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Specification Testing in Random Coefficient Models

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  • Breunig, Christoph

    (Humboldt University Berlin)

  • Hoderlein, Stefan

    (Boston College)

Abstract

In this paper, we suggest and analyze a new class of specification tests for random coefficient models. These tests allow to assess the validity of central structural features of the model, in particular linearity in coefficients, generalizations of this notion like a known nonlinear functional relationship, or degeneracy of the distribution of a random coefficient, i.e., whether a coefficient is fixed or random, including whether an associated variable can be omitted altogether. Our tests are nonparametric in nature, and use sieve estimators of the characteristic function. We provide formal power analysis against global as well as against local alternatives. Moreover, we perform a Monte Carlo simulation study, and apply the tests to analyze the degree of nonlinearity in a heterogeneous random coefficients demand model. While we find some evidence against the popular QUAIDS specification with random coefficients, it is not strong enough to reject the specification at the conventional significance level.

Suggested Citation

  • Breunig, Christoph & Hoderlein, Stefan, 2018. "Specification Testing in Random Coefficient Models," Rationality and Competition Discussion Paper Series 77, CRC TRR 190 Rationality and Competition.
    • Handle: RePEc:rco:dpaper:77
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    Cited by:

    1. Breunig, Christoph, 2021. "Varying random coefficient models," Journal of Econometrics, Elsevier, vol. 221(2), pages 381-408.
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    3. Gautier, Eric & Gaillac, Christophe, 2019. "Adaptive estimation in the linear random coefficients model when regressors have limited variation," TSE Working Papers 19-1026, Toulouse School of Economics (TSE).

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    More about this item

    Keywords

    nonparametric; specification; testing; random coefficients; unobserved heterogeneity; sieve estimation; characteristic function; consumer demand;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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