Estimating the price elasticity of gasoline demand in 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. We use variation across clusters to estimate coefficients with homogeneous slopes (such as time effects) and within-cluster variation to estimate the cluster-specific heterogeneity directly. We then aggregate them to population averages. We demonstrate consistency, showing robustness over standard estimators, and provide analytic standard errors for robust inference. Basic implementation is straightforward using standard software such as Stata. 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. In our setting, we provide evidence of correlation between heterogeneity in the first and second stages, violating a key assumption underpinning consistency of standard estimators. We see significant divergence in the implicit weighting when applying FEIV from the natural weights applied in PCIV. Overlooking effect heterogeneity with standard estimators is consequential. Our estimated distribution of elasticities reveals significant heterogeneity and meaningful differences in estimated averages.