There has been much recent discussion ahout the ultimate sources of macroeco-nomic variability. A number ofauthors attribute most of this variability to only B few sowces, sometimes only one. Although there may be only B few important sources, this is fsr from obvious, since economies seem compliested. The purpose of this paper is to provide qusntitstive estimates of various sowces of vsriability using B U.S. econometric model. Stochastic simulation is used to estimate how much the overall variances of real GNP and the GNP deflator are reduced when various shocks BIG suppressed in the model. I. Ii-4TR0000~10~ There has been much recent discussion about the ultimate sources of macroeconomic variability. Shiller [1987] surveys this work, where he points out that a number of authors attribute most of output or unemployment variability to only a few sources, sometimes only one. The sources vary from technology shocks for Kydland and Prescott [1982], to unanticipated changes in the money stock for Barre [1977], to “unusual structural shifts, ” such as changes in the demand for produced goods relative to services, for Lilien [1982], to oil price shocks for Hamilton [1983], to changes in desired consumption for Hall [1986]. (See Shiller [1987] for more references.) Although it may be that there are only a few important sowces of macroeconomic variability, this is far from obvious. Economies seem complicated, and it may be that there are many important sources. The purpose of this paper is to estimate the quantitative importance of various sources of variability using a macroeconometric model. Macroeconometric models provide an obvious vehicle for esti-mating the sources of variability of endogenous variables. There are two types of shocks that one needs to consider: shocks to the stochastic equations and shocks to the exogenous variables. Shocks to the stochastic equations are easy to handle. They ax simply draws from the postulated distribution (usually normal) of the structural error terms, the distribution upon which the estimation *This paper grew out of discussions with Robert Shiller, to whom I am indebted for many helpful suggestions and comments. Some of the results in this paper are

I. Introduction, 551. — II. The general model, 552. — III. Specification of the model, 555. — IV. The results, 567. — V. Conclusions, 576. — Appendix, 578.

asymptotic variances of multipliers for nonlinear models. It is used to estimate the uncertainty of the results of eight policy experiments for a particular model. ALTHOUGH MACROECONOMETRIC MOI)ELS are widely used to analyze the effects of alternative government actions on the economy, estimates of the uncertainty of these effects are rarely, if ever, presented. This is, of course, not surprising, since most macroeconometric models are nonlinear. Unlike for linear models, formulas for the asymptotic variances of impact and dynamic multipliers are not known for nonlinear models. ’ It is possible, however, to estimate these variances for nonlinear models by stochastic simulation, and the purpose of this paper is to discuss the method by which this can be done. The method is discussed in Section 2, and results of applying the method to eight policy experiments for the model in Fair [7,10] are presented in Section 3.3 Given the obvious importance of knowing how much confidence to place on the results of any particular policy experiment in a model, it is hoped that this study will stimulate others to obtain uncertainty estimates for their models similar to those presented in Section 3. 2. THE METHOD The. method can be applied to a model that is nonlinear in both variables and coefficients. Let G denote the total number of equations in the model, M the number of stochastic equations, and N the total number of predetermined (both exogenous and lagged endogenous) variables. Assume (for exposition.4 con-venience only) that the model is quarterly, and let the ith equation of the model for quarter t be written: (1) CpdYi,, YGh Zlb, ZN,,

The purpose of this paper is to examine within the context of a patieular U.S. exammetric model the sensitivity of fiscal policy effects to alternative assumptions about the behavior of the Federal Reserve. Five cases are considered, four in which Fed behavior is exogenous and one in which Fed behavior is endogenous. In each of the four exogenous cases the Fed is assumed to control a particular variable, which is then taken to be exogenous for purposes of the fiscal-policy experiments. For the endogetmus case an estimated equation explaining Fed behavior is added to the model. and the expanded mcdel is used to perform the experiments. The rewlts of some optimal control experiments are also reported in this paper. These latter experiments are designed to examine the sensitivity of optimal fiscal policies to alternative assumptions about Fed behavior. The main conclusion of this paper is that fiscal policy effects and optimal fiscal policies are quite sensitive to assumptions about the behavior of the Fed. 1. IN-cROD”cTION MOST EXAMINATIONS OF FISCAL POLICY EFFECTS in U.S. econometric models are based on the assumption that the behavior of the Federal Reserve (henceforth called the “Fed”) is exogenous, i.e., that the behavior of the Fed is not influenced by the state of the economy. The typical procedure is to assume that the Feds has control over a particular variable in the model and then to take this variable as exogenous for purposes of the fiscal policy experiments. An alternative procedure, if one believes that the behavior of the Fed is not exogenous, is to estimate an equation explaining Fed behavior (i.e., explaining the variable that the Fed is assumed to control), add this equation to the model, and use this expanded model to perform the fiscal policy experiments. The purpose of this paper is to examine within the context of a particular U.S. econometric model the sensitivity of fiscal policy effects to alternative assumptions about Fed behavior. Five cases are considered, four in which Fed behavior is exogenous and one in which Fed behavior is endogenous. In each of the four exogenous cases the Fed is assumed to control a particular variable, which is then taken to be exogenous for purposes of the fiscal policy experiments. The control variables in the four cases are: (1) the amount of government securities outstanding; (2) the money supply; (3) nonborrowed reserves; and (4) the bill rate. For the endogenous case an estimated equation explaining Fed behavior is added to the model, and the expanded model is used to perform the fiscal policy experiments. Section 2 contains a brief description of the econometric model used for purposes of this paper. The model, which is described in detail in Fair [9], is particularly suited for examining the effects of monetary and fiscal policies ‘The research described in this paper was financed by grant SOC77-03274 from the National

In this paper various methods for the estimation of simultaneous equation models with lagged endogenous variables and first order serially correlated errors are discussed. The methods differ in the number of instrumental variables used. The asymptotic and small sample properties of the various methods are compared, and the variables which must be included as instruments to insure consistent estimates are derived. A suggestion on how to estimate the approximate covariance matrix of the estimators is made.

This paper tests, using U.S. data, the dynamics implied by the NAIRU view of the relationship between inflation and the unemployment rate. The results are somewhat sensitive to the measure of inflation used, but they generally reject the dynamics. An alternative way of thinking about the relationship between inflation and the unemployment rate is suggested.

Abrtmcr-An important question in the study of aging concerns the rate at which people physically deteriorate with age.HOW much, for example.CB~ be physically expected of, say, a healthy, non-injured 75.year-old man or woman relative to what be or she could do at ape 4% This paper applies econometric techniques to data on men's track and field and road racing remrds by age to estimate the rate at which men sknv down with asc.Eight track.eight field.and eleven road racing events me considered.The main econometric technique usad is a combination of the polytwmial-spline method and the frontier-function method.A number of the evetttr have been pooled to provide more et%cient estimates.1.

This paper tests for the existence of expectational effects in very disaggregate price equations. Price equations are estimated using monthly data for each of 40 products. The dynamic specification of the equations is also tested, including whether the equations should be specified in level