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Residual-Based Procedures for Prediction and Estimation in a Nonlinear Simultaneous System

Byran W. Brown
Roberto S. Mariano

Abstract

This paper proposes the residual-based stochastic predictor as an alternative procedure for obtaining forecasts with a static nonlinear econometric model. This procedure modifies the usual Monte Carlo approach to stochastic simulations of the model in that calculated residuals over the sample period are used as proxies for disturbances instead of random draws from some assumed parametric distribution. In comparison with the Monte Carlo predictor, the residual-based should be less sensitive to distributional assumptions concerning disturbances in the system. It is also less demanding computationally. The large-sample asymptotic moments of the residual-based predictor are derived in this paper and compared with those of the Monte Carlo predictor. Both procedures are asymptotically unbiased. In terms of asymptotic mean squared prediction error (AMSPE), the Monte Carlo is efficient relative to the residual-based when the number of replications in the Monte Carlo simulations is large relative to sample size. This order of relative efficiency is reversed, however, when replication and sample sizes are similar. In any event, the amount by which the AMSPE of either predictor exceeds the low bound for AMSPE is small as a percentage of the lower bound AMSPE when sample and replication sizes are at least of moderate magnitude. The paper also discusses the extension of the residual-based and Monte Carlo procedures to the estimation of higher order moments and cumulative distribution functions of endogenous variables in the system.