stability of money demand function in nepal
TRANSCRIPT
STABILITY OF MONEY DEMAND FUNCTION IN NEPAL
A Thesis
Submitted to the Central Department of Economics,
Tribhuvan University, Kirtipur, Kathmandu, Nepal,
in Partial Fulfillment of the Requirements
for the Degree of
MASTER OF ARTS
in
ECONOMICS
By
SIDDHA RAJ BHATTA
Central Department of Economics
Tribhuvan University, Kirtipur
Kathmandu, Nepal
March 2011
LETTER OF RECOMMENDATION
This thesis entitled “STABILITY OF MONEY DEMAND FUNCTION IN NEPAL”
has been prepared by Mr. Siddha Raj Bhatta under my supervision. I hereby
recommend this thesis for examination to the Thesis Committee as a partial
fulfillment of the requirements for the Degree of MASTER OF ARTS in
ECONOMICS.
________________________
Mr. Ananta Kumar Mainaly
Associate Professor
Thesis Supervisor
Date : .............................
APPROVAL SHEET
We clarify that this thesis entitled "STABILITY OF MONEY DEMAND
FUNCTION IN NEAPL" submitted by Mr. Siddha Raj Bhatta to the Central
Department of Economics, Faculty of Humanities and Social Sciences, Tribhuvan
University, in partial fulfillment of the requirements for the Degree of Masters of
Arts in Economics has been found satisfactory in scope and quality. Therefore, we
accept this thesis as a part of the said degree.
Thesis Committee
___________________________
Prof. Dr. Rudra Prasad Upadhyay
Head of Department
___________________________
Dr. Yuba Raj Khatiwada
Governor, Nepal Rastra Bank
External Examiner
________________________________
Associate Prof. Ananta Kumar Mainaly
Thesis Supervisor
Date : ............................
ACKNOWLEDGEMENTS
This thesis entitled "STABILITY OF MONEY DEMAND FUNCTION IN
NEPAL" has been prepared for partial fulfillment of the requirements for the
Degree of Masters of Arts in Economics.
I am pleased to take this opportunity to express my heartfelt gratitude to my
thesis supervisor Associate Prof. Ananta Kumar Mainaly, the Central
Department of Economics, University Campus, Kirtipur, Tribhuvan
University for his valuable guidance, encouragement and suggestions
throughout my work. Similarly, I am grateful to Prof. Dr. Rudra Prasad
Upadhyay, the Head of the Central Department of Economics for his
suggestions and guidance. I also feel privileged to express my gratitude to all
the teachers of Central Department of Economics for their gracious response
to my queries.
I would like to thank all the non-teaching members of Central Department of
Economics and all the staff members of Central library, T.U. Kirtipur, for the
help they extended to me during this study in very many ways.
I want to extend my indebtedness to Dr. Tap Prashad Koirala, Research
Division, Nepal Rastra Bank, and Mr. Dadhi Adhikari, lecturer of Central
Department of Economics for their help in data transformation. Similarly, my
heartfelt thanks goes to Mr. Naveen Adhikari, Mr. Resham Thapa and Mr.
Khagendra Katuwal, the lecturers of Central Department of Economics for
their invaluable guidelines.
I am heartily indebted to my friend Miss Sapana Singh who encouraged me all
the moment to complete this work in time.
I bear sole responsibility for any errors and discrepancies that might have
occurred in this research report.
Siddha Raj Bhatta
March, 2011
TABLE OF CONTENTS
ACKNOWLEDGEMENTS iv
LIST OF TABLES viii
LIST OF FIGURES ix
LIST OF ACRONYMS x
CHAPTER I: INTRODUCTION 1-7
1.1 Background of the Study 1
1.2 Statement of the Problem 3
1.3 Objectives of the study 4
1.4 Significance of the study 5
1.5 Limitations of the study 6
1.6 Organization of the study 7
CHAPTER II : REVIEW OF LITERATURE 8-23
2.1 Introduction 8
2.2 Theoretical Review 8
2.2.1 Classical View 8
2.2.2 Neo-Classical View/Cambridge Cash Balance Approach 9
2.2.3 Keynesian Approach 10
2.2.4 The Inventory-Theoretic Approach 12
2.2.5 The Portfolio Balance Approach 13
2.2.6 Modern Approach 13
2.2.7 McKinnon Approach 14
2.2.8 Implication of the Theories for Nepal 15
2.3 Review of International Empirical Studies 15
2.4 Review of National Empirical Studies 20
2.5 Conclusion 23
CHAPTER III: DATA AND METHODOLOGY 25-43
3.1 Introduction 25
3.2 The General Model 25
3.3 Selection of Variables 25
3.3.1 Scale Variable 25
3.3.2 Opportunity Cost Variable 26
3.4 The Empirical Model 27
3.5 Estimation Methodology 29
3.5.1 Autoregressive Distributed Lag Model (ARDL) to Cointegration
Analysis 30
3.6 Hypothesis 31
3.7 Econometric Tools 32
3.7.1 Time Series Properties of the Variables 32
3.7.2 Cointegration 33
3.7.3 Error Correction Modeling 34
3.7.4 Diagnostic Tests and Other Test 35
3.8 The Data 42
CHAPTER IV : DATA ANALYSIS 44-60
4.1 Time Series Properties of the Variables 44
4.2 Estimation Results 47
4.3 Estimation Results 57
CHAPTER V: SUMMARY, CONCLUSIONS AND RECOMMENDATIONS
61-64
5.1 Summary of the Findings and Conclusions 61
5.2 Recommendations 63
APPENDIX 65
REFERENCES 76
LIST OF TABLES
Table 3.1 : Variable Details 28
Table 4.1 : ADF Test Results 46
Table 4.2 : F-statistics (Bound Test) 47
Table 4.3 : Full-information ARDL Estimate Results(M1 monetary
aggregate) 49
Table 4.4 : Estimated Long Run Coefficients using the ARDL
Approach(M1 Monetary Aggregate) 51
Table 4.5 : Error Correction Representation for the Selected ARDL
Model(M1 Monetary Aggregate) 53
Table 4.6 : Full-information ARDL Estimate Results(M2 monetary
aggregate) 54
Table 4.7 : Estimated Long Run Coefficients using the ARDL
Approach(M2 monetary aggregate) 55
Table 4.8 : Error Correction Representation for the Selected ARDL Model
(M2 monetary aggregate) 57
LIST OF FIGURES
Figure 1 : Time Series Plot of ln m1t, ln m2t and ln yt 45
Figure 2 : Time Series Plot of rsdt and rfdt 45
Figure 3 : Time Series Plot of rrsdt and rrfdt 45
Figure 4 : Plots of CUSUM Statistics (M1 Aggregate) 58
Figure 5 : Plots of CUSUMSQ Statistics (M1 Aggregate) 59
Figure 6 : Plots of CUSUM Statistics (M2 Aggregate) 59
Figure 7 : Plots of CUSUM Statistics (M1 Aggregate) 60
LIST OF ACRONYMS
AIC - Akaike Information Criterion
ARDL - Auto Regressive Distributed Lag Model
CBS - Central Bureau of Statistic
FY - Fiscal year
GDP - Gross Domestic Product
JB - Jarque Berra Test
LM - Lagrange Multiplier Test
IMF - International Monetary Fund
MOF - Ministry of Finance
OLS - Ordinary Least Squares
NRB - Nepal Rastra Bank
RESET - Regression Specification Test
SBC - Schwarz Bayesian Criterian
UK - United Kingdom
USA - United States of America
CHAPTER I
INTRODUCTION
1.1 Background of the Study
The demand for money is one of the key functions in all macroeconomic models of
the economy. A sound monetary policy formulation presupposes theoretically
coherent and empirically robust model of money demand. The stability of money
demand function is crucial for the effectiveness of monetary policy in offsetting the
fluctuations that may arise from the real sector of the economy. Given the importance
attached to money demand in the success or failure of an activist monetary policy, it is
not surprising that the demand for money is one of the most controversial and heavily
researched areas in macroeconomics (Bose and Rahman, 1996).
A good understanding of the determinants of the demand for real money
balances in the economy by investigating the behaviour of the money demand
function is crucial for the formulation and implementation of an effective
monetary policy. Moreover, the identification of a stable relationship between
the demand for money and its determinants provides empirical evidence that
the monetary targeting is an appropriate framework for economic stabilization
policy (Rutayisire, 2010). That is, if the demand for real balances has a
consistent or stable relationship with its determinants, the changes in money
stock has predictable effects on income and output and the required change in
the money stock to restore the equilibrium in the economy can be easily
worked out. This is what needed for the stability of the economy. In such a
case, the central bank can bring the desired changes in the economy by using
monetary aggregate as a target variable. Thus, if the central bank relies on
control of monetary aggregates as its policy instrument, it must believe in a
known and reliable connection between changes in that aggregate and changes
in the arguments of the money demand function in order for its policy to have
predictable effects on those arguments. If instead the central bank relies on
interest rates as targets and adjusts the monetary aggregate through daily
reserve management to whatever level is required to hit them, instability of
the demand for money could make the required reserve changes both large
and unpredictable. Disorderly financial markets might well result (Cameron
1979).
In the monetarists‟ type of transmission mechanism, stability of the demand
for money function has a decisive role for the effect of money supply on
income and prices. If the demand for money is stable, any change in money
supply has a direct effect on aggregate expenditure. Whether this change will
affect real income or price or both depends on whether the economy is at full
employment or less than full employment. If the demand for money is not
stable, (i.e. velocity of money circulation is fluctuating), any change in money
supply can just be offset by equal and opposite change in velocity (through
idle hoarding/dishoarding of cash balance) having no effect on income or
prices. So, to analyze the transmission mechanism of monetary policy, the
specification of the demand for money function, test of its stability and
estimation of its elasticities is highly essential (Laidler, 1971).
Thus, for any central bank, stability issue of the money demand function is
one of the most important guiding policy issues that helps to decide whether
to use the monetary targeting strategy or inflation targeting strategy in the
monetary policy in bringing the desired changes in the economy. This issue
has been triggered further by the abandonment of monetary targeting strategy
by many developed countries such as Canada, Newzeland, Brazil, Turkey,
Norway, Australia etc as they switched to inflation targeting strategy. Stability
of the demand for money function is, therefore, the focus point for any central
bank.
In this context, an assessment of the monetary policy of Nepal requires first to
test the stability of money demand function. The central bank of Nepal has
been using both the narrow money stock and broad money stock as the
intermediate targets of the monetary policy. Especially after the adoption of
financial liberalization in the 1980s, there may have been the forces that might
have caused the instability in money demand and rendered the monetary
policy ineffective. Thus, this study mainly focuses on the stability of money
demand function in Nepal.
1.2 Statement of the Problem
After the implementation of liberalization program in 1980s, the Nepalese
economy has gone through some significant structural and institutional
changes. These changes included the liberalization of the external trade and
payment systems, substantial degree of financial deepening and innovations in
the banking sector, the elimination of price and interest rate controls, changes
in monetary policy, and the emphasis on market determined indirect
instruments of monetary policy. It is conceivable that these developments may
have altered the relationship between money, income, prices, and other key
economic variables; and this may have caused the money demand function to
become structurally unstable. Consequently, determining whether the
financial reforms undertaken under the liberalization program have affected
the stability of the money demand relationship is important to the effective
formulation and implementation of monetary policy. Nepal started the
financial liberalization process with partial deregulation of the interest rate in
1984. Since then, various liberalization measures have been implemented in
phases, which include removal of entry barriers of banks and financial
institutions (1984), reforms in treasury bills issuance by introducing open
market bidding system (1988), introduction of prudential norms (1984), full
deregulation of interest rates (1989), establishment of Credit Information
Bureau for providing information on borrowers (1989), shift in monetary
policy stance from direct to indirect (1989), reform in capital markets through
the establishment of Security Exchange Company and introduction of floor
trading (1992), reduction in statutory reserve requirement (1993), and
enactment of Nepal Rastra Bank Act (2001) and Debt Recovery Act (2002).
The above measures were aimed at “widening” and “deepening” of the
financial sector in Nepal.
Due to the extensive liberalization process, the effects of monetary policy may
be transmitted to the real sector of the economy, because of relaxation of
direct control over the interest rate. So, money demand function might have
been unstable. The implications of this is the change in the relationship among
money, income, interest rate and hence the effectiveness of monetary policy.
Financial market development through reform measures may lead to new
financial assets with attractive yield. This may shift portfolio from the
monetary assets. Transaction costs often go down due to competition among
financial institutions and hence money demand may respond more rapidly to
interest rate changes. The holding of monetary aggregates may be affected by
the development of rural banking through shifting fund from informal sector
to the banking sector. Thus the financial reform have implications for the
stability of the money demand function and hence the conduct of monetary
policy (Khan and Wadud, 2003).
With the passage of time, the scope of monetary policy is getting wider. It
aims at price stability, economic growth, full employment etc. In Nepal also,
Nepal Rastra bank is being entrusted with a number of objectives since its
establishment in 1956. The intermediate target chosen for the conduct of
monetary policy in Nepal are the monetary aggregates M1 and M2. The first
and foremost condition for these intermediate targets to work in achieving
final goals is a stable money demand function. In such a context, the present
study is focused on answering the following questions:
Is there any significant long run equilibrium relationship among real
money balances, the scale variable (real GDP) and the opportunity cost
variable (interest rate) in Nepal?
Is the relationship between demand for real money balances with its
determinants stable in Nepal?
Are the monetary aggregates used as intermediate targets appropriate
for Nepal?
1.3 Objectives of the study
The general objective of this study is to analyze the money demand function
of Nepal for narrow and broad monetary aggregates and examine their
stability so as to provide some policy recommendations to the central
monetary authority for designing the monetary policy.
The specific objectives of this study are:
1. To examine whether there exists a long run cointegrating relationship
between the demand for real money balances and its determinants or
not.
2. To examine the long run money demand function and the short run
dynamics in the money demand function.
3. To examine whether the relationship between the demand for real
money balances and its determinants is stable or not in the long run
and
4. To provide suggestions to the central monetary authority about whether
to use monetary targeting strategy or inflation targeting strategy.
1.4 Significance of the study
A stable money demand function forms the core in the conduct of monetary
policy as it enables a policy-driven change in monetary aggregates to have
predictable influences on output, interest rate and ultimately price. Because of
its importance, many studies have been carried out worldwide in the last
several decades (Sriram, 1999).
Empirical research on the money demand function is of utmost interest
because the information on its structure is very useful for policy makers in
designing effective monetary policy. Due to this importance, many studies on
money demand function in both developed and developing countries have
been conducted in the past.
The study on stability of money demand function in Nepal is of utmost
interest for several reasons. Firstly, demand for money and its stability have
important implications for the selection of the monetary policy instruments
and for the conduct of monetary policy. According to Poole (1970) interest
rate should be selected as the monetary policy instrument when the LM curve
is unstable and money supply should be the instrument when IS curve is
unstable. If the choice of the monetary policy instrument is inappropriate, then
monetary policy will increase the costs of stabilization. Since instability in the
demand for money is a major factor contributing to instability in the LM, it is
important to test for the stability of the demand for money. Many developed
countries have switched to interest rate as the monetary policy instrument
when their money demand functions have become unstable following the
financial reforms from the second half of the 1980s. Secondly, there are
remarkable changes in both financial sector and economy as a whole after the
adoption of liberalization policies in the 1980s as a result of which the number
of financial institutions has been grown rapidly. According to Bordo and Jung
(2004), the development of financial institutions could be a stronger source of
instability of money demand function which can make monetary policy
ineffective. Researches on the stability of money demand in the face of
ongoing financial reform program are still lacking in Nepal. Thus, there is a
need to test the stability of money demand function. Thirdly, estimates of the
demand for money are useful to understand the limits to non-inflationary
seignorage revenue and for the formulation of monetary policy targets.
Fourthly, the unit roots and cointegration literature has made significant
impact on modeling dynamic economic relationships and especially on the
demand for money. Finally, it is widely known that, the currency substitution
phenomenon by the growing number of other financial assets may cause the
instability of money demand function. This affects the effectiveness of
monetary policy. Thus, there is a growing need to test the money demand
relationship in Nepal using the recently developed econometric tools of
cointegration and error correction modeling as it can determine the power of
predictability for the behavior of monetary policy. This study aims at fulfilling
this objective and providing information to the policy makers to the usefulness
of monetary aggregates as intermediate targets of monetary policy.
1.5 Limitations of the study
The study has the following limitations:
1. The study covers the time series data from FY 1974/75 to FY 2008/09
only.
2. It is based on annual data as there is no availability of quarterly data
figures on GDP in Nepal.
3. Current inflation has been used as a proxy for expected inflation.
1.6 Organization of the study
The present study is organized in five chapters. The first chapter is an
introductory part of the study covering the background of the study, statement
of the problem, objectives of the study, rationale and study limitations. The
second chapter covers the review of some of the theories concerning the
demand for money and review of empirical studies at national and
international level. The third chapter provides a glimpse of the methodology
used. The fourth chapter covers the analysis of data and finally, the fifth
chapter presents the summary, conclusions and recommendations.
CHAPTER II
REVIEW OF LITERATURE
2.1 Introduction
In literature, money demand function has been studied using both „velocity‟
and „conventional‟ formulation. In comparison to the relatively limited
literature on the velocity, „conventional‟ money demand function attracted a
large number of researchers, primarily because it is easy to understand the
formulation (Omer, 2010). Even if one starts with the Post Bretton Woods
Period, Goldfeld (1973), Boughton (1981), Arango and Nadiri (1981), Butter
and Fase (1981), Mehra (1991), etc are a few among the vast pool of the
authors who made a significant contribution in this field, banking on the
conventional models. The conventional models also have been analyzed by
using different methodologies. Among them are simple linear model, log
linear model, semi log linear model, partial adjustment model, autoregressive
distributed lag model, Almon polynomial lag model, Vector error correction
model etc. A recent technique is the cointegration analysis and use of error
correction modeling to time series modeling used in the money demand
function. This chapter presents a brief review of some of the theories
concerned with the demand for money in section 2.2. Section 2.3 presents the
review of the empirical studies on the money demand function at international
level; section 2.4 presents a brief review of the studies on money demand
function at national level and conclusion from the reviews has been discussed
in section 2.5.
2.2 Theoretical Review
Different economists have raised their different views regarding the demand
for money. The various views can be outlined as below:
2.2.1 Classical View
Classical economists were not explicitly concerned with the demand for
money but it can be derived from the quantity theory of money as proposed by
Fisher. The classical quantity theory can be written as:
MV=PT………………………………………………………………..... (2.1)
Where,
M=stock of money,
V=transaction velocity of money
P= general price level and
T=volume of transaction in the economy
Here V and T are assumed to be constant in the short run.
Though the equation MV=PT is an equation for determining the price level in
the economy as money supply changes. The variables used in this equation are
significant enough to derive the theory of the demand for money. For this, this
equation can be written as:
Md=
v
1PT…………………………………………………………..... ..(2.2)
Equation (2.2) implies that a constant fraction of the total volume of
transactions is demanded to keep in the form of money for transaction
purposes.
2.2.2 Neo-Classical View/Cambridge Cash Balance Approach
The Cambridge cash balance approach associated particularly with Marshall
and Pigou argues that other things remaining the same, the demand for money
of an individual depends upon his income .i.e.
Md=k(py)……………………………………………............................(2.3)
Where,
Py = nominal income,
k = proportion of money income that one likes to hold as cash balance and k
depends on institutional factors.
This implies that a constant fraction of money income is demanded as demand
for money. This equation seems quite similar to Fisher‟s equation except that
k=1/v. Thus, factors affecting the velocity of money are responsible to
determine k.
The main features of cash balance equation can be outlined as:
i) It makes the demand for money a function of money income and only
of it.
ii) The Cambridge economists did recognize that other variables such as
the rate of interest, wealth etc influence the value of k and thus the
money demand. But they were not able to incorporate these variables
systematically in their analysis.
iii) Md is a proportional function of money income and price,
iv) The income elasticity and price elasticity of money demand are unity
so that money demand is a homogeneous function of degree one in
price.
2.2.3 Keynesian Approach
In the Keynesian view, the desire for money is a demand for liquidity
preference. He presented three motives for holding money: transaction,
precautionary and speculative motives. The first motive arises because money
is needed to finance daily purchase of goods and services or money is required
to bridge the gap between the receipt of income and expenditure and to meet
the time interval between incurring business costs and receipts of sales. The
amount of money demanded for this purpose is expected to vary directly with
the level of income.
The precautionary motive arises to provide for future contingencies like
accident, sickness etc. The money balance for this purpose is also expected to
vary with the level of income.
Keynes has lumped together the transaction and precautionary demand on the
grounds that both are fairly stable functions of income which can be written
as:
M1 = f1(Y) ∂M1/∂Y>0…………………………………………………(2.4)
Where,
M1=amount of money demanded for transaction and precautionary purposes
and,
Y = level of income
The most significant contribution made by Keynes is his analysis of money
demand is the speculative demand for money. To him, people demand some
amount of money for speculation, i.e. for making profit due to rise/fall in the
rate of interest. Considering only two financial asset-world, he concluded that
in deciding whether to hold money or bonds, investors would take account of
the prospective capital gain or loss in holding bonds and interest rate as well
(Cuthberston:1988). If the investors feel that the interest is too low and they
expect it to rise, the value of the bond is expected to fall and the investors hold
cash to avoid capital losses. Similarly, if investors feel that interest rate is too
high so that it cannot rise further and the only expectation is a fall in the
interest rate, in such a case investors hold bonds because with the fall in the
interest rate, bond price will rise and accordingly there will be capital gains.
Thus, the speculative demand for money depends inversely on interest rate
which can be written as:
M2 =f2(r); ∂M2/∂r <0………………………………………………....... (2.5)
Where,
M2 =speculative balances
r = interest rate
Lumping equations (2.4) and (2.5) together,
M = M1+M2 = f1(Y) + f2(r)……………………………………………..(2.6)
Where,
∂M/∂Y>0, ∂M/∂r <0
M=total demand for money balances
Thus in Keynesian approach, the transaction demand follows Cambridge
tradition, but the demand for money in aggregate is determined by the
speculative behavior of individuals also.
2.2.4 The Inventory-Theoretic Approach
Baumol (1952) has argued that the cash held by people for transaction is like
an inventory or stock of capital and thus until otherwise needed, it can be
invested in short term bonds. Thus transaction demand for money is interest
rate sensitive but only at a higher rate of interest. The goal in holding money
balance is to minimize the total cost of holding money which comprises of
brokerage fee and interest cost. The money demand function as argued by
Baumol can be written as:
M/2 = i
bY
2;……………………………………………………….(2.7)
Where M/2 is the average demand for money balance for transaction purpose,
b = brokerage fee per conversion while converting bonds into cash
Y = total nominal income
i = market rate of interest
This demand function shows that:
i) Transaction demand for money is inversely related with the rate of
interest and is thus interest rate-sensitive but only at a higher interest
rate.
ii) Transaction demand is non-proportionately related to income as against
the proportional relationship established by earlier theories.
iii) Elasticity of money demand with respect to interest rate is less than
unity.
iv) Income elasticity of demand for money is less than unity. It shows that
a person with higher income holds less cash and there are economies of
scale in cash management.
2.2.5 The Portfolio Balance Approach
Tobin (1959) has analyzed the speculative demand for money incorporating
the uncertainty and risk and concluded that individuals hold a combination of
cash and bonds so as to optimize the return on bonds and minimize risk. With
this portfolio optimization theory, he reaches the conclusion that the risk
factors and uncertainty also play important role in speculative demand for
money. However, his theory produces similar results as the speculative
demand for money as Keynes.
2.2.6 Modern Approach
Milton Friedman (1959) the leader of monetarism, restated the classical
Quantity Theory of money. To him, money is one kind of asset in the whole
portfolio of assets, a capital good, and a source of productive services. He
attempted to clear the conceptual framework of the quantity theory with the
assertion that the demand for money does not become infinitely interest elastic
but it is relatively interest inelastic (Patinkin:1972).
His money demand function can be written as:
Md = f(Y, h, P, R, π, µ)………………………………………….. (2.8)
Where,
Md = money demand,
Y = permanent income,
h = ratio of human to non-human wealth,
P = price level,
R = vector of interest rates,
π = inflation and
µ = a variable incorporating tastes and preferences
The restrictions to this demand functions are:
fR <0, fh>0, fπ<0, and fy>0
To Friedman, the money demand function represented by equation (2.8) is
homogeneous of degree one in price showing the demand for real balance, i.e.
Md/p = f(Y/P, h, R, π, µ)……………………………...…………….... (2.9)
The major issue raised by Friedman is the stability of the money demand
function. To him, money demand function is highly stable which implies the
stability of the velocity of money.
2.2.7 McKinnon Approach
McKinnon (1973) has opined that due to the underdevelopment of capital and
financial markets and the poor performance in the underdeveloped countries,
the theories for the demand for money in developed countries do not fit the
scenario of underdeveloped countries. He thus has argued that due to
underdevelopment of capital market, there exists complementary relationship
between the demand for money and the demand for physical capital. In such a
case, the money demand function can be represented as:
(M/P)d = f(Y, I/Y, d-
*p )………………………………………………..(2.10)
Where,
fY
'
>0, fYI
'
/>0, and
*
' .d p
f
>0
(M/P) = real money demand,
Y = real income,
I/Y = investment income ratio,
d-
*p = real rate of return from money,
d = nominal rate of return from money,
*p = expected rate of inflation
2.2.8 Implication of the Theories for Nepal
If the financial market imperfections, political instability, risks and
uncertainties are kept in mind, it becomes clear that the demand for money in
Nepal may be less sensitive to interest rate. Since capital and money markets
are not well-developed, the security market, bond market etc are not well-
practiced; the speculative demand for money may be inoperative. Since the
elasticity of interest rate is low, Baumol‟s approach has less significance in
Nepal (Gaudel, 2003). Similar is the case with Tobin‟s and Friedman‟s
analysis. This leads us to the classical economic world. As argued by Prasad
and Sampath (1977), people in underdeveloped countries obtain cash for
transaction purpose first by borrowing it and withdrawing it from investment,
secondly by withholding it from cash receipts and thirdly by withdrawing and
withholding. Thus, interest elasticity of demand for money would become
almost zero. Johnson (1963) has recommended the possibility of keeping a
block of cash by an individual out of his remuneration, investing the rest in
assets thereby reducing the interest elasticity of money demand less than
unity.
This suggests that a simple model on quantity theory approach would perform
better than the Keynesian approach in the context of developing countries like
Nepal.
2.3 Review of International Empirical Studies
Reviews of some of the studies using different approaches at international
level are as follows:
Taylor (1993) has estimated the short run and long run demand for broad
money for United Kingdom using high quality data from 1871-1913 applying
recent econometric technique of Johansen‟s Maximum likelihood approach to
cointegration and has discovered a unique, statistically significant long-run
money demand function relating broad money, prices, real income and the
long-term interest rate, which displays price and income homogeneity and a
plausible long-run interest rate semi-elasticity. Cointegration estimates to
model short-run adjustment in money demand in which short-term interest
rates and the own rate of return on money were found to be important, and
which returned the long-run estimates as the steady-state solution. This short-
run demand function was found to be superior to previous estimates for this
period on statistical grounds. It fitted well with well-determined coefficients
and shows no sign of structural instability.
Lumas and Mehra (1997) have analyzed the stability of demand for money
in USA using annual data for the period 1900 to 1974 using the varying
parameter approach developed by Cooley and Prescott (1973). They found
that the demand for money equations which regress money (M1 or M2) on
income and interest rates but omit a lagged value of the dependent variable are
not stable. This result is consistent with the observation that there are lags in
the adjustment of actual to desired money stock and hence stability requires
the specification of the adjustment mechanism in the money demand function.
Hamori and Hamori (1999) have found the demand for money in Germany
unstable. They have also used cointegration analysis with the quarterly data
from 1969:Q1 to 1996:Q3. The included variables are real GDP, M1, M2, M3
and call rates. They have used chow test to test the stability of the money
demand function.
Bahmani-Oskooee (2001) has tested the stability of money demand in Japan using
ARDL modeling to cointegration analysis by using the quarterly data from 1964 to
1996 and found that demand for broad money is stable. The included variables are
M2, real income and interest rate. With the help of CUSUM and CUSUMSQ test, he
has found a stable relationship in the money demand function.
Bahmani-Oskooee and Chi Wing Ng (2002) have examined the long run demand
for money in Hong Kong using the ARDL cointegration procedure on the quarterly
data from the first quarter of 1985 to the fourth quarter of 1999. They have concluded
that M2 is cointegrated with its determinants real income, domestic interest rate,
foreign interest rate and foreign exchange rate and all the coefficients have been
found to be significant. The long run income elasticity and domestic interest rate
elasticity have been found to be 1.730 and .038 respectively. They have used the
CUSUM and CUSUMSQ test to confirm the stability of the money demand function
and found it stable. Their study has suggested that in addition to the conventional
scale and domestic interest rate variable, the foreign sector consideration do matter in
explaining the variation in the broad money aggregate for a highly open economy like
Hongkong. The coefficient of exchange rate has been found to be positive supporting
the result that currency depreciation would reduce the demand for domestic currency.
Bahmani-Oskooee and Hafez (2005) have also used the ARDL modeling for a
number of countries like Singapore, Malaysia, India, Indonesia, Pakistan, Philippines
and Thailand. The sample period used is 1972:Q1 to 2000:Q4. The included variables
are real M1, real M2, real GDP, inflation rate and exchange rate. Their study has
shown that demand for M1 is stable in India, Indonesia and Singapore while in other
countries M2 is stable.
Halicioglu and Ugur (2005) have empirically analyzed the narrow money
demand function in Turkey over the period 1950 to 2002. The variables
included are real narrow money stock per capita, real national income per
capita, interest rate on alternative assets and nominal exchange rate. The study
has shown that there is a long-run relationship between the narrow money
aggregate (M1) and its determinants: national income, interest rate and
exchange rates. The methodology used is the single equation cointegration
technique, ARDL as proposed by Pesaran et al. (2000). The long run income
elasticity and interest rate elasticity from ARDL (1,0,0,0) model have been
found to be 0.93 and -0.01 respectively. The CUSUM and CUSUMSQ
stability tests indicate that there exists a stable money demand function
implying that narrow money aggregate can be used as an intermediate target
variable of monetary policy in Turkey.
Akinlo (2006) has used the ARDL modeling to test the stability of the demand for
money in Nigeria by using the quarterly data from 1970:Q1 to 2002:Q4 and found
that the variables M2, real GDP, nominal exchange rate and interest rate are
cointegrated. The CUSUM and CUSUMSQ tests reveal that a stable relationship
exists between the variables.
Bahmani-Oskooee and Bahmani (2007) have examined the money demand
function for broad money balances in Iran in the post revolutionary period of
Islamic Revolution 1979 considering the data set from 1979 to 2007. They
also have applied the ARDL modeling approach to cointegration analysis
including the variables: real GDP, inflation, exchange rate and a volatility
measure of the real exchange rate. Their examination has concluded that the
variables included in the money demand function are strongly integrated.
Their conclusion is that the M2 money demand function of Iran in the study
period is stable as such the revolution has not led to the parameter instability
of the money demand function. The estimated long run income elasticity is
1.0086 and the coefficient of inflation -3.18. The long run coefficients of
exchange rate and exchange rate volatility index have been found to be -0.14
and -0.17 respectively. All the coefficients are significant. Thus, their study
has argued that in addition to Mundell‟s theory on exchange rate being an
important determinant of the demand for money, exchange rate volatility also
serves as another important variable that impacts demand for money and
should therefore be included in the money demand function. Further, the study
has revealed that indeed, exchange rate volatility has both short-run as well as
long-run effects on the demand for real M2 monetary aggregate in Iran during
the post revolutionary period of 1979 to 2007, and is therefore a very
important determinant of demand for money.
Ahmed and Islam (2007) have empirically explored the long run equilibrium money
demand relationship as well as the short run dynamics in the context of Bangladesh
for M2, M1 and M0 using the Johansen and Juselius multivariate cointegration
analysis using the quarterly data from 1990 to 2006. This study has revealed that there
exists a statistically significant long run equilibrium relationship among real money
balances of various types, real income and respective nominal interest rates. The long
run demand for broad money and narrow money depend positively on real income
and negatively on the respective interest rates. The demand for real balances in the
economy is strongly dominated by the transaction motive for holding money as shown
by the elasticity of real income.
Bahmani-Oskooee and Wang (2007) have studied the stability issue in Chinese
money demand function with ARDL modeling to cointegration and found that in
China; M1 money demand function is stable while M2 money demand function is not
during the study period 1983:Q1 to 2002:Q2. The included variables are real income,
domestic interest rate, foreign exchange rate and the nominal effective exchange rate.
The estimated income elasticities are 1.28 for narrow money demand and 1.69 for
broad money demand respectively. On the other hand, the domestic interest rate
elasticities are -4.52 for narrow money demand and -1.54 for broad money demand
respectively. They have recommended that Chinese central bank should use M1
monetary aggregate rather than M2 in implementing monetary policy. The stability
issue has been examined by applying CUSUM and CUSUMSQ tests to the residuals
of error correction model.
Samreth (2008) has also used the ARDL modeling to cointegration analysis in
Cambodia with the monthly data from 1994:12 to 2006:12. His study has found that
there exists cointegration among the variables included in the money demand function
which are real income, inflation, exchange rate and real narrow money balances (M1).
The estimated elasticity coefficients of real income and inflation are positive and
negative respectively as expected. The long run income elasticity has been found to be
1.75 while the coefficient of inflation has been found to be -19.91. The coefficient of
exchange rate is negative supporting the currency substitution phenomenon in
Cambodia. The estimated results have further shown that the political turmoil in
Cambodia has no impact on money demand function. The CUSUM and CUSUMSQ
tests have revealed reveal that estimated model is roughly stable.
Ashsani (2010) has compared the estimation results from vector error correction
modeling (VECM) and ARDL modeling to cointegration analysis to money demand
in Indonesia. The results suggest that there was a cointegrating relationship among
real broad money aggregate (M2), real income and interest rate in Indonesia during
the study period. The ARDL modeling was found better than VECM in terms of
stability of the model, significant error correction term and other indicators like R-
square and R-bar square. The ARDL model was stable while VECM was not stable.
The estimated long run income elasticity was 3.20 and interest rate elasticity was
0.0819. The applied stability tests are CUSUM and CUSUMSQ. The study has
covered the sample period from 1990:Q1 to 2008:Q3.
Omer (2010) by using the ARDL Model has found that in Pakistan the
velocities of M0 (reserve money) and M2 are independent of interest rate and
depend on income and business cycle fluctuations where as velocity of M1
significantly depends on interest rate. This implies that M0 and M2 (broad
money) can be used as nominal anchors for operational and the intermediate
targets, respectively. He has also found that there exists a stable and long run
relationship between money velocities and its determinants such as, per capita
real permanent income, and transitory income. His Study has covered the
annual data from 1975 to 2006.
2.4 Review of National Empirical Studies
Empirical studies at the national level using the latest techniques of cointegration and
error correction modeling are still lacking. The main problem behind this is lack of
sufficient data observations, lack of high frequency data etc. Some of the studies
relating to money demand function and test of its stability in Nepalese context are as
follows:
Poudel (1987) has estimated the money demand function of Nepal using the data
sample 1974/75 to 1986/87. He has concluded that:
i) The demand for narrow money in Nepal is highly stable.
ii) Aggregate real income is highly statistically significant determinant of
the demand for all types of money defined in real terms.
iii) The income elasticity of the demand for M1 is greater than unity lying
in the range of 2.31 to 2.47 implying that money is a luxurious
commodity.
iv) The nominal rate of interest is not the appropriate rate in explaining the
demand for real money balances in Nepal but the real rate of interest
turns out to be a significant variable.
v) The income elasticity of the demand for time deposits is 3.77.
vi) The broad money has also more than unitary income elasticity whose
magnitude is 2.72.
vii) The McKinnon hypothesis fits in Nepal.
However, this study has not tested the stability of the money demand
function.
Khatiwada (1997) has analyzed the money demand function in Nepal using the
annual data of 21 years from 1975/76 to 1995/96. He has concluded that demand for
real money balance in Nepal is a stable and predictable function of a few variables
(real income and interest rate). He has concluded that the financial reforms have not
significantly affected the money demand function. He has found the income elasticity
of broad money (1.45) higher than narrow money (1.25). The unit root test shows that
most of the time series in natural logarithmic form of the levels of the data used in the
money demand function are time trended or integrated of order zero or one. Only
GDP deflator is integrated of order three implying the higher degree of non-
stationarity in time series. The Engle-Granger (EG) cointegration test reveals that real
narrow money demand, real income and interest rate represented by 12-months fixed
deposit rate are cointegrated when the time trend variable is included in the
cointegration test. However, the EG test shows that the cointegrating relationship does
not seem significant for broad money definitions of real money balances.
Pandey (1998) by using an error correction dynamic specification found that demand
for narrow money (M1) is highly stable and this has been confirmed by all the
statistical tests that were employed. He also has found that the rate of interest on
savings deposits does not have a significant effect on the demand for M1 balances.
This study has also established the fact that money is a luxurious item for the
Nepalese people and the expected rate of inflation does not seem to have a significant
influence on the demand for M1 in Nepal. However, he has not tested the stability of
the demand for broad money.
Gaudel (2003) has used chow test to investigate the stability for the three alternative
definitions of money in the demand function using OLS estimation and found that a
stable relationship is maintained in all definitions of money. His study has covered
the data set from 1965 to 1994 only. He has estimated the money demand function
using the following various models:
1. Simple Linear Model
2. Simple Modified Model
3. Log Linear Model
4. Semi Log Linear model
5. Auto-regressive Distributed Lag Model
6. Partial Adjustment Model
7. Adaptive Expectations Model
8. The Almon Polynomial Lag Model
9. Simultaneous Equations System
His major findings are:
i) The demand for money in Nepal over the sample period is best
explained as a function of income as a scale variable and rate of
inflation and interest bearing assets as opportunity cost variables.
ii) From the result of the chow test, it is found that a stable relationship is
maintained in all the three definitions of money.
iii) The overall results of the linear models conclude that narrow definition of
money is superior to broad definition of money. It seems to indicate that
narrow definition of money is more appropriate than broad definition
providing the evidence of non-monetized economy.
iv) The income elasticity of the demand for money is positive and less than unity
in all log linear models implying that money is not a luxury asset in Nepal. It
also supports the view of Baumol and Tobin that there is a significant
economy of scale in holding money balances.
v) Money and physical assets in Nepal are more complementary rather than
substitutes.
vi) The long run demand function in comparison to the short run demand function
has performed better.
vii) The interest elasticities in log linear models are found to be low and
statistically insignificant.
2.5 Conclusion
The studies at international level reviewed in section 2.3 imply that most of
the studies in the money demand function in the international level have used
cointegration analysis. It is because the results from OLS estimation can
suffer from spurious regression phenomenon if the data are non-stationary.
When the standard assumption of stationarity breaks down, straightforward
application of regression technique no more remains valid. It therefore
becomes necessary to look for the presence of unit roots, prevalence of
cointegration and consequent application of error correction models (ECMs).
Further, they give support to the use of ARDL modeling over other methods
like Johansen multivariate cointegration technique, Phillips and Hansen
technique, etc in case of annual data and/or small number of observation. It is
because the validity of the result may be questioned in case of small size of
sample in latter methods. They also reveal the fact that the real GDP, interest
rate, inflation and exchange rate are the most common determinants of money
demand. The national literature on the money demand function makes a few
things clear: first, there has been a considerable lapse of time in the empirical
study of money demand function since Khatiwada (1997) and Pandey (1998);
secondly, the available literatures are based on OLS method of estimation
except Pandey (1998) which utilizes Engle-Granger Cointegration Method.
The reviews of studies at national level are relevant to compare the results of
the elasticities and other findings from the present study with the ones from
previous ones. Next, the studies by Poudel (1989), Khatiwada (1997) and
Pandey (1998) help to decide the appropriate scale variable and opportunity
cost variables in the money demand function. These studies prompt one to
apply the recently developed cointegration technique to the formulation of
money demand function to avoid the phenomenon of spurious correlation and
spurious regression. They also help to compare the efficiency and robustness
of the methodologies used in the formulation of money demand function till
now. Therefore, there has arisen the need to re-estimate the money demand
function extending the data set beyond 1997 and examine the stability issue.
This study, thus, aims to overcome these two shortcomings by extending the
data set from 1975 to 2009 and by adopting the ARDL modeling to
cointegration analysis proposed by Pesaran and Shin (1999) to get rid of the
spurious regression problem.
CHAPTER III
METHODOLOGY OF THE STUDY
3.1 Introduction
This chapter is a discussion of the methodology used in this study. Section 3.2
presents the general model used in the money demand function, section 3.3
provides a discussion on the selection of appropriate variables, section 3.4
presents the empirical model and variable details, section 3.5 discusses the
ARDL modeling to cointegration analysis, section 3.6 presents the hypothesis,
section 3.7 provides a discussion on the various econometric tools and tests
used in the study and finally section 3.8 discusses the data sources.
3.2 The General Model
In the literature of money demand function, the basic model of money demand
begins with the following relationship:
M/P = f(S, OC)
Where, the demand for real balances M/P is a function of the chosen scale
variable(S) to represent the economic activity and the opportunity cost of
holding money (OC). M stands for the selected monetary aggregates in
nominal term and P for the price (Sriram, 2000).
3.3 Selection of Variables
3.3.1 Scale Variable
There is a wide controversy among researchers on the selection of appropriate
scale variable. Studies in the developed countries have mostly used wealth
and permanent income as scale variables. The studies in US have been mostly
specified in terms of permanent income as the scale variable [Brunner and
Meltzer(1964), Chow(1966), Laidler (1966), Khan (1974), etc] while there are
some emphasizing the use of wealth as a scale variable [Meltzer(1963),
Hamberger (1966),etc] and some have used the measured income [Goldfeld
(1973), Arango and Nadiri (1981), etc]. However, in the context of developing
countries, measured income has been used in most empirical studies. Several
studies in India [Gujarati (1968), Bhattacharya (1974), Sampath & Husain
(1981), etc] have used current income as the scale variable. The reason for this
may be two-fold: first, the information on wealth is not available in the non-
monetized economy and secondly, permanent income series cannot be
meaningfully constructed because of very short time series national income
data.
In the context of Nepal, several studies [Poudel (1989), Khatiwada (1997),
Pandey (1998), Gaudel (2003) ] have used real GDP as the scale variable and
found significant and stable relationship between real GDP and the stock of
money holding. Thus, following the literature, this study has selected real
GDP as the scale variable.
3.3.2 Opportunity Cost Variable
Selection of opportunity cost variable also is not free of debate. There is the
ongoing controversy as which interest rate is the best indicator of the
opportunity cost of holding money. Some argue that the long-term bond rate is
better choice as it is more representative of the average rate of return on
capital. The Keynesian theory also supports the long term interest rate as it is
the interest rate that is linked with investment decision and hence the level of
income. Since the economic theory on the money demand function does not
provide any clear cut guideline on the choice of interest rate, researchers have
tried different interest rates in modeling the money demand function.
In case of US, Khan (1974) and Jacobs (1974) have used the long term rate of
interest whereas Heller (1965) and Laidler (1971) have used short term
interest rate. In case of India, Gupta (1970) and Bhattacharya (1974) have
used the short term interest variable in the money demand function.
In the context of Nepal, the use of T-bill rate or long term bond rate is
irrelevant as these instruments are not a significant part of asset portfolios.
Further data are not available for long term fixed deposit rate for the whole
study period. Thus, in this study, rate of interest on saving deposit has been
used as a proxy to interest rate on short term financial assets to model the
narrow money demand and the interest rate on one-year fixed deposit has
been used as a proxy for long term interest rate to model the broad money
demand function.
3.4 The Empirical Model
In this study, following Bahmani-Oskooee (2001), the following model has
been considered.
ln mt =a + b ln yt +c rt + et…………………………………………………………………… (3.1)
Where, mt is a monetary aggregate in real term, y the real GDP, r the interest
rate and e is a white noise error term. Based on the conventional economic
theory, the income elasticity coefficient, b, is expected to be positive; whereas
the interest elasticity parameter, r, is expected to be negative.
To model the money demand functions for both narrow and broad money
aggregates, equation (1) can be written in the form of two different models:
Model I for Narrow Money Demand Function and Model II for Broad Money
Demand Function.
Model I (Narrow Money Aggregate): ln m1t =a+b lnyt+c rsdt+et………….(3.2)
Model II (Broad Money Aggregate): ln m2t =a+b lnyt+c rfdt+et…(3.3)
The details of all the variables used in the formulation of equations (3.2), (3.3)
and used in this study have been presented in table 3.1.
Table 3.1
Variable Details
Variables Name Details
m1t Real Narrow Money Stock defined by the
narrow money stock divided by CPI(FY
2000/01=100)
m2t Real Broad money stock defined by the broad
money stock divided by CPI( FY 2000/01=100)
yt Real GDP defined by nominal GDP deflated by
the implicit GDP deflator(FY 2000/01=100)
ln m1t Natural logarithm of real narrow money stock
ln m2t Natural logarithm of real broad money stock
ln yt Natural logarithm of real GDP
rsdt Rate of interest on saving deposit
rfdt Rate of interest on one-year fixed deposit
Narrow money stock(M1) Currency held by public plus demand deposits of
the commercial banks(CC+DD)
Broad money stock(M2) Narrow money stock plus time
deposits(CC+DD+TD)
CPI Consumer price index (FY 2000/01=100)
INF Expected rate of inflation proxied by the actual
rate of inflation defined by ( CPIt -CPIt-1 )/CPIt-
1
rrsd Real rate of interest on saving deposit defined as
nominal interest rate on saving deposit minus
expected rate of inflation
rrfd Real rate of interest on 12-months fixed deposit
defined as nominal interest rate on such deposit
minus expected rate of inflation
3.5 Estimation Methodology
There are various techniques for conducting the cointegration analysis on
money demand function. The popular approaches are: the well-known
residual-based approach proposed by Engle and Granger (1987) and the
maximum likelihood-based approach proposed by Johansen and Julius (1990)
and Johansen (1991). When there are more than two I(1) variables in the
system, the maximum likelihood approach of Johansen and Julius has the
advantage over residual-based approach of Engle and Granger; however, both
of the approaches require that the variables have the same order of integration.
This requirement often causes difficulty to the researchers when the system
contains the variables with different orders of integration. To overcome this
problem, Pesaran et al. (1996, 2001) proposed a new approach known as
Autoregressive Distributed Lag (ARDL) to cointegration test that does not
require the classification of variables into I(0) or I(1). Therefore, adopting the
ARDL approach for cointegration test, there is no need to conduct the unit
root test, which is prerequisite for residual-based and maximum likelihood
based approach. For these advantages, ARDL approach has gained popularity
over recent years and its adoption for empirical analysis on money demand
can be found in many published works.
This study follows the Auto Regressive Distributed Lag Model (ARDL) as
proposed by Pesaran and Shin (1999). There are many advantages of this
approach. First, it can be applied on a time series data irrespective of whether
the variables are I(0) or I(1) (Pesaran and Pesaran, 1997). Second, it takes
sufficient numbers of lags to capture the data generating process in a general-
to-specific modeling framework (Laurenceson and Chai, 2003). Third, a
dynamic Error Correction Model (ECM) can be derived from ARDL through
a simple linear transformation (Banerjee et.al., 1993). The ECM integrates the
short-run dynamics with the long run equilibrium without losing long-run
information.
3.5.1 Autoregressive Distributed Lag Model (ARDL) to Cointegration
Analysis
The ARDL bounds testing approach to cointegration was developed by
Pesaran and Shin (1999) and Pesaran et al. (2001). Due to the low power and
other problems associated with other methods for cointegration test, the
ARDL approach to cointegration has become popular in recent years. The
ARDL cointegration approach has numerous advantages in comparison to
other cointegration methods such as Engle and Granger (1987), Johansen
(1988), and Johansen and Juselius (1990) procedures: (i) The ARDL
procedure can be applied whether the regressors are I(1) and/or I(0), while
Johansen cointegration techniques require that all the variables in the system
be of equal order of integration. This means that the ARDL can be applied
irrespective of whether underlying regressors are purely I(0), purely I(1) or
mutually cointegrated and thus no need for unit root pre-testing, (ii) While
the Johansen cointegration techniques require large data samples for validity,
the ARDL procedure is statistically more significant approach to determine
the cointegration relation in small samples, (iii) The ARDL procedure allows
that the variables may have different optimal lags, while it is impossible with
conventional cointegration procedures, (iv) The ARDL technique generally
provides unbiased estimates of the long-run model and validates the t-
statistics even when some of the regressors are endogenous, (v) The ARDL
procedure employs only a single reduced form equation, while the
conventional cointegration procedures estimate the long-run relationships
within a context of system equations.
Following the ARDL approach proposed by Pesaran and Shin (1999), the
existence of long run relationship could be tested using equation (3.4) below:
ln mt = a0 +
p
j 1
bj ln mt –j +
q
j 0
cj ln yt-j +
r
oj
dj rt-j +1 ln mt–1 + 2 ln
yt–1 + 3 rt-1 + t ……………………………………………………….(3.4)
Where, mt represents real narrow money balances for narrow money demand
model (model I) and real broad money balances for broad money demand
model(model II), r represents interest rate on saving deposit for model I and
interest rate on one-year fixed deposit for model II, similarly, γ1 ,γ2, γ3 are
the long run coefficients while, bj, cj, dj and ζt represents the short run
dynamics and random disturbance term respectively.
3.6 Hypothesis
To test whether the long run equilibrium relationship exists between demand
for real money balances, real GDP and interest rate, this study carries out
Bounds test (F-version) for cointegration as proposed by Pesaran and Shin
(1999). To test the long run level relationship between the variables, the
hypotheses are:
Null Hypothesis: γ1 =γ2 =γ3 =0 i.e. the long run relationship does not exist.
Alternative hypothesis: γ1 ≠ γ2 ≠ γ3 ≠ 0
This hypothesis is tested by means of the familiar F statistic. The distribution
of this F-statistics is non-standard irrespective of whether the variables in the
system are I(0) or I(1). The critical values of the F-statistics in this test are
available in Pesaran and Pesaran (1997) and Pesaran et al. (2001). They
provide two sets of critical values in which one set is computed with the
assumption that all the variables in the ARDL model are I(1), and another
with the assumption that they are I(0). For each application, the two sets
provide the bands covering all the possible classifications of the variables into
I(0) or I(1), or even fractionally integrated ones. If the computed F-statistics is
higher than the appropriate upper bound of the critical value, the null
hypothesis of no cointegration is rejected; if it is below the appropriate lower
bound, the null hypothesis cannot be rejected, and if it lies within the lower
and upper bounds, the result is inconclusive (Samreth, 2008).
Next step is the estimation of the long run relationship based on the
appropriate lag selection criterion such as adjusted R2, Schwarz Bayesian
Criterion (SBC), Akaike Information Criterion (AIC) and Haann Quinn (HQ)
Criterion. Based on the long run coefficients, the estimation of dynamic error
correction will be carried out using formulation of equation (3.5). The
coefficients δ1i, δ2i, and δ3i show the short run dynamics of the model and δ4
indicates the divergence/convergence towards the long run equilibrium. A
positive coefficient indicates a divergence, while a negative coefficient
indicates convergence. The term ECM is derived as the error term from the
corresponding long run model whose coefficients are obtained by normalizing
the equation on m1t and m2t respectively for both money demand models.
ln mt = 0 +
p
j 1
𝛿1j ln mt –j +
q
j 0
𝛿2j ln yt-j +
r
oj
𝛿 3jrt-j + 4 ECMt-
1+t…… (3.5)
For the test of stability, CUSUM and CUSUMSQ tests as proposed by the
Brown et al. (1975) are carried out in this study. Besides these tests, a battery
of other tests are also carried out, such as Augmented Dicky-Fuller
Test(ADF) for testing the order of integration of the variables, Lagrange
Multiplier (LM) test for serial correlation, Ramsey Reset test for functional
form Misspecification, Jarque-Berra Test for normality and KB test for
heteroscedasticity.
3.7 Econometric Tools
3.7.1 Time Series Properties of the Variables
A time series is said to be stationary if its mean, variance and auto covariance
remain the same no matter at what point they are measured; i.e. they are time
invariant. Such a time series will tend to return to its mean and fluctuations
around this mean will have broadly constant amplitude. If a time series is not
stationary, it is called a non-stationary time series (Gujarati, 2007).
A stationary time series is also called a time series integrated of order zero or I
(0) process. If a time series is non-stationary at level but stationary at first
difference, it is said to be integrated of order one or I (1) process. In general, if
a non-stationary time series has to be differenced d times to get a stationary
series, it is said to be integrated of order d or an I(d) process.
Most economic time series are generally I(1); that is , they generally become
stationary only after taking their first differences (Granger,1986).
3.7.2 Cointegration
The regression analysis on time series has been much benefited from the
concept of cointegration by Granger (1981) and Engle and Granger (1987).
They showed that using OLS in case of I(1) variables could be dangerous
because a non-stationary series violates the basic assumptions of OLS and as
such one cannot get the best linear unbiased estimators (BLUE) and also there
may exist the spurious or non-sense correlation between non-stationary
variables. In the case where the variables are non-stationary at levels but are
difference stationary, cointegration methodology allows researchers to test for
the presence of long run equilibrium relationships between economic
variables. If the separate economic time series are stationary after differencing
or they are integrated of order one, but a linear combination of their levels is
stationary, then the series are said to be cointegrated. In other words, two or
more I (l) time series are said to be cointegrated if some linear combination of
them is stationary. Formally, given xt and yt are integrated of order one [I (1)]
or are difference stationary processes, they are said to be cointegrated if there
exists a parameter 𝛼 such that ut = yt-𝛼xt is a stationary process or is
integrated of order zero [I (0)].
Tests for cointegration seek to discern whether or not a stable long-run
relationship exists among such a set of variables. The existence of a common
trend among the variables means that in the long run the behavior of the
common trend will drive the behavior of the variables. Shocks that are unique
to one time series will die out as the variables adjust back to their common
trend.
3.7.3 Error Correction Modeling
Even if Yt and Xt variables are cointegrated, i.e. there is a long run equilibrium
relationship between them, there may be disequilibrium in the short run. Thus
the error term ut = Yt –𝛽1- 𝛽2Xt in the regression equation Yt = 𝛽1+ 𝛽2Xt+ ut is
called the equilibrium error. This error term can be used to tie the short run
behavior of Y to its long run value. The Error correction Models (ECM) first
used by Sargan (1984) and later popularized by Engle and Granger corrects
for disequilibrium. The Granger Representation Theorem says that if two
variables Yt and Xt are cointegrated, then the relationship between the two can
be expressed as Error Correction Modeling as:
𝛥Yt =𝛼0+𝛼1𝛥Xt+𝛼2ut-1+𝜺t………………….…………………........ (3.6)
Where,
𝛥= first difference operator,
𝜺t= a white noise error term,
ut-1= one period lagged value of the error term from the cointegrating
regression(ut-1=Yt-1-–𝛽1- 𝛽2Xt-1)
Equation (3.6) can be arrived through a simple manipulation of the
cointegrating regression Yt = 𝛽1+ 𝛽2Xt+ ut . Adding and subtracting Yt-1 on the
left hand side and adding and subtracting 𝛽2Xt-1 on the right hand side yields:
Yt –Yt-1 + Yt-1= 𝛽1+ 𝛽2Xt+ 𝛽2Xt-1 - 𝛽2Xt-1+ ut
Or, 𝛥Yt= 𝛽1+ 𝛽2𝛥Xt –(Yt-1 - 𝛽2Xt-1)+ ut
Or, 𝛥Yt= 𝛽1+ 𝛽2𝛥Xt –ECMt-1+ ut
The ECM in equation (3.6) states that 𝛥Yt depends on 𝛥Xt and on the
equilibrium error term. If the error term is non-zero, the model is out of
equilibrium. Here the value of 𝛼2 decides how quickly the equilibrium is
restored.
3.7.4 Diagnostic Tests and Other Tests
i) JB Test for Normality
Jarque Bera (JB) Test of Normality is an asymptotic large sample test based
on the OLS residuals. The test statistic is defined by
JB=n [6
2S+
24
)3( 2K]
Where n= sample size, S= skewness coefficient, K = kurtosis coefficient. For
a normally distributed variable, S= 0 and K = 3. Therefore, the JB test for
normality is a test of joint hypothesis that S and K are 0 and 3 respectively. In
that case, the value of the JB statistic is expected to be zero. Under the null
hypothesis that the residuals are normally distributed, Jarque and Bera showed
that asymptotically the JB statistic follows the chi-square distribution with 2
degree of freedom. If the computed p-value of the JB statistic is sufficiently
low or the value of the statistic itself is very different from zero, the null
hypothesis that the residuals are normally distributed is rejected. On the
contrary, if the p-value is reasonably high or the value of the statistic is close
to zero, the normality hypothesis is not rejected (Gujarati, 2007).
ii) LM Test for Serial Correlation
In the models which contain lagged values of the regressand, the Durbin-
Watson d-statistic is often around 2 implying that there is no first order
autocorrelation. Thus, there is a bias against discovering first order
autocorrelation in such models. This does not mean that autoregressive
models do not suffer from autocorrelation problem. To solve this problem,
Durbin has developed Durbin h-test but it is less powerful in statistical sense
than the Breusch-Godfrey test popularly known as the LM test for serial
correlation. The LM test allows for the lagged values of the regressand, higher
order autoregressive scheme and simple or higher order moving averages of
the white noise error term.
The null hypothesis under this test is:
H0: 𝜌1=𝜌2=𝜌3=……𝜌p=0 i.e. there is no serial correlation of any order.
Where ut follows the pth
order autoregressive, AR (p), scheme as follows:
ut = 𝜌1ut-1+ 𝜌2ut-2+………+ 𝜌put-p+𝜺t………………………………………(3.7)
Test statistic is given by
(n-p)R2 ∼𝜒
2
p
Where the R2 is calculated from the auxiliary regression equation given by
tu
=𝛼 0 +𝛼i Xti + 1
1
tu + 2
2
tu +………+ p
ptu
+𝜺t
Where Xti are explanatory variables
For large sample, this statistics follows the chi-square distribution with p df. If (n-
p)R2
exceeds the chi-square critical value at the chosen level of significance in which
case null hypothesis is rejected that is to say there is the presence of serial correlation
of some order.
iii) Koenker- Basset Heteroscedasticity Test
This test for Heteroscedasticity is based on the squared residuals, 2ˆtu but
instead of being regressand on one or more regressors, the squared residuals
are regressed on the squared estimated values of the regressand. Specifically if
the original model is
Yt = 𝛽1 + 𝛽2X2 + 𝛽3X3 + ………. + 𝛽kXk+ ut, …………….…………..(3.8)
Then, the following model is estimated,
2ˆtu =𝛼1 + 𝛼2(𝑌 𝑡)2 +vt
Where, 𝑌 𝑡=estimated Y value from the regression equation (3.8)
And 𝑢 = Yt -𝑌 t
Null hypothesis: 𝛼2=0
This hypothesis is tested by the usual t-test or the F-test. If the null hypothesis
is not rejected, the conclusion is that there is no heteroscedasticity.
iv) Ramsey’s RESET Test
This test is the regression specification error test (RESET). It is used to check
whether the specified functional form is correct or not.
The Procedure for F-Version is as follows:
Let the simple regression model is
Y = 𝛼1 + 𝛼2X + u ……………………………………………………..........(3.9)
From equation (3.9), 𝑌 is found and the following regression is run by adding 𝑌 in
some form as an additional regressors starting with 𝑌 2, e.g.
Y = 𝛽1+ 𝛽2X+ 𝛽3𝑌 2
+ 𝛽4𝑌 3+u………………………………… (3.10)
Let the R2 obtained from equation (3.9) is 2
oldR and that from Equation (3.10) is 2
newR
. Then, the following F statistics is constructed:
F =
(Rnew2 −Rold
2 )number of new regressors
(1−Rnew2 )
(n−numbers of parameters in the new model )
If the computed F value is found significant, say, at 5%, one can accept the hypothesis
that the model is mis-specified.
Alternative to F-version is the LM version where the calculated statistic nR2 follows
the chi-square distribution with df equal to the number of restrictions imposed for
large samples. If the calculated value exceeds the critical value of 𝜒2 at the chosen
level of significance, the null hypothesis is rejected and concluded that the model is
mis-specified.
v) Model Selection Criteria
Model selection criteria are used to choose a model from the alternative models.
Adjusted R2 criterion
It is calculated as:
𝑅 2 = 1-
𝑅𝑆𝑆 𝑛−𝑘
𝑇𝑆𝑆 𝑛−1
Where,
RSS= residual sum of square
TSS= Total sum of square
n = number of observations
k = number of parameters in the regression model
On the basis of this criterion, a model with highest 𝑅 2 is chosen.
Akaike Information criterion(AIC)
AIC is calculated as:
AIC = n
RSSe
nk
/2
Where, k= number of parameters,
It can also be writes as:
ln AIC = 2k/n + ln (RSS/n)
Where, ln = natural logarithm and 2k/n is the penalty factor.
AIC imposes harsher penalty than 𝑅 2 for adding more regressors. In comparing the
models, the lowest value of AIC is preferred.
Schwarz Bayesian Criterion (SBC)
SBC is calculated as:
SBC = n
k. ln n + ln(
n
RSS)
Here, n
k. ln n is the penalty factor. So SBC imposes a harsher penalty than AIC. Like
AIC, lower value of SBC is preferred.
vi) Recursive Residuals, CUSUM Test and CUSUMSQ Test
In recursive least squares, the equation is estimated repeatedly, using ever
larger subsets of the sample data. If there are k coefficients to be estimated in
the regression, then the first K observations are used to form the first estimate
of the parameters. The next observation is then added to the data set and k+1
observations are used to compute the second estimate of parameters. This
process is repeated until all the T sample points have been used, yielding T-
k+1 parameter estimates. At each step the last estimate of the parameters can
be used to predict the next value of the dependent variable. The one-step
ahead forecast error resulting from this prediction, suitably scaled, is defined
to be a recursive residual.
CUSUM Test
The CUSUM test (Brown, Durbin, and Evans, 1975) is based on the
cumulative sum of the recursive residuals. This option plots the cumulative
sum together with the 5% critical lines. The test finds parameter instability if
the cumulative sum goes outside the area between the two critical lines.
The CUSUM test is based on the statistic
Wt=1
t
r
r k s
w
For t=k+1,…….T , where Wt is the recursive residual and s is the standard
error of the regression fitted to all sample points T. If the vector of the
parameter remains constant from period to period, E (Wt) = 0, but if this
vector changes, Wt will tend to diverge from the zero mean value line. The
significance of any departure from the zero line is assessed by reference to a
pair of 5% significance lines, the distance between which increases with t.
The 5% significance lines are found by connecting the points
[k, ± -0.948(T-k)1/2
] and [T, ±3×0.948(T-k)1/2
]
Movement of outside the critical lines is suggestive of coefficient instability.
CUSUMSQ Test
The CUSUM of squares test (Brown, Durbin, and Evans, 1975) is based on
the test statistic
Wt =
2
1
2
1
t
rr k
T
rr k
w
w
The expected value of under the hypothesis of parameter constancy is E (St) =
t-k/T-k which goes from zero at to unity at. The significance of the departure
of from its expected value is assessed by reference to a pair of parallel straight
lines around the expected value. The CUSUM of squares test provides a plot
of against and the pair of 5 percent critical lines. As with the CUSUM test,
movement outside the critical lines is suggestive of parameter or variance
instability.
vi) Bounds Test (F-version)
The F-test can be used to test the hypothesis about one or more parameters of
the k-variable regression model:
Yi = 𝛽1 + 𝛽2X2i+ 𝛽3X3i+ 𝛽4X4i+………..+ 𝛽k Xki + ui…………………………… (11)
Let, the hypothesis to be tested is H0: 𝛽4= 𝛽5= 𝛽6= 𝛽7=0
Then, another regression by dropping the variables X4i, X5i, X6i and X7i is run
as
Yi = 𝛽1 + 𝛽2X2i+ 𝛽3X3i+ 𝛽8X8i+………..+ 𝛽k Xki + ui…………………………… (12)
and residual sum of squares is calculated from both models. Equation (11) is
called unrestricted regression and equation (12) is called restricted regression.
The F statistic is calculated by the formula:
F =
UR
UR
R(RSS RSS
m
RSS(n k)
;
Where,
RSSR =RSS of the restricted regression,
RSSUR = RSS of unrestricted regression,
m= number of restrictions,
k= number of parameters in unrestricted regression and
n=number of observations
According to Pesaran (1997), the bounds test (General F test) can be used test
the long run relationship in equation (3.4)
vii) Augmented Dickey-Fuller (ADF)Test
ADF test statistic is used to examine the stationarity of the time series
variable. The following regression is run in Augmented Dickey-Fuller (ADF)
test to check for unit root of the variables or to check the order of integration:
Δ xt = η+ γt + αxt-1+1
k
j t j
j
x
+ ε1t………….………………... (3.13)
Where xt is any variable used in this study, that is, ln m1t, ln m2t, ln yt,rsdt, and
rfdt, Δ indicates the first difference operator and k is the length of lag which
ensures residuals to have white noise empirically. The ADF statistic is simply
the t-value of the coefficient α in equation (13). The null hypothesis is that xt
has a unit root, that is, H0: α = 0 and is rejected if the calculated ADF statistic
is above the critical value implying that xt has no unit root or xt is stationary.
3.8 The Data
This study is based on the secondary data. The data sources are Quarterly
Economic Bulletin published by Nepal Rastra Bank (NRB), Economic Survey
published by Ministry of Finance(MOF) and the World Economic Outlook by
IMF. The GDP figures have been extracted from the World Economic
Outlook database of IMF available at econstats.com which contains the time
series data on the real GDP figures of Nepal calculated at the base year price
of FY 2000/01 adjusted to the base year price by data splicing chain weighted
method. The information pertaining to the money balances and interest rates
on saving and one-year fixed deposit have been extracted from Quarterly
Economic Bulletin (various issues). The data on the CPI (FY 2000/01=100)
have been extracted from the Economic Survey 2009/10.
CHAPTER IV
ANALYSIS OF DATA
This chapter presents the analysis of data with the estimated results. Section
4.1 presents the results from the ADF test to test the order of integration of the
variables, section 4.2 presents the results from the bounds test to test the long
run relationship between the variables, the estimated short run model, long run
model and the resulting error correction model for both money demand
models and section 4.3 presents the results of the CUSUM and CUSUMSQ
tests for both models.
4.1 Time Series Properties of the Variables
The underlying assumption of ARDL procedure that each variable in narrow
and broad money demand models is I (1) or I (0). Thus, there is no need to
check whether the variable is I (0) or I (1). However, if any variable is
integrated of higher than order one, then the procedure is not applicable
because if any variable is I(2) of of some higher order, the table values given
by Pesaran (1997) do not work. Thus, it is still necessary to perform unit root
tests to ensure that none of the variables in equations is I (2) or higher order.
Augmented Dickey-Fuller (ADF) unit-root test has been applied to test the
order of integration of the variables. Before conducting the ADF test, an
attempt is made on whether to include the trend as a variable in the ADF
regression or not. To confirm this, the time series plot of the variables has
been presented in Fig. 1 and Fig. 2 and Fig. 3.
The time series plot in Fig. 1 shows that ln m1t, ln m2t and ln yt are trended
variables. So, a trend is included in the ADF test for them. On the other hand,
rsdt and rfdt in Fig. 2 and rrsdt, rrfdt and INF in Fig. 3 have no trend as such
intercept only is included while testing their order of integration. From the
time series plot, it is obvious that the relevant ADF statistic for checking the
order of integration in case of ln m1t, ln m2t and ln yt is the ADF statistic from
the ADF regression including constant and trend whereas the relevant ADF
statistic for checking the order of integration in case of rsdt, rfdt, rrsdt, rrfdt and
INF is the ADF statistic from the ADF regression including constant but no
trend.
Fig. 1
Time Series Plot of ln m1t, ln m2t and ln yt
Fig. 2
Time Series Plot of rsd and rfd
Fig. 3
Time Series Plot of rrsdt, rrfdt and INF
2
4
6
8
10
12
1975 1984 1993 2002 2009
m1t m2t ln yt
4
6
8
10
12
14
16
1975 1984 1993 2002 2009
RFD RSD
Table 4.1 presents the results of the ADF test. Since the data is annual,
following Pesaran and Shin (1999), only one lag has been included (p=1).
Table 4.1
ADF Test Results (p=1)
Variables Constant Constant and trend
ln m1t -0.38 -
4.25
ln m2t -0.60 -
5.04
ln yt -0.98 -2.99
rsdt -1.48 -1.96
rfdt -1.80 -2.50
rrsdt -4.60 -4.58
rrfdt -4.38 -4.66
INF -3.51 -3.90
𝛥ln m1t -4.65* -4.42
𝛥ln m2t -5.65* -5.27
𝛥ln yt -4.95* -5.20
𝛥rsdt -4.06* -3.93
𝛥rfdt -3.79* -3.70
𝛥rrsdt -6.93* -6.73
-20
-10
0
10
20
30
1975 1984 1993 2002 2009
RRsd RRfd INF
𝛥rrfdt -7.12* -6.92
𝛥INF -6.46* -6.25
*represents the rejection of null hypothesis at 5% level of significance.
The critical values are -2.966 (constant but no trend) and -3.6008 (constant
and trend) at 5% level of significance. The critical values have been calculated
by stochastic simulation of 32 observations and 20000 replications.
From the results in table 4.1, it becomes clear that none of the variables are
integrated of higher than order one. All the variables are at most integrated of
order one. To confirm the order of integration of the variables besides ADF
test, the autocorrelation function for each variable has been examined which
leads to the conclusion that the variables ln m1t, ln m2t, ln yt, rsdt, rfdt, are
integrated of order one or are I (1) processes whereas the variables rrsdt, rrfdt
and INF are integrated of order zero or are I (0) processes (the graphs of
autocorrelation functions have been provided in Appendix E). If the auto
correlation coefficient starts with a high value and diminishes slowly, the
variables are non-stationary processes at level. Since, the variables are of
mixed order; the ARDL modeling is the most appropriate approach to model
the demand for money as suggested by Pesaran and Shin (1997).
4.2 Estimation Results
Since the main objective of the study is to check the long run cointegrating
relationship between the variables included in the money demand function
and check the stability of the money demand function, an attempt to check
such long run relationship is made first. As this study follows the Auto
Regressive Distributed Lag Modeling (ARDL) to the formulation of money
demand function popularized by Pesaran and Shin (1997), the bounds test (F-
statistics) has been applied to justify the existence of the cointegration or
long-run relationship among variables in the system. Table 4.2 provides the
results of the F-statistics according to various lag orders.
Table 4.2
F-statistics (Bound Test)
Lag order 0 1
F statistic M1 Aggregate 3.7513 4.5580*
M2 Aggregate 7.6529**
4.9437**
Note: The relevant critical value bounds are (with intercept and no trend;
number of regressors = 2) 3.793 – 4.855 at the 95% significance level and
3.182– 4.126 at the 90% significance level.
* denotes that the F-statistic falls above the 90% upper bound and ** denotes
above the 95% upper bound.
The results of Table 4.2 shows that most of the F-statistics are above the upper
bounds of the critical values (CV) of standard significance levels (5 % or
10%) provided by Pesaran and Pesaran (1997). But these critical values were
generated on the basis of 40,000 replications of a stochastic simulation for a
sample of 1,000 observations. So, they are less relevant for a small sample
size. Therefore, following the critical values by Narayan and Smyth (2004)
which are based on 40,000 replication of a stochastic simulation for a sample
of 40 observations with two regressors, the critical value bounds are 2.83 to
3.58 at 10 % and 3.43 to 4.26 for 5% level of significance. On the basis of
these critical values, the calculated F-statistics clearly rejects null hypothesis
of no cointegration at 5 % or 10% level of significance. These values Support
the existence of cointegration or long-run relationship between variables in
the equation. However, Bahmani-Oskooee and Bohl (2000) consider these
results as preliminary, precisely due to arbitrary choice of lag selection, and
rely more on the other stages of estimation for testing cointegration which are
more efficient.
In the second step, equation (3.4) is estimated and different model selection
criteria are used to justify the lag orders of each variable in the system. Only
an appropriate lag selection criterion will be able to identify the true dynamics
of the model. The maximum lag order is set to 2 following Pesaran and Shin
(1999) and Narayan (2004) as the data are annual and there are only 35
observations. With this maximum lag order, the adjusted sample period for
analysis becomes 1977 to 2009. This setting also helps save the degree of
freedom, as our available sample period for analysis is quite small. Using
Microfit 5.0, all the selection criteria have given the same results. Microfit
runs the (p+1)k
numbers of regressions and selects the best model, where p is
the maximum number of lags to be used and k is the number of variables in
the equation. Here then number of regressions to be run are (2+1)3 = 27. The
ARDL (1, 0, 0) model is selected on the basis of all criteria like Adjusted R2,
Schwarz Bayesian Criterion (SBC), Akaike Information Criterion (AIC) and
Haann Quinn criterion for both M1 aggregate and M2 aggregate models.
According to Pesaran (1997), AIC and SBC perform relatively well in small
samples, although the SBC is slightly superior to the AIC (Pesaran and Shin,
1999). Besides, SBC is parsimonious as it uses minimum acceptable lag while
selecting the lag length and avoid unnecessary loss of degrees of freedom.
Therefore, SBC criterion has been used, as a criterion for the optimal lag
selection, in all cointegration estimations.
After selecting the appropriate lag orders for each variable in the system,
equation (3.4) is re-estimated. The Results of such estimation along with the
short run diagnostic statistics are presented in table 4.3.
Table 4.3
Full-information ARDL Estimate Results (M1 monetary aggregate)
Autoregressive Distributed Lag Estimates
ARDL (1,0,0) selected based on Schwarz Bayesian Criterion
Dependent variable is ln m1t
33 observations used for estimation from 1977 to 2009
Regressors
𝛥 ln m1t(-1)
𝛥 yt
𝛥 rsdt
C
Coefficient
.51759*
.67440*
-.001907
-5.2578*
T-
Ratio[Prob]
4.4513[.000]
4.1057[.000]
-.26506[.793]
-3.9985[.000]
R-Squared .99482 R-Bar-Squared
.99428
S.E. of Regression .045336 F-Stat. F(3,29)
1855.9[.000]
Diagnostic Tests
Test Statistics LM Version F
Version
A:Serial Correlation CHSQ(1) = .33333[.564]
F(1,28)=.28571[.597]
B:Functional Form CHSQ(1) = 3.8703[.049] F(1,28) =
3.7202[.064]
C:Normality CHSQ(2) = 1.2077[.547] Not applicable
D:Heteroscedasticity CHSQ(1) = .007825[.930] F(1,31)
=.007353[.932]
A: Lagrange multiplier test of residual serial correlation
B: Ramsey‟s RESET test using the square of the fitted values
C: Based on a test of skewness and kurtosis of residuals
D: Based on the regression of squared residuals on squared fitted values
*denotes the significance of coefficient at 5% level
Table 4.3 indicates that the overall goodness of fit of the estimated ARDL
regression model is very high with the result of adjusted R2 = 0.9942. From
the diagnostic tests, it is clear that the model passes all of the tests. The critical
values of 𝝌2 for one and two degrees of freedom at 5% level of significance
are 3.84 and 5.99 respectively. Thus, null hypothesis of normality of residuals,
null hypothesis of no first order serial correlation and null hypothesis of no
heteroscedasticity are accepted. However, the null hypothesis of no
misspecification of functional form can be accepted at 1% level of
significance only. Since the LM version of misspecification test is a large
sample test, it is more appropriate to conclude on the basis of F-version of
RESET test. On the basis of F-version, the null hypothesis of no
misspecification can be easily accepted even at 5% level of significance. Not
much interpretation can be attached to the short run coefficients. These
coefficients will be interpreted in the error correction ARDL model in table
4.5.
The long-run model of the corresponding ARDL (1, 0, 0) for the demand for
narrow money balances can be written as follows:
ln m1t = -10.899 + 1.398ln yt - 0.00395 rsdt
The long run coefficients are the values of coefficients 𝛾1 to 𝛾3 of equation
(3.4) normalized on ln m1t by dividing the coefficients by the coefficient (-𝛾1).
The long run coefficients are reported in Table 4.4. As expected, the
coefficient of the real income (GDP) is positive and that of short term interest
rate is negative. Quantitatively, the income elasticity of narrow money
demand is 1.398, which is highly significant as reflected by a t-statistic of
27.40. This in turn shows that one percentage increase in real GDP leads to
increase in the real money balance holdings by 1.398 percentages. This shows
that money is a luxury asset in Nepal. This result is in conformity with many
studies done in underdeveloped countries e.g. Poudel (1989) and Khatiwada
(1997) for Nepal, Aghevli et.al.(1979) and Teseng and Corker (1991) for
Asian countries and Simmons (1992) for African Countries. It thus rejects the
conclusion of Gaudel (2003) that income elasticity of demand for money is
less than unitary in Nepal. The more than unity elasticity implies that an
increase in income leads to a higher increase in the demand for real money
balances and a reduction in the velocity of money (Rutayisire, 2010). This
result is attributed to the under-monetization of the economy where the
gradual absorption of the non-monetary sector by the monetary sector is
accompanied by an increase in cash in hand that is faster than income.
Table 4.4
Estimated Long Run Coefficients using the ARDL Approach
ARDL (1,0,0) selected based on Schwarz Bayesian Criterion
Dependent variable is ln m1t
33 observations used for estimation from 1977 to 2009
Regressors
ln yt
rsdt
C
Coefficient
1.3980*
-.0039530
-10.899*
T-Ratio[Prob]
27.4070[.000]
-
.26559[.792]
-
17.9565[.000]
*shows the significance of coefficients at 1% level of significance.
The interest rate despite bearing the correct negative sign is statistically
insignificant which implies that in the long run the demand for narrow money
balances remains independent of the interest rate. Thus, either the interest rate
is not a good proxy of the opportunity cost of holding money or interest rate
does not have a significant effect on the demand for narrow money balances
in Nepal. In an attempt to search for a suitable appropriate opportunity cost
variable in the narrow money demand function, the interest rate on one-year
fixed deposit was tried instead of interest rate on saving deposit but it also did
not appear to be fruitful. Also, the real rates of interest were tried, but none of
them carried significant t-ratio. Lastly, the inflation rate also did not turned
out to be a significant opportunity cost variable in money demand function
(Results are provided in the APPENDIX C and APPENDIX D). These results
strongly support the view of Johnson (1963) that in less developed country,
there is a possibility of keeping a block of cash by an individual out of his
remuneration, investing the rest in assets and thereby reducing the interest
elasticity of money demand to less than unity or even zero. The result that
inflation also is not a significant opportunity cost of holding narrow money
balances is in conformity with Pandey (1998) and in contradiction with
several other studies. This result points to two possibilities: either the actual
rate of inflation is not a good proxy of the expected rate of inflation or
inflation does not have a significant impact upon the demand for real money
balances in Nepal.
The estimates of the error correction representation of the ARDL (1, 0, 0)
model selected by the SBC criterion are presented in Table 4.5. The long run
coefficients are used to generate the error correction term .i.e. ecm = ln m1t-
1.398 ln yt + 0.00395rsdt+10.899. The computed F-statistic clearly rejects the
null hypothesis that all regressors have zero coefficients. The JB test for
normality shows that the residuals of the error correction modeling are
normally distributed. The KB test supports the homoscedasticity assumption.
Importantly, the error correction coefficient has the expected negative sign
and is highly significant as shown by the probability value being zero. This
helps to reinforce the existence of cointegration as provided by the F-test.
Specifically, the estimated value of ecm(−1) is － 0.482. The absolute value
of the coefficient of ecm (−1) is substantially high indicating the fast speed of
adjustment to equilibrium following short-run shocks; about 48% of the
disequilibrium, caused by previous period shocks, converges back to the long-
run equilibrium in one period. The short-run coefficients show the dynamic
adjustment of these variables. The coefficient of income and interest rate give
the short- run elasticities of income and interest rate respectively. The short
run income elasticity thus is 0.677 which is less than the long run elasticity
1.398. On the other hand, as in the long run, the short run elasticity of interest
rate is not statistically significant implying that demand for money even in the
short run remains independent of the interest rate. The adjusted R-square of
the error correction model is rather low but it does not significantly affect our
results [for example see Omer (2010), Samreth (2008), Bahmani-Oskooee and
Chi Wing Ng (2002)]. The low adjusted R square is due to the selection of a
restricted error correction model without a constant term following Pesaran
and Shin (1999).
Table 4.5
Error Correction Representation for the Selected ARDL Model
ARDL(1,0,0) selected based on Schwarz Bayesian Criterion
Dependent variable is 𝛥ln m1t
33 observations used for estimation from 1977 to 2009
Regressors
𝛥ln yt
𝛥 rsdt
ecm(-1)
Coefficient
.67440*
-.0019070
-.48241*
Standard Error
.16426
.0071946
.11628
T-Ratio[Prob]
4.1057[.000]
-.2651[.793]
-4.1488[.000]
R-Squared .37248 R-Bar-Squared
.30756
S.E. of Regression .045336 F-Stat. F(3,29)
5.7379[.003]
JB(Normality) 1.2076[0.5467]
F-stat. (For KB heteroscedasticity test) : 0.0953[0.759]
ecm = ln m1t -1.3980*ln yt + .0039530*rsdt + 10.8990*C
Note: R-Squared and R-Bar-Squared measures refer to the dependent variable
𝛥M1t and in cases where the error correction model is highly restricted, these
measures could become negative.
*shows the significance of coefficients at 1% level of significance.
Next, equation (3.4) is estimated for M2 monetary aggregates. Table 4.6
presents the estimated coefficients along with the diagnostic test statistics. It
indicates that the overall goodness of fit of the estimated ARDL regression
model is very high with the result of adjusted R2 = 0.9975.
Table 4.6
Full-information ARDL Estimate Results (M2 Monetary Aggregate)
ARDL(1,0,0) selected based on Schwarz Bayesian Criterion
Dependent variable is ln m2t
33 observations used for estimation from 1977 to 2009
Regressors
𝛥ln m2t(-1)
𝛥ln yt
𝛥rfdt
C
Coefficient
.59979*
.72642*
-.6579E-3
-5.7054*
Standard Error
.087851
.16415
.0048925
1.3393
T-Ratio[Prob]
6.8274[.000]
4.4253[.000]
-.1345[.894]
-4.2600[.000]
Diagnostic Tests
Test Statistics LM Version F Version
A:Serial Correlation CHSQ(1) = .065072[.799] F(1,28)
=.055322[.816]
B:Functional Form CHSQ(1) = 1.5144[.218] F(1,28) =
1.3467[.256]
C:Normality CHSQ(2) = .64742[.723] Not applicable
D:Heteroscedasticity CHSQ(1) = .0039343[.950] F(1,31) =
.00369[.952]
A:Lagrange multiplier test of residual serial correlation
B:Ramsey's RESET test using the square of the fitted values
C:Based on a test of skewness and kurtosis of residuals
D:Based on the regression of squared residuals on squared fitted values
*shows the significance of coefficients at 1% level of significance.
From the diagnostic tests in table 4.6, it is clear that the model passes all of
the tests. The critical values of 𝝌2 for one and two degrees of freedom at 5%
level of significance are 3.84 and 5.99 respectively. Thus, null hypothesis of
normality of residuals, null hypothesis of no first order serial correlation and
null hypothesis of no heteroscedasticity and null hypothesis of no
misspecification of functional form can be easily accepted at 5% level of
significance. Not much interpretation can be attached to the short run
coefficients. These coefficients will be interpreted in the error correction
ARDL model in table 4.9.
The long run coefficients are the values of coefficients 𝛾1 to 𝛾3 of equation
(3.4) normalized on ln m2t by dividing the coefficients by the coefficient (-𝛾1 )
The long-run model of the corresponding ARDL (1, 0, 0 ) for the demand for
money can be written as:
ln m2t=-14.255 + 1.815 ln y - 0.00164 rfdt
The long run coefficients are reported in Table 4.7:
Table 4.7
Estimated Long Run Coefficients using the ARDL Approach
ARDL(1,0,0) selected based on Schwarz Bayesian Criterion
Dependent variable is ln m2t
33 observations used for estimation from 1977 to 2009
Regressors
ln yt
rfdt
C
Coefficient
1.8151*
-.0016438
-14.2558*
Standard Error
.077302
.012221
.9079
T-Ratio[Prob]
23.4804[.000]
-.13450[.894]
-15.7019[.000]
Note: Figures in parentheses are the probabilities associated with the t-ratios
and the asterisk * shows that the coefficient is significant at 1% level of
significance.
In table 4.7, as expected, the coefficient of the real income (GDP) is positive
and that of one year fixed deposit interest rate is negative. Quantitatively, the
income elasticity of broad money demand is 1.815, which is highly significant
as reflected by a t-statistic of 23.48. This in turn shows that one percentage
increase in real GDP leads to increase in the real money balance holdings by
1.815 percentages. It also implies that the income elasticity for broad
definition of money is higher than narrow money. This result is again in
conformity with Poudel (1989) and Sharma (1997) for Nepal. The interest rate
despite bearing the correct negative sign is again statistically insignificant
which implies that in the long run, either, the demand for broad money
balances remains independent of the interest rate or the chosen interest rate rfdt
is not an appropriate opportunity cost variable. Here also, in search for an
appropriate opportunity cost variable, the real rate of interest was tried but the
coefficient of interest rate did not appear to be significant. This again is in
conformity with the view of Johnson (1963). Finally, the rate of inflation also
did not prove fruitful. As the intercept term is statistically significant, it
implies that unidentified variables including time trend have significant
bearings on real money demand and they have a negative impact on real
money demand (Sharma, 1997).
The error correction representation for broad money aggregate model has
been presented in table 4.8 which reconfirms the cointegrating relationship
between the variables included in the broad money demand function as
revealed by the expected negative sign with the error correction term with a
highly significant probability value of zero. The long run coefficients are used
to generate the error correction term .i.e. ecm = ln m2t- 1.8151*ln yt +
0.0016438*rfdt + 14.2558*C. The computed F-statistic clearly rejects the null
hypothesis that all regressors have zero coefficients. Specifically, the
estimated value of ecm (−1) is -0.40. The absolute value of the coefficient of
ecm (-1) is substantially high indicating the fast speed of adjustment to
equilibrium following short-run shocks; about 40% of the disequilibrium,
caused by previous period shocks, converges back to the long-run equilibrium
in one period. Since, the absolute value of the coefficient of ecm is lower in
case of broad money demand, there is a slower speed of adjustment of short
run disequilibrium to the long run equilibrium in case of broad money demand
function.
Table 4.8
Error Correction Representation for the Selected ARDL Model
ARDL(1,0,0) selected based on Schwarz Bayesian Criterion
Dependent variable is 𝛥ln m2t
33 observations used for estimation from 1977 to 2009
Regressors Coefficient Standard Error T-
Ratio[Prob]
𝛥ln yt .72642 .16415
4.4253[.000]
𝛥rfdt -.6579E-3 .0048925 -
.1344[.894]
ecm(-1) -.40021 0.087851 -
4.5556[.000]
R-Squared .41963 R-Bar-Squared
.35959
S.E. of Regression .038364 F-Stat. F(3,29)
6.9893[.001]
ecm = ln m2t - 1.8151*ln yt + .0016438*rfdt + 14.2558*C
JB(Normality) .6474[.723]
F-stat. (For KB heteroscedasticity test): 0.0238[0.878]
Note: R-Squared and R-Bar-Squared measures refer to the dependent variable
𝛥M1 and in cases where the error correction model is highly restricted, these
measures could become negative.
The coefficient showing the short run dynamics are not all significant: only
the short run income elasticity (0.7264) is significant where as the short run
interest rate elasticity is not significant though having a correct sign implying
that money demand in the short run also remains independent of the interest
rate. All these coefficients show the dynamic adjustment of these variables.
4.3 Stability Test
Finally, the stability of the long run coefficients together with the short run
dynamics is examined. In doing so, Pesaran and Pesaran (1997) have been
followed and the CUSUM and CUSUMSQ tests [proposed by Brown, Durbin,
and Evans (1975) have been applied. The tests are applied to the residuals of
the two models following Pesaran and Pesaran (1997). Specifically, the
CUSUM test makes use of the cumulative sum of recursive residuals based on
the first set of n observations and is updated recursively and plotted against
break points. If the plot of CUSUM statistics stays within the critical bounds
of 5% significance level represented by a pair of straight lines drawn at the
5% level of significance whose equations are given in Brown, Durbin, and
Evans (1975)], the null hypothesis that all coefficients in the error correction
model are stable cannot be rejected. If either of the lines is crossed, the null
hypothesis of coefficient constancy can be rejected at the 5% level of
significance. A similar procedure is used to carry out the CUSUMSQ test,
which is based on the squared recursive residuals. Figure 4 and figure 5,
figure 6 and figure 7 show the graphical representation of the CUSUM and
CUSUMSQ plots applied to the money demand models selected by the SBC
criterion. Neither CUSUM nor CUSUMSQ plots cross the critical bounds,
indicating no evidence of any significant structural instability. Similar results
have been obtained for the broad money demand model. Since all the graphs
of CUSUM and CUSUMSQ statistics stay comfortably well within the 5
percent band, it is safe to conclude that the estimated demand functions for
narrow and broad money balances are stable.
Figure 4
Plots of CUSUM Statistics (M1 Aggregate)
Figure 5
Plots of CUSUMSQ Statistics (M1 Aggregate)
Figure 6
Plots of CUSUM Statistics (M2 Aggregate)
Figure 7
Plots of CUSUMSQ Statistics (M2 Aggregate)
Thus, on the basis of all statistical tests applied, it can be concluded that a
statistically robust demand for money can be modeled for both narrow and
broad monetary aggregates using the ARDL model proposed by Pesaran and
Shin (19997). In case of both monetary aggregates, there exists the long run
cointegrating relationship between real money balances, real GDP and the
corresponding interest rate variable selected.
CHAPTER V
SUMMARY, CONCLUSIONS AND RECOMMENDATIONS
This study is focused on the estimation of money demand function in Nepal
and examination of the stability issue of it over the study period 1975-2009. It
has followed the recently developed ARDL modeling to cointegration and
error correction modeling approach developed and popularized by Pesaran
and Shin (1999) and Pesaran et.al. (2001) in analyzing the demand for both
narrow and broad money balances. It is expected that the results from this
study will provide valuable information to the monetary authority in
determining the intermediate targets of monetary policy. The main objectives
of the study are to examine the long run equilibrium relationship between the
variables included in the money demand function, to examine long run
coefficients and short run dynamics in the money demand function and to
examine the stability of the money demand function. This chapter is the
concluding chapter of the present study. The first part summarizes the
findings from the study and draws some conclusions. The second part lists
some recommendations that can be made from the conclusions of the study.
5.1 Summary of the Findings and Conclusions
The main purpose of this study has been to investigate the money demand
relationship in Nepal empirically and examine the stability of the money
demand function by using the recently developed tools of ARDL modeling to
cointegration and error correction modeling developed by Pesaran and Shin
(1999). It has included the variables that were found relevant by the previous
studies and analyzed the demand function for both narrow and broad money
aggregates over the time period 1975-2009.The major findings and
conclusions from this study are:
1. In both cases of money aggregates M1 and M2, demand for real money
balances has been found to have a long run equilibrium relationship with the
scale variable(real GDP) and corresponding opportunity cost variable( interest
rate on savings deposit in narrow money demand and interest rate on one year
fixed deposit in case of broad money demand). In other words, there exists
cointegrating relationship among the variables included in the money demand
function in case of both monetary aggregates.
2. The most significant determinant of money demand function in case of Nepal
is the scale variable or the real GDP as shown by the correct sign of long run
income elasticity which is highly significant in both cases.
3. The coefficient of interest rate in both cases though bears a correct sign is
statistically insignificant implying that demand for real money balances is
independent of interest rate in the long run in Nepal. Even if rate of interest in
savings deposits is replaced by the interest rate on one-year fixed deposit in
modeling the demand for narrow money, the coefficient is insignificant. This
finding is in conformity with Poudel (1989), and Pandey (1998). However, it
is in contrary to the Keynesian liquidity preference hypothesis which implies
that the chosen interest rate is either not an appropriate opportunity cost
variable or the money holders are sensitive to the return on other alternative
assets. According to Pandey (1998), the financial assets consists a negligible
part in the asset portfolio in Nepal because savings are mostly held in the form
of physical assets. Thus interest rate has a poor performance in modeling the
demand for money. Similarly this conclusion reinforces the findings of
Kaufman and Latta (1996) that interest rate would serve to be significant only
in those countries with well developed money markets. Next, this study has
tried to include the real rates of interest and inflation as opportunity cost
variable in modeling the money demand function but unfortunately they also
appeared insignificant. This conclusion does not support the earlier findings
by Poudel (1989) that real rate of interest is a significant variable in money
demand function where as nominal rate of interest is not. On the other hand,
inflation as an insignificant opportunity cost variable supports the findings of
Pandey (1998). This implies that either the actual rate of inflation is not a good
proxy of the expected rate of inflation or inflation is not a significant
opportunity cost variable in the demand for money function in Nepal.
4. The income elasticity in case of narrow money demand is 1.398 and in case of
broad money demand is 1.815. Since income elasticity is greater than unity in
both cases, money balances is still a luxury in Nepal. The more than unitary
income elasticity implies the under-monetization of the economy. In such a
situation, as the economy moves towards monetization, the demand for cash
increases more than the increases in income. Also, income elasticity in case of
broad money demand is found to be higher than the narrow money demand.
This finding also supports the findings by Poudel (1989) and Khatiwada
(1997).
5. The coefficient of error correction term in both cases has a negative sign
reinforcing the long run equilibrium relationship between the included
variables. Since the coefficient of ecm in case of broad money demand is
smaller in absolute value, disequilibrium errors created by the previous period
shocks are adjusted more slowly in case of broad money demand.
6. Money demand function in case of both monetary aggregates has been found
to remain stable during the time period under study as confirmed by the
CUSUM and CUSUMSQ tests. The financial liberalization process which has
led the economy to deregulation of interest rate, deregulation of financial
sector, deregulation of external sector and exchange rate depreciation has not
significantly resulted in the parameter instability as expected.
7. As the intercept term is statistically significant in both long run models, it
implies that unidentified variables including time trend have significant
bearings on real money demand. As the intercept term in both cases is
negative, it indicates that the unspecified variables including the time trend
have negative impact on real money demand.
5.2 Recommendations
From the conclusions of the study, the following recommendation can be
made:
1. Since the money demand functions in case of both monetary aggregates
are stable in their parameters, the central bank of Nepal can continue
the monetary targeting strategy as a policy in achieving the major
macroeconomic policy goals. NRB can use the narrow monetary
aggregate or broad monetary aggregate as an intermediate target in
conducting the monetary policy. Thus, any of the two definition of
money stock can be taken as an appropriate variable for estimation of
money demand in the policy formulation process.
2. In both models used in the study, none of the interest rates appeared to
be a significant variable in the long run money demand function. To
make the interest rate an effective opportunity cost variable, Nepal
should continue the financial liberalization process developing the
money and capital markets.
3. Since the intercept term is statistically significant in both long run models, it
implies that unidentified variables including time trend have significant
bearings on real money demand. As the coefficient is negative, it indicates that
the unspecified variables including the time trend have negative impact on real
money demand. Thus, further researches should be directed towards including
other determinant variables of money demand like expected inflation rate,
price level, exchange rate etc.
4. In both models, the income elasticity is greater than unity. This implies
the validity of the proposition that less developed countries where the
development of the financial markets is at the low web, money is more
important as a vehicle of saving. Thus, there is the need to develop the
financial market with attractive returns on the financial assets.
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