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Testing the Correlated Random Coefficient Model

Author

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  • Heckman, James J.

    (University of Chicago)

  • Schmierer, Daniel

    (University of Chicago)

  • Urzua, Sergio

    (University of Maryland)

Abstract

The recent literature on instrumental variables (IV) features models in which agents sort into treatment status on the basis of gains from treatment as well as on baseline-pretreatment levels. Components of the gains known to the agents and acted on by them may not be known by the observing economist. Such models are called correlated random coefficient models. Sorting on unobserved components of gains complicates the interpretation of what IV estimates. This paper examines testable implications of the hypothesis that agents do not sort into treatment based on gains. In it, we develop new tests to gauge the empirical relevance of the correlated random coefficient model to examine whether the additional complications associated with it are required. We examine the power of the proposed tests. We derive a new representation of the variance of the instrumental variable estimator for the correlated random coefficient model. We apply the methods in this paper to the prototypical empirical problem of estimating the return to schooling and find evidence of sorting into schooling based on unobserved components of gains.

Suggested Citation

  • Heckman, James J. & Schmierer, Daniel & Urzua, Sergio, 2009. "Testing the Correlated Random Coefficient Model," IZA Discussion Papers 4525, Institute of Labor Economics (IZA).
  • Handle: RePEc:iza:izadps:dp4525
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    References listed on IDEAS

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    More about this item

    Keywords

    power of tests based on IV; testing; correlated random coefficient; instrumental variables;
    All these keywords.

    JEL classification:

    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models

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