« Back to Results

Bayesian and Likelihood Methods

Paper Session

Sunday, Jan. 6, 2019 1:00 PM - 3:00 PM

Atlanta Marriott Marquis, L504
Hosted By: Econometric Society
  • Chair: Molin Zhong, Federal Reserve Board

Bayesian Estimation and Comparison of Conditional Moment Models

Siddhartha Chib
,
Washington University-St. Louis
Minchul Shin
,
University of Illinois
Anna Simoni
,
CNRS and CREST

Abstract

In this paper we consider an extension of the Bayesian exponentially tilted empirical likelihood framework developed in Chib, Shin and Simoni (2017) for unconditional moment condition models to conditional moment models. The basic idea is to transform the conditional moments in a sequence of unconditional moments by using a vector of approximating functions with increasing dimension. We consider both correctly and incorrectly specified conditional moment models and demonstrate that in both cases the Bayesian posterior distribution satisfies the Bernstein-von Mises theorem, subject to a rate condition on the number of approximating functions. We also develop an approach based on marginal likelihoods for comparing different conditional moment restricted models and establish the model selection consistency of the marginal likelihood. Several examples are used to illustrate the framework and results.

Adaptive Bayesian Estimation of Mixed Discrete-Continuous Distributions under Smoothness and Sparsity

Andriy Norets
,
Brown University
Justinas Pelenis
,
Institute for Advanced Studies-Vienna

Abstract

We consider nonparametric estimation of a mixed discrete-continuous distribution
under anisotropic smoothness conditions and possibly increasing number of support points for the discrete part of the distribution. For these settings, we derive lower bounds on the estimation rates in the total variation distance. Next, we consider a nonparametric mixture of normals model that uses continuous latent variables for the discrete part of the observations. We show that the posterior in this model contracts at rates that are equal to the derived lower bounds up to a log factor. Thus, Bayesian mixture of normals models can be used for optimal adaptive estimation of mixed discrete-continuous distributions.

Density Forecasts in Panel Data Models: A Semiparametric Bayesian Perspective

Laura Liu
,
Federal Reserve Board

Abstract

This paper constructs individual-specific density forecasts for a panel of firms or households using a dynamic linear model with common and heterogeneous coefficients and cross-sectional heteroskedasticity. The panel considered in this paper features a large cross-sectional dimension N but short time series T. Due to the short T, traditional methods have difficulty in disentangling the heterogeneous parameters from the shocks, which contaminates the estimates of the heterogeneous parameters. To tackle this problem, I assume that there is an underlying distribution of heterogeneous parameters, model this distribution nonparametrically allowing for correlation between heterogeneous parameters and initial conditions as well as individual-specific regressors, and then estimate this distribution by pooling the information from the whole cross-section together. Theoretically, I prove that both the estimated common parameters and the estimated distribution of the heterogeneous parameters achieve posterior consistency, and that the density forecasts asymptotically converge to the oracle forecast. Methodologically, I develop a simulation-based posterior sampling algorithm specifically addressing the nonparametric density estimation of unobserved heterogeneous parameters. Monte Carlo simulations and an application to young firm dynamics demonstrate improvements in density forecasts relative to alternative approaches.

Likelihood Evaluation of Models with Occasionally Binding Constraints

Pablo Cuba-Borda
,
Federal Reserve Board
Luca Guerrieri
,
Federal Reserve Board
Matteo Iacoviello
,
Boston College
Molin Zhong
,
Federal Reserve Board

Abstract

Applied researchers often need to estimate key parameters of DSGE models. Except in a handful of special cases, both the solution and the estimation step will require the use of numerical approximation techniques that introduce additional sources of error between the "true" value of the parameter and its actual estimate. In this paper, we focus on likelihood evaluation of models with occasionally binding constraints. We highlight how solution approximation errors and errors in specifying the likelihood function interact in ways that can compound each other.
JEL Classifications
  • C1 - Econometric and Statistical Methods and Methodology: General
  • C5 - Econometric Modeling