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Nonparametric estimation of finite mixtures

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Author Info

  • Stéphane Bonhomme

    (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.

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Bibliographic Info

Paper provided by Sciences Po in its series Sciences Po publications with number 2013-09.

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Date of creation: Mar 2013
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Handle: RePEc:spo:wpmain:info:hdl:2441/7o52iohb7k6srk09n8t4k21sm

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

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References

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  1. Jean-Marc Robin & Stéphane Bonhomme, 2009. "Consistent Noisy Independent Component Analysis," Sciences Po publications info:hdl:2441/eu4vqp9ompq, Sciences Po.
  2. Yingyao Hu & Susanne M. Schennach, 2008. "Instrumental Variable Treatment of Nonclassical Measurement Error Models," Econometrica, Econometric Society, Econometric Society, vol. 76(1), pages 195-216, 01.
  3. 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.
  4. Javier Alvarez & Martin Browning & Mette Ejrnæs, 2001. "Modelling Income Processes with lots of heterogeneity," CAM Working Papers, University of Copenhagen. Department of Economics. Centre for Applied Microeconometrics 2002-01, University of Copenhagen. Department of Economics. Centre for Applied Microeconometrics.
  5. Robin, J.M. & Smith, R.J., 1995. "Tests of Rank," Cambridge Working Papers in Economics, Faculty of Economics, University of Cambridge 9521, Faculty of Economics, University of Cambridge.
  6. Richard Paap & Frank Kleibergen, 2004. "Generalized Reduced Rank Tests using the Singular Value Decomposition," Econometric Society 2004 Australasian Meetings, Econometric Society 195, Econometric Society.
  7. Jean-Marc Robin & Stéphane Bonhomme, 2009. "Consistent Noisy Independent Component Analysis," Sciences Po publications info:hdl:2441/eu4vqp9ompq, Sciences Po.
  8. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, Elsevier, vol. 79(1), pages 147-168, July.
  9. Hiroyuki Kasahara & Katsumi Shimotsu, 2009. "Nonparametric Identification of Finite Mixture Models of Dynamic Discrete Choices," Econometrica, Econometric Society, Econometric Society, vol. 77(1), pages 135-175, 01.
  10. Magnus, J.R., 1985. "On differentiating eigenvalues and eigenvectors," Open Access publications from Tilburg University, Tilburg University urn:nbn:nl:ui:12-153213, Tilburg University.
  11. McDonald, James B, 1984. "Some Generalized Functions for the Size Distribution of Income," Econometrica, Econometric Society, Econometric Society, vol. 52(3), pages 647-63, May.
  12. 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.
  13. repec:spo:wpecon:info:hdl:2441/eu4vqp9ompqllr09j01si09a2 is not listed on IDEAS
  14. Ahn, Hyungtaik & Powell, James L., 1993. "Semiparametric estimation of censored selection models with a nonparametric selection mechanism," Journal of Econometrics, Elsevier, Elsevier, vol. 58(1-2), pages 3-29, July.
  15. Peter Hall & Amnon Neeman & Reza Pakyari & Ryan Elmore, 2005. "Nonparametric inference in multivariate mixtures," Biometrika, Biometrika Trust, Biometrika Trust, vol. 92(3), pages 667-678, September.
  16. Magnus, Jan R., 1985. "On Differentiating Eigenvalues and Eigenvectors," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 1(02), pages 179-191, August.
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Citations

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Cited by:
  1. Stephane Bonhomme & Koen Jochmans & Jean-Marc Robin, 2014. "Nonparametric spectral-based estimation of latent structures," CeMMAP working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies CWP18/14, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  2. Marc Henry & Koen Jochmans & Bernard Salanié, 2014. "Inference on Mixtures Under Tail Restrictions," Sciences Po publications 2014-01, Sciences Po.

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