Non-likelihood based methods for the estimation and inference in econometric models

Abstract

This dissertation aims to address estimation and inference in econometric models when the likelihood-based estimations may not be applicable. Chapter 1 proposes simple, robust estimation and inference methods for the transition matrix of a high-dimensional semiparametric Gaussian copula vector autoregressive (VAR) process with unknown, possibly fat-tailed marginal distributions. In this model, the observable variable is a monotonic transformation of the latent variable, and the latent variable follows the Gaussian VAR process. Since the marginal distribution is unknown, conventional approaches that use the sample variance and auto-covariances such as OLS are not applicable. This chapter circumvents the problem by constructing the rank estimators of the variance and auto-covariance matrices of the latent process. This chapter derives rates of convergence of the estimator based on which we develop de-biased inference for Granger causality. Chapter 2 develops a simple, robust method for the estimation and inference in structural models using sliced distances between empirical and model-induced quantile functions (distribution functions). In state-space models, observable variables could be driven by fewer latent variables. This causes stochastic singularity, and the likelihood function does not exist. For the models with parameter-dependent support such as in the one-sided and two-sided models, the likelihood function may not be smooth depending on the parameter. Therefore, the asymptotic theory for MLE may not be robust to the parameter. We handle these issues using sliced distances since they are well-defined for stochastic singular models and models with parameter-dependent support. In contrast to MLE and likelihood-based inference, we show that under mild regularity conditions, our estimator is asymptotically normally distributed, leading to simple inference regardless of the possible presence of ”stochastic singularity” and parameter-dependent supports. Furthermore, our estimator applies to generative models with intractable likelihood functions but from which one can easily draw synthetic samples. We provide simulation results based on a stochastic singular state-space model, a term structure model, and an auction model.