DUMMY ENDOGENOUS VARIABLES IN A SIMULTANEOUS EQUATION SYSTEM

DUMMY ENDOGENOUS VARIABLES IN A SIMULTANEOUS EQUATION SYSTEM

May 1977 | James J. Heckman
This paper presents a general model for simultaneous equation systems with both discrete and continuous endogenous variables. The model is formulated to encompass classical simultaneous equation models for continuous endogenous variables and recent models for purely discrete endogenous variables as special cases. The paper discusses the formulation and estimation of such models, emphasizing the role of dummy variables as proxies for unobserved latent variables and as direct shifters of behavioral equations. It introduces a model with both continuous and discrete endogenous variables, which is analyzed in detail. The paper also discusses the identification and estimation of parameters, including maximum likelihood estimators and alternative estimators. It compares the proposed model with existing models, such as the multivariate probit model, and highlights the importance of the Principle Assumption in ensuring the model's validity. The paper also addresses the challenges of estimating structural parameters in overidentified models and presents methods for consistent estimation. The analysis includes the use of reduced form equations, the role of dummy variables in shifting behavioral equations, and the implications of the Principle Assumption on the identification of parameters. The paper concludes with a discussion of the asymptotic properties of estimators and the challenges of estimating structural covariance terms in the presence of unobserved latent variables.This paper presents a general model for simultaneous equation systems with both discrete and continuous endogenous variables. The model is formulated to encompass classical simultaneous equation models for continuous endogenous variables and recent models for purely discrete endogenous variables as special cases. The paper discusses the formulation and estimation of such models, emphasizing the role of dummy variables as proxies for unobserved latent variables and as direct shifters of behavioral equations. It introduces a model with both continuous and discrete endogenous variables, which is analyzed in detail. The paper also discusses the identification and estimation of parameters, including maximum likelihood estimators and alternative estimators. It compares the proposed model with existing models, such as the multivariate probit model, and highlights the importance of the Principle Assumption in ensuring the model's validity. The paper also addresses the challenges of estimating structural parameters in overidentified models and presents methods for consistent estimation. The analysis includes the use of reduced form equations, the role of dummy variables in shifting behavioral equations, and the implications of the Principle Assumption on the identification of parameters. The paper concludes with a discussion of the asymptotic properties of estimators and the challenges of estimating structural covariance terms in the presence of unobserved latent variables.
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