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Tests for qualitative features in the random coefficients model

Author

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  • Fabian Dunker
  • Konstantin Eckle
  • Katharina Proksch
  • Johannes Schmidt-Hieber

Abstract

The random coefficients model is an extension of the linear regression model that allows for unobserved heterogeneity in the population by modeling the regression coefficients as random variables. Given data from this model, the statistical challenge is to recover information about the joint density of the random coefficients which is a multivariate and ill-posed problem. Because of the curse of dimensionality and the ill-posedness, pointwise nonparametric estimation of the joint density is difficult and suffers from slow convergence rates. Larger features, such as an increase of the density along some direction or a well-accentuated mode can, however, be much easier detected from data by means of statistical tests. In this article, we follow this strategy and construct tests and confidence statements for qualitative features of the joint density, such as increases, decreases and modes. We propose a multiple testing approach based on aggregating single tests which are designed to extract shape information on fixed scales and directions. Using recent tools for Gaussian approximations of multivariate empirical processes, we derive expressions for the critical value. We apply our method to simulated and real data.

Suggested Citation

  • Fabian Dunker & Konstantin Eckle & Katharina Proksch & Johannes Schmidt-Hieber, 2017. "Tests for qualitative features in the random coefficients model," Papers 1704.01066, arXiv.org, revised Mar 2018.
  • Handle: RePEc:arx:papers:1704.01066
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    References listed on IDEAS

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    1. Rudolf Beran, 1993. "Semiparametric random coefficient regression models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 45(4), pages 639-654, December.
    2. Hoderlein, Stefan & Holzmann, Hajo & Meister, Alexander, 2017. "The triangular model with random coefficients," Journal of Econometrics, Elsevier, vol. 201(1), pages 144-169.
    3. Jean‐Pierre Dubé & Jeremy T. Fox & Che‐Lin Su, 2012. "Improving the Numerical Performance of Static and Dynamic Aggregate Discrete Choice Random Coefficients Demand Estimation," Econometrica, Econometric Society, vol. 80(5), pages 2231-2267, September.
    4. Gautier, Eric & Hoderlein, Stefan, 2011. "A triangular treatment effect model with random coefficients in the selection equation," TSE Working Papers 15-598, Toulouse School of Economics (TSE), revised 25 Aug 2015.
    5. Hoderlein, Stefan & Klemelä, Jussi & Mammen, Enno, 2010. "Analyzing The Random Coefficient Model Nonparametrically," Econometric Theory, Cambridge University Press, vol. 26(3), pages 804-837, June.
    6. Jeremy T. Fox & Amit Gandhi, 2016. "Nonparametric identification and estimation of random coefficients in multinomial choice models," RAND Journal of Economics, RAND Corporation, vol. 47(1), pages 118-139, February.
    7. Amil Petrin, 2002. "Quantifying the Benefits of New Products: The Case of the Minivan," Journal of Political Economy, University of Chicago Press, vol. 110(4), pages 705-729, August.
    8. Nevo, Aviv, 2001. "Measuring Market Power in the Ready-to-Eat Cereal Industry," Econometrica, Econometric Society, vol. 69(2), pages 307-342, March.
    9. Andrews, Donald W K, 2001. "Testing When a Parameter Is on the Boundary of the Maintained Hypothesis," Econometrica, Econometric Society, vol. 69(3), pages 683-734, May.
    10. Matthew Masten & Alexander Torgovitsky, 2014. "Instrumental variables estimation of a generalized correlated random coefficients model," CeMMAP working papers CWP02/14, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    11. Andrey Feuerverger & Yehuda Vardi, 2000. "Positron Emission Tomography and Random Coefficients Regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(1), pages 123-138, March.
    12. Steven Berry & Ariel Pakes, 2007. "The Pure Characteristics Demand Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 48(4), pages 1193-1225, November.
    13. Eric Gautier & Yuichi Kitamura, 2013. "Nonparametric Estimation in Random Coefficients Binary Choice Models," Econometrica, Econometric Society, vol. 81(2), pages 581-607, March.
    14. Bai, Z. D. & Rao, C. Radhakrishna & Zhao, L. C., 1988. "Kernel estimators of density function of directional data," Journal of Multivariate Analysis, Elsevier, vol. 27(1), pages 24-39, October.
    15. Sander Greenland, 2000. "When Should Epidemiologic Regressions Use Random Coefficients?," Biometrics, The International Biometric Society, vol. 56(3), pages 915-921, September.
    16. Ichimura, Hidehiko & Thompson, T. Scott, 1998. "Maximum likelihood estimation of a binary choice model with random coefficients of unknown distribution," Journal of Econometrics, Elsevier, vol. 86(2), pages 269-295, June.
    17. Fabian Dunker & Stefan Hoderlein & Hiroaki Kaido, 2017. "Nonparametric Identification of Random Coefficients in Endogenous and Heterogeneous Aggregate Demand," Courant Research Centre: Poverty, Equity and Growth - Discussion Papers 224, Courant Research Centre PEG.
    18. Matthew Masten, 2015. "Random coefficients on endogenous variables in simultaneous equations models," CeMMAP working papers CWP25/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    19. Victor Chernozhukov & Denis Chetverikov & Kengo Kato, 2014. "Central limit theorems and bootstrap in high dimensions," CeMMAP working papers CWP49/14, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    20. Fabian Dunker & Stefan Hoderlein & Hiroaki Kaido, 2017. "Nonparametric identification of random coefficients in endogenous and heterogeneous aggregate demand models," CeMMAP working papers CWP11/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    21. Fabian Dunker & Stefan Hoderlein & Hiroaki Kaido, 2013. "Random Coefficients in Static Games of Complete Information," Boston College Working Papers in Economics 835, Boston College Department of Economics.
    22. Deaton, Angus S & Muellbauer, John, 1980. "An Almost Ideal Demand System," American Economic Review, American Economic Association, vol. 70(3), pages 312-326, June.
    23. Paul Gustafson & Sander Greenland, 2006. "The Performance of Random Coefficient Regression in Accounting for Residual Confounding," Biometrics, The International Biometric Society, vol. 62(3), pages 760-768, September.
    24. Berry, Steven & Levinsohn, James & Pakes, Ariel, 1995. "Automobile Prices in Market Equilibrium," Econometrica, Econometric Society, vol. 63(4), pages 841-890, July.
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    Cited by:

    1. Christoph Breunig, 2018. "Varying Random Coefficient Models," Papers 1804.03110, arXiv.org, revised May 2019.
    2. Christophe Gaillac & Eric Gautier, 2019. "Adaptive estimation in the linear random coefficients model when regressors have limited variation," Working Papers hal-02130472, HAL.

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