This paper fills a gap in the empirical work on the demand for money for Fiji. We allowed for structural breaks in the cointegrating equation, within the Gregory and Hansen framework, and found that there is a cointegrating relationship between real narrow money, real income and the nominal rate of interest in all the three types of their models. However, only the model with an intercept shift for the 1987 political coup yields a meaningful cointegrating relationship. We tested for its temporal stability and found that the demand for money in Fiji is stable.Structural break; Cointegration; Gregory and Hansen; Demand for money; Fiji

Kumar, Saten

Rao, B. Bhaskara

English

Research Papers in Economics

  1 
Structural Breaks and the Demand for Money in Fiji
1 
 
 
B. Bhaskara Rao
2 and Saten Kumar
3 
University of the South Pacific 
 
 
 
 
Abstract 
 
This paper fills a gap in the empirical work on the demand for money for Fiji. We 
allowed for structural breaks in the cointegrating equation, within the Gregory and 
Hansen framework, and found that there is a cointegrating relationship between real 
narrow money, real income and the nominal rate of interest in all the three types of their 
models. However, only the model with an intercept shift for the 1987 political coup 
yields a meaningful cointegrating relationship. We tested for its temporal stability and 
found that the demand for money in Fiji is stable. 
   
 
 
                                                 
1 We thank Mr. Rup Singh for comments and the University of the South Pacific for a research grant (Vote 
Code: 6599-1421) which is partly used for this paper. 
2 Professor of Economics at the School of Economics, the University of the South Pacific. 
3 Graduate student at the School of Economics, the University of the South Pacific.    2 
 
1. Introduction 
 
A countless number of empirical studies have estimated the demand for money in many 
countries and examined its stability. Demand for money and, more importantly, its 
temporal stability have important implications for the selection of the monetary policy 
instruments. In a classic paper Poole (1970) has shown that when the LM curve is 
unstable, central banks should use the bank rate as the instrument of monetary policy, but 
when the IS curve is unstable the appropriate monetary policy instrument is money 
supply. Since a major source of instability in LM is due to instability in the demand for 
money, the stability of the demand for money is important.  
 
In the developed countries the demand for money is found to be temporally unstable, 
since the late 1980s, due to the liberalization of the financial markets. Therefore, central 
banks in the developed countries have switched to bank rate as their main instrument of 
monetary policy. In contrast there is no significant evidence that the demand for money 
in the developing countries has also become unstable; see a recent comprehensive study 
by Oskooee-Bahmani and Rehman (2005). Nevertheless, central banks in many 
developing countries, including Fiji, have also switched to the bank rate as their 
instrument of monetary policy. Such an inappropriate choice of monetary policy 
instrument could actually lead to increased instability and it is important to test the 
stability of the demand for money with some recent developments in time series 
techniques.  
 
The main purpose of this paper is to fill a gap in the existing empirical work on the 
stability of the demand for money in the developing countries by allowing for structural 
breaks in the cointegrating relationship. To limit the scope of this paper, we examine the 
stability of demand for money only in Fiji with the Gregory and Hansen (1996a) 
technique. Needless to say our methodology can be easily used to analyse the stability of 
demand for money (or any other cointegrating relationship) in other countries. The 
outline of this paper is as follows. Section 2 briefly reviews the Gregory and Hansen   3 
model for estimating cointegrating equations with structural breaks. Section 3 presents 
empirical results for Fiji and discusses their implications. Summary and conclusions are 
in Section 4. 
 
2. The Gregory-Hansen Equations 
 
Gregory and Hansen (1996a) have proposed residual based tests for the null of no 
cointegration with structural breaks against the alternative of cointegration. In Gregory 
and Hansen (1996a) there are three models with alternative assumptions about structural 
breaks namely (1) level shift; (2) level shift with trend and (3) regime shift where both 
the intercept and the slope coefficients change. The single break date in these models is 
endogenously determined. These three models can be stated with the following simple 
specifications with two variables.
4 
 
121
1211
12112
(1)
(2)
(3)
ttktt
ttktt
ttktttkt
YX
YtX
YtXX
mmjae
mmjbae
mmjbaaje
=+++
=++++
=+++++
 
 
where Y is the dependent and  X is the independent variable, t  is time subscript, e  is an 
error term, k  is the break date and j is a dummy variable such that 
(4) if
if
tk
tk
tk
j 0
1 = £
> {   
 
It is easy to extend these models for more than one explanatory variable.  
 
                                                 
4 A fourth model developed by Gregory and Hansen (1996b)  is 
 
121112 ttktktttkt YttXX mmjbbjaaje =++++++  
 
We ignore this model in this paper because of some limitations in our software. 
   4 
A limited number of previous studies on the demand for money in Fiji are Luckett 
(1987), Joyson (1997), Jayaraman and Ward (2000), Katafono (2001), Rao and Singh 
(2005a) and more recently Singh and Kumar (2006a and 2006b). The merits and 
weaknesses of these earlier studies were discussed in Rao and Singh (2005a). While 
Katafono found that the demand for money is unstable, Rao and Singh, Jayaraman and 
Ward and Singh and Kumar found that the demand for money in Fiji is well determined 
and temporally stable. In all these previous studies an important issue that was not 
addressed is that the cointegration relationship may have a structural break during the 
sample period. Rao and Singh only briefly discuss this issue. Therefore, we explore the 
stability of the demand for money with the Gregory-Hansen techniques.  Since Rao and 
Singh have obtained similar coefficients for their cointegrating equations with two 
alternative techniques namely the LSE-Hendry GETS and the Johansen maximum 
likelihood systems methods, we shall use their specification which is: 
 
12 lnln(5) tttt MYr maae =+-+  
 
where M  is real narrow money, Y is real GDP and r is the nominal rate of interest.  The 
implied specifications for the three Gregory and Hansen equations with structural breaks 
are as follows. 
 
1212
12112
121111
222
lnln(6)
lnln(7)
lnlnln
(8)
ttkttt
ttkttt
ttkttk
tttkt
MYr
MtYr
MtYY
rr
mmjaae
mmjbaae
mmjbaaj
aaje
=++-+
=+++-+
=++++
--+
 
 
For convenience these equations will be referred as GH-I, GH-II and GH-III respectively. 
 
 The Gregory-Hansen method  is essentially an extension of similar tests for unit root 
tests with structural breaks, for example, by Zivot and Andrews (1992). The break date is 
searched by estimating the cointegration equations for all possible break dates in the 
sample and then selecting a date where the test statistic is the minimum (i.e., where the   5 
absolute value of the ADF test statistic is the maximum). However, the critical values for 
cointegration in this method are different. With regime shifts the distribution theory to 
evaluate the residual based tests is not the same as the standard MacKinnon (1991) 
cointegration tests used in the Engle-Granger two-step procedure. Therefore, Gregory and 
Hansen have tabulated the critical values by modifying the MacKinnon (1991) procedure 
for testing cointegration in the Engle-Granger method with unknown breaks. We follow 
this methodology in this paper. 
 
3. Empirical Estimates of the Break Date 
 
The definitions of variables and sources of data are same as in Rao and Singh (2005a). 
Our sample period is from 1971 to 2002 but due the presence of some lagged variables, 
the three models in equations (6) to (8) are estimated from 1974 to 2002 and the results 
are given below in Table-1.  
   6 
Table-1 
Tests for Cointegration 
with Structural Breaks 
1974-2002 
 
  Brake 
Date 
GH Test 
Statistic 
5%  Critical 
Value 
Reject H0  
of no  
Cointegration 
GH-I  1987  -5.19111  -4.92  YES 
GH-II  1976  -5.95961  -5.29  YES 
GH-III  1987  -6.71172  -5.50  YES 
 
These results, which are self-explanatory, imply that irrespective of which of the three 
models with structural breaks is used, there is a cointegrating relation between real 
money, real income and the nominal rate of interest in Fiji. However, the endogenously 
determined brake date is 1987 in GH-I and GH-III, but different at 1976 in GH-II. Since 
the null is rejected by all the three models, it hard to decide which is the best. Therefore, 
we have estimated the cointegrating equations for the three models with the Engle-
Granger method and the first stage OLS equations are given below in Table-2. 
 
From these estimates it can be said that GH-I is the most plausible model. In this model 
all the estimated coefficients, except the pre 1987 intercept, are significant and their 
values are plausible although the estimate of income elasticity at 0.76 seems be a bit low. 
However, the Wald test could not reject the null that that it is unity at the 5% level. The 
computed test statistic, with its p-value in brackets, is 1.462 (0.227). 
 
In GH-II the estimate of income elasticity is low at 0.262 and insignificant. In GH-III 
income elasticity, after the break, is very high at almost three and the estimates of the two 
interest rate coefficients are insignificant. These results in GH-II and GH-III can be 
rejected as implausible because statistical techniques, as noted by Smith (2000) and Rao 
(2006), are merely tools to summarize facts and are not appropriate to answer questions   7 
that belong to economic theory.
5 Therefore, we shall use the residuals from GH-I to 
estimate the short run dynamic equation for the demand for money with the error-
correction adjustment model (ECM).  
 
Table-2 
Cointegrating Equations 1974-2002
6 
 
  GH-I       GH-II           GH-III 
        Intercept  0.112 
(0.07) 
     3.736 
     (0.98) 
     10.340 
     (5.71)* 
         Trend         0.024 
     (2.91)* 
 
           ln Yt  
 
0.758 
(3.80)* 
     0.262 
     (0.51) 
     -0.625 
     (2.50)* 
             rt  -0.035 
(4.49)* 
     -0.029 
     (2.78)* 
     -0.003 
     (0.20) 
    Dummy 1976         -0.197 
     (2.26)* 
 
    Dummy 1987  0.230 
(4.37)* 
       -22.248 
     (3.68)* 
 Dummy 1987˝ ln Yt           2.912 
     (3.82)* 
  Dummy 1987 ˝ rt           0.027 
     (0.83) 
 
                                                 
5 Smith (2000) distinguishes between three stages in applied economic work namely purpose (or objective), 
summary of facts and interpretation of facts.  Within this threefold classification, statistical techniques are 
seen as tools to develop credible summaries of the observed facts. Purpose and interpretation are left to the 
analyst according to his/her preferred economic theories. Therefore, in evaluating the relative merits of the 
alternative statistical estimates, it is important to ask: how good a particular result is for summarizing the 
observed facts; see also Rao (2006). 
 
6 Absolute t-ratios are reported below the coefficients. * indicates significance at 5% level.   8 
In developing an appropriate ECM model for the short run, we adopted the LSE- 
Hendry’s GETS approach in the second stage. This second stage equation is estimated 
with OLS in which Dln Mt is regressed on its lagged values, the current and lagged values 
of Dln Yt and Drt and the one period lagged residuals from the cointegrating vector of 
Gregory Hansen i.e., from equation GH-I. We have used lags up to 4 periods and using 
the variable deletion tests in Microfit 4.1 and arrived at the following parsimonious 
equation: 
 
Dln Mt = -0.392 ECMt-1 + 1.092 Dln Yt – 0.816 Dln Yt-1 
                (1.80)**            (2.55)*            (1.84)** 
                        + 0.027 D
2rt-1 
                (2.45)*                                                          (9) 
           _ 
           R
2 = 0.532,     SER = 0.098,     Period: 1975-2002 
                X
2
sc1 = 0.691 (0.41), X
2
ff = 4.088 (0.04)*, 
                X
2
n = 0.791 (0.67), X
2
hs = 3.710 (0.05)* 
 
where * and ** indicate significance at the 5% and 10% levels respectively. It may be 
noted from these estimates that it is possible to reduce further the number of estimated 
coefficients to increase the degrees of freedom. The coefficients of Dln Yt and Dln Yt-1 are 
close and opposite in sign. When this restriction is tested, the Wald test computed ?
2(1) 
test statistic with p value in the parenthesis is 0.157 (0.692) is insignificant and the 
constraint could not be rejected. The following ultra parsimonious equation is based on 
this restriction:   
 
Dln Mt = -0.391 ECMt-1 + 0.958 D
2 ln Yt-1 
                (1.83)**            (3.69)*               
                      + 0.026 D
2rt-1 
                (2.46)*                                                         (10) 
            _ 
            R
2 = 0.548,     SER = 0.097,     Period: 1975-2002 
                  X
2
sc1 = 0.749 (0.39), X
2
ff = 3.951 (0.05)*, 
                  X
2
n = 1.039 (0.60), X
2
hs = 2.490 (0.12) 
 
The summary statistics of this equation have marginally improved. All the estimated 
coefficients are significant. The coefficient of the lagged error correction term is 
significant at 10% level with correct negative sign, and serves as the expected negative   9 
feedback function. This implies that if there are departures from equilibrium in the 
previous period, this departure is reduced by about 40% in the current period. The ?
2 
statistics indicate that there is no serial correlation (?
2
sc1), non-normality (?
2
n) and 
heteroscedasticity (?
2
hs) in the residuals. However, it may be noted that the functional 
form misspecification ?
2
ff test is marginally significant at the 5% but not at 1% level. This 
is not unusual for dynamic equations because it is hard to claim that the complex nature 
of dynamic adjustments, with limited data, can be adequately captured with linear 
specifications.  
 
Having obtained the long run equilibrium estimates and the dynamic counterpart, it is 
important to test for the stability of the money demand function. When we subjected our 
preferred equation (10) to CUSUM and CUSUMSQ stability tests, neither the CUSUM 
nor the CUSUM SQUARES showed any instability. The plots of these tests are given in 
Figure 1 and 2 below. They show that the money demand function is temporally stable in 
Fiji. Therefore, following Poole (1970) it can be said that money supply is the appropriate 
monetary policy instrument for the Reserve Bank of Fiji (RBF). However, if the RBF 
follows the advanced countries and target the rate of interest, this would probably cause 
more instability in GDP. In this respect our findings are consistent with those in Rao and 
Singh (2005a), Singh and Kumar (2006) and Jayaraman and Ward (2000) although these 
works did not allow for structural breaks in their cointegration equations. 
 
 
 
                             10 
                         Figure 1: CUSUM TEST FOR EQUATION 10 
 
              Plot of Cumulative Sum of Recursive Residuals 
 
 
 The straight lines represent critical bounds at 5% significance level 
-5 
-10 
-15 
0 
5 
10 
15 
1975  1980  1985  1990  1995  2000  2002 
 
 
                     
 
 
 
                    Figure 2: CUSUM SQUARES TEST FOR EQUATION 10 
          
            Plot of Cumulative Sum of Squares of Recursive Residuals 
 
 The straight lines represent critical bounds at 5% significance level 
-0.5 
0.0 
0.5 
1.0 
1.5 
1975  1980  1985  1990  1995  2000  2002 
 
 
 
 
 
   11 
4. Conclusion 
 
In this paper, we have used the Gregory Hansen procedure to test the stability of the 
demand for money in Fiji. We believe that our study is perhaps the first attempt to 
estimate and test the demand for money in Fiji with structural breaks.  Our estimates  
imply that there exist a cointegrating relationship between real money, real income and 
nominal rate of interest which might have shifted up by about 0.23 after the 1987 coup. 
This may be due to some increased precautionary demand for liquidity. However, the 
major finding of this paper is that there is a well-determined and stable demand for 
money in Fiji from 1971 to 2002. 
 
Our estimates imply that the income elasticity of 0.758 is, although somewhat lower than 
in the earlier studies of unity, the Wald test indicates that our estimate is not significantly 
different from unity. The estimate of interest rate elasticity, at its mean value of 6.97, is 
about –0.244 and consistent with the previous findings.  We hope that our paper will 
encourage further applied work with structural breaks on the demand for money in other 
countries as well as on other relationships. 
 
  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
   12 
 
References 
 
 
 
Gregory, A.W. and Hansen, B.E. (1996a) “Residual-based tests for cointegration in 
models with regime shifts,” Journal of Econometrics, Vol.70, pp.99-126. 
 
--------------- & -------------------- (1996b) “Tests for cointegration in models with regime 
and trend shifts,” Oxford Bulletin of Economics and Statistics, Vol.58, pp.555-559. 
 
Jayaraman, T.K. and Ward, B.D., (2000) “Demand for money in Fiji: An econometric 
analysis,” Pacific Economic Bulletin, Vol. pp.81-93. 
 
Joyson, R. (1997) Money demand in Fiji. Suva: The Reserve Bank of Fiji (Unpublished). 
 
Katafono, R. (2001) “Demand for money in Fiji,” Staff Working paper (03/2001). Suva: 
The Reserve Bank of Fiji. 
 
Luckett, D. (1984) “A preliminary study of the demand for money in Fiji,” Reserve Bank 
of Fiji, Quarterly Review, June, 1984 (RBF: Suva, Fiji). 
 
MacKinnon, J. G. (1991) “Critical values for cointegration tests,” in Engle, R. F. and 
Granger, C.W.J. (eds), Long run Economic Relationships: Readings in Cointegration, 
Oxford University Press, pp.267-276.  
 
Oskooee, M., and Rehman, H. (2005) “Stability of the money demand function in Asian 
developing countries,” Applied Economics, Vol. 37, pp. 773-792. 
 
Poole, W. (1970) “The optimal choice of monetary policy instruments in a simple macro 
model,” Quarterly Journal of Economics, Vol.84, pp.192-216. 
   13 
Rao, B. B., (2006)  “Estimating short and long run relationships: A guide to applied 
economists’, forthcoming in Applied Economics. 
 
Rao, B. and Singh (2005a) “Cointergration and error correction approach to the demand 
for money in Fiji,” Pacific Economic Bulletin, Vol. 20, pp. 72-86. 
 
Singh, R. and Kumar, S. (2006a) “Cointegration and demand for money in the Selected 
Pacific Island Countries,” Staff Working Paper No. 03/2006. Suva: The University of the 
South Pacific. 
 
--------------&-------------- (2006b) “Demand for money in developing countries: 
Alternative estimates and policy implications,” Staff Working Paper No. 05/2006. Suva: 
The University of the South Pacific. 
 
Smith, R. (2000) “Unit roots and all that: The impact of times series methods on 
Macroeconomics,” in Backhouse, R. and Salanti, A. (eds). Macroeconomics and the Real 
World, Oxford: Oxford University Press. 
 
Zivot, E. and Andrews, D.W.K. (1992) “Further evidence on the Great Crash, the oil-
price shock, and the Unit root hypothesis,” Journal of Business and Economic Statistics, 
Vol.10, pp.251-270. 
 
                                                       
 
 
 
 
 
 
 
 
 
 
   14 
 
 
 
  

A preliminary study of the demand for money in Fiji,” Reserve Bank of Fiji, Quarterly Review,

and Singh (2005a) “Cointergration and error correction approach to the demand for money in Fiji,”

Critical values for cointegration tests,” in

Demand for money in Fiji,” Staff Working paper (03/2001). Suva: The Reserve Bank of Fiji.

Demand for money in Fiji: An econometric analysis,”

Estimating short and long run relationships: A guide to applied economists’, forthcoming in Applied Economics.

Further evidence on the Great Crash, the oilprice shock, and the Unit root hypothesis,”

Money demand in Fiji. Suva: The Reserve Bank of Fiji (Unpublished).

Residual-based tests for cointegration in models with regime shifts,”

Stability of the money demand function in Asian developing countries,”

The optimal choice of monetary policy instruments in a simple macro model,”

Unit roots and all that: The impact of times series methods on Macroeconomics,”

Structural Breaks and the Demand for Money in Fiji

Structural Breaks and the Demand for Money in Fiji

Abstract

Similar works

Full text

Available Versions

Research Papers in Economics