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On the stability of demand for money in a developing economy
Journal of Development Economics 72 (2003) 335 – 351 www.elsevier.com/locate/econbase
On the stability of demand for money in a developing economy Some empirical issues Basanta K. Pradhan *, A. Subramanian National Council of Applied Economic Research, Parisila Bhawan, 11-Indraprastha Estate, New Delhi 110002, India Received 1 January 1998; accepted 1 September 2002
Abstract In recent years, a number of developing countries have undergone extensive reforms in the financial sector. The effects of this underlying financial innovation process on the stability of demand for money have seldom been studied in the context of developing countries. Nevertheless, these changes in the financial sector highlight the transition from one regime to the other. This need necessarily follows that such a process has to be accounted for in the long-run demand for money estimation. Here, we use a three-step testing procedure to study the implication of the reform process on the stability of demand for money. To account for the abovementioned changes, we specify the demand for money in an open economy framework using data from India. An estimation procedure accounting for these changes in the specification of demand for money suggests that financial deregulation and innovation did affect the empirical stability of demand for money in India. D 2003 Elsevier B.V. All rights reserved. JEL classification: E41 Keywords: Stability; Money; Developing economy
1. Introduction The stability of the demand for money is one of the most important and recurring issues in macroeconomic policy analysis. The issue at stake here is the set of necessary * Corresponding author. National Council of Applied Economic Research, Parisila Bhawan, 11-Indraprastha Estate, New Delhi 110002, India. E-mail address: [email protected] (B.K. Pradhan). 0304-3878/03/$ - see front matter D 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0304-3878(03)00080-4
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conditions for money to exert predictable influence on the economy so that the central bank’s control of the money supply can be a useful instrument of economic policy. A monetary policy that seeks to limit the supply of money to its demand facilitates the tasks of demand management and contributes to the achievement of price stability. The rate of growth in money supply should be in conformity with the desired rate of growth in output and thus constrain the price increases to an acceptable level. A stable demand for money implies a stable money multiplier and, therefore, stability makes it easier to predict the effect of a given money supply on the aggregate money income. The stability of demand for money has been studied extensively both theoretically and empirically, especially, in the case of USA and UK during the periods of ‘missing money’ and ‘great velocity decline’ in the early 1970s.1 The most widely applied tests to study the implications on the demand for money are residual-based ones in which the null hypothesis of no cointegration is tested against the alternative that the relationship is cointegrated in the sense of Engle and Granger (1987). But this linear combination may have shifted at some unknown point in the sample. In this context, the standard tests for cointegration are not appropriate, since they presume that the cointegration vector is timeinvariant under the alternative hypothesis. Following Johansen (1988) and Johansen and Juselius (1992), some studies estimate using the complete systems analysis of cointegration. However, while statistically appealing, the full system approach has some practical problems, mainly related to the increased dimensionality of the system due to the unconditional use of information. An additional problem is the presence of structural breaks, which may affect particular variables and are difficult to handle statistically in large models. Conditional partial models are attractive because they condition information based on economic theory and increase efficiency. Structural breaks are also easier to handle in small systems than in large ones. In this paper, we follow an alternative route which consists of three steps: (i) estimation of cointegration relationship using full systems model; (ii) models are then reduced from systems formulation to single equations using weak exogeneity tests and then (iii) testing for cointegration between the variables allowing for the possibility of one break in the cointegration vector with unknown timing. Here, we assume that the full system can be partitioned into a vector of endogenous variables and a vector of weakly exogenous variables in the sense of Engle et al. (1983). If the assumption of weak exogeneity is satisfied, then the system of equations in the second step is block recursive.2 The third step is the residual-based tests for cointegration in models with regime shift. We use a class of residual-based test for cointegration which allows for regime shift and are multivariate extension of some of the univariate tests allowing for the possibility of a break using recursive, rolling or sequential approach.3 This method has an advantage over the conventional ADF test, the power of which falls sharply in the presence of a structural break.4 1
See Hendry and Ericsson (1991), Goldfeld and Sichel (1990), etc. The advantage of appropriately partitioning full cointegrated systems into conditional partial models, which can be given a structural interpretation has been emphasised by Johansen (1992) and Ericsson (1995). 3 See Perron (1989), Banerjee et al. (1992), etc. 4 See Gregory and Hansen (1996) for the advantages of this method. 2
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We apply this methodology to the Indian case. The Indian case is especially interesting in the light of reforms undertaken in the last decade for which no attempt has yet been made to study the impact of these reforms on the stability of demand for money. These issues have not caught up with the research on developing countries though the processes of reforms in general and financial sector reforms in particular are an overriding phenomenon in the past decade. The effects of these underlying financial innovation process highlight the transition from one regime to the other which need necessarily follows that such a process has to be accounted for in the long-run demand for money estimation. Fig. 1 shows the velocity of money defined both narrowly (M1) and broadly (M3). The figure reveals a change in the trend behavior of velocity for M3 around the mid-1980s after which the declining trend stabilizes. The trend behavior in the velocity of M1 is somewhat mixed with an increase after the mid-1990s. The behavior that is important is the diverging trend between M1 and M3 in the later half of 1990s. This period has been characterized by important changes in the financial sector. Financial liberalization has been a major target of policy reforms in India since the early 1990s. The reforms in general were concentrated broadly in these four areas, such as interest rate and credit reforms, capital market reforms, exchange rate reforms and fiscal reforms. The interest rate structure was simplified in October 1990 with scheduled commercial banks allowed to freely determine their lending rates on loans for purchase of consumer durables, loans to individuals for purchase of shares and bonds and other nonpriority sector. Since October 1995, scheduled commercial banks were also permitted to fix their own interest rates on domestic term deposits with a maturity of 2 years or more. Later, the norms were further relaxed to cover term deposits with a maturity of over 1 year. Even interest rates on nonresident (external) rupee term deposits over 2 years were freed with effect from April 1996. Since 1991, the capital market in India has been influenced by wide-ranging reforms leading to changes in the number of issues, market capitalization
Fig. 1. Velocity of money.
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and trading volumes. Another important change in the capital market, which has wideranging effects for the money demand is the easy access allowed to the international capital market through euro-equity shares. The Indian rupee was made partially convertible in 1992 –1993. In the following year, full convertibility of the rupee was allowed on the trade account, which was extended for almost all merchandise trade transactions and all receipts on the current or capital account, but not to all payments. In 1994, rupee was made fully convertible on current account. Another important change is the entry of foreign capital in the Indian stock market through foreign institutional investors and joint ventures. The implications these changes have on the trend behaviour of velocity of money can be interpreted along the lines of Bordo and Jonung (1987) analysis. The stylised long-run global pattern of velocity of money behaviour as documented by them suggests that technical progress in the financial sector introduces two competing influences on the trend behaviour of velocity, each dominating at a different stage of development of a particular country. During the first stage of development, the economy is characterised by increasing monetisation. Cash and demand deposits are increasingly used for settling transactions, replacing earlier reliance on barter trade. As a result, demand for transaction balances grows more rapidly than income and velocity is characterized by a negative trend. During the second phase of development, financial liberalization allows for the introduction of a range of widely traded and highly liquid securities. These assets substitute money as a store of value. Additionally, technological innovation in the financial sector and the rapid transfer of funds facilitates the economizing on money balances. As a result, money balances grow slower compared to the volume of transactions and velocity stabilizes or even increases over time. Hence, velocity follows a U-shaped pattern. This change in the trend behavior of velocity, however, presents difficulties in modeling the empirical relationship among the variables in the demand for money function. The features which distinguish this paper from the others addressing the same issues for a developing economy undergoing financial sector reforms are: first, this paper uses an alternative three-step testing procedure to evaluate the stability of demand for money accounting for structural breaks in the demand for money specification. Second, this paper estimates the demand for money using data from India which spans a period from the fourth quarter of 1970 to the third quarter of 2000, the post bank-nationalization period. These years, in fact, have been characterized by important changes in the Indian money market structure: stock market collapse, reforms in the financial sector, progressive dismantling of administered interest rates, government debts and foreign exchange rates are at market rates, etc. As a result of these financial deregulation and innovation, the character of the market and the role of money within the system have been altered by these changes.5 The long-run relationship between real money balances and output may have also changed. In order to test this proposition, we test for cointegration between the variables allowing for the possibility of a break in the cointegration vector with unknown timing.
5 Apart from this, there were some significant changes such as phasing out of interest tax, launching of capital indexed bonds, etc.
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In Section 2, we discuss some of the econometric issues on the demand for money followed by an exploratory analysis of data used in the demand for money specification in Section 3. In Section 4, we test for the existence of long-run relationship in the demand for money function in a systems framework and then the single equation formulation to test for structural breaks. Section 5 provides the concluding remarks.
2. Demand for money: some econometric issues Consider the following simple specification with Mt, the measure of money and Yt, representing both scale and opportunity cost variables and Ut, the error term. DMt ¼ bDYt þ Ut
ð1Þ
The change represented by D in the demand for money from one period to the next is explained by the change in Y variables over the same time interval. In order to understand the dynamics of adjustment in Eq. (1) with an error-correction representation, consider the following transformation. Assume the equilibrium value of Mt is f( Yt) for all t, and hence, at equilibrium, Mt1 ¼ f ðYt1 Þ ¼ CYt1 ðsayÞ
ð2Þ
where C is a linear operator. Let X be defined as a negative parameter, which denotes the degree of adjustment, then an expression such as XðMt1 CYt1 Þ
ð3Þ
represents the level of M in period (t 1) relative to the equilibrium value of M for the same period, CYt 1. Introducing this expression in Eq. (1), we obtain DMt ¼ bDYt þ XðMt1 CYt1 Þ þ Ut
ð4Þ
This gives an error-correction representation of demand for money with X as the errorcorrection coefficient (or adjustment parameter), while C is the long-run multiplier and b, the impact multiplier. Further, Ut is white noise error term, i.e., a mean-zero uncorrelated process. If 2 < X < 0, then the characteristics equation of Eq. (1) implies a stable longrun relationship M = CY. Assume that the explanatory variable is integrated of order 1[l(1)]. If the model is stable, then the linear combination Mt CYt is stationary, although Mt (and Yt if C p 0) are integrated of order 1; i.e., Mt and Yt are cointegrated of order (1,1) with cointegrating vector (1, C). On the other hand, if X = 0, then there is no adjustment towards equilibrium and hence no cointegration.6 The above illustration assumes that Y variables are weakly exogenous for the parameters of the conditioned model (see e.g. Engle et al., 1983). However, this assumption underrepresents the potential relationships when more than one cointegrated vector exists leading to inefficiency. Hence, we adopt a more comprehensive econometric 6
For a more explicit exposition, see Holden and Perman (1994).
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procedure based on the estimation of Vector Autoregressive models (VAR). These models characterize the joint behavior of a group of variables conditional on their past values also including the constant terms, linear trends, seasonal dummies and even specific dummies. A VAR model with n variables takes the following form Zt ¼ Al Zt1 þ . . . þ Ak Ztk þ Ut
t ¼ 1; . . . ; T
ð5Þ
were Zt is (n l) and each of the Al is an (n n) matrix of parameters. Ut is a ndimensional normal process with N(0,r). If the l(1) variables that we are modeling have r stationary equilibrium relationships amongst them, then we can write the system in the Stationary Vector Equilibrium Correction form (e.g. Johansen, 1988) which is given by: DZt ¼ U1 DZt1 þ . . . þ Uk1 DZtk þ pZtk þ hDt þ Ut
ð6Þ
where Ul = (l A1 . . . Al), (l = 1, k 1), and p = (l A1 . . . Ak) representing both short- and long-run adjustment to changes in Zt, respectively. The matrix p has reduced rank equal to r with speed of adjustment to disequilibrium and a matrix of longrun coefficients represented by a and b, respectively. We use the test developed by Johansen (1988, 1991) to test for the number of cointegration relationships amongst the variables – trace statistics. In the Johansen’s procedure, testing for cointegration amounts to a consideration of the rank of p, that is, finding the number of r linearly independent columns in p. In such a procedure, inclusion of stationary variables l(0) by itself form a linearly independent column in p and create identification problem. While inclusion of l(2) variables in such models requires a different procedure. Hence, the knowledge of the order of integration of each of the variables may help in interpreting the initial results obtained from using the Johansen approach. There are several ways of testing for the order of integration. Two generally known tests are the Dickey –Fuller test (DF test) and Augmented Dickey –Fuller test to correct for the autocorrection among the error terms. Perron (1989) showed that if a series is stationary around a deterministic time trend that has undergone a structural break sometime during the period under consideration, the failure to take account of this change in the slope would be mistaken by the usual ADF unit root test as a persistent innovation to a stochastic trend.7 That is a unit root test, which does not take account of the break in the series, will have low power. A structural break essentially corresponds to an intermittent shock with a permanent effect on the series (Hendry, 1996). The opposite can also happen if the break occurs at the beginning of the sample (Leybourne et al., 1998). In order to test for the possibility of a break, a number of univariate tests were proposed such as recursive, rolling, or sequential approach (Banerjee et al., 1992) and further tests of Perron (1989), Perron and Vogelsang (1992) and Zivot and Andrews (1992). Here, we propose to use a more general, residual-based multivariate test allowing for a regime shift in either the intercept alone or the entire coefficient vector (Gregory and Hansen, 1996). This test is a multivariate extension of the univariate test mentioned above. 7 Gregory et al. (1996) have shown that the power of the conventional ADF test falls sharply in the presence of a structural break.
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The general advantage with this test is that they are noninformative about the timing of the regime shifts, which prevents ad hoc selection of structural breaks. We consider three alternative models: (i) a level shifts, (ii) a level shift with a trend, and (iii) a regime shift. The choice of the model is data-dependent. The standard method of testing the null hypothesis of no cointegration is to apply a unit root test, the ADF test, on the residuals of the cointegrating equation. In the presence of structural breaks, cointegration tests involve searching for the largest negative value, ADF*, of the ADF statistic over all possible break dates. The cointegration regression is estimated sequentially with the break occurring at a different data every time between 1 and T, where T is the last observation. The largest negative value in the sequence of the ADF* statistic is then compared with the simulated critical values reported in Gregory and Hansen (1996).
3. The demand for money: an exploratory analysis of the data From the policy standpoint, it is important to identify the correct measure of money as a better guide to monetary policy for the purpose of price stability. We consider both M1 and M2. Secondly, since the policy maker may be interested not only in the forecasting power of such estimations but also about the short-run relevance of the parameters, we use the high frequency monthly data. All the series are monthly, seasonally unadjusted and the estimation sample extends from 1970(04) to 2000(03). The data used in the estimation of money demand are given by the logarithm of real money, M1 and M3, index of Industrial production, and rate of interest and prices. The M1 is defined as currency and demand deposits while M3 is defined as M1 plus time deposits with the banks. The literature on developing countries indicates that the models on narrow money worked better reflecting the weak banking system and low-financial sector development. However, over time narrow money accommodates the new instruments created as a result of the evolving financial system and institutional framework. Hence, we use both money, defined narrowly and broadly, to model the demand for money in India.8 The selection of opportunity cost variable is crucial to the determination of money demand especially in the Indian context where interest rate structure is complex, segmented and pegged by policy till September 1995 (Government of India, 1996). Since the degree of liquidity is different for both M1 and M3, it is essential that the demand specification should incorporate different interest rates as the relevant opportunity cost. Hence, we consider both short- and the medium/long-term interest rates in the specification. Among the range of alternative rates like bank deposit rates, treasury bill rate, etc., we choose call money rates representing short-term and prime-lending rates representing the medium/long-term opportunity cost. The choice is facilitated by the availability of the data as well as the functional importance of these opportunity cost variables in time differentiation. The index of industrial production (1993 – 1994 = 100) is used as the scale variable. It is chosen mainly because monthly data are available only for this measure. Wholesale Price 8 Hafer and Jansen (1991) used money defined broadly to yield a stable function and they preferred a broader definition to evaluate the long-run economic impact of the changes in monetary policy.
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Fig. 2. (a) Log of narrow real money, (b) log of broad real money, (c) short-term interest rate, (d) long-run real rate of interest, (e) log of real exchange rate, (f) log of US treasury bill, (g) log of index of industrial production, and (h) log of wholesale price index.
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Fig. 2 (continued).
Index (WPI) is considered as the price variable though specifications with Consumer Price Index (CPI) were also used in the trial runs. For the sake of brevity, we do not present the results here.
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Fig. 2 (continued).
An informal examination of the data and the graphs, presented in Fig. 2, may be useful in giving a preliminary idea of the time series properties of these variables. While index of industrial production shows quite a regular pattern, real M1 shows two different seasonal patterns before and after 1979. This irregularity is due to the earlier inclusion of the part of savings deposits which was permitted to be withdrawn without notice was added to demand deposits. With effect from March 1, 1978, this accounting procedure was changed and interest accruing saving deposits is now treated as time deposits. Both inflation and real long-run interest rates show regular seasonal patterns through out the period, while short-run rate of interest shows sharp fluctuations after the 1990s which coincide with the policy changes in the structure of interest rates in India. The longrun rate of interest shows a decline in the spread by 0.5 points in January 1997, though varying for individual banks; owing due to RBI’s announcement at the end of 1996 asking banks to announce the maximum spread over the prime rate for all advances.
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4. Empirical results In 1992– 1993, a liberalised exchange rate system was introduced to make the Indian rupee partially convertible. The following year, this system was dispensed with and replaced by a unified exchange rate system where full convertibility of the rupee on the trade account was allowed. This was extended for almost all merchandised trade transaction with all receipts on the current or capital account but not to all payments. In 1994, full convertibility of the rupee on current account was announced. The empirical estimates presented in this section are augmented by variables exerting foreign influence to allow for currency substitution, a decent representation of not so a closed economy. In this context, we introduce two additional variables as the opportunity cost of holding money namely the real exchange rate (LREER) and the yield on the US treasury bills (LTBILL), though London interbank offer rate is the most widely used (Darrant, 1986; Arize, 1994). Before testing for cointegration, the order of integration of the individual time-series needs to be established. The tests used to investigate the existence of unit roots in the variables are based on the Augmented Dickey – Fuller (ADF) test. The regression for ADF tests is presented below in Eq. (7). n X DlnZt ¼ at þ b1 lnZt1 þ b2 T þ nbf DlnZtf þ et ð7Þ f ¼1
where Zt 1 is the 1-year lag of the relevant time series, D is the first difference and et is the residual, and T is a linear deterministic time trend. The null hypothesis that Zt is a stationary series is rejected when the coefficient of Zt 1 is not significantly negative. In Table 1, we present the test results for all the variables. Here, seasonal dummies were included to allow for seasonal changes in the seasonally unadjusted data. The ADF test is done by both including and excluding seasonal dummies. The lag length is calculated using the Schwert’s criterion (Schwert, 1989). In all the cases, the null hypothesis of nonstationarity is not rejected except for the rate of inflation (INF) and short- and long-term real interest rates (SRINT and LRINT), shortrun nominal interest rate (SINT) which are significant at 1% level. Therefore, these four variables are stationary at levels, namely l(0). While real money defined narrowly (LRM1) and broadly (LRM3), wholesale price index (LWPI), long-run nominal rate of interest (LINT), both index of industrial production for manufacturing (LIIPM) and general (LIIPG) are all nonstationary at levels. Proceeding further, we make use of the unit root test to find out if the series becomes stationary after differencing once.9 If the series becomes stationary after differencing once, then the original series is integrated of order one. All the nonstationary series becomes stationary after differencing once. The t values for each of the differenced series presented in the table exceeds the Mackinnon critical value at 1% level of significance ( 3.657). Therefore, first-differenced series do not exhibit unit roots. In other words, the series are stationary in differences which can be represented as l(0) and the original series as l(1). 9
Differencing the logarithmic series.
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Table 1 Results based on unit root test Variables
LRM1 LRM3 INF LWPI LRINT SRINT LINT SINT LIIPG LIIPM LTBIL LREER DLRM1 DLRM3 DLINT DLWPI DLIIPG DLIIPM DLTBIL DLREER
Constant
Constant and seasonal
Constant and trend
Constant, trend and seasonal
Test statistics
Lag length
Test statistics
Lag length
Test statistics
Lag length
Test statistics
Lag length
1.05 0.55 6.66* 1.20 18.69* 18.13* 2.13 4.62* 0.17 0.41 2.09 1.33 9.70* 7.58* 19.26* 3.96* 11.29* 11.68* 5.59* 7.59*
6 6 6 11 0 0 0 3 6 6 10 8 7 6 0 11 5 7 10 7
1.27 0.58 4.95* 1.07 19.04* 18.33* 2.16 4.37* 0.8 1.11 1.77 1.39 7.51* 6.01* 19.10* 3.96* 8.55* 8.84* 10.02* 6.96*
6 6 6 11 0 0 0 3 6 6 6 8 7 6 0 11 5 7 5 7
1.90 2.54 8.12* 3.41 18.68* 18.10* 1.36 4.82* 2.98 2.89 2.46 2.06 9.89* 7.54* 19.41* 4.04* 11.30* 11.77* 5.64* 7.62*
6 6 6 11 0 0 0 3 8 7 10 8 7 6 0 11 5 7 10 7
1.83 2.55 6.17* 3.69** 19.02* 18.30* 1.37 4.55* 2.49 1.92 1.95 2.18 7.72* 6.04* 19.26* 4.02* 8.63* 8.99* 10.01* 6.99*
6 6 6 12 11 0 0 3 7 7 6 8 7 6 0 11 5 7 5 7
* and ** indicate rejection of unit roots at 1% and 5% level of significance, respectively. L and D refer to log and first difference, respectively.
4.1. Testing long-run relationship in the demand for money Given that the data are monthly, we start with the estimation of a VAR with 12 lags for the full sample and, as real money is affected by seasonality, we introduce a set of centered seasonal dummies which are orthogonal to the constant term. Furthermore, the estimation of the unrestricted VAR includes also two impulse dummies one for the 1995(10), introduced mainly to capture some instability in the equation for interest rate, which corresponds to interest rate deregulation. It is worth noting here that inclusion of such Table 2 Tests of the cointegration rank for the demand for money function Ho:r 0 1 2 3 4 5
LRM1
LRM3
k1
ktrace
ktrace(0.95)
k1
ktrace
ktrace(0.95)
0.319 0.096 0.031 0.021 0.015 0.012
180.68* 50.36 25.37 15.56 8.87 0.90
98.15 70.85 45.21 30.56 14.41 3.76
0.169 0.079 0.043 0.027 0.017 0.011
118.02* 59.90 26.60 12.50 5.43 0.80
85.17 65.18 30.21 25.95 13.13 2.85
* and ** indicate significance at 1% and 5%, respectively.
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Table 3 Normalised cointegration coefficients
LRM1 LRM3
LIIPG
LINT
LREER
LTBILL
LWPI
0.94 1.28
0.09 0.29
0.21 0.35
0.01 0.05
0.37 0.23
dummies will affect the underlying distribution of the test statistics and hence the critical values provided in Osterwald-Lenum (1992) are only indicative. For these reasons, we calculate the critical values using the program Disco. The unit root tests show that the variables are either l(0) or l(1). Though stationary variables might play a key role in establishing a sensible long-run relationship between nonstationary variables, inclusion of such variables will increase the cointegration rank. Henceforth, we exclude the stationary variables in the estimation of the demand for money except WPI, which becomes significant at 5% level only when constant, trend and seasonal dummies are included. We now use the Johansen cointegration procedure to determine the rank r and to possibly identify a long-run money demand function amongst the cointegration vectors. Given that the data are monthly, we start with the estimation of a VAR with 12 lags for the full sample and, as real money is affected by seasonality, we introduce a set of centered seasonal dummies which are orthogonal to the constant term. To find a model with the appropriate lag length and to avoid overparameterization, the test is repeated by sequentially reducing one lag at a time until we find the appropriate model free of estimation problem. The cointegration test results are presented in Table 2. This indicates that the trace test rejected zero in favor or at least one cointegrating vector. The results are significant at 1% level. The standardised coefficients of the variables entering into the respective cointegrating vector are presented in Table 3. The coefficients are normalised with a value of one along the principal diagonal of the matrix. The long-run income elasticity for narrow money is close to one as suggested by the quantity theory of money. The long-run demand for real money is positively affected by the own rate of return for money, prices and exchange rate while negatively for foreign interest rate. Generally, a relative increase in the interest rates abroad exert negative influence on the domestic money holders to substitute away from foreign assets by drawing down domestic money holdings. Hence, the foreign Table 4 Test for weak exogeneity for money narrowly defined (M1) Variables
al = 0
v2(l)
Lrm1 Liipg Lint Lreer Ltbill Lwpi
0.386 0.290 0.531 0.004 0.147 0.108
7.88 3.87 15.15 0.45 0.75 3.45
[0.0153]** [0.1153] [0.4305] [0.4203] [0.0681] [0.0021]*
* and ** reject at 1% and 5% significance level, respectively. The probability of getting any number exceeding the v2 value shown above is less than the figure presented with in the squared brackets.
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Table 5 Test for weak exogeneity for money broadly defined (M3) Variables
al = 0
v2(l)
Lrm3 Liipg Lint Lreer Ltbill Lwpi
0.377 0.190 0.431 0.114 0.156 0.019
6.95 2.56 13.13 0.35 0.65 2.95
[0.0165]** [0.1032] [0.352] [0.376] [0.0691] [0.0010]*
* and ** reject at 1% and 5% significance level, respectively. The probability of getting any number exceeding the v2 value shown above is less than the figure presented within the squared brackets.
interest rate such as the US treasure bill rate shows a negative relationship though the influence is substantially lower because of the not so open nature of the Indian economy. 4.2. Model formulation: from the full system to single equation In order to examine the short-run demand for money for a simpler specification, we test for weak exogeneity among the cointegrating relationship. Since one cointegrating relationship has been identified, the weak exogeneity tests are evaluated under the assumption of rank one. The null hypothesis is the existence of weak exogeneity. To test for weak exogeneity in the system as a whole requires a test of the hypothesis that H:aij = 0 for j = 1,. . .,r, where row i contains only zeroes. This test is conducted by placing row restrictions on a to give a new restricted model, and then using a likelihood ratio test involving the restricted and unrestricted models to ascertain whether the restrictions are valid. The results presented in Tables 4 and 5 show that the weak exogeneity is rejected for both LRM1 and LRM3 at 1% and LWPI at 5%. Therefore, a short-run model can be designed with a system of two equations, one each with both narrow and broad money, and another with prices by considering income, interest, exchange rate and foreign interest rate as weakly exogenous. Since the objective is to study the demand for money relationship, we focus our attention only on the single equation specification for money.
Table 6 Testing for cointegration with regime shift M1
M3
Test statistics
Break point
Test statistics
Break point
ADF* Level shifts Level shift with trend Regime shift
5.67** 4.72 5.67
(0.99) (0.75) (0.68)
4.90 3.93 4.38
(0.26) (0.23) (0.27)
ADF Constant Constant with trend
5.59* 5.72*
CV 3.45 (1%) 3.98 (1%)
3.08** 3.12
CV 2.87 (5%) 3.13 (10%)
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Subsequently, this single equation demand for money is used to test if the long-run relationship among variables in the demand for money has changed as a result of financial deregulation and innovation. In order to test this proposition, we follow the methodology of Gregory and Hansen (1996) and test for cointegration between variables in the models with regime shifts. A large number of specifications were tried with different combinations of the weakly exogenous variables. Here in Table 6, we present results only for the full specification, though results did not change much with different specifications. The conventional ADF tests reject the null hypothesis of no cointegration at 1% significance level for M1 while for M3 the null is rejected only for the constant though at 5% level. The selection of lag for both conventional ADF and ADF* is based on Schwert’s criterion and t-test. The maximum lag length was set at 12, given the monthly data, and then progressively reduced until the Schwert’s criterion is the smallest and also the last lag of the first difference included is significant at normal critical value. Across all experi-
Fig. 3. Structural breaks in money demand.
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ments the lag lengths were generally 8 or 9 and, occasionally lower. The smallest test statistics occurred in the later half for M1 and in the first half for M3 as also seen in Fig. 3, which plots the ADF* for level shift (M1C and M3C), level shift with trend (M1CT and M3CT) and regime shift (M1R and M3R). The conventional ADF test rejects the null while ADF* does suggest that structural change in the cointegration vector is important and needs to be taken care of in the specification of demand for money.
5. Some concluding remarks The standard assumption of the recent empirical literature on the long-run relationship of the money demand in the Indian economy is the existence of stable demand for money. Despite financial deregulation and innovation, it is still maintained that demand for money is stable. This issue on the demand for money is subjected to empirical investigation in this paper which, however, casts serious doubts on the stability aspect of the demand for money in the Indian economy. The empirical evidence was based on an elaborate methodology, first identifying the full systems model and then reducing it to the single equation framework with finally testing for the structural break with unknown timing. This test which allows for the possibility of regime shifts seems to suggest lack of stability in the demand for money, given the data set and the model specifications. Hence, a money demand specification with an open economy framework, enveloping the changing financial sector and subjected to residual-based tests for cointegration does raise some important questions on the long-run relationship between the series. However, further research can focus on this issue by using a more robust nonlinear specification, such as the logistics smooth transition functions to model the smooth transitions from one regime to another.
Acknowledgements Previous versions of this paper were presented at the 28th Annual Conference of Economists, 26 –30 September 1999, La Trobe University, Melbourne, Australia and also in the conference on Money and Finance in the Indian Economy, 2 –4 December 1998 held at the Indira Gandhi Institute of Development Research, Mumbai. This paper forms part of MIMAP India project supported by the International Development Research Centre (IDRC), Canada. We thank Sebastian Edwards, K.L. Krishna and the anonymous referee for their comments on the previous version of this paper. However, errors that still remain are our responsibility.
References Arize, A.C., 1994. A re-examination of the demand for money in small developing economies. Applied Economics 26 (3), 217 – 228 (March).
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Banerjee, A., Lumsdaine, R.L., Stock, J.H., 1992. Recursive and sequential tests of the unit-root and trend-break hypothesis: theory and international evidence. Journal of Business and Economic Statistics 10, 271 – 287. Bordo, M.D., Jonung, L., 1987. Long-run Behavior of the Velocity of Circulation: The International Evidence. Cambridge Univ. Press, Cambridge. Darrant, A.F., 1986. The demand for money in some major OPEC members: regression estimates and stability results. Applied Economics 18 (2), 127 – 142. Engle, R.F., Granger, C.W.J., 1987. Cointegration and error correction: representation, estimation and testing. Econometrica 55, 251 – 276. Engle, R.F., Hendry, D.F., Richard, J.F., 1983. Exogeneity. Econometrica 51, 277 – 304. Ericsson, N.R., 1995. Conditional and structural error correction models. Journal of Econometrics 69, 159 – 171. Goldfeld, S.M., Sichel, D.E., 1990. The demand for money. In: Friedman, B.M., Hahn, F.H. (Eds.), Handbook of Monetary Economics, vol. 1. North-Holland, Amsterdam, pp. 299 – 365. Government of India, 1996. Economic Survey, 1995 – 96. Ministry of Finance, New Delhi. Gregory, A.W., Hansen, B.E., 1996. Residual based tests for cointegration in models with regime shifts. Journal of Econometrics 70, 99 – 126. Gregory, A.W., Nason, J.M., Watt, D., 1996. Testing for structural breaks in cointegrated relationships. Journal of Econometrics 71 (1 – 2), 321 – 341 (March). Hafer, R.W., Jansen, D.W., 1991. The demand for money in the United States: evidence from cointegration test. Journal of Money, Credit and Banking 23 (2), 155 – 168. Hendry, D.F., 1996. A Theory of Co-breaking. Paper presented at the time series meeting organized by NBERNSF. Hendry, D.F., Ericsson, N.R., 1991. An econometric analysis of money, U.K., demand in monetary trends in the United States and the United Kingdom by Milton Friedman and Anna J. Schwartz. American Economic Review 81 (1), 8 – 38. Holden, D., Perman, R., 1994. Unit root and cointegration for the economists. In: Rao, B.B. (Ed.), Cointegration: For the Applied Economists. Macmillan, New York, pp. 47 – 112. Johansen, S., 1988. Statistical analysis of cointegrating vectors. Journal of Economic Dynamics and Control 12, 231 – 254. Johansen, S., 1991. A Statistical Analysis of Cointegration for l(2) Variables. University of Copenhagen. Johansen, S., 1992. Cointegration in partial systems and the efficiency of single equations analysis. Journal of Econometrics 52, 313 – 334. Johansen, S., Juselius, K., 1992. Testing structural hypothesis in a multivariate cointegration analysis of the PPP and the UIP for UK. Journal of Econometrics 53, 211 – 244. Leybourne, S., Mills, T., Newbold, P., 1998. Spurious rejections by Dickey – Fuller tests in the presence of a break under the null. Journal of Econometrics 87, 191 – 203. Osterwald-Lenum, M., 1992. A note with quantiles of the asymptotic distribution of the ML cointegration rank test statistics. Oxford Bulletin of Economics and Statistics 54, 461 – 472. Perron, P., 1989. The great crash, the oil shock and the unit root hypothesis. Econometrica 57, 1361 – 1402. Perron, P., Vogelsang, T.J., 1992. Nonstationarity and level shifts with an application to purchasing power parity. Journal of Business and Economic Statistics 10, 301 – 320. Schwert, G.W., 1989. Tests for unit roots: a Monte Carlo Investigation. Journal of Business and Economic Statistics 7 (2), 147 – 159 (April). Zivot, E., 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 10, 251 – 270.
On the stability of demand for money in a developing economy Some empirical issues Basanta K. Pradhan *, A. Subramanian National Council of Applied Economic Research, Parisila Bhawan, 11-Indraprastha Estate, New Delhi 110002, India Received 1 January 1998; accepted 1 September 2002
Abstract In recent years, a number of developing countries have undergone extensive reforms in the financial sector. The effects of this underlying financial innovation process on the stability of demand for money have seldom been studied in the context of developing countries. Nevertheless, these changes in the financial sector highlight the transition from one regime to the other. This need necessarily follows that such a process has to be accounted for in the long-run demand for money estimation. Here, we use a three-step testing procedure to study the implication of the reform process on the stability of demand for money. To account for the abovementioned changes, we specify the demand for money in an open economy framework using data from India. An estimation procedure accounting for these changes in the specification of demand for money suggests that financial deregulation and innovation did affect the empirical stability of demand for money in India. D 2003 Elsevier B.V. All rights reserved. JEL classification: E41 Keywords: Stability; Money; Developing economy
1. Introduction The stability of the demand for money is one of the most important and recurring issues in macroeconomic policy analysis. The issue at stake here is the set of necessary * Corresponding author. National Council of Applied Economic Research, Parisila Bhawan, 11-Indraprastha Estate, New Delhi 110002, India. E-mail address: [email protected] (B.K. Pradhan). 0304-3878/03/$ - see front matter D 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0304-3878(03)00080-4
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conditions for money to exert predictable influence on the economy so that the central bank’s control of the money supply can be a useful instrument of economic policy. A monetary policy that seeks to limit the supply of money to its demand facilitates the tasks of demand management and contributes to the achievement of price stability. The rate of growth in money supply should be in conformity with the desired rate of growth in output and thus constrain the price increases to an acceptable level. A stable demand for money implies a stable money multiplier and, therefore, stability makes it easier to predict the effect of a given money supply on the aggregate money income. The stability of demand for money has been studied extensively both theoretically and empirically, especially, in the case of USA and UK during the periods of ‘missing money’ and ‘great velocity decline’ in the early 1970s.1 The most widely applied tests to study the implications on the demand for money are residual-based ones in which the null hypothesis of no cointegration is tested against the alternative that the relationship is cointegrated in the sense of Engle and Granger (1987). But this linear combination may have shifted at some unknown point in the sample. In this context, the standard tests for cointegration are not appropriate, since they presume that the cointegration vector is timeinvariant under the alternative hypothesis. Following Johansen (1988) and Johansen and Juselius (1992), some studies estimate using the complete systems analysis of cointegration. However, while statistically appealing, the full system approach has some practical problems, mainly related to the increased dimensionality of the system due to the unconditional use of information. An additional problem is the presence of structural breaks, which may affect particular variables and are difficult to handle statistically in large models. Conditional partial models are attractive because they condition information based on economic theory and increase efficiency. Structural breaks are also easier to handle in small systems than in large ones. In this paper, we follow an alternative route which consists of three steps: (i) estimation of cointegration relationship using full systems model; (ii) models are then reduced from systems formulation to single equations using weak exogeneity tests and then (iii) testing for cointegration between the variables allowing for the possibility of one break in the cointegration vector with unknown timing. Here, we assume that the full system can be partitioned into a vector of endogenous variables and a vector of weakly exogenous variables in the sense of Engle et al. (1983). If the assumption of weak exogeneity is satisfied, then the system of equations in the second step is block recursive.2 The third step is the residual-based tests for cointegration in models with regime shift. We use a class of residual-based test for cointegration which allows for regime shift and are multivariate extension of some of the univariate tests allowing for the possibility of a break using recursive, rolling or sequential approach.3 This method has an advantage over the conventional ADF test, the power of which falls sharply in the presence of a structural break.4 1
See Hendry and Ericsson (1991), Goldfeld and Sichel (1990), etc. The advantage of appropriately partitioning full cointegrated systems into conditional partial models, which can be given a structural interpretation has been emphasised by Johansen (1992) and Ericsson (1995). 3 See Perron (1989), Banerjee et al. (1992), etc. 4 See Gregory and Hansen (1996) for the advantages of this method. 2
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We apply this methodology to the Indian case. The Indian case is especially interesting in the light of reforms undertaken in the last decade for which no attempt has yet been made to study the impact of these reforms on the stability of demand for money. These issues have not caught up with the research on developing countries though the processes of reforms in general and financial sector reforms in particular are an overriding phenomenon in the past decade. The effects of these underlying financial innovation process highlight the transition from one regime to the other which need necessarily follows that such a process has to be accounted for in the long-run demand for money estimation. Fig. 1 shows the velocity of money defined both narrowly (M1) and broadly (M3). The figure reveals a change in the trend behavior of velocity for M3 around the mid-1980s after which the declining trend stabilizes. The trend behavior in the velocity of M1 is somewhat mixed with an increase after the mid-1990s. The behavior that is important is the diverging trend between M1 and M3 in the later half of 1990s. This period has been characterized by important changes in the financial sector. Financial liberalization has been a major target of policy reforms in India since the early 1990s. The reforms in general were concentrated broadly in these four areas, such as interest rate and credit reforms, capital market reforms, exchange rate reforms and fiscal reforms. The interest rate structure was simplified in October 1990 with scheduled commercial banks allowed to freely determine their lending rates on loans for purchase of consumer durables, loans to individuals for purchase of shares and bonds and other nonpriority sector. Since October 1995, scheduled commercial banks were also permitted to fix their own interest rates on domestic term deposits with a maturity of 2 years or more. Later, the norms were further relaxed to cover term deposits with a maturity of over 1 year. Even interest rates on nonresident (external) rupee term deposits over 2 years were freed with effect from April 1996. Since 1991, the capital market in India has been influenced by wide-ranging reforms leading to changes in the number of issues, market capitalization
Fig. 1. Velocity of money.
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and trading volumes. Another important change in the capital market, which has wideranging effects for the money demand is the easy access allowed to the international capital market through euro-equity shares. The Indian rupee was made partially convertible in 1992 –1993. In the following year, full convertibility of the rupee was allowed on the trade account, which was extended for almost all merchandise trade transactions and all receipts on the current or capital account, but not to all payments. In 1994, rupee was made fully convertible on current account. Another important change is the entry of foreign capital in the Indian stock market through foreign institutional investors and joint ventures. The implications these changes have on the trend behaviour of velocity of money can be interpreted along the lines of Bordo and Jonung (1987) analysis. The stylised long-run global pattern of velocity of money behaviour as documented by them suggests that technical progress in the financial sector introduces two competing influences on the trend behaviour of velocity, each dominating at a different stage of development of a particular country. During the first stage of development, the economy is characterised by increasing monetisation. Cash and demand deposits are increasingly used for settling transactions, replacing earlier reliance on barter trade. As a result, demand for transaction balances grows more rapidly than income and velocity is characterized by a negative trend. During the second phase of development, financial liberalization allows for the introduction of a range of widely traded and highly liquid securities. These assets substitute money as a store of value. Additionally, technological innovation in the financial sector and the rapid transfer of funds facilitates the economizing on money balances. As a result, money balances grow slower compared to the volume of transactions and velocity stabilizes or even increases over time. Hence, velocity follows a U-shaped pattern. This change in the trend behavior of velocity, however, presents difficulties in modeling the empirical relationship among the variables in the demand for money function. The features which distinguish this paper from the others addressing the same issues for a developing economy undergoing financial sector reforms are: first, this paper uses an alternative three-step testing procedure to evaluate the stability of demand for money accounting for structural breaks in the demand for money specification. Second, this paper estimates the demand for money using data from India which spans a period from the fourth quarter of 1970 to the third quarter of 2000, the post bank-nationalization period. These years, in fact, have been characterized by important changes in the Indian money market structure: stock market collapse, reforms in the financial sector, progressive dismantling of administered interest rates, government debts and foreign exchange rates are at market rates, etc. As a result of these financial deregulation and innovation, the character of the market and the role of money within the system have been altered by these changes.5 The long-run relationship between real money balances and output may have also changed. In order to test this proposition, we test for cointegration between the variables allowing for the possibility of a break in the cointegration vector with unknown timing.
5 Apart from this, there were some significant changes such as phasing out of interest tax, launching of capital indexed bonds, etc.
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In Section 2, we discuss some of the econometric issues on the demand for money followed by an exploratory analysis of data used in the demand for money specification in Section 3. In Section 4, we test for the existence of long-run relationship in the demand for money function in a systems framework and then the single equation formulation to test for structural breaks. Section 5 provides the concluding remarks.
2. Demand for money: some econometric issues Consider the following simple specification with Mt, the measure of money and Yt, representing both scale and opportunity cost variables and Ut, the error term. DMt ¼ bDYt þ Ut
ð1Þ
The change represented by D in the demand for money from one period to the next is explained by the change in Y variables over the same time interval. In order to understand the dynamics of adjustment in Eq. (1) with an error-correction representation, consider the following transformation. Assume the equilibrium value of Mt is f( Yt) for all t, and hence, at equilibrium, Mt1 ¼ f ðYt1 Þ ¼ CYt1 ðsayÞ
ð2Þ
where C is a linear operator. Let X be defined as a negative parameter, which denotes the degree of adjustment, then an expression such as XðMt1 CYt1 Þ
ð3Þ
represents the level of M in period (t 1) relative to the equilibrium value of M for the same period, CYt 1. Introducing this expression in Eq. (1), we obtain DMt ¼ bDYt þ XðMt1 CYt1 Þ þ Ut
ð4Þ
This gives an error-correction representation of demand for money with X as the errorcorrection coefficient (or adjustment parameter), while C is the long-run multiplier and b, the impact multiplier. Further, Ut is white noise error term, i.e., a mean-zero uncorrelated process. If 2 < X < 0, then the characteristics equation of Eq. (1) implies a stable longrun relationship M = CY. Assume that the explanatory variable is integrated of order 1[l(1)]. If the model is stable, then the linear combination Mt CYt is stationary, although Mt (and Yt if C p 0) are integrated of order 1; i.e., Mt and Yt are cointegrated of order (1,1) with cointegrating vector (1, C). On the other hand, if X = 0, then there is no adjustment towards equilibrium and hence no cointegration.6 The above illustration assumes that Y variables are weakly exogenous for the parameters of the conditioned model (see e.g. Engle et al., 1983). However, this assumption underrepresents the potential relationships when more than one cointegrated vector exists leading to inefficiency. Hence, we adopt a more comprehensive econometric 6
For a more explicit exposition, see Holden and Perman (1994).
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procedure based on the estimation of Vector Autoregressive models (VAR). These models characterize the joint behavior of a group of variables conditional on their past values also including the constant terms, linear trends, seasonal dummies and even specific dummies. A VAR model with n variables takes the following form Zt ¼ Al Zt1 þ . . . þ Ak Ztk þ Ut
t ¼ 1; . . . ; T
ð5Þ
were Zt is (n l) and each of the Al is an (n n) matrix of parameters. Ut is a ndimensional normal process with N(0,r). If the l(1) variables that we are modeling have r stationary equilibrium relationships amongst them, then we can write the system in the Stationary Vector Equilibrium Correction form (e.g. Johansen, 1988) which is given by: DZt ¼ U1 DZt1 þ . . . þ Uk1 DZtk þ pZtk þ hDt þ Ut
ð6Þ
where Ul = (l A1 . . . Al), (l = 1, k 1), and p = (l A1 . . . Ak) representing both short- and long-run adjustment to changes in Zt, respectively. The matrix p has reduced rank equal to r with speed of adjustment to disequilibrium and a matrix of longrun coefficients represented by a and b, respectively. We use the test developed by Johansen (1988, 1991) to test for the number of cointegration relationships amongst the variables – trace statistics. In the Johansen’s procedure, testing for cointegration amounts to a consideration of the rank of p, that is, finding the number of r linearly independent columns in p. In such a procedure, inclusion of stationary variables l(0) by itself form a linearly independent column in p and create identification problem. While inclusion of l(2) variables in such models requires a different procedure. Hence, the knowledge of the order of integration of each of the variables may help in interpreting the initial results obtained from using the Johansen approach. There are several ways of testing for the order of integration. Two generally known tests are the Dickey –Fuller test (DF test) and Augmented Dickey –Fuller test to correct for the autocorrection among the error terms. Perron (1989) showed that if a series is stationary around a deterministic time trend that has undergone a structural break sometime during the period under consideration, the failure to take account of this change in the slope would be mistaken by the usual ADF unit root test as a persistent innovation to a stochastic trend.7 That is a unit root test, which does not take account of the break in the series, will have low power. A structural break essentially corresponds to an intermittent shock with a permanent effect on the series (Hendry, 1996). The opposite can also happen if the break occurs at the beginning of the sample (Leybourne et al., 1998). In order to test for the possibility of a break, a number of univariate tests were proposed such as recursive, rolling, or sequential approach (Banerjee et al., 1992) and further tests of Perron (1989), Perron and Vogelsang (1992) and Zivot and Andrews (1992). Here, we propose to use a more general, residual-based multivariate test allowing for a regime shift in either the intercept alone or the entire coefficient vector (Gregory and Hansen, 1996). This test is a multivariate extension of the univariate test mentioned above. 7 Gregory et al. (1996) have shown that the power of the conventional ADF test falls sharply in the presence of a structural break.
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The general advantage with this test is that they are noninformative about the timing of the regime shifts, which prevents ad hoc selection of structural breaks. We consider three alternative models: (i) a level shifts, (ii) a level shift with a trend, and (iii) a regime shift. The choice of the model is data-dependent. The standard method of testing the null hypothesis of no cointegration is to apply a unit root test, the ADF test, on the residuals of the cointegrating equation. In the presence of structural breaks, cointegration tests involve searching for the largest negative value, ADF*, of the ADF statistic over all possible break dates. The cointegration regression is estimated sequentially with the break occurring at a different data every time between 1 and T, where T is the last observation. The largest negative value in the sequence of the ADF* statistic is then compared with the simulated critical values reported in Gregory and Hansen (1996).
3. The demand for money: an exploratory analysis of the data From the policy standpoint, it is important to identify the correct measure of money as a better guide to monetary policy for the purpose of price stability. We consider both M1 and M2. Secondly, since the policy maker may be interested not only in the forecasting power of such estimations but also about the short-run relevance of the parameters, we use the high frequency monthly data. All the series are monthly, seasonally unadjusted and the estimation sample extends from 1970(04) to 2000(03). The data used in the estimation of money demand are given by the logarithm of real money, M1 and M3, index of Industrial production, and rate of interest and prices. The M1 is defined as currency and demand deposits while M3 is defined as M1 plus time deposits with the banks. The literature on developing countries indicates that the models on narrow money worked better reflecting the weak banking system and low-financial sector development. However, over time narrow money accommodates the new instruments created as a result of the evolving financial system and institutional framework. Hence, we use both money, defined narrowly and broadly, to model the demand for money in India.8 The selection of opportunity cost variable is crucial to the determination of money demand especially in the Indian context where interest rate structure is complex, segmented and pegged by policy till September 1995 (Government of India, 1996). Since the degree of liquidity is different for both M1 and M3, it is essential that the demand specification should incorporate different interest rates as the relevant opportunity cost. Hence, we consider both short- and the medium/long-term interest rates in the specification. Among the range of alternative rates like bank deposit rates, treasury bill rate, etc., we choose call money rates representing short-term and prime-lending rates representing the medium/long-term opportunity cost. The choice is facilitated by the availability of the data as well as the functional importance of these opportunity cost variables in time differentiation. The index of industrial production (1993 – 1994 = 100) is used as the scale variable. It is chosen mainly because monthly data are available only for this measure. Wholesale Price 8 Hafer and Jansen (1991) used money defined broadly to yield a stable function and they preferred a broader definition to evaluate the long-run economic impact of the changes in monetary policy.
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Fig. 2. (a) Log of narrow real money, (b) log of broad real money, (c) short-term interest rate, (d) long-run real rate of interest, (e) log of real exchange rate, (f) log of US treasury bill, (g) log of index of industrial production, and (h) log of wholesale price index.
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Fig. 2 (continued).
Index (WPI) is considered as the price variable though specifications with Consumer Price Index (CPI) were also used in the trial runs. For the sake of brevity, we do not present the results here.
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Fig. 2 (continued).
An informal examination of the data and the graphs, presented in Fig. 2, may be useful in giving a preliminary idea of the time series properties of these variables. While index of industrial production shows quite a regular pattern, real M1 shows two different seasonal patterns before and after 1979. This irregularity is due to the earlier inclusion of the part of savings deposits which was permitted to be withdrawn without notice was added to demand deposits. With effect from March 1, 1978, this accounting procedure was changed and interest accruing saving deposits is now treated as time deposits. Both inflation and real long-run interest rates show regular seasonal patterns through out the period, while short-run rate of interest shows sharp fluctuations after the 1990s which coincide with the policy changes in the structure of interest rates in India. The longrun rate of interest shows a decline in the spread by 0.5 points in January 1997, though varying for individual banks; owing due to RBI’s announcement at the end of 1996 asking banks to announce the maximum spread over the prime rate for all advances.
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4. Empirical results In 1992– 1993, a liberalised exchange rate system was introduced to make the Indian rupee partially convertible. The following year, this system was dispensed with and replaced by a unified exchange rate system where full convertibility of the rupee on the trade account was allowed. This was extended for almost all merchandised trade transaction with all receipts on the current or capital account but not to all payments. In 1994, full convertibility of the rupee on current account was announced. The empirical estimates presented in this section are augmented by variables exerting foreign influence to allow for currency substitution, a decent representation of not so a closed economy. In this context, we introduce two additional variables as the opportunity cost of holding money namely the real exchange rate (LREER) and the yield on the US treasury bills (LTBILL), though London interbank offer rate is the most widely used (Darrant, 1986; Arize, 1994). Before testing for cointegration, the order of integration of the individual time-series needs to be established. The tests used to investigate the existence of unit roots in the variables are based on the Augmented Dickey – Fuller (ADF) test. The regression for ADF tests is presented below in Eq. (7). n X DlnZt ¼ at þ b1 lnZt1 þ b2 T þ nbf DlnZtf þ et ð7Þ f ¼1
where Zt 1 is the 1-year lag of the relevant time series, D is the first difference and et is the residual, and T is a linear deterministic time trend. The null hypothesis that Zt is a stationary series is rejected when the coefficient of Zt 1 is not significantly negative. In Table 1, we present the test results for all the variables. Here, seasonal dummies were included to allow for seasonal changes in the seasonally unadjusted data. The ADF test is done by both including and excluding seasonal dummies. The lag length is calculated using the Schwert’s criterion (Schwert, 1989). In all the cases, the null hypothesis of nonstationarity is not rejected except for the rate of inflation (INF) and short- and long-term real interest rates (SRINT and LRINT), shortrun nominal interest rate (SINT) which are significant at 1% level. Therefore, these four variables are stationary at levels, namely l(0). While real money defined narrowly (LRM1) and broadly (LRM3), wholesale price index (LWPI), long-run nominal rate of interest (LINT), both index of industrial production for manufacturing (LIIPM) and general (LIIPG) are all nonstationary at levels. Proceeding further, we make use of the unit root test to find out if the series becomes stationary after differencing once.9 If the series becomes stationary after differencing once, then the original series is integrated of order one. All the nonstationary series becomes stationary after differencing once. The t values for each of the differenced series presented in the table exceeds the Mackinnon critical value at 1% level of significance ( 3.657). Therefore, first-differenced series do not exhibit unit roots. In other words, the series are stationary in differences which can be represented as l(0) and the original series as l(1). 9
Differencing the logarithmic series.
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Table 1 Results based on unit root test Variables
LRM1 LRM3 INF LWPI LRINT SRINT LINT SINT LIIPG LIIPM LTBIL LREER DLRM1 DLRM3 DLINT DLWPI DLIIPG DLIIPM DLTBIL DLREER
Constant
Constant and seasonal
Constant and trend
Constant, trend and seasonal
Test statistics
Lag length
Test statistics
Lag length
Test statistics
Lag length
Test statistics
Lag length
1.05 0.55 6.66* 1.20 18.69* 18.13* 2.13 4.62* 0.17 0.41 2.09 1.33 9.70* 7.58* 19.26* 3.96* 11.29* 11.68* 5.59* 7.59*
6 6 6 11 0 0 0 3 6 6 10 8 7 6 0 11 5 7 10 7
1.27 0.58 4.95* 1.07 19.04* 18.33* 2.16 4.37* 0.8 1.11 1.77 1.39 7.51* 6.01* 19.10* 3.96* 8.55* 8.84* 10.02* 6.96*
6 6 6 11 0 0 0 3 6 6 6 8 7 6 0 11 5 7 5 7
1.90 2.54 8.12* 3.41 18.68* 18.10* 1.36 4.82* 2.98 2.89 2.46 2.06 9.89* 7.54* 19.41* 4.04* 11.30* 11.77* 5.64* 7.62*
6 6 6 11 0 0 0 3 8 7 10 8 7 6 0 11 5 7 10 7
1.83 2.55 6.17* 3.69** 19.02* 18.30* 1.37 4.55* 2.49 1.92 1.95 2.18 7.72* 6.04* 19.26* 4.02* 8.63* 8.99* 10.01* 6.99*
6 6 6 12 11 0 0 3 7 7 6 8 7 6 0 11 5 7 5 7
* and ** indicate rejection of unit roots at 1% and 5% level of significance, respectively. L and D refer to log and first difference, respectively.
4.1. Testing long-run relationship in the demand for money Given that the data are monthly, we start with the estimation of a VAR with 12 lags for the full sample and, as real money is affected by seasonality, we introduce a set of centered seasonal dummies which are orthogonal to the constant term. Furthermore, the estimation of the unrestricted VAR includes also two impulse dummies one for the 1995(10), introduced mainly to capture some instability in the equation for interest rate, which corresponds to interest rate deregulation. It is worth noting here that inclusion of such Table 2 Tests of the cointegration rank for the demand for money function Ho:r 0 1 2 3 4 5
LRM1
LRM3
k1
ktrace
ktrace(0.95)
k1
ktrace
ktrace(0.95)
0.319 0.096 0.031 0.021 0.015 0.012
180.68* 50.36 25.37 15.56 8.87 0.90
98.15 70.85 45.21 30.56 14.41 3.76
0.169 0.079 0.043 0.027 0.017 0.011
118.02* 59.90 26.60 12.50 5.43 0.80
85.17 65.18 30.21 25.95 13.13 2.85
* and ** indicate significance at 1% and 5%, respectively.
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Table 3 Normalised cointegration coefficients
LRM1 LRM3
LIIPG
LINT
LREER
LTBILL
LWPI
0.94 1.28
0.09 0.29
0.21 0.35
0.01 0.05
0.37 0.23
dummies will affect the underlying distribution of the test statistics and hence the critical values provided in Osterwald-Lenum (1992) are only indicative. For these reasons, we calculate the critical values using the program Disco. The unit root tests show that the variables are either l(0) or l(1). Though stationary variables might play a key role in establishing a sensible long-run relationship between nonstationary variables, inclusion of such variables will increase the cointegration rank. Henceforth, we exclude the stationary variables in the estimation of the demand for money except WPI, which becomes significant at 5% level only when constant, trend and seasonal dummies are included. We now use the Johansen cointegration procedure to determine the rank r and to possibly identify a long-run money demand function amongst the cointegration vectors. Given that the data are monthly, we start with the estimation of a VAR with 12 lags for the full sample and, as real money is affected by seasonality, we introduce a set of centered seasonal dummies which are orthogonal to the constant term. To find a model with the appropriate lag length and to avoid overparameterization, the test is repeated by sequentially reducing one lag at a time until we find the appropriate model free of estimation problem. The cointegration test results are presented in Table 2. This indicates that the trace test rejected zero in favor or at least one cointegrating vector. The results are significant at 1% level. The standardised coefficients of the variables entering into the respective cointegrating vector are presented in Table 3. The coefficients are normalised with a value of one along the principal diagonal of the matrix. The long-run income elasticity for narrow money is close to one as suggested by the quantity theory of money. The long-run demand for real money is positively affected by the own rate of return for money, prices and exchange rate while negatively for foreign interest rate. Generally, a relative increase in the interest rates abroad exert negative influence on the domestic money holders to substitute away from foreign assets by drawing down domestic money holdings. Hence, the foreign Table 4 Test for weak exogeneity for money narrowly defined (M1) Variables
al = 0
v2(l)
Lrm1 Liipg Lint Lreer Ltbill Lwpi
0.386 0.290 0.531 0.004 0.147 0.108
7.88 3.87 15.15 0.45 0.75 3.45
[0.0153]** [0.1153] [0.4305] [0.4203] [0.0681] [0.0021]*
* and ** reject at 1% and 5% significance level, respectively. The probability of getting any number exceeding the v2 value shown above is less than the figure presented with in the squared brackets.
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Table 5 Test for weak exogeneity for money broadly defined (M3) Variables
al = 0
v2(l)
Lrm3 Liipg Lint Lreer Ltbill Lwpi
0.377 0.190 0.431 0.114 0.156 0.019
6.95 2.56 13.13 0.35 0.65 2.95
[0.0165]** [0.1032] [0.352] [0.376] [0.0691] [0.0010]*
* and ** reject at 1% and 5% significance level, respectively. The probability of getting any number exceeding the v2 value shown above is less than the figure presented within the squared brackets.
interest rate such as the US treasure bill rate shows a negative relationship though the influence is substantially lower because of the not so open nature of the Indian economy. 4.2. Model formulation: from the full system to single equation In order to examine the short-run demand for money for a simpler specification, we test for weak exogeneity among the cointegrating relationship. Since one cointegrating relationship has been identified, the weak exogeneity tests are evaluated under the assumption of rank one. The null hypothesis is the existence of weak exogeneity. To test for weak exogeneity in the system as a whole requires a test of the hypothesis that H:aij = 0 for j = 1,. . .,r, where row i contains only zeroes. This test is conducted by placing row restrictions on a to give a new restricted model, and then using a likelihood ratio test involving the restricted and unrestricted models to ascertain whether the restrictions are valid. The results presented in Tables 4 and 5 show that the weak exogeneity is rejected for both LRM1 and LRM3 at 1% and LWPI at 5%. Therefore, a short-run model can be designed with a system of two equations, one each with both narrow and broad money, and another with prices by considering income, interest, exchange rate and foreign interest rate as weakly exogenous. Since the objective is to study the demand for money relationship, we focus our attention only on the single equation specification for money.
Table 6 Testing for cointegration with regime shift M1
M3
Test statistics
Break point
Test statistics
Break point
ADF* Level shifts Level shift with trend Regime shift
5.67** 4.72 5.67
(0.99) (0.75) (0.68)
4.90 3.93 4.38
(0.26) (0.23) (0.27)
ADF Constant Constant with trend
5.59* 5.72*
CV 3.45 (1%) 3.98 (1%)
3.08** 3.12
CV 2.87 (5%) 3.13 (10%)
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Subsequently, this single equation demand for money is used to test if the long-run relationship among variables in the demand for money has changed as a result of financial deregulation and innovation. In order to test this proposition, we follow the methodology of Gregory and Hansen (1996) and test for cointegration between variables in the models with regime shifts. A large number of specifications were tried with different combinations of the weakly exogenous variables. Here in Table 6, we present results only for the full specification, though results did not change much with different specifications. The conventional ADF tests reject the null hypothesis of no cointegration at 1% significance level for M1 while for M3 the null is rejected only for the constant though at 5% level. The selection of lag for both conventional ADF and ADF* is based on Schwert’s criterion and t-test. The maximum lag length was set at 12, given the monthly data, and then progressively reduced until the Schwert’s criterion is the smallest and also the last lag of the first difference included is significant at normal critical value. Across all experi-
Fig. 3. Structural breaks in money demand.
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ments the lag lengths were generally 8 or 9 and, occasionally lower. The smallest test statistics occurred in the later half for M1 and in the first half for M3 as also seen in Fig. 3, which plots the ADF* for level shift (M1C and M3C), level shift with trend (M1CT and M3CT) and regime shift (M1R and M3R). The conventional ADF test rejects the null while ADF* does suggest that structural change in the cointegration vector is important and needs to be taken care of in the specification of demand for money.
5. Some concluding remarks The standard assumption of the recent empirical literature on the long-run relationship of the money demand in the Indian economy is the existence of stable demand for money. Despite financial deregulation and innovation, it is still maintained that demand for money is stable. This issue on the demand for money is subjected to empirical investigation in this paper which, however, casts serious doubts on the stability aspect of the demand for money in the Indian economy. The empirical evidence was based on an elaborate methodology, first identifying the full systems model and then reducing it to the single equation framework with finally testing for the structural break with unknown timing. This test which allows for the possibility of regime shifts seems to suggest lack of stability in the demand for money, given the data set and the model specifications. Hence, a money demand specification with an open economy framework, enveloping the changing financial sector and subjected to residual-based tests for cointegration does raise some important questions on the long-run relationship between the series. However, further research can focus on this issue by using a more robust nonlinear specification, such as the logistics smooth transition functions to model the smooth transitions from one regime to another.
Acknowledgements Previous versions of this paper were presented at the 28th Annual Conference of Economists, 26 –30 September 1999, La Trobe University, Melbourne, Australia and also in the conference on Money and Finance in the Indian Economy, 2 –4 December 1998 held at the Indira Gandhi Institute of Development Research, Mumbai. This paper forms part of MIMAP India project supported by the International Development Research Centre (IDRC), Canada. We thank Sebastian Edwards, K.L. Krishna and the anonymous referee for their comments on the previous version of this paper. However, errors that still remain are our responsibility.
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