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This is to certify that the

dissertation entitled

COMPLEMENTARITY BETWEEN MONEY AND
CAPITAL IN THAILAND

presented by

Bun-Ek Hiranpradist

has been accepted towards fulfillment
of the requirements for

Ph.D. Economics

degree in

 

 

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Major professor

Dag February 26, 1982

 

MS U is an Affirmative Action/Equal Opportunity Institution 042771

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COMPLEMENTARITY BETWEEN MONEY AND CAPITAL
IN THAILAND

By

Bun-ER Hiranpradist

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Economics
1982

 

JV

(7// /

ABSTRACT

COMPLEMENTARITY BETWEEN MONEY AND
CAPITAL IN THAILAND

By

Bun-Ek Hiranpradist

The financial sector of economically developed
countries is characterized by smoothly functional capital
markets and highly sophisticated financial instruments
and institutions. The conversion of wealth, held as money,
into other assets (and vice versa) can be accomplished
at_very low transactions cost. Therefore, in neoclassical
theory, money and other assets are viewed as alternative,
competing, means of holding wealth. That is, they are
substitutes in assetholders' portfolios.

In an important study, McKinnon argued that the
conditions that give rise to this neoclassical conception
are absent in developing countries (Money and Capital in
Economic Development, 1973). Capital markets are rudimentary
at best; and small enterprises, especially in agriculture,

are likely to be restricted to self-financed investment.
Money-holding becomes the conduit through which these

enterprises finance their investment projects. Thus,

money-holding is complementary to physical capital, rather
than a substitute for it, as in the neoclassical theory.

Inherent in these two alternative conceptions of the
relation of money to physical capital are important
differences in policy implications. It is therefore
important to determine whether the financial system of a
country is dominated by the substitution or complementarity
relationship between money and capital before making a
policy decision.

It is the purpose of this study to develop and
formulate three empirical models to test whether the
relationship between money and capital in Thailand is
dominated by substitution or complementarity. First, we
discuss the contrasting views of McKinnon and neoclassical
economic thought. This is followed by a review of the
studies which have attempted to determine which view better
fits the facts in developing countries. Second, we show
that the Thai economy satisfies the conditions under
which, according to McKinnon, there may be a complementary
relationship between money and capital. Third, we test this
complementarity hypothesis using three different models:
McKinnon's own two-equation model, a portfolio model, and a
translog production function model. These models discriminate
much more sharply between the complementarity hypothesis
and the neoclassical conception than do those used by
previous researchers. Each of the three models is estimated

using four different definitions of money applied to three

   

-nt geographical regions in Thailand:

the whole

F“, the Bangkok area, and the region outside Bangkdk

Isthe“

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;;‘I

 

DEDICATED TO:
My mother and father. Iadmanee and Nob
My wife and daughter, Barbara and Saranya
My brothers and sisters, Loesjai, Nuannuj ,
Sirisakdi, Panai, Teeranuj, Jurairat,
and our sister who died before being

named.

ii

ACKNOWLEDGMENTS

In writing this dissertation, from inception to
completion I have received prompt responses, valuable advice,
and constant guidance and encouragement from the members of
my thesis committee. I wish to express my sincere gratitude
to my dissertation chairman, Dr. Mark Ladenson, who
generously bestowed an enormous amount of his time providing
detailed guidance on every aspect of the study while it was
in the planning and execution stages, and making major,
detailed, changes in my preliminary drafts as the study
neared completion; to Dr. Edmund Sheehey, who initially
suggested the topic, and unfailingly provided constructive
criticism, additional ideas and much needed encouragement
during the course of the study; and to Dr. Paul W. Strassmann
and Dr. Christine E. Amsler, who also read the entire
manuscript and made many valuable suggestions.

I would like to thank several other faculty members
for providing helpful advice concerning both this study and
my academic pursuits in general, during my years at Michigan
State. These include Dr. Robert H. Rasche, Dr. Kenneth D.
Boyer, Dr. Daniel S. Hamermesh, Dr. David A. Burton, Dr.
Norman P. Obst, Dr. James M. Johannes, Dr. Anthony Y.C. Koo,

Dr. William D. King, and Pamela Japinga.

 

For their congenial comments, suggestions and
encouragement, I would like to thank some of my fellow
graduate students. These include Richard Cervin, Ali Reza
Nasseh, Abdollah Ferdowsi, and Don Wyhowski.

Further thanks go to Dr. Alfred Vanderzandan, who
gave his friendship and provided great help as I struggled
to learn the subject matter of mathematical statistics, and
who also provided editorial assistance through many stages
of this dissertation.

I would also like to thank Mrs. Harriett Posner for
her editorial assistance at the final stage and Terie L.
Snyder for her diligent and accurate typing of this
dissertation.

I consider this dissertation a family team effort and
am grateful to my brothers and sisters, Loesjai, Nuannuj,
Sirisakdi, Panai, Teeranuj, and Jurairat for their loyal
help in locating documents and data available only in
Thailand, and transmitting them expeditiously by airmail,
and overseas telephone. My wife, Barbara, who helped with
the editing in the early stage of the study, and my daughter,
Saranya, deserve special thanks for the grace with which
they bore the stresses and strains to which a family is
typically subjected when one of its members is writing a
dissertation.

Finally, I shall always be grateful to my mother
and father, Iadmanee and Nob, who continually encouraged

and supported me, spiritually and financially, during my

iv

years of study leading to the completion of this disserta—

tion. A most heartfelt thank you.

TABLE OF CONTENTS

LIST OF TABLES.

CHAPTER
I. INTRODUCTION -
II.

III.

IV.

VI.

VII.

MONEY AND CAPITAL IN THE NEOCLASSICAL AND THE

NEOLIBERAL VIEW .
Introduction.

. Money and Capital in the Neoliberal View.

. Policy Implications .

. Empirical Testing of the Complementarity
Hypothesis .

Summary ,

’11 muons»

THE COMPLEMENTARITY HYPOTHESIS AND THE THAI
ECONOMY . . . . . . . . . . . . . . . . .

MCKINNON'S MODEL .

Introduction.
. Regression Model.
. Model Estimation.
. Empirical Results
. Summary , ,

MUOW>

PORTFOLIO MODEL.

A. Introduction. . .

B. Theoretical Framework .

C. Model Estimation and Results.
D. Summary ,

TRANSLOG PRODUCTION FUNCTION MODEL .

. Introduction. . .

. Theoretical Framework .

. Regression Model. . . . . . .
Model Estimation and Results. . . . . . .
. Summary . . . . .

MUOCU>

SUMMARY AND CONCLUSION .

vi

Money and Capital in othe Neoclassical View:

Page
viii

APPENDICES:

A. Measurement of Real Capital Stock at the End
of Year (1960- 1979) Using 1972 as the Base
Year . . .

B. Measurement of Variables for the Translog
Production Function. .

C. Data.

FOOTNOTES,

BIBLIOGRAPHY .

Page

99

102
106

118
123

TABLE
2.1

3.1

LIST OF TABLES

Summary of the Empirical Works on Testing the
Complementarity Hypothesis.

Ratio of Total Commercial Bank Loans to Total
Deposits, 1967- 1977 . . . .

The Results of the Ordinary Lease Squares on
the Single Stacked Equation for the Whole
Kingdom . . . .

The Results of the Ordinary Least Squares on
the Single Stacked Equation for the Bangkok
Area. . . . . . .

The Results of the Ordinary Least Squares on ’
the Single Stacked Equation for the Area
Outside Bangkok . . .

The Results of the IZEF Estimations for the Whole
Kingdom . . .

The Results of the IZEF Estimations for the
Bangkok Area. . . . .

The Results of the IZEF Estimations for the
Area Outside Bangkok. . .

The Results of the Portfolio Model Estimation
for the Whole Kingdom . .

The Calculated Elasticities of Each Financial
Asset (- liability) with Respect to Each
Yield for the Whole Kingdom . . .

The Results of the Portfolio Model Estimation
for the Bangkok Area. .

The Calculated Elasticities of Each Financial
Asset (- liability) with Respect to Each
Yield for the Bangkok Area. .

The Results of the Portfolio Model Estimation
for the Area Outside Bangkok. .

viii

Page

18

24

34

35

36

37

38

39

55

56

57

58

59

 

COCO
O‘Ul-I-‘w

The Calculated Elasticities of Each Financial
Asset (-liability) with Respect to Each
Yield for the Area Outside Bangkok.

The Single Stacked Equation Version for the
First Stage . . .

The Results of the Single Stacked Equation
Version for the Whole Kingdom . . . .

The Results of the Single Stacked Equation
Version for the Bangkok Area. .

The Results of the Single Stacked Equation
Version for the Area Outside Bangkok.

The Results of the IZEF Estimations for the
Whole Kingdom . . . . . . . . . . . . . .

The Results of the IZEF Estimations for the
Bangkok Area. . . . . . . . . . . . .

The Results of the IZEF Estimations for the
Area Outside Bangkok. . . .

The Allen Partial Elasticities of Substitution
for the Whole Kingdom . .

The Allen Partial Elasticities of Substitution
for the Bangkok Area. . . . . .

The Allen Partial Elasticities of Substitution
for the Area Outside Bangkok.

The Estimated Values of Real Capital Stock at
1972 Prices at the End of Year (1962-1979).

Q

Commercial Bank Deposits in Bangkok Metropolis,

Other Provinces, and Whole Kingdom.

Money Supply for the Bangkok Metropolis, Other
Provinces, and the Whole Kingdom. . . . . .

Gross National Product at Current Prices .

Gross Fixed Capital Formation at Current Prices.

Structure of Interest Rates. . . . . . . .

Loans of the Banking Sector Classified by.
Purposes.

Number of Commercial Banks Offices per Capita.

ix

Page

60

82

84

85

86

87

88

89

91

92

93

101

109
110

112

C.8
C.9
C.10
C.11
C.12

Loans by the Banking Sector from BOT.

Population .
Consumer Price Index .
Profit Rates .

Agricultural Wage Income .

Page
113

114
115
116
117

CHAPTER I

INTRODUCTION

It is well known that the role of the financial
system, which encompasses financial instruments, institu-
tions, and markets, is to increase the efficiency of the
economic system in terms of output, employment, and price
stability in the short run and in terms of capital
accumulation and economic growth in the long run. Monetary
authorities believe that by manipulating the money supply
they can fulfill the role of the financial system. In
conventional monetary theory, the two main functions of
money are to serve as a universally acceptable medium of
exchange and as a store of value. Since the financial
system is assumed to be well developed, money is easily
converted to other asset forms with little cost or inconven-
ience. Therefore, as a store of value, money will compete
with other assets in wealth holders portfolios.

The applicability of this view to problems of less-
developed countries (LDCs) has been questioned in an
important study by McKinnon (1973). He observed that there
are no well-organized financial markets in developing
countries. As a result the transaction and inventory costs

.of physical assets are much heavier than those associated

with money holdings. Therefore, individuals are more likely
to prefer money to physical assets as a means of savings.

In this scenario, money holding is viewed as a conduit
through which financing of investment projects can take
place. Thus, money holding can be complementary to,

rather than a substitute for, physical capital.

This contrasting relationship between money and
capital leads to different economic results. Therefore, it
is important to determine whether the financial system of
a country is dominated by the substitution effect or the
complementarity effect before making a policy decision. It
is the purpose of this dissertation to develop and formulate
three empirical models to test whether the relationship
between money and capital in Thailand is dominated by
substitution or complementarity.

The dissertation is organized in the following way:
Chapter Two summarizes McKinnon's exposition of contrasting
views about the relationship between money and capital. The
policy implications will be demonstrated. A survey of the
literature concerning empirical testing of the complementar-
ity hypothesis will be presented.

In order to determine whether money and capital in
Thailand are substitutes or complements, Chapter Three will
present an overview of the Thai economy. McKinnon asserted
that the main cause of the complementary relationship
between money and capital is the extremely imperfect state

of capital markets that constrains investment projects to

 

be self-financed prior to conducting the empirical test his
statement will be evaluated to see how accurately it
describes the Thai economic environment.

The empirical tests of the complementarity hypothesis
are performed in Chapters Four, Five, and Six. In Chapter
Four we use McKinnon's model. In Chapter Five we use the
portfolio model, and in Chapter Six we use the translog
production function model. All three models will be
presented in the same way. First, the economic concept
behind each is explained. Then, based on this concept, we
demonstrate how to develop and formulate a regression
model. Next, we explain the estimation methodology. Finally,
the empirical results are presented and interpreted.

The concluding chapter summarizes our results, which
almost uniformly provide support for the complementarity
hypothesis, and suggests some directions for further

research.

 

CHAPTER II

MONEY AND CAPITAL IN THE NEOCLASSICAL
AND THE NEOLIBERAL VIEW

A. Introduction

In an important study, McKinnon (1973) argues that
the hypotheses concerning the financial system and the
conduct of monetary policy, which he designates the "neo-
classical view" and which have been widely applied in
advanced industrial countries, may not be applicable to
less-developed countries (LDCs). In contrast to the neo-
classical view that money and capital are substitutes,
McKinnon argues that they may well be complements. The
purpose of this chapter is to summarize McKinnon's exposition
of these contrasting hypotheses and to explain their

differing policy implications.
B. Money and Capital in the Neoclassiggl View

In neoclassical monetary theory, the salient role of
money in the economy has been discussed, interpreted, and
formulated in a number of theoretical models. Two of these
are the portfolio model and the monetary growth model.

Portfolio models treat money as an asset that is an

alternative to other financial and real assets and view

monetary policy as operating through the substitution
relations among these. By changing the quantity of money
and other assets, the monetary authority will cause
changes in the rate of return on these and consequently
influence the demand for real assets and money. This, in
turn, will affect the rate of investment in new capital.
Often—quoted statements of this process are to be found in
Tobin (1960, 1969), Friedman and Schwartz (1963), and
Brunner and Meltzer (1963).

In some monetary growth models, money or real cash
balances enter as a factor input in the production function.
In these models, changes in the money supply will influence
the amount of capital, labor, and other factor inputs
through the substitution and complementary relationships
among the inputs. These models are reflected in the
Austrial transaction-cost model by Gabor and Pearce (1958)
and the neoclassical monetary growth model by Johnson
(1968), Stein (1970), Levhari and Patinkin (1968), and
Fischer (1974).

Now consider two of the most important neoclassical
assumptions, namely:

(1) Capital markets operate perfectly and costlessly

to equate return on all real and financial
assets with a single, real rate of interest.

(2) Inputs, including capital, and outputs are
perfectly divisible.

Neoclassical monetary theory, based on the above
two assumptions, generates a demand for money function that

McKinnon writes as

6

(M/P)D - H<Y/P.r.d-be) (2.1)

where (M/P)D = the demand for real cash balances;

(Y/P) = the aggregate real income;
r a the real rate of return on both

physical capital and all non-
monetary financial assets;

d = the nominal interest rate on
deposits;
be = the expected future rate of
inflation;

p = the actual rate of inflation;

(d-pe) = the real return on holding money.

[an/3(Y/P)] > 0
(EH/3 r) < 0
[an/3 (d-ée>1> o

In this neoclassical demand for money function, money
and real capital are substitutes. With a rise in r,
individual asset holders switch from money to more lucrative
physical capital. In doing so, they give up some of the
transaction advantages of using money, (Hr < O). Symmetri-
cally, an increase in the real return on holding money,
d-pe, for a given Y and r, will increase the real cash
balances and reduce the demand for physical capital in the
private saver's portfolio, (H(d_ée) > 0). "This is the
substitution effect between money and real capital which
dominates neoclassical monetary theory."1

That money and capital are substitutes is also

 

reflected in the neoclassical monetary growth model. Citing
Levhari and Patinkin, McKinnon writes "the neoclassical
investment function that holds in equilibrium growth"2 as
I = dK/dt = sY+ (s-1)(M-P)(M/P) (2.2)
where I = the aggregate annual flow of
investment in physical capital;
K = the stock of physical capital;
t = an index of time;

M - the rate of expansion in nominal
cash balances;

Y - the current output of goods and
services;

3 = MPS = the marginal propensity to
save;

g = the actual rate of inflation;

(M/P) = real money balances.

Since (s-l) < 0 and (according to McKinnon) (M-P) > 0,
we obtain a result similar to that obtained from the static
model. That is, an increase in the real stock of money,
(M/P), may reduce the real rate of investment. Because the
savings propensity is fixed and savings can be directed only
toward real balances or toward physical capital, they are

substitutes.
C. Money and Capital in the Neoliberal View

McKinnon (1973) pointed out that the neoclassical
assumptions are inapplicable and unreal with respect to the

economic environment in less-developed countries (LDCs).

8

The lack of organized finance and the fragmented economic
environment in these countries seem to suggest opposite
assumptions. Therefore, he proposed that economic models
for LDCs be based on the following assumptions:

(1) The capital market is highly imperfect, which
confines all economic units to self-finance,
with no useful distinction to be made between
savers (households) and investors (firms).
These firm-households do not borrow from, or
lend to, each other.

(2) The small size of firm-households implies that
indivisibilities in investment are of consider-
able importance.-

These two assumptions lead to a complementary

relationship between money and capital in LDCs.

This complementary relationship can be expressed in the

money-demand function as
D -e
(M/P) = L(Y.I/Y.d—p ) (2.3)

where (M/P)D = the real money demand;
Y - the current income;
I/Y = the investment-income ratio;
d - the nominal interest rate on deposit;

pa = the expected future rate of

inflation;

(d-pe) s the real return on holding money.

McKinnon's two assumptions indicate that, in LDC's
imperfect capital market environment, if an individual
saver-investor, being limited to self-finance, wants to

purchase physical capital, he has to accumulate cash balances

for this purpose. Therefore, real cash balances have a
tendency to be positively related to the propensity to
invest. In other words, money and capital complement,
rather than compete against, each other.

In order to compare this with the traditional model,
McKinnon replaces (I/Y) with the average return to capital,
r, as in the neoclassical money-demand function. This
implies that if there are exogenous changes in the environ-
ment that could raise f, such as opening an economy to
foreign trade or introducing a "green revolution" in agri-
culture, this will raise desired investment and the demand
for cash holding. Therefore, we can summarize the demand

for money in a more familiar form as
(M/P)D = L(Y,f,d-pe) (2.4)

The complementary relationship in equation (2.4)
is reflected as LE > 0, in contrast to the neoclassical
substitution effect that Hr < 0.

McKinnon suggested that complementarity between money
and capital is also reflected in the investment function as

given by equation (2.5)
(I/Y) = Mid-15% (2.5)

where (as/3E) > 0 (2.5.1)

owe-.38» 20. (2.5.2)

The partial derivative (2.5.1) implies that a rise

in the average rate of return to capital, P, will increase

10

the investment-income ratio.

The partial derivative (2.5.2) is of ambiguous sign,
the result of the mixture of the traditional "competing-
asset" effect and the "conduit" effect. If the conduit
effect prevails, the increase in real return, (d-pe), will
augment the importance of money as a store of value. This
will enlarge the financial conduit for capital accumulation
and increase the investment-income ratio. The partial
derivative will have a positive sign. Conversely, if the
competing-asset effect prevails, this means the real return
of holding money is already high. Therefore, further
increases in the return may induce net portfolio substitution
away from the accumulation of capital toward cash balances
as earning assets in their own right instead of as the
financial conduit. The partial derivative (2.5.2) in this

case will be negative.

D. Policy Implications

 

The complementarity hypothesis contains policy
implications that differ markedly from those contained in
the neoclassical view. Several examples of these differences
are presented in this section, and further implications of
the complementarity hypothesis are stated.

As a first example, suppose that there is an exogenous
improvement in real rates of return to physical investment
such as a "green revolution" in agriculture. This will

result in an increase in investment and, where the

13

ll

complementarity hypothesis is operative, will Egigg the
quantity demanded of real balances. To prevent deflation,
the money stock should be increased. In contrast, in a
static neoclassical model the increase in the rate of
return on investment would not affect the quantity of real
balances demanded. In that model, if the money stock were
increased in these circumstances, a rise in the price level
would result.

Our second example is drawn from the experience of
Chile in the 19503. The threat of hyperinflation was very
real in Chile in 1955. Orthodox deflationary measures wggg
successful in lowering the inflation rate to 17 percent in
1957. But these measures also caused an industrial
recession severe enough to discredit orthodox deflationary
advice throughout Latin America. To combat this recession,
the monetary reins were loosened in 1958, and the inflation
rate doubled to 33 percent. In these years, per capita
income actually declined. "Chile seemed to have chosen for
itself the worse of several possible worlds since it had
'neither stability nor development,‘ to quote the title of
a brochure by one of its most articulate economists."4

Is there a better way to fight inflation in LDCs?
The complementary hypothesis would recommend an alternative
monetary policy. The central bank should géigg the nominal
deposit rate, which will, in turn, increase the real rate
of return to the holding of cash balances. This will

increase the demand for money, decrease consumption, and

12

slow down aggregate demand. At the same time, the central
bank should increase the nominal money supply. This will
increase bank credit through the conduit effect and will
stimulate the growth of working capital and increase the
aggregate supply of goods and services. By conducting
monetary policy based on the complementarity hypothesis,
the central bank will be able to stabilize the price level.

These examples show that the complementarity

hypothesis has the following implications:

(1) The formulation of the money-demand function
for LDCs should include (I/Y) as an independent
variable.

(2) The imperfect capital market indicates the need
for expanding the banking system in order to
increase the degree of saving mobilization
(McKinnon 1973, p. 5 ).

(3) Because of imperfect capital markets, the
central bank should encourage the creation of
liquid assets with attractive yields (Aghevli,
Khan, Narvekar, and Short 1979, p. 90).

(4) The conduit effect, which is implied by the
complementarity hypothesis, is the result of
financial repression and negative real rates
of return to holding money. Therefore, this
hypothesis indicates the need for interest

rate reform policy that will deregulate interest
rates and let them respond to market forces.

E. Empirical Testing of the Complementarity Hypothesis

Several authors have attempted to test the complemen-
tarity hypothesis using data on LDCs in Latin America and
South Asia. In this section we survey these tests.

McKinnon (1973) did not use any econometric technique

to test the complementarity hypothesis. To support his

l3

hypothesis, he simply discussed the relationships among real
cash balances (defined as the sum of currency, demand,
saving, and time deposits), aggregate investment, and growth

in Korea and Taiwan from 1960 to 1972.5

Vogel and Buser

The first test of the complementarity hypothesis to
appear in the literature was conducted by Vogel and Buser
' (1976).6 McKinnon had noted that one way the authorities
can increase the real return to holding money is to reduce
the rate of inflation. According to his complementarity
hypothesis, this will increase the volume of (self-financed)
investment. To test these relationships, Vogel and Buser
first compared inflation rates, growth rates of holdings
of real money balances, and the growth rate of real
investment in sixteen Latin American countries over the
1950-1971 period. Inflation and holdings of real time and
savings deposits were, indeed, inversely related. Inflation
was also inversely related to the growth rate of real
investment, but the relation was much weaker.

Second, pooling their time series data across all
countries, Vogel and Buser regressed ratios of various
components of money to income on the inflation rate and real
GNP. They found that a one percentage point rise in the
rate of inflation reduces the ratio of currency holdings to
national income by 0.1 percentage points, reduces the ratio

of demand deposit holdings to national income by 0.07

14

percentage points, and reduces the ratio of time deposit
holdings to national income by 0.5 percentage points. Third,
they mention that they regressed the ratio of investment to
income on "both levels and changes in the rate of inflation
for both current and past time periods...in various combi-
nations," but that "none of the inflation variables has a
significant impact on the share of investment in gross
domestic product." (p. 58).

Fourth, Vogel and Buser regressed the ratio of invest-
ment to income on the ratios of currency, demand deposits,
and time deposits to income. As a fourth independent
variable to test the complementarity hypothesis, they
wanted to use the ratio of nonmonetary to monetary assets.
Their theoretical work (see my footnote 6) suggested that
this variable was an appropriate index of financial
repression. Since data on nonmonetary assets were lacking,
they used gross domestic product as a proxy. Their fourth
independent variable, then, was the ratio of gross domestic
product to the sum of demand and time deposits. All
estimated coefficients had the correct signs, but only the
positive coefficients on the ratio of time deposits to
income and the negative coefficient on the index of financial
repression were significant.

In sum, all tests except the third support the
complementarity hypothesis. Vogel and Buser recognize that
since thev find. in the first two tests. that inflation

adversely affects the size of the financial sector and. in

15

the fourth test, that the size of the financial sector is
directly related to the share of investment in output, it is
paradoxical that the third test fails to show an inverse
relation between inflation and the ratio of investment to
output. They suggest, as McKinnon had argued, that orthodox
inflation fighting policy does not stress financial
liberalization and hence "may appreciably reduce aggregate
supply as well as aggregate demand; this not only makes it
more difficult to curb inflation, but also tends to reduce
capital formation... A lower rate of inflation, if brought
about through orthodox policies, may thus have an adverse
impact on the share of capital formation in national income"

(p. 62).
m

Yoo (1977) tested the complementarity hypothesis by
developing a two-equation model with independent investment
and saving functions. McKinnon's conduit effect appears in
the net investment function through inclusion of the lagged
money stock as an independent variable. The saving function
also contains the lagged money stock as an independent
variable. These two functions were estimated for each of
five developing countries (the Phillipines, South Korea,
Taiwan, Israel, and Brazil) and three industrial countries
(Norway, New Zealand, and the United States) with data for
the 1953-1970 period. For all five developing countries,

the coefficient of money in the investment function was

16

positive and significant, thus giving support to the notion
of a conduit effect. While this coefficient was also posi-
tive for the three developed countries, for two of them it

was not significantly different from zero.

:22

Fry estimated a variant of equation (2.3) using
pooled time series-cross section data for ten Asian LDCs
over the period 1962-1972. Rather than using the ratio of
investment to income as an independent variable in the demand
for money function, he asserted that "domestic saving is
equal by definition to domestically financed investment,"
and used the ratio of saving to income as an independent
variable. The coefficient of this variable was negative
and significant. Fry interpreted this finding as evidence

against the complementarity hypothesis.
Galbis

Galbis estimated the parameters of equation (2.3)
for each of nineteen Latin American countries for the period
1961-1973. He also estimated a variant of the investment
function, equation (2.5), in which the rate of inflation
appears as an independent variable. The coefficient of the
ratio of investment to income in the demand for money
function was positive and significant in only four of the
nineteen regressions. The coefficient was actually negative

in twelve of the regressions. Like Vogel and Buser, Galbis

17

was unable to find a significant negative relation between
the share of investment in national income and the rate of
inflation. The coefficient of inflation in the investment
equation was negative for only seven countries. In not one
of these cases was the coefficient significantly different
from zero. The study provided, at best, very weak support

for the complementarity hypothesis.

F. Summary

The above review of the literature on empirical
tests of the complementarity hypothesis disclosed that, on
balance, the hypothesis acquired different degrees of
support that ranged from "strong" to "moderate" to "weak"
depending on the analysis and the variables employed by
each researcher. Nevertheless, these empirical tests have
a common ground: all used only the two—equations model,
namely, the model using the money-demand and the investment-
income ratio equations.

In this dissertation we will use this model, but we
will also break new ground by using the portfolio and
production function models to test the complementarity

hypothesis.

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CHAPTER III

THE COMPLEMENTARITY HYPOTHESIS AND THE THAI ECONOMY

Thailand is a country located in the center of the
Southeast Asian peninsula. It has an area of about
200,000 square miles and a total population (in 1979) of
46.14 million. Bangkok-Thonburi, the capital city, is
the only major concentration of commerce, manufacturing,
and finance; its population in 1979 was about five million.
However, more than 80 percent of the population live in
rural areas and participate in agriculture.

. The growth rate of the gross national product

during the 19703 was approximately 6 to 7 percent, as
targeted for the period of the Fourth National Economic and
Social Development Plan. The breakdown of the gross
domestic product in 1979 was as follows: agriculture
(crops, livestock, fisheries, and forestry) 25.8 percent,
and the nonagricultural sectors (mining and quarrying,
manufacturing, construction, power generation, water supply,
and so forth) 74.2 percent.

In the nonagricultural sector, which contains a
vast number of small-scale, family-run enterprises, capital
inputs are becoming much more important in the production

process than labor.l

19

20

Capital inputs require financing. Therefore, the
question is how can these inputs be financed? In countries
with well-developed financial markets and institutions,
private enterprise may be financed either through self-
finance, or by borrowing from the market. In contrast,
in countries with under-developed financial markets,
investing entities must accumulate savings from within.

The latter description appears to characterize
accurately certain sectors of the Thai economy. According
to several research studies concerning the Thai financial
system,2 although 70 to 80 percent of the population are
involved in agriculture, only 30 percent of the gross
domestic product comes from this sector. Prior to 1975,
agriculture accounted for approximately two percent of total
bank credits. The remaining funds financed mainly trade,
industry, housing, and consumption in Bangkok and a few
other cities. Since only a small fraction of savings in
many rural areas and provinces has been channeled back into
these areas, farmers have had little choice in financing
investment projects. They have had to obtain financing
from direct reinvestment of funds by the owners or by
borrowing from noninstitutional private lenders at
exorbitant interest rates.

Unakul and Panitchpakdi (1978, p. 10).described the
role of the banking sector in this saving—investment process

as follows:

21

"When left to the financial institutions, funds
are naturally channelled into projects or sectors
that promise the highest yield under certain risk
conditions. Most commercial banks traditionally
concentrate on financing foreign trade and domestic
commerce. When they diversify, the direction is
usually towards urban-based activities such as real
estate projects and service industry. The credit
needs of agriculture, small business and industry
including a large number of traditional enterprises
have to be met by non-institutional lenders.

The inefficiency of the financial system in
allocating funds is also reflected through the
so-called 'banking collateral syndrome.‘ This
describes the rigidly risk-averting attitude of
lending institutions in insisting on approved
securities as collateral, for example real estate or
government securities, rather than basing their
judgment on project appraisal or on the borrower's
characters. This attitude has deprived many
deserving borrowers lacking in these assets of the
chance to qualify for bank loans. It has been found
in many LDCs that the rigid insistence on collateral
requirements rather than the prevailing rates of
interest is the major factor in curtailing the
availability of credit. This rationing of credit on
a narrow interpretation of risk criteria results in
substantial social costs in terms of foregone
economic opportunities and activities. It is mis—
leading to consider uncollateralised loans more risky
than a fully secured loan under all circumstances.
To improve the credit allocating function of the
financial system, it is therefore necessary that
financial policies be geared to growth and employment
potential rather than being constrained by the
availability of collateral."

A study by Baker (1979) also finds this problem.
His results indicate that one of the impediments to the
development of rural financial markets is a lack of funds
available for lending. Regulatory authorities caused this
lack by imposing a ceiling on interest rates in the fund
market. This limits the rates that can be charged to
borrowers and paid to savers. Unsatisfied demand then

shifts either to informal lenders, who will charge higher

 

22

interest rates, or to self-finance.

The consequences of the existing self-finance
investment situation on an economy with a less-organized
financial market are well known, namely, arbitrary and
wasteful allocation of capital.3 Official documents
indicate that the Bank of Thailand (BOT),the monetary
authority in Thailand, is also aware of this condition.4
Consequently, in 1975 BOT adopted a policy that required each
commercial bank to increase agricultural loans to an amount
not less than a certain percentage of its total deposits.
Outstanding agricultural credits increased from 1.2 percent
in 1974 to 14.3 percent in 1977. The ratio of loans to
deposits, a measure of saving mobilization, indicates that
only 63 percent of the total deposits in rural areas were
lent back to these areas. The corresponding ratio for the
Bangkok-Thonburi area was 1.118, which is greater than one.

Hence, it can be concluded that investment projects
in the rural areas still depend on self-financing, while
most investment projects in the Bangkok-Thonburi area are

likely to be financed by the banking system.

Summary

McKinnon stresses that a necessary condition for
validity of the complementarity hypothesis is that capital
markets operate so imperfectly that large sectors of the
economy are essentially limited to self-financed investment.

In this chapter, we have shown that this situation appears

 

23

to prevail in the Thai economy. The latter, therefore,

provides an appropriate setting for tests of the comple-

mentarity hypothesis. These tests are explained and

performed in the next three chapters.

 

24

TABLE 3.1

RATIO OF TOTAL COMMERCIAL BANK LOANS TO TOTAL
DEPOSITS, 1967-77 WEIGHTED MEAN BY REGION

 

Ratio for All Central Northeast Northern Southern
Bangkok- Changwads* Region*’ Region Region Region
Year Thonburi

1967 0.927 0.420 0.366 0.426 0.436 0.468
1968 0.887 0.443 0.363 0.434 0.532 0.480
1969 0.954 0.459 0.377 0.440 0.599 0.464
1970 1.054 0.451 0.407 0.417 0.513 0.493
1971 0.990 0.442 0.427 0.357 0.487 0.496
1972 0.861 0.410 0.372 0.359 0.462 0.480
1973 1.013 0.454 0.415 0.415 0.496 0.522
1974 1.114 0.424 0.401 0.410 0.459 0.445
1975 1.154 0.476 0.444 0.487 0. 525 0.477
1976 1.142 0.512 0.487 0.512 0.566 0.506
1977 1.118 0.633 0.615 0.651 0.713 0.565

 

* excluding Bangkok-Thonburi.

Source: Meesook (1978).

CHAPTER IV

MCKINNON'S MODEL

A. Introduction

In this chapter we will present the test of the
complementarity hypothesis based on the earlier
discussion of McKinnon's two-equation model. The two
equations are the money-demand equation and the investment-

income ratio equation.

B. Regression Model
The Money-Demand Equation

Let the demand for money in the multiplicative

form be

C C C C
(M/P)tD = mt = CoYt1<I/Y)t2<dt>3<15§>4 (4.1)

where c0,c1,c2,c3 and c4 are constant terms.
The coefficient c2 is the elasticity of demand for
real balances with respect to the investment-income ratio.

Since the deposit rate, d has not fluctuated much during

t)
the estimation period, this variable will be dropped from

equation (4.1). Then, equation (4.1) becomes

25

26

c c , c
(WP)? = mt = COYt1(I/Y)t2(p:) “ (4.2)

Taking the natural logarithm of (4.2), we get
lnmt -= 1nco + cllnYt + c21n(I/Y)t + c4ln(p:) (4.3)

Since the expected rate of inflation, pe, is not
directly observable, let us propose that expectations are
formed by the adaptive expectation or error learning

hypothesis,1 which is

 

 

fie fi (l-A)
.g = .9? (4.4)
pt-l pt-l
where 0 s A s l.
or
'e 'e . 'e
lnpt--lnpt_l = (l-A)(lnpt - lnpt_1) (4.5)

Equation (4.5) states that the expectations of the
inflation rate are revised each period by a fraction (1-1)
of the gap between the actual and the expectation rate of

the inflation rate. Equation (4.5) can also be written as
'e 2 - . 'e
lnpt (l A)lnpt + Alnpt_1 (4.6)

Equation (4.6) shows that the expected inflation
rate at time t is a weighted average of the actual value
of the inflation rate at time t and its expected value in
the previous period, with weights of (l-A) and A, respec—

tively. If A = 0, lnp: = lnpt, meaning that expectations

27

are realized immediately and fully in the same time period.
If, however, A = 1, Inp: = Inp:_l, meaning that expectations
are static.

Substituting (4.6) into (4.3) we obtain
lnmt = lnco+ cllnYt + c21n(I/Y)t+ c4((l-A)1npt+ Alnp:_1)
= lnc0+ cllnYt + c21n(I/Y)t + c4(1-A)lnpt
+ c4 11.11354 (4.7)
Lag (4.3) one period and multiply by A to obtain
Alnmt_l - Alnc0 + AcllnYt_l + Ac21n(I/Y)t_1
+ Ac4ln(p:_l) <48)
Subtracting (4.8) from (4.7), we get
lnmt - Alnmt_l = (1-A)1nco+-c11nYt- AcllnYt_1
+ c21n(I/Y)t - Ac21n(I/Y)t_1

+ c4(1-A)1npt (4.9)
or

lnmt s (l-A)1nc0 + cllnYt- AcllnYt_1+c21n(I/Y)t
- Ac21n(I/Y)t_l + c4(1-A)lnpt + Alnmt_1 (4.10)

01'

 

28
mm = (1-A)1nco + cllnYt ' A‘3111‘Ytrl
+ c2(lnIt-lnYt) ‘ AczanIt-l'lnYt-l)
+ c,(:-A>1né, + Alnmt-l

= (l-A)lnco+-(c1-c2)lnYt- A(cl-c2)lnYt_l-l-c21nlt
— AczlnIt__l + c4(l-A)lnpt + Alnmt_l (4.11)

Equation (4.11) could be written in linear form as

follows:

lnmt = a0+allnYt + azlnYt_1 + a3lnIt + a4lnIt_1

+ aslnpt + a61nmt_1 (4.12)

However, there is no unique correspondence between the
coefficients of these two equations. In particular,
inherent in equation (4.12) are four separate estimates of
the coefficient cl, and two separate estimates of the
coefficient c2. Therefore, rather than estimate equation
(4.12), we estimate the parameters of equation (4.11) using

a nonlinear least squares method.

The Investment Equation

 

Following McKinnon, let the investment function in

the multiplicative form be

h1 h2 'e h3
(I/Y)t - h0(fi/K)t (dc) (pt) (4.13)

29

where ho, hl’ h2 and h3 are constant terms and (n/K), the
ratio of profits to capital, is the proxy for the average
return to capital, E.

Since the deposit rate, d has not fluctuated much

t!
during the estimation period, this will be dropped from
equation (4.13). Equation (4.13) becomes
h . h
(Imt = ho<w/K)t1<p§) 3 (4.14)
Taking the natural logarithm of (4.14) we get
ln(I/Y)t - lnho + hlln(n/K)t + h3ln(p:) (4.15)
Next, substitute (4.6) into (4.15) to obtain
ln(I/Y)t = lnho + hlln(n/K)t + h3((l-A)lnpt+Alnp:_1)
= lnho + hlln(:r/K)t + h3(l—A)lnpt
+ h3Alnp:_l (4.16)
Lag (4.15) one period and multiply by A to get

= .e
Aln(I/Y)t_l Alnh0 + Ah11n(:r/K)t_l + h3Aln(pt_l)
(4.17)
Finally, subtracting (4.17) from (4.16) leads to

1n(I/Y)t - Aln(I/Y)t_1 = (l-A)lnho + hlln(1r/K)t
- Ahlln(n/K)t_l + h3(l-A)lnpt

or

30
1n(I/Y)t = (l-A)1nho + h11n(1r/K)t - Ah11n(1r/K)t_1
+ h3(l-A)lnpt + Aln(I/Y)t_1 (4.18)

Equation (4.11) and (4.18) are results of the
derivations of the adaptive expectation hypothesis for the
expected inflation rate. They have the same coefficient,
lambda. This fact will be taken into account in the
estimation procedure. Equation (4.18) could be written in

linear form as follows:
ln(I/Y)t = b0 + blln(n/K)t + b21n(n/K)t_1
+ b3lnpt + b4ln(I/Y)t_1 (4.19)

However, there is no unique correspondence between the
coefficients of these two equations. In particular,
inherent in equation (4.19) are two separate estimates of
the coefficient hl. Therefore, rather than estimate
equation (4.19), we estimate the parameters of equation

(4.18) using a nonlinear least squares method.
C. Model Estimation

Our nonlinear least squares estimation of McKinnon's

two-equation model will proceed in two stages.2

The First Stage

Any nonlinear least squares procedure requires
starting estimates for the parameters c0, c1, c2, c3, hO’

hl’ h3, and A. The purpose of the first stage of the

31

estimation procedure is to determine reasonable values for
these starting points. The estimation is obtained by
stacking the two equations (4.12) and (4.19) into a single
matrix equation in order to enforce the equality restriction
of the lambda parameter in both equations.

The dependent variable contains 34 observations.
The first 17 are those on the log of money (lnmt) for the
period 1962 to 1979. The last 17 observations are those on
the log of the investment income ratio for the same period.

The independent variables consist of eight columns
of data groups of explanatory variables from equation
(4.12) and (4.19). The first 17 observations of the first
five columns consist of the constant term one, the log of
income (lnYt), the log of investment (lnlt), the log of
the actual inflation rate (lnpt), and the log of real
money balances lagging one period (lnmt_1). The last three
columns of the first 17 observations consist of zeros.
For the last 17 observations, the first four columns consist
of zeros, while the last four columns consist of the log of
the investment-income ratio lagged one period (ln(I/Y)t_1),
the constant term one, the log of the profit rate (ln(n/K)t),
and the log of the actual inflation rate (lnpt). The
single equation that represents the stacking of equation
(4.12) and (4.19) is given in equation (4.20). The reason
for estimating the two equations as the single stacked
equation (4.20) is to force the starting estimate of A(a6)

obtained from the money-demand equation to equality with

32

the starting estimate of A obtained from the investment—
income ratio equation, in accord with the derivations of

these equations.

 

ilnmt
Lln(I/Y)t
8o
r . 81
1 1nYt lnIt 1npt lnmt_1 0 0 0 :3
. 86
L0 0 0 0 ln(I/Y)t_1 l ln(n/K)t lnpt E:
b3
(4.20)

For the Thai financial environment, Tengpratrip (1978)
recommended that the narrow definition of money, M =
currency, should also be tested since demand deposit is
still not generally accepted as a means of payment in
Thailand.3 Therefore, the stacked equation (4.20) will be
estimated by the ordinary least squares method using four

different definitions of real money balances:

M1 8 C + DD;
M2 8 C + DD + SD; and
M3 = C + DD + SD + TD.

MO represents the currency; M1 is currency plus
demand deposit, which is a narrow definition of money;

M2 is currency plus demand and saving deposits; and M3 is

33

currency plus demand, saving, and time deposits. Both M2

and M3 are broad definitions of money.
The Second Stage

The second stage of the procedure is to estimate
equations (4.11) and (4.18) using a simultaneous equations
nonlinear least squares method.4 The values of the
parameters estimated in the first stage will be used as the
starting points for estimating the values of the parameters
c0, c1, c2, c4, ho, hl’ h3, and A.

The estimation procedure for both stages will be
conducted on the whole kingdom, the Bangkok area, and the
area outside Bangkok using each of M0, M1, M2, and M3.

D. Empirical Results

 

The results of the ordinary least squares procedure
on the single stacked equation for the first stage for the
whole kingdom, the Bangkok area, and the area outside
Bangkok are presented in tables (4.1.a), (4.1.b), and
(4.1.c), respectively. The determination of the money-
demand equation and the investment equation, as the
results of the IZEF estimation corresponding to each region,
are shown in tables (4.2.a), (4.2.b), and (4.2.c),
respectively. The estimated equations are (4.11) for the
money-demand equation and (4.18) for the investment equation.
The derived numerical values for the parameters as starting

points, which are derived from the coefficients of the

34

 

 

 

 

 

 

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40

single stacked equation in the first stage, are provided
for the IZEF estimation for each region. The number of
iterations required to achieve convergence are presented
for each equation. The multiple coefficient of determina-
tion adjusted for degrees of freedom (R2), Durbin-Watson
statistic (DW), and standard error of estimate (SEE) are
calculated from the residuals for each of the two dependent
variables.

Since equations (4.11) and (4.18) are autoregressive
models, they include the lagged values of the dependent
variables among the explanatory variables. Therefore, we
provide the Durbin h statistic which is the appropriate
check on autocorrelation of residuals for such equations.5
Since at the five percent level of significance, the
critical h value from the normal distribution table is
1.645, and all the computed h statistics are greater than
the critical h, we can reject the hypothesis that there is
no (first-order) serial correlation in the data. There-
fore, the t ratios given in these tables may contain an
upward bias.

The empirical findings for all three regions can be
summarized as follows. First, the results show that for
the whole kingdom and the Bangkok area the coefficients
of the log of the investment-income ratio in the money—
damand equation are positive and significant for all four
definitions of money, thus giving support to the complemen—

tarity hypothesis. For the area outside Bangkok, this

41

coefficient is positive and significant only for the case
of money defined as the sum of currency plus demand and
saving deposits. From these results we may infer that by
holding income and the expected inflation rate constant,

a one percent increase in the investment-income ratio leads
to an increase in the demand for money that ranges from
15.4743 to 30.7639 percent for the whole kingdom, from
7.02787 to 16.243 percent for the Bangkok area, and 15.6672
percent for the area outside Bangkok.

Second, the empirical results show that over the
period of study (1962 to 1979), holding the investment-
income ratio and the expected inflation rate constant, a
one percent increase in income led to an increase in the
demand for money that ranged from 0.722639 to 1.49345
percent for the whole kingdom, from.0.499635 to 1.27381
percent for the Bangkok area, and from 1.35057 to 2.41041
percent for the area outside Bangkok.

Third, by holding income and the investment-income
ratio constant, a one percent increase in the expected
inflation rate led to a decrease in the demand for money
that ranged from 0.149706 to 0.293182 percent for the
whole kingdom, from 0.107621 to 0.24989 percent for the
Bangkok area, and from.0.0406634 to 0.0699731 percent for
the area outside Bangkok. This is because an increase in
the inflation rate decreases the real return of holding
money, (d-pe), and depreciates its value while it leads

to a decrease in the demand for money.

42

Fourth, the t values of the coefficients in the
investment-income ratio equation for all three regions and
all four definitions of money are insignificant. These
poor results are due to the unusual difficulty in measuring
the rate of return on investment. Other researchers have
had difficulty measuring this variable. The problem caused
Galbis (1978) to drop the variable in his estimation.

Vogel and Buser (1976, p. 50) also remind readers of the
well-recognized deficiencies in data for LDCs.

E. Summary

In this chapter we tested the complementarity
hypothesis by estimating the parameters of McKinnon's two-
equation model with data on the Thai economy.

The empirical results, generally, support the
complementarity hypothesis. They indicate that for the
whole kingdom money holding will increase on the average‘
of 15 to 30 percent if an increase of one percent in invest-
ment is desired. For the Bangkok area, the demand for
money will increase on the average of 7 to 16 percent in
response to an increase in investment of one percent.
Finally, for the area outside Bangkok, the money demand will
.increase on the average of 15 percent in response to a one

percent increase in investment.

CHAPTER V

PORTFOLIO MODEL

A. Introduction

 

The preceding chapter discussed tests of the
complementarity hypothesis that used McKinnon's two-equation
model. This chapter will present tests of the complemen-

tarity hypothesis that use a portfolio model.
B. Theoretical Framework

In the general portfolio model, the private non-
banking sector portfolio contains more than two assets.
The interrelationships between assets in the portfolio is
constrained by a balance sheet identity. Each pair of
assets may be substitutes or complements depending on the
sign of their cross-elasticities. MOdels of this sort
are presented in Brainard and Tobin (1968), Silber (1971),
Hendershott (1977), and Mathieson (1979).

In general, following Hendershott (1977) and
Mathieson (1979), we will assume that the demand for any

financial asset takes the following form.

FAi = fi(r1,r2,...,ri,...,rn,TFA) i = l,2,...,n.
(5.1)

43

44

where FAi = quantity demanded of the igh financial asset;
r1 a yield on the ith asset;
TFA

total financial assets.

The linear form of equation (5.1) can be written as

FAi 8 a10 + ailr1 + a12r2+...+aiiri+ ...+
+ ainrn + biTFA;
i - 1, 2,...,n (5.2)

A matrix representation of the set of equations (5.2) is

FA - A0 1 + A R + B TFA
nxl nxl 1x1 nxn nxl nxl 1x1
(5.2')

Diagonal elements of A should be positive. The demand for
any financial asset should be positively related to its own
rate of return. If a particular off-diagonal element, aij’
is positive, an increase in the rate of return on asset j
increases the demand for asset i, and so the two assets are
complements. If aij is negative, an increase in the rate of

return on asset j decreases the demand for asset i, and
1

 

the two assets are substitutes.

In choosing the assets to be included in our portfolio
model, we adopt as our point of departure the framework
proposed by Mathieson (1979). Mathieson assumed the nonbank
sector portfolio contains the following assets and

liabilities:

45

 

Assets Liabilities
Currency (C) Bank Loans (L)
Demand Deposits ~ (DD)
Time Deposits (TD)
Government Securities (GS)
Foreign Assets (FA)
Real Capital (K)

In the Thai economic environment, government
securities and foreign assets are not significant items
in household portfolios (Park 1973; wattanasiritham.l978,
p. 322). Therefore, these two items will be omitted in
the following modification. Since the complementarity

hypothesis involves money, we consider
C+DD+TD = M (5.3)

Therefore, the modification of Mathieson's model

for household portfolios in Thailand will be:

Assets Liabilities

Money (M) Loans (L)
Capital (K)

The total assets (TA) for this modified portfolio
. will be :

X

TA = M+K+(_-L) = A1+A2+A3 =- 1.6.16.4)

where TA = total assets;
A1 - M - money;
A2 = K a capital;
A = (-L) = (-Loans) .2

46

The demand for (or supply of) a particular asset
(or liability) is assumed to depend, on two variables in
addition to total financial assets and yields on each asset
(equation 5.1). In Thailand, the Bank of Thailand (BOT)
has pursued the traditional goals of a central bank. It
attempts to attain internal and external stability and to
improve the financial structure at the same time. One
financial development policy BOT pursued was aimed at
mobilization of savings. BOT has encouraged commercial
banks to open branches in rural areas throughout the country
in order to attract more saving. Thus, one of our additional
variables is the number of commercial banks per capita.

Another policy goal of BOT is to increase the
allocation of credit to the rural sector. To achieve this,
BOT offers rediscount facilities for agricultural credit
at the subsidized rate of five percent, subject to the
condition that the maximum discount rate chargeable by
commercial banks and the Bank for Agriculture and Agricultu-
ral Cooperatives (BAAC) is ten percent. These facilities
are used mostly by the BAAC, but are not popular with banks
because the amount refinanced is not included in the
fulfillment of the agricultural credit target. Our other
additional variable, then, is the volume of loans and
rediscounts provided by BOT to the banking sector.

we can write these relationships in functional form

as

47

fi(r1,r2,r3,TA,Zl,Zz) (5.5)

nominal holding of asset i or liability i
(-Ai); i - 19293;

the expected real yields on assets and
liabilities held by the private sector;

total assets;

the exogenous variable j; j = 1,2.

We will assume that the demand for the financial

asset is homogenous of degree one in total financial assets.
This means, other things being equal, a given proportional
change in total assets will cause that same proportional
change in holdings of all individual financial assets.
Therefore, equation (5.5) takes the form
A1 a ailrlTA + ainZTA + a13r3TA + biTA + c1121
+ c1222 (5.6)
where aij’bi’ and cij are fixed coefficients. Specifically,
A1 = allrlTA + alzrzTA + a13r3TA + blTA + c1121
+ c1222 (5.7.1)
A2 - a21r1TA + a22r2TA + a23r3TA + b2TA + c2121
+ c2222 (5.7.2)
A3 = a31rlTA + a32r2TA + a33r3TA + b3TA + c3121
+ (5.7.3)

c3222

3

48

Mathieson (1979) imposes the following restrictions:

(1) A Change in one of the interest rates, with TA
fixed, can only change the distribution between
the three financial asset demands. Thus, the
interest rate coefficients must sum to zero
across the three portfolio equations.

3 3
1&1 aij - 0, 121 cij = O (5.8)

(2) The proportions of total assets must sum to one.
3
12-1 A1 a (b1 + b2 + b3)TA

= TA 1,3 - 1, 2, 3. (5.9)

One way of enforcing this balance sheet constraint
is to build the linear restrictions into the coefficients,
as suggested by Hendershott (1971, 1977), and estimate all
the equations together by placing one equation on top of
another. This is the so-called stacking method. (The

complete stacked equation will appear as follows:

49

A1 rlTA 0
A2 - all 0 +a21 rlTA +a31
A 0 0

Z

+ c22 22 +c32 0
0 Z2
We shall impose the following constraints:

+a +a

(812 22 32 = 0) '*322

(a13 + a23 + a33 = 0) +a33

(2) (b1+b2+b3=l) +b =

r1

(5.10)

‘a21 ’ 831
(5.11.1)

‘812 ’ 832
(5.11.2)

‘313 ‘ 823
(5.11.3)

.132
(5.11.4)

l-bl

_ (3)

(°11

50

+c +c

'0)+C

21 31 11 3 ‘°21 °31

(5.11.5)

(812 + c22 + c32 ‘ 0) * c22 ‘ ‘°12 ‘ c32

(5.11.6)

Therefore, the stacked equation with the balance sheet

constraints imposed on the coefficient becomes

 

 

 

 

 

 

 

 

-r1TA -r1TA ‘rzTA
321 r1TA + 8131 ° + 312 'rzTA
0 rlTA 0
0 r3TA 0
a32 -r2TA + a13 0 + a23 r3TA
r2TA -r3TA -r3TA
TA 0 0
b1 0 + b2 TA + (1) 0
-TA -TA TA
r ‘ r ‘ ‘ f
21) r 0 22 o W
c11 0 + c21 Z1 + c12 0 + c22 22
('21. (‘21. .‘221 ,'zz.
(5.12)
0

The coefficient of 0 is known with certainty to be one.

TA

Therefore, it is combined with the dependent variable to

give

51

 

 

 

 

 

 

 

 

 

 

 

 

 

 

A1 -r1TA -r1TA rZTA
A3-TA 0 rlTA 0

r o 1 (1:31.40 r o 1
LrZTA) L-r3TA. -r3TAJ
(TA‘ f o ‘ (21) V o 1

+-b1 0 +‘b2 TA +-cll O '+ c21 Zl
-TA -TA -Z -Z
L J L J L 11 1J
F ‘ f ‘

22 0

+ C12 0 + c22 Z2 (5.13)

L-ZZJ 1-227

 

 

 

 

The symmetry constraint is also imposed on the interest rate
coefficient in the financial asset demand equation.4 That

is,
(aAi/arj) = (aAj/ari)
Therefore, aij = aji where i # j. (5.14)

Symmetry constraints are imposed in the stacking procedure
by using interest rate spreads, instead of individual rates,
as independent variables. Rearranging the stacked equation,

we get

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

r 1 r- - 1 r- - 1
A1 (r1 r2)TA (r1 r3)TA
A2 = a12 (rl-r2)TA + a13 0
,A3-TA, L O L (r2-r3)TAJ
r 0 rm1 f o ‘
+ a23 -(r2-r3)TA 1+ b1 0 +‘b2 TA
r 1 r 1 r
21 o 22)
+ cll o + c21 21 + C12 0
- -z -
1 21. L 1. 1 7'21
r 0 ‘
;+ c22 22 (5.15)
-2
L 21
In tabular form we have
rlTA rzTA r3TA TA 21 22
A1 ‘312‘313 a12 a13 b1 c11 c12
A2 812 ‘312’323 823 b2 c21 c22
A3 813 823 ‘313‘323 1“b1'bz '°11‘°21 '°12‘°22
Z - TA 0 o o 1 o o

 

In matrix equation form we have

53

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

F
' ‘ r- - 1 - _ 1r 1
A1 (r1 r2)TA (r1 r3)TA 0
A2 = (rl-r2)TA 0 -(r2-r3)TA
(AB-TA, LL 0 , (rl-r3)TAJL (rz-r3)TAJ
) (812‘
rTAUVOWZIWOMZZWOW a13
a23
0 TA 0 Z1 0 22 1;:
"TA 'TA '2 'Z "Z -Z C11
L 1L 4L 11L 11L 211 21) CZI
c12
chz
(5.16)
or
Y = X B (5.17)
The stochastic form of equation (5.17) is
Y(3cx1) ' x(3tx9) B(9x1) + E(3tx1) (5°13)

where E = the disturbance term;

E' = (e11...e1t,e21...ezt,e31...e3t).

Our dominant interest is in the sign of 812' The complemen-
tary relationship between money and capital holds if

812 (' 321) > 0-
C. Model Estimation and Results

In Chapter Four, separate estimates of McKinnon's
model were obtained using four different definitions of

money. ‘We use those same four definitions as alternative

54

measures of the asset Al in estimating the parameters of
the stacked equation (5.18), and thus obtain four separate
sets of estimates. Also, as in Chapter Four, we obtain
separate estimates for the Bangkok area, for the rest of
the country, and for the two areas together.5

In equation (5.16) the "dependent variable" is
actually three separate variables stacked one over the
other. The average values of these three variables differ
considerably, introducing the problem of heteroscedasticity.
we use the adjustment for this problem presented in
Hendershott (1977, pp. 56-58).

Table 5.1 presents estimates of the parameters
of equation (5.15) using data for the entire kingdom,
Table 5.2 presents such estimates using data for the
Bangkok area, and Table 5.3 presents the estimates for
that part of the country outside the Bangkok area.

As can be seen, the R2 is quite respectable for
each equation for the whole kingdom, the Bangkok area, and
the area outside Bangkok models. Exceptions are equations
M1 and M2 for the whole kingdom model, which are 0.503611
and 0.330596, respectively. The Durbin-Watson ratios for
the area outside of Bangkok are not far from two, while for
the whole kingdom they range from 0.98969 to 2.98265; and
for the Bangkok area they range from 0.8867 to 1.6273.

The elasticity of each financial asset with respect
to each yield is shown in Table 5.1.1 for the whole

kingdom, Table 5.2.1 for the Bangkok area, and Table 5.3.1

 

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61

for the area outside Bangkok. In general, the elasticities

are calculated as

nRj,Ai = (aAi/aRjMRj/Ai) = (paij.TAk)(Rj/Ai)6

where i,j = 1,2,3;
k = 0,1,2,3;
the barred values refer to sample means;

TAk - Mk + K‘+ (-L) = A1 + A2 + A3.

Of greatest interest to us is the estimated sign
of the coefficient relating the real return on capital to
the demand for real balances, a12’ since, as mentioned
earlier, it constitutes a direct test of the complementarity
hypothesis. As shown in tables 5.1, 5.2, and 5.3, all
twelve -- three regions times four definitions of real
balances -- of our estimates of this coefficient are
positive. In many cases, the t ratios approach or exceed
a value of two. These estimates providerather strong
support for the complementarity hypothesis.

Admittedly, our estimates of the elasticities of
the demand for real balances with respect to the rate of
return on capital, and of the demand for capital with
respect to the real deposit rate7, shown in tables 5.1.1,
5.2.1, and 5.3.1, are very small. The former range only
from .002 to .03 and the latter from .0004 to .003. This
seems, however, to be a standard outcome of imposing the
linear homogeneity condition on the system of equations

(5.5). Similarly low estimates of elasticities have been

62

obtained by authors who applied U.S. data to the system of
equations (5.6).8 Our low elasticity estimates notwith—
standing, therefore, we conclude that the positive, often
significant, estimates of 3M/8R2.TA, in tables 5.1, 5.2,
and 5.3, do provide notable support for the complementarity
hypothesis.

Turning to our estimates of the own-elasticity of the
demand for money, it must first be noted that only M0 is
an individual asset. M1,M2, and M3 are aggregations of
several assets, each of which, in principle, has its own
rate of return. Strictly speaking, therefore, the own-
elasticity of demand for M2, for example, measures the
percentage change in quantity demanded of M2 caused by a one
percent change in an appropriately weighted index of the
three rates of return on the three assets that comprise M2.
Since only data on the rate of return on one—year time
deposits were available to us, we could not construct and
use such indexes. Rather, we have used the real rate of
return on one-year time deposits as "the" return on money
for all our definitions. Thus, the partial derivatives in
the first row and first column of each panel of tables 5.1,
5.2, and 5.3 and the elasticities in the first row of
tables 5.1.1, 5.2.1, and 5.3.1 are not true ggnrpartial
derivatives and ggnfelasticities, respectively.

This is most apparent in considering the relation
between M0 and/or M1 and the rate of return on one year

time deposits. We expect a true own-elasticity to be

63

positive. We also expect an increase in the rate of
return on one-year time deposits to decrease the demand for
both currency and demand deposits, and we do, in fact, obtain
this result. However, the failure of our estimates of the
partial derivatives to achieve reasonable significance
levels is disappointing. In contrast, we have no §_priori
expectation on the signs of the partial derivatives and
elasticities of M2 and M3 with respect to the rate of
return on one-year time deposits. We expect an increase in
that rate to decrease the demand for same of the assets
(currency and demand deposits) comprising these aggregates
and to increase the demand for one of the other assets (time
deposits). The effect on the demand for the remaining asset
(savings deposits) depends on whether or not its rate of
return (for changes in which we have not been able to control)
is held constant. Our actual result, an average of these
conflicting expected effects, is that for Bangkok and the
entire kingdom.an increase in the rate of return on one—
year time deposits lowers the demand for M2 and raises the
demand for M3. For the region outside Bangkok, an increase
lowers the demand for both assets. In no case are the
estimates different from zero at a level of reasonable
significance.

We next must note that the negative signs of our
estimates of the partial derivative of the demand for
capital with respect to its own rate of return are clearly

at variance with our expectation. One reason for this

64

may be our implicit assumption that the observed level of
capital is the desired level. One of the basic themes in
empirical work on investment functions is that investment
is a process of adjusting the actual capital stock to its
desired level, and that the time required for this adjustment
may be very long. If the period exceeds a year, then even
with annual data it will not be appropriate to relate
observed levels of capital to contemporaneous rates of
return on capital. A second reason may be that our data,
both on the quantity of capital and on its rate of return,
are extremely rough.

The signs of our estimates of the partial derivatives
of the demand for loans with respect to its own interest
rate vary. They are negative for the whole kingdom and
for Bangkok and, therefore, not in accordance with our
expectation. They are positive, but not significantly
different from zero for the area outside Bangkok. This
latter result perhaps confirms the appropriateness of our
implicit assumption that, outside Bangkok, rural investment
projects are largely limited to self-finance.

we conclude this discussion of our estimates of
the coefficients aij by reiterating our major finding: The
always positive, often significant, estimates of the
coefficient 812 constitute reasonably strong support for
the complementarity hypothesis.

Turning next to our estimates of the coefficients

b.

1, we find that for all three regions the proportion of a'

65

given increase in total assets, held in the form of real
balances, increases as we broaden the definition of money.
Nevertheless, for the whole kingdom and for Bangkok these
proportions are less than 10 percent for MO,M., and M2.
For these three assets they are between 15 and 30 percent
for the region outside Bangkok. These proportions rise in
varying degrees when M3 is the definition of money. The
proportion of a given increase in total assets taking the
form of capital generally ranges from 88 to 118 percent.9
For each region and definition of money, of course, the
proportion of a given increase in total assets held in the
form of loans equals the sum of the proportions held as
money and capital minus one. This amounts to between 15
and 20 percent for the whole kingdom and for Bangkok, and
to about 4 percent for the region outside Bangkok.

We expect an increase in the number of commercial
bank branches per capita to increase all three balance
sheet items - money, capital, and loans. In general, these
expectations are not borne out. The only assets that rise
in response to an increase in the per capita number of
bank branches are Mb, M1, and M2 for the whole kingdom and
the Bangkok area, and capital for the region outside
Bangkok.

Finally, we expect an increase in borrowing from
the Bank of Thailand to increase the quantity of bank loans

outstanding. This expectation is borne out in every case.

66

D. Summa Z.

The results of the portfolio model testing exhibited
some expected and some unexpected signs. But the importance
of the tests is in the supporting evidence they provide for
the complementarity hypothesis for the whole kingdom,

Bangkok, and the area outside Bangkok.

CHAPTER VI

TRANSLOG PRODUCTION FUNCTION MODEL

A. Introduction

 

In the preceding two chapters, tests of the
complementarity relationship between money and capital in
the Thai economy were conducted using MbKinnon's two-equation
model and a portfolio model. In this chqpter, we will
demonstrate that real cash balances can also be considered
factors of production, as are capital and labor. Then we
‘will develop a model to test the complementarity hypothesis
'by estimating the parameters of a translog production

function.

B. Theoretical Framework

 

The Role of Money in the Production Function

 

In the past, economic models seldom included cash
balances or money as a productive physical input. Labor
must be hired, capital services rented, and factors combined
at various physical locations so that production can occur.
In the barter system, production could conceivably take

place without money, and the removal of a unit of any other

67

68

factor would immediately reduce the product.

A number of authors discuss the role of real cash
balances in production.1 Most, in essence, regard money
as "working capital". Thus real money balances can be
considered just like any other inventory which enters into

2

the productive process. On this basis, they implicitly

or explicitly insert real balances as a third factor in

the production function, along with capital and labor.3
Y = f(L,K,M/P) (6.1)
where Y = real output of goods and services;

L a labor input;
K = divisible physical capital;
(M/ P)

real cash balances.

The results of a number of attempts to estimate
the parameters of such a function using U.S. aggregate data
have been published. Nadiri (1969) obtained a demand
function for real balances by minimizing a cost function
that includes real balances, subject to the production
function (6.1). Assuming the variables entered this demand
function in multiplicative fashion, he estimated its
parameters. His results indicated that there are substantial
economies of scale with respect to holdings of real cash
balances and that money and capital are substitutes. Sinai
and Stokes (1972) used the Cobb-Douglas production function
in their estimation. Their results indicated that real

money balances, however defined, are of substantial

69

importance when added to the standard Cobb-Douglas production
function.

Dennis and Smith (1978) included real balances as one
of four factors in a translog cost function. For each of
eleven U.S. manufacturing industries, they tested whether
the underlying production function displays separability
with respect to the factors of production. (This involves
testingeajoint null hypothesis that certain parameters of
the translog cost function are all equal to zero.)' For all
industries the null hypothesis of absence of separability
was rejected at the five percent level, indicating that
"real cash balances must be treated as an individual input
to the production process of each of these 11 industries"
(p. 803). In addition, for each industry, they used their
estimates of the parameters of the translog cost function
to calculate both Allen partial elasticities of substitution
between all pairs of inputs and the elasticity of demand for

4 The

real cash balances with respect to each input price.
results provide almost uniform support for the notion that
money and capital are substitutes. Estimates of the partial
elasticity of substitution between money and capital, and of
the demand for real balances with respect to the price of
capital, are positive for all but one of the eleven indus«
tries.

Subrahmanyam (1980) applied Dennis and.Smith's methods

to a three-variable translog cost function using aggregate

U.S. data for the 1946 to 1967 period. He also obtained

70

positive estimates of the partial elasticity of substitution
between capital and money, and of the elasticity of demand
for money with respect to the cost of a unit of capital
services.

These empirical studies both support the procedure
of entering real balances as a factor in the production
function, and the notion that money and capital are substi-

tutes in production, in the U.S. economy.

Self-Finance Investment and Money in the ProductiOn FunCtion

 

In this section, we show why it is natural to include
money as a factor in the production function in economies
in which investment is largely limited to self-finance.
Let the production function that describes the transformation
of a set of inputs into output for the Thai economy be

written as

Y = f(Lt’Kt) (6.2)

where Y output;
L - labor output;
K - capital input;

t = indicate the time period t.

As discussed in Chapter Three, the capital market in
Thailand has had a highly limited role in mobilizing savings
and bridging the gap between investors and savers. Invest-

ment projects in Thailand depend to a major extent on

71

self-finance, which means that to acquire additional capital
a firm has to accumulate or "build up" cash balances from
the prior period. This process is also recognized by Gabor
and Pearce (1958, p. 544).

Therefore, the following capital function can be

written

K = Kt(K (6.3)

t t-1’Mt-1)

According to equation (6.3) the amount of capital
in period t will depend on the amount of capital, and on
the build-up in cash balances, in period t—l. We substitute
equation (6.3) in (6.2) to get

Yt = fELt,Kt(Kt_l,Mt_1)] (6.4)

We will assume that the production structure is
weakly separable into the inputs Lt and Kt (Humphrey and
Moroney 1975, p. 63; Fuss 1977, p. 90; Denny and Fuss
1977, p. 408, and Grant 1977, Chapter 1.3). This means the
marginal rate of substitution between Lt and Kt is indepen-

dent of the quantities of Kt-l and M. demanded. Therefore,

t-l
the weakly separable production function allows us to

write equation (6.4) as

Yt - f(Lt,Kt_1,Mt_l) (6.5)

Therefore, the production function (6.5) has Mt-l
as an input factor as well as Lt and Kt-l' This function

states that because of the self-finance investment

72

environment, firms must accumulate their own cash balances

to finance investment projects. In this situation, the
production function depends on cash accumulation as well as
on capital and labor. Since cash balances are viewed as

a financial conduit through which accumulation takes place.
the demand for money increases with the demand for physical
capital. This is a reflection of the complementary relation-
ship between money and capital. Equation (6.5) will be used
in this study as the aggregate production function for the
whole kingdom, the Bangkok area, and the area outside

Bangkok.

The Translongroduction Function

Several forms of the production function are widely
employed as tools of econometric research. These include
the input-output (I-O) production function, the Cobb-Douglas
(C-D) production function, the constant elasticity of
substitution (CES) production function, and the translog
pro duct ion function .

For purposes of empirically measuring substitution
relationships between inputs, the translog function is the
least restrictive. The other functions force the elasticity
of substitution to take on a value of one, or at least, a
constant value. In contrast, in the translog function the
elasticity of substitution can vary along an isoquant (as
it normally does). Since our interest is, indeed, in

measuring substitution relationships - specifically, whether

73

money and capital are substitutes or complements — we use
the translog function for this purpose.

Our strategy is to obtain estimates of the parameters
of the translog function. These, in turn, are used to
derive estimates of the Allen partial elasticity of
substitution (AES) between each pair of inputs. The AES
between factors i and j measures the effect on the quantity
of factor i due to a change in the price of factor j, holding
output and other input prices constant. The two factors are
substitutes in production if this elasticity is positive
and are complements if it is negative.

Our main interest is in deriving an estimate of the
AES between money and capital. A negative estimate would
indicate that the two factors are complements in production
and would, thus, support the complementarity hypothesis. A
positive estimate would be evidence against the hypothesis.

Recall the production function introduced in equation

(6.5).

Yt - f(Lt’Kt-1’Mt-l) (6.5)
or

Yt - f(X1,X2,X3) (6.6)
where Yt = output in period t;

X1 - Lt - labor in period t;

X2 - Kt-l - the capital from period tel;

X3 = Mt-l = the build-up cash balances from period

t-l.

74
Taking logarithms of function (6.6) we get

lnY = q(lnX1,lnX2,lnX (6.7)

t 3)

The translog function is a specific form of equation (6.7),

3 3

3 .
lnY = 1na + 2 a lnX. + (1/2) E b. 1nX lnX
t 0 i=1' i 1 i=1 3’1 ij i j

= lna0 + allnXl + azlnx2 + a31nX3

+ (1/2)(b111nX 1nX + blzlnxllnx2

l l

+ bl3lnX11nX3

+ b211nX21nX + bzzlnlenX2

1

+ib231nX21nX3

+ bBllnXBlnX1 + b321nX3lnX2

+ b 1nX lnX

33 3 3) (6'8)

where a0 = the constant term representing the state of
technological knowledge;
a. bij = the coefficients representing the technologi-
cally determined production parameters.
It is assumed that the production function (6.8) is

linear homogeneous (exhibits constant return to scale),

which imposes the following parameter restrictions.

8 1 . (6.9)

b . = 0 (6.10)

75

bij = 0 (6.11)

bij

II
C)

i,j = 1,2,3. (6.12)

L]. M LJOM

2

The function (6.8) is further assumed to satisfy the

symmetry restriction

bij = bji i,j = 1,2,3. (6.13)

The definition of the output elasticity of input 1, Ei’ is

E. = (alnYt/alnxi)

1 (aYt/axi) (Xi/Yr)

= fi'(xi/Yt) (6.14)
By taking the partial derivatives of (6.8) we also obtain

E. = (alnYt/alnxi) = a. + f b .

1 (6.15)

Combining (6.14) and (6.15) we find that the marginal product
of X1, fi’ is given by

fi = (Yt/xi)(ai + jgl bijlnxj ) (6.16)
The direct second-order derivative for X. is
fii = (Y t:/xi)[bii+ (ai + £1 bij1nxj-1)
(a a1 + jil bijlnxj.)1 (5.17)

The cross-partial derivative with respect to xk is

76
3 .
fki = (Yt/kaixbki + (ak + 3.21 bkjlnxj)

3
(a1 + jzl bijlan)] (6.18)

where i,j,k - 1,2,3.

Assuming that inputs and product markets are
competitive (the relaxation of or derivation from this
assumption will be discussed in the regression model section),
the necessary condition for profit maximization or minimiza-

tion of loss is

fi = pi i = 1,2,3. (6.19)

where pi is the factor price of the input i.5

Condition (6.19) implies that the output elasticity

of each factor equals its share of total output, Si'

Si ' (pixi/Yt) "" (fixi/Yt) " Ei

lnXj

The estimation of equation (6.20), which will be

3
= a1 + jzl bij

(6.20)
performed in the regression model section, will give the
estimated values of the production function parameters in
(6.8). This will allow us to compute estimates of f1, fii
and fki’ respectively. These, in turn, are used to derive
estimates of the Allen partial elasticity of substitution

between any two factors 1 and j, Oij’ as follows:

3 -

77

where IFI is the determinant of the bordered Hessian matrix

f
f

[o f
f

1 2

11 12
'F' ‘ f2 f21 f22 f23

f

 

 

f

31 32

and [Fijl is the cofactor of the i,j, element, fij’ of |F|.
To repeat the point made at the beginning of this

section, our main interest is in 023, the Allen partial

elasticity of substitution between money and capital.

A negative estimate of 023 would imply that these two

factors are complementary in production and would support

the complementarity hypothesis. A positive estimate would

be evidence against the hypothesis.

C. Regression Model

 

We estimate the parameters of equation (6.8) by
using the stochastic version of the distributive shares
equation (6.20). Accordingly, the system of cost share;

equations for this translog production function can be

written as follows.6

S1 = a1+b111nX1-l-b121nX2+bl31nX3-l-u1 (6.22.a)

+b lnx +b221nx2+b lnX +u (6.22.b)

S2 82 21 1 23 3 2

S3 = a34-b311nX14-b321nX24-b331nX34-u3 (6.22.c)

78

Imposing the linear homogeneity restrictions, a
system of any n equations of the above type is a singular
system.7 However, parameters of the kth equation can be
expressed in terms of the parameters in the remaining k-l
equations. Hence, a nonsingular set of share equations

would be

S1 = a1 + g bijln(Xi/xk) + ui (6.23)

where k is the index of the deleted equation, and i and j
are not equal to k.

From the estimated parameters of any two equations
in (6.22), using version (6.23), together with the
assumption of linear homogeneity and the symmetry restric-
tions, we will be able to identify exactly all parameters

of the production function (6.8).

Case I: If we choose to estimate equations (6.22.a) and
(6.22.b), then the nonsingular set of share

equations (6.22) would appear as follows.
S1 = a1 + b111n(Xl/X3) + b121n(X2/X3) + 111 (6.24)
82 = a2 + b211n(X1/X3) + b221n(X2/X3) + u2 (6.25)

The remaining parameters are determined from the
linear homogeneity condition and the symmetry restriction

using

79

a3 = 1-(a1 + a2) b13 - -(611 + 612)
b23 ‘ ‘(b21 + bzz) b31 ‘ b13
b32 ' b23 b33 ‘ ‘(b31 + b32)

Case II: If we choose to estimate the equations (6.22.a)
and (6.22.c), then the nonsingular set of share

equations (6.22) would appear as follows:
S1 = a1 + b111n(X1/X2) + b131n(X3/X2) + 111 (6.26)
S3 = a3 + b3lln(X1/X2) + b33ln(X3/X2) + 113 (6.27)

The remaining parameters are determined as follows:

b21 ’ b12 b32 ‘ '(b31 + b33)
b23 ‘ b32 b22 ‘ '(b21 + b23)

Case III: If we choose to estimate the equations (6.22.b)
and (6.22.c), then the nonsingular set of share

equations (6.22) would appear as follows:
82 = a2 + b221n(X2/X1) + b23ln(X3/Xl) + 112 (6.28)
83 = a3 + b231n(X2/X1) + b331n(X3/X1) + 113 (6.29)

The remaining parameters are determined as follows:

80

a1 = 1-(a2 + a3) b21 = -(b22 + b23)
b31 ‘(b32 + b33) b12 ‘ b21
b13 ‘ b31 b11 ’ '(b12 + b13)

For each system of the share equations (either in
Case I, Case II, or Case III), the disturbances are likely
to be correlated across equations. Random deviations from
profit maximization are likely to affect all input
quantities (Lt' Kt-l’ and Mt-l)‘ Hence, the two-stage
estimation procedure suggested by Zellner (1962), which is
known as Zellner efficient estimation or ZEF, will yield
efficient parameter estimates. However, the estimates
obtained by ZEF estimation depend on which two equations
in the system equation (6.22), that is, Case I, Case II, or
Case III, are chosen.

A.maximum likelihood procedure would provide para-
meter estimates that are independent of which equations
were selected. In a series of Monte Carlo experiments,
Kmenta and Gilbert (1968) found that maximum likelihood (ML)
and iterated Zellner efficient estimation (IZEF) led to
identical estimates in all samples.8 Therefore, in this
study parameters will be estimated using the IZEF method.
Parameters of all three cases will be estimated in order to
determine whether the results are identical, as suggested by
Kmenta and Gilbert (1968). In addition, the symmetry
restriction, (6.13), will be imposed in the estimation of

81

each case.

From the estimated parameters a1 and bij (i,j-=l,2,3),
and the level of input services, we will proceed to calculate
the value of the first derivative, f1, and second derivative,
fij‘ Equations (6.16), (6.17), and (6.18) indicate that
the values of f1 and fij’ and therefore the numerical values
of IF] and [Fijl’ generally vary with the levels of input
usage. Therefore, we will present point estimates of these

partial derivatives evaluated at the sample means.

D. Model Estimation and Results

 

As was the case for the models in Chapters Four and
Five, we estimate the parameters of equations (6.20), using
four alternative definitions of money and three alternative
regions. Variables and sources of data are explained in
Appendix B.

Our estimation of the parameters of the three pairs
of equations (6.24) through (6.29) will proceed in two
stages. The purpose of the first stage is to find the
starting points for the parameters that will be estimated
using IZEF estimation in the second stage. The estimation
in the first stage is obtained by stacking the selected two
equations into a single matrix equation in order to enforce
the symmetry constraint. The single equation that represents
the stacking of equations (6.24) and (6.25) is given in
Table 6.1. The second stacked equation in Table 6.1

represents the stacking of equations (6.26) and (6.27), and

82

TABLE 6.1

THE SINGLE STACKED EQUATION VERSION
FOR THE FIRST STAGE

 

 

 

 

 

Case I:
r 81 1
S1 = l ln(X1/X3) ln(X2/X3) 0 0 b11
b12
82 0 0 ln(Xl/X3) l ln(X2/X3) a2
L - b22J
Case II:
Hal
S1 1 ln(X1/X2) ln(X3/X2) 0 0 b11
= b13
83 0 0 ln(X1/X2) l ln(X3/X2) g3
33
Case III:
32
83
S3 0 0 ln(X2/Xl) 1 ln(X3/X1) b33

 

83

the third stacked equation represents the stacking of
equations (6.28) and (6.29). In the first stage, each of
the three stacked equations in Table 6.1 will be estimated
by the ordinary least squares procedure using each of the
four different definitions of real money balances (M0, M1'
M2, and M3).

The purpose of the second stage is to estimate the
system of share equations in Case I, Case II, and Case III
by IZEF estimation. The estimates obtained in the first
stage will be provided as the starting estimates for the
respective parameters. From the estimated parameters
obtained by IZEF estimation, together with the assumption
of linear homogeneity and the symmetry restrictions, we
will be able to identify each of the remaining parameters
of the production function.9

we turn now to a discussion of our empirical

results.10

The results of ordinary least squares estimation
of the first stage single stacked equation are presented in
Table 6.2.a, Table 6.2.b, and Table 6.2.c for the whole
kingdom, the Bangkok area, and the area outside Bangkok,
respectively. The IZEF estimates of the system of cost-
share equations for each case and for each definition of
money are presented in Tables 6.3.a, 6.3.b, and 6.3.c.

Using the estimated parameters implied by the restrictions
bij
for each definition of money and for each system of share

- bji (ifj) and constant return to scale, we compute,

equations, estimates of the elements of F and of

84

TABLE 6.2.a

THE RESULTS OF THE SINGLE STACKED EQUATION VERSION

FOR THE WHOLE KINGDOM MODEL

 

 

$12 $13 823
MO al - 0. 685732 a1 - 0.672902 a2 - 0. 136944
bll - -0 . 02114754 bll - -0. 025076 b22 ' 0.0254962
b12 - -0 . 00526437 b13 - 0 . 0302761 b23 - -0 . 0154844
a2 - 0. 152075 33 - 0.17816 a3 - 0.202509
b22 - 0 . 0260015 b33 - -0 . 00836374 b33 - -0 . 0272734
Ml a1 =- 0.612701 a1 - 0.561393 3‘2 - 0.146627
bll -' -0 . 0282298 bll - -0 . 0411283 b22 - 0. 0328612
b12 - 0 . 00681251 b13 - 0 . 0343619 b23 - -0 .30283236
612 - 0.193402 a3 - 0.253029 a3 =- 0.341458
b22 - 0 . 0322638 b33 = 0 . 00766542 b33 - -0 . 0369796
M2 a1 - 0.596941 a1 - 0.579157 32 - 0. 113311
bll - -0 . 0367337 bll -0 . 0382284 b22 - 0 . 0418927
b12- -0.00267385 b13= 0.0360773 b23= -0.0335985
a2 - 0.138713 a3 = 0.281557 a3 = 0.315515
b22 - 0 . 0409812 b33 - 0. 0150948 b33 =- -0 . 0209457
M3 al -' 0. 651443 a1 = 0. 748807 a2 - -0.177049
bll -0 . 0263069 b11 - -0 . 0199404 b22 =- 0 . 107283
b12- -0.0208215 b13- 0.0789833 b23- -0.576421
a2 - 0. 174659 _ a3 - 0.57407 a3 - 0.448146
1322 - -0. 0148643 b33 = 0 . 0268697 b33 - -0. 126603

TABLE 6.2.b

85

THE RESULTS OF THE SINGLE STACKED EQUATION VERSION
FOR THE BANGKOK MODEL

 

 

Case I Case II Case III
S12 S13 S23
MO a1 0.989252 a1 - 0.798728 a2 0.049441
b11 0.0409344 b11 - 0.00505939 b22 0.0322156
b12 -0.00960811 b13 = 0.00527472 b23 -0.0130767
a2 0.110404 a3 - 0.101845 a3 0.32314
b22 0.0292110 b33 = 0.0157881 b33 -0.0381665
Ml a1 0.809537 al - 0.64765 a2 0.0633226
b11 0.0107228 b11 - -0.0166255 b22 0.0385314
b12 -0.00393773 b13 - 0.0202012 b23 -0.0236755
a2 0.138871 a3 - 0.221184 a3 0.420267
b22 0.0343858 b33 = 0.0142125 b33 -0.0353451
M2 a1 0.753779 a1 = 0.655693 a2 0.0371467
b11 0.000802818 b11 = -0.015l655 b22 0.0417640
b12 -0.00515532 b13 - 0.0193270 b23 -0.0235896
a2 0.120967 a3 - 0.230138 a3 0.39843
b22 0.0394919 b33 = 0.0208405 b33 -0.0311896
M3 a1 0.701927 a1 = 0.669673 a2 -0.279l47
bll -0.0157l49 b11 = -0.0l97310 b22 0.138891
b12 -0.0364421 b13 = 0.0533305 b23 -0.09989
a2 -0.103673 a3 = 0.718158 a3 0.585656
b22 0.0592025 b33 = 0.124579 b33 - 0.0431316

TABLE 6.2.c

THE RESULTS OF THE SINGLE
FOR THE OUTSIDE

86

STACKED EQUATION VERSION
BANGKOK MODEL

 

 

 

S12 13 23
MD a1 0.874875 81 = 1.09161 82 -0 123289
bll -0.0453486 b11 = 0.0100199 b22 0 115045
b12 -0.0885094 b13 8 0.11854 b23 -0.0818187
a2 -0.434384 83 - 0.444707 33 0.41334
b22 0.198845 b33 8 -00044657 b33 -0.0160833
M1 31 0.636691 a1 = 0.957238 a2 -0.0230622
b11 -0.114156 bll 3 -0.0277422 b22 0.0889068
b12 -0.0946425 b13 3 0.169066 b23 0.0634954
32 -0.449545 a3 = 0.515905 a3 0.478408
b22 0.223466 b33 = -0.l4735 b33 -0.0656372
M2 a1 0.804947 31 = 1.04987 32 -0.100393
bll -0.0492568 b11 ' 0.0100207 b22 0.111675
b12 -0.109622 b13 = 0.143919 b23 -0.0668778
32 -0.441629 33 3 0.535365 a3 0.472135
b22 0.208876 b33 3 -0.0821146 b33 -0.0534495
M3 a1 1.09523 a1 = 1.47391 a2 -0.124994
b11 0.0383365 bll = 0.122357 b22 0.940666
blz -0018483 b13 = 0.145934 b23 -000254522
a2 -0.673853 a3 = 0.568065 a3 0.437574
b22 0.239933 b33 = -0.101133 b33 -0.0894245

87

TABLE 6.3.a

THE RESULTS OF THE IZEF ESTIMATIONS FOR
THE WHOLE KINGDOM
(The Numbers in Parentheses are t-Statistics)

 

 

ffi i t
Coe c en M0 M1 M2 M3
Case I: a 0.669834 0.576896 0.590467 0.634757
(7.10139) (3.77648) (4.98659) (4. 85891)
b11 -0.0268206 -0.0378472 -0.0377454 -0.0273312
(-0.958884) (-0.881839) {-1.10909) (-1.13083)
b12 -0.00620949 0.00581611 -0.0017194 -0.0140886
(-0.36795) (0.285418) (-0.0622008) (-0.433217)
a2 0.146301 0.185253 0.137253 0.264998
(1.63859) (1.95943) (1.34907) (0.733297)
b22 0.0268133 0.0339023 0.0432253 -0.04807
(1.51767) (1.66901) (1.30481) (-0.385099)
Case II: a1 0.669834 0.576833 0.590468 0.634748
(7.10136) (3.77568) (4.98715) (4.85904)
b11 -0.0268207 -0.0378687 -0.0377424 -0.0273319
{-0.958886) (-0.882331) {-1.1091) (-l.l309)
b13 0.0330302 0.0320614 0.0394573 0.0414172
(0.888035) (0.575012) (0.726991) (1.035564)
a3 0.183865 0.237948 0.272268 0.100215
(1.92497) (1.29506) (1.76307) (0.329791)
b33 -0.0124265 0.00764774 0.00205655 -0.103586
(-0.228291) (0.0981813) (0.0205731) (-l.148)
Case III: a1 0.146301 0.185219 0.137236 0.26504
(1.63859) (1.9589) (1.34898) (0.733414)
b22 0.0268132 0.0339017 0.0432217 -0.0480843
(1.5177) (1.66935) (1.30487) {-0.385214)
b23 -0.0206035 -0.0397089 -0.0414959 0.0621695
(-0.974008) (-l.35145) {-0.788076) (0.633111)
a3 0.183866 0.237947 0.272305 0.100213
(1.92499) (1.29503) (1.7632) (0.329786)
b33 -0.0124274 0.00764765 0.00201924 -0.103587

(-0.228308)

(0.0981785)

(0.0201998)

(-1.14800)

88

TABLE 6.3.b

THE RESULTS OF THE IZEF ESTIMATIONS FOR
THE BANGKOK AREA
(The Numbers in Parentheses are t-Statistics)

 

 

Coefficient M0 M1 M2 M3
Case I: a1 0.732876 0.676414 0.687828 0.713797
(5.24377) (3.87104) (4.31468) (5.90253)
b11 -0.00831116 -0.0119295 -0.00984545 -0.0142152
(-0.334885) {-0.395964) (-0.345839) {-0.715687)
b12 -0.0121981 -0.00399214 -0.00428604 -0.0374162)
(-l.19793) {-0.340131) {-0.293224) (-2.343312)
a2 0.0876955 0.130661 0.117347 0.00311151
(0.982673) (1.42897) (1.16092) (0.0152625)
b22 0.0319255 0.0372768 0.0428394 0.00228016
(2.60772) (2.60084) (2.55428) (0.0256266)
Case II: a1 0.733331 0.677353 0.688278 0.713782
(5.24984) (3.87932) (4.32017) (5.90074)
b11 -0.00821718 -0.ll7499 -0.00975078 -0.0142185
(-0.331182) (-0.390172) {-0.342634) (-0.715837)
b13 0.0203997 0.0156989 0.0139927 0.0516381
(0.780434) (0.459940) (0.381589) (1.69122)
a3 0.178879 0.1917 0.194113 0.283384
(1.32395) (1.00797) (1.00427) (1.14905)
b33 -0.000660014 0.0176172 0.0246057 -0.0866493
(-0.0224476) (0.422091) (0.47495) (-0.860056)
Case III: al 0.0877404 0.130873 0.117435 0.00319121
(0.983461) (1.43272) (1.16189) (0.0156533)
b22 0.0319239 0.0372683 0.0428412 0.00224336
(2.60783) (2.59838) (2.55335) (0.025213)
b23 -0.0197332 -0.0333082 -0.0385706 0.0351719
(-2.56270) (-2.26382) {-1.80549) (0.387306)
a3 0.179168 0.192020 0.194612 0.283008
(1.32616) (1.00966) (1.00696) (1.14737)
b33 -0.000724196 0.0175512 0.0244827 -0.0868014
(-0.0246314) (0.420544) (0.472689) {-0.861352)

89

TABLE 6.3.c

THE RESULTS OF THE IZEF ESTIMATIONS FOR
THE OUTSIDE BANGKOK
(The Numbers in Parentheses are t-Statistics)

 

 

Coefficient Mb M1 M2 M3
a1 0.807626 0.501339 0.686676 0.872711
(7.59279) (3.07468) (5.42181) (3.98276)
b11 -0.0587208 -0.l38606 -0.0742113 -0.00960263
(-2.12843) {-2.81269) (-1.98871) (-0.l62825)
b12 -0.0719412 -0.0558635 -0.0809102 -0.129371
(-2.9l36) {-1.66369) (0.0258267) (-4.3924)
a2 -0.363769 -0.296231 -0.31951 -0.420406
(-3.09994) (-l.92755) (-2.75832) (-3.24584)
b22 0.184196 0.197097 0.185031 0.180601
(6.04251) (4.36792) (6.09489) (5.90175)
Case II: a1 0.807380 0.501168 0.686763 0.872715
(7.58889) (3.07065) (5.42374) (3.98282)
b11 -0.0587625 -0.138599 -0.0741956 -0.0096017
(-2.12899) {-2.81047) (-1.98885) (-0.16281l)
b13 0.130636 0.194354 0.155132 0.138974
(5.61214) (3.78934) (3.8067) (2.01761)
a3 0.556058 0.79442 0.632873 0.547696
(8.50175) (5.37557) (5.64725) (2.24162)
b33 -0.0183916 -0.0532079 -0.0510055 -0.0877439
7 {-0.58841) (0.792055) (-0.948129) (-1.01084)
Case 111: a2 -0.360452 -0.293417 -0.31912 -0.420373
(~3.07200) (-l.90893) {-2.755) (-3.24564)
b22- 0.183406 0.19633 0.184933 0.180593
'(6.0237) (4.35405) (6.0233) (5.90149)
b23 -0.112149 -0.141000 -0.104103 -0.512287
{-6.02158) (-3.84537) {-5.05145) (-2.52418)
a3 0.555291 0.793249 0.632709 0.547688
(8.46279) (5.35679) (5.63934) (2.24148)
b33 -0.0182471 -0.0530227 -0.0509863 -0.0877436
{-0.584993) (-0.790457) (-0.948124) (-l.01085)

90

IF12|, IF13l, and IFZBI. Using equation (6.21), we then
calculate estimates of Allen partial elasticities of
substitution, 012, 013, and 023, which are given in Tables
6.4.a, 6.4.b, and 6.4.c.11

In examining Tables 6.3.a, 6.3.b, and 6.3.c, we
first note that our results are in agreement with those of
Kmenta and Gilbert (1968). In each table, the two estimates
of each parameter a1 and bii’ obtained from estimating two
different cases, are very close. we also note that
although estimates having t ratios with values well below
two abound in tables 6.3.a and 6.3.b, in view of the
complicated relation (b) in footnote 11, it does not
automatically follow that the elasticity estimates in
tables 6.4.a and 6.4.b are similarly subject to large
standard errors.

Turning to a discussion of these elasticity estimates,
the most important results in tables 6.4.a, 6.4.b, and
6.4.c concern the sign of our estimates of OKM‘ The results
strongly support the complementarity hypothesis. For the
area outside Bangkok, our estimates of this parameter have
negative signs no matter which definition of money is used.
For the whole kingdom and the Bangkok area, our estimates
have negative signs except when money is defined as
consisting only of currency. According to these estimates,
money and capital are complements in production.

All point estimates of °LK are positive for the

Bangkok area and negative for the area outside Bangkok.

TABLE 6.4.8.

91

THE ALLEN PARTIAL ELASTICITIES OF SUBSTITUTION (01 j)
FOR THE WHOLE KINGDOM MODEL

 

 

oLK °LM UKM
Msc $12 A 1.42619 -3.12281 10.0251
313 1.42619 -3.12276 10.0250
523 1.42620 -3.12289 10.0250
MbC+DD s12 0.176413 5.18979 -19.0563
313 0.173019 5.20914 ~19.1237
323 0.172994 5.20931 -19.1245
MéC+DD+SD 312 -0 664479 9.04313 -32.l708
$13 -0.660374 9.02163 ~32.0957
$23 -O.670188 9.07285 -32 2740
MeC+DD+SD¥TD $12 0.914136 0.266453 -1.89373
$13 0.914117 0.266527 -1.89396
$23 0.914111 0.266503 -1.89405

TABLE 6.4.b

92

THE ALLEN PARTIAL ELASTICITIES OF SUBSTITUTION (0
FOR THE BANGKOK MODEL

ij)

 

 

OLK OLM OKM
MO-C 812 13.4599 -137.837 430.925
313 22.6501 -240.716 753.609
823 16.6074 -l73.071 541.428
M1=C+DD 812 0.807112 2.40990 -8.87583
$13 0.812249 2.37373 -8.76297
823 0.810928 2.38301 -8.79179
M2=C+DD+SD 812 0.864864 1.88025 -7.15077
$13 0.867032 1.86599 -7.10617
S23 0.865551 1.87561 -7.13594
M3=C+DD+SD+TD S12 1.05253 -0.0701509 -1.11925
S13 1.05289 -0.0717305 -1.11457
$23 1.05243 -0.0696926 —1.12057

93
TABLE 6.4.c
THE ALLEN PARTIAL ELASTICITIES OF

SUBSTITUTION (oij)

 

 

FOR THE OUTSIDE BANGKOK MODEL
.OLK oLM °KM
Nee $12 -0.184088 1.50921 -7 17032
$13 -0.183999 1.50957 -7.17170
$23 -o.183227 1.51254 -7.18427
MeC+DD S12 -0.313883 1.12515 ~5.50987
813 -o.314223 1.12642 -5.51492
s23 -0.314244 1.12927 -5.52661
MeC+DD+SD 812 -0.511523 1.52635 -7.32452
813 -0.511455 1.52610 -7.32346
$23 -0 511718 1.52719 -7.32789
M#C+DD+SD+TD s12 -1.50523 2.56581 -12.4406
813 -1.50521 2.56580 -12.4406
823 -1.50535 2.56615 -12.4415

94

These results imply that labor and capital are substitutes
in the Bangkok area but are complements in the area outside
Bangkok. In other words, an increase in the price of
capital input in the production process will increase the
amount of labor in the area outside Bangkok. The latter
result is rather implausible and may be due to the poor
quality of the capital stock data.

All point estimates of OLM for the area outside
Bangkok are positive, while in the Bangkok area these point
estimates exhibit both negative and positive values.

This implies that cash balances and labor in the area
outside Bangkok are substitutes, while in the Bangkok area
these two factors can be either complements or substitutes

depending on the definition of money.

E. Summary

In this chapter, we examined the relation between
meney and capital in production. We estimated the parameters
of an aggregate production function containing three inputs
- labor, capital, and real cash balances. We used these
estimates to calculate the value of Allen partial elasticities
of Substitution (AES) between each pair of factors. A
negative value of the AES for any such pair indicates that
they are complements in production.

The major finding was that for all but one of our
twelve combinations of definition of money/region of the

country, our calculated value of the AES between real cash

95

balances and capital was negative. This finding indicates
that the two factors are complements in production in the
Thai economy, and it adds support to that developed in

earlier chapters for the complementarity hypothesis.

CHAPTER VII

SUMMARY AND CONCLUSION

The purpose of this study was to develop empirical models
to test McKinnon's complementarity hypothesis using data
on the Thai economy for the period 1962 to 1979. Prior
empirical tests of this hypothesis have all simply
employed variants of McKinnon's two-equation model. While
this study also estimated the parameters of such a model,
it broke new ground by devising and executing additional
tests of the complementarity hypothesis. Specifically,

it employed.the portfolio model and the translog production
function model. While these are familiar enough to
economists, they have not been used, prior to this study,
to test the complementarity hypothesis.

The most important finding of this study is that
results from all three models provide varying degrees of
support for the complementarity hypothesis. For McKinnon's
two-equation model, we found that a one percent increase
in the desired investment-income ratio would increase the
demand for money by 15 percent on the average outside the
Bangkok area, by 7 percent to 16 percent in the Bangkok

area, and by 15 to 30 percent for the whole kingdom,

96

97

depending on the definition of money.

Our estimates of the parameters of the portfolio
model all indicated that money and capital are complementary
assets in the Thai economy. A change of given sign in the
rate of return on capital was uniformly found to lead to
a change in the demand for real cash balances of the same
sign (although the latter change was always very small
relative to the former).

Finally, our estimates of the translog production
function model in almost all cases indicate that money and
capital are complements in production. An increase in the

price of capital services decreases the demand for real

 

balances conceived as a factor of production.

It is interesting to note that when comparing the
degree of complementarity between money and capital among
the regions, all three models led to similar results. That
is, for each model, the whole kingdom displayed the
greatest degree of complementarity, while the area outside
Bangkok exhibited greater complementarity than did the
Bangkok area. Another interesting finding was that capital
has a stronger complementary relationship with money defined
as currency plus other deposits than with money defined only
as currency. This result suggests that an increase in the
number of bank branches may play a role in increasing the
conduit effect of money in the saving-investment process.

Future extension of this study can be achieved by

elaboration of the complementarity hypothesis to provide a

98

consistent and efficient policy framework. Furthermore, if
complementarity between money and capital is due to an
imperfect capital market environment in which self-financed
investment dominates, then further research on how to
increase the efficiency of the financial market in LDCs is
called for.

While writing this dissertation, it was learned that
the Bank of Thailand was aware of MoKinnon’s complementarity
hypothesis. In cooperation with the International Monetary
Fund.and the World Bank, BOT has produced several research
studies on the nature of the Thai financial system. There-
fore, it is hoped that BOT will use and synthesize the
empirical findings of this study in their future policy
meking.

APPENDIX A

MEASUREMENT OF REAL CAPITAL STOCK AT THE END F
YEAR (1960-1979) USING 1972 AS THE BASE YEAR

We shall adopt Trescott's (1967) method for
measuring capital stock (see Tengpratip 1978).2 Trescott
(1967) estimated capital stock for the period 1945 to 1965
using 1956 as the base year. He used the formula that
total capital stock equals fixed capital stock plus
inventory, and assumed that the whole kingdom capital
stock is the sum of the agricultural and nonagricultural
capital stock. At the end of 1962, the capital stock for
the whole kingdom was estimated to be 97.1 billion baht
with 28.1 billion baht belonging to the agricultural
sector and 69.0 billion baht belonging to the nonagricultural
sector.3
Tengpratip (1978) used 1962 as the base year.
Therefore, capital stock for the year 1962 is 99.7 billion
baht, rather than 97.1. In our study we changed the base
year from 1962 to 1972, making the capital stock for the
year 1962 122.93 billion baht and that for 1959 96.08 billion
baht.

We will use 96.08 as the base to generate the

series of the real capital stock at 1972 prices for the

99

100

period 1960-1979 for the whole kingdom, the nonagricultural
sector, and the agricultural sector.

Columns A and B in Table A.l show the values of the
gross fixed capital formation at year end in current prices
and 1972 prices, respectively. Columns C and D give
capital depreciation or provision for the consumption of
fixed capital in current prices and 1972 prices, respectively.
Column B shows the net capital formation for the whole
kingdom at 1972 prices. Column E is obtained by subtracting
column D from column B. Column F shows the values of net
capital formation accumulated from 1960 to 1979. Column G
gives the estimated values of net capital stocks for the
whole kingdom. Column G is the sum of column F and the
estimated capital stock of 1959, that is, 96.078 billion
baht.

Column H shows the ratio of gross fixed capital.
formation in Thailand's agricultural sector to the nation's
total gross fixed capital formation. Column I gives the
estimated values of net capital stocks for agricultural
purposes. Column I is the product of columns G and H.

The last column J, gives the estimated values of net capital
stock for nonagricultural purposes. Column J is obtained

by subtracting column I from column G. We used the
estimated real capital stocks in Table A.l as a proxy for the

real net capital stock in this study.

101

 

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~.< mgm<H

APPENDIX B

MEASUREMENT OF VARIABLES FOR
THE TRANSLOG PRODUCTION FUNCTION

The data for the distributive shares and the quantity
inputs in the translog production function are constructed
as follows. Assume that the distributive shares of the

1 The total annual costs of

inputs exhaust total cost.
production in period t are thus apportioned among the
wage bill in the same period, total capital costs from the
previous period, and the cost of holding money in the
previous period. Total cost is computed by total labor
costs (the wage bill) plus total capital costs plus the
cost of holding money. The distributive shares are
calculated by dividing the cost attributable to each input

2 Therefore,

by total cost.
(Total Cost)t = (Labor Cost)t + (Capital cost)t-1
+ (Cost of Holding Mbney)t_l

= (Compensation)t + (Income from

Property)t_1 +[(d--13>.M>1,:_1
(3.1)

102

103

and
S = Labor Shares 8 (Labor Costs)t/(Total Cost)t

(8.2)

1

= Capital Shares = (Capital Costs)t_l/(Total Cost)t

S
2 (B.3)

83 a Money shares as [(d-p).M]t_l/(T0ta1 COSt)t (B.4)

The labor costs or wage bill for the whole kingdom,
the Bangkok area, and the area outside Bangkok are

determined as follows. Christensen and Jorgenson (1970.

p. 24) proposed to measure the labor cost (or the wage bill)
using data on labor compensation found in the national income
accounts. This concept will be adopted in the whole

kingdom model. Data on compensation of employees for the

whole kingdom is available in the National Income Accounts

 

of Thailand. The compensation of employees for the Bangkok

 

area will be the difference between the labor compensation
for the whole kingdom and that for the area outside Bangkok.
We assumed that the latter grows at the same rate as does
the rate of nominal gross domestic product. We used this
assumption and the 1979 value of labor costs in agriculture
(19.6 billion baht) to generate a data series on these costs
for earlier years.3

Capital costs for the whole kingdom are measured
using property income (see Christensen and Jorgenson 1969,
p. 306). The data for property income between 1962 and 1979

are available from the National Income Accounts of Thailand

104

(see Table c.1l). Capital costs for the Bangkok area are
calculated by subtracting capital costs for the area outside
Bangkok from those of the whole kingdom. Capital costs for
the area outside Bangkok are calculated by multiplying the
value of capital costs for the_whole kingdom by the ratio
of investment in the agricultural sector to total investment
(Column H, Table A.l). The ratio of capital costs to labor
costs for the area outside Bangkok was found to be approxi-
mately 20 to 40 percent. This rate is confirmed by the
micro study of the cost of production in the agricultural
sector by Akrasanee and Wattananukit (1977, p. 94).

The cost of holding money is defined as (d-p).M.4
The real money balances will be measured by the following
four definitions.

Mo-C:

M1 = C + DD;

M2 = C + DD + SD; and

M3 = C + DD + SD + TD.

M.0 represents the currency. M1 is currency plus
demand deposits. M2 is currency plus demand and saving
deposits. M3 is currency plus demand, savings, and time
deposits.

The value of the output for the whole kingdom is
defined as the gross national product (GNP). The value of
the output for the Bangkok area is computed by subtracting
GNP from the value of the output for the area outside

Bangkok. The value of the latter area is defined as the

105

agricultural component of GNP. Sources of data are the
National Income Accounts of Thailand (see Table C.3).
This current market price data will be transformed into

constant price data using 1972 as the base year.

 

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108

TABLE C.3

GROSS NATIONAL PRODUCT AT CURRENT PRICES
(Millions of Baht)

 

Whole Kingdom Ban kok Outside Bangkok
(Gross National) (Non-Agricultural) (Agricultural)

 

 

 

Year Product Products Products
1979 564,431.0 418,815.0 145,616.0
1978 441,950.0 321,525.0 120,425.0
1977 381,043.0 273,364.0 107,679.0
1976 336,220.0 233,450.0 102,770.0
1975 296,993.0 202,930.0 94,063.0
1974 272,166.0 187,431.0 84,735.0
1973 214,770.0 141,794.0 72,976.0
1972 161,744.0 112,447.0 49,297.0
1971 143,938.0 103,852.0 40,086.0
1970 l36,318.0 97,532.0 38,786.0
1969 128,792.0 88,471.0 40,321.0
1968 117,578.9 80,616.8 36,962.1
1967 108,39l.8 73,248.7 35,143.1
1966 101,282.l 64,360.6 36,921.5
1965 84,291.9 54,909.0 29,382.9
1964 73,730.4 49,121.3 24,609.1
1963 68,921.4 43,811.8 25,109.6
1962 65,208.6 40,901.8 24,306.8
Source: (a) BOT Statistical Bulletin

Agricultural Products Include Crops, Livestock,
Fisheries and Forestry.

(b)

(c) Non-Agricultural Products = GNP w.Agricu1tural

Products

109

TABLE C.4

GROSS FIXED CAPITAL FORMATION AT CURRENT PRICES
(Millions of Baht)

 

 

Whole Kingdom Ban kok
(Non-Agriculture)

Outside Bangkok

 

 

(Agriculture)’

1979 146,057.0 131596.0 14460.77
1978 120,204.0 108174.0 12030.00
1977 99,522.0 88749.0 10773.00
1976 77,418.0 69199.0 8219.00
1975 68,830.0 62259.0 6571.00
1974 59,109.0 53274.0 5835.00
1973 44,244.0 40258.0 3986.00
1972 34,591.0 31487.0 3104.00
1971 32,772.0 29144.0 3628.00
1970 32,776.0 29231.0 3495.00
1969 30,774.0 27355.7 3418.26
1968 27,477.0 24374.5 3102.46
1967 24,927.0 22068.8 2858.21
1966 20,364.1 17943.0 2421.14
1965 15,935.5 13297.4 2638.10
1964 14,518.5 12052.8 2465.70
1963 12,084.9 9970.1 2114.80
1962 ll,639.l 9533.2 2105.90
Source: (a) BOT Statistical Bulletin

(b) Office of the National Economic Development
Board (1965. Table 40)

(c) United Nations: "Yearbook of National Accounts
Statistics: 1979, Vol. 1: Individual Country
Data," Table 9A.

Note: Under the guidance of Dr. Mark Ladenson, data for the
outside Bangkok (1966-1979) are generated by using
the interpolation method by Chow and Lin (1971).
on the existing data the regression equation will
appear as follows:

IA 8 470.545 + 0.0957861 IWK
(O.886131)(13.5041)

Based

110

TABLE C.5
STRUCTURE OF INTEREST RATES
Bank of Thailand Commercial Banks

Year Loan Rate 12 Months and Over
Time Deposits Rate

1979 0.125 0.09
1978 0.125 0.08
1977 0.09 0.08
1976 0.09 0.08
1975 0.10 0.08
1974 0.11 0.08
1973 0.10 0.07
1972 0.08 0.07
1971 0.09 0.07
1970 0.09 0.07
1969 0.11 0.07
1968 0.07 0.07
1967 0.07 0.07
1966 0.07 0.07
1965 0.07 0.07
1964 0.08 0.07
1963 0.08 0.07
1962 0.08 0.08

Source: BOT Statistical Bulletin

111
TABLE C.6

LOANS OF THE BANKING SECTOR CLASSIFIED BY PURPOSES

 

CB Loans For

 

.. Agricultural

Year Total CB Loans Purposes BAAC Loans
1979 l98363.2 10774.9 10943.5
1978 160878.5 8656.9 9703.3
1977 122810.0 6340.5 8521.8
1976 96377.3 4121.4 6778.4
1975 82898.8 2823.7 4714.8
1974 68815.7 1305.3 2650.7
1973 51291.2 990.5 1952.1
1972 35845.7 771.2 1736.8
1971 31709.8 742.7 1439.5
1970 28234.2 637.4 1208.7
1969 23390.2 660.5 999.0
1968 14630.1 565.2 690.5
1967 12590.7 473.1 381.7
1966 10577.3 401.0 217.4
1965 8930.7 324.8 223.6
1964 7401.3 292.8 211.2
1963 6188.2 239.6 226.0
1962 5392.3 201.6 245.5
Source: BOT Statistical Bulletin

112

TABLE C.7

THE NUMBER OF COMMERCIAL BANK OFFICES PER CAPITA

The Number of Bank Offices‘

4_._

The # of CB Offices Per Capita
(Office per 100 ,000 Populations

 

BangkOk-
Year Thonburi Provinces Kingdom

 

1979 419
1978 406
1977 364
1976 344
1975 323
1974 303
1973 283
1972 271
1971 259
1970 234
1969 214
1968 197
1967 182
1966 169
1965 161
1964 153
1963 145
1962 134
Sources:

OEher Whole
944 1,363
893 1,299
820 1,184
721 1,065
572 895
543 846
496 779
460 731
423 682
413 647
390 604
371 568
353 535
325 494
313 474
305 458
302 447
291 425

(b) Alex A. Rozental
(c) The Thai Military Bank: Annual
(d) Paul B. Trescott (1971)

 

’BangkOk- Other Whole
Thonburi Provinces Kingdom
.38168 2.29455 2.95405
.33676 2.21974 2.88027
.67609 2.08662 2.68847
.56876 1.87687 2.47905
.42699 1.52448 2.13757
.03016 1.48889 2.07455
.59213 1.40125 1.96271
.39603 1.33943 1.89476
.19321 1.27417 1.82451
.66998 1.28729 1.78680
.25540 1.25652 1.72031
.05517 1.24526 1.68596
.87936 1.21934 1.63709
.73522 1.15531 1.55836
.66937 1.14686 1.54196
.59597 1.15133 1.53588
.61636 1.16787 1.54138
.55937 1.16117 1.51786

hbbbbbmumo‘ma‘wuuumm

(a) Kanitta M. Meesook (1978).
(1971).

Report (1978)

113

TABLE C.8
LOANS WHICH THE BANKING SECTORS BORROW FROM THE BOT

 

CBs Borrowed Discount and Rediscount Loans from Ministry
Year From BOT at BOT by BAAC of Finance by BAAC

 

1979 16733.0 2500.0 375.4
1978 8140.8 1992.2 511.5
1977 5952.2 1020.8 293.4
1976 5530.3 981.1 275.9
1975 7297.0 515.5 189.3
1974 3984.9 420.3 220.0
1973 2881.7 256.8 47.9
1972 1263.4 184.7 11.2
1971 1296.3 ----- 16.3
1970 787.3 129. 21.1
1969 296.6 130.0 29.1
1968 397.9 65.8 37.7
1967 298.5 ----- 53.3
1966 336.9 ----- 91.3
1965 244.3 ----- 77.9
1964 164.7 ----- 75.3
1963 98.0 ----- 80.1
1962 103.6 ----- 88.5
Source: BOT Statistical Bulletin.

114

TABLE C.9
POPULATION (Millions)

 

 

Year Whole Kingdom Metropolitan Non-Metropolitan
1979 46.14 4.999 41.141
1978 45.10 4.870 40.230
1977 44.04 4.742 39.298
1976 42.96 4.545 38.415
1975 41.87 4.349 37.521
1974 40.78 4.310 36.470
1973 39.69 4.293 35.397
1972 38.58 4.237 34.343
1971 37.38 4.182 33.198
1970 36.21 4.127 32.083
1969 35.11 4.072 31.038
1968 33.69 3.897 29.793
1967 32.68 3.730 28.950
1966 31.70 3.569 28.131
1965 30.74 3.448 27.292
1964 29.82 3.329 . 26.491
1963 29.00 3.141 25.859
1962 28.00 2.939 25.061
Sources: (a) IMF: International Financial Statistics

(e)
(d)

Charsombuti and Wagner (1969)

Thailand National Statistical Office:
"Bulletin of Statistics".

Thailand's Current Economic Situation (1967)

115

TABLE C.10
CONSUMER PRICE INDEX

 

 

gnf1ation
. t' t-l ,
Year (19723100) Pt-(_PE:I__) (100)
1979 212.59 14.99
1978 184.88 7.81
1977 171.49 8.87
1976 157.52 4.20
1975 151.17 5.30
1974 143.56 24.34
1973 115.46 15.46
1972 100.00 4.92
1971 95.31 0.43
1970 94.90 (-0.08) -‘- 0.01*
1969 94.98 2.43
1968 92.73 1.79
1967 91.10 4.31
1966 87.34 3.85
1965 84.10 0.78
1964 83.45 1.98
1963 81.83 0.90
1962 81.10 2.46

Source: BOT Statistical Bulletin.

* Since the computer cannot operate on the log of the
negative value, Dr. Mark Ladenson recommended to use
0. 1 as the close approximation for (-0.08).

116

TABLE C.11
PROFIT RATE (At 1972 Price)

 

 

INCOME FROM SAVING OF PROFIT RATE OF RETURN
PROPERTY DIVIDEND CORPORATIONS -DVD+SCP ON CAPITAL OR
YEAR (YPP) (DVD). (SOP) (1r) PROFIT RATE-(n/K)
1979 23318.1 1418.69 5842.70 7261.40 0.0128325
1978 23210.2 1359.26 5911.94 7271.20 0.0140669
1977 21096.3 1088.11 4308.12 5396.23 0.0114697
1976 20268.5 971.94 3466.23 4438.17 0.0103468
1975 18128.6 974.40 3414.04 4388.44 0.0111070
1974 16851.5 815.69 4459.46 5275.15 0.0145175
1973 17070.8 758.70 3640.22 4398.93 0.0131474
1972 14296.0 722.00 3509.00 4231.00 0.0136900
1971 12825.5 657.85 3161.26 , 3819.12 0.0132927
1970 12243.4 569.02 2561.64 3130.66 0.0118115
1969 10663.0 547.87 2873.03 3420.90 0.0141670
1968 9943.6 510.97 2793.59 3304.50 0.0151300
1967 8818.55 453.10 2479.25 2932.36 0.0148923
1966 9933.13 510.37 2047.52 2557.89 0.0144944
1965 8079.69 414.98 1519.38 1934.37 0.0121684
1964 7689.28 395.08 1553.62 1948.70 0.0133930
1963 7672.25 394.20 1001.71 1395.91 0.0104809
1962 7307.40 375.46 817.38 1192.84 0.00969846
Source: "National Income of Thailand" Office of the National
Economic and Social Development Board.

Note: Since the dividend data was not available prior to

1970, Dr. Mark Ladenson recommended this series be
generated for the period 1962-1969 by the following

 

X (DVD./ )
* 1-1970 1 YPPi .
DVD = YPR ( J=1960, . . . ,1969.
.1 J . 10
L J

 

 

117

TABLE C.12
AGRICULTURAL WAGE INCOME (Millions of Baht)

 

 

Year A B C D

1979 14.99 564,431 2.83 19,600.00
1978 7.81 477.341 12.66 16,270.50
1977 8.87 393,030 6.92 14,051.40
1976 4.20 337,635 8.44 12,475.00
1975 5.30 298,816 7.46 11,063.40
1974 24 34 264,077 -0.83 8,957.48
1973 15.46 214,160 14.30 6,902.92
1972 4.92 162,273 6.35 6,203.60
1971 0.43 145,425 7.04 5,772.29
1970 0.01 135,276 3.66 5,573.14
1969 2.43 130,612.7 8.70 5,014.90
1968 1.79 117,306.7 6.48 4,631.58
1967 4.31 108,224.3 2.35 ' 4,342.56
1966 3.85 101,374 7 15.78 3,629.63
1965 0.78 84,303.0 12.03 3,217.44
1964 1.98 74,667.3 7.55 2,937.53
1963 0.90 68,078.6 5.77 2,753.95
1962 2.46 63,793 0 5.58 2,548.98

Sources: (a) Kanitta M. Meesook (October, 1980, p. 20)
(b) BOT Statistical Bulletins

Note: (a) The Actual Inflation Rate
(b) Gross Domestic Product at Current Prices
(c) Growth Rate of Gross Domestic Product
(d) Wage Bill in the Agricultural Sector

FOOTNOTES

FOOTNOTES

 

Chapter II:
lMcKinnon (1973), p. 45.
21bid.
3Ibid, p. 56.
4Hirschman (1963), p. 211.
5

McKinnon (1973, 1976).

6In addition to reporting their empirical research,
Vobel and Buser extend MoKinnon s theoretical analysis of
complementarity to a model in which the variability of
rates of return on money and capital, as well as the
expected values of the rates, plays a systematic role.
However, our empirical analysis in chapters Four, Five, and
Six is limited to the complementarity hypothesis as
developed by MeKinnon.

 

Chapter III:

 

1Trescott (1971), p. 9.

2Rozental (1970), chapter three, Trescott (1971),
pp. 7-10, and Meesook (1978), p. 2.

3
4

See Cheng (1980) for a detailed discussion.
Unakul and Panitchpakdi (1978).

Chapter IV:

 

1Cagan (1956). P. 37.

2The period of estimation is 1962-1979. We deflated
data in nominal termson gross fixed capital formation and on
gross national product by data on the consumer price index
(1972-100). We calculated the rate of inflation as the

118

119

percentage change in the consumer price index. As will be
noted shortly, four alternative measures of money were used.
Data on all these variables were obtained from various
issued of the Bank of Thailand Monthly Bulletin. Data on
the value of profits, n, were taken from various editions
of National Income of Thailand. The construction of data
used in this study on the capital stock variable is
explained in Appendix A.

3

 

 

Tengpratrip (1978), p. 29.

4The method used is iterative Zellner efficient
estimation (IZEF).

SDurbin (1970). p. 410-421.

Chapter V:

 

1Economic theory distinguishes between gross and net
subatitutes. Gross substitutability includes income effects
of a change in relative prices or yields; net substitutability
excludes these effects. Hendershott (1977), pp. 347-351
shows that if data on asset values are not adjusted for
price changes (for example, they represent book rather than
market values), the ai-s represent net substitution terms.
Since our data are rec8rded at book value, the values of the
aijs we estimate represent the net substitute concept.

2Endogenous liabilities (-L) is entered in the
equation negatively to emphasize the constraints on the
total portfolio responses (Hendershott 1977, p. 120).

3Hendershott (1977), p. 46. In addition, Gramlich
and Hulett (1972) used this framework for their empirical
work, while Brainard and Tobin (1968) used this framework
for their simulation.

4The symmetry result of consumer demand theory
applies only to the substitution effect (Hendershott, 1977,
p. 347). As noted in footnote one of this chapter,
Hendershott has shown that when all assets are measured at
book rather than at market value, as in our sample, the
coefficients a1: measure only substitution effects, and thus
imposition of tfie symmetry constraint is appropriate.

5Sources of data on the four measures of money, on
the rate of inflation, on the capital stock, and on the
variable n/K.were given in footnote two in Chapter Four.
For the Bangkok area, the data on bank loans exclude loans
to the agricultural sector, while for the rest of the
country these data consist only of such loans. The nominal
return on money was measured as the rate of interest on

120

one-year bank deposits. For lack of a better series on the
rate of interest on bank loans, we used the Bank of Thailand
discount rate. Data on these variables as well as on the
volume of loans and rediscounts extended by BOT were taken
from various issues of the Bank of Thailand Monthly Bulletin.
Data on bank branches per capita were taken from various
issues of the Bank of Thailand Annual Report.

 

 

6Hendershott (1977), p. 92. Note that while aij'aji’
"111,53 7‘ ”133,2: .
7

As noted in footnote six of this chapter, even
though we impose symmetry restrictions on the matrix of
partial derivatives, A, in equation (5.2)', our estimates of
the corresponding cross-elasticities will not be symmetric.

8Hendershott (1977), Hendershott and Lemmon (1971),
and Gramlich and Hulett (1972).

9The only exceptions occur in the region outside
Bangkok when the two broadest definitions of money are used.

Chapter VI:

 

1Johnson (1969, pp. 40-45), Nadiri (1969, p. 175),
Levhari and Patinkin (1968, pp. 737-740), Moroney (1972), and
Fisher (1974). For money and the aggregate production
function see Nadiri (1969, p. 177), Levhari and Patinkin
(1968, p. 737), Sinai and Stokes (1972, p. 291), and
Subrahmanyan (1980, p. 281); for money and the firm production
function see Dennis and Smith (1978, p. 798).

2

3Gabor and Pearce (1958) is a notable exception. More
recently, Fisher (1974) has argued "that to treat real
balances as a factor of production is in general a dangerous
procedure" (p. 517).

Levhari and Patinkin (1968, p. 737).

4The relation between these two sorts of elasticities
is set out in Allen (1938, pp. 503-509). The Allen partial
elasticity of substitution between factor i and j measures
the effect on the quantity of factor 1 due to a change in the
price of factor j holding output and other input prices
constant. If this elasticity is positive, the two factors
are substitutes in production. If it is negative, they are
complements.

5Condition (6.19) allows the translog production
function to capture the negative price or negative return of
holding deposit; This negative price, (d—pe), arises because
the rate of inflation has been higher than the rate of

121

deposit since 1974.

6The equality of E and Si in the distributive shares
equation (6.20) is estab11shed by profit maximizing behavior
in competitive markets. Introducing the disturbance terms
into the stochastic versions of (6. 2.a), (6.22.b), and
(6.22.c) will allow the model to deviate from the gurely
competitive markets. This relaxation may be attri uted
to a variety of forces, including imperfectly competitive
markets and the inability of entrepreneurs to instantaneously
'maximize profits (Mundlak and Hock 1965, Zellner, Kmenta and
Dreeze 1966, p. 65, Grant 1979, p. 38, and Subrahmanyam
1980, p. 281).

7Grant (1979).p. 8, Dennis and Smith (1978), p. 801,
footnote 15.

8For further discussions of IZEF estimation based on
unrestricted estimates of the cross equation disturbance
variance-covariance matrix see Kmenta and Gilbert (1968);
for IZEF estimations based on restricted estimates of the
variance-covariance matrix see Johannes (1978).

 

 

9See pages 79-80.

10A production function is well behaved if and only
if both the monotonicity condition and the concavity
condition are satisfied. The monotonicity condition requires
that the marginal product of each input be positive, while
the concavity condition requires that the Hessian matrix of
partial second derivatives be negative semi—definite. These
two conditions were tested in this study and were found to
be satisfied over all three regions and for most definitions
of money. Therefore, we conclude that the aggregate
production function for the whole kingdom, the Bangkok area,
and the area outside Bangkok seem to be well behaved
according to the economic theory; that is, each of the three
inputs is characterized by a diminishing marginal rate of
factor substitution.

11we do not obtain estimates of the standard errors
of these estimates. Although it is possible, in principle,
to derive these, the computational burden, without the aid
of computers, is enormous, and there is no standard computer
package to execute the task.

Klein (1953, p. 258) gives the following formula.
Let

wi - fi(x1,...,xn) (a)

Then

122

var(_wi )- 2 (Bf/3x1) 2.var(x )

i-l
+- E (Bf/3x1)(Bf/axj)cov(xi,xj ) (b)
#3
When equation 6.21 plays the role of equation (a), oij plays
the role of wi, and the x1 are fi’xi Xj, lFfl |, and IFI in

that equation. To use relation (b) to calculate and estimate
of the standard error of our estimate of oi , we need
estimates of the variances and covariances of fi,Xi,X ,
lfijl’ and IFI, it would be necessary to let equation (15)
and the definitions of IFijl and IF] in terms of the ais and
bijs’ in turn play the role of equation (a) and use relation
(b) to evaluate their variances. This alone would be an
enormous computational task, even ignoring the necessity

for evaluation of the covariances and partial derivatives

in relation (b).

Appendix A:

 

1Discussion and derivation in this appendix is based
on Tengpratip (1978), Appendix A.

2Trescott (1967).
31bid, p. 40.
Appendix B:

 

1Christensen and Jorgensen (1969), p. 24.

2Humphrey and Moroney (1975), p. 66, Dennis and Smith
(1978), p. 810.

3As shown in Table C.12, our actual data series was
generated using data on the sum of the growth rates of real
gross domestic product and the consumer price index, rather
than directly on the growth rate of nominal gross domestic
product. The figure of 19.6 billion baht is taken from
Meesook (1980b, Table 5). That author uses an assumption
similar to ours about the growth rate of income in the
agricultural sector.

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