Estimating nonlinear dynamic equilibrium models by matching impulse responses

This paper examines the proposition that using a nonlinear - instead of a linear - auxiliary model for the indirect inference estimation of a nonlinear dynamic equilibrium model should deliver more efficient estimates and statistical inference. Focusing on the widely-used impulse-response matching procedure, it is pointed out that a nonlinear dynamic equilibrium model generates impulse responses that depend on the sign, size, and timing of the shock. This is also the case for impulse responses generated by a nonlinear auxiliary model. In contrast, impulse responses generated by a linear auxiliary model are independent of the sign, size, and timing of the shock. Monte-Carlo results show that both auxiliary models deliver estimates close to their true values, but that using a nonlinear auxiliary model yields more efficient estimates because it exploits information on the mean of the variables and the curvature of the economic model. (C) 2020 Elsevier B.V. All rights reserved.