# Deficits and the demand for money.

I. Introduction

In recent years, the large budget deficits of the Federal Government have renewed interest in the effects of government debt on private sector behavior. To date, empirical research has focused on the relationship between debt and two key variables, consumption and interest rates.(1) By contrast, empirical research on the effects of government debt on other variables of interest to macroeconomists is limited. This paper examines the relationship between government debt and one such variable, real money balances. The neglect of government debt as a determinant of money demand is surprising. Many traditional macroeconomic models, such as Blinder and Solow's |9~ influential work, include government debt as an argument to the money demand function. Moreover, macroeconomic theorists have long been aware that a government debt -- money demand relationship has important implications for the efficacy of fiscal policy.(2)

This paper examines the relationship between government debt and real money holdings over the 1950-1990 period. A positive money -- debt relationship was previously noted by Butkiewicz |12~ and Deravi, Hegji, and Moberly |15~ (hereafter referred to as DHM). Our work improves upon this research in two ways. First, in contrast to Butkiewicz |12~ and DHM |15~, we investigate the time-series properties (stationarity, cointegration) of relevant variables. Second, we distinguish between supply-side and demand-side explanations of the debt-money relationship. The explanation advanced by Butkiewicz |12~ and DHM |15~ is that an increase government debt is perceived by the private sector as an increase in net wealth and hence should increase money demand.(3) This explanation ignores a potentially important connection between government debt and money supply. If the Federal Reserve monetizes debt, and if the private sector's adjustment to this monetization is lagged, then debt and real money balances will exhibit a positive correlation in the short run (but not the long run) even in the absence of a net wealth effect in money demand. It is thus crucial to distinguish between money demand and supply effects in empirical work on debt and real money holdings. To distinguish between these effects we develop a two-equation model of money demand and supply. Our model draws on Carr and Darby's |13~ "shock-absorber" framework, as well as work by Mishkin |39; 40~ and Bohara |10~.

The empirical results reported in this paper are stronger than those reported by Butkiewicz |12~ or DHM |15~. Their research found a contemporaneous relationship between money demand and government debt over the 1950-1973 period. We confirm this finding. We also find a strong evidence of lagged demand-side effects of changes in real government debt on real money holdings over the entire 1950-1990 period as well as the 1973-1990 period. However, we find no evidence that deficits are monetized. Thus, the positive correlation between money demand and government debt appears to be purely a result of demand-side factors.

The paper is organized as follows. In section II, we discuss the role of government debt in money demand and supply functions. In section III, we present the empirical analysis. We first test for the stationarity of the relevant variables. The evidence suggests that these variables are level non-stationary but difference stationary. Therefore, we perform co-integration tests on the money demand and monetary base reaction functions. For both functions, the null hypothesis of no-cointegration is not rejected. Finally, we bring demand and supply elements together using a "shock-absorber" money demand model. We jointly estimate money demand and monetary base reaction functions using the technique suggested by Mishkin |39; 40~. We find strong evidence that deficits increase the demand for money. By contrast, we find little evidence for a supply-side relationship. Section IV presents our concluding comments.

II. Deficits and the Demand for and Supply of Money

In this section, we discuss the role of government debt in money demand and supply. We begin with money demand. Economic theory suggests that money demand is related to a scale variable (i.e., transactions or wealth) and an opportunity cost measure. In equation (1), |m.sup.d~ is real money demand, y is real income, R is the nominal interest rate.

|m.sup.d~ = f(y, R, b) (1)

The inclusion of real government debt (b) in a money demand equation such as (1) can be justified on several grounds. The simplest justification is a net wealth effect, as discussed by authors such as Blinder and Solow |9~, Butkiewicz |12~, Mankiw and Summers |35~ and DHM |15~. Of course, if government bonds are part of net wealth, Ricardian Equivalence does not hold. However, there are models which imply a relationship between real money balances and government debt that do not rely upon a net wealth effect. One such model was suggested by Rodriguez |45~. He demonstrates that, in a cash-in-advance model, issuance of government debt increases transactions and hence money demand. Moreover, recent work on the liquidity effect by Grossman and Weiss |26~, Rotemberg |46~, Lucas |33~ and Christiano |14~ also derive conditions under which an open market operation increases real money holdings.(4)

There is also a supply-side explanation for a money-debt relationship that is not considered in previous work. Increases in government debt may be monetized by the government. If the private sector's adjustment to money supply shocks is not instantaneous, then positive money supply surprises lead to short run increases in real money holdings. This mechanism requires both that real money balances act to absorb real money shocks, as in the model of Carr and Darby |13~, and that deficits are monetized. Many papers, including Niskanen |41~, Hamburger and Zwick |27~, Allen and Smith |2~, Allen and McCrickard |1~, and Joines |29~, have investigated whether deficits are followed by increases in the money supply. To date, however, the empirical results on this question are mixed and the issue remains unsettled.

The theoretical foundations for a money supply reaction function are not well-developed. Our choice of explanatory variables for this function is therefore determined by earlier studies. Previous research found that the Federal Reserve has targeted interest rates (R), output (y), unemployment rates (U), and the price level (P).(5) Debt monetization by the Federal Reserve implies that we must include nominal debt (B) in the base money (H) reaction function.(6) Thus, the money supply reaction function can be written as:

H = g(y, R, B, P, U). (2)

III. The Interaction of Supply and Demand Factors in a "Shock-Absorber" Framework

In this section, we investigate the effects of government debt on the demand and supply of money. The analysis proceeds in the following steps. First, we test for the level and difference stationarity of all variables included in equations (1) and (2). We find that these variables are level non-stationary but difference stationary. Second, we test for a long-run cointegrating relationship for money demand and supply. In accordance with previous research, we find little evidence of cointegration for either relationship. Finally, we consider the short-run relationship between real money holdings and government debt implied by a first-difference formulation of equations (1) and (2), using Carr and Darby's |13~ shock-absorber model.

Recent work in econometrics has stressed the importance of time-series properties of the data, such as the degree of integration. As a preliminary step, we tested for the stationarity of all the variables in equations (1) and (2). Table I reports the results of three standard tests for stationarity, the Augmented Dickey-Fuller (ADF), and the Z|Alpha~ and Zt, tests developed by Phillips |43~ and Phillips and Perron |44~. (These tests are described in Appendix I. The data are described in Appendix 2.) The results suggest that all variables are level non-stationary but difference stationary. For some variables, notably the inflation rate and nominal money base growth, the Z|Alpha~ and Zt tests provide stronger evidence in favor of stationarity than the ADF tests. Nonetheless, all three tests can reject the null hypothesis of difference non-stationarity for most variables.(7)

TABULAR DATA OMITTED

Cointegration is a long-run equilibrium relationship between non-stationary variables. As the above results support the hypothesis of non-stationarity, a natural extension is to test for cointegration. We tested for the cointegration of variables in equations (1) and (2) by applying the ADF, Z|Alpha~ and Zt stationarity tests to the residuals of equations (1) and (2). The results for both equations strongly suggested that no cointegration exists. The null hypothesis of no cointegration was not rejected for any period for either equation.(8) Our failure to find a cointegrating relationship in money demand confirms earlier work by Miller |38~ and Friedman and Kuttner |21~.

However, the absence of cointegration does not preclude the existence of short-run relationships between the variables in (1) and (2). We test for short run relationships by expressing equations (1) and (2) in first difference form. In addition, we estimate the demand and supply relationships jointly.

The first building block of our model is a money demand equation.(9) In the absence of a long-run (cointegrated) relationship, we posit the following short-run money demand function where m* are desired money balances.

|Mathematical Expression Omitted~

Next, we incorporate a monetary base reaction function (along the lines of Barro |5; 6~, Mishkin |39; 40~, and Bohara |10~) into the analysis.

|Mathematical Expression Omitted~

Note that this specification permits a different response of the monetary base to changes in nominal indebtedness (||Mu~.sub.3i~) and inflation (||Mu~.sub.4i~).

The "shock absorber" money demand function of Carr and Darby |13~ provides a convenient way to jointly estimate the money demand and reaction functions. In this model, money surprises induce temporary increases in real money holdings as agents respond passively to money supply shocks. This relationship is given by equation (2|double prime~):

|Mathematical Expression Omitted~.

We estimate equations (1|prime~) and (2|double prime~) jointly using a non-linear generalized least squares technique. Carr and Darby's |13~ original work used a linear generated regressor method similar to that of Barro |5; 6~. The non-linear method is superior to the generated regressor method for three reasons, as Pagan |42~ and Mishkin |39; 40~ point out. First, the non-linear method yields more efficient parameter estimates. Second, the test statistics for the joint technique allow us to account for contemporaneous cross-equation correlations of the error terms ||Epsilon~.sub.t~ and ||Eta~.sub.t~. Finally, this method allows us to impose and test non-linear cross-equation restrictions.

In our empirical work we tested four restrictions:

(i) |Theta~ = 0 Monetary base shocks do not affect real money holdings

(ii) ||Phi~.sub.3i~ = 0 No effect of the real deficit on real money demand, i = 0 to 4.

(iii) |Theta~ = ||Phi~.sub.3i~ = 0 No effects of real deficits or money base surprises on real money holdings, i = 0 to 4.

(iv) ||Mu~.sub.3i~ = 0 No effects of nominal deficits on nominal money base movements, i = 0 to 4.

We used Gallant and Jorgensen's |23~ statistic to test these restrictions. This test statistic is n(|S.sub.r~ - |S.sub.u~), where n is the number of observations, |S.sub.r~ and |S.sub.u~ are the sums of squared errors for the restricted system and unrestricted system, respectively. This statistic is distributed Chi-squared with degrees of freedom equal to the number of restrictions.

Restriction (i) tests the "shock absorber" approach. The second restriction tests whether or not an increase in the real deficit increases the demand for real balances. Restriction (iii) is a joint test of restrictions (i) and (ii). The final restriction is a test of the debt monetization hypothesis.

We determined the lag length for each equation using the Akaike Information Criteria. The results suggested that the optimal lag length for both equations on all explanatory variables was 4.(10) In addition, we split the sample at 1972:4. We choose this breakpoint given the widespread evidence of instability in money demand after this date |24~.

The results are reported in Tables II, III, and IV. Table II provides the tests results and the adjusted system R-squares as well as Durbin's F-Test for serial correlation as suggested by Maddala |34, 248~.(11) Table III reports the sums of the estimated coefficients on |Theta~, |Phi~, and |Mu~. Finally, Table IV presents the individual coefficient estimates of ||Phi~.sub.3i~, i = 0 to 4, for the unrestricted version of equation (2|double prime~).

The results suggest that deficits increase the demand for real money balances. With respect to the entire 1950-1990 period, we find a strong positive relationship between changes in debt and changes in money demand. From Table III, the restriction (ii) that ||Phi~.sub.3i~ = 0, is always rejected at better than the 95 percent level. From Table III, note that the coefficients on the deficit sum to 0.18. In addition, note from Table IV that most of the explanatory power for the debt terms in money demand is due to lags 3 and 4.

With respect to the 1950-1972 sub-period, a strong contemporaneous relationship between changes in debt and changes in money demand is present. Our results are similar to those of DHM |15~, who found a contemporaneous money-deficit relationship during the same period. As well, lags 3 and 4 are significantly different from zero (||Phi~.sub.33~ = 0.07, ||Phi~.sub.34~ = -0.09) at the 90 percent level or better. With respect to the 1972-1990 sub-period, a stronger relationship between changes in debt and changes in money demand is apparent. The first lag is positive and significantly different from zero at the 90 percent level, while lags 3 and 4 are positive and significantly different from zero at the 95 percent level or better. As Table III shows, restriction (ii) that ||Phi~.sub.3i~ = 0, is again rejected at the 95 percent level. Over this period the deficit terms sum to 0.43.

The results suggest that, in accordance with the "shock-absorber" approach, money supply shocks increase real money holdings. Note also that both restrictions (i) (|Theta~ = 0) and (iii) (|Theta~ = ||Phi~.sub.3i~ = 0) are rejected at the 95 percent level or better for the whole period, as well as the two sub-samples. As shown in Table IV, most values of |Theta~ lie between 0.3 and 0.4, suggesting that a one-percent shock to the monetary base corresponds to an increase in real money balances of between 0.3 percent and 0.4 percent.

However, there is little evidence of a supply-side relationship between money and debt. Table III shows that restriction (iv), (||Mu~.sub.4i~ = 0) cannot be rejected at conventional significance levels in either period. Moreover, as shown by Table IV, the ||Mu~.sub.4i~ parameter estimates are highly sensitive with respect to the choice of sample and imposition of restrictions. Therefore, it would appear that the money-debt relationship is not explainable in terms of debt monetization. Our TABULAR DATA OMITTED results confirm those of Joines |29~ who found that previous evidence in favor of the debt monetization hypothesis resulted from seasonality. Thus, the positive correlation between real money balances and government debt is due to demand factors.

IV. Concluding Comments

This paper has analyzed the relationship between real money demand (|m.sub.1~) and the government deficit (adjusted for inflation and measured at market value). We found that increases in the deficit raised the demand for real balances especially for the post-1972 period. In addition, we found TABULAR DATA OMITTED TABULAR DATA OMITTED that the positive correlation between deficits and real money holdings is not explainable by money supply factors. Indeed, for no period did we find evidence that deficits were monetized by the monetary authorities.

However, the existence of a positive relationship between the deficit and real money holdings is not necessarily evidence against Ricardian Equivalence as implied by DHM |15~. Rather, the presence of transactions costs or a financial transactions demand for money can give rise to a positive debt-money relationship, even if Ricardian Equivalence holds. Thus, the underlying origins of the positive correlation between debt and money established in this paper remains a question for further research.

Appendix 1: The Z|Alpha~ and Zt Tests

Phillips's |43~ and Phillips and Perron's |44~ non-parametric Z|Alpha~ and Zt for any variable V are calculated by first running the regression

|Mathematical Expression Omitted~.

Next, the test statistics are defined as

|Mathematical Expression Omitted~

|Mathematical Expression Omitted~

where

|Mathematical Expression Omitted~

and

|Mathematical Expression Omitted~.

A modification of the above is made for the case in which the trend term is included.

Appendix 2: Data Description

1. |m.sub.1~: Nominal Money (M1) deflated by GNP Deflator. Source: Federal Reserve Bulletin, National Income and Product Accounts. Seasonally adjusted by authors with X-11 procedure.

2. H: Nominal Monetary Base. Source: Federal Reserve Bulletin. Seasonally adjusted by authors with X-11 procedure.

3. y: Real Gross National Product, Seasonally Adjusted. Source: National Income and Product Accounts

4. P: Gross National Product Deflator, Seasonally Adjusted. Source: National Income and Product Accounts

5. R: Nominal Commercial Paper Rate. Source: Federal Reserve Bulletin

6. B, b: Nominal, Real Government Indebtedness at Market Value. Source: W. Michael Cox, Federal Reserve Bank of Dallas.

7. U: Unemployment rate, Seasonally Adjusted. Source: Bureau of Economic Analysis, U.S. Department of Commerce.

The authors are indebted to an anonymous referee for helpful comments.

1. Barro's |4~ article on Ricardian Equivalence stimulated much of this work. Empirical studies of debt and consumption include Feldstein |18~, Kormendi |30~, Aschauer |3~, Barth, Iden, and Russek |8~, Kormendi and Meguire |31; 32~, Modigliani and Sterling |36; 37~, and Feldstein and Elmendorf |19~. Empirical studies of deficits and interest rates include Feldstein and Eckstien |20~, Evans |16~, and Barro and Sala-i-Martin |7~.

2. In the IS/LM model a deficit induces a leftward shift in the LM curve (in addition to the expected rightward shift of the IS curve) if government debt is an argument of money demand. See the debate surrounding Milton Friedman's Monetary Framework in Gordon |25~ and especially Brunner and Meltzer |11~. More recently, see Mankiw and Summers |35~.

3. However, as discussed in section II, a net wealth effect is not necessary for deficits to affect money demand. Increases in government indebtedness may induce additional transactions (and hence increase money holdings). Thus, a money demand -- debt relationship does not imply a refutation of the Ricardian Equivalence Hypothesis.

4. These papers use variants of the cash-in-advance constraint. Critical to their results is the timing of monetary and consumption transactions. For example, the papers of Grossman and Weiss |26~ and Rotemberg |46~ rest on the assumption that not all agents can conduct financial transactions simultaneously.

5. The date after which the Federal Reserve ceased to target interest rates is generally taken to be 1979. However, Hoelscher |28~ claims that there is little difference between the pre- and post- 1979 behavior of the Fed with respect to interest rate targeting.

6. Empirically, our results reported below are unchanged if real debt is used.

7. The reported results do not include a time-trend. For most variables, inclusion of a time-trend does not change results. Two variables, unemployment (U) and the nominal interest rate (R) appear to be level-stationary if a time trend is included. However, for these variables, the time-trend is not statistically significant. Thus, we enter U and R into subsequent estimations in first difference form. When the detrended levels of these variables were used, we obtained identical results.

8. For example, the ADF t-statistic with 4 lags, ADF(4) for the residual of the money demand equation estimated over the entire period was 2.89. The 95% critical value is 4.02, as shown in Engle and Yoo |17~. Complete results are available from the authors on request.

9. The original Carr-Darby |13~ formulation included lagged adjustment. Our empirical results are unchanged if a lagged dependent term is included.

10. The criteria were applied to each equation separately.

11. The F-statistic is a test of the restriction |a.sub.1~ = 0 in the regression |e.sub.t~ = |a.sub.0~ + |a.sub.1~|e.sub.t - 1~ + |a.sub.2~|y.sub.t - 1~ + |Sigma~||Beta~.sub.i~|x.sub.i~ + error, where e is the residual of regressions (1|prime~) or (2|double prime~), y is the dependent variable (real |m.sub.1~ or the monetary base H) and the |x.sub.i~ are the explanatory variables. This test is an alternative to Durbin's H. The null hypothesis of no serial correlation is not rejected only for restriction (iv). In all other cases, the null hypothesis of serial correlation is rejected.

References

1. Allen, Scott D., and Douglas D. McCrickard, "Deficits and Money Growth in the United States: A Comment." Journal of Monetary Economics, January 1983, 143-53.

2. ----- and M. D. Smith, "Government Borrowing and Monetary Accommodation." Journal of Monetary Economics, November 1983, 605-16.

3. Aschauer, David Alan, "Fiscal Policy and Aggregate Demand." American Economic Review, March 1985, 117-27.

4. Barro, Robert, "Are Government Bonds Net Wealth?" Journal of Political Economy, November-December 1974, 1095-117.

5. -----, "Unanticipated Money Growth and Unemployment in the United States." American Economic Review, March 1977, 101-15.

6. -----, "Unanticipated Money, Output, and the Price Level in the United States." Journal of Political Economy, August 1978, 548-80.

7. ----- and Xavier Sala-i-Martin. "World Real Interest Rates" in NBER Macroeconomics Annual, edited by O. J. Blanchard and S. Fischer. Cambridge: MIT Press, 1990, pp. 15-59.

8. Barth, James, George A. Iden and Frank S. Russek, "Government Debt, Government Spending, and Private Sector Behavior: Comment." American Economic Review, December 1986, 1158-67.

9. Blinder, Alan and Robert Solow, editors. The Economics of Public Finance. Washington: The Brookings Institution, 1974, pp. 3-118.

10. Bohara, Alok K., "Testing The Rational-Expectations Hypothesis: Further Evidence." Journal of Business Economics and Statistics, June 1991, 337-40.

11. Brunner, Karl and Allan H. Meltzer, "Friedman's Monetary Theory" in Milton Friedman's Monetary Framework: A Debate With His Critics, edited by R. Gordon. Chicago: University of Chicago Press, 1970.

12. Butkiewicz, James L., "Outside Wealth, the Demand for Money, and the Crowding Out Effect." Journal of Monetary Economics, April 1979, 249-81.

13. Carr, Jack L. and Michael R. Darby, "The Role of Money Supply Shocks in the Short-Run Demand for Money." Journal of Monetary Economics, September 1981, 183-99.

14. Christiano, Laurence, "Modeling the Liquidity Effect of a Money Shock." Quarterly Review, Federal Reserve Bank of Minneapolis, Winter 1991, 3-34.

15. Deravi, M. Kevin, Charles E. Hegji, and H. Dean Moberly, "Government Debt and the Demand For Money: An Extreme Bounds Analysis." Economic Inquiry, April 1990, 390-401.

16. Evans, Paul, "Do Large Budget Deficits Produce High Interest Rates?" American Economic Review, March 1985, 68-87.

17. Engle, Robert F. and Byong Sam Yoo, "Forecasting and Testing in Cointegrating Systems." Journal of Econometrics, May 1987, 143-59.

18. Feldstein, Martin S., "Government Deficits and Aggregate Demand." Journal of Monetary Economics, January 1982, 1-20.

19. ----- and Douglas W. Elmendorf, "Government Debt, Government Spending, and Private Sector Behavior Revisited: Comment." American Economic Review, June 1990, 589-99.

20. ----- and Otto Eckstein, "The Fundamental Determinants of the Interest Rate." Review of Economics and Statistics, November 1972, 363-75.

21. Friedman, Benjamin and Kenneth Kuttner, "Money, Income, Prices and Interest Rates." American Economic Review, June 1992, 472-92.

22. Fuller, Wayne A. Introduction to Statistical Time Series. New York: Wiley 1976, pp. 371-73.

23. Gallant, A. Ronald and Dale W. Jorgensen, "Statistical Inference for a System of Simultaneous, Nonlinear, Implicit Equations in the Context of Instrumental Variables Estimation." Journal of Econometrics, October/December 1979, 275-302.

24. Goldfeld, Stephen M., "The Demand for Money Revisited." Brookings Papers on Economic Activity 1973; 3, 577-638.

25. Gordon, Robert, Milton Friedman's Monetary Framework: A Debate With His Critics. Chicago: University of Chicago Press, 1970.

26. Grossman, Sanford and Laurence Weiss, "A Transactions-Based Model of The Monetary Transmissions Mechanism." American Economic Review, December 1983, 871-80.

27. Hamburger, Michael J. and Burton Zwick, "Deficits, Money, and Inflation." Journal of Monetary Economics, January 1981, 141-50.

28. Hoelscher, Gregory, "1979-1982: Rules or Discretion in Monetary Policy?" Economic Inquiry, April 1990, 249-56.

29. Joines, Douglas H., "Deficits and Money Growth in the United States, 1872-1983." Journal of Monetary Economics, November 1985, 329-51.

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

31. ----- and Phillip Meguire, "Government Debt, Government Spending, and Private Sector Behavior: Reply." American Economic Review, December 1986, 1180-87.

32. -----, "Government Debt, Government Spending, and Private Sector Behavior: Reply and Update." American Economic Review, June 1990, 604-17.

33. Lucas, Robert E. Jr., "Liquidity and Interest Rates." Journal of Economic Theory, April 1990, 237-64.

34. Maddala, G. S. Introduction to Econometrics. New York: MacMillan, 1992.

35. Mankiw, N. Gregory and Larry Summers, "Consumption, Money Demand, and Fiscal Policy Effects." Journal of Money, Credit and Banking, November 1986, 415-29.

36. Modigliani, Franco and Arlie Sterling, "Government Debt, Government Spending, and Private Sector Behavior: Comment." American Economic Review, December 1986, 1168-79.

37. ----- and -----, "Government Debt, Government Spending, and Private Sector Behavior: A Further Comment." American Economic Review, June 1990, 600-603.

38. Miller, Stephen M., "Monetary Dynamics: An Application of Cointegration and Error-Correction Modeling." Journal of Money, Credit, and Banking, May 1991, 139-54.

39. Mishkin, Fredrick S., "Does Anticipated Monetary Policy Matter: An Econometric Investigation." Journal of Political Economy, February 1982, 22-51.

40. -----, "Does Anticipated Aggregate Demand Policy Matter? Further Econometric Results." American Economic Review, September 1982, 788-802.

41. Niskanen, William A., "Deficits, Government Spending, and Inflation: What Is the Evidence?" Journal of Monetary Economics, August 1978, 591-602.

42. Pagan, Adrian R., "Econometric Issues in the Analysis of Regression With Generated Regressors." International Economic Review, February 1984, 221-47.

43. Phillips, Peter C. B., "Time Series Regressions with a Unit Root." Econometrica, March 1987, 277-301.

44. ----- and Pierre Perron, "Testing for a Unit Root in Time-Series Regressions." Biometrika, June 1988, 335-46.

45. Rodriguez, Alvaro, "The Debt-Money Ratio: What Are The Limits." Rivista di Politica Econonomica, December 1990, 330-51.

46. Rotemberg, Julio J., "A Monetary Equilibrium Model With Transactions Costs." Journal of Political Economy, February 1984, 40-58.

In recent years, the large budget deficits of the Federal Government have renewed interest in the effects of government debt on private sector behavior. To date, empirical research has focused on the relationship between debt and two key variables, consumption and interest rates.(1) By contrast, empirical research on the effects of government debt on other variables of interest to macroeconomists is limited. This paper examines the relationship between government debt and one such variable, real money balances. The neglect of government debt as a determinant of money demand is surprising. Many traditional macroeconomic models, such as Blinder and Solow's |9~ influential work, include government debt as an argument to the money demand function. Moreover, macroeconomic theorists have long been aware that a government debt -- money demand relationship has important implications for the efficacy of fiscal policy.(2)

This paper examines the relationship between government debt and real money holdings over the 1950-1990 period. A positive money -- debt relationship was previously noted by Butkiewicz |12~ and Deravi, Hegji, and Moberly |15~ (hereafter referred to as DHM). Our work improves upon this research in two ways. First, in contrast to Butkiewicz |12~ and DHM |15~, we investigate the time-series properties (stationarity, cointegration) of relevant variables. Second, we distinguish between supply-side and demand-side explanations of the debt-money relationship. The explanation advanced by Butkiewicz |12~ and DHM |15~ is that an increase government debt is perceived by the private sector as an increase in net wealth and hence should increase money demand.(3) This explanation ignores a potentially important connection between government debt and money supply. If the Federal Reserve monetizes debt, and if the private sector's adjustment to this monetization is lagged, then debt and real money balances will exhibit a positive correlation in the short run (but not the long run) even in the absence of a net wealth effect in money demand. It is thus crucial to distinguish between money demand and supply effects in empirical work on debt and real money holdings. To distinguish between these effects we develop a two-equation model of money demand and supply. Our model draws on Carr and Darby's |13~ "shock-absorber" framework, as well as work by Mishkin |39; 40~ and Bohara |10~.

The empirical results reported in this paper are stronger than those reported by Butkiewicz |12~ or DHM |15~. Their research found a contemporaneous relationship between money demand and government debt over the 1950-1973 period. We confirm this finding. We also find a strong evidence of lagged demand-side effects of changes in real government debt on real money holdings over the entire 1950-1990 period as well as the 1973-1990 period. However, we find no evidence that deficits are monetized. Thus, the positive correlation between money demand and government debt appears to be purely a result of demand-side factors.

The paper is organized as follows. In section II, we discuss the role of government debt in money demand and supply functions. In section III, we present the empirical analysis. We first test for the stationarity of the relevant variables. The evidence suggests that these variables are level non-stationary but difference stationary. Therefore, we perform co-integration tests on the money demand and monetary base reaction functions. For both functions, the null hypothesis of no-cointegration is not rejected. Finally, we bring demand and supply elements together using a "shock-absorber" money demand model. We jointly estimate money demand and monetary base reaction functions using the technique suggested by Mishkin |39; 40~. We find strong evidence that deficits increase the demand for money. By contrast, we find little evidence for a supply-side relationship. Section IV presents our concluding comments.

II. Deficits and the Demand for and Supply of Money

In this section, we discuss the role of government debt in money demand and supply. We begin with money demand. Economic theory suggests that money demand is related to a scale variable (i.e., transactions or wealth) and an opportunity cost measure. In equation (1), |m.sup.d~ is real money demand, y is real income, R is the nominal interest rate.

|m.sup.d~ = f(y, R, b) (1)

The inclusion of real government debt (b) in a money demand equation such as (1) can be justified on several grounds. The simplest justification is a net wealth effect, as discussed by authors such as Blinder and Solow |9~, Butkiewicz |12~, Mankiw and Summers |35~ and DHM |15~. Of course, if government bonds are part of net wealth, Ricardian Equivalence does not hold. However, there are models which imply a relationship between real money balances and government debt that do not rely upon a net wealth effect. One such model was suggested by Rodriguez |45~. He demonstrates that, in a cash-in-advance model, issuance of government debt increases transactions and hence money demand. Moreover, recent work on the liquidity effect by Grossman and Weiss |26~, Rotemberg |46~, Lucas |33~ and Christiano |14~ also derive conditions under which an open market operation increases real money holdings.(4)

There is also a supply-side explanation for a money-debt relationship that is not considered in previous work. Increases in government debt may be monetized by the government. If the private sector's adjustment to money supply shocks is not instantaneous, then positive money supply surprises lead to short run increases in real money holdings. This mechanism requires both that real money balances act to absorb real money shocks, as in the model of Carr and Darby |13~, and that deficits are monetized. Many papers, including Niskanen |41~, Hamburger and Zwick |27~, Allen and Smith |2~, Allen and McCrickard |1~, and Joines |29~, have investigated whether deficits are followed by increases in the money supply. To date, however, the empirical results on this question are mixed and the issue remains unsettled.

The theoretical foundations for a money supply reaction function are not well-developed. Our choice of explanatory variables for this function is therefore determined by earlier studies. Previous research found that the Federal Reserve has targeted interest rates (R), output (y), unemployment rates (U), and the price level (P).(5) Debt monetization by the Federal Reserve implies that we must include nominal debt (B) in the base money (H) reaction function.(6) Thus, the money supply reaction function can be written as:

H = g(y, R, B, P, U). (2)

III. The Interaction of Supply and Demand Factors in a "Shock-Absorber" Framework

In this section, we investigate the effects of government debt on the demand and supply of money. The analysis proceeds in the following steps. First, we test for the level and difference stationarity of all variables included in equations (1) and (2). We find that these variables are level non-stationary but difference stationary. Second, we test for a long-run cointegrating relationship for money demand and supply. In accordance with previous research, we find little evidence of cointegration for either relationship. Finally, we consider the short-run relationship between real money holdings and government debt implied by a first-difference formulation of equations (1) and (2), using Carr and Darby's |13~ shock-absorber model.

Recent work in econometrics has stressed the importance of time-series properties of the data, such as the degree of integration. As a preliminary step, we tested for the stationarity of all the variables in equations (1) and (2). Table I reports the results of three standard tests for stationarity, the Augmented Dickey-Fuller (ADF), and the Z|Alpha~ and Zt, tests developed by Phillips |43~ and Phillips and Perron |44~. (These tests are described in Appendix I. The data are described in Appendix 2.) The results suggest that all variables are level non-stationary but difference stationary. For some variables, notably the inflation rate and nominal money base growth, the Z|Alpha~ and Zt tests provide stronger evidence in favor of stationarity than the ADF tests. Nonetheless, all three tests can reject the null hypothesis of difference non-stationarity for most variables.(7)

TABULAR DATA OMITTED

Cointegration is a long-run equilibrium relationship between non-stationary variables. As the above results support the hypothesis of non-stationarity, a natural extension is to test for cointegration. We tested for the cointegration of variables in equations (1) and (2) by applying the ADF, Z|Alpha~ and Zt stationarity tests to the residuals of equations (1) and (2). The results for both equations strongly suggested that no cointegration exists. The null hypothesis of no cointegration was not rejected for any period for either equation.(8) Our failure to find a cointegrating relationship in money demand confirms earlier work by Miller |38~ and Friedman and Kuttner |21~.

However, the absence of cointegration does not preclude the existence of short-run relationships between the variables in (1) and (2). We test for short run relationships by expressing equations (1) and (2) in first difference form. In addition, we estimate the demand and supply relationships jointly.

The first building block of our model is a money demand equation.(9) In the absence of a long-run (cointegrated) relationship, we posit the following short-run money demand function where m* are desired money balances.

|Mathematical Expression Omitted~

Next, we incorporate a monetary base reaction function (along the lines of Barro |5; 6~, Mishkin |39; 40~, and Bohara |10~) into the analysis.

|Mathematical Expression Omitted~

Note that this specification permits a different response of the monetary base to changes in nominal indebtedness (||Mu~.sub.3i~) and inflation (||Mu~.sub.4i~).

The "shock absorber" money demand function of Carr and Darby |13~ provides a convenient way to jointly estimate the money demand and reaction functions. In this model, money surprises induce temporary increases in real money holdings as agents respond passively to money supply shocks. This relationship is given by equation (2|double prime~):

|Mathematical Expression Omitted~.

We estimate equations (1|prime~) and (2|double prime~) jointly using a non-linear generalized least squares technique. Carr and Darby's |13~ original work used a linear generated regressor method similar to that of Barro |5; 6~. The non-linear method is superior to the generated regressor method for three reasons, as Pagan |42~ and Mishkin |39; 40~ point out. First, the non-linear method yields more efficient parameter estimates. Second, the test statistics for the joint technique allow us to account for contemporaneous cross-equation correlations of the error terms ||Epsilon~.sub.t~ and ||Eta~.sub.t~. Finally, this method allows us to impose and test non-linear cross-equation restrictions.

In our empirical work we tested four restrictions:

(i) |Theta~ = 0 Monetary base shocks do not affect real money holdings

(ii) ||Phi~.sub.3i~ = 0 No effect of the real deficit on real money demand, i = 0 to 4.

(iii) |Theta~ = ||Phi~.sub.3i~ = 0 No effects of real deficits or money base surprises on real money holdings, i = 0 to 4.

(iv) ||Mu~.sub.3i~ = 0 No effects of nominal deficits on nominal money base movements, i = 0 to 4.

We used Gallant and Jorgensen's |23~ statistic to test these restrictions. This test statistic is n(|S.sub.r~ - |S.sub.u~), where n is the number of observations, |S.sub.r~ and |S.sub.u~ are the sums of squared errors for the restricted system and unrestricted system, respectively. This statistic is distributed Chi-squared with degrees of freedom equal to the number of restrictions.

Restriction (i) tests the "shock absorber" approach. The second restriction tests whether or not an increase in the real deficit increases the demand for real balances. Restriction (iii) is a joint test of restrictions (i) and (ii). The final restriction is a test of the debt monetization hypothesis.

We determined the lag length for each equation using the Akaike Information Criteria. The results suggested that the optimal lag length for both equations on all explanatory variables was 4.(10) In addition, we split the sample at 1972:4. We choose this breakpoint given the widespread evidence of instability in money demand after this date |24~.

The results are reported in Tables II, III, and IV. Table II provides the tests results and the adjusted system R-squares as well as Durbin's F-Test for serial correlation as suggested by Maddala |34, 248~.(11) Table III reports the sums of the estimated coefficients on |Theta~, |Phi~, and |Mu~. Finally, Table IV presents the individual coefficient estimates of ||Phi~.sub.3i~, i = 0 to 4, for the unrestricted version of equation (2|double prime~).

The results suggest that deficits increase the demand for real money balances. With respect to the entire 1950-1990 period, we find a strong positive relationship between changes in debt and changes in money demand. From Table III, the restriction (ii) that ||Phi~.sub.3i~ = 0, is always rejected at better than the 95 percent level. From Table III, note that the coefficients on the deficit sum to 0.18. In addition, note from Table IV that most of the explanatory power for the debt terms in money demand is due to lags 3 and 4.

With respect to the 1950-1972 sub-period, a strong contemporaneous relationship between changes in debt and changes in money demand is present. Our results are similar to those of DHM |15~, who found a contemporaneous money-deficit relationship during the same period. As well, lags 3 and 4 are significantly different from zero (||Phi~.sub.33~ = 0.07, ||Phi~.sub.34~ = -0.09) at the 90 percent level or better. With respect to the 1972-1990 sub-period, a stronger relationship between changes in debt and changes in money demand is apparent. The first lag is positive and significantly different from zero at the 90 percent level, while lags 3 and 4 are positive and significantly different from zero at the 95 percent level or better. As Table III shows, restriction (ii) that ||Phi~.sub.3i~ = 0, is again rejected at the 95 percent level. Over this period the deficit terms sum to 0.43.

The results suggest that, in accordance with the "shock-absorber" approach, money supply shocks increase real money holdings. Note also that both restrictions (i) (|Theta~ = 0) and (iii) (|Theta~ = ||Phi~.sub.3i~ = 0) are rejected at the 95 percent level or better for the whole period, as well as the two sub-samples. As shown in Table IV, most values of |Theta~ lie between 0.3 and 0.4, suggesting that a one-percent shock to the monetary base corresponds to an increase in real money balances of between 0.3 percent and 0.4 percent.

However, there is little evidence of a supply-side relationship between money and debt. Table III shows that restriction (iv), (||Mu~.sub.4i~ = 0) cannot be rejected at conventional significance levels in either period. Moreover, as shown by Table IV, the ||Mu~.sub.4i~ parameter estimates are highly sensitive with respect to the choice of sample and imposition of restrictions. Therefore, it would appear that the money-debt relationship is not explainable in terms of debt monetization. Our TABULAR DATA OMITTED results confirm those of Joines |29~ who found that previous evidence in favor of the debt monetization hypothesis resulted from seasonality. Thus, the positive correlation between real money balances and government debt is due to demand factors.

IV. Concluding Comments

This paper has analyzed the relationship between real money demand (|m.sub.1~) and the government deficit (adjusted for inflation and measured at market value). We found that increases in the deficit raised the demand for real balances especially for the post-1972 period. In addition, we found TABULAR DATA OMITTED TABULAR DATA OMITTED that the positive correlation between deficits and real money holdings is not explainable by money supply factors. Indeed, for no period did we find evidence that deficits were monetized by the monetary authorities.

However, the existence of a positive relationship between the deficit and real money holdings is not necessarily evidence against Ricardian Equivalence as implied by DHM |15~. Rather, the presence of transactions costs or a financial transactions demand for money can give rise to a positive debt-money relationship, even if Ricardian Equivalence holds. Thus, the underlying origins of the positive correlation between debt and money established in this paper remains a question for further research.

Appendix 1: The Z|Alpha~ and Zt Tests

Phillips's |43~ and Phillips and Perron's |44~ non-parametric Z|Alpha~ and Zt for any variable V are calculated by first running the regression

|Mathematical Expression Omitted~.

Next, the test statistics are defined as

|Mathematical Expression Omitted~

|Mathematical Expression Omitted~

where

|Mathematical Expression Omitted~

and

|Mathematical Expression Omitted~.

A modification of the above is made for the case in which the trend term is included.

Appendix 2: Data Description

1. |m.sub.1~: Nominal Money (M1) deflated by GNP Deflator. Source: Federal Reserve Bulletin, National Income and Product Accounts. Seasonally adjusted by authors with X-11 procedure.

2. H: Nominal Monetary Base. Source: Federal Reserve Bulletin. Seasonally adjusted by authors with X-11 procedure.

3. y: Real Gross National Product, Seasonally Adjusted. Source: National Income and Product Accounts

4. P: Gross National Product Deflator, Seasonally Adjusted. Source: National Income and Product Accounts

5. R: Nominal Commercial Paper Rate. Source: Federal Reserve Bulletin

6. B, b: Nominal, Real Government Indebtedness at Market Value. Source: W. Michael Cox, Federal Reserve Bank of Dallas.

7. U: Unemployment rate, Seasonally Adjusted. Source: Bureau of Economic Analysis, U.S. Department of Commerce.

The authors are indebted to an anonymous referee for helpful comments.

1. Barro's |4~ article on Ricardian Equivalence stimulated much of this work. Empirical studies of debt and consumption include Feldstein |18~, Kormendi |30~, Aschauer |3~, Barth, Iden, and Russek |8~, Kormendi and Meguire |31; 32~, Modigliani and Sterling |36; 37~, and Feldstein and Elmendorf |19~. Empirical studies of deficits and interest rates include Feldstein and Eckstien |20~, Evans |16~, and Barro and Sala-i-Martin |7~.

2. In the IS/LM model a deficit induces a leftward shift in the LM curve (in addition to the expected rightward shift of the IS curve) if government debt is an argument of money demand. See the debate surrounding Milton Friedman's Monetary Framework in Gordon |25~ and especially Brunner and Meltzer |11~. More recently, see Mankiw and Summers |35~.

3. However, as discussed in section II, a net wealth effect is not necessary for deficits to affect money demand. Increases in government indebtedness may induce additional transactions (and hence increase money holdings). Thus, a money demand -- debt relationship does not imply a refutation of the Ricardian Equivalence Hypothesis.

4. These papers use variants of the cash-in-advance constraint. Critical to their results is the timing of monetary and consumption transactions. For example, the papers of Grossman and Weiss |26~ and Rotemberg |46~ rest on the assumption that not all agents can conduct financial transactions simultaneously.

5. The date after which the Federal Reserve ceased to target interest rates is generally taken to be 1979. However, Hoelscher |28~ claims that there is little difference between the pre- and post- 1979 behavior of the Fed with respect to interest rate targeting.

6. Empirically, our results reported below are unchanged if real debt is used.

7. The reported results do not include a time-trend. For most variables, inclusion of a time-trend does not change results. Two variables, unemployment (U) and the nominal interest rate (R) appear to be level-stationary if a time trend is included. However, for these variables, the time-trend is not statistically significant. Thus, we enter U and R into subsequent estimations in first difference form. When the detrended levels of these variables were used, we obtained identical results.

8. For example, the ADF t-statistic with 4 lags, ADF(4) for the residual of the money demand equation estimated over the entire period was 2.89. The 95% critical value is 4.02, as shown in Engle and Yoo |17~. Complete results are available from the authors on request.

9. The original Carr-Darby |13~ formulation included lagged adjustment. Our empirical results are unchanged if a lagged dependent term is included.

10. The criteria were applied to each equation separately.

11. The F-statistic is a test of the restriction |a.sub.1~ = 0 in the regression |e.sub.t~ = |a.sub.0~ + |a.sub.1~|e.sub.t - 1~ + |a.sub.2~|y.sub.t - 1~ + |Sigma~||Beta~.sub.i~|x.sub.i~ + error, where e is the residual of regressions (1|prime~) or (2|double prime~), y is the dependent variable (real |m.sub.1~ or the monetary base H) and the |x.sub.i~ are the explanatory variables. This test is an alternative to Durbin's H. The null hypothesis of no serial correlation is not rejected only for restriction (iv). In all other cases, the null hypothesis of serial correlation is rejected.

References

1. Allen, Scott D., and Douglas D. McCrickard, "Deficits and Money Growth in the United States: A Comment." Journal of Monetary Economics, January 1983, 143-53.

2. ----- and M. D. Smith, "Government Borrowing and Monetary Accommodation." Journal of Monetary Economics, November 1983, 605-16.

3. Aschauer, David Alan, "Fiscal Policy and Aggregate Demand." American Economic Review, March 1985, 117-27.

4. Barro, Robert, "Are Government Bonds Net Wealth?" Journal of Political Economy, November-December 1974, 1095-117.

5. -----, "Unanticipated Money Growth and Unemployment in the United States." American Economic Review, March 1977, 101-15.

6. -----, "Unanticipated Money, Output, and the Price Level in the United States." Journal of Political Economy, August 1978, 548-80.

7. ----- and Xavier Sala-i-Martin. "World Real Interest Rates" in NBER Macroeconomics Annual, edited by O. J. Blanchard and S. Fischer. Cambridge: MIT Press, 1990, pp. 15-59.

8. Barth, James, George A. Iden and Frank S. Russek, "Government Debt, Government Spending, and Private Sector Behavior: Comment." American Economic Review, December 1986, 1158-67.

9. Blinder, Alan and Robert Solow, editors. The Economics of Public Finance. Washington: The Brookings Institution, 1974, pp. 3-118.

10. Bohara, Alok K., "Testing The Rational-Expectations Hypothesis: Further Evidence." Journal of Business Economics and Statistics, June 1991, 337-40.

11. Brunner, Karl and Allan H. Meltzer, "Friedman's Monetary Theory" in Milton Friedman's Monetary Framework: A Debate With His Critics, edited by R. Gordon. Chicago: University of Chicago Press, 1970.

12. Butkiewicz, James L., "Outside Wealth, the Demand for Money, and the Crowding Out Effect." Journal of Monetary Economics, April 1979, 249-81.

13. Carr, Jack L. and Michael R. Darby, "The Role of Money Supply Shocks in the Short-Run Demand for Money." Journal of Monetary Economics, September 1981, 183-99.

14. Christiano, Laurence, "Modeling the Liquidity Effect of a Money Shock." Quarterly Review, Federal Reserve Bank of Minneapolis, Winter 1991, 3-34.

15. Deravi, M. Kevin, Charles E. Hegji, and H. Dean Moberly, "Government Debt and the Demand For Money: An Extreme Bounds Analysis." Economic Inquiry, April 1990, 390-401.

16. Evans, Paul, "Do Large Budget Deficits Produce High Interest Rates?" American Economic Review, March 1985, 68-87.

17. Engle, Robert F. and Byong Sam Yoo, "Forecasting and Testing in Cointegrating Systems." Journal of Econometrics, May 1987, 143-59.

18. Feldstein, Martin S., "Government Deficits and Aggregate Demand." Journal of Monetary Economics, January 1982, 1-20.

19. ----- and Douglas W. Elmendorf, "Government Debt, Government Spending, and Private Sector Behavior Revisited: Comment." American Economic Review, June 1990, 589-99.

20. ----- and Otto Eckstein, "The Fundamental Determinants of the Interest Rate." Review of Economics and Statistics, November 1972, 363-75.

21. Friedman, Benjamin and Kenneth Kuttner, "Money, Income, Prices and Interest Rates." American Economic Review, June 1992, 472-92.

22. Fuller, Wayne A. Introduction to Statistical Time Series. New York: Wiley 1976, pp. 371-73.

23. Gallant, A. Ronald and Dale W. Jorgensen, "Statistical Inference for a System of Simultaneous, Nonlinear, Implicit Equations in the Context of Instrumental Variables Estimation." Journal of Econometrics, October/December 1979, 275-302.

24. Goldfeld, Stephen M., "The Demand for Money Revisited." Brookings Papers on Economic Activity 1973; 3, 577-638.

25. Gordon, Robert, Milton Friedman's Monetary Framework: A Debate With His Critics. Chicago: University of Chicago Press, 1970.

26. Grossman, Sanford and Laurence Weiss, "A Transactions-Based Model of The Monetary Transmissions Mechanism." American Economic Review, December 1983, 871-80.

27. Hamburger, Michael J. and Burton Zwick, "Deficits, Money, and Inflation." Journal of Monetary Economics, January 1981, 141-50.

28. Hoelscher, Gregory, "1979-1982: Rules or Discretion in Monetary Policy?" Economic Inquiry, April 1990, 249-56.

29. Joines, Douglas H., "Deficits and Money Growth in the United States, 1872-1983." Journal of Monetary Economics, November 1985, 329-51.

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

31. ----- and Phillip Meguire, "Government Debt, Government Spending, and Private Sector Behavior: Reply." American Economic Review, December 1986, 1180-87.

32. -----, "Government Debt, Government Spending, and Private Sector Behavior: Reply and Update." American Economic Review, June 1990, 604-17.

33. Lucas, Robert E. Jr., "Liquidity and Interest Rates." Journal of Economic Theory, April 1990, 237-64.

34. Maddala, G. S. Introduction to Econometrics. New York: MacMillan, 1992.

35. Mankiw, N. Gregory and Larry Summers, "Consumption, Money Demand, and Fiscal Policy Effects." Journal of Money, Credit and Banking, November 1986, 415-29.

36. Modigliani, Franco and Arlie Sterling, "Government Debt, Government Spending, and Private Sector Behavior: Comment." American Economic Review, December 1986, 1168-79.

37. ----- and -----, "Government Debt, Government Spending, and Private Sector Behavior: A Further Comment." American Economic Review, June 1990, 600-603.

38. Miller, Stephen M., "Monetary Dynamics: An Application of Cointegration and Error-Correction Modeling." Journal of Money, Credit, and Banking, May 1991, 139-54.

39. Mishkin, Fredrick S., "Does Anticipated Monetary Policy Matter: An Econometric Investigation." Journal of Political Economy, February 1982, 22-51.

40. -----, "Does Anticipated Aggregate Demand Policy Matter? Further Econometric Results." American Economic Review, September 1982, 788-802.

41. Niskanen, William A., "Deficits, Government Spending, and Inflation: What Is the Evidence?" Journal of Monetary Economics, August 1978, 591-602.

42. Pagan, Adrian R., "Econometric Issues in the Analysis of Regression With Generated Regressors." International Economic Review, February 1984, 221-47.

43. Phillips, Peter C. B., "Time Series Regressions with a Unit Root." Econometrica, March 1987, 277-301.

44. ----- and Pierre Perron, "Testing for a Unit Root in Time-Series Regressions." Biometrika, June 1988, 335-46.

45. Rodriguez, Alvaro, "The Debt-Money Ratio: What Are The Limits." Rivista di Politica Econonomica, December 1990, 330-51.

46. Rotemberg, Julio J., "A Monetary Equilibrium Model With Transactions Costs." Journal of Political Economy, February 1984, 40-58.

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Publication: | Southern Economic Journal |

Date: | Oct 1, 1993 |

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