Federal deficits and money growth in the United States

Journal of Banking and Finance 13 (1989) 137-149. North-Holland

FEDERAL DEFICITS AND MONEY GROWTH IN THE UNITED STATES A Vector Autoregressive Analysis Scott W. BARNHART* Clemso, Unir,er¢ity~ C!e.m..~onSC 29634-1323, US4

Ali F. DARRAT* Louisiana Tech University, Ruston, LA 71272, USA Received May 1987, final version received April 1988 A multivariate VAR modelling technique is employed in this paper to test for causality between federal deficits and money growth in the United States. Four alternative causality hypotheses, including the common accommodation view, are examined. In addition to the two policy variables, four other related macro variables are included in the empirical analysis; namely, short-term interest rates, prices, real output, and exchange rates. The VAR results consistently reject the accommodation hypothesis and indicate that monetary and fiscal policy actions are set independently in the United States. Other causality inferences are also obtained and their implications are discussed.

1. Introduction

Large and growing U.S. federal budget deficits have recently attracted a great deal of attention in academic and policy circles alike. This concern stems mainly from the popular view that large budget deficits result in high interest rates, thus impeding formation and economic growth? This deficitto-interest rate linkage has also lead to the claim that federal deficits are inflationary. The upward pressure on interest rates could induce the Federal Reserve (Fed) to monetize at least part of the debt, leading to an increase in the rate of money growth and thus inflation. This theoretical linkage between deficits and money growth is often called 'the accommodation hypothesis. However, the empirical evidence on the accommodation hypothesis for the United States has been remarkably mixed~ For example, Barro (1978) and Joines (1985) have found no association between federal deficits and money *The authors, whose names appear alphabetically, would like to thank H.E. Neiman, G.P. Szeg6 and two anonymous referees for helpful comments and suggestions. The vsual disclaimer applies. ~For further discussion of these issues, see B. Friedman (1983) and Kopcke (1983). 0378-4266/89/$3.50 ~g~)1989, Elsevier Science Publishers B.V. (North-Holland)

J.B.F.--F

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S.W. Barnhart and A.F. Darrat, Federal deficits

growth, while Allen and Smith (1983) and Hoffman, Low and Reinberg (1983) have reported results in support of the accommodation hypothesis. In this article, we reexamine the empirical validity of the accommodation hypothesis using the vector-autoregression (VAR) technique. The VAR is used in conjunction with Akaike's Information Criterion (AIC) to test for Granger-causality between money growth and federal deficits. Most empirical studies in this area, including those cited above, are based on some type of regression analysis, which is void of any causality implications.' Support for the accommodation hypothesis that deficits 'cause' money growth is typically proclaimed if the coefficient(s) on the deficit variable in a money growth equation proves statistically significant. Clearly, regressions like these can only reveal whether a statistical correlation between deficits and money growth exists. Yet, the accommodation hypothesis not only implies the presence of a significant positive correlation between federal deficits and money growth, but also that the former causes the latter without significant feedback. In addition to the familiar deficit-to-money causal relationship, one could further argue for a reverse money-to-deficit relationship which is also consistent with a high association between the two variables. For example, Bradley and Potter (1986), extending work by Abrams, Froyen and Waud (1983), derive a theoretical reaction function for 5seal policy that specifies budget deficits as a function of money growth and other macroeconomic variables. In such situations, it is of course inappropriate to argue that budget deficits cause money growth. Interestingly, both regression studies of Hoffman, Low, and Reinberg (1983) and Joines (1985) do imply some empirical support for the notion that budget deficits have induced money growth in the United States. Further support for a possible money-to-deficit relationship is also implied in the model proposed by Barro (1979). In that model, Barro theorized that the government is primarily concerned with the real value of its deficit. Thus, the government would increase nominal deficits in order to keep pace with the rate of inflation. Inflation, however~ is primarily the result of excessive money growth. Therefore, it is reasonable to postulate that higher money growth, through the inflation channel, would lead to higher budget deficits, contrary to the implication of the accommodation hypothesis. These theoretical considerations, then, imply three alternative hypotheses regarding the relationship between budget deficits and money growth. There 2To our knowledge, only Dwyer {19821, Ahking and Miller (1985), and McMillin (1986) have employed some form of causality procedures to test for the effect of federal deficits on money growth. McMillin used a single equation model, ignoring the possibility that money growth could also cause deficits, while Dwyer's study has been criticized for the use of a common lag on all ~'ariables in his VAR. Ahk~ng and Miller on the other hand, omitted other potentially important variables from their system of equations.

S.W. Barnhart and A.F. Darrat, Federal deficits

139

is first the accommodation hypothesis that budget deficits cause money growth. Secondly, there is the reverse (Barro) hypothesis that money growth causes budget deficits. A third possibility is that both hypotheses are valid, in which case bidirectional causality exists between money growth and budget deficits. In this situation, previous studies that treat deficits as an exogenous variable are both biased and inconsistent due to the presence of simultaneous-equation bias. Returning for a moment to the accommodation hypothesis, it should be noted that this deficit-to-money relationship is premised upon two implicit assumptions. The first assumption is that the Fed is preoccupied with stabilizing interest rates as the main policy goal. The second is that budget deficits have a strong positive effect on interest rates. Neither assumption, however, is necessarily valid. It is possible, indeed likely, that the Fed has other more compelling policy goals such as price stability and economic growth. Contrary to the second assumption, the Ricardian equivalence proposition [see Bar~'o (1974)] denies on theoretical grounds any effect of the deficits on interest rates. Consistent with this view, Hoelscher (1983) and Evans (1985, 1987), among others, have found no empirical evidence of a positive effect of defic:its on interest rates. The preceding discussion suggests the possibility of a fourth hypothesis; namely, that no causal relationship between budget deficits and money growth exists. It is conceivable, as Granger (1980) pointed out, that two variables be highly correlated yet causally independent. Under such a scenario, the observed correlation between budget deficits and money growth may simply be the result of both variables responding to causal effects emanating from other factors (e.g., interest rates, prices, and real output). Recent international evidence by Protopapadakis and Siegel (1987) and Barnhart and Darrat (1988) underscores the importance of this fourth proposition. These studies, which examine the accommodation hypothesis in a number of industrialized countries, provide no evidence of a positive effect of deficits on money growth) The next section of the paper briefly desc~ibes the VAR technique and the data used. The resultant VAR model is discussed in section 3. Concluding remarks follow in section 4.

2. Data and methodology The empirical analysis in thi., paper is based on a multivariate vector 3Whereas Protopapadakis and Sie,~el employed the common correlation-based analysis, this study is based o,a testing for causali'y in the context of a multivariate VAR model. Moreover, Protopapadaki~ and Siegel did not Ciscuss any of the other alternative hypotheses that form the basis of this study.

140

S.W. Barnhart and A.F. Darrat, Federal deficits

autoregression modelling technique. The estimated VAR model consists of six related macroeconomic variables. They are: the monetary base adjusted for reserve requirement changes (to represent monet:-~ry policy); highemployment federal budget deficits scaled by potential GNP (to represent fiscal policy); the three-month Treasury bill rate (to represent policy concern over financial market stability); the implicit price deflator (to represent policy concern over price stability); movements in the trade-weighted average of the exchange rate (to approximate policy concern over external balance); and real GNP (to represent policy concern over real economic activity). 4 Note that, in measuring the thrust of fiscal policy, high-employment (in contrast to actual deficits are used here to filter out movements due to changes in business conditions. Recent studies in this area have also employed a similar measure [See, for example, Sheehan (1985) and Grier and Neiman (1987)]. The VAR technique has been recommended by Sims (1982) as.a reliable alternative to the conventional 'structural modelling' procedure which restricts the relationship between interrelated variables on the basis of 'arbitrary' considerations. Moreover, the results of testing for causality within a multivariate VAR system are much more general and realiable compared with the typical bivariate tests. As Sims (1980) and Lutkepohl (1982) p,~int out, bivariate tests are suspect due to the omission of variables. In addition, the VAR is preferable to a vector autoregressive moving average (VARMA) model because joint VARMA representations lack uniqueness [for further details, see Tjostheim ( 1981)]. In similar fashion to Hsiao (1981. 1982) and Caines, Keng and Sethi (1981), we utilize a lag order selection criterion (Akaike's Information Criterion, AIC) to determine the appropriate lag structure for each equation in the VAR system. Once each individual equation is specified, the six equation system is then reestimated in an Iterative Seemingly Unrelated Regressions (ISUR) framework to gain statistical efficiency. The ISUR variance-covariance matrix is then used with Wald chi-square statistics to perform the Granger-causality tests, as discussed below. ['he AIC procedure is a very general method for determining either lag orders or choosing among alternative classes of models. For a covariance stationary Gaussian process, the AIC from a mode~ with q independently adjusted parameters is defined as: "2 AIC(q)=ln aq + 2q/n,

(1)

4Data for the fiscal policy measure, prices aad real GNP were obtained from Survey of Current Business. The Federal Reserve Bank of St. Louis provided data on base money. The interest rate data was obtained from OECD Main Economic Indicators, and the Board of Governors of the Federal Reserve System provided data on the exchange rate. Tile high employment deficit data are constructed by Frank De Leeuw and Thomas Holloway and reported in Sur,:ey of Current Business. The sample period starts at 1961:1 to mark the beginning of the 'Keynesian' period in U.S. policy-making. See McMillin (1986~.

S.W. Barnhart and A.F. Darrat, Federal deficits

141

where o¢ ~r2 is the maximum likelihood estimate of the residual variance? A stationary trine series { Y,} is said to Granger-cause another stationary series {X,} if the prediction error of current X declines by using past values of Y in addition to past values of X. A tegt ef the hypothesis that { g,} does no" Granger-cause {X,} may be conducted by testing the null hypothesis that 6(L) =0 in the following equation:

X,=ot + ~( L)X, + 6( L) Yt + u,,

(2)

where//(L) and J(L) are polynomials of order h and k respectively and L is the lag operator. To test this hypothesis a Waid test statistic of the form

WT=n(~2u - ~~r2 u ,~/,,q.2 ,~

(3)

is calculated, where tru --2 is the maximum likelihood estimate of the variance of ut when the constraint t~(L)=O is imposed, and b~ is the maximum likelihood estimate of the variance of u, in the unconstrained model of eq. (2). Under the null hypothesis, the test statistic WT in (3) is distributed approximately as X~k}[see Silvey (1975)]. The theory underlying the Granger tests presumes the use of stationary data. The test results, however, are known to be sensitive to the method used to achieve stationarity [see, for example, Feige and Pearce (1979) and Kang (1985)]. In this paper, the degree of differencing needed to achieve station.arity is determined by examining the empirical autocorrelation function of each variable, a standard tool in time series analysis. This differencing method has been recommended by PIosser and Schwert (1978), and Wasserfallen (1986). The procedure used to specify each of the six equations in the VAR system is similar io that adopted by Caines, Keng and Sethi (1981). In the first step, we determine the appropria~,~- lag order of the autoregression model for each of the prefiltered variables (say for Xt) by minimizing the AIC over thirteen autoregressive lags.6 Next, the orders of bivariate regressions are determined by minimizing the AIC in a regression equation coasisting of the appropriate own lag of Xt (determined above) a~d each of thirteen lags of the remaining five variables, considered one at a time. If none of the AIC values calculated for a particular variable are smaller than the minimum AIC 5For an autoregressive model, this estimate of the residual variance is the mean square error of the one-step ahead prediction error. Therefore, when the appropriate order of the model is reached, the prediction error will be smallest. The AIC reaches a minimum because the decline in the residual variance from including the additional lag outweighs the increase iu ~he number ofparameters in the second term in eq. (1). °If the minimum AIC was obtained at lag 13, we allowed the lag length to extend by two additional quarters to ensure that the appropriate lag length was indeed 13.

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calcula:ed in the first step, that variable is said not to Granger-cause Xt and is temporarily dropped from further analysis.7 Proceed in a similar fashion adding to each subsequent step the variables with at least one AIC value that is smaller than the minimum AIC obtained in the preceding step. The process continues with trivariate (quadrivariate, etcetera) models until all variables under consideration have either been added to the model (causal) or temporarily dropped from the analysis (non-causal). Once each of the six eeuations have beei~ specified, we combined them to form a system and obtain ISUR estimates. Next, we perform tests of model adequacy by over- and under-fitting the model and by testing for white noise in the residuals. The final step in the procedure is tne additional joint testz of parameter significance using the Wald test and the ISUR covariance matrix. A final point concerning the estimation procedure is that two Chow tests of structural change were cgnducted for each equation. The first test corresponds to the switch in 1972:3 from the fixed to flexible exchange rate regimes, and the second corresponds to the change in the Federal Reserve operating strategy in 1979:3 from targeting the federal funds rate to targeting non-borrowed reserves. The stability hypothesis was rejected only for the interest rate and exchange rate equations, and then only for the date corresponding to the change in the Federal Reserve operating strategy. Consequently, these two equations were reestimated adding only those slope and intercept dummy variables that proved to be statistically significant, s

3. Results Using the VAR/AIC technique described in the previous section and the quarterly data over 1961"1 to 1984:4, the following VAR model (4) was obtained: D

m

m

Bt Ft

Rt Pl

Et Xt - = ~

aat, ( L) 0 0 a~2{L) 0 0 0 0 0 iO a~z(L)

aS~3(L) 0 a]3(L) 0 a~°(L) a~3(L)

0 0 a~,,(L) a34(L) a~4(L) a~4(L)

a~s(L) 0 ezSs(L) 0

B

t

Fr

0 a~(L) a9s(L) 0

Rt P

a~s(L)

a~6(L)

a'~s

0 m

7The w riable is only 'temporarily' dropped because the final model v.ili~ade~go diagnostic checks by liftingthat restriction. SThc F-statisticfor a structural change in the interest rate equation with 15 and 50 degrees of freedom is 1.85,and that for the exchange rate equation with 21 and 39 degrees of freedom is 1.91. The d u m m y variables that arc statisticallysignificant in the interest rate equation are the

S.W. Bare,hart and A.F. Darrat, Federal deficits

143

! elt

a2l +

e2t

a3 I +

!e3t

a4 I

e4~

as I

est

a6l m

-...a

e6t m

(4)

where B, =(1 - L)(I - L)4 In MB. MB is the monetary base adjusted for reserve requirement char~ges and measured as the averages of monthly fir:,.~res; Ft=(HDFJPGNFt), HDF is high-employment federal budget deficits, and PGNF is potential GNP; R t = ( l - L ) l n TBR. TBR is the three-month Treasury bill rate; Pt=(1-L) In GNPD. GNPD is the implicit G N P deflator; Et=(1-L)ln WEt, WE is the trade-weighted average of the exchange value of the dollar; Xt=(1-L)InRGNP. RGNP is real GNP; L is the lag operator; aik is the k lag coemcients on variable j in equation i; ai are constants; and ei are white noise error terms. The coefficient estimates are not presented here to conserve space but are :?,vailable from the authors upon request. Note, however, that these coefficient estimates are difficult to interpret due to the reduced-form nature of the model [see Sims (1980)]. It should also bt. pointed out that applying the VAR modelling technique on an equation-by-equation oas~s resulted in a model similar to, but slightly different from, model (4). When an extensive series of specification tests (similar to those reported in table 1) were perfermed within the ISUR system, certain modifications were suggested to ~mprove the original model. Initially, the specification procedure included the foilowing elements: a]3(L), aa2(L) and a~6(L), ttowever, these elements were subsequently dropped from the model as they proved to be statistically insignificant in the system. [The chi-square statistics for testing that the above elements are zero are respectively X~3)=5.25, Z~3~=3.49 and X~=0.33.] Moreover, over-fitting the model indicated that the elements a24(L) and a~4(L) should be added to the model. [The corresponding chi-square values are respectively ;(~2~=10.43 and X~,,,= 11.79.] Table 1 summarizes a series of specification tests. Tests 1 through 28 impose zero restrictions on the non-zero elements, both individually and jointly. Tests 29 through 45 ease the zero restrictions of the model. Tests 46 through 51 examine whether the fit of the model could be improved by extending the existing lag lengths (over-fitting). Finally, tests 52 throu,~h 71 third lag of the interest rate and the first, third, and tenth lags of real GNP. For the exchange rate equation, the significant dummy variables are the intercept and the fourth lag of the interest rate.

144

S.W.. Barnhart and A.F. Darrat, Federal deficits Table 1 Specification tests using system (4) as the maintained hypothesis. Hypotheses

(1) a~t(L) = 0 (2) (3) (4) (5) (6) (7) (8) (9)

Wald chi-square test statistics ~

Degrees of freedom

94.20** 34.81"* 19.88" 136.40"*

8 S 8 1

a,5s(L) = 0

18.04"*

a~3(L) = 0 a~,(L) =0 a[~(L)=O

43.24** 8.97* 93.30** 5.04* 30.40** 30.14"* 65.70** 10.21"* 5.38* 24.09** 13.08* 35.47** 4.75* 20.08** 164.31"* 23.44** 92.29** 121.11* *

5 4b 2 14b

aSia(L) = 0 a~s(L) = 0 a~2(L) = 0

a~t(L) = 0

(1o) a~(L) = 0 (11) a94s(L) = 0

(12) aiO,f~ s3~'-~ =O (13) a~4(L) = 0

(14) a~5(L) =0 (15) al6(L) = 0 (16) a~2(L) = 0 (17) %3(I-,) = u (18) a~4(L) =0 (19) a~s(L) =0 s I - -- 0 (20) a~3(L)=.,t°,r~-a "s3~1 ...... 6~{~') (21) a~,,(L) = a~4(L) = ao~4(L)= 0 (22) a~s(L)=a~s(L)=a~s(L)=a~s(L)=O (23) a~(L) = ~ ( L ) = 0 (24) al83(L) = a~ ~(L ) = 0 (25) a3Z4(L)= a[~(L)= 0 (26) a~ t ( L) = a]s( L) = 0 (27) a[ O(L) = a~4(L) = a~6(L) = 0 (28) a~2(L)=a~3(L)=a~4(L)=a~s(L)=O {29) a~2(L) =0 (30) a~4(!.)= 0 (31) ai46(L) = 0 (32) a'~:{L) = 0 (33) a~a(L)=0 (34) a~4(L) = 0 (35) a'~d L) =0 (36) a'~t(L)=O (37) a'~2(L)=O (38) a~s(L) = 0 (39) a~2(L) = 0 (40) a43(L) = 0 (41) a~6(L) = 0 (42) a~(L) = 0 (43) a~2(L) = 0 (a4) a'~l(L)=O (45) a~6(L) = 0 (46) al O(L), al o{L), al O(L) (47) a,2(L), a25(L) (48) a~3(L), a~4(L), a~63(L) (49) a ~ (L), a~,(L), at ~(L) 12 5 (50) asa(L), as4(L),a~ s{L),a~s6(L) 6 lo 3 L), a~s(L) ~51) a62(L), a63(L}, a6a(

60.44** 95.74** 35.71"* 96.3 2 ** 88.18"* 1.67 2.86 3.11 4.88 6.09. 2.06 0.99 1.58 1.48 1.31 3.34 2.74 5.78 4.36 5.28 2.39 3.40 3.88 3.26 6.44 7.43 7.74

2.09

I

3 9 II b 4 1

5 4 8 1 4

27 b 7 26 19b 16 16 10 20 b 17 4 4 4 4 4 4

4 4

4 4

4 4 4 4 4 4 4 6 4 4 6 8 8

S.W. Barnhart ard A.F. Darrat, Federal deficits

145 '

Table 1 (continued) Hypotheses

(52) a~l(L) (53) at63(L) (54) a6s(L) (55) aSs(L) {56) a[a(L) (57) aa4(L) l {58) a~6(L) (59) aL,{L) (60) a~s{L) (61) aSs3(L) (62) a2s4(L) (63) a3s6(L)

(64) a~z(L) (65) a~,s(L) (66) a6Zs(L)

(67) a 6l l(L), al63(L), al6s(L) (68) a~a(L),a~4(L),a~6(L) (69) a~4(L),a7s(L) (70) aass(L),a~4(L),a~6(L) (71) a~2(L),a63(L),aZ6s(L)

Wald chi-square test statistics a

Degrees of freedom

15.04"* 7.21" 4.94c 15.79"* 43.18"*

2 2 2 2 3b

8.71"* 26.33** 16.32"* 9.28** 12.29"* 7.44** 15.20"* 10.28"*

1 3b 2 2 2 2 2 2

i i.93"* 16.43"*

2 2

28.07** 86.84** 32.51"* 37.16"* 34.10"*

6 sb 4 6 6

a, indicates rejection of the hypothesis at the 5 percent level of significance, while ** indicates rejection of the hypothesis at the 1 percent level of significance. bThe degrees of freedom are increased due to the inclusion of some dummy variables to correct for possible coefficient instability (see section 2 for details). CThis chi-square value achieves significance at the 10 percent level.

assess whether the improvement in the fit of the model could be gained by shortening the existing lag lengths (under-fitting). All of the Wald test statistics reported in table 1 consistently indicate that the specification of model (4) is an adequate representation of the data. Moreover, two additional diagnostic checks were finally employed to test for residual white, noise in each equation; namely, the modified Ljung-Box and the Kolmogorov-Smirnov tests. Both tests could not reject the null hypothesis of white noise residuals? We come now to analyzing the causal inferences implied by model (4) and the associated tests displayed in table 1. Of particular importance is the finding that federal deficits and base money are not causally related. Specifically, the proposition that federal deficits do not cause base money cannot be rejec~,ed at the 5 percent level, as is evident in test 29 in table 1. The reverse hypothesis that base money does not cause federal deficits cannot be rejected either according to test 32. These results are thus consistent with the view that monetary and fiscal policies are independent of 9To economize on space, the details of these tests are omitted here but are available from the authors upon request.

146

S.W. Barnhart and A.F. Darrat, Federal deficits

each other. This finding supports, at least in spirit, the evidence reported recently by Dwyer (1982), Joines (1985), Sheehan (1985), Protopapadakis and Siegel (1987) and Barnhart and Darrat (1988) though none of these studies were performed within a VAR-causality framework. The causal linkages between each of the two policy variables and the other macro variables of the model are also of interest. Test statistic 16 suggests that federal deficits exert a causal impact upon real GNP. One might then argue that fiscal policy could be seen as a tool for stabilizing real economic activity. Stephens (1980a, b) provides some theoretical rationale for this finding, while Laumas and McMillin (1984) and Darrat (1986) present supporting empirical evidence using a different methodology. Test 35 suggests the absence of any significant feedbacks frora real output to the deficit measure which, together wifl-, the earlier finding, imply that deficits could be treated as an exogenous variable in real output equations. As to the remaining variables, the results show that iederal deficits have no causal impact on interest rates (test 37), on prices (test 39), nor on er,ehange rates (test 43). The finding that deficits do not cause changes in interest rates is consistent with evidence reported recently by Hoelscher (1983) and Evans (1985, 1986, 1987). As the work of Darby (1979) suggests, however, the absence of a significant causal effect of federal deficits on interest rates does not necessarily support the Ricardian equivalence proposition. For example, in contemporary open economies, budget deficits could be fully or partially financed by an inflow of capital from abroad. Thus, even when the Ricardian proposition is incorrect and government bonds do represent private wealth, the process of foreign financing coald weaken any effect of budget deficits on domestic interest rates. Indeed, this seems to be the case over the estimation period because federal deficits are causally prior to real GNP, although deficits have no causal effect on interest rates. The results from the federal deficit equation reveal that, aside from past movements in the deficit measure, only changes in exchange rates cause significant movements in fiscal policy over the estimation period. In other words, it seems that there is little concern on the part of the fiscal authorities for other policy goals such as financial market stability or inflation. Taken together, the results imply that federal deficits are causally independent of both interest rates and price3. For the monetary policy variable, the results or table 1 show tha~ base money has a causal influence only on prices (test 9), without significant feedback (test 30). This finding supports the typical treatment of base money as an exogenous variable in an inflation equation and attests ~o the importance of moaetary policy as a key anti-inflation measure. However, the results further suggest that base money does not cause interest rates (~est 36), does not cause exchange rates (~est 42), and does not cause real output (test 44). The finding tha~ base money does not cause changes in interest r a~es may

S.W. Barnhart and A.F. Darrat, Federal deficits

147

seem surprising given the dominant role usually attributed to monetary policy in determining interest rates. Note, however, that the results suggest that inflation unidirectionally causes changes in interest rates (test 7 and 40) in accordance with the familiar Fisher effect. Thus, base money can still influence interest rates, albeit indirectly, through its causal influence on inflation. Base money can also influence exchange rates and real output indirectly through the price channel. Test 18 indicates that inflation (resulting primarily from changes in monetary base) causes changes in real output and, interestingly, the sign of the causal effect (not shown here ~, is negative. This raises the possibility that the Phillips' curve is positively sloped as expounded by Friedman (1977) in his Nobel Lecture. It is also worth noting that tests 12 and 38 suggest that interest rates cause changes in exchange rates without feedback. This result supports the conventional view as elaborated in Dornbusch (1976), and affirms the regression evidence reported in Hutchison and Pigott (1984), among others. Finally, the estimated base morley equation shows that, aside from lagged base-money growth rates, financial market stability and movements in the exchange rate appear to be the major factors shaping monetary policy moves over the estimation period.

4. Concluding remarks This article employs a vector autoregressive (VAR) modelling technique to reexamine the important accommodation hypothesis that the Federal Reserve has tended to expand money growth in response to higher federal deficits. A six variable VAR model is estimated consisting of the highemployment federal deficit scaled by potential GNP, monetary base, shortterm interest rates, prices, real output, and exchange rates. Given their theoretical relation to both fiscal and monetary policy, the latter four variables are included in the analysis to avoid the 'omission of variables' problem. In contrast to the typical correlation-based analysis used in most previous studies in this area, the VAR technique is capable of discriminating among four alternative hypotheses. These are: (a) that federal deficits cause base money (the accommodation hypothesis), (b) that base money causes federal deficits, (c) that causali~ty between the two policy variables is bidirectional, and (d) that the two policy variables are causally independent. A s~g,~ific~nt correlation between federal deficits and base money is consistent with any of these four hypotheses. The VAR results cota~sistently reject the accommodation hypothesis and indicate that federal deficits and base money are causally independent. Therefore, our analysis supports the view that monetary policy is independent of fiscal policy. The results further indicate the presence of z significant unidirectional causal influence from federal deficits to real output, and from

148

S.W. Barnhart and A.F. Darrm, Federal deficits

base money to prices. The deficit measure has no causal effect on prices, on exchange rates, or on interest rates. This last finding could perhaps explain the lack of relationship between federal deficits and base money. With the exception of prices, our results suggest that base money does not cause any of the macro variables in the model. However, by virtue of its causal influence on prices, base money can still indirectly cause changes in interest rates, in exchange rates, and in real output. Interestingly, the results also reveal that prices are causally prior to real output, and that the causal effect of prices is negative. This finding supports Friedman's conjecture that the Phillips curve exists though with a positive slope.

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