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Cointegration, real exchange rate and modelling thedemand for broad money in JapanAugustine C. Arize a & Steven S. Shwiff aa College of Business and Technology, East Texas State University , Commerce, TX,75429, USAPublished online: 28 Jul 2006.

To cite this article: Augustine C. Arize & Steven S. Shwiff (1993) Cointegration, real exchange rate and modelling thedemand for broad money in Japan, Applied Economics, 25:6, 717-726, DOI: 10.1080/00036849300000124

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Applied Economics, 1993, 25, 717-726

Cointegration, real exchange rate and modelling the demand for broad money in Japan

A U G U S T I N E C . ARIZE and STEVEN S. S H W I F F

College of Business and Technology, East Texas State University, Commerce, T X 75429, U S A

The literature on the demand for the Japan's broad money addresses two controversial issues: the form (log level or log difference) in which variables enter the money demand function and the question of whether financial innovation and deregulation caused shift(s) in the money demand relationship. Log-level specifications of the money demand function have been shown to exhibit large shifts, whereas log-first-differences and error-correction specifications do not. Our paper demonstrates that the appropri- ate specification for the Japanese money demand function is that which uses cointegration and error-correction procedures.

I . I N T R O D U C T I O N

The literature on the demand for Japan's broad money [M2 plus certificate of deposits (CDs)] has grown immensely over the last two decades. This literature addresses two inter- esting and controversial issues: the form (log level or log difference) in which variables enter the money demand function and the question of whether financial innovation and deregulation caused shift(s) in the money demand relationship. Because a majority of these studies are not available in English, Yoshida and Rasche (1990, p. 10) have provided a summary of the empirical findings, whereas Corker (1990, p. 419) has reviewed the trends in broad money over the 1970-88 period. See also Arize (1990a) for the effects of financial innovations on Japan's money de- mand function.

Yoshida and Rasche report that a majority of these studies use a log-level Goldfeld (1973) type model. One of the findings from these studies is that the demand for broad money shifted between 1973-74. Whereas this shift was influenced by structural changes in the financial system and by financial innovation, there is no evidence that further shifts have occurred in the post-1974 period.'

Much of Hendry's work (for example, Hendry, 1980,1985) has been devoted to showing that parameter instability

claimed to prevail in the US and British money demand functions is a spurious phenomenon due to incorrect speci- fication. Work by Granger and Newbold (1974) has shown that the log level of many economic variables are non- stationary and, thus, subject to the 'spurious regression phenomenon.' Moreover, Phillips (1986) has shown that the use of a log-level model generates spurious inferences, because the usual t- and F-ratio test statistics do not have even the limiting distribution. These specification issues raise questions about the observed instability in the Gold- feld (1973) type models of Japan's broad-money demand function.

Quite recently, the appropriateness of the log-level speci- fication has been questioned by Ito (1989). His findings suggest that the log-level money demand model exhibits a large shift, whereas a log-first-difference shows little signs of instability. Ueda (1988), using the 'error-correction' model (ECM) advocated by Hendry and others, found no evidence of a shift in Japan's broad-money demand relationship. Corker's (1990) findings, using ECM, corroborate those of Ueda (1988), who found parameter stability over the quar- terly period, 1970-88.

The ECM appears to have four desirable features. First, it avoids the possibility of spurious correlation among strong- ly trended variables. Second, the long-run relationships that

'See Suzuki (1984) for more on this.

0003-6846 0 1993 Chapman & Hall

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A. C. Arize and S . S . Shwifl

may be lost by expressing the data in differences to achieve stationarity are captured by including the lagged levels of the variables on the right-hand side. Third, the specification attempts to distinguish between short-run (first-differences) and long-run (lagged-levels) effects. Finally, it provides a more general lag structure, which does not impose too specific a shape on the model (Hendry, 1980).

Recent work in econometrics by Engle and Granger (1987) has shown that a full error-correction representation would exist if the variables in question were properly 'cointegrable.' Given the cointegrability condition, reliable, or consistent, values for the steady-state parameters can be obtained by estimating the static 'cointegration' relation- ship. While their results established the validity of the traditional ECM, Engle and Granger go on to suggest a two- step estimation procedure that allows explicit tests of the underlying assumption of cointegration. This procedure is well known and will not be discussed in this paper. However, it is worth mentioning that the procedure allows questions of the appropriate specification of the dynamic elements of the model to be handled independently of the specification of long-run parameters. Yoshida (1990) is the first study to apply this procedure in estimating the demand for broad money in Japan. Following Ueda's (1988) suggestion concer- ning the impacts of wealth and land prices, Yoshida (1990) includes stock price variability as a regressor, in addition to real income and the coupon of five-year bank debentures in his cointegrating regression for the sample period 1968:Ql-1989:Ql. His findings suggest that the relationship between real broad-money balances and its determinants have remained stable.

However, in a more recent study, Yoshida and Rasche (1990) suggest that a shift in broad-money demand relation- ship occurred in 198542. This outcome conflicts with Corker (1 990).

The present study provides empirical support for the presence of a stable money demand function in Japan. Previous studies are extended in at least six respects. First, data for the floating exchange rate period, 1973:Ql-1988:Q4, are utilized. A characteristic of these previous studies is that the money demand equations are estimated with pooled data of both fixed and flexible exchange rate periods without justification for the equations being symmetrical during the periods. Second, the influence of international monetary influences on domestic money holdings in open economies is considered by including real exchange rate as another determinant of the demand for money. See, for example, Bahmani-Oskooee and Pourhey- darian (1990), whose work supports Arango and Nadiri (1981). Third, an ECM is estimated by application of the two-step estimator of cointegrated systems as developed in Engle and Granger (1987). Fourth, by considering both restricted and unrestricted ECMs, we distinguish between short- and long-run real exchange rates effects. Finally, particular attention is given to testing for higher-order

autocorrelation, functional form misspecification, simultan- eous equation bias, heteroskedasticity, and non-normal residuals.

It is important to mention that previous studies do not examine extensively the validity of their econometric model. For example, Corker (1990) overlooked his maintained hypothesis of cointegration and, consequently, interprets his empirical results mistakenly as evidence that the regressions determine long-run equilibrium money demand. As shown below, there is no evidence of cointegration between real broad money and the regressors in his model. Furthermore, Corker uses the instrumental variable (IV) procedure due to the presence of contemporaneous log-first-difference vari- able (interest rate spread). However, it is not clear whether the instruments used are statistically valid since a Sargan (1958) test is not applied. Similar comments can be made about the study by Yoshida (1990).

Finally, previous studies (see, for example, Corker, 1990) pay only lip-service to the issue of parameter stability without examining it in detail. These studies rely on the Chow (1960) test, but fcrget that the null hypothesis of parameter stability between split samples is conditional on the residuals being homoskedastic for the whole sample. Thus, the correct sequence is to test the uniformity of residuals across both samples before calculating the Chow statistic (see Arize, 1990a for more on this). Moreover, the reliance of previous studies on only a Chow test is perhaps unjustified, especially in the presence of a multitude of alternative tests.

The remainder of this paper is set out as follows. Section I1 describes the model. The estimation is carried out on quarterly data, over the period 1973-88. Section 111 repre- sents and discusses the empirical results of our preferred equation. The main conclusions are summarized in Section IV. Data definitions and sources are cited in the Appendix.

11. M O D E L S P E C I F I C A T I O N

The error-correction money demand has two parts. The first is a long-run equilibrium money demand that may be written as follows:

where m is the desired real M2 balance, Y is real income (Gross National Product), R is opportunity cost of holding money, Wis real wealth, K is real exchange rate, and e is the error term. It is expected that f l , > 0, f12 < 0, b, > 0, and f14 >O. The inclusion of real income and interest rate variab- les in the empirical broad-money demand function is stand- ard and needs little elaboration here. Corker (1990) has postulated that the broad money in Japan is held to finance transaction and as a store of value. As a result, a wealth measure to capture portfolio decisions among financial

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Demand for broad money in Japan

assets and real gross national product (GNP) have been included in Equation 1. The deflator used is GNP (1980 = 100). Furthermore, Equation 1 takes into account the fact that a large portion of broad money is interest bearing. Therefore, the opportunity-cost variable was proxied by the three-month average Gensaki rate minus the average return on holding broad money. Note that the Gensaki rate is market determined, whereas the call rate used in Yoshida and Rasche (1990) is largely regulated.

To account for the effects of international monetary developments on the demand for broad money, real ex- change rate is also included in our specification. Recently, several analysts, such as Bahmani-Oskooee (1991), and Arango and Nadiri (1981) found some success with a proxy for international monetary influences on domestic money holdings in their money demand functions. Furthermore, as will be shown below, the null hypothesis of non-cointegr- ation is rejected only when the real exchange rate variable is included with some variables that appear in the long-run model of Corker (1990), that is, real GNP, real wealth and net interest rate.

The estimation of Equation 1 raises several econometric issues. First, the time-series properties of the data should be investigated. For instance, are the variables stationary in levels or in first differences? Estimation of Equation 1 using non-stationary data will lead to unreliable t-statistics, as the underlying time series would have theoretically infinite variances. Even if each individual time series is level-non- stationary, is the linear combination of these series as suggested by Equation 1 level-stationary? Second, the dy- namic adjustment of the demand for money is neglected. Notably, are its determinants instantaneous? If not, how should the dynamic adjustment be modelled?

The present discussion leads to the second part of Equa- tion l . Collective wisdom, based mainly on intuition, sugges- ts that actual money balances do not always equal what the public wishes to hold on the basis of long-run factors specified in Equation 1. Therefore, the second part of the model is a dynamic error-correction equation of the form

where all variables are as defined above. Note that other variables such as AlnP, may be included in the equation, where P is GNP deflator. Further, E is the short-run random disturbance term. A refers to the first-difference operator; C j (j = 1-5) represents the number of lags, and el - , is the lagged value of the long-run random disturbance term. Equation 2

gives the short-run determinants of broad money, which include, among others, current and past changes in the scale; opportunity cost and exchange rate variables; and the lagged value of the residual from the long-run money- demand function, that is, Equation 1. The parameter I that appears on el-, in Equation 2 is the error-correction coefficient. The presence of el-, in Equation 2 reflects the presumption that actual money balances do not always equal what the public wishes to hold on the basis of the long- run factors given in Equation 1. In the short-run, the public attempts to adjust its money balances to correct any dis- equilibrium in its long-run money holdings. The parameter L in Equation 2 measures the role such disequilibria play in explaining the short-run movements in money balances, and it is expected to be negative.

Jenkinson (1986, p.248) has suggested an alternative ECM as well. In this case, the restriction implied by the cointegra- ting regression is relaxed. That is, e,-, in Equation 2 is replaced by the lagged levels of the variables in Equation 1, so that the short- and long-run parameters are jointly estimated. Estimates of the level variables then reveal the long-run effects of the regressors. The t-statistics corres- ponding to level variables are asymptotically valid. To shed more light on this issue, substitute Equation 1 into Equation 2 to obtain a combined ECM equation:

c 1 c2

Aln mi= KO + x Y ,,Aln m,-I + x Y2,A1n W,- , i = 1 i = O

where KO =('Po-POL), T, = 2, T2 = -?,PI, T3 =AD2, r4 =

- LP3, r5 = -A/?,+. Equation 3 can be estimated using consistent estimation

procedures, and all parameters of Equations 1 and 2 can be recovered from those of Equation 3. For example, the error- correction coefficient I is T,; the long-term real income elasticity (PI) is T, divided by T; the long-term interest rate elasticity (P,) is T3 divided by TI; the long-term real wealth elasticity (P3) is T4 divided by TI; and the long-term exchange rate (8,) is T, divided by TI . As suggested by Jenkinson and Hall, a more robust check of the validity of the cointegrating regression as a long-run solution may be conducted by testing the joint restriction that the coefficients of lagged-level variables in Equation 3 are zero. If the computed F-statistic exceeds its critical value from the F table, it will be concluded that lagged coefficients have a joint significant effect on the demand for money. Hence, the restriction is rejected and cointegration is supported.

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720 A. C . Arize and S. S. Shwiff

An alternative approach towards estimating the long-run coefficients is also utilized in this study. That is, one can estimate long-run elasticity directly by allowing for the accumulation of the short-run effects. This method is based on the approach suggested by Bewley (1979). The next section examines empirical results related to the specifica- tion and stability of Japan's broad-money demand.

111. E M P I R I C A L RESULTS

Cointegration, error-correction modelling involves four steps. First, determine the order of integration for each of the variables under consideration. Second, estimate cointegra- ting regressions with ordinary least squares, using variables with the same order of integration. Third, test for stationary residuals of cointegrating regressions. Finally, construct the error-correction models.

The analysis of time-series properties - in particular, the order of integration of economic time series -has become an important aspect of econometric modelling in recent years. The analysis led to rejection of a Goldfeld-type log-level specification of the Japan demand for money, as well as the log-difference specification. It was found, as by other re- searchers, that the variables commonly used in money demand studies are non-stationary stochastic processes - even in log form - and, thus, may be characterized as integrated of order one.2 We performed Dickey-Fuller, augmented Dickey-Fuller, and Phillips-Perron tests on the log of real broad money (lnm,), the log of real GNP (In Y,), the log of real wealth (In W,), the log of real exchange rate (In K,), inflation rate (Aln P,), the log of implicit GNP deflator (In PY,), and log of net interest rate (ln(1 + R),). The Phillips-Perron test (Phillips and Perron, 1988) is perhaps the mQst general of the tests used, due to its non-parametric nature. The values of the test statistics were: lnm,= -9.48, ln Y,= -12.23, ln W,= -4.61, lnK,= -5.81, AlnP,= - 17.1,lnP Y, = - 3.4, ln(1 + R), = - 16.4. These results were achieved with six lags of the differenced process and a time trend and should be compared with a 95% critical value of -20.7 (Fuller, 1976, p.371). All variables failed to reject stationarity in the first differences of each time series.

Before discussing the empirical results from the cointegra- ting regressions, it is important to provide some evidence for the statistical adequacy of the ADF models, which are based on the residuals of the cointegrating equations. In Table 1 three ADF models are presented. These are labelled A*, R*, and C*, whereas their corresponding cointegrating regres- sions are labelled as A, B, and C, respectively. The ADF

model A* is consistent with Equation 1; B* is also consistent with Equation 1 but examines the long-run proportionality between money and prices, and C* is consistent with Corker (1990), in that the cointegrating regression excludes real exchange rate.

In estimating each ADF model, the Said and Dickey (1984) version of the Dickey and Fuller test is emphasized. The augmented regressions initially included differences at lags 1-12 as suggested by Schwert's (Schwert, 1987) for- m ~ l a . ~ The lagged terms were tested for significance in groups of four, deleting and sequentially testing until signifi- cance was found or all lags were exhausted. To assess the reliability of the ADF models, this paper tests whether the residuals exhibit serial independence, homoskedasticity and normality. The predictive failure of the models was exam- ined by a Chow forecasting test (see Johnston, 1984, p.507). To test the first of these residuals properties, the paper applies the Breusch and Godfrey (1981) test that all the coefficients of AR(4) and AR(12) for the residuals are equal to zero. The hypothesis of homoskedasticity is tested by ARCH and Het statistics. To test for normal residuals, the paper uses a JB statistic suggested by Jarque and Bera (1980) for skewness and kurtosis. Arize (1990a, b) gives a more detailed account of these tests. The diagnostic test results in Table 1 suggest that the ADF models do not suffer from any misspecifications. Table 1 reports 't-ratios' derived from White's (White, 1980) consistent covariance matrix. These t-ratios are - 4.15, - 3.57 and - 3.16 for A*, B" and C*, respectively. The critical value of - 3.99 at the 5% level was interpolated from Table 3 in Engle and Yoo (1987) for A* and C". The null hypothesis of non-cointegration is rejected if the computed t-ratio is smaller than -3.99. Therefore, Corker's (1990) long-run Equation C is not cointegrated, whereas A shows strong evidence of cointegr- ation. For B, the calculated value of -3.96 is smaller than -3.91, interpolated from Table 3 of Engle and Yoo at the 10% level. Note that the coefficient of 0.87 on In P, is close to one, statistically. Furthermore, using the Perron (1988) Za* statistic with a truncation lag of 4, it was found that for A and B, the null hypothesis of non-cointegration is easily rejected. The computed values are -20.82, -21.7 and - 12.97 for A, B and C, respectively, whereas the critical value at the 5% level is - 13.7 (see Fuller, 1976).

Several interesting features emerge from the estimated long-run coefficients of the cointegrating regressions (A and B) in Table 1. First, note that the estimates in model A are biased but consistent. Importantly, the extent of the small- sample bias is related to (1 -R2) of model A, which suggests that, in the present case, the bias is not large (Banerjee et al.,

'A variable is integrated of order I(0) when it is stationary in its level. A time series requiring first-order differencing to achieve stationarity is said to be I(1). If the series are integrated of different orders, they cannot be cointegrated. 3Schwert (1987) presents evidence that economic time series are likely to contain moving-average components. However, Said and Dickey (1984) show that the ADF is appropriate for mixed models of unknown orders. In the present paper, the maximum lag length is set equal to 12 and then the Said and Dickey procedure is followed.

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Table 1. Cointegrution results und tests

A. Inm,= -0.16+0.641In Yl+0.3781n W,+0.0941nkt+e, (0.96) (9.42) (8.45) (4.99)

R2 =0.998, D W =0.45, ADF= -4.36, Za* = -20.82

A'. Ae,= -0.001 -0.464el-, +0.31Ael-, +0.327Aet-, +0.26Ae1-, (0.47) (4.36) (2.36) (2.65) (2.00)

AR 1-4 F[4,50] = 1.98, ARCH(4) = 2.78, Vj = F[16,44] = 0.44 AR 1-12 F[12,42] = 1.67, Het(l)=0.79, JB(2)=0.51

B. In M,= -0.789 +0.995 In Y,+0.325 In W,+0.045 In k,+0.87 In P,+ o, (2.94) (9.54) (7.75) (2.22) (6.8)

R2 =0.999, D W =0.54, ADF= - 3.57, Za* = -21.07

B'. Au,=O.OOl -0 .335~~- , +0.20Av,~2+0.271Av,~4 (0.08) (3.57) (1.66) (2.19)

AR 1-4 F[4,51] = 1.31, ARCH(4)= 2.36, Vj= F[10,37] =0.60 AR 1-12 F[12,43] =0.63, Het(l)=0.81, JB(2)=0.81

C. In m, =0.552 +0.395 In Y, + 0.576 In W, -0.451 In (1 + R), + z, (1.92) (4.18) (1 3.18) (2.77)

C'. Az, = 0.008 -0.2532, - , + O.266Azt - , + 0.226Azl-, (0.08) (3.16) (2.06) (1.83)

Note: The numbers in parentheses beneath the estimated coefficients are the absolute t-values derived from White (1980) consistent standard errors. R2 is the coefficient of multiple determination. ADF is the augmented Dickey and Fuller statistic. Za* is the Perron's statistic. AR is the Breusch-Godfrey statistic for autocorrelation. ARCH is Engle's statistic for the presence of autoregressive process in the error term. Het tests for heteroskedasticity. Vj is the Chow forecasting test. JB is a test of non-normal residuals. Note that A, B and C are cointegrating regressions whereas A', B' and C' are augmented Dickey-Fuller regressions.

1986).4 Second, like Yoshida and Rasche (I 990), it was found that interest rate spread does not have any significant effect on the long-run demand for money in Japan. Therefore, this finding conflicts with Corker (1990). Third, the present finding supports the hypothesis that real exchange rate is a n important determinant of long-run demand for money in Japan during the floating exchange rate period. An increase in the real exchange rate, that is, depreciation of the Japan- ese Yen, would increase the demand for broad money, leading to a decrease in the effectiveness of a given monetary policy, evidence consistent with Bahmani-Oskooee (1991) for the United Kingdom and Bahmani-Oskooee and Pour- heydarian (1990) for the United States and Canada. Fourth, like Corker (1990) and Ueda (1988), it was found that wealth and real income have long-run effects on the demand for broad money, evidence that supports the argument that broad money in Japan is held to finance transactions and as a store of value. Finally, there are two other encouraging aspects of our results: (a) the income and wealth elasticities sum approximately to one - a finding that conforms to the theoretical money demand function described in Tobin

(1969); and (b) the hypothesis of long-run proportionality between money and prices is supported by the data; hence, the money demand equation in real terms can be specified.

Having established that model A is the preferred cointe- grating regression, the next step is the estimation of a dynamic relationship, such as Equation 2 that includes the lagged residuals of model A, called EC,- ,, as a representa- tion of the feedback toward the long-run money demand equilibrium and the estimation of Equation 3 by imposing the restriction that the long-run income and wealth elastici- ties should sum to one. Alternatively, one can estimate Equation 3 without imposing this restriction. The first two approaches were opted for. The estimates of the final equations are given in Table 2 as Equations D and E. Because the data used are those supplied to us by Corker, we have attempted to replicate his final equation, and this is shown as Equation F.

As can be seen, Equations D and E appear to be satis- factory, based on the usual criteria. In particular, all variab- les have the expected signs and are statistically significant a t the 5% level. The exception is the interest rate variable in

,The authors are grateful to a referee for suggesting the Johansen-Juselius (1990) maximum-likelihood procedure. We tested whether there is one cointegrating vector using the likelihood ratio statistics. The results (available from the authors) suggest that there is one cointegrating vector which is qualitatively similar to the OLS cointegrating equation preferred here.

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Table 2. Error-correction regressions for Japan money demand (1973:Ql-1988:Q4)

D. Inm,=0.0093+0.617A1nm1~, -0.8866111 P1+0.497AIn PI-, -0.105AIn(I +R),-, -0.025Aln Kt- , - 132EC,- , (3.99) (6.35) (10.97) (4.3 1) (1.93) (2.2) (2.95)

R~ =0.913, SEE=0.003, F1(6, 55)= 107.5, DW = 1.97, AR1-4 F[4,51] = 1.58 AR1-12 F[12,43] = 1.02, ARCH(4)=2.9, Het(l)=2.19, RESET F[1,54] =0.73 JB(2) = 0.24, BP(20) = 18.6, LB(20) = 23.07, T= 62[1973(3b1988(4)]

E. Inn~,=0.041+0.619A1nml~,-0.920InP,+0.529AInP,~,-0.094AIn(l+R),~, (2.49) (6.35) (10.5) (4.32) (1.9 1)

-0.023Aln K t - , -0.057(ln m , - , -In W,- ,)-0.081(lnrnf-, -In Y,- ,)+0.0201n Kt- , (2.07) (2.93) (4.3) (3.50)

~ ~ = 0 . 9 1 2 , SEE=0.003, F1(7,54)=90,Z, DW=2.0, AR1-4F[4,50]=1.68 AR1-12 F[12,42] = 0.89, ARCH(2)=4.2, Het(l)= 1.99, RESET F[1,53] = 1.13 JB(2)= 1.14, BP(20) = 17.74, LB(20)= 22.14, T = 62[1973(3k1988(4)]

Note: The numbers in parentheses beneath the estimated coefficients are the absolute t-values derived from White (1980) consistent standard errors. SEE is the standard error of estimate. DW is the Durbin-Watson statistic. AR is the Breusch-Godfrey F-statistic for serial correlation. ARCH and Het statistics are for heteroskedasticity. F,tests the null hypothesis that all right-hand side variables as a group except the constant have a zero coefficient. RESET is the specification test for departures from the linearity assumption in the structure of the model. JB tests if the residuals originate from a normal distribution. BP is the Box-Pierce statistic. LB is the Ljung-Box statistic.

Model E, which is significant at the 10% level. The dia- gnostic test statistics reported show no evidence of function- al form misspecification, no higher-order serial correlation, no problems of non-constant residual variances, and no problems of non-normal residuals.

An examination of CUSUM and CUSUMSQ graphs reveals no problem of within-sample instability. Three other coefficient stability tests were employed, namely Chow (1960), Farley and Hinich (1970) and Ashley ( 1 984) to avoid reliance on a single statistic. The calculated values are F (7,48) = 1.13 and F(6,49) = 1.45 for the Chow and Farley and Hinich statistics, respectively. The calculated values of Ash- ley statistics are 0.1 1, 1.3, 1.06, 0.70 and 0.93 for Alnm,-,, Aln PI, Aln(1 + R),- ,, Aln K t - ,, EC,-, and Aln PI- ,, re- spectively. The Ashley values are to be compared to F(5,62) = 2.37. Note that the three statistics corroborate the findings of CUSUM and CUSUMSQ in every case. Because of the space limits, the implementation of these tests is not ex- plained in detail. Interested readers are referred to Arize (1992) for a detailed discussion.

The test of parameter restriction against the general model, which resulted in Model D, suggests that the re- stricted ECM is not dynamically misspecified. The com- puted F value is F(19,33)= 1.41, which is not significantly different from zero at the 5% level. To relax the restriction imposed on EC,-, by virtue of the cointegrating regression, EC,-, is excluded and the lagged-level variables of the

cointegrating regression are included. Then we tested whether In m,- ,, In Y,- ,, In W , - , and In K t - , are jointly zero. The computed F(4, 52)=5.6 is significant at the 5% level. As Jenkinson (1 986) pointed out, given the correspond- ence between cointegrated and error-correction models, the test of the lagged-level variables is a more robust check of the validity of the cointegrating regression as a long-run solu- tion. Hence, the cointegrating regression is strongly sup- ported. The advantage of Model D is that the EC,-, variable reduces the number of parameters in the estimating equation by four.

As a further test of dynamic specification of Model D in Table 2, the Wallis (1986, p.189) and Hendry and Ericsson (1991) procedures are used. The Wallis procedure involves including EC ,-,, EC,-, and EC,-, as regressors, whereas the Hendry and Ericsson procedure amounts to adding higher powers of EC,-,, such as the squares and cubes of EC,- ,, into the short-run dynamic model. The computed value for Wallis is F(3,50)=0.09, whereas for the Hendry and Ericsson procedure it is F(2,53)= 2.05. Neither of the F- values is significant at the 5% level.

Turning next to the exogeneity assumption of Model D, it has so far been assumed that the contemporaneous variable AP, is weakly exogenous, choosing to interpret the coeffic- ients of the model as those of a money demand f u n c t i ~ n . ~ As demonstrated earlier, Model D is statistically stable over the sample period; however, inverting the model by treating AP,

'Using dummy variables, 1985:Q2 and 1987 were also examined. None of the dummies proved significant at even the 15% level.

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as endogenous and the growth rate of nominal money, (In M,) as exogenous yields an equation which, unlike Model D, is not constant (see Appendix B for details). Furthermore, note that Model D is unchanged by adding AP, to both sides of the model, in which case the regressand becomes Aln M, and the coefficient of AP, becomes +0.114.

To test directly the super-exogeneity assumption, the variable addition test procedure suggested by Favero and Hendry (1990) is used. First, a single-equation model of AP, is developed:

R2 =0.78, SEE = 0.0066, F1(3, 60) = 69.43,

DW = 1.92 JB(2)= 3.5, AR 1-4 F[4,56] = 2.66,

ARCH(4) = 5.43 RESET F[1,59] = 0.6, BP(21)= 9.08 LB(21) = 11.65

In Equation 4, the numbers in parentheses beneath the estimated coefficients are absolute t-statistics derived from White (1980) heteroskedasticity-consistent estimated stand- ard errors. The diagnostic tests are explained briefly in Table 2. Second, the residuals from Equation 4 denoted as U[P], the squared residual u[P]~, the distributed lags of u[P]~, and four-period moving standard deviation of U[P], denoted as JUCP], were added to Model D and tested for significance. Specifically, U[P],, U[P],-, and JUCP], are added to Model D, and a test of the joint restriction, that the coefficients on the added variables are zero, was performed. The calculated F(4,50)= 1.24 is below the 5% critical value of 2.56. It is also below the 10% critical value of 2.06. Longer or shorter lags on the squared residuals yielded similar outcomes; in no case were any of the added terms testing for weak or super exogeneity significant. Third, two standard tests used to check for structural stability were performed on Equation 4. The Chow test, with the sample period split at the mid-point to maximize the empirical power of the test, yields F(4,36) = 3. I . The two periods are 1973:Ql-1980:Q4 and 1981:Ql-1988:Q4. Given the sensi- tivity of the Chow test to the particular choice of the breaking date, applying an alternative test seems prudent. A test that does not require splitting the sample into two parts is the Farley and Hinich (1970) procedure. The calculated F(3,57) = -9.78 corroborates the Chow test in rejecting the stability hypothesis. One can, thus, argue that the marginal model is non-constant, whereas the conditional Model D is constant.

Fourth, a dummy variable D74Q1 is used, coded one for the period 1973:Q2-1974:Ql and zero otherwise (to repres- ent oil price shock), to capture the parameter non-constancy

of Equation 4:

R2=0.82, SEE=0.005, Fl(4,56)=64.7,

DW =2.2 JB(2)=4.1, A R 1 4 F[4,52] = 1.3,

ARCH(4)= 1.92 RESET F[1,59] =0.59,

Equation 5 suggests that 'the oil-crisis' dummy is positive and significant at the 5% level.6 The equation is reasonably constant relative to Equation 4. Invariance implies that the variables helpful in explaining the in-sample non-constancy of Equation 4 should be unimportant if added to Model D. When D74Q1 is added to Model D, the partial F-value is F(1,54)= 1.84, which is non-significant at the 5% level (see Engle and Hendry, 1991 for details).

Fifth, the White (1980) test was applied, which is a joint test for heteroskedasticity and simultaneous equation bias on Model D. The calculated chi-square value of 29.1 with 21 degrees of freedom is below the critical value of 32.7 at the 5% level. Furthermore, note that the Breusch and Pagan (1979) test for heteroskedasticity applied on Model D yields a chi-square value of 3.29, which is non-significant. There- fore, according to White's procedure, exogeneity is sup- ported. Finally, Model D was estimated using instrumental variable estimation and the best results were obtained using the following instrument set: { 1 , t, Apt-,, Apt-,, AP ,-,, AY,-,, AY,-,, AR,-3, AP:, AP:- ,, APF-,,I, where P* is the world price level. The estimated structural parameters are very close to the OLS estimates of Model D and the standard error of estimate o=0.0043, which is also close to the OLS estimate, a=0.003. Furthermore, the Sargan stat- istic for the validity of the instruments yields a value of 4.06, which is distributed as a x2(5) under the null and is not significant at the 5% level. Although these results are by no means conclusive without further tests, they do, to some extent, support the exogeneity assumptions underlying the conditional model, that is D.

In sum, the above diagnostic tests indicate a well-fitting money-demand equation that fullfills the condition of serial non-correlation, homoskedasticity, structural stability, zero disturbance mean (i.e. no specification errors) regressor- error term non-correlation and normality of residuals.

IV. S U M M A R Y A N D C O N C L U S I O N

The purpose of the present paper has been to estimate an appropriate money demand function for Japan using coin- tegration and error-correction procedures. In so doing, a

recession period dummies (1974-75, 1977 and 1980-82) were 'They are consistent with those of the Johansen procedure (not rep0

tried without success. lrted here).

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A . C . Ar ize and S . S . Shwifl

modest attempt has been made to incorporate explicitly the effects of international monetary developments on domestic money holdings as summarized in the movements of real exchange rates. The temporal stability of the estimated money demand model has also been examined. The princi- pal conclusions of the present empirical paper can be summarized briefly as follows.

First, in the model considered, the explanatory variables that significantly influence the real broad money demand in the short-run are changes in real exchange rates, inflation and interest rate spread. This contrasts markedly with Corker (1990), who found that the short-run dynamics are driven by income and interest rate spread. This finding appears surprising because, except for real exchange rate, the data are identical. Note that Corker's model excludes infl- ation. However, like Corker, it is found that changes in financial wealth have no immediate effects on money de- mand. Note that the findings conform with Yoshida and Rasche (1990) and Yoshida (1990) on the short-run inflation effects; with Bahmani-Oskooee and Pourheydarian (1990) on real exchange rate effects and with Corker (1990) on net interest rate effects. When the inflation term is excluded, the Chow statistic yields a value of F(5,52)= 2.47, which exceeds the critical value of 2.4 at the 5% level. Furthermore, the inflation terms dominate the income and interest rate terms in Corker's model. An encompassing test yields a value of F(5,50) = 20.03 in favour of the present model. Exclusion of interest rate spread does not affect the stability of the model or result in autocorrelated residuals; however, the test of the dynamic specification turns up significant at the 5% level F(15,38)=2.21. When real exchange rate is excluded from the model, the Breusch and Godfrey statistic for AR(1) and AR(4) results in F(1,56) = 4.6 and F(4,53) = 2.6, respectively. Both are significant at the 5% level. It should be mentioned that the model variance dominates Corker's because the standard error of estimate of 0.003 is preferable to 0.007.

Second, an interesting result emerging from the study concerns not only the structural stability of the money demand function but also the evidence regarding the long- run path of real money balances. The study shows that the long-run path is driven by real income, wealth and the real exchange rate. Like Yoshida and Rasche (l990), no long-run interest rate effects were found. This finding conflicts with Corker (1990). Note that, when the Bewley (1979) procedure is used to estimate the long-run coefficients, the interest rate variable is insignificant. Furthermore, as noted before, our cointegrating equation is supported by the augmented Dic- key and Fuller statistic, Perron's Z(a*), and Jenkinson's joint restriction test. It is noteworthy that the coefficients estim- ated with Bewley's procedure are very close to those of the cointegrating regression. Moreover, the significance of the error-correction term suggests also the validity of the equi- librium relationship, indicating the existence of market forces in the money market that operate to restore long-run equilibrium after a short-run shock. The error-correction

coefficient of 13% per quarter is an improvement over 1 1 % reported by Corker (l990), 5% reported by Yoshida (1990), and 5.2% reported by Yoshida and Rasche (1990). Although the coefficient on the error-correction feedback term is small, it is similar to those reported for the US and UK (see Baba et al., 1988; Hendry, 1985).

Finally, the study shows that the neglect of a proxy for external monetary developments can produce biased results. According to the present results, real exchange rate has short- and long-run effects; therefore, monetary policy ac- tions aimed at stabilizing the economy and counteracting the impact of external shocks must take into account the response of domestic money demand to these external factors. If the adjustments in money demand induced by external monetary influences are ignored, monetary policy action can generate, at best, only uncertain results.

A P P E N D I X A: DATA S O U R C E S A N D D E F I N I T I O N S

The data sources and definitions are given in Corker (1990, p. 429). As Corker points out, 'the data sources were Nihon Keizai Shimbun, Inc.'s Nikkei Telecom: Japan News and Retrieval (Tokyo); and the International Monetary Fund's International Financial Statistics (Washington). All data, except for interest rates, were seasonally adjusted. For money and wealth, seasonal adjustment was carried out by the author using the XI1 program.'

The definitions of most of the data are described in the text, with the exception of financial wealth and the oppor- tunity cost of holding money. Corker (1990) indicates that

financial wealth was defined from flow-of-funds data as the average of beginning-and-end period stocks of the sum of the total positive financial assets of the personal and corporate sectors. The opportunity cost of holding money was defined as the three-month Gensaki rate minus the average return on holding money. The latter was defined as a weighted average of the interest rate on three-month certificates of deposit and the guideline three-month deposit rate. The weight on the CD was equal to the share of liberalized time deposits and banking sector money market certificates plus CD's in broad money. The weight on the guideline deposit rate was equal to the share of quasi- money, excluding liberalized time deposits, money market certi- ficates, and CD's in broad money.

The world price level and MERM exchange rates were provided by the statistics department of the International Monetary Fund (Washington).

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Demand for broad money in Japan

A P P E N D I X B

Long-run elasticities: Bewley procedure

In m, = - 0.426 - 0.4041n (1 + R), + 0.78 1 ln Y, + 0.39 In W, + 0.057 In K, (1.1 7) (1.05) (5.14) (4.83) (1 34)

In m, = - 0.242 + 0.75 In Y, + 0.39 ln W, + 0.083 In K , (0.96) (6.56) (6.14) (3.1 5)

Adding Aln P, t o both sides of Model D

In m, =0.0093 +0.617Aln m,-, +O. 114Aln P, +0.497AIn PI-, (4.54) (7.04) (1.48) (4.43)

-0.105Aln(l+ R),-, -0.025Aln Kt- , -0.132EC,-, (1.69) (2.1 2) (3.21)

R"O.57, SEE =0.003, F1(6,55)= 14.4 DW = 1.96

Inversion of Model D

Aln P, = 0.007 +0.087Aln m,-, + 0.299Aln Mt+0.82A1n P,-, (1.85) (0.45) (1.37) (4.64)

+ 0.30Aln(l + R ) , - , + 0.002Ain K t - , + 0.1 09EC, - , (3.24) (0.08) (1.56)

R 2 =0.80, SEE =0.0059, F1(6, 55)=40.6 DW = 2.65 AR1-4 F[4,51] =3.14, RESET F(1,54)=7.07, JB=(2)=2.6 Het(l)= 1.06, Chow F(7,48)=2.77, FH F(4,49)=4.9

Notes: For an explanation of notation see notes in Tables 1, 2, and Appendix A. Chow F breaking date is 1973:Ql-1980:Q4 and 1981:Ql-1988:Q4. FH is the Farley and Hinich (1970) parameter stability test. Note that the absolute t-values in parentheses beneath the estimated coefficients are consistent and have been estimated by the IV estimation as suggested by Bewley (1979). Equation 1, therefore, suggests that interest rate spread is insignificant.

A C K N O W L E D G E M E N T S

We are grateful for the comments and suggestions of Ed Manton, Ray Ballard, Kathleen Smith and Trezzie Pressley. Special thanks to Karan Huggins for excellent typing. Part of the work was conducted under a CBT-ETSU grant and part under an ETSU Research Council grant.

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