Research related to high dimensional econometrics
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This dissertation consists of three chapters related to high dimensional econometrics dealing with the estimation of nonlinear panel data models and networks models. The first chapter proposes a fixed effects expectation-maximization estimator for a class of nonlinear panel data models with unobserved heterogeneity modeled as individual and/or time effects or an arbitrary interaction of the two. The estimator is obtained through a computationally simple iterative two-step procedure, both steps having a closed form solution. I show that the estimator is consistent in large panels, derive the asymptotic distribution for a probit model with interactive effects, and develop analytical bias corrections to deal with the incidental parameter problem. The second chapter considers estimation and inference for semiparametric nonlinear panel single index models with interactive effects. These include static and dynamic probit, logit, and Poisson models. An iterative two-step procedure to maximize the likelihood is proposed. The estimator is consistent, but has bias due to the incidental parameter problem. Analytical and jackknife bias corrections are developed to remove the bias without increasing variance. The third chapter proposes Quantile Graphical Models (QGMs) to characterize predictive and conditional dependence relationships within a set of random variables in non-Gaussian settings. These characterize the best linear predictor under asymmetric losses and the conditional dependence at each quantile. Estimators based on high-dimensional techniques are proposed. Each QGM represents the tail interdependence and the associated tail risk network and can be used to measure systemic risk contributions for the study of financial contagion and hedging under a market downturn.