“Inference for High-Dimensional Factor Models with an Application to Demand”
Summary: I propose an estimator and an inference method for the low-dimensional parameters of interest in models with high-dimensional controls. The estimator uses principal components regression (PCR) to estimate relevant components of the high-dimensional controls. I adopt the Neyman orthogonalized moment conditions to obtain root-N-consistency of my estimator. I derive asymptotic normality and develop a consistent estimator for the asymptotic variance. I extend these results to allow for endogeneity of the variables of interest when an instrumental variable is available. In Monte Carlo simulations, I compare the mean-squared error and the coverage rate of corresponding confidence intervals of my estimator with several competitors for a parameter of interest in different setups. PCR results show correct coverage rate and the smallest mean-squared error when underlying data generating processes are high-dimensional factor models. I apply my estimator and other parametric alternatives to the estimation and inference of the price coefficient in logit demand models for the U.S. ready-to-eat cereal market. Using an instrumental variable does change the estimate of the coefficient for the price significantly, which implies that researchers should consider potential endogeneity problems even under high-dimensional controls.
“Incorporating a Possibly Misspecified Over-Identifying Inequality by Model Averaging”
“Inference for Functions of Two-Stage Partially Identified Models”