Two-stage residual inclusion estimation: Addressing endogeneity in health econometric modeling

Abstract

The paper focuses on two estimation methods that have been widely used to address endogeneity in empirical research in health economics and health services research B two-stage predictor substitution (2SPS) and two-stage residual inclusion (2SRI). 2SPS is the rote extension (to nonlinear models) of the popular linear two-stage least squares estimator. The 2SRI estimator is similar except that in the second stage regression, the endogenous variables are not replaced by first-stage predictors. Instead, first-stage residuals are included as additional regressors. In a generic parametric framework, we show that 2SRI is consistent and 2SPS is not. Results from a simulation study and an illustrative example also recommend against 2SPS and favor 2SRI. Our findings are important given that there are many prominent examples of the application of inconsistent 2SPS in the recent literature. This study can be used as a guide by future researchers in health economics who are confronted with endogeneity in their empirical work.

Does the extension of primary care practice opening hours reduce the use of emergency services?

“…Terza, Basu and Rathouz (2008) extend the previously suggested residual inclusion strategies (Rivers and Vuong, 1988;Smith and Blundell, 1986) to a broader class of nonlinear models. This structural equation approach can also be interpreted as an extension of the Hausman (1978) endogeneity test suitable for non-linear models.…”

“…Terza, Bradford and Dismuke (2008) show that addressing endogeneity by applying conventional linear IV methods that ignore the non-linear specification of the relationship of to an endogenous regressor, and a set of additional confounders, can lead to biased estimates of the causal effect in question. Mullahy (1997) and Terza, Basu and Rathouz (2008), among others, have suggested alternative estimators in order to deal with endogeneity in count/exponential regression models. In keeping with these studies, we employ two different IV strategies to estimate the model in (5) where the (binary) regressor %&' is allowed to be endogenous to the outcome variable.…”

Does Quality Affect Patients’ Choice of Doctor? Evidence from England

“…We implement our IV estimates using two‐stage residual inclusion (Terza et al ., 2008). We first estimate an OLS model of practice quality for all practices in the choice sets of LSOAs in the East Midlands.…”

The Role of Education and Family Background in Marriage, Childbearing and Labor Market Participation in Senegal

“…The underlying hypothesis is that, while the average characteristics of the department have an impact on the individual fertility decision, the relative position of a department does not affect individual fertility choices, and it can thus represent a valid instrument for the placement decision. We then compute the generalized residuals (Gourieroux et al, 1987) from the first stage, including them as auxiliary regressors in the non-linear fertility model together with the endogenous variables (Terza et al, 2008). Results show that the generalized residuals are positive -suggesting that fertility planning services are placed in areas where the age at first child is lower -but they are not significant at conventional confidence level -thus reducing our concerns about the endogeneity of condoms availability.…”