“Econometric Estimation with High-Dimensional Moment Equalitites” by Zhentao Shi
The Chinese University of Hong Kong
We consider a structural model in which the number of moments is not limited by the sample size, and where the econometric problem is to estimate and perform inference on a finite-dimensional parameter. We develop a novel two-step estimation procedure. We call the first step the Relaxed Empirical Likelihood, which relaxes the moment constraints of the primal problem of empirical likelihood. As the relaxation introduces first-order bias, the second step selects a small subset of moments in a computationally efficient manner to correct the bias. To the best of our knowledge, this paper provides the first asymptotically normally distributed estimator in such an environment. The new estimator is shown to have favorable finite sample properties in simulations. Estimating an international trade model with massive China datasets, we find Chinese firms are of low cost efficiency.