THREE ESSAYS ON MONETARY ECONOMICS by

Transcription

THREE ESSAYS ON MONETARY
ECONOMICS
by
LINYUAN CAI
JAMES COVER, COMMITTEE CHAIR
JUN MA
HAROLD ELDER
SHAWN MOBBS
CECIL ROBINSON
A DISSERTATION
Submitted in partial fulfillment of the requirements
for the degree of Doctor of Philosophy
in the Department of Economics, Finance and Legal Studies
in the Graduate School of
The University of Alabama
TUSCALOOSA, ALABAMA
2013
Copyright Linyuan Cai 2013
ALL RIGHTS RESERVED
ABSTRACT
The study of monetary economics encompasses a broad range of directions, and this
research aims to address several different areas of monetary economics through empirical and
theoretical work. The first essay uses annual data from twenty-seven countries to determine
whether unexpected inflation has an effect on unexpected output, as suggested by the Lucas
Supply Function. Additional specifications are added to show that Lucas’ base model is
incomplete. Once money level equations were included, the results suggest money affects output
through prices, as well as through other means. The second essay seeks to find stable predictors
of the money demand function. The money demand function has been unstable since the 1970s,
and this study focuses on the definition of money stock and adding measures of risk as solutions
in stabilizing money demand. The results show that replacing the traditional measure of money
stock (M2) with Money Zero Maturity, in addition to adding market risk and inflation risk to the
specification for money demand, stabilizes the money demand function significantly. In this
case, we have discovered a money demand function that is stable both in the short run and the
long run, according to the LWZ criterion. The third essay attempts to verify Carl Menger’s
theory on the emergence of money through the observation of an online gaming economy. The
results show that, while most of the observations were identical to Menger’s theories, one
interesting difference has emerged due to modern day technology and communication tools.
Menger suggested that the creation of currency was due to trade being extremely unproductive
under the “Double Coincidence of Wants,” but our observations show that a barter system can
coexist with a currency due to technology making search costs almost negligible.
ii
DEDICATION
This dissertation is dedicated to my parents, Tianyi Cai and Jie Li, whose guidance and
support have motivated me to complete my doctoral degree. I would also like to dedicate it to
my loving wife, Anna, who has endured this entire process with me.
iii
LIST OF ABBREVIATIONS AND SYMBOLS
BIC
Bayesian Information Criterion
FFR
Federal Funds Rate
GDP
Gross Domestic Product
LSF
Lucas Supply Function
LWZ
Liu, Wu, Zidek Criterion
MZM
Money Zero Maturity
POW
Prisoner of War
RPG
Role-Playing Game
SoJ
Stone of Jordan
VAR
Vector Autoregression
iv
ACKNOWLEDGMENTS
I would like to thank my family, friends, and faculty members who have helped and
inspired me during this process. Notably, I would like to thank the members of my dissertation
committee for their guidance, expertise, and ingenuity. These faculty members include my
committee chair, Dr. James Cover; Dr. Jun Ma; Dr. Harold Elder; Dr. Shawn Mobbs; and Dr.
Cecil Robinson.
I would like to present a special thanks to Dr. James Cover for directing me through this
entire journey, allowing me to study under him, and giving me numerous inspirational ideas over
these years.
I would also like to thank Dr. Billy Helms for giving me the opportunity to study in this
department. I have learned a lot from him as his TA, and I truly feel that this department was a
helpful family under his leadership.
v
CONTENTS
ABSTRACT............................................................................................................ ii
DEDICATION ....................................................................................................... iii
LIST OF ABBREVIATIONS AND SYMBOLS .................................................. iv
ACKNOWLEDGMENTS .......................................................................................v
LIST OF TABLES ................................................................................................ vii
LIST OF FIGURES ............................................................................................. viii
1. INTRODUCTION ..............................................................................................1
2. INTERNATIONAL EVIDENCE ON THE EFFECTS OF UNEXPECTED
INFLATION ON OUTPUT ................................................................................3
3. MONEY DEMAND, RISK, AND A BETTER MEASURE OF THE
MONETARY AGGREGATE ..........................................................................22
4. THE THEORY OF MONEY DESCRIBED BY ONLINE GAMING .............46
5. CONCLUDING REMARKS ............................................................................69
vi
LIST OF TABLES
Table 2.1. Most Parsimonious Processes with White Noise Residuals ...................7
Table 2.2. Results of Covariance-Bounds Tests Using Box-Jenkins.....................10
Table 2.3. Results of Covariance-Bounds Tests Using VAR ................................11
Table 2.4. Countries with Positive Values of 𝑎 Using Box-Jenkins......................14
Table 2.5. Countries with Negative Values of 𝑎 Using Box-Jenkins ....................14
Table 2.6. Countries with Positive Values of 𝑎 Using VAR .................................15
Table 2.7. Countries with Negative Values of 𝑎 Using VAR................................15
Table 3.1. Results from Bai-Perron Structural Break Test ....................................39
Table 3.2. Structural Break Dates ..........................................................................40
Table 3.3. Estimated Values of Coefficients .........................................................43
Table 4.1. SoJ and Runes Occurrence Rates..........................................................65
vii
LIST OF FIGURES
1
Figure 2.1. Trend of 𝑎|𝑐 = 2 with Box-Jenkins Method .......................................16
Figure 2.2. Trend of 𝑎|𝑐 = 1 with Box-Jenkins Method.......................................17
1
Figure 2.3. Trend of 𝑎|𝑐 = 2 with VAR ................................................................18
Figure 2.4. Trend of 𝑎|𝑐 = 1 with VAR ................................................................19
Figure 3.1. Coefficients using M2 with No Measures of Risk ..............................28
Figure 3.2. Coefficients using MZM with No Measures of Risk ..........................29
Figure 3.3. Coefficients using M2 with Market Risk ............................................32
Figure 3.4. Coefficients using MZM with Market Risk ........................................33
Figure 3.5. Coefficients using M2 with Inflation Risk ..........................................35
Figure 3.6. Coefficients using MZM with Inflation Risk ......................................36
Figure 3.7. Coefficients using M2 with Market Risk and Inflation Risk ..............37
Figure 3.8. Coefficients using MZM with Market Risk and Inflation Risk ..........38
Figure 3.9. Actual MZM Versus Fitted MZM .......................................................43
Figure 4.1. Example Posts from August 2000 Trading Forums ............................60
Figure 4.2. Example Posts from October 2000 Trading Forums ...........................60
Figure 4.3. Example Posts from December 2000 Trading Forums .......................61
Figure 4.4. Example Posts from March 2001 Trading Forums .............................61
Figure 4.5. Example Posts from August 2001 Trading Forums ............................62
Figure 4.6. Example Posts from April 2002 Trading Forums ...............................63
viii
CHAPTER 1
INTRODUCTION
Over the last several decades, the field of monetary economics has seen tremendous
growth. In particular, research in the trade-off between inflation and output, as well as finding a
stable money demand function, have been widespread; however, the success of these efforts has
been limited. The first essay tackles the former topic by using annual data from twenty-seven
countries to determine whether unexpected inflation has an effect on unexpected output, as
predicted by Lucas (1973) and more recently tested by Fendel and Rülke (2012). A set of
Covariance-Bounds Tests derived by Cover (1989) is applied to the variances and covariances
obtained from a VAR. We expect that unexpected inflation will affect unexpected output to
some degree, but we also expect that unexpected money will account for a larger portion of the
fluctuations in output.
The second essay attempts to discover a stable money demand function. Finding a stable
money demand function has been a difficult task since the 1970s. Much of the related literature
suggests this is because the definition of money stock changes when technology and policies
change the liquidity of different types of money. If our definition of money is inaccurate, then it
is impossible to predict the behavior of money demand in the future. Another approach points to
the fact that the traditional money demand equation does not include measures of risk when risk
should affect the amount of money consumers hold. This essay combines these two contentions
by using Money Zero Maturity (MZM) instead of M2 as the measure
1
of money and by including market risk and inflation risk in the estimation of money demand in
order to find stable predictors of money demand.
Although much of the research conducted in monetary economics has been empirical,
theory should also be explored. The third essay discusses the origin and evolution of money by
showing how an online gaming economy mirrors the development of money, as described by
Carl Menger in his On the Origins of Money. As one might expect, it is difficult to verify some
of Menger’s theories on money, since trades that occurred before the existence of currency were
not well documented. His theories are also difficult to model because it is nearly impossible to
discover a developing community in which a currency has not already been established. An
online gaming economy was chosen to model his theories because a digital market emerges in
every new game, and we are able to freely observe the interactions in these markets. The
forecast for this paper is that there is most likely a great deal of truth in Menger’s theories, but
there may also be certain deviations produced by the advancement of modern communication. A
secondary purpose of this paper is to urge economists to delve more deeply into virtual world
experiments. There is still much territory to be explored, since the virtual world can offer us the
outcomes of different policies in fields such as money and trade without the negative impacts
they would impose on society if said policies did not perform as expected.
2
CHAPTER 2
INTERNATIONAL EVIDENCE ON THE EFFECTS OF
UNEXPECTED INFLATION ON OUTPUT
2.1
Introduction
Since Lucas’ (1973) milestone paper on inflation and output tradeoff, the Lucas Supply
Function (LSF) has become a major foundation of most modern day macroeconomics textbooks.
Fendel and Rülke (2012) tested the Lucas Supply Function using actual inflation surprises across
nineteen industrialized economies and found strong evidence of a relationship between the
inflation forecast errors (unexpected inflation) and variations of real output around its trend
(unexpected output). Prior to Fendel and Rülke, Madsen (1997) also tested the LSF; however,
Madsen failed to find evidence of it. Although Fendel and Rülke’s paper is the first to find
evidence supporting the LSF using actual inflation surprises, the model has certain endogeneity
issues that should not be overlooked. Fendel and Rülke used the following equation, a Lucastype aggregate supply equation, for their empirical analysis:
𝑦𝑡 − 𝑦𝑡𝑡𝑟𝑒𝑛𝑑 = 𝛼 + 𝛽(𝜋𝑡 − 𝐸𝑡−4 𝜋𝑡 ) + 𝜀𝑡
(2.1)
where 𝑦𝑡 is the current GDP, 𝑦𝑡𝑡𝑟𝑒𝑛𝑑 is the trend GDP, 𝜋𝑡 is the inflation rate, and 𝐸𝑡−4 𝜋𝑡 is the
one year ahead forecast of the inflation rate (quarterly data was used). 𝜋𝑡 − 𝐸𝑡−4 𝜋𝑡 reflects the
inflation forecast error or “unexpected inflation” and 𝜀𝑡 is the error term. The endogeneity issue
occurs because there is a loop of causality between the endogenous and exogenous variables in
3
equation (2.1). Whenever there is unexpected inflation, output should unexpectedly rise. With
this rise in output, unemployment decreases and workers demand higher wages. This eventually
leads to firms raising prices because input costs increase. The endogeneity problems can also be
observed by noting that 𝜋𝑡 − 𝐸𝑡−4 𝜋𝑡 is dependent on its previous lags, so it is trivial that 𝜀𝑡 is
serially correlated in this case. Although Fendel and Rulke are using expected price levels from
a survey, the actual price level is still endogenous; therefore, their estimation suffers from
simultaneous equation bias.
To account for these endogeneity issues, I will add the money level estimation to Fendel
and Rülke’s model to make our residuals serially uncorrelated. I will also implement a group of
covariance-bounds tests developed by Cover (1989) to provide analysis on inflation-output
sensitivity. Then, conditional estimates of the sensitivity of output to unexpected inflation will
be presented. The procedure directly employs each country’s price level information. The
results presented by Fendel and Rülke suggested a strong relationship between unexpected
inflation and variations in output; however, these series of tests show that once an unbiased
model has been introduced, the relationship is not quite as strong as Fendel and Rülke suggest.
The following section will introduce the model, with the remaining sections discussing the
results of the covariance-bounds tests and conditional estimates.
2.2
Model
Consider the following model from Cover (1989):
𝑦𝑡 − 𝐸𝑡−1 𝑦𝑡 = 𝑎(𝑝𝑡 − 𝐸𝑡−1 𝑝𝑡 ) + 𝑢𝑡
(2.2)
𝑚𝑡 − 𝑝𝑡 = 𝑏 + 𝑐𝑦𝑡 + 𝑑𝐸𝑡−1 (𝑝𝑡 − 𝑝𝑡−1 ) + 𝜀𝑡
(2.3)
𝑚𝑡 − 𝐸𝑡−1 𝑚𝑡 = 𝜉𝑡
(2.4)
𝑒𝑡 = 𝜉𝑡 − 𝜀𝑡
(2.5)
4
where 𝑢𝑡 , 𝜀𝑡 , and 𝜉𝑡 are mutually and serially uncorrelated, mean-zero disturbances; 𝑦𝑡 , 𝑝𝑡 , and
𝑚𝑡 are the logarithms of output, price, and money supply, respectively,;and 𝐸𝑡−1 is the
expectation of a variable conditional on information available during period 𝑡 − 1. Equation
(2.2) is the aggregate supply equation similar to that used by Fendel and Rülke. The parameter 𝑎
represents the relationship between output fluctuations and unexpected inflation. Equation (2.3)
is a portfolio balance equation, and the parameter 𝑐 is the income elasticity of money demand.
The parameter 𝑑 is the inflation elasticity of money demand, which we assume is negative, since
people will hold less money when inflation is high. Equation (2.3) assumes that the real interest
rate is constant over time, in order to keep the model simple. This leads to the result that the
nominal interest rate varies only with the inflation rate. Equation (2.4) is defined as unexpected
money, and equation (2.5) is the net monetary disturbance.
Solving equations (2.2) – (2.5) for 𝑦𝑡 and 𝑝𝑡 , we obtain:
𝑦𝑡 = 𝐸𝑡−1 𝑦𝑡 + 𝑎(𝑝𝑡 − 𝐸𝑡−1 𝑝𝑡 ) + 𝑢𝑡
(2.6)
𝑝𝑡 = 𝐸𝑡−1 𝑝𝑡 + 𝑎(𝑦𝑡 − 𝐸𝑡−1 𝑦𝑡 ) + 𝑒𝑡
(2.7)
Buiter (1983) found these two equations to be unidentified. These equations cannot be estimated
without additional restrictions. Notice that introducing additional exogenous variables to the
system does not help identify the equations because 𝐸𝑡−1 𝑦𝑡 and 𝐸𝑡−1 𝑝𝑡 are on the right side of
both of them. Any expression added to the right side of equation (2.6) will also appear in
equation (2.7). With these considerations, tests for the hypothesis 𝑎 = 0 are still possible to
implement.
Equations (2.6) and (2.7) can be rewritten as follows:
𝑎
1
(2.8)
1
𝑐
(2.9)
𝑦𝑡∗ = 𝑦𝑡 − 𝐸𝑡−1 𝑦𝑡 = 1+𝑎𝑐 𝑒𝑡 + 1+𝑎𝑐 𝑢𝑡
𝑝𝑡∗ = 𝑝𝑡 − 𝐸𝑡−1 𝑝𝑡 = 1+𝑎𝑐 𝑒𝑡 − 1+𝑎𝑐 𝑢𝑡
5
where 𝑦𝑡∗ and 𝑝𝑡∗ represent unexpected output and unexpected inflation, respectively. Using
equations (2.8) and (2.9), we can verify that the covariance matrix of 𝑦𝑡∗ and 𝑝𝑡∗ can be
constructed with the following equations:
𝑣𝑎𝑟(𝑦𝑡∗ ) =
𝑣𝑎𝑟(𝑝𝑡∗ ) =
𝑎2 𝜎𝑒2 +𝜎𝑢2
(2.10)
(1+𝑎𝑐)2
𝜎𝑒2 +𝑐 2 𝜎𝑢2
(2.11)
(1+𝑎𝑐)2
𝑐𝑜𝑣(𝑦𝑡∗ , 𝑝𝑡∗ ) =
𝑎𝜎𝑒2 −𝑐𝜎𝑢2
(2.12)
(1+𝑎𝑐)2
With the intention to implement the tests developed by Cover (1989), we must first
estimate the covariance matrix by fitting the annual data on output and price level for each
country to univariate Box-Jenkins models. Following Cover (1988), it can also be shown that
the output and price level processes should be univariate because past values of price and money
supply contain no information that can improve predictions of the output and past values of
output and money supply contain no information that can improve predictions of the price level.
It follows that we should use the most parsimonious univariate models that yield white-noise
residuals for output and price level. Table 2.1 summarizes these models in addition to the
sample periods used.
6
Table 2.1. Most Parsimonious Processes with White Noise Residuals
Country
Argentina
Australia
Bolivia
Canada
Colombia
Ecuador
France
Germany
Iceland
Ireland
Italy
Japan
Korea
Mexico
Netherlands
New Zealand
Norway
Paraguay
Philippines
Russia
Singapore
South Africa
Spain
Sweden
Turkey
United Kingdom
United States
2.3
Y – Process
P – Process
(0,1,0)
(1,0,0)
(1,1,0)
(1,0,0)
(1,1,0)
(0,1,0)
(2,0,0)
(1,1,0)
(1,1,0)
(1,1,0)
(1,0,0)
(1,0,0)
(1,0,0)
(1,0,0)
(2,0,0)
(0,1,0)
(2,0,0)
(1,1,0)
(1,1,0)
(0,1,0)
(0,1,0)
(2,0,0)
(1,0,0)
(1,1,0)
(0,1,0)
(1,1,0)
(0,1,0)
(2,1,0)
(1,1,0)
(1,1,0)
(1,1,0)
(1,1,0)
(1,1,0)
(2,1,0)
(2,1,0)
(1,1,0)
(1,1,0)
(2,0,0)
(2,0,0)
(2,0,0)
(3,1,0)
(2,0,0)
(1,1,0)
(2,0,0)
(1,1,0)
(1,1,0)
(1,0,0)
(0,1,1)
(1,1,1)
(2,0,0)
(1,1,0)
(1,1,0)
(2,0,0)
(2,1,0)
Sample Period
1953-2011
1962-2011
1971-2010
1953-2011
1971-2010
1968-2010
1953-2011
1963-2011
1963-2011
1953-2011
1973-2011
1960-2011
1969-2011
1954-2011
1959-2011
1957-2011
1969-2011
1953-2011
1961-2011
1998-2011
1963-2011
1957-2011
1957-2011
1953-2011
1970-2011
1991-2011
1953-2011
Analysis
Here, two methods of estimating the covariance matrix are used. First we use the Box-
Jenkins method to estimate the most parsimonious univariate models that yield white-noise
residuals, and then we use the cmoment command in RATS to estimate the covariance matrix of
unexpected output and unexpected inflation. Second, a VAR system was set up in order to
estimate the covariance matrix. Using VAR to estimate the covariance matrix should not yield
significantly different results if these are truly univariate models.
7
2.3.1 Covariance-Bounds Test 1
As we discussed earlier, the hypothesis for each of these tests should be 𝑎 = 0. This will
give us information on whether unexpected inflation affects unexpected output. Cover (1989)
calls this first test a strong covariance-bounds test, and it begins by following equation (2.12) and
noting that the covariance between 𝑦𝑡∗ and 𝑝𝑡∗ can be positive only if 𝑎 is positive. Table 2.2
shows 𝑐𝑜𝑣(𝑦𝑡∗ , 𝑝𝑡∗ ) estimates for twenty-seven different countries using the Box-Jenkins method.
The covariance is positive for eleven countries. We may conclude that unexpected inflation has
an effect on output for these eleven countries; however, we cannot say with certainty that there is
no effect for the remaining sixteen countries because the covariance can be negative even if 𝑎 is
positive. The estimates of 𝑐𝑜𝑣(𝑦𝑡∗ , 𝑝𝑡∗ ) using VAR are presented in Table 2.3. The covariance is
positive for the same eleven countries, so the results from these two methods of estimation are
consistent for this first covariance-bounds test.
This test follows equation (2.12) and notes that the covariance can be zero only if 𝑎 is
positive. The hypothesis is that the covariance matrix is a diagonal matrix. The test statistic is
the square of the correlation coefficient times the number of observations and has a chi-square
distribution with one degree of freedom (Judge et al. 1985). The hypothesis that the correlation
coefficient is zero is rejected in nine of the twenty-seven countries, according to the estimates
from the Box-Jenkins method. Five of these countries are in the top ten of the highest variances
of unexpected prices, but the remaining four have comparatively low variances. These results
suggest that unexpected prices have an effect on output in eighteen of the twenty-seven
countries. Also note that, of the eleven countries that had a positive 𝑎 from the first covariancebounds test, eight of these eleven countries correspondingly have a positive 𝑎 according to this
8
second covariance-bounds test. Based on estimates produced from VAR, the hypothesis that the
correlation coefficient is zero is rejected in ten of the twenty-seven countries. The same five
countries are within the top ten highest variances of unexpected prices, and the remaining five
countries have three in common with the previous Box-Jenkins method results. Of the eleven
countries with a positive 𝑎 from the first covariance-bounds test, again, eight of these eleven
countries have a positive 𝑎 using the second covariance-bounds test. The VAR estimates give us
consistent results compared to the estimates found using the Box-Jenkins method.
This covariance-bounds test is derived by solving for 𝑐 from equations (2.10) and (2.12)
with the hypothesis that 𝑎 = 0. This yields the following expression:
𝑐=
−𝑐𝑜𝑣(𝑦𝑡∗ ,𝑝𝑡∗ )
(2.13)
𝑣𝑎𝑟(𝑦𝑡∗ )
Here, 𝑐 is the conditional estimate of the income elasticity of money demand given unexpected
prices have no effect on output. Using the Box-Jenkins method estimates, 𝑐 falls between onethird and one-half for two of the countries, which is credible under the Miller-Orr (1966) model
of money demand. Using VAR estimates, 𝑐 falls between one-third and one-half for only one of
these two countries, however, the other country has a 𝑐 that was extremely close to one-third. For
three additional countries, the 𝑐 found from the Box-Jenkins method estimates falls between onehalf and one, which is reasonable under the transaction theory of money demand presented by
Barro (1976). For these same three countries, 𝑐 falls between one-half and one using VAR
estimates. This final covariance-bounds test suggests that it is realistic to assume that 𝑎 is zero
in only five of the twenty-seven countries.
9
Table 2.2. Results of Covariance-Bounds Tests Using Box-Jenkins
𝑣𝑎𝑟(𝑦 ∗ )
Country
𝑣𝑎𝑟(𝑝∗ )
𝑐𝑜𝑣(𝑦 ∗ , 𝑝∗ )
𝜌
Bolivia
0.0120
16.9265
-0.0694
-0.1540
Argentina
0.1534
11.3689
-0.6531
-0.4946c
Mexico
0.0511
0.5926
-0.0626
-0.3596c
Turkey
0.0688
0.4687
-0.0605
-0.3367b
Ecuador
0.0860
0.4087
-0.0308
-0.1641
Iceland
0.0582
0.2939
-0.0247
-0.1890
Philippines
0.0350
0.2242
-0.0510
-0.5754c
a
Paraguay
0.0729
0.1753
0.0183
0.1619
Russia
0.0333
0.1111
0.0023a
0.0385
Korea
0.0443
0.0645
-0.0248
-0.4649c
Colombia
0.0146
0.0593
-0.0027
-0.0917
France
0.0119
0.0489
-0.0036
-0.1474
Singapore
0.0806
0.0427
0.0191a
0.3254b
Ireland
0.0352
0.0402
0.0024a
0.0627
New Zealand
0.0319
0.0332
-0.0071
-0.2181
Spain
0.0536
0.0318
0.0070a
0.1701
Japan
0.0438
0.0265
-0.0057
-0.1660
Sweden
0.0244
0.0258
-0.0018
-0.0703
Australia
0.0138
0.0175
-0.0015
-0.0974
South Africa
0.0224
0.0174
0.0004a
0.0197
Norway
0.0083
0.0131
-0.0048
-0.4579c
United States
0.0296
0.0124
0.0022a
0.1126
a
Canada
0.0264
0.0113
0.0021
0.1218
Italy
0.0135
0.0100
0.0017a
0.1427
Netherlands
0.0196
0.0090
0.0031a
0.2302b
Germany
0.0311
0.0041
0.0038a
0.3369b
United Kingdom
0.0066
0.0014
-0.0005
-0.1776
a
Positive Covariance suggests 𝑎 > 0.
b
Significant at 10% level.
c
d
1
e
𝑐|𝑎 = 0 is between and 1 – Possible under transaction theory of money demand.
f
2
1
1
3
2
𝑐|𝑎 = 0 is between and – Possible under the Miller-Orr model of money demand.
10
𝑐|𝑎 = 0
5.7847
4.2583
1.2251
0.8787e
0.3579f
0.4246f
1.4561
-0.2510
-0.0703
0.5607e
0.1847
0.2988
-0.2370
-0.0670
0.2228
-0.1310
0.1291
0.0724
0.1096
-0.0174
0.5760e
-0.0727
-0.0797
-0.1230
-0.1560
-0.1230
0.0822
Table 2.3. Results of Covariance-Bounds Tests Using VAR
𝑣𝑎𝑟(𝑦 ∗ )
Country
𝑐𝑜𝑣(𝑦 ∗ , 𝑝∗ )
𝜌
Bolivia
-0.2021
2.8445E-04
3.9040E-01
-2.1300E-03
Argentina
-0.5319d
2.4000E-03
1.8937E-01
-1.1340E-02
Turkey
-0.3337c
1.5900E-03
1.0600E-02
-1.3700E-03
Mexico
-0.3673d
8.1908E-04
1.0170E-02
-1.0600E-03
Ecuador
-0.1357
1.8100E-03
9.1600E-03
-5.5267E-04
Russia
0.1256
2.2900E-03
6.2400E-03
4.7473E-04a
Iceland
-0.1947
1.1800E-03
5.6800E-03
-5.0418E-04
Philippines
-0.5793d
6.3887E-04
4.1000E-03
-9.3751E-04
a
Paraguay
0.1620
1.2400E-03
2.9600E-03
3.1039E-04
Korea
-0.4375d
8.9824E-04
1.3500E-03
-4.8174E-04
Colombia
-0.1031
3.6299E-04
1.1500E-03
-6.6591E-05
Singapore
0.2419b
1.4200E-03
9.0464E-04
2.7420E-04a
France
-0.1518
1.9123E-04
7.6653E-04
-5.8137E-05
a
Ireland
0.0653
5.8495E-04
6.4734E-04
4.0154E-05
New Zealand
-0.2824c
5.5077E-04
5.5275E-04
-1.5581E-04
Spain
0.2097
8.3586E-04
5.2037E-04
1.3830E-04a
Japan
-0.1440
7.8421E-04
4.2910E-04
-8.3533E-05
Sweden
-0.0384
3.6209E-04
3.8710E-04
-1.4374E-05
Australia
-0.1301
1.9884E-04
3.4423E-04
-3.4047E-05
Norway
-0.4648d
1.7826E-04
2.7340E-04
-1.0262E-04
South Africa
0.0735
3.0601E-04
2.7339E-04
2.1256E-05a
Italy
0.3026b
2.3108E-04
2.3214E-04
7.0095E-05a
Canada
0.1245
4.2912E-04
1.9179E-04
3.5728E-05a
a
United States
0.0838
4.1385E-04
1.7190E-04
2.2345E-05
Netherlands
0.1985
3.3537E-04
1.4387E-04
4.3600E-05a
Germany
0.3374c
5.6586E-04
7.2255E-05
6.8229E-05a
United Kingdom
-0.2426
1.2839E-04
6.0786E-05
-2.1433E-05
a
Positive Covariance suggests 𝑎 > 0.
b
c
d
1
e
𝑐|𝑎 = 0 is between and 1 – Possible under transaction theory of money demand.
f
2
1
1
3
2
𝑐|𝑎 = 0 is between and – Possible under the Miller-Orr model of money demand.
11
𝑐|𝑎 = 0
7.4881
4.7250
0.8616e
1.2941
0.3053
-0.2073
0.4273f
1.4674
-0.2503
0.5363e
0.1834
-0.1931
0.3040
-0.0686
0.2829
-0.1655
0.1065
0.0397
0.1712
0.5757e
-0.0695
-0.3033
-0.0833
-0.0540
-0.1300
-0.1206
0.1669
2.3.4 Conditional Estimates of 𝑎
Cover (1989) noted that the theory used to derive an aggregate supply function like (2.2)
does not inherently imply that 𝑎 > 0. What the model suggests is that if 𝑎 ≠ 0, then the absolute
value of 𝑎 decreases as the variance of unexpected prices increases. If a firm observes a rise in
the nominal price of the good it produces and believes it is a real increase, then it will increase its
output if the substitution effect outweighs the income effect. If the income effect is greater than
the substitution effect, then the firm will reduce output (Barro 1984). What we want to do now is
check if 𝑎 decreases in absolute value as the variance of unexpected prices increases for the
countries with 𝑎 > 0 for this given data set.
Solving equations (2.10)-(2.12) for 𝑎, 𝜎𝑒2 , 𝜎𝑢2 , we obtain the following expressions:
𝑐𝑜𝑣(𝑦 ∗ ,𝑝∗ )+𝑐 𝑣𝑎𝑟(𝑦 ∗ )
𝑡
𝑡
𝑎 = 𝑣𝑎𝑟(𝑝𝑡∗)+𝑐
𝑐𝑜𝑣(𝑦 ∗ ,𝑝∗ )
(2.14)
𝜎𝑒2 = (1 + 𝑎𝑐)[𝑣𝑎𝑟(𝑝𝑡∗ ) + 𝑐 𝑐𝑜𝑣(𝑦𝑡∗ , 𝑝𝑡∗ )]
(2.15)
𝜎𝑢2 = (1 + 𝑎𝑐)[𝑣𝑎𝑟(𝑦𝑡∗ ) − 𝑎 𝑐𝑜𝑣(𝑦𝑡∗ , 𝑝𝑡∗ )]
(2.16)
𝑡
𝑡
𝑡
Equation (2.14) allows us to estimate the sensitivity of output to unexpected inflation with a
given value of the income elasticity of money demand, while equations (2.15), (2.16), and (2.10)
allow us to estimate the percentage of the variance of output due to real and monetary
disturbances.
1
The conditional estimate of 𝑎 when 𝑐 = 2 for the three countries (Turkey, Korea, and
Norway) with 𝑐 between one-half and one in the third covariance-bounds test is extremely close
to zero or negative, according to both the Box-Jenkins method and VAR results, so unexpected
1
changes in price have no effect on output when 𝑐 = . Estimates of 𝑎 are negative and extremely
2
close to zero for Bolivia, Argentina, Mexico, and the Philippines. These four countries have
12
variances of prices within the top eight highest variances using both the Box-Jenkins method and
VAR results, meaning that the variance of prices rises as 𝑎 decreases. (Results are shown in
Table 2.5 for the Box-Jenkins method and Table 2.7 for VAR.) This is consistent with Lucas
1
(1973). Table 2.4 and Table 2.6 offer conditional estimates of 𝑎 given 𝑐 = 2 and 𝑐 = 1 for the
countries with a positive 𝑎 in either case. We may observe that 𝑎 decreases as the variance of
unexpected prices increases, and the percentage of the variance of output explained by the real
disturbance increases as the variance of prices increases. This is, once again, consistent with
Lucas’ proposition (notice the downward trend of 𝑎 in Figures 2.1 – 2.4).
The results in Tables 2.4 – 2.7 suggest that the real theories of business cycles depend on
1
the value of the income elasticity of money demand. If 𝑐 = 2, then nine of these twenty-seven
countries have more than 25% of their variance of output explained by monetary disturbances,
using the Box-Jenkins method estimates, while eight of the twenty-seven countries have more
than 25% of their variance of output explained by monetary disturbances, using VAR estimates.
If 𝑐 = 1, then monetary disturbances account for over 50% of the variance of output for eleven
countries and over 25% for another five countries, using the Box-Jenkins method estimates,
while it accounts for over 50% of the variance of output for twelve countries and over 25% for
another five countries, using VAR estimates. While Fendel and Rülke’s (2012) results show
strong evidence that unexpected changes in prices account for a large portion of the changes in
output, the results presented in Tables 2.4, 2.5, 2.6, and 2.7 suggest that the price level only has a
1
large effect on the variance of output in nine of the twenty-seven countries when 𝑐 = 2 and
seventeen of the countries when 𝑐 = 1. The percentage of the variance of output due to the
monetary disturbance is heavily dependent on the value of 𝑐, and there is not strong evidence of
unexpected inflation affecting unexpected output unless the income elasticity of money demand
13
is nearly unity. Note that results from VAR estimates are once again rather consistent with
results from the Box-Jenkins method estimates, providing further support that the output and
price level processes are univariate.
Table 2.4. Countries with Positive Values of 𝑎 Using Box-Jenkins
Country
Percenta
𝑎|𝑐 = 1/2
Turkey
0.4687
Ecuador
0.4087
0.0311
99.6%
Iceland
0.2939
0.0156
99.9%
Paraguay
0.1753
0.2970
80.6%
Russia
0.1111
0.1691
91.1%
Korea
0.0645
Colombia
0.0593
0.0796
97.6%
France
0.0489
0.0508
99.0%
Singapore
0.0427
1.1358
46.6%
Ireland
0.0402
0.4827
78.0%
New Zealand
0.0332
0.2973
92.8%
Spain
0.0318
0.9586
59.1%
Japan
0.0265
0.6862
81.1%
Sweden
0.0258
0.4183
85.2%
Australia
0.0175
0.3220
89.2%
South Africa
0.0174
0.6584
74.4%
Norway
0.0131
United States
0.0124
1.2627
55.7%
Canada
0.0113
1.2375
55.7%
Italy
0.0100
0.7744
65.2%
Netherlands
0.0090
1.2208
50.3%
Germany
0.0041
3.1979
23.3%
United Kingdom
0.0014
2.4143
54.3%
a
Percent of 𝑣𝑎𝑟(𝑦∗ ) accounted for by the real disturbance.
𝑎|𝑐 = 1
Percenta
0.0204
0.1461
0.1245
0.4714
0.3142
0.4912
0.2107
0.1840
1.6120
0.8831
0.9469
1.5627
1.8298
0.9408
0.7691
1.2805
0.4215
2.1895
2.1240
1.2967
1.8786
4.3812
6.9547
99.8%
91.8%
93.6%
59.9%
74.4%
85.5%
85.8%
89.1%
23.7%
50.0%
62.2%
31.0%
43.7%
55.0%
61.3%
42.9%
87.4%
26.4%
26.6%
36.6%
24.6%
8.6%
19.8%
Table 2.5. Countries with Negative Values of 𝑎 Using Box-Jenkins
Country
Percenta
𝑎|𝑐 = 1/2
Bolivia
16.926
-0.0038
98.0%
Argentina
11.368
-0.0522
79.9%
Mexico
0.5926
-0.0660
95.1%
Turkey
0.4687
-0.0594
97.7%
Philippines
0.2242
-0.1684
82.4%
Korea
0.0645
-0.0517
99.7%
Norway
0.0131
-0.0587
99.5%
∗
a
Percent of 𝑣𝑎𝑟(𝑦 ) accounted for by the real disturbance.
14
𝑎|𝑐 = 1
Percenta
-0.0034
-0.0466
-0.0217
98.4%
84.1%
99.5%
-0.0922
95.4%
Table 2.6. Countries with Positive Values of 𝑎 Using VAR
Country
Percenta
𝑎|𝑐 = 1/2
Mexico
1.06E-02
Ecuador
0.0397
99.2%
9.16E-03
Russia
0.2501
84.3%
6.24E-03
Iceland
0.0158
99.9%
5.68E-03
Paraguay
0.2987
80.5%
2.96E-03
Korea
1.35E-03
Colombia
0.1029
96.9%
1.15E-03
Singapore
0.9448
55.5%
9.05E-04
France
0.0508
99.0%
7.67E-04
Ireland
0.4984
77.3%
6.47E-04
New Zealand
0.2518
95.1%
5.53E-04
Spain
0.9435
57.3%
5.20E-04
Japan
0.7967
77.6%
4.29E-04
Sweden
0.4387
83.4%
3.87E-04
Australia
0.1998
94.0%
3.44E-04
Norway
2.73E-04
South Africa
0.6136
73.3%
2.73E-04
Italy
0.6948
58.6%
2.32E-04
Canada
1.1938
56.4%
1.92E-04
United States
1.2523
57.3%
1.72E-04
Netherlands
1.2753
50.9%
1.44E-04
Germany
3.3013
22.7%
7.23E-05
United Kingdom
0.8540
80.1%
6.08E-05
∗
a
Percent of 𝑣𝑎𝑟(𝑦 ) accounted for by the real disturbance.
𝑎|𝑐 = 1
Percenta
0.0238
0.1461
0.4117
0.1306
0.4741
0.4797
0.2736
1.4372
0.1879
0.9093
0.9950
1.4790
2.0276
0.9329
0.5313
0.4429
1.1107
0.9965
2.0431
2.2456
2.0215
4.5136
2.7178
99.7%
91.1%
64.8%
93.4%
59.8%
85.0%
82.5%
29.6%
89.0%
49.1%
64.2%
30.5%
40.2%
53.7%
71.2%
87.0%
43.7%
34.9%
27.3%
27.1%
24.4%
8.3%
39.1%
𝑎|𝑐 = 1
Percenta
-0.0048
-0.0502
96.9%
80.3%
-0.0264
-0.0944
99.2%
95.1%
Table 2.7. Countries with Negative Values of 𝑎 Using VAR
Country
Percenta
𝑎|𝑐 = 1/2
Bolivia
-0.0051
96.4%
3.90E-01
Argentina
-0.0552
76.0%
1.89E-01
Mexico
-0.0580
97.8%
1.06E-02
Turkey
-0.0675
94.5%
1.02E-02
Philippines
-0.1702
82.0%
4.10E-03
Korea
-0.0294
99.9%
1.35E-03
Norway
-0.0607
99.5%
2.73E-04
a
Percent of 𝑣𝑎𝑟(𝑦 ∗ ) accounted for by the real disturbance.
15
𝟏
Figure 2.1. Trend of 𝒂|𝒄 = 𝟐 with Box-Jenkins Method
2.5
2.0
Germany
United Kingdom
a|c=1/2
1.5
United States
Netherlands
Canada
1.0
Italy
0.5
Singapore
Spain
Japan
South Africa
Ireland
Sweden
Australia
Paraguay
New Zealand
Russia
Colombia
France
Iceland
Ecuador
0.0
0.0
0.1
0.2
0.3
0.4
Var(p*)
16
0.5
0.6
0.7
Figure 2.2. Trend of 𝒂|𝒄 = 𝟏 with Box-Jenkins Method
3.0
United Kingdom
2.5
Germany
a|c=1
2.0
United States
1.5
Netherlands
Canada
Italy
1.0
Australia
Japan
Singapore
Spain
South Africa
New Zealand
Sweden Ireland
Paraguay
Russia
0.5
France
Colombia
Iceland
Ecuador
0.0
0.0
0.1
0.2
0.3
0.4
Var(p*)
17
0.5
0.6
0.7
𝟏
Figure 2.3. Trend of 𝒂|𝒄 = 𝟐 with VAR
2.0
Germany
1.8
1.6
1.4
a|c=1/2
1.2
1.0
0.8
0.6
Netherlands
United States
Canada
Spain Singapore
United Kingdom
Japan
Italy
South Africa
Ireland
Sweden
Paraguay
New Zealand
Australia
0.4
Russia
Colombia
France
0.2
Ecuador
Iceland
0.0
0.00
0.02
0.04
0.06
Var(p*)
18
0.08
0.10
0.12
Figure 2.4. Trend of 𝒂|𝒄 = 𝟏 with VAR
2.5
Germany
2.0
United Kingdom
United States
1.5
a|c=1/2
Netherlands Canada
Japan
Spain
Singapore
South Africa
New Zealand
Italy
Ireland
Sweden
1.0
Australia
Paraguay
Colombia
France
0.5
Russia
Iceland
Ecuador
0.0
0.00
0.02
0.04
0.06
Var(p*)
19
0.08
0.10
0.12
2.4
Conclusions
According to the covariance-bounds tests presented, it is plausible that unexpected
inflation affects output in nineteen of the twenty-seven countries presented. From the
conditional estimates presented, in seven of the countries (Bolivia, Argentina, Mexico, Turkey,
Philippines, Korea, and Norway) 𝑎 is either negative or zero. This means that unexpected
inflation has either a negative or no effect on output in these countries. In only nine of the
remaining twenty countries (Singapore, Spain, South Africa, United States, Canada, Italy,
Netherlands, Germany, and United Kingdom) does the price level account for a large portion of
the variance of output.
These results are not consistent with the results of Fendel and Rülke (2012), who found
that unexpected inflation has a large effect on output. The reason that these results differ is
because Fendel and Rülke only used real disturbance in their estimation. Once the portfoliobalance equation is added, it can be seen that it is unexpected money that has the main effect on
output. While there is some evidence that unexpected inflation affects output, the results here
suggest that unexpected money affects output through the price level and other means.
20
References
Abbot, B. and C. Martinez. “An Updated Assessment of the Lucas Supply Curve and the
Inflation Output Trade-off.” Economic Letters 101 (1988): 199-201.
Barro, Robert J. “Integral Constraints and Aggregation in an Inventory Model of Money
Demand.” The Journal of Finance 31 (March 1976): 77-88.
Buiter, Willem H. “Real Effects of Anticipated and Unanticipated Money: Some
Problem of Estimation and Hypothesis Testing.” Journal of Monetary Economics 11
(1983): 207-224.
Cover, James Peery. “A Keynesian Macroeconomic Model With New-Classical
Econometric Properties.” Southern Economic Journal 54 (April 1988): 831-839.
Cover, James Peery. “International Evidence on Output-Inflation Trade-Offs: Results
From a Covariance-Bounds Test.” Journal of Macroeconomics 11 (Summer
1989): 397-408.
Fendel, Ralf and Jan-Christoph Rülke. “Some International Evidence on the Lucas
Supply Function.” Economic Letters 114 (2012): 157-160
Judge, George E., W.E. Griffiths, R. Carter Hill, Helmut Lutkepohl, and Tsoung-Choa
Lee. The Theory and Practice of Econometrics. 2nd ed. New York: John Wiley
and Sons, 1985.
Lucas, Robert E., Jr. “Some International Evidence on Output-Inflation Tradeoffs.”
American Economic Review 63 (June 1973): 326-334.
Madsen, J.B., “Tests of the Lucas Supply Curve with Price Exceptional Data.” Applied
Economic Letters 4 (1997): 195-197.
Miller, Merton H., and Daniel Orr. “A Model of the Demand for Money by Firms.”
Quarterly Journal of Economics 70 (August 1966): 413-435.
21
CHAPTER 3
MONEY DEMAND, RISK, AND A BETTER MEASURE OF
THE MONETARY AGGREGATE
3.1
Introduction and Theory
Estimating the money demand function in the past thirty years has not been an easy task.
Before the 1970s, the partial adjustment model was generally accepted, but several works
emerged in the 70s which reshaped the view of modern monetarism. Prior to 1974, evidence
suggested that the only variables needed to explain the movements in money demand were
income, interest rates, and lags of these variables. Goldfeld (1976) demonstrated that data
extrapolated prior to 1974 tends to significantly over-predict actual money demand post-1974,
and the forecasting errors seemed to magnify as time progressed. Goldfeld stated that the results
of his paper were difficult to characterize. The paper did not formulate an improved
specification of the demand function for M1; however, it did pinpoint the business sector as a
prime source of the errors in the current specification. Following Goldfeld’s paper, the demand
equation for M1 and M2 was more rigorously analyzed by economists.
In the last several decades, the idea that a stable money demand function exists has
received a tremendous amount of attention; however, there no general consensus on the stability
or instability of money demand functions has emerged. Through the early 1990s, much of the
literature related to money demand was unable to specify a stable demand for money function,
and, instead, only warned researchers of potential causes of instability. Arize (1994) introduced
22
the idea that the majority of money demand function specifications have been unstable due to the
neglect of the “value-of-time” hypothesis. He suggested that a variable representing the value of
time, such as wage rate, should be included as an additional argument in the money demand
function. In testing the stability of the money demand function, Arize used three tests (the Chow
test, the Farley-Hinich test, and the Ashley Stabilogram test). He tested the traditional
specification of the money demand function versus the specification with the introduction of real
wage rates. Results from all three tests showed the function of U.S. real M2 demand was
structurally stable with the time-value variable (real wages) included. With the real wage
variable dropped, all three tests revealed the money demand function as extremely unstable.
Arize concluded that the empirical results from 1963:1 – 1991:4 strongly support the value-oftime hypothesis and that U.S. policy-makers should take into account the movements of real
wages when setting their targets for the M2 aggregate.
Reynard (2004) made the claim that although time-series studies on money demand often
show that money holdings are not stable functions of interest rates, time-series estimations of
money demand functions are fundamentally flawed and incorrectly demonstrate instability.
Reynard stated that, as a consequence of the results shown by time-series analysis, interest in this
line of research had declined and the progression of financial market participation had prompted
an instability in money demand: “Persistent change in interest rate, wealth or cost of holding
non-monetary assets, affect persistently the level of aggregate money holdings and the sensitivity
of money demand to interest rate fluctuations.” Reynard’s main contribution to the field was
showing that cross-sectional analysis would be needed to illustrate the true structural parameters
of money demand relationships.
23
As we approach the topic of money demand today, we see that current results have not
been achieved easily. Research in the field remains wide open, as new results emerge from new
estimation techniques and new theory. For a new model to be considered reasonable, it should
not only predict money demand well, but it needs to explain why previous theories have failed.
In formulating a more accurate model, which explains the flaws of previous models, while
attempting to stabilize money demand, I have replaced the traditional measure of money stock
(M2) with Money Zero Maturity (MZM) and also included a measure of risk in the estimation.
Teles and Zhou (2005) argued that it was not true that money demand and its
determinants (income, interest rates, and a lag term) had unstable relationships, but rather that
the measure of money was not a stable measure. They stated that technology advancement and
changes in the way money was regulated have played a role in making other monetary
aggregates as liquid as M1. In doing so, the definition of money stock should be adjusted in
order to find a stable relationship between money and its determinants. These changes reduced
the funds that were classified as M1 by almost 50%. MZM was reasoned to be a better measure
of money stock because it included only balances that could be used for transactions at zero cost.
Teles and Zhou concluded that using MZM, rather than M2, as money stock helped the
estimation of money demand become quantifiably more stable.
Using a measure of risk in estimating money demand was first suggested by Friedman
(1956) in his restatement of the Quantity Theory of Money. He suggested that “variables
affecting the usefulness of money,” such as interest rates and uncertainty about the future, should
be considered when determining the demand for money. Following Friedman, Tobin (1958)
proposed that risk averse consumers hold money due to the uncertainty of future interest rates.
24
Cover (2009) introduced the use of market risk to help explain certain macroeconomic
phenomena. Additionally, he tested whether Moody’s BAA rate minus Moody’s AAA rate (a
measure of market risk) would help stabilize the demand for money. Cover argued that, as the
economic environment became more risky, individuals tended to hold assets whose nominal
value is less likely to change. Since the components of M2 are believed by consumers to be less
risky than other assets, the demand for money should increase whenever the market becomes
more risky. He also argued that if this measure of risk was an important determinant of money
demand, then a specification that includes risk should be more stable than a specification that
does not include risk. Cover found that this spread helped stabilize the predictors of money
demand significantly.
The measures of risk I will use include the difference between Moody’s BAA rate and
AAA rate (𝑠𝑝𝑟𝑒𝑎𝑑𝐴) and the difference between the long-term treasury yield and the short-term
treasury yield (𝑠𝑝𝑟𝑒𝑎𝑑𝐵). 𝑠𝑝𝑟𝑒𝑎𝑑𝐴 will show how market risk affects the demand for money,
while 𝑠𝑝𝑟𝑒𝑎𝑑𝐵 will show how inflation risk affects money demand. With these two measures
of risk included, we could see two different results. The demand for money function could
become more stable, or it could remain unstable. The second result could suggest that the model
is still mis-specified; however, the first result could help a great deal in predicting money
demand in the future.
3.2
Methodology
The base model I have decided to use in the estimation of money demand is the same as
that used by Goldfeld. The estimation includes money demand, gross domestic product, the
25
federal funds rates (a measure of the opportunity cost of holding money), and a lag of the
dependent variable. It will take the following form:
𝑚
𝑦
𝑚
𝑙𝑛 𝑝 𝑡 = 𝜆 (𝛼0 + 𝛼1 𝑙𝑛 𝑝𝑡 + 𝛼2 𝑓𝑓𝑟𝑡 ) + (1 − 𝜆)𝑙𝑛 𝑝 𝑡−1 + 𝜀𝑡
𝑡
𝑡
𝑡−1
(3.1)
Here, 𝑚 includes different measures of money stock, 𝑦 is the gross domestic product, and 𝑓𝑓𝑟 is
the federal funds rate. Cover (2009) stated that the parameter 𝜆 represents the speed of
adjustment towards the long-run equilibrium holdings of real money balances. This means that
𝜆𝛼1 is the short-run income elasticity of money demand and 𝛼1 is the long-run elasticity of
money demand. Our prediction is that 𝛼1 will be positive, since more income should lead to a
higher demand for money; 𝛼2 will be negative because individuals will hold less money as the
opportunity cost of holding money rises; and 1 − 𝜆 will be positive, as it is the coefficient of the
lag of money demand.
I will begin by estimating the traditional money demand equation stated in equation (3.1),
while using M2 as the measure of money stock. Then, M2 will be replaced by MZM to see the
effect on the stability of money demand when the definition of money stock is changed. Finally,
the different measures of risk will be added to each specification to see if risk can aid in the
stabilization of money demand. An in-depth look at these models should also include crosssectional analysis, as Reynard (2004) concluded that cross-sectional analysis would be needed to
illustrate the true structural parameters of money demand relationships. I hope that this research
will assist in discovering if adding risk will improve the specification of money demand.
3.3
Results and Analysis
I began the estimation of money demand by running 30-year cross-sectional rolling
regressions. Figure 3.1 and Figure 3.2 show the results for two different estimations. Figure 3.1
26
represents the coefficients of the estimation using M2 as money stock, and Figure 3.2 represents
the coefficients using MZM as money stock. Without any measures of risk in the estimation,
changing the measure of money stock from M2 to MZM does not improve 𝛼1 , 𝛼2 , or 1 − 𝜆 as
predictors of money demand. The Bai-Perron structural break test was also applied to these
coefficients, and Table 3.1 shows that changing the money stock, alone, did not reduce the
number of structural breaks.
27
Figure 3.1. Coefficients using M2 with No Measures of Risk
1.6
0
-0.002
-0.004
-0.006
-0.008
-0.01
-0.012
-0.014
-0.016
-0.018
1.4
1.2
1
0.8
0.6
0.4
0.2
0
1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009
GDP Coefficients
Standard Error Bands
FFR Coefficients
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009
Lag Term Coefficients
28
Figure 3.2. Coefficients using MZM with No Measures of Risk
2.5
0
-0.01
2
-0.02
1.5
-0.03
1
-0.04
-0.05
0.5
-0.06
0
1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009
GDP Coefficients
FFR Coefficients
1
0.8
0.6
0.4
0.2
0
1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009
-0.07
1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009
29
Figure 3.3 and Figure 3.4 present the results for the following specification:
𝑚
𝑦
𝑚
𝑙𝑛 𝑝 𝑡 = 𝜆 (𝛼0 + 𝛼1 𝑙𝑛 𝑝𝑡 + 𝛼2 𝑓𝑓𝑟𝑡 + 𝛼3 𝑠𝑝𝑟𝑒𝑎𝑑𝐴𝑡 ) + (1 − 𝜆)𝑙𝑛 𝑝 𝑡−1 + 𝜀𝑡
𝑡
𝑡
𝑡−1
(3.2)
𝑠𝑝𝑟𝑒𝑎𝑑𝐴 is a measure of market risk. We can expect the 𝑠𝑝𝑟𝑒𝑎𝑑𝐴 coefficient to be positive
since, as market risk increases, individuals will hold more money because it is a low-risk asset.
First, we use M2 as the measure of money stock to determine if adding market risk helps
stabilize money demand, then we do the same while using MZM as the measure of money stock.
The coefficients of GDP seem to be relatively unstable, whether we are using M2 or MZM.
Adding 𝑠𝑝𝑟𝑒𝑎𝑑𝐴 to the equation does not seem to help. These coefficients were also
significantly positive throughout the series, as previous authors have suggested. The coefficients
of 𝑓𝑓𝑟𝑡 seem to be unstable when 𝑠𝑝𝑟𝑒𝑎𝑑𝐴 is added while M2 is used to measure money stock,
but when MZM is used to measure money stock, the coefficients of 𝑓𝑓𝑟𝑡 become quite stable, as
Figure 3.4b illustrates. These coefficients were significantly negative throughout the series, and
this is consistent with our prediction that, as the opportunity cost of holding money rises, the
demand to hold money would fall. The coefficients of the lag term display the same properties
as the coefficients of 𝑓𝑓𝑟𝑡 in terms of stability. Once M2 is replaced with MZM and 𝑠𝑝𝑟𝑒𝑎𝑑𝐴 is
added to the specification, the coefficients are quite smooth throughout the series. The
coefficients of 𝑠𝑝𝑟𝑒𝑎𝑑𝐴 with both M2 and MZM are not what we expected. These coefficients
are significantly negative for about 60% of the series when M2 is the measure of money stock
and significantly negative for almost the entire series when MZM is the measure of money stock.
The implications of this result may lead to new views on the understanding of money demand.
Overall, we can see from these results that 𝑠𝑝𝑟𝑒𝑎𝑑𝐴 does contain information in explaining the
demand for money, since the predictors of money demand have become rather stable compared
to these coefficients without 𝑠𝑝𝑟𝑒𝑎𝑑𝐴. After applying the Bai-Perron structural break test on the
30
coefficients, we can see that the LWZ criterion suggests that there are no structural breaks in any
of the coefficients; however, there are still several problems according to the BIC criterion
(Table 3.1).
31
Figure 3.3. Coefficients Using M2 with Market Risk
1.6
0
-0.002
-0.004
-0.006
-0.008
-0.01
-0.012
-0.014
-0.016
1.4
1.2
1
0.8
0.6
0.4
0.2
0
1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009
GDP Coefficients
FFR Coefficients
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009
0.04
0.03
0.02
0.01
0
-0.01
-0.02
-0.03
-0.04
-0.05
1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009
Market Risk Coefficients
32
Figure 3.4. Coefficients Using MZM with Market Risk
2.5
0
-0.005
2
-0.01
-0.015
1.5
-0.02
1
-0.025
-0.03
0.5
-0.035
0
1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009
GDP Coefficients
FFR Coefficients
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009
0.04
0.02
0
-0.02
-0.04
-0.06
-0.08
-0.1
-0.12
-0.14
1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009
33
Figure 3.5 and Figure 3.6 show the results from the following specification:
𝑚
𝑦
𝑚
𝑙𝑛 𝑝 𝑡 = 𝜆 (𝛼0 + 𝛼1 𝑙𝑛 𝑝𝑡 + 𝛼2 𝑓𝑓𝑟𝑡 + 𝛼4 𝑠𝑝𝑟𝑒𝑎𝑑𝐵𝑡 ) + (1 − 𝜆)𝑙𝑛 𝑝 𝑡−1 + 𝜀𝑡
𝑡
𝑡
𝑡−1
(3.3)
𝑠𝑝𝑟𝑒𝑎𝑑𝐵 is the difference between the ten-year treasury yield and the three-month treasury
yield. This spread measures inflation risk and should be negatively correlated with money
demand. Whenever inflation risk is expected to be high, individuals will hold less money in
order to prevent loss of real money through inflation. The results of the above estimation
suggest that the coefficient of 𝑠𝑝𝑟𝑒𝑎𝑑𝐵 is significantly negative. This result is consistent with
our prediction that higher inflation risk leads to lower holdings of real money balances. Figure
3.5, Figure 3.6, and Table 3.1 shows us that 𝑠𝑝𝑟𝑒𝑎𝑑𝐵 has very little effect on the stability of
money demand. The coefficients of GDP, the federal funds rate, and the lag term were almost
identical to the corresponding coefficients when 𝑠𝑝𝑟𝑒𝑎𝑑𝐵 was not used. The Bai-Perron
structural break test also shows that there are still several structural breaks in all of the
coefficients. This leads me to conclude that 𝑠𝑝𝑟𝑒𝑎𝑑𝐵 does contain useful information in
determining the demand for money, but additional variables may be needed to stabilize money
demand.
Since both 𝑠𝑝𝑟𝑒𝑎𝑑𝐴 and 𝑠𝑝𝑟𝑒𝑎𝑑𝐵 were significant when added to the partial adjustment
model by themselves, the obvious next step was to add both of them, together, to the
specification. This resulted in the following model:
𝑚
𝑦
𝑙𝑛 𝑝 𝑡 = 𝜆 (𝛼0 + 𝛼1 𝑙𝑛 𝑝𝑡 + 𝛼2 𝑓𝑓𝑟𝑡 + 𝛼3 𝑠𝑝𝑟𝑒𝑎𝑑𝐴𝑡 + 𝛼4 𝑠𝑝𝑟𝑒𝑎𝑑𝐵𝑡 )
𝑡
𝑡
𝑚
+(1 − 𝜆)𝑙𝑛 𝑝 𝑡−1 + 𝜀𝑡
(4)
𝑡−1
When both measures of risk are added to the money demand specification, our predictors
become rather stable (Figure 3.4 and Table 3.1).
34
Figure 3.5. Coefficients Using M2 with Inflation Risk
1.6
0
1.4
-0.005
1.2
1
-0.01
0.8
0.6
-0.015
0.4
0.2
-0.02
0
1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009
GDP Coefficients
FFR Coefficients
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009
0.015
0.01
0.005
0
-0.005
-0.01
-0.015
Inflation Risk Coefficients
35
Figure 3.6. Coefficients Using MZM with Inflation Risk
2.5
0
-0.01
2
-0.02
1.5
-0.03
1
-0.04
-0.05
0.5
-0.06
0
1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009
GDP Coefficients
FFR Coefficients
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009
-0.07
1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009
0.01
0
-0.01
-0.02
-0.03
-0.04
-0.05
-0.06
1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009
36
Figure 3.7. Coefficients Using M2 with Market Risk and Inflation Risk
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0
-0.005
-0.01
-0.015
2005
2007
2009
2007
2009
2003
2001
2005
2003
2001
1999
1997
1995
0.01
0.005
0
-0.005
-0.01
2009
2007
2005
2003
2001
1999
1997
1995
-0.015
1993
1999
1995
0.015
1991
1997
-0.06
1989
0
2009
-0.04
2007
0.2
2005
-0.02
2003
0.4
2001
0
1999
0.6
1997
0.02
1993
0.8
1991
0.04
1989
1993
1995
1993
FFR Coefficients
1991
GDP Coefficients
1
1989
1991
1989
2009
2007
2005
2003
2001
1999
1997
1995
1993
1991
1989
-0.02
37
2009
2003
2001
1999
1997
1995
2009
2007
2005
2003
2001
1999
1997
1995
1993
1991
1993
0.005
0
-0.005
-0.01
-0.015
-0.02
-0.025
-0.03
-0.035
1989
1991
1989
2009
2007
2005
2003
2001
1999
1997
1995
1993
1991
0.04
0.02
0
-0.02
-0.04
-0.06
-0.08
-0.1
-0.12
1989
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
2009
2007
2007
FFR Coefficients
2005
GDP Coefficients
2005
2003
2001
1999
1997
1995
1995
1993
-0.05
1989
0
2009
-0.04
2007
0.5
2005
-0.03
2003
1
2001
-0.02
1999
1.5
1997
-0.01
1993
2
1991
0
1989
2.5
1991
Figure 3.8. Coefficients Using MZM with Market Risk and Inflation Risk
38
Table 3.1. Results from Bai-Perron Structural Break Test
Monetary Aggregate
And Measure of Risk
M2 – No Risks
BIC
LWZ
M2 – Spread A
BIC
LWZ
M2 – Spread B
BIC
LWZ
M2 – Spread A and B
BIC
LWZ
MZM – No Risks
BIC
LWZ
MZM – Spread A
BIC
LWZ
MZM – Spread B
BIC
LWZ
MZM – Spread A and B
BIC
LWZ
𝛼1
GDP
Number of Structural Breaks
𝛼2
𝛼3
𝛼4
1−𝜆
FFR
Market Risk Inflation Risk Lag
4
4
0
0
N/A
N/A
N/A
N/A
4
0
3
3
0
0
1
0
N/A
N/A
3
3
4
2
0
0
N/A
N/A
1
1
4
0
4
3
2
0
1
0
0
0
4
3
4
4
4
1
N/A
N/A
N/A
N/A
4
3
0
0
3
0
0
0
N/A
N/A
4
0
4
3
2
1
N/A
N/A
4
0
3
0
0
0
0
0
0
0
0
0
2
0
39
Table 3.2. Structural Break Dates
Monetary
Aggregate and
Measure of Risk
M2 – No Risk
BIC
M2 – No Risk
LWZ
M2 – Spread A
BIC
M2 – Spread A
LWZ
M2 – Spread B
BIC
M2 – Spread B
LWZ
M2 – Spread A
and Spread B
BIC
M2 – Spread A
and Spread B
LWZ
MZM – No Risk
BIC
MZM – No Risk
LWZ
MZM – Spread A
BIC
MZM – Spread A
LWZ
MZM – Spread B
BIC
MZM – Spread B
LWZ
MZM – Spread A
and Spread B
BIC
MZM – Spread A
and Spread B
LWZ
𝛼1
GDP
𝛼2
FFR
𝛼3
Market Risk
𝛼4
Inflation Risk
1−𝜆
Lag
1991:4
2000:1
2003:1
2006:2
1991:4
2000:1
2003:1
2006:2
1991:4
2000:3
2006:2
1991:4
2000:3
2006:2
1991:4
2000:2
2003:2
2006:2
1991:4
2000:3
1991:4
1997:2
2000:3
2006:2
1991:4
2000:3
2006:2
1991:4
1997:3
2000:3
2006:2
1991:4
1997:3
2000:3
2006:2
No Breaks
No Breaks
N/A
N/A
No Breaks
N/A
N/A
1991:4
2000:1
2003:1
2006:2
No Breaks
No Breaks
1991:4
N/A
No Breaks
No Breaks
N/A
No Breaks
N/A
1991:4
No Breaks
N/A
1991:4
1992:1
2004:1
2004:1
No Breaks
No Breaks
No Breaks
No Breaks
1991:4
1997:3
2000:3
2003:3
1991:4
N/A
N/A
N/A
N/A
1991:4
1994:4
2000:3
No Breaks
N/A
No Breaks
No Breaks
No Breaks
N/A
1991:4
1997:3
2000:3
2006:2
1991:4
1997:3
2000:3
No Breaks
1991:4
2003:2
N/A
1991:4
N/A
1991:4
1994:4
2000:3
2004:1
No Breaks
No Breaks
No Breaks
No Breaks
1991:4
1997:3
No Breaks
No Breaks
No Breaks
No Breaks
No Breaks
40
1991:4
1999:4
2006:2
1991:4
1999:4
2006:2
1991:4
2000:1
2003:1
2006:2
No Breaks
1991:4
1994:4
2003:1
2006:2
1991:4
2003:1
2006:2
1991:4
1997:3
2000:3
2005:3
1991:4
1997:3
2000:3
1991:4
1996:1
1999:3
2002:4
No Breaks
1991:4
1996:3
2000:1
No Breaks
The Bai-Perron structural break test was applied to each of the coefficient series for M2
and MZM as money stock and all combinations of risks included in the specification. The
Bayesian information criterion (BIC) and Liu, Wu, and Zidek (1997) criterion (LWZ) are two
commonly used methods of the Bai-Perron test for determining the number of structural breaks.
Yao (1988) showed that the BIC can be used to estimate the number of structural breaks
consistently for a normal sequence of random variables with shifts in the mean. The LWZ is a
modified BIC, and both methods perform well when there is no serial correlation present. When
a lag-dependent term is present, the BIC does not perform well when the coefficient of the lagdependent term is large; however, the LWZ performs better under this condition. The number of
breaks estimated by the BIC is larger than the number of breaks estimated by the LWZ when the
coefficient of the lag-dependent term is large.
The results from Table 3.1 show that, initially, the coefficient series are quite unstable, as
the BIC criterion suggests that there are 4 structural breaks in both the 𝑔𝑑𝑝 and 𝑙𝑎𝑔 series.
Although adding 𝑠𝑝𝑟𝑒𝑎𝑑𝐴 and 𝑠𝑝𝑟𝑒𝑎𝑑𝐵 to the specification did reduce the number of structural
breaks slightly, the behavior of most of the series is still quite unstable. Once M2 is replaced
with MZM, adding measures of risk seems to stabilize the predictors rather successfully. When
𝑠𝑝𝑟𝑒𝑎𝑑𝐴 is added with MZM as money stock, the LWZ criterion suggests that there are no
structural breaks in 𝑔𝑑𝑝, 𝑓𝑓𝑟, 𝑙𝑎𝑔, or 𝑠𝑝𝑟𝑒𝑎𝑑𝐴; however, the BIC criterion suggests that the
𝑓𝑓𝑟 series has 3 breaks, while the 𝑙𝑎𝑔 series has 4 breaks. Further testing, by adding 𝑠𝑝𝑟𝑒𝑎𝑑𝐴
and 𝑠𝑝𝑟𝑒𝑎𝑑𝐵 with MZM as money stock, yielded significant improvements. The LWZ criterion
suggests that there are no structural breaks in any of the coefficient series, and the BIC criterion
suggests the same, with the exception of the 𝑙𝑎𝑔 series having 2 structural breaks. These results
demonstrate that, with market risk and inflation risk introduced into the model, the long-run
41
predictors of money demand are stable. Since 𝛼1 , 𝛼2 , 𝛼3 , and 𝛼4 are the long-run elasticities of
money demand, the Bai-Perron test suggests that we have found a stable money demand function
in the long run. Only the BIC criterion suggests that there is still short-run instability in money
demand. This is a substantial improvement from any previous specifications tested. These
results suggest that replacing M2 with MZM or adding measures of risk, on their own, do not
stabilize the predictors of money demand; however, once both provisions are implemented, the
demand for money becomes reasonably stable.
Table 3.2 shows the dates of the structural breaks from both the BIC and LWZ criterion.
The two most common dates for breaks are the fourth quarter of 1991 and the second quarter of
2006. There is a significant jump for all of the coefficients in 1991 when M2 is used as the
measure of money stock and 𝑠𝑝𝑟𝑒𝑎𝑑𝐴 is present, as demonstrated in Figure 3.3 and Figure 3.7,
but the break in 2006 is not significantly noticeable from the graphs of coefficients. When M2 is
replaced with MZM, none of the break dates are noticeably visible in the graphs. Notice that the
break dates are usually the same when several coefficients have the same number of breaks using
the BIC. This is most likely due to the BIC being inaccurate when the coefficient of the lagdependent term is large. Since the BIC tends to overestimate the number of breaks when the
coefficient of the lag-dependent term is large, it is reasonable to rely more on the results from the
LWZ.
Since the LWZ suggests that there are no changes in the coefficients of any of the
predictors of money demand, I have presented the estimates of the coefficients for the entire
sample period in Table 3.3. All coefficients are significant at the 1% level, except for the lagdependent term, which is significant at the 10% level. A graph of the values of MZM versus the
fitted values of MZM is presented in Figure 3.9. The estimated coefficients seem to estimate the
42
demand for money quite well for the entire sample period. Note that there is still the possibility
of serial correlation for estimates of the entire sample period, which is an area of possible future
research.
Table 3.3. Estimated Values of Coefficients
Explanatory
Variables
𝛼1 – GDP
𝛼2 – FFR
𝛼3 – Market Risk
𝛼4 – Inflation Risk
1 − 𝜆 – Lag
a
b
Estimated Value
1.127
-0.028
-0.020
-0.017
0.537
T-Statistic
5.29a
-7.84a
-1.80a
-2.83a
10.83b
Significant at the 1% level.
Sifnificant at the 10% level.
Figure 3.9. Actual MZM Versus Fitted MZM
4
3.8
3.6
3.4
3.2
3
2.8
2.6
2.4
2.2
1959
1961
1963
1965
1967
1969
1971
1973
1975
1977
1979
1981
1983
1985
1987
1989
1991
1993
1995
1997
1999
2001
2003
2005
2007
2009
2011
2
Actual MZM
Fitted MZM
43
3.4
Conclusions
The results of this paper suggest that replacing M2 with MZM as a measure of money
stock, alone, does not help stabilize money demand, while adding measures of risk, such as
𝑠𝑝𝑟𝑒𝑎𝑑𝐴 and 𝑠𝑝𝑟𝑒𝑎𝑑𝐵, to the money demand equation, with M2 as the measure of money
stock, also does not stabilize money demand tremendously. Note that 𝑠𝑝𝑟𝑒𝑎𝑑𝐴 added to the
equation with M2 as money stock did help stabilize money demand to some degree. This is
consistent with Cover’s (2009) findings. The most significant result is that the combination of
replacing M2 with MZM and adding 𝑠𝑝𝑟𝑒𝑎𝑑𝐴 and 𝑠𝑝𝑟𝑒𝑎𝑑𝐵 stabilized the coefficients of 𝑓𝑓𝑟,
𝑔𝑑𝑝, 𝑠𝑝𝑟𝑒𝑎𝑑𝐴, and 𝑠𝑝𝑟𝑒𝑎𝑑𝐵 as predictors of money demand, while the coefficients of the lag
term remained unstable.
The finding that the coefficients of market risk are negative and significant is puzzling
and may suggest that our current interpretation of money demand is flawed. Being concerned
with endogeneity issues in the specification, I implemented a GARCH model in order to fix the
sign of this coefficient; however, the results still suggested that the coefficients of market risk
should be negative. An alternative approach to the analysis of the sign of this coefficient is to
examine why it can be negative. When risk is low in the economy, businesses are doing well and
banks are more willing to lend money. Because banks are lending more money, the equilibrium
of money demand and money supply is higher, leading to a negative relationship between market
risk and money demand.
The final result of this paper is that we have found stable predictors of money demand in
the long term (and short term suggested by the LWZ). All long-run coefficients of the variables
used in equation (3.4) have no structural breaks in their series. Future analysis may include
defining an even better measure of money stock or assessing additional measures of risk that
contain useful information about money demand that 𝑠𝑝𝑟𝑒𝑎𝑑𝐴 and 𝑠𝑝𝑟𝑒𝑎𝑑𝐵 did not contain.
44
References
Amihud, Yakov. “An Empirical Note on the Bond-Yield Uncertainty and the Demand
for Money.” Economic Letters 5 (1980): 63-69.
Arize, Augustine C. “The Value of Time and Recent U.S. Money Demand Instability.”
Southern Economic Journal (1994): 564-578.
Bai, Jushan, and Pierre Perron. “Estimating and testing linear models with multiple
structural changes.” Econometrica 66 (1998): 47-78.
Cover, James Peery. “Risk and Macroeconomic Activity.” Journal of Economic
Literature (2009).
Friedman, Milton. “The Quantity Theory of Money - A Restatement.” Studies in the
Quantity Theory of Money (1956).
Friedman, Milton. “A Theoretical Framework for Monetary Analysis.” Journal of
Political Economy (1970): 193-238.
Goldfeld, Stephen M. “The Demand for Money Revisited.” Brookings Papers on
Economic Activity (1973): 557-638.
Goldfeld, Stephen M. “The Case of the Missing Money.” Brookings Papers on
Economics Activity (1976): 683-739.
Liu, Jian, Shiying Wu, and James V. Zidek. “On segmented multivariate regressions.”
Statistica Sinica 7 (1997): 497-525.
Reynard, Samuel. “Financial Market Participation and the Apparent Instability of Money
Demand.” Journal of Monetary Economics 51 (2004): 1297-1317.
Teles, Pedro, and Ruilin Zhou. “A Stable Money Demand: Looking for the Right
Monetary Aggregate.” Economic Prespectives Q1 (2005): 50-63.
Tobin, James. “Liquidity Preference as Behavior Towards Risk.” Review of Economic
Studies 25 (1958): 65-86.
Yao, Yi-Ching. “Estimating the number of change-points via Schwarz’ Criterion.”
Statistics and Probability Letters 6 (1988): 181-189.
45
CHAPTER 4
THE THEORY OF MONEY DESCRIBED
BY ONLINE GAMING
4.1
Introduction
Video games have become an increasingly popular pastime for Americans, especially for
those who were school-aged in the 80s and 90s. Video games offer more scope for the
imagination than other hobbies, which is one reason they have captured the attention of millions
around the world. According to TechRadar News, video games became the most popular
pastime in 2008, outselling both music and film. With so many resources devoted to gaming, it
would be a shame to ignore it as a field for economic research. The world of video games is
filled with repeated interactions between players--the perfect setting for economists to observe
behavior and conduct experiments. Scholarly research involving virtual economies has increased
rapidly in the past decade. For example, Castronova et al (2009) tested whether aggregate
economic behavior mapped from the real world to the virtual world and found that “virtual world
economic behavior followed real world patterns.” The Southern Economic Journal published a
symposium on the game Second Life in 2011, covering a broad range of topics including trust,
economic decision making, and stock markets.
Over the past decade, Massively Multiplayer Online Role-Playing Games (MMORPG)
have exploded onto the gaming scene, with popular incarnations such as World of Warcraft
(WoW), Everquest II, and Final Fantasy XI. In Role-Playing Games (RPG) prior to 2003,
46
currencies were not well established and trading interfaces were primitive. With the emerging
popularity of MMORPGs, companies have begun to implement standard currencies in new
releases in order to provide a user-friendly interface. The focus of this paper is the game Diablo
II, an RPG1 released by Blizzard Entertainment on June 30, 2000. The Diablo II economy will
be used to illustrate that the development and evolution of currency is as Carl Menger suggests in
his works. The reason Diablo II was chosen to model Menger’s theories is because its in-game
currency was not useful to players, which allowed another currency to develop endogenously
within the game.
In this paper, I will introduce several theories on how currency developed, and then I will
discuss how a currency emerged in Diablo II. I will also discuss the parallels and differences
between Diablo II and Menger’s theories and illustrate these parallels through descriptive and
numerical analysis. The official trading forums of Diablo II were partially archived, and this
data will be used to demonstrate the development of currencies in Diablo II. The concluding
section will examine possible future research and what we have learned, thus far, from the virtual
world.
4.2
Theory
Menger (1892) suggested that before the establishment of currency, people brought what
they could produce to the market and traded for what they needed. The reason that people
engaged in trade was to obtain items of higher value or usefulness to themselves than the items
1
Diablo II is not strictly considered a MMORPG by the gaming community because it did not put everyone within a
server in the same game. In traditional MMORPGs, every player on the same server was placed in the same world,
where they could freely interact with thousands of other players. Diablo II only allowed eight players to be in the
same world at once, but players were allowed to create as many worlds as desired, in addition to being able to
move freely between these worlds. This allowed Diablo II to be classified as an Action RPG.
47
they currently held. Menger concluded that trading under these conditions would have been
extremely difficult because each trader needed to satisfy two specific conditions:
1. Trader A must find Trader B, who has exactly what Trader A needs.
2. Trader B also needs what Trader A has, but values these goods in precisely the
opposite way.
This is our classical definition of the “Double Coincidence of Wants,” even though Menger did
not give it this name. Given these conditions, Menger suggested that when Trader A needed
something specific, it is not necessary that Trader B even exist. If Trader B did exist, it was even
more unlikely for the two traders to find each other. Due to these circumstances, Menger
insinuated that it was highly unlikely that trade was extremely productive before the
development of currency, and, naturally, some form of currency had to develop as a middle
ground for traders.
Menger described cattle as the earliest form of currency amongst nomadic societies.
Cattle was effortlessly transported, easy to store, had a low maintenance cost, and was something
that most people could use. He stated that the reason cattle was used as currency was because it
was extremely useful and sought after. Cattle satisfies our modern day definition of money in
that it was used as a medium of exchange, a unit of account, was highly liquid, and could even be
used as a store of value, since cattle lived for a long period of time.
Eventually, the currency transitioned into precious metals made into coins because these
precious metals became the most useful commodity in society. Copper, silver, and gold were
commonly used for making weapons, armors, silverware, and tools, so small pieces of these
types of metal were sought after as a medium of exchange. Menger noted that commodity
money changed as different types of goods were deemed the most useful by society.
48
Another monetary theorist, William Stanley Jevons (1876) first used the phrase “Double
Coincidence of Wants” as the reason money was needed for transactions. Jevons insisted that it
would be quite difficult for a person to find another trader who has exactly what he wants but
also wants exactly what he has. Money must naturally emerge in this economy, in order to give
both traders a common medium of exchange. They could both trade their own goods for money
and then buy the goods they needed. This description is almost identical to what Menger
described in On the Origins of Money. Jevons’ theories were developed independently from
Menger at around the same time. It is clear that most sources agree on these theories as the
origin of money.
More recently, Surowiecki (2012) suggested that coins naturally became the medium of
exchange over cattle because they were easier to carry around and did not age or die like cattle.
The first written record of money appeared around 3000 B.C. in Mesopotamia; however, it was
not until 700 B.C. that the world’s first standardized metal coins were minted in the kingdom of
Lydia, located in modern day Turkey. The currency system of Lydia spread quickly throughout
the Mediterranean kingdoms, which followed suit in introducing their own coins. The
widespread use of money also created more markets around the world. Money made
transactions so much easier that it drove out other economic organizations, such as barter and
feudal systems.
Although these theories on the origin of money are commonly accepted, they are difficult
to verify because isolated and newly emerging economies without a currency are exceedingly
rare in today’s world. An example of such an economy was described by Radford (1945), in
which the author showed that currency developed in a World War II POW camp in a manner
similar to the theories introduced by Menger and Jevons. In his description, prisoners in the
49
POW camp initially gave each other goods or cigarettes as a show of good will, but this was
immediately realized as a mistake because prisoners soon began maximizing their personal
economic well-being. In doing so, the prisoners needed to trade their food and cigarette rations
with each other in order to obtain the goods that were most useful to themselves. Soon,
cigarettes emerged as the currency amongst prisoners. Radford explained the reasons for
cigarettes becoming the currency in a similar fashion to Menger suggesting cattle and coins as
currencies. Cigarettes were used as currency because they were extremely sought after as well as
being quite useful to many prisoners. They were easy to store and transport, and they did not
have a shelf life like most of the other foods distributed in the camp.
In Radford’s description of the POW camp, he stated that supplies were distributed
equally amongst the prisoners, but everyone soon discovered that there was no need to distribute
everything equally. This was another reason trade emerged. Soon after this realization, people
began trading for what they needed. The behavior of prisoners in the camp mimicked those of
people in everyday life, and, therefore, created an interesting study in terms of economic
organization.
As mentioned before, these isolated economies are extremely rare to find and observe in
the modern world. This is the reason online gaming is of interest to us. We are able to freely
observe a newly emerged economy with the release of every new game. Unlike the scenario
described by Radford in the POW camp, players within the game actually produce goods they
initially own, instead of having supplies distributed to them from an organization like the Red
Cross. Due to the more robust resources available to players in online gaming, the economic
organization can even better imitate that of real world economies.
50
In modern day games, economic activity is extremely well organized. Markets are built
into the games, and transportation of goods is instant, due to all items being digital. There are
both advantages and disadvantages in studying gaming economies. We can freely observe how
an economy will behave in response to certain policies within the game (gaming companies do
have currency policies) without having real life consequences. However, we may not be able to
account for every real life factor inside a game, such as the transportation costs of trading.
Studying these economies can be useful in helping us discover problems in current theory or
reaffirming other policies that positively impact our economy. As stated previously, the focus of
this paper is the gaming economy of Diablo II, as it can be used to help us understand the origin
and evolution of money and currency.
4.3
The Development of Currency in Diablo II
Online RPGs have always had their own currencies, which are created by their respective
gaming companies. These exogenous currencies enhance the games and make them more user
friendly. These companies are obviously economic actors trying to maximize their own profits,
and it is apparent that their profits are higher when customers are satisfied. As stated earlier, the
reason that Diablo II was chosen to model Menger and Jevons’ theories is because the currency
created by Blizzard Entertainment for Diablo II held no intrinsic value2, allowing for an
endogenous currency to develop. When Diablo II was released, online RPGs were still in the
early development stages, and gaming companies did not always know how to implement viable
currencies. Although most games released before and after Diablo II had their share of currency
problems, most did not have Diablo II’s extreme problem of a worthless currency. This problem
2
Of course, in modern times, fiat money is a viable currency in most countries, even though it has no intrinsic
value. However, there is not enough confidence in the Diablo II administrators for a fiat currency to exist.
51
allowed another currency to develop endogenously, rather than the exogenously developed
currency experienced in most other games.
Much like other Role-Playing Games (RPG), Diablo II was a game where players worked
to build their own characters, while questing through the storyline provided by the gaming
company. Characters gained experience and grew stronger as they defeated villains, and they
could also wear an assortment of equipment, including rings, amulets, shoes, armors, weapons,
and shields. Diablo II, like any other RPG, began with players finding the equipment they
needed within the playing aspect of the game. When a player defeated a villain, an item would
often drop from the villain, and this would frequently be a useful piece of equipment for the
character. A trading interface was included with the game, so players could trade equipment
they did not need for equipment they did need. This system is quite similar to what Menger and
Jevons described, as people immediately began offering to trade what they had for what they
needed. Although the trading tools available to players in the game were more robust than those
of nomadic times, the initial interactions were still quite similar Menger’s descriptions. Between
trading channels in the game and trading forums on the internet, the economy of Diablo II
developed a currency within several months of the game’s launch. This illustrates how modern
communication is able to accelerate what could have taken hundreds of years to develop in
ancient times.
4.3.1 The Intrinsic Value of the Stone of Jordan and Establishment as Currency
The first currency used in Diablo II was a ring called The Stone of Jordan. The Stone of
Jordan is described as follows by DiabloWiki: “The Stone of Jordan ring, mostly referred to as a
‘SoJ,’ is likely to be the most classic item in the Diablo series. The ring has an iconic status and
52
has, since the release of the game, been considered as high-end gear, and is still considered so in
the days of patch 1.12. It was very common to collect this item in large quantities.” The SoJ
became the currency in the Diablo II economy because it was the most sought after item. It was
also easy to store. In the Diablo II trading interface, a forty-space inventory was allowed to be
traded. Rings required the minimum amount of space: one. It was much easier to make
transactions in terms of SoJs rather than items that required six or eight spaces out of the fortyspace inventory. As the game progressed and SoJs became more numerous, it established itself
as the currency of the Diablo II economy.
4.3.2 Increase in Supply of the Stone of Jordan
The SoJ began as the rarest unique item in Diablo II. Nickolas Reynolds and Michael
Loucas (2012 Interviews – Players) recall the first SoJ selling for over $500 on eBay
approximately one week after the release of Diablo II. Initially, the SoJ was so rare that only
players of the highest status were able to obtain it. Only players who traded very frequently (and
successfully) or players who played the game extensively were able to acquire the ring. After
some time, players with programming experience began reading the code for Diablo II and
discovered methods to exploit the rate of SoJ occurrence3. This played a large role in the
3
The SoJ was classified as a unique ring, and most players would be quite excited to find an unidentified
unique ring; however, players would often be disappointed once they identified the ring. When an item dropped
from defeating a monster in the game, it was initially unidentified (the bonuses the item would provide to players
were hidden) and players would have to pay a fee to discover the attributes of each item. Unlike other unique
items, there were three unique rings in Diablo II: Nagelring, Manald Heal, and Stone of Jordan. At first players
believed that the SoJ had the lowest occurrence rate and decided that the low number of SoJs found was a matter
of the game’s programming giving it a lower chance to be found. After studying the code to the game, players
discovered that unique rings were found in a sequence. If a player was carrying a Nagelring when a unique ring
dropped, then the new ring was guaranteed to be a Manald Heal. If a player was carrying both a Nagelring and a
Manald Heal when a unique ring dropped, then the new ring was guaranteed to be a Stone of Jordan. Once this
information was widely spread, the number of SoJs found increased dramatically.
53
increase in the availability of the SoJ. It is worth noting that this was not public information, and
although literal stocks were not traded in this instance, this practice was similar to insider
trading.
Interviewed players recalled that, as the supply of SoJs increased, the price plummeted to
around $30 each on eBay (October 2000). This method of increasing the number of SoJs
allowed the SoJ to become common enough for any moderate gamer to obtain it easily, while
still rare enough casual gamers to find it quite difficult to acquire. This essentially marked the
SoJ as the currency of Diablo II for anyone who played the game consistently.
4.3.3 Counterfeiting, Inflation, and Contractionary Monetary Policy
As the SoJ strengthened in its role as the currency of Diablo II, knowledgeable
programmers began seeking other methods of exploiting the game. Some discovered a method
of sending illegal packets to the servers, which allowed the duplication of items. This permitted
these specific players to freely duplicate the SoJ (or any other item). This method of duplication
is comparable to counterfeiting; however, there was no process which could distinguish a
duplicated item from its original. As one might imagine, the duplication of items was much
more devastating to the economy of Diablo II than previous methods of increasing its
availability. The same interviewed players recalled the price of SoJs dropping to $5 on eBay by
April 2001. The SoJ became so common that players traded SoJs in bundles of thirty to forty for
an item which would have previously commanded a price of three to four SoJs. Because there
was no failsafe in detecting duplicated items, this phenomenon became the same as the
government printing too much money and resulted in tremendous inflation in the Diablo II
54
economy. The inflation became such a problem that players stopped recognizing the SoJ as a
legitimate currency. Blizzard Entertainment realized this was a problem because it allowed even
the newest players to easily obtain the SoJ. When a player could obtain the best item in the game
within a day of playing Diablo II, it left them with little interest in continuing to play.
On June 29, 2001, Blizzard released Diablo II: Lord of Destruction (LoD), an expansion
of Diablo II, and implemented several public and private methods to reduce the abundance of
SoJs. The public method was quite simple: it allowed players to destroy SoJs, themselves, in
order to help their own characters. When LoD was released, Blizzard announced a recipe that
allowed items to be upgraded using a mechanism called the Horadric Cube. The upgrade
required an item and a Stone of Jordan to be placed in the Horadric Cube. The item would then
be transmuted to a more valuable item, and the SoJ would be destroyed. The process could not
be reversed. This method was quite effective in stopping inflation, and it was an example of
monetary policy enforced by Blizzard Entertainment. Not only did this method reduce the
quantity of SoJs, but it also increased the demand, since it introduced another use for SoJs.
The private methods for stopping inflation were eventually discovered by players.
Although Blizzard worked diligently to stop duplication, new methods were constantly being
developed by savvy players. When LoD was released, Blizzard implemented an algorithm that
created a unique identification code for every item on a server. Whenever the item was
duplicated, this code was copied with it; if two items with the same identification code were ever
in the same game, one of them would be destroyed. While this was not a perfect solution to the
counterfeiting problem, it did reduce the number of counterfeit items in existence. This method
actually created some problems, as players began complaining about their items disappearing.
As the frequency of disappearing items increased, players became more aware of who these
55
items had been obtained from. Once a player was labeled a counterfeiter, it became more
difficult for him or her to trade duplicated items. As the number of SoJs in the market dwindled,
it reestablished itself as the currency of Diablo II. It was not until the emergence of runes that
the SoJ lost its status as the currency of Diablo II forever.
4.3.4 Transition to a New Currency
Another parallel to monetary theory offered by the Diablo II world is the rise of a second
form of currency. Through his description of desirability, Menger clearly suggested that
different types of currencies arose due to the change in desirability of new commodities. In On
the Origins of Money, Menger discusses that it was a peculiar phenomenon that pieces of metal
had been commonly accepted as currency even though they had no particular use to those people
accepting the money. The question he raised was “why it is that the economic man is ready to
accept a certain kind of commodity, even if he does not need it, or if his need of it is already
supplied, in exchange for all the goods he has brought to market, while it is none the less what he
needs that he consults in the first instance, with respect to the goods he intends to acquire in the
course of his transactions.” His ultimate conclusion was that these items were the most saleable
commodities historically. Whether it was cattle or precious metals, all the commodities used as
currency had an extremely high level of desirability. It did not matter if these items were
desirable because they could be used as food or merely as jewelry, desirability created a high
demand for these goods and, hence, their status as a form of currency.
Runes are another item in Diablo II released with LoD. Runes were not useful initially,
but Blizzard slowly increased their usefulness through different updates of the game. Runes
created new items in Diablo II that were so essential to characters that they definitively replaced
56
the status of the SoJ as the most significant piece of equipment. The parallel illustrated here is,
as desirability changed, the currency of the economy changed as well. Over time, the SoJ was
discarded as a currency, and runes became the established currency.
4.3.5 Differences from Theory
One major difference from Menger and Jevons’ theories that the Diablo II trade forums
illustrate is that the “Double Coincidence of Wants” problem does not limit trade as much as
they suggested. We can observe from Table 4.1 that the highest occurrence rate of SoJs or runes
was still less than 40%. They proposed that trade was extremely unproductive without a
currency due to high search costs, and it was unlikely to find someone to trade with if a person
who wanted this specific transaction even existed. In modern times, however, trade has become
significantly less costly due to the advent of the internet and other contemporary communication
tools. Even while the SoJ is an established currency, players continued to barter. Often items
would be listed for sale (in terms of SoJs) and for trade at the same time. The search costs on
forums are rather low. Players can advertise for what they want by simply typing a post for
everyone to view, and if they cannot find someone to make the exchange, then they are willing to
sell their items. This is much simpler than traveling around a marketplace asking each person if
they want to perform a specific exchange. Yanis Varoufakis (2012), the economist for online
game Team Fortress 2, discovered a similar phenomenon while studying its economy. He
stated, “A close study of our Team Fortress 2 economy revealed a more complex picture; one in
which barter still prevails even though the volume of trading is skyrocketing and the
sophistication of the participants’ economic behavior is progressing in leaps and bounds.” His
57
finding is consistent with my discovery that, even with the development of an accepted currency,
there are still a large number of transactions taking place without currency.
The trade forums of a collectible card game, Magic: The Gathering, is another excellent
example of how the “Double Coincidence of Wants” is more easily satisfied through technology
and the internet. On these forums, players are allowed to create a “have list” and a “want list,”
and they are also allowed to search other people’s lists using a search engine provided by the
forum. Additionally, a player can enter any cards he or she is looking for and any cards he or she
has into the search engine and a list of players with exact matches will be returned. If a match is
not found, then players will know that the best alternative is to sell their cards for currency and
buy the cards they want. In Menger and Jevons’ descriptions of the “Double Coincidence of
Wants,” finding someone to trade with was the largest issue. This made search costs high, since
a trader could spend days looking for an item, with no guarantee of finding it. A search engine
greatly reduces search costs, since it only takes a few minutes to type a list of “wants” and
“haves.” Although players are allowed to buy and sell on these forums, a majority of
transactions do not involve money. One reason players prefer trading to buying and selling is
that using third party companies, such as PayPal or Western Union, to transfer money introduces
high transaction costs, since these companies charge a fee for each transaction. Because
technology has made communication increasingly easier, foregoing the transaction costs of one
medium of exchange is preferred by many players.
58
4.4
Analysis
Online archives of the Diablo II trading forums were used to document and further
analyze the process of currency emergence in Diablo II. A detailed descriptive analysis is
followed by a numerical summary.
Diablo II was offered to players on six different servers around the world: USEast,
USWest, Europe, Asia1, Asia2, and Asia3. While players outside of the United States did not
use Blizzard’s trading forums reliably, players on USEast and USWest used Blizzard’s trading
forums consistently. The forums were archived on www.archive.org, a website that has archived
websites for over 15 years. Its selection of websites is based on traffic volume. Since Diablo II
was a fairly popular game, this data is available to us; however, since battle.net, the server for
playing Diablo II, was not the website on the internet with the most traffic, data was only
archived once every two to three months. We will be studying data from the USWest forums
because, as the most populous and traffic-heavy server, it is most well archived. I will note that
the same pattern of trade is illustrated on the trade forums of the other servers, and the SoJ
emerged as the currency in all of them, despite players on different servers not being able to
interact with each other in the game.
4.4.1 Descriptive Analysis
The first data point available to us is from August 2000, approximately two months after
the game’s release. The forum posts in August demonstrate that a currency has not yet emerged.
The following are some sample posts from August:
59
Figure 4.1. Example Posts from August 2000 Trading Forums
“i NEED A GOTHIC BOW 110+ DAMAGE I GOT A LOT”
“Have axe, want sword”
“Have infernal torch lookin 4 mage plate 300+”
“Ancient Sword, Bow, or Xbow for Hammer”
“I will trade Goldskin and Wormskull for Silks”
The posts demonstrate that most traders advertise the items they have and also ask for the items
they are looking for. This is the exact pattern of trade described by Menger. The SoJ is rarely
mentioned. When traders did reference the SoJ, they dedicated entire posts to having or wanting
a single SoJ, as it was clearly an extremely uncommon item.
In October 2000, the quantity of SoJs began increasing significantly:
Figure 4.2. Example Posts from October 2000 Trading Forums
“+1 Amulets for an EYE of Etlich”
“Frostburn & Wormskull 4 stone”
“this for silks + 2 stones”
“SILKS4TRD I WANt BOWS or Dual LEACH r EyeAMMY”
“MY SILKS 4 2 STONES”
Although players were still listing items they had for items they wanted, many more players were
requesting SoJs. Players were also asking for more than one SoJ for their items, as they realized
that everyone was working towards finding as many SoJs as possible.
By December 2000, the trade forums were beginning to look like this:
60
Figure 4.3. Example Posts from December 2000 Trading Forums
“10 stone of jordans for trade”
“Cool rare and many stones 4 ORNATE plate”
“4 Stones for 140+ Bow with nice stats...”
“EXECSORWD FOR SOJs”
“8 SOJs for GLOVES”
Two dramatic changes occur between October and December. The first change is that the
quantity of SoJs offered and wanted by traders has increased dramatically. In October, most
people asked for 1 to 5 SoJs in trade, but by December they were asking for numbers around 10.
A majority of the traders offering and accepting a common good in large quantities in trade is a
clear sign that the economy is converging towards a shared currency. The second change that
occurred was that players began calling the Stone of Jordan by its abbreviated name: SoJ. This
confirms that the term was used so often that players needed an easier way to express it; typing
“Stone of Jordan” just took too much time when every trade involved the unique ring. These two
changes marked a major milestone in the SoJ becoming a currency.
In March 2001, the trade forums of USWest were littered with posts similar to the
following:
Figure 4.4. Example Posts from March 2001 Trading Forums
“13sojs for 310+dmg lance”
“doom grip ring for 10soj”
“40+SOJS FOR 130+ZWEIHANDER SWORD”
“10 sojs for life leech ring with 24%+ mf”
“Up to 12 soj for +2 Amazon, 70+ Mana Amulet”
61
One noticeable change is that, again, the number of SoJs offered and requested has increased.
Now a majority of posts involving SoJs ask for 10 or more SoJs, and only the lower quality items
command a low number of SoJs. It is difficult to pinpoint the precise moment that the SoJ
became an accepted currency in the economy, but we can easily see that the pattern of trade
described by Menger has led us to this point. Based on the forum data available to us, we can
conclude that the SoJ began being traded in multiples between August and October 2000 and that
it become commonly accepted as a currency between October and December 2000. As the
months went by, players began storing SoJs only for the purpose of trading them, a clear
indication that it has emerged as a currency in the Diablo II economy.
By August 2001, the use of SoJs had progressed significantly. The trade forums
appeared as follows:
Figure 4.5. Example Posts from August 2001 Trading Forums
“40 SOJS for your SKULLDER'S IRE!!!”
“need eaglehorn offering 45 sojs”
“Looking for LightSabre 25soj I'm on B.Net”
“20 SOJS for ber rune”
“40 SoJs for your Shako”
The quantity of SoJs offered and requested had changed significantly, as well. By this point, the
SoJ was already a well-accepted currency in the economy of Diablo II. Another development
since the March data set was the release of Diablo II: Lord of Destruction. With this addition,
there were some new items added to the economy. One noticeable item mentioned in the fourth
post in Figure 5 is a rune. The currency of Diablo II eventually transitioned to runes.
By April 2002, the development of runes as a substitute for SoJs as a currency had
advanced further:
62
Figure 4.6. Example Posts from April 2002 Trading Forums
“25 SOJS FOR UR BER RUNE”
“sojs 4 ur Ohm rune”
“high runes for your windforce!”
“My 15 sojs for your perfect arreat and more..”
“Trading Zod+Jah Rune For Cham”
We can see that while SoJs were still being offered for items, players were beginning to trade
large amounts of SoJs for runes. Runes were also being offered in exchange for other items.
This transition is as Menger described, in that players were exchanging their former currency for
the more sought after and useful item.
4.4.2 Numerical Analysis
Table 4.1 shows the available dates selected by archive.org from the USWest server and
the percentage of forum posts that contain the terms “Stone of Jordan” or “SoJ” during those
dates. As we can see, there is a low occurrence of these terms toward the beginning, but the
occurrence slowly rose as SoJs became common. By October 2000, the occurrence had risen
from 4.22% to 9.33%. As indicated earlier, this is when I suggest that the SoJ began to be traded
in multiples. By December 2000, the occurrence rate had reached 15.6% of all posts, and this is
the time I indicate that the SoJ had become a standardized currency. The SoJ continued to thrive
as the dominant currency for more than a year, and by December 2001, the occurrence rate in
forum posts had reached 31.24%.
Another significant development demonstrated by Table 4.1 was the number of posts that
used the term “SoJ” as a percentage of the number of posts that used “SoJ” or “Stone of Jordan.”
The last column in Table 4.1 shows that not a single post referred to the Stone of Jordan as an
63
SoJ in August 2000, but a low percentage of players were beginning to call it “SoJ” by October
2000. By November 2000, a large percentage of players referred to the ring as the SoJ, instead
of the Stone of Jordan, and this continued to be the case. As stated earlier, this is an indication
that the Stone of Jordan had become a currency. The name was used so often that players chose
to abbreviate its name in order to save time. This frequency of use ensured that all players would
recognize the abbreviation.
In 2002, the occurrence rate of SoJs drastically declined in the trade forums. Although
players still traded with SoJs, the percentage of posts requesting or offering SoJs was
consistently lower than in the 2001 months displayed. The primary reason for this change is the
introduction of runes as tools to create items that were much more beneficial to characters than
the SoJ. Table 4.1 also shows the occurrence rate of the terms “rune” and all high level runes that
were used as currency on the USWest server. Runes were beginning to be requested or offered in
trade towards the end of 2001, but the occurrence rate was relatively low until it began to rise
steadily in 2002. This also corresponded with a fall in the occurrence rate of SoJs, which
documents the transition of currency from SoJs to runes, mirroring Menger’s theories.
In this online gaming economy, we witness noticeable similarities to the theories Menger
proposed. The trade patterns and emergence of currency described by Menger may have taken
hundreds of years to develop, but we were able to observe them within mere months due to the
robustness of modern communication tools such as trade forums. This shows that online gaming
can be a useful tool in studying the field of economics.
64
Table 4.1. SoJ and Runes Occurrence Rates
Date
SoJ and
Stone %a
Runes
2000-08
2000-10
2000-11
2000-12
2001-01
2001-03
2001-08
2001-12
2002-04
2002-05
2002-06
2002-07
2002-08
2002-10
2002-12
4.22%
9.33%
9.21%
15.60%
10.98%
15.20%
15.60%
31.24%
11.46%
6.90%
10.58%
8.99%
4.13%
8.93%
3.29%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
6.03%
6.72%
16.21%
23.45%
28.31%
25.84%
30.58%
25.55%
25.18%
a
%b
SoJ vs
Stone %c
0.00%
16.07%
100.00%
61.07%
88.89%
89.62%
96.44%
98.38%
96.55%
100.00%
100.00%
100.00%
100.00%
97.78%
97.83%
This is the number of posts that had the terms “SoJ” or “Stone of Jordan” as a percentage of the total number of
posts that month.
b
This is the number of posts that had the terms “rune,” “zod,” “cham,” “jah,” or “ber” as a percentage of the total
number of posts that month.
c
This is the number of posts that used the terms “SoJ” as a percentage of all posts that used either “SoJ” or “Stone
of Jordan.”
65
4.5
Conclusions
What I have offered is not a flawless proof of Menger’s theories; however, we cannot
deny that there are a large number of similarities between the Diablo II world and Menger’s
descriptions of the origin of money. Although the correctness of Menger’s theories has been
highly debated over the past century, there is no doubt that studying newly emerged economies
can give us some level of clarity and insight as to their accuracy. One difference from theory
that this paper has demonstrated is that in our current economy, individuals barter more
frequently than Menger and Jevons suggested. Because modern day communication is far more
advanced than when currency first developed, we are able to satisfy the conditions specified in
the “Double Coincidence of Wants” much more effortlessly. This shows that the world of online
gaming has a great deal to offer to the field of economics. Here, we have demonstrated that
existing theories can be reinforced, while certain details can also change over time; however,
there is much more to be explored. The virtual world offers a wide array of economic research
topics. With the cooperation of gaming companies, we could conduct controlled experiments
that would help us understand different types of monetary policies.
Today, many gaming companies hire their own economists to manage the economic
policies of their games. They have learned from previous mistakes and know the importance of
a stable currency. They know that having an unstable currency will drive players away, resulting
in a loss of income. The most significant problem companies have dealt with has been
hyperinflation of currency, as demonstrated in Diablo II, through counterfeiting; however, some
games continue to tackle this problem. In Diablo III, the successor to Diablo II, the problem of
hyperinflation continues because Blizzard Entertainment did not implement enough game
mechanics to ensure that the currency would hold intrinsic value. Peter Earle (2013) attributed
66
the hyperinflation in Diablo III to an insufficient control over the growth of money supply.
While Blizzard dealt with the problem of counterfeiting and the exogenous currency lacking
intrinsic value, they were unsuccessful in implementing a stable monetary policy. It is apparent
that the fate of online games rests in the hands of their respective economists and that having a
seasoned economist at the helm could benefit each company tremendously. Even companies that
do not hire economists recognize that a rapidly increasing money supply is the source of
hyperinflation, and these companies do their best to actively control the money supply. It is clear
that there is ample room for economists to delve into this field and observe the economic
interactions transpiring.
Another benefit provided by experimenting within the virtual world is that we can more
easily discover real world weaknesses and problems. The counterfeiting problems of Diablo II
illustrate how careful we need to be when selecting ways to invest our assets. With so much
asset transfer taking place virtually, we must insure that the companies we have chosen are
taking extra measures to protect their servers from malicious attacks. Further development of
economic research in the gaming world will undoubtedly broaden our understanding of
economic interaction and behavior in the future.
67
References
Castronova, Edward, Dmitri Williams, Cuihua Shen, Rabindra Rata, Li Xiong, Yun
Huang, and Brian Keegan. “As real as real? Macroeconomic behavior in a large-scale
virtual world.” New Media and Society 11 (2011): 685-707.
Chacksfield, Marc. “Video Games Become Most Popular Pastime.” Techradar 5
November 2008 <http://www.techradar.com/us/news/gaming/videogamesbecome-most-popular-pastime-482039>
Earle, Peter C. “A Virtual Weimar: Hyperinflation in a Video Game World.” Mises
Daily Index. May 2013 < http://mises.org/daily/6435/>
Jevons, William Stanley. Money and the Mechanism of Exchange. New York: D.
Appleton and Co. 1876.
Menger, Carl. “On the Origin of Money.” Economic Journal 2 (1892): 239-55.
Radford, R.A. “The Economic Organisation of a P.O.W. Camp.” Economica 12
(1945): 189-201.
Surowiecki, James. “A Brief History of Money.” IEEE Spectrum 49 (2012): 44-79.
“The Stone of Jordan.” DiabloWiki. May 2010
<http://diablo.gamepedia.com/The_Stone_of_Jordan>
Varoufakis, Yanis. “Arbitrage and Equilibrium in the Team Fortress 2 Economy.” Valve
Economics. June 2012 < http://blogs.valvesoftware.com/economics/arbitrage-andequilibrium-in-the-team-fortress-2-economy/>
68
CHAPTER 5
CONCLUDING REMARKS
This dissertation successfully explores three different areas of monetary economics;
furthermore, it does so by utilizing econometric tools for empirical work and by observing
virtual economies to reaffirm theory. The results of the first essay suggest that, while there is a
relationship between unexpected inflation and unexpected output in some countries, prices are
endogenously derived through money and other variables. We can actually find more
information on output through the money level equation. The second essay combines two
different ideas in stabilizing money demand and is able to find a stable money demand function
through this method. The final essay confirms Carl Menger’s theory of money with the caveat
that modern communication tools have allowed a barter system to coexist with currencies. The
discoveries of the third essay may even have an effect on money demand in the future, as people
progressively use money less as a medium of exchange, and this could redefine what we use as a
measure of money stock.
69

THREE ESSAYS ON MONETARY ECONOMICS by

Transcription

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