ACCURACY OF SIMULATIONS FOR STOCHASTIC DYNAMIC MODELS By Manuel S. Santos and Adrian Peralta-Alva 1 This paper is concerned with accuracy properties of simulations of approximate solutions for stochastic dynamic models. Our analysis rests upon a continuity property of invariant distributions and a generalized law of large numbers. We then show that the statistics generated by any sufficiently good numerical approx- imation are arbitrarily close to the set of expected values of the model’s invariant distributions. Also, under a contractivity condition on the dynamics we establish error bounds. These results are of further interest for the comparative study of stationary solutions and the estimation of structural dynamic models. Keywords: Stochastic Dynamic Model, Invariant Distribution, Numerical Solution, Approximation Error, Simulated Moments, Convergence. 1 Introduction Economists perform computational experiments to analyze quantitative properties of equilib- rium solutions, but relatively little is known about the biases that may result from numerical approximations. The purpose of this paper is to set forth easily verifiable conditions for the accuracy of statistics obtained from numerical simulations. This work provides theoretical foundations for the widespread use of numerical techniques in the simulation and estimation of dynamic economic models. In the simulation of dynamic models approximation errors may cumulate over time, and hence they may change drastically the evolution of sample paths. In order to establish accuracy properties of the statistics obtained from numerical simulations we address the 1 We have benefitted from several discussions with various seminar participants at Arizona State University, Universidad Carlos III of Madrid, the University of Minnesota, the Federal Reserve Bank of Minneapolis, and the SED meetings (Paris, June 2003). We are grateful to Jorge Aseff and to three anonymous referees for several detailed comments to an earlier draft. This research was partially supported by the Spanish Ministerio de Ciencia y Tecnologia, Grant SEC 2002-4318. 1