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Atlanta Marriott Marquis, L504
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Econometric Society
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.
Bayesian and Likelihood Methods
Paper Session
Sunday, Jan. 6, 2019 1:00 PM - 3:00 PM
- Chair: Molin Zhong, Federal Reserve Board
Adaptive Bayesian Estimation of Mixed Discrete-Continuous Distributions under Smoothness and Sparsity
Abstract
We consider nonparametric estimation of a mixed discrete-continuous distributionunder 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
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
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