- Email: [email protected]
The relationship between government deficits, money growthm and inflation
FRANCIS W. AHKING STEPHEN M. MILLER University
of
Connecticut
The Relationship Between Government Deficits, Money Growth, and Inflation* We model the time-series relationship between Federal government deficits, basemoney growth, and inflation as a trivariate autoregressive process. The technique is a generalization of Hsiao’s (1979; 1981) b ivariate autoregressive modeling method, but also incorporates several recent contributions by Caines, Keng, and Sethi (1981) and Lutkepohl (1982). The results indicate that for the 196Os, both government deficits and inflation are econometrically exogenous. But, for the 1950s and the 197Os, government deficits, money growth, and inflation are all causally related.
1. Introduction There is a “popular view” among policy makers that government deficits are inflationary. Most economists, however, subscribe to the position that inflation is a monetary phenomenon, at least in the long run. Friedman (1968) argued that the monetary authorities can control the inflation rate, especially in the long run, with the control of the money supply. Deficits can lead to inflation, but only to the extent that they are monetized. Thus, money-financed deficits are inflationary; bond-financed deficits need not be.’ Whether bond-financed deficits are inflationary or not depends upon the current approach to policy of the monetary authorities. If they are stabilizing (pegging) interest rates, then bond-financed deficits are inflationary. That is, bond sales push up interest rates and lower bond prices. Because the monetary authorities are stabilizing interest rates, this calls forth an expansion in the money supply that ultimately leads to rising prices. Sargent and Wallace (1981) questioned Recently, however, whether it is possible that with continuing deficits, monetary au*The authors are assistant professor and professor of economics, respectively, at the University of Connecticut. Comments of two anonymous referees significantly improved the paper; we alone are responsible for any remaining errors. We also acknowledge the support of the University of Connecticut Computer Center. ‘Buchanan and Wagner (1977), however, argued that government deficits will be monetized due to political pressure; the monetary authorities do not have a true choice.
Journal Copyright
of Macroeconomics, 0 1986 by Wayne
Fall 1985, Vol. State University
7, No. 4, Press.
pp.
447-467
447
rrancas W. Ahking
and Stephen M. Miller
thorities will never be obliged to monetize a portion of the government debt. The reason is that in a long-run growth context, the private sector’s demand for government bonds imposes an effective constraint on the degree of independence between monetary and fiscal policy. The ultimate question is who, monetary or fiscal authorities, dominates policy making. Assume that the fiscal authorities dominate and that they are expanding the stock of government indebtedness-both privately and publicly [i.e., the Federal Reserve (Fed)] held-at a rate faster than the monetary authorities are expanding base money. That is, the Fed is adding to its holding of government bonds less rapidly than the fiscal authorities are expanding total debt. Thus, privately held government debt is growing more rapidly than base money. This implies a portfolio shift into privately held government debt; the private sector will absorb this increase only as interest rates on government debt rise. This cannot continue forever. Either interest rates will become too high and/ or the demand for government debt will become perfectly inelastic. At this point, monetary policy must accommodate the needs of fiscal policy. If the Fed dominates, then it can control inflation in the long run. It now falls on the fiscal authorities to structure their revenue and expenditure patterns to be consistent with monetary policy. That is, given the private sector’s demand for government bonds, the fiscal authorities cannot on a continuing basis expand the stock of government indebtedness more rapidly than the growth in base money. An alternative view, expounded by Miller (1983), argues that government deficits are necessarily inflationary irrespective of whether the deficits are monetized or not. According to Miller, deficit policy leads to inflation through three channels. The Fed might be forced into monetary accommodation of the deficits as argued by Sargent and Wallace (1981). But, even if the Fed does not monetize the deficit, deficits are still inflationary through private monetization and/ or crowding out. That is, nonmonetized deficits lead to higher interest rates. Higher interest rates crowd out private investment, reduce the rate of growth of real output, and with a given money supply, lead to higher prices. Higher interest rates also spur the financial sector to innovate in the payment system and makes government bonds more substitutable for money.’ ‘In do not
448
an earlier article, Miller imply a future tax liability
(1980) argued that current to society. The government
bond-financed deficits will issue more bonds
Government
Deficits,
Money
Growth,
Inflation
Although most discussions on the relationship between government deficits and inflation focus on the role of deficits in causing inflation, the “fiscal-dividend” hypothesis argues that inflation leads to adjustments in the government deficit. That is, in a progressive tax system, inflation pushes tax payers into higher marginal tax brackets. Thus, if the government holds the ratio of government expenditure to gross national product constant, then inflation should lower (increase) the deficit (surplus). This allows legislators to simultaneously reduce tax rates and expand government expenditure. Thus, inflation leads to changes in government deficits. Barro (1979) h as also offered a theory of public debt that bears on the issue of (anticipated) inflation and government deficits. In a nutshell, the model assumes that the objective of government is to ‘1 , minimize the present value of revenue-raising costs . . .” [(%79), p. 9441. This assumption produces the conclusion that the ratios of real government expenditure to real income and real tax revenue to real income are constant over time. The consideration of inflation and the government budget constraint demonstrates that increases in anticipated inflation lead to larger government deficits.3 The theoretical arguments suggest that government deficits can be inflationary while at the same time they can also be the result of inflation. Empirical studies, however, have not yet reached a consensus. Barro (1978), Niskanen (1978), and McMillin and Beard (1982) found no evidence that government deficits are systematically related to money growth, and hence, inflation. On the other hand, Levy (1981), Hamburger and Zwich (1981, 1982), Dewald (1982), Dwyer (1982), Allen and Smith (1983), and Hoffman, Low, and Reineberg (1983) found some evidence that government deficits are systematically related to money growth or inflation. The inconclusive empirical evidence may be due to a number
to cover the maturing indebtedness as well as any new addition to total indebtedness. Hence, since government bonds are not backed by tangible assets or by future taxes, the bonds are in essence a part of the money supply. Cox (undated) argued analogously that if interest payments on government bonds are financed by deficits (bonds are infinitely lived assets), then government bonds are net nominal wealth. An increase in government debt will therefore have the same effect on the price level as an increase in the money supply. 3It should also be mentioned that both Siegel (1979) and Jump (1980) have noted similar relationships between inflation and government deficits. Their main concern, however, was not the causal relationship between inflation and government deficits.
449
of estimation problems. Researchers, with the exception of Dwyer (1982) and Hof&n an, Low, and Reineberg (1983),4 have estimated monetary reaction functions, Barre’s (1978) specification being the most popular. Barro’s reaction function has been criticized extensively;’ but, more generally, all monetary reaction functions are subject to the problem of being a joint test of the reaction-function specification and the existence of a relationship between deficits, money growth, and inflation. Since general agreement on the appropriate monetary reaction function does not exist, any conclusions concerning the relationship between deficits, money growth, and inflation should be considered tentative. A further problem with the existing empirical literature, with the exception of Levy (1981) and Dwyer (1982), is that conclusions are based on single-equation estimates. The general approach is to include a deficit variable in a monetary reaction function. The maintained assumption is that deficits are exogenous in the reaction function; their effect on inflation is implicit (i.e., if monetized, then deficits are necessarily inflationary). We argue that the single-equation approach is too restrictive when examining the links between deficits, money growth, and inflation. For example, the possibility that there may be a direct effect of deficits on inflation, as argued by Miller (1983), or that changes in deficits may be a result of inbetween flation are ruled out, a priori6 In sum, the relationship deficits, money growth, and inflation should be examined in a system-of-equations framework. In this paper, we examine the relationships between deficits, money growth, and inflation in a trivariate autoregressive fi-amework, thus allowing us to treat each variable as endogenous within a three-equation system. In addition to the obvious advantage of not imposing a priori exogeneity assumptions, this framework also
4Dwyer’s empirical methodology was different from the empirical literature cited in that he used the vector-autoregressive approach. He found that inflation was important in explaining deficits, but deficits were not important in explaining inflation, the growth of nominal GNP, the growth rate of the money stock, or the level of interest rates. Hoffman, Low, and Reineberg regressed money growth on future and past deficits. sSee Allen and Smith [(1983), p. 898, Footnote 31 for a partial list of researchers who are critical of Barro’s monetary reaction function. ‘Niskanen (1978) did develop a monetary reaction function including the deficit as an exogenous variable and a reduced-form inflation equation including both the deficit and lagged money growth. He estimated his two equations, however, as single equations.
Government
Deficits,
Money
Growth,
Inflation
relieves us of the burden of having to specify the structural relationships between deficits, money growth, and inflation. This is because the trivariate autoregressive model can be interpreted as a general system of reduced-form equations for the three variables. Yet, within this framework, meaningful economic hypotheses can be tested. The remainder of the paper is as follows. Section 2 discusses the empirical methodology and the data; Section 3 presents the empirical results; and Section 4 is the conclusion.
2. Empirical
Methodology
and Data
A trivariate autoregressive and inflation is as follows:
model for deficits,
money
growth,
where D,, H,, and Pt are deficits, money growth, and inflation, respectively; a, b, and c are constants; L is the lag operator such, that for any variable X,, tiX, = Xtj; a,(L), hi(L), and C,(L), i = 1, 2, and 3, are polynomials in the lag operator [e.g., al(L) = E~zlaU(Lj)]; and Ult,U2tr and U,, are innovations. The innovations are zero-mean whitenoise stochastic processes with constant covariances. The literature suggests several methods for identifying the system of Equations (1). Lutkepohl (1982) assumed the autoregressive lags for all the variables to be identical and determined the optimal system lag length by using Akaike’s Information Criterion (AIC) after searching over a lag length from one to a maximum of M. After determining the optimal system lag length, Lutkepohl conducted formal statistical tests to determine whether any of the off-diagonal operators can be excluded. Lutkepohl’s method is relatively inexpensive to implement. But, the assumption of equal lag lengths for all variables is rather restrictive. Caines, Keng, and Sethi (1981) modeled a system of iV(>2) variables in stages. First, bivariate autoregressive models are estimated for each ordered pair of variables. The two variables in each bivariate autoregressive process are assumed to have equal lag lengths, and the optimal lag length is determined by Akaike’s Final Prediction Error (FPE) criterion, which is equivalent to Lutkepohl’s 451
AIC, after searching over lag length from one to K. The objective of this stage is to determine the relationships between the two variables, i.e., endogeneity, exogeneity, or independence, and to determine the order in which variables should be entered into higherdimension multivariate autoregressive processes. Second, information obtained from the bivariate analysis is used to build a multivariate autoregressive process, and, finally, hypothesis testing is performed. The modeling strategy of Caines, Keng, and Sethi has certain appeal. The bivariate autoregressive modeling reduces the computational burden for later multivariate analysis. The assumption of equal lag lengths for the two variables in a given bivariate autoregressive process, however, is rather restrictive. Furthermore, the determination of the relationship between two variables at the bivariate modeling stage may not be appropriate. As Lutkepohl (1982) has pointed out, a low-dimension subprocess may not contain sufficient information about the structure of a higher-dimension process. Our empirical methodology is essentially a trivariate extension of Hsiao’s (1979; 1981) b ivariate autoregressive modeling method. We do incorporate, however, several features from Caines, Keng, and Sethi (1981) and Lutkepohl (1982). In the first-stage modeling, we treat each equation in (1) independently and, thus, all estimations use ordinary least squares (OLS). Three steps are involved in the first stage for each equation in (1). The modeling of the deficit equation, for example, would P-+ proceed as follows: (i) Search over a lag length from one to a maximum of M and determine the optimal lag length for the univariate autoregressive process for D by means of Akaike’s minimum FPE criterion. Denote the optimal lag length for D as m and the minimum FPE as FPEo(m). (ii) Maintaining the autoregressive lag for D at m, construct autoregressive processes for (Dt, H,) and (Dl, PJ by varying the lag length of H and P from one to M and compute the FPEs at each lag. Use the minimum FPEs for the autoregressive processes for (Dt, H,) and (D,, Pt) to determine the optimal lag lengths for H and P which we designate as n and r, respectively. Denote the minimum FPEs as FPEn,H(m, n) and FPEn,r(m, r), respectively. (iii) To determine the order that H and P should enter the D 452
equation, identify the minimum of FPE&m, n) and FPE,,p(m, r). Assume that FPE&vz, n) is smaller (i.e., H is ranked as more important than P in the D equation).7 Maintain the lag lengths for D and H at m and n, respectively; construct an autoregressive model for (D,, H,, Pt) by varying the lag length of P from one to M; and compute FPEs at each lag. Determine the optimal lag length for P by the minimum FPE criterion. The second-stage modeling involves the analysis of the system of Equations (1). It proceeds in three steps as follows: (iv) Pool the single equations for D, H, and P as determined in the first stage to give a tentative identification for the system of Equations (1). To obtain asymptotically efficient estimates, estimate the system using three-stage least squares to account for possible correlations between the innovations. (v) Perform diagnostic checks, treating the tentatively identified system as the maintained hypothesis. Use the tests in this step to determine if any of the off-diagonal operators in (1) can be excluded. (vi) Identify the final model based on the results in step (v). Finally, using the final model as the maintained hypothesis, test the nonzero off-diagonal operators of (1) to determine the relationships between D, H, and P, if any. The two-stage multistepped approach outlined above is used in our empirical analysis. Before turning to the results, we will briefly discuss our data base. A list of data sources and a description of how the variables were constructed are contained in the Appendix. The variables employed in the econometric analysis are as follows: P E annual rate of inflation; H = annual rate of growth of base money; and D = annual rate of growth of privately-held government debt. These variables differ from most previous studies in several respects. First, we employ base money rather than the money sup‘This method of ranking is equivalent to ordering the variables by their specific gravity [see Gaines, Keng, and Sethi (198l)l. Note, however, that we differ from Hsaio (1979, 1981) and Caines, Keng, and Sethi (1981) in that we not exclude any variable from further consideration at this stage.
453
I rU,~~~~YV.nntczng ancl Stephen M. Miller ply. The relationship between deficits and money growth is best addressed, in our opinion, by examining base money. That is, if the Fed monetizes the deficit, it does so by expanding base money. Moreover, base money is linked to the money stock through the banking multiplier. If the multiplier is stable, then base-money and money-supply growth should be highly correlated. Second, our measure of the government deficit is computed as the annual rate of change of privately held public-debt securities, including the debt held by the Fed.’ The national-income accounts measure of the deficit has been used frequently [e.g., Barro, (1978)]. Its use in the present context is problematic because it is on an accrual rather than a cash-flow basis. The Fed when altering base money does so through open-market operations. Thus, whether or not the Fed monetizes the deficit depends upon whether it purchases government securities as the Treasury sells them to the private sector to finance a cash-flow imbalance. The change in privately held public debt is on a cash-flow basis; it also includes debt financing of off-budget items. The analysis uses post-WWII quarterly data. The sample extends from 1947i to 198Oiii. Since seasonally unadjusted data are preferred in time-series studies, the data are not seasonally adjusted. We do include, however, seasonal dummy variables. This is equivalent to assuming that the seasonahty is deterministic, which is a debatable assumption. But, even if we are willing to explicitly analyze the deterministic and stochastic causes of seasonality, it is not clear whether an optimal, or even an adequate, seasonal adjustment procedure can be constructed.’ Thus, it is not obvious whether the use of seasonal dummies is necessarily worse, or better, than other seasonal adjustment procedures. It is required that the time series of D, H, and P are stationary. Since the variables are already rates of change, this has the effect of removing any trend from the data. Additional analysis of the autocorrelation functions for D, H, and P revealed some residual trend in P with an autocorrelation coefficient at lag one of 0.65. This is significantly different from unity, however. First differencing
‘The time series on’ privately held public-debt securities used is equivalent to the series used by Levy (1981) and Dwyer (1982) except for some minor adjustments described in the Appendix. ‘See the volume edited by Zellner (1978), especially the two papers by Granger and Wallis for a discussion of the problems with seasonal adjustment of economic time-series data.
454
Government
Deficits,
Money Growth,
Inflation
thus does not appear appropriate. Therefore, we included a linear time trend in each equation to account for any residual trend. We present estimates of the system of Equations (1) for three time periods: 19471 to 196Oiv, 1961i to 197Oiv, and 1971i to 1980iii. This allows us to examine whether or not the relationships between deficits, money growth, and inflation are stable over time. The break in 1961i is chosen to correspond roughly to what Hamburger and Zwich (1981) called the “Keynesian” period and the break at 1971i is to separate the unusual events that occurred during the 1970s (e.g., the wage-price controls, the oil-price shocks, and the collapse of the Bretten Woods system). There is no reason to expect the final model identified for one period to be the same for another period;” thus, we follow the six-step method described above to identify a final model for each period.
3. Empirical Results Table 1 presents the summary statistics from the single-equation estimations.” The optimal lag length for each variable is given in parentheses next to the variable. In each case, the variable listed last was the variable for which a search over lagged values was conducted. Variables preceeding, if any, had their lag length determined in the previous step(s). The single-equation results [i.e., steps (i) to (iii)] lead us to
“In fact, Levy (1981), using a quarterly reaction-function model, and Allen and Smith (1983), using a quarterly version of the basic Barro specification, reported structural breaks that correspond roughly to our break points. Both approaches identified break points one at a time. Thus, the identification of one structural break required the assumption of structural stability across the second break point in all the tests. In the only exception, Allen and Smith used post-196lii data to identify the second break point after identifying 1961ii as the first break point; they did use data through 1974io, however, to identify the first break. Levy used the full sample in all his tests for structural breaks. We did not undertake a search for structural breaks due to the high cost of repeating our six-step methodology. “A maximum order of twelve is assumed for the autoregressive process and given the calculation of rates of change, the sample for the first period begins at 1959ii. Thus, the first sample period includes some observations from the preTreasury-Federal-Reserve-Accord period. Degrees-of-freedom considerations led us to include the pre-Accord data. Also, Friedman (1982) argues that there was no significant change in FED behavior in the period immediately after the Accord. Nevertheless, alter obtaining the single-equation results (i.e., steps (i) to (iii) completed), we redid steps (iv) to (vi) using data from 1953i to 1960io. The same model was identified and our conclusions are unaltered.
455
1.
NOTFX experienced
D(12)
D(2)
H(l)
H(l) P(Q) H(l) P(Q)D(Q) P(l) P(1) DO) P(l) H(5) P(l) H(5) D(7)
H(l)
D(Q)H(1) D(Q)P(l) D(Q)P(l)
values is the
and Lags
1961i-197Oiv
indicate the number of lagged values from one to twelve. FPE
1.051 0.983 0.992 0.974 0.577 0.364
1.651 1.686 1.700 1.237 1.307
D(Q)
Variables
Lag Lengths
FPE X 10M3 1.779
Numbers in parentheses a search over lagged
D(l) Wll) H(ll)
DO)
P(6)
H(l) H(l) PO) P(l) P(1) P(1)
P(6)
HO) PW H(l) pw D(l)
and Lags
195Oii-lQ6Oiv
FPEs and Optimal
D(l) D(l) DO) H(l) WV
Variables D(l)
TABLE
of the variable. minimum value
0.177 0.179 0.182 0.189
0.350
0.385
2.819 2.791 2.868 0.421 0.460
FPE x lob3 2.730
In each over the
case, twelve
last
0.534
0.511 0.517 0.776 0.805 0.814
2.416 1.758 1.712 0.561 0.596
has
FPE x 10e3 2.292
the variable listed lagged values.
W9 P(8) D(7)
H(l) P(5) P(5) H(l) D(2)
and Lags
D(l) HO) P(8) DO) WW
H(1) H(1) f’(8) P(8) W3)
D(l) D(l) D(l) H(l)
Variables DO)
1971i-1980iii
i g$ -
5 s ;
:
i : 2 E E
Government identify tentatively three periods.
Deficits,
the following
Period:
Money Growth,
matrices
of lag operators
Inflution for the
195Oii-1960iv
(2)
Period:
1961i-1970iv
(3)
Period:
1971i-1980iii
(4)
where lag.
a superscript
denotes
the optimal
order
of the polynomial
Step (iv) in the identification process is to estimate the tentatively identified system with three-stage least squares; step (v) performs diagnostic checks that test whether any of the off-diagonal operators of (2), (3), and (4) can be excluded. F-statistics are used for the diagnostic tests [see Theil (1971), pp. 312-141. We tested nine hypotheses for each period and summary statistics are reported in Table 2. For the 1950ii to 1960iv period, the results suggest that none of the off-diagonal operators can be excluded. The two operators b:(L) and $‘(L) are not significantly different from zero individually. Jointly, however, they are significantly different from zero at the 10% level. We conducted two additional diagnostic checks: (i) Constrain b:(L) to zero in (2) .and test the hypothesis that $(L) equals zero; and (ii) constrain c:O(L) to zero and test the hypothesis that b&L) equals zero. In both cases, the hypothesis can be rejected at the 10% level. It appears that H and P are highly correlated and that this explains the seeming inconsistency between the joint. and 457
Francis W. Ahking TABLE
2.
and Stephen M. Miller
F-statistics
for Zero Restrictions F-statistic
Hypothesis b,(L) = c,(L) b,(L) c,(L) az(L) = q(L) at(L) q(L) a,(L) = b3(L) a,(L) b&)
= = = = = = = = =
0 0 0 0 0 0 0 0 0
195Oii-196Oiu
.2961i-197Oiv
1971i-198Oiii
1.75** 1.24 1.43 3.05* 2.99** 2.85* 9.77* 5.11* 10.11*
0.76 0.70 0.92 4.36* 2.82* 5.07* 1.37 1.28 2.77*
2.77* 1.67 3.32* 2.37* 1.46 2.75* 3.02* 11.58* 3.14*
NOTE: The maintained hypothesis for the F-statistics (4) for columns 1, 2, and 3, respectively. *The hypothesis can be rejected at the 5% level. **The hypothesis can be rejected at the 10% level.
are
matrices
(2),
(3),
and
individual tests. The diagnostic tests, in sum, imply the retention of (2) as the final model specification for the first period. For the 1961i to 197&u period, the results in Table 2 suggest that &:(I.$, c#J, and a&) all equal zero. But, when these operators are constrained to zero in (3), further diagnostic checks reveal that the hypothesis b@) equals zero cannot be rejected at the 10% level. This result, however, is not entirely surprising for two reasons. First, from Table 1, we see that the lowest FPE in the set of inflation equations occurs for the univariate specification. Second, from Table 2, we cannot reject the joint hypothesis that both a:(L) and b!(L) equal zero at the 10% level. The hypothesis that wJ> 4(L)> d(L), and b@) are jointly zero (i.e., the test statistic is F = 1.28) cannot be rejected at the 10% level. Thus, we conclude that the final model for the 1961i to 19i’Oiu period is as follows:
For the period 1971i to 198Oiii, the results in Table 2 suggest that both b:(L) and &?J e q ua 1 zero. The hypothesis that these two operators are jointly zero in (4) (i.e., the test statistic is F = 1.48) 458
Government
Deficits,
Money
Growth,
cannot be rejected at the 10% level. Thus, for the third final model is given as:
(;
bl&
Znflation period,
the
(4’)
ii).
So far, we have been deliberately overfitting the models initially and using a series of diagnostic checks to arrive at the final models. As a last check of the adequacy of the final models, we sequentially over-fitted the final models by adding one additional lag and then two additional lags to each variable, including those variables that were not significantly different from zero in the final models. Next, we sequentially underfitted the final models with one lag and then two lags. In all cases with overfitting, the F-statistics indicated that the extra lags were not significantly different from zero at the 10% level. On the other hand, in all the underfitting cases, the F-statistics indicated that the omitted lags were significantly different from zero at the 5% level. The results, available from the authors upon request, reveal no inadequacy in the final models. Using (2), (3’), and (4’) as the final models, Table 3 presents the results of the various tests of the relationships between D, H, TABLE
3.
Tests of the Final
Models F-statistics
Hypothesis b,(L) = c,(L) b,(L) c,(L) a&) = q(L) a&) q(L) a,(L) = b&J a&) ML) (4’)
195Oii-1960iv = = = = = = = = =
0 0 0 0 0 0 0 0 0
1.75** 1.24 1.43 3.05* 2.99** 2.85” 9.77* 5.11* 10.11*
1961i-1970iv
1971i-198Oiii
3.17* 5.66* 6.55* 3.50*
NOTE: The maintained hypothesis for the F-statistics for columns 1, 2, and 3, respectively. *The hypothesis can be rejected at the 5% level. **The hypothesis can be rejected at the 10% level.
2.37* 3.59* 12.59* 3.75* are
matrices
(2),
(3’),
and
459
Francis W. Ahking
and Stephen M. Miller
and P. The results for the I95Oii to 1960iu period are unchanged from Table 2 but are included for completeness. For the latter two periods, the tests confirm (3’) and (4’) as the final models. The results imply that the causal relationships between D, H, and P have not been stable for the three periods.r2 The 1950s present the most complex set of interactions between the variables generated in the three periods. We find that all variables are directly causally related to each other. The results for the 1970s differ from those of the 1950s only in that there is no evidence of direct temporal causality between government deficits and base-money growth. There is, however, two-way causality between deficits and basemoney growth via the inflation rate (i.e., indirect causality). Thus, in the 1950s and the 197Os, none of the three variables is exogenous. In contrast, the results for the 1960s identify both government deficits and inflation as best represented by univariate models i.e., they are exogenous), Base-money growth, however, is caused ( by both deficits and inflation. Comparing the three periods yields the following set of consistent results. First, inflation causes base-money growth in all three periods. Second, government deficits cause base-money growth in all three periods, but the causal relationship is indirect through the inflation rate in the 1970s. Third, for the 1950s and the 197Os, twoway causality is indicated between government deficits and inflation, between base-money growth and inflation, and between government deficits and base-money growth. Thus, in these two periods, both government deficits and base-money growth cause inflation; the effect of the deficit on inflation, moreover, is direct and independent of the effect of money growth on inflation. In contrast, the 1960s indicate that inflation is best represented by a univariate model. On an equation-by-equation basis, the base-money growth equations come closest to exhibiting a consistent pattern across the three periods. This is interesting because base money is directly affected by the general controls of monetary policy, including, most importantly, open-market operations. Thus, the causality uncovered in these equations is probably a reflection of monetary policy. The
‘*It should be emphasized that temporal causality. That is, the future cannot cause the past [See has provided a detailed criticism a personal viewpoint on causality 480
the concept of causality used here is &anger’s past and present can cause the future, but the Granger (1980), p. 330, Axiom A]. Zellner (1979) of C&anger causality, but see Granger (1980) for testing.
Government TABLE
4.
Variance
Deficits,
Money
Growth,
Inflation
Decomposition
Time Period
Dependent Variableb
195&i-196&u 196%197Oiu 197%198Oiii
Percentage of Dependent Variance Explained
Variable’s by” Unexplained
D
H
P
S
D(H, P) D D
0.2 20.6 31.7
4.8 -
13.9 10.2
58.3 51.8 43.6
22.8 27.6 14.5
195Oii-196Oiv 1961i-197Oiu 1971i-198Oiii
H(P, D) H(P, D) H
0.9 1.0 -
0.8 0.0 0.0
5.5 1.9 3.3
85.4 96.1 92.6
7.4 1.0 4.1
WOii-196% 1961i-1970iv 1971i-198Oiii
P(H, D) P P(D, H)
18.1 0.6
50.3 17.6
10.3 0.3 32.9
14.2 69.5 40.1
7.1 30.2 8.8
‘S includes a constant, a time trend, and seasonal dummy variables; D, H and P are defined in the Appendix. The columns indicate the percentage of the dependent variable’s variance (e.g., variance of D) explained by adding sequentially S, lagged values of the dependent variable, and lagged values of the other significant variables (e.g., H and P); the last variables are added in the order determined in Table 1. An entry of 0.0 means that the reduction in variance was less than 0.05%. A dash occurs for those variables that are not significant in the previous analysis. Wariables in parentheses indicate the order that they are added in the variance decomposition. For example, D(H, P) means that lagged values of H are added prior to lagged values of P in the variance decomposition.
results suggest that monetary policy has responded to both inflation and government deficits, although the latter ceases its direct effect during the 1970s.r3 Our empirical results so far only provide qualitative information on the causal relationships between D, H, and P. Further insight is obtained by decomposing the variance of the dependent variable into components explainable by significant explanatory variables. The results are reported in Table 4.14 IsThese results are generally consistent with Levy’s (1981) results in a reactionfunction framework. He found that both expected inflation, proxied by a distributed lag of actual inflation, and privately held government debt affected base money. “Our variance decomposition method is different from that employed by Sims (1980; 1982). where the variance of the n-period ahead forecast errors of the dependent variable is decomposed into components attributable to the innovations uf the explanatory variables. Since the residuals are correlated across equations, Sims’s technique requires that they are first transformed into orthogonal form. To do this,
461
rrancis
W. Ahking
and Stephen
M. Miller
Several findings are noteworthy. First, 58% to 75% of The variance of the deficit is explainable by its own lagged values and by the vector of variables in S, which consists of a constant, a linear time trend and three seasonal dummy variables.- Of the remaining two explanatory variables, inflation is quantitatively more important than base-money growth in explaining the variations in the deficit. Second, between 85% and 96% of the variance in base-money growth is accounted for by the variables in S alone, while its own lagged values, deficits, and inflation accounted for a small fraction of the variance. Finally, other than its own lagged values and the variables in S, the most important explanatory variable of inflation is basemoney growth. The variance decomposition results appear to explain partially the differences in the autoregressive results across the three time periods. Thus, although deficits are caused by base-money growth only in the 195Os, its effect on deficits is quantitatively small. Similarly, deficits cause base-money growth in the 1950s and the 1960s but not in the 1970s. Again, the quantitative effect of deficits on base-money growth in these two time periods is small. Finally, deficits cause inflation in the 1950s and the 197Os, but not in the 1960s. The quantitative effect of deficits on inflation is small in the 197Os, but not in the 1950s. In contrast, inflation causes deficits in the 1950s and the 197Os, but not in the 1960s. Here the effects are quantitatively large. Also, deficits and base-money growth do not cause inflation in the 1960s but have quantitatively large effects in
(Note
cont.
from
p. 461)
the system of equations is triangularized by selecting a particular order in which the variables are entered into the system with the variables placed in the lower order included as regressors contemporaneous values of variables placed in the higher order [see Sims (1980)]. The selection of the ordering, however, is arbitrary and amounts to imposing ad hoc identifying restrictions to achieve a recursive system, which is quite contrary to the spirit of autoregressive modeling. Furthermore, the variance decomposition results could be quite sensitive to the particular ordering of the variables chosen. Our variance decomposition method, we believe, provides similar information as Sims’s method but without having to first triangularize the system of equations. Our approach also requires the selection of an ordering of the explanatory variables. The results in Table 1, however, provide a natural selection of ordering. There are two shortcomings in our method, however. First, we do not incorporate any information about contemporaneous correlations among the residuals of the system’s equations. Second, because we are not examining forecast errors, our approach provides no information on the system’s dynamics.
462
Government the 195Os, while only base-money effect on inflation in the 1970s.
Deficits, growth
Money
Growth,
Inflation
has a quantitatively
large
4. Conclusion Most empirical studies on the relationship between government deficits and money growth or inflation have adopted a singleequation approach, treating government deficits as exogenous. Moreover, money growth is also typically considered as exogenous in an inflation equation. Our results, treating government deficits, base-money growth, and inflation all as endogenous variables in a trivariate autoregressive model, suggest that the exogeneity assumptions are not generally supported by the data. Moreover, the causal relationships have not been stable overtime. Although we do not have a complete account as to why the causal relationships have changed, the results do suggest, however, that tests of hypotheses relying upon a single-equation specification between deficits, basemoney growth, and inflation are inappropriate. The results indicate that for the 1960s government deficits and inflation are exogenous and cause base-money growth. In addition, government deficits and inflation cause base-money growth in all three periods;” in the 1950s and the 197Os, the causality is two-way so that base-money growth causes government deficits and inflation. The causal relationship from deficits to base-money growth, although statistically significant, is quantitatively small. Finally, a two-way causal relationship occurs for the 1950s and the 1970s between government deficits and inflation. Thus, government deficits appear to be inflationary in the 1950s and the 1970s. Contrary to most theoretical arguments and empirical studies, however, the effect of government deficits on inflation is direct and independent of the effect that base-money growth may have on inflation. In other r5A referee suggested that the 1970s’ sample period end prior to the October 1979 Fed announced change in policy. Although our sample only contains four quarters in the post-October 1979 period, we did run some tests. As in the additional Treasury-Federal-Reserve-Accord tests, we began with the single-equation results for the 1971i to 198Oiii period. Redoing steps (iv) to (vi) for the 1971i to 1979iii period produced the same causality results with one exception; in the shortened sample, we now have a significant direct link implying that deficits cause basemoney growth. This further strengthens the argument that deficits affect monetary policy, but, at the same time, it suggests that monetary policy might have ceased to respond to deficits after October 1979. Of course, this is highly speculative. More time will have to elapse before tests of such conjuctures can be performed.
Francis W. Ahking
and Stephen
M. Miller
words, our empirical results do not support the contention that government deficits are only inflationary if they are monetized.16 But, it should be noted that the quantitative effect of deficits on inflation is small in the 1970s. Received: January 1984 Final version received: May
1985
References Allen, S.D., and M.D. Smith. “Government Borrowing and Monetary Accommodation.” Journal of Monetary Economics 12 (November 1983): 605-16. Barro, R. J. “Comment From an Unreconstructed Ricardian.” Journal of Monetary Economics 4 (August 1978): 569-81. -. “On the Determination of the Public Debt.” Journal of POlitical Economy 87 (October 1979): 940-71. Buchanan, J. M., and R. Wagner. Democracy in Deficit: The Z’olitical Legacy of Lord Keynes. New York: Academic Press, 1977. Caines, P.E., C.W. Keng, and S.P. Sethi. “Causality Analysis and Multivariate Autoregressive Modeling with an Application to Supermarket Sales Analysis. ” Journal of Economic Dynamics and Control 3 (August 1981): 267-98. Cox, W.M. “Is There a Rule for Financing Public Debt? The Wealth Content of U.S. Government Bonds, 1950-1981.” Department of Economics Working Paper, Virginia Polytechnic Institute and State University, undated. Dewald, W.G. “Disentangling Monetary and Fiscal Policy.” Federal Reserve Bank of San Francisco Economic Review (Winter 1982): 7-18. Dwyer, G.P. “Inflation and Government Deficits.” Economic Znquiry 20 (July 1982): 315-29. Friedman, M. “The Role of Monetary Policy.” American Economic Review 58 (March 1968): 1-17. -. “Monetary Policy: Theory and Practice.” Journal of Money, Credit and Banking 14 (February 1982): 98-118. Granger, C. W. J. “Testing for Causality: A Personal Viewpoint.” Journal of Economic Dynamics and Control 2 (November 1980): 329-52. 160ur results entiate between
464
are consistent “deficit policies”
with Miller’s and “deficit
(1983) hypothesis realizations.”
but
do
not
differ-
Government Hamburger,
Money
Growth,
lnflation
“Deficits, Money and Inflation.” 7 (January 1981): 141-50. -, and -. “Deficits, Money and Inflation: Reply.” Journal of Monetary Economics 10 (September 1982): 279-83. Hoffman, D.L., S.A. Low, and H.H. Reineberg. “Recent Evidence on the Relationship Between Money Growth and Budget Deficits.” Journal of Macroeconomics 5 (Spring 1983): 223-31. Hsiao, C. “Autoregressive Modeling of Canadian Money and Income Date.” Journal of the American Statistical Association 74 (September 1979): 553-60. “Autoregressive Modelling and Money-Income Causality -. Detection. ” Journal of Monetary Economics 7 (January 1981): 85106. Jump, G.V. “Interest Rates, Inflation Expectations, and Spurious Elements in Measured Real Income and Saving.” American Economic Review 70 (December 1980): 990-1004. Levy, M.D. “Factors Affecting Monetary Policy in an Era of Inflation.” Journal of Monetary Economics 8 (November 1981): 35173. Lutkepohl, H. “Non-Causality Due to Omitted Variables.” Journal of Econometrics 19 (August 1982): 367-78. McMillin, W.D., and T.R. Beard. “Deficits, Money and Inflation: Comment.” Journal of Monetary Economics 10 (September 1982): 273-77. Miller, P. J. “Deficit Policies, Deficit Fallacies.” Federal Reserve Bank of Minneapolis Quarterly Review (Summer 1980): 2-4. -. “Higher Deficit Policies Lead to Higher Inflation.” Federal Reserve Bank of Minneapolis Quarterly Review (Winter 1983): 8-19. Niskanen, W.A. “Deficits, Government Spending and Inflation: What Is the Evidence?” Journal of Monetary Economics 4 (August 1978): 591-602. Sargent, T.J. and N. Wallace. “Some Unpleasant Monetarist Arithmetic. ” Federal Reserve Bank of Minneapolis Quarterly Review (Fall 1981): 1-17. Siegel, J. J. “Inflation-Induced Distortions in Government and Private Savings Statistics.” Review of Economics and Statistics 61 (February 1979): 83-90. Sims, C. “Macroeconomics and Reality.” Econometrica 48 (January 1980): l-48. -. “Policy Analysis with Econometric Models.” In Brookings Papers on Economic Activity. W. Brainard, and G. Perry, eds.
Journal
M.J.,
Deficits,
and B. Zwick.
of Monetary
Economics
465
I~~~U~CES W. Ahking
and Stephen M. Miller
Washington, D.C.: The Brookings Institution, 1982, pp. 107-52. Tatom, J.A. “Issues in Measuring an Adjusted Monetary Base.” Federal Reserve Bank of St. Louis Review 62 (December 1980): 11-29. Theil, H. Principles of Econometrics. New York: John Wiley and Sons, 1971. Zellner, A., ed. Seasonal Analysis of Economic Time Series. Washington, D.C.: U.S. Department of Commerce, Bureau of the Census, 1978. -. “Causality and Econometrics.” Carnegie-Rochester Conference on Public Policy 10 (Spring 1979): 9-54.
Appendix The definitions
of variables
and data sources are as follows:
P: The monthly not-seasonally-adjusted Consumer Price Index was obtained from the Citibank Data Base. The last month of each quarter was used to calculate the quarterly rate of inflation. This was converted into the equivalent annual rate of change. H: The monthly series on not-seasonally-adjusted base money constructed by Tatom (1980) was utilized. The last month of each quarter was used to calculate the quarterly rate of change. This was converted into the equivalent annual rate of change. D: The monthly series on not-seasonally-adjusted privately held public debt securities including Fed holdings. The last month of each quarter was used to calculate the rate of change. This was converted into the equivalent annual rate of change. The source is the Treasury Bulletin, various issues. As noted by Dwyer [(1982), p. 3281, the privately held public debt series needs to be adjusted due to a redefinition in 1968 of the amount of government agency debt held by the private sector. The redefinition increased the privately held public debt series after 1968. We do have observations using both pre- and post-1968 definitions at the end of the fiscal year (i.e., the second quarter) from 1960 to 1967 as well as all four quarters in 1968. The ratio of postto pre-1968 observations is fairly stable from 196Oii to 1965ii. We compute the average value over these six years (i.e., 1.038) and use this to inflate all the debt observations from 1947i to 1965iu. In 466
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Deficits,
Money
Growth,
Inflation
19fXii and 1967ii, the ratios are 1.059 and 1.080, respectively. These numbers are used to inflate the debt observations in each quarter of the corresponding year. The data series splices nicely in 19682’ because the ratio is also equal to 1.080. As a final minor adjustment, the pre-1968 data included the holdings of special international issues (e.g., IMF issues) that are excluded from the post-1968 data. We have excluded this data in the pre-1968 data used.
467
of
Connecticut
The Relationship Between Government Deficits, Money Growth, and Inflation* We model the time-series relationship between Federal government deficits, basemoney growth, and inflation as a trivariate autoregressive process. The technique is a generalization of Hsiao’s (1979; 1981) b ivariate autoregressive modeling method, but also incorporates several recent contributions by Caines, Keng, and Sethi (1981) and Lutkepohl (1982). The results indicate that for the 196Os, both government deficits and inflation are econometrically exogenous. But, for the 1950s and the 197Os, government deficits, money growth, and inflation are all causally related.
1. Introduction There is a “popular view” among policy makers that government deficits are inflationary. Most economists, however, subscribe to the position that inflation is a monetary phenomenon, at least in the long run. Friedman (1968) argued that the monetary authorities can control the inflation rate, especially in the long run, with the control of the money supply. Deficits can lead to inflation, but only to the extent that they are monetized. Thus, money-financed deficits are inflationary; bond-financed deficits need not be.’ Whether bond-financed deficits are inflationary or not depends upon the current approach to policy of the monetary authorities. If they are stabilizing (pegging) interest rates, then bond-financed deficits are inflationary. That is, bond sales push up interest rates and lower bond prices. Because the monetary authorities are stabilizing interest rates, this calls forth an expansion in the money supply that ultimately leads to rising prices. Sargent and Wallace (1981) questioned Recently, however, whether it is possible that with continuing deficits, monetary au*The authors are assistant professor and professor of economics, respectively, at the University of Connecticut. Comments of two anonymous referees significantly improved the paper; we alone are responsible for any remaining errors. We also acknowledge the support of the University of Connecticut Computer Center. ‘Buchanan and Wagner (1977), however, argued that government deficits will be monetized due to political pressure; the monetary authorities do not have a true choice.
Journal Copyright
of Macroeconomics, 0 1986 by Wayne
Fall 1985, Vol. State University
7, No. 4, Press.
pp.
447-467
447
rrancas W. Ahking
and Stephen M. Miller
thorities will never be obliged to monetize a portion of the government debt. The reason is that in a long-run growth context, the private sector’s demand for government bonds imposes an effective constraint on the degree of independence between monetary and fiscal policy. The ultimate question is who, monetary or fiscal authorities, dominates policy making. Assume that the fiscal authorities dominate and that they are expanding the stock of government indebtedness-both privately and publicly [i.e., the Federal Reserve (Fed)] held-at a rate faster than the monetary authorities are expanding base money. That is, the Fed is adding to its holding of government bonds less rapidly than the fiscal authorities are expanding total debt. Thus, privately held government debt is growing more rapidly than base money. This implies a portfolio shift into privately held government debt; the private sector will absorb this increase only as interest rates on government debt rise. This cannot continue forever. Either interest rates will become too high and/ or the demand for government debt will become perfectly inelastic. At this point, monetary policy must accommodate the needs of fiscal policy. If the Fed dominates, then it can control inflation in the long run. It now falls on the fiscal authorities to structure their revenue and expenditure patterns to be consistent with monetary policy. That is, given the private sector’s demand for government bonds, the fiscal authorities cannot on a continuing basis expand the stock of government indebtedness more rapidly than the growth in base money. An alternative view, expounded by Miller (1983), argues that government deficits are necessarily inflationary irrespective of whether the deficits are monetized or not. According to Miller, deficit policy leads to inflation through three channels. The Fed might be forced into monetary accommodation of the deficits as argued by Sargent and Wallace (1981). But, even if the Fed does not monetize the deficit, deficits are still inflationary through private monetization and/ or crowding out. That is, nonmonetized deficits lead to higher interest rates. Higher interest rates crowd out private investment, reduce the rate of growth of real output, and with a given money supply, lead to higher prices. Higher interest rates also spur the financial sector to innovate in the payment system and makes government bonds more substitutable for money.’ ‘In do not
448
an earlier article, Miller imply a future tax liability
(1980) argued that current to society. The government
bond-financed deficits will issue more bonds
Government
Deficits,
Money
Growth,
Inflation
Although most discussions on the relationship between government deficits and inflation focus on the role of deficits in causing inflation, the “fiscal-dividend” hypothesis argues that inflation leads to adjustments in the government deficit. That is, in a progressive tax system, inflation pushes tax payers into higher marginal tax brackets. Thus, if the government holds the ratio of government expenditure to gross national product constant, then inflation should lower (increase) the deficit (surplus). This allows legislators to simultaneously reduce tax rates and expand government expenditure. Thus, inflation leads to changes in government deficits. Barro (1979) h as also offered a theory of public debt that bears on the issue of (anticipated) inflation and government deficits. In a nutshell, the model assumes that the objective of government is to ‘1 , minimize the present value of revenue-raising costs . . .” [(%79), p. 9441. This assumption produces the conclusion that the ratios of real government expenditure to real income and real tax revenue to real income are constant over time. The consideration of inflation and the government budget constraint demonstrates that increases in anticipated inflation lead to larger government deficits.3 The theoretical arguments suggest that government deficits can be inflationary while at the same time they can also be the result of inflation. Empirical studies, however, have not yet reached a consensus. Barro (1978), Niskanen (1978), and McMillin and Beard (1982) found no evidence that government deficits are systematically related to money growth, and hence, inflation. On the other hand, Levy (1981), Hamburger and Zwich (1981, 1982), Dewald (1982), Dwyer (1982), Allen and Smith (1983), and Hoffman, Low, and Reineberg (1983) found some evidence that government deficits are systematically related to money growth or inflation. The inconclusive empirical evidence may be due to a number
to cover the maturing indebtedness as well as any new addition to total indebtedness. Hence, since government bonds are not backed by tangible assets or by future taxes, the bonds are in essence a part of the money supply. Cox (undated) argued analogously that if interest payments on government bonds are financed by deficits (bonds are infinitely lived assets), then government bonds are net nominal wealth. An increase in government debt will therefore have the same effect on the price level as an increase in the money supply. 3It should also be mentioned that both Siegel (1979) and Jump (1980) have noted similar relationships between inflation and government deficits. Their main concern, however, was not the causal relationship between inflation and government deficits.
449
of estimation problems. Researchers, with the exception of Dwyer (1982) and Hof&n an, Low, and Reineberg (1983),4 have estimated monetary reaction functions, Barre’s (1978) specification being the most popular. Barro’s reaction function has been criticized extensively;’ but, more generally, all monetary reaction functions are subject to the problem of being a joint test of the reaction-function specification and the existence of a relationship between deficits, money growth, and inflation. Since general agreement on the appropriate monetary reaction function does not exist, any conclusions concerning the relationship between deficits, money growth, and inflation should be considered tentative. A further problem with the existing empirical literature, with the exception of Levy (1981) and Dwyer (1982), is that conclusions are based on single-equation estimates. The general approach is to include a deficit variable in a monetary reaction function. The maintained assumption is that deficits are exogenous in the reaction function; their effect on inflation is implicit (i.e., if monetized, then deficits are necessarily inflationary). We argue that the single-equation approach is too restrictive when examining the links between deficits, money growth, and inflation. For example, the possibility that there may be a direct effect of deficits on inflation, as argued by Miller (1983), or that changes in deficits may be a result of inbetween flation are ruled out, a priori6 In sum, the relationship deficits, money growth, and inflation should be examined in a system-of-equations framework. In this paper, we examine the relationships between deficits, money growth, and inflation in a trivariate autoregressive fi-amework, thus allowing us to treat each variable as endogenous within a three-equation system. In addition to the obvious advantage of not imposing a priori exogeneity assumptions, this framework also
4Dwyer’s empirical methodology was different from the empirical literature cited in that he used the vector-autoregressive approach. He found that inflation was important in explaining deficits, but deficits were not important in explaining inflation, the growth of nominal GNP, the growth rate of the money stock, or the level of interest rates. Hoffman, Low, and Reineberg regressed money growth on future and past deficits. sSee Allen and Smith [(1983), p. 898, Footnote 31 for a partial list of researchers who are critical of Barro’s monetary reaction function. ‘Niskanen (1978) did develop a monetary reaction function including the deficit as an exogenous variable and a reduced-form inflation equation including both the deficit and lagged money growth. He estimated his two equations, however, as single equations.
Government
Deficits,
Money
Growth,
Inflation
relieves us of the burden of having to specify the structural relationships between deficits, money growth, and inflation. This is because the trivariate autoregressive model can be interpreted as a general system of reduced-form equations for the three variables. Yet, within this framework, meaningful economic hypotheses can be tested. The remainder of the paper is as follows. Section 2 discusses the empirical methodology and the data; Section 3 presents the empirical results; and Section 4 is the conclusion.
2. Empirical
Methodology
and Data
A trivariate autoregressive and inflation is as follows:
model for deficits,
money
growth,
where D,, H,, and Pt are deficits, money growth, and inflation, respectively; a, b, and c are constants; L is the lag operator such, that for any variable X,, tiX, = Xtj; a,(L), hi(L), and C,(L), i = 1, 2, and 3, are polynomials in the lag operator [e.g., al(L) = E~zlaU(Lj)]; and Ult,U2tr and U,, are innovations. The innovations are zero-mean whitenoise stochastic processes with constant covariances. The literature suggests several methods for identifying the system of Equations (1). Lutkepohl (1982) assumed the autoregressive lags for all the variables to be identical and determined the optimal system lag length by using Akaike’s Information Criterion (AIC) after searching over a lag length from one to a maximum of M. After determining the optimal system lag length, Lutkepohl conducted formal statistical tests to determine whether any of the off-diagonal operators can be excluded. Lutkepohl’s method is relatively inexpensive to implement. But, the assumption of equal lag lengths for all variables is rather restrictive. Caines, Keng, and Sethi (1981) modeled a system of iV(>2) variables in stages. First, bivariate autoregressive models are estimated for each ordered pair of variables. The two variables in each bivariate autoregressive process are assumed to have equal lag lengths, and the optimal lag length is determined by Akaike’s Final Prediction Error (FPE) criterion, which is equivalent to Lutkepohl’s 451
AIC, after searching over lag length from one to K. The objective of this stage is to determine the relationships between the two variables, i.e., endogeneity, exogeneity, or independence, and to determine the order in which variables should be entered into higherdimension multivariate autoregressive processes. Second, information obtained from the bivariate analysis is used to build a multivariate autoregressive process, and, finally, hypothesis testing is performed. The modeling strategy of Caines, Keng, and Sethi has certain appeal. The bivariate autoregressive modeling reduces the computational burden for later multivariate analysis. The assumption of equal lag lengths for the two variables in a given bivariate autoregressive process, however, is rather restrictive. Furthermore, the determination of the relationship between two variables at the bivariate modeling stage may not be appropriate. As Lutkepohl (1982) has pointed out, a low-dimension subprocess may not contain sufficient information about the structure of a higher-dimension process. Our empirical methodology is essentially a trivariate extension of Hsiao’s (1979; 1981) b ivariate autoregressive modeling method. We do incorporate, however, several features from Caines, Keng, and Sethi (1981) and Lutkepohl (1982). In the first-stage modeling, we treat each equation in (1) independently and, thus, all estimations use ordinary least squares (OLS). Three steps are involved in the first stage for each equation in (1). The modeling of the deficit equation, for example, would P-+ proceed as follows: (i) Search over a lag length from one to a maximum of M and determine the optimal lag length for the univariate autoregressive process for D by means of Akaike’s minimum FPE criterion. Denote the optimal lag length for D as m and the minimum FPE as FPEo(m). (ii) Maintaining the autoregressive lag for D at m, construct autoregressive processes for (Dt, H,) and (Dl, PJ by varying the lag length of H and P from one to M and compute the FPEs at each lag. Use the minimum FPEs for the autoregressive processes for (Dt, H,) and (D,, Pt) to determine the optimal lag lengths for H and P which we designate as n and r, respectively. Denote the minimum FPEs as FPEn,H(m, n) and FPEn,r(m, r), respectively. (iii) To determine the order that H and P should enter the D 452
equation, identify the minimum of FPE&m, n) and FPE,,p(m, r). Assume that FPE&vz, n) is smaller (i.e., H is ranked as more important than P in the D equation).7 Maintain the lag lengths for D and H at m and n, respectively; construct an autoregressive model for (D,, H,, Pt) by varying the lag length of P from one to M; and compute FPEs at each lag. Determine the optimal lag length for P by the minimum FPE criterion. The second-stage modeling involves the analysis of the system of Equations (1). It proceeds in three steps as follows: (iv) Pool the single equations for D, H, and P as determined in the first stage to give a tentative identification for the system of Equations (1). To obtain asymptotically efficient estimates, estimate the system using three-stage least squares to account for possible correlations between the innovations. (v) Perform diagnostic checks, treating the tentatively identified system as the maintained hypothesis. Use the tests in this step to determine if any of the off-diagonal operators in (1) can be excluded. (vi) Identify the final model based on the results in step (v). Finally, using the final model as the maintained hypothesis, test the nonzero off-diagonal operators of (1) to determine the relationships between D, H, and P, if any. The two-stage multistepped approach outlined above is used in our empirical analysis. Before turning to the results, we will briefly discuss our data base. A list of data sources and a description of how the variables were constructed are contained in the Appendix. The variables employed in the econometric analysis are as follows: P E annual rate of inflation; H = annual rate of growth of base money; and D = annual rate of growth of privately-held government debt. These variables differ from most previous studies in several respects. First, we employ base money rather than the money sup‘This method of ranking is equivalent to ordering the variables by their specific gravity [see Gaines, Keng, and Sethi (198l)l. Note, however, that we differ from Hsaio (1979, 1981) and Caines, Keng, and Sethi (1981) in that we not exclude any variable from further consideration at this stage.
453
I rU,~~~~YV.nntczng ancl Stephen M. Miller ply. The relationship between deficits and money growth is best addressed, in our opinion, by examining base money. That is, if the Fed monetizes the deficit, it does so by expanding base money. Moreover, base money is linked to the money stock through the banking multiplier. If the multiplier is stable, then base-money and money-supply growth should be highly correlated. Second, our measure of the government deficit is computed as the annual rate of change of privately held public-debt securities, including the debt held by the Fed.’ The national-income accounts measure of the deficit has been used frequently [e.g., Barro, (1978)]. Its use in the present context is problematic because it is on an accrual rather than a cash-flow basis. The Fed when altering base money does so through open-market operations. Thus, whether or not the Fed monetizes the deficit depends upon whether it purchases government securities as the Treasury sells them to the private sector to finance a cash-flow imbalance. The change in privately held public debt is on a cash-flow basis; it also includes debt financing of off-budget items. The analysis uses post-WWII quarterly data. The sample extends from 1947i to 198Oiii. Since seasonally unadjusted data are preferred in time-series studies, the data are not seasonally adjusted. We do include, however, seasonal dummy variables. This is equivalent to assuming that the seasonahty is deterministic, which is a debatable assumption. But, even if we are willing to explicitly analyze the deterministic and stochastic causes of seasonality, it is not clear whether an optimal, or even an adequate, seasonal adjustment procedure can be constructed.’ Thus, it is not obvious whether the use of seasonal dummies is necessarily worse, or better, than other seasonal adjustment procedures. It is required that the time series of D, H, and P are stationary. Since the variables are already rates of change, this has the effect of removing any trend from the data. Additional analysis of the autocorrelation functions for D, H, and P revealed some residual trend in P with an autocorrelation coefficient at lag one of 0.65. This is significantly different from unity, however. First differencing
‘The time series on’ privately held public-debt securities used is equivalent to the series used by Levy (1981) and Dwyer (1982) except for some minor adjustments described in the Appendix. ‘See the volume edited by Zellner (1978), especially the two papers by Granger and Wallis for a discussion of the problems with seasonal adjustment of economic time-series data.
454
Government
Deficits,
Money Growth,
Inflation
thus does not appear appropriate. Therefore, we included a linear time trend in each equation to account for any residual trend. We present estimates of the system of Equations (1) for three time periods: 19471 to 196Oiv, 1961i to 197Oiv, and 1971i to 1980iii. This allows us to examine whether or not the relationships between deficits, money growth, and inflation are stable over time. The break in 1961i is chosen to correspond roughly to what Hamburger and Zwich (1981) called the “Keynesian” period and the break at 1971i is to separate the unusual events that occurred during the 1970s (e.g., the wage-price controls, the oil-price shocks, and the collapse of the Bretten Woods system). There is no reason to expect the final model identified for one period to be the same for another period;” thus, we follow the six-step method described above to identify a final model for each period.
3. Empirical Results Table 1 presents the summary statistics from the single-equation estimations.” The optimal lag length for each variable is given in parentheses next to the variable. In each case, the variable listed last was the variable for which a search over lagged values was conducted. Variables preceeding, if any, had their lag length determined in the previous step(s). The single-equation results [i.e., steps (i) to (iii)] lead us to
“In fact, Levy (1981), using a quarterly reaction-function model, and Allen and Smith (1983), using a quarterly version of the basic Barro specification, reported structural breaks that correspond roughly to our break points. Both approaches identified break points one at a time. Thus, the identification of one structural break required the assumption of structural stability across the second break point in all the tests. In the only exception, Allen and Smith used post-196lii data to identify the second break point after identifying 1961ii as the first break point; they did use data through 1974io, however, to identify the first break. Levy used the full sample in all his tests for structural breaks. We did not undertake a search for structural breaks due to the high cost of repeating our six-step methodology. “A maximum order of twelve is assumed for the autoregressive process and given the calculation of rates of change, the sample for the first period begins at 1959ii. Thus, the first sample period includes some observations from the preTreasury-Federal-Reserve-Accord period. Degrees-of-freedom considerations led us to include the pre-Accord data. Also, Friedman (1982) argues that there was no significant change in FED behavior in the period immediately after the Accord. Nevertheless, alter obtaining the single-equation results (i.e., steps (i) to (iii) completed), we redid steps (iv) to (vi) using data from 1953i to 1960io. The same model was identified and our conclusions are unaltered.
455
1.
NOTFX experienced
D(12)
D(2)
H(l)
H(l) P(Q) H(l) P(Q)D(Q) P(l) P(1) DO) P(l) H(5) P(l) H(5) D(7)
H(l)
D(Q)H(1) D(Q)P(l) D(Q)P(l)
values is the
and Lags
1961i-197Oiv
indicate the number of lagged values from one to twelve. FPE
1.051 0.983 0.992 0.974 0.577 0.364
1.651 1.686 1.700 1.237 1.307
D(Q)
Variables
Lag Lengths
FPE X 10M3 1.779
Numbers in parentheses a search over lagged
D(l) Wll) H(ll)
DO)
P(6)
H(l) H(l) PO) P(l) P(1) P(1)
P(6)
HO) PW H(l) pw D(l)
and Lags
195Oii-lQ6Oiv
FPEs and Optimal
D(l) D(l) DO) H(l) WV
Variables D(l)
TABLE
of the variable. minimum value
0.177 0.179 0.182 0.189
0.350
0.385
2.819 2.791 2.868 0.421 0.460
FPE x lob3 2.730
In each over the
case, twelve
last
0.534
0.511 0.517 0.776 0.805 0.814
2.416 1.758 1.712 0.561 0.596
has
FPE x 10e3 2.292
the variable listed lagged values.
W9 P(8) D(7)
H(l) P(5) P(5) H(l) D(2)
and Lags
D(l) HO) P(8) DO) WW
H(1) H(1) f’(8) P(8) W3)
D(l) D(l) D(l) H(l)
Variables DO)
1971i-1980iii
i g$ -
5 s ;
:
i : 2 E E
Government identify tentatively three periods.
Deficits,
the following
Period:
Money Growth,
matrices
of lag operators
Inflution for the
195Oii-1960iv
(2)
Period:
1961i-1970iv
(3)
Period:
1971i-1980iii
(4)
where lag.
a superscript
denotes
the optimal
order
of the polynomial
Step (iv) in the identification process is to estimate the tentatively identified system with three-stage least squares; step (v) performs diagnostic checks that test whether any of the off-diagonal operators of (2), (3), and (4) can be excluded. F-statistics are used for the diagnostic tests [see Theil (1971), pp. 312-141. We tested nine hypotheses for each period and summary statistics are reported in Table 2. For the 1950ii to 1960iv period, the results suggest that none of the off-diagonal operators can be excluded. The two operators b:(L) and $‘(L) are not significantly different from zero individually. Jointly, however, they are significantly different from zero at the 10% level. We conducted two additional diagnostic checks: (i) Constrain b:(L) to zero in (2) .and test the hypothesis that $(L) equals zero; and (ii) constrain c:O(L) to zero and test the hypothesis that b&L) equals zero. In both cases, the hypothesis can be rejected at the 10% level. It appears that H and P are highly correlated and that this explains the seeming inconsistency between the joint. and 457
Francis W. Ahking TABLE
2.
and Stephen M. Miller
F-statistics
for Zero Restrictions F-statistic
Hypothesis b,(L) = c,(L) b,(L) c,(L) az(L) = q(L) at(L) q(L) a,(L) = b3(L) a,(L) b&)
= = = = = = = = =
0 0 0 0 0 0 0 0 0
195Oii-196Oiu
.2961i-197Oiv
1971i-198Oiii
1.75** 1.24 1.43 3.05* 2.99** 2.85* 9.77* 5.11* 10.11*
0.76 0.70 0.92 4.36* 2.82* 5.07* 1.37 1.28 2.77*
2.77* 1.67 3.32* 2.37* 1.46 2.75* 3.02* 11.58* 3.14*
NOTE: The maintained hypothesis for the F-statistics (4) for columns 1, 2, and 3, respectively. *The hypothesis can be rejected at the 5% level. **The hypothesis can be rejected at the 10% level.
are
matrices
(2),
(3),
and
individual tests. The diagnostic tests, in sum, imply the retention of (2) as the final model specification for the first period. For the 1961i to 197&u period, the results in Table 2 suggest that &:(I.$, c#J, and a&) all equal zero. But, when these operators are constrained to zero in (3), further diagnostic checks reveal that the hypothesis b@) equals zero cannot be rejected at the 10% level. This result, however, is not entirely surprising for two reasons. First, from Table 1, we see that the lowest FPE in the set of inflation equations occurs for the univariate specification. Second, from Table 2, we cannot reject the joint hypothesis that both a:(L) and b!(L) equal zero at the 10% level. The hypothesis that wJ> 4(L)> d(L), and b@) are jointly zero (i.e., the test statistic is F = 1.28) cannot be rejected at the 10% level. Thus, we conclude that the final model for the 1961i to 19i’Oiu period is as follows:
For the period 1971i to 198Oiii, the results in Table 2 suggest that both b:(L) and &?J e q ua 1 zero. The hypothesis that these two operators are jointly zero in (4) (i.e., the test statistic is F = 1.48) 458
Government
Deficits,
Money
Growth,
cannot be rejected at the 10% level. Thus, for the third final model is given as:
(;
bl&
Znflation period,
the
(4’)
ii).
So far, we have been deliberately overfitting the models initially and using a series of diagnostic checks to arrive at the final models. As a last check of the adequacy of the final models, we sequentially over-fitted the final models by adding one additional lag and then two additional lags to each variable, including those variables that were not significantly different from zero in the final models. Next, we sequentially underfitted the final models with one lag and then two lags. In all cases with overfitting, the F-statistics indicated that the extra lags were not significantly different from zero at the 10% level. On the other hand, in all the underfitting cases, the F-statistics indicated that the omitted lags were significantly different from zero at the 5% level. The results, available from the authors upon request, reveal no inadequacy in the final models. Using (2), (3’), and (4’) as the final models, Table 3 presents the results of the various tests of the relationships between D, H, TABLE
3.
Tests of the Final
Models F-statistics
Hypothesis b,(L) = c,(L) b,(L) c,(L) a&) = q(L) a&) q(L) a,(L) = b&J a&) ML) (4’)
195Oii-1960iv = = = = = = = = =
0 0 0 0 0 0 0 0 0
1.75** 1.24 1.43 3.05* 2.99** 2.85” 9.77* 5.11* 10.11*
1961i-1970iv
1971i-198Oiii
3.17* 5.66* 6.55* 3.50*
NOTE: The maintained hypothesis for the F-statistics for columns 1, 2, and 3, respectively. *The hypothesis can be rejected at the 5% level. **The hypothesis can be rejected at the 10% level.
2.37* 3.59* 12.59* 3.75* are
matrices
(2),
(3’),
and
459
Francis W. Ahking
and Stephen M. Miller
and P. The results for the I95Oii to 1960iu period are unchanged from Table 2 but are included for completeness. For the latter two periods, the tests confirm (3’) and (4’) as the final models. The results imply that the causal relationships between D, H, and P have not been stable for the three periods.r2 The 1950s present the most complex set of interactions between the variables generated in the three periods. We find that all variables are directly causally related to each other. The results for the 1970s differ from those of the 1950s only in that there is no evidence of direct temporal causality between government deficits and base-money growth. There is, however, two-way causality between deficits and basemoney growth via the inflation rate (i.e., indirect causality). Thus, in the 1950s and the 197Os, none of the three variables is exogenous. In contrast, the results for the 1960s identify both government deficits and inflation as best represented by univariate models i.e., they are exogenous), Base-money growth, however, is caused ( by both deficits and inflation. Comparing the three periods yields the following set of consistent results. First, inflation causes base-money growth in all three periods. Second, government deficits cause base-money growth in all three periods, but the causal relationship is indirect through the inflation rate in the 1970s. Third, for the 1950s and the 197Os, twoway causality is indicated between government deficits and inflation, between base-money growth and inflation, and between government deficits and base-money growth. Thus, in these two periods, both government deficits and base-money growth cause inflation; the effect of the deficit on inflation, moreover, is direct and independent of the effect of money growth on inflation. In contrast, the 1960s indicate that inflation is best represented by a univariate model. On an equation-by-equation basis, the base-money growth equations come closest to exhibiting a consistent pattern across the three periods. This is interesting because base money is directly affected by the general controls of monetary policy, including, most importantly, open-market operations. Thus, the causality uncovered in these equations is probably a reflection of monetary policy. The
‘*It should be emphasized that temporal causality. That is, the future cannot cause the past [See has provided a detailed criticism a personal viewpoint on causality 480
the concept of causality used here is &anger’s past and present can cause the future, but the Granger (1980), p. 330, Axiom A]. Zellner (1979) of C&anger causality, but see Granger (1980) for testing.
Government TABLE
4.
Variance
Deficits,
Money
Growth,
Inflation
Decomposition
Time Period
Dependent Variableb
195&i-196&u 196%197Oiu 197%198Oiii
Percentage of Dependent Variance Explained
Variable’s by” Unexplained
D
H
P
S
D(H, P) D D
0.2 20.6 31.7
4.8 -
13.9 10.2
58.3 51.8 43.6
22.8 27.6 14.5
195Oii-196Oiv 1961i-197Oiu 1971i-198Oiii
H(P, D) H(P, D) H
0.9 1.0 -
0.8 0.0 0.0
5.5 1.9 3.3
85.4 96.1 92.6
7.4 1.0 4.1
WOii-196% 1961i-1970iv 1971i-198Oiii
P(H, D) P P(D, H)
18.1 0.6
50.3 17.6
10.3 0.3 32.9
14.2 69.5 40.1
7.1 30.2 8.8
‘S includes a constant, a time trend, and seasonal dummy variables; D, H and P are defined in the Appendix. The columns indicate the percentage of the dependent variable’s variance (e.g., variance of D) explained by adding sequentially S, lagged values of the dependent variable, and lagged values of the other significant variables (e.g., H and P); the last variables are added in the order determined in Table 1. An entry of 0.0 means that the reduction in variance was less than 0.05%. A dash occurs for those variables that are not significant in the previous analysis. Wariables in parentheses indicate the order that they are added in the variance decomposition. For example, D(H, P) means that lagged values of H are added prior to lagged values of P in the variance decomposition.
results suggest that monetary policy has responded to both inflation and government deficits, although the latter ceases its direct effect during the 1970s.r3 Our empirical results so far only provide qualitative information on the causal relationships between D, H, and P. Further insight is obtained by decomposing the variance of the dependent variable into components explainable by significant explanatory variables. The results are reported in Table 4.14 IsThese results are generally consistent with Levy’s (1981) results in a reactionfunction framework. He found that both expected inflation, proxied by a distributed lag of actual inflation, and privately held government debt affected base money. “Our variance decomposition method is different from that employed by Sims (1980; 1982). where the variance of the n-period ahead forecast errors of the dependent variable is decomposed into components attributable to the innovations uf the explanatory variables. Since the residuals are correlated across equations, Sims’s technique requires that they are first transformed into orthogonal form. To do this,
461
rrancis
W. Ahking
and Stephen
M. Miller
Several findings are noteworthy. First, 58% to 75% of The variance of the deficit is explainable by its own lagged values and by the vector of variables in S, which consists of a constant, a linear time trend and three seasonal dummy variables.- Of the remaining two explanatory variables, inflation is quantitatively more important than base-money growth in explaining the variations in the deficit. Second, between 85% and 96% of the variance in base-money growth is accounted for by the variables in S alone, while its own lagged values, deficits, and inflation accounted for a small fraction of the variance. Finally, other than its own lagged values and the variables in S, the most important explanatory variable of inflation is basemoney growth. The variance decomposition results appear to explain partially the differences in the autoregressive results across the three time periods. Thus, although deficits are caused by base-money growth only in the 195Os, its effect on deficits is quantitatively small. Similarly, deficits cause base-money growth in the 1950s and the 1960s but not in the 1970s. Again, the quantitative effect of deficits on base-money growth in these two time periods is small. Finally, deficits cause inflation in the 1950s and the 197Os, but not in the 1960s. The quantitative effect of deficits on inflation is small in the 197Os, but not in the 1950s. In contrast, inflation causes deficits in the 1950s and the 197Os, but not in the 1960s. Here the effects are quantitatively large. Also, deficits and base-money growth do not cause inflation in the 1960s but have quantitatively large effects in
(Note
cont.
from
p. 461)
the system of equations is triangularized by selecting a particular order in which the variables are entered into the system with the variables placed in the lower order included as regressors contemporaneous values of variables placed in the higher order [see Sims (1980)]. The selection of the ordering, however, is arbitrary and amounts to imposing ad hoc identifying restrictions to achieve a recursive system, which is quite contrary to the spirit of autoregressive modeling. Furthermore, the variance decomposition results could be quite sensitive to the particular ordering of the variables chosen. Our variance decomposition method, we believe, provides similar information as Sims’s method but without having to first triangularize the system of equations. Our approach also requires the selection of an ordering of the explanatory variables. The results in Table 1, however, provide a natural selection of ordering. There are two shortcomings in our method, however. First, we do not incorporate any information about contemporaneous correlations among the residuals of the system’s equations. Second, because we are not examining forecast errors, our approach provides no information on the system’s dynamics.
462
Government the 195Os, while only base-money effect on inflation in the 1970s.
Deficits, growth
Money
Growth,
Inflation
has a quantitatively
large
4. Conclusion Most empirical studies on the relationship between government deficits and money growth or inflation have adopted a singleequation approach, treating government deficits as exogenous. Moreover, money growth is also typically considered as exogenous in an inflation equation. Our results, treating government deficits, base-money growth, and inflation all as endogenous variables in a trivariate autoregressive model, suggest that the exogeneity assumptions are not generally supported by the data. Moreover, the causal relationships have not been stable overtime. Although we do not have a complete account as to why the causal relationships have changed, the results do suggest, however, that tests of hypotheses relying upon a single-equation specification between deficits, basemoney growth, and inflation are inappropriate. The results indicate that for the 1960s government deficits and inflation are exogenous and cause base-money growth. In addition, government deficits and inflation cause base-money growth in all three periods;” in the 1950s and the 197Os, the causality is two-way so that base-money growth causes government deficits and inflation. The causal relationship from deficits to base-money growth, although statistically significant, is quantitatively small. Finally, a two-way causal relationship occurs for the 1950s and the 1970s between government deficits and inflation. Thus, government deficits appear to be inflationary in the 1950s and the 1970s. Contrary to most theoretical arguments and empirical studies, however, the effect of government deficits on inflation is direct and independent of the effect that base-money growth may have on inflation. In other r5A referee suggested that the 1970s’ sample period end prior to the October 1979 Fed announced change in policy. Although our sample only contains four quarters in the post-October 1979 period, we did run some tests. As in the additional Treasury-Federal-Reserve-Accord tests, we began with the single-equation results for the 1971i to 198Oiii period. Redoing steps (iv) to (vi) for the 1971i to 1979iii period produced the same causality results with one exception; in the shortened sample, we now have a significant direct link implying that deficits cause basemoney growth. This further strengthens the argument that deficits affect monetary policy, but, at the same time, it suggests that monetary policy might have ceased to respond to deficits after October 1979. Of course, this is highly speculative. More time will have to elapse before tests of such conjuctures can be performed.
Francis W. Ahking
and Stephen
M. Miller
words, our empirical results do not support the contention that government deficits are only inflationary if they are monetized.16 But, it should be noted that the quantitative effect of deficits on inflation is small in the 1970s. Received: January 1984 Final version received: May
1985
References Allen, S.D., and M.D. Smith. “Government Borrowing and Monetary Accommodation.” Journal of Monetary Economics 12 (November 1983): 605-16. Barro, R. J. “Comment From an Unreconstructed Ricardian.” Journal of Monetary Economics 4 (August 1978): 569-81. -. “On the Determination of the Public Debt.” Journal of POlitical Economy 87 (October 1979): 940-71. Buchanan, J. M., and R. Wagner. Democracy in Deficit: The Z’olitical Legacy of Lord Keynes. New York: Academic Press, 1977. Caines, P.E., C.W. Keng, and S.P. Sethi. “Causality Analysis and Multivariate Autoregressive Modeling with an Application to Supermarket Sales Analysis. ” Journal of Economic Dynamics and Control 3 (August 1981): 267-98. Cox, W.M. “Is There a Rule for Financing Public Debt? The Wealth Content of U.S. Government Bonds, 1950-1981.” Department of Economics Working Paper, Virginia Polytechnic Institute and State University, undated. Dewald, W.G. “Disentangling Monetary and Fiscal Policy.” Federal Reserve Bank of San Francisco Economic Review (Winter 1982): 7-18. Dwyer, G.P. “Inflation and Government Deficits.” Economic Znquiry 20 (July 1982): 315-29. Friedman, M. “The Role of Monetary Policy.” American Economic Review 58 (March 1968): 1-17. -. “Monetary Policy: Theory and Practice.” Journal of Money, Credit and Banking 14 (February 1982): 98-118. Granger, C. W. J. “Testing for Causality: A Personal Viewpoint.” Journal of Economic Dynamics and Control 2 (November 1980): 329-52. 160ur results entiate between
464
are consistent “deficit policies”
with Miller’s and “deficit
(1983) hypothesis realizations.”
but
do
not
differ-
Government Hamburger,
Money
Growth,
lnflation
“Deficits, Money and Inflation.” 7 (January 1981): 141-50. -, and -. “Deficits, Money and Inflation: Reply.” Journal of Monetary Economics 10 (September 1982): 279-83. Hoffman, D.L., S.A. Low, and H.H. Reineberg. “Recent Evidence on the Relationship Between Money Growth and Budget Deficits.” Journal of Macroeconomics 5 (Spring 1983): 223-31. Hsiao, C. “Autoregressive Modeling of Canadian Money and Income Date.” Journal of the American Statistical Association 74 (September 1979): 553-60. “Autoregressive Modelling and Money-Income Causality -. Detection. ” Journal of Monetary Economics 7 (January 1981): 85106. Jump, G.V. “Interest Rates, Inflation Expectations, and Spurious Elements in Measured Real Income and Saving.” American Economic Review 70 (December 1980): 990-1004. Levy, M.D. “Factors Affecting Monetary Policy in an Era of Inflation.” Journal of Monetary Economics 8 (November 1981): 35173. Lutkepohl, H. “Non-Causality Due to Omitted Variables.” Journal of Econometrics 19 (August 1982): 367-78. McMillin, W.D., and T.R. Beard. “Deficits, Money and Inflation: Comment.” Journal of Monetary Economics 10 (September 1982): 273-77. Miller, P. J. “Deficit Policies, Deficit Fallacies.” Federal Reserve Bank of Minneapolis Quarterly Review (Summer 1980): 2-4. -. “Higher Deficit Policies Lead to Higher Inflation.” Federal Reserve Bank of Minneapolis Quarterly Review (Winter 1983): 8-19. Niskanen, W.A. “Deficits, Government Spending and Inflation: What Is the Evidence?” Journal of Monetary Economics 4 (August 1978): 591-602. Sargent, T.J. and N. Wallace. “Some Unpleasant Monetarist Arithmetic. ” Federal Reserve Bank of Minneapolis Quarterly Review (Fall 1981): 1-17. Siegel, J. J. “Inflation-Induced Distortions in Government and Private Savings Statistics.” Review of Economics and Statistics 61 (February 1979): 83-90. Sims, C. “Macroeconomics and Reality.” Econometrica 48 (January 1980): l-48. -. “Policy Analysis with Econometric Models.” In Brookings Papers on Economic Activity. W. Brainard, and G. Perry, eds.
Journal
M.J.,
Deficits,
and B. Zwick.
of Monetary
Economics
465
I~~~U~CES W. Ahking
and Stephen M. Miller
Washington, D.C.: The Brookings Institution, 1982, pp. 107-52. Tatom, J.A. “Issues in Measuring an Adjusted Monetary Base.” Federal Reserve Bank of St. Louis Review 62 (December 1980): 11-29. Theil, H. Principles of Econometrics. New York: John Wiley and Sons, 1971. Zellner, A., ed. Seasonal Analysis of Economic Time Series. Washington, D.C.: U.S. Department of Commerce, Bureau of the Census, 1978. -. “Causality and Econometrics.” Carnegie-Rochester Conference on Public Policy 10 (Spring 1979): 9-54.
Appendix The definitions
of variables
and data sources are as follows:
P: The monthly not-seasonally-adjusted Consumer Price Index was obtained from the Citibank Data Base. The last month of each quarter was used to calculate the quarterly rate of inflation. This was converted into the equivalent annual rate of change. H: The monthly series on not-seasonally-adjusted base money constructed by Tatom (1980) was utilized. The last month of each quarter was used to calculate the quarterly rate of change. This was converted into the equivalent annual rate of change. D: The monthly series on not-seasonally-adjusted privately held public debt securities including Fed holdings. The last month of each quarter was used to calculate the rate of change. This was converted into the equivalent annual rate of change. The source is the Treasury Bulletin, various issues. As noted by Dwyer [(1982), p. 3281, the privately held public debt series needs to be adjusted due to a redefinition in 1968 of the amount of government agency debt held by the private sector. The redefinition increased the privately held public debt series after 1968. We do have observations using both pre- and post-1968 definitions at the end of the fiscal year (i.e., the second quarter) from 1960 to 1967 as well as all four quarters in 1968. The ratio of postto pre-1968 observations is fairly stable from 196Oii to 1965ii. We compute the average value over these six years (i.e., 1.038) and use this to inflate all the debt observations from 1947i to 1965iu. In 466
Government
Deficits,
Money
Growth,
Inflation
19fXii and 1967ii, the ratios are 1.059 and 1.080, respectively. These numbers are used to inflate the debt observations in each quarter of the corresponding year. The data series splices nicely in 19682’ because the ratio is also equal to 1.080. As a final minor adjustment, the pre-1968 data included the holdings of special international issues (e.g., IMF issues) that are excluded from the post-1968 data. We have excluded this data in the pre-1968 data used.
467