Asymptotic theory for differentiated products demand models with many markets

This paper develops asymptotic theory for differentiated product demand models with a large number of markets T. It takes into account that the predicted market shares are approximated by Monte Carlo integration with R draws and that the observed market shares are approximated from a sample of N consumers. The estimated parameters are consistent and asymptotically normal as long as R and N grow fast enough relative to T. Both approximations yield additional bias and variance terms in the asymptotic expansion. I propose a bias corrected estimator and a variance adjustment that takes the leading terms into account. Monte Carlo simulations show that these adjustments should be used in applications to avoid severe undercoverage caused by the approximation errors.