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Econometric estimation with high-dimensional moment equalities

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  • Shi, Zhentao

Abstract

We consider a nonlinear structural model in which the number of moments is not limited by the sample size. The econometric problem here is to estimate and perform inference on a finite-dimensional parameter. To handle the high dimensionality, we must systematically choose a set of informative moments; in other words, delete the uninformative ones. In nonlinear models, a consistent estimator is a prerequisite for moment selection. We develop in this paper a novel two-step procedure. The first step achieves consistency in high-dimensional asymptotics by relaxing the moment constraints of empirical likelihood. Given the consistent estimator, in the second step we propose a computationally efficient algorithm to select the informative moments from a vast number of candidate combinations, and then use these moments to correct the bias of the first-step estimator. We show that the resulting second-step estimator is n-asymptotic normal, and achieves the lowest variance under a sparsity condition. To the best of our knowledge, we provide the first asymptotically normally distributed estimator in such an environment. The new estimator is shown to have favorable finite sample properties in simulations, and it is applied to estimate an international trade model with massive Chinese datasets.

Suggested Citation

  • Shi, Zhentao, 2016. "Econometric estimation with high-dimensional moment equalities," Journal of Econometrics, Elsevier, vol. 195(1), pages 104-119.
  • Handle: RePEc:eee:econom:v:195:y:2016:i:1:p:104-119
    DOI: 10.1016/j.jeconom.2016.07.004
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    as
    1. Han, Chirok & Orea, Luis & Schmidt, Peter, 2005. "Estimation of a panel data model with parametric temporal variation in individual effects," Journal of Econometrics, Elsevier, vol. 126(2), pages 241-267, June.
    2. Carrasco, Marine & Florens, Jean-Pierre, 2014. "On The Asymptotic Efficiency Of Gmm," Econometric Theory, Cambridge University Press, vol. 30(2), pages 372-406, April.
    3. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    4. Bai, Jushan & Ng, Serena, 2010. "Instrumental Variable Estimation In A Data Rich Environment," Econometric Theory, Cambridge University Press, vol. 26(6), pages 1577-1606, December.
    5. Whitney K. Newey & Richard J. Smith, 2004. "Higher Order Properties of Gmm and Generalized Empirical Likelihood Estimators," Econometrica, Econometric Society, vol. 72(1), pages 219-255, January.
    6. Carrasco, Marine & Tchuente, Guy, 2015. "Regularized LIML for many instruments," Journal of Econometrics, Elsevier, vol. 186(2), pages 427-442.
    7. Koenker, Roger & Machado, Jose A. F., 1999. "GMM inference when the number of moment conditions is large," Journal of Econometrics, Elsevier, vol. 93(2), pages 327-344, December.
    8. Chirok Han & Peter C. B. Phillips, 2006. "GMM with Many Moment Conditions," Econometrica, Econometric Society, vol. 74(1), pages 147-192, January.
    9. Joseph G. Altonji & Anthony A. Smith Jr. & Ivan Vidangos, 2013. "Modeling Earnings Dynamics," Econometrica, Econometric Society, vol. 81(4), pages 1395-1454, July.
    10. Jonathan Eaton & Samuel Kortum & Francis Kramarz, 2011. "An Anatomy of International Trade: Evidence From French Firms," Econometrica, Econometric Society, vol. 79(5), pages 1453-1498, September.
    11. Hansen, Christian & Kozbur, Damian, 2014. "Instrumental variables estimation with many weak instruments using regularized JIVE," Journal of Econometrics, Elsevier, vol. 182(2), pages 290-308.
    12. Hahn, Jinyong, 2002. "Optimal Inference With Many Instruments," Econometric Theory, Cambridge University Press, vol. 18(1), pages 140-168, February.
    13. Angrist, Joshua D, 1990. "Lifetime Earnings and the Vietnam Era Draft Lottery: Evidence from Social Security Administrative Records," American Economic Review, American Economic Association, vol. 80(3), pages 313-336, June.
    14. Whitney K. Newey & Frank Windmeijer, 2009. "Generalized Method of Moments With Many Weak Moment Conditions," Econometrica, Econometric Society, vol. 77(3), pages 687-719, May.
    15. Yuichi Kitamura & Michael Stutzer, 1997. "An Information-Theoretic Alternative to Generalized Method of Moments Estimation," Econometrica, Econometric Society, vol. 65(4), pages 861-874, July.
    16. Carrasco, Marine & Florens, Jean-Pierre, 2000. "Generalization Of Gmm To A Continuum Of Moment Conditions," Econometric Theory, Cambridge University Press, vol. 16(6), pages 797-834, December.
    17. A. Belloni & D. Chen & V. Chernozhukov & C. Hansen, 2012. "Sparse Models and Methods for Optimal Instruments With an Application to Eminent Domain," Econometrica, Econometric Society, vol. 80(6), pages 2369-2429, November.
    18. Liao, Zhipeng, 2013. "Adaptive Gmm Shrinkage Estimation With Consistent Moment Selection," Econometric Theory, Cambridge University Press, vol. 29(5), pages 857-904, October.
    19. John C. Chao & Norman R. Swanson, 2005. "Consistent Estimation with a Large Number of Weak Instruments," Econometrica, Econometric Society, vol. 73(5), pages 1673-1692, September.
    20. Chao, John C. & Swanson, Norman R. & Hausman, Jerry A. & Newey, Whitney K. & Woutersen, Tiemen, 2012. "Asymptotic Distribution Of Jive In A Heteroskedastic Iv Regression With Many Instruments," Econometric Theory, Cambridge University Press, vol. 28(1), pages 42-86, February.
    21. Fan, Jianqing & Hall, Peter & Yao, Qiwei, 2007. "To How Many Simultaneous Hypothesis Tests Can Normal, Student's t or Bootstrap Calibration Be Applied?," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1282-1288, December.
    22. Donald, Stephen G. & Imbens, Guido W. & Newey, Whitney K., 2003. "Empirical likelihood estimation and consistent tests with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 117(1), pages 55-93, November.
    23. Breusch, Trevor & Qian, Hailong & Schmidt, Peter & Wyhowski, Donald, 1999. "Redundancy of moment conditions," Journal of Econometrics, Elsevier, vol. 91(1), pages 89-111, July.
    24. A. Belloni & V. Chernozhukov & L. Wang, 2011. "Square-root lasso: pivotal recovery of sparse signals via conic programming," Biometrika, Biometrika Trust, vol. 98(4), pages 791-806.
    25. Hong, Han & Preston, Bruce & Shum, Matthew, 2003. "Generalized Empirical Likelihood–Based Model Selection Criteria For Moment Condition Models," Econometric Theory, Cambridge University Press, vol. 19(6), pages 923-943, December.
    26. Alastair R. Hall & Fernanda P. M. Peixe, 2003. "A Consistent Method for the Selection of Relevant Instruments," Econometric Reviews, Taylor & Francis Journals, vol. 22(3), pages 269-287, January.
    27. Alexandre Belloni & Victor Chernozhukov & Christian Hansen, 2011. "Estimation of treatment effects with high-dimensional controls," CeMMAP working papers CWP42/11, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    28. Angrist, Joshua D, 1990. "Lifetime Earnings and the Vietnam Era Draft Lottery: Evidence from Social Security Administrative Records: Errata," American Economic Review, American Economic Association, vol. 80(5), pages 1284-1286, December.
    29. Chen, Xiaohong, 2007. "Large Sample Sieve Estimation of Semi-Nonparametric Models," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 76, Elsevier.
    30. Otsu, Taisuke, 2010. "On Bahadur efficiency of empirical likelihood," Journal of Econometrics, Elsevier, vol. 157(2), pages 248-256, August.
    31. Joshua D. Angrist & Alan B. Keueger, 1991. "Does Compulsory School Attendance Affect Schooling and Earnings?," The Quarterly Journal of Economics, Oxford University Press, vol. 106(4), pages 979-1014.
    32. Caner, Mehmet, 2009. "Lasso-Type Gmm Estimator," Econometric Theory, Cambridge University Press, vol. 25(1), pages 270-290, February.
    33. Hansen, Lars Peter & Heaton, John & Yaron, Amir, 1996. "Finite-Sample Properties of Some Alternative GMM Estimators," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 262-280, July.
    34. Jushan Bai & Serena Ng, 2009. "Boosting diffusion indices," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(4), pages 607-629.
    35. Andrews, Donald W. K. & Lu, Biao, 2001. "Consistent model and moment selection procedures for GMM estimation with application to dynamic panel data models," Journal of Econometrics, Elsevier, vol. 101(1), pages 123-164, March.
    36. Hall, Alastair R. & Inoue, Atsushi & Jana, Kalidas & Shin, Changmock, 2007. "Information in generalized method of moments estimation and entropy-based moment selection," Journal of Econometrics, Elsevier, vol. 138(2), pages 488-512, June.
    37. Otsu, Taisuke, 2007. "Penalized empirical likelihood estimation of semiparametric models," Journal of Multivariate Analysis, Elsevier, vol. 98(10), pages 1923-1954, November.
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    2. Hao, Bowen & Prokhorov, Artem & Qian, Hailong, 2018. "Moment redundancy test with application to efficiency-improving copulas," Economics Letters, Elsevier, vol. 171(C), pages 29-33.
    3. Tang, Niansheng & Yan, Xiaodong & Zhao, Puying, 2018. "Exponentially tilted likelihood inference on growing dimensional unconditional moment models," Journal of Econometrics, Elsevier, vol. 202(1), pages 57-74.
    4. Zhentao Shi & Liangjun Su & Tian Xie, 2020. "High Dimensional Forecast Combinations Under Latent Structures," Papers 2010.09477, arXiv.org.

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    More about this item

    Keywords

    Bias correction; Empirical likelihood; Greedy algorithm; High-dimensional estimation;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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