On Modeling the Effects of Government Policies

By RAY C. FAIR*

An important question in macroeconomics III the testing of the model is discussed. Two is how government policies affect the ccono- types of tests arc considered in this section: my. The fact that this question is still being tests of individual hypotheses and tests of the debated forty-three years after John May- accuracy of the overall model. The main nard Keynes wrote The General Theory and points of the paper are summarized in Section thirty-nine years after Jan Tinbergen did his 1v. pioneering econometric study of business cycles for the League of Nations indicates the difficulty of answering it. Although it is easy to construct theoretical models in which The proposition that government tax rates government policies do or do not have impor- and transfer payments affect the decisions of tant effects on, say, real output, it is difficult households and firms is familiar from micro- to test alternative models. One difficulty is economics. In the theoretical model upon the relative ease with which aggregate time- which my econometric model is based (see the series data can be fit well within the sample author, 1974, 1976), the “micro-economic” period. Because of this, a good within-sample aspect of individual decisions has been fit is by no means a guarantee that the stressed. The decisions of the individual particular equation or model is a good repre- agents in the model (households, firms, and sentation of the actual process generating the banks) are derived from the solutions of data. It is also dificult to make comparisons multiperiod optimization problems. At the of predictive accuracy across models because beginning of each period each agent solves its of dill&aces in the number and types of optimization problem, knowing all past variables that are taken to be exogenous. values, receiving in some cases information These difficulties are annoying and have from others regarding certain current-period undoubtedly contributed to giving macro- values, and forming expectations of future economics a bad name. values. A number of government policy vari- The purpose of this paper is to review that ables affect the solutions of these problems, part of my recent work that relates to model- and so through this channel government ing the effects of government policies. In my actions affect the economy. Tax rates and econometric model, government actions, even transfer payments, for example, affect the if they are anticipated, can have important labor-leisure choice of the utility-maximizing effects on real output, and in Section 1 the households. theoretical basis for this property is reviewed. Although these micro-economic effects are In Section II the sensitivity of policy effects in fairly well accepted in the profession, they do the model to a number of alternative assump- not exist in a popular class of rational expec- tions is examined. These assumptions concern tations macro models (see Robert J. Barre, 1) the behavior of the Federal Reserve, 2) Robert E. Lucas, Jr., Thomas J. Sargent, whether or not there are rational expectations 1973, 1976, and Sargent and Neil Wallace). in the bond and stock markets, and 3) Elsewhere (1978b), I have criticized this class whether or not government bonds are treated of models for postulating that individuals are as wealth by the household sector. In Section rational with respect to their expectation formation but not rational with respect to their overall behavior. This is an important ‘Cowks Foundation, department of economics, Yale criticism of these models in that their key University.The research dexrikd in this paper was financed by grant SOC77-03274 from the National property regarding the ineffectiveness of Science Foundation. anticipated government actions on real output

86 VOL. 69 NO. 2 THE EFFECTIVENESS OF FISCAL POLICY 87

no longer holds if rationality with respect to prices and wages may not always clear overall behavior is introduced into the models. markets. In my model, on the other hand, In a “completely” rational model the govern- such an explanation is provided, namely the ment can affect real output by affecting, possibility of expectation errors on the part of among other things, the labor-leisure choice firms. ln short, my model, unlike Barre and of households. Grossman’s, is “choice theoretic” with respect There is also in my theoretical model to the determination of prices and wages. another reason government actions can affect Because of this weakness of the Barro- the economy. The model allows for the exis- Grossman model, Grossman is now advocat- tence of disequilibrium, and if there is ing another theory of employment fluctua- disequilibrium, the government can, by tions, a theory in which market transactions conventional means, help to correct it. Dis- are viewed as involving implicit contractual equilibrium takes the form of banks arrangements for mitigating risk. constraining firms and households in how much money they can borrow at the current II. The Sensitivity of Policy EtTects loan rates and of firms constraining house- to Alternative Assumptions holds in how much they can work at the current wage rates. Binding constraints in the The properties of macro-econometric loan market are due to mistakes on the part of models tend to be sensitive to alternative banks in setting loan rates, and binding assumptions. Given the difficulty of testing constraints in the labor market are due to assumptions, this means that any policy mistakes on the part of firms in setting prices recommendations that result from analyzing and wages. These mistakes are the result of a model must be interpreted with consider- expectation errors. No agent knows the able caution. Some assumptions are, however, complete model, and so expectations can turn more important than others in this regard, out to be wrong even though there are no and the purpose of this section is to review the random shocks in the model. There is, howev- sensitivity results that 1 have obtained with er, a continual adjustment to past mistakes in my model. that each period the individual agents form Fiscal policy effects in the model are, as a new set of expectations and reoptimize on reported in my 1978a paper, quite sensitive to the basis of information from the previous assumptions about monetary policy. The period. results of five experiments are presented here. The key premise of my theoretical work is Each experiment corresponded to the same thus that agents each period first form a set of fiscal policy shock (an increase in government expectations of future values and then given purchases of goods). For four of the experi- these expectations base their decisions on the ments the behavior of the Fed was assumed to solutions of multiperiod optimization prob- be exogenous: in each of these cases the Fed lems. The expectations may be in error, and was assumed to control a particular variable, so banks and firms may set values of loan which was then taken to be exogenous for the rates, wages, and prices that are not market experiment. (By exogenous here is meant that clearing. Both the micro-economic and dis- for the experiment the variable was kept equilibrium aspects of this premise imply that unchanged each period from its base-simula- the government can affect real variables in tion value.) The control variables in the four the economy. cases were: 1) the amount of government One important difference between my securities outstanding; 2) the money supply; theoretical model and a disequilibrium model 3) nonborrowed reserves: and 4) the bill rate. like that of Barre and Herschel Grossman For the fifth experiment the Fed was assumed should be noted. In the Barre-Grossman to behave according to an estimated equation. model, prices and wages are not decision The behavior that is reflected in this equation variables of firms (or any other agents), and is behavior in which the Fed “leans against no explanation is provided as to why it is that the wind.” As the economy expands or as 88 AMERlCAN ECONOMIC ASSOCIATION MAY ,979 inflation increases, the Fed is estimated to Higher long-term rates have, other things cause interest rates to rise. being equal, a contractionary effect on the The results of these experiments are briefly economy, and this is the main reason for the as follows. When the Fed behaved according smaller increases in real output in Model 2 to the estimated equation, the sum of the than in Model 1. For Mode1 3 the sum of the increase in real output over the first twelve output increase was 61 percent of the sum for quarters after the fiscal policy change was 61 Model I. In Model 3 people also know that percent of the sum when the bill rate was kept profits are going to be higher in the future as unchanged. When the money supply was kept a result of the stimulus, and this information unchanged, the sum was 45 percent of the gets incorporated immediately into stock sum in the constant bill-rate case. The most prices. Stock prices are thus higher in Model expansionary case was the one in which the 3 than they are in Model 2, and this leads, amount of government securities outstanding through a wealth effect on the household was kept unchanged. In this case the govern- sector, to a slightly more expansionary econ- ment deficit that results from the fiscal policy omy in Model 3 than in Model 2. This change is tinanced by an increase in high difference is, however, much smaller than the powered money. The sum in this case was 107 difference between the results for Models 1 percent of the sum in the constant bill-rate and 2, and so in this sense expected future case. Finally, the sum in the case in which profits in the model are less important than nonborrowed reserves was kept unchanged expected future interest rates. was 72 percent of the sum in the constant The experiment just described was an bill-rate case. In short, these results indicate unanticipated fiscal policy change. I also ran that fiscal policy effects are quite sensitive to an experiment in which the change was what is assumed about Fed behavior. announced thirteen years before it was Policy effects in the model are also sensitive actually made. In this case in Models 2 and 3 to what is assumed about expectations in the (but not in Model 1) people. begin to adjust to bond and stock markets. In my forthcoming the higher expected future interest rates and paper 1 have examined policy effects in three profits before the change is actually made. versions of the model: I) the regular version For Model 3 the sum of the change in output (Model I), in which expectations of future between the time of the announcement and interest rates and stock prices are not ration- twelve quarters after the change was actually al; 2) a version (Model 2) in which expecta- made was 29 percent of the sum for Model 1. tions of future interest rates are rational; and The anticipated policy change was thus about 3) a version (Model 3) in which expectations half as stimulative as the unanticipated of future interest rates and stock prices are change (29 vs. 61 percent). rational. The fiscal policy shock described Although the results just described are above was used, and the Fed was assumed to clearly tentative and are in no way a test of behave according to the estimated equation the assumption of rational expectations, they mentioned above. do indicate that this assumption is of consid- The results for these three versions of the erably quantitative significance in macro- model are as follows. For Model 2 the sum of econometric models. the increase in real output over the first For purposes of the present paper I have twelve quarters after the fiscal policy change also examined the sensitivity of policy effects was 51 percent of the sum for Model 1. In to the treatment of government debt as wealth Model 2 people know that the Fed is going to by the household sector. The wealth of the respond to the fiscal policy stimulus by household sector is an explanatory variable in increasing interest rates in the future, and this the four consumption equations in the model information gets incorporated immediately and in one of the three labor supply equations. into long-term rates. In Model I, on the other In the regular version of the model govern- hand, long-term rates adjust only to the ment debt is included in this wealth variable. current and lagged increases in the short rate. For an alternative version I reestimated the VOL. 69 NO. 2 THE EFFECTWENESS OF FISCAL POLICY 89 five equations with government debt sub- appears in the four consumption equations tracted from the wealth variable. I then and in two of the three labor supply equations, applied the same fiscal policy shock described with t-values for the most recent set of esti- above to this version (with the Fed behaving mates, (see my 1978, paper), of 1.49, 3.37, according to the estimated equation). The 4.43, 2.17, 3.92, and 2.36. results from this exercise are easy to summa- With respect to possible tests of the rize. First, the fits of the five equations in the assumptions examined in the previous section, alternative version were almost identical to I have already mentioned that it seems the corresponding fits in the regular version. unlikely that the data are adequate for testing It is clear that the macro data are not the hypothesis that government debt is adequate for discriminating between these treated as wealth by households. It may, on two versions of the model. Second, and for the other hand, be possible to test the hy- once fortunately, the policy properties of the pothesis of rational expectations in the bond two versions are quite similar. Jn other words, and stock markets, although this is by no policy effects in the model are not sensitive to means a straightforward exercise. I have whether or not government debt is treated as outlined in my forthcoming paper (fn. 13) one wealth by the household sector. The sum of possible way in which this hypothesis might the increase in output over the twelve quarters be tested. Regarding the assumption about in the alternative version was 98 percent of Fed behavior, the equation that I have esti- the sum in the regular version. mated to explain Fed behavior seems quite good by conventional statistical standards, III. Tests of the Model although again conventional tests of individ- ual equations must be interpreted with Given that my model does allow for antici- considerable caution. pated government actions to have effects on Tests of the significance of individual coef- real output, it is of considerable interest to ficient estimates do not allow one to test one test this model against models that do not model against another (unless the models are allow for these effects. In this section the tests nested). I have, however, recently proposed a of the model that I have performed will be method for estimating the uncertainty of a reviewed. forecast from an econometric model that There are, first of all, t-tests of the individ- allows one to make comparisons of predictive ual coefficient estimates. A number of the accuracy across models (see my 1978~ paper), explanatory variables in the consumption and and I have applied this method to three other labor supply equations that one expects from models besides my own (1978d). The three micro-economic theory to all&t the decisions other models are the classical macro-econo- of households are significant by conventional metric model of Sargent (1976), the six- standards. In addition, the “disequilibrium” equation unconstrained vector autoregression variable that 1 have used to try to account for model of Chistopher A. Sims, and a “naive” possible work constraints on the household model in which each variable is regressed on a sector is significant in a number of the equa- constant, time, and its first eight lagged tions. One must, of course, be skeptical of values. These three models have quite differ- f-tests because of the ease with which good ent policy implications from mine, and so t-values can be obtained in macro data and of estimating the accuracy of my model against the general problem of data mining, and the these provides one test of the hypothesis that purported significance of my micro-economic anticipated government actions affect real and disequilibrium explanatory variables is no variables. In Sargent’s model anticipated exception to this. At least with respect to the government actions have no effect on real disequilibrium variable, however, it does seem output, and in Sims’ model and in the naive unlikely to me that the results would be as model there are no exogenous variables. they are if there were no disequilibrium Space limitations prevent a detailed discus- effects in the economy. The variable (ZJ) sion of the method of comparison. The method accounts for the four main sources of that even anticipated government actions uncertainty of a forecast: uncertainty due to affect real variables. On a macro-economic 1) the error terms, 2) the coefficient esti- level this proposition has received some mates, 3) the exogenous variable forecasts, support in my work in the sense that a number and 4) the possible misspecification of the of “micro-economic” explanatory variables model. It is based on successive reestimation are significant in my estimated equations. and stochastic simulation of the model. 2. The possible existence of disequilib- Because it accounts for all four sources, it can rium in the economy provides another justifi- be used to make comparisons across models. cation for the effectiveness of government A sampling of the comparison results is as policies. The proposition that disequilibrium follows. For real GNP the estimated standard at times exists in the economy has received errors of the eight-quarter-ahead forecast, some support in my work through the signifi- taking into account all four sources of uncer- cance of my “disequilibrium” variable (ZJ). tainty, are 4.74 percent for the naive model, 3. Policy effects in my model arc sensi- 5.10 percent for Sargent’s model, 7.79 tive to assumptions about Fed behavior and percent for Sims’ model, and 2.27 percent for about expectations in the bond and stock my model. For the eight-quarter-ahead fore- markets. They are not sensitive to whether or cast of the GNP deflator the corresponding not government debt is treated as wealth by estimated standard errors arc 6.20,8.53,6.26, households. It may be possible in the future, and 3.48 percent; and for the eight-quarter- as outlined in my forthcoming paper, to test ahead forecast of the unemployment rate the the assumption of rational expectations in the corresponding errors in percentage points are bond and stock markets, but it is unlikely that 2.19, 1.88, 2.23, and 0.71. Although these the macro data can be used to decide how results are quite tentative, they do seem to government debt is treated by households. indicate that my model is more accurate than The equation that 1 have estimated to explain the other three with respect to these three Fed behavior, an equation in which the Fed is variables. So as not to leave the impression estimated to lean against the wind, appears to that I feel I have found the ultimate model, it be good when judged by conventional statisti- should also be pointed out that my model is cal standards. not as accurate as either the naive model or 4. A method that I have proposed for the Sims model with respect to forecasts of estimating the expected predictive accuracy the money supply. The estimated standard of econometric models indicates that my errors for the eight-quarter-ahead forecast model is more accurate than Sargent’s model, arc 3.70 percent for the naive model, 6.79 Sims’ model, and a naive model with respect percent for Sims’ model, and 7.50 percent for to forecasts of real GNP, the GNP deflator, my model. (The money supply is exogenous in and the unemployment rate. These results Sargent’s model.) Also, my model is not as thus provide some tentative support for the accurate as the naive model with respect to proposition that even anticipated government forecasts of the nominal wage rate. The esti- actions can affect real variables. mated standard errors for the eight-quarter- To conclude, it is interesting to speculate ahead forecast arc 2.04 percent for the naive what the status of the debate about the model, 5.69 percent for Sims’ model, and 4.16 effectiveness of government policies will be percent for my model. (The wage rate is not a forty-three years from now in 2021. By this variable in Sargent’s model.) time 172 more quarterly observations will have been generated, and my hope is that the use of these additional data and methods like the one I have proposed for comparing models The main points of this paper can be will have considerably narrowed the range. of summarized as follows: disagreement. At the least, one would hope 1. There is strong theoretical justifica- that we will have advanced beyond the point tion from microeconomics for the proposition where the best model available is only fair. “OL. 65’ NO. 2 THE EFFECTIVENESS OF FISCAL POLICY 91

REFERENCES 15, 1978,” mimeo., Yale Univ. 1978. _, “An Analysis of a Macro-Economet- R. J. Bnrro, “Rational Expectations and the ric Model with Rational Expectations in Role of Monetary Policy,” J. Monet. Econ., the Bond and Stock Markets,” Amer. Jan. 1976, 2, l-32. Econ. Rev., forthcoming. ~ and H. I. Grossman, “A General Dis- H. 1. Grossman, “Why Does Aggregate equilibrium Model of Income and Employ- Employment Fluctuate?,” Amer. Econ. ment,” Amer. Econ. Rev., Mar. 1971, 61, Rev. Prof., May 1979, 69, 64-69. 82-93. John Maynard Keynes, The General Theory of Ray C. Fair, A Model of Macroeconomic Employment, Interest, and Money, New Activity, Volume I: The Theoretical Mod- York 1939. el, Cambridge, Mass. 1974. R. E. Lucas, Jr., “Some International Evidence -1 A Model of Macroeconomic Activi- on Output-Inflation Tradeoffs,” Amer. ty, Volume II: The Empirical Model, Econ. Rev., June 1973,63, 326-34. Cambridge, Mass. 1976. T. 1. Sargent, “Rational Expectations, the Real -, (197%~) “The Sensitivity of Fiscal- Rate of Interest, and the Natural Rate of Policy Effects to Assumptions about the Unemployment,” Brookings Papers, Behavior of the Federal Reserve,” Econe Washington 1973, 2, 429-80. metrica, Sept. 1978, 46, 116s-79s. _, “A Classical Macroeconometric -7 (1978b) “A Criticism of One Class of Model for the United States,” J. Polit. Macroeconomic Models with Rational Ex- Econ., Apr. 1976,84, 207-37. pectations,” J. Money, Credit, Banking, __ and N. Wallace, “Rational’ Expecta- Nov. 1978, 10, 411-17. tions, the Optimal Monetary Instrument, ~, (197%) “Estimating the Expected and the Optimal Money Supply Rule,” J. Predictive Accuracy of Econometric Mod- Polil. Econ., Apr. 1975, 83, 241-54. els,” Cowles Foundation disc. paper no. C. A. Sims, “Macro-Economics and Reality,” 480, Yale Univ., rev. Oct. 1978. paper presented as the 1977 Fisher-Schultz -9 (1978d) “An Analysis of the Accu- Lecture, Vienna, Sept. 1977: rev. Nov. racy of Four Macroeconometric Models,” 1977. Cowles Foundation disc. paper no. 492, Jan Tinbergen, Business Cycies in the United Yale Univ., Aug. 11, 1978. States of America, 1919-1932, Geneva ~, (1978e) “The Fair Model as of April 1939.

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