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Determinants of income velocity in the United Kingdom: multivariate Granger causality.

1. Introduction

The behavior of the income velocity of both narrow and broad measures of money in the United Kingdom in the 1980s was a surprise to many monetary economists. After an upward trend during the 1970s, income velocity showed virtually no growth during the 1980s.(1) This decline in income velocity has been interpreted as undermining a basic principle of monetarism, that is, the generally well-established predictable link between prior changes in money stock and in nominal income.(2)

Discussion of the behavior of velocity has focused upon whether the process generating velocity underwent a shift, perhaps due to the financial innovation and deregulation in the 1980s or whether the behavior of velocity merely reflects the underlying variability in its determinants. Goodhart (1989:318-322) and Temperton (1991) provide summaries of this debate.

A different explanation for the decline in income velocity is to be found in the work of Milton Friedman (1983). This was written in the context of the decline in income velocity that occurred in the United States from 1981. Friedman rejects the argument that the decline in income velocity in the United States undermines the case for a monetary policy which emphasizes controlling the growth of M1. Rather, he attributes the velocity decline, in part, to the unprecedented volatility of money growth following the Federal Reserve's 1979 shift to targeting nonborrowed reserves. Friedman's main argument is that increased volatility of money growth raised the degree of perceived uncertainty with regard to standard economic measures, such as interest rates, output, and prices and thereby contributed to increasing the demand for money or, equivalently, reducing the velocity of money.(3) This argument appears consistent with the recent money demand literature that has stressed the role of money as a shock absorber which temporarily smooths the response of the economy to unexpected changes in the money supply. See, for example, Boughton and Tavlas (1990:434). From this viewpoint, declines in velocity associated with an increased growth in money supply are seen as temporary, and the money growth as a predecessor of future inflation. Poole (198), B. Friedman (1988) and others argue that a significant weight must be given to such factors as: (a) declining inflation (and presumably inflationary expectations); (b) interest rate volatility; (c) the introduction of interest payments on transaction accounts; (d) decreasing cost of intermediation as a result of increased competition and innovation in the financial sector; and (e) the rise in the real exchange value of the domestic currency. Existing empirical work on U.S. data, such as Hall and Noble (1987), find a causal relation between monetary variability and velocity, as suggested by Friedman. However, their results have recently been questioned by Mehra (1989) and Brocato and Smith (1989). Mehra found that first differencing the volatility measure (as is indicated by tests for a first-order unit root) led to the conclusion that money growth volatility does not Granger-cause velocity. A similar conclusion was reached by Brocato and Smith using monthly (instead of quarterly) data. Nonetheless, in the case of the United States, this issue is by no means resolved. A recent study (Fisher and Serletus, 1989) using nine measures of velocity and monthly data has concluded that monetary growth variability did in fact Granger-cause velocity over the 1970-1985 sample period. Furthermore, Belongia (1984) found that increased quarter to quarter variation in the growth of M1 has some permanent reductions on the level and growth rate of nominal GNP. There is also evidence that Friedman's hypothesis is supported by data from selected developing economies over the period, 1974Q1 through 1985Q4. See Shams (1989) for details. To our knowledge, Friedman's hypothesis has not been examined for the United Kingdom, an economy that also experienced substantial declines in income velocity on both narrow and broad measures of money beginning in 1980. This paper employs two methodologies that are used to establish the causal relationship between income velocity and monetary growth volatility. The first relies on the multivariate rather than a bivariate Granger causality test in order to avoid distorting the causality inferences due to the omission of relevant variables |See Lutkepohl (1982)~. These additional variables are real output, treasury bill rate, interest rate volatility, and real effective exchange rate. Thus, in testing for the causal relationship between monetary volatility and income velocity, the results provide some evidence of whether income velocity has been causally determined by these other macro variables.

The second relies on an error-correction model (ECM) approach outlined by Engle and Granger (1987). Granger (1988) shows that the causal impact of one variable on another can take place in an ECM in two ways. One way is through the impact of lagged changes in the regressors. The second occurs through the error (EC) correction term, which itself is a function of lagged levels of the variables. The remainder of this paper is as follows: Section 2 discusses our empirical methodology. Section 3 presents the empirical results. Some concluding remarks are provided in Section 4. The sample period examined is the recent flexible exchange rate era 1973Q1 through 1990Q2.(4) Data definitions and sources are cited in the appendix.

2. The Empirical Methodology

In this study we are investigating whether real output (Y), treasury bill rate (R), interest rate volatility (VR), real effective exchange rate (|p.sup.f~|center dot~E/P) and money growth volatility (VOL) causes changes in income velocity (V).(5) The estimating equation (seasonal dummies excluded for simplicity) considered is:

|Mathematical Expression Omitted~

where T is the number of observations; |p.sup.f~ is the world price level measured by weighted average of consumer price index (CPI) of industrial countries (1980=100); E is the index of effective exchange rate; P is domestic price level measured by CPI (1980=100); and e is a disturbance term.

Tests of Granger-causality presume the use of covariance stationary data. To achieve stationarity, all the variables in the above equation (except the seasonal dummies) were expressed in growth rate or first difference form. This is justified by the results of our unit root tests which are not reported here because of limited space.(6)

Another requirement of Granger-causality tests is that the stationary series should have a zero mean. To achieve this, each stationary series should be mean corrected, either by subtracting the appropriate mean or by including a constant term in the equation. The latter approach is adopted in this paper.

In order to determine the appropriate lag lengths of the regressors in equation (1), we used Hsiao (1981) sequential procedure which combines the minimum final prediction error (FPE) criterion developed by Akaike (1969) with Granger's definition of causality.

First, |Delta~1nV is treated as a one-dimensional autoregressive process. That is,

|Delta~ln|V.sub.t~ = ||Alpha~.sub.0~ + |summation of~ |Alpha~1|center dot~s|Delta~ln|V.sub.t-s~ where s=1 to P + |e.sub.t~ (2)

where P is the maximum lag length allowed for all regressors and is set at four, in order to preserve a reasonable number of degrees of freedom. The minimum FPE is then computed by varying the maximum order of lags from one to four. Let this value of s which minimizes FPE(s) be K1.

Second, once the lag operator for the |Delta~lnV is set, it is treated as the controlled variable. then, a set of bivariate regressions are estimated consisting of the appropriate own lag (K1) and the lags of each of the remaining variables in equation (1), taken one at a time. By varying the order of lags from one to four and computing FPE each time, the optimum lag length for each of the variables is chosen.

Third, the specific gravity criterion of Caines, Keng and Sethi (1981) is used to determine the order in which the variables from the bivariate equations are added in each stage. Among the five variables in the bivariate regressions, the one with the least minimum FPE is considered to be most important to |Delta~lnV and is added to equation (2). Let this variable be |Delta~lnY and its optimum lag length be K2.

Fourth, trivariate equations are estimated with |Delta~lnV and |Delta~lnY as controlled variables with order of lags set at K1 and K2, respectively. Then the same steps outlined above for the bivariate model are followed for the trivariate (quadrivariate, etc.) models. Finally, the joint significance of the coefficients is tested by using the F-test.

As indicated before, causality testing conducted with differenced time series will likely yield invalid causal inferences in those situations where the series are cointegrated since the (EC) term is omitted from the specification. To this end, we examine whether our use of first differenced variables to test for causality is appropriate. For this purpose, we employ the procedures suggested in Engle and Granger (1987). If the variables are cointegrated then we should introduce a lagged residual term into equation (1) before conducting Granger-causality tests.

3. Empirical Results

In this section, the results of using the above statistical procedures are reported for both narrow and broad money velocity of circulation. First, according to our lag length and model building criteria, the following equation was obtained for M1-velocity over the period 1973Q1 through 1989Q2 using ordinary least squares (OLS):

|Mathematical Expression Omitted~.

For M2-velocity, the following model was obtained over the period 1973Q1 through 1990Q2 using OLS:

|Mathematical Expression Omitted~.

To conserve space, the results of estimating equations (3) and (4) are not reported here, but are available upon request. It should be noted that breaking the sample at different dates for stability tests did not reveal any structural break in either equation. Also, the models show no evidence of serially correlated or heteroskedastic residuals.

The results of Granger-causality reported in Table 1, suggest that changes in the rate of interest, the real exchange rate and interest rate volatility provide information that helps predict future movements in M1-velocity. These results also suggest that changes in money growth volatility, interest rate and interest rate volatility are statistically useful in predicting M2-volatility, at either the 5% or 10% significance level.

Because all the variables are nonstationary time series, it is important to examine whether they could be cointegrated as discussed in Engle and Granger (1987). If the variables are cointegrated, Granger-causality could occur through the (EC) term. In that case, the results presented in Table 1, may be affected by the omission of EC term in our specifications. To this end, we report the following preferred (ECM) results for M1-velocity (absolute t values in parentheses):

|Mathematical Expression Omitted~


For M2-velocity, the preferred equation is

|Mathematical Expression Omitted~

Equations (5) and (6) are derived from an unrestricted model with four lagged values of the regress and other regressors. To save space, we simply note that both models pass the diagnostic tests employed in Arize (1991).

Several features of the estimated ECMs are worth emphasizing. First, according to the DW and Godfrey (|F.sub.j~) tests, the equations exhibit the desired property of serially uncorrelated errors. Second, the estimated velocity equations seem to fit the data quite well as about half of the total variation in the growth of velocity is explained by each equation. Third, according to the Chow test, these equations appear structurally stable. Fourth, in regard to causality, equation (5) suggests that changes in real output, interest rate, interest rate volatility and real exchange rate provide information that helps predict future movements in M1-velocity. Note that these findings are consistent with those of multivariate Granger causality except that real output enters the function with a time lag of two quarters.

According to equation (6), the lagged changes in the interest rate volatility, money growth volatility and interest rate represent the short-run causal impact on M2-velocity. Note that these findings corroborate multivariate Granger causality results in supporting Friedman's hypothesis.(7) Fifth, observe that the EC term in each equation has the correct negative sign. It is also statistically significant at the 5% level, lending support to the validity of cointegration between income velocity and its determinants.(8) In addition, it indicates the existence of market forces in the money market that operate to restore long-run equilibrium after a short-run disturbance. Therefore, the significance of EC terms introduces an additional channel through which Granger causality can emerge.

4. Conclusion

The present study has been designed to provide meaningful empirical evidence not only about Granger-causality in the velocity-money growth relationship, but also on the issue of whether income velocity has been causally determined by other macro variables. The empirical results suggest the following inferences: There is a significant causal impact of money growth volatility upon M2-velocity even when the effects of other macro variables are controlled for in the equation. This evidence appears to support Friedman's hypothesis and is consistent with Belongia (1984), Hall and Noble (1987), Shams (1989) and Fisher and Serletus (1989).

Furthermore, although perhaps best regarded as tentative, the results suggest that money growth volatility may have long-run impact on both M1 and M2 velocity through EC term. While such an interpretation is attractive, Granger (1988) warns that it is unclear that such a view is in fact justified until work similar to Geweke (1982) is done to explore the frequency decomposition of the EC term.

Finally, the results show that besides money growth volatility, there is significant causal impact especially of interest rate volatility and real exchange rate upon income velocity. These findings are in line with the conclusion drawn by Goodhart (1989:318) that "there are a variety of suggested answers, none of them fully satisfactory, though all of them may possess some validity."


1. During the 1970s, M1-velocity growth (measured from the fourth quarter of one year to the fourth quarter of the next) increased by about 14.5% whereas M2-velocity growth increased by about 29%. For each monetary aggregate, income velocity reached a peak in 1980 and declined sharply thereafter--M1-velocity fell by about 21% whereas M2-velocity fell by 26.7%.

2. Gordon (1983) has described this drop in velocity as the "demise of monetarism."

3. See Hall and Noble (1987:114) for a more detailed discussion.

4. Some justification should, perhaps, be given for restricting the sample period to the flexible exchange rate period, apart from the fact that it enables comparison with previous studies examined below. Given several breaks in the U.K. monetary data prior to 1973 (see, topping and Bishop, 1989 for details) we use data for the flexible exchange rate period to avoid criticism raised against pooling data from these different exchange rate regimes. See Bank of England Quarterly Bulletin (August 1989:352) and Papell (1989): 1106). 5. Data or the Money GDP, treasury bill rate and real GDP are from Economic Trends, Annual Supplement 1991, Central Statistical Office, London. Data for the world price level, index of effective exchange rate, consumer prices, M1 and M2 are from International Financial Statistics, IMF (various issues) including Supplement on Prices. Note that the world price level is measured by a weighted average of consumer prices of industrial countries (1980-100). Because the IMF defines MERM (line amx) as units of foreign currency per unit of domestic currency, we had to invert the MERM series to get effective exchange rate defined as units of domestic currency per unit of foreign currency. Monetary and interest rate volatility are proxied by an eight-quarter (current and seven lags) standard deviation of the quarterly percentage change in each variable. 6. The tests used are those described in Arize and Walker (1992a), Arize and Ndubizu (1992b) and Arize and Shwiff (1992c).

7. Other alternative measures of volatility were used to check the sensitivity or robustness of the results. No evidence to the contrary was found.

8. Results of Johansen and Juselius (1990) procedure which are available from the author upon request are consistent with these findings.


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Author:Arize, Augustine C.
Publication:American Economist
Date:Sep 22, 1993
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