Estimating correlated random coefficient models with endogeneity

We propose a per-cluster instrumental-variables approach (PCIV) for estimating correlated random coefficient models in the presence of contemporaneous endogeneity and two- way fixed effects using Stata. Our estimator uses variation across clusters to estimate coefficients with homogeneous slopes (such as time effects) and within-cluster variation to estimate the cluster-specific heterogeneity. We aggregate cluster-specific estimates to population averages. We demonstrate consistency, showing robustness over standard estimators, and provide analytic standard errors for robust inference. Our Stata package allows for straightforward implementation. In Monte Carlo simulation, PCIV performs relatively well against pooled 2SLS and fixed-effects IV (FEIV) with a finite number of clusters or finite observations per cluster. We apply PCIV in estimating the price elasticity of gasoline demand using state fuel taxes as instrumental variables. PCIV estimation allows for greater transparency of the underlying data. It produces graphs depicting divergence in the implicit weighting when applying FEIV from the natural weights applied in PCIV and evidence of correlations between heterogeneity in the first and second stages, violating a key assumption underpinning the consistency of standard estimators. In our application, overlooking effect heterogeneity with standard estimators is consequential. Our estimated distribution of elasticities reveals significant heterogeneity and meaningful differences in estimated averages.