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dissertation entitled

We TYomsacti‘ons Money Demand Fri Ewan: Ana/fix
ofi 3105“] (Md the Importance 0+ the Innova'bbns

in the Common Stochos‘u‘c Tfencls
presented by

Lee, Ch‘ngnuw

has been accepted towards fulfillment
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Cbpartmen‘t of ' Economics .

 

 

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MSU In An Affirmative Action/Equal Opportunity Intuition
Wm:

THE TRANSACTIONS MONEY DEMAND IN TAIWAN: ANALMSIS OF
STABILITY AND THE IMPORTANCE OF THE INNOVATIONS
IN THE COMMON STOCHASTIC TRENDS

BY

Chingnun Lee

A DISSERTATION

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

DOCTOR OF PHILOSOPHY

Department of Economics

1994

ABSTRACT

THE TRANSACTIONS MONEY DEMAND IN TAIWAN: ANALYSIS OF
STABILITY AND THE IMPORTANCE OF THE INNOVATIONS
IN THE COMMON STOCHASTIC TRENDS

BY
Chingnun Lee

This dissertation studies the stability of transactions
money (M18) demand in Taiwan using the statistical technique
developed by Johansen (1988,1991), and Hansen and Johansen
(1993). A long-run equilibrium transactions money demand
function is identified and estimated along with the three-
variable vector error correction model (VECM). The results
suggest that the transactions money demand function shifted
downwards in the fourth quarter of 1982, while leaving the
income and interest rates elasticities unchanged. The
tentative explanation to the shift is the financial
deregulations in the early 1980's, and historically
jpersistently high interest rates at the same time. The results
in the estimated equilibrium transactions money demand
function are further used as a long-run restriction in the
Gussian VAR.model to identify two common stochastic trends in
the nonstationary money demand variables. These two common
stochastic trends explain a considerable portion of the

variance of major economic variables in Taiwan.

Dedicated to my parents:

Chen-Hsiung and Hung-Chin

iii

ACKNOILEDGEMINTS

First and foremost, I would like to express my sincere
gratitude to Professor Robert H. Rasche, my dissertation
chairman, for all the time, patience, encouragement, guidance
he ‘has given to ‘me throughout. the jpreparation of this
dissertation. I wish to thank the other dissertation committee
members, Professor Jeffrey M. Wooldridge and Christine Amsler
for their invaluable comments.

I also wish to express my deepest appreciation to Professor
Anthony Koo for his providing me crucial economic data about
Taiwan, to Professor Ching-Fan Chung, whose constant
encouragement kept me on track and to Professor Rodger Jackson
for his editorial assistance on my first draft.

Finally, I would like to express my indebtedness to my
family for their support throughout my graduate study at
Michigan State University. To my brothers, Ching-Chang and
Ching-Fung for sending me the much needed review literatures
in Chapter Two of the dissertation, and to my parents for
their unflaggingly spiritual and financial support, without
which I would have never been able to complete my doctoral

degree.

iv

TABLE OF CONTENTS

Chapter 1. IntrOductionooooooooooooooooooooooooooooooooooooool

Chapter 2. Brief Review of Theories of Demand for Money and
Empirical Analysis in Taiwan.

I. Theories of the demand for money..................6

(A).Theclassicsapproach........................6
(1). Irving Fisher's version of the

Quantity Theory........................6

(2) . The Cambridge approach.................7

(B). Keynesian Theory.............................7

(1) . Thetransactionsmotive.. . ......8

(2) . Theprecautionarymotive. . . . . . . . . . . . . . . .8

(3) . Thespeculativemotive. .. .. .9

(C).ModernQuantityTheory.......................9

II. Empirical analysis on the demand for transaction
moneyinTaiwan.... 11
(A). Lu, F.C.(1970)..............................l3
(B). Chen, J.N. and Shu, J.H.(1974)..............13
(C). Liang, M.I., Chen, K. and Lou, S.(1982).....14
(D). Wu, C.S. andYen, C.F.(1987)................15
(E). Chang, J.Y.(l989)...........................16
(F). San, K.L.(1991).............................17

III. Problems with the lag-dependent variable
specification:
(A). From economic theory
( 1) . Real balance adjustment assumption. . . . . 18
(2) . Nominal balance adjustment assumption. . 20
(B). Fromeconometrictheory. . . . . . . . . . . . . . . . . . . . .22

IV. Problems with single equation error correction
mweJ-OOOI...OIOOOOOOOOOIOOOOOOO0.0.0.000000028

Chapter 3. The Present Structure of the Financial System in
' Taiwan.

I. Financial institutions in Taiwan. . . . . . . . . . . . . . . . . 29
(A). Monetary institutions

(1) . The Central bank of China......... ...30
(2). Domestic banks.........................3O
(3) . Local branches of foreign banks. . . . . . . .31
(4).Mediumbusinessbanks..................31
(5) . Credit cooperative association. . . . . . . . . 31
(6). Credit departments of farmers' and
fishermens' association................31
(B). Other financial institutions.
(1) . Investment and trust companies. . . . . . . . .32
(2). Postalsavingssystem..................32
(3). Lifeinsurancecompanies...............33
(C). "Near financial institutions”
(1). Property and casualty insurance company
.......................................35
(2) . Central deposit insurance corporation. . 35
(3) . Bills financecompanies................35
(4) . Fuh-Hwa securities finance company. . . . . 35
(5) . Offshorebankingunits.................35

II. Financialmarket inTaiwan.......................36
(A). Money market

(1) O “finition O O O O O O O O O O O I O O ....... O O O O O O O O 36
(2) O BaCRground. O O O O O O O O O O O O O O O O O ........ O O O 36
(3).Curbmoneymarket..... ........ .........37

(B). Capital market
(1). Definition.............................39
(2). Background.............................39

III . Some important economic indicators. . . . . . . . . . . . . . 40

IV. Major liberalization and reforms of the
financial system since 1980. . . . . . . . . . . . . . . .43

Chapter 4 . Equilibrium Transactions money Demand in Taiwan. .45

I . Unit root in aggregate economic variables. . . . . . . . 46
(A). Dickey-Fuller test..........................48

(B) . Augmented Dickey-Fuller test. . . . . . . . . . . . . . . . 50

(C). Phillips-Perron test........................51

II. Cointegration....................................53

III. Johansen maximum likelihood method. . . . . . . . . . . . . . .58
IV. Identification of cointegration vector. . . . . . . . . . . 70
V. Empirical results

(A) . Data
(1) . Measurement and sources ...... . . . . . . . . . . 73

vi

(2). Data characteristics...................81
(B).Unitroottest..............................84
(C) . Model misspecifications test. . . . . . . . . . . . . . . .88
(D). Johansen cointegration estimation and test

(1). Log-log specifications.................91

(a) . Results under restriction on p. . . . .91
(b) . Results under restriction on a. . . . 112
(c). Results under restriction on.fi and a

..................................115

(2). Semi-log specifications...............117
(E) . Stock-Watson dynamic OLS estimation. . . . . . . . 124

Chapter 5. The Importance of the Common Stochastic Trends
on the Fluctuations of Major Aggregate Economic
Variables in Taiwan .................. ..........128

I. Common trend representations of a cointegration
system.0.0...O00.........OOOCOIOOOOOOOOOO0.0.128

II . Identification of common stochastic trends. . . . 130

III. Impulsion response function and variance
decomPOSitions.0......0......0.0.0.00000000000133

IV. Empirical results. ..... .......................135

Chapter 6. Conclusions....................................143

Appendix A. Test for price homogeneity in Taiwan money demand
function: fromL-Rtest........................145
Appendix 8. Test for price homogeneity in Taiwan money demand
function: fromWaldtest.......................147
Appendix C. Test for absence of linear trends in the
nonstationary processes........................149
Appendix D. How to invert the estimated VECM to a multivariate
version of Wold's decomposition in first
difference.....................................152
Appendisz. The roots in the characteristic polynomial of the
VAR(5) model...................................155

Bibliwraphy.O..0...00......COO...O0.0...00.00.000.00000000158

Table
(3.1).

(3.2).

(4.1).
(4.2).

(4.3).
(4.4).

(4.5).

(4.6).
(4.7).

(4.8).
(4.9).
(4.10).

(4.11).

(4.12).

(4.13).

(4.14).
(4.15).

(4.16).

(4.17).

(4.18).

LIST OF TABLES

Assets and Units of Financial Institutions in
Taiwan..............................................34
Assets and Units of "Near-Financial” Institutions in
Taiwan..............................................35
How Money stock is Defined in Taiwan. . . . . . . . . . . . . . . .76
The Percent of Postal Passbook Savings Deposits
RelativetoMlBinTaiwan...........................78
Unit Root Test Statistics (logarithms) . . . . . . . . . . . . . .85
Unit Root Test Statistics (First Difference of
Logarithms).........................................86
0,05 Critical Values of Unit Root Test by Schwert
(1989)..............................................87
Box-Pierce-Ljung Test Statistics. . . . . . . . . . . . . . . . . . .89
Residual Diagnostics for Fourth Order Vector Error
Correction Model....................................90
Test for Cointegration: Real M18, Real GNP, and One-
month time Deposits Interest Rates (T=69) . . . . . . . . . . . .93
Test for Cointegration: Real M18, Real GNP, and One-
month time Deposits Interest Rates (T=80) . . . . . . . . . . . .96
Recursive Estimates of the Money Demand Specification
in Taiwan, 61:3--92:4, Johansen's Estimates. . . . . . . . .99
Recursive Estimates of the Money Demand Specification
in Taiwan, 61:3--92:4, With D824 (begin at 1982:4),
Johansen's Estimates...............................102
Test for Cointegration: Real M18, Real GNP, and One-
month time Deposits Interest Rates(T=121), with
0824...............................................104
Recursive Estimates of the Money Demand Specification
in Taiwan, 61:3--92:4. Income elasticity constrain to
be 1.70, with D824(begin at 1982:4) . . . . . . . . . . . . . . . .106
Recursive Estimates of the Money Demand Specification
in Taiwan, 61:3--92:4, with 8824 and a' 6=0. . . . . . . .111
Recursive Estimates of the Money Deman Specification
in Taiwan, 61:3--92:4, with D824 and a =a3=0. . . . . . .114
Estimates for the Taiwan Money Demand and the
Corresponding fl and a vector under various hypothesis
about 8 and a. sample Period: 1961:3--1992:4, with a
D824 Dummy variable................................115
Test for Cointegration, Real M18, Real GNP, and One-
Month-Time Deposit Interest Rates. . . . . . . . . . . . . . . . . . 116
Recursive Estimates of the Money Demand Specification
in Taiwan, Semi-Log Model, 61:3--92:4, Johansen's
Estimates..........................................118

viii

(4.19) .

(4.20).

(4.21).

(4.22).

(5.1).

(5.2).

(A.1).

Recursive Estimates of the Money Demand Specification
in Taiwan, Semi-Log Model, 61:3--92:4, With D824
(begin at 1982:4) , Johansen's estimates. . . . . . . . . . . . 120
Estimated Cointegrating Model. Semi-Log Specification.
Long-run Income Elasticity restricted to be 1.70. . . 122
Estimated Cointegrating Model. Semi-Log Specification.
Long-run Income Elasticity restricted to be 1.70,
Adding D824........................................123
Stock and Watson' 3 Dynamic OLS Estimate of Money
Demand Function in Taiwan, Log-Log specification, add
D824...............................................127
Fraction of the Forecast Error Variance Attributed to
”Nominal” Permanent Shock..........................142
Fraction of the Forecast Error Variance Attributed to
”Natural Output" Permanent Shock. . . . . . . . . . . . . . . . . . . 142

The Eigenvalues and the Corresponding Test Statistics
forTestingRestrictions onfi......................142

ix

Figures
Figures
Figures
Figures
Figures
Figures
Figures
Figures

Figures

Figures

Figures

Figures

Figures

Figures

1.

2.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

LIST 0? FIGURES

Consumer Price Inflation Rate..................41
Annual Growth Rate of M18 in Taiwan............41
Growth Rate of GNP at Current Price............42
Annual Growth Rate of Real GNP.................42
LogarithmofReal M1882
Logarithmof Real GNP82
VelocityofM18................................83
One-Month-Time Deposits Interest Rates. . . . . . . . .83

Real M18 in Response to One Standard Deviation
in "Nomina1'. ShOCROOOOO...00.0.0000000000000000138

Real M18 in Response to One Standard Deviation
in"Natura10utput"Shock......................138

Real GNP in Response to One Standard Deviation
in "nominal" ShOCROOOOOOOO0.00000000000000000139

Real GNP in Response to One Standard Deviation
innNaturaloutPut'.ShOCkO0.00...00.0.000000000139

Real r in Response to One Standard Deviation
in "Nominal" Shock...........................140

Real r in Response to One Standard Deviation
in"NaturalOutput"Shock......................140

CHAPTER 1

INTRODUCTION

This study investigates the structure and the stability of
the long-run transactions money demand in Taiwan by
cointegration analysis of’ Johansen's (1988,1991) maximum
likelihood.method. Once the issue of stability is answered, I
further identify the common stochastic trends that prevail in
the money demand variables by the procedures described by
King, Plosser, Stock, and Watson (1991) and observe how these
variables respond to innovations in the common stochastic
trends.

A stable money demand function is one that can be shown to
be a function of relatively few variables and exists under
differing institutional arrangements, changes in the social
and political environment, and changes in economic conditions,
or to explain the effects of such changes on the functions‘.

The importance of a stable money demand functions is
stressed by both Milton Friedman (1956): "The quantity
theorist not only regards the demand function for money as
stable, he also regards it playing a vital role in determining
variables that he considers of great importance for the
analysis of the economy as a whole, such as the level of money

income or of price.", and by Gordon (1984b): ”The concept of

 

1See Meltzer (1963), p222.

1

2
the long-run demand for money plays such a central role in
macroeconomic theory that it is difficult to imagine living
without it. Similarly, stable long-run money demand function,
both at home and abroad, are key ingredients in the monetary
theory of the balance of payments and the more recent monetary
theory of exchange rate determination".

The body of empirical evidences on the issue of money
demand stability both from lag-dependent variable
specification (for example, Liang, Chen, and Lou (1982): Wu
and Yen (1987)) and single equation error correction model
(for example, Chang (1989); San (1991)) provide overwhelming
support for the hypothesis that there exists a stable money
demand function in Taiwan. However, recent advances in
econometrics and time series methodology have made it clear
that a model in levels such as lag-dependent variable
specification that ignore the nonstationarity of individual
series may lead to spurious regression results, while a model
in first differences will be misspecified if the series are
cointegrated and converge to a stationary long-term
relationships. On the other hand, a single equation error
correction model may suffer from simultaneous equations bias.

I choose the possible dynamic specifications based on the
maximum likelihood procedures developed by Johansen (1988,
1991) to reexamine this issue of the stability'of'money demand
function by multivariate autoregressive analysis. This
procedure allows systematic tests for nonstationarity and
cointegration without imposing a prior restrictions on the

coefficients or the numbers of the possible long-term

3
relationships. The question of stability is answered by the
latest test developed by Hansen and Johansen (1993) for
testing constancy in the cointegration space.

The primary' conclusions of ‘this study' are that. with
attention to the time series properties of available data, the
estimated equilibrium income and interest rates elasticities
of transactions money demand (M18) in Taiwan remain stable for
the entire samples when we consider the structural break in
fourth quarter of 1982. The hypothesis of the equilibrium real
income (GNP) elasticity being equal to 1.70 generally cannot
be rejected. Further, the estimates of equilibrium interest
rates (one-month time deposit) elasticity are approximately
-0.46 to -0.65. However, in contrast to any other studies on
this issue of money demand function stability, this structural
break is shown to be the shift down of the constant term in
the money demand function by statistical decomposition of this
shift (dummy) variable. The shift-down of the demand for money
in the fourth quarter of 1982 is tentatively attributed to the
financial deregulation in 1980's and historically high
interest rates at that time in Taiwan.

In Chapter 2, I briefly review the theories of money demand
and present a summary of the empirical literatures on the
demand function for real transactions money in Taiwan. The
possible problems of the existing literature in model
misspecification, simultaneous equations bias and
nonstationarity in the variables are also addressed.

In Chapter 3, I shortly introduce the present structure of
the financial system in Taiwan. With the introduction of the

4
financial institutions, markets, and deregulation, it makes
clear to the question for the choice of the data and the
explanation of structural break in money demand function in
Chapter 4.

In Chapter 4, I first review the recent.developments in the
statistical theory of testing for unit root in the individual
variable. A thorough explanation of the Johansen maximum
likelihood procedures for testing cointegration, linear
constraints in the cointegrating vector, and weakly exogeneity
of certain variables is then presented. Empirical results from
various unit root test support the evidence of a single unit
root in Taiwan«data for real M18, real GNP, and one-month time
deposits interest rate. Results from recursive estimation of
Johansen ML method in this chapter suggest that a single
cointegrating relationship exists among the real M18, real
GNP, and one-month time deposits interest rates when we
consider the 1982:4 structural break. Therefore the evidence
supports a stable equilibrium demand function for real M18 in
Taiwan economy. A tentative explanation of this structural
change is also provided. An alternative results from dynamic
OLS for estimating a known number of cointegrating vectors
developed by Stock and Watson (1993) are also presented in the
final section of Chapter 4. This dynamic OLS estimation
assumes some variables are weakly exogenous. Therefore, these
results provided a good example for comparison of the
estimates from the constrained Johansen's method of testing
exogeneity.

In Chapter 5, I apply the procedures of King, Plosser,

5

Stock, and Watson (1991) to identify and to estimate the
common stochastic trends from the estimated cointegrated
system in Chapter 4. The system dynamic then is determined by
means of forecasts error variance decompositions and impulse
response function. The results in this chapter reveal that
:movements in these common stochastic ‘trends account for
significant portion in the variations of real M18, real GNP,
and nominal interest rate in Taiwan.

Chapter 6 presents the summary and conclusions.

CHAPTER 2

BRIEP REVIEN OP THEORIES OP DEMAND TOR MONEY AND EMPIRICAL
ANALYSIS IN TAIWAN

The nature of the demand for money has been an area of
great interest in macroeconomics and has had important
implications for the conduct of monetary policy. Under the
assumptions of direct control over the manipulating variables
in the money supply functions, the monetary authorities can
exert a systematic influence on at least some of the factors
on which the quantity of money demand depends. Some of the
factors that might influence money demand are interest rates,
real national income (and therefore employment), and the
general price level. The importance of the behavior of these
variables for the well-being of the economy is quite obvious,
and a detailed knowledge of the demand for money function is
an essential prerequisite to the active use of monetary

policy.

I.Theories of the demand for money:
(A). The classics approachz:
(1). Irving Fisher's Version of The Quantity Theory:
Irving Fisher, the economist most closely associated with

this approach, built on ideas that emerged from the 19th
century on monetary economics in his book MW

 

2The detail of classical theory of money demand can be
found in Laidler (1985, Chapter 5).

6

7
gfi_ngn§y_112111. The demand for nominal money depends on the
current values of the transactions to be conducted in the
economy and is equal to a constant fraction of those
transactions, which in turns bears a constant relationship to

the level of national income. This can be written as

M,,,-k,.1>1T

where P is the price level, and T is the volume of
transactions.
(2). The Cambridge Approach:

In the Cambridge approach, as epitomized in the work of
Marshall and Pigou (1917) , the principle determinant of
people's demand for money holding is the fact that it is a
convenient asset to have, being universally acceptable in
exchange for goods and services. The more transactions an
individual has to undertake, the more cash he will want to
hold. The emphasis, however, is on desire to hold, rather’than
necessity to hold; and this is the basic difference between
Cambridge monetary theory and the Fisher framework. They write

the demand equation for money:
Md=kPY ,
where Y is aggregate nominal national income.

(8) . Keynesian Theory: The three theories we are about to

review correspond to Keynes's famous three motives for holding

8
money3 and are refined by subsequent authors.
(1). The Transactions Motive:

The 'transactions demand for' money arises Ibecause the
receipt of income by an individual or a firm is not perfectly
synchronized with the payments that have to be made. In order
to be sure that payment can be made when it is due,
individuals and firms maintain money balances in the form of
cash and demand deposits. Specific models of the theory of
money demand for transactions were constructed by Baumol
(1952), Tobin (1956) for the individual; by Miller and Orr

( 1956) for the firm. This well-known equation for money demand

is
£14.24:
p 2 R ’

where b stands for cost (brokerage fee) of conversion between
money and bonds, T is the total value of transactions during
a period, R is the interest paid on bond-holdings‘.
(2). The Precautionary Motive:

This theory concentrates on the demand for money that
arises because people are uncertain about the payments they
might want to, or have to, make. The more money an individual

holds, the less likely he is to incur the cost of liquidity

 

38» J. 24- Keynes. WW
1W (1936. Chap. 13).

‘McCallum (1989, Chapter 3) also provides a formal model
from utility-maximization individuals to get a transaction
money demand as a function of consumption expenditure and an
interest rate.

9
(that is, not having money immediately available). But the
more money he holds, the more interest he is giving up. See,
for' example, 'Whalen. (1966), Gray' and. Parkin (1973), and
Goldman (1974).
(3). The Speculative Motive:

An individual who has wealth has to hold that wealth in
specific financial assets. Those assets make up a portfolio.
Money has an expected yield of zero, but it is riskless
because its money value is certain. Bonds, on the hand,
usually have a positive expected yield, although there is a
possibility that unanticipated capital gains or losses will be
incurred. Unanticipated capital gains or losses affect the
actual yield and therefore make bonds risky. Uncertainty about
the return on risky assets leads to a diversified portfolio
strategy. Tobin (1958) argued that money would be held as the
safe asset in the portfolios of investors.

Tobin's portfolio theory explained why relatively low
interest, riskless savings accounts (M2) are jpart of a
portfolio that also include high-yield but risky bonds. The
transactions demand for money explains why cash and demand
deposits (M1) are held along with riskless assets such as
savings accounts that do pay interest. Noninterest-earning
money is convenient for settling transactions. In short, the
theories of transactions and speculative demand for money are
complementary rather than alternatives.

(C). Modern Quantity Theory:
The modern quantity theory was developed by Milton Friedman

(1956). Friedman's view of money is similar to Tobin's

10
portfolio theory in that money is seen as one asset among

many. Friedman writes the aggregate money demand function as:

M 1 dP Y
—"f I I I l _—l W, _I I
P ( b 9 P dt P u)

where r5 and r; represent expected real return from holding

bonds and equities. (1/P) (dP/dt) stands for expected price
inflation which is considered as the foregone rate of return
from holding money instead of physical goods. w is the ratio
of non-human to human wealth. Y/P stands for real wealth and
u is any variables that can be expected to affect tastes and
preferences. The key distinguishing feature of Friedman's
demand for money function is the inclusion of the rate of
return (and therefore, expected inflation rate) on physical
assets which directly substitute for money. Keynesians
emphasize the substitutability of money and financial assets
such as bonds and stock. On a strict transactions view of
demand for money, a variable measuring anticipated inflation
seems to have no place. Under suitable assumptions by Ando and
Shell (1975), inflationary expectations will be reflected to
some extent in nominal interest rates and thus will indirectly
affect the demand for money, therefore expected inflation

should not appear in the money demand function again.

II. Empirical Analysis on the Demand for Transaction MOney in

Taiwan
As it is pointed out in the last section on theories of

money demand, different approaches lead to various views of

11
money' stock, and/or' appropriate {arguments ‘that influence
demand for money. For example, from a transaction view of
money demand, short term interest rates and real national
income are appropriate factors that affect demand for currency
and demand deposit (M1). It is easier to make payments with
currency and demand deposits than with savings and time
deposits although the later are safe and pay interest. On the
other hand, the Keynesian speculative motive and Friedman's
new quantity theory seem to suggest that long-term interest
rates and.wealth affect the portfolio choice because time and
savings deposit (M2) are safer assets relative to bonds and
stocks which pay a higher expected yield. The new quantity
theory even incorporates the expected rate of inflation as an
argument of the demand for money. It is an empirical problem
to test which approach is relevant to the real motive for
holding money by individuals. A great deal of work has been
done in United State. I will not go deeply into this debate.
In this paper, I will only concentrate on the transactions
demand for money in Taiwan for two data reason. First, there
are no non-human wealth data available in Taiwan‘. As Laidler
(1985, p87) said: "Sufficiently detailed data on nonhuman
wealth measured over a time span long enough to be useful do
not exist for economies other than the United States". Second,
it is hard tijut a appropriate variable in the long-run money

demand function to measure unobservable expected rate of

 

sMany use permanent income to represent for wealth. As
explained by Rasche (1990), in full equilibrium transitory
income is zero, so real income equals permanent income as the
argument of the equilibrium demand for real balances.

12
inflation.

There is general agreement among economists on the
specification of a long-run transactions money demand
function. In doing empirical work when using annual data, it
is usually assumed all adjustment is complete within a year,
so there is no need to specify a short run dynamic function
form for the estimation.( For example, Meltzer (1963), Laider
(1966)). In the 1970's, as quarterly data became available, a
short-run dynamic specification was used. The argument is that
optimal quantity of money balance is only approached slowly,
due to the presence of adjustment costs, which means that the
approach to equilibrium balances cannot be completed within a
quarter. (See Goldfeld (1973, 1976), Hamburger (1977),
Lieberman (1980), Judd. and. Scadding (1982), and. Boorman
(1982)).

In Taiwan, quarterly data on national income were not
available until June 1981 when the Directorate-General of
Budget, Accounting and Statistics (DGBAS) first publish
Quarterly National income Statistics in Taiwan ALE: which
retrieved data from.January, 1961. For this reason, empirical
research on money demand in Taiwan used annual data in the
70's. Since then analyses using quarterly data with Goldfeld's
type of partial adjustment are popular. The following are most
of the notable work on transactions demand for money in
Taiwan, each is chosen for its representation of advances in
various methodology in model specifications of money demand

functions in the past twenty years (mostly in Chinese).

13
(A).Lu, F.C. (1970):
He uses annual data to get the equation (2) in his paper
ln(m)=-3.5948 + 1.4809 ln(y) - 0.0861 ln(r)
(7.81) (0.60)
18-0.9312, o.w=0.9329, sample period: 1947--1968
where m is real M1 at 1964 constant price
y is real GDP at 1964 constant price
r is interest rate on secured loans charged in curb
money market in Taipei city.
He concluded money is a luxury good.
(8).Chen, J.N. and Shu, J.H. (1974):
They use annual data from 1953 to 1972 and obtain an even
higher income elasticity of money demand. Equation (10) in
their paper is

ln(m)=-0.8736 + 1.5441 ln(y) - 0.0073 ln(r)
(17.06) (-0.047)

R2=0.9928, Sz=0.0048, DW=1.3796

No explanation of the definitions of data and the low t
value in interest rate is given.

(C).Liang, M.I., Chen, K. and Lou, S. (1982):

This was the first paper that uses quarterly data to do
empirical analysis of the demand for money function in Taiwan.
They first argue that Lu (1970) and Chen, J.N. (1974)'s work
does not adjust for serial correlation in the disturbances
which is apparent from low D-W value. They specify a Goldfeld
type of partial adjustment mechanism in the demand for real
balances to take advantage the availability of quarterly data.

The following' equation in their’ paper (equation. 4) has

14
corrected for serial correlation in the residuals by the
Hildrth-Lu method.
In NIB-0.326 + 0.284111 y +0.79? ln In,1 - 0.079 ln r
(2.89) (3.83) (13.85) (2.83)

18-0.9947: p=0.22: DW=2.03: Sample period:1961:3--1981:2
where msreal M1 at 1976 constant price

y-real GNP at 1976 constant price

r=interest rate on one-month time deposits.

long-run elasticity of income =1.40

long-run elasticity of interest rate =-0.39

They also tested stability by Chow test and recursive

estimation. The Chow test was performed by splitting the
entire sample at 1973:4 to see if Taiwan's money demand
function had shifted like that in the United States at this
time. The test statistic they obtain (F value) was 2.23 and is
insignificant. Recursive estimation began from 1961:3 to end
of each of the following years. Stable coefficients were
obtained from this estimation. The estimated long-run
elasticity of income was in the order of 1.26 to 1.40, and
interest rate elasticity ranged from -0.35 to -0.45. They
conclude money demand function in Taiwan is stable during that
period. For comparison with my study with seasonal dummies in
the equation, Iialso include the result of their equation with
seasonal dummies, although a variable representing expected
inflation was also included in the equation (equation 11 in
their paper).

ln m=-0.247+0.191 1n y+0.881 In 10.1 -0.078 1n r
(2.16) (2.48) (14.77) (2.98)

15

-0.811 ln (p/p4)+0.041 Q1+0.026 02+0.015 Q3
(6.89) (6.05) (2.85) (2.00)

18-0.9949, p=0.45, DW=1.94, sample period: 1961:3--1981:4
long-run elasticity of income =1.61

long-run elasticity of interest rate = -0.66

(D).wu, c.s., Yen, C.F. (1987)

This paper mainly concentrates on the role played by
expected inflation in a model specification of real or nominal
adjustment as suggested by Milbourne (1983) . The equation that
is related with my study is their equation (10):

ln Mt/Pt=-0.4310+0.2230 1n yt-0.0627 ln Rt+0.8662 ln MM/Pt
(-2.60) (2.78) (-2.45) (16.77)

+0.0192 01+0.0255 02+0.0450 03+0.0104 01-0.0048 02
(3.17) (3.38) (7.62) (0.55) (—0.28)

18:0.9966, DW=1.95, p=0.52, sample period: l961:3--1986:l
long run elasticity of income=1.67
long run elasticity of interest rate=-0.47
where M : M18
P: GNP deflator at 1981 constant price
R: interest rate on one month time deposit
y: real GNP at 1981 constant price
Qi: seasonal dummy variable: i=1,2,3.
Oi: oil price shock dummy variable:
Ol=1 , 73:3--74:3: =0 otherwise.
02=1, 79:2--81:1: =0 otherwise.
Stability was checked by recursive estimation. The results
showed short-run money demand function in Taiwan was quite
stable with the long run elasticity of income in the order of

1.76 to 1.92 and the interest rate elasticity ranged from

16
'-().69 to -0.79.
(E) .Chang, J.Y. (1989):

She was among the first to use the Engle-Granger two step
cointegrating test and single equation error correction.model
to estimate long-run and short-run money demand function in
Taiwan. In the first step to test cointegration, she found no
cointegrating relation existed among real M186, real income
and one-month time deposit rates over the sample 1964:1--
1987:4. A cointegrating relation did exist among real M2, real
income and the interest rate over the same period. Next she
specified a single equation error correction model by adding
'arbitrary' explanatory variables to capture the dynamics of
short-run money demand function (M2) . Her complete equation is

(her equation 5.35)7:

A1nm2t- 0 . 02 6+0 . 113A1nyt_2-0 . 079A1nrt_1-1 . 030PGt+0 . 544P(:‘:t,.l
+0.1555PG“,--0.079A1nCRt_,1--l-0.045AlnESt.2
-0. 062AlnTYM+0. 483A1nm2H-0. 07280:,1
‘ -0.00lDl-0.014D2-0.001D3.
where PG=GNP deflator

CR=(net currency issued)/(deposit money).8

 

6She also found.no»cointegrating relation among real MIA,
income, and the interest rate over the same period.

7It is unclear why a stable money demand function like
this has so many variables. Judd and Scadding (1982): "a
stable demand function for money should has relatively few
arguments; a relationship that requires knowledge about a
large number of variables in order to pin it down is, in
effect, not predictable".

8The definition of the deposit money will be clear in
Chapter 3.

17
Es=geometric average of growth rate of real GNP in every
six quarters.
TY-(volume of trade/GNP) .
EC=='error correction term'=lnm2t+4.245-1.699lnyt+0.309lnrt
(F).San, K.L. (1991):

She first used the Johansen maximum likelihood method to
test cointegration among real GDP, real M18 and six-month time
deposit interest rate over the sample 1965:1--1988:4. After
rejecting the null of no cointegration, she specified the

single equation error corrections model as (her equation 4.3)

A1nm1b=0.016+0.18 Alny;+0.22 Ayb4-0.52 A1nr;-0.18 Pt

+0.3 Alnmt_1+0.16 Alnmt_,.-0.08 ECM.

Strangely enough, the important error correction term ECP1
was not shown explicitly in her paper. The stability of this
equation as a description of money demand in Taiwan was
checked by the cumulative sums of squared recursive residuals,
and she concludes that there is no evidence of any structural

break over the entire sample period.

III. Problems with the lag dependent variable specification:

Although the estimation of long run money demand in Taiwan
seems to perform well when relying on the lag dependent
variable type of short-run money demand function, this method
suffers at least three problems from economics as well as

econometric theory for its bad performance both in United

18
States and Japan’.
(A).From Economic Theory:
(1). Real balance adjustment assumption:
A long-run money demand function is assumed to depend on

current income and interest rates:

(M-P):=po+p1yt+fizrt.

We assume the optimal real balance adjustment process to be

(M-P).-(M-P)..1= fl3[ m-m'.- (M-P) ...J .

where 83 represents the portion that the gap between desired
and actual real balance that is closed in a single discrete
time period. Therefore a short-run money demand function based
on the assumption that real money demand function depends on
current income but with real balance partial adjustment can be

written as

(2 . 1) (M-P) t=fi3fio+fisfi1yt+fi3fizrt+ (1-33) (M-P) H , 0<fl3<1 .

Because the price is not under the control of the public,
price is an exogenous variable. It is not obvious that.agents'
adjustment to price level changes should be instantaneous when
their adjustment to changes in other situations is slow.

An alternative assumption to derive the lag-dependent

 

9See for example, R.H. Rasche (1990).

19
variable type of short-run money demand function is that real
money demand depends on expected (permanent) income and

interest rates:

(M'P):=30+B1Y=+pzz‘i

We assumed people form their expectation of income and
interest rates from calculating weighted average of past level

measured income and interest rates:

yt=ly.+ (1-1) v.3, .

rt=lrt+ (1-1) rtf1 .

A short-run money demand function under these assumptions

therefore is

(2 . 2) (M-P) t430+“?1373182134» (1-1.) (M-P)t_1.

However, the estimated results from equation (2.1) is
undistinguished from those of equation (2.2). Also, Rational
Expectations must imply that the adaptive error-learning is a
very doubtful formulations of the relationship between
expected (or permanent) income and current income. Therefore,
the empirical demand for money functions utilizing lagged
dependent variables must be interpreted with care since they
do not necessarily reflect the working of adjustment

mechanisms. See Boorman (1982, p75), Laider (1985, p108).

20

(2). Nominal balance adjustment assumption:

(2-3) (H'P).=B3f(z)+(1'fi3) (HM-P.) ,

(2 . 4) < dPt/th=1/ps>1.

We must distinguish the individual experiment and the
market experiment. If we regard equation (2.3) as an
individual short-run.money demand function, in a economy with
an exogenously fixed money supply (Mt=MM=M') , the lag
dependent variable should not even appear in the aggregate
short-run money demand function equation (2.3.1), which is
added from all individuals short-run money demand function

equation (2.3).

(2 . 3 . 1) M*-Pt=fi3f (z) + (1-fl3) (if-Pt) ,

M'-Pt=f (Z) .

If we do not distinguish the difference of an individual
and aggregate money demand function, there will be an unreal
overshoot on the money stock change to the price change in
equation (2.4) under the assumption that people slowly adjust
their portfolio back to equilibrium. But this overshoot would
not happen in the aggregate short-run money demand function in
equation (2.3.1). (See Laider (1982, Chapter 2), Gordon(1984,
p412)).

The portfolio adjustment cost adjustment explanation is
logically invalid, and the expectations lag explanation does

not consistently stand up to empirical testing. The lag

21

dependent variable specifications may in fact be capturing the
true relationship in the way in which the money supply and the
arguments of the money demand function interact over time. The
importance of the presence of lagged dependent variables in
empirical work on the aggregate demand for money function can,
as Laider (1982, p54, equation 23) has shown, be explained in
term of price stickiness. When price level is sticky, such
variables as interest rate and real income will tend to change
as the money market attempts to clear itself when the Central
Bank targets the growth rate of nominal money stock to combat
inflation. 80 real income and interest rate should be regarded
as endogenous and money demand function is best estimated as
part of a complete macro system, rather than as a single
equation. But Cooley and Leroy (1981) raised the problem of
how to identify the coefficient of short run money demand
function in a complete macro system. Rasche (1990) also uses
a quite general macro model of the Japanese economy to show
that the structural parameters in Japan's short-run money
demand function can't be identified from the coefficients
estimated from the reduced form of a vector error corrections
model.
(8). From Econometric Theory

Econometrics issues are important even if the above model
misspecification problems do not occur. Lieberman (1980)
reestimated Chow's (1966) equation but used Cochrane-Orcutt
technique to adjust for serial correlation. His results
revealed that previous studies such as Chows' overstated the

magnitude of permanent income and he concluded that the

22
transactions model of money demand appears to be more
appropriate than the asset or utility demand.model. Therefore
we should carefully use the econometric technique before any
conclusions can be made.

The econometrian can no longer ignore the properties of the
variables with which he is concerned. The fact that much
macroeconomic data in levels or in logarithms are near random
walks or integrated processes means that considerable care has
to be taken in specifying one's equations.

For an independent stochastic linear regression model of

Goldberger (1964):

Y=Xfi+63 x=[x1' , . . . .x.']'; xt'=[xt1, . . .xtk] ,

where

E(e) -0;E(ee’) -0"I,

the stochastic process generating x is assumed to be
independent of the stochastic process generating 6.

The ordinary least square estimator b is consistent since
plim b=plim (B+(X'X)"X'e)
=p+p11n (X'X/T)’1plim (X's/T)

=5... 3;" * o=p

The asymptotic distribution of the least square estimator b is

23

fi(b-B) ".gyN(oI 022;) I

where Eu=plim (X'X/T) .

From this asymptotic normal distribution, the test
statistics such as t and F are derived. However, the
asymptotically' normal distribution. is *valid only' if ‘the
regressor X is sampled from a stationary multivariate
stochastic process with nonsingular contemporaneous moment
matrix En=Extxt'=plim (X'X/T) and expectation E,‘(X'X)’1 exists
(Fomby, 1984, p76). This is an assumption that sample means of
squares and cross-products gives a consistent estimator of the
matrix of expected squares and cross-products of the
population. When this condition is not met, all the
conclusions such as b is a consistent estimator of 8 and test
statistics would not apply directly.

For example, assume the AR(1) process

xt=pr+et , |p|<1, E(8t)=0, var(et)=az.

(2.5) var(x.>=o'/(1-p'). E<x.)=o.

is estimated by least square.

We know that Exx=plim (X'X/T)=plim T423931 = az/(l-pz) , that
is, the sample second moment is a consistent estimator of
population second moment as long as the second moment exists.

So, we would conclude that

fi(fi'P)~N(0.1-Pz)

24

But when p=1, the process become a random walk and 2:“ above
will not exist since it make no sense to set p=1 in equation
(2.5). Since the underlying process is non-stationary, there
is no second moment in the process as we can see the variance
of a random walk is to2 which explodes as time passes and is
not a constant. The asymptotic theory set out above does not
apply so neither do the test statistics that are derived.
Indeed, there is a limiting distribution, but it is for T(3-1)
rather than for T"2(3-p) , the conventional inference. The more
important point about the limiting distribution is that it is
not a normal distribution and the usual test statistics
dependent upon the asymptotic normality of the estimator do
not apply.

The lag dependent variable models that most of short—run
money demand functions employ do not fit entirely the example
of this classical stochastic regression”. The point is that
when we face nonstationarity in the regressor, special
attention should be paid to interpreting the result from
regression. Granger and Newbold (1974) used simulation to warn
how dangerous it is when a regression of two independent
random walks results in spurious relations which are not
easily detected by conventional t test statistics. Phillips
(1986) went further to use asymptotic theory showing that

regression of nonstationary variables has, three results. First

 

1"Mann and Wald (1943) show that the asymptotic properties
of estimator of a model with lag dependent variable should
rely on the stationarity in the regressor.

25
it is an entirely spurious relation11 as Granger and Newbold
(1974) . When dealing with two rather general independent
integrated process of order one whose first difference are
weakly dependent and possibly heterogeneously distributed
innovations, he shows that the conventional t-ratio that are
used to assess the significance of the coefficients in
regression analysis do not have a limiting distribution. 80
there are no asymptotically correct critical values for the
conventional significance tests. He also shows that DW-vo,
whereas R2 has non-degenerate limiting distribution as T-m.
Second, let a scalar y and m-vector x which are all quite
general integrated processes of order one be estimated by
least squares. It is not necessary to require that y and X be

independent. The main requirement is that the vector time

 

"Phillips (1986):
T‘“2 tron/v1”, where
u-fw t) m t) dt-fw t) dtfm t) dt
,v-{fw t) 2dt- (fv( t) dt) “HIM t) 2dt— (fun 1:) dt) 2}

-{fV( t) W( t) dt-fw t) dtfwt t) dtlz;
and
R2- HIM t) 2dt- (fan 1:) dt) 2};
fV(t)2dt- (IN 1:) dt)2

 

finally,
DIV-'0 .

where W(t) and V(t) are independent Wiener processes on C[0, l]
and integration are from 0 to 1.

 

26

series (y,X') is not cointegrated in the sense of Granger and
Engle (1987). Phillips shows that even under these condition
that y and X are dependent, the distribution of both F and t
diverge as M. So there are no asymptotically corrected
critical values for these statistics. As in the first case,
DW»0 and R2 has a non-degenerate limiting distribution as M.
Third, let X and y as defined above be cointegrated. Phillips
and Durlauf (1987), Stock (1987) had investigated these case.
Stock. shows 'the least squares. estimator' of’ cointegrated
variables has asymptotic properties different from those of
least squares estimator in the stationary time series model:
convergence to their probability limits occurs faster than
usual, and their limiting distribution is nonnormal.

For any equation from a traditional lag-dependent variable
short-run money demand function, (for example, equation (4)

from Goldfeld (1973)):

In m=0.271+0.193 ln y+0.717 lnm4-0.019ln RCP -0.045 ln RTD

if the variables are nonstationary as many studies of most
economic data in the United States suggest“, then there are
three conclusions that all invalidate the Goldfeld's results.
(i). The relation is entirely spurious. There exists no
relation between real balance, real income and interest rates.
Although Hildreth-Lu search procedure which.minimized.the sum

of square errors for the cochrane-Orcutt transformation is

 

12For example, Nelson and Plosser (1982).

27

applied to find the possibly autocorrelated disturbance”,
when the p is found and used in the transformed equation, the
variable still is random walk as they were before“. The high
R2 of the transformed regression might well come from
independent random walks and the relation may still be
spurious.

(ii).The three variables are correlated time series but not
cointegrated. However, the t test and R2 all are not
comparable with that of conventional inference with stationary
process.

(iii) .They are cointegrated. However, as shown by Stock
(1987), the limiting distribution of a standardized least
square estimators of the cointegrating vector be nonnormal, so
the t value is not applicable.

Given the three possibilities above, there are serious
doubts about the credibility of the results from conventional
lag dependent variable short run money demand function from an
econometrics standpoint. With a model of lag-dependent
variable specification, we must first check the individual
data properties, if nonstationarity is found, we should check
if they are cointegrated or not (among m, y and r). If there

exists one or more vectors describing the long run equilibrium

 

"Other method such as two step method of Cochrane-Orcutt,
Theil (1971), and Durbin (1960) are improper for the
contemporaneous correlation between lag dependent variable and
autocorrelated disturbance.

1‘A random walk yt= , +ut: a constant p<1, such that pyma
pyt_2+put_1. Cochrane-Orautt transformation is: Yt‘th-1=Yt-1'PY:-
fut-put,“ that is xt=xt_1+et, another random walk: where xt=yt-
PYM. et=ut-put_1 and is stationary.

28
conditions to which the variable tend to return, then a model
of short-run lag-dependent variable15 (or other possible
dynamic specification) model will be meaningful, otherwise, it
is not. To the extent that the level of economic time series
are non-stationary and non-ergodic, regressions of short-run
money demand function that relate such variables as real
money, real income and interest rate will require the use of
asymptotic methods and results that are quite different from
those that are well established in current econometrics theory

and practice.

IV. Problem with single equation error correction model (ECM):

Methodologically, it is fair to say that ECM is superior to
conventional partial adjustment model for its more flexible
dynamic structure and considerations of long-run equilibrium
relations in its model. However, Yoshida and Rasche (1990)
have explained that ECM is less than satisfactory. It could
possible that results of the estimation of money demand
function suffers from simultaneous equation bias. Unbiased
estimation in a single equation framework is possible as long
as weak exogeneity conditions holds. Therefore, we should
first check this condition before specifying a single equation
ECM. Thus. we will analyze the data in a full system of
equations, allowing for possible interactions in the
determination of money, income, and interest rate in this

study.

 

1"‘If m , and r are cointegrated, so will be mt, y” and
rbk, for any k. See Granger (1991).

CHAPTER 3

THE PRESENT STRUCTURE OP THE PINANCIAL SYSTEM IN TAINAN

Taiwan's financial system consists of financial
institutions and markets, with the former being much more
well-developed than the latter. The Ministry of Finance and
the Central Bank are at the apex of the financial system
regulating and supervising the financial system in Taiwan. The
Ministry of Finance is responsible for the formulation of
financial regulatory policies and for the licensing of
financial institutions, while the Central Bank is responsible
for the conduct of monetary and financial regulatory policies.
Although the credit cooperatives are supervised by the
Provincial Cooperative Bank, the Central Bank oversees most

financial institutions.

I. Financial institutions in Taiwan

Current financial statistics issued by the Central Bank
divide financial institutions in Taiwan into two categories --
Monetary Institutions and Other Financial Institutions, on the
basis of whether they can create money or not. The data in
Table (3.1) below provides a more precise indication of the
relative importance, as measured by total assets of all
different types of financial institutions. Although property
and casualty insurance companies, bills finance companies and

securities finance companies also provide financial services,

29

30
generally speaking, they differ greatly from financial
institutions in terms of the financial debt that they
provide‘. For this reason, the Economic Research Department
of Central Bank does not include them with the Other
Financial Institutions when compiling financial statistics,
but instead treats them as if they belong to the private
sectorz. Their assets are thus shown separately for reference
purposes’. I will thus call them "Near-Financial"
Institutions. (See Table (3.2)).
(A) .Monetary Institutions: The monetary Institutions hold
about 84 percent of the assets of all financial institutions,
with about two-thirds of total assets belonging to the Central
Bank (18 percent) and domestic banks (43 percent).
(1).Central Bank of China (Taiwan):

The Central Bank of China (hereafter, C8C) is Taiwan's
central bank. It was established under W
W of 1935 in China and reestablished in Taiwan in July
1961. From the liberation of Taiwan from Japan in 1945 to the
rehabilitation of the Central Bank of China in Taiwan in 1961,
the Bank of Taiwan (which now is a major government bank)
acted as Central Bank.

(2).Domestic Banks:

There are 33 domestic full service banks in Taiwan, of

 

'See 2inangia1_statietiee_nentnix._cec. May 1993. p188.

2see Einangial_Statistigs_ngnthlxi_sfisi may 1993. 9188.

3'I'able 1 in Emery, R.F. (1988) incorrectly includes the
"near" financial institutions in his computation of the assets
of financial institutions.

31

which, 21 are managed as private enterprises, i.e, they have
independent boards of directors, and thus their managers have
much more liberty in management, without the rigid restriction
of government banks. As is noted, the private share in the
government bank (as is defined: more than 50 percent of bank's
share are government owned) is increasing.

(3).Local Branches of Foreign Banks:

The United States has the largest commercial bank presence,
with eleven banks and sixteen branches at the end of April
1993. A foreign commercial bank can engage in most of the
business activities that are permitted for their domestic bank
counterparts.

(4).Medium Business Banks:

There are 8 medium business bank in major metropolitan
areas in Taiwan. They are privately owned by shareholders.
They can only conduct banking business within their respective
regions, with the main purpose of financing medium and small
business.

(5).Credit Cooperative Association:

These are regional institutions and are authorized to deal
with their members only. They engage in all or some of the
following activities: acceptance of deposits, extending loans
and discounts, accepts of bills, collection and disbursement
of funds.

(6).Credit Department of Farmers' and Fishermens'
Associations:
They are authorized to accept deposits, to extend loans to

members, to handle remittance, and to serve as agents for

32
government agencies in the provision of agriculture and
fishery credit.
(B).Other Financial Institutions:
(1).Investment and Trust Companies: Their main functions are
to provide housing loans, to invest in properties and to
accept trust funds, which are in effect a disguised way of
taking fixed deposits because investment and trust companies
are not allowed to accept deposits from the public.
(2).Postal Savings System: It is organized mainly for
collecting savings deposits from the general public and
redepositing the funds in the Central Bank, or government
banks‘, or investing the funds in government securities rather
than lending to the public. It is because of this non-money-
creating function that it is not considered a monetary
institutions. The postal savings system is relatively
important: its share of the assets out of all financial
institutions rose from less than 1 percent in 1961 to about 10
percent in April 1993. Two major factors have contributed to
rapid rate of growth in the postal saving system's assets
since the mid-708. One is the fact that with 1230 post office
and 349 postal agencies as end of April 1993, it is convenient
for most residents to deposit in the system. The other factor
is that the interest received by the depositors on their
deposits is marginally higher than that offered by the bank

(Semkow, 1992, p43). For example, the after-tax yields are

 

‘Postal savings system redeposits at Bank of
Communications, Land Bank of Taiwan, The Farmer Bank of China,
and Medium Business of Taiwan other than CBC. See p52 of

Wm- May 1993-

33

much more attractive as interest on deposits not exceeding NT$
700,0005 is tax-exempt, whereas interest from banks is tax-
free for deposits under NT$ 360,000.

(3) .Life Insurance Companies: These companies are comprised of
eight local companies and twelve U.S. companies with four
local companies dominating the market with over 85 percent
market share, and the 0.8. companies having a 2 percent market

share of assets (Semkow, 1992, p47).

 

5Hereafter, the sign NT$ means New Taiwan Dollars with a
exchange rate to US$ about 1 US$=27 NT$.

Assets and Units of Financial Institutions in Taiwan

34

lel. (3.1)

(NT$ billions)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

F
Institutes No. of No. of Assets As a percent of
units. branches total assets of
Financial ‘
Institutions
Monetary 465 2494 13689 84.02
Institutions
(1):

#Central bank 1 0 2990 18.35 I
Domestic 33 915 6983 42.86
bank
Local Branch 37 26 336 2.06
of Foreign
Banks J
Medium 8 332 1061 6.51
Business
Bank
Credit 74 447 1322 8.11
Cooperative
Associations

; Farmer's & 312 774 997 6.11
Fishermen's
Credit
Associations
(1)+(2) 493 4214 16291 100.00
Other 28 1720 2602 15.97
Financial
Institutions
(2):

Investment 7 60 403 2.47
and Trust

Company.

Postal 1 1579 1589 9.75
Saving

System

Life 20 81 610 3.74
Insurance

Company 7

0 e: No. 0 oranc es are or e eno 0 Apr , 1"

Source: Financial Statistics Monthly, Taiwan District, ROC.
1993.

MaYI

35

(C)."lear-Financial Institutions":

(1).Property and Casualty Insurance Company.

(2).Central Deposit Insurance Corporation.

(3).Bills Finance Companies: Taiwan's three bill finance

companies are the primary intermediaries of the country's

money market. The principal functions of these companies are

to facilitate the supply and demand of short-term funds in the

bill market.

(4).Fuh-Hwa Securities Finance Company: It was established in

1980 to finance margin trading and advancing securities in the

stock market, with a view to facilitating the order of the

market.

(5).Offshore banking units

 

 

 

 

 

 
  

 

 

 

 

 

 

 

 

 

 

Table (3.2)
Assets and Units of "Near-Financial" Institutions in Taiwan
Institutes No.of No.of Assets As a
units branches percent to
total
assets of
financial
institution
Property & Casualty 22 81 46 0.2
Insurance Companies
Central Deposit 1 0 4.8 0.0
Insurance Corporation
Bills Finance 3 21 32 0.2
Companies
Fuh-Hwa Securities 1 2 81 0.5
Finance Company
Offshore Banking units 39 0 698 4.2
Asse un : n ons 63-NTS. 18 end of-Apr 993.

No. of branches is for the end of April

1993.

Source: Financial Statistics Monthly, Taiwan District, ROC.

36
II. Financial market in Taiwan: Taiwan's financial market
consists of money, capital, and a stock market although the
latter is not discussed in this study.
(A). Money market:
( 1) .Definition‘: This includes the interbank call-loan market
and the short-term accommodation market, as well as securities
with a maturity of less than one year that are transacted on
the open market i.e. on the primary market and secondary
market. Instruments transacted include commercial paper,
negotiable certificates of deposits, banker's acceptances,
commercial acceptances, Treasury bills and government bonds,
bank debentures, and corporate bonds, etc, all with a maturity
of less than one year.
(2).Background: There was no open short-term money market in
Taiwan until the mid-19708. Because of large cumulative budget
surpluses, the government had no need to issue short-term
securities for Treasury financing. As an experiment to start
a money market, The Central Bank of China started issuing
Treasury bills in October 1973. Bankers' acceptance and
negotiable certificates of deposits were introduced in the
money market in 1975. The W and the
promulgation of the 'Regulations Governing the Dealers of
Short-Term Negotiable Instruments' in December 1975 ushered in
the money and discount market, with the establishment of three
bill finance companies that are mentioned above. Commercial

paper and negotiable certificates of deposit are two of the

 

6This definition is from CBC.

37

main money market instruments of bill finance companies. The
open-money market has grown substantially since its
establishment in 1976. The volume of money market instruments
outstanding increased from NT$ 8 billion in 1976 to NT$ 9397
billion in end of 1992. The inter-bank, called the loan sub-
market, also experienced rapid growth from its beginning in
April of 1980. The trading volume in a year on the inter-bank
call loan market increased from NT$ 390 billion in 1980 to NT$
12662 billion in the end of 19923. The development of the
money market had increased the options for business finance
and had also provided a market-determined money market
interest rate. This has been helpful to the central bank in
conducting its interest rate policy, since for many years the
authorities have controlled banks deposits and loan rates (see
Section III).

(3) .Curb (informal) money market: There was no open short-term
money market in Taiwan until 1976, but it does not mean that
there was no money market over the same period. On the
contrary, the aggregate size of the curb market, that has
existed for decades, in term of financial assets was
'probably' as large as all the financial institutions put

together”. In theory, as the money and capital market becomes

 

7898 p122 in W: Hay.
1993.

8See P125 in W: Hay.
1993.

9In 1986 domestic funds borrowed by business enterprises
(including public and private ones), come from the curb money
market to the extent of about 30%, from bank and financial
institutions 47%, open-money market 7 %, and from the capital

38
more developed, the curb money market should lose its
significance. However, the share of the curb money market is
no lower than in 1964”. Lying outside regulated channels,
activities in the curb market take a wide assortment of forms
and employ a large variety of instruments. They include
suppliers' credit, leasing or installment credit companies,
postdated check, private lottery club, loanshare, and
businesses that surreptitiously accept deposits from staff and
outsiders.11 In the early days, curb money market undoubtedly
made a great contribution to financing Taiwan's particular
economy type--mostly small and.medium sized business. Because
the interest rate paid is much higher (generally by two or
three times) than the financial institutions, most people are
willing to run the risk of being defrauded and invest their
saved money little by little in a mutual aid associations.
Small and medium businesses whose credit standing can not
match that of large companies and which therefore find it
difficult to borrow from financial institutions, can use this
channel to obtain funds to enable the business to operate and
grow. For this important financing channel existing in Taiwan
for a long time, The Central Bank of China even has formal

survey data recording the interest rates of this market as

 

market 14%. See Table 3.4 of Lee, S.Y. (1990).

‘wIn 1986, The flow of savings funds into time and saving
deposits with financial institutions was 66.2%, money market
4.79%, capital market 8.91%, and curb money market 19.69%. See
Table 3.5 of Lee, S.Y. (1990).

"For a detailed study of these market, see Liu and Wu,
et. al (1984).

39
early as 1961 (see Chapter 4).
(8). Capital Market
( 1) . Definition: This refers to securities with a maturity in
excess of one year or no established time limit (such as
shares) that are transacted on the open market. Instrument
transacted include government bonds, corporate bonds,
financial securities, saving bonds/securities of the Central
Bank of China, negotiable certificates of deposits of the
Central Bank of China and shares, etc.
( 2) . Background: Taiwan's capital market consists of stock and
bond markets. The stock exchange was established in February,
1962. The number of listed companies increased from 18 in 1962
to 264 at the end of April 1993. Total market value increased
from NT$ 7 billion in 1962 to NT$ 3636 billion”, equivalent
to 22.31 percent of the total asset value of financial
institutions, over the same period. On the other side of the
capital market, since firms prefer bank financing, and
corporate bond issue typically require a bank guarantee, the
corporate bond market is very small. As mentioned above, since
the government ran a persistent budget surplus from 1964 to
1981 and hence felt no need to borrow and incur interest cost,
the government bond market is small also. However, volume has
been increasing significantly in both corporate and government
bond market. In 1961, the corporate and government bonds
outstanding accounted for NT$ 0.1 billion and NT$ 0.8 billion

respectively : by the end of April 1993, they had grown to NT$

 

12s.. p118 in W. May 1993-

40
60 billion and NT$ 647 billion respectively”. One thing to
notice is that the outstanding government bonds are NT$ 188
billion at the end of 1990. In a short.period of about 2 years
(1991--1992), this amount has increased 3.4 times, which is
mostly attributed to central government issues reflecting the

deteriorated budget deficit in recent years.

III. Some Important Economic Indicators:
The following figures (1)--(4) give a concise summary of
Taiwan's economic developments (quarterly) in the past three

decades.

 

13see 9129 in W May 1993.

 

41

CONSUMER PRICE INFLATION RATE

IN TIIIII(1962--l”1)

 

‘0
35 L
30 —
25 h
20 b

15 _

INFLATION III!

10)—

 

 

 

 

 

Figure 1

ANNUAL GROWTH RATE OF MlB IN TAIWAN

C 1963--1992 )

 

‘0

33 —

30 ~

35 F

20 ’

RATE

 

 

 

-1o 111+LL 11 L411: 1 l 1 1

 

TIME PERIOD

Figure 2

42

GROWTH RATE OF GNP AT CURRENT PRICE

35

30

as
g 20
1

5 15

10

Figure 3

ll
16
14
12

10

Figure 4

11‘ WUJSR- '1992)

 

 

 

 

 

62 66 70 74 7S .2 .6 ’0 ’4

ANNUAL GROWTH RATE OF REAL GNP

AT 1986 PRICE IN ram (1962--1’92)

 

 

 

 

 

 

 

 

43

Despite monetary (M18) growth being higher than income
growth in almost all periods as shown in Figures (2) , ( 3) , and
(1), price inflation is stable except in 1974 and 1981“, due
to the lag-effect of the two oil crises. The most important
objective of monetary policy of Taiwan was to achieve price
stability (Lee, S.Y., p117) . Therefore, the monetary authority
in Taiwan was quite successful in achieving the goal of
restraining inflation through massive sterilization operations
(Emery, p397). Taiwan also has experienced a extraordinarily
high level of the real output growth rate for most of the
periods as shown in Figures (4) with real GNP growing from NT$
31,003 millions in 1961 to NT$ 4,525,237 millions in the 1992.

That is about 146 times in thirty years”.

IV. Major liberalization and reforms of the financial system
since 1980:

(A). Interest rate liberalization

(1) . On 7 November 1980, the Central Bank announced "the Major
points of Consideration of Interest Rate of Banks", which
stated that (i) Banks could propose to the Central Bank a
range of deposit rates, although the maximum deposit rate was
still determined by the Central Bank. (ii) Banks could propose
to the Central bank a range of lending rates for the latter's

approval: the ranges was to be widened to allow flexibility in

 

1‘Therefore, the velocity of M18 has historically trended
downward. See figure (7) in Chapter 4.

1""Population increases about two times over the same
period.

44
operation. (iii) Interest rates in money market and Negotiable
Certificate of Deposits are not subject to the limitation of
the maximum deposit rate.(Lee, S.Y., p158).
(2) . On 1 March 1985, banks were allowed to announce their
basic lending rates.
(3). On 20 January 1986, deposit categories on which the CBC
determined interest rate ceilings were reduced from thirteen
to four, giving banks greater latitude in competing for
deposits by paying higher rates for deposit-type categories
(Semkow, p96).
(4). The New Bank Act on July 19, 1989 was passed, which
liberalized further the financial system. Both local and
foreign banks are allowed to set their own.deposit and lending
rates freely according to their funding cost.
(8). Other financial deregulation:

Including bank entry deregulation, financial products
deregulation, foreign exchange deregulation, . .etc. can be
found in detail in Lee, Y.S. (Chapter 8), Semkow (Chapter 6,
7), Lee, J.C. and Lin, J.Y. (1990), and Cheng, H-S. (Chapter
11) .

CHAPTER 4

THE EQUILIBRIUM TRANSACTIONS MONEY DEMAND IN TAINAN

The assumption of the existence of a stable long-run.money
demand function has been an integral part of all macroeconomic
theory. The estimation of this function, using data with a
high degree of time aggregation (such as annual data) has its
costs. The number of observations in any time series is
obviously reduced and other variations average out. A "short-
run" lag-dependent money demand function with many more
observations for precise estimation is introduced to recover
the elasticity of income and interest rate in the long run
demand function, although serious doubts about the importance
of this short-run money demand function are raised by Garden
(1984b).

The lag-dependent variable specification suffers from so
many problems such as model misspecification, simultaneous
equation bias as stated in Chapter 2. An estimation that use
data of a low degree of aggregation (quarterly or even monthly
data) but avoid the above stated problems is introduced to
derive the income and interest rate elasticity in the long run
demand function and even short run dynamic adjustment. A
'naive' multivariate time series model explains the behavior
of a set of variables in term of their own past. Unlike a
dynamic simultaneous equation model in which a priori

restrictions have been imposed the on parameters on the bases

45

46
of economic theory, a multivariate time series model does not
specify a tight form of the dynamics. In a multivariate time
series model all the variables are potentially endogenous. A
vector autoregressive model (VAR) is employed in this study
that regards real money (m), real income (y), and interest
rates (r) as jointly determined and are treated as all

endogenous variables.

I. Unit root in aggregate economic variables:

We have seen from Chapter 2 that nonstationarity in the
regressors will invalidate the traditional statistical
inference which depends upon the asymptotic normality from the
stationarity in the regressors. It is important to check the
character of the stochastic processes of each individual
variable in the money demand function before specifying any
econometric model to estimate the relation among these
variables. There are two fundamentally different class of non-
stationary processes as alternative hypotheses. The first
class of processes consists of those that can be expressed as
a deterministic function of time, called a trend, plus a
stationary stochastic process with a mean zero. We refer to
this as a trend stationary (TS) process. The second class of
non-stationary process considered is that class for which the
first difference or higher order difference is a stationary
and invertible ARMA process (DS process). How to correctly
represent the true process of the variable in a econometric
(or specify, money demand) model is critical both from

economics and econometrics points of view. In economics, 8 TS

47
process means uncertainty is bounded and neither current nor
past events will alter long-term expectations. A DS process,
on the contrast, will always be influenced by historical
events and variances of forecast error will increase without
bound. Any shock to the process will persist permanently. In
econometrics, when modelling TS variables, a linear time trend
is added in addition as an independent variable (for example,
Roley 1985, p629). Inclusion of a time trend in a regression
between variables of interest is of course equivalent to
detrending of the variables prior to regression (Lovell,
1963)‘. On the other hand, as suggested by Granger and Newbold
(1974), taking the first difference of the variables in a
regression model is appropriate when the variables are DS
processes (for example, Hafer and Hein, 1980: Fackler and
Mcmillin, 1983)2. An incorrect representation of the process
will result in "spurious periodicity" in a regression of a
random walk on time trends (Nelson and Kang, 1981).
Overdifferencing of TS processes produces unit roots in

moving-average polynomials and make them noninvertible’.

 

1However it is not true anymore that Q=lim (X'X/T) is
finite. The regressor matrix is said to be asymptotically
uncooperative. Extensive discussions of uncooperative
regressors can be found in Dhrymes (1971, pp84-88), and
Schmidt (1976, pp86-88). One of the results of these
investigations is that the presence of a time trend regressor
doesn't nullify the consistency of the least square estimator.

2Differencing is subject to the criticism of generally
application of difference form. yt=bo+b1x +e : x, y are in first
difference form. In the equation above, if bo=0 and e is white
noise, then there in no long-run relationship between the
levels of Y and X. (See Gordon, 1984b, p421).

3See, Diebold and Nerlove (1990)

48

Therefore, which process (TS or DS) provides good stochastic
approximations to the variables (real national income, real
money stock, and interest rate) that appear in Taiwan money
demand function is important before we specify this function.
There are three commonly used tests to detect the possible
presence of unit root in economic variables.
(A).Dickey-Fuller Test:

Dickey (1976) and Fuller (1976) used the Monte Carlo method
to calculate the percentage points of the finite sample as
well as the asymptotic distribution of the LS estimator of the
autoregressive parameter as well as its ”t-statistic," when
the true autoregressive parameter is unity.

Consider the null model

Ho: xt=x

2 _

and the alternative‘

(4.1) H1: xt=a+pxt,1+et, et~N(0,oz), p-fil, xo=0.

The least square estimator an is obtained from.a sample of
size T. Under the null hypothesis (Bu-1)=OP(T"), the
convergence is faster than for |p|<1, in which case (3“-
p)=Op(T"’2) . It follows that the appropriate quantity for which

percentage should be calculated under the null is 90:9(3u-1) .

 

‘The alternative hypothesis originates from a model
without a constant in Dickey-Fuller Test.

49

They also make use of the usual "Student's t" for testing p=1,

e - 9‘1

" [39:11-11

t-2
‘where s2 is the usual unbiased variance estimator. Under the

1/2

 

null, ’r‘u =0p(1) , but it does not have the t distribution. The
corresponding statistics 7“ and fh have been tabulated under
the null of (a,p)=(0,l) by Dickey (1976) and Fuller (1976).

Similarly, the alternative might include a trend
(4 . 2) xt=a+fit+pxm+et
Under the null hypothesis that fi=0, p=1

xt=cz+xH+et .
This random ‘walk. with drift is a null hypothesis. that
frequently arises in economic applications: stationary
deviations from linear trend are a natural alternative. Dickey
(1976) and Fuller (1976) tabulate the distribution of
normalized-Bias and studentized statistics, 9, and 7,
respectively under H5: (a,8,p)=(0,0,1). Furthermore, Dickey
and Fuller (1979) show that the null distributions of the two
test statistics are unaffected by the value of a. They also
show that the limiting distributions also hold for et that are

independent and identically distributed nonnormal random

variables (white noise). However, a practical issue is that in

50
most series et is not white noise. There are two popular
corrections which might be called a parametric and a non-
parametric solution.
(B). Augmented Dickey-Fuller test:
The parametric solution suggested by Dickey and Fuller
(1979) is to augment the regression equation (4.1) by adding

sufficient terms in ax to whiten the residual.

t-i

Consider the AR(p) process with non-zero mean

(xc-u) +1138 1 (xt,j-u) -et, et~N(0, 02) , xo-O.

We can immediately put this in the form

xt-k+plxt-l+j§pj (xt-j+1"xc-j) +et’

where k=1==u(1+£i':1 aj) , p22 ,
and

p1--j§aj. pi-jéajl 1'2I - - - - ID

If there is a unit root, then p1=1. Dickey (1976) and

Fuller (1976) consider the distribution of 31 under the null
of p 1=1 and show that for any particular process there exists
a scalar c such that Tc($1-1) has the same asymptotic
distributions as §u=T((A> "-1) , the statistic discussed earlier
for the first order case. In addition, the studentized
statistic for the null hypothesis of p1=1 has the same

asymptotic distribution as ’7‘“. The same augmented Dickey-

51
Fuller test extends naturally to the model with a time trend.
It is an immediate generalization of earlier result to show
that the studentized statistics on 31 has (asymptotically) the
7, distribution.
(C).Phillips-Perron Test:

A general approach, which exploits developments in
functional central-limit theory to obtain nonparametric
corrections for infinite dimensional nuisance parameters, has
been taken by Phillips (1987) , and Phillips and Perron (1988) .
They develop modifications of the statistics In and T(3u-1)
that have the same asymptotic distributions tabulated by
Dickey-Fuller, when the data follow an ARIMA(p,0,q) processs.
The basic idea is to estimate a non-augmented Dickey-Fuller

regression equation (4.1):
xt=0z+pxm+et ,

and then use residual from the regression to correct the
Dickey-Fuller normalized-bias Ir“ and studentized statistics ’7‘“
for general forms of serial correlation and/or
heteroskedasticity that might be presented in et. The modified

normalized-bias statistics is

t 1 - — -
fp-T(fi,.-1)--2- (sh-s3) [T 2§2(x._1-x.1)21 1.

 

5Actually, Phillips (1987) allows for more general
dependence, including conditional heteroskedasticity.

52
where

2 -1 2 2 2 —1
s-(T fie) s -s+2T fw fee_
9 t-2 t I T): e 1-1 Jkt-j+1 c c j!

and the weights wjk={1-j/ (1+k) } ensure that the estimate of the
variance 3“ is positive‘. The modified studentized

statistics is constructed in a similar fashion, and is given
by

-1/2
€;-?p(s,/su) ——%— (sfik-sfi) sfikT'zcé (Jed-27.1) 2

The Phillips and Perron procedure has been extended to
allow trends under the alternative hypothesis that the process
is a stationary ARIMA(p,0,q) around a deterministic time
trend. The first step in performing these tests is to estimate

an AR(l) model
xt=a+fit+pxt_1+et ,
and then use the residual autocovariances to adjust the

Dickey-Fuller statistics. The modified normalized bias from

the nonaugmented Dickey-Fuller regression is

fJ-T(6,-1) + (sfik—si) (T‘/24Dxx) .

 

“This method is suggested by Newey and West (1985) .

53
and has the same asymptotic distribution that Dickey and
Fuller tabulate for T(p,-1) in the AR(l) case, where Du is the
determinate of the regressor cross-product.matrix. Similarly,

the studentized statistic is modified to be

1:4.(89/sm) - (Si-33) T3 mama”) 1/2] -1.

The statistics should have asymptotic distribution tabulated
by Dickey and Fuller fom'77, even if the regression errors in
equation (4.2) are autocorrelated or/and heteroskedasticity.

Schwert (1987,1989) argued many economic time series are
not pure AR processes. Simulation evidence indicates that the
convergence of the augmented Dickey-Fuller statistics to their
asymptotic distributions may be quite slow in the presence of
moving-average errors, and similarly for the Phillips-Perron
statistics. Therefore, the critical value implied by the
Dickey-Fuller simulations can be misleading. He presents
critical values for various regression 7 and T(p-1) test for
a unit root in the autoregressive polynomial of the ARIMA
model, where the simulated data follows a different moving

average parameter 0 in ARIMA(0,1,1) model.

II. Cointegration.

It is widely observed that many time series of economic
interest follow a nondeterministic trend in levels or in
logarithms, but that these variables appear to be stationary

after first differencing. At the same time, however, these

54
variables often trend together: certain linear combinations of
contemporaneous observations seem to be stationary in the
sense that they do not require further differencing to exhibit
limited dependence. The following from Engle and Granger
(1987) are formal definition of the variables that possess

these properties stated above.

W: A series with no deterministic component which has
a stationary, invertible, ARMA representation7 after
differencing d times, is said to be integrated of order d,
denoted xt~I (d) .

W: The components of the vector xt are said to be
cointegrated of order d, b, denoted Xt~CI(d,b), if (i) All
components of Xt are I(d): (ii) There exists a vector 8(410)
such that zt=B'Xt~I(d-b), b>0. The vector 8 is called the

cointegrating vector.

When it is the case d=b=1, cointegration would mean that if
the components of Xt were all 1(1), then zt=(fi'xt)~I(0) is the
equilibrium error which will not drift far from zero. If Xt
has p components, then there may be more than one
cointegrating vector 8. It is clearly possible for several

equilibrium relations to govern the joint behavior of these

 

7A trend stationary series is not an integrated series
although difference of 2it is also stationary. For example:
z=a+fit+c : c ~i. i. d(0, 02). First difference of zt, zt =(1-
:z)z=p+c-1, which is noninvertible because of the unit root
nthe moving-average polynomials.

55
variables.” When there are r(Sp-1) linearly independently
cointegrating vectors, we can gather these r cointegrating
vectors into the pxr array 8. By construction, the rank of B
will be r which will be called the ”cointegrating rank" of Xt.
A cointegrating vector puts a special constraints on their
representation. The following Granger Representation Theorem

states these constraints:

WW” If the 9x1 vector X. is

cointegrated with d=1, b=1 and with co-integrating rank r,
then:
(i).If a finite vector autoregressive representation is
possible, then it will have the form
A(L)Xt=et, where E(8t8; =A , t=s:
=0 , otherwise.
with the properties that A(1) has rank r
(ii).There exist pxr matrices, a, B, of rank r such that
A(1)=aB'.
(iii).There exist an error correction representation with
Zt=fi'xt, a rxi vector of stationary random variables,
such that

A*(L) (l-L)Xt=-afi'zt_1+et.

The autoregressive and error correction representation

 

8For example, three and six variables in King, Plosser,
Stock, and Watson (1991).

9The Granger Representation Theorem extends to vector
ARMA representation.

ti
in

ar

SY
Gr
th.
Ph.
Pa:
"at
(ls
tes

at

Pro.
sine
dYna
that

56

given above differ in an important fashion from typical VAR
applications. The cointegration of the variables x, generates
a restriction which makes A(1) in (i) singular. Cointegration
is implied by the presence of the levels of the variables in
equation (iii), so a pure VAR in difference will be
misspecified if the variable are cointegrated. Thus vector
autoregressions estimated with cointegrated data will be
misspecified if the data are differenced by omitting the
equilibrium error term, and will have omitted important
constraints (Rank A(1)=r) which make estimation inefficient if
the data are used in levels. So before we specify a model
involving integrated variables, we should first check if they
are cointegrated or not.

Several tests and estimation procedures for cointegration
systems have been proposed in the past years. Engle and
Granger (1987) suggested a two-step regression procedure and
these estimators have been investigated by Stock (1987) ,
Phillips (1987), Phillips and Durlauf (1987), Phillips and
Park (1988,1989), Phillips and Quliaris (1990), Stock and
Watson (1987). Johansen (1988,1991), Johansen and Juselius
(1990) propose the maximum likelihood method to estimate and
test the cointegration system. Stock and Watson (1993) present
estimation of cointegrating vectors by dynamic GLS or OLS.

Engle and Granger (1987) first proposed the two-step
procedure to estimate a cointegration relation by static least
square regression without worrying about the complicated
dynamic structure. Engle and Granger's two step method assumes

that cointegrating rank is known (r=1) and estimates the long-

57
run parameters by regressing some of the variables on the
others. This gives a consistent estimator of B as shown by
Stock (1987) , but the asymptotic distribution theory is
complicated, which makes inferences on structural hypothesis
difficult. The estimates converge to the true cointegration
coefficient at the rate of T rather than the usual Tm, and so
are superconsistent under the null. The two step procedure
suffers another drawback by assuming a unique cointegration
relation between variables. When there is more than one
cointegration relation between the variables, the static least
square regression is not able to discriminate among the
different relations. Johansen's maximum likelihood estimation
for the Gaussian case not only derives likelihood ratio tests
of cointegration rank and finds the asymptotic distribution of
the test statistics,*but also characterizes the cointegrating
relation and formulates tests of structural hypotheses about
these relations. The reason for expecting the estimators to
behave better than the regression estimates is that they take
into account the error structure of the underlying process,
while the regression estimates do not. Gonzalo's (1989)
simulation finds, not surprisingly, that if the data are
generated by an error correction model, the likelihood method
has a better performance than several other procedure. I will
base my analysis on the procedures prescribed by Johansen
(1988,1991,1992) , Hansen and Johansen (1993) , and Johansen and
Juselius (1990) to test for the existence of cointegration,
and estimate income and interest rate elasticities in Taiwan

in this study. A brief introduction of these methods is

58

presented in the following.

III. Johansen maximum likelihood method:
This method begins with the following multivariate p
dimension stochastic process”: Consider a general p-

dimension VAR model with Gaussian error

(4 O 3) H1: xt=u+QDt+n1xt-1+O O O . 0+mxt-k+et' t=1’ O O O O O O O IT

where 81, . . . . ,81 are IINp(0, A) and X491, . . . .,Xo are fixed. Dt
are seasonal dummies orthogonal to the constant term u. Using
a=l-L, where L is the lag operator, it is convenient to

rewrite the model in equation (4.3) as

(4 . 4) H1: Axt=ll+ODt+r1AXt_1+-. . . °+rk-1‘Xt-k+1+nxt-k+3t’

where
I‘i=-(I-II1-. . .-IIi) , i=1, . . . . . ,k-l,
and

n=-(1-n,-. . .410 .

The reason for doing so is that now all the long-run
information in the Xt process is summarized in the "long-run
impact matrix", H. The main procedures of Johansen method are
to investigate whether the coefficient matrix II contains

information about long-run relations (that is, cointegrating

 

10Note at this point that individual components of Xt can
be either 1(0) or I(l) at this moment.

59

relations) among the variables in the data vector from the
knowledge of rank of H . There are three possible cases:
(i). Rank(I[)=p, i.e. the matrix II has full rank, indicating
the vector process is stationary. All elements in Xt are
1(0)".

(ii). Rank(n)=0,i.e. H is a null matrix, all the p-variables
in Xt are individually 1(1) and there is no cointegration, and
the model in equation(4.4) corresponds to a traditional
differenced vector time series model. That is Xt is the
traditional p-dimension multivariate ARIMA(k-1,1,0) process.
(iii). 0<rank(I[)=r<p, implying that there are pxr full column
rank matrix (1,8 such that II=afi' . That implies Axt and B'Xt are
stationary and Xt is nonstationary, with a linear trend
according to Johansen's (1991) proof of Granger Representation

12

Theorem .

The main hypothesis we are going to consider is

 

11Anderson (1971, p170) shows that under quite general
condition Xt can be represented as an infinite linear
combination of the 8t's,

Xt-A '1 (L) (e c411+4ch) .

12The Granger Representation Theorem is based on X is
I(1). Johansen (1991) shows that the distribution properties
of the estimators and the test statistics we are going to
derive below are based on the assumption that the
characteristic polynomial in the equation (4.4) is

II (2) - (1-z) I—E’flil‘i (1-z) z 1-IIz *,

it holds that III(z)I=0 implies that Izl>1 or z=1. This
guarantees that the nonstationarity of X can be removed by
differencing. The condition needed for the process Xt to be
integrated of order 1 is that a'itfii have full rank p-r. Then
the process xt is integrated of order 1, but has pxr
cointegration vectors 8.

60
15: H=ap',

where both a, B are pxr matrices. When this hypothesis is
true, then equation (4.4) can be interpreted as a‘vector error
correction model (VECM), B is the cointegrating vector, a the
adjustment coefficients, since it loads past stationary
equilibrium errors (B'ka) into the system for error
correction. The maximum likelihood method described by
Johansen for equation (4.4) is to estimate a, B, I}, A , u,
and 0 and to test the number of cointegrating vectors under
the null hypothesis (8%).

Under the H2 hypothesis II=afi' , we can write the process for
Xt in H2 as
(4 . 5) Axt=u+0ot+r1axt,1+. . . .+rk_,Axt-m+afi 'xmnt.

Next, we can simplify the estimation of a and B by first
concentrating out the short-run dynamics. This is accomplished
by regressing AXt and X” on (1,Dt,aXH, . . . ,XHM) which define
the residual vectors, Rat and R". The concentrated likelihood

function up to a proportional constant became

1.34%. 0.11) -w exp {T4251 (Rat—afl’Rn)’A'1(Rec—aB’RnH.

The concentrated likelihood function then has the form of a

61

"reduced rank regression"”

I
R°t= up R “terror.

For fixed 8, it is easy to estimate a and A by regressing R0t
on B'Rkt to obtain:

(4.6) 3<B)=s,,§(fi's,,fi)":

80

(4.7) fi=3fs' ,

Further

(4.8) K<B>=soo-so,fi(fi 'skkfi) "9's...
where

Sij-T-12€.1R1thtl i,j'o,k.

The coefficients on constant, seasonal dummy, and lagged

difference I‘=(u,o,I‘1,I‘2, . ”1"“) can be calculated as“

(4.9) P-MmMR-HMMH

The maximum likelihood estimator of B is found by the

following procedures:

 

13See, for example, Velu, Reinsel, and Wichern (1986).
1"'In Johansen and Juselius ( 1990) notation, ZOt=AXt: Z1: are

the stacked variables (1,Dt,AXH, . . ,AXHM) , and zkt=xt,k. The Mij
are defined as:

T
— I ' C

62
First solve the eigenvalues and eigenvectors of the

equation

( 4 - 10) |Asu-skasggsog-0

giving the eigenvalues 3.93.2» .>ip and corresponding
eigenvectors V=(G1, . . ,GP) normalized such that Vska=I:

The choice of 8 is now

A

(4.11) p=($1,...,$r),

which gives

IT:J{T(H2) 'ISool 11:11 (1-1 1)

When H is unconstrained, all p eigenvalues are retained and

the unconstrained maximum likelihood function is

LEW.) -|S..| film-I.)

The likelihood ratio test statistics for the hypothesis H2:ha

IL therefore is:

(4.12) -21n(Q;H, I H1)--T1£ ln(l—Ii)

-l'+1

The statistics -21n(Q:H2HL) has a limit distribution, which,
if aflueo, an is a px(p-r) matrix1s chosen orthogonal to a, can

be expressed in term of a (p-r)-dimensional Brownian motion 8

 

15That is, a; is in the null space of a' such that a'afo.

63

with i.i.d. component as

(4.13) cnfws) F’ [fFF’du] '1fF(dB)’};

where F'=(F1' 'Fz') , and
F" (t)=18i (t) 48‘ (u)du i=1, . . . . ,p-r-l,

Fz(t)=t-1/2 .

Here, and in the following, the integral are all on the unit
interval, where the Brownian motions are defined.
The statistics from likelihood ratio test for Hatr)'versus

Ig(r+1) is given by
(4.14) -21n(Q:H2(r) :H2(r+1))=-Tln(1-1M)

which has a limit distribution (under the condition a' ;mm) as

(4.15) lm{f(dB) F’ [fFP'du] -1fzr<d8)’}.

where 1.u{M) denotes the maximal eigenvalue of M.

The tabulated quantile of equation (4.13) and equation
(4.15) can be found in Johansen and Juselius (1990). The
tables have been extended by Osterwald-Lenum (1992). Equation
(4.12) and equation (4.14) are referred as trace and A-max
statistics respectively.

We have seen that the limit distribution of the likelihood
ratio test are derived by the assumption that a'*u¢0. The

assumption is equivalent to the presentence of a linear trend

64
in the nonstationary process Xt. Under the condition, the

constant u can be decomposed into two parts:

(4.16) E(B'Xt)=-(a'a)"a'u + (a'a)"a'YBJa'lYBJ'M'Lu,

(4.17) E(AXt)=r=Cu,

where equation (4.16) and equation (4.17) are mean (constant)
in cointegrating vector and linear trend in nonstationary
process Xt respectively. C and Y are defined in Johansen
(1991) .‘6

Further development by Johansen is the estimation and
testing under the linear restriction.on.fi, or, a or'both.given
the correctness of the hypothesis H2. Because these hypothesis
are heavily used in the following empirical tests, a brief
introduction is presented for easier understanding of the

notations in the text.

H3: fi=H¢, where H is pxs known matrix.

This is a linear restriction on the cointegrating vectors.
Certain components in the cointegrating vector are shown up
with a fixed relation specified by economic theory. This

restriction may be also imposed for precise estimation if it

 

1“"In practical computation:
Y-r-‘E‘ri—ur-ini)
1'1 1'1

Johansen(1991) show C=fil(a'LYB*)"a'L. The linear trend 7(=Cu)
disappears when a' lu=0.

65
is correct. The estimation and test is:

First solve

[AH/SuH-H’Skosggsofi |-0 ,

for $3.1” ”£3.31 and V3=($3.1, . . $3..) . Notices here the
eigenvalue and eigenvector have been reduced from p-dimension

to s. Choose
(4.18) ¢=(v11,..,vlr), and B=H¢,

The likelihood ratio test of the hypothesis H3 in H2 is

(4.19) —21n(Q;H3 I H2)-T1f:1n{(1-13.1)/(1-Xi)}
-1

The asymptotic distribution of the statistics is shown in
Johansen (1991) to be a x2 with r(p-s) degree of freedom."

Another test for the linear restriction in the
cointegrating vectors can also be calculated by the Wald test.
This test only requires estimation under HE, instead of the
likelihood ratio test which requires both H2 and H3. Johansen
(1991) shows that if only 1 cointegration ‘vector’ 8 is
presented (r=1), and if we want to test the hypothesis K'fi=0,
then the statistics

(4.20) T(K’B)’[(x;1-l) (K’W’Io 1 '1

 

"If r=1, it is equivalent to the difference of two Max-1
test statistics computed for test r=0.

66

is asymptotically 12 with 1 degree of freedom. Here 11 is the
maximal eigenvalue and the 3 is the corresponding eigenvector

of equation (4.10)

[ASH-skasggsoj-o

The remaining eigenvectors form 3. Thus if there is only one

cointegrating vector, one can think of the matrix

(4-21) (I?-—1)W’/T

as giving an estimate the asymptotic "variance" of 3.
Another linear restriction is on the parameters of the
adjustment coefficient matrix a. A frequent restriction in a
is that certain components of a are zero. When some i row(s)
of a, ai=0, then the corresponding i component X“ in Xt is
”weakly exogenous" in the sense that it is not "Granger caused
” by the levels of the other of variables in X}. (see Hoffman

and Rasche (1991b)).

la: a=At, A is pxm known matrix.

67

First solve the equation18

I A"31:1.N536».8557841.!»5'nir.1: |"'°

we then get the ordered eigenvalues and corresponding

eigenvectors
A A A
=- 0:1‘.p=ol and VA: (v4.1 ' . . 'v‘09)

The dimension of eigenvalue and eigenvector remain p, but the
estimated eigenvalue have (p-m) zero components.

Now take

(4.21) §=(G,.,,..,$,or) ,

which gives

$=<A'A) "9...... 3

and

(4.22)

A A

a4= At.

The likelihood ratio test statistics of H‘:hil§ is

 

‘“In particular, B=Ai is a (px(p-m)) matrix, such that
B'A=0.

Sak.b'A/30k'AlsooB (3,5003) 43/50): '
I I I -1 I
Ska,b-SOkA-SOKB (B 3008) B 500A .
Sn. b-su- 33,,8 ( B’SOOB) 43’s“.

S

., b-A’SooA-A’SOOB (B’SOOB) 48490011.

68

(4.23) -21n(Q:H,|H,)-T1tlln{(1-l‘.1)/(1-11)}

The asymptotic distribution of the test statistics is given
by a x2 distribution with r(p-m) degree of freedom.
The restrictions can be simultaneously imposed on 8 as well

as on :1,
H5: B=H¢, and a=At.

By solving the eigenvalue problem"

PHISkk.bH’HISka,bSa-:.b5.k,fl I'O.

A A A A
for 15_,>. also“, and V5=(v5.1, . . ,VSJ) .

Choose

(4.24) fi=(vi1,..,vir),
which give the estimates

(4.25) 35=A(A'A)'1 Sam, 2}.

The likelihood ratio test statistics of H5 in H2 is

 

”Johansen and Juselius (1990, p201) mistakenly print this

equations to be

llH/Skk. bH-H/Ska. 1354:. bSka. 12”" O '

69

(4-26) —21n(o.-H5|H,) -T1t11n{(1—15.1)/(1—11)}

which is asymptotically x2 distributed with (p-m)r+(p-s)r
degrees of freedom.

There is a final point to mention about the assumption of
a constant u explicitly in the hypothesis H2. A hypothesis
concerning the existence of the cointegrating vectors but not
allowing a linear trend in the nonstationary variables is the
hypothesis H2 augmented by the restriction a' lu=0. Let u=afio' .

The hypothesis becomes:
If: H=afi', and a'iu=0;
We can rewrite H1 under H; as
AXt=§Dt+P1AXt_1+. . . .+rk_1axt,k,1+ap*'x‘t_k+et,

where B*=(fi', 80')',and X*t_k=(X't_k, 1) '. Then the estimation
procedure proceeds as H2. The only difference is the constant
now is in the left hand side of the regression AXt and X“, on
AXH (i=1, . .,k-l) , therefore the estimated eigenvalues and
eigenvectors will be (p+1) dimension.

A check that the maintained assumption about the absence of
trend in the nonstationary variables for a given r

cointegrating vector is the test that

70

-21n(Q,-H; I H2) --T f: 1n{(1—X‘,)/(1-X,)}

1-141

where A" are eigenvalues calculated by assumption H5. The test
statistic is asymptotically distributed as x2 with (p-r)
degree of freedom. Subsequent hypothesis H, (i=3, .,5) or H:
should depend upon whether H2 or H; is maintained. So this test
should be regard as primary among future test such as linear
restriction on cointegrating vectors.

Finally, the test developed by Hansen and Johansen (1993)
for the forward recursive analysis is to detect the possible
non-constancy of the cointegrating space when there is no

prior knowledge of structural breaks. Consider the hypothesis
H6: sp(b)=sp(fi) , where b is a known pxr matrix.

In a recursive analysis we can perform a sequence of
likelihood ratio tests in which the estimate 3 is based on
different samples 1, . . . .,t, for t=T0, ,T: T the full sample.

The familiar eigenvalues problem again is to find the roots in

|Ab’Skk( t) b-b’Skosoo ( t) ”130,3 t) b [-0, t-To, . . . , T,
and get a sequence of likelihood ratio statistics

(4.27)

1-x6'1(t)
1‘x1(t)

 

-21n(Q;H,(t)|H2(t))-t1tlln[ ], t-To, . . .,T.

71

where $6.,(t) are the roots of equation(4.27) and 3.,(t) are the
roots under Hz with the moment matrix SU based on the sample
1, . . . ,t. For each estimation period the L-R test has the same
form, and is distributed asymptotically as a 12 with r(p-r)
degree of freedom. Hansen and Johansen (1993) suggest setting

b=B(T), where B(T) is the full-sample estimates of B.

IV. Identification of cointegration vector

The analysis so far does not impose a prior economic
structure relation between the variables in Xt to conduct
inferences on the numbers as well as the structure of
cointegration relations. It is seen that the parameters a, B
are not identified in model H2, since for any choice of an rxr
matrix 6', the matrices oi" and Bi' imply the same
distribution. A VAR model may be thought as a reduced form of
some unspecified economic model. Reduced form can be estimated
directly, but in itself does not provide any information about
the structure of the economic model. However, when the set of
variables in the VAR model are cointegrated, as shown in
Granger Representation Theorem the special constraint on the
impact matrix H has to be specified in the model, which is
always from the knowledge of long-run economic structure among
the variables. Therefore cointegration system bridges the link
between the traditional econometrics model and time series
model with integrated variables. Hoffman and Rasche (1991b)
demonstrate it is possible to assign a unique economic

interpretation to a particular cointegrating vector only when

72

a certain exclusion restrictions are imposed. Economic theory
must provide the exclusion restrictions that allow one to
identify specific long-run economic relations among an
arbitrary set of cointegrating vectors or cointegration space.
They specify the conditions for identification of a specific
long-run relation from the knowledge of the number of the
cointegrating vectors that prevail in a given menu of
integrated variables. The basic method stated briefly as
follows:

Given the pxr error correction parameter and cointegrating
matrix a, B; a and B are not unique as discussed above, since
given an arbitrary rxr transformation matrix £', EB' is also
cointegrating. We must impose some restriction on B to make
the only admissible transformation matrix to be diagonal.
Identification for the first row of B' , as denoted by B'1(a lxp
row vector), may be established by considering the pxm
restriction matrix 8 so that B38 =0. The "restriction” matrix
may be traced to specific long-run relationships as predicted
by economic theory that prevail among the set of integrated
variables in the VAR model. For identification of the first
row in the cointegrating matrix, the transformation matrix is

"admissible" if and only if {'1'B 8=0, where E: is the first

0
(1)

row of i except first element, and B are the (r-1)xp matrix

in
from the exclusion of B; in B. This method applies naturally
to identify other rows. The condition for the transformation
matrix being "admissible" is equivalent to saying that the
rank of (B'e) equals r-l. This is called "rank" condition for

identification of any row in cointegrating matrix. Another

73
necessary but not sufficient condition for identification is
that mar-1, that is the numbers of 6 restrictions are greater
than or equal to the number of cointegrating vectors less one.
This is called "order" condition. In practice for
identification, upon knowing the number of cointegrating

vectors (r), we can always normalize B' to be the form

(4.28) B’.— (Wm-16’-

where c'=[Ir:O]. Then B'c will be of the form [IJB'J] where
B'c* are the last columns of B'c.20 Therefore, the
cointegrating vector can always be normalized to impose (r-l)
zero order restrictions on each row vectors of B'21 where (r-
1) is the exact number of restrictions necessary for
identifying among an arbitrary set of cointegrating matrix.
Economic theory serves as a guide for the restriction for
identification and therefore ultimately controls the choice of

normalization.

 

20For the example of our estimation, in the latter
empirical result, a cointegrating vector (r=1) prevails among
m, y, and r (in order, p=3). Normalization is performed by

fl'c=[ (31:32:33) (1,0,0) ' 1.1(B1IBZIB3)

£2. 2..
'61'31

-(1

21Arxr identity matrix I, has (r-l) zeros in each rows,
and therefore put (r-l) exclusion constrain in each rows of
normalized cointegrating matrix.

'74
IV.Empirical Resultszz:
(A).Data
(1).Measurement and sources
Official quarterly national income (GNP) data are available
from the beginning of 1961. The real (at 1986 constant price)

and nominal GNP are not seasonally adjusted, published in

 

(1961:1--
1991:4) by the Directorate-General of Budget, Accounting and
Statistics (DGBAS) , Executive Yuan”. The GNP deflator at
1986 constant price is used to construct real M18.

We concentrate on M18 because it is the definition of the
money stock that corresponds most closely to the role of money
as medium of exchange, or as the means of making transactions

in Taiwan. The current definition of M18 is:

M18 = Qurrsnsx_ln_§ir2ulatign + Dsnosit§_n9n2¥.

where QuIren2!____ln____sirsulatign refers to all

sectors/departments besides Monetary Institutions (as mentioned
above) that hold currency, Deposithugngy refers to checking
accounts, passbook deposits and passbook savings deposits of
enterprises and individuals in Monetary Institutions. (note:
Postal Passbook Savings Deposits are excluded in the
definition of M18)

The reason for passbook (and saving) deposit being included

 

”The computer program written in GAUSS is used to do all
the computation in this chapter.

JBProfessor Day, T.S. kindly gave me this data.

75
in 1418 is the different transactions custom in Taiwan relative
to United State. A check is usually not an acceptable medium
of exchange for individuals. So a money stock describing the
transactions activity in Taiwan would include passbook
(saving) deposit.

The other definitions of money stock are

H1A= M18 - Passbook Savings Deposits“;

M2= M13 + Quasi Money,

where Quasi money = Deposits Replaced by Postal Saving System-
Time savings Deposits + foreign Currency Deposits of
enterprises and individuals in Monetary Institutions.

The Passbook savings deposit was introduced in September
1968 and had been listed as a part of Qgpggitg_flgn§y since
January 1970. However, in July 1972 a penalty of a 30%
discount on the interest paid for the deposits had been
imposed when the number of withdrawals was in excess of 19
times over a period of'6 months. As a result, the moneyness of
the deposits was reduced. The deposit has since been excluded
from deposit money and included in M2 instead. However, the
above—mentioned penalty was lifted on December 21, 1979
according to the promulgation by the Ministry of Finance. In

this connection, beginning from June of 1982 the deposit was

 

2“Passbook Savings Deposits differ from Passbook deposit
in two ways: First, it can only be deposited by individuals
and nonprofit organizations. Second, the interest rate is
higher for the amounts under NT$ 1,000,000, over that amounts
the interest rate is the same with that of Passbook Deposits.

76
re-included in 1118.25 The following Table ( 4.1) show the
definition.of various money aggregates and the relatively very
small amount of checking accounts to passbook (and savings)

deposits in Taiwan.

Table“. 1)
now Honey stock is Defined in Taiwan

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(1) Currency in Circulation 436,139 I
(2) Checking Accounts 286,727 I
(3) Passbook Deposits 636,058 I
H1A=(1)+(2)+(3) 1,358,924
(4) Passbook Savings Deposits 1,075,551 I
MlB=M1A+(4) 2,434,475
(5) Deposits Re-Placed by P.P.S 1,529,720
(6) Time & Savings Deposits 4,799,546
(7) Foreign Currency Deposits 100,950
M2=MlB+(5)+(6)+(7) 8,864,691 !
At end 0% In M1 ions 0

From above definition of M18 in Taiwan we find a major
problem that is Postal Passbook Saving Deposit are excluded
from M18 (as does Japan, see Rasche, (1990)) because of the
non- money-creating functions of Postal Savings System. It is

recategorized in Deposits Re-Placed by Postal Saving System

 

25'As this reason, any researcher who tries to find M18
data before 1982 in Taiwan should consult to the second
(October, 1982) and third (October, 1987) edition of ,5
_-- eu- t . .1c . _ tis cs H'Jt! 1 I :
for a homogenous definition of M18 from 1961: 1 to date, rather
than using the individual monthly issues from 1961.

77
with Postal Time Saving Deposits since January, 1987. As is
mentioned in Chapter 3, Postal Saving System is categorized in
”Other Financial Institutions" which can't create money. In
fact, Postal Saving System put only 0.2 percent of its asset
in loans, 4 percent in buying government securities, 95
percent in redeposit with Central Bank and four government-
owned specialized banks, and the rest in cash at the end of
April 1993. Table (4.2) shows a non-constant portion of postal
passbook savings deposits relative to H18. The fraction
increase steadily since the early 80's and peaks in 1985. All
of the postal passbook savings deposits of course engage in
making everyday's transactions in Taiwan but they are not

counted in M18.

78

lel.(4.2)

The Percent of Postal Passbook Saving”
Relative to 1:18 in Taiwan

, 7 unit: millions of N.T dollars

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

END or (1) .POSTAL Passaoox (2) .1113 [(1)/(2)]uoo
MONTH SAVING DEPOSITS
I65:12 902 16914 5.33
70:12 4156 35042 11.86
I 75:12 21045 131227 16.03
I 80:12 93194 396382 23.51
I81:12 123744 451560 27.40
F82:06 151742 466162 32.55
82:07 159730 468037 34.12
82:08 161582 471952 34.29
82:09 162665 480204 33.87
82:10 167107 485216 34.43
82:11 169415 480764 35.23
82:12 177290 517480 34.26
[83:12 224575 612902 36.64
[84:12 260022 669619 38.83
85:12 304015 751469 40.45
I86:12 402776 1137863 35.39
[87:12 506400 1568225 32.29
88:12 554515 1950473 28.42
89:12 470162 2068759 22.72
90:12 476286 1931897 24.65
I92:12 597364 2434475 A 24.53
cums Mon y, a wan. ay, 3.

 

2"Including Transfer Account for homogeneous definition.

79

Official monthly data in.MlB are available with two bases:
end-of-month and average figures which are only available from
January 1980 to December 1981 for the average of weekly
figures ending Tuesday, and from.January 1982 to date for the
average of daily figures. In this study, quarterly average
series for M18 is measured as the geometric average of the
three end-of-month observations from July 1961 to the end of
1992. Again, the data are not seasonally adjustedal

Many interest rates in Taiwan have been regulated during
much of the sample period considered in this study. Current
interest rates data available are categorized into five groups
by W
(i).Rate on accommodations to bank by Central Bank
(ii).Rate of Commercial Bank
(iii) .Money Market interest rate”3
(iv).Capita1 Market Interest rate
(v).Interest rates in Unorganized money markets,
where money and capital market were introduced in Chapter 3,
and the Unorganized money market is the curb money market
mentioned. The interest rate on capital market can be measured

by the yield that bonds offer if held to maturity. Only data

 

27One thing to mention, Central Bank of China was
reestablished in July of 1961. For this reason, most studies
of Taiwan M1 demand began from third quarter of 1961. Monthly
data on M1 are available from Bank of Taiwan for the period
between 1945 to 1961. But as Central Bank revised her data on

all money aggregate since July, 1961 in A Supplement to
' 1:! . S 1 °St s 01 9, ‘ 912 . o, e .,- ..

. 1

— 7 ' I
the money data before July 1961 from Bank of Taiwan thus are
unsuitable as a homogeneous data series M1.

28Including interbank call-loan money market interest
rate.

80
on primary market rates, which are weighted by the volume of
new issues in the corresponding month or year, are available.
The capital market interest rates contain mostly one to seven
year bonds of government and corporations considered to be a
long-term rate and are not suitable for this study on M18
demand (see section on money demand theory). For a short-term
interest rate, the best data should come from ‘market-
determined rates since they reflect market forces. But as we
know, Taiwan's formal money market was established in 1976,
91-days of Treasury bill was issued from October 1973: 182-
days was issued from April 1975. Both of them are considered
to be too short a sample period for precise estimation. The
commercial paper interest rate is only available from 1980
that is also the year which interbank call-loan market was
established. My only choice for market determined interest
rate is the Unorganized Money Market interest rate in Taipei
city, which is a survey information list on data source
‘mentioned.above. But the interest rate is much higher relative
to other interest rates of the same time and is not
homogeneously defined in the data source”. The data source
does not explain whether the rate is a long-term or short-term
rate”, however, the latter is what transactions money (M18)

demand really is concerned with in this study. The interest

rates such as rediscount in Central Bank are of no doubt

 

”For example, many of them are above 25 percent per annum
and there is a different figure on the interest rate of
November 1970 from the issues of December 1970 and April 1971.

30This was also pointed out by Liang, Chan, and Lou (1982,
p27).

81

highly regulated in order to conduct monetary policy. What I
use in this study is one-month time deposits interest rate, as
do most of the studies in Taiwan money demand, to capture the
nature of a short-term rate for the shortest maturity of one-
month time deposits relative to hold money. Prior to January
20 1986, the interest rates on bank deposits were prescribed
by The Central Bank of China. From that time on, the banks in
Taiwan were allowed to set their own interest rate on deposits
under the official ceilings. Beginning July 19 1989, based on
the revised Banking Law, the ceilings on deposit rate have
been entirely removed. In this study, I use one-month time
deposit rates from W11 under the
title mum: RATE ON DEPOSITS from 1961 tO 1985. After 1986
the title is DEPOSIT RATES OFFERED 3! FIRST COMMERCIAL 3m
which is a major government bank in Taiwan. I use the daily
average interest rate actually offered during each quarter to
bypass the problem that only the DNTE OF CHANGE is listed on
the data source.
(2) Data Characteristics

It would be better to draw figures to get clear image of
the data characteristics. Figure (5)--(8) is real M1B (m),
real GNP (y), Velocity of MlB, and one-month time deposit

interest rate (R) respectively.

15

10.5

13.5

13

12.5

IIAL I1.

12
11.5
11
10.5

10

Figure 5

16.2

14
13.8
13.6
13.6

11.2

s 12.:
12.6
a 12.4
12.2

11..
11.6
11.4
11.2

11

Figure 6

82

LOGARITHM OF REAL MlB

I” rarwan (1961-'1992)

 

 

 

LOGARITHM OF REAL GNP

IN Thrill (19‘1--1992)

 

’T

r

l 4Ti4T

 

 

 

 

1)

12

11

10

m1! 0' l1.
4

Figure 7

12
11

10

Figure 8

83

‘IIEI.C)CEITI“Y' (DI? hdiLIB

fl TAM (1’61 ' .1992)

 

 

 

 

 

 

 

l l l l l l 1 g L l I l 4 i I
so 64 as 12 n so u u 92
m Palm
CDDJIB"DdCDIngT{"frf[hdlE"IDIBIPCDESIEIF
m IN!" no nmuuyouea)
l l l L A i l l l l l i 1 l J
so 64 so 72 76 no u u n

 

 

84

From figure (5) and (6) , we see that Taiwan's real M18 and
GNP are upward trending. Figure ( 7) shows that velocity of M18
in Taiwan is downward trending which will be proved by a
greater-than-one income elasticity of money demand function in
the latter section. There is also an apparent drift up in the
historically downward trend in velocity since the early 80's.
Figure (4) correctly shows two peaks with a lag in interest
rates of one-month time deposits at two oil shocks in 1973 and
1979. Subsequent to the complete interest rate deregulation in
1989, more volatility can be observed.
(B).Unit Root Test:

The following unit root tests are based on the critical
value, Table (3), set by Schwert (1987, p89 and p95)31

Table (4.3) and (4.4) are the results from various unit
root tests. The shorter sample periods are from 1961:3 to
1979:4, which are chosen to be the maximum number of
observations possible before the major financial deregulation
and second oil shock in Taiwan. The longer one covers the

entire sample from 1961:3 to 1992:432.

 

31They are 0. 05 fractiles of the sample distribution of
the regression t-test and normalized bias T(p- 1) against the
alternative. Schwert's table is based on 10, 000 replications
of an ARIMA(Q,1,,1) process,“ (x -x 1)— =e -Oc However, the
distribution r , and r are nvar ant with respect to
the introduction of a nonzero drift in the generating process.
Thus there is no loss in generality by assuming no drift in
data generating process. See Dickey & Fuller (1979) and
Phillips & Perron (1988).

”Non-seasonally adjusted date are used and no seasonal
dummy variables are added to equation, although which is added
to in cointegration test later.

85

Tlh1.(4.3)
Unit Root Test statisticsuogarithns)”

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Test GNP MlB RATE GNP MlB RATE
Statistics AR 61:3 61:3 61:3 61:3 61:3 61:3
-92:4 -92:4 -92:4 -79:4 -79:4 -79:4

?u 4 -2.72 -1.03 -3.08‘ -2.16 -1.14 -l.65
£IL-T(3u-1) 4 -1.12 -o.41 -1o.o -1.13 -o.52 -3.47
Tc(3d+1) 4 -o.39 -o.63 -23.4* -o.39 -o.67 -6.99
?, 4 -o.75 -3.14 -3.23 -o.04 -2.99 -3.39
£,=T(3,-1) 4 -5.08 -12.6 -11.2 -0.36 -14.1 -11.4
Tc(3;<1) 4 -1.32 -26.3 -27.1 -o.12 -28.5 —23.1
?L 4 -1.63 -o.69 -2.35 -1.44 -o.7o -1.52
?L 4 -o.59 -o.37 —11.1 -0.68 -o.4o -5.04
9; 4 -5.07 -1.42 —2.32 -5.10 -1.51 -2.52
?’ _ 4_ _f4o.z_ -7.17 -11.0 -48.46 -7.98 -11.7

 

33* means signification by critical value of Schwert

(1937)

86

le10(4.4)
Unit Root Test (First Difference of Logaritbns)

 

lfilB
61:3
-92:4

-4.02’
-64.47*
-45.04*

 

 

 

 

-7.56*
-81.6‘
E:

 

 

 

 

 

 

 

 

 

 

Note: 7

T and r7 are test statistics, as defined in the context, of

‘7 r“: f!

the regression
k
xc-a +pxc_1+}:j-2p j ( xt_ 1+1'Xc- j) + e, .

or

k
xc'“+p t+pxc-1+Ej-Zp 1(xc-j+1‘xc-j)+ec'

c is computed as l/(l-pZ-p3-p‘) as suggested by Watson in Schwert (1987, p75) .
7""' and T: are adjusted Dickey-Fuller test suggested by Phillips. f“ and r:
are Phillips corrected normalized bias test. All are calculated with 4 lags
of the residual autocorrelations as suggested by Schwert (1987). That is
k—Inc{4(128/100)1/‘}-4.34

 

“Schwert (1987) did not explain in detail of the choice
of k (=Int{4[T/100]’“} which is all the same under different
assumed true moving average parameter 0. Huang (1993) use
Monte Carlo to explain the correct choice of k under different
moving average parameter 0.

87

Table(4.5)
0.05 Critical Values of Unit root Test by Schwert (1989)

 

 

 

  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

__ __
Test AR 6=-o . 5 the 6=o . 5 _-I
Statistics

’1‘“ 4 -3.02 -2.87 -2.93 I
9“ 4 -29.2 -14.4 -9.80 I
Tc(3u-1) 4 -19.9 -16.6 -17.4 I
?, 4 --3.61 -3.41 -3.49 I
i; 4 -44.2 -22.4 -15.6
Tc(3,-1) 4 -33.8 -23.3 -3o.4

’1‘” 4 -5.30 -2.93 -2.73

E, 4 -44.9 -14.3 -11.9

'7", 4 -6.59 -3.53 -3.15 I
9’, 4 -65.8 -21.8 -17.6 I

 

From Table (4.3) above, all of the tests fail to reject a
unit root in real M13 and income”. The unit root test on the
one-month time reposit interest rate rejects only two out of
ten tests under the hypothesis of a unit root.

The question of a second unit root in these data series is
examined by performing the first difference of the data series
on the same unit root test (assuming no determined trend). The
computed test result is in Table (4.4). In contrast to the

level data, the maintained hypothesis of a unit in the

 

”Kwiatkowski, Phillips, Schmidt, and Shin (1992) argue
that it is very common to fail to reject a unit root. The
explanation for it is simply that most economic time series
are not very informative about whether or not there is a unit
root, or equivalently, that standard unit root tests are not
very powerful against relevant alternatives. See also DeJong
et al. (1989), and Diebold and Rudebusch (1991).

88
difference of data is strongly rejected in all data series.
Therefore, we conclude that real money, income, and one-month
time deposit interest rates in Taiwan are integrated of order
less than 2. For the statistical analysis that'utilized.in.the
study here, it is critical for the time series to be

integrated of order 1.

(C).Model Misspecifications test

The maximum likelihood method is applied to estimate the
equation (4.4) without any constraints under 8,. The data is
fitted into this model starting with lag length.k=2, thenwwith
k=3, and so on, until the test statistics for the residuals in
each equation pass the test for being uncorrelated. Table
(4.6) show the choice of k by the test suggested by Box and
Pierce, which was refined by Ljung and Box (1979). This test
has been criticized for the difficulty with the choice of L,

though I chose L=12 in the test below.

89

lel.(4.6)
Box-Pierce-Ljung test statistics“

 

   
  
   

 

 

 

 

Test statistics AM1 AY
under various k
k=2 9.45 214.65.
7.28 172.87‘
7.41 46.77‘
10.77 14.83

 

 

 

 

 

From table above, a VECM37 with k=5 in equation (4.4) is
used in the basic model for subsequent reduced rank tests for
its autocorrelated-free :residuals. Table (4.7) reports. a
summary of the residual diagnostics obtained from the VECM

with k=5 for the model misspecification test.

 

:“The Box-Ljung-Pierce Q statistics defined as

2
Q-T(T+2) if I’.
.r17LJ

 

which converge to’x2(12) under the null hypothesis that there
is no serial correlation of the residuals of any order, where
r3 is the j-th order autocorrelation.

InStrictly speaking, the model at this moment can not yet
be said a VECM, because the rank of H has not shown to be
reduced.

90

Table(4.7)
Residual diagnostics For Fourth order Brror'CorrectionMModel

 

Autocorrelation

Lag 1 2 3 4 5 6 7 8 9 10 11 12

Am . 01 “.02 .00 “.03 “.06 .08 “.03 .03 .16 “.12 “.16 “.01
AY “.06 .08 .14 “.05 “.10 .00 “.15 .00 “.18 .08 “.02 “.08
Ar .00 .03 .03 “.05 “.04 “.12 .11 .07 .05 “.09 .04 “.06

Contemporaneous Residual Correlation Matrix

Am Ay Ar
Am 1.0 0.211 -0.416
Ay 0.211 1.0 -0.082
Ar -0.416 -0.082 1.0

Eq Standard Skewness Excess Normality Q-Test

deviation kurtosis test 12(2) 12(12)
Am 0.034 0.153 “0.119 0.461 10.77
AY 0.018 0.103 “0.142 0.269 14.83
Ar 0.079 2.027 10.893 574.256 7.78

The residual of interest rate equation does not pass the

normality test from Jarque & Bera (1980)”. They are due

 

inThe Jarque & Bera test statistics defined as

_ (T‘In) 3 3K2
7 -—7;——(smr+—7r-)

converge to x2(2) under the null hypothesis of normality,
where m is the number of regressors, SR is skewness and ER is
excess kurtosis. Lin and Kao (1992) noted that these
statistics Q and 7 might not converge to traditional 12
distribution since the model involves integrated series.

91
largely to excess kurtosis than to skewnessfi” There may be
a potential problem for this skewed distribution in applying
the assumption of Gaussian errors to derive the test
statistics and estimator in the reduced rank hypothesis. The
robustness of the ML cointegration procedure for deviations

for normality has not been investigated so far“t

(D).Johansen Cointegration Estimation and Test
(1) Log-Log specifications

(a). Results under restriction on B

From'Table (4.6) and (4.7) above, a model of equation (4.4)
with k=5 is fitted to the Taiwan money demand data. Price
homogeneity is first tested and since it is clearly accepted
by data (see Appendix A, B), the empirical analysis here will
be for real money (m), real income (y) and interest rate (r)
for ease in interpreting the results from the data measured
in logarithms. The constant plays a crucial role for the
interpretation of the model, as well as for statistical and
the probability analysis as we have seen above. On the basis
of the plots of the series (see figure 5, 6, and 8) and a
formal test (see Appendix C), a constant is added explicitly

in the estimation and test under our maintained hypothesis

 

39A even larger lag-length k is fitted, but interest rate
equation still does,not pass normality test. The huge skewness
and excess kurtosis only result from sample extending through
l989:3, that happened to be the time when Taiwan interest rate
was completely deregulated.

‘wJohansen (1991, p1566) states that the assumption of a
Gaussian distribution is not so serious, as long as the
process 2&5 can be approximated by a Brownian motion.

92
(H,,i-2,.,5) which assumes the nonstationary process Xt-(mt,

"‘ has linear trends with coefficients which are

y.. r.)
functions of u only through alu. A 3x1 season dummy variable
matrix D: orthogonal to the constant is added to the model
because of non-seasonally-adjusted data being used.

The initial estimation is performed over a sample through
the end of 1979. The sample is chosen for its maximum possible
number of samples before major financial deregulations in

Taiwan in the 1980s'. The results of this estimation are

presented in Table (4.8)

 

“In this order through all Chapter 4.

93

Table(4.8)
Test for Cointegration Real M13, Real GNP, One-Month-
Tine-Deposit Interest Rates.

 

Sample Period 1961:3--1979:4
(k=5, T=69)

3:388.“ I: m===

Unconstrained

Johansen Test Statistics

H2 r=0 r<=1 r<-2
Trace Test 24.78. 5.37 0.35
Maximum Eigenvalue Test 19.40 5.02 0.35
Estimated Eigenvalues .2451 .0702 .0051
m y R
Estimated Cointegration Vector 16.97 -28.25 6.88
Estimated Standard Errors (2.67) (3.73) (0.82)
Estimated long-run (Y/P) elasticity 1.66
Estimated long-run R elasticity -0.40
x2(1) for income elasticity=1.00 12.27:
12(1) for interest rate elasticity=0.0 11.24

Estimated Eigenvalue 0.2415 0.0191
Hfiflz: 12(1) Test Statistics For Constraint(LR)= 0.3315
H5: x2(1) Test Statistics For Constraint(WALD)= 0.4472

m y R
Estimated Cointegration Vector 15.09 -25.66 7.26
Estimated Standard Errors (1.12) (1.90) (0.53)
Estimated long-run R elasticity -0.48

 

* reject the null at 10%
** reject the null at 5%
See Table (4.10) for critical value of trace and max-1 test.

94
where trace test is from equation (4.12), maximum eigenvalue
test from equation ( 4.14) , estimated eigenvalues from equation
(4.10), cointegrating vector from equation (4.11), long-run
income and interest rate elasticities from equation (4.28),
12(1) for LR test from equation (4.19), 1261) for Wald test
from equation (4.20), cointegrating vector under income
constraints from equation (4. 18) , and estimated standard
errors from equation (4.21). From Table (4.8) above, maximum
eigenvalue test statistics rejects the hypothesis that rank of
H is zero (m, y, r are nonstationary and not cointegrated) at
0.1 level, although trace test does not. Both statistics fail
to reject the hypothesis that rank of Hiis <= 2 at 0.01 levels
which are consistent with the results from unit root test that
the individual variables are nonstationary. As is noted by
Kasa (1992) the trace test will tend to have greater power
than max-1 test statistics when the 1‘ are evenly distributed.
On the other hand, max-1 will tend to give better result when
the 1, are either large or small. In practice, the value of r
is best chosen at a judicious consideration of both
statistics, along' with. an inspection. of’ the eigenvalues
themselves. A visual inspection of the eigenvalues, we see
that the eigenvalues are not evenly distributed and with a
single large one dominating the others. Therefore, the
statistics from max-1 give evidence that there exists a unique
cointegrating vector among m, y and r in Taiwan through end of
1979. For r=1, the order condition for identifying is
satisfied automatically. The stationary process B'xt (B after

normalization) is called the estimated equilibrium error of

95

money demand function describing how'the three variables inxt
trend together. Finally, the signs of individual elements of
the cointegrating vector are consistent with a positive
equilibrium real income elasticity 1.66 and a negative
equilibrium interest elasticity -0.40 of money demand
function. From 13(1) test, the income elasticity is
significantly greater than 1 and interest rates elasticity is
significantly greater than 0. The estimated standard error is
not particularly large. A constraint that income elasticity
equals to 1.70 is estimated to consider problems generated by
potential multicolinearity between real balance and real
income. Both 12(1) statistics from LR and wald test fail to
reject this hypothesis. The precision of the estimation
improves, but not profoundly. The estimated interest rate
elasticity is -0.48 which is not quite different from the
estimation from unrestricted model -0.40.

A forward recursive estimation is performed from 1961:3 to
subsequent quarters of 1979:4 until the full sample period
ending 1992:4. The result in Table (4.8) is unaffected until
the samples extend through 1982:3. The detailed results are

reported in Table (4.9) for these expanding sample periods.

96

Table(4.9)
Test for Cointegration Real M18, Real GNP, One-Month Time
Deposit Interest Rates.

 

Sample Period 1961:3--1982:3
(k=5, T=80)

 

Unconstrained

Johansen Test Statistics

H2 r=0 r<=l r<=2
Trace Test 26.33. 6.52 0.75
Maximum Eigenvalue Test 19.81 5.77 0.75
Estimated Eigenvalues .2193 .0696 .0093
m y R
Estimated Cointegration Vector 16.10 -26.92 7.54
Estimated Standard Errors (3.03) (4.40) (0.65)
Estimated long-run (Y/P) elasticity 1.67
Estimated long-run R elasticity -0.46
x2(1) for income elasticity=1.00 11.02:
12(1) for interest rate elasticity=0.0 12.16

(y) Elasticity Constrained to be 1.70

Estimated Eigenvalue 0.2178 0.0150

M3IH2: x2(1) Test Statistics For Constraint(LR)= 0.156
35: 12(1) Test Statistics For Constraint(WALD)= 0.223

m y R
Estimated Cointegration Vector 14.74 -25.07 7.82
Estimated Standard Errors (1.68) (2.86) (0.08)
Estimated long-run R elasticity -0.53

 

* reject the null at 10%
** reject the null at 5%

97

Table(4.9) (cont'd)

&- “0.0209 103*A- 0.121 0.271 “0.007
“0.1839 “0.855 “0.007 2.807

-o.1413 0.2402 -0.0749
in--0.0209 0.0355 -0.0110
-0.1839 0.3129 -0.0975

“1.1043 0.0138 -0.0072 -0.0469

u--0.1711 0- 0.0640 -0.0019 0.0702

-1.4323 -0.0632 -0.0215 -0.0657
0.0860 0.1967 -0.2364 “0.1641 -0.1871 -0.0604
P1- 0.0956 -0.0597 -0.0093 Pz- -0.0278 -0.5978 -0.0563
-0.4761 -0.5521 0.4183 0.2251 -0.1477 -0.1184
-0.1877 0.0566 -0.0967 -0.0939 -0.1153 -0.0715
P3- 0.1761 -0.0944 0.0406 P‘- -0.1222 0.2641 -0.1302
0.4965 -0.4013 0.0117 0.1386 0.0728 -0.0832

 

where a is estimated from equation ( 4.6) , A from equation
(4.8), H from equation (4.7), and the other coefficients in
VECM from equation (4.9). The max-1 test again rejects the
hypothesis of no cointegrating at the 0.1 level, but fails to
reject the hypothesis of one or fewer cointegrating vectors at
the 0.01 level. However, the precision in the estimation of
the individual elements of the unrestricted cointegrating
vector deteriorates a bit. Restricting income elasticity to be

1.70 again improves the precision of the estimation with a

98

somewhat lower estimated asymptotic standard error. Both x2
tests fail to reject this hypothesis. The implied unrestricted
income and interest rate.elasticity are 1.67 and -0.47 and.are
great than 1 and 0 significantly. The estimated interest rate
under income restriction is -0.53. The full set of estimates
of the parameters of the restricted error correction model
equation (4.5) are also shown in Table (4.9). The estimated a
has been normalized by the estimated parameter in
cointegrating vector corresponding to money(m) with a correct
a:1 sign that shows excess money demand in last period is
downward corrected in current period.

However, the evidence of the existence of a cointegrating
vector is not maintained (not to mention the stability ) as
samples are extended beyond the third quarter of 1982. Values
of the tests statistics drop noticeably. Both trace and max-1
test statistics cannot reject the hypothesis that there is no
cointegrating relation among these three variables.” The
complete sets of theses test statistics from recursive

estimation (unconstrained) are shown in Table (4.10).

 

‘QA same restriction that income elasticity is equal to
1.70 (H3) will make the trace and max-1 test statistics
significantly reject the no cointegrating hypothesis. However,
this procedure is inappropriate because H is a subset of H2.
If there is no cointegrating relation estimated from H2, no
further restrictions Should apply in B.

99

le10(4.10)
Recursive Estimates of the Money Demand Specification in
Taiwan, 61:3--92:4

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

SAMPLE Estimated 12 ( 2 ) Trace A-MAX
END Cointegrating 36‘ sp (b) test test
Vector (r=0) (r-O)
=spw)“

79:4 16.97 -28.25 6.88 5.38* 24.78 19.40*
80:4 17.17 “28.66 6.89 6.55** 25.54 20.10*
‘81:4 17.21 “28.75 7.20 6.47** 26.64 21.07**
82:1 17.35 “28.98 7.23 6.71** 26.95* 21.34**
82:2 16.31 “27.37 7.53 5.00* 27.22* 20.86**
82:3 16.10 -26.92 7.54 3.90 26.33 19.81*
82:4 15.77 -26.30 7.54 2.75 25.98 18.41
483:4 15.52 -25.55 7.33 1.14 25.24 17.13
84:4 15.07 -24.19 6.57 0.02 22.24 14.50
85:4 17.48 -26.23 3.14 2.04 17.43 10.11
86:4 17.15 -26.15 3.87 1.86 17.18 11.72
87:4 15.46 “24.07 4.57 0.63 19.41 13.55
I88:4 11.97 “19.12 5.09 0.02 20.35 13.44
89:4 9.75 -15.98 5.15 0.72 21.57 13.23
90:4 11.30 “17.98 4.76 0.03 24.29 18.76*
91:4 11.25 -17.96 4.71 0.02 26.86* 19.08*
92:4 11.56 -18.43 4.69 0.00 27.79* 18.35

 

 

 

 

 

 

“The estimation of subsample between end of 1982:4 and
The "cointegrating vector"
between these periods just present for purpose of comparison.

1989:4 show no cointegrating.

“This hypothesis again is a sub set of H2, it can be
tested only when a knowing numbers of cointegrating vector
exist. For this reason, the test statistics listed between end
of 1982:4 and 1989:4 are only for illustrations.

100

Table(4.10) (cont'd)

90% Critical Value of trace test“ = 26.79
95% Critical Value of trace test = 29.68

90% Critical Value of Max-1 test - 18.60
95% Critical Value of Max- 1 test a 20.97

* :significant at 90%
** :significant at 95%

 

where the 78(2) test is the test for the hypothesis H6:
sp(b)=sp(B), that is, the estimated cointegrating vectors lie
in the same space with the one estimated from full sample
periods b. It is from equation (4.27) and the b(=B(121)) is
the estimated cointegrating vector of all sample period
through 1992:4. From the Table above, there is no evidence of
cointegrating relation among most of samples after 1982:3. A
cointegrating vector does exist when we estimate from all
sample periods, however, the constancy of parameter is not
maintained from the x2(2) test which shows that the space
spanned by the cointegrating vector estimated from full sample
period is different from. those of before 1982:3. If a
cointegrating relation does exist among the three variables,
and this relation is stable, then the model such as equation
(4.5) must describe the process inadequately after 1982:3.

A dummy variable D824 to shift the constant term is added

 

‘“This critical value taken from Table 1 of Ostrewald-
Lenum (1992), allows an unrestricted intercept in the error
correction representation in the statistical model (SM) and
data generating process (DGP).

101
to the error correction model of Taiwan money demand
function“. The impact of the addition of this variable to
the existence of a cointegrating vector is remarkable and the
estimated parameters are stable for most of sample periods.
This can be seen in Table (4.11) which show that the recursive
estimation of equilibrium real income and interest rate
elasticity as well as the related test statistics from the

unconstrained model.

 

“In particular the dummy variable, D824, is 0.0 for all
quarter through 1982:3 and 1.0 for all subsequent quarters.

Taiwan, 61:3--92:4, with 0824 (begin at 1982:4).

 

102

Table(4.11)
Recursive Estimates of the Money Demand Specification in

Johansen Estimates

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

SAMPL c y r x2 (2 ) Trace 1-MAX
E END H :sp (b) test test ( r=0
=82 ( fl) (1‘0) )

79:4 “7.54 1.66 “.40 2.29 24.78 19.40*
80:4 “7.66 1.66 “.40 2.72 25.54 20.10*
81:4 “7.61 1.67 “.41 2.82 26.64 21.07**
82:1 “7.61 1.67 “.41 3.01 26.95* 21.34**
82:2 “7.59 1.67 “.46 1.57 27.22* 20.86*
82:3 “7.53 1.67 “.46 1.14 26.33 19.81*
82:4 “7.62 1.67 “.46 1.16 26.66 20.05*
83:4 “7.84 1.68 “.49 0.95 28.44* 21.30**

I84:4 “7.94 1.68 “.49 0.94 29.02* 21.55**
85:4 “7.66 1.64 “.38 1.43 24.01 16.78
86:4 “7.69 1.63 “.38 1.89 26.38 20.60*
87:4 “7.88 1.65 “.43 1.77 26.53 23.46**
88:4 “8.43 1.72 “.61 0.13 25.81 22.35**
89:4 “10.4 1.96 “1.25 1.01 25.77 18.20
90:4 “8.44 1.73 “.65 0.04 29.52* 24.48**
91:4 “8.58 1.75 “.70 0.00 34.16** 24.22**
92:4 “8.56 1.75 “.69 0.00 33.93** 23.12**

90% Critical Value of trace test = 26.79

95% Critical Value of trace test = 29.68

90% Critical Value of Max-1 test = 18.60

95% Critical Value of Max-1 test = 20.97

:significant at 90%
:significant at 95%

103
where the constant in the cointegrating vector is estimated
from equation (4.16).

In sharp contrast to Table (4.10), Table (4.11) shows that
there is strong evidence of one cointegrating vector among m,
y, and r in Taiwan. The hypothesis r-O is rejected at the 5
percent level against the possible stationarity both from
trace and max-1 test statisticS". The estimated income and
interest rate elasticity remain stable in most sample periods.
The stability is reinforced by the test in H6 that shows all
the parameters lie in the same space spanned by the one
estimated from all sample period. The full set of estimation
through 1992:4 is listed in Table (4.12) for comparison with

the results of sample ending in 1982:3 in Table (4.9).

 

"Because the hypothesis r<=1 is never rejected, I do not
report them here.

104

Table(4.12)
Test for Cointegration Real M18, Real GNP, One-month Time-
Deposit Interest Rates. With a D824 Dummy Variable.

 

Sample Period 1961:3--1992:4
(k=5, T=121)

 

Unconstrained

Johansen Test Statistics

H5 r=0 r<=1 r<=2
Trace Test 33.93: 10.80 1.79
Maximum Eigenvalue Test 23.12 9.00 1.79
Estimated Eigenvalues .1739 .0717 .0147

m y R
Estimated Cointegration Vector 8.89 -15.58 6.18
Estimated Standard Errors (2.01) (2.99) (0.32)
Estimated long-run (Y/P) elasticity 1.75
Estimated long-run R elasticity -0.69

Estimated Eigenvalue 0.1717 0.0329

33:32:12”) Test Statistics For Constraint(LR) =0.3313
lg: 12(1) Test Statistics For Constraint(WALD)=0.510

 

m y R
Estimated Cointegration Vector 10.01 -17.03 5.92
Estimated Standard Errors (1.36) (2.31) (0.24)
Estimated long-run R elasticity -0.59
* reject the null at 10%
** reject the null at 5%
-0.1108 1.034 0.123 ..1.097
8- 0.0126 103*A- 0.123 0.297 -0.009

-0.0508 -1.097 -0.009 5u676

105

Table(4.12) (cont'd)

.01213 -0.1108 0.1884 -0.0655
:-.01152 n- 0.0126 -o.0215 0.0074
.01262 -0.0508 0.0863 -0.0300
-.8949 -.0229 -.0033 .0004 .0330
u--.1190 D824--.0034 0- .0084 .0030 .0127
-.3822 -.0182 -.0176 -.0288 -.0669
.1775 .1622 -.1113 -.0434 -.l368 -.0628
1‘1- .1498 -.2267 .0409 I‘,-—.0076 —.3483 -.0514
-.2763 -.4622 .2742 .1203 -.2612 -.1593
-.1632 -.0563 -.0692 -.0740 -.0676 -.0670
P3- .1524 -.2595 .0213 1‘,--.0958 .4846 -.0652
.6621 -.2004 .2844 .4542 -.0348 .0146

 

where 7 from equation (4.17) are the estimated trends in the
nonstationary variables.

Constraining the income elasticity to be 1.70 improves the
precise of the estimation again. The estimated interest rate
under income constraint is -.59 which is not too :much
different from that of the sample ending at 1982:3, -.53. The
first coefficient in the a matrix corresponding to the error
correction speed of excess money demand remains stable.
Positive trend 7 in the variables is consistent with figure
(5).(5).(8)-

From the Table (4.9) and (4.12) above, the constraint that

income elasticity equal to 1.70 is never rejected, and this

106
constraint make the parameters estimation even more stable,
particularly for the sample ending between 1989:2 and 1990:1,
I therefore list a complete set of constrained estimation in

Table (4.13).

Table(4.l3)
Recursive Estimates of the Honey Deaand Specification
in Taiwan, 61:3--92:4. Income elasticity constrain to
be 1.70. Begin from 1982:4, add D824 dummy variable.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

SAMPLE r Mean r 12(1) Trace A-Max
END (LéR) Test(r=0) Test(r=0)
79:4 -7.81 -0.48 .331 20.41** 19.07**
80:4 -7.90 -0.46 .266 20.31** 19.84**
81:4 -7.84 -0.48 .236 21.30** 20.83**
82:4 -7.65 -0.53 .158 21.13** 19.89**
83:4 -7.92 -0.53 .062 22.49** 21.23**
84:4 -8.05 -0.52 .058 22.77** 21.49**
85:4 -8.15 -0.52 .497 17.57** 16.29**
86:4 -8.24 -0.52 .726 21.17** 19.87**
87:4 -8.23 -0.51 .404 23.78** 23.05**
88:4 -8.11 -0.56 .115 22.94** 22.24**
89:4 -7.91 -0.65 1.768 18.99** 16.43**
90:4 -8.07 -0.58 .198 26.97** 24.28**
91:4 -8.03 -0.59 .398 27.70** 23.82**
92:4 ‘-8103‘_ :0.39>_.331 26.84** 22.79**

90% Critical Value of trace test = 13.33
95% Critical Value of trace test = 15.41
90% Critical Value of Max-l test = 12.07
95% Critical Value of Max-A test = 14.07

107

Some kind of change has occurred in the relationship
between real M18 (m) , real income (y), and short-term interest
rates (r) in Taiwan since 1982:3. The question is what kind of
change has happen and if the answer to this question can be
found, what had caused the change ?

The same kind of dummy variable to shift the constant term
in addition to the original vector error correction model are
also found in Rasche (1990), Rasche and Yoshida (1990),
Hoffman and Rasche (1991), and Orden and Fisher(1993) in the
study the money demand in Japan, United States, New Zealand
and Australia. In Rasche (1990), the hypothesis that the D82
dummy variables reflects a shift in the drift of real money,
real income and the call rate, without a shift in equilibrium
real balances is not rejected in Japan. Rasche and Yoshida
(1990) interpreted the D85 variabLe as a one-time shift in
equilibrium real M2+CD balances after the deregulation of
large time deposits in Japan. Hoffman and Rasche (1991) argued
that the estimated coefficients on the D82 dummy variables
represent a shifts in the deterministic trends of the real
balances series while both.the slopes and.the constants of the
equilibrium demand for real balances remain constant during
the eighties in the United States. Orden and Fisher (1993)
argued a deterministic shift variable should be included in
the models to account for the financial deregulation effect in
1984 in New Zealand to get the evidences of cointegration
through the 1980's among money, price and output, but they do
not identify the effect of this dummy variable.

It is informative to interpret the 0824 that is added to

108
shift the constant term in the error correction model. As we
have shown that a estimated constant can be decomposed into

two part:

Em 'Xt)=-(a'a) "a'u+(a'a) "a'YpJa'JfiJ "a'Lu,

E (Axt) =r=Cu;

where C=fi*(a';!fi‘)"a'u
and

T-I-ifl‘i—kU-illi).
-1

1-1

The former is the constant term (mean) in the cointegrating
vector, and the later represents the linear trend in real
balances series. The presence of a dummy variables such as
D824 in error correction model with coefficient vector 6,
indicates a shift in the constant vector from u to (n+6) . This
reflects either a change in the mean of cointegrating vectors,
a change in the deterministic trends of the variables, or
both. When a and B remain unchanged in the presence of a dummy
variables, the change in the mean and trend caused by the

addition of D824 can be calculated as

(4.29) -(a'a)"a'6+(a'a)"a'! A(a'gply‘a'ts,
and

(4.30) Bi(a'l!fil)"a'L6.

109

When a'*6=0 the change in trend caused by 6 is zero while 6
still affects the mean in the cointegrating vector up to

-(a'a)”a'6. The estimated a in subsample through 1982:3 and
1992:4 is not particularly changed, and the estimated 8 is
lying in the same spanned space. This ”informal" calculation
shows the shift in the mean of cointegrating vector due to the
addition of 0824 is -0.1718 (after normalization of
cointegrating vector, estimated through 1992:4) and the shift
in the deterministic trend due to 0824 is -0.000263 for the
real money series, -0.003808 for the real income series, and -
0.010511 for the interest rate series. It is hard to judge its
magnitude of the shift in means and trends without comparing
other studies. A -0.1718 shift in the mean of the normalized
cointegrating vector is moderate when compared with other
studies“. A formal test suggested by Yoshida and Rasche
(1990) is a modified Johansen test about the absence of a
linear trend in the variable. We have seen from equation
(4.30) that when a' 16:0! there is no change in the trend in
the variables. The hypothesis Hafiz to test a'lu=0 introduced
above can be modified to test a" 6 =0 by substituting 0824
for the constant vector in the construction of the test

statistics. The test statistics thus computed is 3.85“

 

“Rasche (1990) estimated the shift in the mean of
cointegrating vector in Japan's H1 is -0.112. Yoshida and
Rasche (1990) estimated shift in Japan M2+C0 is 0.418, and
Hoffman and Rasche (1991) estimated a 0.047 shift in mean of
equilibrium money demand function in United States.

“That is, 30.69-26.84. However, I am using constrained
(income elasticity) model, this test involves H3 (r) ,H3(r) in
Johansen (1990) notation. It is unclear this test statistics
possess the same property as Johansen' 3 since he only show the

110

(estimated from whole sample period), and is not significant
at x2(p-r-2) . Therefore the hypothesis that the addition of a
dummy variable represents no change in the deterministic trend
cannot be rejected. The 0824 means a downward shift in the
means of cointegrating vector. The empirical result of there
being a downward shift in the equilibrium money demand in the
early 803 is consistent with figure (7) that shows a upward
drift in the velocity in early 808. This upward drift has
changed the historic trend of the H18 velocity since that
time.

The test a" 6 =0 is a modified Johansen's hypothesis H;:H2
to test a' 1“=°° Since Johansen and Juselius (1990) did not
provide the asymptotic distributions of the other hypotheses
such as H;{H3, HuH‘, and H"s “is”, the following Table (4.14)
is the recursive estimates of the model under H2 after 1982:3

but subject to the constraint that a" 6 =0.

 

statistics (r) 'H2 (r). A statistics in unconstrained model
also is ca culated, the estimated statistics is 37. 78-
33. 93=3. 85, which is also not significant.

5°Intuitively, H. or H (i=3, 4 ,5) are applied depending
upon whether H2 or H 2 is maintained in the first step.
Therefore there are no needs for the test for H;}H3, HHH‘, and

Hsnns

111

Tab1e(4.14)
Recursive Estimates of the Honey Demand
Specification in Taiwan, 61:3--92:4, With 0824
(begin at 1982:4). a'i6 =0, Johansen Batimates.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Constant y r 12(2)
11;:32 (ans =0)
-7.70 1.67 -.48 6.00 *
-7.81 1.68 -.49 3.85
-7.85 1.68 -.49 3.62
-7.55 1.65 -.42 6.12 *
-7.53 1.65 -.41 3.73
-7.70 1.66 -.44 6.89 *
-8.17 1.73 -.63 7.14 *
-9.92 1.95 -1.22 4.17
-8.22 1.74 -.68 4.07
-8.36 1.76 -.73 2.94
-8.35 1.75_ -.72 3.85 ,
* re ec e nu a '1.

Beside only a few subsample estimates reject the hypothesis
a'i6 ==0 (no change in the trends caused. by 0824), the
estimated income and interest rates elasticities almost remain
identical to Table (4.11). Therefore the hypothesis that the
0824 dummy variable reflects a "shift down" in the mean of
cointegration vector, without a shift in the equilibrium real
income and interest rates elasticity is not rejected.

The interesting question is what has made a one time shift
down in the late 1982 in the equilibrium Taiwan money demand

function but has not changed the income and interest rate

elasticity? The shift is consistent. with the ‘view ‘that

112
investments in money capital as a response to increasingly
higher interest rates will lower the demand for transaction
money”. With a major interest rate deregulation in November
1980 (see Chapter 3) which completely deregulated interest
rates on negotiable certificates of deposit and other money
market instruments, coincided with the historically
persistently higher interest rate in Taiwan during 1980-1982
(see Figure 8) , it might motive people in Taiwan to make
investments for cash management that allowed them to hold
permanently lower level of money whose yield is regulated
below the competitive level in money market. Evidence from the
data shows this "ratchet" effect shifts down Taiwan's money
demand around forth quarter of 1982Ӥ Another possible (but
not satisfactoryflb explanation is that the portion of Postal
Passbook Savings relative to H18 increases in the early
1980's. The Postal Passbook Savings deposits, of course, enter
into everyday transactions in Taiwan. A monetary aggregate
measuring transactions activity such as H18 therefore
underestimates the true transactions money if there is a shift
up in this portion.
(b). Results under restriction on 0

Next, a test that certain variables may be exogenous is

 

51See for example, Porter, Simpson, and Hauskopf (1979),
Judd and Scadding (1982), and Ochs and Rush (1983).

52This view might be consistent with Lee, J .C (1986) that
velocity of H18 had occurred permanent shift from temporary
change around early 80's due to high inflation rate (interest
rate) in Taiwan.

53However, there are no 'clear-cut' of the jump of this
increasing portion, see Table (4.2).

 

113
performed. Table (4.11) show that second and third parameters
in the a matrix are close to zero. A test statistics 23.12-
21.68=1.44, is not significant at 12(r(p-m) =2) . The hypothesis
that 02 and 03 are zero cannot be rejected.

The results from the hypotheses that 02 and as are zero from
the Hde are comparable to the results from the following
Stock-Watson's dynamic OLS which already assume that income
and interest rates are exogenous (see section(E)). Therefore
I further present the recursive Johansen's estimates under the
constraints that 022 and :13 in Table (4.15) for the comparison

in due text.

114

Table(4.15)
Recursive Estimates of the Honey Demand Specification
in Taiwan, 61:3-92“. ctr-0:50. Johansen method.
Begin from 1982:4, add 0824 dummy variable.

 

 

 

 

 

 

 

 

 

 

 

 

 

  

 

    

 

 

 

 

SAMPLE Hean y r H‘ } H2 -T ln ( 1-
END 2 A.)
x (2)
79:4 -7.48 1.62 -0.29 3.90 15.50
80:4 -7.49 1.62 -0.29 3.21 16.89
81:4 -7.45 1.62 -0.32 3.36 17.71
82:4 -7.32 1.62 -0.34 3.24 16.81
83:4 -7.44 1.62 -0.34 3.80 17.50
84:4 -7.49 1.62 -0.34 3.73 17.82
85:4 -7.36 1.60 -0.29 1418 15.60
86:4 -7.50 1.61 -0.31 1.61 18.99
87:4 -7.77 1.64 -0.39 1.53 21.93
88:4 -8.19 1.69 -0.53 2.16 20.19
89:4 -8.59 1.75 -0.71 2.34» 15.86
90:4 -8.15 1.70 -0.58 1.71 22.77
91:4 -8.16 1.71 -0.60 1.21 23.01
92:4 '8.06 1:70w_”_Hfl=0:58n‘L__ 1.44 V 21.68

 

 

115
(c). Results under restriction on 3 and a
A. complete set. of .results of ‘various. hypotheses are

presented in Table (4.16) to illustrate the tests so far.

Table(4.16)
Estimates for the Taiwan.Honey Demand and the Corresponding p
and a vector under various hypothesis about a and 8.
Sample period:1961:3--1992:4. With a 0824 Dummy variable

 

B-restrictions

a-restrictions
A1

 

. -Tln(1-AQ

 

 

 

 

 

 

 

Since Hs never be rejected from Table (4.16) , a complete
set of estimated parameters based on H5 is reported in Table
(4.17) which form the basis for constructing a common

stochastic trends model in Chapter 5 below.

 

5"H is not tested above. I directly test H5:83 in the
constrained model.

116

Table(4.17)
Test for Cointegration Real HlB,Real GNP, One-Honth-Time-
Deposit Interest Rates. With a 0824 Dummy Variable.

 

Sample Period 1961:3--l992:4
(k=5, T=121)

Hs a2=a3=0 3 813-1 . 78,

Estimated Eigenvalue 0.1640 0.0000

H5:I-13:xz(2) Test Statistics For Constraint(LR) =l.10
m y R
Estimated Cointegration Vector 10.10 -17.18 5.93
Estimated long-run R elasticity -0.59
-0.1254 1.036 0.125 -1.103
8- 0.0000 103*A- 0.125 0.298 -0.009
0.0000 -1.103 -0.009 5.720
.01157 -0.1254 0.2132 -0.0737
t-.01131 II- 0.0000 0.0000 0.0000
.01304 0.0000 0.0000 0.0000
-.9644 -.0252 -.0033 .0003 .0330
u- .0200 D824--.0054 Q- .0085 .0029 .0127
.0141 -.0102 -.0178 —.0284 -.0667
.1607 .1537 -.1161 -.0574 -.1377 -.0669
P1- .1346 .2348 .0346 P2--.0201 -.3482 -.0553
-.2154 -.4297 .2921 .1707 -.2615 -.1439

-.1763 -.0539 -.0754
I3- .1407 -.2582 .0154
.7090 -.2055 .3078

-.0886 -.0656 -.0713
I;--.1088 .4898 -.0693
.5065 -.0560 .0308

117
(2). Semi-Log Specification:

This section present the results from an alternative
specification that uses the level (R) rather than logarithms
(r) of interest rate. Three variables Xt=(mt,yt,Rt) ' are fitted
in the equation (4.5) again. The results from recursive

estimations are given in Table (4.18).

 

118

Table(4.18)
Recursive Estimates of the Honey Demand Specification:
Taiwan, semi-log Hodel, 61:3--92:4, Johansen Estimates

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

SAMPLE Estimated 12 (2) Trace
END Co integrat ing H6: sp (b) Test

Vector55 (r=0)

=sp(m 5‘

79:4 16.47 -27.28 1.14 4.71* 26.26
80:4 16.88 -28.04 1.08 6.29** 25.03
81:4 17.60 -29.13 1.06 7.18** 25.98
82:1 17.50 -29.00 1.07 7.26** 26.42
82:2 15.92 -26.57 1.14 5.36** 27.60
82:3 15.47 -25.80 1.15 4.30 27.00* 20.54* I
82:4 14.89 -24.74 1.15 2.76 26.50 18.95*
83:4 14.63 -23.96 1.10 1.13 26.26 17.82
84:4 14.06 -22.43 0.98 0.02 22.92 14.97
85:4 -16.56 24.76 -0.49 2.01 18.29 10.56 I
86:4 15.50 -23.73 0.65 1.02 19.54 12.90
87:4 14.50 -22.52 0.71 0.47 20.26 14.35
88:4 11.90 -18.78 0.79 0.05 20.34 14.05
89:4 9.57 -15.45 0.82 0.59 21.56 13.63
90:4 10.91 -17.26 0.72 0.01 24.85 19.30*
91:4 10.77 -17.12 0.72 0.03 26.92* 19.07*
92:4 11.08 -17.56 0.71 0.00 27.62* 18.06 J

 

* :significant at 90%
** :significant at 95%

 

55'The estimation of subsample between end of 1982:4 and
1989:4 show no cointegrating. The "cointegrating vector" of
this period just present for purpose of comparison.

5"This hypothesis again is a sub set of H2, it can be
tested only when a knowing numbers of cointegrating vector
exist. For this reason, the test statistics listed.between.end
of 1982:4 and 1989:4 was only for illustration.

119

The same pattern of problems with trace and max-1 test
statistics dropping noticeably after 1982:3 occurs”. The
same dummy variable to capture the possible shift in the
constant is added, and again its work in 'recovering ' the
cointegrating relationship is remarkable. The estimated income
elasticity and interest rate semi-elasticity are stable for
most subsample estimation. The parameter constancy is again
enhanced by the test from hypothesis H . All estimated
parameters lie in the same space spanned by the one estimated
over all sample periods. The estimated constant and income
elasticity are almost identical to that of estimation from
log-log specification. Table (4.19) shows the results from
adding this shift-variable.

 

57However, the tests does not reject the null of no
cointegrating beginning at 1983:1 in this specification, that
is a quarter behind log-log specifications.

120

Table(4.19)
Recursive Estimates of the Money Demand Specification:
Taiwan, semi-log Model, 61:3--92:4, With 0824 (begin

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

at 1982:4). Johansen Estimates
y R x2 (2) Trace MAX-l
H6: sp (b) test test
=39“) (1‘0) (1‘0)
1.65 -.069 1.74 26.26 20.57*
1.66 -.064 2.48 25.03 19.53*
1.65 -.060 4.06 25.98 20.30*
1.65 -.061 4.06 26.42 20.77*
1.66 -.071 1.94 27.60* 21.21**
1.66 -.074 1.25 27.00* 20.54*
1.66 -.074 1.26 27.33* 20.80*
1.67 -.078 1.09 29.54* 22.46**
1.67 -.078 1.08 30.33** 22.84**
1.64 -.064 1.34 25.87 18.46
1.66 -.071 1.23 30.33** 23.52**
1.67 -.077 1.16 28.50* 25.02**
1.72 -.100 0.23 27.48* 24.49**
1.90 -.179 1.13 27.35* 21.01**
1.73 -.107 0.01 30.08** 24.15**
1.75 -.116 0.02 33.58** 23.52**
1.73 -.111 0.00 32.57** 21.72**
90% Critical Value of trace test = 26.79
95% Critical Value of trace test = 29.68

90% Critical Value of Max-1 test = 18.60
95% Critical Value of Max-1 test = 20.97

* :significant at 90%
** :significant at 95%

121

For comparison with the full set of estimated parameters
from both specifications, the following presents the complete
set of estimated parameter in Table (4.20) and (4.21) which
correspond to their counterparts in Table (4.9) and (4.12).
The data do not distinguish between the logarithmic and the
semi-logarithmic alternative specifications. The estimated
coefficients remains almost identical except for those

involving interest rates.

122

Table(4.20)
Estimated Cointegrating model. Semi-logarithmic specification
Long-run income Elasticity Restricted to be 1.70

 

 

 

 

Sample Period 1961:3--1982:3
(k=5, T=80)
Estimated Eigenvalue 0.2243 0.0108
m y R

Estimated Cointegration Vector 13.86 -23.57 1.20
Estimated Standard Errors (1.74) (2.97) (0.01)
Estimated long-run R elasticity -.086

-0.1340 1.078 0.102 -6.052

a- -0.0392 103*A- 0.102 0.259 -0.S34
-1.1298 -6.052 -0.534 131.159

-0.1340 0.2779 -0.0116
II- -0.0392 0.0667 -0.0033
-1.1298 1.9206 -0.0978

—1.0972 .0157 -.0069 .0519
u- -0.3269 0- .0631 -.0021 .0698
-9.1703 -.5690 -.1103 -.6365
.0972 .1602 -.0335 -.1490 -.2430 -.0060
P1- .0691 -.1263 -.0046 P2--.0438 -.6385 -.0067
-3.2854 -3.6154 .4247 1.5526 -.0567 -.0326
-.2031 .0296 -.0164 -.1215 -.1678 -.0138

F3- .1485 -.1302 -.0012 P‘--.1448 .2352 -.0218
3.1472 -3.3264 -.0999 .7698 1.4673 -.0667

123

Table (4 . 2 1) .
Estimated Cointegrating model . Semi-logarithmic specification
Long-run income Elasticity Restricted to be 1.70, Adding 0824

 

Sample Period 196l:3--1992:4
(k=5, T=121)

 

 

Estimated Eigenvalue 0.1633 0.0329
m y R
Estimated Cointegration Vector 9.51 -16.17 .94
Estimated Standard Errors (1.41) (2.40) (0.04)
Estimated long-run R elasticity —.098
-0.1022 1.062 0.113 -7.383
a- -0.0001 103*A- 0.113 0.292 -0.545
-0.4619 -7.383 -0.545 240.390
.00956 -.1022 .1738 -.0101
t- .01156 II--.0001 .0002 -.0000
.09513 -.4619 .7853 .0456
-0.8249 -.0221 -.0027 -.0006 .0339
u- 0.0210 D824--.0066 0- .0075 -.0027 .0117
-3.7295 -.1275 -.1836 -.2020 -.5118
.2052 .1222 -.0170 -.0175 -.1872 -.0069
[y- .1372 -.2580 -.0051 I;--.0130 -.3651 -.0079
-2.4005 -2.3203 -.3136 0.5202 -.1786 -.1982
-.1457 -.0953 -.0103 -.0649 -.1091 -.0103
P3- .1297 -.2738 -.0010 P‘--.1049 .4811 -.0115

3.1678 -.3193 -.1931 2.8842 .8787 .0154

124

(E) .Stock-Watson Dynamic OLS Estimation”:

Another method to estimate cointegrating vector suggested
by Stock and Watson (1993) is in the following:

let Xt be a p-dimensional time series, whose elements are
individually I(l) . Suppose that pxr matrix of r cointegrating
vectors is fi=(Ir, -0) ' , where 1.. is the rxr identity matrix and
8 is the rx (p-r) submatrix of unknown parameters to be

estimated. The triangular representation for x, is

(4 . 31) xg=u+0xf+vt1 ,

(4.32) Ax§=v§,

where Xt is partitioned as (xt‘, Xf)‘ with x: being rx1, and X5
being (p-r)x1. vt=(vt",vt2') ' is a stationary stochastic
process. The proposed estimator is to rewrite equation (4.31)

as
(4 . 33) xg=u+exf+d (L) 6x3“: ,
where 6:=vt‘-E[vt‘}{vf}], {v5} denote (vs, t=0,il, 3:2,...}.

and d(L)AXt2=E[vt1: {vf)], d(L) is in general two sides.

Stock and Watson (1993) shows that when it is the case that

 

5"A major difference of the Stock-Watson estimation with
that of Johansen's is that the former employs the
normalization prior to estimation and assumes weakly
exogeneity of p-r variables. Also the Johansen procedure
estimates the number of cointegrating vectors and the
cointegrating space simultaneously, while the Stock-Watson
approach is based on the particular normalization that
requires prior knowledge of the numbers of cointegrating
space. (See Hoffman and Rasche, 1991a).

125
r=1, one can simply regress one of the variables onto
contemporaneous levels of the remaining variables, leads and
lags of their first differences, and a constant, using either
ordinary least squares or generalized least square. The
resulting "dynamic OLS" estimators are asymptotically
equivalent to Johansen estimator.

In our case, three dimensional vector Xt= (mt,yt,rt) ' in
Taiwan has a unique cointegrating vector(r=1) over the whole
sample period after taking consideration of structural break
in 1982:4. The Stock—Watson dynamic OLS is easily applied from
equation (4.33) . Let xg=mt, Xf=(yt,rt) ' . One can simply get the
income and interest rate elasticities, and the constant in the
equilibrium money demand relation (0,u) in equation (4.31)
from dynamic OLS in equation (4.33) with the proper choice of

number of leads and lags d(L)”. The following Table (4.22)

K

5"’Professor Rasche suggests me the following idea:
In Johansen and Juselius (1990) Corollary 6.2:" If m=r=1 then
the maximum likelihood estimate of H is found as the
coefficients of XH in the regression of A'AXt on XH‘, B'Axt,
and Axt, ,...,xt_m, 0t and the constant." In my case, p=3 and
I‘§1, an if cz=(¢z11 0 0) ', where the data are ordered as Am"

A)?“ and Art, then

1 00
A-O, B-10.
0 01

$0 the regression in Johansen & Juselius Corollary 6.1 would
e :

Amt=b0+b1Ayt+b2Art+b3mt_k+b,yt_k+b5rt_k+o . . - . .
wh :ich is equivalent to the regression
A111,:==co+c1Ayt+c,_,Art-i-c3mt_,a-c,.yt_1+c5rH+. . . . . . ,

which is also equivalent to the regression

126
are the results by applying this procedure with the same 0824
dummy variable. The estimated parameters do not show too much
difference among choices of k (numbers of leads-lags) . The
constant estimated from this procedure is consistent with that
of Johansen method. The income and interest rate elasticities
are a little bit smaller than Johansen approach“, however,
all the parameters from recursive estimation remain stable for

entire sample period.

mt=do+d1Yt+dzrt+d3Amt+d4AYt+dsArc”: . . . .+f1Amt,k+iz‘szt.,,,+1f;,Ar't..K ,

wh ich is a lot like the Stock-Watson DOLS regression without
the leads. Therefore the choice of k=5 at Table (4.22) make it
comparable case to Johansen method and we can even try to
test if the lead changes in 001.8 regressions are significant
Or not ‘? However the conventional test (such as F test) is not
sIlitable because of the nonstationarity of the regressor.

“The smaller elasticities estimated from dynamic OLS
I‘elative to Johansen MLE also can be found in applying to

In(31"ley demand in the United States. See Hoffman and Rasche
(1991a) .

Stock and Watson's Dynamic OLS Estimate of Honey Demand
function In Taiwan. Log-Log Specification, add 0824. k=no. of

127

TRb1.(4.22)

leads-lags, 1961:3--1992:4

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

——
Sample k Mean y r k
End

79:4 4 -7.08 1.57 -0.20 5
80:4 4 '-7.22 1.59 -0.21 5
81:4 4 -7.20 1.59 -0.21 5
82:4 4 -7.24 1.59 -0.23 5
83:4 4 -7.23 1.59 -0.23 5
84:4 4 -7.22 1.59 -0.22 5
85:4 4 -7.06 1.56 -0.17 5
86:4 4 '-6.84 1.54 -0.11 5
87:4 4 '-6.83 1.54 -0.10 5
88:4 4 -7.09 1.57 -0.19 5
89:4 4 -7.10 1.58 -0.22 5
90:4 4 -7.07 1.57 -0.22 5
91:4 4 '-7.17 1.58 -0.23 5
92:4 4 -7.21 1.59 -0.24 5

 

 

 

 

 

 

 

 

 

CHAPTER 5

Th. IIPORTANCI Ol' COIIIION STOCHASTIC TRENDS OI m FLUCTUATIONS
Ol' NOR AOGRBGATB ECONOMIC VARIABLES IN TAI'AN

We have seen that there exist a unique cointegrating vector
among the three variables real H18 Cm), real GNP (y), and one-
month time deposit interest rate in Taiwan. A cointegrating
system puts special constraints on the variables in their
multivariate Wold, and ARMA representations and there exist an
error corrections representations among these cointegrating
variables as made clear by Granger Representation Theorem.
Stock and Watson ( 1988) , King, Plosser, Stock, and Watson
(1987) (hereafter, KPSW) have proposed an alternative
representation for such a cointegration system by calling them
the "common trends representations". This form is convenient
for discussing long-term forecasts. The study1 in this chapter
uses multiple cointegrating variables to examine empirically
the effect of shifts in these common stochastic trends on

major aggregate economic variables in Taiwan.

(I). Common Trends Representation of a Cointegration System:
Suppose that each component of the pxl vector Xt is I(l) ,
then Xt has a moving average representation in first

difference, perhaps with a nonzero pxl drift 6:

 

1The recent other studies includes Blanchard and Quah
(1989), Clark (1987), Cambell and Hankiw (1987), and Shapiro
and Watson (1988).

128

129

(5. 1) AX,=6+C(L) 6,, with Co=I ,
and
E(e,6,')=0, tats,
=A, t=s.

When it is the case that X, is cointegrated with a pxr (rSp)
cointegrating matrix )9, such that fl'X, are stationaryz, it can
be shown that X, has a common trend representation with (p-r)

common stochastic trends as equation (5.2).

(5. 2) X,=y+A‘r,+D(L) 6,, r,=u+7,-,+r),,

where y is a pxl vector of constants, A is a px(p-r) full
column rank matrix such that fi'A=0, r, is a (p-r)x1 vector of
random walks with drift u and innovation 1),. r, can be thought
as the "common stochastic trends" of X,. Because certain (r)
linear combination of X,, fi'X, are stationary, the numbers of
trends in X, has been reduced from p to be (p-r)3. The
elements of 0(L)6, have finite variances and are stationary.

The equation (5.2) decomposes the integrated vector X, into

 

2It can also be shown that the rank of C(1) is (p-r), and
B'C(1)=0.

3The number of common trends in a cointegrating system
can easily be shown by a system of linear equations. When a
pxl vector X~I(1), but a rxl vector fi'X,~I(0) with rSp.
Suppose that 8'X,=0,, the solution of X, will be in the (p-r)
dimensional subspace of RP because there will be (p-r) ”free
variables". Those (p-r) free variables govern the integrated
process of X, and will be called the common stochastic trends.

130
permanent and transitory components. Whi-le 0(L) 6, is
stationary, A1, is not‘. Thus Xf=Ar, can be thought of as the
permanent component of X,, while X,=0( L) 6, can be thought as

a stationary or transient component. That is,

(5.3) X,= x‘,’ + X2.

The permanent innovations r), and the transient innovations 6,
are related by r),=F6,, where F is a (p-r)><p matrix as defined
in KPSW (1987). In this formulation the vector of permanent
innovations is completely determined by the vector of
transitory innovationss. The interesting questions are the
importance of the innovations n, in the common stochastic

trend 7, to the fluctuations of X, and give an interpretation

of these innovations.

(II). Identification of Common Nominal interest rate and
Natural Output Trends.
The estimation of A in equation (5.2) is not unique since
if B'A=0, then fi'AR=O for any arbitrary transformation (p-
r)x(p-r) matrix R. The choice of R must be based on some

priori considerations that generally involve economic theory.

 

‘This decomposition leads naturally to the multivariate
version of the Berverige and Nelson (1981) decomposition of a
single variable ARIMA(p,1,q) process into a stochastic trend
and a stationary component, where a stochastic trend is
defined as a random walk, possibly with drift.

sIn Beveridge and Nelson (1981) the innovations in the
stochastic trend and transitory component are also perfectly
correlated.

131
We can rewrite the common trend representations equation

(5.2) in a "structural-form" model“:

(5.4) Ax,=6+H(L)fi, ,

where n: =(r),' , 7),") is a px1 vector of transformed innovations
with r), the (p-r)x1 vector of permanent innovations as in
equation (5.2) and the r): the rxl vector of transformed
transitory innovations. The complicated procedures by KPSW
(1991) recover this representation, equation (5.4), from the
data process equation (5.1): AX,=6+C(L)6,.

The identification problem can be stated as follows’: under
what conditions is it possible to deduce the structural
disturbances n; , and the matrix of lag polynomials H(L) in
equation (5.4) from the reduced form error 6, and matrix of
lag polynomials C(L) in equation (5.1.)8 ? The identification
is achieved KPSW (1987,1991) through two sets of restrictions

by as

 

‘The structural form must always be specified on the
basis of a prior knowledge on the structure of the
relationship between the variables of interest, while the
reduced form is just used to describe the variation of the
data.

7That is to say under what suitable assumptions can we
identify H06 and the related reduced form with the structural
model by Han: and H(L)=C(L)Ho. In Sims (1980), the
identificateion is through the assumption that Er is diagonal
and that H0 is lower triangular.

8The other methods of identification the structural shock
through a factorization of the reduced form error covariance
matrix can be found for example in Sims (1980), Bernanke
(1986), and Blanchard and Quah (1989).

132

(5. 5) Hon,'=6,,
and
(5-5) H(1)=[A000],

where Ho" exists and A0 is a known px (p-r) full column rank
matrix chosen in a way that associates each shock with a
familiar economic mechanism and satisfying fi'Ao-O, n is a (p-
r)><(p-r) lower triangular matrix with full rank and 1's on the
diagonal, and 0 is a pxr matrix of 0's.

The covariance matrix of the structural disturbance in
equation (5.4) is assumed to be

e 0’ 2‘1 o
En‘-E(n tn t) - 0 2‘1 '

where E, is partitioned conformably with n," =(r),', 172') ' and E,
is diagonal.

The calculations of n can be the Cholesky decomposition of
the transformed reduced formed covariance matrix 02,0' and
normalized to be 1 on the diagonal, where matrix 0 is equal to
(AO'A0)"A0'C(1), and C(1) can be calculated from Johansen
(1991, p1559)’. The permanent innovations are identified by
n,=Ge,, where G=n"0. The dynamic multipliers for r), are
C(L)E,G'E;,1.

Therefore after estimating VECH such as equation ( 4.24) , we

 

9See also footnote 15 in Chapter 4.

133
can invert it to be the reduced form in equation (5.1)10 and
relate it to the estimated structure model in equation (5.4)
by suitable factorization on the reduced form error covariance

matrix as stated above.

III. Impulse Response Functions and Variance Decompositions:

One device used in the multivariate study to measure the
importance of the innovations (1),) in the permanent component
of the stochastic process X, are the concepts variance
decompositions and impulse response function, which Sims
(1980) has applied to VAR models".

The long-term forecasts of X, are easily expressed from the
"structural model" equation (5.4): AX,=6+H(L)r),' as

(5.7) Xc-tb+1$1§Hjn‘1l Xo-O;

and for h21,

t+ -.i -
5.8 - ‘. '
( ) X,,), (t:+h)5+i}:31 jg H11] 1+§1§§H1n“1'

The forecast of X,+h given the information at time t is simply

the first two terms of equation (5.8) or

 

1°See appendix for how to invert the estimated VECH to the
multivariate Wold representation in first difference of X,.

"The only difference here is that X, is in first
difference in his Wold representation.

134

+ -1
(5.9) X,,H,-(t+h)6+ftf2 8111'}.

1-1 j-O

The effect of a unit shock in period t on the forecast in

period t+h therefore simply is

(5.10) 134-3511, when h-m ,-H(1).
-0
8

Thus equation (5.10) describes the response of a shock to X,
and the response depends upon the sum of the moving average
coefficients of the first differences of X, in its structural
model. The impulse response function thus is defined. We
therefore can measure the dynamic response of X, to the
innovations in the common stochastic trend in different time
horizon.

We next consider the forecast error variance. Denoting the

h-step ahead forecast error by e ,, we have

6M

(5 . 11) et+Ht-Xt+h-Xt+Ht-1§:¥:H j" 2+1 '

When the forecast error can be traced to a particular factor
in r),', it is reasonable to conclude that this factor is
important in determining the evolution of X,. It follows from
equation (5.11) that the variance of the h-step ahead forecast

error is

135

(5 . 12) var [euucl' £12321)” ”(32139”

Forecast error variance decompositions therefore build on this
intuition by quantitatively attributing the errors in
forecasting the different variables in X, to the various

innovations in n: of the systems.

IV. Empirical Results“:

For identification the two permanent shocks n,from our
estimated cointegrating vector from the constrained model in
equation (4.24) , we must have a known A0 matrix as in equation
(5.6) which is orthogonal to the cointegrating vector 3.

We choose13

-B, B

.AAAC) y 1. 0
- 0 - 0 1 “’21 1 .
1 0

In the case that “m=0 and the coefficients in the error

 

12A method suggested by Runkle (1987) to estimate the
confidence intervals for the impulse response functions and
variance decompositions is not performed here.

13I originally ordered the "natural output" shock first,

BY '9’ 1 0
A-AOQ- 1 o .
0 1

But the estimated 0 1=-1.209, which makes the permanent natural
output and nomlnal shocks deviate seriously from
orthogonality.

136

corrections loading matrix 0:2 and a, are equal to 0, we can
interpret the first common trend as a nominal shock“ and the
second one as a natural output shock. The first common trend
is interpreted as a nominal shock since a one-unit increase of
this shock leads to a 8, change in the real balances and 1
unit change in nominal interest rates by a Fisher relation”.
The second common trend is a natural output trend since a
shock in the trend leads to a one-unit long-run increase in
real output. Through the money demand relation, this natural
output shock also leads to a fly increase in real balances.

The following are the empirical results based on the

cointegrating vector estimated under assumption H5. We get

-0.59 1.70 0.0000 0.9618 —O.6163
Aw- 0 1 , C(1)- 0.0000 0.8066 -0.1065
1 0 0.0000 0.6969 0.7405
-0.2192 0.5233 1.0 3.16x104 0 0
110- 0.0424 1.1026 0.0 2,.- 0 2.41x10" 0
1.3103 -1.0375 0.0 o o 7 .84x10“
0.0000 0.6969 0.7405 1 0]
0.0000 0.8066 -0.1065 -0.1054 1'

We have shown that az=a3=0 from Table (4.15) and 021 in n

 

1‘We can also interpret it, like KPSW (1991), as a long-
run neutral inflation shock since it has no long-run effect on
real income and has a unit long-run effect on nominal interest
rates.

15Amacroeconomic model to derive similar interpretation
can be found in Hoffman and Rasche (1991).

137
matrix is close to 0“. The interpretation of the two common
trends as nominal shock and natural output shock therefore is
of economic consequence.

The estimated impulse response of m, y, and r to a one
standard deviation of the innovation in the common stochastic
trends are plotted in Figure (9)--(14). The response of real
money to nominal and natural output shocks are negative and
positive, respectively, as predicted by money demand theory.
Income response to nominal shock is negligible in all time
horizon. The response of income to shocks from natural output
is consistent with how one might think income would response
to news about positive natural output innovation (such as
technological developments). However the response is
oscillatory for a long period.before it is back to new steady-
state equilibriumnfl The model is normalized so that nominal
shocks have a long-run unitary effect on the nominal interest
rate. The initial response.of nominal interest rate to natural
output shock is negative which is consistent with the
prediction from classical IS-LH model that a increase in the
aggregate supply from positive natural output shock would

lower nominal interest rate. However, the effect dies out in

the long—run.

 

‘“A test suggested by Hoffman and Rasche (1991) to test
the diagonality of the covariance matrix of the permanent
shocks 02,0' is not performed here. If 02,0' is diagonal, then
0 is an identity matrix.

17See Appendix E for the explanation of the oscillatory
dynamics in the responses.

138

 

 

Impulse Responses
I
01
O
l

 

 

 

‘. 90 r I 7’ T I r T f l I
0 H3 20 30 4O 50 60 7O 80 9O
Quarters .

Figure 9. IRF of Log Real H18 to a One-Standard-Deviation
Innovation in the Nominal Permanent Component.

 

225

200"

L75‘ ee— 1. __

 

L50“

L25“

Impulse Responses

LOO“

.75“

 

 

 

SO I l I T I I I l T Y
O l O 20 30 40 50 60 7O 80 9O
Quarters

Figure 10. IRF of Log Real M18 to a One-Standard-Deviation
Innovation in the Natural Output Permanent Component.

 

139

 

 

 

a
Q
Li)
O
1

l
O
(n
O
1

Impulse Responses

 

 

 

.I80 I I I I I I I I I I
0 ll 22 33 4‘} 55 66 77 88 99

Quarters

Figure 11. IRF of Log Real GNP to a One-Standard-Deviation
Innovation in the Nominal Permanent Component.

 

1.40
1.30-
1.20~ I
LlO‘ ‘
1.009
.90«

I
.704
.60- I
.50 0 1‘0 20 30 4'0 50 6’0 70 80 9o

Quarters

 

 

 

 

 

Impulse Responses

 

 

 

 

 

Figure 12. IRF of Log Real GNP to a One-Standard-Deviation
Innovation in the Natural Output Permanent Component.

140

 

2.00

1.80“

in
O
1

 

Imp: Ilse Responses

Ix) Ln
0 O
I 1

 

1.00 " ‘

 

 

 

80 I I I I I I I I I I
O 10 20 30 40 SO 60 7O 80 90
Quarters

Figure 13. IRF of Log Nominal Rate to a One-Standard-Deviation
Innovation in the Nominal Permanent Component.

 

 

Impulse Responses
I
U1
1

..IS—l

-2.0 7

 

 

 

"2.8 l V I I I I I
0 10 20 30 40 50 60 77‘ 80 90
Quarters

Figure 14. IRF of Log Nominal Rate to a One-Standard-Deviation
Innovation in the Natural Output Permanent Component.

141

Are these responses large enough to explain a substantial
fraction of the short-run variation of the variables? The key
answer is provided in Table (5.1) and (5.2), which show the
fraction of the forecast-error variance attributed to
innovations in the common stochastic trend at horizons of 1-
100 quarters. Table (5.1) shows that.the first ”nominal shock”
explains about two-fifths of the money movements in the 1-4
quarter horizon. The nominal shock explains more than four-
fifths in the movements in nominal interest rate in the short-
run. In the long run, the nominal shock.has.a dominant role in
the movements of both money and nominal interest rate. That
the nominal shock has less important effects on real income
movement in the short and long-run is consistent with figure
(11) . The second "natural output" trend still has a non-
negligible role in the short-run movements of real money, it
alsojplay'a dominant role in the variation of real output. The
natural output shock does not affect the movement of nominal
interest rate significantly. However, movements in the two
common stochastic trends totally account for about one-half in
the variation of real balance, and more than ninety percent of
the variation of real income, and almost all the variation in
the movement of nominal interest rate in Taiwan in the short-

run 1-4 quarter.

142

Table(s.l) Forecast Error Variance Decompositions

Fraction of the Forecast Error Variance
Attributed to Nominal Permanent Shock.

 

Horizon

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table(5.2) Forecast Error Variance Decompositions

Fraction of the Forecast Error Variance
_Attributsét9 "Naturaloutput"Permanent succk-

Horizon

 

 

 

 

 

 

 

 

 

 

 

 

 

 

CHAPTER 6

CONCLUSION

This study has presented evidence consistent with the
hypothesis that a long run cointegrating relation exists among
nonstationary real H18, real GNP, and one-month time deposits
interest rates in Taiwan at quarterly frequency when we take
into accounts the structural break in the fourth quarter of
1982. Our primary concern is not simply with the existence of
cointegration but also with the stability of estimated money
demand coefficients. The recursive estimates of the parameters
of cointegration ‘vectors remains stable for' most sample
periods from the third quarter of 1961 through fourth quarter
of 1992. The conclusions are robust to choice of estimator
(Johansen's HLE and Stock & Watson's DOLS), and logarithmic
specification. The issue of money demand stability is enhanced
by the results from the latest method developed by Hansen and
Johansen (1993) to test constancy in the cointegration space.
For Taiwan, the equilibrium real income elasticity of real H18
is not significantly different from 1.70, and the equilibrium
interest rate elasticity is on the order of -0.46 to -0.65.
The structural break is shown to be the shift down in the
constant term of money demand function.

In the cases for which I have established evidence for a
stable long-term stationary relationship among real H18, real
income, and nominal interest rate, hypothesis concerning that
real income and nominal interest are weakly exogenous receives

143

144

overwhelming support, and the hypothesis that levels of money
and prices are proportional in the long-run generally can not
be rejected“; The nonstationary variables also are shown to
contain positive deterministic trends. Weak exogeneity of the
nominal interest rates is quite consistent with the fact that
interest rates in Taiwan have been regulated for most of the
sample periods.

I further examine the importance of innovations in the
common stochastic trends in the money demand variables by
impulse responses and forecast error variance decompositions.
The two common stochastic trends is identified by the
procedures developed by KPSW (1991) and interpreted as nominal
and natural output permanent shock. The results suggests that
a remarkable portion of the variance in the money demand
function variables can be explained by these two stochastic
trends. In general, the results are quite consistent with the
views of real business cycle theory since the natural output

trends explains nearly all of the variance in real output.

 

18See Appendix A, and 8.

APPENDICES

APPENDIX A

Test for Price Homogeneity in Taiwan Honey Demand Function:
From L-R Test

Four variables nominal H18 (M), real income (y), interest
rate (r), and GNP deflator (P) in logarithms based on the

model of1

Md-kyplruzpp3 ,

are fitted into equation (4.4) to test if 53=1 or not. That is
to test the equality of parameters in the cointegratinngector

if such a cointegrating vector exists.

H1: AX,=11+0D,+I‘1AX,-1+. . . .+I‘,,,AX,_,,,+I[ X,.k+€,;

The result under H2: lI=afi' and 83: fi=H¢ are in Table (A.1)

below.

 

1Unit root tests are first performed on nominal M18 and
GNP deflator. The augmented Dickey-Fuller test statistics Tu
are -1. 28 and -0. 86 respectively, both can not reject the unit
root hypothesis.

145

146

Table 1.12
The eigenvalue and the corresponding test statistics for

testing restrictions on p

 

 

Eigenvalue
H2: .179 .106 .081 .002 H3: .165 .103 .028
trace l-max trace l-max
r33 0.23 0.23
r52 10.51 10.28 rS2 3.45 3.45
r51 24.17 13.65 r51 16.65 13.19
r=0 48.10* 23.93 r=0 38.53* 21.87
*:significant at 10%.
where
-1 0 0
0 1 0
Ht
0 0 1
1 0 0

and o is a 3xr matrix.
From Table (A.1), a cointegrating vector (r=1) exist in
original four variables model (p=4). To test.the constraint of

price homogeneity, the test statistics is computed as

121*[1n(l-0.165)-ln(l-0.179)]=121*(-0.180+0.197)=2.05

which is not significant at 12(1). Therefore, price

homogeneity is assumed and three variables model with real
money(m), real income(y) and interest rate(r) are used in the

text.

 

2Sample period: 1961:3--l992:4, and a 0824 dummy variable
is added for the same reason.

APPENDIX E

Test for Price Homogeneity in Taiwan Honey Demand Function
from Wald Test:

Johansen (1991) shows that if only 1 cointegration vector
6 is presented (r=1), and if we want to test the hypothesis

K'fi=0, then the statistics

T(K’B) 3 I (if-1) (K’W’K) 1 '1

is asymptotically xg‘with 1 degree of freedom. Here i, is the
maximal eigenvalue and the 3 is the corresponding eigenvectors

of the equation

psu-skosggsog-o

The remaining eigenvectors form 6.
From Appendix.A‘we know that 4 variable (M, y, r, and P) in
Taiwan have a cointegration vector. Their eigenvector

(columnwise) by the descending order of eigenvalue are :

H -5.274 -13.876 0.239 -0.652
y 7.028 24.075 6.647 2.931
r -7.082 0.159 -0.054 1.632
P 9.303 10.657 -8.178 -5.451

147

K is {l O 0 1)‘ in this case. The estimated test statistics
therefore is 3.881 which is on the margin of 90 percent of
12(1) and not significant at 97.5 percent. Again, we do not
reject the hypothesis of price homogeneity from the Wald.Test

(although it is not so strong).

148

APPENDIX C

Test for Absence of Linear Trend In the Wonstationary Process

The constant term in an autoregressive model for
nonstationary variables gives rise to a trend. A constant
plays a crucial role for the interpretation of the model, as
well as for the statistical and the probabilisitic analysis.
In the context, a model with a constant is assumed, the
asymptotically distribution of the estimate and the test
statistics are all under the presence of the constant in the
model. I further investigate the hypothesis about the absence
of a linear trend in the stochastic process of the variables.

A model with real money (10) , real income (y), and interest

rate (r) are fitted into the model as equation (4.4) before :
H1: AX,=u+TD,+P1AX,.1+. . . .+I‘,.1AX,.,+,+IIX,_,+6,.

A constraint u=afi'o, or alternatively a'1u=0, which is a

hypothesis about the absence of a linear trend in the process,

is added in addition to the original H2 hypothesis. That is,

H2: =afi' and u=¢zfl'o

In calculation, we can write

149

150

“B’Xt-k+ U'GBIXt_R+GBS-¢B.’Xz_k

where B'=(fi', £0) and X',_,=(X',_,, 1).

The eigenvalues and eigenvectors (not normalized) under H;

are as fol lowing-I:

Eigenvalues 1':

0.1813 0.0999 0.0656 0

Eigenvectors V’

m 8.028 7.275 7.849 1.883
y -14.089 -11.928 -10.442 -4.645
r 5.962 0.997 -1.945 -0.721
1 64.546 61.570 37.468 34.985

Note that the eigenvectors under H; are of dimension 4. The
last rows of coefficients in the eigenvectors are the
estimated intercept (mean) in the cointegration vectors.

The test statistics for the hypothesis H; and H2 (repeated

 

3Sample period: 1961:3--1992:4. A 0824 dummy is added for
the same reason.

 

151

for ease of comparison) are in the following:‘

“2 Hz
trace l-max trace l-max
r52 8.22 8.22 r52 1.79 1.79
r51 20.96 12.74 r51 10.80 9.00
r-O 45.16* 24.20 r=0 33.93* 23.12*

* significant at 10 percent quantile.

There is no evidence in the data for more than one
cointegration relation both from hypothesis H; and H2. The
maintained assumption about the absence of trend in the data
is inconsistent since the test statistics for H; (r51) in H2

(r51) is:

(A- 1) -21n(Q;H; (1)IH2 (1) ) -T1nlls;ol(1-X§) /|s,,ol(1-11)}

--T1t 1n{(1-X‘,) / (1-1 1)}-45.16-33 .93-11.23 ,
-2

where I850} is defined in Johansen and Juselius (1990) and
Johansen (1991). The statistics is asymptotically distributed
as 12 with (p-r)=3-1=2 degree of freedom and therefore is
significant. We reject the hypothesis of the absence of a
linear trend in the nonstationary process of variables in
Taiwan money demand function. A constant is added in the VAR
1model explicitly and all sequent inferences are based on this
model.

‘Note: the critical value of the statistics are different
from that of Hz.

APPENDIX D

How to invert the Estimated VECH to a Hultivariate Version of
Wold's Decomposition in First Difference.
A VECH X, estimated by Johansen ML method,
AX,=u+§D,-l-I‘,AX,_1+. . . .+r,,,4X,_,,,+IIx,,,+6,,
We can easily invert it into a "reduced form" such as

equation (5.1). In the spirit of Baillie (1987), it is

particularly convenient to express the VECH in companion form

 

 

 

 

 

 

 

 

as
AX: ‘ - P1 . . . . I‘ _2 I',,_1 I a 'AXt-l 1 P3 :+U+°Dc.
AXt-l I 0 . . . . 0 I 0 AXt-z 0
0 I 0 I 0
- I e ' +
. . l . AXHM
[mym 0 0 . . . I 0 l 0 AxHm .
/

_B/Xt-k+1, .01.),p 0 . . . . fl I If, _ B’Xt-k. _ 0
or,
(A: 2) Yt=AYt-1+Ct

where Y, and C, are (p(k-1)+r)x1 in dimension and A is
(p(k-1)+r)x(p(k-1)+r) . The first p rows of this companion form
expression give the original VECH, while all the other rows

are identities.

152

 

153
From the VECH expressed as the enlarged stationary VAR(1)

in equation (A.2) we can by successive substitution show that

Y,-§A 1cm“! W0.

Hence eventually,
(11.3) lit-£301! Kw.
On defining a px(p(k-1)+r) dimensional selection matrix
N'=[IpI°].
we can premultiply equation (A.2) by N' to obtain

N ' Y,=N 'AY,-,+N' C, ,

hence,
AX,=(N'Y,,1)+(6,+u+§0,) .

That is again the original VECH form since N 'Y, is the first
p rows of A in equation (A.2). On premultiplying equation

(A.3) by N':

AX, - J'fiN’A th-j - 123(N’A’N) (e,_j+u+¢Dc_j) .
..o -0

 

154

=C (L) (6,+u+§D,) ,

which just is the expression in equation (5.1) that

AX,=y+C (L) 6, .

Hence for the VECH model the infinite HAR in first difference

coefficient matrices Cjare calculated as

C,=N'A’N, CO=I .

 

APPENDIX E

The goats in the Characteristic Polynomial of the man
Hodel

Consider a p-dimensional VAR(k) process as in equation

(4.3):
X,=u+§D,+II,X,,,+. . .+II,X,_,+6, , t=1, . . . ,T,
It can be written as
II (L) X,=u+00,+6, ,

where H(L)=Ip-II,L-...II,L", and L is the lag operator.

Hultiplying from the left by the adjoint H110. of H(L) gives
:II(L) :x,=II(L)*(u+40,+e,) .

Thus, the VAR(k) process can written as a VARHA process with
univariate AR operator, that is, all components have the same
AR operator {H(L) I . If gnu.) :=0 has d unit roots‘5 and
otherwise all roots7 outside the unit circle, the AR operator

can be written as

 

5Professor Rasche kindly provides me the calculation in
this appendix.

6:H(L): will totally have (pxk) roots.

7The modulus of the complex conjugates roots are greater
than one.

155

156

mu.) l=e(L) (1-L)‘=e(L)A'.

where 8(L) is an invertible operator. This guarantees that the

nonstationarity of X, can be removed by differencing“.

In our case estimated from a VAR(S) model’, the fifteen
roots in the form of (a+bi) are (a, b)=(l, 0), (l, 0), (1.06,
-0.24), (1.06, 0.24), (-1.07, 0), (1.16, -0.64), (1.16, 0.64),
(1.20, -1.05), (1.20, 1.05), (-.44, -1.38), (-.44, 1.38),

(-2.09, -1.11), (-2.09, 1.11), (.39, -1.94), (.39, 1.94).

Three roots are real (b=0) , and two of them are unit roots.
All roots other than the two "unit root" are outside the unit
circle as judged from the modulus of each root.

There is a negative real root (-1.07, 0), such that

 

I’This is a basic assumption of Johansen's HLE. See also
footnote 11 in Chapter 4.

9The estimated coefficient matrices are

1.1607 0.1537 -0.1161‘ -0.2182 -0.2915 0.04915
“1' 0.1346 0.7651 0.0364 11,- -0.1548 -0.1134 -@.09176
-0.2154 -0.4297 1H2921. 0.3862 0.1681 -0.4360
-0.1188 0.0838 -0.0084‘ 0.0876 -0.0066 0.0041

113- 0.1609 0.0900 0.0707 II,--0.2496 0.7481 -0.0847
0.5383 0.0560 0.4517, -0.2025 0.1495 -0.2769

 

-0.0368 0.2738 -0.0023
Ig- 0.1088 -0.4898 0.0693
-0.5065 0.0560 -0.0308

157

-0.93.

 

 

-1.07

It makes a slow decaying to the process since

1 2 2 3 4 4
— - -. .9 L - . g _ ....... '
[1,033 ] 1 93L+( 3) ( 93) L+( 93) L

which made the process oscillatory for a long period before it
is fully dominated by the unit roots as seen in figure (9)--
(14).

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