modelling the demand for broad money in the united states

Modelling the Demand for Broad Money in the United States

AUGUSTINE C. ARIZE*

The demand for money function occupies a central role in most theories of aggregate economic activity, especially in the formulation and execution of effective monetary policy. In this paper, estimates of the short- and long-run demand for broad money in the United States are obtained. The empirical evidence suggests that the relationship between the growth of money balances and its economic determinants is more stable than some have argued. Importantly, the out-of-sample forecasts presented here suggest that M2 growth in the 1980s is welI predicted by an error-correction model that includes a variable representing the value of time and also uses real consumer spending as the short-run scale variable. (JEL E40)

I. Introduction

Until recently, econometric analysis of broad money behavior has proceeded on the basis of a level or first-difference equation, and it generally has emphasized short-term interest rates and real-income elasticities. Recent advances in cointegration and dynamic- modelling techniques have integrated the two specifications using theories of error correction and cointegration.

The current specification strategies can be classified into two main groups according to whether the long-run equilibrium and the short-run dynamics are modelled jointly or in successive steps. The simultaneous specification of the long-run equilibrium relation and short-run dynamics is suggested by Hendry in a series of papers [Hendry, 1985; 1979].

Work by Engle and Granger [1987] suggests a two-step specification strategy. In the first step, the long-run equilibrium relation is super-consistently estimated by means of a static OLS regression [Stock, 1987]. Residuals from this regression are then used, in the second step, as an error-correction model (ECM) term around which the short-run dynamics are modelled.

This paper presents an error-correction model of M2 demand. Several stability tests indicate that this M2 demand function is stable over the sample period 1955:1-1992:1.

II. Model Specification and Empirical Results

The error-correction model estimated here is:

lnmt = /30 + 131 lnYt + /3z lnRt + /33 lnRm2, + /34 lnw t + e, and (1)

*East Texas State University. The author would like to thank Ed Manton, Keith McFarland, and Ray Ballard for helpful comments on an earlier draft. Special thanks to Kathleen Smith for excellent research assistance. The research is funded by a GSRF-ETSU grant.

37

38 S E P T E M B E R A F J : V O L U M E 22, NO. 3

A l n m t = a o nl n2 n3

+ E all Alnmt-i + £ a2i AlnYt-i + ~-, a3i z~lngt-i i = 1 i = 0 i = 0 n4 n5

+ E a 4 i AlnRm2t_ i + ~ asi A l n w t _ i + Xe,_~ + e t, i =0 i = 0

(2)

where m is real M2 balances; Y, the real GDP; R, the commercial paper rate (4-6 month); Rm2, the own rate of return on M2; w, the real wages; e and e, the random-error terms; A, the first difference operator; ~,, the error-correction coefficient; and In, the natural logarithm. It should be noted that other variables such as ,5 lnPt may be included in the equation, where P is the GDP deflator (1987 = 100)F

Equation (1) is a long-run equilibrium money-demand function, where the parameter estimates are the long-run elasticities. 2 The expected signs are 31, 33, 34> 0 and 32< 0. 3

Equation (2) is a dynamic ECM of the short-run behavior of money demand, where nj(j= 1 to 5) represents the number of lags. If the variables employed in equation (1) have a single unit root but are cointegrated, then equation (2), which is a restricted ECM, is likely to give meaningful results, i.e., ~.#0. [Engle and Granger, 1987]. In this paper, equations (1) and (2) are estimated jointly, as in Small and Porter [1989] and Mehra [1991, 1992]. To do this, equation (1) is solved for et. 1, and then et. ~ is substituted into equation (2) to obtain the following:

n l

Alnmt = ko + ~_, ali Alnmt- i i = 1

n4

n2 n3

+ £ aziAlnYt- i + E a3iAlnRt-i i =0 i =0

.5 (3) + ~ a4iAlnRm2t-i + ~ , asiAlnw,-i + % l n m t _ 1 + 3,21nY~_ 1

i =0 i =0

+ y31nRt_~ + T41nRm2t_l + ,yslnwt_l + e t,

1Data used here (except wages) are the same as in Mehra [1992]. The GDP deflator is the price level variable used for constructing AlnPt and Inmt is measured as nominal M2 deflated by the implicit GDP price deflator; real wage is measured by the index of average hourly earnings deflated by the GDP deflator. The series for wages was obtained from a Citibank data tape.

2Wage rate is included as a proxy for the value of time. Dutton and Gramm [1973], Karni [1973], Dotsey [1988], Dowd [1990], and Lahiri [1991] provide empirical evidence that real wage is an importam determinant of money demand in both the short-run and long-run. Dutton and Gramm [1973, p. 652] note, "If the use of money saves transactions time, it increases the amount of leisure. This suggests an additional determinant of the demand for money, the consumer's valuation of time, i.e., the wage rate." The underlying thesis of Baumol's money-demand approach is that the holding of money saves transaction time, the cost of which varies with the value of time.

3Laidler [1985] argues that failure to allow for the role of the wage rate in the "standard" transactions models of money demand could result in serious misspecification. It is conceivable that such misspecification may have caused instability in the U.S. money-demand function. Ironically, none of the previous studies examining the effect of the time factor on money demand noted its implication for the stability property of the estimated function. Therefore, real wage is included in the author's model.

ARIZE: DEMAND FOR MONEY 39

where k o = (a o -X3o); 3'~ = X; 3'z = -•31; 3`3 : -X32; 3`4 = -X~3; a n d ~[5 : -)k34. Equation (3) may be estimated using consistent estimation procedures as tong as some

of the level variables are cointegrated. It should be noted that all of the parameters of equations (1) and (2) can be recovered from those of equation (3). For example, the error- correction coefficient X is 3'1, and the long-term real income elasticity (31) is 3'2 divided by 3"1.

Prior to estimating equation (3), the time series properties of the individual series were tested. The sample period is 1955:1-1992:1. The tests used are the augmented Dickey- Fuller (ADF), and Z(~), Z(toO and Z(ff3) developed by Phillips [1987] and Perron [1988]. In view of the findings of Schwert [1987], the Johansen [1988] unit root test was also computed. 4 Following Dickey and Pantula [1987], higher order unit roots were also tested by the application of the same tests to the data in first and second differences. Table 1 gives the relevant test statistics.

Except for the net interest rate variable, nonstationarity cannot be rejected for all series at the 5 percent significance level. In contrast, when the data are differenced, nonstationarity can be rejected in all cases. Because net interest rate is integrated of order 0 (i.e., stationary), it should not be included in the long-run part of equation (3). However, it should be noted that lnRm2 t and lnR t are individually integrated of order 1 and therefore can be included in the long-run part of equation (3).

TABLE 1

Time-series Properties Of The Variables, 1955:1-1992:1

Series/ Statistics Into t lnYt lnRt l n R m 2 t l n Y c t lnwt ln(R - Rm2) t

Level

ADF -1.87 -1.59 -2.43 -1.36 -1.38 0.28 -3.98 Z (07) -4.72 -5.44 -13.04 -4.84 -2.40 0.34 -23.65 Z (t6) -1.33 -1.44 -2.32 -1.06 -0.75 0.26 -3.45 Z (4~3) 1.47 1.59 3.17 1.42 1.60 15.55 6.30

J 1.33 1.66 8.49 7.02 1.66 6.60 12.62

4The Johansen procedure is generally used to test for cointegration. However, with one variable, it can be viewed as testing for stationarity.

40 SEPTEMBER AEJ: VOLUME 22, NO. 3

TABLE 1 (CONT.)

First Difference

ADF -3.61 -5.29 -4.36 -3.92 -5.01 -3.90 -5.27 Z(o7) -57.30 -103.61 -106.15 -101.03 -132.39 -177.35 -101.27 Z (t07) -6.00 -8.83 -9.95 -8.93 -10.01 -14.44 -9.75 Z (~b3) 18,44 39.24 49.70 40.22 50.24 -104.05 47.86

J 20.20 29.70 30.83 13.80 20.20 17.99 33.83

Second Difference

ADF -8.60 -10.30 -11.54 -11.50 -10.24 -9.04 -12.53 Z(oT) -153.34 -176.44 -129.04 -137.55 -191.50 -204.88 -129.17 Z(td~) -16.59 -21,79 -21.07 -20.66 -24.74 -36.56 -20.22 Z (q~3) 135.09 233.03 216.18 208.28 300.16 656.37 199.22

J 96.30 100.03 154.10 132,20 139.70 144.02 173.96

Notes: The critical value at the 5 percent level for the ADF and Z (tc~) statistics is -3.44 [MacKinnon, 1991]; that for Z (&) is -21.8, and Z (43) is 6.25 [Perron, 1988]. The 5 percent region for the J-statistic is {J c R/J > 9.24}. A fourth-order univariate autoregression was used to calculate J. Varying the lag truncation parameter between 1 and 7 yielded qualitatively similar results.

The results of testing for the number of significant cointegrating vectors in lnm,, lnF. lnR. lnRm2 t and lnw~ are reported in Table 2. The maximum eigenvalue results imply that there are three cointegrating vectors, although only the signs of the third vector make economic sense. By normalizing on that vector yields:

lnm t = -3.57 + 0.891nY r - 0.281nR t + O.141nRm2 t + .841nw t. (4)

This cointegration claim is reinforced by the ADF test of residuals from the equation, which yields a value of -5.3.

As a further check of the long-run solution, an unrestricted autoregressive distributed lag model was estimated with seven successive lags on each variable (lnm, lnY, lnR, InRm2 and Inw), with zero-one dummies (CC1, CC2) for Carter credit controls in 1980:1 and 1980:2,~ and a zero-one dummy (D83:1) to capture the transitory effects of Money Market Deposit Accounts (MMDA) in 1983:1. No significant loss of information was


found in restricting the model to two lags. (See Appendix for the results). The solved long-run solution is:

0.62 0.731nY 0.271nR 0.181nRm2 0.8311nw , (5) lnm = (0.10) ÷ (0.04) - (0.09) + (0.11) ÷ (0.05)

The standard errors given in equation (5) are computed following the Bardsen [1989] procedure. As can be seen, the elasticities in equation (5) are similar to those in equation (4) and are consistent with Baumol and Tobin theory of money.

TABLE 2

Johansen Test For Cointegration (1953:1-1987:4)

Number of Cointegrating

Vector (r)

Likelihood Ratio Statistic

VAR lag length = 1 Eigenvalues 10 Percent

Critical Value

r _< 4 3.4 .02 7.53 r < 3 13.4 .06 17.85 r < 2 32.5 .13 32.0 r <__ t 64.8 .21 49.6 r = 0 267.1 .76 71.8

Note: Preferred parameter estimates qualitatively unchanged for VAR lag lengths 1-5. As one extends the lag length in the VAR for a given finite sample size [Hall, 1991l, the maximum number of unique cointegration vector (r) tends to increase, but the parameter estimates from the eigenvectors are relatively invariant. A similar qualitative result is found in the application of the Johansen procedure in this study, but a cointegrating relationship that is acceptable on a priori grounds can always be found.

Table 3 presents the results of estimating equation (3) by ordinary least squares (OLS) and by instrumental variables (IV) methods. As the results suggest, the statistical fits of models to the data are satisfactory, as indicated by values of the standard error of estimate (SEE); and the F-value for testing the null hypothesis that all the right-hand-side variables as a group, except for the constant term, have a 0 coefficient.

Considering that each dependent variable is cast in first-difference format, the congruency of the models with the data is also supported by Theil's R 2 of about 0.85 in both the OLS and IV equations. All of the diagnostic tests support the statistical

42 SElYFEMBER AEJ: VOLUME 22, NO. 3

appropriateness of the estimated models. 5 Figure I in the Appendix shows that the actual and fitted values from the OLS for the rate of change in real M2 are fairly close to one another.

TABLE 3

Estimates Of The Error-Correction Money-Demand Models: 1955:1-1992:1

Regressors OLS (1) IV (2)

Constant 0.075 (0.98) 0.044 (0.40) Alnmt_ 1 0.369 (6.39) 0.359 (5.48) AlnP t -0.869 (10.39) -0.819 (4.59) AlnPt-1 0.367 (3.69) 0.321 (2.04) Alnwt 0.144 (1.92) 0.215 (0.99) A(R-Rm 2)t -0.003 (6.28) -0.003 (2.76) A(R-Rm2)t-1 -0.003 (5.89) -0.003 (4.83) AYc t 0,107 (1.95) 0.151 (0.89) mrct . 1 0. 127 (2.32) 0. 130 (2.28) Inmt-1 -0.051 (2.92) 0.056 (2.81) lnYt. l 0.041 (2.25) 0.045 (2.18) lnRt-1 -0.010 (3.84) -0.009 (3.32) lnRm2 t 1 0.004 (1.66) 0.004 (1.47) lnwt, 1 0.096 (4.31) 0.093 (3.40) CC1 -0.011 (2.83) -0.011 (1.970 CC2 0.007 (1.86) 0.007 (1.57) D83:1 0,021 (5.83) 0.002 (5.73) SEE 0.00358 0.00361 F(16,132) 54.16 53.24 /~2 0.8518 0.8496 DW 1.96 1.88 BG(4) 1.74 7.50 BG(5) 1.53 9.50 BG(12) 19.3 13.6 BP(24) 28.4 29.13 LB(24) 32.6 34.41

5The model is unchanged by adding AlnP t to both sides, in which case the regressand becomes the growth of nominal money Alnm~, and the coefficient on AlnPt becomes + .31. Switching the positions of Alnmt and AlnP t and re-estimating yields a statistically unstable, autocorretated, and heteroskedastic equation.


TABLE 3 (CONT.)

Regressors OLS (1) IV (2)

Het(1) 32.6 34.41 JB(2) 2.96 1.61 RESET(l) 0.54 0.09

Notes: SEE is the standard error of regression; F tests the null hypothesis that R2=0 against the alternative hypothesis RE>0; ~2 is the Theil's R E (coefficient of determination adjusted for degrees of freedom); BG, Breusch-Godfrey statistic for residual autocorrelation; BP is the Box-Pierce statistic for autocorrelation; LB is the Ljung-Box statistic for serial correlation; Het is the Koenker and Basset statistic for homoskedasticity; JB statistic is for normality of the residual; and RESET is for functional form misspecification [Pesaran and Pesaran, 1991]. Absolute value of t-statistic is in parenthesis beside the estimated coefficients. BG(4) refers to the chi-square statistic with 4 degrees of freedom.

Economically, all estimated coefficients are fairly consistent with the theory's a priori expectations and are generally statistically significant at the 5 percent level. In particular, the significance of the error-correction term (lnm t_ 1) reconfirms the validity of an equilibrium relationship between the variables in the cointegrating equation. Work by Hall [1986] and Boswijk and Franses [1992] suggests that, given the correspondence 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 solution. When the variables {1, lnm t_ 1, lnY,_ 1, ]nRt-i, lnRm2,. 1, and lnwt_ 1} were tested for being jointly 0, using the OLS equation, the computed F(6,131)=6.4 was significant at the 5 percent level. This result lends further support to the finding of cointegration among the variables.

Finally, it should be noted that the estimated structural parameters of the IV equation are fairly close to the OLS estimates and that the standard error of the estimate (SEE)=0.0037 for the IV equation is also close to the OLS estimate, (SEE)=0.0036. Furthermore, the Sargan statistic for the validity of the instrument set yields a value of 14.27, which is below ~ ( 9 ) = 16.91 for the 5 percent level. The instruments are a constant CC1, CC2, D83:1, four lagged values of AlnYc.,, Aln(R-Rm2)t, Alnw,, and AInP,, one lagged value of Alnmt, and a lagged value of lnY, Inw, lnR, lnRm2t, and lnm r

The evidence supporting the adequacy of the estimated error-correction model of U.S. M2 demand equation having been provided, the actual behavior of real M2 balances over 1988:1-1992:1 is tested for its consistency with a stable M2 demand behavior. 6 This is examined by means of the Dufour [1980] test. This test procedure uses separate (0,1) dummy variables entered for each individual observation beyond a selected breakpoint.

6The relevance of the money stability issue is due to its implications for the conduct of monetary policy. A stable money-demand function generally implies a stable monetary multiplier; stability makes it much easier to forecast the impact of a given money supply on the aggregate money income.

44 S E P T E M B E R AEJ : V O L U M E 22, NO. 3

In the present study, a dummy variable D1 was entered as 1.0 for 1/1988 and as 0 elsewhere; D2 was entered as 1.0 for 11/1988 and as 0 elsewhere and so on, through 1/1992. 7

An F-statistic was used to test the joint significance of the dummy variables. It should be noted that the estimated coefficients on the dummy variables represent post-sample static forecast errors. The results of the Dufour test appear in Table 4. A small F-statistic indicates structural stability. As can be seen, the individual coefficients that appear on the shift dummies are generally not statistically significant, with the exception of the one for the third quarter of 1991. The F-statistic that tests the null hypothesis that these shift dummies are 0 yields a value of 0.96, whereas the critical value is F(17,115)= 1.72 at the 5 percent level, indicating that, as a group, the shift dummies are statistically insignificant.

TABLE 4

Estimates Of Post-1987 Forecast Errors

Variables Estimates t-statistic

1/1988 0.0024 0.63 II 0.0023 0.60 III -0.0024 0.61 IV 0.0000 0.10 1/1989 -0.0019 0,48 II 0.0067 0.47 III 0.0028 1.64 IV 0.0028 0.69 1/1990 0.0027 0.65 II -0.0020 0.48 III 0.0000 0.00 IV 0.0032 0.77 1/1991 0.0023 0,53 II 0.0002 0.05 III -0.0102 2.44* IV -0.0031 0.72 1/1992 -0.0017 0.39

7In 1987, the Federal Reserve System dropped Mt from its list of intermediate policy targets, and M2 became the system's principal monetary aggregate. As with M1, the decision to focus on M2 was made on the basis of the long-run stability of its relationship with nominal GDP.

ARIZE: DEMAND FOR MONEY

TABLE 4 (CONT.)

45

Summary Statistics

F(17, 115) Mean Error Root-Mean-Squared-Forecast Error Theil Inequality Coefficient (u) Fraction of Error due to:

(a) Bias (u m) (b) Variation (u s) (c) Covariation (u c)

0.96 -0.0027 0.00363

0.39

0.012 0.126 0.862

*Denotes significance at 5 percent level.

As can be seen in Table 4, the root-mean-squared forecast error (RMFE) is 0.00363, which is very close to the in-sample standard error of 0.0036. Also, the Theil inequality coefficient (u) is relatively small and below 1 with a reasonable decomposition. The Theil bias coefficient (u") indicates that only 1 percent of the forecast error is attributable to bias, that is, one-sided prediction errors, whereas 86 percent of the RMFE is attributed to unsystematic deviations. Finally, it should be observed that the model over-predicts real money balances in only 8 out of 17 times. Given these few, statistically insignificant over- predictions, it can be argued that a major part of the deceleration in M2 growth reflects movements in real consumer spending and wages. For example, the rate of growth in M2, which averaged 8.84 percent in the 1971-88 period, decelerated to 4.67, 3.93, and 2.78 in 1989, 1990, and 199I, respectively. Similarly, the rate of growth in real consumer spending averaged 3.13 percent in the 1971-88 period and decelerated to 1.21, 0.2, and 0.03 in 1989, 1990, and 1991, respectively. Also, the rate of growth in real wages, which averaged 0.2 percent in the 1971-88 period, was much smaller in 1989, 1990, and 1991, i.e., -1.6, -.47, and .03, respectively.

In order to gain further insight into the size and importance of these prediction errors, Table 5 presents static simulations of M2 growth conditional on actual values of the regressors. The predicted values were generated using regression estimated over 1955:1- 1987:4 and then simulated over 1981:1-1991:4. 8 Actual M2 growth and prediction errors are also reported. It should be observed that the mean error and root-mean-squared simulation error (RMSE) are fairly small. Also, the number of negative signs (over- predictions) is only 5 out of 11 years. As indicated by the correlation of 0.975 between

8The Theil inequality coefficient is 0.16; the bias coefficient is 1 percent, and 98 percent of the root- mean-squared forecast error is attributed to unsystematic error.


the actual and the forecasted growth rates, the model used here captures the swings in M2 growth reasonably well. Figure II in the Appendix also reflects this strong correlation.

If these forecasts over such annual intervals are unbiased, then a regression of actual M2 growth on forecasted growth should result in an intercept term (a) of 0 and a slope coefficient (b) of 1. As shown in Table 5, the F-statistic for testing the null hypothesis (a,b)=(0,1) has a marginal significance level of 0.96, indicating that the forecasts are indeed unbiased.

TABLE 5

Actual And Predicted M2 Growth; 1981-91

Year A G PC, E

1981 8.9 8.45 0.45 1982 8.7 9.45 -0.73 1983 11.5 12.35 -0.85 1984 7.7 7.55 0.15 1985 8.3 7.93 0.37 1986 8.8 7.96 0.84 1987 4.2 4.61 -0.41 1988 5.1 4.85 0.25 1989 4.7 4.12 0.58 1990 3.9 4.16 -0.26 1991 2.8 3.90 -1.10

Mean Error -0.06 RMSE 0.37 fAG, P G .98 Cumulative Prediction Error by 1992:1:

(a) Level 108.69 (b) Percentage .2

Notes: AG is actual M2 growth; PG is predicted M2 growth; and E is the predicted error. The predicted values are generated by using OLS regression (see Table 3) estimated over 1955:1-1987:4 and simulated over 1981:1-1992:1. r is the correlation betweenAG and PG. Regression of AG on PGyieldsAG = -0.0 (.34) + 0.95PG (3.91). F-test of the null hypothesis (a, b) = (0, 1) is 0.06 with a marginal significance level of 0.96.

Recently, Wenniger and Partlan [1992, p. 28] reported that the conventional broad money equation "over-predicted M2 by nearly $200 billion or 5.6 percent, by the fourth quarter of 1991," and Mehra [1992, p. 31] reported that his best models "cumulate to an


over-prediction of M2 of only $144 to $149 billion" over 1990:1-1992:2. Because the same data as Mehra [1992] are used here, it is important to address the over-prediction in terms of the levels of M2 for comparison purposes.

Using the model, the cumulative errors in the level of M2 from 1988:1-1992:1 is -26 billion, which is fairly small. Also, the prediction errors cumulate to over-prediction of only $108.69 billion between 1988:1 and 1992:1. Considering that the total level of M2 between 1988:1 and 1992:1 is about $54,859 billion, this over-prediction is only about 0.2 percent. These results suggest that the model provides a more accurate forecast of M2 than previous studies.

To avoid reliance on a single test statistic such as the Dufour test, the estimated model is examined to discover whether it can survive slightly more demanding tests of the stability of the estimated coefficients and the stability of the error structure. This dichotomy is important because tests for coefficient stability in the presence of heteroskedasticity can be misleading.

First, the Hendry forecast (HF) test [Johnston, 1984, p. 508] indicates numerical parameter constancy over the forecast periods: 1988:1-1988:4, HF(4)=1.37 (X~=9.5); 1988:1-1989:4, HF(8)=6.1 (X2c=15.5); 1988:1-1990:4, HF(12)=7.89 (X2c=21.03); 1988:1-t992:1, HF(17) =17.48 (XZ~=26.3). Second, the Chow forecast test [Johnston, 1984, p. 507], with shift points located at or after 1988, also indicates that the M2 demand equation estimated here is stable. For example, for shift points 1988:1, 1988:4, 1989:4, and 1990:4, the computed F-values were, in general, around 1, -0.97, 0.33, 0.68, and 0.62, respectively.

Third, the conventional Chow test was also implemented through use of the dummy variables approach [Johnston, 1984, p. 226] with alternative breakpoints. These breakp0ints are consistent with the recommendation that the sample be split at the midpoint to maximize the empirical power of the test [Farley, Hinich, and McGuire, 1975]. This form of the Chow test is implemented by estimating a version of equation (3), shown below as equation (6):

Alnm, = c o + nl

E i=1

n4

E i=0

n2 n3 c l i A l n m t - i + E c2 iA lnY t - i + E c 3 i A l n ( R - R m Z ) t - i

i =0 i =0

c4iAlnwt_i + cs lnmt_ 1 + c61nYt_ 1 + cvlnR~_ 1

nl c81nRm2,_ 1 + c91nwt_ 1

n2

+ E ~2iDt- iAlnYt- i i=0

n4

+ E t54iDt-iAlnwt-i i = o

+ 87Dt_l lnRt_ 1

+ hoD t + ~., 61 iDt_iAlnmt_i i = 1

n3

+ E 63iDt-i A l n ( R - R m 2 ) t - i i = 0

+ 65Dt_ l lnmt_ t + 66D,_ l lnYt_ 1

+ 6 8 D t _ l l n R m 2 t _ 1 + 69Dt_ l lnwt_ j + u t . (6)


The calculated Chow-F statistics are 1.70, 1.71, 1.67, 1.66, 1.56, 1.55, 1.58, 1.59, 1.51, and 1.49 for breakpoints 1972:4, 1973:1-4, 1974:1-4, and 1975:1, respectively, The critical value at the 5 percent level is F(14, 118)= 1.78. The F-values are below their critical value, and are thus consistent with the hypothesis of no significant shift in M2 demand. Furthermore, the stability of the error structure is confirmed by the Breusch and Pagan [1979] statistic (4) for heteroskedasticity. The computed value is 4(14)= 17.3, X2c=23.7. Therefore, the null hypothesis of a stable error structure is also accepted.

In sum, the above diagnostic tests indicate a well-fitting money-demand equation that fulfills the condition of serial non-correlation, homoskedasticity, zero-disturbance mean, regressor-error term non-correlation, normality of residuals, and structural stability.

IIl. Conclusion

A conventional money-demand function can describe the recent developments in M2 growth in the United States quite well. However, the money-demand function must properly take into account the following suggestions: (a) include a measure of real wage to proxy the value of time [Laidler, 1985]; Co) use a split-format on the opportunity-cost variable instead of constraining the effects of the market rate to be equal in magnitude but opposite in sign to the rate of return on M2 (see integration results in Table 1); and (c) use real consumer spending as the short-run scale variable and real GDP as the long-run scale variable [Small and Porter, 1989; Mehra, 1991]. When these refinements are made, it does not appear, as some have argued, that money-demand behavior has changed significantly during recent years.

The finding on the significant effects of real wage supports Higgins [1992, p. 21], who pointed out that the character of M2 demand cannot be "explained by traditional relationships to income and interest rates." Significant effects of real wage are consistent with Lahiri [1991], Dowd [1990], Dotsey [1988], Karni [1973], and Dutton and Gramm [1973]. Furthermore, the results support Hendry [1979], who showed that the parameter instability claimed in both the U.S. and British money-demand functions is a spurious phenomenon due to incorrect specification.

It should be noted that, when real wage is excluded from the equation, the forecast errors all become negative (over-prediction) except in 1988:3. Also, the t-statistics for the forecast errors become significant at the 10 percent level in 1988:3, 1989:1, 1989:2, 1990:2, 1990:3, 1990:4, and 1991:3. Furthermore, the normality (JB) and autocorrelation BG(5) statistics rise to 5.83 and 10.71, respectively. Both are significant at the 10 percent level.

From the policy perspective, empirical results clearly show that monetary policies relying on quarter-to-quarter or annual interval forecasts of money demand growth should fare well because there is no random, unpredictable component inherent in the estimated relationship. The results further suggest that policy-makers should take into account the value of time, e.g., movements in real wages, when setting targets for the M2 aggregate.

ARIZE: DEMAND FOR MONEY

APPENDIX

Autoregressive Distributed Lag Representation for lnm t Lagj (or index)

49

Variable 0 1 2 E~ = 0

lnm t.j -1.0 lnw t .j 0.37859 lnRt_ J -0.0215148 lnRm2, 4 -0.0052059 lnK_j -0.0209922 CC1 -0.0185 CC2 0.0065 D83:1 0.22 Constant -0.0313

1.3464822 -0.3967827 -0.0503 -0.5781784 0.2417508 -0.0136 -0.0081035 0.0159754 0.0094 0.0138641 0.0007249 0.0366 0.234331 -0.1748185

Notes: T=149 [1955:1-1992:2]; AR 1-4F(4, 127)=1.23; AR 1-12F(12, 119)=0.85; R2=0.999; BPX2(16)=20.66; LBX2(36)=24.05; JB(2)= 1.89; RESET F(1, 130)=0.22; SEE=0.0049; DW=2.04; HET F(1, 147)=0.02. (See notes in Table 3).

F I G U R E I

A C T U A L AND FITTED REAL M O N E Y BALANCES

0.04

0.03

0.02

0.01

0.00

-0.01

-0.02

-0.03- 955

i

J

' " P ' l ' q m l " l ' q m l ' q ' q " ' p ' l ' q ' ' q ' ' l ' ' l ml ~ ' l ' q m l ' q " q ' q ~ H l ' q ' q J ' l m U ' H ' P ' q ' ' l m l " q ' q ' ' l a ' l ' ~ 1960 1965 1970 1975 1980 1985 1990

ACTUAL . . . . . FITTED

50

0.06

SEPTEMBER AEJ: VOLUME 22, NO. 3

FIGURE II

ACTUAL AND FITTED MONEY GROWTH

0.05

0.04

0.03

0.03

0.01

0.00 1955

m p . I H , l . , l l . [ ,~ q . q , ~'1 " q , , q l " l i, , p . I ' I ' i " q i ' q ' b'l " ' l ' " I ' " l " '1 " ' I' " I u q m i i . lu q . q M q m ] m p ,, pl q H q , ,~IH q . ,

1960 1965 t970 1975 t980 1985 1990

_ _ MM . . . . . FITMM

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