An instrumental variable random-coefficients model for binary outcomes

Area of Science:

• Econometrics
• Statistics
• Binary Outcome Models

Background:

• Endogeneity is a common challenge in econometrics, particularly in models with binary outcomes.
• Traditional methods like control functions require strong assumptions on the joint distribution of endogenous variables and instruments.
• Random-coefficients models offer flexibility but often face identification issues when endogeneity is present.

Purpose of the Study:

• To develop and analyze a random-coefficients model for binary outcomes that accommodates arbitrary endogeneity.
• To extend generalized instrumental variable (GIV) methods to address endogeneity in this specific model class.
• To characterize the identified set for the distribution of random coefficients under endogeneity.

Main Methods:

• The study employs a generalized instrumental variable (GIV) framework.
• It utilizes conditional moment inequalities to define the identified set for the random coefficients.
• Identification results from prior GIV studies are adapted and applied.

Main Results:

• The paper characterizes the identified set for the distribution of random coefficients in the presence of endogeneity.
• It demonstrates the applicability of GIV identification results to this model.
• Numerical illustrations are provided to explore the structure of the identified sets.

Conclusions:

• The proposed GIV approach provides a robust method for analyzing binary outcome models with endogeneity.
• The characterization of the identified set offers valuable insights into the model's estimability.
• This work contributes to the literature on identification and estimation in econometric models with complex error structures.