust
LN_SALES
COEF
ROBUST
STD.ERR
T
P>│t│
95%
CONF.
INTERVA
L
LN_labour
.529**
.256
2.06
.041
.022
1.036
LN-CAPITAL
.272***
.100
2.71
.008
.073
.4713
LN_INTERMEDIATE
.069
.0695
1.00
.319
-.068
.2071
LN_ELECTRICITY
.669***
.1711
3.91
.000
.331
1.008
_CONS
.313
1.173
.79
.79
-2.01
2.633
Source: Authors estimation
Note: level by significance *** for 1%; ** for 5% and * for 10% statistical significance
91
Our multiplicative Cobb-Douglas model may be described as follows:
Sales=1.13LAB0.53CAPITAL0.27INTERMEDIATE0.07ELECTRICITY0.67
According to the results the variables in the model are significant at conventional
significance levels, except the intermediate materials input. The corresponding elasticity
coefficients of the inputs in the model are: 0.466 for labor; 0.123 for capital and
approximately 0.7 for electricity. The output elasticity of intermediate goods used in the
production is relatively small and result insignificant in conventional levels of
significance. The evidence is in accordance with the theory since the model estimation
displays positive and decreasing returns to inputs. The elasticity of output with respect to
production factors imply that if capital (labor, electricity) increases by 1% , the output
increases by 0.46%, (0.122%, 0.699%) respectively on average, ceteris paribus. Again the
coefficient on labor is larger compared to capital but smaller than electricity, an input
added in this model.
The results suggest that firms are experiencing increasing returns to scale on average.
Increasing returns to scale results both in the original 2-input Cobb-Douglas production
function and the 4-input production function. Again increasing returns to scale suggest
that a 1% increase in the inputs leads to more than 1% increase in output. Further more
the resulting increasing returns may suggest that firms do not operate with minimum
costs, respectively they are not Pareto efficient.
Additionally we performed another test to test the elasticity of substitution estimating:
Log Q/L = β0+ βLog w;
Where w = real wage rate, Q/L = labor productivity and β= elasticity of substitution.
Wage is measures as monthly compensation of full time employee.
The results are shown in table below:
Table 13 Estimating elasticity of substitution
Laborproductivity
COEF
STD.ERR T
LN_wage
1.03*** .094
10.96 .000
.844
1.21
_CONS
-3.8***
-7.52
-4.87
-2.84
.513
P>│t│ 95%
CONF.
.000
INTERV
AL
Source: Authors estimation
Note: level by significance *** for 1%; ** for 5% and * for 10% statistical significance
The estimation results suggest that the elasticity of substitution is unitary; on average a
percentage point increase in wage will result with a percentage point increase in labor
productivity. According to Klein‟s viewpoint if elasticity of substitution is near about
unity a Cobb-Douglas production function can be estimated. Wage rates have impact on
labor productivity.
92
We suggest that incentives related to wage levels in these countries are same as
incentivizing labor productivity which on the other hand is evidence that using wage
incentive instruments is aligning companies‟ goal and may not lead to principle agent
problem. Again this is evidence that labor productivity may be explained by employee
earnings. The general idea is in line with Lazear that wages may be as incentives for
increasing labor productivity. We may propose that recognized forms of financial
participation both theoretically and empirically, that result with increased productivity
may be used in transition countries for their expected potential benefits. Examples of this
kind are employee share ownership and profit sharing. The introduction of Financial
Participation in transition countries can be identified with the privatization process; it was
a bridge for the transformation of the ownership of state owned enterprises. In recent
years there is no evidence that these countries are incentivizing and creating a legal
framework for such schemes. Increasing wages that may potentially increase labor
productivity is a desirable outcome for both employees and employers and is not a
Principle-Agent problem. In line whith this we propose:
1. Aligning the goals of the Principle and the Agents will lead to increased
productivity;
2. Linking the effort with income may increase the performance.
4.9.
CONCLUSIONS
The free market, open economies and globalization all may lead to the companies’
necessity to innovate. We can identify that most of the markets can be classified as
monopolistic competition. Therefore we urge that companies that try to be competitive
and stay in the market for a longer time period should intensively work on differentiating
products and introducing innovation and new products. In this study we provide evidence
on what may possibly influence the odds to innovate. We estimate a logit model and find
that companies that have a credit increase the odds to innovate compared to the ones that
do not have also that the increase in sales increases the odds to innovate.
Reviewing the literature and evidence for innovation in transition countries we may
conclude that innovation may be beneficial for customers, employees, companies and in
the macroeconomic perspective it may increase employment. That is why the research on
the topic is broad and an ongoing area of interest. Our estimation suggests that possible
determinants that may increase the probability to innovate are: competition, internet
broadband, R&D investment and access to finance. Thus if we want to encourage
innovation we suggest the encouragement of the latter.
SME are recognized as engine for growth by academicians and researches and a large
number of studies note that the expected benefit of innovation are efficiency and
productivity. Our estimates resulted that there is statistically difference in the probability
to innovate between large enterprises and SME where the latter innovate less. Innovation
is a costly process and therefore the ease of financing may encourage enterprises to
innovate. Another crucial factor that induces innovation is informal competition.
Concluding a friendlier environment for SME should be created in respective countries in
order to stimulate them to innovate more. Finally according to our results a friendlier
93
environment may be enhancing a competitive market for SMEs and no obstacles for
financing. Innovation we suggest is driven by firm specific and market factors.
The results suggest that enterprises that innovate, have an internet broadband, face
informal competition and large enterprises compared to small and medium have higher
probability to be engaged in R&D investments. R&D investment should be encouraged
even for small and medium enterprises because it may be a potential source for growth.
We conclude that labor productivity is important and that firms in Macedonia and
Albania operate with increasing returns to scale. The elasticity of substitution is unitary
and we suggest that labor productivity is incentivizes by wage growth. Our estimation
suggest that policies regarding employee incentivizing for working more productively,
employing adequate skilled workforce, incentivizing and subsidies for innovation and
R&D may improve the productivity in the countries referenced.
94
5. CONCLUSION, POLICY RECOMANDATION, LIMITATIONS
AND FUTURE RESEARCH
The purpose of this study is to empirically analyze production function and productivity
for companies in Albania and Macedonia. The main contribution to knowledge derived
from this thesis is the evidence for describing productivity and also factors that influence
productivity. The main hypothesis of the study is: companies in respective countries
possibly do not operate at their minimum cost.
The aim of the study is to measure productivity function and scale of economies for small
and medium sized enterprises in transition countries respectively in Albania and
Macedonia. The research on productivity is large both at micro and macro level and the
research is build on using different approaches of measuring productivity and therefore is
also subject to different measurement challenges and problems.
For empirical analyses data are extracted from BEEPS dataset. Due to lack of data, times
series or panel analyses could not be undertaken. In the thesis the first part was to set up
the theoretical framework for the research question which is then empirically tested. A
comparative assessment of enterprise characteristics between the two countries is
provided. The Cobb-Douglas production function and MLE are used and advantages and
disadvantages of the two estimation techniques are critically appraised.
This chapter is organised as follows: Section 5.1 summarizes main findings derived from
this thesis; Section 5.2 outlines policy recommendations; main conclusions of the
research are highlighted in Section 5.3 and the chapter concludes by identifying further
research areas and limitations of the study.
5.1 SUMMARY ON THE LITERATURE REVIEW
Studies on productivity have as stakeholders the employees, owners and the government.
On our literature review on studies on productivity we find that different measures of
productivity, input, and output are used to study the nature and the determinants of
productivity. We note that researches should be cautious when proposing policies
depending on the measurement of individual variables used in the estimation process. We
conclude that the definition of variables used in the model and the estimation
methodology are crucial for the results we will obtain. We suggest that identification of
drawbacks of each empirical estimation is crucial for deciding the choice of empirical
estimation.
A large body of studies finds that SMEs‟ are boosting the economy as a whole and also a
lot of studies study the profitability issue of firms. There may be drawn two strands of
researches studying profitability the first one structure –conduct performance strand and
the other strand is on the firm effects model. On the other hand there can be identified
two main groups of studies: studies describing productivity and studies describing factors
that determine productivity. Firm employing more efficiently their inputs will tend to be
more profitable. The main hypothesis is that industry characteristics and firm
characteristics both affect the profitability of firms. SCP models may relate profitability
95
to suboptimal welfare while firm effects model may not find relationship between
profitability and welfare losses. Empirically both models find evidence.
The literature on productivity is diverse and looking at different aspects of productivity.
In the firm level being productive may be understood as incentivizing employees to work
efficiently while in the macro level studies on productivity we may be interested in GDP
and employment. Most of macroeconomic studies finish noting the limitations on
macroeconomic studies and suggesting micro studies to capture the channels to which
business climate enhances growth (Durlauf et al. (2008); Straub (2008); Pande and Udry
(2005).Micro data in studying productivity are important in different fields of economics:
microeconomics, macroeconomics, labor economics, international trade and industrial
organization. According to empirical research we find that variables correlated with
productivity are: institutional change, technological progress, IT investment, innovation
and R&D.
There is a large “menu” of methodologies used in productivity studies but we are looking
at the most common used methodologies such as Index Numbers, Production Function,
Distance Function and DEA analysis. Malmquist index and Törnqvist index are the most
common used indexes on productivity studies. For example they are used in studies such
as: Fare et al (1994), Ball et al (2004); Camanho and Dyson (2006); Grifell-tatjé and
Lovell (1998).The production function relates the amount of the output to the amount of
input used – a function that describes the technology. For example they are used in
studies such as: Solow (1957); Banda and Verdugo (2011); Grimes, Arthur Ren, Cleo
Stevens, Philip (2011); Fernandes (2008).Distance function studies: Saal et al. (2007);
Conceição et al. (2006) while Dea analyzis studies: Feng-Cheng Fu and Chu-Ping C.
Vijverberg and Yong-Sheng Chen (2007).The general conclusion that we may draw from
the literature review is that productivity is likely to generate desired results for the
stakeholders and therefore should be a goal for firms and countries.
We presented the formal formulation of nonlinear models with specific reference to logit
model, the method used to estimate and how they are interpreted. We sum that the
interpretation of nonlinear models is not straightforward and the difficulty arises
especially with dummy variables. We also noted the confusion that is usually about
product term and interaction variables in logit models. The problems with logit model
(mentioned in the study) may be problems of the nature of sampling, missing data,
variable bias and heteroscedascity. Despite the above mentioned logit model is applied in
different fields of economics such as: industrial relations, game theory, labor market,
mergers, transport, consumer choice and demand, economics of education, emigration,
banking, mergers. The extensive use of nonlinear models in different fields of economics
suggest us that we should acknowledge more understating and research in the nature,
scope, advantages and disadvantages of these models in economics analysis.
5.2 POLICY RECOMANDATION
The benefits from innovation and productivity may be captured from customers,
employees, companies. That is why the research on the topic is broad and an ongoing
96
area of interest. In this study one focus was to look what may possibly influence the odds
to innovate. We estimated a logit model and find that companies that have a credit
increase the odds to innovate compared to the ones that do not have also that the increase
in sales increases the odds to innovate. Our estimation suggests that possible
determinants that may increase the probability to innovate are: competition, internet
broadband, R&D investment and access to finance. Thus if we want to encourage
innovation we suggest the encouragement of the latter.
Our estimates resulted that there is statistically difference in the probability to innovate
between large enterprises and SME where the latter innovate less. Another crucial factor
that induces innovation is informal competition. Concluding a friendlier environment for
SME should be created in respective countries in order to stimulate them to innovate
more. Finally according to our results a friendlier environment may be enhancing a
competitive market for SMEs and no obstacles for financing. Innovation we suggest is
driven by firm specific and market factors.
We have analyzed a cross section production function and during our research we noticed
the urge of a micro panel dataset so that researchers will be able to look far beyond the
scope of the provided research here. The evidence from estimated Cobb-Douglas
production function is that companies in Macedonia and Albania show increasing returns
to scale and the sign of corresponding input elasticities are in line with the theory.
We urge the necessity of micro panel dataset especially for transition countries because
this limitation results with the scarcity of research in this kind of countries who need
policy recommendation in order to improve and grow economically.
Policy recommendation that respective institutions should follow is to encourage firms to
show increasing returns to scale or constant returns to scale or identify the firms
operating with increasing returns to scale and incentivize them to stay in the business.
Government policy should be to attract efficient firms. We also propose that company
level studies should be incentivized. As a consequence of the transition process and
privatization which is the case of both Macedonia and Albania it is expected that in the
short run there will be a large number of small and medium enterprises, but on the other
perspective as both countries are adhering the EU in order to survive in the open market
economy they should be competitive and productive. The legislation and policy response
therefore should be in line with the international market. Finally the awareness of policy
makers should be focused that both productive firms and productive workers should be
incentivized otherwise we encourage them to seek better off opportunities somewhere
else. We propose that policies should be oriented toward:
1. Aligning the goals of the Principle and the Agents will lead to increased
productivity;
2. Linking the effort with income may increase the performance.
5.3 MAIN CONCLUSIONS
Costs will depend on productivity which responses to the law of diminishing marginal
returns and our findings in this work are in line with theory and give supporting evidence
97
for our hypothesis. Our estimation suggest that policies regarding employee incentivizing
for working more productively, employing adequate skilled workforce, incentivizing and
subsidies for innovation and R&D may improve the productivity in the countries
referenced.
We may list the main conclusions of this research:
 Stakeholders: employees, the owners and the government.
 Performance measure
 Productivity may enhance growth.

Important in different fields of economics
 Approaches for studying productivity: index number studies, production
function, distance function and DEA analysis.
 Concluding we suggest that identification of drawbacks of each empirical
estimation is crucial for deciding the choice of empirical estimation.
 The nature of the firm, the structure of the market and financing are possible
determinants of innovation.
 Enterprises that innovate, have an internet broadband, face informal competition
and large enterprises compared to small and medium have higher probability to be
engaged in R&D investments
 Cobb-Douglas estimates suggest that firms are experiencing increasing returns to
scale on average which suggests that the businesses in these countries do not
operate at their minimum average costs
 Aligning the goals of the Principle and the Agents will lead to increased
productivity;
 Linking the effort with income may increase the performance.
We estimated models for factors describing productivity using MLE and Cobb-Douglas
estimation for a sample representative enterprises drawn from BEEPS dataset. Following
we provide the empirical evidence from estimation results.
According to the estimated MLE model for innovation the following resulted: For a
standard deviation increase in sales the odds of innovating increase by 27.6% holding
other things constant. Odds for innovation are: 74.4% greater to firms that have credit
than those who don‟t, holding all other covariates constant; 52.2% greater for enterprises
that compete with informal competition than those who don‟t, holding all other covariates
constant; 59.3% higher for SME than for large companies, holding all other covariates
constant. Thus our results are in line with Schumpeterian view.
In sum our estimates suggest that for our sample data the size of sales has increased the
probability to innovate, also companies that face informal competition and have a line of
credit or loan have higher probability to innovate compared to companies that do not face
informal competition respectively companies that do not have a credit. Thus the nature of
the firm, the structure of the market and financing are possible determinants of
innovation.
98
In the second model estimating for predictors of R&D using MLE estimation results that
wwe are 95% confident that the probability to have R&D is between 0.3 and 0.6 given
that it innovates. The estimates suggest that predictors of R&D are innovation, internet
broadband, competition and size. According to our estimation results it is suggested that
firms that do innovate are more likely for 0.3 to have invested in R&D than the ones who
don‟t, holding other things constant. The estimated results also suggest that having
comepetition (in our case informal one) and having internet broadband increases
probability to invest in R&D at sample means by 0.2 respectively by 0.244 holding other
covariates constant.
Cobb-Douglas production function is used extensively in productivity studies and such a
function is estimated in the thesis. The very first estimation of input-output relationship
was in Cobb and Douglas (1928). Their work was object of discussions among
researchers criticizing and giving credit to the same. We estimate an equivalent linear
function of logarithms of Cobb-Douglas production function. The resulting estimated
coefficients of the Cobb-Douglas production function are output elasticity‟s of respective
inputs and in our estimation ( after testing and correcting for multicolinearity and
heteroscdedascity) output elasticity of capital is 0.46 and output elasticity of labor is 0.78.
In the four input Cobb-Douglas estimation the corresponding elasticity coefficients of the
inputs in the model are: 0.466 for labor; 0.123 for capital and approximately 0.7 for
electricity. Thus, our results are in accordance with the economic theory which tells us
that marginal products of capital and labor are both positive, and these inputs individually
exhibit diminishing returns. The results suggest that labor contributes more than capital
in the output i.e. in order to add output the distribution of input goods should be toward
labor in order to have higher increase in the output level. Thus our estimates are evidence
of applied Cobb-Douglas production function with statistically valid results. Finally our
results are in line with the theory and we provide supporting evidence for Schumpeterian
view and Lazears‟ theory of incentive wages.
The empirical evidence in the study suggests that the enterprises in respective countries
are experiencing increasing returns to scale. The positive economies of scale on the other
hand suggest that industries can produce and export at competing prices and may grow
employing more inputs. If this is the case these firms may generate revenues for the
economy.
5.4 LIMITATIONS OF THE STUDY AND RECOMANDATIONS
FOR FUTURE RESEARCH
This study is subject to some limitations which are mainly related to lack of data. The
first limitation is that the study does not capture industry and country differences;
secondly; examination is done by using cross section data; thirdly we do not calculate
total factor productivity and its convergence within industries and countries.
We propose and suggest that further research should be done using a trans-log production
function or taking the Levinshon-Petrin approach. This approach is a technique that uses
the cost of material as a proxy of companies‟ information about productivity. Another
approach that may be applied is Olley and Pakes if the dataset has information about
investment which is their proxy for companies‟ information about productivity.
99
Concluding we may state some suggestions for the road ahead are to pursue the following
approaches: Legros and Galia (2011)-simultaneous equations; Levinshon-Petrin
approach; Olley and Pakes approach; Translog production function and comparative
studies .
The problem of availability of data for large samples and longer time periods is a
limitation for conducting studies on productivity. Therefore we suggest that preparing
questionnaire and colecting micro- panel dataset may be helpful in solving estimation and
comparison models in productivity studies.
In closing I would like to add that increasing productivity is multilevel complex
framework and a better understanding of the problem may be attained by disaggregating
the problem in micro level studies.
100
APPENDIX
A.1 LIST OF ABREVIATIONS
ABREVIATION
EXPLANATION
TFP
Total factor productivity
GDP
Gross domestic product
BEA
Bureau of economic analysis
BLS
The Bureau of Labor Statistics
TTP
Total technology progress
PPP
Purchasing power parity
OECD
The Organization
Development
R&D
Research and development
GML
General maximum likelihood
CRS
Constant returns to scale
LP
Labor productivity
ALS
Asymptotic least square
MPI
Malmquist productivity indicator
DEA
Data envelopment analysis
CEE
Central and east Europe
MLE
Maximum likelihood estimation
LSDV
Least square dummy variable
GLS
Generalized least square
WITHIN
Model proposed by Conweli et al. (1990)
BC
Battese and Coelli ( 1992) model
FEM
Fixed effect model
ECM
Error component model
REM
Random effects model
ACF
Ackerberg, Cavez and Frazer
IT
Information Technology
101
for
Economic
Co-operation
and
A.2 SUMMARY OF LITERATURE REVIEW
Author
/TITLE
 1953- Sten Malmquist
Zvi Griliches
1984
Chapter Title: R&D and
Productivity: The Unfinished
Business
Griliches Chapter Author: Zvi
Type of
data;analyses&method
Malmquist
Index
originates from and
introduced by Caves
et al. (1982)
Literature
review
Review
production
function Log of sales
output R&D capital
Physical capital
Labor other variables
R capital
&D Physical capitalQ
= AXPKT, where Q is
output, X is
an
index
of
conventional
inputs
including
physical
capital,
K is the “stock of
knowledge”
(or
R&D),
A is the level of
disembodied
technology, and p and
y
are the parameters of
interest
Innovation
and
productivity
 Baily and Chakrabarti
(Innovation
and
productivity in US
industry, 1985)

Holzer (1988)
Their
dependent
variable is wage and
productivity on a scale
from 1-100
 Fare et al. (1994)

Index studies
102
Conclusion
Econometric issues:
(1) the simultaneity
of the R&D decision,
(2) heterogeneity and
endogeneity
of
individual
product
prices,
(3) heterogeneity of
the
underlying
production functions,
and ( the role of
spillovers
They find evidence
that
tenure
and
training are positively
linked with wage and
productivity
decomposed
Malmquist index in
efficiency change and
Bernard and Jones (1996)
Cobb-Douglas
 : Brynjolfson and Hitt
(1998)
 Lazear (2000)
technological change
Countries in 70s‟ and
80s‟
converge.
Convergence
is
industry specific and
comparison
of
countries may be
misleading. They find
evidence
on
aggregate
convergence and no
evidence
on
convergence
in
manufacturing.
IT investment may
lead to productivity
Incentive wages
productivity as a
result of incentive
effect
and Factors that influence Productivity paradox
productivity
 : Stratapoulos
Dehning (2000)

 De Toni and Tonchia Build a performance
(2001)
measurement
framework
and
classify productivity
measurement as cost
measurement.
Steindal and Stiroh (2001)
Review of measures draw
difference
of productivity
between two concepts
of
output:
value
added and gross
output
 Neelu et al. ( 2005)
.
also
classify
productivity
as
performance measure
 Audretsch, David B. :
- institutional change
Elston, Julie Ann
and productivity
(2006)

 Fernandes (2008)
575
firms
in Reverse casualty of
Bangladesh
corruption
and
productivity
 Rungsuriyawiboon,
TFP and technological
Supawat
Stefanou, progress:
103
Spiro E. (2008)

 Diewert (2008)
discusses
measurement
problems
 R. Fare, S. Grosskopf Time
series; Productivity may be
and D. Margaritis Benet_Bowley
addressed to R&D:
(2008)
productivity index

Profit may be e
Andreas Stierwald
function of time trend.
(2009)
Lagged
dependent
variable accounts for
dynamic component
of profitability. Firm
profits are computed
as the ratio of profit
level to the value of
total The level of
profit is defined as the
difference
between
sales revenue and total
operating expenses.
Total
factor
productivity refers to
the level of costefficiency
in
the
production
process
and
is defined as the logdifference
between
predicted
and
empirical cost:
More
borrowed
capital more risk.
 Oh (2010)
26 OECD countries
Propose
global
MalmquistLuenberger Index and
suggest
that
productivity
is
addressed mainly to
technological change
 Grimes et al. (2011)
Cobb-Douglas
Firms with internet
broadband
more
productive
 Banda and Verdugo AIS data (1993-2006) Capital
elasticity
104
(2011)
 GrifellTatje
Lowell
and
GUSTAVO CRESPI
Sussex University, AIM, and
CeRiBA
CHIARA CRISCUOLO
LSE, AIM, and CeRiBA
JONATHAN HASKEL
Queen Mary, University of
London, AIM, CeRiBA, CEPR,
and IZA
DENISE HAWKES
Centre
for
Longitudinal
Studies, Institute of Education,
University of London
1
between 0.28 and
0.34
and
labor
elasticity
between
0.56 and 0.66
Decompose
Malmquist index in
technical
change,
technical efficiency
and returns to scale
Are
output
data Quarterly measures
reliable to measure problems:
productivity?
1.some sectors are not
good measure of
productivity
2. employment uses
productivity
adjustment (what it
is)
3. income and
expenditure might
give other estimates
Review
LMD
productivity studies
Eric J. Bartelsman
Reviews:
Richard
and
Caves (1998) and ,
Mark Doms
James Tybout (2000)
methods
of
calculating
TFP,
choices
can be made among
index
number
approaches,
econometric
estimation of cost or
production
functions,
or
nonparametric
methods, such as data
envelopment analysis.
 Durlauf et al. 2008; Macroeconomic
Straub (2008); Pande studies
and Udry (2005).
105
the
most
significant
contribution LMDs
have made is to
revisit the ideas of
heterogeneity and
Schumpeter‟s
creative destruction.
Productivity as a
measure of TFP
finish noting the
limitations on
macroeconomic
studies and
suggesting micro
studies to capture the
channels to which
business climate
enhances growth
 Barteslamn and Doms Review on literature
(2000); Mawson et al.
(2003).
106
A.3 DATASET QUESTIONS OF INTEREST/QUESTIONARE
Questions of interest in the panel data:
 Industry




Manufacturing
Service
other
SIZE- the size of the industry:
Small
Medium
Large
 Does this establishment have an internationally-recognized quality certification?
 Yes 1
 No 0
 Over fiscal year 2007, did this establishment experience power outages?
 Yes 1
 No 0
 What percentage of total sales does the main product represent?
 In fiscal year 2007, what were this establishment‟s total annual sales?
 In fiscal year 2007, which of the following was the main market in which this
establishment sold its main product?
 Local
 National
 International
 In fiscal year 2007, for the main market in which this establishment sold its main
product, how many competitors did this establishment‟s main product face?
 0-1
 >2
 Comparing the last month to the first month of the fiscal year 2007 have monthly
sales of this establishment‟s main product increased, remained the same, or
decreased?
 Increased
 Same
 Decreased
 Does this establishment compete against unregistered or informal firms?
 Yes 1
107
 No 0
 In the last three years, has this establishment introduced new products or
services?
 Yes 1
 No 0
 In fiscal year 2007, did this establishment spend on research and development
activities, either in-house or contracted with other companies (outsourced)?
 Yes 1
 No 0
 In fiscal year 2007, how much did this establishment spend on research and
development activities either in-house or contracted with other companies
(outsourced)?
 At this time, does this establishment have an overdraft facility?
 Yes 1
 No 0
 At this time, does this establishment have a line of credit or a loan from a
financial institution?
 Yes 1
 No 0
 Is access to finance, which includes availability and cost, interest rates, fees and
collateral requirements, No Obstacle, a Minor Obstacle, a Moderate Obstacle, a
Major Obstacle, or a Very Severe Obstacle to the current operations of this
establishment?
 NO OBSTACLE: no obstacle, minor obstacle
 OBSTACLE: moderate, major and very
 At the end of fiscal year 2007, how many permanent, full-time employees did
this establishment employ? Please include all employees and managers
 At the end of fiscal year 2007, how many permanent, full-time employees were:
 Skilled
 Unskilled
 For fiscal 2007 please provide:
 Total annual cost of labour (including wages, salaries, bonuses, social security
payments)
 Total annual cost of raw materials and intermediate goods used in production
 Average monthly compensation for full-time production employee
 At the end of fiscal year 2007, what was the net book value, that is the value of
assets after depreciation, of the following:
108
 Machinery, vehicles, and equipment
 Land and buildings
109
A.4 SUMMARY STATISTICS OF THE QUESTIONARE: AFTER
CORRECTIONS
First we provide summary statistic for variable individually and then the overall variables
after correcting for don‟t know possibility answer or/and missing data.
SIZE
We have the classification for Macedonia only for year 2009 for size:
SME
Freq.
Percent
Cum.
0
1
90
276
24.59
75.41
24.59
100.00
Total
366
100.00
We have the classification for Albania: only for year 2009 for size:
SME
Freq.
Percent
Cum.
0
1
1
53
1.85
98.15
1.85
100.00
Total
54
100.00
For both countries we have the following statistics:
SME
Freq.
Percent
Cum.
0
1
91
329
21.67
78.33
21.67
100.00
Total
420
100.00
Summary statistics for the variable:
Variable
Obs
Mean
SME
420
.7833333
Std. Dev.
.4124649
Min
Max
0
1
INNOVATION
Frequencies for innovation for Macedonia:
innov
Freq.
Percent
Cum.
0
1
148
218
40.44
59.56
40.44
100.00
Total
366
100.00
110
Frequencies for innovation for Albania:
innov
Freq.
Percent
Cum.
0
1
34
20
62.96
37.04
62.96
100.00
Total
54
100.00
Frequencies for our sample data:
innov
Freq.
Percent
Cum.
0
1
182
238
43.33
56.67
43.33
100.00
Total
420
100.00
Summary statistics for innovation:
Variable
Obs
Mean
innov
420
.5666667
Std. Dev.
.4961266
Min
Max
0
1
INTERNET
Frequencies for the variable internet for Macedonia:
internet
Freq.
Percent
Cum.
0
1
37
105
26.06
73.94
26.06
100.00
Total
142
100.00
Frequencies for the variable internet for Albania:
internet
Freq.
Percent
Cum.
0
1
45
113
28.48
71.52
28.48
100.00
Total
158
100.00
Frequencies for the variable internet for overall sample:
111
internet
Freq.
Percent
Cum.
0
1
37
105
26.06
73.94
26.06
100.00
Total
142
100.00
Summary statistics for variable internet:
Variable
Obs
Mean
internet
158
.7151899
Std. Dev.
Min
Max
0
1
.452759
R&D’
Frequencies for the variable R&D for Macedonia area:
RandD
Freq.
Percent
Cum.
0
1
215
151
58.74
41.26
58.74
100.00
Total
366
100.00
Frequencies for the variable R&D for Albania:
RandD
Freq.
Percent
Cum.
0
1
248
172
59.05
40.95
59.05
100.00
Total
420
100.00
Frequencies for the variable R&D for all:
RandD
Freq.
Percent
Cum.
0
1
248
172
59.05
40.95
59.05
100.00
Total
420
100.00
Summary statistics for the variable R&D:
Variable
Obs
Mean
RandD
420
.4095238
Std. Dev.
.4923324
Min
Max
0
1
Another question for R&D is the amount spent on R&D. But the question on the amount
of R&D is resulting with missing data as can be seen from the summary statistics below:
112
. tab
accessfin if
accessfin
country15&year1
Freq.
Percent
Cum.
0
96
64.00
64.00
1
54
36.00
100.00
. tab
accessfin if
albania&year1
Total
150
100.00
accessfin
Freq.
Percent
Cum.
. tab
accessfin
if country15&year2
Variable
Obs
Mean
Std. Dev.
Min
0
96
65.31
65.31
accessfin
Freq.
Percent
Cum.
1
51
34.69
100.00
amountRandD
52
33511.41
90244.29
1
0
92
50.27
Total
147
100.00
1
91
49.73
. tab
accessfin if
albania&year2
Total
183
100.00
accessfin
Freq.
Percent
. tab
accessfin if country15&year3
no observations
0
116
59.49
1
79
40.51
. tab
accessfin if country15&year4
Total
195
100.00
accessfin
Freq.
Percent
. tab
accessfin if
albania&year3
0
168
45.90
1
198
54.10
accessfin
Freq.
Percent
. sum labour if
Total 0
366
163
100.00
53.62
46.38
country15&year1
1
141
Cum.
59.49
100.00
Cum.
45.90
100.00
Cum.
53.62
100.00
Variable
Obs
Mean
Std.
Dev.
Total
304
100.00
For Albania we
have the following
frequencies:
labour
. tab
accessfin
if
albania&year4
167
118.0719
373.9862
. sum labour if accessfin
country15&year2Freq.
Variable
labour
. sum labour if
. sum labour if
EMPLOYEESVariable
Variable
0
Obs
1
34
Mean
20
200
94.21
Total
Percent
62.96
Std.
Dev.
37.04
Min
Max
2
3600
Cum.
62.96
Min
100.00
Max
2
3100
299.8724
54
625980.7
50.27
100.00
ACCESS TO FINANCE
For Macedonia we have the following frequencies:
Max
100.00
country15&year3
albania&year1
Obs
Mean
Obs
Mean
Std. Dev.
Std. Dev.
labour
0
Summary statistics
for the variable
labor for Macedonia:
labour
170
97.47647
340.2755
Min
Min
2
Max
Max
3360
.. sum
labour if
if albania&year2
country15&year4
sum labour
Variable
Variable
Obs
Obs
labour
labour
365
204
. sum labour if
Variable
Mean Std.Std.
Mean
Dev.Dev.
91.63562 240.3428
220.6412
80.35294
Min
Min
Max
Max
2
1
2100
2146
albania&year3
Std. Dev.
Min
Max
Summary statistics
for the variable
labor for Albania:
labour
297
35.86532
80.65577
2
1120
. sum labour if
. sum
Obs
albania&year4
skilledlab if country15&year1
Variable
Obs
Variable
Obs
skilledlab
163
labour
. sum
Mean
54
Mean
Mean
23.14815
64.58282
Std. Dev.
Std. Dev.
45.01254
195.0228
Min
Max
Min
Max
0
1600
Min
Max
0
2170
2
320
skilledlab if country15&year2
Variable
Obs
Mean
Std. Dev.
The aboveskilledlab
definition is of labor
with44.625
no classification.
200
174.1098
Now we .will
at the classification
in skilled and unskilled for Macedonia and
sum look
skilledlab
if country15&year3
Albania: Variable
Obs
Mean
Std. Dev.
Min
Max
skilledlab
Skilled Macedonia:
. sum
0
skilledlab if country15&year4
Variable
Obs
Mean
skilledlab
115
74.43478
Std. Dev.
112.4755
For Albania:
113
Min
Max
0
730
skilledlab
. sum
203
skilledlab if
Variable if
unskilllab
. sum
skilledlab
Variable
115.4416
Obs
Mean
country15&year1
110
Obs
unskilllab
Variable if
Std. Dev.
25.14545
79.26808 Min
Mean
Std. Dev.
908
Min
Max
9.607362
41.9458
albania&year4
country15&year2
Obs
Mean
0 Max
0
Std. Dev.
Min
740
Max
Std. Dev.
Min
Max
203
20.90148
64.76584
Obs
Mean
Std. Dev.
. tab if
qualcert
if country15&year1
. sum
unskilllab
albania&year3
unskilllab
115
12.09565
36.27671
qualcert
Freq.
Percent
Variable
Obs
Mean
Std.
Dev.
0
673
Max
unskilllab if
. sum
Variable
unskilllab if
90.73663
Std. Dev.
0 Max
1008
Max
unskilllab
Macedonia:
23.53012
Mean
Max
0
. sum
166
Obs
albania&year2
0
Obs
Mean
country15&year4
unskilllab
Variable
Albania unskilled
. tab
Min
qualcert if
Min
0
Cum.
Min
290
Max
albania&year1
153
90.53
90.53
unskilllab
16.45455
38.84588
0
294
16
9.47
100.00
qualcert
Freq.
Percent
Cum.
. sum
unskilllab if
albania&year4
Total
169
100.00
87.27
Variable
Obs 0
Mean 144 Std. Dev.
Min 87.27 Max
1
21
12.73
100.00
. tab qualcert
if country15&year2
unskilllab
20
4.9
7.09262
0
26
qualcert
Freq. 165 Percent
Cum.
Total
100.00
. tab
0
110
1
0
89.00
qualcert
if178 albania&year2
1
22
qualcert
Cum.
0
. tab qualcert
if
1
no observations
170
83.33
country15&year3
83.33
100.00
. tab
country15&year4
204
100.00
qualcert
if
Total
Freq.
200
89.00
100.00
Percent
100.00
Total
QUALITY CERTIFICATION
Macedonia:
11.00
34
16.67
Freq. albania&year3
Percent
. qualcert
tab qualcert if
qualcert
1
0
235
Freq.
131
Total 0
366 220
100.0072.37
Total
304
100.00
1
Albania:
. tab
qualcert if
84
Cum.
64.21
64.21
Percent 100.00
35.79
27.63
Cum.
72.37
100.00
albania&year4
qualcert
Freq.
Percent
Cum.
0
1
43
11
79.63
20.37
79.63
100.00
Total
54
100.00
114
800
360
Variable
Obs
Std. Dev.
skilledlab
20 Mean 27.95
63.76971 Min
. sum
unskilllab if
albania&year1
unskilllab
200
15.695
70.26448
0
.
Variable
Obs
Mean
Std. Dev.
Min
. sum
unskilllab if
country15&year3
Unskilledunskilllab
labor
Variable
0
albania&year3
unskilllab
163if
. sum skilledlab
. sum
36.62069
294
A.5 SUMMARY STATISTICS OF VARIABLES
Sample data
Variable
Obs
Mean
sales_output
ln_sales
RandD
labour
ln_labour
420
420
420
419
419
3384308
11.13629
.4095238
82.80907
3.272071
innov
SME
qualcert
compete_un~d
credit
420
420
420
420
420
powerout
accessfin
internet
compete_in~l
skilledlab
Std. Dev.
Min
Max
1.02e+07
5.554266
.4923324
207.7936
1.432095
1
0
0
1
0
1.12e+08
18.53658
1
2146
7.671361
.5666667
.7833333
.3380952
.6571429
.5880952
.4961266
.4124649
.4736253
.4752303
.492765
0
0
0
0
0
1
1
1
1
1
420
420
158
420
135
.4357143
.5190476
.7151899
.6571429
67.54815
.4964415
.5002329
.452759
.4752303
107.7678
0
0
0
0
0
1
1
1
1
730
unskilllab
amountRandD
averagewage
netbookmach
netbookland
135
52
135
135
135
11.02963
33511.41
277.9276
821107.8
803323.1
33.66449
90244.29
148.0133
2604167
2317725
0
1
1
1
1
290
625980.7
871.9016
2.21e+07
1.74e+07
lnamountRa~D
lnnetbookm~h
lnnetbookl~d
labourprod~t
lncapital
52
135
135
419
135
7.298771
9.570401
7.266376
59874.51
16.83678
4.281841
5.24607
6.444171
166854.1
10.69095
0
0
0
.0028571
0
13.34707
16.91186
16.6716
2038163
32.43742
electricity
ln_electri~y
intermediate
ln_interme~e
293
293
135
135
56664.65
8.132479
1421451
8.580796
316294.9
3.309198
5550820
5.957968
1
0
1
0
4121479
15.23172
4.58e+07
17.63881
Albania year 4:
115
Variable
Obs
Mean
Min
Max
sales
ln_sales
RandD
labour
ln_labour
54
54
54
54
54
685822.3
7.601991
.3888889
23.14815
2.54949
Std. Dev.
1723862
6.468326
.4920756
45.01254
.9358211
-.0995268
0
0
2
.6931472
9289169
16.04436
1
320
5.768321
ln_spent_RD
innov
SME
qualcert
compete_un~d
3
54
54
54
54
9.84594
.3703704
.9814815
.2037037
.4444444
.291267
.4874383
.1360828
.406533
.5015699
9.509809
0
0
0
0
10.02391
1
1
1
1
accessfin
internet
compete_in~l
skilledlab
unskilllab
54
16
54
20
20
.3703704
.5
.4444444
27.95
4.9
.4874383
.5163978
.5015699
63.76971
7.09262
0
0
0
0
0
1
1
1
294
26
amountRandD
averagewage
netbookmach
netbookland
lnskilledlab
6
20
20
20
19
9695.149
260.5557
1437045
382787.7
2.556082
11100.76
131.3365
4890052
1230850
1.10251
1
187.9951
1
1
.6931472
22559.41
774.0974
2.21e+07
5529268
5.68358
lnunskilllab
lnamountRa~D
lnnetbookm~h
lnnetbookl~d
wage
10
6
20
20
20
1.99877
4.92297
9.529253
7.190054
260.5557
.8514837
5.395989
5.860659
5.843625
131.3365
.6931472
0
0
0
187.9951
3.258096
10.02391
16.91186
15.52557
774.0974
labourprod~t
growth
54
54
33121.96
2.299725
62004.46
3.620878
.0111111
-7.370534
368617.8
8.02218
The table suggests that with variable amount spent on R&D we have missing data
therefore we may not include it in regression analysis as it is.
Macedonia year 4
Variable
Obs
Mean
Min
Max
sales
ln_sales
RandD
labour
ln_labour
366
366
366
365
365
3782445
11.65775
.4125683
91.63562
3.378973
Std. Dev.
1.09e+07
5.217086
.4929703
220.6412
1.462436
-.2012081
0
0
1
0
1.12e+08
18.53658
1
2146
7.671361
ln_spent_RD
innov
SME
qualcert
compete_un~d
37
366
366
366
366
9.459412
.5956284
.7540984
.3579235
.6885246
1.694876
.4914418
.43121
.4800457
.4637306
6.508312
0
0
0
0
13.34707
1
1
1
1
accessfin
internet
compete_in~l
skilledlab
unskilllab
366
142
366
115
115
.5409836
.7394366
.6885246
74.43478
12.09565
.4989997
.4404958
.4637306
112.4755
36.27671
0
0
0
0
0
1
1
1
730
290
amountRandD
averagewage
netbookmach
netbookland
lnskilledlab
46
115
115
115
113
36617.88
280.9487
713988.2
876459.7
3.351492
95554.79
151.0444
1976838
2454660
1.554081
1
1
1
1
0
625980.7
871.9016
1.52e+07
1.74e+07
6.593045
lnunskilllab
lnamountRa~D
lnnetbookm~h
lnnetbookl~d
wage
50
46
115
115
115
2.471365
7.608658
9.577558
7.279649
280.8861
1.292429
4.085679
5.159907
6.566606
151.1617
0
0
0
0
-.2012081
5.669881
13.34707
16.5375
16.6716
871.9016
labourprod~t
growth
365
366
63832.43
.936664
176886.4
2.583574
.0028571
-8.562719
2038163
9.079048
The same situation is with data collected for Macedonia.
116
A.6 SUMMARY TABLE OF SUMMARY STATISTICS
Variable
Obs
Mean
sales
ln_sales
RandD
labour
ln_labour
22825
22825
16777
26788
26787
4.50e+09
12.39943
.2803839
115.4018
3.274152
ln_spent_RD
innov
qualcert
transpobst
cust_trade
3144
24925
26854
26697
25576
compete_un~d
overdraft
credit
powerout
accessfin
Min
Max
6.62e+11
4.551746
.4492002
468.2949
1.600346
-17.51683
0
0
0
0
1.00e+14
32.23619
1
37772
10.53932
10.0425
.4365496
.1942727
.2269543
.1567485
2.161312
.4959677
.3956472
.4188707
2.08564
.6931472
0
0
0
-7
19.11383
1
1
1
4
11558
11660
11660
26625
26117
.3865721
.4030017
.4745283
.4346667
.4655205
.4869852
.4905221
.4993722
.4957225
.4988193
0
0
0
0
0
1
1
1
1
1
prod_sale_~p
publiclist
private
soleprop
partner
4713
26911
26911
26911
26911
.8226183
.0681506
.3890602
.263907
0
.3820319
.2520088
.4875461
.4407576
0
0
0
0
0
0
1
1
1
1
0
limpartner
otherprop
internet
compete_in~l
skilledlab
26911
26911
19128
11558
19674
.0369737
.1228122
.5904433
.3865721
62.80919
.1887008
.3282277
.4917648
.4869852
236.4475
0
0
0
0
0
1
1
1
1
8217
unskilllab
amountRandD
lnskilledlab
lnunskilllab
lnamountRa~D
19487
8186
17089
9774
8186
17.62888
153488.5
2.695414
2.134367
3.857028
98.37284
3369531
1.704775
1.587288
5.064998
0
1
0
0
0
7600
2.00e+08
9.013961
8.935904
19.11383
.
117
Std. Dev.
A.7 NATURE OF DATA
Frequency of the questionnaire:
. tab
panel if a1==44
Panel: Firm interviewed
in these years
Freq.
only in 2009
only in 2007
only in 2005
only in 2002
only in 2002, 05
only in 2005, 09
only in 2002, 05, 09
37
304
127
105
120
24
15
5.05
41.53
17.35
14.34
16.39
3.28
2.05
Total
732
100.00
. tab
Percent
Cum.
5.05
46.58
63.93
78.28
94.67
97.95
100.00
panel if a1==66
Panel: Firm interviewed
in these years
Freq.
only in 2009
only in 2005
only in 2002
only in 2002, 05
only in 2005, 09
only in 2002, 05, 09
279
97
136
32
138
54
37.91
13.18
18.48
4.35
18.75
7.34
Total
736
100.00
118
Percent
Cum.
37.91
51.09
69.57
73.91
92.66
100.00
A.8 ESTIMATION OUTPUTS
A.8.1 INNOVATION MODEL
. logit
innov sales SME
Iteration
Iteration
Iteration
Iteration
Iteration
0:
1:
2:
3:
4:
log
log
log
log
log
compete_unregistered credit
likelihood
likelihood
likelihood
likelihood
likelihood
=
=
=
=
=
-287.37734
-278.18506
-278.07192
-278.07173
-278.07173
Logistic regression
Number of obs
LR chi2(4)
Prob > chi2
Pseudo R2
Log likelihood = -278.07173
innov
Coef.
sales
SME
compete_un~d
credit
_cons
2.38e-08
.4657748
.4200596
.5559567
-.7653765
if (albania | country15)&year4
Std. Err.
1.38e-08
.2615244
.212123
.2063587
.2992028
z
P>|z|
1.72
1.78
1.98
2.69
-2.56
0.085
0.075
0.048
0.007
0.011
=
=
=
=
420
18.61
0.0009
0.0324
[95% Conf. Interval]
-3.32e-09
-.0468036
.0043062
.1515011
-1.351803
5.09e-08
.9783532
.835813
.9604123
-.1789497
Marginal effects after logit
y = Pr(innov) (predict)
= .5702615
variable
sales
SME*
compet~d*
credit*
dy/dx
5.83e-09
.1152712
.1034227
.1362639
Std. Err.
z
.00000
.06477
.05222
.05022
1.72
1.78
1.98
2.71
P>|z| [
95% C.I.
0.085 -8.0e-10 1.2e-08
0.075 -.011674 .242217
0.048 .001079 .205767
0.007 .037825 .234702
(*) dy/dx is for discrete change of dummy variable from 0 to 1
119
]
X
3.4e+06
.783333
.657143
.588095
. estat classification
Logistic model for innov
True
Classified
D
~D
Total
+
-
201
37
126
56
327
93
Total
238
182
420
Classified + if predicted Pr(D) >= .5
True D defined as innov != 0
Sensitivity
Specificity
Positive predictive value
Negative predictive value
Pr( +| D)
Pr( -|~D)
Pr( D| +)
Pr(~D| -)
84.45%
30.77%
61.47%
60.22%
False
False
False
False
Pr( +|~D)
Pr( -| D)
Pr(~D| +)
Pr( D| -)
69.23%
15.55%
38.53%
39.78%
+
+
-
rate
rate
rate
rate
for
for
for
for
true ~D
true D
classified +
classified -
Correctly classified
. sum
innov
sales SME
61.19%
compete_unregistered
Variable
Obs
Mean
innov
sales
SME
compete_un~d
credit
420
420
420
420
420
.5666667
3384308
.7833333
.6571429
.5880952
credit
Std. Dev.
if (albania |
Min
Max
0
1
0
0
0
1
1.12e+08
1
1
1
.4961266
1.02e+07
.4124649
.4752303
.492765
Correlation matrix of coefficients of logit model
e(V)
innov
sales
SME
compet~d
credit
_cons
sales
SME
compete_un~d
credit
_cons
1.0000
0.3260
0.0239
-0.0682
-0.3360
1.0000
-0.0575
0.0973
-0.7395
1.0000
-0.0984
-0.3839
1.0000
-0.4068
1.0000
innov
. prvalue
logit: Predictions for innov
Confidence intervals by delta method
Pr(y=1|x):
Pr(y=0|x):
x=
sales
3384307.7
95% Conf. Interval
[ 0.5217,
0.6188]
[ 0.3812,
0.4783]
0.5703
0.4297
SME
.78333333
compete_un~d
.65714286
120
credit
.58809524
country15)&year4
logit: Predictions for innov
Confidence intervals by delta method
Pr(y=1|x):
Pr(y=0|x):
x=
0.6486
0.3514
sales
3384307.7
SME
1
95% Conf. Interval
[ 0.5818,
0.7154]
[ 0.2846,
0.4182]
compete_un~d
.65714286
credit
1
%
in oddspercent help
. change
listcoef,
logit (N=420): Percentage Change in Odds
Odds of: 1 vs 0
innov
sales
SME
compete_un~d
credit
b
z
P>|z|
%
%StdX
SDofX
=
=
=
=
=
=
b
z
P>|z|
0.00000
0.46577
0.42006
0.55596
1.720
1.781
1.980
2.694
0.085
0.075
0.048
0.007
%
0.0
59.3
52.2
74.4
%StdX
27.5 1.0204e+07
21.2
0.4125
22.1
0.4752
31.5
0.4928
raw coefficient
z-score for test of b=0
p-value for z-test
percent change in odds for unit increase in X
percent change in odds for SD increase in X
standard deviation of X
Significance test: single
and
joint tests
. test
credit
( 1)
[innov]credit = 0
chi2( 1) =
Prob > chi2 =
( 1)
[innov]SME = 0
chi2( 1) =
Prob > chi2 =
( 1)
3.92
0.0477
[innov]sales = 0
chi2( 1) =
Prob > chi2 =
( 1)
( 2)
3.17
0.0749
[innov]compete_unregistered = 0
chi2( 1) =
Prob > chi2 =
( 1)
7.26
0.0071
2.96
0.0855
[innov]SME = 0
[innov]credit = 0
chi2( 2) =
Prob > chi2 =
121
9.59
0.0083
SDofX
(
(
(
(
1)
2)
3)
4)
[innov]SME = 0
[innov]credit = 0
[innov]compete_unregistered = 0
[innov]sales = 0
chi2( 4) =
Prob > chi2 =
16.99
0.0019
A.8.2 R&D MODEL
. logit RandD
Iteration
Iteration
Iteration
Iteration
Iteration
0:
1:
2:
3:
4:
innov powerout internet
log
log
log
log
log
likelihood
likelihood
likelihood
likelihood
likelihood
=
=
=
=
=
compete_unregistered
-106.25422
-89.019955
-88.664148
-88.663269
-88.663269
Logistic regression
Number of obs
LR chi2(5)
Prob > chi2
Pseudo R2
Log likelihood = -88.663269
RandD
Coef.
innov
powerout
internet
compete_un~d
SME
_cons
1.414821
.284185
1.161377
.9840382
-1.352051
-1.848304
SME if (albania |
Std. Err.
z
.4067508
.3754238
.4442525
.4488389
.681335
.825426
3.48
0.76
2.61
2.19
-1.98
-2.24
P>|z|
0.001
0.449
0.009
0.028
0.047
0.025
=
=
=
=
158
35.18
0.0000
0.1656
[95% Conf. Interval]
.6176036
-.4516321
.2906584
.1043301
-2.687443
-3.466109
2.212038
1.020002
2.032096
1.863746
-.016659
-.2304992
. mfx
Marginal effects after logit
y = Pr(RandD) (predict)
= .36688979
variable
innov*
powerout*
internet*
compet~d*
SME*
dy/dx
.304585
.0664155
.2448809
.2098799
-.3256939
Std. Err.
.07721
.08817
.08142
.08501
.15183
z
3.95
0.75
3.01
2.47
-2.15
P>|z|
0.000
0.451
0.003
0.014
0.032
[
95% C.I.
.153263 .455907
-.1064 .239231
.085296 .404466
.043258 .376502
-.62328 -.028108
(*) dy/dx is for discrete change of dummy variable from 0 to 1
122
]
X
.613924
.398734
.71519
.734177
.911392
country15)&ye
. sum RandD
innov powerout internet
Variable
Obs
Mean
RandD
innov
powerout
internet
compete_un~d
420
420
420
158
420
.4095238
.5666667
.4357143
.7151899
.6571429
SME
420
.7833333
compete_unregistered
Std. Dev.
Min
Max
.4923324
.4961266
.4964415
.452759
.4752303
0
0
0
0
0
1
1
1
1
1
.4124649
0
1
. lstat
Logistic model for RandD
True
Classified
D
~D
Total
+
-
43
20
20
75
63
95
Total
63
95
158
Classified + if predicted Pr(D) >= .5
True D defined as RandD != 0
Sensitivity
Specificity
Positive predictive value
Negative predictive value
Pr( +| D)
Pr( -|~D)
Pr( D| +)
Pr(~D| -)
68.25%
78.95%
68.25%
78.95%
False
False
False
False
Pr( +|~D)
Pr( -| D)
Pr(~D| +)
Pr( D| -)
21.05%
31.75%
31.75%
21.05%
+
+
-
rate
rate
rate
rate
for
for
for
for
true ~D
true D
classified +
classified -
Correctly classified
74.68%
. lfit
Logistic model for RandD, goodness-of-fit test
number of observations
number of covariate patterns
Pearson chi2(17)
Prob > chi2
123
SME if (albania |
=
=
=
=
158
23
19.32
0.3107
country
. estat vce, correlation
Correlation matrix of coefficients of logit model
RandD
innov powerout internet compet~d
e(V)
SME
_cons
1.0000
-0.6512
1.0000
RandD
innov
powerout
internet
compete_un~d
SME
_cons
1.0000
-0.0077
-0.0441
-0.0223
-0.1641
-0.1949
1.0000
0.0499
0.0359
-0.1150
-0.1274
1.0000
0.0873
0.0279
-0.4732
1.0000
-0.0941
-0.3919
. sum predictR_D if (albania | country15)&year4
Variable
Obs
Mean
predictR_D
158
.3987342
Std. Dev.
.2221505
Min
Max
.0391524
.8803887
.
. prvalue,
x(innov=1)
logit: Predictions for RandD
Confidence intervals by delta method
Pr(y=1|x):
Pr(y=0|x):
0.5002
0.4998
innov
1
x=
95% Conf. Interval
[ 0.3911,
0.6092]
[ 0.3908,
0.6089]
powerout
.39873418
internet
.71518987
compete_un~d
.73417722
SME
.91139241
. prvalue, x(innov=1 SME=1)
logit: Predictions for RandD
Confidence intervals by delta method
Pr(y=1|x):
Pr(y=0|x):
innov
1
x=
95% Conf. Interval
[ 0.3606,
0.5799]
[ 0.4201,
0.6394]
0.4702
0.5298
powerout
.39873418
internet
.71518987
compete_un~d
.73417722
SME
1
. prvalue
logit: Predictions for RandD
Confidence intervals by delta method
Pr(y=1|x):
Pr(y=0|x):
x=
innov
.61392405
0.3669
0.6331
powerout
.39873418
95% Conf. Interval
[ 0.2805,
0.4533]
[ 0.5467,
0.7195]
internet
.71518987
124
compete_un~d
.73417722
SME
.91139241
. listcoef, percent help
logit (N=158): Percentage Change in Odds
Odds of: 1 vs 0
RandD
innov
powerout
internet
compete_un~d
SME
b
z
P>|z|
%
%StdX
SDofX
=
=
=
=
=
=
b
1.41482
0.28418
1.16138
0.98404
-1.35205
z
3.478
0.757
2.614
2.192
-1.984
P>|z|
%
%StdX
SDofX
0.001
0.449
0.009
0.028
0.047
311.6
32.9
219.4
167.5
-74.1
99.6
15.0
69.2
54.7
-32.0
0.4884
0.4912
0.4528
0.4432
0.2851
raw coefficient
z-score for test of b=0
p-value for z-test
percent change in odds for unit increase in X
percent change in odds for SD increase in X
standard deviation of X
A.8.3 COBB DOUGLAS ESTIMATION
TWO INPUT MODEL estimation
COBB-DOUGLAS
TWO INPUT
. regres ln_sales ln_labour
ln_land_capital
Source
SS
df
MS
Model
Residual
1005.99008
2493.7328
2
132
502.99504
18.8919152
Total
3499.72288
134
26.1173349
ln_sales
Coef.
ln_labour
ln_land_ca~l
_cons
.7822951
.4603108
3.855015
if (albania |
country15)&year4
Number of obs
F( 2,
132)
Prob > F
R-squared
Adj R-squared
Root MSE
=
=
=
=
=
=
135
26.62
0.0000
0.2874
0.2767
4.3465
Std. Err.
t
P>|t|
[95% Conf. Interval]
.2708306
.0720827
1.24557
2.89
6.39
3.09
0.005
0.000
0.002
.2465653
.317724
1.391153
Breusch-Pagan / Cook-Weisberg test for heteroskedasticity
Ho: Constant variance
Variables: fitted values of ln_sales
chi2(1)
Prob > chi2
=
=
27.70
0.0000
125
1.318025
.6028975
6.318876
. imtest
Cameron & Trivedi's decomposition of IM-test
Source
chi2
df
p
Heteroskedasticity
Skewness
Kurtosis
27.34
16.94
10.59
5
2
1
0.0000
0.0002
0.0011
Total
54.86
8
0.0000
. estat vif
Variable
VIF
1/VIF
ln_labour
ln_land_ca~l
1.03
1.03
0.968218
0.968218
Mean VIF
1.03
. estat vce
Covariance matrix of coefficients of regress model
e(V)
ln_labour
ln_land_~l
_cons
ln_labour
ln_land_ca~l
_cons
.07334924
-.00191328
-.25161408
.00519592
-.04655895
1.5514454
Correlation matrix of coefficients of regress model
e(V)
ln_lab~r
ln_lan~l
_cons
ln_labour
ln_land_ca~l
_cons
1.0000
-0.0980
-0.7459
1.0000
-0.5186
1.0000
. estat summarize
Estimation sample regress
Variable
Mean
ln_sales
ln_labour
ln_land_ca~l
11.50099
3.699627
10.32298
Number of obs =
Std. Dev.
5.110512
1.393104
5.234199
126
135
Min
Max
0
1.09861
.693147
18.1581
7.16472
17.135
. regres
ln_sales ln_labour
ln_land_capital if (albania |
Linear regression
country15)&year4, robust
Number of obs
F( 2,
132)
Prob > F
R-squared
Root MSE
ln_sales
Coef.
ln_labour
ln_land_ca~l
_cons
.7822951
.4603108
3.855015
Robust
Std. Err.
t
.2507319
.1038046
1.237605
3.12
4.43
3.11
=
=
=
=
=
135
27.92
0.0000
0.2874
4.3465
P>|t|
[95% Conf. Interval]
0.002
0.000
0.002
.2863226
.2549749
1.406909
1.278268
.6656466
6.30312
+++++++++++++++++++++++++++++++++++++++++++++++++++
COBB-DOUGLAS FOUR INPUT
THE FOUR INPUT MODEL:
Source
SS
df
MS
Model
Residual
1526.85489
1972.86799
4
130
381.713723
15.1759076
Total
3499.72288
134
26.1173349
ln_sales
Coef.
ln_labour
ln_land_ca~l
ln_interme~e
ln_electri~y
_cons
.5291978
.2722208
.0696127
.6695686
.3133278
Std. Err.
.2468409
.0740647
.0639537
.1261129
1.270661
Number of obs
F( 4,
130)
Prob > F
R-squared
Adj R-squared
Root MSE
t
P>|t|
2.14
3.68
1.09
5.31
0.25
=
=
=
=
=
=
135
25.15
0.0000
0.4363
0.4189
3.8956
[95% Conf. Interval]
0.034
0.000
0.278
0.000
0.806
.0408526
.1256927
-.056912
.4200694
-2.200524
1.017543
.4187489
.1961375
.9190678
2.827179
Breusch-Pagan / Cook-Weisberg test for heteroskedasticity
Ho: Constant variance
Variables: fitted values of ln_sales
chi2(1)
Prob > chi2
=
=
7.97
0.0048
Cameron & Trivedi's decomposition of IM-test
Source
chi2
df
Heteroskedasticity
Skewness
Kurtosis
22.90
14.27
8.27
14
4
1
0.0620
0.0065
0.0040
Total
45.43
19
0.0006
127
p
Variable
VIF
1/VIF
ln_interme~e
ln_electri~y
ln_land_ca~l
ln_labour
1.89
1.84
1.52
1.06
0.530350
0.542456
0.656660
0.939897
Mean VIF
1.58
Covariance matrix of coefficients of regress model
e(V)
ln_labour
ln_land_~l
ln_inter~e
ln_elect~y
_cons
ln_labour
ln_land_ca~l
ln_interme~e
ln_electri~y
_cons
.06093043
-.00034997
.00023669
-.00557387
-.17536948
.00548557
-.00143473
-.00277582
-.0188839
.00409008
-.00199208
-.00383857
.01590446
-.07193078
1.6145804
.
Correlation matrix of coefficients of regress model
e(V)
ln_lab~r
ln_lan~l
ln_int~e
ln_ele~y
_cons
ln_labour
ln_land_ca~l
ln_interme~e
ln_electri~y
_cons
1.0000
-0.0191
0.0150
-0.1791
-0.5591
1.0000
-0.3029
-0.2972
-0.2007
1.0000
-0.2470
-0.0472
1.0000
-0.4489
1.0000
Estimation sample regress
Variable
Mean
ln_sales
ln_labour
ln_land_ca~l
ln_interme~e
ln_electri~y
11.50099
3.699627
10.32298
8.580796
8.695702
Number of obs =
Std. Dev.
5.110512
1.393104
5.234199
5.957968
3.073648
128
135
Min
Max
0
1.09861
.693147
0
0
18.1581
7.16472
17.135
17.6388
14.9916
Linear regression
Number of obs
F( 4,
130)
Prob > F
R-squared
Root MSE
ln_sales
Coef.
ln_labour
ln_land_ca~l
ln_interme~e
ln_electri~y
_cons
.5291978
.2722208
.0696127
.6695686
.3133278
(
(
(
(
1)
2)
3)
4)
Robust
Std. Err.
t
P>|t|
.2563157
.1006164
.0695286
.1711543
1.17272
2.06
2.71
1.00
3.91
0.27
0.041
0.008
0.319
0.000
0.790
=
=
=
=
=
135
33.55
0.0000
0.4363
3.8956
[95% Conf. Interval]
.0221078
.0731633
-.0679413
.3309603
-2.006758
1.036288
.4712783
.2071668
1.008177
2.633414
ln_land_capital = 0
ln_electricity = 0
ln_intermediate = 0
ln_labour = 0
F(
4,
130) =
Prob > F =
33.55
0.0000
The multicolinearity test suggests that the model does not suffer from multicolinearity
while the heteroscedacity test suggests that we have heteroscedascity problem.
A.8.4
ELASTICITY
OF SUBSTITUTION
OUTPUT
. regres
loglabprod ln_wage
if (albania | country15)&year4
Source
SS
df
MS
Model
Residual
234.657155
259.852364
1
133
234.657155
1.95377717
Total
494.509519
134
3.69036954
loglabprod
Coef.
ln_wage
_cons
1.030584
-3.861981
Std. Err.
.0940381
.5134944
t
10.96
-7.52
129
Number of obs
F( 1,
133)
Prob > F
R-squared
Adj R-squared
Root MSE
P>|t|
0.000
0.000
=
=
=
=
=
=
135
120.10
0.0000
0.4745
0.4706
1.3978
[95% Conf. Interval]
.8445801
-4.877654
1.216588
-2.846309
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