Estimating nonlinear dynamic equilibrium models by matching impulse responses

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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.