I want to estimate a model correcting for self-selection based endogeneity in a cross-sectional sample. In my case, my outcome y is binary and I observe it for everyone irrespective of treatment or not, but my treatment is assigned non-randomly. In fact, individuals in my random example, self-select into the treatment. Additional details that I am disregarding for now are that the data are nested, such that I observe individuals in regions, and I am interested in the effect of a level 2 variable that is potentially endogenous (correlated with covariates).
To address the self-selection based endogeneity, I am relying on the suite of what Stata calls the extended regression models, available starting in Stata 18, using the following pseudocode:
where y is my binary outcome, x1 is my potentially endogenous independent variable, x2 and x3 are my exogenous control variables, and w is an instrument that serves as exclusion criterion.
My starting point for correcting the self-selection based endogeneity was Clougherty et al. (2016). They introduce and discuss two models to correct for self-selection: the switching regression model and the treatment effects model. According to them, the key assumption is whether the treatment merely has an intercept effect, i.e. endogenous treatment or whether it also affects the coefficients, i.e. endogenous switching effect. I have searched and read parts of the help file for the extended regression models, but I could not find information on which assumption the extended regression models apply. I am also interested in any treatise discussing when either assumption applies.
References
Clougherty, J. A., Duso, T., & Muck, J. (2016). Correcting for Self-selection Based Endogeneity in Management Research: Review, Recommendations and Simulations. Organizational Research Methods, 19(2), 286–347. https://doi.org/10.1177/1094428115619013
To address the self-selection based endogeneity, I am relying on the suite of what Stata calls the extended regression models, available starting in Stata 18, using the following pseudocode:
Code:
eprobit y x1 x2 x3, entreat(z = x1 x2 x3 w),
My starting point for correcting the self-selection based endogeneity was Clougherty et al. (2016). They introduce and discuss two models to correct for self-selection: the switching regression model and the treatment effects model. According to them, the key assumption is whether the treatment merely has an intercept effect, i.e. endogenous treatment or whether it also affects the coefficients, i.e. endogenous switching effect. I have searched and read parts of the help file for the extended regression models, but I could not find information on which assumption the extended regression models apply. I am also interested in any treatise discussing when either assumption applies.
References
Clougherty, J. A., Duso, T., & Muck, J. (2016). Correcting for Self-selection Based Endogeneity in Management Research: Review, Recommendations and Simulations. Organizational Research Methods, 19(2), 286–347. https://doi.org/10.1177/1094428115619013
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