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An instrumental variable random-coefficients model for binary outcomes.

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This study introduces a new random-coefficients model for binary outcomes, addressing endogeneity by allowing arbitrary correlations. It uses instrumental variables to identify the model, offering a flexible approach for analyzing complex data relationships.

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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.