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Nonparametric Identification of a Binary Random Factor in Cross Section Data

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  • Yingying Dong

    (California State University, Fullerton)

  • Arthur Lewbel

    () (Boston College)

Abstract

Suppose V and U are two independent mean zero random variables, where V has an asymmetric distribution with two mass points and U has a symmetric distribution. We show that the distributions of V and U are nonparametrically identified just from observing the sum V+U, and provide a rate root n estimator. We apply these results to the world income distribution to measure the extent of convergence over time, where the values V can take on correspond to country types, i.e., wealthy versus poor countries. We also extend our results to include covariates X, showing that we can nonparametrically identify and estimate cross section regression models of the form Y=g(X,D*)+U, where D* is an unobserved binary regressor.

Suggested Citation

  • Yingying Dong & Arthur Lewbel, 2009. "Nonparametric Identification of a Binary Random Factor in Cross Section Data," Boston College Working Papers in Economics 707, Boston College Department of Economics, revised 01 Jul 2010.
  • Handle: RePEc:boc:bocoec:707
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    1. Carrasco, Marine & Florens, Jean-Pierre, 2000. "Generalization Of Gmm To A Continuum Of Moment Conditions," Econometric Theory, Cambridge University Press, vol. 16(06), pages 797-834, December.
    2. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    3. Powell, James L, 1986. "Symmetrically Trimmed Least Squares Estimation for Tobit Models," Econometrica, Econometric Society, vol. 54(6), pages 1435-1460, November.
    4. Heckman, James J. & Robb, Richard Jr., 1985. "Alternative methods for evaluating the impact of interventions : An overview," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 239-267.
    5. Li, Qi & Racine, Jeff, 2003. "Nonparametric estimation of distributions with categorical and continuous data," Journal of Multivariate Analysis, Elsevier, vol. 86(2), pages 266-292, August.
    6. Bianchi, Marco, 1997. "Testing for Convergence: Evidence from Non-parametric Multimodality Tests," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 12(4), pages 393-409, July-Aug..
    7. Xiaohong Chen & Oliver Linton & Ingrid Van Keilegom, 2003. "Estimation of Semiparametric Models when the Criterion Function Is Not Smooth," Econometrica, Econometric Society, vol. 71(5), pages 1591-1608, September.
    8. Kumbhakar, Subal C. & Park, Byeong U. & Simar, Leopold & Tsionas, Efthymios G., 2007. "Nonparametric stochastic frontiers: A local maximum likelihood approach," Journal of Econometrics, Elsevier, vol. 137(1), pages 1-27, March.
    9. Xiaohong Chen & Yingyao Hu & Arthur Lewbel, 2007. "Nonparametric Identification and Estimation of Nonclassical Errors-in-Variables Models Without Additional Information," Boston College Working Papers in Economics 676, Boston College Department of Economics.
    10. Hiroyuki Kasahara & Katsumi Shimotsu, 2007. "Nonparametric Identification and Estimation of Multivariate Mixtures," Working Papers 1153, Queen's University, Department of Economics.
    11. Altonji, Joseph G & Segal, Lewis M, 1996. "Small-Sample Bias in GMM Estimation of Covariance Structures," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 353-366, July.
    12. Arthur Lewbel & Oliver Linton, 2007. "Nonparametric Matching and Efficient Estimators of Homothetically Separable Functions," Econometrica, Econometric Society, vol. 75(4), pages 1209-1227, July.
    13. 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.
    14. Lewbel, Arthur, 2007. "A local generalized method of moments estimator," Economics Letters, Elsevier, vol. 94(1), pages 124-128, January.
    15. Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, vol. 71(5), pages 1565-1578, September.
    16. Chunrong Ai & Xiaohong Chen, 2003. "Efficient Estimation of Models with Conditional Moment Restrictions Containing Unknown Functions," Econometrica, Econometric Society, vol. 71(6), pages 1795-1843, November.
    17. Yingyao Hu & Arthur Lewbel, 2007. "Identifying the Returns to Lying When the Truth is Unobserved," Economics Working Paper Archive 540, The Johns Hopkins University,Department of Economics.
    18. Chen, Xiaohong & Hu, Yingyao & Lewbel, Arthur, 2008. "Nonparametric identification of regression models containing a misclassified dichotomous regressor without instruments," Economics Letters, Elsevier, vol. 100(3), pages 381-384, September.
    19. Dong, Yingying, 2011. "Semiparametric binary random effects models: Estimating two types of drinking behavior," Economics Letters, Elsevier, vol. 112(1), pages 79-81, July.
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    Cited by:

    1. Dong, Yingying, 2011. "Semiparametric binary random effects models: Estimating two types of drinking behavior," Economics Letters, Elsevier, vol. 112(1), pages 79-81, July.
    2. Park, Byeong U. & Simar, LĂ©opold & Zelenyuk, Valentin, 2017. "Nonparametric estimation of dynamic discrete choice models for time series data," Computational Statistics & Data Analysis, Elsevier, pages 97-120.

    More about this item

    Keywords

    Mixture model; Random effects; Binary; Unobserved factor; Unobserved regressor; Nonparametric identification; Deconvolution; Treatment;

    JEL classification:

    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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