Random coefficients on endogenous variables in simultaneous equations models

This paper considers a classical linear simultaneous equations model with random coefficients on the endogenous variables. Simultaneous equations models are used to study social interactions, strategic interactions between ï¬rms, and market equilibrium. Random coefficient models allow for heterogeneous marginal effects. For two-equation systems, I give two sets of sufficient conditions for point identiï¬cation of the coefficients’ marginal distributions conditional on exogenous covariates. The ï¬rst requires full support instruments, but allows for nearly arbitrary distributions of unobservables. The second allows for continuous instruments without full support, but places tail restrictions on the distributions of unobservables. I show that a nonparametric sieve maximum likelihood estimator for these distributions is consistent. I apply my results to the Add Health data to analyze the social determinants of obesity.