On the estimation of a binary response model in a selected population

Area of Science:

• Econometrics
• Biostatistics
• Statistical Modeling

Background:

• Selectivity bias can distort findings in binary response models.
• Traditional Probit models may not adequately address complex selection mechanisms.
• Unobserved factors influencing selection require careful consideration.

Purpose of the Study:

• To propose a generalized Probit model incorporating an extended skew-normal distribution.
• To model binary response variables in the presence of selectivity bias.
• To provide methods for parameter estimation and inference on selection parameters.

Main Methods:

• Generalization of the Probit model using extended skew-normal cumulative distribution as a link function.
• Maximum Likelihood (ML) estimation for model parameters.
• Inference on parameters quantifying the degree of selection.

Main Results:

• The proposed model effectively handles selectivity bias when the selection mechanism influences unmeasured factors.
• The model remains valid even when the standard assumption of selection independence from explanatory variables is violated, provided other conditional independencies hold.
• Instrumental variable approaches are applicable within this framework, particularly at the second stage of estimation.

Conclusions:

• The extended skew-normal Probit model offers a flexible approach to binary data analysis with selection bias.
• The methodology provides a robust framework for estimating selection effects and their impact.
• The model's derivation ensures applicability in scenarios where instrumental variables are relevant for addressing endogeneity.