Random coefficients on endogenous variables in simultaneous equations models

Citation

Masten, Matthew A. (2018). Random coefficients on endogenous variables in simultaneous equations models. Review of Economic Studies. vol. 85 (2) pp. 1193-1250

Abstract

This article 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 firms, and market equilibrium. Random coefficient models allow for heterogeneous marginal effects. I show that random coefficient seemingly unrelated regression models with common regressors are not point identified, which implies random coefficient simultaneous equations models are not point identified. Important features of these models, however, can be identified. For two-equation systems, I give two sets of sufficient conditions for point identification of the coefficients’ marginal distributions conditional on exogenous covariates. The first allows for small support continuous instruments under tail restrictions on the distributions of unobservables which are necessary for point identification. The second requires full support instruments, but allows for nearly arbitrary distributions of unobservables. I discuss how to generalize these results to many equation systems, where I focus on linear-in-means models with heterogeneous endogenous social interaction effects. I give sufficient conditions for point identification of the distributions of these endogenous social effects. I propose a consistent nonparametric kernel estimator for these distributions based on the identification arguments. I apply my results to the Add Health data to analyse peer effects in education.

URL

http://doi.org/10.1093/restud/rdx047

Keyword(s)

Cross-sectional models Spatial models Treatment effect models Quantile regressions Social interaction models Semiparametric and nonparametric methods Instrumental variables estimation Model construction and estimation

Reference Type

Journal Article

Journal Title

Review of Economic Studies

Author(s)

Masten, Matthew A.

Year Published

2018

Volume Number

85

Issue Number

2

Pages

1193-1250

Edition

August 18, 2017

DOI

10.1093/restud/rdx047

Reference ID

8423