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Tests of Hypotheses Arising In the Correlated Random Coefficient Model
James J Heckman1, Daniel Schmierer
1University of Chicago, University College Dublin, Cowles Foundation, Yale University, and the American Bar Foundation.
Economic Modelling
|December 21, 2010
Summary
This study introduces the correlated random coefficient model, expanding on Swamy's foundational work. New methods are presented for analyzing its properties and testing its validity against uncorrelated models.
Area of Science:
- Econometrics
- Statistical Modeling
Background:
- The uncorrelated random coefficient model, pioneered by Swamy (1971), is a cornerstone in econometric analysis.
- Existing models often assume independence between coefficients and regressors, limiting their applicability.
Purpose of the Study:
- To introduce and analyze the correlated random coefficient model.
- To extend the theoretical framework established by Swamy (1971).
- To develop novel statistical tests for model validation.
Main Methods:
- Derivation of the properties of the correlated random coefficient model.
- Development of a new representation for the variance of the instrumental variable estimator.
- Formulation of hypothesis tests comparing correlated and uncorrelated models.
Main Results:
- The paper establishes the theoretical properties of the correlated random coefficient model.
- A novel variance representation for the instrumental variable estimator is derived.
- New tests are developed to distinguish between correlated and uncorrelated random coefficient models.
Conclusions:
- The correlated random coefficient model offers a more flexible framework for economic analysis.
- The derived estimator and tests provide valuable tools for empirical econometrics.
- This work advances the understanding and application of random coefficient models.
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