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 develops a generalized Bayes framework for conditional moment restriction models, where the parameter of interest is a nonparametric structural function of endogenous variables. We establish contraction rates for a class of Gaussian process priors and provide conditions under which a Bernstein-von Mises theorem holds for the quasi-Bayes posterior. Consequently, we show that optimally weighted quasi-Bayes credible sets achieve exact asymptotic frequentist coverage, extending classical results for parametric GMM models. As an application, we estimate firm-level production functions using Chilean plant-level data.

We study the Gaussian sequence compound decision problem and analyze a Bayesian nonparametric estimator from an empirical Bayes, regret-based perspective. Motivated by sharp results for the classical nonparametric maximum likelihood estimator (NPMLE), we ask whether an analogous guarantee can be obtained using a standard Bayesian nonparametric prior. 

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.