The Macroeconomic Impacts of Government Debt: An Empirical Analysis of the 1980s and 1990s

Atlantic
Economic
Journal

VOLUME 27
NUMBER 3

September 1999

Pages 273-284

This study examines the macroeconomic impacts of government debt. Unlike previous studies, the current study restricts the estimation period to the 1980s and 1990s. The analysis is conducted using variance decompositions and impulse response functions derived from a vector autoregressive model. The results presented here support an extreme form of the Ricardian equivalence hypothesis. In this view, wealth falls as government debt rises. Because wealth falls as government debt rises, an increase in government debt leads to decreases in interest rates, output, and the price level. (JEL E3)

This study examines the macroeconomic impacts of government debt in the U.S. The estimation is conducted using a vector autoregressive (VAR) model. The VAR is used to derive variance decompositions (VDCs) and impulse response functions (IRFs). Unlike previous studies, this study restricts the estimation period to the 1980s and 1990s.

The 1980s and 1990s are of interest because of the record amount of government debt created during this period. In January 1980, the market value of privately held gross federal debt was $510,436.00 million. By December 1995, the market value of privately held gross federal debt had risen to $3,511,280.00 million.

The conventional view of deficit financing holds that an increase in government debt leads to an increase in private sector wealth. Adherents of this view argue that the increase in wealth, in turn, leads to an increase in private sector spending, which then leads to increases in the price level, output, and interest rates.

Barro [1974] has proposed an alternative to the conventional view. Known as Ricardian equivalence, this view holds that an increase in government debt does not lead to additional private sector wealth. Instead, the increase in government debt is seen as leading to increased future tax liabilities of the same present value as the debt. According to the Ricardian equivalence hypothesis, because government debt is not viewed as private sector wealth, then an increase in government debt does not alter private spending. Hence, changes in government debt do not cause changes in the price level, output, or interest rates.⁽²⁾

Empirical studies of the Ricardian equivalence hypothesis have taken many forms. Several authors test Ricardian equivalence using consumption functions in which a measure of government debt or the deficit are included as regressors. Statistical insignificance of the debt or deficit variable provides support for the Ricardian view.

Of the consumption function studies, Kochin [1974], Tanner [1979], Kormendi [1983], Seater and Mariano [1985], and Aschauer [1985] find empirical support for Ricardian equivalence, while Yawitz and Meyer [1976] and Feldstein [1982] do not. A comparison of the consumption function studies published prior to 1985 indicates that seemingly trivial changes in specification can dramatically alter the results. However, Seater and Mariano [1985, pp. 196] note, "The earlier studies suffer from several methodological weaknesses, the most serious of which turns out to be failure to correct adequately for simultaneity bias." They go on to show that when a correction for simultaneity is made, the earlier studies yield results supporting Ricardian equivalence.

Several studies have tested Ricardian equivalence using single-equation reduced-form models.⁽³⁾ Most of these studies test Ricardian equivalence by estimating reduced-form equations where the interest rate is the dependent variable, and the list of regressors includes a measure of government debt or the deficit. However, there are exceptions to this. Eisner and Pieper [1984] reject Ricardian equivalence based on regressions of real gross national product (GNP), or the unemployment rate, on various measures of the deficit. De Leeuw and Holloway [1985] regress nominal GNP on a vector of explanatory variables, including changes in government debt and the level of government debt, and conclude that their data does not support Ricardian equivalence.

The remaining single-equation studies use an interest rate as the dependent variable. On balance, these studies support the Ricardian equivalence hypothesis. An exception to this is Makin [1983]. Unlike other studies, Makin uses a transfer function model of the short-term interest rate and rejects Ricardian equivalence.

McMillin [1986b] finds empirical support for Ricardian equivalence based on Granger-causality tests using the short-term interest rate. Evans [1985] finds no link between the deficit and short- and long-term rates, while Evans [1987] finds that both the actual deficit and the anticipated deficit have no impact on both short- and long-term interest rates. Hence, Evans [1985,1987] supports Ricardian equivalence.

Hoelscher's [1983] results support Ricardian equivalence using a short-term interest rate, but rejects Ricardian equivalence using a long-term interest rate. In a comment on Hoelscher's [1986] work, Goff [1990] argues that the Ricardian equivalence theorem should be tested by examining the effects of the anticipated deficit and not by examining the effects of the actual deficit. He goes on to show that when the deficit is divided into its anticipated and unanticipated components, Ricardian equivalence is supported using both short- and long-term interest rates.

Swamy et al. [1990] find a negative relationship between their deficit measure and the short-term interest rate. They interpret this result as a rejection of Ricardian equivalence. However, other authors have interpreted a negative relationship between various economic aggregates and deficit or debt measures as support for Ricardian equivalence. See, for example, Barro [1974], Fackler and McMillin [1989], Kormendi [1983], and Evans [1987].

As in this study, several previous studies test for Ricardian equivalence using VAR models. The VAR studies tend to confirm Ricardian equivalence. Dwyer [1982], Plosser [1982], Fackler and McMillin [1989], and Darrat [1989,1990] find support for the Ricardian equivalence hypothesis using postwar data, while Miller and Russek [1996] present mixed results. Beard and McMillin [1991] present results which support the Ricardian equivalence hypothesis using a VAR model estimated for the interwar years.

Unlike this study, none of the above studies analyze data from the 1990s. Furthermore, only Miller and Russek [1996] include data from the late 1980s in their estimation period. Given the record amount of government debt created in the late 1980s and 1990s, a study that examines this period is warranted.

The Ricardian equivalence hypothesis is tested by examining the impact of government debt on output, the price level, and interest rates. Six variables are included in the analysis. The selected variables are standard endogenous variables found in most textbook macroeconomic models. Monthly data are employed to obtain sufficient observations for estimation over the 1980s and 1990s only.⁽⁴⁾

The debt measure used in this study is the real market value of privately held gross federal debt (D).⁽⁵⁾ Commonly used debt measures (for instance, the par value of government debt) do not adequately account for the effects of inflation on outstanding federal debt.⁽⁶⁾ Real military expenditures (G) are included in the model as a proxy for the exogenous elements of fiscal policy.⁽⁷⁾ If government expenditures were excluded, then macro effects due to variations in government expenditures might be incorrectly attributed to government debt because government expenditures and government debt are correlated.

The money stock is measured as real M2 (M2). Industrial production (Y) is included in the model as a measure of output, while the price level is measured by the consumer price index (P).⁽⁸⁾⁽⁹⁾ The interest rate is measured with the AAA bond rate (R). A long-term interest rate is used because, as Fackler and McMillin [1989] note, investment decisions follow long-term interest rates much more closely than short-term interest rates. With the exception of R, all variables are seasonally adjusted.

This study employs VDCs and IRFs to examine the impact of government debt on the macroeconomy. The VDCs and IRFs are derived from the moving average representation of a VAR model of the macroeconomy which contains G, D, M2, R, Y, and P.

VDCs show the portion of the variance in the prediction error of each variable in the system that is attributable to its own innovations (shocks) and to innovations to the other variables in the system. The current study is most concerned with the portion of the forecast error variance in R, Y, and P explained by innovations to D. If innovations to D explain significant portions of the forecast error variance in R, Y, or P, then government debt has an impact on the macroeconomy. However, if innovations to government debt do not explain significant portions of the forecast error variance in R, Y, or P, then government debt has no impact on the macroeconomy. In the latter case, Ricardian equivalence is supported.

IRFs show the predictable response of each variable in the system to an innovation (shock) to one of the system's variables. Fischer [1981] notes that IRFs can be viewed as dynamic multipliers that give the current and subsequent effects on each system variable of a shock to one of the system's variables. The current study is most concerned with the paths taken by R, Y, and P in response to a shock to D.

Ohanian [1988], among others, cautions against interpreting results derived from VARs estimated with potentially integrated regressors. Hence, the empirical analysis begins by examining the time series properties of the data. In particular, this study tests for unit roots in the univariate representation of each variable and for a cointegrating relationship among all system variables.

The estimation period runs from January 1980 to December 1995, and data from 1978 and 1979 are used as presample data.⁽¹⁰⁾ With the exception of R, all variables are expressed in logs. A series of Dickey-Fuller [1981] unit root tests indicate that the null hypothesis of a unit root in the level of each variable is not rejected at the 5 percent level of significance. Further estimation reveals that the unit root hypothesis is rejected for the first difference of each series. This implies that each of the six series included in this study is integrated of order one and should be differenced once to attain stationarity.

Engle and Granger [1987] have pointed out that a VAR estimated with differenced data will be misspecified if the variables are cointegrated and the cointegrating relationships are ignored. Because of this, Johansen's [1988] (trace) cointegration test has been conducted.⁽¹¹⁾ At the 5 percent level of significance, the results of the Johansen test provide no evidence of cointegration. Thus, the six variables in this study constitute a system with no cointegrating vector. Because of the presence of a unit root in each of the variables, and the absence of cointegration among the variables, the VAR model is estimated in first differences.

As suggested by Spencer [1989], Akaike's Information Criterion (AIC) is used to determine the lag length for the VAR model.⁽¹²⁾ The maximum lag length considered is 12 months. The AIC is not applied blindly. The residuals from each VAR equation are required to be white noise. Q-statistics are used to determine if the residuals are white noise. The AIC and Q-statistics point to a lag length of seven months. Because Hafer and Sheehan [1991] argue that policy recommendations derived from VARs can be quite sensitive to the lag length employed, VARs are also estimated with 3, 6, and 12 lags.

The main results of this paper are contained in the VDCs and IRFs. To compute VDCs and IRFs, the VAR residuals must be orthogonalized. There are several ways to do this. Bernanke [1986] and Blanchard and Quah [1989], among others, recommend that structural models be estimated using the residuals from various VAR equations. The restrictions in these structural models are used to produce the orthogonal residuals necessary for the VDCs and IRFs. However, Bernanke and Blinder [1992] have recently argued against using structural VARs. They note that inferences drawn from structural VARs are typically sensitive to the choice of the specification of the structural model. McMillin and Parker [1994, pp. 492] note, "This is a critical problem since there is no general agreement on the 'best' structural model."

Due to the problems associated with structural VARs, this study uses a Choleski decomposition to produce the orthogonal residuals necessary to compute VDCs and IRFs.^(13)(14) The Choleski decomposition requires that variables in the VAR be ordered in a particular fashion. Because of cross-equation residual correlation, when a variable higher in the ordering changes, then all variables lower in the ordering are assumed to change.⁽¹⁵⁾ The extent of the change depends on the degree of the residual correlation. The ordering employed in this study is G, D, M2, R, Y, P.

The key element of this ordering is the placement of policy variables (G, D, and M2). Policy variables are placed first in the ordering.⁽¹⁶⁾ This allows policy variables to affect other system variables contemporaneously (within the same month). However, R, Y, and P have no impact on policy variables within the same month. R, Y, and P do have an impact on policy variables through the lags of the VAR. Hence, it is assumed that the information set available to policymakers contains only lagged values of R, Y, and P.⁽¹⁷⁾ This assumption seems reasonable in light of information lags and the use of monthly data.

G is used in the model as a proxy for the exogenous elements of fiscal policy. Therefore, G is placed first among the policy variables. M2 is placed last among the policy variables. This allows monetary policy to respond contemporaneously to fiscal policy changes, while fiscal policy cannot respond to monetary policy changes in the current period. Given the use of monthly data and the relative flexibility in the implementation of monetary policy, as compared to fiscal policy, this assumption seems reasonable.⁽¹⁸⁾

Given that R, Y, and P are placed below the policy variables in the ordering, the placement in the ordering of R, Y, and P relative to each other is a matter of indifference. The ordering G, D, M2, R, Y, P will produce the same impacts of D shocks on R, Y, and P as any other ordering where G, D, and M2 are the first, second, and third variables in the ordering.⁽¹⁹⁾ This is the case because D is given the credit for any contemporaneous relationships between D and M2, R, Y, and P.

The VDCs are reported in Table 1. Point estimates and standard errors are both reported. The estimates of the proportion of forecast error variance explained by each variable are judged as significant if the point estimate is at least twice the estimated standard error. Given that this study tests the Ricardian equivalence hypothesis, Table 1 reports only the VDCs for the proportion of the forecast error variance in R, Y, and P, explained by innovations to D. VDCs at horizons 12, 24, 36, and 48 months are reported to convey the dynamics of the system. Due to the arguments of Hafer and Sheehan [1991], VDCs are reported for VARs estimated with lag lengths of 3, 6, 7, and 12.

An analysis of Table 1 reveals that innovations to D explain significant portions of the forecast error variance in R, Y, and P at each time horizon.⁽²⁰⁾ Furthermore, the results are unchanged when the VAR lag length is altered. Altering the VAR lag changes point estimates somewhat. However, the significance of the point estimates is unchanged when the VAR lag is altered.

The VDCs in Table 1 show that government debt has important macroeconomic effects. However, the VDCs provide no indication of the direction of the effects of government debt. The direction of the effects of government debt are shown in IRFs. IRFs showing the impact of a shock to D on R, Y, and P are shown in Figures 1, 2, and 3. A two-standard-deviation confidence interval is reported for each IRF.⁽²¹⁾ A confidence interval containing zero indicates a lack of statistical significance.

Figure 1 indicates that a shock to D initially produces a negative impact on R. This impact remains significant for two periods and then becomes insignificant. Figure 2 indicates that a shock to D produces a significant, and negative, impact on Y for three periods. Figure 3 shows that a shock to D produces a negative impact on P. The impact on P of a D shock is significant for six periods and insignificant thereafter.

The negative initial impacts of D shocks to R, P, and Y are consistent with the evidence presented by Fackler and McMillin [1989], Kormendi [1983], and Evans [1987]. Fackler and McMillin find negative initial impacts of government debt on the AAA bond rate, real GNP, and the GNP deflator. Kormendi finds some evidence of negative effects of government debt on consumption. Evans finds evidence of negative effects of deficits on interest rates.

Negative effects of government debt on macroeconomic activity are not consistent with the conventional view that government debt is private sector wealth. The negative effects of government debt also appear to be at odds with the Ricardian equivalence hypothesis. However, Barro [1974], Kormendi [1983], and Fackler and McMillin [1989] argue that this is not the case. Fackler and McMillin [1989, pp. 1000] state that:

"...because of uncertainty about the individual's share of future taxes and the timing of these taxes, individuals may save more than the present value of the income streams associated with bonds issued to finance a deficit. In this view, wealth falls as deficits rise, so one would expect declines in interest rates, output, and prices."

This study has examined the relationship between macroeconomic activity and government debt over the period January 1980 to December 1995. This is the only study focusing on the 1980s and 1990s. The analysis was conducted using VDCs and IRFs derived from a VAR model.

The VDCs indicate that government debt has significant impacts on the interest rate, price level, and output. The IRFs indicate that shocks to government debt have significant and negative impacts on the interest rate, price level, and output. On balance, these results support an extreme form of the Ricardian view. In this view, wealth falls as deficits rise. In this case, an increase in government debt leads to decreases in interest rates, output, and prices.

Aschauer, David A. "Fiscal Policy and Aggregate Demand," American Economic Review, 75, 1, 1985, pp. 117-27.

Barro, Robert J. "Are Government Bonds Net Wealth?," Journal of Political Economy, 82, 6, 1974, pp. 1095-117.

Beard, Thomas R.; McMillin, W. Douglas. "The Impact of Budget Deficits in the Interwar Period," Journal of Macroeconomics, 13, 2, 1991, pp. 239-66.

Bernanke, Ben S. "Alternative Explanations of the Money-Income Correlation," Carnegie-Rochester Conference Series on Public Policy, 25, Autumn 1986, pp. 49-99.

Bernanke, Ben. S.; Blinder, Alan. "The Federal Funds Rate and the Channels of Monetary Transmission," American Economic Review, 82, 4, 1992, pp. 901-21.

Blanchard, Olivier J.; Quah, Danny. "The Dynamic Effects of Aggregate Demand and Supply Disturbances," American Economic Review, 79, 4, 1989, pp. 655-73.

Cox, W. Michael. "The Behavior of Treasury Securities: Monthly, 1942-1984," Journal of Monetary Economics, 16, 2, 1985, pp. 227-40.

Darrat, Ali F. "Fiscal Deficits and Long-Term Interest Rates: Further Evidence from Annual Data," Southern Economic Journal, 56, 2, 1989, pp. 363-74.

_____. "Structural Federal Deficits and Interest Rates: Some Causality and Co-Integration Tests," Southern Economic Journal, 56, 3, 1990, pp. 752-9.

de Leeuw, Frank; Holloway, Thomas M. "The Measurement and Significance of the Cyclically Adjusted Federal Budget and Debt," Journal of Money, Credit and Banking, 17, 2, 1985, pp. 232-42.

Dickey, David A.; Fuller, Wayne A. "Likelihood Ratio Statistics for Autoregressive Times Series with a Unit Root," Econometrica, 49, 4, 1981, pp. 1057-72.

Dwyer, Gerald P. "Inflation and Government Deficits," Economic Inquiry, 20, 3, 1982, pp. 315-29.

Eisner, Robert; Pieper, Paul J. "A New View of Federal Debt and Budget Deficits," American Economic Review, 74, 1, 1984, pp. 11-29.

Enders, Walter. Applied Econometric Times Series, New York, NY: John Wiley and Sons, 1995.

Engle, Robert F.; Granger, C. W. J. "Co-Integration and Error Correction: Representation, Estimation and Testing," Econometrica, 55, 2, 1987, pp. 251-76.

Evans, Paul. "Do Large Deficits Produce High Interest Rates?," American Economic Review, 75, 1, 1985, pp. 68-87.

_____. "Interest Rates and Expected Future Budget Deficits in the United States," Journal of Political Economy, 95, 1, 1987, pp. 34-58.

Fackler, James S.; McMillin, W. Douglas. "Federal Debt and Macroeconomic Activity," Southern Economic Journal, 55, 4, 1989, pp. 994-1003.

Feldstein, Martin. "Government Deficits and Aggregate Demand," Journal of Monetary Economics, 9, 1, 1982, pp. 1-20.

_____. "The Effects of Fiscal Policies When Incomes Are Uncertain: A Contradiction of Ricardian Equivalence," American Economic Review, 78, 1, 1988, pp. 14-23.

Fischer, Stanley. "Relative Shocks, Relative Price Variability, and Inflation," Brookings Papers on Economic Activity, 2, 1981, pp. 381-431.

Goff, Brian L. "Federal Deficit Effects on Short and Long Term Rates: A Note on Hoelscher," Southern Economic Journal, 57, 1, 1990, pp. 243-7.

Hafer, R. W.; Sheehan, Richard G. "Policy Inference Using VAR Models," Economic Inquiry, 29, 1, 1991, pp. 44-52.

Hoelscher, Gregory. "Federal Borrowing and Short-Term Interest Rates," Southern Economic Journal, 50, 2, 1983, pp. 319-33.

_____. "New Evidence on Deficits and Interest Rates," Journal of Money, Credit and Banking, 18, 1, 1986, pp. 1-17.

Johansen, Soren. "Statistical Analysis of Cointegration Vectors," Journal of Economic Dynamics and Control, 12, 2/3, 1988, pp. 231-54.

Kochin, Levis. "Are Future Taxes Anticipated by Consumers?," Journal of Money, Credit and Banking, 6, 3, 1974, pp. 385-94.

Kormendi, Roger C. "Government Debt, Government Spending, and Private Sector Behavior," American Economic Review, 73, 5, 1983, pp. 994-1010.

Makin, John H. "Real Interest, Money Surprises, Anticipated Inflation and Fiscal Deficits," Review of Economics and Statistics, 65, 3, 1983, pp. 374-84.

McMillin, W. Douglas. "Federal Deficits, Macrostabilization Goals, and Federal Reserve Behavior," Economic Inquiry, 24, 2, 1986a, pp. 257-69.

_____. "Federal Deficits and Short-Term Interest Rates," Journal of Macroeconomics, 8, 4, 1986b, pp. 403-22.

McMillin, W. Douglas; Parker, Randall E. "An Empirical Analysis of Oil Price Shocks in the Interwar Period," Economic Inquiry, 32, 3, 1994, pp. 486-97.

Miller, Stephen M.; Russek, Frank S. "Do Federal Deficits Affect Interest Rates? Evidence from Three Econometric Methods," Journal of Macroeconomics, 18, 3, 1996, pp. 403-28.

Ohanian, Lee E. "The Spurious Effects of Unit Roots on Vector Autoregressions: A Monte Carlo Study," Journal of Econometrics, 39, 3, 1988, pp. 251-66.

Plosser, Charles I. "Government Financing Decisions and Asset Returns," Journal of Monetary Economics, 9, 3, 1982, pp. 325-52.

Sawa, Takmitsu. "Information Criteria for Discriminating Among Alternative Regression Models," Econometrica, 46, 6, 1978, pp. 1273-91.

Seater, John J.; Mariano, Roberto S. "New Tests of the Life Cycle and Tax Discounting Hypothesis," Journal of Monetary Economics, 15, 2, 1985, pp. 195-215.

Spencer, David E., "Does Money Matter? The Robustness of Evidence from Vector Autoregressions," Journal of Money, Credit and Banking, 21, 4, 1989, pp. 442-54.

Swamy, Paravastu A. V. B.; Kolluri, Bharat R.; Singamsetti, Rao N. "What Do Regressions of Interest Rates on Deficits Imply?," Southern Economic Journal, 56, 4, 1990, pp. 1010-28.

Tanner, J. Ernest. "An Empirical Investigation of Tax Discounting," Journal of Money, Credit and Banking, 11, 2, 1979, pp. 214-8.

Yawitz, Jess B.; Meyer, Laurence H. "An Empirical Test of the Extent of Tax Discounting," Journal of Money, Credit and Banking, 8, 2, 1976, pp. 247-54.

1. Western Michigan University--U.S.A. This work was supported by a grant from the Faculty Research and Creative Activities Support Fund of Western Michigan University. The author wishes to thank Nancy S. Barrett, James S. Fackler, W. Douglas McMillin, Susan Pozo, and Paul D. Thistle for comments and suggestions.
(Return to Text)

2. Barro [1974] also argues that a stronger form of Ricardian equivalence is possible. In this stronger form and due to uncertainty about the individual's share of future taxes and the timing of future taxes, an increase in government debt leads to a decrease in private sector wealth and in spending. However, Feldstein [1988] has argued that increased income uncertainty can lead to increased spending and a rejection of Ricardian equivalence. Hence, whether uncertainty leads to a stronger form of Ricardian equivalence or a rejection of Ricardian equivalence is an empirical question.
(Return to Text)

3. In some cases, the models are estimated using both ordinary least squares and instrumental variables, such as two-stage least squares. Instrumental variables are used to correct for possible simultaneous equation bias. However, ordinary least squares and instrumental variables produce consistent results (see, for example, Hoelscher [1983] and Evans [1985]).
(Return to Text)

4. Using monthly data greatly restricts variables available for estimation. However, restricting the estimation period to the 1980s and 1990s leaves little choice but to use monthly data. If quarterly data were used, the estimation period would contain only 64 observations.
(Return to Text)

5. The nominal market value of privately held gross federal debt was provided by W. Michael Cox. This series originally appeared in Cox [1985]. He provides the series in seasonally unadjusted form. The X-11 procedure in the Statistical Analysis System was used to produce a seasonally adjusted nominal debt series. This series was then deflated by the consumer price index (CPI) to produce the real market value of privately held gross federal debt (D).
(Return to Text)

6. McMillin [1986a] notes that inflation tends to raise market interest rates and reduce the real market value of outstanding government debt. This causes a transfer of wealth from bondholders to the government. The change in the real market value of privately held government debt incorporates this effect.
(Return to Text)

7. Using monthly data greatly reduces the options for fiscal variables. Military expenditures are one of the few spending variables available on a monthly basis. Ideally, tax rates would be included in the model. However, reliable monthly series on tax rates are not available.
(Return to Text)

8. D, G, and M2 are defined as the relevant nominal variable divided by the CPI (P). A model is also estimated with D, G, and M2 placed in nominal terms. Policy implications remain unchanged if G, D, and M2 are placed in nominal terms.
(Return to Text)

9. A VAR that employs the producer price index instead of the CPI has also been estimated. VDCs and IRFs derived from the VAR that contains the producer price index produce implications consistent with the VDCs and IRFs derived from the VAR that contains the CPI.
(Return to Text)

10. The fiscal disruptions at the beginning of 1996 make December 1995 a good candidate for the end point of the estimation period.
(Return to Text)

11. As suggested by Enders [1995], the lag length used for the Johansen [1988] test is selected using the AIC for a VAR estimated with undifferenced data. The minimum AIC, for which all VAR equations have white noise errors, is produced with a lag of 7. Q-statistics are used to determine if residuals are white noise.
(Return to Text)

12. Sawa [1978] has argued that the AIC tends to choose models of higher order than the true model. However, Sawa states that the bias is negligible when the selected lag length is less than (N/10), as it is here (where N equals number of observations).
(Return to Text)

13. The Choleski decomposition is not without problems. A major criticism of the Choleski decomposition is that it places a recursive structure on contemporaneous relationships.
(Return to Text)

14. As a check on the VDC and IRF results reported in this paper, VDCs and IRFs have also been constructed using a Blanchard-Quah [1989] decomposition. Policy implications derived from the Blanchard-Quah decomposition are the same as those derived from the Choleski decomposition. The program used for the Blanchard-Quah decomposition was provided by William D. Lastrapes. VDCs and IRFs derived using the Blanchard-Quah decomposition are available from the author upon request.
(Return to Text)

15. Variables lower in the ordering are not allowed to influence variables higher in the ordering contemporaneously.
(Return to Text)

16. An argument can always be made that the interest rate, not the money stock, is the relevant policy variable. Because of this, VDCs and IRFs have been constructed with M2 and R switched in the ordering. This change has no impact on the results.
(Return to Text)

18. Switching D and M2 in the ordering does not alter the policy implications derived from the VAR.
(Return to Text)

19. The amount of forecast error variance in, for example, P, explained by shocks to R, will be altered by changing the relative placement of R, P, and Y in the ordering. However, this study is concerned with Ricardian equivalence, that is, with the impact of shocks to D on R, Y, and P.
(Return to Text)

20. Although not reported in Table 1, innovations to D also explain a significant portion of the forecast error variance in M2 at each time horizon. Innovations to D never explain a significant portion of the forecast error variance in G.
(Return to Text)

21. The IRFs reported in Figures 1, 2, and 3 are derived from a VAR estimated with the AIC selected lag length of 7. Conclusions are not altered if the VAR lag is set at 3, 6, or 12. One-thousand bootstrap simulations were used to construct the confidence intervals.
(Return to Text)