Estimating the Uncertainty of Policy Effects in Nonlinear Models

Abstract

ALTHOUGH MACROECONOMETRIC MODELS 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.2 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 expositional convenience only) that the model is quarterly, and let the ith equation of the model for quarter t be written: (1) 4ki(yit, * * * , YGt, Zlt, * * *, ZNt, 1i) = Eit (i = . ), where the Yit are the endogenous variables, the zit are the predetermined variables, fli is the vector of unknown coefficients in equation i, and sit is the error term corresponding to equation i. For identities, sit is zero for all t. Also, let fl denote the vector of all the unknown coefficients in the model, and let Et denote 1 The research described in this paper was financed by grant SOC77-03274 from the National