Click for Abstract
Abstract: This paper proposes a Sieve Simulated Method of Moments (Sieve-SMM) estimator for the parameters and the distribution of the shocks in nonlinear dynamic models where the likelihood and the moments are not tractable. An important concern with SMM, which matches sample with simulated moments, is that a parametric distribution is required but economic quantities that depend on this distribution, such as welfare and asset-prices, can be sensitive to misspecification. The Sieve-SMM estimator addresses this issue by flexibly approximating the distribution of the shocks with a Gaussian and tails mixture sieve. The asymptotic framework provides consistency, rate of convergence and asymptotic normality results, extending sieve theory to more general dynamics with latent variables. Monte-Carlo simulations illustrate the finite sample properties of the estimator. Two empirical applications highlight the importance of the distribution of the shocks. The first provides evidence of non-Gaussian shocks in macroeconomic data and their implications on welfare and the risk-free rate. The second finds that Gaussian estimates of stochastic volatility are significantly biased in exchange rate data because of fat tails.