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Nonparametric estimation of finite mixtures

Author

Listed:
  • Stéphane Bonhomme

    (Centro de Estudios Monetarios y Financieros (CEMFI))

  • Koen Jochmans

    (Département d'économie)

  • Jean-Marc Robin

    (Département d'économie)

Abstract

The aim of this paper is to provide simple nonparametric methods to estimate finitemixture models from data with repeated measurements. Three measurements suffice for the mixture to be fully identified and so our approach can be used even with very short panel data. We provide distribution theory for estimators of the mixing proportions and the mixture distributions, and various functionals thereof. We also discuss inference on the number of components. These estimators are found to perform well in a series of Monte Carlo exercises. We apply our techniques to document heterogeneity in log annual earnings using PSID data spanning the period 1969–1998.

Suggested Citation

  • Stéphane Bonhomme & Koen Jochmans & Jean-Marc Robin, 2013. "Nonparametric estimation of finite mixtures," Sciences Po Economics Discussion Papers 2013-09, Sciences Po Departement of Economics.
  • Handle: RePEc:spo:wpecon:info:hdl:2441/7o52iohb7k6srk09n8t4k21sm
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    References listed on IDEAS

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    1. Kleibergen, Frank & Paap, Richard, 2006. "Generalized reduced rank tests using the singular value decomposition," Journal of Econometrics, Elsevier, vol. 133(1), pages 97-126, July.
    2. Martin Browning & Mette Ejrnæs & Javier Alvarez, 2010. "Modelling Income Processes with Lots of Heterogeneity," Review of Economic Studies, Oxford University Press, vol. 77(4), pages 1353-1381.
    3. McDonald, James B, 1984. "Some Generalized Functions for the Size Distribution of Income," Econometrica, Econometric Society, vol. 52(3), pages 647-663, May.
    4. Bonhomme, Stphane & Robin, Jean-Marc, 2009. "Consistent noisy independent component analysis," Journal of Econometrics, Elsevier, vol. 149(1), pages 12-25, April.
    5. Yingyao Hu & Susanne M. Schennach, 2008. "Instrumental Variable Treatment of Nonclassical Measurement Error Models," Econometrica, Econometric Society, vol. 76(1), pages 195-216, January.
    6. repec:spo:wpecon:info:hdl:2441/eu4vqp9ompqllr09j01si09a2 is not listed on IDEAS
    7. Robin, Jean-Marc & Smith, Richard J., 2000. "Tests Of Rank," Econometric Theory, Cambridge University Press, vol. 16(02), pages 151-175, April.
    8. Peter Gottschalk & Robert Moffitt, 1994. "The Growth of Earnings Instability in the U.S. Labor Market," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 25(2), pages 217-272.
    9. Peter Hall & Amnon Neeman & Reza Pakyari & Ryan Elmore, 2005. "Nonparametric inference in multivariate mixtures," Biometrika, Biometrika Trust, vol. 92(3), pages 667-678, September.
    10. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
    11. Robert A. Moffitt & Peter Gottschalk, 2012. "Trends in the Transitory Variance of Male Earnings: Methods and Evidence," Journal of Human Resources, University of Wisconsin Press, vol. 47(1), pages 204-236.
    12. Magnus, Jan R., 1985. "On Differentiating Eigenvalues and Eigenvectors," Econometric Theory, Cambridge University Press, vol. 1(02), pages 179-191, August.
    13. Ahn, Hyungtaik & Powell, James L., 1993. "Semiparametric estimation of censored selection models with a nonparametric selection mechanism," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 3-29, July.
    14. Magnus, J.R., 1985. "On differentiating eigenvalues and eigenvectors," Other publications TiSEM f410e3a5-ba9b-4787-b8cc-4, Tilburg University, School of Economics and Management.
    15. Bura, E. & Pfeiffer, R., 2008. "On the distribution of the left singular vectors of a random matrix and its applications," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2275-2280, October.
    16. Hiroyuki Kasahara & Katsumi Shimotsu, 2009. "Nonparametric Identification of Finite Mixture Models of Dynamic Discrete Choices," Econometrica, Econometric Society, vol. 77(1), pages 135-175, January.
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    Citations

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    Cited by:

    1. Jean-Marc Robin & Stéphane Bonhomme & Koen Jochmans, 2014. "Estimating Multivariate Latent-Structure Models," Sciences Po Economics Discussion Papers 2014-18, Sciences Po Departement of Economics.
    2. Marc Henry & Koen Jochmans & Bernard Salanié, 2014. "Inference on Mixtures Under Tail Restrictions," Working Papers hal-01053810, HAL.
    3. Brodaty, Thomas & Gary-Bobo, Robert J. & Prieto, Ana, 2014. "Do risk aversion and wages explain educational choices?," Journal of Public Economics, Elsevier, vol. 117(C), pages 125-148.
    4. Stéphane Bonhomme & Koen Jochmans & Jean-Marc Robin, 2014. "Nonparametric spectral-based estimation of latent structures," CeMMAP working papers CWP18/14, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

    More about this item

    Keywords

    finite-mixture model; nonparametric estimation; series expansion; simultaneousdiagonalization system.;

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