Abstract
This paper presents a method for estimating the average treatment effects (ATE) of an exponential endogenous switching model where the coefficients of covariates in the structural equation are random and correlated with the binary treatment variable. The estimating equations are derived under some mild identifying assumptions. We find that the ATE is identified, although each coefficient in the structural model may not be. Tests assessing the endogeneity of treatment and for model selection are provided. Monte Carlo simulations show that, in large samples, the proposed estimator has a smaller bias and a larger variance than the methods that do not take the random coefficients into account. This is applied to health insurance data of Oregon.
Highlights
The conventional instrumental variable methods fail to consistently estimate the Average Partial Effects (APE) when the individual heterogeneity enters the model in a non-additive way (Heckman and Vytlacil 1998; Card 2001; Browning and Lechene 2003; Browning and Carro 2007; Imbens 2007)
One of the simplest models, which allows for non-additive heterogeneity, is the Correlated Random Coefficient (CRC) model, where the heterogeneity interacts with the covariates to create random coefficients
This paper provides the identification and the estimation of the average treatment effect (ATE) for an exponential model that has two regimes induced by an endogenous treatment
Summary
The conventional instrumental variable methods fail to consistently estimate the Average Partial Effects (APE) when the individual heterogeneity enters the model in a non-additive way (Heckman and Vytlacil 1998; Card 2001; Browning and Lechene 2003; Browning and Carro 2007; Imbens 2007). The second is due to Angrist and Imbens (1994) under Rubin’s counterfactual setting, where the heterogeneous treatment effect, i.e., the individual-specific difference of outcomes in two regimes, appears as the coefficient on the binary regime indicator. Wooldridge (2015), in a linear setting with a continuous dependent variable, allows the coefficients on all other covariates to be random and correlated with the treatment. This study extends Terza (2009)’s exponential ES regression model by allowing the coefficients on the covariates in each regime to be correlated with the binary regime indicator. This is an exponential version of the linear two-regime CRC model.
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