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Finite underidentification

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  • Sentana, Enrique

Abstract

I adapt the Generalised Method of Moments to deal with nonlinear models in which a finite number of isolated parameter values satisfy the moment conditions. I also study the closely related class of first-order underidentified models, whose expected Jacobian is rank deficient but not necessarily zero. In both cases, my proposed procedures exploit the underidentification structure to yield parameter estimators and underidentification tests within a standard asymptotically normal GMM framework. I study nonlinear models with and without separation of data and parameters. I also illustrate my proposed inference procedures with applications to production function estimation and dynamic panel data models.

Suggested Citation

  • Sentana, Enrique, 2024. "Finite underidentification," Journal of Econometrics, Elsevier, vol. 240(1).
    • Handle: RePEc:eee:econom:v:240:y:2024:i:1:s0304407624000381
    DOI: 10.1016/j.jeconom.2024.105692
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    1. Maurice J.G. Bun & Frank Kleibergen, 2013. "Identification and inference in moments based analysis of linear dynamic panel data models," UvA-Econometrics Working Papers 13-07, Universiteit van Amsterdam, Dept. of Econometrics.
    2. de Paula, Aureo & Rasul, Imran & Souza, Pedro, 2018. "Identifying Network Ties from Panel Data: Theory and an Application to Tax Competition," CEPR Discussion Papers 12792, C.E.P.R. Discussion Papers.
    3. Bun, Maurice J.G. & Kleibergen, Frank, 2022. "Identification Robust Inference For Moments-Based Analysis Of Linear Dynamic Panel Data Models," Econometric Theory, Cambridge University Press, vol. 38(4), pages 689-751, August.
    4. Arthur Lewbel, 2012. "Using Heteroscedasticity to Identify and Estimate Mismeasured and Endogenous Regressor Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(1), pages 67-80.
    5. Dovonon, Prosper & Gonçalves, Sílvia, 2017. "Bootstrapping the GMM overidentification test under first-order underidentification," Journal of Econometrics, Elsevier, vol. 201(1), pages 43-71.
    6. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    7. Alvarez, Javier & Arellano, Manuel, 2022. "Robust likelihood estimation of dynamic panel data models," Journal of Econometrics, Elsevier, vol. 226(1), pages 21-61.
    8. Jean-Marie Dufour, 2003. "Identification, weak instruments, and statistical inference in econometrics," Canadian Journal of Economics, Canadian Economics Association, vol. 36(4), pages 767-808, November.
    9. Dovonon, Prosper & Hall, Alastair R. & Kleibergen, Frank, 2020. "Inference in second-order identified models," Journal of Econometrics, Elsevier, vol. 218(2), pages 346-372.
    10. Francisco Peñaranda & Enrique Sentana, 2015. "A Unifying Approach to the Empirical Evaluation of Asset Pricing Models," The Review of Economics and Statistics, MIT Press, vol. 97(2), pages 412-435, May.
    11. Bramoullé, Yann & Djebbari, Habiba & Fortin, Bernard, 2009. "Identification of peer effects through social networks," Journal of Econometrics, Elsevier, vol. 150(1), pages 41-55, May.
    12. Lee, Ji Hyung & Liao, Zhipeng, 2018. "On Standard Inference For Gmm With Local Identification Failure Of Known Forms," Econometric Theory, Cambridge University Press, vol. 34(4), pages 790-814, August.
    13. Rothenberg, Thomas J, 1971. "Identification in Parametric Models," Econometrica, Econometric Society, vol. 39(3), pages 577-591, May.
    14. Prosper Dovonon & Alastair Hall, 2018. "The Asymptotic Properties of GMM and Indirect Inference under Second-order Identification," CIRANO Working Papers 2018s-37, CIRANO.
    15. Gorodnichenko, Yuriy & Mikusheva, Anna & Ng, Serena, 2012. "Estimators For Persistent And Possibly Nonstationary Data With Classical Properties," Econometric Theory, Cambridge University Press, vol. 28(5), pages 1003-1036, October.
    16. Gabriele Fiorentini & Enrique Sentana, 2016. "Neglected serial correlation tests in UCARIMA models," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 7(1), pages 121-178, March.
    17. Wright, Jonathan H., 2003. "Detecting Lack Of Identification In Gmm," Econometric Theory, Cambridge University Press, vol. 19(2), pages 322-330, April.
    18. Jean‐Marie Dufour, 2003. "Identification, weak instruments, and statistical inference in econometrics," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 36(4), pages 767-808, November.
    19. Stock, James H & Wright, Jonathan H & Yogo, Motohiro, 2002. "A Survey of Weak Instruments and Weak Identification in Generalized Method of Moments," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(4), pages 518-529, October.
    20. Prosper Dovonon & Eric Renault, 2013. "Testing for Common Conditionally Heteroskedastic Factors," Econometrica, Econometric Society, vol. 81(6), pages 2561-2586, November.
    21. Áureo de Paula & Imran Rasul & Pedro CL Souza, 2018. "Recovering social networks from panel data: identification, simulations and an application," CeMMAP working papers CWP58/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    22. Ahn, Seung C. & Schmidt, Peter, 1995. "Efficient estimation of models for dynamic panel data," Journal of Econometrics, Elsevier, vol. 68(1), pages 5-27, July.
    23. Ackerberg, Daniel A. & Frazer, Garth & Kim, Kyoo il & Luo, Yao & Su, Yingjun, 2023. "Under-identification of structural models based on timing and information set assumptions," Journal of Econometrics, Elsevier, vol. 237(1).
    24. Arellano, Manuel, 2003. "Panel Data Econometrics," OUP Catalogue, Oxford University Press, number 9780199245291.
    25. Breusch, Trevor & Qian, Hailong & Schmidt, Peter & Wyhowski, Donald, 1999. "Redundancy of moment conditions," Journal of Econometrics, Elsevier, vol. 91(1), pages 89-111, July.
    26. Manresa, Elena & Peñaranda, Francisco & Sentana, Enrique, 2023. "Empirical evaluation of overspecified asset pricing models," Journal of Financial Economics, Elsevier, vol. 147(2), pages 338-351.
    27. Hillier, Grant H, 1990. "On the Normalization of Structural Equations: Properties of Direct Estimators," Econometrica, Econometric Society, vol. 58(5), pages 1181-1194, September.
    28. Dovonon, Prosper & Hall, Alastair R., 2018. "The asymptotic properties of GMM and indirect inference under second-order identification," Journal of Econometrics, Elsevier, vol. 205(1), pages 76-111.
    29. Arthur Lewbel, 2019. "The Identification Zoo: Meanings of Identification in Econometrics," Journal of Economic Literature, American Economic Association, vol. 57(4), pages 835-903, December.
    30. Davidson, Russell & MacKinnon, James G, 1998. "Graphical Methods for Investigating the Size and Power of Hypothesis Tests," The Manchester School of Economic & Social Studies, University of Manchester, vol. 66(1), pages 1-26, January.
    31. Yildiz, Neşe, 2012. "Consistency Of Plug-In Estimators Of Upper Contour And Level Sets," Econometric Theory, Cambridge University Press, vol. 28(2), pages 309-327, April.
    32. Papadopoulos, Georgios & Santos Silva, J.M.C., 2012. "Identification issues in some double-index models for non-negative data," Economics Letters, Elsevier, vol. 117(1), pages 365-367.
    33. Cragg, John G. & Donald, Stephen G., 1993. "Testing Identifiability and Specification in Instrumental Variable Models," Econometric Theory, Cambridge University Press, vol. 9(2), pages 222-240, April.
    34. 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.
    35. Frank Kleibergen, 2005. "Testing Parameters in GMM Without Assuming that They Are Identified," Econometrica, Econometric Society, vol. 73(4), pages 1103-1123, July.
    36. Bertille Antoine & Eric Renault, 2012. "Efficient Inference with Poor Instruments: a General Framework," Discussion Papers dp12-04, Department of Economics, Simon Fraser University.
    37. Manuel Arellano & Stephen Bond, 1991. "Some Tests of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(2), pages 277-297.
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    1. Ackerberg, Daniel A. & Frazer, Garth & Kim, Kyoo il & Luo, Yao & Su, Yingjun, 2023. "Under-identification of structural models based on timing and information set assumptions," Journal of Econometrics, Elsevier, vol. 237(1).
    2. Dovonon, Prosper & Hall, Alastair R., 2018. "The asymptotic properties of GMM and indirect inference under second-order identification," Journal of Econometrics, Elsevier, vol. 205(1), pages 76-111.

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    More about this item

    Keywords

    Finite set; Generalised Method of Moments; Identification test;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General

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