The thesis includes three chapters. The first chapter studies a type of partially identified models defined by moment equalities with latent variables and proposes a novel method to identify and estimate the parameters of interest. The second chapter applies the method in chapter one to demand estimation when the observed market shares cannot correctly represent the true market shares. The third chapter studies price competition models when firms are facing capacity constraints, and provides methods to partially or point identify and estimate the parameters of interests in both demand and supply function.