Latent variable models are widely used to account for unobserved determinants of economic behavior. This paper introduces a quasi-Bayes approach to nonparametrically estimate a large class of latent variable models. As an application, we model U.S. individual log earnings from the Panel Study of Income Dynamics (PSID) as the sum of latent permanent and transitory components. Simulations illustrate the favorable performance of quasi-Bayes estimators relative to common alternatives.
This paper studies quasi-Bayesian estimation and uncertainty quantification for an unknown structural function that is identified by a nonparametric conditional moment restriction. We derive contraction rates for a class of Gaussian process priors. Furthermore, we provide conditions under which a Bernstein–von Mises theorem holds for the quasi-posterior distribution. This extends classical results on the frequentist validity of quasi-Bayes credible sets for parametric generalized method of moments (GMM) models.
We introduce two practical methods for estimation and inference on a nonparametric structural function and its derivatives. The first is a data-driven choice of sieve dimension. The second is a data-driven approach for constructing uniform confidence bands. Both procedures are simple to implement, have strong theoretical justification, and do not require prior information about the smoothness of the unknown structural function. Simulations illustrate the good performance of our procedures in empirically calibrated designs. As an application, we estimate the elasticity of the intensive margin of firm exports in a monopolistic competition model of international trade.
Kernel-weighted test statistics are widely used for inference. We introduce the expected small ball probability as a tool to study the local behavior of kernel smoothed statistics. We then develop the limit theory for a kernel-weighted specification test of a parametric conditional mean when the law of the regressors may not be absolutely continuous to the Lebesgue measure. In the special case of absolutely continuous measures, our approach weakens the usual regularity conditions. This approach is of independent interest and may be useful in other applications that utilize kernel smoothed statistics.