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 is concerned with the problem of estimating demand and supply schedules in disequilibrium markets. The results of Fair and Jaffee are expanded in three ways. (1) Their directional method I is modified to yield consistent estimates. (2) A maximum likelihood alternative to their quantitative method is proposed. (3) The price equation is generalized to be a multivariate, stochastic function, and a method is proposed for estimating demand and supply schedules in this case.

[This paper is concerned with the econometric problems associated with estimating supply and demand schedules in disequilibrium markets. The general problem is that in the absence of an equilibrium condition the ex ante demand and supply quantities cannot in general be equated to the observed quatity traded in the market. Four methods of estimation, differing primarily in their use of information on price-setting behavior, are developed in this paper. The first method is a generalization of an earlier meothd developed by R. Quandt and is based upon the maximization of a likelihood function. The method does not require any specific assumption about price-setting behavior, and it allows the sample separation (into demand and supply regimes) to be estimated along with the coefficient estimates. The second and third methods use the change in price as a qualitative proxy in determining the sample separation. The fouth method uses the change in price as a quantitative proxy for the amount of excess demand (supply) in the market. In the final section of the paper the four methods are used to estimate a a model of the housing and mortgage market in an effort to gauge the potential usefulness of each of the methods.]

A solution method and an estimation method for nonlinear rational expectations models are presented in this paper.The solution method can be used in forecasting and policy applications and can handle models with serial correlation and multiple viewpoint dates.When applied to linear models, the solution method yields the same results as those obtained from currently available methods that are designed specifically for linear models.It is, however, more flexible and general than these methods.The estimation method is based on the maximum likelihood principal.It is, as far as we know, the only method available for obtaining maximum likelihood estimates for nonlinear rational expectations models.The method has the advantage of being applicable to a wide range of models, including, as a special case, linear models.The method can also handle different assumptions about the expectations of the exogenous variables, something which is not true of currently available approaches to linear models.