Money demand in an open economy

JOURNAL

OF

THE

JAPANESE

Money

AND

INTERNATIONAL

Demand

ECONOMIES

6, 176-198 (1992)

in an Open Economy*

C. R. MCKENZIE Faculty of Economics,

Osaka University,

Toyonaka, Osaka 560, Japan

Received November 6, 1989; revised November 25, 1991 McKenzie,

C. R.-Money

Demand in an Open Economy

This paper considers the specification of the demand for money in Japan in an open economy context. The importance of considering the rates of return on foreign-currency-denominated assets and disaggregating money by currency denomination and the residence of the holder is emphasized. Estimated money demand equations for resident holdings of yen-denominated Ml and M2 are presented. These equations are used to determine the quantitative impact of the 1980 foreign exchange law on portfolio substitution between domestic money and foreign assets. Portfolio shifts in response to changes in economic variables and the foreign exchange law do not seem to have had a significant influence on the demand for money in Japan. J. Japan. fnt. Econ., June 1992, 6(2), pp. 176-198. Faculty of Economics, Osaka University. Toyonaka, Osaka 560, Japan. c 1992 Academic

Press. Inc.

Journal

qf Economic Literature Classification Numbers C5, El41, F41, Gl I.

This paper attempts to m o d e l the demand for money in Japan in an open economy setting. The shift from a closed economy setting to an open setting raises issues related to the appropriate alternative rates of return that should be considered, the currency denomination of the money stock and the importance of the liberalization of capital controls. In an open economy, foreign-currency-denominated money and assets become potential avenues of investment and so the rates of return on these assets may influence the demand for money. As the demand for assets denominated in different currencies or held by different agents can be expected to * The author thanks Yoshiharu Oritani, Yoichi Shinkai, seminar participants at the Bank of Japan, the editor, and two anonymous referees for helpful comments and suggestions. In addition, the author acknowledges the financial support of the Nihon Keizai Kenkyu Shorei Zaidan (Foundation to Promote Research on the Japanese Economy) and the University of Western Australia. 0889-1.583/92$5.00 Copyright 0 1992 by Academic Press, Inc. All rights of reproduction in any form reserved.

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respond differently to changes in economic variables, it may be important to disaggregate money demand by currency denomination and holder. G iven that capital controls limit investment opportunities in foreign assets, liberalization of these controls by opening up new investment avenues may also influence the demand for money. Over the past ten years, there has been significant liberalization of regulations on both capital inflows and outflows as well as significant liberalization of the domestic financial system. Broadly speaking the former preceded the latter. The choice of the sample period used in this paper reflects this by focusing on the period prior to the significant domestic liberalization. The previous points suggest that Japanese money demand equations previously estimated are potentially misspecified. This is because Japanese money demand studies typically do not contain any reference to money demand in an open economy and to how open economy effects might influence the specification of the demand for money function. The principal exception is Boughton (1979), who found that external factors like the Eurodollar deposit rate and the rate of change of the effective (tradeweighted) exchange rate did not have any significant influence on the demand for money (Ml or M2) in Japan. Since Boughton (1979) used a sample period (1960-1977) that includes periods of both fixed and flexible exchange rates but does not cover the important change in the foreign exchange law in 1980 and also used a potentially inappropriate estimator, ordinary least-squares, it is possible that the choice of a different sample period, different proxies for the expected change of the exchange rate, and/or different estimators could overturn his results. The specification of the money demand function in an open economy with particular emphasis on the need to consider the rates of return on foreigncurrency assets and to disaggregate money by currency denomination and the residence of the holder is elaborated on in Section 1. Section 2 presents money demand equations estimated using Japanese data on the holdings of M 1 and resident holdings of yen-denominated M2 with Japanese banks. Estimated equations for these demands based on closed economy influences alone are presented in Section 2.1. These estimated equations are used in Section 2.2 to determine the quantitative impact of shifts between yen-denominated money and foreign-currency-denominated assetsfor Japan in the floating exchange rate period and the impact of the Foreign Exchange and Foreign Trade Control Law of 1980 on these shifts. Section 2.3 discusses problems associated with proxy variables for the expected change of the exchange rate. Section 3 contains some concluding remarks. 1. MONEY DEMAND

IN AN OPEN ECONOMY

In the economics literature, attention has focused on the demand for money in a closed economy. In contrast, little attention seems to have

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been given to open economy effects (see, for example, the surveys by Cuthbertson, 1988, and Leventakis and Brissimis, 1991). Following this closed economy tradition, money demand functions for either Ml or M2 estimated for Japan have typically been of the form M, = b, + b,M,-, + b2Y, + b,R,, + b,R,, + b,pdot, + E,, forMl:b,>Oandb,,b,,b,
(1)

for M2: b,, b, > 0 and b4, b, < 0,

where M, is the log of the real money stock, Y, is a transactions variable like the log of real Gross National Product (GNP), RI, is an own rate of return like the log of the one year time deposit rate, R,, is the rate of return on an alternative asset like the log of the call rate, pdot, is the inflation rate, and E, is a disturbance term. The expected signs of the coefficients for the two money stocks appear under Eq. (1). Illustrations of studies that are encompassed by Eq. (1) are Tsutsui and Hatanaka (1982) and Suzuki (1988) who set b, = b5 = 0, Hamada and Hayashi (1983) who set b, = 0, and Boughton (1979) who sets b, = 0. Shinkai (1984) also includes a moving standard deviation of the inflation rate but does not find it to be a significant explanatory variable. One notable feature of all these studies is their simple treatment of dynamic behavior by only including a single lagged dependent variable. More recent studies have considered more complicated dynamic behavior and a wider range of explanatory variables including wealth, stock price volatility, and return on investment in shares (Ueda, 1988; Corker, 1989; Rasche, 1990; Yoshida, 1990; Yoshida and Rasche, 1990; Boughton 1991; Shiba 1991). A consideration of money demand in an open economy raises a number of potentially important issues. The variety of assets available for portfolio diversification is wider as foreign-currency-denominated assets are now available. In the general Tobin-type model where all relevant asset returns are included in every asset demand, the demand for money will be influenced by the rate of return on foreign assets, that is, the assets’ nominal returns plus the expected return resulting from exchange rate changes. If foreign bonds are a relevant investment alternative, then their rate of return plus the expected rate of exchange rate appreciation could be expected to appear in the money demand function. With foreign money a relevant investment alternative, the expected rate of change of the exchange rate, could be expected to appear. The expected rate of change of the exchange rate is also the focus variable in the direct currency substitution literature that stresses portfolio shifts between domestic and foreign money (Miles, 1978; Cuddington, 1983) while the foreign interest rate is the focus variable in the indirect currency substitution literature (McKinnon, 1982, 1984; Traa, 1985). To the extent that these variables are important

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and have been excluded from the money demand functions estimated previously, it could be expected that the money demand functions would exhibit some instability. The second difference arising in the open economy is that nonresidents may hold yen deposits. Argy (1989) estimates nonresident nonbank holdings of deposits in Japan in 1985 at about 4% of M2 although nonresident yen deposits are always under 1% between 1980 and 1984. A number of reasons for nonresidents holding yen deposits can be suggested (Swoboda, 1968; Chrystal, 1977). First, these deposits may be used by nonresidents to diversify their portfolios, although given the interest ceilings on yen time deposits with Japanese banks until 1985, time deposits are likely to have been dominated by Gensaki and Euroyen deposits. Second, central banks may wish to diversify their portfolios. Central bank motives for holding and changing their holdings of time deposits are likely to differ from the motives of private sector investors (Nicholl and Brady, 1992). In addition, agreements between central banks aim to prevent central banks using their holdings in the same way as private investors. Third, traders may wish to use them to pay for Japanese exports by acquiring yen now as a hedge against exchange rate movements. Fourth, traders may use them to deposit the proceeds of export contracts to Japan; that is, the yen has been acquired and is held as yen pending expected favorable movements of the exchange rate. This last sort of activity is likely to be small given that the proportion of Japanese imports denominated in yen has been small (Fujii, 1992). Therefore, the influences on holdings of yen deposits by nonresidents could differ substantially from those of residents. The reasons why Japanese residents would want to hold foreigncurrency deposits are very similar. Private individuals and corporations may wish to diversify their portfolios. Japanese importers who have to pay for imports in foreign currency may use foreign-currency deposits for hedging purposes. Japanese exporters may use them to deposit the proceeds of export contracts for the purpose of hedging. Argy (1989) estimates Japanese resident holdings of foreign-currency deposits abroad at about 2% of M2 in 1985. The possibility of different investor portfolio behavior between residents and nonresidents suggests it may be important to disaggregate money demand by the residence of the investor and the currency of denomination. This is consistent with Goldfeld’s (1973, 1976, p. 708) argument for disaggregation of domestic money demand by the type of money and the type of individuals involved. Not only may lag structures and response sizes differ but the response of different types of money to changes in say domestic interest rates may differ (Mussa, 1979). For example, the responses of the demand for dollar time deposits to changes in yen and dollar

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time deposit interest rates are expected to be the opposite of the responses of yen time deposits to changes in the same variables. The transactions variable driving residents and nonresidents could also be expected to differ. Thus, attention needs to be paid to the currency composition of Ml and M2. On the basis of the arguments about open economy influences and the need to consider dynamics more carefully, the following extended form of (1) is used as a starting point, M, = 6, + b,M,-, + b,Y, + b,R,, + b,R,, + b,pdot, + b,M,-, + b,Yt-, + bsR,,-, + b9R2,-, + b,,pdot,-, + b,,DER: + b,,R; + c,,

(2)

where DER; is the expected rate of change of the exchange rate and R{ is a foreign interest rate. It should be noted that the significance of DER: and/or R{ is not necessarily evidence of currency substitution as these variables may be capturing the rate of return on holdings of foreign bonds, not monies. Where both foreign bonds and money are available, it becomes difficult to disentangle the influences of their respective returns on domestic money and to specify a priori the signs of b,, and b,, (see Cuddington, 1983). The demand for two money stocks, Ml and resident holdings of yendenominated M2, is investigated. As the definition of Japanese Ml excludes both nonresidents’ holdings of yen and foreign-currency deposits with Japanese banks, no adjustment is required. Given that the Japanese definition of M2 includes both yen-denominated and foreign-currencydenominated deposits and given the previous arguments, foreign-currency deposits have been excluded from the figures for M2. The foreigncurrency-denominated component of M2 rises steadily from 3.3% of M2 in 1980 to 5.1% in 1984. Since the extent of foreign influences on money demand is the focus of this paper, considering an M2 that includes foreign-currency deposits would mask any shifts that occurred between yen-denominated deposits and foreign-currency-denominated assets. If foreign-currency deposits are to be excluded, the aggregation of foreigncurrency deposits and nonresident yen deposits in official statistics prior to December 1980 also requires the exclusion of nonresident holdings of yen deposits. This adjustment is of the order of 2.3% up to 1980. In any case, the earlier arguments regarding the potentially differing investment motives of residents and nonresidents provide additional reasons for their exclusion. Certificates of Deposit (CDs), introduced in May 1979, were not added to M2 to form a broad monetary aggregate. When estimating the demand for a broad monetary aggregate for Japan, some authors have estimated equations for M2 + Certificates of Deposit (for example, Tsutsui and

MONEY DEMANDIN

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181

Hatanaka, 1982; Hamada and Hayashi, 1983). However, the characteristics of the assets in M2 and the characteristics of CDs are likely to differ significantly. For the period examined here (up to 1984), interest rates on the deposits contained in M2 are either zero or fixed at a government determined rate, whereas the rates on CDs are market determined (see McKenzie, 1992). CDs are also negotiable instruments and thus are more similar to bonds than money. Aggregation of these different assets could mask responses both between M2 assets and CDs and between M2 and foreign assets, while disaggregation may permit a clearer identification of these responses. After their introduction in May 1979, CDs are between 1 and 3% of M2 over the sample period.

2.

DEMAND

FORMONIESISSUED

DOMESTICALLY

The equations for M l and resident holdings of yen-denominated M2 (hereafter denoted M2) are estimated on quarterly data from 1973:11 to 1984:IV so that there are 47 observations. The estimation period is chosen to include only observations on the floating exchange rate period and to exclude observations for 1985 and onward where significant domestic financial liberalization has occurred. The estimation period is chosen to favor finding portfolio shifts between domestic money and foreigncurrency-denominated assets as much as possible. The justification for lim iting the data to the floating exchange rate period is that it is only in a period of volatile exchange rates and price instability that hard currencies like the yen or the mark become competitive stores of value and units of account for the dollar (McKinnon and Tan, 1983). 2.1 A Closed Economy Approach McAleer et al. (1985) have recently stressed the importance of dynamics in the specification of econometric models and of starting from a general model and working toward a specific model by the application of testable restrictions. Here the short sample of 47 observations prevents the consideration of long lags for each variable and a strict application of the general to specific modeling methodology. Instead, the modeling procedure adopted here was to attempt to find a satisfactory equation for the money demands based on wholly domestic influences by setting b,, = b,, = 0 in Eq. (2). Then, the variables suggested by open economy arguments, the expected change of the exchange rate and a foreign interest rate, are added to determine if they significantly improve the explanatory power of the closed economy model. Although recent econometric work has stressed the importance

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of unit roots and the nonstationarity of time series, the approach adopted here is to follow standard procedures given the low power of tests for unit roots (Christian0 and Eichenbaum, 1990). The variables included in the model were taken from those selected by other investigators (Boughton, 1979; Tsutsui and Hatanaka, 1982; Hamada and Hayashi, 1983; Corker, 1989; Rasche, 1990; Yoshida and Rasche, 1990; Boughton, 1991). Following Eq. (2), four domestic variables, the three-month’Gensaki rate (R3) as a rate of return on competing assets, the three-month bank deposit rate (RT) as a rate of return on competing assets for Ml and as an own rate of return for M2, the inflation rate’ (INF) as another rate of return on competing assets, and real Japanese Gross National Product (GNP) as a transactions variable, were considered as potential explanatory variables for Ml and M2. The price deflator used was the GNP price deflator. All regressors except the inflation rate were in logs and three seasonal dummies and a constant were included in each equation. Further details on the specification of the variables used and the sources of the data are given in the Appendix. Ordinary least-squares (OLS) was used to estimate the equations. For Ml the estimate of Eq. (2) assuming b,, = 6,, = 0 was 641, = 0.177 M&e1 + 0.037 GNP, + 0.051 RT, + (0.11) (1.25) (1.44 + 0.293 Ml,-, + 0.317 GNP,-I - 0.038 RT,m, (1.08) (0.91) (2.45) + seasonal dummies and constant, SEE = 0.159,

0.040 R3, + 0.106 INF, (1.77) (0.W 0.120 R3,-, + 0.169 INF,-l (1.13) (3.61)

R= = 0.985,

(3)

where the figures in parentheses are the absolute values of the t-statistics. SEE and R2 denote the equation’s standard error and the coefficient of determination, respectively. In this equation, only Ml,-, and R3,-, are statistically significant at the 5% level. It is interesting that the initial impact of rises in both R3 and RT is to raise the demand for Ml (suggesting short-term complementarity). The positive long-run impact of GNP and the negative long-run impact of R3 are consistent with a priori expectations. A little surprising are the positive long-run impact of RT given that RT is a rate of return on a competing asset and the positive long-run impact of inflation but both these long-run impacts are statistically insignificantly different from zero. For M2, the estimate of Eq. (2) assuming 6,, = b,, = 0 was ’ While a case could be made for using the expected inflation rate rather than the actual inflation rate, the approach of previous studies has been followed on this point (see, for example, Boughton, 1979; Yoshida, 1990).

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IN AN OPEN ECONOMY

183

ti2, = 0.654 M2,-, + 0.152 GNP, + 0.014 RT, - 0.002 R3, - 0.319 INF, (0.86) (0.22) (3.36) (4.52) (0.92) + 0.216 M2,-, + 0.002 GNP,-, + 0.015 RT,-, - 0.044 R3,-, + 0.244 INF,-, (2.72) (0.01) (1.05) (3.42) (1.77) + seasonal dummies and constant, SEE = 0.0074,

R= = 0.999.

(4)

In this equation, the signs on R3, RT, and GNP are consistent with a priori expectations and the long-run negative impact of inflation on money demand is what m ight be expected if money is held as a substitute for real assets. Both inflation variables, the Gensaki rate lagged one period and the money stock lagged one period, are individually statistically significant at the 5% level. A specification search2 led to the following preferred equations for M l and M2: tilt = 0.248 M l,+, + 0.290 GNP, + 0.039 R3, + 0.289 M l,-, - 0.100 R3,_, (2.07) (2.59) (5.32) (4.83) (2.07) + seasonal dummies and constant, SEE = 0.0157,

R= = 0.983;

(5)

ti2, = 0.828 M2,-, + 0.203 GNP, - 0.321 INF, - 0.019 R3- r + 0.237 INF,- , (4.01) (3.56) (2.56) (14.17) (3.44) + seasonal dummies and constant, SEE = 0.0076,

R= = 0.999.

(6)

In the preferred model, M l is a function of GNP, an interest rate on a competing asset and the lagged money stock. The long-run income elasticity of M l is a little on the low side at 0.63 as it is significantly different from unity (asymptotic standard error is 0.040). The long-run interest elasticity of M l was 0.13. As with the initial equation, the initial response to a rise in R3 is an increase in the demand for M l followed by a fall in demand. The preferred model was an acceptable simplification of Eq. (3) as the test statistic for the exclusion restrictions was 1.44 and the critical value F(5, 33, 0.01) = 3.70. The preferred model for M2 is very much like the model estimated by Boughton (1979) in the variables that it includes but the dynamics are a little richer. The long-run income elasticity of 1.18 is similar to that obtained in other studies and is insignificantly different from unity (asymptotic standard error is 0.097). The long-run interest elasticity is a little on the low * Details of the specification search are omitted because of space limitations and the open economy focus of the paper.

184

C. R. MCKENZIE TABLE 1 DIAGNOSTIC TESTS FOR Ml AND M2 EQUATIONS

Aggregate

Statistic type

Statistic value

Critical value

Ml

RESET” Normalityb Heteroskedasticity’ ACF of residuals’ ACF of squared residuals’ Exogeneity’ RESET Normality Heteroskedasticity ACF of residuals ACF of squared residuals Exogeneity

3.21 1.04 0.02 (1) 0.56, (2) 0.30, (3) 0.13, (4) 0.52 (I) -0.34, (2) 0.08, (3) 0.28, (4) - 1.60

x$,(0.01) = 9.21 ~\~>(0.01) = 9.21 xii,(O.Ol) = 6.63

1.03 4.96 1.72 0.31 (1) 0.52, (2) 0.41, (3) 0.17, (4) 0.21 (I) 1.90, (2) 0.18, (3) 0.09. (4) 1.51

x+(0.0’) = xY,(O.Ol) = ~~~~(0.01)= ~~~~(0.01)=

4.48

~;~,(0.01) = 9.21

M2

9.21 9.21 9.21 6.63

a RESET. This tests whether the coefficients of the predictions squared and cubed are significantly different from zero in the regression of the residuals against these and the other explanatory variables: see Ramsey (1%9). b Normality. The normality test of Bera and Jarque (1981). c Heteroskedasticity. The LM heteroskedasticity test derived in Pagan ef a/. (1981) to test that 01 = 0 in u; = a2[E(y,)p, where y, is the dependent variable in the regression. d ACF of residuals. If the model is y, = p’ x, + e,, these are the f-statistics that the coefficient of the lagged residual u,-, is zero in the regression of u, against x, and y,-,. These r-statistics are asymptotically distributed as standard normal under the null hypothesis of no sertal correlation: see McAleerer a[. (1985). * ACF of squared residuals. These f-statistics are the r-statistics of I$, in the regression of ~43against uf-, and are asymptotically distributed as standard normal (see Granger and Anderson (1978)). ‘The exogeneity test was conducted by obtaining the predictions from the regressions of GNP,, R3,, and INF, on an instrument set, augmenting the preferred model for Ml by the predictions for GNP, and R3, and the preferred model for M2 by the predictions for GNP, and INF,, and testing the joint significance of the added predictions in each equation. For further details on these tests see Hausman (1978) and McAleer and Deistler (1986). In calculating the predictions used in the MI equation the instrument set was Ml,_,, Ml,+,, GNP,_,, GNP,+L, R3,_,, R3,-,, INF,-,, INFUS,-,, REUD,-,, DER,-r, a time trend, and seasonal dummies. For the predictions used in the M2 equation the instrument set was M2,-,, M2,+2, GNP,-,, GNP,_!, R3,-,, INF,_,. INF,-,, INFUS ,_,. REUD,-,, DER3,-,, a time trend, and seasonal dummies. INFUS,, REUD,, and DER3, are respectively the inflation rate in the United States, the threemonth Eurodollar rate, and the actual rate of change of the exchange rate over the next quarter.

side at 0.11 when compared with the corresponding elasticity for M 1 of 0.13. The preferred model was an acceptable simplification of Eq. (4) as the test statistic for the exclusion restrictions was 1.42 and the critical value F(5, 33, 0.01) = 3.70. To determine the adequacy of the preferred models for Ml and M2, each model was subjected to a number of diagnostic tests that are designed to detect functional form misspecification, heteroskedasticity, serial correlation and nonnormality of the errors, and general misspecification. Table I contains the results of these tests and a brief description of each test (see McAleer and Deistler, 1986, for a more detailed discussion of these tests). These tests provide no striking evidence of any serious deficiencies in either model. An attempt was made to generalize the specification of each model by including a time trend and by estimating the model assuming the

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disturbances followed up to a fourth-order autoregression. These changes did not contribute significantly to the explanatory power of the model. The use of ordinary least-squares to estimate both models assumes that all of the explanatory variables are exogenous. Should any of the explanatory variables be endogenous it would be necessary to use an instrumental variable estimation technique. The exogeneity of GNP, and R3, in the Ml equation and GNP, and INF, in the M2 equation was tested. As indicated by the exogeneity tests in Table I, the hypothesis of exogeneity was not rejected, justifying the use of ordinary least-squares. Having found what appear to be satisfactory equations for Ml and M2, the investigation proceeds to examine the stability of these equations. One check of parameter stability is to estimate the equation over a particular sample and then use the equation to generate out of sample forecasts. As few Japanese investigators have calculated the confidence intervals of these out of sample predictions, it has been difficult to determine whether there has been statistically significant over- or underprediction (cf. Tsutsui and Hatanaka, 1982). A note of caution is also warranted as to what can be inferred if instability is found. In addition to the failure to consider open economy influences (including currency substitution), a number of competing causes of instability in the money demand function have been suggested, including financial innovation and deregulation (Enzler ef al. 1976) and general misspecification of the money demand function (Hamburger, 1977). This suggests that if instability is detected it should not automatically be ascribed to open economy influences or currency substitution (cf. McKinnon, 1982). The preferred models for Ml and M2 in Eqs. (5) and (6) were reestimated using data up to 1980: IV and then one-step ahead prediction errors were generated for the next 16 periods using a dummy variable technique (see Salkever, 1976; Pagan and Nicholls, 1984). For Ml and M2, 15 of the 16 prediction errors were positive. This is not the pattern of prediction errors that would be expected if the prediction errors were uncorrelated but theoretically the prediction errors will be correlated. However, the F-test that the 16 coefficients associated with the dummy variables were jointly zero was 0.81 for Ml and 0.89 for M2, well below the critical value of F( 16,22,0.01) = 2.95. An examination of the individual t-tests of the dummy variables for the Ml equation indicated that the only significant prediction error had a t-value of 2.52 and this occurred in 84:III. For M2, the most significant prediction error was in 1981:11with a f-value of 2.11. With 16 predictions and a significance level of 5%, the likelihood of at least one significant t-value is quite high. Therefore, these results seem to suggest quite a degree of stability for both equations. One of the reasons for predicting from 1981:1 was that rules governing the use of foreign-currency deposits held with Japanese banks were sig-

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C. R. MCKENZIE

nificantly altered in December 1980. Prior to December 1980, foreigncurrency deposits acquired by yen conversion (rather than as a result of export or other external transactions) were limited to 3 million yen. This rule was eliminated in December 1980 and, simultaneously, the interest rate payable on foreign-currency deposits was liberalized. In addition, the principle governing foreign exchange control was reversed from prohibition in principle to freedom in principle (see McKenzie, 1992, for further details). These changes may have provided the Japanese with a greater ability to shift their funds between domestic money and foreign-currency assets and this could have caused the parameters in the money demand function to become unstable. Had significant shifts between domestic money and foreign-currency assets occurred in the period 198l:I to 1984:IV, it could be expected that sizable prediction errors would have been observed. The prediction test provides no evidence to support this notion. A Chow test was implemented by augmenting the preferred equation with each of the variables multiplied by a dummy that took the value zero up to 198O:IV and the value unity thereafter. These Chow tests also provided no evidence of instability with values of 0.84 for Ml and 1.01 for M2 (critical value: F(9, 29, 0.01) = 3.10). As a further test of parameter instability, the cusum and cusum of squares tests of Brown et al. (1975) were applied. These tests also suggested no parameter instability, since for both Ml and M2 the value of the cusum and cusum of squares statistics lay well within the bounds prescribed for each observation. Since both Eqs. (5) and (6) contain lagged dependent variables, there is a slight theoretical difficulty in interpreting these tests. However, there is no theoretical reason to believe that in the presence of lagged dependent variables the tests are biased toward accepting the null hypothesis (Pagan and Volker, 1981, p. 389). 2.2.

Open Economy

Influences

Having found what appears to be adequate equations for Ml and M2 that exhibit no parameter instability, open economy influences are investigated by the inclusion of the expected rate of change of the yen/dollar exchange rate, DER:, and a foreign interest rate, the three-month Eurodollar rate. The reason for focusing on dollar assets is that dollar denominated assets are the most important assests for Japanese investors.3 Based on Eqs. (5) and (6), the estimated equations for Ml and M2, respectively, were of the form 3 A referee suggested that there might be some value in examining a broader country average for both the foreign interest rate and the expected change of the exchange rate. Considering country averages raises the conceptual problem that the corresponding weighted average assets are not usually the assets investors consider. In addition, there is a problem of how to choose the weights.

MONEY

Ml, = c,, + c,Mll-,

DEMAND

IN

AN

OPEN

ECONOMY

+ cZR3, + c,GNP, + c‘,M~,-~ + cSR3,-, + c,DER; + c7REU, + seasonaldummies + elt,

187 (7)

M2, = d, + d,M2,-, + &GNP, + d,INF, + d,R3,-, + d,INF,-, + d,DER; + d,REU, + seasonal dummies + c2,, (8) where tit are disturbances. The parameters of interest are cg and c7 in Eq. (7) and d6 and d7 in Eq. (8). The inclusion of the expected change of the exchange rate makes it necessary to make an assumption about how those expectations are formed. Here, rational expectations are assumed and the realized change of the exchange rate, DER,, is used as a proxy for the expected value of the change of the exchange rate (see McCallum, 1976). Under rational expectations DER, = DER: + qr, where r), is an error uncorrelated with information available at the time expectations were formed. This means there is essentially an errors-in-variables problem associated with using the realized value of the change of the exchange rate as a proxy variable and this necessitates the use of an instrumental variables estimator. In addition, there is the possibility that the error in Eqs. (7) and (8) will follow a first-order moving average process [MA(l)] (Cumby et al., 1983). The relevant test statistics associated with the parameters of interest are contained in Table II. The Joint Test refers to the test of the hypothesis that cg = c7 = 0 in Eq. (7) and d6 = d7 = 0 in Eq. (8) and is distributed as a x$ under the null hypothesis. Three different instrument sets labeled I, II, and III were used. Instrument set I included information dated at time t or earlier, instrument set II included information dated at time t or earlier excluding the values of R3,, REU,, and DER,- , dated at time t, and instrument set III included only information dated at time t - 1 or earlier. In all instrument sets, lagged dependent variables are included as instruments. Cumby et al. (1983) argue that if the error is likely to be an MA(l) process because of a McCallum (1976) type substitution then the dependent variable at lag one will be an invalid instrument. This proposition is incorrect and the results in Fair (1984) indicate that for Eqs. (7) and (8) all lags of the dependent variable are valid instruments. As shown in Table II, for both Ml and M2, the three-month Eurodollar rate and the expected change of the exchange rate were neither separately nor jointly significant. A result that was independent of the instrument set or estimator used (two-stage least-squares (2SLS) or two-stage two-step least-squares estimator allowing for a moving average error of order one (2S2SLS [MA(l)])). Despite Cumby et al.‘s (1983) theoretical argument, there did not appear to be any serial correlation when either equation was estimated by 2SLS (see Note to Table II). Equations (7) and (8) were also estimated subject to the restrictions that cg = c7 and de = d,, respectively,

TABLE II TEST FOR OPEN ECONOMY

Aggregate Ml

Estimation method”

I-Statistics

Instrument set’

REU,

I II III I I1 III I II III

0.72 0.53 0.69 0.84 0.22 0.28 -

1 II III 1 11 III I II III

1.42 0.32 0.18 1.72 0.63 0.28 -

2SLS

ZSZSLS[MA( I)] OLSP

M2

INFLUENCES

2SLS

2S2SLS[MA( I)] OLSP

DER; 0.21 0.27 0.004 0.22 0.48 0.41 0.21 0.01 1.04 - 0.45 0.19 -0.18 -0.55 0.19 -0.30 -0.48 0.35 1.52

Joint test 2.53 0.77 0.62 3.33 0.66 0.44 2.46 1.21 3.58 2.14 0.37 0.03 3.07 1.06 0.09 2.47 2.36 4.70

Note. Consider the simple autoregressive process E,, = p,.sirmj+ u,, and the simple moving average process sir = ui, + P,u,,_~,where ui, is a white noise process. LM, is the test of the null hypothesis Ho: p, = 0 against the alternative hypothesis H,: pJ # 0. This test statistic is distributed as a standard normal variate under the null hypothesis. Instrument set

LMI

LM>

LM3

MI

I II III

0.35 -0.15 0.07

0.04 -0.55 0.06

0.25 0.31 0.80

0.08 -0.31 - 0.46

M2

I II III

0.28 - 0.80 -0.14

0.63 0.28 I .03

0.64 0.73 0.47

0.62 0.68 0.48

Aggregate

LM4

0 2SLS denotes two-stage least-squares. 2S2SLS [MA(l)] denotes the two-stage two-step least-squares estimator of Cumby et al. (1983) assuming the errors follow a moving average of order one. OLSP denotes ordinary least-squares where the predictions from a regression of the realized change of the exchange rate on the instrument set are used as a proxy for the expected change of the exchange rate. b For Ml, instrument set I was Ml,-,, MI,-,, GNP,, GNP,-,, R3,, R3,-1, INF,, INF,+,, REU,, DER ,-,, and INFUS,. Instrument set II was Ml,-,, Ml,_,, GNP,, GNP,_,, R3,_,, R3,-*, INF,, INF ,-,, REU ,-,, DER,-r. and INFUS,. Instrument set III was Ml,-,, Ml,-?, GNP ,-,, GNP,_*, R3,-,, R3,-r, INF,-,, INFUS,-,, REU,-,, DER,-r, and a time trend. All instrument sets included a constant and seasonal dummies as well. For M2, instrument set I was M2,- ,, M2,-,, GNP,, GNP,-, , R3,, R3,-, , INF,, INF,_, , REU,, DER,- , , and INFUS,. Instrument set II wasM2,_,, M2,-r, GNP,, GNP,_,, R3,-,, R3,_r, INF,-,, INF,-2, REU,-,, DER,-r, and INFUS,. Instrument set III was M2,- i, M2,-r, GNP,_ ,, GNP,-r, R3,-,, INF,_ ,, INF,_2, INFUS,_ ,, REU,-,, DER,-,, and a time trend. All instrument sets includedaconstant and seasonal dummies as well. 188

MONEY DEMAND

IN AN OPEN ECONOMY

189

so that it is REU, + DER: that appears. This variable was also insignificant, a conclusion that was robust to the choice of the instrument set and estimation technique used. To test the robustness of these results to the choice of proxy for the expected change of the exchange rate, an alternative proxy obtained as the predictions from a regression of the realized change of the exchange rate on an information set was used.4 These predictions were then used as a proxy for DER: and Eqs. (7) and (8) were estimated by OLS. The tests associated with this proxy variable are denoted by the estimation method OLSP in Table II. The information sets used to form the predictions are the same as the instruments used in the 2SLS and 2S2SLS [MA(l)] regressions. In general, the application of ordinary least-squares to this type of equation which contains a generated regressor, the predicted change of the exchange rate, will lead to inconsistent parameter estimates and inconsistent hypothesis tests (Nelson, 1975; Pagan, 1984). These problems arise because the measurement error associated with the generated regressor is potentially correlated with explanatory variables in the equation. However, where the hypothesis being tested includes the hypothesis that the coefficient associated with the generated regressor is zero, the usual test statistics from an OLS regression can be used to provide a consistent test (Pagan, 1984, p. 229). The results from these OLS based tests in Table II suggesting that DER; and REU, are not statistically significant are consistent with the results obtained from the other estimation methods. No test statistic is provided for the test of whether the coefficient on REU, is zero in the OLSP regressions as the hypothesis being tested does not include the hypothesis that the coefficient on DER: was zero. Including only DER; in the preferred models indicated that DER: was not a significant explanator when the equation was estimated by 2SLS, 2S2SLS [MA(l)], or OLSP. When the preferred models were augmented by REU, only and estimated by OLS, REU, was not significant. It is possible that it was only after the change in the foreign exchange law and the rules governing the use of foreign-currency deposits in December 1980 that agents could freely engage in shifts between domestic and foreign-currency deposits. To take account of this possibility a dummy variable, DFE,, that takes the value zero up to and including 1980:111and unity thereafter was defined. It was included together with appropriate expected change of the exchange rate and foreign interest rate variables (DFE, . DER; and DFE, * REU,) to capture the possibility of “new” 4 A referee suggested that other proxies might be used for the expected change of the exchange rate. The use of three instrument sets together with the OLSP technique can be interpreted as using slightly different proxies for the expected change of the exchange rate.

190

C. R. MCKENZIE

investor sensitivity to foreign rates of return following the regulatory change. The equations estimated were Ml, = c0 + c~MI,-~ + c,R3, + c,GNP, + c~MI,-~ + cSR3,-, + c,DFE, + c,DFE, . DER; + c,DFE, . REU, + seasonal dummies + cl,

(9)

M2, = do + d,M2,-, + d,GNP, + d,INF, + d4R31-, + &INF,-i + d,DFE, + d,DFE, . DER: + d,DFE, * REU, + seasonal dummies + c2,, (10) where the coefficients of interest are now cg, c7, and cs in Eq. (9) and d6, d7, and d8 in Eq. (10). The test statistics associated with these coefficients are presented in Table III. The Joint Test refers to the test of the hypothesis that c6 = c7 = cs = 0 in Eq. (9) and d6 = d7 = d, = 0 in Eq. (10) and is distributed as x& under the null hypothesis. As before, three different instruments sets were used and these are labeled IV, V, and VI. Instrument set IV included information dated at time t or earlier, instrument set V included information dated at time t or earlier excluding the values of R3,, DFE,- , * DER:- , , and DFE, . REU,, and instrument set VI included only information dated at time t - 1 or earlier. There was no sign of any serial correlation in either equation when estimated by 2SLS (see Note to Table III). For M 1, neither the individual nor the joint tests indicate that any of the “open economy” variables are significant. When only DFE, was added to the preferred model for Ml it was insignificant. For M2, only two of the individual t-tests associated with DFE, indicate any significant variables at the 5% level. However, over half the joint tests indicate rejection at the 5% level of the hypothesis that the coefficients on DFE,, DFE, * DER,, and DFE, * REU, are jointly zero (critical value: &(0.05) = 7.81). As in Table II, no test statistics are provided for DFE, and DFE, * REU, for the OLSP estimation method as the usual test statistics from an OLS regression are not valid. An examination of the individual t-statistics for the M2 equation in Table III suggests that DFE, could be significant and could be the cause of the significant joint tests observed. This is certainly confirmed when only DFE, is added to Eq. (6) and the equation is reestimated by OLS. M2, = 0.822 M2,-, + 0.162 GNP, - 0.325 INF, - 0.022 R3,-, (2.20) (4.44) (4.45) (15.37) + 0.213 INF,-, + 0.013 DFE, + seasonal dummies and constant. (2.89) (3.36) SEE = 0.0070,

R2 = 0.999.

(11)

MONEY

DEMAND

IN

AN

OPEN

191

ECONOMY

TABLE III TESTS FOR OPEN ECONOMYINFLUENCESAFTER DECEMBER1980 t-Statistics Aggregate Ml

Estimation method” 2SLS

2S2SLS [MAC 1)I

OLSP

M2

2SLS

2S2SLS [MA(l)]

OLSP

No&.

The definition

Instrument set” IV V VI IV V VI IV V VI

DFE,

DFE,

0.87 0.19 -0.05 0.98 0.20 0.33

-

IV V VI IV V VI IV V VI

DER:

DFE,

REU,

Joint test

-0.27 -0.27 -1.27 -0.30 -0.36 -0.96 - 0.27 -0.27 0.86

-0.05 0.11 0.58 -0.06 0.17 0.51 -

3.14 2.46 2.99 4.06 4.09 4.91 3.21 3.54 3.93

I .02 1.16 -0.14 I .08 0.95 -0.61 1.03 1.21 I .36

-0.95 - 1.22 -0.78 - 1.13 -1.13 -0.68 -

9.51* 6.70 1.14 17.96* 12.54* 6.94 9.63* 10.11* 10.59*

1.93 1.81 1.66 2.52* 2.04* 1.49 -

of LM, is as in the Note to Table II. Instrument set

I-M,

LM,

LM,

LM,

Ml

IV V VI

0.20 -0.62 -1.14

0.07 0.37 -0.06

-0.07 -0.13 -0.02

-0.35 0.18 0.01

M2

IV V VI

-1.40 -1.35 -1.10

0.01 -0.19 1.19

0.05 -0.14 0.14

-0.51 -0.65 -0.07

Aggregate

” See footnote n of Table II for details. b For Ml, instrument set IV was Ml ,-,, M1,-2, GNP,, GNP ,-,, R3,, R3 ,-,, INF,, DFE,, DFE, REU,, DFE,-, . DER,- ,, DFE, INF,, and DFE, INFUS,. Instrument set V was Ml,_ I, Ml,_*, GNP,, GNP,_ ,, R3,_,, R3,_2, INF,, DFE,, DFE,_, REU,_,, DFE,_, REU,_,, DFE, INF,, and DFE, INFUS,. Instrument set VI was MI,-,, M1,_Z, GNP,-,, GNP,_?, R3,_,, R3,_2, INF ,_,, DFE,, DFE,+, REU ,-,, DFE,-, DER,_,, DFE,_, INF,_ ,, and DFE,-, INFUS,_ t. All instrument sets included a constant and seasonal dummies as well. For M2, instrument set IV was M2,_ ,, M2,_*, GNP,, GNP,_ ,, R3,, R3,_ ,, INF,, INF,-, , DFE,, DFE, . REU,, DFE,_, . DER,_ i, DFE, INF,, and DFE, INFUS,. Instrument set V was M2 ,-,, M2,-*, GNP,, GNP ,A,, R3,-,, R3,->, INF,, INF ,-,, DFE,, DFE,-, REU ,-,, DFE,_, DER,_:, DFE,-, INF,_ ,, and DFE,- i INFUS,_ ,. Instrument set VI was M2,_ i, M2,_?, GNP,_ ,, GNP,_?, R3,_ ,, INF,-t, INF,_2, DFE,, DFE,_ t . REU,_ ,, DFE,-, DER,_:, DFE,_, INF ,+,, and DFE,_, INFUS,_ ,, All instrument sets included a constant and seasonaldummies as well. * Significant at the 5% level.

The variable DFE, indicates that there has been a statistically significant upward shift in the demand for M2. This upward shift ties in with the pattern of prediction errors observed earlier, namely, that in the equation without DFE,, the predictions seemed to underpredict the observed value. However, the error for any single observation was not usually large enough to make the prediction error significantly different from zero. The positive sign on DFE, is a little unexpected. If M2 were used to finance a “one-

192

C. R. MCKENZIE TABLE IV DIAGNOSTIC TESTS FOR M2 EQUATION

Statistic type RESET Normality Heteroskedasticity ACF of residuals ACF of square residuals

Statistic value

Critical value

1.16 0.82 0.10 (1) 1.84, (2) 0.31, (3) 0.06, (4) 0.14 (I) 0.12, (2) 0.05, (3) - 1.02, (4) -0.91

&,(O.Ol) = 9.21 x$,(0.01) = 9.21 xf,,(O.Ol) = 6.63

Note. See footnotes to Table I for details of the tests.

off’ shift into foreign assets, a downward shift in the demand for M2, that is, a negative sign, might have been expected. However, the sign would be consistent with complementarity between M2 and the foreign assets into which funds might have moved with the funds possibly coming from yen-denominated bonds. Table IV contains a diagnostic evaluation of Eq. (11) and does not provide any evidence of misspecification. Performing the one-step-ahead prediction test for Eq. (11) over the period 1983:1 to 1984:IV gave rise to a test statistic of 0.410 (critical value: F(8, 29, 0.01) = 3.20). The largest individual t test was a mere 1.09 and occurred in 1984:111, so that Eq. (11) appears to be quite stable. 2.3

On Proxies for the Expected Change of the Exchange Rate

One of the problems encountered in estimating Eqs. (7)-(10) was the need to find a proxy for the expected change of the exchange rate. The realized change of the exchange rate was the first choice and this required the use of an instrumental variable estimation technique. Instrumental variable estimation requires a degree of correlation between the instruments and the “problem” variable. In the equations estimated here, the correlation between the realized value of the change of the exchange rate, DER, (dated at time t + I), and the instruments (dated at time t or t - 1) was rather low (R2 around 0.15). In actual time, this separation is three or six months. The correlation was higher for the variable DFE, . DER, (R2 around 0.35). An alternative proxy was to use the predictions from a regression of the realized value of the change of the exchange rate on an information set. These regressions also suffer from a low correlation between the predictions and the realized value. If the change of the log of the exchange rate is white noise (that is, the log of the exchange rate is a random walk) and is largely dominated by unanticipated events as suggested by Meese and Rogoff (1983), such low correlations could be expected. Taken at face value, the random walk

MONEY

DEMAND

IN AN OPEN ECONOMY

193

hypothesis suggests that it may be impossible to identify the effect of expected changes of the exchange rate on any economic variable. The low correlations are also to be expected since the realized value of the exchange rate and the variables in the information set are three or six months apart. It may be that the insignificance of DER: and DFE, * DER; in the money demand equations is attributable to this lack of correlation between DER, and DFE, * DER,, and the instruments. A number of examples where the expected values of variables are included as explanatory variables in econometric models are the expected inflation rate in an output equation (Taylor, 1979; Cumby et al., 1983), the expected output gap in an inflation equation (Taylor, 1979; Cumby et al., 1983), the expected inflation rate in a Phillips’ curve (McCallum, 1976), and the expected rate of return (including the expected rate of change of the exchange rate) on foreign bonds in a bond demand equation (Danker et al., 1987). In none of these cases is the lack of correlation between the realized value used to proxy the expected variable and the instrument set remarked on as being a problem. However, it should be noted that the variables that proxy the expectations variable tend to have coefficients that are statistically insignificant. Given the results in this paper, a problem with a lack of correIation might have been expected in the estimation of the bond demand equations in Danker et al. (1987). The lack of a good instrument set leading to large standard errors is one potential explanation for the tendency to accept the hypothesis that coefficients associated with expectations variables are not insignificantly different from zero. Using the McCallum (1976) substitution approach may also mean that attempts to find significant movements in the demand for bonds and short- and longterm capital flows in response to expected rate changes may prove difficult. 3.

CONCLUSION

The results presented here suggest that a foreign interest rate and the expected change of the exchange rate are not important influences on the demand for Japanese Ml or on the resident demand for yen-denominated M2. Thus, the results justify the closed economy focus of earlier studies. For Ml, the relevant explanatory variables appear to be an interest rate on competing assets, a transaction variable, and lagged values of the money stock. For M2, in addition to these variables, the rate of inflation was also a relevant variable. The preferred equations differ from those traditionally estimated for Japan by allowing for different dynamic behavior in the response of money demand to changes in the explanatory variables. The results indicate that this difference is of some importance. Following changes to the foreign exchange law and the rules governing

194

C. R. MCKENZIE

the usage of foreign-currency deposits in December 1980 there does seem to have been a significant upward shift in the resident demand for yendenominated M2. Since nonresident demand for domestic money issued by Japanese banks appears to be small and stable, this result suggests that a money demand equation for resident and nonresident yen-denominated M2 issued in Japan, as well as the traditionally used M2 variable which includes foreign-currency deposits, would also be unstable. One possible explanation for this shift is complementarity between yen-denominated deposits and foreign assets so that an increased demand for foreign assets may have also lead to an increase in yen-denominated deposits. The demand for Ml does not seem to have been significantly affected. The equations seem to be quite stable when one-step-ahead predictions and confidence intervals for these predictions are calculated, a result that seems inconsistent with the existence of currency substitution suggested by McKinnon (1982). It may be that investor sensitivities to expected exchange rate changes occur over periods much shorter than three months. An investigation using monthly rather than quarterly data may provide a sharper test of open economy influences hypothesis and may also give rise to instruments that are more highly correlated with the realized exchange rate change. However such an investigation will probably be hampered by the lack of a suitable monthly transactions variable. APPENDIX: DATA DEFINITIONS AND SOURCES

Unless otherwise stated, all interest rates and asset stocks are end of period and all variables are seasonally unadjusted. The units of measurement for each variable are in parentheses. In the construction of some variables, it was necessary to splice a number of series together because of changes in base number. This is indicated by [S:Xl], where Xl denotes the point(s) where splicing occurred. The sources of the data are the Economic Planning Agency Data Base (EPA); Bank of Japan-Economic Statistics Monthly (ESM); International Monetary Fund-Znternational Financial Statistics (IMF); International Monetary Fund (198 1)-Supplement on Price Statistics (IMPPS); Kinyli Zuisei Jij6 (KZJ); and Morgan Guaranty Trust-World Financial Markets (WFM). Data Dejinitions “Cash in circulation” in Japan, the amount of banknotes CASCIR issued minus the amount of cash currency held by financial institutions surveyed by the Bank of Japan: ESM (100 million yen).

MONEY

CURDEP

DER DFE FCD GNP GNPNOM INF INFUS Ml MINOM M2 M2NOM MZYNOM NRY NRYFCD

P* PGNP REU

DEMAND

IN AN OPEN ECONOMY

195

“Deposit money” in Japan, the total of demand deposits (current deposits, ordinary deposits, deposits at notice, special deposits, and deposits for tax payments) among public and private deposits with financial institutions surveyed by the Bank of Japan minus the checks and bills held by them: ESM (100 million yen). 400 * (log S,+, - log S,). Dummy variable taking the value zero until the third quarter 1980 and then unity thereafter. Foreign-currency deposits with all banks in Japan (data available only from December 1980): ESM (100 million yen). Japanese gross national product at constant prices (annual rate, seasonally adjusted): IMF line 99ar (billion yen) [S: 1974:1, 1980:1]. Japanese gross national product at market prices (annual rate, seasonally adjusted): IMF line 99a (billion yen). Japanese annual inflation rate, calculated using gross national product price deflator as (PGNP, - PGNP,&/ PGNP,-,. United States’ annual inflation rate calculated using U.S. consumer price index as (PF - P,*_,)/P,*_,. Japanese (real) Ml constructed as MlNOM/PGNP. Japanese (nominal) Ml constructed as CASCIR + CURDEP (100 million yen). Japanese resident (real) holdings of yen-denominated M2 constructed as M2YNOM/PGNP. Japanese (nominal) M2 constructed as MlNOM + TIMDEP (100 million yen). Japanese resident (nominal) holdings of yen-denominated M2, constructed as M2NOM-NRYFCD (100 million yen). Nonresident yen deposits with all banks in Japan (data only available from December 1980): ESM (100 million yen). Prior to December 1980, free-yen deposits and foreigncurrency deposits with Japanese banks, since December 1980, NRY + FCD: ESM (100 million yen). Consumer price index for U.S.: IMFPS and IMF line 64 [S: 1982:6]. Japanese gross national product price deflator, calculated as 100 * GNPNOM/GNP. Three-month Eurodollar rate: WFM (percent p.a.)

196 RT R3 s TIMDEP

c. R. MCKENZIE

Three-month yen-denominated time deposit rate with Japanese banks: ESM (percent p.a.) Three-month Gensaki rate: EPA and KZJ (percent p.a.) Yen/dollar exchange rate: IMF line ae “Quasi-money” in Japan, the total of private deposits, public deposits, and installment of Sdgti banks minus demand deposits with financial institutions surveyed: ESM (100 million yen).

REFERENCES ARGY, V. (1989). “International Financial Deregulation-Some Macroeconomic Implications,” Pacific Economic Paper 168, Australia-Japan Research Centre. BERA, A. K., AND JARQUE, C. M. (1981). “An Efficient Large-Sample Test for Normality of Observations and Regression Residuals,” Working Paper in Economics and Econometrics 040, Australian National University. BOUGHTON, J. M. (1979). Demand for Money in Major OECD Countries, OECD Econ. Outlook, Occasional Stud. 35-57. BOUGHTON, J. M. (1991). Long-run money demand in large industrial countries, IMF Staff Pap. 38, l-32. BROWN, R. L., DURBIN, J., AND EVANS, J. M. (1975). Techniques for testing the constancy of regression relationships over time, J. Roy. Statist. Sot. Ser. B 37, 149-192. [With discussion] CHRISTIANO, L. J., AND EICHENBAUM, R. (1990). Unit roots in real GNP: Do we know and do we care? Carnegie-Rochester Conf. Ser. Public Policy 32, 7-82. [With discussion] CHRYSTAL, K. A. (1977). Demand for international media of exchange, Amer. Econ. Rev. 67,840-850. CORKER, R. (1989). Wealth, financial liberalization, and the demand for money in Japan, mimeograph, International Monetary Fund. CUDDINGTON, J. T. (1983). Currency substitution, capital mobility and money demand, J. Inr. Money Finan. 2, 111-133. CUMBY, R. E., HUIZINGA, J., AND OBSTFELD, M. (1983). Two-step two-stage least squares estimation in models with rational expectations, J. Econometrics 21, 333-355. CLJTHBERTSON,K. (1988). “The Supply and Demand for Money,” Blackwell, Oxford. DANKER, D. J., HAAS, R. A., HENDERSON, D. W., SYMANSKY, S. A., AND TRYON, R. W. (1987). Small empirical models of exchange market intervention: Applications to Germany, Japan and Canada, J. Policy Modelling 9, 143-173. ENZLER, J., JOHNSON, L., AND PAULUS, J. (1976). Some problems of money demand, Brookings Pap. Econ. Act. 261-282. FAIR, R. C. (1984). “The Use of Expected Future Variables in Macroeconometric Models,” NBER Working Paper 1445. FUJII, M. (1992). The role of the yen in the world economy, forthcoming in “Japanese Financial Markets and the Role of the Yen” (C. R. McKenzie and M. Stutchbury, Eds.), Allen & Unwin, Sydney.

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DEMAND

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