Productivity Dynamics in a Large Sample of Countries: A Panel Study Abstract

Productivity Dynamics in a Large Sample of
Countries: A Panel Study
By
Nazrul Islam
Department of Economics
Emory University
Abstract
Recent research shows that productivity differences are more important than
differences in input intensity in explaining income differences across countries. In this
paper we use the panel approach to study productivity dynamics in a large sample of
countries. We use a modified version of the Minimum Distance estimator to estimate the
capital share parameter in a way that avoids both omitted variable bias and possible
endogeneity bias. Productivity levels are then computed for two different time periods.
This reveals productivity dynamics in the sample. Better data and more flexibility in
parameter values will certainly help in further refining the picture. However the evidence
is strong that countries vary widely in terms of productivity dynamics. The task ahead is
to find out what accounts for the observed dynamics.
First Draft: November 1999
Current Draft: February 2000
---------------------------------------------------------------------------------------------This is a preliminary version of the paper. Please do not quote without permission
of the author. Send your comments to [email protected].
Productivity Dynamics in a Large Sample of Countries:
A Panel Study
1. Introduction
Recent research has shown that productivity differences are more important than
differences in input intensity in explaining income differences across countries. Some
studies indicate that the productivity levels of the developed countries have converged.
However, studies also indicate that such convergence has not occurred either among the
developing countries or between them on the one hand and the developed countries on
the other. This makes study of productivity dynamics in a large sample of countries
interesting and perhaps more useful.
Several different approaches have been used so far for international comparison
of total factor productivity (TFP). Among these are the time series approach, the panel
approach and the cross-section approach. Data limitations do not allow application of the
sophisticated version of the time series approach to many of the developing countries.
The panel approach was used earlier in Islam (1995) to produce productivity indices for a
sample of 96 countries. Recently Hall and Jones (1996, 1999) have used the cross-section
approach to produce productivity indices for 127 countries for the year of 1988.
However, such static snapshot pictures cannot reveal the productivity dynamics.
Yet it is these dynamics that can better reveal the determinants of productivity
improvement. In this paper we apply the panel approach to produce productivity indices
for two different time periods and thereby reveal the productivity changes. We begin by
adapting Cahmberlain’s (1982, 1884) Minimum Distance estimator to estimate the
parameters of the production function free of both omitted variable bias and possible
endogeneity bias. The sample consists of 83 countries for which the Penn World Table
(PWT) allows construction of five-year panels ranging over 1960 to 1990. The two subperiods distinguished are: (a) an initial sub-period ranging from 1965 to 1980, which
mainly represents the 1970s; and (b) a subsequent period ranging from 1975 to 1990,
which mainly represents the 1980s.
The results indicate that the value of the capital share parameter for the 1980s is
significantly higher than for the 1970s. Two possible explanations for this result are (a)
shift in distribution in favor of capital and (b) greater role of human capital in the
production process in the 1980s compared to that in 1970s.
Productivity indices computed on the basis of the estimated parameter values
show much turbulence in relative productivity levels across the countries. There is some
persistence at the top and lower end of the spectrum. Seven countries make to the list of
the top ten performers in both the periods. Similarly, eight countries are found to be
common in the list of bottom ten in both the periods. However, the relative positions
change even within these smaller lists. The major change in the short list of top ten
performers is replacement of the US by Hong Kong as the top performer in the 1980s.
In general, only three countries of the sample retain their productivity rank across
the periods. For 25 percent of the countries, the change in rank (in either direction) ranges
between 6 to 10. For another 12 percent each, this change ranges between 11 to 15 and
1
between 16 to 20. Five countries experience such substantial change in productivity that
their ranks change by more than twenty. For the remaining 34 countries (forty-one
percent) the change in rank ranges between 1 to 5.
Underlying these rank-changes are real shifts in productivity levels. A cardinal
measure of productivity change is obtained by expressing the productivity level of each
country as percentage of the US productivity level. This allows productivity dynamics to
be expressed as changes (in percentage points) in the relative productivity level of a
country, with the US as the common benchmark. All the countries undergo change in
terms of this yardstick. For a majority (thirty-four) of the countries the absolute value of
this change remain limited to one to five percentage points. Fourteen of this group of
countries experience change in the positive direction, while the remaining witness
negative change. For about one-third (twenty) of the countries the absolute magnitude of
the change (in either direction) ranges between six to ten percentage points. For another
fifteen percent the change ranges between eleven to fifteen percent. Seven countries
experience change that range higher than twenty percentage points. Happily for most of
this group of countries the change is positive. For another five countries this change
range between sixteen and twenty percentage points. For most of the countries of this
latter group, however, the change is negative.
We want to view the results presented in this paper as exploratory. There are
several reasons for this. First, the results of any empirical exercise are often as good as
the data used for the purpose. The PWT, despite their wide use and their purchasing
power parity (PPP) feature, have drawn some criticisms. Some researchers have doubted
the validity of the data and questioned the merit of research done on its basis. While we
do not share the extreme variants of this criticism, we recognize that some aspects of the
results may owe more to data construction than to the economic processes of interest.
Second, despite use of an estimation procedure that avoids problems of both omitted
variable bias and endogeneity bias, there remains scope for further improvement in the
econometric methodology.
Despite these possible shortcomings the work presented in this paper shows that is
possible to move the analysis of international productivity differences forward from that
of levels to that of changes. Instead of limiting to a static snapshot it is possible to capture
the dynamics. The picture that one gets from such an attempt reveals enormous variation
in productivity dynamics. Documentation of this variation is a necessary first step in
understanding the productivity determinants. Analysis of these determinants and dealing
with remaining methodological issues are some of the lines along which future research
can proceed.
The paper is organized as follows. Section-2 provides the background to the study
question pursued in this paper. Section-3 discusses various issues related to the panel
approach to productivity study. Section-4 presents the modified version of the Minimum
Distance estimator that avoids the potential endogeneity problem. Sections 5 and 6
present and explain the results. Section-7 discusses various issues of interpretation of the
results and the questions that remain to be investigated further. Section-8 contains the
concluding remarks.
2
2. Importance and State of International Productivity Study
Recent research has shown that productivity differences, rather than differences in
input intensity, play a more important role in accounting for observed per capita incomedifferences across countries. For example, Hall and Jones (1999) note that of the 35-fold
difference in per capita income between the US and Nigeria, difference in capital
intensity accounts for a factor of 1.5, and the difference in educational level accounts for
another factor of 3.1. Productivity difference accounts for the remaining 7.7 factor.
Similar large differences in productivity were reported in Islam (1995).
By “productivity” we are referring here to “total factor productivity (TFP).”
However, “productivity” is sometimes also understood to mean “labor-productivity,” and
per-capita income, because of its easy availability, is often used as a proxy for labor
productivity. Numerous studies have been conducted with level or growth of per-capita
income as the dependent variable. In fact, it is this genre of analysis that has led to or
reinforced the finding that difference in “total factor productivity,” and not difference in
input-intensity, is the main source of per-capita income difference.
Some recent studies have shown that productivity levels of the developed
countries have largely converged to each other. This productivity-convergence has been
portrayed as part of the income-convergence process in this sample of countries. 1
However, research has also shown that such income-convergence and productivityconvergence have not occurred either among the developing countries themselves or
between them on the one hand and the developed countries on the other. Hence, the
larger sample of countries contains more variation in productivity performance, making
study of productivity dynamics in such a sample more interesting and perhaps more
useful.
Separating out the contribution of total factor productivity from that of input
growth is a thorny issue. Many large debates have been waged on this subject, and these
debates are still continuing. Many researchers are skeptical about using aggregate
production function in computing total factor productivity. 2 Others contend that it is not
possible to separate out contribution of productivity from that of the inputs even within
the aggregate production framework. 3 Despite these reservations, total factor productivity
continues to be studied, and the aggregate production function continues to be the
dominant paradigm within which this study is conducted. In part, this is because of
Solow’s (1957, 1962) advice to accept the aggregate production function as a useful
parable necessary to learn the lesson, if not the whole truth. Another reason for the
prevalence of the aggregate production function approach is that there hardly exists any
alternative operational concept that allows quantification of productivity differences
across economies.
However, there are different approaches to take even after adopting the aggregate
production function framework for studying total factor productivity. The oldest among
these is the “time-series growth accounting” approach. Starting with Tinbergen (1942/
1959), this approach has attained a great degree of sophistication in the hands of
1
There is obviously a “selection” problem in this finding. See De Long (1988) and Baumol and Wolff
(1988) for a discussion of this issue.
2
For a recent discussion of this issue, see Felipe (1999)
3
See, for example, the discussion by Abramovitz (1956, 1993) and Abramovitz and David (1973).
3
Jorgenson and his associates. 4 The approach requires disaggregated data on different
types of capital and labor and their respective compensation. It is difficult to find this
kind of disaggregated data for wider samples of countries. This limits the application of
the sophisticated version of the time-series approach for large samples.
This limitation, in part, has led to the emergence of other approaches for
computation of productivity levels in large samples of countries. For example, Islam
(1995) uses a panel regression approach to estimate productivity levels in a sample of 96
countries. On the other hand, Hall and Jones (1996, 1999) use a cross-section approach to
compute productivity levels in a sample of 127 countries. Islam (1999) provides a
discussion of these various approaches and compares the results produced by them. 5
Productivity analysis has therefore progressed from its earlier focus on laborproductivity to its current focus on total factor-productivity and from small sample to
large sample. However, productivity levels computed for large samples of countries have
so far been limited to only one particular time period. Thus, the productivity level
estimates presented in Hall and Jones (1996, 1999) are for 1988. Those of Islam (1995)
are for the 1960-85 period as a whole. These provide one-shot pictures of relative
productivity levels across countries. But, these do not show how productivity changes
over time across countries.
In this context it is worth noting that growth researchers are no longer satisfied
with analyzing such “proximate” sources of growth as investment rate and labor force
growth rate, etc. The quest is now for ultimate or fundamental sources of growth and
productivity. 6 Unfortunately, one-shot pictures of productivity differences are not
adequate for this task. Productivity analysis with such one-shot pictures has to substitute
cross-section variation for temporal change. This limits the analysis. It is therefore
necessary to unearth the productivity dynamics, document them, and start analyzing
them.
In this paper, we take a step in that direction by employing the panel methodology
to compute productivity levels at two different points in time. This reveals productivity
dynamics across the periods. We begin by discussing in the following section the
arguments for using the panel method and the issues that arise in using this methodology.
2. The Panel Approach to Productivity Study
The Cross-section vs. the Panel Approach
A comparison between the cross-section approach and the panel regression
approach shows that both of these have their methodological strengths and weaknesses. 7
One merit of the cross-section approach implemented in Hall and Jones (1996) was it’s
4
For a recent compilation of Jorgenson and his associates’ work on productivity in the US and on
international productivity comparison, see Jorgenson (1995a) and (1995b), respectively
5
Another approach to productivity analysis and efficiency comparison is often referred to as the stochastic
frontier production function (SFPF) approach. Important works using this approach include Fare et al.
(1994), Nishimizu and Page (1983). However, application of this approach requires data that are not
available for large sample of countries.
6
See for example, Barro (1997), Hall and Jones (1999), and Sachs and Warner (1997).
7
See Islam (1999) for details.
4
allowance for the capital share parameter, α , to differ across countries. This however
required the assumption of a common rate of return to capital for all countries. The
method also required prior ordering of the countries according to some criterion. The
productivity results obtained on the basis of these assumptions yielded some surprising
candidates at the apex of the productivity ranking. In Hall and Jones (1999) the authors
abandon the assumption of country specific α and opt for a common value of α .
However, they choose the value of α arbitrarily. From this point of view, the panel
regression approach has a certain advantage. It also assumes a common value of α for
the sample. However, instead of imposing it arbitrarily, it lets the sample data determine
the best-fit value of α . The cross-section approach also requires construction of capital
stock data, which in turn requires assumptions regarding the initial capital stock values
and the depreciation profiles. These may act as additional sources of noise in the data.
The panel approach on the other hand can work directly with the investment rates. 8
These considerations persuade us to use the panel approach in this study, although we
continue to regard the cross-section approach to be also viable.
The panel approach itself has many issues to confront with. We now turn to a
brief discussion of these issues.
Issues of the Panel Approach
The panel approach originates from the fact that the growth-convergence equation
can be reformulated as a dynamic panel data model, and panel estimators can be used to
estimate it. Since Islam (1993, and 1995) and Knight et al. (1993), the panel approach to
growth empirics has become quite popular. This has led to some controversies too. For
example, Barro (1997) expresses the view that panel estimation is not appropriate for
estimation of the growth-convergence equation because it throws away the cross-section
variation and relies on the within variation only. This contention is true of the fixedeffects model. Most of the other panel methods use both between and within variation.
Also, it is a moot point whether the between-variation or the within-variation is more
appropriate for estimation of the convergence parameters. 9
Nerlove (1999) highlights the issue of small sample bias in the context of panel
estimation of the growth-convergence equation. He explores with a variety of panel data
estimators and finds significant difference in results from their application. However,
except for the Least Squares with Dummy Variable (LSDV) estimator (based on the
fixed-effects assumption), all other estimators considered by Nerlove rely on the randomeffects assumption. It is important to note that the random-effects assumption regarding
the country effect term (denoted by, say, µ i ) is not appropriate for the growthconvergence equation. In typical specifications of this equation the right hand side
variables include savings rate, labor force growth rate, etc. The very rationale for
discarding the cross-section regression and adopting the panel approach to estimate the
8
Also of note is that Hall and Jones have now moved away from the Hicks-neutral specification of
technological progress that they used in their earlier (1996) paper. In Hall and Jones (1999), they adopt the
Harrod-neutral specification, which has been also the specification of choice by most of the panel studies of
growth.
9
On this issue, see Islam (1996).
5
growth-convergence equation is that the country effects µ i ’s are correlated with such
right hand side variables.
Notice also that the large samples used to estimate this equation include almost all
countries of the world. Thus, almost the entire population is included in estimation,
leaving little scope for random sampling of µ i . Finally, the deFiniti condition of
interchangeability is clearly not satisfied in this context. For example, it is difficult to
claim that such components of µ i as institutions and resource endowments of the US and
Sierra Leone can be interchanged without affecting the outcome. All these considerations
suggest that panel estimators based on random-effects assumption are not suitable for
estimating the growth convergence equation.
There are some panel-estimators that proceed by first-differencing the equation in
order to get rid of the country effect term µ i . For such estimators it matters less whether
the µ i ’s are random or not. Anderson and Hsiao (1981, 1982) take this approach and use
further lagged values of the dependent variable as instrument. Arellano and Bond (1991)
extend this approach and suggest using all possible lagged values of the dependent
variable as instrument within a GMM framework. Others have taken this idea further. For
example, Ahn and Schmidt (1995) show that there are non-linear moment conditions that
are not exploited in Arellano-Bond, and efficiency can be improved by using them.
Blundell and Bond (1998) show that several restrictions on the initial variables yield
more linear moment conditions, and a GMM estimator inclusive of the latter
encompasses Ahn and Schmidt’s non-linear GMM estimator.
Caseli et al. (1996) actually use an Arellano-Bond (1991) type GMM estimator
(henceforth referred to as AB-GMM) to estimate the growth-convergence equation.
However, the AB-GMM estimator has generally been found to display significant small
sample bias. Alonso-Borrego and Arellano (1996), Kiviet (1995), Harris and Matyas
(1996), Islam (1993), Judson and Owen (1997) Ziliak (1997) and several other studies
report such bias. In fact, one of the motivations for Blundell and Bond’s variant of the
GMM estimator has been to reduce this bias.
On the other hand, several studies have shown good small sample performance of
the fixed-effects estimator (LSDV). This is despite the fact that in a model with lagged
dependent variable, the LSDV estimator is consistent only in the direction of T and not N,
as shown by Nickell (1981) and others. Kiviet (1995) has recently worked out some
analytical results regarding small sample bias of the LSDV estimator and has proposed a
bias-corrected LSDV. His simulations show that the bias-corrected LSDV performs
better than the AB-GMM type estimators do. Judson and Owen (1997) also reach similar
conclusions. The Monte Carlo study by Islam (1993) also shows relatively poor
performance of the AB-GMM estimator in estimating the growth-convergence equation
using the Penn World Table (PWT) data. These findings indicate that the results
presented in Caseli et al. (1996) may suffer from significant small sample bias.
The Endogeneity Problem
However, Caseli et al. (1996) correctly draws attention to a potential endogeneity
problem. To illustrate this, we introduce here the growth-convergence equation that has
6
dominated the recent empirical growth literature. A generic version of this equation can
be written as follows:
y it = γ y i, t−1 + β xi, t−1 + µ i + η t + ν it .
(1)
Here y it represents log of per capita GDP of country i at time t, yi , t −1 is the same lagged
by one period, and x i, t −1 is the difference in log of investment and population growth rate
variables of country i at time t-1. Finally, µ i is the individual country effect, ηt is the
time (period) effect, and ν it is the transitory error that varies across both country and
period. The derivation of this equation is available in many recent papers and hence is not
reproduced here. 10 It proceeds from the following Cobb-Douglas production function
with Harrod-neutral technological progress
α
Yt = K t ( At Lt )1−α ,
(2)
where Y, K, and L are output, capital, and labor respectively. A is the labor-augmenting
technology which grows exponentially at the exogenous rate g. The derivation yields the
following correspondence between coefficients of equation (1) and structural parameters
of the production function (equation (2)):
(3)
γ = e − λτ ,
(4)
β = (1 − e − λτ )
(5)
α
,
1− α
µ i = (1 − e − λτ ) ln A0 i , and
(6)
η t = g ( t 2 − e − λτ t 1 ) .
Here τ is the length of time between t 2 and t1 , which correspond to t and (t-1) of
equation (1), respectively. Finally, λ = (1 − α )( n + g + δ ) .
Notice that by itself equation (1) does not suffer from endogeneity. The
explanatory variable x i, t −1 is pre-determined. So, even if there is a contemporaneous
feedback effect of y it on x it , this cannot affect x i, t −1 . Hence the problem of endogeneity
arises via the estimation procedure. For example, LSDV estimates the equation on the
basis of within variation, and it amounts to application of OLS to the following
transformed equation:
(7)
where y i =
( y it − yi ) = γ ( y i,t −1 − y i, −1 ) + β ( xi, t−1 − xi , −1 ) + (vit − v i ) ,
1 T
∑ y it ,
T t=1
y i, −1 =
1 T −1
1
y i, t −1 , x i, −1 =
∑
T t= 0
T
10
T −1
∑ xi , t −1 , and
t =0
vi =
1 T
∑ v it .
T t=1
See for example Barro and Sala-i-Martin (1992, 1995), Mankiw, Romer, and Weil (1992), Islam (1995),
Mankiw (1995), and other related works.
7
There are now two problems with this equation. The first is the correlation
between ( y i, t −1 − y i, −1 ) and ( vit − v i ) that arises from the dynamic nature of the equation.
This problem has been studied earlier by Nickel (1981) and others. However, now a
second problem arises because of endogeneity. The term xi ,−1 contains all future values
of x it . Hence if there is a feedback effect of y it on x it , then there is a correlation between
( xi, t−1 − xi , −1 ) and ( vit − v i ) .
Estimation of dynamic panel data models with predetermined regressors has
received considerable attention in recent years. Arellano and Bover (1995) consider this
issue in the context of the AB-GMM type estimators. Their suggestion is to transform the
system using the ‘forward orthogonal deviations operator’ and then to use lagged values
of the predetermined variables as instruments. Keane and Runkle (1992) suggest the
forward filtering method of Hayashi and Sims (1983) as an alternative way of conducting
panel estimation with pre-determined variables, including lagged dependent variables.
They show that this method can be applied even to the level-equation when the effects
are random. On the other hand, if the effects are fixed and correlated, then the method has
to be applied to the first-differenced equation. Schmidt, Ahn, and Wyhowski (1992) show
that filtering becomes irrelevant if all available instruments are used. Ziliak (1997)
presents an application of several panel estimators in a situation of pre-determined
variables. He finds that the GMM estimators suffer from severe bias, though the forwardfilter GMM estimator performs better.
4. The Modified Minimum Distance Estimator
The endogeneity problem affects the Minimum Distance (MD) estimation
procedure too. In case of the MD estimation, the problem enters through the specification
of the individual, country effect term µ i . Under strict exogeneity, the MD procedure
assumes the following specification of µ i :
(8)
µ i = κ C + κ 0 x i0 + κ 1 xi1 + L + κ T −1 xi ,T −1 + ψ i ,
where E (ψ i | xi 0 ,K, x i,T −1 ) = 0 . Substituting this into equation (1) yields
(9)
y it = κ C + γ yi ,t −1 + κ 0 xi 0 + κ 1 x i1 + L + ( β + κ t ) xit + L + κ T −1 xT −1 + (ψ i + v it )
However, in presence of endogeneity, x it through x i, T −1 will be correlated with v it , and
this will bias the estimation results.
In the standard MD procedure, the right hand side term y i, t −1 is reduced to yi , 0
through repeated backward substitution. Then in order to conduct unconditional
estimation, yi , 0 ’s are substituted by their following specification in terms of x it ’s:
8
(10)
y i0 = φ C + φ 0 x i0 + φ1 x i1 +L+ φ T −1 xi , T −1 + ζ i ,
where E (ζ i | x i0 , K, xi , T −1 ) = 0 . In presence of endogeneity, this substitution adds to the
correlation problem above.
However, unlike the LSDV estimator, the MD estimator can still be made to work
in presence of endogeneity. One way to do this is to modify the specifications of µ i and
yi , 0 . The basic idea behind the MD estimation is that µ i ’s are correlated with the x it ’s,
and the estimation procedure strives to offer as general a (linear) specification of this
correlation as possible. However, it is not necessary to specify this correlation only in
terms of those x it ’s that fall within the period for which estimation is conducted. It is
quite valid to specify this correlation in terms of lagged values of x it . Note that even in
the standard format, the specification of µ i in the equation for the T-th period turns out to
be entirely in terms of lagged x it ’s.
Specification of µ i in terms of lagged x it increases the set of right hand side
variables and may make the resulting Π -matrix wider. However, in principle, it is still
possible to squeeze out estimates of the structural parameters from the elements of the
Π -matrix using the usual MD format, and the usual properties of the MD estimator
should hold. Chamberlain (1982, 1983) shows that the Π -matrix can have many different
structures depending on the concrete nature of the estimation problem at hand.
In the following we illustrate the procedure on the basis of a set up where T = 3.
To simplify the exposition we ignore the time effects and suppress the subscript i. The
equation for the periods T, T-1, and T-2 can then be written as:
y iT = γ y i, T −1 + β xi, T −1 + µ i + ν iT
(11)
y i,T −1 = γ yi , T −2 + β xi, T − 2 + µ i + ν i,T −1
y i, T − 2 = γ y i, T −3 + β xi, T − 3 + µ i + ν i, T − 2
Assuming that y i, T −3 ’s are the initial values of y, we can use repeated backward
substitution to express the system only in terms of initial y and the x’s. This yields the
following familiar system expressed in matrix form:
 y i, T − 2   β

 

(12) y i, T −1  =  γβ


 y i, T   γ 2 β


0
β
γβ
 u i, T − 2 
0  x i, T −3   γ 
1



 2






0  x i,T − 2 +  γ  y i, T −3 + 1 + γ
 µ i + u i, T −1  ,





2
 u i, T 
β  x i, T −1   γ 3 
1 + γ + γ 


where u i, T − 2 = v i, T − 2 , u i, T −1 = γ v i, T − 2 + vi , T −1 , and u iT = γ 2 vi, T − 2 + γ vi , T −1 + v iT . Now
suppose, we have lagged values of x such as x i, T −4 , x i,T − 5 , and x i, T −6 . We can use these
lagged x’s to specify µ i and the initial y as follows:
9
(13)
µ i = κ C + κ T −6 xi , T −6 + κ T −5 xi ,T −5 + κ T − 4 xi ,T − 4 + ψ i
(14)
y i, T −3 = φ C + φ T −6 xi ,T −6 + φ T −5 xi ,T −5 +φ T −4 xi , T −4 + ζ i
Substituting these into equation (12) we get a Π -matrix of the following type:
(15)
where
(16)
 π 10 π 11 π 12 π 13 π 14 π 15

Π = π 20 π 21 π 22 π 23 π 24 π 25
π
 30 π 31 π 32 π 33 π 34 π 35
π 16 

π 26  ,
π 36 
π 10 = γ κ C + φ C
π 20 = γ 2 κ C + (1 + γ ) φ C
π 30 = γ 3 κ C + (1 + γ + γ 2 ) φ C
π 11 = γ κ T − 6 + φT − 6
π 21 = γ 2 κ T − 6 + (1 + γ ) φ T − 6
π 31 = γ 3 κ T −6 + (1 + γ + γ 2 ) φ T −6
π 12 = γ κ T −5 + φ T −5
π 22 = γ 2 κ T −5 + (1 + γ ) φ T −5
π 32 = γ 3 κ T − 5 + (1 + γ + γ 2 ) φ T − 5
π 13 = γ κ T − 4 + φT − 4
π 23 = γ 2 κ T −4 + (1 + γ ) φ T − 4
π 33 = γ 3 κ T − 4 + (1 + γ + γ 2 ) φ T − 4
π 14 = β , π 15 = 0 , π 16 = 0 ,
π 24 = γ β , π 25 = β , π 26 = 0 ,
π 34 = γ 2 β , π 35 = γ β , and π 36 = β .
Equation for each period now has only predetermined variables on the right hand
side. Hence consistent estimates of the π ’s are readily available. Ignoring the first
column, which contains the intercept terms, this Π -matrix contains eighteen elements,
which are in turn functions of eight underlying parameters, namely
(γ β κ T −6 κ T − 5 κ T − 4 φ T − 6 φ T −5 φ T −4 ) . We may denote these parameters together by the
vector θ .
The process of estimation of θ from the elements of Π -matrix can proceed in the
usual fashion. In other words, we want θˆ such that
(17)
ˆ − g (θ ))' AN (vecΠ
ˆ − g (θ )) ,
θˆ = arg min( vecΠ
10
where g (θ ) is the vector-valued function mapping the elements of θ into vec(Π ) , and
AN is the weighting matrix. Chamberlain shows that the optimal choice for the weighting
matrix AN is the inverse of
Ω = E[( yi − Π 0 x i )( y i − Π 0 xi ) ′ ⊗ Φ −x1 ( x i xi′ ) Φ −x1 ] ,
(18)
where Π 0 is the matrix of true coefficients, Φ x = E ( x i xi′) , and yi and x i are vectors
containing y it ’s and x it ’s of the relevant time periods, respectively. It may be noted that
Ω is a heteroskedasticity consistent weighting matrix. In actual implementation, it is
replaced by its consistent sample analog
N
$ = N −1 ∑ [( y − Π
$ x )( y − Π
$ x ) ′ ⊗ S − 1 ( x x ′) S −1 ] ,
Ω
i
i
i
i
x
i i
x
(19)
i
N
where S x = ∑ x i xi′ / N . Since only predetermined x’s appear in the system, the inference
i =1
theory for the standard MD estimator should apply. Therefore under standard regularity
assumptions, we should have
D
(20)
N (θˆ − θ ) → N ( 0, [G ' Ω −1G] −1 )
where G = ∂g (θ ) ∂θ ′ . The estimated asymptotic variance-covariance matrix of θˆ is
given by
(21)
1
ˆ −1G ] −1 .
Est. Asy Var ( θˆ ) = [G ′Ω
N
We now proceed to apply this modified MD estimator to study productivity
dynamics in a large sample of countries.
5. Estimation and Results
For estimation we focus on the 98-country sample that has figured widely in the
recent studies of growth and productivity. 11 We begin by constructing the five-year
panels in a similar fashion as in Islam (1995). The main reason for considering the data in
five-year panels instead of in the yearly form is to minimize the role of short-term
(business cycle) fluctuations in the estimation process. The recent version of the Penn
World Tables allows the time period to be extended to 1990. For reasons that will be
soon clear, having another five-year panel covering the period of 1990-1985 is important
for the current study. However, not all the countries of the original 98-country sample
have data for the year 1990. Hence, we have to drop the thirteen countries for which data
11
See for example, Barro (1991), Mankiw, Romer, and Weil (1992) and Islam (1995).
11
are missing and thereby reduce the sample size to eighty-three. The entire period extends
from 1960 to 1990, and we have six five-year panels, namely 1990-85, 1985-80, 1980-75,
1975-70, 1970-65, and 1965-60. The list of the countries included in the sample is
provided in the Appendix Table-A1.
While T = 6 is a reasonable size (with N = 83) for MD estimation, our task is
made difficult by the following two facts. First, we need to distinguish two sub-periods
within this overall period. Second, we need to leave some lagged observations so as to
make it possible to specify µ i (and y i0 ) entirely in terms of pre-determined x it ’s. These
two requirements put important constraints on the set ups that can be used. We adopt the
following compromise formula. We consider two sub-periods, the first of which consists
of the panels of 1965-70, 1970-75, and 1975-80. As is clear, this sub-period represent
mainly the 1970s. The second sub-period consists of the panels of 1990-85, 1985-80, and
1980-75. This more recent sub-period represent mainly the 1980s. This allows the µ i for
the first period to be specified in terms of x it ’s for 1965 and 1960. To keep the
symmetry, the µ i for the second sub-period is specified in terms of x it ’s for 1975 and
1970, although more lagged x it ’s are available for this purpose for this sub-period. 12
With this setup, the Π -matrix for each period contains 12 elements (not counting
the elements of the first column, which collects the terms involving the constants and the
time effects). The number of parameters (again, not counting the constants and the time
effects) to be estimated is six, thus leaving us with six degrees of freedom.
We do not report the results on entire parameter vectors for consideration of
space. Instead, we focus on only the implied values of α , the capital share. These values
are reported in Table-1 below.
Table-1
Minimum Distance Estimation of α , the Capital Share
Time period
1970-1980
1980-1990
Estimated Value of
α
0.2581
0.4574
Standard Error of
Estimate
0.0923
0.1236
Value of the
MD-statistic
0.3868
0.9666
Note: The MD statistic has a Chi-square distribution with six degrees of freedom. The critical values are
10.64, 12.59, and 16.81 for ten, five, and one percent level of significance, respectively.
A few observations are in order here. First, we notice that the parameter α is
estimated with considerable precision. Second, The value of the MD-statistic indicate that
the restrictions imposed on the Π -matrix by the main dynamic equation (1) and the
specifications of µ i and y i0 as given by equations (8) and (10) are sustained.
These two observations are of econometric nature. From growth theory’s point of
view however the main point to observe is the significance increase in the value of α
12
Notice that the panel for 1980-75 appears in both the sub-periods. This is to have some degrees of
freedom for the estimation to be successful.
12
from the earlier to the more recent period. Two factors might have worked for this
increase. First, notice that the production function (equation (2)) used to derive the
dynamic model (equation (1)) does not include “human capital” as a separate input. The
L stands for labor, and in implementation L is measured by head count of population or
workers. There is no way for human capital to enter the picture through L. On the other
hand, development of human capital requires some physical investment too (school
buildings, equipment, etc.). It is therefore possible that capital K, implemented through
the investment rate variable, captures some of increased importance of human capital in
the production processes of the more recent period compared to those of the earlier
period.
The second possible reason for the increase in the value of α is purely of
distributional nature. It is widely perceived that the balance of social forces has moved
more in favor of the owners of capital in the 1980s compared to that in the 1970s. This is
reflected by the waning strength of the labor unions, rising income and wealth inequality,
etc. The higher value of α for the more recent period is likely to be a reflection of these
shifts in distribution.
This rise in the value of α in the recent period may not be an artifact of MD
estimation. Some corroborative evidence from LSDV estimation can illustrate this.
Table-2 presents the values of α obtained from LSDV estimation for two
correspondingly similar periods.
Table-2
LSDV Estimation of α , the Capital Share
Time period
1960-1975
1975-1990
Estimated Value of
α
0.2258
0.3160
Standard Error of
Estimate
0.0388
0.0383
Note that the time periods are not exactly the same as those used for MD
estimation. However, it is clear from the above that the estimated value of α does indeed
prove to be much higher for the recent period compared to the earlier period.
Recall the earlier discussion about problems with LSDV estimation in presence of
lagged dependent variable and endogeneity. Hence, no claim is made here regarding
inference-quality of the LSDV results. These are presented here for illustrative purpose
only. In the remaining of this study, we will use the MD values of α . Note that we need
estimated α values only to compute the productivity indices. The relative standing of
countries within a sample and within a period is not likely to be that affected by small
differences in the value of α . Nevertheless, use of an α obtained from a consistent
estimator such as the modified MD estimator above should be a better option compared
to setting α arbitrarily. It is to the task of computation of the productivity indices that we
now turn.
13
6. Productivity Levels and Changes
The estimated coefficients of the dynamic model (equation (1)) can be used to
obtain the estimated values of µ i ’s. The correspondence given by equation (3) and (5)
can then be used to recover the estimated values of A0i . The appendix Table-A1
compiles the results. The columns (2)-(4) show results on relative productivity levels for
the initial period, and the columns (5)-(7) show the results for the subsequent period. The
numbers in columns (8) and (9) give the ordinal and cardinal measures of change in
productivity level of the individual countries between the two periods.
To help assimilate the information provided in Table-A1, we present several
tables. Table-3 shows the top ten and the bottom ten performing countries in terms of
total factor productivity in the two periods. Several things come to notice. First is
persistence. We see that seven countries are common in the list of top ten for both the
periods. It is only France, Belgium, and Japan who, while being in the top ten in the
initial period, fail to do so in the subsequent period. Hong Kong, the UK, and Denmark
replace them. Similarly eight of the bottom ten remain common in both the initial and
subsequent periods. Two countries, namely the Central African Republic and Chad, lift
themselves to higher productivity levels in the subsequent period, and Nigeria and
Zimbabwe replace them. Second, most of the high-performing countries are from North
America and Europe (and Australia). Other than these only Japan, Trinidad, and Hong
Kong enter this top list. Third, Hong Kong replaces the US as the country with the
highest total productivity level in the 1980s. Fourth, most of the countries of the least
performing countries are from Africa. The only notable exception is India. In terms of
productivity India finds herself in this bottom rung in both the periods.
The persistence of countries in the top and bottom list should not overshadow the
wide-ranging movements that occur between the two periods. On can look at these
dynamics from two points of view, namely the ordinal and the cardinal. The ordinal view
is presented in Table-4. It summarizes the extent of movement in terms of change in rank.
The following observations can be made. First, there are three countries whose rank does
not change. These are El Salvador, Mexico, and Sweden, having the ranks of 49, 24, and
6 respectively. Second, a few countries undergo productivity improvement of such
magnitude that the ranks of a large number of countries go down. Thus while thirty
countries’ productivity rank improves, as many as fifty countries’ rank suffers. There are
5 countries whose rank improves by more than 20. Of the remaining, the number of
countries whose rank improves by 1-5, 6-10, 11-15, and 16-20 are 9, 9, 3, and 4
respectively. On the deterioration side, the number of countries whose rank deteriorates
by 1-5, 6-10, 11-15, and 16-20 prove to be 25, 12, 7, and 6 respectively. There is no
country whose rank suffers by more than 20.
More useful for subsequent analysis are the cardinal shifts in productivity. For
cardinal analysis we express the productivity level of the individual countries as
percentage of the US productivity level in both the periods. Thus the numbers in column
(9) give the change (in percentage points)13 in the productivity level of a country relative
to that of the USA. We summarize this information in Table-5. On the improvement side,
we see that the number of countries whose productivity level relative to that of the USA
13
Obviously, after multiplying by hundred.
14
improve by 0-5, 6-10, 11-15, and 16-20 percentage points are 14, 8, 4, and 1 respectively.
For another six countries, this improvement exceeds twenty percentage points. On the
deterioration side, the number of countries whose productivity relative to that of the USA
declines by 0-5, 6-10, 11-15, and 16-20 percentage points are 20, 16, 8, and 4,
respectively. This decline exceeds twenty percentage points for one country only.
Graph-1 presents both the ordinal and cardinal information in the form of a
picture. The X-axis represents the relative (to the US) productivity level in the initial
period. The Y-axis does the same for the subsequent period. The 45-degree line represents
the points where the relative levels in the two periods are the same. The graph is selfexplanatory. All that we observed above in terms of the Tables can now be perused in the
context of this graph.
These results confirm that significant productivity movements are occurring
among the countries over time. The picture is complex. The movements are in different
directions and are of widely different magnitudes. This information can now be used to
find out and analyze the determinants of productivity.
7. Interpretation and Issues
It cannot be claimed that all issues regarding estimation of the productivity
indices have been resolved, and all is well with the results presented in this paper. First of
all there are some data issues. The present exercise is based on the Penn World Tables
(PWT). Relative productivity indices cannot be computed unless data for different
countries are brought to a common base. From this point of view the PWT is particularly
appealing because it has a common base and the conversion is done using the purchasing
power parity (PPP) principle. Also, almost all the recent papers on growth and
productivity have used this data set. 14 Yet the PWT is not above some criticism. Several
researchers have questioned the validity of the data and hence the merit of research done
on its basis. 15 While we do not share the extreme variants of this criticism, we recognize
that some aspects of the results may actually owe to problems of data construction rather
than to the economic processes of interest.
From methodological point of view, some issues concerning assumptions about α
and g remain. To the extent that we are ready to assume a common α across countries,
the estimation procedure used in this paper has the attractive properties of being free from
omitted variable bias and endogeneity bias. However, one may remain squeamish about a
common α . Although it is difficult to either obtain or econometrically estimate countryspecific α , particularly for different periods, the effort in this direction can certainly
continue.
The same can be said of g. In this paper we continue to assume a common g
within a period. This allows treating the ratio of initial productivity level as the relative
productivity level for the period as a whole. This can be illustrated through equation (22)
below.
14
The American Economic Association (AEA) has even awarded prize to Robert Summers and Alan
Heston for putting together this data set.
15
See for example Bardhan (1995). Temple (1998) also discusses the data issues.
15
(22)
Ait
A e gt
A
= 0i gt = 0i .
A jt A0 j e
A0 j
However, this also leaves unexplained what leads to change in the relative productivity
level from one period to the other. Thus the assumption of a within-period common g has
a contradiction with substantial changes in relative productivity level that this study
reveals. Future research may focus on this issue.
An important issue concerns interpretation of A0i or “total factor productivity
(TFP).” It is well known that A0i and TFP is an omnibus term that encompasses many
different elements. 16 In his Nobel address, Solow approvingly mentions “unpacking” by
Denison of “technological progress in the broadest sense” into “technological progress in
the narrow sense” and several other constituents. (Solow, 1987). Among the latter are, for
example, “improved allocation of resources” (which refers to movement of labor from
low productivity agriculture to high productivity industry), economies of scale, etc. So
interpreting the changes in relative productivity levels that we observe through this study
is not easy. This will require an entire separate level of study.
However, we may take note of one particular aspect of this issue, particularly to
facilitate comparison with other studies such as of Hall and Jones (1996, 1999). This
concerns human capital. Unlike Hall and Jones we have refrained from including humancapital in the production function. There are two reasons for this, both relating to data.
First, human capital data are generally fraught with problems. In most cases the schooling
years are not adjusted for differences in quality. Also the estimates of returns to schooling
for one region may not hold for others. There is also the issue of appropriate definition
and measurement of human capital. Etc. Thus, incorporation of human capital into the
analysis is likely to lead to considerable noise in the data. Second, unlike Hall and Jones,
which is a level exercise for one particular year, the present exercise requires human
capital data for all the quinquennial years. Such data are difficult to get for a large sample
of countries. Moreover, research shows that the time series dimension of available human
capital data is worse than the cross-section dimension. 17
The decision to leave human capital out of the production function does not imply
that human capital is not important. What this means is that the productivity dynamics
presented in this paper in part captures the variation and dynamics of human capital
formation. This relationship may be more clearly seen as follows. Proceeding from
equation (2) we have
(23)
ln Y − α ln K − (1 − α ) ln L = (1 − α ) ln A S .
The notation A S indicates that this A comes from the original Solow production function
given by equation (2). On the other hand, if we proceed from the following Mankiw,
Romer, and Weil (1992)’s version of human capital augmented production function,
(24)
16
17
Y = K α H β ( A MRW L )1−α − β ,
See Islam (1999) for a discussion of this and the related issues.
See for example, DeGregorio (1992), Benhabib and Spiegel (1994), Islam (1995), and others.
16
where H is the stock of human capital, then we have
(25)
ln Y − α ln K − (1 − α ) ln L = (1 − α − β ) ln A MRW + β (ln H − ln L )
= (1 − α ) ln AMRW + β (ln h − ln A MRW )
.
Here h is human capital per unit of L. Together with (23) this implies that
(26)
β
1 − α − β 
S
MRW
ln A = 
+
ln h .
 ln A
1−α
 1− α 
This shows that A computed on the basis of equation (2) contains a component coming
from human capital.
This relationship between A S and human capital is simpler in the context of the
following production function used by Hall and Jones (1999):
(27)
Y = K α ( A HJ H ) 1−α ,
They specify H to be e φ ( E ) L , where E is years of education. With this specification the
relationship between A S and AHJ is simply given by
(28)
ln A S = ln A HJ + φ ( E)
All this makes clear that part of the story of productivity dynamics displayed in
this paper has to be told in terms of variation and change in human capital accumulation.
However, that will not be the entire story. Many other factors have to be distinguished
and identified. It is to this intriguing but promising task that we may look forward.
8. Concluding Remarks
Recent research has shown that productivity differences far overshadow
differences in capital accumulation in accounting for (per capita) income differences
across countries. However, analysis of international productivity differences has not kept
up with it importance. For a long time cross-country growth regularities were studied
under the assumption of identical technology. Recent research has broken that mold and
this has led to some attention to productivity differences across countries. This has also
given rise to new methodologies for estimation of productivity indices in large sample of
countries, such as the panel regression approach and the cross-section growth accounting
approach. These methodologies have so far produced one-shot pictures of productivity
differences across countries. However, for a deeper understanding of productivity
determinants, it is necessary to unearth and analyze the productivity dynamics.
This paper takes a step in that direction by computing productivity indices in a
sample of eighty-three countries for two periods, namely the seventies and the eighties.
17
For this purpose it uses an estimation procedure that avoids both the omitted variable bias
problem and the endogeneity problem. The results show enormous diversity in
productivity dynamics across countries. Almost all countries undergo change in relative
productivity level. Some experience movement in the upward direction while others
witness movement in the downward direction. The intriguing question is what determines
the direction and magnitude of these movements. The information produced by this paper
can therefore provide a useful point of departure for analyzing the determinants of
productivity.
The methodology used in this paper can be perfected further. In particular, efforts
may continue to allow the capital share parameter as well as the rate of technological
progress to be country-specific. The wide-ranging productivity dynamics revealed by this
paper enhances the necessity of the latter.
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22
Table-A1
Productivity Dynamics in a Large Sample of Countries
Country
Initial
( µi − µ )
(1)
(2)
Initial
Initial
Subsequent Subsequent Subsequent Change in Change in
Productivity Productivity
Productivity Productivity Productivity Relative (to
Rank
Relative to ( µ i − µ )
Rank
Relative to
Rank
the US)
the USA
The USA
Productivity
(3)
(4)
(5)
(6)
(7)
(8)
(9)
Algeria
Benin
-0.04487
-0.28107
45
68
0.223815
0.118916
-0.23175
-0.28715
62
65
0.175408
0.157365
-17
3
-0.04841
0.038449
Burundi
-0.52267
80
0.062275
-0.46905
74
0.110186
6
0.047911
Cameroon
-0.24427
Ctr. Afr. Rep -0.50157
65
78
0.131229
0.065894
-0.16995
-0.39115
58
72
0.197986
0.128355
7
6
0.066757
0.062461
Chad
-0.47727
76
0.070324
-0.22055
60
0.179299
16
0.108975
Congo
Egypt
-0.08977
-0.05857
50
47
0.198464
0.215754
0.079347
0.244547
34
27
0.322677
0.446004
16
20
0.124213
0.23025
Ghana
-0.34627
70
0.099868
-0.13825
55
0.210673
15
0.110805
Ivory Coast
Kenya
-0.14247
-0.46997
54
74
0.172346
0.071712
-0.28445
-0.57315
64
78
0.1582
0.089856
-10
-4
-0.01415
0.018144
Madagascar -0.15387
55
0.167165
0.289647
22
0.487209
33
0.320043
Malawi
Mali
-0.59097
-0.57697
83
82
0.051868
0.053849
-0.76995
-0.49935
81
77
0.061106
0.103835
2
5
0.009239
0.049987
Mauritania
-0.47997
77
0.069817
-0.74665
80
0.063961
-3
-0.00586
Mauritius
Morocco
0.078428
-0.09447
33
51
0.311358
0.195982
0.360747
-0.01865
16
45
0.560035
0.266304
17
6
0.248676
0.070323
Mozambique -0.19977
62
0.147834
0.163547
31
0.380553
31
0.232718
Nigeria
Rwanda
-0.24167
-0.19687
64
61
0.132146
0.148987
-0.64845
-0.07625
79
51
0.077531
0.237884
-15
10
-0.05462
0.088898
Senegal
-0.29087
69
0.115837
-0.01275
44
0.269401
25
0.153564
S. Africa
Togo
0.032728
-0.51437
36
79
0.2755
0.063674
-0.07865
-0.86245
52
83
0.236768
0.050977
-16
-4
-0.03873
-0.0127
Tunisia
-0.07607
48
0.205878
-0.03075
47
0.260065
1
0.054187
Uganda
Zambia
-0.44377
-0.53277
73
81
0.076923
0.060613
-0.07105
-0.78675
50
82
0.24032
0.059128
23
-1
0.163397
-0.00149
Zimbabwe
-0.35827
72
0.096711
-0.47315
75
0.109305
-3
0.012594
Canada
Costa Rica
0.506528
0.088028
2
32
0.979595
0.319465
0.595047
0.040047
3
39
0.886306
0.298763
-1
-7
-0.09329
-0.0207
Dom. Rep.
-0.05207
46
0.219542
-0.22335
61
0.178319
-15
-0.04122
El Salvador
Guatemala
-0.08687
0.001928
49
39
0.200011
0.253693
-0.06985
0.030447
49
41
0.240886
0.293196
0
-2
0.040875
0.039503
Honduras
-0.26527
66
0.124055
-0.29745
67
0.154221
-1
0.030166
Jamaica
Mexico
-0.16837
0.259328
59
24
0.1608
0.505368
-0.31435
0.265947
68
24
0.149198
0.465102
-9
0
-0.0116
-0.04027
Nicaragua
-0.15687
56
0.165828
-0.28885
66
0.156842
-10
-0.00899
Panama
Trinidad
0.007328
0.494728
37
3
0.257387
0.94913
-0.16105
0.520747
56
4
0.201469
0.766233
-19
-1
-0.05592
-0.1829
USA
0.514228
1
1
0.656647
2
1
-1
0
Argentina
Bolivia
0.240028
-0.19657
26
60
0.479917
0.149106
0.126047
-0.32105
32
69
0.353594
0.147252
-6
-9
-0.12632
-0.00185
Brazil
0.133628
30
0.360949
0.026247
42
0.290793
-12
-0.07016
Chile
0.003428
38
0.254713
0.070847
35
0.317347
3
0.062634
23
Initial
Country
( µi − µ )
(1)
(2)
Initial
Initial
Subsequent Subsequent Subsequent Change in Change in
Productivity Productivity
Productivity Productivity Productivity Relative (to
( µi − µ )
Rank
Relative to
Rank
Relative to
Rank
the US)
the USA
The USA
Productivity
(3)
(4)
(5)
(6)
(7)
(8)
(9)
Colombia
-0.01247
41
0.244098
-0.00615
43
0.272907
-2
0.028809
Ecuador
Paraguay
-0.00997
-0.02737
40
42
0.245737
0.234552
-0.19565
-0.10835
59
53
0.188264
0.223384
-19
-11
-0.05747
-0.01117
Peru
-0.03837
44
0.227744
-0.23525
63
0.174209
-19
-0.05354
Uruguay
Venezuela
0.185128
0.299228
28
23
0.414314
0.562344
0.060447
0.254947
38
26
0.310946
0.455185
-10
-3
-0.10337
-0.10716
Bangladesh
-0.28067
67
0.119044
0.258547
25
0.458407
42
0.339364
Hong Kong
India
0.373028
-0.47347
13
75
0.685197
0.071043
0.663347
-0.47535
1
76
1.013214
0.108834
12
-1
0.328017
0.037791
Israel
0.309428
22
0.577913
0.318747
19
0.515794
3
-0.06212
Japan
Jordan
0.380728
-0.09697
10
52
0.69947
0.194674
0.312347
-0.37465
21
71
0.509367
0.132572
-11
-19
-0.1901
-0.0621
S. Korea
0.062928
35
0.298701
0.063147
37
0.312596
-2
0.013894
Malaysia
Pakistan
0.074828
-0.35577
34
71
0.308372
0.09736
0.038447
-0.16955
40
57
0.297828
0.198142
-6
14
-0.01054
0.100781
Philippines
-0.16577
58
0.161923
-0.34495
70
0.140516
-12
-0.02141
Singapore
Sri Lanka
0.315928
-0.15767
21
57
0.588059
0.165473
0.188347
-0.05585
29
48
0.399501
0.247585
-8
9
-0.18856
0.082112
Syria
0.188728
27
0.418326
0.183947
30
0.396071
-3
-0.02225
Thailand
Austria
-0.10837
0.361528
53
17
0.188822
0.664421
-0.02085
0.317547
46
20
0.265159
0.514583
7
-3
0.076337
-0.14984
Belgium
0.384328
9
0.706244
0.394647
12
0.598495
-3
-0.10775
Denmark
Finland
0.362228
0.330828
16
20
0.665668
0.611993
0.398947
0.269247
10
23
0.603559
0.468119
6
-3
-0.06211
-0.14387
France
0.404628
7
0.745692
0.379947
13
0.581503
-6
-0.16419
Germany
Greece
0.380728
0.169028
11
29
0.69947
0.396834
0.366847
0.064147
14
36
0.566768
0.313209
-3
-7
-0.1327
-0.08362
Ireland
0.372528
14
0.68428
0.398847
11
0.603441
3
-0.08084
Italy
Netherland
0.346428
0.398228
19
8
0.638095
0.733023
0.340547
0.423347
18
9
0.538302
0.633114
1
-1
-0.09979
-0.09991
Norway
0.379928
12
0.697973
0.364147
15
0.563778
-3
-0.1342
Portugal
Spain
0.117428
0.258728
31
25
0.345628
0.504556
0.088947
0.214147
33
28
0.328804
0.420214
-2
-3
-0.01682
-0.08434
Sweden
0.417028
6
0.770864
0.465747
6
0.687956
0
-0.08291
Switzerland
Turkey
0.453028
-0.03317
4
43
0.848864
0.230937
0.430347
-0.12625
8
54
0.641857
0.215685
-4
-11
-0.20701
-0.01525
U. K.
0.367328
15
0.674819
0.491547
5
0.723626
10
0.048807
Australia
0.435628
New
0.354028
Zealand
P. N. Guinea -0.22827
5
18
0.810225
0.651212
0.461147
0.360047
7
17
0.681783
0.559267
-2
1
-0.12844
-0.09195
63
0.136973
-0.41305
73
0.122964
-10
-0.01401
Note: The
shows:
µi
’s are the estimated country effects obtained from estimation of equation (1). As equation (5)
µi =(1− e −λτ ) ln A0i
. The
µ
is the average of
µi
over i, where i is the subscript for the countries.
24
Table-3
Best and Worst TFP Performers
Rank
Top ten in
the initial
period
Top ten in the
subsequent
Period
1
USA
Hong Kong
2
Canada
3
Rank
Bottom ten
in the
initial period
Bottom ten in
the subsequent
period
83
Malawi
Togo
USA
82
Mali
Zambia
Trinidad
Canada
81
Zambia
Malawi
4
Switzerland
Trinidad
80
Burundi
Mauritania
5
Australia
UK
79
Togo
Nigeria
6
Sweden
Sweden
78
Ctrl. Afr. Rep
Kenya
7
France
Australia
77
Mauritania
Mali
8
Netherlands
Switzerland
76
Chad
India
9
Belgium
Netherlands
75
India
Zimbabwe
10
Japan
Denmark
74
Kenya
Burundi
Note: The ranks are on the basis of estimated values of
µi
. Under the assumption the
µi
remain unchanged
within the period. The “Initial Period” mostly refers to the 1970s, and the “Subsequent Period” to the
1980s.
25
Table-4
Productivity Dynamics: Change of Rank
Improve
-ment
in rank
by
No
Of
countries
1-5
9
6-10
Countries
Countries
Deterior
-ation
in rank
by
No.
of
Coun
tries
Benin, Malawi, Mali, Tunisia,
Chile, Israel, Ireland, Italy,
New Zealnd
1-5
25
Kenya, Mauritania, Togo,
Zambia, Zimbabwe, Canada,
Guatemala, Honduras,
Trinidad, USA, Colombia,
Venezuela, India, Korea,
Syria, Austria, Belgium,
Finland, Germany,
Netherlands, Norway,
Portugal, Spain, Switzerland,
Australia
9
Burundi, Cameroon, Ctrl. Afr.
Rep., Morocco, Rwanda, Sri
Lanka, Thailand, Denmark,
the UK
6-10
12
Ivory Coast, Costa Rica,
Jamaica, Nicaragua,
Argentina, Bolivia, Uruguay,
Malaysia, Singapore, France,
Greece, Papua New Guinea
11-15
3
Ghana, Hong Kong, Pakistan
11-15
7
Nigeria, Dom. Rep., Brazil,
Paraguay, Japan, Philippines,
Turkey
16-20
4
Chad, Congo, Egypt,
Mauritius
16-20
6
Algeria, South Africa,
Panama, Ecuador, Peru,
Jordan
More than
20
5
Bangladesh, Madagascar,
Mozambique, Senegal,
Uganda
More than
20
0
Note: The ranks are on the basis of estimated values of
within the period.
26
µi
. Under the assumption the
µi
remain unchanged
Table-5
Productivity Dynamics: Change in Relative Productivity
Countries
Deterior
-ation
in relative
pdvty by
(pct.
Points)
0-5
No. of
Count
ries
Countries
20
Algeria, Ivory Coast,
Mauritania, South Africa,
Togo, Zambia, Costa Rica,
Dom. Rep., Jamaica, Mexico,
Nicaragua, Bolivia, Paraguay,
Peru, Malaysia, Philippines,
Syria, Portugal, Turkey,
Papua New Guinea
Cameroon, Ctr. Afr. Rep.,
Morocco, Rwanda, Chile,
Pakistan, Sri Lanka, Thailand
6-10
16
Nigeria, Canada, Panama,
Brazil, Ecuador, Uruguay,
Israel, Jordan, Denmark,
Greece, Ireland, Italy,
Netherlands, Spain, Sweden,
New Zealand
4
Chad, Congo, Ghana, Senegal
11-15
8
Argentina, Venezuela, Austria,
Belgium, Finland, Germany,
Norway, Australia
16-20
1
Uganda
16-20
4
Trinidad, Japan, Singapore,
France
More than
20
6
Bangladesh, Egypt, Hong
Kong, Madagascar, Mauritius,
Mozambique
More than
20
1
Switzerland
Improve
-ment
in relative
pdvty by
(pct.
points)
0-5
No
Of
Countries
14
Benin, Burundi, Kenya,
Malawi, Mali, Tunisia,
Zimbabwe, El Salvador,
Guatemala, Honduras,
Colombia, India, Korea, the
UK.
6-10
8
11-15
Note: Relative productivity level signifies the ratio of
A0 of a country to A0 of the USA for the same
period. Under the assumptions this ratio remain the same within the same period.
27
Graph-1
Productivity Dynamics in a Large Sample of Countries
Productivity Dynamics in a Large Sample of Countries
1.1
1.1
HKG
Subsequent Relative Productivity
1
USA
.9
CAN
.8
1
.9
.8
TTO
GBR
.7
.7
SWE
AUS
CHE
NLD
DNK
IRL
BEL
DEUFRA
MUS
NZLNOR
ITA
ISR
AUT
JPN
MDG
MEX VEN FIN
BGD
EGY
ESP
SGP
SYR
MOZ
ARG
PRT
COGCHL
KOR
GRC
URY
CRIBRA
GTMMYS
COL
SEN THA
MAR
TUN
LKA
UGA RWASLV
ZAF
PRY
TUR
GHA
PAN
PAK
CMR
ECU
TCD
DOM
DZA
PER
CIV
BEN
HND
NIC
BOL
JAM
PHL
JOR
CAR PNG
BDI
IND
ZWE
MLI
KEN NGA
MRT
MWI
ZMB
TGO
.6
.5
.4
.3
.2
.1
.6
.5
.4
.3
.2
.1
0
0
0
.1
.2
.3
.4
.5
.6
.7
Initial Relative Productivity
.8
.9
1
Note: “Initial Relative Productivity” refers to productivity relative to the US in the 1970s,
and “Subsequent Relative Productivity” refers to productivity relative to the US in the
1980s. Relative productivity is measured by the ratio
A
0i
A
0 ,US
given in columns (4) and (7) of the Appendix Table-A1.
28
. The data for the graph are