Money and economic activity revisited

Money and economic activity revisited

~ Pergamon PII: Journal of International Mott 0' and Finance, Vol. 16, No. 6, pp. 955-968, 1997 © 1997 Elsevier Science Ltd. All rights reserved Pri...

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Pergamon PII:

Journal of International Mott 0' and Finance, Vol. 16, No. 6, pp. 955-968, 1997 © 1997 Elsevier Science Ltd. All rights reserved Printed in Great Britain S0261-5606(97)00038-7 0261-5606/97 $17.00 + 0.00

Money and economic activity revisited M A R K S DAVIS*

Eastern Europe and Central Asia Division, The World Bank, 1818 H. Street, N.W., Washington, D.C. 20433, USA AND

J ERNEST TANNER~

Department of Economics, Tulane University, New Orleans, LA 70118, USA Recent literature has concluded that money no longer plays a fundamental role in determining US economic activity, especially when post-1982 data are included in the analysis. We re-examine the issue using annual and quarterly data sets ranging back to the Civil War. Cointegration tests show that an equilibrium relationship holds between money and income in all data samples of 35 years or longer, but frequently fails to hold for many shorter samples. However, when the normal monetary lags are explicitly imposed, a cointegrating relationship is frequently captured, even in quite short samples. Examining the issue in a standard five-variable VAR model, we find that money is the most important variable in explaining real output for the full 1874-1993 as well as 1952-1993 periods, even allowing for interest rate effects. Finally, using monthly data over the troublesome 1983-1994 sample, we show that when appropriate adjustments are made to capture recent structural changes, such as the growing importance of the international economy on US output, money still Granger-causes economic activity. (JEL E40). © 1997 Elsevier Science Ltd. All rights reserved. *This research is dedicated to the memory of Patrick C. McMahon. Though we knew him far too briefly, Patrick uplifted both of our personal and professional lives. As Davis' classroom teacher and initial thesis director, Patrick methodically constructed a framework of the macroeconomy and the international financial system, which he then illuminated with the full realm of modern empirical research, of which he was so familiar and so much a part. As a colleague and through personal conversations, Patrick made each day more rewarding and enjoyable. His wit and humor were enjoyed by everyone within earshot. Professor McMahon is sorely missed by his students and friends around the globe. We thank John Boschen, Phil Cagan, Mike Cox, Milton Friedman, Russ Robins and Ed Tower for numerous comments and helpful suggestions on earlier drafts of this manuscript. ¢~J. Ernest Tanner passed away while this issue was in press. The editors and his fellow contributors mourn his untimely passing.

955

Money and economic activity revisited: M S Davis and J E Tanner

In recent years, money growth has lost much of its appeal in predicting changes in US economic activity. In contrast to the early 1980s when laymen and professional economists alike were following every squiggle, money growth is now largely ignored by the public, by most professional economists, and is even attributed less importance by the policy makers at the Federal Reserve. Has the decline in the apparent importance of money been the result of a sharp increase in the variability of velocity following the Monetary Control Act of 1980? Or was money's fall in stature simply the result of it having been placed on too high a pedestal in 1980 after an abnormally stable money-to-income relationship during the 1950-1980 period? ~ Using new statistical techniques and data sets which were not available to researchers in 1980, we examine these and other questions. Results suggest that the 1980s may look different from some earlier periods, but that this is not due to a fundamental breakdown of the money growth-output relationship. Rather, the US economy is now more open and more subject to international influences than in the past, and monetary policy in the 1980s, especially since 1982 seems to have been more contra-cyclical than in many earlier periods. As a result, the simple m o n e y income correlations of the 1950-1980 period may well have changed, but the fundamental proposition that changes in money supply growth affect economic activity remains in tact. The plan of the paper is as follows. In Section I, we perform long-run equilibrium (cointegration) tests of the money-income relationship using fulland sub-sample data sets ranging back to the Civil War. In Section II, we make small macro (vector-autoregression) model estimates of the US economy. In Section III, we re-examine the post-1982 experience in light of the increasing importance of the international economy and the forward-looking nature of interest rates. Section IV summarizes the paper's major findings.

I. Testing for an equilibrium money-income relationship It has been widely assumed by monetarists since the 1960s that there is a long-run relationship between the respective levels of money and income and between money and prices. While Milton Friedman's statement 'inflation is always and everywhere a monetary phenomenon' was more controversial when first published in 1963 than when reprinted in Friedman 1968, p. 39), Friedman now says that it is 'perhaps the single most important and most thoroughly documented.., proposition' (Friedman, 1992, p. 262). Yet, the 1970s' criticism that inflation results from the Federal Reserve's policy of base drift has faded, and recent tests do not find a stable relationship between money and income. 2 To wit: 'In sum, whatever the situation may have been before the 1980s, it is no longer possible to discern from the data a stable long-run relationship between income and the monetary base, M1, or credit, either with or without allowances for the effect of interest rates, and the evidence of such stability in the case of M2 strictly depends on the inclusion of data from the 1960s... The evidence in favor of the kind of long-run stability of the m o n e y - i n c o m e relationship.., has become weaker over time, so much so that any 956

Money and economic activity revisited: M S Davis and J E Tanner 30 II

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FIOURE 1. Four-year growth rates: M2, nominal GNP and real GNP.

presumption in favor of such a relationship must reflect prior beliefs, rather than the evidence contained in the data now available.' (Friedman and Kuttner, 1992, p. 490.)

We begin our reexamination in Fig. 1 by plotting 4-year growth rates (about the average business cycle length) of M2, nominal GNP and real GNP annual data since the Civil War. The graph shows a very close relationship between growth rates in money and nominal income, especially since about 1910. Additionally, the money-nominal income relationship for the past 35 years appears as good as for earlier periods. However, over the past 35 years, while very short-run movements in money appear to be related to very short-run movements in real output, longer term trends of real GNP and M2 appear quite unrelated. The 4-year growth rate in M2 rises from 1960 to a peak about 1980 and then erratically declines through the end of the sample. Real GNP growth shows no comparable swings since 1960. Thus over the past 125 years, the 1960-1993 sample shows the longest sustained gap between 4-year growth rates in the real economy and the nominal money supply, suggesting to many observers that the money-income relationship began falling apart in the 1970s before a final break with the Monetary Control Act of 1980. 3 To monetarists, however, the relevant link is between nominal income and money, not real income and money. When we break the 1966-1993 gap about in the middle with the 1980 Act, M2 growth for the 1966-1980 period averaged 8.7% while nominal GDP growth averaged 0.5% higher at 9.2%, and from 1980 to 1994, M2 growth averaged 6.1% while nominal GDP growth averaged 0.6% higher at 6.7% - - certainly not evidence that the money-income equilibrium relationship broke apart. 4 Recent advances provide statistical tests of long-run equilibrium. In terms of these tests, an equilibrium holds between economic series if a linear combination of them is stationary. Thus, even if money, prices and output are individu957

Money and economic activity revisited." M S Davis and J E Tanner

ally integrated of order greater than zero (i.e. each is non-stationary), they may be 'cointegrated' in the sense that some linear combination is integrated of a reduced order. In the M V = Y relationship, for example, a finding that M and Y are I(1), but velocity is stationary, implies that M and Y are cointegrated. 5 A finding that velocity is non-stationary does not, however, rule out the existence of a long-run equilibrium because M V = Y imposes a unit income elasticity of money demand and because other variables may be necessary. 6 We thus hypothesize the equilibrium relationship: (1)

y-

flm=e

where y is nominal GNP, m is the M2 money stock and e is a stochastic error process. In such relationships, Engle and Granger (1987) showed that cointegrating variables can be viewed as part of an error-correction process where the change in a variable depends upon deviations from the equilibrium relationship. For example, in the M V = Y relationship, if we assume that the dynamics of the system are captured by a 1st order vector-autoregression in differences, then changes in income can be expressed as a function of the lagged differences of money and income and of the lagged deviation in levels of money and income: (2)

Ay, = aAy,_ l + A~mt-l

- T ( Y , - l - t i m , _ l) + u,

In this specification, if gamma is non-zero, Eq. (2) error corrects, and money and income are said to be 'cointegrated' since income will eventually adjust to any change in the money supply. Johansen (1988) and Johansen and Juselius (1990) provide a maximum likelihood testing procedure for error-correction models which amounts to testing the dimensionality of the error-correction parameter matrix (i.e. the number of cointegrating vectors in the equation system). Johansen and Juselius propose two alternative tests to ascertain the number of non-zero eigenvalues (and therefore the rank) of the error-correction parameter matrix. The A-Max test poses the null that there are k against the alternative of k + 1 cointegrating vectors while the Trace test has as its null that the number of cointegrating vectors is < k. In either case, a rejection of the null of k = 0 will be sufficient to establish a long-run relationship. 7 Critical values at the bottom of Table 1 are from Table A2 of Johansen and Juselius (1990). s Before turning to the test results, two remaining issues need to be discussed. First, in order to use established critical values, each variable of the system must be individually integrated of order one. Phillips and Perron tests of real income and real money (Phillips and Perron, 1988) support an 1(1) specification for the full- and sub-samples. 9 Second, since much previous research has indicated that there are substantial lags in the effects of monetary policy, we examined whether such lags are important in rejecting the hypothesis of a long-run equilibrium relationship. Lag structure in cointegrating relationships has largely been ignored. This is because, theoretically, a short-run lag should have no impact on long-run correlations. The intuition runs as follows: any differenced stationary variable 958

Mom:v and econotnic activi~ revisited." M S Davis and J E Tanner

TABLE 1. Johansen test for money-output cointegraton [equilibrium hypothesis: y - / 3 ( m - p ) = e] Annual data (2nd-order ECM) Sample 1876-1993 1946-1993 Quarterly data (4th-order ECM)

1878:4 1994:1 1878:4-1913:4 1878:4-1896:4 1897:1-1913:4 1920:1-1939:4 1952:1- 1994:1 1952:1- 1982:4 1983:1-1994:1 1960:2-1979:3 1960:2-1990:4 1970:3-1990:4 1960:2-1994:1 1970:3-1994:1 Monthly data (18th-order ECM)

Contemporaneous money

Money lagged 1 year

Money lagged 3 years

h-Max

Trace

h-Max

Trace

h-Max

Trace

20.18 17.68

23.86 26.43

27.88 13.75

30.91 20.98

32.12 20.83

33.30 21.51

Contemporaneous money

Money lagged 3 quarters

Money lagged 10 quarters

A-Max

Trace

A-Max

Trace

A-Max

Trace

33.27 21.25 1i. 12 21.48 5.62 21.38 15.98 7.11 15.57 13.41 10.06 15.83 12.56

33.28 21.43 12.31 21.68 9.33 31.00 25.73 8.31 26.42 24.27 18.34 25.39 19.07

37.16 21.70 11.70 17.58 9.38 21.56 14.45 12.35 14.72 12.59 8.70 15.64 11.25

37.16 21.86 12.32 17.64 8.21 25.10 17.70 13.20 21.99 19.32 14.77 22.72 16.76

29.97 31.64 21.17 17.50 15.08 37.05 24.99 17.83 25.87 27.47 16.47 29.69 18.24

29.97 31.80 23.28 19.38 18.74 49.01 33.32 21.42 32.39 34.71 27.78 38.94 31.07

Contemporaneous money

Money lagged 9 months

Money lagged 30 months

h-Max

Trace

h-Max

Trace

h-Max

Trace

1952:1-1994:06 1952:1-1982:12 1960:1-1982:12 1960:1-1994:06 1970:1 1994:06 1983:1-1994:06

19.43 15.57 18.72 20.86 11.22 10.52

21.66 16.82 22.36 25.62 15.69 12.66

11.09 7.70 7.16 8.93 5.75 14.40

13.34 9.03 9.98 13.68 10.69 17.02

18.23 14.22 8.53 14.75 10.77 27.17

20.93 16.46 9.17 18.19 17.73 30.57

Critical values h-Max Trace

1% 18.78 21.96

2.5% 16.40 19.61

5% 14.60 17.84

10% 12.78 15.58

is cointegrated with its own lag; therefore, if a second variable is cointegrated with the first, it must also be cointegrated with the lag o f the first and so on back to any relevant lag] ° In practice, however, researchers have limited samples with which to capture the error-correcting relationship. Referring back to Eq. (2), for instance, if we know the bulk o f the impact of m o n e t a r y policy on o u t p u t takes place in the 3rd period, a short-sample c o n t e m p o r a n e o u s

959

Money and economic activity revisited: M S Davis and J E Tanner

regression would likely not capture the underlying error-correcting relationship, unless the entire money series were appropriately lagged by 3 periods. Increasing the frequency of sampling will not solve the problem, because if the lags exceed 2 years as implied by Barro (1978) or are 3 years as used by Heinemann (1994), then long samples are required, not frequent observations.~l We therefore ran each of the hypothesized cointegration specifications with income and money contemporaneously, money lagged by 1 and 3 years for the annual data, money lagged by 3 quarters and 10 quarters for the quarterly data and by 9 and 30 months for the monthly data. We did not experiment with other lag lengths. Table 1 tests for a long-run money-income equilibrium. The annual data show significant tests statistics at the 1% significance level for all lag specifications, indicating an equilibrium money-income relationship for the whole 1876-1993 period. For the shorter post-WW2 period, the A-Max test is significant at 2.5% for contemporaneous money, significant at 10% when money is lagged 1 year, but significant at 1% when lagged 3 years. The results using quarterly data are also supportive. As with the annual tests, the evidence in favor of cointegration decreases and then increases as the lag length is increased, and in no sample is the hypothesis of cointegration not accepted at the 5% level when money is allowed to precede income by 10 quarters. In contrast, without allowance for lags, cointegration is not accepted at the 5% level in six sub-samples using the A-Max test (three sub-samples using the Trace test). Using a three-lag specification, cointegration is not accepted seven times under both tests. One important implication of these results to the recent data is that cointegration is least likely to be accepted in short data samples. Under the gold standard period, for instance, cointegration appears more likely during the full 1878-1913 sample than for either the 1878-1896 sample or for the 1897-1913 sub-samples. Likewise, evidence for cointegration during the 1920-1939 sample is weak for both the no-lags and three-lags case, but significant in the 10-lags case. Post-World War 2 pattems seem similar in that the whole 1952-1994 sample shows cointegration at the 1% level for all lags. Yet no sub-sample of the 1952-1994 period appears this robust. The monthly tests are for the post-1951 Treasury-Federal Reserve Accord period and use industrial production as a proxy for output. Given the above results, these monthly tests are not surprising. Again, the longest sample periods provide the strongest evidence in support of cointegration. The usual contemporaneous tests show cointegration at the 1% level for the 1952-1994 period. Cointegration is also indicated for the 1960-1982 and 1960-1994 periods, but not for the 1970-1994 or 1983-1994 periods. However, if money is lagged by 30 months, the tests for cointegration are significant at the 1% level for the 1983-1994 sample. These results are consistent with the results of Friedman-Kuttner in that, when lags are ignored, cointegration appears to exist over the 1952-1994 and 1960-1994 periods, but not for 1970-1994 or 1983-1994 periods. However, the introduction of substantial lags often suggests cointegration even for the post-1970 samples.

960

Money and economic activity revisited: M S Davis and J E Tanner

II. The vector-autoregression evidenee Much of the recent research regarding money's influence on economic activity has used the vector-autoregression model (VAR) because simultaneous equation bias is prevalent in many older estimations of the money-real output relationship. In many ways, V A R is statistically superior to the reduced form estimation procedures of the 1970s. However, it may not accurately test the 'money matters' model implicit in much of the work of Milton Friedman and others of the monetarist bent, who place the predominant emphasis on 'sustained' changes in money growth rates, because it is viewed that 'transitory' changes (occurring over 1 month or 1-2 quarters) matter little, either for short-run output changes or for inflation. Rather, monetarists contend that only sustained changes in money supply growth result in comparable changes of nominal economic growth. Thus, 'innovations', especially innovations in shorter-term monthly and quarterly data, are unlikely to properly evaluate the original monetarist hypothesis. ~2 Nevertheless, because of the criticism 'monetarism' has received from researchers using monthly and quarterly data in the V A R context, it is worthwhile to reexamine the money-income relationship in the same framework, Additionally, improved annual data estimated by Romer (1989) and new quarterly estimates by Balke and Gordon (1986) allow us to extend the analysis back to the 1870s. We are thus able to provide a clearer picture, both of the money-income relationship over the last century and a quarter, and of how recent episodes compare to a longer history of money and economic activity. Table 2 presents the marginal significance levels for M2 on real GNP in a five-variable V A R model. The model includes an output variable, inflation, an interest rate, a private-government rate spread, and M2 growth. All series were made stationary by appropriate transformations, as defined in the table, before estimation. Significance levels of the F-statistics tell a very impressive story about the importance of money in all periods. In the annual data case (the case most closely related to the monetarist proposition that only sustained changes in money supply matter), M2 is clearly the most important variable in explaining real GNP for every sample period. Lagged innovations in annual money growth explain economic activity at the 2% significance level in all but the 1952-1993 sample (where it was 5.6%). In contrast, in no sample is the change in the 6-month commercial paper rate significant at even the 10% level, likewise for the 6-month Treasury-commercial paper spread and inflation, and in only one case is the lagged dependent variable significant. Results are similar for the four-variable equivalent nominal GNP VARs (not reported), where money is clearly the most important variable for explaining nominal output for all sample periods. In the quarterly data set, the evidence for innovations in money is only slightly less robust. Money is significant at the 5% level in all samples except the 1952-1982 sub-sample. This result should not be unexpected if one

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Money and economic activi~_ revisited." M S Davis and J E Tanner

TABLE 2. Marginal significance levels of VAR model of output Annual data (four-lag model) 1874-1993 Non-War 18741993 DGNP$82 DPrices Spread DCP DM2

0.018 0.861 0.741 0.875 0.005

0.515 0.368 0.287 0.536 0.000

18741913

19521993

0.537 0.128 0.774 0.261 0.012

0.856 0.218 0.845 0.894 0.056

Quarterly data (six-lag model) 1876:4-1 Non-War 1876:4- 1876:4- 1920:1- 1952:1- 1952:11994:1 1994:1 1913:4 1939:4 1982:4 1993:4 DGNP$82 DPrices Spread DCP DM2

0.000 0.002 0.004 0.007 0.000

0.000 0.000 0.019 0.021 0.000

0.007 0.027 0.408 0.480 0.003

0.130 0.065 0.019 0.022 0.039

0.419 0.135 0.025 0.233 0.207

0.270 0.025 0.007 0.234 0.007

Monthly data (12-1ag model) Sample: 1983:01-1993:06 DIIP DIIP (resids) DCPI DCP DCP (resids) Spread Spread (resids) DM2

(1)

(2)

0.302

0.042

0.437 0.247

0.306

(3)

(4)

0.013 0.215 0.038

0.103 0.375

0.186 0.318 0.163

0.49 0.0169

0.317 0.076

0.028

0.354 0.011

Notes: DGNP$82, first differences of logged real GNP in 1982 dollars; DIIP, first differences of logged index of industrial production; DIIP (resids), residuals of regression of DIIP on constant, trend and four lags of industrial production growth rates in Canada, Japan, Mexico and Germany, to capture the growing impact of foreign economies in the United States; DCPI, first differences of logged consumer price index; DCP, first differences of the 6-month commercial paper rate; DCP (resids), residuals of a regression of DCP on DM2, 0-6 months ahead, to capture the effect of current and anticipated future money growth on observed interest rates; Spread, 6-month commercial paper rate less the 6-month Treasury bill rate; Spread (resids), residuals of Spread regressed on 0-6 months ahead DM2; DM2, first differences of the logs of the M2 definition of money.

c o n s i d e r s m o n e t a r y policy p r i o r to 1979. R e g a r d l e s s o f o n e ' s p e r s u a s i o n , m o s t o b s e r v e r s o f the F e d e r a l R e s e r v e o v e r the 1 9 5 1 - O c t o b e r 1979 p e r i o d m a i n t a i n t h a t the F e d was targeting interest rates. C o n s e q u e n t l y , d u r i n g m o s t o f the 962

Money and economic activity revisited: M S Davis and J E Tanner

1952-1982 sub-sample, innovations in Fed policy are more accurately measured by innovations in interest rates than by innovations in money. 13 Thus, because monetary policy is essentially an interest rate policy from 1951 to 1979, it should be expected that money supply changes do not play a significant role in a V A R model including an interest rate over that period.

III. Monthly data since 1983 As noted earlier, although the spirit of monetarism is not accurately reflectcd by monthly VARs, they have been widely used to criticize the main monetarist proposition 'that money matters.' Becausc of this, we re-examine the cvidence for the rcccnt past. Wc concentratc on thc post-1982 period for thrce reasons. First, McCallum (1983) showed that during a period of Federal Reserve interest rate targcting, innovations in monetary policy are most accurately captured by innovations in intercst ratcs, not by innovations in money. Second, when interest ratcs and money growth rates are plotted, there is an obvious brcak in the relationship ncar the end of 1982 when the Federal Reservc abandoned the 1979-1982 policy of targeting non-borrowed reserves. 14 Thus, we avoid this structural break by estimating only the post-1982 period. Finally, wc usc only post-1982 data bccause this period scems to bc thc most problematic in tcrms of the robustness of the conclusions in the literature. The statistical significance levels of money innovations are at the bottom of Table 2. In contrast to Friedman and Kuttncr who specify 12 lags for all variables except for money which they specify with six lags, we specify 12 lags for all variablcs: industrial production, consumer prices, the 6-month commercial paper ratc, thc 6-month commcrcial papcr-trcasury bill spread, and M2. In addition, the model is specified with a constant and trend term and is estimated ovcr the 1983:1 through 1993:12 period with 1982 used as initial observations and early 1994 data bcing used for interest rate adjustmcnts. (Discussed below.) As shown by Column 1 (the Friedman-Kuttner preferred specification), no variablc is significant in causing innovations in industrial production. M2 is most significant, but at 16.3% it hardly qualifies. For Column 2, consider an efficient market in the context of a central bank which has monetary levers at its control. In this context, innovations in interest ratcs may reflect unexpected innovations in actual money growth rates as well as expected innovations in future moncy growth rates. Because the 6-month commercial papcr rate and the spread reflect not only cxpcctations about future monetary policy, but also about current policy [as discussed in Friedman and Kuttner (1993)], we regressed the interest rate variables on current and future M2 growth rates up to 6 months ahead to generate intcrest rate variables not contaminated by cxpcctations about currcnt and future monetary policy. Thc results show that the significance of interest rate effects are marginally improved, while the significance of money rises quite sharply. For Column 3, we note that thc industrial sector has been declining as a share of the nation's economy for several years and is now significantly less important than the service sector. However, bccause other researchers [follow963

Money and economic activity revisited." M S Davis" and J E Tanner

ing Sims (1980)] have often used industrial output to measure the real economy on a monthly basis, we follow them. Still, as the economy becomes more open and intemational trade becomes more important, innovations in industrial production are increasingly likely to reflect changes in foreign demands for our products, and these are not likely to respond to domestic monetary innovations. To capture these world influences, Column 3 uses residuals of US industrial production regressed on industrial production indexes ([IP) and IIP interacted with trend in Canada, Mexico, Japan and Germany using lags up to 4 months. When these foreign demand adjustments are made, the significance of all variables increases, with the significance of money climbing to 2.8%. Column 4 makes both adjustments (i.e. the adjustment for interest rates reflecting current and expected monetary policy and the adjustment for foreign influences on our industrial output). This yields money significant at the 1.1% level. IV. Conclusions

Over the past several years, the monetarist proposition 'that money matters' has come under serious attack as velocity showed extreme volatility in the post-1982 period and as statistical tests showed that inclusion of data from the 1980s tended to nullify earlier conclusions about money's predictiveness for subsequent economic activity. Our analysis suggests that the demise of monetarism is premature. First, in contrast to recently published test results, we find that cointegration tests accept the cointegration hypothesis for longer data sets ranging back into the latter half of the 19th century. When cointegration is not accepted, the sample period is almost invariably quite short. Because lags from money to economic activity may be 2 years or longer, especially nominal income which includes price adjustments, it should not be surprising that the equilibrium cointegrating relationship does not show up in recent tests which are based on short sample periods. However, when lags are allowed, the evidence for cointegration generally increases and cointegration is frequently accepted even for shorter samples like those beginning in 1970 or later. Second, our VAR tests show that money (M2) is a statistically exogenous factor causing real as well as nominal output over all extended samples. The only exception occurs during the 1952-1982 sub-sample, a period characterized by a Fed policy of targeting interest rates. During such periods, innovations in monetary policy are more appropriately measured by an interest rate variable than by the money supply. Third, we argue that the proposition of monetarism is not well captured by the more extreme, short-term innovations of a monthly model. Rather, since monetarism maintains that only sustained monetary changes matter, in a VAR context annual data is more appropriate for evaluating the monetarist proposition, quarterly data is marginal, and monthly data may be quite unreliable. Indeed, all of our V A R tests using annual data show that money innovations are more significant than any other variable's innovations in causing innova-

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Money and economic activity revisited: M S Davis and J E Tanner

tions in income. In general, we do not find this to be true for either monthly or quarterly data. Fourth, we find that many previous monthly tests may have been flawed because of the use of poor measures of total real output, because V A R regressions were performed over the 'interest rate targeting' period, and because current innovations in forward looking interest rates reflect expected monetary policy innovations. When appropriate adjustments are made, i.e. using foreign demand adjusted output, limiting the sample to the 1983-1994 period, and making interest rates orthogonal to current and anticipated monetary policy (but not to past policies), money growth rates are found to be a statistically exogenous factor explaining real output in the post-1982 US economy. Notes 1. Even many strong monetarists have lost their faith in the ability of a stable money growth path to ameliorate the business cycle. For example, Poole, a strong advocate of a more stable and slow money growth policy in the 1970s, writes: '...I now believe that 1980-1985 experience has demonstrated quite decisively that the gradualist prescription is unreliable. The decline of velocity was far greater than economists had predicted and it seems very unlikely that the economy could have adjusted satisfactorily (to a simple rule of just slowing money growth)...' (Poole, 1988, p. 97). 2. In the 1970s, Federal Reserve critics often complained that the Fed was contributing to rising inflation because of 'base drift'. As the Fed often exceeded its target money growth, re-basing money growth for the coming year on too high a base because of excessive money growth during the past year was said to have contributed to the high inflation rate. Rather, critics argued that excessive money growth during the past year should be justification to lower target money growth next year so that the combined multi-year money growth did not exceed target. See, for example, Poole (1976). 3. In the early 1970s, the demand for money appeared to shift, indicating that the money-income relationship was breaking down. See, for example, Goldfeld (1976). 4. In commenting on this period, Dewald (1994) points out that both money growth and nominal GNP growth slowed approx. 2.5% since deregulation in 1980, real output growth slowed only slightly to 2.5% from 2.8% and inflation declined more significantly to 4.2% from 6.5%. If more recent data were taken into account, real growth would have slowed even less while inflation would have been down even more. 5. In this context, Phillips and Perron unit-root tests of quarterly M2 velocity for several different sample periods between 1878:4 and 1994:1, as well as over the entire period, showed little evidence of cointegration. Given the lags between money and income, we tested three alternate M2 velocity specifications: (i) GNPt/M2t; (ii) G N P J M 2 , 3; and (iii) GNP,/M2 t ~0. For all samples and all specifications a four-lag truncation of the sample autocorrelations was used for consistent estimation of o-2 [in the notation of Phillips (1987)]. Results were not found to be sensitive to other lag lengths. Since the data appear to be trending, we base our tests upon Phillip's Z(t, ~) statistic, however, they are also invariant to the testing strategy of Perron (1988). The samples tested were 1878:4 1994:1, 1878:4-1896:4, 1897:1-1913:4, 1878:4-1913:4, 1920:1-1939:4, 1952:1-1994:1, 1952:1-1982:4, 1983:1 1994:1, 1960:2-1990:1, 1970:3-1990:1 and 1960:2-1979:3. The last three samples are those tested by Friedman and Kuttner (1993). Although these Phillips Perron tests indicated that M2 velocity is non-stationary for every specification and sample tested, results were less consistent when the Augmented Dickey-Fuller test was applied as a check. Using the A D F t-test (with four lags of the dependent variable and a constant and trend included in the regression), we found stationarity at a 5% or greater significance level for all specifications during the 1878-1994 sample, and for ( G N P J M 2 t 10) during the 1952-1982 and 1960-1970 965

Money and economic activity revisited: M S Davis and J E Tanner

6.

7.

8.

9.

10.

11.

12. 13.

14.

sub-samples. We attribute these inconsistencies to the low power of the tests. [See Schwert (1989) for a simulation-based comparison of power in the PP and ADF tests.] Tanner (1993), for example, used interest rates, stock returns, real asset returns and a measure of policy tightness to obtain a predicted velocity relationship. When the money supply was multiplied by predicted velocity to form 'effective money', cointegration tests showed that effective money and income were cointegrated through the 1980s. In effect, the Trace test differs from the h-Max test by considering not only the largest eigenvalue, but the sum of all of the eigcnvalues as an indication that at least one is significantly different from zero. As suggested by Johansen and Juselius, we use Table A2 since money and output exhibit trends. This is advised because the broader tails in this table provide a more conservative test. Although the current literature analyzes real income and real money, monetarists feel that the interesting question for Federal Reserve policy is to test the cointegration of nominal money and nominal income. Statisticians would argue that it doesn't matter because both sides of the money-income identity are divided by the same price level. However, since the Fed controls only the nominal quantity of money while the public determines the real quantity of money [see, for example, Friedman (1969)], testing for cointegration in the real quantities may be irrelevant since the amount of wealth the public holds in the form of real money balances may bear only a scant relation to real GNP. Applying Phillips-Perron tests to nominal M2 and nominal GNP over the Pre-War, Inter-War and full 1879-1994 sample, we found both M2 and nominal GNP to be integrated of order 1, except M2 during the post-WW2 sample and its sub-samples and over the 1897-1913 sub-sample where it tests •(2). This enabled us to conduct quarterly cointegration tests of the nominal aggregates over the full sample as well as over the pre-war and inter-war sub-samples. For purposes of brevity we have excluded the table, but we note that results are similar to those reported using real aggregates, though slightly less significant. Leads and lags should have no effect on the results of cointegration tests when the sample goes to infinity. Suppose Y~ is a simple random walk so that Yt = Y~- k + e, where k = 1, 2, 3 .... and e is an iid distributed error. Then, in the limit, Y, and X t have the same long-run relationship as Y~ k and X,. While the lag in the effects of monetary policy is debatable, there is moderate agreement that the real effects take roughly 3 quarters while the inflation effects are significantly longer. Heinemann (1994) uses 36 months, Selden (1981) estimates the lag for many countries in the 5- to 13-quarter range and Barro (1978) argues that his lags are consistent with Selden's. For more complete analysis and discussion of this point, see Cagan (1989) and McCallum (1983). McCallum (1983) shows that if the Fed targets an interest rate based upon an observable information set, then stochastic disturbances in the interest rate rule is the appropriate variable to use in measuring the effects of monetary policy. As McCallum concludes, during interest rate targeting periods, monetary policy innovations in the VAR model may 'not be well represented by money stock innovations...' (p. 168). Gordon and Leeper (1994) use only post-December 1982 data in tests of their model of the effects of money in a money demand-money supply framework as this period 'produced a fairly stationary policy environment' (p. 1231). Tanner and Pescatrice (1998), also find a significant change in the money supply function at the end of 1982.

References Balke, N. and Gordon, R.J. (1986) Appendix ]3, Historical Data. In TheAmerican Business Cycle, ed. R.J. Gordon, pp. 781-850. University of Chicago Press, Chicago. 966

Money and economic activity revisited:M S Davis"and J E Tanner Barro, R.J. (1978) Unanticipated money, output and the price level. Journal of Political Economy 86, 549-580. Cagan, P. (1989) Money-income causality: a critical review of the literature since A Monetary History. In Money, History and International Finance: Essays in Honor of Anna J. Schwartz, ed. M,D. Bordo, pp. 117-151. The University of Chicago Press, Chicago. Dewald, W.G. (1994) Deregulation and trends in M2, GDP and inflation. Monetary Trends, Federal Reserve Bank of St. Louis, September 1. Engle, R.F. and Granger, C.W.J. (1987) Cointegration and error correction representation, estimation, and testing. Econometrica 5, 251-276. Friedman, B.M. and Kuttner, K.N. (1992) Money, income, prices, and interest rates. American Economic Review 82, 472-492. Friedman, B.M. and Kuttner, K.N. (1993) Why does the paper-bill spread predict real economic activity? In New Research on Business Cycle Indicators and Forecasting, eds. J.H. Stock and M.W. Watson, pp. 213-249. University of Chicago Press, Chicago. Friedman, M. (1968) Dollars and Deficits: Inflation, Monetary Policy and the Balance of Payments. Prentice Hall, Englewood Cliffs, NJ. Friedman, M. (1969) The optimum quantity of money. In The Optimum Quantity of Money and Other Essays, Chapter 1. Aldine, Chicago. Friedman, M. (1992) Money Mischief." Episodes in Monetary History. Harcourt Brace Jovanovich, New York. Goldfeld, S,M. (1976) The case of the missing money. Brookhlgs Papers on Economic Activity 3, 683-730. Gordon, D.B. and Leeper, E.M. (1994) The dynamic impacts of monetary policy: an exercise in tentative identification. Journal of Political Economy 1228-1247. Heinemann, H.E. (1994) The cost of go-stop-go. Shadow Open Market Committee: Policy Statement and Position Papers, September 11-12, 9 28. Johansen, S. (1988) Statistical analysis of cointegration vectors. Journal of Economic Dynamics and Control 12, 231-254. Johansen, S. and Juselius, K. (1990) Maximum likelihood estimation and inference on cointegration - - with applications to the demand for money. Oxford Bulletin of Economics and Statistics 52, 169-210. McCallum, B.T. (1983) A reconsideration of Sims' evidence concerning monetarism. Economics Letters 13, 167 171. Perron, P. (1988) Trends and random walks in macroeconornic time series. Journal of Economic Dynamics and Control 12, 297-332. Phillips, P.C.B. (1987) Time series regression with a unit root. Econometrica 55, 277-301. Phillips, P.C.B. and Perron, P. (1988) Testing for a unit root in time series regression. Biometrika 75, 335-346. Poole, W. (1976) Interpreting the Fed's monetary targets. Brookings Papers on Economic Activity, 247-259. Poole, W. (1988) Monetary policy lessons of recent inflation and disinflation. Journal of Economic Perspectives 2, 73-100. Romer, C. (1989) The pre-war business cycle reconsidered: new estimates of gross national product, 1869-1908. Journal of Political Economy 97, 1-37. Schwert, W. (1989) Tests for unit roots: a monte carlo investigation. Journal of Business and Economic Statistics 7, 147 159. Selden, R.T. (1981) Inflation and monetary growth: experience in fourteen countries of Europe and North America since 1958. Economic Review, Federal Reserve Bank of Richmond, 19-35. 967

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Sims, C.A. (1980) Comparison of interwar and postwar business cycles: monetarism reconsidered. American Economic Review (Papers and Proceedings) 70, 250-257. Tanner, J.E. (1993) Did monetarism die in the 1980s? Journal of Economics and Bushtess 45, 213-229. Tanner, J.E. and Pescatrice, D. (1998) Monetary policy: impotent or simply contracyclical? Journal of Macroeconomics, forthcoming.

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