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THE LONG-RUN DEMAND FOR MONEY FUNCTIONS IN TAIWAN
(1961:4-1997z3): COINTEGRATION AND STABILITY

presented by

Ching-yi Chiang

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1M animus-m4

THE LONG-RUN DEMAND FOR MONEY FUNCTIONS IN TAIWAN

(1961:4-1997z3): COINTEGRATION AND STABILITY

BY

Ching-yi Chiang

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements

for the degree of

DOCTOR OF PHILOSOPHY

Department of Economics

1999

ABSTRACT
THE LONG-RUN DEMAND FOR MONEY FUNCTIONS IN TAIWAN
(196l:4-1997:3): COINTEGRATION AND STABILITY
BY

Ching-yi Chiang

This dissertation compares the performance of the long-
run demand functions for alternative new definitions of
money (MIA, MlB, MlBP, and M2) in Taiwan for the same sample
period (1961:4-1997z3). Various unit—root tests cannot
reject that the variables chosen for each function (real
balances, real GNP, and short-term interest rates) are
characterized as IICl) processes. Using residual-based
cointegration tests (Phillips and Ouliaris 1990, Gregory and
Hansen 1996), rue found cointegration evidence 1J1 all four
demand functions for real balances. However, the parameter
stability ‘tests cflf Hansen (1992b) suggest that the :most
stable long-run relationship occurs in the demand for real
MlB equation. MlB being stable is consistent with the
transactions-demand theory which links real money balances
demanded with a measure of the volume of real transactions
(real GNP) and opportunity costs of holding money balances.
Instability detected in the demand for broadly defined money

(M18? and M2) is explained by misspecification. Low

liquidity in the non-M18 components suggests that the demand
for broader measures may be justified by portfolio or
speculative-demand. theory; hence, wealth instead of .real
GNP, or a measure of volatility of alternative assets'

returns enters the equation.
Johansen's (1991) trace and max-K test establish that

there is only one cointegrating vector in the system. For
the demand for real MlB function, the equilibrium income
elasticity! is around 1.50, and interest elasticity is -
0.41, which are robust to four alternative estimators. While
the price homogeneity is not rejected, the unitary income
elasticity is rejected by the data. The rejection of weak
exogeneity status of the variables invalidates the inference
conducted in single equation error correction model in
estimating the long-run. demand. for real MlB function in

Taiwan.

To my Mother, Kwey-jen Deng Chiang

and my Father, Ching-jen Chiang

ACKNOWLEDGMENTS

I wish to express my deepest gratitude to Professor
Robert H. Rasche for years of assistance and guidance
throughout this research. As my research adviser, he has
been very generous to give me valuable comments and
suggestions and also been very patient to guide to be a
researcher' so that I cxui grow' professionally. His broad
knowledge of Macroeconomics and Monetary Economics expand my
ways of thinking about these fields. Through his lectures, I
obtained the first hand knowledge of these fields and
constant intellectual stimulation as well. This enables me
to fit disarranged pieces of knowledge together in an
efficient way and then to form a clearer picture of the
multi-dimensional jigsaw puzzle—Monetary Economics. His
interpretations (ME economic theories vnifli thoughts spiced
with interesting examples, sometimes jokes, inspired me to
study Economics not only with discipline but also with
pleasure. Moreover, Ii greatly' appreciate Professor's
assistance in constructing the interest rate variables in my
study, which shortened the length of time for me to complete
this dissertation. Without his assistance, I must have been
still struggling with the data problem, which would take

years to resolve without such expertise and experience. I am

very grateful for all of what I have learned from Professor
Rasche during these years at MSU.

I also wish to thank. the other two members of' my
guidance committee, Professor Jeffrey' Wooldridge and
Professor Christine E. Amsler. Their valuable comments and
suggestions encouraged we tx> think further how tx> improve
this study. I greatly appreciate that they generously gave
me their time and support. I would also like to thank
Professor Peter Schmidt for kindly providing me references.
I also appreciate Professor Chingnun Lee for his help with
the data and for his generosity of allowing me to get access
to Taiwanese economic data through internet.

I want to mention some friends I made at MSU. Ling—
Huang Yu is a friend whose warm heart, perseverance, and
critical mind are what I admire her most about; we went
through good times and bad times together during my graduate
career. II also greatly appreciate Jing-I Ina, Mei-Yu Teai,
and Meihsin Chou for their support and encouragement. These
unique individuals enrich my life at MSU in several ways. I
wish them the very best.

Last but most I would like to thank my mother, Kwey-jen
Den Chiang, and my father Ching-jen Chiang, for their
unconditional love, continuos encouragement, and financial
support. Words are unable to express my gratitude to them.

All the accomplishments I have made belong to them. Their

vi

devotion to children is beyond what I can understand.
Besides, I also thank my aunt Fang—kwey, who constantly
calls me to eat properly. Her words turned out to be more
nutritious than food. I would also like to thank my sister
Chiu-juan for being very considerate of me, providing me
suggestions, sharing her experience in life with me, and

frequently forwarding jokes to me.

vii

TABLE OF CONTENTS

LIST OF TABLES ........................................... xi

LIST OF FIGURE ......................................... xiv
CHAPTER 1

INTRODUCTION .............................................. 1
CHAPTER 2

THE DEMAND FOR MONEY: THEORY .............................. 6

I: THEORY REVIEW ........................................ 6

l The Motives of the Demand for Money ................ 6

2 A Missing Chapter in the Theoretical Money Demand
Literature: The Time (Energy, Resources) Saving

Aspect of the Use of Money ......................... 7
II: TRANSACTIONS DEMAND FOR MONEY MODEL: A SHOPPING
TIME MODEL ......................................... 10
1 Assumptions ....................................... 10
(1) Preferences ................................... 10
(2) Time constraint ............................... ll
(3) The multiperiod budget constraint ............. 15
2 The Constrained Multiperiod Utility Maximization
Problem ........................................... 20
3 Properties of the Money Demand Function ........... 24
4 Stability of the Money Demand Function ............ 28
5 Cash—in-Advance Model versus the Shopping Time
Model ............................................. 32
6 Empirical Issues: Arguments in the Money Demand
Function .......................................... 34

III: THE STABILITY OF THE AGGREGATE MONEY DEMAND

FUNCTION AND ITS POLICY IMPLICATION ............... 37

1 Quantity Theory of Money and Monetarism ........... 39
IV: THE ARGUMENTS IN THE TAIWANESE DEMAND FOR MONEY

FUNCTIONS: DATA DESCRIPTION ....................... 43

1 Measure of Money .................................. 45

2 Scale Variable .................................... 48

vm

3 Measure of the Opportunity Cost of Holding Money..49

(1) The own rate on money ......................... 51
(2) Unorganized money market rate ................. 52
CHAPTER 3

STATISTICAL PROPERTIES OF UNIVARIATE TIME SERIES IN
THE DEMAND FUNCTIONS FOR REAL BALANCES IN TAIWAN:

1961:4-1997:3 ............................................ 60
I: INTRODUCTION ........................................ 60
II: UNIVARIATE UNIT-ROOT TESTS ......................... 63

1 The HEGY Seasonal Unit—Root Tests ................. 67
2 The Dickey-Fuller Unit-Root Tests ................. 78
3 The KPSS Stationarity Tests ....................... 84

CHAPTER 4

THE LONG-RUN DEMAND FOR MONEY FUNCTIONS IN TAIWAN

(1961:4-1997:3): COINTEGRATION AND STABILITY ............. 91
I: EQUILIBRIUM RELATIONSHIP AND COINTEGRATION .......... 91
II: RESIDUAL BASED COINTEGRATION TESTS ................. 93

1 Introduction ...................................... 93
2 Phillips and Ouliaris (1990) Z; and 22 tests ...... 95
3 OLS Estimates: Asymptotic Results ................. 99
4 Inference of Cointegrating Vectors .............. 100
5 Empirical Study: The Existence of the Long-Run
Money Demand Functions in Taiwan (1961:4-1997:3)
................................................ 101
(1) The demand for real MIA equation ............ 104
(2) The demand for real MlB equation ............ 105
(3) The demand for real MlBP equation ........... 105
(4) The demand for real M2 equation ............. 105
(5) Summary ..................................... 111
III: THE STABILITY OF THE LONG-RUN DEMAND FOR MONEY
FUNCTIONS IN TAIWAN (1961:4—1997z3) ............. 112
1 Residual Based Tests for Cointegration in Models
with Regime Shifts: Gregory and Hansen (1996) Z;
and Z: Tests .................................... 113
2 Hansen (1992b) LM Tests for Parameter Instability
in Cointegrating System ......................... 118

3 Empirical Study: The Stability of the Long-Run
Money Demand Functions in Taiwan (1961:4-1997z3) 121
(1) The demand for real MlA equation ............ 123
(2) The demand for real MlB equation ............ 126
(3) The demand for real MlBP equation ........... 128

k

(4) The demand for real M2 equation ............. 131
(5) Summary ..................................... 132

IV: JOHANSEN’S FULL INFORMATION MAXIMUM LIKELIHOOD
ESTIMATION ....................................... 151

1 Introduction .................................... 151
2 Empirical Study: The Number of the Cointegrating
Vectors in Taiwanese Money Demand Data

(1961:4-1997z3) ................................. 153
(1) The Taiwanese demand for real MIA data ...... 155
(2) The Taiwanese demand for real MlB data ..... 161

V: ESTIMATION AND TESTS OF LINEAR RESTRICTIONS ON THE
LONG-RUN PARAMETERS OF DEMAND FOR REAL MlB IN TAIWAN
.................................................. 167

1 Estimation of the Long-Run Income and Interest
Elasticities .................................... 167
2 Tests of Linear Restrictions on Cointegrating

Vectors (B) and the Adjustment Coefficients (a). 180

(1) Tests of linear restrictions on B ........... 180
(2) Weak exogeneity tests ....................... 182
3 Estimation of the Long-Run Impact Matrix II ...... 184
4 Summary ......................................... 185
CHAPTER 5
CONCLUSIONS ............................................ 189
APPENDIX 1
THE REDEFINED MONETARY AGGREGATES IN TAIWAN ............ 193
APPENDIX 2
SOURCES OF FUNDS BORROWED BY PRIVATE ENTERPRISES IN
TAIWAN ................................................. 197
APPENDIX 3
TESTING FOR PRICE HOMOGENEITY OF THE MONEY DEMAND
FUNCTIONS IN TAIWAN (1961:4-1997z3) .................... 199
APPENDIX 4

TESTING FOR NO COINTEGRATION BETWEEN THE UNORGANIZED
MONEY MARKET RATE AND THE OWN RATE OF MONEY IN TAIWAN
(196l:4-1997:3) ........................................ 202

BIBLIOGRAPHY ........................................... 206

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

2:

10:

11:

12:

LIST IF TABLES

HEGY tests for seasonal unit roots in

quarterly aggregate series for the Taiwanese
demand functions for real balances:

1961:4-1997:3 .................................. 74

DF tests for unit roots at zero frequency in
quarterly aggregate series for the Taiwanese
demand functions for real balances:

1961:4-1997:3 ................................... 80

KPSS stationarity tests for quarterly aggregate

series for the Taiwanese demand functions for real
balances (1961:4-1997:3): Model I: Regression with
an intercept .................................... 87

KPSS stationarity tests for quarterly aggregate
series for the Taiwanese demand functions for real
balances (1961:4-1997:3): Model II: Regression with
an intercept and a trend ........................ 88

DF-t tests for unit roots in the first difference
of the aggregate series for the Taiwanese demand
functions for real balances: 1961:4-1997:3 ...... 89

Testing for no cointegration in Taiwanese

demand real MIA data .......................... 107
Testing for no cointegration in Taiwanese
demand for real MlB data ...................... 108
Testing for no cointegration in Taiwanese
demand for real MlBP data ..................... 109
Testing for no cointegration in Taiwanese
demand for real M2 data ....................... 110
Critical values for residual-based
cointegration tests .......................... 111
Cointegration tests with regime shifts and
parameter constancy tests: real MIA data ..... 134
Cointegration tests with regime shifts and
parameter constancy tests: real MlB data ..... 136

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

13:

14:

15:

16:

17:

18:

19:

20:

21:

22:

23:

24:

25:

26:

27:

28:

29:

Cointegration tests with regime shifts and
parameter constancy tests: real MlBP data.... 138
Cointegration tests with regime shifts and
parameter constancy tests: real M2 data ...... 139
Critical values for Z; and Z: tests .......... 141
Critical values for Lt, MeanF, and SupF tests 141
Residual misspecification tests .............. 157
Tests of the cointegration rank .............. 158
The eigenvector associated with the largest
eigenvalue (vi) and the corresponding weights

(W1) .......................................... 160
Residual misspecification tests .............. 161
Trace and 2““ tests .......................... 163
Normalized cointegrating vectors (fl) and error
correction coefficients (a) ................. 166
Critical values for trace and 2m“ tests ...... 167
Estimated cointegrating relations:

RMlB, = u + Oyy, + 8,fi + e, ................. 172
Estimated cointegrating relations:

RMlB, = p + ny, + Gnmumm, + 8, ............. 173
Weak exogeneity tests: VAR(4) model .......... 186
Weak exogeneity tests: VAR(3) model .......... 187
VAR(4): Estimated long-run coefficients matrix:

1'] = afl’ .................................... 188
VAR(3) Estimated long—run coefficients matrix:

11 = afl’ .................................... 188

X“

Table
Table

Table

Table

A1:
A2:

A3:

A4:

New measures of money ........................

Sources of funds borrowed by private

enterprises in Taiwan ........................

Testing for price homogeneity ................
Testing for no cointegration between the

unorganized money market rate (umm) and
the own rate of money (i) ....................

xiii

194
197

200

203

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure
Figure
Figure
Figure

Figure

Figure

10:

II:

12:

13:

I4:

15:

16:

LIST OF FIGURES

Taiwanese money demand Data .................... 58

Growth rates

of Taiwanese money demand data

(1961:4-1997:3) ................................ 59
Time plot of Z(t) statistics for the demand
for real MIA ................................. 142
Time plot of Z(a) statistics for the demand
for real MIA ................................. 143
Time plot of Z(t) statistics for the demand
for real MIB ................................. 144
Time plot of Z(a) statistics for the demand
for real MIB ................................. 145
Time plot of Z(t) statistics for the demand
for real MIBP ................................ 146
Time plot of Z(a) statistics for the demand
for real MIBP ................................ 147
Time plot of Z(t) statistics for the demand
for real M2 .................................. 148
Time plot of Z(d) statistics for the demand
for real M2 ................................. 149
SupF test for demand for real MIA ........... 150
SupF test for demand for real MIB ........... 150
SupF test for demand for real MIBP .......... 150
SupF test for demand for real M2 ............ 150
The Actual and estimated MIB/P
(Four-variable system) ...................... 174
The Actual and estimated MIB/P
(Three-variable system) ..................... 175

xw

Figure 17: The Actual and estimated MIB/P:
OLS estimation .............................. 176

Figure 18: The Actual and estimated MIB/P:
DOLS estimation ............................. 177

Figure 19: The Actual and estimated MIB/P:
FM estimation ............................... 178

Figure 20: The Actual and estimated MIB/P:
JOH ......................................... 179

XV

CHAPTER 1

INTRODUCTION

The aggregate demand for nmney function, which links
money balances demanded with a scale variable and a measure
of the opportunity cost of holding money balances, is an
essential ingredient in macroeconomic analysis and its
importance is associated with efficacy of monetary policy.
As Keynes (1936) postulated long before, while a stable
money demand relation under different state of nature does
not guarantee the potence of the monetary policy, its
instability certainly undermines the usefulness of
manipulation of quantity of money in an economy as a central
stabilizing device. Many macroeconomic models are built on a
notion that the»:money' demand relation remains stable to
analyze the effect of monetary policy on economic activity,
such as Monetarist (Friedman, 1956, 1974), New Classical
model (Sargent and Wallace, 1975), New Keynesian model
(Mankiw, 1991), and the empirical real business cycle model
(King, Plosser, Stock, and Watson, 1991). Finding an
empirical stable money demand relation provides these models
an empirical content.

Numerous attempts to estimate money demand relations in

Taiwan have been undertaken. Studies on Taiwanese money

demand function concentrate on the Goldfeld-type (Goldfeld,
1973, 1976) partial adjustment model. Empirical evidence on
the issue of stability based on Taiwanese data is mixed,
depending (N1 the functional form, 'variables used, sample
period studied, and the choice of estimating and testing
procedure, see Hwang and Wu (1994) and Lin (1997) for a
review. Using Engle-Granger (1987) ADF cointegration tests,
Chang (1989) finds that there is TM) evidence of
cointegration among real balances, real GNP, one-month time
deposit rate for two monetary aggregates (real MIA and real
MIB) but cointegration occurs in real M2 equation (using the
same scale variable, and interest rate variable). The
evidence from. the error-correction. model shows that the
short-run specification for the demand for real M2 remains
stable over the sample period (1964:1-1987z4). Lee (1994)1
examines the equilibrium relationship between real MIB, real
GNP, and one—month time deposit rate over the sample period
(1961:3-1992:4) using Johansen (1991) and Hansen and
Johansen (1993) testing procedures. He finds that the demand
for real MIB function shifted downward in the fourth quarter
of 1982, while leaving the income and interest elasticity

unchanged.

 

1 Ph.D dissertation, C.N. Lee, 1994, Department of

Economics , Michigan State University. Also see the
published version of Lee’s Ph.D dissertation (in Chinese)
(1996).

Conventionally, studies on Taiwanese money demand use
bank deposit rates as a measure of opportunity cost of
holding money balances. However, the characteristics of the
financial structure in Taiwan — flourishing unorganized
money markets (U.M.M.) - have been overlooked in the
Taiwanese money demand literature. In the study, we argue
that the interest rate on U.M.M., which has been recorded
since 1947 but omitted in most of the early studies, is a
relevant variable entering tflua money demand relationships
and this interest rate may also play an important role in
the macroeconomic analysis in Taiwan.

The objective of this study is to investigate the
stability of the long-run demand for money functions for
four alternative new definitions of money by incorporating
the characteristics of the financial structure in Taiwan. We
estimate the equations using quarterly data from 196I:4
through I997:3. The sample period covers several regime
shifts (two oil crises 1973, 1979, shifts from a fixed
exchange rate regime 1x3 a floating' exchange rate regime
1978, and financial deregulation since 1980). Since VH3 do
not have theories suggesting the appropriate definition of
money for monetary analysis and particular empirical
measures as clearly superior to others which yield more
stable money demand relationships, we estimate the money

demand functions for four measures of money (MIA, MIB, MlBP,

and M2) and then compare their performance over the same
sample period using the same econometric techniques to
reveal which measure may serve a better guide to monetary
policy.

This dissertation is organized as follows. In Section I
of CHAPTER 2, we briefly review the theories of the demand
for money in the literature. In Section II, we derive a
transactions demand for money model from a multiperiod
utility maximization framework without imposing a cash-in-
advance constraint. This model has solutions similar to
those in Lucas (1988) and possesses some properties which
help understand some empirical findings. In Section III the
importance of aa stable aggregate money demand function in
macroeconomic analysis is discussed. In Section IV we
clarify some questions regarding the appropriate interest
rate variable in the Taiwanese money demand functions a
priori and describe the data series used in the study.

In CHAPTER 3 the statistical properties of the data
series are investigated in order to choose appropriate
econometric techniques to study the money demand
relationships. In Section I there is a brief discussion of
how the time series analysis of models with unit roots has
had a major impact on our understanding of the response of
economic system.tx> shocks. In Section II vwa apply various

univariUe unit root tests (Hylleberg, Engle, Granger, and

Yoo 1990, Fuller 1976, Dickey and Fuller 1979, I981,
Kwiatkowski, Phillips, Schmidt, and Shin 1992) incorporating
seasonality in the data to establish the order of
integration of the individual time series.

In CHAPTER 4 the empirical evidence of the long-run
money demand relationships for four measures of money (MIA,
MIB, MIBP, and M2) is explored and their stability during
I961:4-1997:3 is examined. In Section I equilibrium concepts
in terms of cointegration are sketched. In Section II the
econometric methods for analyzing relationship among I(1)
variables are introduced enui the empirical cointegration
evidence in the four money demand functions is examined.
Parameter stability in these four functions is investigated
in Section III. In Section IV the order of cointegration
rank in the demand for real MIB data is first examined and
linear restrictions on the long-run parameters are estimated
and tested using Johansen (I99I)'s general deterministic
trend model. The robustness of the equilibrium income
elasticity and interest elasticity is checked using four
alternative estimators, (OLS, Stock and Watson 1993,
Phillips and Hansen 1990, Johansen 1991).

In CHAPTER 5 the conclusions are presented.

CHAPTER 2

THE DEMAND FOR.MONEY: THEORY

I: THEORY REVIEW

1 The MOtives of the Demand for MOney

Keynes (1936) articulates three motives for liquidity-
preference, namely, the transactions-motive, the
precautionary-motive, and the speculative-motive. These
three sources of liquidity-preference generate the demand
for money. Baumol (I952), Tobin (1956), Miller and Orr
(1966)1, by emphasizing the choice-making behavior of
individuals and giving the transactions demand for money a
microfoundaton, go further to investigate the optimal
transactions cash holdings for the economic agent. They find
that even the transactions demand for cash can be interest-
elastic due to the existence of transactions costs between

cash and interest-bearing assets. This contrasts with the

 

1 These models emphasize that the necessity of holding
cash is to bridge the gap between receipts and expenditures.
Under the assumptions that transactions are perfectly
foreseen and occur in a steady stream, Baumol’s and Tobin's
models apply reasonably well to salary-earning households.
In constrast to the deterministic Baumol/Tobin model, Miller
and Orr make the opposite assumption that the net cash flows
are completely stochastic, building a money demand model for
business firms.

demand for transactions money developed from the quantity
theory of money Fisher (1911) and the Cambridge approach
(Marshall, Pigou), or Keynes (1936) who postulated that the
effect of interest rates on the transactions money is
negligible. Tobin (1958) explains that the speculative money
demand comes from the risk averse behavior of the agent. The
agent is uncertain of the future rate of interest on
variable market yield monetary asset so he holds money in
his investment balances to diversify the risk from the
portfolio to avoid a loss from holding the non-money asset.
Other than for the transactions purpose, economic agents
hold idle balances in money even when money is dominated by

many other monetary assets as a store of valuez.

2 A Missing Chapter in the Theoretical Mbney Demand
Literature: The Time (Energy, Resources) Saving Aspect of
the USe of Money

 

The distinguishing feature between a barter economy and
a money economy is the use of a medium of exchange
(generally acceptable media of payment, money) in conducting
transactions. In a barter economy, economic agents exchange
goods and services for goods and services, whereas in a

money economy, economic agents sell goods and services for

 

2 It is possible that a risk averter would choose to

hold all his investment balances in non-money asset and not
to hold.:money' at all. If the agent is risk lover,, he
certainly plunges his entire investment balances into
variable yield monetary assets (see Tobin I958).

money and use money to purchase goods and services3. However

money is defined empirically“, or whatever form it is held
in, strictly speaking, by money we mean that money serves
four functions: (1) as a medium of exchange, (2) as a
standard of unit of account, (3) as a store of value (a
temporary abode of purchasing power), and (4) as a final
discharge of debts.

The use of money as a medium of exchange and a store of
value allows purchases and sales to be conducted
independently cflf one another so ii: effectively eliminates
the requirement of a “double coincidence of wants” in the
exchange search process of a barter economy. As a unit of
account and a final discharge of debts, it also reduces the
number of rates of exchange (prices) between different items
quoted in the market and simplifies the information in any
transaction. The use.of money greatly reduces the time and
resource devoted to exchange and therefore facilitates
transactions.

Without recognizing the time saving aspect of the use
of money, it is hard to explain why money is used at all in
the economy. The literature cited above recognizes that

money 1i; indispensable III conducting transactions aumi the

 

3 Some transactions, of course, may be conducted

through barter in a money-economy.

transactions purpose is the reason why it is included in the
portfolit> even. when. other assets with higher yields are
available. The analyses presume that money is used in the
transactions so the demand for money is always positive,
which amounts to imposing a cash-in-advance (Clower)
constraint in the model. However the fundamental reason for
the use of money is unstated in these models, there is a
missing chapter in the theoretical literature in explaining
the money demand behavior.

Saving (1971) fills this missing chapter in the money
demand literature by emphasizing the medium-of—exchange role
of money and time saving aspect of money. In his
sophisticated model, it is demonstrated that without
imposing a cash-in-advance restriction, we can still obtain
a positive transactions demand for money.

In the spirit of Saving (1971) and McCallum (Chapter 3,
1989) models, we build a transactions demand for money model
from a utility maximization framework. The model tries to
capture the notion in Friedman's (1956) restatement of the
quantity theory of money that money is an asset held for the
services which it provides and that these services and the
low transactions cost associated with exchange of money for

other assets (including physical goods) explain the

 

4 Empirical money is defined according to the relative
ease (liquidity) with which an asset may be converted into
“money”, a means of payment.

existence a positive demand for money. Without a cash-in-
advance restriction, the solutions of the model have similar
properties to those in Lucas (1988), so our model provides a
possible explanation for the cash-in-advance constraint in
his model. The resulting money demand function also has some
properties which may help understand some empirical findings

in the money demand literature.

II: TRANSACATIONS DEMAND FOR.MONEY MODEL:
A SHOPPING TIME MODEL

1 Assumptions

 

We assume complete certainty in order to abstract from
precautionary and speculative demand for money and to

concentrate on the transaction motive for holding money.

(1) Preferences

 

The agent is assumed to live for T periods. He gets
utility out of real consumption of goods and services (c)
and leisure time (L) enui he prefers to smooth out the
consumption over the lifetime by borrowing and lending.
Thus, at any point in time, e.g. period 1, preferences are

described by the explicit multiperiod utility function as,

10

U = U(CI’CZ'HH'CT’.LI'LZ’"..'LT)

T T
= Zfl"'lnc, + aZa)"'lnL, 0 < (1,8,(9 < 1 (1,1)
r=l

(=1

where B and w are the intertemporal elasticities of

consumption and leisure, respectively. a is the

contemporaneous elasticity between consumption and leisure.
U has properties of positive marginal utility, and

diminishing marginal utility with respect to each c and L.

(2) Time constraint

 

The agent allocates each period of time (normalized as

1) into leisure (1;), work. (N}) and shopping (transaction

time, 8,). The agent is assumed to be locked in a labor

-

contract, supplying' labor services inelastically (Ah) at

real wage rate my, which is equivalent to assuming that the

household receives real income )4 (== w.N)), the amount of

which unaffected by the household's choice. So the agent

faces the time constraint

ll

Since barter transactions take time, the transaction time S
is assumed as an increasing function of the volume of
transactions undertaken (consumption). For a given volume of
transactions, the amount of time (and energy) spent is
reduced by additional money holding so S is a decreasing

function of real money holdingss. Therefore, S, = g(c,,

m,_l ) , where m,_l = M,_l /p, and g possesses partial
derivatives g3>0, and g5<0, and diminishing marginal
effects, gH<0 and gn>0. Since the greater the time spent in
shopping, the smaller the amount left over for leisure, it

implies that leisure time is a decreasing function in c, and

a2 L,

. . I I 82L!
increaSing in m,.,, 23:—I<0 and ohm >0; 7413—») and 2 <0.

I r-l

 

 

Specifically, it is assumed to take the form of homogeneous

function:

I“
ll

’ Cr-hmf-l' [ = 1,2, ......... IT (1.3)

0 < a, b < 1

where (1 and l) stand for transaction technology parameters

or transactions costs variables.

 

55 Money' holdings facilitate transactions. It is ‘the

real quantity of money that matters. With higher prices,
greater nominal amounts of money are needed for given real
consumption quantities.

The parameter “a” characterizes the time saving aspect
of the use of money and may represent the revolution of
money and payments technology6. For different definitions of
money, the parameter “a” differs. For example, we may

reason that the use of fiat money is less time consuming

than the use of commodity money, in this case a] > a

(.0

Hence, when there is a monetary reform (e.g. from metallic
money to paper money), we may observe changes in the
parameter “a” to reflect alterations in service flows from
a given. real money holdings. We :may also infer that a
broader measure of money has smaller “0” than a narrow
measure because the former has a large proportion of less
liquid assets than the latter. In other words, whenever the
agent needs to Hake payment, he has to transfer the less
liquid components of his transactions balances into a means
of payment first, ‘consequently, this incurs financial
transactions costs (costs like in the Baumol-Tobin model),
and then reduces the convenience of the use of money.

Similarly, for the same definition of money, changes in “a”

 

6 Saving (1971) deals with the model in a disaggregate
manner, deriving demand function for multiple “moneys”
(currency, demand deposits, etc.). In this case, the service
flow (being a means of payment) from different “money” is
not the same because liquidity in various assets differs and
this should be reflected in the transaction time function.
That is, different parameter “a” for each “money” may
appear i11.L. Whereas in our model we consider “money” as an
aggregate so the parameter “cf’ may be thought of an index
of average service flows from various components of nmmey
whatever it is defined.

may reflect some regulatory changes or innovations in
payments system which alter the liquidity of money over time
and in turn simplify (complicate) the payment process7. In
other words, for a given volume of transactions, the

improvement (deterioration) in payments technology saves

even more (less) energy and time by additional money
holding.
The parameter “b" represents the transactions

technology, being determined by geographical factors, or the
nature of transactions. For example, we may expect that
exchange of goods and services is easier in an economy where
the transportation system 115 highly developed than If} an
economy where the transportation system is poor. In this
sense, we reason that the parameter “b” may change over
time due to the development of the transportation conditions

in an economy.

 

7 For example, the automatic transfer from savings to

demand accounts (ATS) authorized by depository institutions
significantly increase the liquidity of savings deposits,
making these deposits serve as transactions balances,
consequently, the transaction costs involved in the transfer
of less liquidity asset to a medium-of—exchange are reduced.

14

(3) The multiperiod budget constraint

To specify the multiperiod budget constraint, we first
describe the trading process. Following Lucas (1988), we
assume that the agent alternates between portfolio
transactions and goods trading in lockstep fashion.

At the beginning of each period (t), the agent

allocates his nominal wealth (M1,) carried from the end of
last period (t-I) into one-period risk free bonds (lfl4) and
money (A44), by trading bonds and money in a single

centralized market. That is,

The bond market is perfectly competitive and the agent is
free to borrow or lend at a same rate of r,. Other than
bonds, money is tine only asset functioning as ea store of
value. The direct cost of holding money is 5,. If 8,>0, the
own rate of money is positive; for example, in the modern
fiat-money world, deposits in the banking system pay
positive interest. 8,<0 may occur in a commodity-money
economy in which perishable goods are used as money and its

real (and nominal) value diminishes over time, other things

15

being the same. We assume that the agent enters period 1
with a given initial exogenous nominal wealth "38.

When security trading is concluded, all agents disperse
the money acquired in the portfolio transactions to produce

or purchase consumption goods at a nominal price p,.

Hence, at the end of period I, the agent's nominal

wealth Wfi is

W, = (1+r,)B0 + (1+5,)M0 + p,y, — p,c, (1.5)

From (1.4) using W0 = B0 + M,,, and W, = B, + M,, we can

rewrite (1.5) as

Bl + M1: (1+r,)W0 ’ (’1'51)Mo 1’ PIJ’I - Pic: (1'6)

Similarly, we generalize the case

”/1 = (1+rI)B-i + (1+8I)MI-l + ply! - plcl

I

B, + M,, x: 1,2, ..... ,T (1.7)

Thus, the bond holding at the beginning of each period up to

T+1 is

 

8 This initial condition allows us to solve the model.

16

By recursive substitution, we obtain the bond holdings at

the beginning of period T+1 (8,):

i.”
l

(1+r,) (1+r2) ----- (1+r,._,) (1+r,) W0
+ (1+5) (1+r3) """ (1+rT-l) (1+r1‘) PI (yl-ci)

+ (1+5) """ (1+r7‘—l) (1+r,)p2(y2-cz)

+ (1+r,._,) (1+ r7.) p,._2 (y7._2-C,-_2)

+ (1+r,) 1),.I (y,-_,-C,-_I )

+ p, (y,.-c,.)

- (r,-8,)(1+r2)(1+r3) ----- (1+r,._,) (1+r,) M,,

- (r2-82)(1+r_,) ..... (1+’7‘_1)(1+"7-)Mi _ _
— (r,._2—5,._2) (1+r,._,) (1+r,) M,_3

- (rm-67.4) (1+r,) M.,._2

- (r,.-6,.) M,._,

- M, (1.9)

To obtain maximum utility, the agent has to consume all his

nominal wealth at the end of his life T, that is, the

l7

terminal constraint (B, = 0 and A4, = 0). Thus, the agent's
multiperiod budget constraint at period 1 is obtained by

dividing both sides of (1.9) by (1+n)(1+5) ..... (1+rfl,)(l+n)

Ply: + szz + pryr

 

 

 

 

 

 

 

O = ”/0 + ..... +
(1+r,) (l+r,)(1+r2) (1+r,)(1+r,)----(1+r,)
_ __P1_C1__ _ P262 _ _ Prcr
(1+r,) (1+r,)(1+r2) (1+r,)(1+r2)----(1+r,.)
_ (rt-‘51)mopi _ (r2-62)mlp2 _ ..... _ (rr‘57')mr—1PT
(1+r,) (l+r,)(1+r2) (1+r,)(1+r2)--~(1+r.,.)

(1.10)

(1.10) can be interpreted as follows.

1
Multiplying both sides of (1.10) by (1+n)-—- and rearranging
1

terms, we obtain

W
(1+n)-;9+ y, + :EI](l+r)4£ly,

l II=2

7 I

= c, + Z“(l+r)"p'

I I==2
T

+ <r,-s. m. + ZU<1+n)‘—p—'(r «m...

I I22

Equivalently,

W T I
(1+r,)p—° + y. + ZU<I+n)"(1-z.)"y,

l I :22

= c, + zn(l+r})"(l—7r,)"c,

I I-2

T I
T ("1"51)mo+ ZI—I(1+rI)-l(1—”I)-l(rl-6I)mI-l’ t = 2,3,-",T

I I32

where n, = £1:iii (1.11)

pr

The left hand side of (1.11) is the agent’s life-time
resources in terms of period 1 consumption at the end period

1, which is the sum of the real value of non-human wealth
(WO/p,) and the present discounted value of current and

future real labor income streams. The right lunui side of
(1.11) represents the present discounted values of

consumption service flows and real service flow from holding

nominal money balances. Note (r,-8,)M, is the opportunity

cost of holding nominal money; (1+n)(1-n,) is real rate of

interest over the course of period t.

19

2 The Constrained MUltiperiod Utility.Maximization Problem

The agent at period 1 is to choose {c,}h, and {ny,}£,
sequences, subject to the time constraint (1.2),
transactions technology (1.3), and the multiperiod budget
constraint (1.10), so as to maximize the multiperiod utility

function (1.1). Therefore, the Lagrangian (I) for the

constrained maximization problem is

f: imaxfiU = 1D(C,) + [3111(62) + B21n(c3) + + BT-lln(c,,.)
+ a[- bln(c,) - (obln(c2) - m2b1n(c3) — w""b1n(c,.)

+ aln(mo)+-waln(mfl + wzaln(m2)+-mr4aln(mflfi]

 

 

 

 

 

 

 

_,_ A, W + ply] + P2J’2 + ..... + PI‘J’T
0 (1+q) (L+nX1+q) (L+nXl+5)~~U+4,)
PIC] _ P262 _ _ pTCT
(1+n) , (L+nXl+Q) (L+nX1+Q)”“U+47)
_ (r, '- 6l)m0pl _ (r2 - 52)m,p2 _ ..... _ (r, - 6T)mT-lpT
(1+n) (L+nX1+Q) (L+nX1+q)~~U+4y)

where X is a Lagrange multiplier.

The first order conditions for the constrained maximization

problem are

20

 

 

 

 

 

 

(”If
E,’ = [l-ba(%)’“'1fl"'c;‘ - rip,(l+r.)"(l+r2)" (1+r,)“
= 0 if c, > 0
< o if c, = o, t = 1,2, ,T (1.12)
i - amo"'m“- It ( -5 )(1+ " 1+ " 1+ "
fink, " I-l pr ’1 I 7“,) ( r2) m( ’7)
= o if m,_, > o
< 0 if m,_, = 0,
t = 1,2,-~-,T (1.13)
1 - 0
at ’
= 0 + 112’:— + szz + ..... _,_ p'l'y’l'
(1+r,) (l+r,)(1+r2) (l+r,)(1+r2)°---(l+r,.)
_ _Pi_c_|_ _ P252 _ _ pTCT
(1+r,) (1+r,)(1+r2) (l+r,)(l+r2)-~-(l+r,.)
_(rI-5I)mopi __ (r2_62)m1p2 _ "_._ (rr"5r)mT—IPT
(1+r,) (1+r,)(l+r2) (l+r,)(1+r2).---(1+r,)

(1.14)

Note if r,<5,, that is, bonds are dominated by money as a

store of value, money is definitely held whereas no bonds

would be held. This is a less interesting case for our
analysis. So we assume that r,>6, Vt and investigate the

case where a positive money demand is possible even when

money is dominated as a store of value. In this case, the

21

only reason for the agent to hold money is to carry out

transactions, therefore the restriction

M,_, _<_ p,c,, or — S 1 (1.15)

must hold.

Assuming that {c,};, and {ny,}£, are all positive, we

can solve for their optimal values in terms of exogenous

variables (demand functions) as follows.

To eliminate A and express {c,}£, and {ny,}f in terms

I=l

07

of "q, using 6%: == aawg' - A;q(1+n)" = 0 and other first
0

 

order conditions from (1.12) and (1.13), we obtain

 

q = (r,-6,)m0 (1.16)

Note that 0 < b,a < I so (I—ba) > 0.

(I) I- I-
[1-(78) '13 I p
c, = m (r,-6,)(1+r,)(1+r,)----(1+r,)—'m,,

l

t=2,3,----,T (1.17)

Ix)
I‘d

 

 

 

 

 

 

_ I—l rl—(Sl &
In4 — m ( )(1+G)(1+fi)””(l+fi) "q
7,—6, ' I
t=2,3, ~,T (1.18)
Substitute (1.16)-(1.18) into (1.14), divide both sides by
(1+r,)’l and then let
"I =
P2J’2 P3J’3 PI'YI‘
1+ W’ + —————
H r') 0 p'y' (1+r,) (1+r,)(1+r,) (1+r,)----(1+r,.)]/p'
”/0 T I ‘1 -|
= (1+r,)—— + y. + 2mm.) (I—m y,
pi I I=2
we obtain the demand for real money balances at the
beginning of period 1:
’ 1 D"W (1 19)
m - acz .
0 rl‘ai
T-l 7‘~1 ,_ 'l‘ l—(UT
where D = [Zfl’+ (a—b)a2w'] = [ '6 + (a-b)0t ].
I=0 I=0 1_fl 1—(0
1
Note that as T—Mt, D = [ + (a-b)a———-]
L—fl L—w
Therefore, the demand function for {C,}L, and {ny,}£,
sequenes are obtained from (1.16)—(1.18) as

c,‘ (1-ba)D"W (1.20)

 

 

 

c,‘ = [1—(3)"'JB"' (1+5) (1+r3>----<1+r,>£iD"W
)6 p.
= [1-(£)H]B'-l (1+r,) (1+r,)-"-(l+r,)LDL&~~‘DT’l D"W
I6 P2 p3 PT
wI-l I-l ' -l
= 11%;) 1B [LI(1—zr.)(1+r.)JD W
I82
t = 2,3, -,T (1.21)
m' =0)"'aa 1 (I+r)(1+r)----(I+r)£'—D"W
I—l (r,—5,) 2 3 I pl
1 I
=(NTaa' [ U-nfifl+n)]an’
(rI—(SI) 1:21
t= 2,3,"~,T (1.22)
where n, = £1:£EL
pr

3 Properties of the Money Demand Function

 

From the multiperiod utility maximization framework, we
obtain the current desired money holdings written as
0 l _l
m0 = aa D W, (1.19)
0"d

This can be expressed in the log form

24

ln(m0) = 1n(aaD") - 1n(r,-5,) + ln(W) (1.23)

 

 

W TI
where H7 = (1+q)-;9 + )5 + 2:1](1+n)4(L—fl04}3 and
l Ii=2
L—fl’ l-afl
D_[1-,6 + (a-b)a,_w]

Therefore, the desired real money balances depends on four

major factors:

(a) the agent’s life-time resources (W’).

(b) the nominal return on money (5,) and on the alternative
asset (bond) (n).

(c) the tastes and preferences of the agent represented by
parameters (a,B,w).

(d) transactions technology (a,b)

To simplify, we write (1.19) as

m0 = f(r,,8,;u)W (1.24)

where u contains (a,B,w,a,b).

From above, a number of properties are in order about
this function:
First, two rates of interest rates entering the function are

one-period rates and no other future rates appear. In other

25

words, given real wealth IV, it is the short-term interest

rate that is relevant in this model.

The directions of the response of "Q to n and 8, are

 

 

5"; a—-—l D"W < o (1 25)
= —a ’

07‘, ("i-(5))2

01"; - aa—L—D"W > o (1 26)

0‘51 — ("1"51)2 .

which display usual substitution effect.

Second, as in all demand analyses resting on maximization of
a utility function defined in terms of “real" nagnitudes,
this function is independent of nominal units used to
measure money variables. If the unit in which prices and
money income are expressed is changed, the amount of money

demanded should change proportionately. That is, nominal
money demand (M5) function is homogeneous of the first
degree in "Q and 1%. As seen in (1.19), the demand for real
balances is expressed as a function of “real” wealth
independent of nominal monetary values. In particular, nfi

is proportional to W’, and it has a unitary wealth
elasticity, other things being the same. As Friedman’s
(1957) permanent income hypothesis suggests that permanent

income is treated as the income flow resulting from a stock

26

of wealth, we define y, = rPV, where r is the yield

applicable to wealth so (1.19) can also be expressed as

. f(’.,5);u)

m0 = -—-r—--y,, (1.27)

and (1.27) in nominal terms becomes

AL,v = I’ (1.28)

[f(r]96|;u) ] -1 .

r

where v = In this form (1.28) is in the usual

quantity theory form. v is (permanent) income elasticity.

Third, other ‘than time wealth. constraint and. substitution
effect on the demand for money, the tastes and preferences
of the agent and the transactions condition also determine

the form of the demand function. These effects are
summarized by a variable tI== u(d,B,dncI,b). The effect of u

may be better examined as that of the issue of the stability

of the money demand function.

27

4 Stability of the Money Demand Function

 

The empirical issue regarding the stability of money

demand function can be investigated by understanding the
preference parameters (0t,[3,d)) and transactions technology

parameters (a,b). Note any changes in tastes (U) or the
transactions technology (L) induced tax social, political
and economic changes can fundamentally change in the
specification of U and L and then alter the functional
fonn of the Honey demand function, which certainly causes
instability of tflua money demand function. Nevertheless we
assume 'that 'these functional specifications aux; the same
under different circumstances. 131 other words, we ck: not
complicate the issue by considering the problem of the Lucas

critique (1976). In the following, we consider the effect of

the parameters'“a” and “b” (n1 mg. The partial derivatives

are computed as

 

 

 

 

 

an; 1 l-fl’ 1-w"
— b D'ZW 1.29
a; ar,—c5,[1—,B 0‘ l—w] ( )
a"; 2 1 (l-w7l)D‘2W > o (1 30)
= acz .
d7 n-d l—w
As mentioned before, changes in the parameter “a” may

reflect the shift of the monetary regime (e.g. commodity

versus money economy), financial regulatory changes or

28

innovations in payment technology, which in turn affect the
costs of using :money' and, then change the desired. money

holdings, for a given wealth and opportunity cost. The

direction of the effect of the parameter “a” (N1 m5 depends

1—flr_bal—af

l—fl l—a)

 

 

on sign of [ ]; when

(l—w)(1-fl") @;
a(1-fl)(1—a)")’ a:

 

O< b s 20

Furthermore, a change in the parameter “b” alters "Q in the

same direction. Intuitively, when a direct exchange of goods
and services becomes harder, the agent is motivated to use a
medium of exchange to conduct transactions to reduce
transactions costs and therefore hold more money.

The effect of transactions costs (N1 the structure of

transactions (barter versus money exchange) can be

understood. by «examining the relationship between ”Q and
transactions c; from (1.16)
. aa 1 .

= 1.16
"q l—bary—d Q ( )

 

Define the average amount of money held per dollar of

transactions

29

mo aa 1
c, l—ba r, —-(5,

 

 

As we argued above, (1.15) must hold, that is h .<. I,
therefore,

aa.<. (1-ba)(r,-6,) (1.31)
and

0 S (l-baX’i—6I)

 

a

The partial derivative of h with respect to the parameters

\\ an and \\ b” are

 

 

9'— — a 1 > o 1 32
d2 — l-ba r,—5, ( ° )
fl — ““2 1 > 0 1 33
ab " (1-ba)2 r,—5, ( ' )

That is, the ratio of transactions with money to total

transactions is increasing in transactions costs parameters

\\

a” and “b”. If payments become easier or barter
transactions become cumbrous, the use of money is encouraged

in the exchange process so the proportion of the trades

30

through barter are reduced. Note the amount of transactions

with money is "n, therefore,

(‘ '>—<1 “a 1)‘>o 134
c, m0 — 1—bar,—5, c,_ (' )

 

is the quantity of transactions via direct barter.

Note (1.16) is not a demand function in our model.
However, this relationship between desired consumption, the
demand for real balances, and the nominal interest rates is
frequently studied in empirical work so we also investigate
the stability of this relationship. As in time analysis of
the “true” money' demand function (1.19), a stable
relationship between the desired real balances, transactions

variable and opportunity cost variable is determined by the

constancy of tastes (a,B) and transactions technology
(a,b). Ihi practice, measured income ()M such as CHHU is
frequently used as a proxy of transactions variable (c). If

transactions and income (or final output) obey ea constant

relationship over time, say c, ‘= njq, where n is a

constant, (1.16) can be written in terms of y as

 

mO l—ba rl_é-ln)l ( )

3|

Thus, we expect (1.35) has same properties as (1.16).
Furthermore, the ratio of money to income, the reciprocal of

(current) income velocity, can be expressed as

m0 1 aa 1
— n
y, v l—baI3—d

 

(1.36)

which is independent of income and negatively related to the

spread of interest rates, other things being equal.

5 Cash—in—Advance MOdel versus the Shgpping Time.Model

Next we compare the transactions money demand model
developed ‘by ZLucas (1988) anmi our' model. By assuming a
constant relative risk aversion utility function of a
homogeneous of degree one function of consumption and

imposing a cash-in-advance constraint,

I’a c S A4 (Eq.4 in Lucas) (1.37)

where 1’ is the price of goods, at and c: are vectors; a. 6

[0,1] is the fraction of purchases of good i that must be
covered by money, Lucas (1988) derives a proportional
relationship between desired real money balances and

consumption

32

A! .
77 = Za,g,(r)c = h(r)c (Eq.15 in Lucas) (1.38)

where c = k(Q)W, (Eq.16 in Lucas); Q are securities
prices; W’ is wealth.
Interestingly, we notice that (1.38) has a similar form

to be

. _ aa 1 .
nq _ l-barq-d q

 

(1.16)

in our model. From his cash-in-advance constraint (1.37), we
reason that Lucas (1988) implicitly recognizes that barter

exchange is possible since

However, he does not consider it explicitLy in the nmdel.
Hence, by assuming a lcgarithm utility function of
consumption and leisure9 (a monotonic transformation of
Cobb-Douglas function) and the Cobb-Douglas leisure function

of consumption and real balances, our model gives a possible

 

9 When we considered different specifications of the

1 c"" -1 L1” -1

 

utility functions, l/(c,,L,) = [ ' -+d ]“’, see
l—y l—a l-fl

(Mankiw, Rotemberg, and Summers, 1985), the proportional

relationship between real balances and wealth (or

consumption) is no longer maintained in the model.

33

missing explanation for the existence of his cash-in—advance
constraint, namely, the time saving aspect of the use of
money. Note the utility function is also a constant relative
risk aversion functionuk (mrr model demonstrates that even
without imposing that money must be used, we can still
generate 23 positive money demand for transactions purpose

even when money is dominated as a store of value.

6 Empirical Issues: Arguments in the Meney Demand Function

Since an agent cannot hold all the money he might want,
in practice, there is the question of the constraint that is
imposed on money balances - whether the appropriate
constraint is a measure of wealth, permanent income, or
current income. In our model, the first two legitimately
enter the “demand function” for money, which can be seen
from (1.19) and (1.27).

Traditionally the use of current income as an argument
in the demand function for money often has been associated
with the notion that money is used primarily to effect a
given transactions volume (Keynes I936, Baumol I952, Tobin

1956, Miller and Orr 1956), and that a demand for cash

 

10 , , . , —-u"(c,)c,
The risk averSion coeff1c1ents are -—;?—;-== 1 and
CI
—u"(L,)L,
—-——-— l.
u'(L,)

34

balances depends on costs and yields. In our model, even the
money demand function is subject to a wealth constraint, the
model is also able to capture this relationship. This can be

seen from

. aa 1 .

m0 = l-ba ’1’5) c, (1.16)

 

This relationship is frequently studied in the empirical
work. Interestingly, the desired money holdings are
proportional to consumption and negatively related with the
opportunity cost variable. Several empirical studies, such
as, (Lucas I988, Rasche 1990, Hoffman and Rasche 1991, Stock
and Watson 1993, Hoffman, Rasche, and Tieslau I995, Rasche
and Hoffman 1996) find a unitary income elasticity and a
negative short-term interest effect. These studies find this
relationship as a steady-state equilibrium property. If, in
addition, in the steady—state c-vty is stationary, then the
results follow our model. Thus, this model may help
understand these empirical findings.

A second issue is concerned with whether a short-run
interest rate or a long-term rates is the relevant variable

mm the money demand function”. Unlike Poole (1988), among

 

n The importance of this issue can be understood
through the following paragraph quoted from Laidler (1966).
‘If investment is more sensitive to long rates of interest
and if the first impact of a change in the money supply is
on short rates, then in order to have a theory as to how

35

others, who has advocated the use of a long-term in the
money-demand function, our model suggests that a short-term
rate is the appropriate argument since, given real wealth,

no other future rates appear in the function.

 

changes in the money stock affect the economy, one must have
a theory as to how interest rates of various terms are

interrelated. Thus, -~- the theory of term structure of
interest rates comes to be a central topic, essential to any
description of the mechanism by which changes in the money

supply affect the real variables in.en1 economy.’ (pp.554—
555).

36

III: THE STABILITY OF THE AGGREGATE MONEY DEMAND FUNCTION
AND ITS POLICY IMPLICATION

Although the Keynesian and Monetarists have emphasized
the “demand” side of the economy in their policy
prescriptions, they held a different view of the
stability/instability of the aggregate demand for money
relationship.

For example, Keynes (1936) explicitly postulated
potential instability in the aggregate demand for money
function, which was asserted to shift erratically and
unpredictably with rumor and expectations so he doubted the
effectiveness of monetary policy”. Keynesian analysis
usually treated. monetary' policy' as subsidiary to fiscal
policy as EH1 income-stabilization device. (hi the contrary,
Friedman (1956) stated that the demand for money was
“empirically” stable function of a few arguments. He argued
that a stable money demand for money function played a vital

role in the analysis of the economy as a whole, such as the

 

12 Keynes (I936) viewed that money affected the economy
through its direct effect on the interest rate, which in
turn affected the investment and employment, and finally
through the nudtiplier process (if nerginal propensity to
consume is less than 1) to affect the aggregate demand and
the output (or' employment) However, he doubted that the
quantity of money was able to work its way into the economy
in the end. For example, the changes in interest rate may be
small since the speculative demand for money may shift
around due to the expectation of the monetary policy or the
investment is inelastic to the interest rate (see Chapter
13, Keynes I936).

37

level of money income or of price. Although he believed that
money mattered in the short-run and recognized that
manipulation of the quantity of money was a powerful
(perhaps dangerous) policy tool, Friedman (1968) doubted the
ability of the use of money to stabilize the economy due to
both inside lag and outside lag in the monetary policy of a
central bank. Consequently, he developed a policy idea of
the money-supply growth rule.

Although the stability/instability of money demand
relationship is not the only difference and would not be the
decisive factor which distinguished Monetarism from
Keynesian”, we recognize that the stability issue is the
central assertion in Monetarism and it is certainly
associated with the importance of the quantity of money in
the economy. To fix the idea that money matters and how a
stable money demand relationship can help formulate monetary
policy, as a first step we need to understand the quantity

theory of money.

 

13 In a simple IS-LM analysis framework, how effective

monetary policy can depend more than the slope of the LM
curve. The responsiveness of aggregate demand to changes in
interest rates as well as the direct responsiveness of
expenditures to changes in the quantity of money are just as
important. A stable money demand function does not guarantee
the potence of monetary policy.

38

1 Quantity Theory of Mbney and Mbnetarism

The ultimate objectives of monetary policy are to
promote price stability and economic growth. The efficacy of
using monetary aggregate targets to achieve ultimate policy
objective depends importantly on the existence of a stable
or predictable demand for money. To put it another way, the
velocity of money must be reasonably stable and predictable.

From the equation of exchange (Fisher 1911), we know

AJV == PY (1.39)

in terms of growth rates

 

I! + I’ = I’-+ Y. (1.40)
Substituting M“ = M‘],
PY
V == A!”

where A4, Y} enmi.P denote the nominal money stock (however
defined), real GNP, and general price level, respectively; V
represents income velocity, interpreted as a measure of how
much money firms and households desire to hold relative to

the level of nominal income. If, in the extreme case where

39

V is constant, as Fisher (1911) claimed, determined. by

social and economic factors, or the demand for money is

inelastic with respect tx> the variables 1J1 A4“, (1.39) is
the model of the determination of money income. In addition,
if, in the long-run, the real output (income) is determined
by “real” side of economy (factors of production, technology
and relative prices) such that output is fixed at full
employment level, (1.39) says that the money stock
determines the general price level. Keeping the nominal
supply on a stable growth will stabilize the behavior of the
price level.

Friedman (1956) reformulated the quantity theory' by
arguing that I’ did not have to be numerically constant over
time, but required the stability in the functional relation
between V (or the quantity of money demanded) and the
variables that determine it. From (1.39)-(1.40), we learn
that as long as I’ is predictable or if the growth in the
demand for money accompanying a given growth of income can
be predicted, the monetary authority can influence growth of
money income (aggregate demand) by controlling monetary
growth. Inaccurate predictions of velocity growth can lead
to monetary targets that are incompatible with ultimate
objective. For example, underestimation (overestimation) of
the growth in velocity can lead the monetary authority to

follow monetary policies that are unduly expansionary

40

(restrictive), resulting in unacceptably high inflation (or
recession).

The principal of the quantity theory of money is easy
to understand through the real-balance effect”; changes in
the money stock may result in changes in real output or
prices or both in the short-run. The monetary authority can
attempt to achieve the short-run output-inflation
combination most consistent with its policy objective by
influencing the level of aggregate demand (nominal income).
However, (1.39) does not tell us how much a change in PY is
reflected in Y and how much in P. To infer this, we need to
specify all the determinants of the variables associated
with (1.39) to capture the complicate transmission from
money to price and output which is hidden in (1.39).

Economists may have different views of the way an
economy works and. then build their own view of
macroeconomic models, however, we will not go further about

these models, (for the macroeconomic models of Monetarism,

 

14 Friedman (1974) illustrated time quantity theory (Hf

money as follows. ‘Suppose that the nominal quantity that
people hold at a particular moment of time happens to
correspond at current prices to real quantity larger than
the quantity that they wish to hold. Individuals will then
seek to dispose of what they regard as their excess money
balances; they will seek to pay out a larger sum for the
purchase of securities, goods and services, for the payment

of debts, and as gifts ----- ’, 'If prices and income are free
to change, the attempt to spend more will raise the volume
of expenditures and receipts, expressed 1J1 nominal units,
which will lead to a bidding up of prices and perhaps also

4l

see Friedman 1974, Monetarism, edited by Stein, 1976). We

 

have seen that a stable money demand function is the central
proposition of monetarist models. We also observe that this
relationship is an important element in the new classical
economics models Sargent and Wallace (1975), New Keynesian
analysis (Mankiw, 1991), and in some empirical real business
cycle models (King, Plosser, Stock, and Watson, 1991) as
well.

We should note that the monetary authorities may use a
dynamic macroeconomic model to compare alternative monetary
policies (e.g. pegging interest rates versus pegging
monetary aggregates) in order to choose a preferable policy
instrument to achieve its policy goal. As Lucas (1976)
suggests, in making policy comparisons, it is necessary that
the model of private behavior, such as the consumption
function, the investment function, and the money demand
function, be “structural”, that is, invariant to the policy
rule in effect. A shift in the empirical money demand
function due to a policy regime shift (or due to other
reasons) certainly invalidates these policy analyses.

From above, we may realize how empirical evidence
against a stable money demand function can invalidate these
macroeconomic models and undermine the importance of the

monetary policy. In the CHAPTER 3 and CHAPTER 4, we will

 

to an increase in output (pp.2-3, “A Theoretical Framework

42

investigate the empirical evidence of the stability of the
aggregate money demand functions in Taiwan over the period
of I961:4—1997:3 using various econometric techniques. First
we describe the variables chosen for the study of the
Taiwanese demand for money in the final section of CHAPTER

2.

IV: THE ARGUMENTS IN THE TAIWANESE DEMAND FOR.MONEY
FUNCTIONS: DATA DESCRIPTION

Economic theories (Keynes 1936, Baumol 1952, Tobin
1956, 1958, Friedman 1956, Miller and Orr 1966, Saving 1971,
Lucas 1988, McCallum 1989) suggest that the demand for money
can be explained by functional relationships which include a
relatively small number of arguments. They can 1x2 a scale
variable, such as permanent income, wealth, or current
income, and an opportunity cost variable such as a nominal
interest rate or some measure of the expected inflation
rate. If nominal balances have been the dependent variable,
the general price level is also included in the function.
Algebraically, the demand for money conventionally takes the

form of log linear function

ny = jr(y,,R,)-+ p,, f, > 0, j} < 0 (1.41)

 

for Monetary Analysis”, Friedman 1974).

43

where m: is the log of quantity of money demanded; y is

scale variable; R a vector of interest rates on the

alternatives tx> money; p the log (Hf the general price

level. Since economic theory predicts that the demand for
money is a demand for “real” balances (money holdings
measured in constant purchasing power terms), a price level
elasticity of demand for nominal balances is frequently

constrained to one. In addition, j" is increasing in y and

decreasing in the elements of R.

Many empirical studies estimate the specification

(m, - p.) = (m,- p.) = f<y,,R.> <1-42>

(1.42) is empirically referred to the long-run (equilibrium)

money demand function which assumes that the observed

quantity of real money balances (nt- 1;) corresponds to the

quantity of real balances that are desired at the current
value of the arguments of the money demand function. It is

distinguished from the short-run demand function15 (Goldfeld

 

15 The widespread practice in the short-run money
demand analysis is to add a lagged dependent variable to the
equilibrium specification (1.42). Such stock adjustment
specifications are motivated by cost minimizing behavior in
the presence of quadratic costs of adjustment toward the
agent’s long-run demand for money functrmn. In the short-
run, some dynamics may appear in the equilibrium
specification so that the current money balances can be
explained not only by current values of the arguments but
also by the lagged real balances and lagged values of the

44

1973, 1976) developed from the partial adjustment model
(Chow 1966), see Rasche and Hoffman 1996 for the
clarification of the long-run specification, and the
criticisms on the partial adjustment models.

The choice and the measurement of the variables for the
study of Taiwanese demand for money which reflect the
corresponding economic notions and time data available are

described in the following.

1 Measure of MOney

 

A stable aggregate demand for money function is an
important element in macroeconomics, however we do not have
theories suggesting the appropriate definition of money for.
monetary analysis and particular empirical measures as
clearly superior to others which yield more stable money
demand relationships. To compare the performance of the
money demand functions in Taiwan for alternative definitions
of money for the same time period (1961:4-1997:3), we will
study four measures of money, namely MIA, MIB, MlBP, and M2.

Currently, the Central Bank in Taiwan has three
definitions of monetary aggregates, MIA, MIB, and M2,

publishing these three series on a monthly basis. MIA and

 

arguments. Hence more general specification of the demand
for real balances can be written as m, = f(y,,R,; lagged

yr! RI' ml)'

45

MIB are narrowly defined monetary aggregates consisting of
currency in circulation and the demand deposits of the
individuals and enterprises in the monetary institutions”;
they largely serve as transactions balances. M2 is a broader
concept of money; it consists of MIB and a large proportion
of less liquid assets including time and time saving
deposits, foreign currency deposits of individuals and
enterprises in the monetary institutions, all the deposits
in the Postal Savings System (P.S.S), and others. Data on
these three aggregates are available from July 1961 in
Financial Statistics Monthly. In February 1997, the Central
Bank in Taiwan changed the definition of money, especially
in the definition of M2 by excluding less liquid
components”, and including new components18 to take account
of financial innovations. The data used in our study are
redefined monetary aggregates and are retrieved from the FSM
data bank of the Taiwan Economic Data Center”. We report

the components in the Appendix 1.

 

16 Monetary institutions are defined as financial

institutions which are able to create money (Financial
Statistics Monthly, November 1997, pp.190).

17 These include bank debentures issued, savings bonds
and treasury bills-B issued by the central bank held by
enterprises or individuals and foreign exchange trust funds.

18 They are repurchase agreements and non-resident NT
(New Taiwan dollar) deposits.

19 I wish to thank Professor Lee, C.N. for his
assistance with the data in my study. The web site address

46

(I)

*v

v‘

I‘-

l).

 

We notice that tine passbook savings deposits 11) the
Postal Saving System (P.S.S.)20 are included in.bfl2 but are
excluded in MIBZK These postal deposits are also
transactions related deposits and are similar to the
deposits included in MIB. Furthermore, the amount of this
component is nontrivial, around 30% of MIB (on average
1980:12 - 1992:12, see Table 4.2 1J1 (3J0 Lee Ph.D
dissertation, Department of Economics, Michigan State
University, 1994). A priori we will reason that the
aggregation of the same type of deposits may reveal similar
money demand behavior of Taiwanese people. Thus, for
experimentation, we construct another monetary aggregate

(MlBP) by adding these transactions related deposits of the

 

of Taiwan Economic Data Center is
http://I40.lll.l.22/moecc/rs/pkg/tedc/tedc2.htm.

x) The Postal Savings System is a major financial
competitor in the deposit market, competing with the
domestic banks for demand and time deposits (Semkow 1992,
pp.43-44). According tx> the Central Bank’s compilation of
monetary aggregates, the Bank groups monetary assets by the
type of institution (monetary versus financial
institutions), not by the similar type of deposits. Because
the Postal Savings System is not defined as a monetary
institution, its deposits are not supposed to be counted in
the monetary aggregates. However, in the new definition, all
deposits are included in M2 as a non-MIB component.

21 In the study of the equilibrium M1 demand for Japan,
Rasche (1990) makes the observation that deposits in the
Postal Savings System are excluded in M1 measure which is
the most comprehensive measure of transactions money
available for Japan.

47

P.S.S into MIB22 to see if this seemingly homogeneous
monetary aggregate yields quantitativeLy and qualitatively
different conclusions from MIB.

The quarterly average series for each monetary
aggregate is measured as the geometric average of the three

end-of—month observations for 1961:7 - l997:9.

2 Scale variable

 

Whether' the appropriate constraint imposed on inoney
balances is a measure of wealth, or income remains an open
question.

The use of income as a constraint in the money demand
function is often associated with the notion that money is
used principally to carry out a given transactions volume,
for example, (Baumol I952, Tobin 1956, Miller and Orr 1966).
The wealth constraint emphasizes the role of money as a
productive asset and focuses attention on the equilibrium of
the balance sheet, and the allocation of assets and the
services that money provides, (e.g. Friedman 1956, Tobin
1958, Saving 1971, Lucas I988, McCallum 1989). The model we
derived in Section II suggests that both a measure of wealth
and of income are relevant variables entering the demand for

money relationship. As in many empirical money demand

 

22

The aggregate (MIBP) is constructed by the sum of
the components with retrieval codes listed in the FSM
databank MlBP = MIB + LPSSGSD@TA + LPSS@SD@PSD.

48

 

.'

~-

HI

-..

‘2-

'5

'f‘

~‘\

amv

~~.

¥..

 

studies, we use real GNP as a measure of the scale variable
for the four specifications of the money—demand functionza
The data are from the NIAQ databank of Taiwan Economic Data
Center.

The four measures of money and real GNP are deflated by
the GNP deflator (1991 = 100). In the following study, they

are denoted as RMIA, RMIB, RMIBP, RM2, and y.

3 Measure of the Opportunity Cost of Holding Mbney Balances

The rate of interest entering the demand function is an
important variable in a macroeconomic model since it carries
the transmission mechanism from a change in the money policy
to other sectors in the economy. Hoffman and Tahiri (1994)
point out that there is no conclusive evidence as to whether
money demand in the developing countries is sensitive to an
interest rate measure. Hence, to find.aa theoretically and
empirically relevant variable would help us understand the
working of the economy in Taiwan and help the monetary
authority select an appropriate policy.

Conventionally, bank deposits rates (e.g. one-, three-,

six- month time deposit rate) are employed as a

 

23 In the Taiwanese money demand literature, Lyo (1970)
used both wealth and real GNP (and unorganized money market
rate as an opportunity cost variable) to study the long-run
demand for real M1 (currency + demand deposits) and real M2
(M1 + time and savings deposits). The data are annual data
(1947-1968).

49

representative of “the” interest rate variable in the study
of the ‘money' demand functions in ‘Taiwan. Perhaps it is
because of the availability of the data. In Financial
Statistics Monthly, the banks rates have longest records
(starting 1961:7) and the data (N1 the money market rates,
which are frequently used in the money demand studies in the
developed countries, are not available until November
1980“. It appears that the choice of “the” rate is
underdiscussed in the Taiwanese money demand literature
since we observe that some. studies mistakenly treated a
proxy of the own rate as the opportunity cost of holding M2.
Moreover, a negative coefficient on the own rate is
frequently obtained in the demand for M2 studieszs. Shen
(1995) first makes this observation but does not provide
suggestion of an appropriate measure of opportunity cost of
holding M2. This fundamental issue should not be overlooked
before we go any further to examine the money demand
relationships otherwise interpretations of results can be

very misleading.

 

24 The money market was established in 1976. Note the

treasury-bill (TB) market was established in April, 1973 and
that the TB rates are available from October 1973 on in
Financial Statistics Monthly.

25 See Lin (1997) for demand for M2 function literature
review.

50

Since bank rates were subject to the ceiling rates set
by the central bank before 1989ufl the structure of deposits
rates did not vary freely with the money market condition
during much of the sample period considered in this study.
They may not adequately capture changes in the opportunity
cost of holding money balances. Hence, the market determined
rate may be a better measure. We argue that another interest
rate should also be included in Taiwanese researchers’
choice list of opportunity cost variables in the money
demand study. In the following, we discuss why we regard the
own rate of money and the unorganized money market (U.M.M.)

. - - 7
rate as relevant variables a prioriz.

(1) The own rate on money

 

Since deposits (money) in the commercial banks pay
interest and a higher (lower) deposit rate attracts
(discourages) the public to hold these assets (due to the
same direction of both substitution and income effect), the

own rate is a relevant variable in the money demand

 

26 Interest rate regulation in Taiwan dates back to

1947. Since then, the maximum rates for various kinds of
deposits and loans were determined by the central bank
(Wu,1995). The process of interest rates deregulation began
in 1980. In 1989, the interest rate regulation was totally
removed (Semkow Ch.6 I992).

27 A couple of Taiwanese money demand studies employed
the U.M.M. rate as a cost variable of holding money (e.g.
Lyo I970, Shui 1983, Lin 1997) but little was said about its
relevance and its importance.

5]

relation. Unless the own rate is close to zero, we should
include it in the study to see if the effect of the own rate
is of statistical significance. Since all the components
except currency and demand deposits in MIA earn non-zero
interest and we observe that the interest rates paid are not
negligible, which can be confirmed by the constructed own
rates in Figure: I, we construct the own rate for each
measure of money.

The proxy of the own rate for each monetary aggregate
is constructed on a monthly basis from the own rates on the
individual components28 and is characterized as a short—term
rate. The weights are the share of the components in
monetary aggregates during the previous month. The own rate
on the individual component is from the Financial Statistics
Monthly (FSM), listed as “Rates of Banks”. The quarterly

rates are obtained from the arithmetic average of monthly

m2

. . -h .I, .
observations and we denote themII”, I , I”, and I

(2) Unorganized money market rate

 

The importance of the role played by the unorganized
money market (a curb market) in the financial structure in
Taiwan has been emphasized by several studies in the

Taiwanese (economic literature (e.g. Pk) I981, Shea I979a,

 

28 The own rate for time deposits is the average of

one— three and six— month “Rates of Banks” listed in FSM.

1979b, 1983, 1986, I991, Liang and Chen 1985, Yang 1984). As
pointed out by Wijnbergen in a series of studies for South
Korea (1982, 1983a, 1983b, and 1985), the typical financial
structure for developing countries is characterized by
undeveloped primary securities markets and the existence of
the unorganized money market (U.M.M.). This is also observed
in Taiwan. Appendix 2 exhibits the source of funds borrowed
by private enterprises during 1976-1988 in Taiwan.

Due to severely rationed bank credit, the public lends
directly to firms via the unorganized money markets,
bypassing the banking system. In Taiwan, the private
enterprises actively borrow from the U.M.M.29 despite the
existence of the organized money market (established in
1976) and substantial reforms launched. to :modernize the
Taiwanese financial system in 19805 (see Semkow 1992, 1994).
These loans made to the firms are supplied by friends,
relatives, and professional money lenders. When looking at
the balance sheet of Taiwanese people (private enterprises
and individuals), we observe two major monetary assets money

(currency anmi bank deposits) and time loans outstanding at

 

29 Postdated checks are one example of the U.M.M.

instruments. They are very popular means of raising funds in
Taiwan, especially among small firms. Invoices for goods are
stated on the basis of cash payment, but are negotiated into
60 to 90 days postdated check payments, often including rate
of interest for the supplier of the purchaser’s loan. The
rate is about three times that of money market rate and bank
rates, (rate on postdated check = 22.44%, I-month commercial
paper rate = 7.86%, October 1997, FSM November 1997).

53

UMM appearing on the sheet30 so that money and loans
extended at U.M.M. are gross substitutes, obeying the adding
up constraint. On a priori we have reason to regard the
U.M.M. rate as tflua relevant opportunity' cost of Iholding
money in Taiwan before testing its significance.

Finding a statistically significant negative effect of
the U.M.M. rate has an important policy message. Wijnbergen
(I982, 1983a,b, 1985), by incorporating facts about the
financial sector of LDCs (absence of security markets,
existence of aa curb merket), analyzes credit policy in 51
macro-model in which the money demand function and the
aggregate supply function are negatively related to the
U.M.M. rate. He uses the existence of the curb market to
explain the empirical observation that monetary policy in
the developing countries has effects that differ from what
we would expect given.the predictions of the standard macro-
model. For example, tight credit policies may lead to higher

inflation and less output (stagflation) in the short run

 

30 It is not argued that there are not other paper
assets (e.g. bonds and equities) appearing on the balance
sheet of Taiwanese households and firms. The assumption is
made on observations, for example, that capital markets in
Taiwan are still in the infancy (see Semkow 1994) and most
treasury bills are bought and held by commercial banks as
liquidity assets (Ch.8, Semkow 1992). So those paper assets
may comprise only small portion in their portfolio. Of
course, we may observe more varieties of assets held in
their portfolio because liberation of financial markets and
financial renovation since the 19808 provide Taiwanese
people with more financial opportunities.

54

rather than an lower inflation and less output as
traditionally assumed because of additional transmission
channel of monetary policy into the supply side of the
economy via the real costs of working capital (“Cavallo-
effect”) other than demand side transmission channel of
monetary policy. If this is the case, policy makers should
be aware of the adverse effects of the monetary policy
documented in these papers and select appropriate measures
to offset these short-term macro-economic consequences.

The U.M.M. rates are survey data”; The survey was
initially conducted by the Bank of Taiwan until 1970:3. The
data are available monthly from September 1961 in the
Financial Statistics Monthly. In our study we use the
“Unsecured Rates in Taipei City” recorded in FSM. However,
the series appears inconsistent before and after 1970:3 due
to changes in the way of surveying. In order to remove the
inconsistency and obtain the longest series for this
variable”, the two series obtained in FSM: series 1
(1961:9-197I:2) and series 2 (1970:3-1997:9) are chained at
March 1970 in! first multiplying 1961:9-1970:2 data tnl the

ratio of the average of series 2 to the average of series 1

 

31 The earliest records on the U.M.M. rate dates back

to May 1947. See Yuan (1986) for detailed research on the
unorganized money market rate in Taiwan.

32 Professor Rasche suggested that :U: was problematic
to obtain credible statistical results if the sample period

55

during 1970:3-I971:2 and then this adjusted series is linked
with the series 2 to obtain the entire series. The quarterly
data are arithmetic average of the monthly data, denoted
umm.

All the data series are seasonally unadjusted. The four
real monetary aggregates and real GNP are in logarithms. We
plot these series and the spread between the umm rate and
the own rate of money (umm—i) in Figure I. The annual
growth rates for y, RMIA, RMIB, RMIBP, RM2 and inflation
rates (computed from GNP deflator) are presented in Figure
2.

Figure 1 suggests that the own rate and the interest
spread for each aggregate display similar trend. They peak
in 1973 and 1979 when two oil crises occurred and inflation
rate climbed up to double-digit. Taiwan does not have a
particular high inflation rate over the whole sample period
except the episode of two oil price shocks. On average,
inflation rate is 5.30% annually. As Figure 2 suggests that
real GNP grows at an average annual rate of 8.75% over the
sample period and displays the mid-70’s and early 80's
recessions common to developed countries. The annul rates of
growth for four real monetary aggregates have been very
similar 11) one another, both.cn1 a trend and.cx1 a cyclical

basis; with the two oil price shocks, four real monetary

 

is too short, especially in conducting cointegration

56

aggregates grow at a negative rate. The average annual
growth rates for four measures of money are RMIA 11.59%,

RMIB 14.05%, RMIBP 14.62%, and 15.48% for RM2.

 

analysis.

57

 

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59

CHAPTER 3

STATISTICAL PROPERTIES OF UNIVATIATE TIME SERIES IN THE
DEMAND FUNCTIONS FOR REAL EALNACES IN TAIWAN: 1961:4-1997:3

I: INTRODUCTION

The rapid development of time series analysis of models
with unit roots has had a major impact on our understanding
of the response of economic systems to shocks.

It is common practice in macroeconomics to decompose
real variables such as output into a growth component, which
is associated with real factors such as capital
accumulation, population growth, and technological change,
and a cyclical component. According to the conventional view
of the business cycle, for example, Monetarist (e.g.
Friedman 1974) and neo-Keynesian theories, fluctuations in
output are assumed. to 1x2 driven. primarily' by shocks to
aggregate demand, such as monetary policy, fiscal policy, or
animal spirits, and shocks to aggregate demand are assumed
to have only a temporary effect on output; in the long-run
the economy returns to the natural rate. The time series of
real output has a tendency to return to a deterministic
path, or to revert toward a trend, following a shock. Since

transitory fluctuations are assumed to dissipate over time,

60

a decline in real GNP below trend today has no effect on
forecasts of the level of real GNP in the far future. This
class of stationary processes is called trend-stationary
processes. Many empirical examinations on real GNP using the
United States data, for example, Nelson and Plosser (1982)
and Campbell and Mankiw (1987), find a great deal
persistence in real GNP and are skeptical about this
implication, suggesting that shocks to GNP are largely
permanent. Instead of modeling the growth component as a
deterministic trend and attributing all variations in output
changes to the cyclical component, a series whose
fluctuations are partly temporary and partly permanent can
be modeled as a combination of a stationary series and a
random walk (stochastic trend, Beveridge and Nelson 1981).
The random walk carries the permanent part of a change and
the stationary component carries transitory part of a

Changel. Thus, real business cycle models (Kydland and

‘

1 Any first-difference stationary process can be

decomposed as the sum of stationary(x',‘) and random walk
Qc3mponent(x,”): Let Ax,= u + c(L)s, , where the roots of C(L)
lie outside the unit circle; x, = x‘,‘+ x,”. There are two

kinds of decompositions commonly used in the literature:
(1) The Beveridge and Nelson (1981) decompositions: x, =

*i ‘,‘+ x,", where x,” = p + x,”_,+ C(1)8, and x',‘ = d(L)8,, d,= -
ac
c,. Note the innovations in x’,‘ and x,” are identical so
"i-H.
t hey are perfectly correlated.
( 2) An unobserved components model: x, = x‘,"+ x,”, where x,” =
H + x,”_,+ r], and x‘,‘ = b(L)5,, E(n,5,) arbitrary. See Nelson

6]

Prescott 1982), which attribute a major role to supply
shocks in fluctuations of real output, and the traditional
view of demand shocks, can coexist to explain the business
cycle. In addition, if the output is characterized as an
integrated stochastic process, we may question the natural
rate hypothesis; aggregate demand shocks may have permanent
effects of the level of output as described by models of
Inultiple equilibria (e.g. Diamond 1984).

From a forecasting perspective, the implication of
integrated series is that if fluctuations in output are
dominated by the permanent components, the series has a
tendency to move farther away from any given initial state
as time goes on. Thus a decline in output today lowers
forecasts of output into the infinite future.

rFrom a purely statistical viewpoint, many statistical
procedures rely critically on whether the series is
integrated or stationary (including trend stationarity) . The
presence of a unit root in its autoregressive representation
produces serious problems of statistical inference. Granger
and Newbold (1974) find that two independent integrated

S'eries can display spurious correlation, characterized by

1”nigh coefficient of multiple correlation R2 and an

QNitremely low value for the Durbin—Watson statistic in the

\

and Plosser (1982), Cochrane (1987), and Stock and Watson
1988) . Note the variance of the random walk is the same for

62

regression. Phillips (1986) provides asymptotic theory for
spurious regressions that relates general integrated random
processes. He demonstrates that the usual t-ratio and F

significance test do not possess a limiting distribution,

but diverge as the sample size becomes large. The use of

conventional asymptotics in setting the critical values of
these tests leads to the rejection of no relationship at a
rate increases with the sample size.

In order to avoid the spurious regressions and non-
standard limiting distribution of coefficients in the
regressions which involve integrated variables and to choose
appropriate tests and estimation procedures to study the
relationships among the variables, we first need to
investigate the nature of the individual time

Carefully

S eriesj

II: UNIVARIATE UNIT-ROOT TESTS

A standard procedure of detecting unit roots in a data
S:eries is to apply Dickey-Fuller type univariate unit root

tests (Fuller 1976, Dickey and Fuller 1979, 1981), or

Phillips (1987), Phillips and Perron (1988) unit-root tests.

S.‘ane all of our data series in the study are seasonally

\
any decomposition of a unit root process into stationary

63

unadjusted, they exhibit substantial seasonality in the
levels, especially in real GNP, which can be seen in Figure
1. We should account for the effects of seasonality in the
unit root tests.

In the literature, three classes of time-series models
aare commonly used to medel seasonality: (1) purely
deterministic seasonal processes, (2) stationary seasonal
gprocesses, and (3) integrated seasonality process (see
fiylleberg, Engle and Granger, Yoo, 1990). The use of
seasonal dummies variables, as in Barsky and Miron (1989),
j.s; not appropriate if the observed seasonality is generated

k3}! an integrated process. When applying seasonal difference

ffilter, for example, for quarterly data, (I-L‘), as
advocated by Box and Jenkins (1970), analysts implicitly
)Eissume that there are seasonal unit root roots. Hence
Vvithout careful detection of the presence of seasonal unit
IToots, the mechanical application of the seasonal difference
ifilter is likely to produce series misspecification.
IFurthermore, Dickey-Fuller type tests assume that the root
C>f interest not only has a modulus of one but is precisely
Clne. Such a root corresponds to a zero—frequency peak in the
5Spectrum. In addition, Dickey—Fuller tests assume that there
are no other unit roots in the system. The properties of

l:3_‘.‘i.ckey-fuller tests in the presence of unit roots at

\
C3<3mponents and random walk components (Cochrane 1987).

64

frequency other than zero have been investigated by Ghysels,
Lee and Noh (1994). They show Dickey-fuller t-statistics
remain valid even when seasonal unit-roots are present if at

least three lagged dependent variables are included in the

usual regression model. However, the normalized—bias

statistic should be divided by four to have the same

limiting distribution as that in Dickey-Fuller (1979). To

see this, let x, be a univariate stochastic process:

>1
II
D
‘H
l
b
+
"I:
N
ll
...:
N
*3
N
1...:

where u, is either a stationary process with zero mean and

Constant variance or, alternatively, depending on the

Context and test u, is a martingale difference sequence

following the regularity conditions appearing in Phillips

(1987) and Chan and Wei (1988). We can rewrite the time

Series in (2.1) as follows:

Ax =¢lxl-l+¢2Axl-l+¢3Axl—2+¢4Axl-3+ul

I

Where¢,=a-land¢,=¢3=¢4=-a.

Under the hypothesis that a = I (or ¢, = 0) Ghysels, Lee,

and Noh (1994) show the following relations holds:

65

 

(T/4)$>, —) {W(r)2- 1) / 2f W(r)dr

I,I —-) {W(r)2- 1} / 2[£ W(r)2dr]”2

where W(r) denotes a standard Brownian motion on [0,1] .

The investigation of seasonal unit roots logically
Forecedes the examination of other kinds of seasonality since
tests can produce spurious results if seasonal unit roots
are present but not accounted for. Our investigation of
seasonal unit roots is conducted using the approach
developed by Hylleberg, Engle, Granger and Yoo (HEGY) (1990) .
This is a general procedure that allows tests for unit roots
at some seasonal frequencies in processes that may also
exhibit deterministic or stationary stochastic seasonality
Without maintaining that unit roots are present at all

8 easonal frequencies .

66

l The HEGY Seasonal Unit-Root Testsz

 

Suppose x, is the series of interest and generated by

a general autoregression of the form:

where <p(L) is a polynomial in the lag operator and e, is a
white noise process. Let y, be the roots of the

characteristic polynomial associated with (p(L). Assume for

the moment that deterministic terms, such as seasonal

dummies or time trend, are known to be absent from the
process for x,. In general, some or all of the 7,, may be

Complex.

The frequency associated with a particular root is the

Value of o) in e‘”, the polar representation of the root. A

root is seasonal if (n = 27tj/S, j = 1, ...... ,S-I, where S is
the number of observations per year. For quarterly data, the
Seasonal unit roots are -l, i, -i , which correspond to 2

Cycles per year and one cycle per year. The last root, -i,

2 I wish to thank Professor Schmidt for providing me

Some related references regarding the effect of seasonal
filter on unit-root tests which lead me to find the
appropriate procedures to implement unit-root tests when
L«‘lsing seasonally unadjusted data series. I am totally
Fesponsible for all the mistakes which I may possibly make
ll") my study.

67

is indistinguishable from the one at i with quarterly data

(the aliasing phenomenon) and is therefore also interpreted
as the annual cycle.

'Do test the hypothesis that the roots of uflL) lie on
‘the unit circle against the alternative that they lie
(outside the unit circle, the testing procedure developed by
HEGY (1990) consists of linearizing the polynomial (p(l.)

around the zero frequency unit root (1) plus three seasonal

Linit roots (-1, i, -i). Thus, write ¢(L) as
4 1-6 L .
<p(L) = Z l,Acp(L) "( ) (Licp (L) (2 2)
1.. 51(L)
1 ¢(6k) 4
Where6(L)=l-—L,?t =—-—-,A(L)= 6L.
I 6k k n5j(0k) (P g k( )

junk
(0(L) is a remainder with roots outside the unit circle with
(I) (0) = 1; the (9,, are the unit roots (1, -I, i, -i).

Thus, (2.2) becomes,

(p(L) = A, L (1+L) (1+L2) + i, (-L) (1-L) (1+L2)
+ 7., (—i L) (1—L) (1+L) (l-i L)
+ 7., (i L) (1-L) (1+L) (1+i L)

+<p'(L>(1-L“) (2.3)

68

It is clear that the polynomial <p(L) will have a root at (9,
if and only if I, = 0. Thus testing for unit roots can be
carried out equivalently by testing for parameters A, = 0.
Since (p(L) is real, It, and It, must be complex conjugates.
Let It, = —l,, 7122 = -12, 2}», = -m, + in“ and 27L, = -1t3-i1t,

After some algebraic manipulation, (2.3) can be re-written

as
cp' (L)y., = 7r,y,,_, + fl2y2,_, + 7r,y,,_2 + 7:,y,,_, + g, (2.4)
where y,, = (1+L+L2+L3)x,3
y,, = —(1-L+L2—L3)x,
y,, = -(1-L2)x,
y,, = (l-L4)x, = A4x,

which renders a testable regression.

(2.4) can be estimated by ordinary least squares,

possibly with additional lags of y,, to whiten the errors.

For the root 1 this is simply a test for 7:, = 0 by use of
the ‘t’ value on It, and for -1 by using ‘t' value to test

TC2 = 0. These two t values are distributed as the usual

3 In y,,, we have removed the seasonal unit roots at

frequency rt/2, and 1t and preserved the zero frequency unit
root, while y,, and y,, contain the It and 7t/2 frequencies
unit root but not the unit roots at other frequencies.

69

Dickey-Fuller t and the tables supplied by Fuller (1976) can

be used. For the complex roots, I, will have absolute value
of zero only if both m3 and m, equal zero, under m4= 0, the

t value on n, has a distribution like the one developed by

Dickey, Hasza, and Fuller (1984) for a process

iFhe proposed HEGY t-statistics for m,, m2, and n, if (1t4 =

C)) will be denoted t, through t,.

In order to obtain power against relevant alternatives,
tLhe hypothesis tests can be extended to the case where the
éalternative includes a constant, and seasonal dummies,
and/or a time trend4. The equation is still estimated by
CDLS, but the asymptOtic and finite sample distributions
<2hange5. Thus, the HEGY tests involve running 51 different

:regression,

4 From his simulation results, Ghysels et al (1994)

ssuggests when the data-generating processes have
(deterministic seasonal components, the regression. without
sseasonal dummies leads to a large size distortion and too
J_ow power. In empirical applications, inclusion of
Cieterministic terms (i.e. a constant, seasonal dummies,
Eand/or ea trend (possible irrelevant) in time model, which
t:ends to reduce the power of the tests, is the safe strategy
(pp.436).

5 As HEGY (1990) noted, the intercept and trend
lEbortions of the deterministic mean influence only the

70

A4 x, = ”12’11-1 1' ”2 ”:4 + ”3 yar—z 1’ ”4 y3I-l
I

+ Z c,,.A4 x,_,. + [set of fixed regressors] + s,
.I=|

\Nhere the set of fixed regressors include a constant,
:seasonal dummies, and a linear trend. We consider four
ealternatives and denote them as I (with an intercept), ISD
(with an intercept and seasonal dummies), IT (with an
:intercept and a linear trend), and ISDT (with an intercept,
sseasonal dummies and time trend). Since autocorrelation
cieestroys the properties of the test, the correct
eatigmentation in the regression is crucial to the
interpretation of test resultss. The lag length k in the
augmented regression is selected on the basis of a t-test
following a procedure suggested by Perron-and Vogelsang

(1992). l< is chosen such that the coefficient on the last

included lag of the fourth-differences of the data is

‘—

distribution of It, because they have all their spectral
rnass at zero frequency. Once the intercept is included, the
remaining three seasonal dummies do not affect the limiting
distribution. Beaulieu and Miron (I993) explicitly derive
the distribution of the HEGY t-statistics for monthly data
Vvhen the regression includes deterministic terms. They show
t, is invariant to the inclusion of seasonal dummies as
long as a constant is included; the distributions of

t 7 ...... t,2 are independent of constant and trend terms.

6 If the number of lags is above/below the number
Ifiecessary to render the errors white noise, the test power
find size are subject to bias; that is, too many lags reduce

7l

significant at 0.05 level (that is, t-statistic of the OLS

A

estmator c, is greater than 1.6 in absolute value) and the
coefficient on the last included lag in higher order
autoregressions is insignificant up to some a priori

specified maximum order (kmn). Initially, we set kmax == 12;

if the last lag (12) is still significant, k = 16.

max

In Table 1, we present the results of applying the HEGY
test procedure to the variables in the Taiwanese demand
function for real balances. The quarterly series are (y),

four monetary aggregates deflated by GNP deflator (RMIA,

RMIB, RMIBP, and RM2), the interest rates (i",W,i"fli“2,umm)
and the spreads between the own rate and umm rate (umm—i).
All variables are in log level except the interest rates.
The sample period is l961:4 to I997:3.

From Table 1, the p-values for Q statistic suggest the
residuals of the regression are white noise. The results
strongly indicate that there is a unit root at the zero
frequency in all of the series except RM2 since we cannot

reject the null hypothesis in any of the auxiliary

regressions at the 5% level. The assumption of 1t,= 0 is

rejected marginally for RM2 in the regression (IT) at the

0.05 level but not at the 0.10 level.

 

the power and too few lags distorts the test size. See
Hyllberg (1995).

72

Next we consider a unit root at 7t/2. In order to
establiSh a unit at n/2, we need both n, == 0 and n, == 0.

Since we fail to reject both hypothesis simultaneously for
each series at either 5% or 10% level, we reject the
existence of a root at this frequency for all series.

Moreover, the tests reject that there are any seasonal unit

roots in all of the interest rates except i” because t,, t ,

3

and t, are all below the 5% critical values in four models.

At n, we cannot reject n, = 0 for y and RM2 in ISD and
ISDT at either 10% (n: 5% level. For i”, m = () cannot be

2
rejected at the 5% level in all models.

To summarize, we fail tx> reject the hypothesis of aa
unit root at frequency zero for all series. The data reject

the presence) of any seasonal unit roots in all of the
interest rates except i”. Series y, RM2, and i” may contain

a unit root at the biannual frequency (m).

73

Table 1
HEGY tests for seasonal unit roots in quarterly aggregate
series for the Taiwanese demand functions for
real balances: 1961:4 - 1997:3

Model I: Regression with an Intercept

 

 

 

0 m n/2 Q"

Series Lags(k) tI T2 t3 t, p-value
y 5 -2.46 -1.79* -2.54** -1.96** 0.22
RMIA 7 -1.36 -2.77** -0.60 -2.79** 0.34
RMIB 7 -1.15 -3.11** -0.32 -3.00** 0.57
RMIBP 7 -I.61 -3.00** -0.33 -3.24** 0.76
RM2 6 -0.98 -1.86* -1.84* -3.20** 0.75
umm-I" 0 -2.13 -8.32** —4.46** -7.40** 0.66
umm-I“ 0 —2.32 -8.41** -4.70** -7.14** 0.66
umm-fir 0 -2.56 -8.51** -4.89** -6.87** 0.61
umm-r"2 0 -1.92 -1.97** -5.47** ~6.35** 0.98
,. 9 —1.49 -I.60* —0.58 -2.64** 0.99
,~ 9 —1.31 —2.66** -I.11** —3.05** 0.98
,M 6 -1.80 -3.42** —I.80* -2.79** 0.52
,m 2 -2.88 -5.69** -3.31** -0.06 0.93
umm I -2.06 -6.66** -3.75** -6.90** 0.93
Critical Values”

5% ** -2.89 -1.91 -1.88 -1.68
10% * -2.58 -1.58 -I.53 -1.31

 

An * and ** indicates significance at
respectively.

(a) This is the marginal significance level of the Ljung-Box
Q statistic (1979) for the test of no serial correlation in
the residuals of the regression.

(b) Critical values are from Hylleberg,
Yoo (1990).

the 10% and 5% levels,

Engle, Granger, and

74

Table 1 (cont’d)
Model ISD: Regression with an intercept and seasonal dummies

 

 

 

O n m/2 Q

Series Lags(k) tI T, t, t, p—value
y 5 —2.45 -I.25 -2.15 -2.77** 0.16
RMIA 5 -1.55 -2.72* -I.45 -4.73** 0.21
RMIB 7 -l.08 -3.04** -0.53 —3.86** 0.65
RMIBP 7 —1.54 -3.10** -0.47 -3.91** 0.78
RM2 6 —0.94 -2.17 -l.79 -3.33** 0.58
umm-I" 0 -2.12 -7.95** -4.37** -7.44** 0.77
umm-I" 0 -2.33 -7.98** —4.63** -7.21** 0.78
umm-W' 0 -2.57 —7.97** -4.88** -6.98** 0.76
umm-r’ 0 -1.95 —7.59** —5.49** -6.4l** 0.99
r 9 -1.38 -2.84* -1.35 -4.01** 0.99
r 1 -I.4l -6.54** -4.15** —7.68** 0.20
m 6 —1.75 -3.58** -I.99 -3.20** 0.42
m2 1 -2.84* -6.54** -3.64** -7.92** 0.84
umm I -I.99 -6.66** -3.87** -7.06** 0.81
Critical values

5% ** -2.94 —2.90 -3.44 -1.96

10% * -2.62 -2.59 -3.11 -1.52

 

75

Table 1 (cont'd)

Model IT: Regression with an intercept and a

linear trend

 

 

 

0 n n/2 Q

Series Lags(k) tI T2 t, t, p-value
y 5 —1.15 -1.78* -2.53** -1.92** 0.34
RMIA 7 -l.73 -2.72** -0.65 —2.82** 0.37
RMIB 7 -1.66 -3.03** -0.39 -3.03** 0.59
RMIBP 7 -0.61 -2.97** -0.34 —3.24** 0.77
RM2 5 -3.48** -3.47** -1.96** -1.56* 0.52
umm-i“ 0 -2.26 -8.30** —4.49** -7.38** 0.64
umm-r” 0 —2.35 -8.37** -4.70** -7.12** 0.65
umm-I”r 0 -2.59 -8.46** -4.89** -6.85** 0.61
umm-i"2 0 —2.11 —7.94** -5.49** -6.33** 0.90
r 9 -2.63 -I.57 -0.57 -2.57** 0.99
p 6 -2.49 —3.56** -2.23** -3.15** 0.92
m 6 -1.44 -3.41** -1.78* -2.78** 0.53
H’ 1 —2.98 -6.44** -3.53** -7.69** 0.93
umm 1 -2.24 —6.60** -3.76** —6.86** 0.72
Critical values

1% -4.09

5% ** -3.46 -I.96 -1.90 -1.64

10% * -3.l6 -I.63 -1.52 -1.23

 

76

Table 1 (cont’d)

model ISDT: Regression with an intercept, seasonal dummies
and a linear trend

 

 

 

0 n/2 n/2 Q

Series Lags(k) tl T2 t, t, p—value
y 5 -1.08 -I.24 -2.15 -2.73** 0.26
RMIA 5 -2.47 -2.64* -l.49 -4.45** 0.26
RMIB 5 -2.57 -2.72* -1.56 -4.52** 0.16
RMIBP 5 -1.58 —2.83* -1.45 -4.88** 0.15
RM2 3 -2.72 -2.52 -3.73** -6.00** 0.20
umm-I" 0 -2.27 -7.92** -4.41** -7.43** 0.75
umm-I” 0 -2.37 -7.95** -4.64** -7.20** 0.77
umm-I”r 0 -2.61 -7.92** -4.88** -6.97** 0.76
umm-r"2 0 -2.16 -7.56** -5.52** -6.41** 0.99
p 9 -2.36 -2.78* -1.33 -3.86** 0.99
p 1 -I.98 -6.40** -4.16** -7.34** 0.26
w 6 -I.39 -3.56** -1.98** -3.19** 0.43
r2 1 -2.88 -6.51** -3.62** -7.83** 0.84
umm l -2.18 -6.61** -3.89** —7.01** 0.80
Critical values

5% ** -3.52 -2.93 -3.44 -1.94
10% * -3.21 -2.61 —3.12 -1.51

 

77

2 The Dickey-Fuller Unit-Root Tests

Even the presence of the seasonal unit roots, we can
still apply the Dickey-Fuller tests to test for a unit root
at zero frequency; Table 22 presents the ‘values of 'test
statistics of the DF-t test and normalized bias test. We

compute DF statistics based on

It
x, = ax,_, + Za,Ax,_, + [set of fixed regressors] + .9,
Fl

where set of fixed regressors are the same as before; k is

chosen according the same procedure as described in the HEGY

A A

test. A t-statistic is based on a, the OLS estimator; Tc(a

- 1) is the normalized bias test, where T is the number of
the observations, c = (l-Za,)". As we mentioned earlier,

in the case of the presence of the seasonal unit root, k
should be no less than three and the normalized bias
statistic should be divided by four. From the HEGY tests, we

observe no seasonal unit roots in any of the interest rates

'0

except I , so k is not restricted for the interest rates.

From Table 2, the results unambiguously indicate that

Y. RMIB, RMBP, and sud. interest rates except V’ and V”

contain a unit root, since none of the tests can reject the

78

null hypothesis of a unit root. The null is rejected at the

A

5% level by normalized bias tests Tc(a - 1), for RMIA in
ISDT, for RM2 in IT, ISDT, for i" in I, IT, and for i’"2 in

ISD but not by the statistic for the presence of seasonal

unit root, ZSZLD. Thus, the outcome depends on whether these
4

two series have a unit root at frequency m (since we have
ruled out m/2, see above).
From the HEGY test, the t2 test cannot reject a unit

root at m at the 5% level for RMIA in ISDT, RM2 in ISDT, and

(I

i in IT so we may use KEELD for inference. Hence, the null
4

hypothesis of a unit root is rejected for these series in

the corresponding models.

79

Table 2
DP tests for unit roots at zero frequency in quarterly
aggregate series for the Taiwanese demand functions for
real balances: 1961:4 - 1997:3

Mbdel 1: Regression with an intercept

 

 

 

Series Lags A“ t-test Tc(&—1) 7ué-n Q“
(R) a 4 p-value
y 9 0.996 -2.20 - 0.47 -O.12 0.25
RMIA 10 0.995 -1.29 - 0.85 —0.21 0.41
RMIB 11 0.997 -l.12 - 0.49 -0.12 0.56
RMIBP 11 0.996 -1.56 - 0.63 -0.16 0.75
RM2 11 0.999 -0.74 - 0.21 -0.05 0.98
umm-I“ 2 0.961 -l.95 - 8.09 -2.02 0.65
umm-I” 2 0.954 -2.11 - 9.19 -2.30 0.62
umm-f” 2 0.944 -2.32 -10.86 -2.71 0.54
umm-I"2 0 0.958 -1.76 - 6.07 -1.52 0.80
r 9 0.936 -2.36 -23.3** -5.84 0.37
r 12 0.982 -l.3l -2.67 -0.67 0.98
w 10 0.978 -1.77 -5.89 -1.47 0.53
W2 1 0.928 -2.92 -10.20 -2.55 0.92
umm 2 0.961 -l.96 -8.52 -2.13 0.77
Critical value‘
5% ** -2.89 -l3.70 -13.70

 

An ** indicates significance at 5% level.

A

(a) a is the OLS estimate of the parameter (a) in the
autoregressive representation of the variable, x, = cth, +

k

EEGQAXF, + [set of fixed regressors] + a.

I=I

(b) This is the marginal significance level of the Ljung-Box

Q statistic (1978) for the test of no serial correlation in

the residuals of the regression.

(c) Critical values are taken from Ghysels, Lee, and Noh
(1994).

80

Table 2 (cont’d)
Model ISD: Regression with an intercept and seasonal dummies

 

 

 

Series Lags A t—test Tc(&-1) 783-0 Q
(R) a 4 p-value

y 12 0.995 -2.11 - 0.46 -0.12 0.21
RMIA 9 0.996 «1.40 — 1.04 -0.26 0.21
RMIB 11 0.999 -1.09 - 0.47 —0.12 0.61
RMIBP 11 0.996 -1.56 - 0.61 -0.15 0.76
RM2 11 0.999 -0.73 - 0.21 -0.05 0.94
umm-I" 2 0.961 —1.98 - 8.59 -2.15 0.79
umm-I” 2 0.954 -2.15 - 9.86 -2.47 0.78
umm-W‘ 2 0.943 -2.36 —11.77 -2.94 0.71
umm—r"2 0 0.960 -1.69 - 5.78 -1.45 0.93
r 12 0.965 -1.38 —5.16 -1.29 0.99
r 6 0.982 -1.50 -4.51 -1.13 0.70
pr 10 0.979 -1.76 -5.81 —1.45 0.42
m2 2 0.927 -2.86 -I7.6** -4.35 0.83
umm 2 0.961 -I.98 —8.64 -2.16 0.83

Critical value
5% ** -2.89 -I3.70 -I3.70

 

8|

Table 2 (cont’ d)
Model IT: Regression with an intercept and a linear trend

 

 

Series Lags A t-test Tc(&-1) 7u3-D Q
(R) a ‘—7_‘ p-value

y 9 0.985 -0.52 - 1.61 - 0.40 0.29
RMIA 11 0.947 —1.90 -20.06 — 5.01 0.47
RMIB 11 0.948 -1.66 —14.89 - 3.72 0.62
RMIBP 11 0.987 —0.54 - 2.40 - 0.60 0.77
RM2 11 0.917 -2.22 -36.08** - 9.02 0.97
umm-I" 2 0.958 -2.08 - 8.92 - 2.23 0.64
umm-I" 2 0.954 —2.14 - 9.40 - 2.35 0.61
umm-I"r 2 0.943 —2.34 -11.06 - 2.76 0.54
umm-I"2 0 0.953 -l.91 — 6.77 - 1.69 0.80
r 13 0.890 -2.42 —36.9** -9.13 0.99
p 11 0.950 —1.69 -12.91 —3.23 0.99
,» 12 0.979 -1.24 -4.34 —I.09 0.84
m1 2 0.923 -2.92 -I8.39 —4.60 0.92
umm 2 0.957 -2.12 -9.57 -2.39 0.76

Critical value
5% ** -3.45 -21.40 -21.40

 

82

Table 2 (cont'd)
Model ISDT: Regression model contains an intercept,
seasonal dummies, and a linear trend

 

 

 

Series Lags A t-test Tc(&—1) 7d;_n O
(k) a 4 p-value
y 9 0.986 -0.49 - 1.54 -0.39 0.25
RMIA 9 0.941 -2.31 -28.40** -7.10 0.28
RMIB 11 0.950 -1.61 -14.05 -3.51 0.65
RMIBP 11 0.987 -0.52 - 2.31 -0.58 0.78
RM2 11 0.918 -2.18 -34.95** -8.74 0.94
umm-I" 2 0.958 -2.11 - 9.50 -2.38 0.79
umm-I” 2 0.953 -2.18 -10.10 -2.52 0.78
umm-VP 2 0.942 —2.39 -11.95 -2.99 0.72
umm-I“2 0 0.955 -I.86 - 6.51 -1.63 0.93
, 12 0.909 -2.36 -21.24 -5.31 0.99
,. 6 0.944 -2.32 -16.91 -4.23 0.76
,v 10 0.978 —1.34 —6.02 -1.51 0.42
,M 2 0.923 —2.91 —18.43 -4.61 0.83
,»w 3 0.952 -2.31 -10.27 -2.57 0.82
umm 2 0.957 -2.15 - 6.19 -1.55 0.85
Critical value
5% ** -3.45 -21.40 -21.40

 

83

3 The KPSS Stationarity Tests

 

Several studies have argued that the Dickey-Fuller
test, has low power against reasonable alternatives, for
example, DeJong et al. (1989) provides evidence that the
Dickey—Fuller tests have low power against a unit root near
unity. Ghysels, Lee, and rkfli (1994) evaluated. the small
sample properties of the HEGY test, finding the HEGY also
has low power against the relevant alternatives. Unlike the
Dickey—Fuller tests and the HEGY tests whose the null
hypothesis is aa unit root pmocess, Kwiatkowski, Phillips,
Schmidt, and Shin (KPSS) (1992), propose a test of the null
hypothesis of stationarity (short-memory) against the
alternative of a unit root. The tests complement unit root
tests, such as the Dickey-fuller tests. By testing both the
unit root hypothesis and the stationary hypothesis, we can
distinguish series that appear to be stationary, series that
appear to have a unit root, and series for which the data
(or the tests) are not sufficiently informative to be sure
whether they are stationary or integrated. To ensure the
existence cfifaa unit root at zero frequency, we also apply
the KPSS test to the data series.

In the study we consider two null hypotheses7; one is

the level stationarity' hypothesis” the other is aa trend

 

7 Canova and Hansen (1993) extend the KPSS test to the

seasonal case and propose a test, the CH test, based on the
residuals from a regression extracting the deterministic

84

statonarity. The resulting statistics are denoted n”, and

n,, respectively. For each test, we will consider values of

the lag truncation parameter (q) from 2 to 88.

The test results are presented in Table 3 and 4. First
we consider the null hypothesis of stationarity around a
level. From 'Table 3, VH3 reject the hypothesis of level

stationarity for all series except the interest rates (all

-n:2

the spreads, 1 , and umm) no matter what value of q we

n12

choose. The outcome for the spreads and i and umm depends
on the lag truncation parameter (q). Since obvious
deterministic trends are present in real GNP and four real
monetary aggregates (see Figure 1A, the rejection (n? the
null is not surprising. We then proceed to test the trend

stationary hypothesis. From Table 4, for all of the series

 

seasonal components and other deterministic components, see
Hylleberg (1995). We also consider the regression with
seasonal dummies for txflji hypotheses, however, we ck) not
report the results in the study because the values of the
statistics are almost identical to those in the
corresponding regression without seasonal dummies.

3 Since the data series are highly dependent over time
and the residuals from the regressions are serially
correlated, it is not realistic to assume iid errors under
the null and use q = 0, no correction for autocorrelation,
in estimation of the long-run variance. The choice of eight
as the maximal value of q, is based on the observation that
the value of the test statistic has settled down by the time
we reach.c1== 8 and the simulation results in KPSS (1992),
which suggest q = 8 is a compromise between the large size
distortion under the null for l = 4 and the very low power
under the alternative for l = 12.

85

except RM2 the null is rejected at either 5% or 10% level

for all values of q.
For the interest rates, KPSS tests of level
stationarity , the ADF-t, ADF-F and HEGY-tI tests of a unit

root against level stationarity unambiguously suggest that

. .h .h . . .
N,z , and 1” contain a unit root at zero frequency Since we

can reject the trend stationary hypothesis and we cannot
reject a unit root hypothesis. Similarly, combining the KPSS

test of the trend stationarity and the ADF—t, ADF—F, and
HEGY t.l test of ea unit root against the trend stationary

alternative, we find that all the series except RM2 appear

to have a unit root at zero frequency. For RM2 and interest

I»,

rates (the spreads and i , umm), since both the null of a
unit root and the null of stationarity are rejected, they
may be characterized as long memory processes. In the
following analysis, hwe will treat them as integrated
processes.

In order to determine the order of integration
maintained in each variables, we apply the ADF-t test to the
first—difference of the series. The alternative models
considered are again I, ISD, IT, and ISDT as defined above.
We report the results in Table 5. From Table 5, we reject
the null hypothesis of 53 unit root against all of ‘the

alternatives for all series at 5% level. Therefore, we model

86

each of the variables under study in the Taiwanese demand

for real balances as an 1(1) process.

Table 3
KPSS stationarity tests for quarterly aggregate series for
the Taiwanese demand functions for real balances
(l961:4 - 1997:3)

Model 1: Regression with an intercept

 

Lag truncation parameter (q)
Series 2 3 4 5 6 7 8

 

n”: 5% critical value is 0.463
10% critical value is 0.347

y 3.39** 2.62** 2.20** 1.96** 1.82** 1.73** l.70**
RMlA 3.34** 2.58** 2.17** l.9l** l.79** 1.7l** l.68**
RMlB 3.38** 2.61** 2.20** l.94** l.81** 1.73** l.69**
RMBP 3.38** 2.61** 2.20** 1.96** l.81** l.73** l.69**
RM2 3.39** 2.62** 2.20** 1.97** 1.82** l.74** 1.70**
umm-i" 0.59** O.46** 0.39* 0.35* 0.33 0.32 0.31
umm-i" 0.44* 0.34* 0.29 0.27 0.25 0.24 0.24
umm-VP 0.34* 0.27 0.23 0.21 0.20 0.19 0.19
umm-1“"2 0.63** 0.49** 0.42* 0.38* 0.35* 0.34* 0.33
P 1.76** 1.37Mr l.l7** l.05** 0.98** 0.94** 0.92**
r 2.70** 2.09** l.77** 1.58** 1.46** l.40** l.37**
W 1.78** l.38**- l.l7** l.05** 0.97** 0.93** 0.90**
rd 0.42** 0.33 0.29 0.27 0.26 0.25 0.25
umm 0.64** 0.50** 0.42* 0.38* 0.36* 0.34 0.34

 

Test statistics are computed using a Newey-West procedure
and the Bartlett lag window as suggested in KPSS (1992).

An * and ** indicates significance at 10% and 5% level,
respectively.

Critical values are taken from Kwiatkowski, Phillips,
Schmidt, and Shin (1992)

87

Table 4
KPSS stationarity tests for quarterly aggregate series for
the Taiwanese demand functions for real balances
(1961:4 - 1997:3)

Model IT: Regression with an intercept and a trend

 

LAG truncation parameter (q)
Series 2 3 4 5 6 7 8

 

 

n,: 5% critical value is 0.146
10% critical value is 0.119

Y 0.62** 0.50** 0.42** 0.38** 0.36** 0.35** 0.34**
RMlA 0.31** 0.25** 0.22** 0.20** 0.19** 0.18** 0.18**
RMlB 0.26** 0.21** 0.18** 0.17** 0.16** 0.16** 0.15**
RMIBP 0.43** 0.34** 0.30** 0.27** 0.26** 0.25** 0.25**
RM2 0.11* 0.09 0.08 0.08 0.07 0.07 0.07
umm-i 0.45** O.35** 0.30** O.27** 0.26** 0.25** 0.24**
umm-i 0.43** 0.33** 0.29** 0.26** 0.24** 0.23** 0.23**
umm-r” 0.34** 0.27** O.23** 0.21** 0.20** 0.19** O.19**
umm-r"2 O.46** 0.36** 0.31** 0.28** 0.26** 0.25** 0.25**
, 0.24** 0.19** 0.16** 0.15** 0.14* 0.13* 0.13*
r 0.42** 0.33** 0.28** 0.26** 0.24** 0.23** 0.23**
w 0.64** 0.49** 0.42** 0.38** 0.35** 0.34** 0.33**
r2 0.23** 0.19** 0.17** 0.15** 0.15** 0.14* 0.14*
umm O.44** 0.35** 0.30** 0.27** 0.25** 0.24** 0.24**
See notes

to Table 3.

88

Table 5
DF-t tests for unit roots in the first difference of the
aggregate series for the Taiwanese demand functions for
real balances: 1961:4 - 1997:3

 

 

 

Regression I(with an intercept) ISD(with an intercept
and seasonal dummies)
Lags t-test Q" Lags t-test Q
(k) p-value (k) p-value
y 7 - 3.88** 0.38 7 -3.86** 0.29
RMIA 8 - 3.33** 0.07 6 -4.37** 0.07
RMlB 10 - 4.04** 0.61 10 -4.09** 0.60
RMIBP 10 - 4.04** 0.80 10 -4.03** 0.81
RM2 10 - 3.88** 0.98 10 -3.84** 0.94
umm-i" 0 - 8.20** 0.55 0 —7.90** 0.76
umm-i“ 0 — 8.43** 0.52 0 —8.12** 0.75
umm-W‘ 0 — 8.67** 0.42 0 -8.36** 0.69
umm-r"2 0 -10.08** 0.89 0 -9.75** 0.98
,n 9 - 3.75** 0.16 10 -4.67** 0.99
y 11 - 3.82** 0.98 9 -3.53** 0.81
i» 9 — 3.63** 0.51 10 -4.33** 0.97
in 10 - 4.00** 0.82 10 -4.04** 0.70
umm 0 - 8.21** 0.70 0 —7.98** 0.82
Critical value"
5% ** -2.89 —2.89

 

 

See notes to Table 2.

89

Table 5 (cont'd)

 

 

Regression IT(with an intercept ISDT(with an intercept,
and a trend) trend and seasonal
dummies)
Lags t—test Q Lags t-test Q
(k) p—value (k) p-value

y 7 - 4.61** 0.20 7 -4.60** 0.15
RMlA 10 - 3.58** 0.40 9 —3.54** 0.19
RM1B 10 — 4.15** 0.56 7 -4.19** 0.60
RMIBP 10 - 4.33** 0.74 10 -4.32** 0.75
RM2 9 - 4.53** 0.98 9 -4.43** 0.93
umm-I" 0 — 8.17** 0.56 0 -7.87** 0.76
umm-1‘ 0 - 8.41** 0.52 0 —8.09** 0.75
umm—W 0 - 8.67** 0.43 0 -8.35** 0.69
umm—i”2 0 —10.06** 0.90 O -9.73** 0.69
p 10 - 4.94** 0.99 10 -4.65** 0.99
p 11 - 3.84** 0.98 10 -4.36** 0.96
,v 9 — 3.80** 0.45 11 -3.64** 0.77
w: 10 — 4.12** 0.82 10 -4.05** 0.68
umm O - 8.19** 0.71 0 —7.95** 0.82
Critical values

5% ** —3.45 ** —3.45

 

 

See notes to Table 2.

90

CHAPTER 4

THE LONG-RUN DEMAND FOR.MDNEY FUNCTIONS IN TAIWAN
(1961:4-1997z3): COINTEGRAITON EVIDENCE

I: EQUILIBRIUMIRELAIIONSHIP AND COINTEGRATION

Economic theories suggest that the long-run money

demand relationship can be explained by functional

relationships:
ml — p: = f(yl’Rl) (3'1)
m, p, y, and R are defined as in (1.42). We can write a

stochastic version for the long-run equilibrium relationship

(3.1) as

ml - pl = f<yl’Rl) + V, (3-2)

v, are disturbances. let .X, be a vector consisting of (n:-

p,,y,, R,), if f (-) is linear in y and R (or some
transformations thereof, the equilibrium relationship in
(3.1) can be stated as a“.X, = 0. In most time periods, .Y

I

will not be in equilibrium and the univariate quantity

9]

can be called the equilibrium error.

In the unit root tests, we have established that all
series chosen for the demand for money functions in Taiwan
are individually I(l). It means that an individual economic
variable can wander extensively whenever it is hit by
shocks. As far as the demand. for money function is
concerned, economic theories suggest that the variables in
the function are expected to move so that they do not drift
too far apart at least in the long-run, if not in the short
run. An economic theory involving equilibrium concepts can
be interpreted in terms of the concept of cointegration in

econometric literature (Engle and Granger 1987). If each

element of aa vector series .X, first achieves stationarity
after differencing, 'but a linear combination a' X, is

already stationary, the time series X; are said to be

cointegrated with cointegrating vector a. Interpreting

as a long-run equilibrium, cointegration implies that
deviations from equilibrium are stationary, with finite
variance, even though the series are non-stationary and have

infinite variance.

However the theories suggest, there is no prior belief
that these I(1) variables in the study necessarily obey the
functional form as theories predict. Whether cointegration
occurs or not is an empirical question. In this chapter, we
examine the empirical evidence of cointegration in the
Taiwanese long-run demand for real balances for four
measures of monetary aggregates (RMlA, RMIB, RMlBP, and

RM2). The choice of scale variable is real GNP (y). The
cost of holding money for each measure of money is the

difference between the own rate of money (i”,i",i””,i"'2) and
the unorganized money market rate (umm) . We first introduce

how to test cointegration between I(l) variables.

II: RESIDUAL BASED COINTEGRATION TESTS

1 Introduction

 

Engle and (Granger (1987) suggest that the residuals
from OLS estimation of the cointegrating regression can be
examined for the pmesence of ea unit root 1J1 the
autoregressive representation. If time I(1) series are rmm
cointegrated then there must be a unit root in these
residuals; this is therefore the null of no cointegration.
If the series are cointegrated, then the residuals will be

stationary.

93

Let observed data A; be a pxl dimensional time series,

partitioned as A3 = (x“,xv'), where x“ is a scalar and x”
is an m-vector, where p = m + 1, and each element of .Y, is
known to be I(1). Regressing one of the variables, say x“,

on the other using ordinary least squares gives the

cointegrating regression:

x“ = a'le + V], (3.3)

where X; may' also contain a constant, time trend, or

A
seasonal dummiesl, other than x”; 1n are the residuals. The

null hypothesis of no cointegration corresponds to the null

hypothesis that v, is I(l):

V, = pv,-] + 6], p = 1, (3'4)

that is to test p = 1.

 

1 Engle and Granger (1991) point out “in almost all

cases, there should be an intercept in the cointegrating
regression. Only strong priors should set it to zero. With
seasonal process which have deterministic seasonals,
seasonal dummy variables can be added either in the

94

2 Phillips and Ouliaris (1990) Z0 and Z, Tests

 

The testing procedure of no cointegration is first to
run the cointegrating regression (3.3) by OLS as described
above and then apply an standard unit root test, such as the

Dickey-fuller unit root test (1976 and 1979), or

Phillips’(1987) Z and Z, tests on the residuals of the

a
cointegrating regression (3.4). The test statistics are
calculated as in the context of univariate unit root
testing, but the asymptotic distributions of the test

statistics differ. Phillips and Ouliaris (1990) examine both

the ADF test and Phillips' Z and Z, tests under the

a

assumption that no deterministic trends are present in the
regressors or the regression equation. The tabulated
distributions are also provided. Hansen (1992a) further
discovers that such cointegration tests depend on the actual
trends in the data if the data is not detrended. Since the
distributions under the null and alternative hypotheses are
sensitive to the true trend process and detrending
procedures, careful consideration of the nature of the
trends in the regressors must be given if tests of the
cointegration hypothesis are to have the correct size and
optimal power. From unit root tests, we have established all

individual series contain a unit root. However many

 

cointegrating regression cu :Ui the error correction form.”
(PP.11)

95

variables, for example, the series (y, RMlA, RMlB, RMIBP,

and RM2) appear to have deterministic trends. This can be
seen from visual inspection of the graph (Figure 1). These
series may be actually best thought of as “I(l) with drift”,
which is the sum of an I(1) process with zero—mean
increments and a linear trend. In the following analysis, we
will conduct tests incorporating this data propertyz.
Although. a simple Dickey—Fuller test would be

appropriate in the model, we consider Z and Z, tests,

0

which have advantages to correct potential serial
correlation and heteroskedasticity in the cointegrating
errors.

While the null hypothesis of no cointegration in (3.4)

A A

holds when p = 1, the alternative holds for p < 1.
Following Hansen (1992a), we consider two pmocedures. The
first is to run the unrestricted OLS regression in which a

time trend is included to test no cointegration of series

 

2 We employed Dickey—Fuller F tests (Dickey and Fuller

1981) of the hypothesis (a,B,p) = (0,0,1) and of the
hypotheses (a,B,p) == (a,0,1) in X = a + ,flt +~ I’Kq +
I

Za,AY,_, + e,, where Y, is univariate time series. The

likelihood ratio test of the hypothesis that the true model
is a unit root process with zero drift (a,B,p) = (0,0,1) is
rejected at the 5% level and that (a,B,p) = (a,0,1) is not
rejected for these series (y, RMIA, RMIB, RMlBP, RM2)(the
estimated a ranges from 0.17 to 0.96). Hence the formal

tests suggest that the series (y, RMIA, RMlB, RMlBP, and
RM2) contain a unit root with possible drift.

96

which have a drift3; this is equivalent to detrending the

series firstqz

+ a'xz, + fit + v, (3.5)

t)

x, =

I

The second is the restricted OLS regression which excludes a

time trend by constraining fl = 0.

Hansen (1992a) notes that cointegration tests based on the
restricted regression are more powerful than cointegration
tests based on the unrestricted regression. Note when some
or all of the I(l) variables are involved deterministic time
trends, cointegration implies that cointegrating vectors
should be sufficient to eliminate both the trend components
and stochastic components of the series for the linear
combination of these variables being stationary (see pp.574-

575, Hamilton 1994).

 

3 Engle and Granger (1991, pp.14) note that this is a
test that the series are not cointegrated even after
extracting a linear time trend.

4 The inclusion of time trends in the regression has
the advantage of rendering estimates of the cointegrating
vector invariant to the presence of trends in the regressors
and simplifies the asymptotic theory, see Phillips and
Hansen (1990), Hansen (1992a).

97

The Phillip's (1987) test statistics Z and Z, are

(1

formed using a “bias—corrected” serial correlation

coefficient estimates

A

2(3) VIA—I " A*)

 

b)

and are computed as

Z = T(;7 - 1), T: sample size (3.6)

 

 

Z,== , s = (3.7)

A 7 l A A A A AA
where A = EEaKj/AI);EE£m,5;, £,=vf—pvt.; vat) is kernel
1" I
.2 1 .2 A
weight; 0' = 7:28, + 2,1.
l
The statistics for the restricted regression are constructed

1 A2
from v, in the same way. The long-run variance (0') is

estimated using a prewhitened quadratic spectral kernel

(QS)5 with a first-order autoregression for the

 

5 Any kernel that yields positive semi-definite

estimates can be used. These include the Bartlett, Parzen,

98

prewhitening6 anmi an automatic Ibandwidth estimator7 (see

Andrews 1991, Andrews and Monahan, 1992).

3 OLS Estimates: Asymptotic Results

 

If the hypothesis of no cointegration is rejected, the
OLS estimates are consistent for the true cointegrating
coefficient (Stock 1987) even though there exist
simultaneous equation bias and serial correlation. This

estimator is superconsistent converging to its true value at

a rate of T"l rather than the usual T'm.

In the case with
r>1 cointegrating vectors, Wooldridge (1991) shows that OLS
estimation. selects time relation. ‘whose residuals are
uncorrelated with any other I(O) linear combinations of
regressors, also see Chapter 19, Hamilton 1994.

Since the OLS estimator has a non-normal limit

distribution, which 'involves three parts: a mixture of

normals, the unit root term, and the term caused by

 

and quadratic spectral (QS) kernel. As Andrews (1991) shows
that QS kernel has the best performance with respect to
asymptotic truncated mean square error (M83).

6 Monte Carlo results in Andrews and Monahan (1992)
show that prewhitening is very effective in reducing bias,
and reducing over-rejection of t statistics constructed
using standard kernel heteroskedasticity and autocorrelation
consistent (HAC) covariance matrix estimator.

7 Since the test outcomes sometimes depend on the
choice of bandwidth (M), the use of a data dependent
bandwidth parameter removes the arbitrariness associated
with the choice of bandwidth.

99

simultaneous equation bias arising from the endogeneity of
the regressors, (Phillips and Loretan 1991). Note that the
last two terms produce a finite sample bias (asymptotically
the bias will vanish) in median and mean and invalidate the
use of standard distributions for testing hypothesis about
the cointegrating vector. The inference about the
cointegrating vectors based on the smandard least squares
output can. be 1misleading. The usual test statistics (t-
ratios and Chi-squared criteria) need to be modified to
allow for the serial dependence in disturbances from

cointegrating errors and endogeneity of the regressors.

4 Inference of Cointegrating Vectors

 

Although the estimates based on least squares
estimation are consistent, there exist alternative estimates
that are superior. Asymptotically efficient estimation of
long-run equilibrium relationship can be achieved by a
variety7 of’ methods, for example, full systems MLE
(restricted by the imposition of unit roots)(Johansen 1988,
1991), fully modified OLS (with semiparametric serial
correlation and endogeniety corrections) (Phillips and
Hansen 1990, Hansen 1992a), and leads and lags estimator

(dynandt: OLS) (Stock anui Watson8 1993), (for' other

 

8 Unlike Johansen and Phillips and Hansen’s estimation
in which each series is individually I(l), DOLS is developed

100

estimators see an informative review of Phillips and Loretan
1991, Gonzalo 1994). Each of these methods achieves full
efficiency in the limit by working to estimate and eliminate
the effects of long-run feedback between the errors on the
long-run equilibrium relationship and the errors that drive

the regressors. These methods are asymptotically equivalent

and lead to conventional chi-squared criteria for
inferential purposes with respect to cointegrating
coefficients.

5 Empirical Study: The Existence of’ the Long—Run .MOney
Demand Functions in Taiwan (l96l:4 — l997:3)

 

Since residual-based cointegration tests are developed
from single-equation regression models, they depend (N1 an
arbitrary normalization of the cointegrating regression. As
far as the demand for money function is concerned, the long-
run money demand relation with no structural breaks may be

written as

I I I

(ng—ii) ==zz~+ ayy, + czi -+ v

Therefore, the natural normalization is to take real balance

(m,—p,) as the dependent variable. Without prior knowledge

 

for cointegrating regressions among general I(le) variables
with general deterministic components.

101

about whether the two interest rates (the own rate i,, and
unorganized money market rate umm) have equal coefficients
with opposite signs, for each test we consider two basic
models (with no structural break).

Model I: the interest rates enter the regression

unrestricted

lllflfll

(m,-p,) = u + ayy, + a,i, + a umm, + [,Btrend]+ v, (3.8)

Model II: the spread is used in the regression

(ml-pl) : ll + ayyl + durum—I(umml - it) + [mend] + VI

(3.9)
Relaxing price homogeneity restriction, we find that the
tests results from the nominal specifications are similar to
those in the real specifications. In Appendix 3, we show
that the price homogeneity is not rejected by the data using
the t-ratios constructed from the fully modified estimator
of Philips eumi Hansen (1990). Therefore, ix) the following
study, we only consider the real specification (3.8)-(3.9).

In Table 6-99, for each aggregate, we report the Zn and

A

Z, tests, and the data dependent band width parameter Ad.

 

9 Although the data are not seasonally adjusted, we do
not add deterministic seasonal dummies in the regressions.
However, the test results generated from the regressions
with these dummies are very close to those in Table 6-9.
Besides, the seasonal dummies are INN: significantly

102

The OLS estimates and their standard errors are also
presented. Note as we mentioned above, the OLS estimates is
a poor candidate for inference, so we should be cautious
when using these standard errors to construct t-ratios to

test significance of parameters of interest. In the bottom

-2

of each table, three outputs from OLS (DW, R and SEE) are
presented. Because of its simplicity, the Durbin-Watson
statistic (DW) was used by Engle and Granger (1987) to test
the hypothesis of no cointegrationuh Although a low DW
might be expected as all dynamics are omitted, it should not
be too low if the variables are cointegrated. Since the
critical values for the test DW=0 are only available for bi-
variable system in Engle and Granger (1987)”, no inference
is made from this statistic for our three- and four—variable

system. We report it just for a quick check if we have a

-2
symptom of spurious regression: high R and a too low DW

(Granger and Newbold 1974, Phillips 1986).

 

different from zero, individually, and jointly using the t-
ratios anui Wald statistics, respectively, which are
constructed from FM estimation. Therefore, the results are
not reported here but are available upon request.

10 Other than the DW statistic, six alternative tests
of no cointegration (e.g. DF, ADF, restricted VAR(RVAR),
augmented RVAR, unrestricted VAR (UVAR), augmented UVAR) are
also considered in Engle and Granger (1987).

l03

(1) The demand for real MlA equation

 

From Table 6, the null hypothesis of no cointegration
is rejected at the 5% level by the Z,, and Z, tests only

when the regression includes a time trend. It suggests that
there is some sort of long-run cointegrating relationship
between the variables in demand for real MlA equation. It
appears that the time trend is important to the conclusion
of cointegration. Comparing test results from.bkxkfl. I and
II, we note that these test results do not depend on how the
opportunity cost variable enters the regression. That is,
two interest rates enter restricted, or the spread is used.
From the OLS estimates, we notice that the coefficient
on income in Regression (B) and (D) (where time trend is
included) is huge. It is not only greater than unity, which
suggests that MlA is a luxury for Taiwanese people, but also
greater than two, which is rarely seen for the narrow
aggregate in the literature. Without the time trend, the
coefficients from Regression (A) and (Cs) aux; 1.28, which

look more reasonable for this aggregate. Moreover, the
coefficients on interest rates are correct. a,n> 0 as the

A A
theories predict and a,,,,,,,<0 and a,,,,,,,_,-a<0 as we conjecture

 

11 Note the empirical distribution of the DW statistic

in Engle and Granger (1987) is generated without considering
a time trend in the cointegrating regression.

104

that the umm rate is a measure of the opportunity cost of

holding real M1A in Taiwan.

(2) The demand for real MlB equation

 

From Table 7, we find that all of the tests reject the
null of no cointegration at the 5% level. The results
strongly suggest that there is a long-run relationship
between the variables in this equation. The coefficients on
interest rates have correct signs and the magnitudes are

similar in the regressions with/without a trend.

(3) The demand for real MlBP equation

Like the demand for real MlB equation, from Table 8 we
find that the null hypothesis of no cointegration is
rejected at the 5% level by all of our tests. It strongly
suggests that there exists a long—run relationship between
the variables in the demand for real MlBP data. The signs
are correct and the magnitudes of the estimates are similar
to those in the real MlB equation. This seems no surprise
because MlBP was constructed by aggregating similar deposits

in the commercial banks and the Postal Savings System.

(4) The demand for real M2 equation

 

From Table 9, we reject the no cointegration hypothesis

at the 5% level for all of the tests. It appears that there

105

is also 51 long-run relationship 1J1 this specification fer
the full sample period (1961:4—1997z3) in Taiwan.

We should note that the coefficients on income are very
different in the regressions with/without a trend. From
Regression (A) and (C), the income elasticity is about 1.71,
which suggests that M2 is a luxury. It becomes less than 1

(0.72) in Regression (B) and (D), indicating that there is
economy of large scale in holding M2. Although cnmm<0 as we

conjectured, dwa>0, which contrasts with the prediction of
theories.

Note that adopting' different normalization, that is
using )2 as the dependent variabLe, we find that the test
results are similar to those in Table 6-9 for each
aggregate. .After re-normalizing time obtained. coefficients
such that the coefficient equals -l.00, we find that the re-
normalized coefficients from the regressions without a trend
are close to those in Table 6-9. However, with a trend in
the regression, different normalization produces
substantially different coefficients.

We also test if the umm rate and the own rate on each

money are cointegrated. Regardless of normalization, Z, and

Z tests cannot reject the hypothesis of IN) cointegration

(I

occurred between these two interest rates. We report the

results in Appendix 4.

106

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107

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108

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109

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0 .fidnua

110

(5) Summary

From the residual based cointegration test, there is
strong evidence suggesting that cointegration occurs over
1961:4 - l997:3 in the variables chosen for the Taiwanese
demand for real MIB, real MlBP, and real M2 equations. These
results are invariant to the detrending procedures. However,
the time trend is important to the conclusion of

cointegration for real MlA equation.

Table 10
Critical values for residual-based cointegration tests

 

 

 

 

Model I Model II

Test 5% 10% 5% 10%

Z.

C -4.20 -3.89 -3.85 —3.55
C/T —4.53 -4.23 —4.20 —3.89
20

C -31.02 -26.94 -26.00 —22.33
C/T -35.30 -31.02 -31.02 -26.94

 

Note: Critical values for Z and Z are from Mackinnon

I a

(1990) and Haug (1992), respectively.

111

III: THE STABILITY OF THE LONG-RUN DEMAND FOR.MDNEY
FUNCTIONS IN TAIWAN: 1961:4-1997:3

In CHAPTER 2, we discussed how important role a stable
long-run money demand function played in the macroeconomic
analysis. In this section, we examine the empirical evidence
of the stability in the long-run money demand relationships
in Taiwan.

From the analysis above, while the conventional
residual based cointegration tests in the previous section
provide us evidence of a long-run relationship in money
demand for real MlA, MlB, MlBP, and M2 in Taiwan for entire
sample period, they do not provide us with much information
concerning the question of whether or not there is a regime
shift in these cointegrating relationships. Moreover,
another unsettled issue in time money' demand. analysis is
whether the narrowly. defined or broadly defined monetary
aggregates yield a more reliable long-run relationship:
“under differing institutional arrangements, changes in the
social anui political environment aumi changes 1J1 economic
conditions” (Meltzer 1963). Lucas (1988) also argues that
the demand for money function will be stable over time
provided that preferences and trading technology are stable.
The following events in Taiwan may play a part in explaining

potential changes in the long—run parameters.

112

1963: the New Taiwan dollar was pegged to the US dollar

1973:3-4: the first oil crisis

1976: the creation of the organized money market

1978: the adoption of a floating exchange rate system

1979: the second oil crisis

1980: interest rate deregulation (ending in 1989)

1987: liberalization of the foreign exchange control
system

1989: bank entry deregulation

With these events in mind, we investigate the stability in
these four demand equations for real balances (RMlA, RMlB,
RMlBP, and RM2) in Taiwan (1961:4-1997z3).

In order to examine the stability in the cointegrating
relation and to search for a correct model, we apply the
extended cointegration tests with regime shifts developed by
Gregory and Hansen (1996) and the parameter stability tests

of Hansen (1992b).

1 Residual-Based’ Tests for Cointegration in .Models with
Regime Shifts: Gregory and Hansen (1996) Z, and z; Tests

 

In the standard tests for no cointegration introduced
iji the jprevious section, it i1; presumed. that the
cointegrating vector is time-invariant under the alternative

hypothesis:

H3

e — I
HI e x, — u + a x2, + v, , I

I

1,2,”.,n

where X3 = (x“,x¢’)' are 1(1) and v; is I(O). In this model
the parameters p. and a are cointegrating vector and are

considered as tinEwinvariant. Zhi our empirical study
(especially for the demand for real MlA data), we wish to
entertain the possibility that the series are cointegrated,
in the sense that a linear combination (the cointegrating
vector) has shifted at one unknown point in the sample;

hence, the standard cointegration tests are not appropriate.

Gregory and Hansen (1996) extend the ADF, Z', and 2, tests

I
designed to test the ruflJ.<0f no cointegration against the
alternative of cointegration in the presence of a possible
regime shift. Such tests can detect cointegrating relations
when there is a change in the intercept and/or slope
coefficient occurring at unknown date. Rejection of the null
hypothesis, therefore, provides evidence 1J1 favor cflf this
specification.

The principle of testing for cointegration in model
with regime shifts is the same as the standard cointegration
procedure as introduced in Section II, which is 53 test of

unit root in the cointegrating residuals. While the standard

testing procedure is to set up the null of no cointegrationf

against the alternative of cointegration, the extended tests

set the alternative Ihypothesis tx> be cointegration. while

114

allowing for the structural change which is reflected in
changes in the intercept and/or changes to the slope.

Specifically, Gregory and Hansen (1996) consider three
alternative hypotheses. In order to model structural change,
we first define a dummy variable. As in Perron and Vogelsang
(1992) and Zivot and Andrews (1992), we assume that there is
at most one change and we denote the date of break, should
it occur, by 1,, with 1 < t, < n, where n is the sample
size. Hence, the dummy variable is defined as

D(t,,) =lift>t,,

I

= 0, otherwise.

We also define the location of the break fraction 1 = th/n,
t 6 (0,1).

Three alternative hypotheses of cointegration with
structural changes (Hz-H4) are
IQ: Level Shift (C)

x, = uI + u2D(t,,)

I

, + d’xm -+ m, t = 1,2. ,n (3.10)

This model specifies that there is a level shift in the
cointegrating relationship, which is modeled as a change in

the intercept u, while the slope coefficients a are held

115

constant. This implies that tflma equilibriunl equation. has

shifted in a parallel fashion. u, represents the intercept

before the shift, and p2 represents the change in the

intercept at the time of the shift. As in Gregory and Hansen

(1996), we also denote this model C.

It: Level shift with trend (C/T)

x11: “1 + uzDIIb): + a'xzr + :6! + V:

t = 1,2,“.,n (3.11)

In this model, we allow for a time trend into the level

shift (C) model.

It: Regime shift (C/S)

x“ = u,'+ u2[)(n)

t = 1,2”.,n (3.12)

This model allows both the intercept and the slope vector to
shift. This permits the equilibrium relation tx> rotate as

well as shift parallel. In this case p, amuiliz are as in

the level shift model (C), 0:, denotes the cointegrating

H6

slope coefficients before the regime shift, aumi<12 denotes

the change in the slope coefficients.
We use the same approach described. in ‘the standard

residual. based. cointegration. tests, but take account the
unknown break date to compute the statistics Z, and 2;. For

each possible I (or t,,), we estimate one of the models C,

C/T, C/S by OLS, yielding the residuals v”. The subscript t
on the residuals denotes the fact that the residual sequence

depends (N1 the choice» of change point ‘L. The resulting

Phillips’ test statistics for each for each I (or 1,) is
denoted Z, (T) and Z0, (1') for each 12 (or t,). The testing

scheme is to choose the breakpoint that gives the least
favorable result for the null hypothesis of no
cointegration; the statistic of interest is the then

smallest value of Efiufll of the above statistics across all

values of T, denoted by Z, and 2;. In other words, I (or Q)

is chosen to minimize Za(T) and Z,(T) for testing that v,r

is I(1).

As suggested in the earlier literature, such as,
Banerjee, Lansdaine, Stock (1992), and Andrews (1990), we
apply some trimming such that .15 < I < .85. For our study,
the sample size n = 144, so the possible break dates

t,,e([22, 122]).

117

2 Hansen (1992b) LM’ Tests for Parameter Instability’ in
Cointegrating System

 

The test statistics proposed. by .Hansen (1992b) are
designed to test the hypothesis of no regime shift against
the alternative of a regime shift. Unlike the tests in the
previous section whose null hypothesis is no cointegration,
the null hypothesis of Hansen’s tests is Engle-Granger
cointegration. Hansen’s (1992b) tests are joint tests on all
regression parameters in a cointegrating regression. A
statistically significant test statistic i1; taken as
evidence against the standard cointegration in favor of the
regime shift model.

Under the null hypothesis of cointegration, we assume

that the generating :mechanism. for AZ: (x“,xh')’ is the

cointegrated system

x“ = a’xm +-zm (3.13)
x2, = Flt + 82, (3.14)
A5,, = uz, (3.15)
As before 19 = (u“,um')' is p-vector stationary series; the
assumption characterizing the innovation vector u, see
Hansen (1992a) . (3.13) can be thought of as a stochastic

version of the linear long—run equilibrium relationship xh

118

= a'xm with u“ representing stationary deviations from
equilibrium. (3.14)-(3.15) is a reduced form which specifies
x” as a general integrated process, the outcome of

superimposed shock u%(sSt) that influence the process

period after period.
Since the asymptotic distributions cflf the test

statistics depend on the nature of the trends in the
regressors x” (Hansen 1992b), as in Section II we estimate

both unrestricted model:

x“ = u + fl! + a’xh + u“ (3.16)

and the restricted model:

x“ = u + a’xh +.u“ (3.17)

For simplicity, we rewrite (3.13) and (3.14) as

x, = A.XD + u“ (3.18)

I
where JYW = (constant, I, x”).

The constancy tests require an estimation of A in
(3.18) that has ea mixed normal asymptotic distribution so

estimators can be the fully modified (FM) estimator of

H9

Phillips and Hansen (1990), the maximum likelihood estimator
(MLE) of .Johansen (1998b,1991), or' the “leads and lags”
estimator of Saikkonen (1991) and Stock and Watson (1993)”.
an3 test statistics using these asymptotically equivalent
estimators would. have the same .asymptotic distributions.
Following Hansen (1992b), we also consider the FM estimator
of Phillips and Hansen (1990), which uses semiparametric
methods for serial correlation and for endogeneity.

The LM tests for parameter stability are L,., MeanF,

and SupF tests”. The three proposed tests are all tests of
the same null hypothesis of cointegration with stable
parameters but differ in their choice of alternative

hypothesis. The SupF test is appropriate to discover whether
there is a swift shift in regime, like Z, and 2; which

assume a single structural break occurring at unknown date

A

(I. The other two statistics capture the notion of an
unstable model that gradually shifts over time. If the

parameter 'variation 1&5 relatively' constant throughout the
sample, the L, is the appropriate choice. In practice, all

of the tests will tend to have power in similar directions.

 

m Also see Phillips and Loretan (1991) for a review

13 For constructing these statistics, see Hansen 1992b.

120

3 Empirical Study: The Stability' of the Long-Run .MOney
Demand Functions in Taiwan (1961:4 - l997:3)

 

 

In Table 11 - 14, we report the extended tests
(ZL,Z,), parameter stability tests — (LC, MeanF, and SupF),
the FM estimates, and their standard errors. In each

specification, the covariance parameters for constructing
statistics are estimated using a QS kernel on residuals
prewhitened with a VAR(l) for Hansen (1992b) procedure, and
AR(1) for Gregory and Hansen (1996) procedure, respectively.
In both procedures, the bandwidth parameter is selected
according to the recommendations of Andrews (1991), using
univariate .AR(1) approximating :modelshk All of the
statistics are computed using the trimming region (.15.85)
as in Section II.

In the Hansen's (1992b) tests and estimation procedure,
we will proceed in a “general to simple” specification
search. We first examine the unrestricted regression in

which a simple time trend is included and the two interest

rates enter the regression unrestricted

Un—pfl = u-+a,x +(Li +cx umm,+ flt-+v,

I IIIIIIII

 

14

1996.

For details, see Hansen 1992b, Gregory and Hansen

12]

Subsequently, we re-estimate the regression by dropping
insignificant variables and cmmstraining the tun) interest
rates to have equal coefficients with opposite sign if the
restriction is compatible with the data. We use the usual t
ratio constructed from FM to test the significance of the

individual coefficients; and the Wald statistics to test the

linear restriction a, -+ a == 0. Under the ruflj. the Wald

statistic is distributed as a x2(1).

For comparison we present all the results from the un-
restricted anmi restricted regressions. However, time final
conclusion is drawn from the restricted regression in which
all the coefficient are significant. We label these
regressions by (A), (B), etc.

For each aggregate, the results from the restricted
regression, where the conclusion is drawn, are also

presented graphically in Figure 3-10, which contains time

plot of Z,(t) and Za(t) over the truncated sample along with

5% and 10% critical values for the minimum Z, and 2;

statistics”. Figure 11-14 plot the sequence of F statistics
along with the 5% critical value for the SupF statistic for

the truncated sample.

 

15 For comparison, we graph all extended tests Z, and

Z. even when time trend is not significant.

a

122

A

t, denotes the estimated break point which is the point

in the sample where the smallest value of the test statistic
(Z, and 2;) :MS obtained and where the largest value of E‘

statistic (SupF) is obtained.

(1) The demand for real MIA equation

 

From unrestricted regression (B) in Table 11, we found

that i" is insignificant and has a negative sign, which
contrasts with the prediction of the theories. Using DOLS
estimation (Stock and Watson 1993), the coefficient has the
correct sign inn: still insignificant, with/without ea time

trend in the regression”:

RMIA, = -16.24 + 2.38)¢ + 0.13i”, - 0.02umng - 0.02! + v,
(6.79) (0.61) (0.23) (0.01) (0.01)

RMIA, = - 3.88 + 1.27y, + 0.141’", - 0.01umm, + v,
(0.63) (0.05) (0.26) (0.01)

Dropping i", we rewestimate regression an. In regression

(D), all coefficients are significant at either 5% (n: 10%
level (the critical values of the t-ratio i1; 1.65 for 5%,

1.28 for 10%) and have correct signs (the time trend is

 

18 The leads and lags in the DOLS estimation are
included in the regressions but their coefficients are not
reported here.

negative from data information). Therefore, the conclusion

from test results are based on this regression.

In regression (D), all three stability tests L,, MeanF
and SupF are not rejected at the 5% level, implying this
long-run relationship remains stable over the whole sample
period. Hansen (1992b) discovered that the L, can be
regarded as a test of the null of cointegtration against the
alternative of rm) cointegration since the lack of
cointegration is aa special case cfif the alternative
hypothesis (an unstable intercept) where the intercept
follows a random walk. Since all of the parameters appear
stable, including the constant, this implies that the null
of cointegration hypothesis is not rejected.

From Panel B of Table 11, we can see that the null

hypothesis of no cointegration is rejected at the 5% level
by z; and 2: tests only when the regression includes a time
trend (the C/T formulation). We should note that although
the null is rejected by z; and 2, tests, providing evidence

in favor of C/T specification (Eq.(3.10)), we are unable to
conclude from these two tests that there is ea structural
break. The reason is that the alternative hypotheses .Hg-ffl

(Eq.(3.10)-(3.12)) in the extended tests contain as a
special case the standard model of cointegration with no

regime shift, a conventional cointegrated system with

124

constant parameters could produce results of cointegration

from these extended regressions. Using the umm rate alone,

we' also conduct. the standard. cointegration. tests Z,(= —

5.80**) and Za(= -53.80**), finding that the null of no

cointegration is also rejected.

Turning to the FM estimates in Regression (D), we
notice that the income elasticity (1.86) is huge as the OLS
estimates in Table 6 and significantly different from unity.
As we mentioned earlier that this is rarely seen in the
literature for this narrow aggregate. The estimates obtained
in the regressions without a time trend Regression (A), (C),
and (E) are more reasonable.

The conclusion of cointegration depends on the
detrending procedure and it appears that the linear
combination of the I(1) variables under study reverts to a
trend. However the significant trend gives us difficulty in

interpreting time results. Firstly, economic theories only

suggest that (ny-zL) -df(yg,R ) should have an equilibrium,

I

that is, the discrepancy should not contain a trend.
Moreover, to accept this long—run relationship, VH3 need a
reasonable explanation for a huge income elasticity.
Balancing the evidence we have obtained, we doubt this
equilibrium relationship.

We notice that the test results and coefficients from

the regression (F) in which the spread is used are very

125

close tx> those from regression H” where the tumn rate is

used.

Finally we present the test results 2:, and 2; fer C,

C/T, and C/S (Panel B in Table 11) graphically in Figure 3-

4, and the sequence of F statistic from Regression (D) in

Figure 11. We can see that the sequences of Z,(T) and 20(1)

for C/T regression cross the 5% 2' and 2; cxitical values

I
several times, suggesting rejection of the no cointegration.
The sequence of F statistics for structural change is well
below the 5% critical value, indicating the parameters are

stable.

(2) The demand for real.MlB equation

 

From the unrestricted regression (B) in Table 12, the

estimated coefficient of V and the time trend are not

significant at the 5% level, which is also robust to the
DOLS estimation, so we re-estimated regression by dropping
them. In Regression (C), all of the coefficients are
significant at the 5% level and possess correct signs. The
following analysis is based on Regression (C).

The Inn. MeanF and SupF tests cannot reject the null
hypothesis of a stable cointegrating relationship at the 5%

level. As in the analysis of demand for real MlA, the L,

126

test implies that the hypothesis of cointegration is not

rejected.

Turning to the 2; and 2: tests (Panel B in Table 12),

the null of no cointegration is rejected at the 5% level for

all of the tests (10% for the C formulation). It is

consistent with the L, test, suggesting strong evidence of

cointegration among real MlB data. Again, the 2; and 2:

tests do not provide us with much information about any
shift in this relationship for the reason we mentioned in
the analysis of the demand for real MlA. Using one single

interest rate, umm, we compute the standard cointegration
tests as Z,(= -5.80**) and Za(= —53.80**). Hence the null

of no cointegration. is also rejected. We note that the
stability tests results are robust to the regressions we
used; the only test which rejects the null at both 5% and 1%
level is the L, test in Regression (A). This suggests that

this long-run relationship among the variables we chose is
quite stable over the sample period. This result contrasts
with that in Lee (1994) who finds a downward shift in the
demand for real MlB around 1982:4.

In Regression (C), the estimated income elasticity
(1.56) is significantly different from unity at the 5% level
so MlB is a luxury to Taiwanese people. The interest semi—

elasticity is around - 0.015. Using the sample mean value of

umm rate (24.12%) to convert the interest semi-elasticity,

we obtain the interest elasticity is of the order of —0.36.
Constraining cy.==‘-amm, which is not rejected by the
Wald statistic, and then using the interest rate spread, we
find that the test results and estimates in regression (E)
are similar to Regression (C).
Finally we present the test results 2:, and 2; for C,

C/T, and C/S graphically (from Panel B in Table 12) in
Figure 5-6, and the sequence of F statistic from Regression

(C) in Figure 12, along with the critical values.

(3) The demand for real.MlBP equation

 

From the unrestricted regression (B) in Table 13, we
find that the time trend is not significant, which is also
observed in DOLS, so we drop it and re-estimate Regression
(A). The coefficients in Regression (A) are all significant
at the 5% level and the signs are consistent with we
predicted. Thus we interpret the results based on Regression
(A) in the following.

All of three parameter stability tests reject the null

at the 5% level, casting some doubt about the existence of a

stable long-run relationship in this specification. All 2;

and 2: tests (from Panel A in Table 13) reject the null of

no cointegration at the 5% level in favor of the structural
break specification.

As we mentioned, this monetary aggregate is obtained by
grouping seemingly' homogenous deposits ix) the commercial
banks (MIB) and in the Postal Savings System (passbook
savings deposits). Since we have shown that the demand for
real MlB displays considerably constant over the same sample
period, the instability in this equation may arise from the
behavior’ of ,postal saving deposits. After examining the
graphs of data series (RMIB, RMlBP, and interest rates) in
Figure 1 for these two equations, we found that the trend
and cycle of two data set exhibit similar pattern over the
whole sample period. Casual inspection of the time series
provides us with little information about the possible
source CHE nonconstancy. However, parameters instability in
the demand for real MlBP may be explained by the difference
in. liquidity' characteristics ill MIB eumi passbook. savings
deposits in the Postal Savings System. J.C. Lee (1994) finds
that the annul turnover rate of the demand deposits in the
Postal Savings System is significantly lower than those in
the commercial banks”. Deposit holders seem to “regard” the

deposits in the commercial banks to be more liquid than

 

I7 The turnover rates Emu: year‘ for 'various deposits

are: 2.9, and 0.7 for passbook savings deposits and time
deposits in the Postal Savings System, respectively. 200 for
checking accounts, EM) for‘ passbook. deposits, and 20 for

129

those in the Postal Savings System even though there is no
substantial difference in the easiness to convert the
deposits into a medium of exchange. This indicates that
these postal deposits on the average are not being actively
used for transaction purpose, and they may be more like
investment balances or savings vehicles to deposit holders,
therefore, their behavior may be influenced by wealth, for
example, instead of a measure of transactions (real GNP) or
other factors. Thus, the specification for this monetary
aggregates might not adequately capture a stable money
demand relationship.

To summarize, the existence of cointegration in this
specification is problematic. This specification appears
subject to a structural change and may not be correctly
specified.

The sequences of Z,(t) and 20(1) (from Panel A in Table

13) in Figure 7 and 8 indicate that there is a well—defined
minimum from these six tests. The smallest statistic is

obtained roughly at one third of the sample (1:0.34,

Ih=73:3); the break date coincides the first oil crisis. In
Figure 13, we plot the sequence of F statistic for the

restricted Regression (A).

 

passbook savings deposits in commercial banks, J.C. Lee
(note 9, Chapter 9, 1994).

130

(4) The demand for real M2 equation

 

From the unrestricted regression (B) in Table 14, each

of the coefficients is significant at either 5% or 10%

A

level. However we notice that (Ln ‘< 0, which is frequently

obtained :hi the studies of time Taiwanese literature and

A

contrasts with the prediction of the theories. (mm ‘< 0 is
also observed in the estimation of OLS (Table 9), DOLS, and
Johansen's procedure with/without a trend.

Based on Regression (B), the null of cointegraion with

constant parameters is rejected by the I“. test, MeanF and

SupF at the 5% level. A stable long-run relationship in the
demand for real M2 is doubtful. The negative coefficient on
the own rate seems to signal this instability. Because of
the instability occurred in real MlBP equation instability
for this equation seems no surprise. Since this
specification may be subject to a structural break, it may
not kme correctly specified. Before i1; is re-examined, we
cannot provide any explanation for the negative own rate
coefficient in this study. It needs further research which
is beyond the scope of this study. Note the results of
instability are robust tie the detrending procedure, which

can be seen from Regression (A).

131

'r‘

I!

L)

I T

(D

The sequence of Z,(t) and 20(1) for (L. CWT, and C/S

(from Panel A in Table 14) are presented in Figure 9 and 10,

and, the sequence of F statistic for regression in Figure

14.

(5) Summary

From the analysis above, it appears that the narrowly
defined monetary aggregate (M1B) yield more reliable long-
run money-demand relationship in Taiwan in spite of several
potential regime shifts over the whole sample period (1961:4
- 1997z3). The broadly defined monetary aggregates (MlBP,
and M2) do not provide evidence of a stable long-run
relationship; the specifications in our study may not
adequately describe the “true” money demand behavior for
these two aggregates. Moreover, the most stable long-run
money demand relationship occurs in the demand for real MlB.
The time trend is important to the conclusbmi of a stable
long-run demand for real MlA function; however, to accept
this relationship, one need to provide a reasonable
explanation for a huge income elasticity.

One the one hand, that M1B yields most stable money
demand relationship (mu) be justified tn; the transactions-
demand theory, with money held as a medium of exchange. The
real quantity of money demanded is an increasing function of

some measure of the volume of real transactions (real GNP)

132

and a decreasing function of the opportunity cost of holding
money (umm or the spread).

On the other hand, the demand for broadly defined money
(RMIBP and RM2) might be associated with the portfolio and
speculative demand, with money as (Mme of several possible
assets in which wealth may be held. Thus, instability
detected in these two aggregates is explained by
misspecification. That is, the resulting money demand
depends on *wealth rather than income (the proxy of ‘the
volume of transactions) and some measure of the volatility
of alternative assets’ returns in addition to their expected
returns. However, we leave this conjecture unanswered in our

study.

133

 

 

 

 

 

 

 

 

 

 

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140

Table 15
Critical values for z; and 2; tests

 

 

 

 

 

 

 

 

m = 3 m = 2
Test 5% 10% 5% 10%
Z?
C —5.28 -5.02 -4.92 -4.69
C/T -5.57 —5.33 -5.29 -5.03
C/S -6.00 —5.75 -5.50 —5.23
22.
C —53.58 -48.65 -46.98 —42.49
C/T -59.76 -54.94 -53.92 -48.94
C/S -68.94 -63.42 -58.33 -52.85
Note: n1:hs the number of I(1) regressors. Critical values
for 2: and 2; are taken from Gregory and Hansen (1996).
Table 16:
Critical values for L,, MbanF, and SupF, tests
m = 3, p = l m = 2, p = 1
5% . 1% 5% 1%

L, 0.90 1.29 0.778 1.13
MeanF 9.21 12.00 7.69 10.3
SupF 19.3 23.9 17.3 21.4
Note: m is the number of I(1) regressors; p: the power of

trend in the data. Critical values are from Hansen (1992b).

141

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150

IV: JOHANSEN’S FULL INFORMEIIONIMAXIMUM
LIKELIHOOD ESTIMATION

I Introduction

 

From 'the residual based cointegration tests in the
Section II and III, we have found evidence of cointegration
with stable coefficients between the variables in the demand
for real MlA and real MlB equations. However, we cannot
determine from those tests whether the cointegrating
relation is unique or whether there are other linearly
independent cointegrating vectors in the system. Approaches
other than residual-based tests for cointegration are
available, for example, the likelihood ratio tests of
cointegration rank of Johansen (1988b, 1991), Johansen and
Juselius (1990), and a common stochastic trends test
proposed by Stock and Watson (1988). Such tests developed
from systems methods enable researchers to avoid invalid
restriction from arbitrary normalization in the
cointegrating regression of the residual-based tests”. Ebr
example, the variable on the left hand side of the
regression may not appear in the cointegrating relation at
all, but a unitary coefficient is wrongly imposed on this
variable. These tests also have the advantage of testing for

the number of cointegrating relations. Since the Johansen

 

19 Conflicts may arise in empirical work where the test

outcome depends on the normalization selected.

U]

(1988b, 1991) maximum likelihood methods for the analysis of
cointegration can simultaneously detect the INflMKH? of the
cointegration rank :Ui the system, estimate and test for
linear hypothesis about the cointegrating vectors and their
adjustment coefficients, we will apply them to continue our
study of long-run money demand equations in Taiwan.

Testing for the number of cointegrating relations and
estimating the cointegrating vectors starts with ea VAR(p)
representation expressed in first order difference and

lagged levels

where x, :hs a p-dimensional vector of I(l) variables; D,

are centered seasonal dummies which sum to zero over a full

year and where 8,, ------ , 8,. are IINP(O,A) and x_,HI ------ x0 are

fixed. The H matrix conveys the long-run information in the

data. The hypothesis of 1: cointegrating vectors is

formulated as a reduced rank of the HFmatrix

H2(rd: 11 = aB’ (3.20)

where a and B are pxr matrices of full rank.

152

Under H2 (r): Hi: aB’, (3.19) can be interpreted as an

error correction model (see Engle and Granger 1987, and

Johansen 1988a).

2 Empirical Study: The NUmber of the Cointegrating vectors
in Taiwanese Money Demand Data (1961:4 — 1997:3)

We apply Johansen’s maximum likelihood method tx> the
study of the long-run money demand relations (MlA and MlB)20

in Taiwan. For a comparison with the results in the previous

sections (II and III), we consider both 4-dimensional VAR
(where x = (m,y,i,umm)) and 3-dimentional VAR (where x =
(m,y,umm-i) for the basic model for each money-demand

relation, where m denotes the log of real balances.

Since the intercept vector (uo) can be decomposed into
linear trends :hi the data and intercepts in the
cointegrating relationship (Johansen and Juselius 1990,
Johansen 1991b) and the trend coefficient p, can be
decomposed into quadratic trend coefficients in the data and

linear trend. coefficients 1J1 the cointegrating relations

(see Osterwald-Lenum 1992), the assumptions about the

properties of the trend and linear restrictions about no

 

20 We also consider the order of the cointegration rank
for the other two aggregates (MlBP and M2). We cannot reject
the hypothesis of no cointegraion (r=0) at either 5% or 10%
even 20% level from the trace and max-A tests. These add
more evidence against ea stable long-run relationship for

153

and th are important in distinguishing the correct

asymptotic distributions of the test statistics.

Since all of time variables except for the interest
rates are characterized as I(1) processes with drift, we
estimate all of the models under the assumption of a linear
trend in the I(1) variables. Specifically, (3.19) without a
time trend and centered seasonal dummie521.is fitted to the
Taiwanese demand for real MlB data

Model I:

H2: Ax, = rlel-l + """ + rk—leI-IHI + an—k + “o + 5:

(3.21)

Because the time trend_ is crucial to our conclusion of
cointegration with stable parameters for the demand for real
MlA data from the single equation methods, we also consider
model (3.19) under the assumption of the existence of linear
trend in the cointegrating relations (but the absence of

quadratic trend) to take into account of a significant

 

these two aggregates. We do not report the results here but
the results are available upon request.

“ Although our data are not seasonally adjusted, *we do
not include the centered seasonal dummies in the model,
because the results obtained in the regression with seasonal
dummies are similar to those we report in the text. In
addition, from the fully modified estimation we found three
seasonal dummies are not significant either individually or
jointly for each demand for money equations.

154

linear trend in FM estimation”. That is, under the null we

estimate
Model II : H;

= IUILE4 4. ...... + FLJAXHMJ + a(B',Bl)(xhl',t)’+ uO-+ q

(3.22)
(see Osterwald-Lenum 1992).

The lag length (k) was chosen as the minimum length for
which there is no significant autocorrelation in the
estimated VECM residuals using the Ljung-Box Q statistics
(1979). The misspecification tests for normal iid assumption
for the residuals in the model are reported. The normality
assumption is tested by the Jarque and Bera statistic

(Jarque and Bera, 1980).

(I) The Taiwanese demand for real MIA data

 

(A) Misspecification tests

 

The misspecification tests for the model are reported
in Table 17. For the two data sets (three- and four—
variable), the choice of k renders the residuals white
noise. However, there are indications of excess skewness and
kurtosis in the residuals of the interest rate equations,

causing the Jarque—Bera test statistic to become

 

’2 Explicit inclusion of a linear trend in the
cointegrating relations implies that there :hs some linear
growth which our model cannot account for given the chosen
data set.

155

significant. We conclude that the residuals from RMIB and y
can be assumed to follow a Gaussian process, those from

interest rate equations follow an innovation processZ3.

(B) Testing for reduced rank

 

For VAR(4), Model I (3.21) is fitted to the data“,- for

VAR(3) we consider both Model I and II (3.22).

From Table 18, the trace and 1mm tests fail to reject

r = 0 at either 5%‘ and 10% level even 20% level
(significant at 20% for VAR(4)) for all of the model we
considered. Since the time trend is important to the
conclusion of cointegration with stable coefficients from

the residual based tests (Table 6 and 11), the inability to

reject Pa in VAR(3) adds more evidence against the

hypothesis of cointegration with constant coefficients among
the variables in the. demand for real MlA. Using a single

interest rate, umm, we reach the same conclusion of no

 

23 The deviation from normality is not a serious
problem. As long as the cumulative sums of errors converge
to a Brownian motion, the asymptotic analysis gives the same
results as those under the assumption of normality (see
Johansen 1991b, Johansen and Juselius 1992, Gonzalo 1994).

24 We also consider model II under the assumption of a
linear trend 1J1 the cointegration relations. Although the

trace and AW tests reject r = 0 at the 5% level, the

estimated income elasticity and interest semi-elasticity are
perverse, having wrong signs enui being economically

A

meaningless. (AMAJflnrfl.,,..,..r/3.> = (1.00, 12.28, -5.08, -
0.28, —0.28).

l56

cointegration which also differs from the conclusion we

reached in previous sections (II and III).

Table 17
Residual misspecification tests

 

 

 

 

VAR(4) with k = 8, x = (RMlA,y,i”,umm)
Eq. S.E.E” Sk” BK” r,“ Tz‘~
x2(34)
ARMlA 0.03 -0.33 0.14 1.97 34.18
Ay 0.01 0.21 -0.04 0.77 37.44
A?’ 0.05 0.37 5.37** 132.37** 45.76
Aumm 0.58 1.06** 3.51** 75.62** 23.22
VAR(3) with k = 5, x = (RMlA,y,umm-i”)
Eq. 5.3.3 Sk EK Tl 12~
x’(34)
ARMlA 0.03 -0.14 0.26 0.70 42.00
Ay 0.02 0.13 -0.03 0.36 42.56
Aumm-r' 0.66 0.89** 5.19** 150.39** 26.78

 

Note: a. S.E.E (denotes the standard_ error' of regression
estimate. b. SK and EK are the skewness and kurtosis
statistics. A ** indicates the test of the null hypothesis
that each is zero is rejected at the 5% level. d. The Jarque

and Bera test for normality (Jarque and Bera, 1980), I, =
T—n1 2 EK2
S

6 ( 4

 

) ~ x2(2), where m is the number of

 

M ,3
regressors. C. The Ljung-Box Q-statistic T(T+2)[§:7,Ij),
.hl ‘

where r, is the jth lag autocorrelation of the residuals. M

is the number of autocorrelations used, and is selected

according t1) the formula D4 = ndn(T/4,3T2),. with aa maximum
value of 36.

H7

Table 18
Tests of the cointegration rank

 

 

 

Panel A
Model I: VAR(4)' with k = 8, x = (RMlA,y,i",umm)
‘33 fit!)
It)" 10"“7'
H2 eigenvalue trace/ ma
r = 0 0.131 41.90 19.07
r S 1 0.095 22.83/ 13.51
r S 2 0.041 9.31 5.74
r S 3 0.026 3.57 3.57
Panel B

Model I: VAR(3)2 with k = 5, x = (RMlA,y,umm-i°)

 

H2 eigenvalue trace Am“

r = 0 0.092 23.92 13.41

r S 1 0.055 10.52 7.94

r S 2 0.018 2.58 2.58
Panel C

Model II: VAR(3)2 with k = 5, x = (RMlA,y,ummri”)

 

 

H; eigenvalue trace 1m“

r = 0 0.107 30.12 15.67

r S 1 0.064 14.45 9.25

r S 2 0.037 5.20 5.20

Note: 1 Model I: Ax, = FIAxP,-+ ------ + I“,,_,Ax,_,‘+l +IH x“, + pa
+ s, is estimated.

2 Under the null of cointegration rank = r, Model II Ax, =
rt Axl-l +""+ rk—let-k+l + “(B' 1B1) (XI-l, ,t) ' + “0 + 8: is
assumed.

See Table 23 for critical values.

158

To conclude the cointegration analysis for the demand
for real MlA, we represent the normalized eigenvector
associated with the largest eigenvalue and the corresponding
weight in Table 19. We notice that the coefficients in panel
(c), under the assumption of a linear trend in the
cointegrating relation, the obtained income elasticity is
not only greater than unity, is also greater than two, as
mentioned above, which is rarely seen in the literature for
this narrow monetary aggregate.

The time trend is important to the conclusion of a
stable cointegrating relationship in the demand for real M1A
from single equation methods (Section II and III). To accept
this conclusion, we need to accept the huge income
elasticity. Based on economic theories and all the evidence
we have obtained as well, we conclude that there is no such

long-run relationship for the demand for real MlA data.

159

Table 19
The eigenvector associted with tho largest aigonvslue (v.)

and the corresponding weights (uh)

 

Panel A
(RMlA,y,i”,umm)

 

 

 

 

 

Model I: VAR(4)l with k = 8, x =
m y i” umm
A 1.00 -1.27 -0.76 —0.014
V1
(0.21) (0.27) (0.17) (0.008)
A 0.01 0.05 0.03 1.15
“’1
Panel B
Model I: VAR(3) with k = 5, x = (RMlA, y, umm-i“)
m Y umm-i"
A 1.00 —l.26 0.003
VI
(0.14) (0.24) (0.26)
A —0.10 0.001 1.36
WI
Panel C
Model 11: VAR(3)? with k = 5, x = (RMlA, y, umm-i")
m Y umm-f' t
A 1.00 -2.33 0.019 0.023
V1
(0.04) (0.42) (0.008) (0.009)
A -0.13 0 01 0.83
WI

 

See notes to Table 18.
computed using the

Figures in ( ) are standard errors
procedure suggested by Johansen (1991).

I60

(2) The Taiwanese demand for real MIB data

(A) Misspecification tests

 

The misspecification tests for this model are reported
in Table 20. As in the demand for real MlA data, the

normality hypothesis is rejected for the interest rate

variables U*,umm,umm-W) chm; to excess skewness and
kurtosis. Thus, the residuals from. real RMlB and. y are
assumed to follow a Gaussian process and the residuals from

the interest rates follow an innovation process.

Tabla 20
Rasidnal misspecification tests

 

 

 

 

 

VAR(4) with k = 7, x = (RMlB,y,ih,umm)
Eq. S.E.E SK BK t, 12
712(34)
ARMlB 0.03 -0.28 0.81 4.18 29.73
Ay 0.02 0.13 -0.03 0.30 53.06
Ajb 0.09 0.47** 3.26** 51.80** 31.32
Aumm 0.63 -0.72** 4.07** 84.04** 21.30
VAR(3) with k = 5, x = (RMlB,y,umm-i")
ARMlB 0.03 -0.25 0.72 3.85 45.82
Ay 0.02 0.09 -0.08 0.19 41.09
Aumm-fl' 0.65 0.85** 5.20** 149.61** 26.61
Note: Model Ax, = f,Ax,_, + ------ + l",,_,Ax,_,,+1 + H x,_,, + 110 + s,

is fitted to the data.

16]

(B) Testing for reduced rank

 

From the trace and Am“ test results in Table 21, the

null hypothesis of no cointegration (r=0) cannot be rejected
at either 5% or 10% level for the two data sets. However,
the null is rejected at the 20% level, which appears
consistent with the results from the residual-based
cointegration tests (see Table 7 and 12). Although the
acceptance of one cointegration vector in the system relies
on the test size of 20%, which usually would be considered
too high, Johansen and Juselius 1990 suggests that when the
cointegrating relation is quite close to the nonstationary
boundary, the powers of the test are likely to be low. Hence
it seems reasonable to LHKB a higher critical value higher
than the usual 5%.

In order to make final decision of the order of the

cointegration rank, we also examine the stationarity of the

cointegrating relation 03x,) constructed from. the full-
sample point estimates. The ADF-t statistic (= —2.64 for
VAR(4), = -3.22 for VAR(3)) (using 9 lagged differences)

rejects the unit root hypothesis at the 10% level for VAR(4)
model, at the 5% level for VAR(3), suggesting that the
cointegrating relations for these two data sets are
stationary.

Since we reject r = 0 and we cannot reject the

hypothesis of r S 1 at 20% level, we conclude that there is

162

only one cointegrating vector between the variables in the

models. Note in APPENDIX 4, we show that there is no

cointegration. between lumn and. W. Thus, we rule out the

possibility that this cointegrating relationship comes from
these two variables alone. When using the umm rate alone, we
obtain similar results as those from the model using the
spread. Therefore, the result is consistent with the

conclusion we drawn in Section 111.

Table 21
Trace and km“ tests

 

VAR(4) with k = 7, x = (RMlB,yyib,umm)

 

 

 

 

H2 eigenvalue trace Am”

r = 0 0.116 40.45 16.84

r S 1 0.095 23.60 13.73

r S 2 0.052 9.87 7.26

r S 3 0.019 2.61 2.61
VAR(3) with k = 5, x = (RMlB,y,umm-V)

H2 eigenvalue trace Am“

r = 0 0.095 24.60 13.91

r S 1 0.057 10.69 8.23

r S 2 0.018 2.46 2.46

See note to Table 20. See Table 23 for critical values.

163

Next. we report. the :normalized. cointegrating 'vector25
and the error correction coefficients in Table 22. The
standard errors of the normalized cointegrating vectors are
obtained using the procedure suggested by Johansen (1991).
We will use the obtained point estimates and their standard
errors to test the significance of each regressor.

For the VAR(4) model, the signs of coefficients on
income and the own rate are consistent with the prediction
of the theories and both are significantly different from
zero. The sign on umm rate is consistent with an conjecture
that the umm rate is a Heasure of the opportunity cost of

holding real MlB in Taiwan, however, it is not significantly

different from zero. Since the constraint (,6, = -,6,,,,,,,,)26

cannot be rejected by likelihood ratio test (LR = 1.37), so
we reestimate the model. We find that not only that the
interest rate spread is significant, but also that the trace

test turns out to reject the r‘== 0 at the 10% level. All

 

2” We present the results normalized by the

coefficients of real MlB variable such that /£.== 1.00. The
parameters a and B are not identified since given any choice

of the matrix §(rxr), (dé) and [3(§’)‘I also produces the same
matrix I], and hence determine the same probability
distribution for the variables. The data can only determine
the space spanned by the columns in B, and the space spanned

by a. For identification of long-run parameters, see Rasche
and Hoffman (Chapter 3, 1996).

I64

estimates have smaller standard deviations than unrestricted
estimates. The constrained estimated are reported in the
Panel B of Table 22.

Turning tx> the error correction coefficients U1), we

can see that equilibrium errors cause real MlB and the umm
rate to adjust downward, real GNP and the own rate to adjust
upward. We also notice that the weight of the equilibrium
errors loading to the change of real balances is very small
in unrestricted VAR(4) model (Panel A, Table 22). Ihl both
models, the equilibrium error enters the umm equation with
largest. weights Chi absolute ‘value), suggesting' that 'the
cointegration relation is important to the adjustment of the
unorganized money market rates.

For the VAR(3) model, the income elasticity (= 1.56) is
significantly different from zero and unity. The interest
semi—elasticity F= --0.017) has ea negative sign as
conjectured but becomes insignificant. The error correction
coefficients suggest that the equilibrium errors cause real
MlB to adjust downward, real GNP and the spread to adjust

upward.

 

26 The restriction ix; imposed (N1 the long-run
information but not on the short—run dynamics, (see Hoffman,
Rasche, and Tieslau 1995).

165

Table 22

Normalised cointegrating vectors (fl) and error correction

coefficients (a)

 

 

 

 

 

 

 

Panel A
Unrestricted VAR(4) with k = 7, x = (RMlB,y,i",umm)
flm fly flib flumm
b 1.00 —1.45 -0.35 0.05
(0.23) (0.32) (0.07) (0.07)
Eq. ARMlB Ay ,Afl Aumm
& -0.003 0.04 0.16 -0.29
Panel B
Restricted VAR(4) with ,6, = -,BW (LR = 1.37)‘
flu: fly fli" flumm
& 1.00 -1.61 -0.02 0.02
(0.14) (0.20) (0.01) (0.01)
Eq. ARMlB Ay ,Afl Aumm
A -0.03 0.04 0.07 —0.72
a
Panel C
VAR(3) with k = 5, x = (RMlB,y,umm-i")
fl” fly flmmn-i‘
A 1.00 —1.56 0.017
fl
(0.27) (0.23) (0.090)
A -0.12 0.01 0.41
a
Note: Figures ( ) are standard deviations. Also see notes to

Table 20. LR is the log likelihood ratio test stastistic for

A

5, =

-flmm against H2 (Eq.3.20), which is asymptotically

distributed as 1595(1) = 3.84.

166

Table 23
Critical values for trace and km“

 

 

p—r 80% 90% 95% 80% 90% 95%
Model I Model 11

Trace Trace
1 1.66 2.69 3.76 8.65 10.49 12.25
2 11.07 13.33 15.41 20.19 22.76 25.32
3 23.64 26.79 29.68 35.56 39.06 42.44
4 40.15 43.95 47.21 54.80 59.14 62.99

Amax A’max

1.66 2.69 3.76 8.65 10.49 12.25

10.04 12.07 14.07 14.70 16.85 18.96
16.20 18.60 20.97 20.45 23.11 25.54
21.98 24.73 27.07 26.30 29.12 31.46

bWNP—J

 

 

Note: Critical values are taken from Table 1.amui Table 2'
in Osterwald-Lenum 1992.

V} ESTIMATION AND TESTS OF LINEAR RESTRICTIONS ON THE LONG-
RUN PARAMETERS OF DEMAND FOR REALIMIB IN TAIWAN

1 Estimation of the Long—Run Income and Interest
Elasticities

 

 

The long-run demand for money plays an important role
in the quantitative analysis of the effects of monetary
policy; buxfll of the empirical money demand literature has
focused on the search for a stable short-run money demand
function. In such cases, the efficient estimators can be
used in subsequent stages of the analysis by imposing the
estimated cointegrating vectors, for example in a VBCM

(King, Plosser, Stock enui Watson 1991), or :hl a, single-

167

equation error correction framework (Hendry and Ericsson
1991). In this section, we compare estimates of the long-run
parameters for the demand for real MlB using four asymptotic
efficient estimators, OLS (Engle and Granger 1987, Stock
1987), the fully modified estimators of Phillips and Hansen
(1990) (FM) and Johansen’s (1988b) VECM maximum likelihood
estimator (JOH) and Stock and Watson (1993) DOLS. The last
three estimators have an asymptotic distribution that is a
random mixture of normals and produce Wald test statistics
with asymptotic chi-squared distribution.

In each estimation, again we consider both four-

variable system x,= (RMlB,y,V,umm) and three-variable
system >g== (RMlB,y,unmvib). Estimates cu? the cointegrating
vectors are normalized such that am = -1.00 and are

reported in Table 24. We use the cmmained point estimates
and their standard errors to test the significance of each
regressors.

In the VAR(4) model, the estimates are very close
across the estimators and the coefficients on each variable
have the expected signs. The income elasticity is around
1.50 and is significantly different from zero and unity at

either 5% or 10% (unrestricted JOH in VAR(4)) level for all

estimators. The interest semi—elasticity (the own rate 6%)

is significantly from zero only for the Johansen estimator,

168

A

which is largest among the estimators. HWW is similar
across estimators and significantly different from zero

except in Johansen’s estimation. Under the constraint ,Q, =

-,B,,,,,,,,, which cannot be rejected by the data (LR = 1.37, see
Panel B, Table 22), the interest rate spread in Johansen's
estimator becomes significant.

In VAR(3), the income elasticity and interest semi—
elasticity are almost identical across estimators.
Surprisingly, Johansen estimates have the largest standard
deviation among all the estimators. The interest variable is

not significant in the Johansen estimation at either 5% or

10% level. Under the constraint 8, == -1.50, the interest

semi-elasticity from JOH becomes more precisely estimated
(with much smaller standard deviation) and turns out to be
significant. Since the own rate is run: significant across
the estimators except JOH, in Table 25, we also report the
results obtained in the regressions only using the umm rate.
We find that the estimates are similar to those using the

spread (the right three columns of Table 24). In all cases,

0 is significantly different from unity at time 5% level;

1

E) is significantly different from zero at either 5% and

”NH”

10% level.
From Table 24, although all four asymptotic efficient

estimators generate qualitatively' and. statistically close

169

estimates, Johansen estimator generally produces larger
standard, deviations among' all estimators considered.
Surprisingly, the analysis based on a complete model
(Johansen 1991), where the different variables are jointly
modeled and a full information analysis is pursued, does not
have efficiency gains in estimating the long—run
parameters”. This is consistent with the simulation results
in Stock and Watson (1993). Our study provides an empirical
example that single equation methods (xvi also efficiently
estimate long-run equilibria, as advocated in Phillips and
Loretan (1991), Stock and Watson (1993).

To conclude the estimation of the long-run demand for
real MlB in Taiwan, we present the graphs for the actual
real MlB (denoted RLMlB in figures) and the estimated real
MlB generated by the estimates of Table 24 to see how well
these regressions track the data. Figure 15 and 16 plot the
comparison of the estimated values across estimators for the
four-variable system (denoted OLS4, DOLS4, FM4, JOH4,
REJOH4) and three—variable system (denoted OLSB, DOLS3, FM3,
JOH3), respectively. For each estimator, we also compare the
estimated real MlB obtained from the four- and three-
variable system with the actual real MlB; they are presented

in Figure 17 - 20.

 

27 I thank Professor" Wooldridge. for the comments on

this empirical finding.

170

From Figure 15 - 20, we can see all the estimators
except unrestricted JOH (JOH4) track the data well either we
use two interest rates or the spread in the regression. We
notice that the actual MlB/P is above the estimated value
across estimation during 1986-91; this period coincides the

boom of the stock exchange market in Taiwan.

171

Table 24
Estimated Cointegrating relations:

 

 

 

 

 

 

 

 

RMlB,=-p.+9yy,+0,i,+e,
OLS
x = (RMlB,yyi",umm) x = (RMlB,y,umm-ih)
£1 &, é,‘ émfl [Al av guano—I.
—6.50 1.52 0.05 -0.021 -6.80 1.55 -0.023
(0.29) (0.02) (0.03) (0.004) (0.13) (0.01) (0.003)
DOLS'

—6.21 1.50 0.10 —0.025 -6.89 1.55 -0.017
(1.27) (0.09) (0.14) (0.016) (0.65) (0.04) (0.012)
PM2
-6.42 1.53 0.06 -0.025 -6.81 1.55 —0.017
(0.89) (0.07) (0.09) (0.010) (0.48) (0.03) (0.010)
JOH

VAR(4) VAR(3)
—5.05 1.45 0.35 -0.050 -6.92 1.56 -0.017
(0.32) (0.07) (0.075) (0.23) (0.092)
Restricted VAR(4) with '6)" = - m” VAR(3) with ,6, = -1.50
-7.57 1.61 0.02 -0.02 -6.83 1.50 -0.016
(0.20) (0.01) (0.01) (0.28) (0.004)

 

Note: 1 DOLS estimation regression:

k k
RMlB = p. + (ivy, + 9,i, + Zd,L-’Ay, + 2g,L-’Ai, + a,

I=-k j=-k
where i is a vector containing interest rates. We set the
number of leads and lags k = 2 and use AR(2) error process

to implement DOLS covariance matrix and estimate the
standard errors.

2 The frequency zero spectral estimator required for FM are
computed. using" prewhitened. quadratic spectral kernel and
automatic bandwidth estimator(see Section II eumi 111 this
Chapter). Figures in parenthesis are standard deviations.

172

Table 25

Estimated Cointegrating relations:

RMIB, = u + Oyy, + 0

III!!!”

um, +8,

 

)

 

 

 

 

 

 

 

 

[1 av an"!

OLS

-6.96 1.56 -0.016

(0.12) (0.01) (0.003)
DOLS

-7.04 1.56 -0.015

(1.47) (0.04) (0.011)
PM

—6.96 1.56 —0.015

(0.44) (0.03) (0.009)
JOH

—7.05 1.57 -0.016

(0.26) (0.008)

 

 

 

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179

2 Tests of Linear Restrictions on Cointegrating vectors (6)
and the Adjustment Coefficients (a)

Because we are not only interested in inference about
the~ cointegrating' relations tun; also 1J1 their" adjustment
coefficients, the Johansen’s likelihood ratio tests provide

us tests for linear structural hypothesis CH1(X and 8. Note

that the Wald statistics for linear restrictions on

cointegrating vectors constructed from DOLS and FM also have
asymptotic x2 distribution.

The likelihood ratio test (M? the linear restrictions
about [3 and a, H4 : ,B =IH¢ and a = Ay/ are constructed from

solving both the unrestricted eigenvalue problem and
restricted eigenvalue problem. (for detail see Johansen and
Juselius 1990, Jehansen. 11991). Since tflma asymptotic
distribution of the maximum likelihood estimator is mixed

Gaussian, the hypotheSis about cointegrating relations is to

use the x2 distribution.

(1) Tests of linear restrictions on,fl

First, we test the unitary income elasticity hypothesis

for the VAR(4) model

H1: flm = — fly

180

The likelihood ratio (LR) for H; against H2 is computed as

LR = 0.85, which is compared x395<1> = 3.84 so the unit

income elasticity hypothesis cannot be rejected an: the 5%
level. The inability of rejection is also consistent with t
test constructed from Johansen estimates, however it is
inconsistent with t-ratios constructed by DOLS and PHFM. As
pointed out in Hoffman, Rasche and Tieslau (1995), the
difference in inference between the Johansen and the single
equation estimation (FM here) follows from the ex ante and
ex post normalization that distinguishes the two estimators.

Next the hypothesis that the coefficients for the own

rate of MlB and the umm rate are equal with opposite sign

is tested. The likelihood ratio for Hg is computed as LR =

1.37. Thus we fail to reject Hi at the 5% level, which is

consistent with the Wald test from FM (Table 12). Since we

fail to reject both H; and Hi, we go on to test the joint

hypothesis of

H; : ,8," = — ,6, and 6,. = "13...”. against H2

181

The likelihood ratio is 7.00, which is compared x§_95(1) =

3.84. Interestingly, H; is rejected at the 5% level even

though both flm = — fl, and (”*‘="flmm are rejected as shown

above.
Moving to VAR(3) model, we compute the likelihood ratio

for Lg :,fly = -1.50 versus H2 as LR = 1.60. Therefore, we

fail to reject the null at the 5% level.

(2) Weak exogeneity tests

 

We examine whether some variables in the system are

weakly exogeneous for the long-run parameters a and B, i.e.
for some i, a, = 0, where i is an index of variables in the
system. If Ax” is weakly exogenous for a and 8 in the sense
that the conditional distribution of Ax, given Ax" as well
as the lagged values of x, contains the parameters a and 8,
whereas all distribution of Ax,, given the lagged x, does

not contain the parameters a and 8. Furthermore, the

parameters in the conditional and marginal distribution are
variation free, (Johansen and Juselius 1990, 1992, Johansen
1991a). Urbain (1992) demonstrates. that the .rejection. of
weak exogeneity status of the various variables sufficiently

invalidates inference conducted in single error correction

182

model (for' both long-run. and short-run parameters)fla In
other words, the single equation ECM has parameters which
are themselves a function of the parameters of the marginal
process. Under such circumstance, one needs to conduct the
analysis based on both marginal and conditional model, i.e.

the full model.

In VAR(4) model, since the hypothesis ,6, = -,3,,,,,,,,

cannot be rejected by the data, we test hypothesis about a

in the restricted model under A. = -flm,,, that is, HQ: 01. =

I

0 and 6,, = -,Bumm versus Hi: ,8, = ":an For VAR(3), we test

the hypothesis of H: ,6, -1.50 and a, = 0 against ,8}, = -

1.50.

Table 26-27 reports the likelihood ratio (LR), which is

asymptotically' distributed. as ea x2(1) distribution under

the null hypothesis (for our case r'== 1). We can see the
test statistic for each hypothesis that the cointegrating
relations are not present in the equation determining each
variable in the system is rejected at the 5% level for both
VAR(4) and VAR(3) model. It indicates none of variables in
the system can be treated as weakly exogenous in estimation

of the long-run parameters a and E5<if the demand for real

 

28 See proposition 1 and 2 in Urbain (1992) for the

case r=l.

183

MlB in Taiwan. There is a loss efficiency if we attempt to
consider partially specified systems where only some of
variables are treated as endogenous and model these
conditional on the remaining variables. We note that
imposing invalid weak exogeneity hypothesis about some
variable, for example, causes the estimates for the interest
variables to posses wrong signs (the 3rd and 5th column in
Table 26, the 3rd and 4th column in Table 27), and the
standard deviations of estimates become very large. Thus,
when estimating the long-run parameters of time demand for

real M18 in Taiwan, we should treat all (n? the variables

(real MlB, y, i”, umm) as endogenous.

3 Estimation of the Long-Run Impact.Matrix [7

Finally, we conclude our cointegration analysis of the
Taiwanese demand for money by a comparison of the estimated
long—run coefficients matrix H = 08’ and the restricted HI:

0113 under the constraint ,6, = -flumm for VAR(4), and under [3y

= -1.50 for VAR(3). The estimates for VAR(4) and VAR(3) are

reported in Table 28 and 29, respectively.

184

4 Summary

Using the system method, we establish that there is one
cointegrating vector among real MlB, real GNP, the interest
rate spread (or the umm rate). The income elasticity is
around 1.50 and significantly different from zero and unity.

The semi-interest elasticity is around -0.017 and

significantly different from zero under a. = 36”,”. Using

the sample mean value of the umm rate (24.12%) the interest
elasticity is calculated as -0.41. These results are robust
to the choice of estimators. Furthermore, all the variables
should be treated as endogenous in estimating the long-run
Taiwanese demand for real MlB. The rejection of weak
exogeneity of the variables in the system suggests that it
is invalid to conduct inference from the single equation

conditional ECM only.

185

Table 26
Weak exogeneity tests: VAR(4) model

 

 

 

 

 

H4

fl!"b =-'6mmn fl!"b =-flwm ’61" =-flmmu fii” =- umm 461‘” =-flmm
a, = 0 a} = 0 a, = 0 awm = 0
LR 1.37 5.87** 7.36** 8.97** 3.99**
2 0.11 0.07 0.06 0.06 0.08
I

k 1.00 1.00 1.00 1.00 1.00
(0.14) (0.25) (0.17) (0.25) (0.23)

k -1.61 —1.70 -1.49 -1.28 —l.62

' (0.20) (0.37) (0.33) (0.39) (0.33)

k -0.02 0.010 -0.008 0.005 —0.04
(0.01) (0.002) (0.01) (0.02) (0.06)

2 0.02 —0.010 0.008 -0.005 0.04
(0.01) (0.002) (0.01) (0.02) (0.06)

g -0.03 0.00 -0.07 —0.03 -0.04

A 0.04 ' 0.03 0.00 -0.01 0.03

a,

& 0.07 -0.003 0.04 0.00 0.11

A —0.72 -0.20 0.83 0.39 0.00

aumm

Note: A. is the largest eigenvalue obtained in the

restricted eigenvalue problem.

186

Table 27
weak exogeneity test: VAR(3) model

 

 

 

 

 

,6, = -1.50 ,By a -1.50 ,3, = -1.50 fly = -1.50
a", = O a}, = O Mint-i” = 0
LR 1.60 12.31** 12.31** 12.31**
2 0.08 0.00 2.0e006 4.0e-006
1
g 1.00 1.00 1.00 1.00
(0.28) (154.18) (59.37) (41.90)
A -1.50 -1.50 -1.50 -1.50
5,
(0.28) (154.18) (59.37) (41.90)
8 0.016 -0.02 —0.03 0.018
_ (0.004) (0.96) (6.80) (7.73)
A —0.11 0.00 -2.7e-004 -7.0e-004
am
A -0.01 2.5e-005 0.00 -9.1e—005
a,
& 0.75 2.4e-003 4.7e-003 0.00
Note: A. is the largest eigenvalue obtained in the

restricted eigenvalue problem.

187

Table 28

 

 

 

 

 

 

 

 

 

VAR(4): Estimated long-run coefficients matrix: fl 8 258'
Hz: H = 018’

RMlB y i” umm
-2.8e-004 4.0e004 9.6e-005 -1.4e-005
0.0406 -0.0579 -0.014 0.0020
0.2079 -0.2962 -0.0710 0.0103
—0.1798 0.2561 0.0614 -0.0890

Hi: H = 018’ and fl,. = ’16...“
-0.0321 0.0518 -7.0e-004
0.0446 -0.0719 9.7e-004
0.0661 -0.1067 0.0014
—0.7216 1.1643 -0.0157
Table 29
VAR(3): Estimated long-run coefficients matrix: 13 I 88'
H2: H = 018’
m Y umm-i"
-0.1204 0.1847 -0.0020
0.0131 —0.0203 2.3e-004
0.4070 -0.6334 0.0070
11.3: r1 = a8' and ,6, = -1.50
—1.3482 -0.0211
-0.1502 -0.0023
8.9325 0.1400

 

188

CHAPTER 5

CONCLUSIONS

This dissertation has examined the stability of the
long-run (equilibrium) demand functions for four alternative
new definitions of money in Taiwan since 1961:4. Unlike many
money demand studies in the Taiwanese literature which use a
single bank deposits rate as a proxy for the opportunity
cost of holding money balances, we employ the interest rate
spread between the own rate of money and the unorganized
money market rate to incorporate the characteristics of the
financial structure in Taiwan.

After considerations have been undertaken to account
for data that exhibit both stochastic and deterministic
trends and seasonality as well, using various econometric
techniques we find that there is a strong evidence for the
existence of stationary linear combinations of real
balances, real GNP, and the short-term interest rates in
each money demand equation spanning 1961:4-1997:3 in Taiwan.
However, the stability tests detect apparent parameter
nonconstancy in broadly defined money equations (real MlBP,
real M2). On the one hand, parameter instability may be
explained by regime shifts over the sample period, including

the oil crisis in 1973, 1979, the shift from fixed to

189

floating exchange rate regime in 1978, and the financial
deregulation since 1980. On the other hand, the absence of
constant parameter may be explained by a misspecification in
econometric model thereof while the “true” long-run
relationship remains constant in spite of these
institutional changes. Although results from single equation
methods (Phillips and Ouliaris 1990, Gregory and Hansen
1996, and Hansen 1992b) suggest that real MlA, real GNP, and
the short-term interest rate (umm or the spread) are
cointegrated with stable parameters while a deterministic
trend. remains in time cointegration. relations, the system
method (Johansen and Juselius 1990, Johansen 1991) suggests
otherwise. Based on economic theories and an implausible
huge income elasticity' as well, we doubt this long-run
relationship. Results reveal that the most stable long-run
relationship occurs in the demand for real MlB data (real
MlB, real GNP, the short-term interest rate (the umm rate or
the spread)), indicating that the narrow MlB aggregate is
the preferable measure with which to consider the long—run
economic impacts of changes in Monetary policy in Taiwan.
Moreover, it also provides a useful anchor for study of
error correction or short-run dynamic and can also be used
in common trend exercises designed to reveal the underlying
source of nonstationarity of an economic system. The

contrasting results on the issue of stability from the

190

demand for two seemingly homogenous monetary aggregates
(real MlB, and real MlBP) are explained by the difference in
liquidity characteristics in these two measures of money.
Unlike insignificant role for an interest rate as the
opportunity cost (n5 holding money 1J1(a developing country
setting, we find that the demand for real MlB is interest
(the umm rate) elastic. The unorganized money market rate
has shown to be an empirically relevant variable in the
study of MlB demand in Taiwan, which may have important
policy message as documented in Wijnbergen (1982, 1983a,b,
and 1985). The estimated equilibrium income elasticity is
significantly different from unity and is (N1 the order of
1.50. The estimated equilibrium interest elasticity is (Hi
the order of -0.41. The transactions money demand model
derived 1J1 CHAPTER 14 which. :possesses steady-state
properties of unitary income elasticity and a negative
effect of the short-run interest rate and appears consistent
with several empirical findings in the money demand
literature using the data from developed countries, is
inadequate t1) explain the empirical findings 1J1 our study

for the long-run demand for real MlB in Taiwan.

191

APPENDIX 1

192

APPENDIX 1

THE REDEFINED MDNETARI AGGREGATES IN TAIWAN

The central bank in Taiwan (the Central Bank of China,
CBC) redefined time monetary aggregates 111 February, 1997.
The definitions of money supply are revised to include the
total deposits in the Postal Savings System. For the M2
definition, repurchase agreements and non-residents N.T.
(New Taiwan dollar) deposits are also added, while the
foreign exchange trust funds and the bank debentures,
savings bonds and Treasury bills held by the public are
excluded from the original definition. The new aggregates

are presented in Table A1

193

Table A1
New measures of money
Millions of New Taiwan (NT) dollars, seasonally unadjusted,
August 1997

 

Mlh 1,721,421
Currency in circulation1 493,057
Checking accounts2 325,415
Passbook deposits2 902,949

M18 3,728,568
M1A 1,721,421
Passbook savings deposits2 2,007,147

MZ 14,520,631
MlB 3,728,568
Time and time savings deposits3 7,855,219
Postal savings deposits4 2,299,346
Foreign currency deposits5 399,206
Repurchase agreements issued by monetary institution

and Postal Savings System6 182,952

Non-resident N.T.(New Taiwan dollar) deposits7 55,340
Notes:

1 This component equals currency issued by (xx: - cash in

vaults held by monetary institutions and the Postal Savings
System.

2 These deposits are also referred as monetary deposits,
held by enterprises and individuals in monetary
institutions. According to Banking Law, savings deposits can
only be held by individuals and non-profit organizations.

3 Time deposits include general time deposits and negotiable
certificates of deposit (NCDs). Time savings deposits also
include deposits replaced by the Postal Savings System.

4 This component includes giro accounts, passbook savings

deposits anui time savings deposits of time Postal Savings
System.

5 It includes foreign currency deposits, and foreign
currency certificates of deposits of enterprises and
individuals in monetary institutions.

194

Notes (cont’d)

(5 It represents repurchase agreements sold 11) enterprises
and individuals tn! monetary' institutions enui the Postal

Savings System. Prior to January 1994, the data are not
available.

7 It includes demand and time deposits held by foreign non-
financial institutions. Prior to January 1994, the data are
not available.

Source:

Financial Statistics Monthly, November 1997, the Central
Bank of China (the Republic of China, Taiwan).

195

APPENDIX 2

196

APPENDIX 2

SOURCES OF FUNDS BORROWED BY PRIVATE ENTERPRISES IN TAIWAN

Table A2 displays the sources of funds borrowed by
private enterprises in Taiwan during 1976-1988. From Table
A2, we can see that the private enterprises actively borrow
from the unorganized money market (U.M.M.) (around one-third
of borrowing comes from U.M.M. during 1976-1988), despite
the existence of the organized money market since 1976. It
appears that there is no sign showing that the importance of
the U.M.M. has declined over time regardless substantial
financial reforms have been launched to modernize the

financial system in Taiwan.

 

 

 

Table A2
Source of funds borrowed by private enterprises in Taiwan
End of year Financial Key U.M.M. %
Institution Market

1976 67.30 0.57 32.13 100.00
1977 63.31 2.89 33.80 100.00
1978 59.98 4.02 36.00 100.00
1979 57.15 8.13 34.72 100.00
1980 54.95 8.91 36.14 100.00
1981 52.80 11.71 35.49 100.00
1982 53.42 13.38 33.20 100.00
1983 54.88 14.31 30.81 100.00
1984 54.71 15.11 30.18 100.00
1985 51.69 13.26 35.05 100.00
1986 50.58 8.41 40.01 100.00
1987 56.22 6.65 37.13 100.00
1988 63.67 5.76 30.57 100.00
Average 56.97 8.97 34.33 100.00

 

Source: The Efficiency of Allocation of Funds in the Taiwanese Financial System
(Table 6, Shea 1991).

197

APPENDIX 3

198

 

APPENDIX 3

TESTING FOR PRICE HOMDGENEITY OF THE MONEY DEMAND FUNCTIONS
IN TAIWAN (1961:4-1997:3)

Since economic theories predict that the demand for
money is a demand for “real” balances (money holdings
measured in constant purchasing power terms), a price level
elasticity of the demand for nominal balances is frequently
constrained to one. In this appendix, we use the fully
modified estimator (FM) of Phillips and Hansen (1990) (see
Section 111, CHAPTER 4) to estimate 6? in the nominal money

(MlA, MlB, MlBP, and M2) cointegrating relation

and to test whether 0 = 1 using t-ratio constructed from FM
estimates, where y, i, (umm are the same as defined before;
p is GNP deflator (1991 = 100). In Table A3, we report the
(FM) estimates, their standard deviations, and Hansen
(1992b) parameter stability tests.

As seen in Table A3, the coefficients on price in all

equations are not significantly different from one at the 5%

199

level.

Note that the coefficient

in MlA equation is not

significantly different from zero at either 5% or 10% level.

Table A3

Testing for price homogeneity: 6

= 1

m, = u + a_,y, + a,i, + ammumm, + 0?, + v,

 

 

 

 

 

Regression MlA MlB MlBP M2
L. 4.69** 1.81** 4.45** 23.18**
MeanF 33.26** 3.11 5.95 60.51**
SupF 280.89** 10.17 27.61** 442.67**
[67:1] [74:2] [67:2] [67:1]
FM estimates
Regressors MlA MlB MlBP M2
constant 3.29 -2.30 - 0.64 -10.10
(0.38) (0.31) (0.25) (0.15)
y 0.45 0.95 0.71 - 2.05
(0.24) (0.18) (0.15) (0.10)
i - 0.36 -0.10 - 0.03 - 0.01
(0.23) (0.10) (0.04) (0.02)
umm - 0.08 -0.05 - 0.05 - 0.02
(0.02) (0.01) (0.01) (0.01)
p 2.40 2.05 2.48 1.54
(1.95) (1.40) (1.15) (0.80)
Note: rn is the log of nominal money supply. p is the log of

the GNP deflator.

** indicates significance at the 5% level.
See Table 15-16 for critical values.

200

APPENDIX 4

201

APPENDIX 4

TESTING FOR.NO COINTEGRATION BETWEEN THE UNORGANIZED MONEY
MARKET RATE AND THE OWN RATE OF MONEY IN TAIWAN
(1961:4-1997:3)

In this appendix, we use standard residual based

cointegration tests Z, enui Za (see Section II, CHAPTER 4)

to test the hypothesis of no cointegration occurred between

the unorganized money market rate (umm) and the own rate on

each measure of money (i“,i”,i"”,i"'2). Test results and the
OLS estimates (and standard errors) are reported ixl'Table
A4.

From Table A4, we find that the hypothesis of no
cointegration is not rejected for each pair of (umm,i) at
the 5% level. The results are invariant to the normalization

selected.

202

Table.A4

Testing for no cointegration between the unorganized.money

market rate (umm) and the own rate (i)

 

 

 

 

 

 

 

 

 

umm, = constant + at“, + 8,
0L5. constant i” —2 SEE DW
estimates R
22.78 2.16 0.009 3.13 0.06
(0.91) (1.40)
Z! 20 £4
-1.56 -4.40 1.10
i“, = constant + aumm, + 8,
m5_ constant umm -2 SEE DW
estimates R
0.44 0.008 0.009 0.19 0.08
(0.12) (0.005)
Z, Z. A“,
-l.77 —6.03 0.33
umm, = constant + ad”, + 8,
CL? constant i” -2 SEE DW
estimates R
20.30 2.51 0.32 2.58 0.08
(0.51) (0.30)
Z. Z. 3,
-1.98 -6.58 1.16
i”, = constant + dumm, + 8,
“5 constant umm —2 SEE DW
estimates R
-1.65 0.13 0.33 0.59 0.04
(0.38) (0.02)
Z, Z. (,
-1.78 -4.42 1.18
Critical Values
Z, Z.
5% -3.37 —20.5
10% -3.07 -17.0

 

An * indicates significance at the 10% level.

Critical values are from Table 1 and 2
(1992a).

AB

(n=1,in=0)

in Hansen

Table A4 (cont’ (1)

 

 

 

 

 

 

 

 

 

umm, = constant + aflw, + 8,
m5_ constant 1” -2 SEE DW
estimates R
19.84 2.05 0.53 2.15 0.11
(0.51) (0.16)
Z. Z. X,
-2.53 -9.97 1.19
i”, = constant + aumm, + 8,
ms. constant umm -2 SEE DW
estimates R
—4.23 0.26 0.53 0.77 0.07
(0.50) (0.02)
Z, Z. x,
-2.55 -8.33 1.30
umm, = constant + cf”, + 8,
ms. constant in -2 SEE DW
estimates R
13.04 2.37 0.65 1.87 0.20
(0.70) (0.15)
Z. Z. (,
—2.77 -14.51 0.80
V”, = constant + aumm, + 8,
“5. constant umm -2 SEE DW
estimates R
0.64 0.64 0.24
-1.93 0.27
(0.41) (0.02) Z, Z0 11:!
-3.11* —17.69* 0.84
Critical Values
Z. Z.
5% -3.37 -20.5
10% -3.07 -17.0

 

An * indicates significance at the 10% level.

Critical values are from Table 1 and 2
(1992a).

(11:1,

204

I]=0)

in Hansen

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