Structural breaks, cointegration, and speed of adjustment Evidence from 12 LDCs money demand

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1 International Review of Economics and Finance 8 (1999) Structural breaks, cointegration, and speed of adjustment Evidence from 12 LDCs money demand Augustine C. Arize a, *, John Malindretos b, Steven S. Shwiff a a College of Business and Technology, Texas A&M University-Commerce, Commerce, TX 75429, USA b Global Management and Financial Consulting Inc., Clifton, NJ 07013, USA Received 25 February 1998; accepted 5 November 1998 Abstract This article estimates a theoretically coherent and empirically robust money demand function for 12 developing countries. The modeling procedure not only tests for a regime shift in the cointegrating equation, but also in the error correction model. Five specific hypotheses are examined. The article demonstrates that a long-run equilibrium relationship exists between real M1 or M2 balances, real income, inflation, exchange rate, foreign exchange risk, and foreign interest rates in the countries studied. The study provides information on the speed of adjustment to equilibrium and the median and mean time lags for adjustment of real money balances to changes in each determinant. Although our results provide more evidence against M1 than M2, this study clearly establishes that both M1 and M2 must be considered as viable policy tools for less developed countries Elsevier Science Inc. All rights reserved. JEL classification: E41 Keywords: Structural breaks; Cointegration; Adjustment; LDCs money demand 1. Introduction Economists and policymakers now widely agree that a theoretically coherent and empirically robust money demand function (MDF) is crucial for sound monetary policy formulation in less developing countries (LDCs), yet empirical work in this area has remained extremely sparse. See Domowitz and Elbadawi (1987) for more on this issue. This article deals with the relationship between real money balances and their determinants in 12 LDCs. The countries examined in the analysis include eight Asian * Corresponding author. Tel.: address: Chuck Arize@tamu-commerce.edu /99/$ see front matter 1999 Elsevier Science Inc. All rights reserved. PII: S (99)

2 400 A.C. Arize et al. / International Review of Economics and Finance 8 (1999) countries India, Korea, Malaysia, the Philippines, Singapore, Sri Lanka, Taiwan and Thailand; and four African countries Ghana, Morocco, South Africa and Tunisia. This sample includes low- and middle-income LDCs, manufacturing and primary exporters, as well as service and remittance countries. This diversity makes the sample reasonably representative of LDCs, and the results of the study can at least be suggestive of some general conclusions regarding LDCs and provide a basis to which future studies can be compared. The results may also provide a valid comparison to the single-country studies, such as Domowitz and Elbadawi (1987) for Sudan, and Chowdhury (1997) for Thailand. Recent studies of long-run money demand in LDCs have employed cointegration procedure (i.e., Chowdhury, 1997; Arize, 1994), and some additionally have tested for parameter stability of the error-correction model (i.e., Arize, 1994), but not for a regime shift in the long-run cointegrating relationship. This article differs from the existing literature, not only in its data set, but also in its empirical method. We are explicitly concerned with the stability of the long-run money demand in LDCs and the validity of a number of hypotheses. In this study, the five hypotheses examined are: (1) that the MDF is homogeneous of degree one with respect to the price level; (2) that the long-run real income elasticity of the demand real money balances is unitary; (3) that real money balances measured by the narrow definition of money are preferable to those measured by the broad definition in determining the long-run effect of monetary policy actions; (4) that the speed of adjustment is instantaneous for both a narrow definition of money (real M1) and a broad definition of money (real M2); and (5) that domestic money holdings in LDCs are not influenced by movements in the openness variables: exchange rates, foreign interest rates and real exchange rate variability. These hypotheses are important for a number of reasons: first, knowledge of whether the demand for nominal money balances is proportional to changes in the price level, which, as Hafer and Kutan (1994, p. 937) pointed out, allows us to consider which monetary measure is preferable in determining the long-run effect of monetary policy actions. Second, knowledge of the size of real income elasticities allows one to determine whether there are economies of scale in cash holdings in LDCs. Aghevli et al. (1979, p. 790) have pointed out that, for financially developed economies, one would expect a proportional relationship between real income and real money balances, but in developing countries the demand for money may well rise at a faster rate than income because of monetization, limited opportunities to economize on cash balances, and the paucity of other financial assets in which to hold savings. Third, while the long-run effects of the determinants of real money balances are of interest, the short-run adjustment of money demand to changes in these variables also is frequently important, especially in a policy sense. How quickly real money balances respond to changes in real income, expected inflation, exchange rate and foreign exchange risks is important for understanding future effects that may occur as a result of changes in monetary or exchange-rate policy and for interpreting recent events. The traditional view is that speed of adjustment to equilibrium in most LDCs is close

3 A.C. Arize et al. / International Review of Economics and Finance 8 (1999) to unity because of higher risks and uncertainties attributable to economic and sociopolitical instability and the lack of a variety of financial assets available for the wealth holders to undertake portfolio switches (Adekunle, 1968; Aghevli et al., 1979). Finally, if the variables exchange rates, foreign interest rates and real exchange rate variability turn out to be important determinants of real money balances, this may affect the design of monetary policy because it creates uncertainty in the outcome of monetary policy or, as Marquez (1987, p. 168) noted, results in a loss of government seigniorage and could precipitate a balance of payments crisis. The remainder of this article is set out as follows. Section 2 describes the money demand model. The empirical results are presented in Section 3, and concluding remarks close the article in Section Model specification and theoretical considerations From an empirical standpoint, there is a consensus in the literature on developing countries (Arize, 1994) that the error-correction model may be written as: m* t 0 1 y t 2 t 3 e t 4 (φ) t 5 rt f t (1) m t k 0 t 1 2 ( j y t j 2 j t j 4 j e t j 6 j (φ) t j 8 j r f j 1 2 j m t j 1 (2) j 0 where m* t is the logarithm of desired holdings of real money balances (real M1 or real M2); real M1 consists of currency outside the banks and demand deposits at the scheduled banks divided by the consumer price index; real M2 consists of M1 plus quasi-money divided by the consumer price index; 1 y t is the logarithm of real GDP; t is the expected inflation rate obtained from the consumer price index; e t is the exchange-rate variable, defined as the number of units of each country s currency per unit of U.S. dollar (a similar definition is employed by Domowitz & Elbadawi, 1987); (φ) t is a measure of real exchange-rate variability; r f t is a measure of foreign interest rates; and is the first-difference operator. The stochastic disturbance terms are t and t. Eq. (1) has assumed that the money market is in equilibrium and it may be viewed as a cointegrating model. The basic idea of cointegration is that two or more nonstationary time series may be regarded as defining a long-run equilibrium relationship if a linear combination of the variables in the model is stationary (converges to an equilibrium over time). 2 Thus, if the money demand function describes a stationary longrun relationship among the variables in Eq. (1) this can be interpreted to mean that the stochastic trend in real money balances is related to the stochastic trends in the real income, the rate of inflation, exchange rate and foreign exchange risk. In other words, even though deviations from the equilibrium should occur, they are mean reverting. t j)

4 402 A.C. Arize et al. / International Review of Economics and Finance 8 (1999) In Eq. (1), real money balances are assumed to be an increasing function of real income (i.e., real GDP), as the usual budget conditions dictates; that is, 1 is expected to be positive. On the other hand, an increase in the expected inflation rate should lead to a substitution away from money to other real assets (i.e., houses, farms or durable consumer goods), so 2 is expected to be negative. The inclusion of exchange rate in the empirical money demand equation was originally postulated by Mundell (1963, p. 484), who wrote, The demand for money is likely to depend upon the exchange rate in addition to the interest rate and the level of income. Arango and Nadiri (1981) have argued that, when domestic currency depreciates, it increases the value of foreign securities held by domestic residents. If this increase is considered as an increase in wealth, the demand for domestic money may rise. On the other hand, Bahmani-OsKooee and Pourheydarin (1990) and Arize (1989) have argued that, as a weak domestic currency yields expectations for further weakening, asset holders would shift some of their portfolios away from domestic currency and into foreign currencies. Therefore, an increase in the exchange rate (i.e., depreciation) could have a positive or negative effect on the demand for money. Other theoretical justifications for the inclusion of the exchange-rate variable are given in Branson and Buiter (1984) and Warner and Kreinin (1983). The effect of foreign exchange risk on real money balances also is an empirical issue. Zilberfarb (1988) suggests that there can be the substitution effect whereby increased foreign exchange risk tends to reduce holdings of the more risky asset and thus increase holdings of domestic balances (i.e., 3 will be positive). On the other hand, Akhtar and Putnam (1980, p. 787) have argued that the direct effect of transactor responding to increases in the riskiness of currency values is a tendency to diversify and hold smaller amounts of domestic money. Domestic currency no longer provides the same informational content concerning international transactions as previously and may no longer serve as an optimal store of value for a given level of transactions. Therefore, exchange risks could have a negative effect on real money balances (i.e., 3 will be negative). The impact of exchange-rate risk on real money balances is an empirical issue, because theory alone cannot determine the sign of 3. The effect of the foreign interest rate variable is inversely related to the demand for real money balances. Work by Hamburger (1977) and Arango and Nadiri (1981) has shown that an increase in foreign interest rates ceteris paribus may induce market participants to transfer their financial assets to the high-yielding capital markets. Such transfers will be financed by drawing down domestic money holdings, so 5 will be negative. Eq. (2) gives the short-run determinants of money demand and embodies both the short-run dynamics and the long-run relation of the series. t 1 is the error-correction (one-lagged error) term generated from the Phillips and Hansen (1990) multivariate procedure. The presence of the t 1 in Eq. (2) reflects the presumption that actual real money balances do not adjust instantaneously to their long-run determinants. Therefore, in the short-run, adjustments are made to correct any disequilibrium in the long-run money demand. The parameter is the error-correction coefficient and measures the response of the real money balances in each period to departures from equilibrium conditions. The Error-Correction Model (ECM) therefore reflects how

5 A.C. Arize et al. / International Review of Economics and Finance 8 (1999) the system converges to the long-run equilibrium implied by Eq. (1), with convergence being assured when is between 0 and 1. In addition, the value of depends on the normalization of the cointegrating vector (Arize & Darrat, 1994). 3. Empirical results 3.1. The data and the unit root tests The data for this study are taken from the International Monetary Fund s (IMF) International Financial Statistics in the case of 11 countries, and the data for Taiwan are drawn from the Taiwan Financial Statistics and Taiwan Financial Monthly. All the data used in this article are annual observations of the variables, and the estimation period is 1961 through The sample period is determined by the availability of consistent measures of the aggregate in question. 3 For each of the 12 countries, we have more than 30 observations, so that the problems of using small samples are arguably minimized. In addition, it is, now known from the studies by both Hakkio and Rush (1991) and Campbell and Perron (1991) that the ability of cointegration tests to detect cointegration is a function of total sample length and not a function of data frequency. That is, using annual data over is just as good as using quarterly or monthly data over the sample period. Data on prices (Consumer Price Index, ), exchange rate (domestic price of U.S. dollar) and the narrow and broad money stock were compiled from various issues of the IMF s International Financial Statistics. The consumer price index of each country is used to measure inflation. The real exchange rate was created by multiplying the U.S. consumer price index by the domestic exchange rate and then deflating by the domestic consumer price index. The proxy for foreign exchange-rate risk was obtained from a time-varying measure of real exchange-rate volatility. 4 The U.S. lending rate is used as a proxy for the foreign interest rate. This can be justified on the grounds following Wickens (1972). Because cointegration tests require a certain stochastic structure of the time series involved, the first step in the estimation procedure is to determine if the variables are stationary or nonstationary in levels. The common practice is to use the augmented Dickey-Fuller (ADF) test and the 90% confidence intervals for the largest autoregressive root. The intervals are constructed using Stock s (1991) procedure. However, a number of authors (i.e., Perron, 1989) have pointed out that the standard ADF test is not appropriate for the variables that may have undergone structural changes. To examine the stationarity of variables with a structural break, we use the recursive version of the Banerjee et al. (1992) test. The latter test is based on asymptotic-distribution theory, which treats break dates as unknown a priori. The results are given in the Appendix Table A1. 5 The null hypothesis of a unit root is tested against the alternative of stationarity and is investigated for real money balances, real GDP, the inflation rate, the official exchange rate, foreign interest rate and foreign exchange-rate risk. The lag structures were determined on the basis of a t-test following a procedure proposed by Ng and Perron (1995). The results in Table A1 suggest that, while it is reasonable to conclude

6 404 A.C. Arize et al. / International Review of Economics and Finance 8 (1999) that the null hypothesis of a unit root (i.e., nonstationarity) is accepted for the variables, some caution is necessary. It is thus assumed that these series are integrated of order one Structural break Given that we have I(1) variables, an Ordinary Least Squares (OLS) equation linking some of these variables will not be a mere spurious regression only if the I(1) variables are cointegrated. A possible reason for the failure to find cointegration using the Engle and Yoo (1987) methodology 6 may be due to structural instability in the long-run relationship given in Eq. (1), especially since their test for linear cointegration presumes that the parameters of the equation are time-invariant and is therefore inappropriate during a period undergoing institutional changes. Gregory and Hansen (1996) propose extensions of the ADF test that allow for a regime shift in either the intercept or the entire coefficient vector. As Gregory and Hansen (1996, p. 101) noted, their residual-based tests are useful in helping lead an applied researcher to a correct model specification. A major advantage of this procedure is that it allows one to search for a break at an unknown shift point and to test for cointegration. Here, we imposed a priori, as well as estimated endogenously the breakpoints. 7 The results of applying the Gregory and Hansen (1996) method are summarized in Table 1. It presents the test statistics for cointegration at the estimated breakpoints and, for comparison, the test statistics achieved for pre-selected breakpoints. The timing of the structural break is shown in years and expressed in proportion to the sample sizes. Three key points are highlighted by the results. First, the endogenously estimated break dates vary across countries and real balances. Second, for most of the countries (i.e., 9 out of 12) the results show that the variables bear a stationary relationship after accounting for a structural break. This finding suggests that there is a long-run equilibrium relationship among either real M1 or real M2, real income, inflation and openness variables in at least nine out of 12 countries. The null hypothesis of no cointegration with structural change is not rejected in Morocco, South Africa and the Philippines. However, the absolute values of the calculated Gregory and Hansen (1996) test statistic for the three countries are close to the 10% critical values, although not significant. The lack of cointegration may simply be the product of the low power of the test for samples below 50 (Gregory & Hansen, 1996, p. 110) when the autocorrelation coefficient is close to one. Finally, in general, the pre-selected breakpoints are not statistically significant Multivariate cointegration A system-based cointegration procedure has been developed by Johansen (1988, 1992) to test for the presence or absence of long-run equilibria among the variables in Eq. (1). The optimality of this technique has been shown by Phillips (1991) in terms of symmetry, unbiasedness and efficiency properties. It should be preferred over other estimators because it does not suffer from problems associated with normalization

7 A.C. Arize et al. / International Review of Economics and Finance 8 (1999) Table 1 Gregory and Hansen (1996) tests for regime shifts Imposed time break Estimated Estimated breakpoint Countries Variables breakpoint test statistic Asia India M1,y,,e [0.52] 7.22 M2,y,,e [0.48] 5.38 Korea M1,y,,e, (φ) [0.38] 7.72 M2,y,,e, (φ) [0.44] 5.42 Malaysia M1,y,,e,r f [0.36] 6.31 M2,y,,e,r f [0.79] 5.24 Philippines M1,y,,e [0.54] 6.24 M2,y,,e [0.37] 5.24 Singapore M1,y,,e, (φ) [0.42] 6.01 M2,y,,e, (φ) [0.48] 6.37 Sri Lanka M1,y,,e [0.56] 6.25 M2,y,,e [0.38] 5.24 Taiwan M1,y,,e, (φ) [0.50] 6.73 M2,y,,e,r f [0.51] 6.47 Thailand M1,y,,e, (φ) [0.61] 4.26 M2,y,,e, (φ),r f [0.61] 8.41 Africa Ghana M1,y,,e,r f [0.56] 5.33 M2,y,,e,r f [0.56] 5.32 Morocco M1,y,,e,r f [0.41] 6.01 M2,y,,e [0.68] 4.28 S. Africa M1,y,,e, (φ) [0.42] 6.01 M2,y,,e, (φ),r f [0.73] 5.24 Tunisia M1,y,,e [0.54] 6.25 M2,y,, (φ) [0.45] 5.30 The critical values at the 10% level are 5.75 for m 3 (i.e., for India, m is 3 and for Singapore, m is 4 and 6.17 for m 4. The critical values are from Table 1 of Gregory and Hansen (1996). There are no critical values for m 5. The imposed time breaks represent oil price shocks and the Plaza Accord of (Johansen, 1995), and it is robust to departures from normality (Cheung & Lai, 1993; Johansen, 1995) and heteroskedasticity (MacDonald & Taylor, 1991; Johansen, 1995). Furthermore, Johansen (1995) points out that the power of the Johansen test is better than that of the residual-based tests. The test utilizes two likelihood-ratio (LR) test statistics for the number of cointegrating vectors: namely, the trace and the maximum eigenvalue ( -max) statistics. To perform the test, the conditioning vector includes the step and impulse or spike dummy variables (where applicable). 8 Similar dummies are included in the studies by Hoffman et al. (1995, p. 322) and Hendry and Doornik (1994, pp ). Optimal (smallest order) lag length of the Vector Autoregression (VAR) was determined by a LR test and the F-version of the Breusch and Godfrey statistic for

8 406 A.C. Arize et al. / International Review of Economics and Finance 8 (1999) serial correlation. 9 After deciding the lag length in the VAR, we then followed the procedure in Johansen (1995) to test the joint hypothesis of both the rank order and the deterministic components. The presence of a significant cointegration vector or vectors indicates a stable relationship among the relevant variables. Table 2 reports the estimated the -max and trace test statistics and their attendant critical values. These estimated test statistics have been adjusted by Reinsel and Ahn scaling factor discussed in Cheung and Lai (1993). For space reasons, we report only tests for the null hypotheses r 0 and r 1. To facilitate an appropriate interpretation of our results, we also report the results with and without shift or step dummies. 10 Focusing on the -max test results, the null hypothesis tested is that there is no cointegrating vector, r 0 and the null hypothesis of at most one cointegrating vector (H o : r 1) is not rejected in any country (except the real M1 and real M2 results for Singapore and Ghana, respectively). 11 In each of the 12 cases, we can reject the hypothesis of no cointegration. Thus, a stable demand for real money balances (real M1 and real M2) exists during the period for each country. 12 We also tested for evidence of cointegration among real money balances, real income and expected inflation, and the results (not reported here) show that there is no evidence of cointegration in both real M1 and real M2 equations of Korea, Malaysia, Morocco and Tunisia. These results suggest that the openness variables are important in the MDF of these countries in order for cointegration to be achieved Long-run equilibrium estimates Given the relatively small sample available and the presence of one cointegrating relationship in the results of each country, we estimate and test the coefficients of Eq. (1) using two alternative approaches, the dynamic ordinary least squares (DOLS) estimator of Stock and Watson (1993) and the fully modified ordinary least-squares (FM-OLS) estimator of Phillips and Hansen (1990). 13 The former allowed the inclusion of the dummies mentioned earlier, whereas the latter procedure does not allow these dummies. Examining the results reported in Table 3 enables us to determine to what degree these estimates are affected by the inclusion of dummies. Focusing on the results obtained from the FM-OLS estimator, the hypothesis that MDF is homogenous of degree one with respect to the price level is tested first with only the traditional variables and second with both the traditional and openness variables. These results are reported in Table 3. With only the traditional variables (i.e., without openness variables) this hypothesis is rejected in 12 (i.e., five cases for real M1 and seven cases for real M2) out of 24 cases. With both the traditional and openness variables included, the hypothesis is rejected in only seven (i.e., four cases for real M1 and three cases for real M2) out of 24 cases. This latter finding showing that only seven are rejected and the cointegration results discussed above lend credence to the importance of the openness variables in the MDF of LDCs. Given that employing the DOLS procedure yielded similar results on price homogeneity, a possible question is: What are the implications of a price elasticity different from unity? The first implication of a price elasticity greater than unity is that a 1%

9 A.C. Arize et al. / International Review of Economics and Finance 8 (1999) Table 2 Testing for cointegration using Reinsel and Ahn s (1992) small-sample correction Maximum likelihood rank tests M1 M2 -Max -Max Trace Trace -Max -Max Trace Trace Country r 0 r 1 r 0 r 1 r 0 r 1 r 0 r 1 r 0 r 1 r 0 r 1 r 0 r 1 r 0 r 1 Asia India Korea Malaysia Philippines Singapore Sri Lanka Taiwan Thailand Africa Ghana Morocco S. Africa Tunisia Critical values 95% a 90% % b 90% % c 90% The test statistics are adjusted for degrees of freedom following Reinsel and Ahn (1992) and the critical values are taken from Pesaran and Pesaran (1997) (unrestricted intercepts and no trends in VAR model). -Max and Trace show test statistics when step dummines are included. a Number of variables 4. b Number of variables 5. c Number of variables 6.

10 408 A.C. Arize et al. / International Review of Economics and Finance 8 (1999) Table 3 Estimates of the cointegrating relationships Tests Tests Zero price level Zero price level Phillips and Hansen (1990) estimates elasticity Stock and Watson estimates elasticity Traditional With Without Traditional With Without variables Openness variables openness openness variables Openness variables openness openness variables variables variables variables Country y e (φ) r f y e (φ) r f Asia India M [17.26] [2.01] [3.06] [0.07] [0.18] [11.09] [2.60] [3.28] [1.03] [1.36] M [35.07] [2.52] [3.59] [1.20] [1.04] [32.75] [1.96] [4.23] [0.52] [1.82]* Korea M [44.87] [0.95] [6.10] [13.97] [0.65] [0.50] [19.71] [2.70] [2.11] [10.24] [0.73] [0.99] M [12.43] [0.04] [1.30] [6.78] [5.70]* [1.19] [10.29] [1.05] [2.53] [8.67] [1.76]* [0.95] Malaysia M [49.14] [2.76] [1.91] [3.78] [1.32] [1.64] [20.50] [3.30] [1.54] [2.07] [0.96] [0.38] M [81.92] [5.17] [5.24] [3.59] [1.09] [3.78]* [61.90] [4.04] [2.94] [3.62] [0.39] [0.82] Philippines M [5.65] [2.53] [1.60] [0.83] [0.88] [15.19] [2.62] [3.29] [0.70] [0.76] M [5.60] [3.38] [5.61] [1.66] [5.44]* [5.45] [5.75] [2.74] [0.22] [2.62]* Singapore M [32.05] [7.40] [6.32] [2.82] [1.11] [0.85] [22.36] [1.96] [4.71] [1.73] [3.73]* [2.34]* M [16.88] [1.74] [2.20] [2.56] [0.90] [1.12] [20.40] [3.13] [2.08] [2.04] [1.14] [1.54] Sri Lanka M [8.44] [0.99] [2.64] [1.40] [2.14]* [8.96] [2.58] [2.32] [3.41]* [1.48] M [9.24] [0.57] [1.74] [3.67]* [1.09] [5.39] [1.14] [1.89] [1.19] [0.55] Taiwan M [83.43] [5.13] [3.25] [2.46] [1.53] [0.40] [50.69] [10.56] [5.63] [3.83] [0.18] [2.03]* (continued)

11 A.C. Arize et al. / International Review of Economics and Finance 8 (1999) Table 3 (Continued) Tests Tests Zero price level Zero price level Phillips and Hansen (1990) estimates elasticity Stock and Watson estimates elasticity Traditional With Without Traditional With Without variables Openness variables openness openness variables Openness variables openness openness variables variables variables variables Country y e (φ) r f y e (φ) r f Asia Taiwan M [56.89] [4.02] [7.47] [2.05] [0.34] [2.87]* [76.85] [9.34] [4.88] [3.94] [0.22] [3.00]* Thailand M [24.40] [2.04] [3.31] [1.42] [7.51]* [4.98]* [27.42] [2.38] [2.27] [3.18] [2.49]* [7.41]* M [83.42] [2.51] [8.37] [2.45] [1.48] [0.90] [2.93]* [326.5] [12.79] [46.9] [53.60] [30.15] [1.35] [1.10] Africa Ghana M [15.30] [2.21] [10.8] [3.70] [0.95] [6.02]* [10.79] [0.41] [4.13] [2.22] [1.65] [4.77]* M [17.64] [1.70] [8.84] [1.78] [1.35] [5.77]* [12.06] [1.18] [3.10] [2.25] [0.23] [6.79]* Morocco M [21.59] [0.95] [1.88] [3.55] [6.36]* [0.50] [17.79] [0.18] [3.72] [3.34] [4.96]* [1.55] M [24.41] [1.24] [1.85] [9.31]* [3.72]* [39.88] [2.77] [1.77] [1.88]* [1.48] S. Africa M [6.65] [3.59] [5.13] [1.77] [4.82]* [4.48]* [4.27] [6.13] [5.97] [5.29] [0.05] [3.56]* M [9.68] [2.14] [1.91] [2.29] [2.12] [0.96] [2.84]* [8.21] [3.51] [1.76] [1.82] [3.59] [0.16] [1.72]* Tunisia M [18.17] [0.14] [2.09] [2.26]* [3.59]* [16.83] [3.47] [2.11] [0.93] [1.58] M [58.56] [0.72] [1.90] [0.08] [0.24] [45.15] [2.27] [2.32] [0.03] [2.28]* The numbers in brackets below the individual coefficient estimates are the absolute values of t-statistics. For testing price homogeneity, we report the estimated coefficient on the price level variable, in addition, to the t-statistic to test whether this coefficient is different from 1. * Significant at the conventional levels.

12 410 A.C. Arize et al. / International Review of Economics and Finance 8 (1999) increase in the price level and money balances leads to a different level of real money balances. Assuming that M2 is chosen as the monetary target by the monetary authorities in Korea, our results imply that a 1% increase in the price level leads to a 2.02% increase in the demand for nominal M1. A possible explanation for this may be that, as the price level, increases the real cost of transactions experienced by economic agents also rises. This is different from the results reported for nominal balances in the United States. For instance, Arize and Darrat (1994) reported a price elasticity of less than one for the U.S. economy. Our results for Korea s M2 suggest that to control inflation under 10%, the growth rate of M2 should be 29.8%, assuming the economy grows at 10% per year. 14 Finally, as Hafer and Kutan (1994) noted, if the demand for money is a demand for real balances, a price elasticity inconsistent with unity should cast doubt on whether the reported relationship is indeed a function of the money demand. The long-run real income elasticities are also reported in Table 3 for real M1 and real M2, respectively. For the FM-OLS, the long-run elasticity of money demand with respect to real GDP has the expected positive signs in all countries. They range from 0.58 (Sri Lanka) to 1.50 (Taiwan) for real M1 and 0.89 (Sri Lanka) to 1.77 (India) for real M2. For the DOLS method, real income is positive and significant in all cases and ranges from 0.56 to 1.43 for real M1, whereas for real M2, the range is from 0.70 to This implies a fairly large response of real money balances to changes in real income. A test of whether long-run real income elasticities of the demand for real money balances is unity indicates that this hypothesis is rejected in most of the countries, a verdict that is corroborated by the work of Aghevli et al. (1979). This finding implies that, as income rises, velocity tends to decline. Although there are exceptions, it can be argued that there is absence of economies of scale in money holdings in LDCs. The sign, magnitude and significance of the long-run elasticity of money demand with respect to inflation is consistent with previous studies (i.e., Zilberfarb, 1988) and range from 0.01 to 0.03 for real M1 and 0.01 to 0.02 for real M2. For real M1, we do not believe that the positive sign in the case of Malaysia is credible. For the DOLS method, the range is 0.01 to 0.04 for real M1; however, significantly positive coefficients are obtained for Malaysia and Tunisia. For real M2, the inflation coefficients in India, Korea, Sri Lanka, Ghana and Thailand are negative but nonsignificant. An appealing aspect of the results is that exchange rate is statistically significant in all countries (except Tunisia s broad MDF). For real M1, it has a negative sign in seven countries and ranges from 0.01 to 0.21, whereas the sign is positive in India, Malaysia, the Philippines, Sri Lanka and South Africa (0.01 to 0.14). For real M2, it has a negative sign in four countries ( 0.01 to 0.28) and a positive sign in six countries (0.01 to 0.26). The DOLS estimates are similar to those of the FM-OLS method. It is worth mentioning that the effect of exchange rate on real money balances is largely positive (i.e., consistent with the Arango and Nadiri (1981) hypothesis) when it is the broad MDF and negative when it is the narrow MDF. 15 For the FM-OLS method, foreign exchange-rate risk enters significantly into the long-run real M1 equations for Korea, Singapore, Taiwan and Thailand. The coefficient

13 A.C. Arize et al. / International Review of Economics and Finance 8 (1999) Table 4 Speed of adjustments and mean time lags for adjustments of real balances [estimates from Phillips and Hansen (1990) procedure] Speed of Mean time lags for adjustments of real balances* adjustments M1 M2 Country M1 M2 y e (φ) r f y e (φ) r f Asia India Korea Malaysia Philippines Singapore Sri Lanka Taiwan Thailand Africa Ghana Morocco South Africa Tunisia * Absolute values. on the risk measure is 0.20 for Korea and 0.02 for Thailand. These results support the Akhtar and Putnam (1980) hypothesis, whereas the estimates for Singapore (0.02) and Taiwan (0.05) are consistent with the Zilberfarb (1988) hypothesis of a positive effect of exchange-rate risk on real money balances. For real M2, the foreign exchange risk variable is statistically significant in five countries. The estimated coefficients are 0.36, 0.06, 0.02, 0.09 and 0.04 for Korea, Singapore, Thailand, South Africa and Tunisia, respectively. These results are similar to those obtained using the DOLS estimates. For the FM-OLS method, the foreign interest rate variable is significantly negative, and the semi-elasticity is about 0.02 in the long-run real M1 equations for Malaysia, Ghana and Morocco. For the real M2 equations, the long-run semi-elasticity is about 0.01 in Malaysia, Taiwan, Thailand and Ghana, and 0.02 in South Africa. These results are consistent with those reported for the DOLS estimator Speed of adjustment and mean time lags This section provides information on the speed of adjustment to equilibrium and identifies how quickly real balances respond to changes in the determinants. Table 4 reports the coefficient of the error-correction term and the mean time lag of each explanatory variable. 16 These results were obtained by estimating Eq. (2) for each of the 12 countries. 17 The speed of adjustment is represented by the absolute value of the error-correction term, which can be interpreted as the change in real money balances per year that is attributed to the disequilibrium between the actual and equilibrium levels.

14 412 A.C. Arize et al. / International Review of Economics and Finance 8 (1999) For both real M1 and real M2, there is considerable inter-country variation in the adjustment speed to the last period s disequilibrium. In the case of real M1, the coefficient of the error-correction term ranges from a low of 0.35 for Tunisia to a high of 0.73 for Korea, whereas for real M2, the range from a low of 0.29 for Singapore and Morocco to a high of 0.73 for Thailand. For example, in Singapore and Morocco, only about 29% of adjustment occurs in a year, whereas the figure is 73% for Thailand. Our results imply that the adjustment of real money balances to changes in the regressors may take about three years in Singapore and Morocco to a little below one and a half years in Thailand. This indicates the existence of market forces in the monetary sector that operate to restore long-run equilibrium after a short disturbance. Three points are worthy of mention. First, our results are not consistent with the hypothesis of an instantaneous adjustment of the rate of growth of real money balances to departure from their equilibrium value in the previous period. Second, our relatively large speeds of adjustment suggest that the predictive content of the relationship between real balances and their determinants have not deteriorated over time. Finally, because M2 contains a savings component, the speed of adjustment is below that of M1. 18 The mean time shows that the average time lag for adjustment of real money balances to changes in each independent variable. The results suggest that the mean lag for adjustment of real money balances to changes in real income is approximately one year in almost all cases. In the case of inflation, it takes about two years in the majority of the countries when the model is real M1, except for Malaysia, Sri Lanka and Taiwan, where it is about a year. For real M2, it takes more than one year in all countries and close to three years in Morocco. Given the open nature of LDCs, another interesting aspect of our study is that the average time lag for the adjustment of real money balances to changes in the openness variables is fairly short. 19 For the majority of the countries, the mean time lags for exchange rate, foreign exchange risk and foreign interest rate are below two years for both real M1 and M2. 20 In sum, the response of real money balances to changes in real income is similar to the response to changes in the openness variables Choice of a monetary aggregate Our results are directly relevant to concerns about which monetary aggregate best determines the long- and short-run effects of monetary policies in LDCs. Our empirical results provide evidence in support of either M1 or M2 as the preferred monetary aggregate. Our results, however, provide more evidence against M1 than M2. There are more reasons against relying on M1 as a measure with which the long-run economic effects of monetary policy actions on major macroeconomic variables, such as prices and real income could be gauged (Hafer & Kutan, 1994, p. 943). This is because more real M1 estimated equations showed structural instability using the Gregory and Hansen (1996) procedure and also failed the price homogeneity test. In addition, some of the estimated coefficients of the inflation variable are positive and statistically significant in the real M1 equations. It is worth mentioning that our finding is consistent with those of Aghevli et al. (1979, pp ), who found that either

15 A.C. Arize et al. / International Review of Economics and Finance 8 (1999) M1 or M2 can be used to achieve the objective of price stability. Our findings also support the conclusion by Chowdhury (1997, p. 407) that the appropriate MDF for Thailand is real M2. Like Bahmani-Oskooee and Rhee (1994), our results point to real M1 as the appropriate MDF for Korea. Concerning the short-run dynamics, the results favor both M1 and M2. First, we employed Sargan s likelihood criterion recommended in Pesaran and Pesaran (1997, pp ). The results of this measure favor both M1 and M2. For example, Sargan s criterion chose M2 for Malaysia, the Philippines, Sri Lanka, Thailand, Singapore and Morocco, whereas for India, Korea, Taiwan, Ghana, South Africa and Tunisia, it chose M1. Second, following the procedure outlined in Baye and Jensen (1995, pp ), we found that the estimated slope coefficient of a three-year moving average of M2 growth is positive and larger in size than those obtained using M1 growth in six out of 12 countries (i.e., India, South Africa, Tunisia, Morocco, Taiwan and Ghana), whereas in the other six countries, this procedure favored M1. These results imply that if the objective of the monetary authorities is the achievement of greater price stability, then either M1 or M2 can be used as a monetary target. 4. Conclusions This article has presented the first conclusive evidence on the long-run equilibrium relationship among the following variables: the real balance of M1 or M2, real income, inflation, exchange rate, foreign exchange risk and foreign interest rates in LDCs. As far we know, there is no such study in the literature for a diverse sample of developing countries. Because the unit root properties of the data play a key role in the analysis, we used two sets of statistics that examine the unit root hypothesis without allowing for trend breaks: (1) ADF t-statistics and (2) 95% confidence intervals for the largest autoregressive root. We then employed the recursive minimum ADF test recommended in Banerjee et al. (1992), which treats break dates as unknown a priori. The results from these tests provide evidence in favor of a single unit root in all variables. Therefore, treatment of this nonstationarity is essential for meaningful results. After testing for cointegration using the Engle and Yoo (1987) approach, we applied the Gregory and Hansen (1996) pre-test procedure to search for a structural break in the long-run relationship between the real balance of M1 or M2 and its determinants. Where concern was warranted, the results from Johansen s multivariate procedure were obtained by treating the dummy variable (representing the structural break revealed by the Gregory and Hansen (1996) method), as a weakly exogenous variable. The empirical results suggest that the demand for money balances and its economic arguments not only are cointegrated but also tie closely together in their short-run dynamics. Our results are directly relevant to concerns about which monetary aggregate best determines the long-run effects of monetary policy actions in 12 LDCs. The results suggest that both M1 and M2 must be considered as viable policy tools in LDCs and

16 414 A.C. Arize et al. / International Review of Economics and Finance 8 (1999) they imply that monetary authorities can use monetary policy successfully, both in the conduct of stabilization policy as well as in their efforts to mobilize the necessary capital for non-inflationary investment spending. In addition, the results also suggest that monetary policy actions aimed at stabilizing the domestic economy can generate at best only uncertain results if the effects of the openness variables (i.e., exchange rate) are ignored in the execution of monetary policy. Acknowledgments The authors would like to thank Ed Manton, Keith McFarland and Lee Schmidt for helpful comments on an earlier draft. Special thanks to Kathleen Smith for excellent research assistance. We are grateful to Craig Hakkio for his valuable suggestions in calculating the median lags. This research is funded by a GSRF-TAMU-C grant. Notes 1. See Domowitz and Hakkio (1990, p. 30) for a detailed explanation of the importance of deflating by consumer price index and using real GDP as scale measure. 2. The consequences of nonstationarity is the inapplicability of the standard sampling theory. The cointegration approach is attractive in that it can properly account for the nonstationary series. 3. Some observations were lost due to the construction of the real exchange-rate risk and the inflation variables, so the effective estimation period is 1961 through It is worth mentioning that the inclusion of exchange rate, foreign interest rate and real exchange-rate risk in the model also handles the problem of estimating over two exchange-rate periods. Nonetheless, the data may contain several structural breaks. Later, we will test if the data show any structural breaks in the long-run money demand function of these countries. 4. This proxy is constructed by the moving-sample standard deviation expressed as (φ) t m [ 1 m m i 1 (R t i 1 R t i 2 ) 2 ] 1/2 where R is the natural logarithm of real exchange rate, and m 3 is the order of the moving average. Work by Baba et al. (1988, pp ) and Koray and Lastrapes (1989) gives the advantages of employing this measure. Although this measure is certainly a complicated nonlinear function of the first differences, because it is made up of a stationary component (first-difference) and a nonstationary component (large persistence because of the moving-average effect), the theoretical results reported in Granger (1988) show that aggregating a stationary process with a nonstationary component results in a nonstationary aggregate process. Furthermore, Campbell and Perron (1991) have suggested that it would be advantageous to econometrically treat a stationary variable

17 A.C. Arize et al. / International Review of Economics and Finance 8 (1999) Table A1 Unit root tests: standard ADF tests and recursive ADF tests of Banerjee et al. (1992) Real Real Country M1 M2 Y e (φ) r f India ADF DF min T B Korea ADF DF min T B Malaysia ADF DF min T B Philippines ADF DF min T B Singapore ADF DF min T B Sri Lanka ADF DF min T B Taiwan ADF DF min T B Thailand ADF DF min T B Ghana ADF DF min T B Morocco ADF DF min T B S. Africa ADF DF min T B Tunisia ADF DF min T B T B is the estimated break date. The critical values are 3.45 (approx.) for ADF and 4.33 for DF min at the 5% significant level. with great persistence as a nonstationary one. A final point is that if the series is nonetheless stationary its coefficient has the usual properties of OLS estimator. 5. Our confidence interval estimates show that, while it is reasonable to carry out cointegration tests, our results should be interpreted with caution. For space considerations, we do not report these confidence interval estimates. Note,

18 416 A.C. Arize et al. / International Review of Economics and Finance 8 (1999) Table A2 Description and sources of data Mean of Mean of Country Sample period Observations inflation exchange rate Asia India Korea Malaysia Philippines Singapore Sri Lanka Taiwan Thailand Africa Ghana Morocco South Africa Tunisia Series and sources. International Financial Statistics (International Monetary Fund): money balances (M1), Line 34; quasi money, Line 35; broad money (M2), Line 34 35; prices, Line 64; U.S. lending rate, Line 60b; real GDP, Line 99b.p or line 99b scaled by prices; official exchange rate, Line rf (domestic currency/u.s. dollar rate). however, that some of the intervals are wide, suggesting a large amount of uncertainty. For example, the real M1 data in Thailand and South Africa are consistent with the hypothesis that the process is I(1), but also are consistent with the hypothesis that the data are trend stationary with autoregressive root close to Because it is difficult to discriminate between trend stationarity and simple I(1) processes, we prefer to operate under the assumption of a stochastic trend in the series. 6. Some experimentations using the Engle and Yoo (1987) methodology and Bardsen (1989) approximate standard errors for testing the significance of the parameters of Eq. (1) indicate that we either fail at the 5% level or we find weak evidence of a stationary money demand function in most of the countries. Further, some of the openness variables proved statistically nonsignificant in some of the countries. For the rest of the article, we utilize our preferred equations for each country since our objective is to obtain a fairly parsimonious equation for each monetary aggregate. 7. Following Gregory and Hansen (1996), we compute ADF statistics for each breakpoint in the interval, 0.15T to 0.85T (where T is the number of observations), and then we choose the breakpoint associated with the smallest value as that point at which the structural break occurred. 8. Conditioning variables are used to eliminate unwanted influences that might affect the estimates of cointegrating vectors. Although they are not in any hypothesized vectors, they do improve the stochastic properties of the vector error-correction model because they are not modelled themselves and have only short-run effects.