Bayesian and non-Bayesian methods for the elimination of high-dimensional nuisance parameters

Empirical economics makes increasing use of panel data. To control for unobserved heterogeneity (e.g., heterogeneity in technology across firms, heterogeneity in preferences across consumers, heterogeneity across teachers and students in matched student-teacher data), a common practice is to introduce agent-specific parameters (e.g., additive fixed effects) into panel data models. Such parameters are high-dimensional nuisance parameters and, in many models, this leads to an incidental parameter problem: standard estimation methods such as least squares or maximum likelihood fail to consistently estimate the model parameters that are assumed common to all agents. This research proposal seeks to extend recently proposed exact or approximate solutions to incidental parameter problems in the following new and important directions: (i) Bayesian bias corrections of the likelihood function via the posterior predictive density or via refined implementation of bias-reducing priors; (ii) empirical-likelihood based adjustments for incidental parameter bias in the GMM framework; (iii) deriving theoretical bounds on the incidental parameter bias in regression models with censoring (where simulations suggest that the bias is small). To summarize, there are many model and data settings where applied researchers are naturally led to introduce agent-specific parameters. My goal is to provide researchers with reliable methods of inference in those situations.