IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2011.06753.html
   My bibliography  Save this paper

Weak Identification in Discrete Choice Models

Author

Listed:
  • David T. Frazier
  • Eric Renault
  • Lina Zhang
  • Xueyan Zhao

Abstract

We study the impact of weak identification in discrete choice models, and provide insights into the determinants of identification strength in these models. Using these insights, we propose a novel test that can consistently detect weak identification in commonly applied discrete choice models, such as probit, logit, and many of their extensions. Furthermore, we demonstrate that when the null hypothesis of weak identification is rejected, Wald-based inference can be carried out using standard formulas and critical values. A Monte Carlo study compares our proposed testing approach against commonly applied weak identification tests. The results simultaneously demonstrate the good performance of our approach and the fundamental failure of using conventional weak identification tests for linear models in the discrete choice model context. Furthermore, we compare our approach against those commonly applied in the literature in two empirical examples: married women labor force participation, and US food aid and civil conflicts.

Suggested Citation

  • David T. Frazier & Eric Renault & Lina Zhang & Xueyan Zhao, 2020. "Weak Identification in Discrete Choice Models," Papers 2011.06753, arXiv.org, revised Jan 2021.
  • Handle: RePEc:arx:papers:2011.06753
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2011.06753
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Carolin E. Pflueger & Su Wang, 2015. "A robust test for weak instruments in Stata," Stata Journal, StataCorp LP, vol. 15(1), pages 216-225, March.
    2. Keith Finlay & Leandro M. Magnusson, 2009. "Implementing weak-instrument robust tests for a general class of instrumental-variables models," Stata Journal, StataCorp LP, vol. 9(3), pages 398-421, September.
    3. Li, Chuhui & Poskitt, D.S. & Zhao, Xueyan, 2019. "The bivariate probit model, maximum likelihood estimation, pseudo true parameters and partial identification," Journal of Econometrics, Elsevier, vol. 209(1), pages 94-113.
    4. Chaudhuri, Saraswata & Renault, Eric, 2020. "Score tests in GMM: Why use implied probabilities?," Journal of Econometrics, Elsevier, vol. 219(2), pages 260-280.
    5. Guido W. Imbens & Whitney K. Newey, 2009. "Identification and Estimation of Triangular Simultaneous Equations Models Without Additivity," Econometrica, Econometric Society, vol. 77(5), pages 1481-1512, September.
    6. Arendt, Jacob Nielsen, 2005. "Does education cause better health? A panel data analysis using school reforms for identification," Economics of Education Review, Elsevier, vol. 24(2), pages 149-160, April.
    7. Nathan Nunn & Nancy Qian, 2014. "US Food Aid and Civil Conflict," American Economic Review, American Economic Association, vol. 104(6), pages 1630-1666, June.
    8. Antoine, Bertille & Renault, Eric, 2020. "Testing identification strength," Journal of Econometrics, Elsevier, vol. 218(2), pages 271-293.
    9. Whitney K. Newey & James L. Powell & Francis Vella, 1999. "Nonparametric Estimation of Triangular Simultaneous Equations Models," Econometrica, Econometric Society, vol. 67(3), pages 565-604, May.
    10. 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.
    11. Richard W. Blundell & James L. Powell, 2004. "Endogeneity in Semiparametric Binary Response Models," Review of Economic Studies, Oxford University Press, vol. 71(3), pages 655-679.
    12. Lance Lochner & Enrico Moretti, 2004. "The Effect of Education on Crime: Evidence from Prison Inmates, Arrests, and Self-Reports," American Economic Review, American Economic Association, vol. 94(1), pages 155-189, March.
    13. Jean-Marie Dufour & Joachim Wilde, 2018. "Weak identification in probit models with endogenous covariates," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(4), pages 611-631, October.
    14. Jeffrey M Wooldridge, 2010. "Econometric Analysis of Cross Section and Panel Data," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262232588.
    15. repec:hrv:faseco:30410811 is not listed on IDEAS
    16. Bertille Antoine & Eric Renault, 2009. "Efficient GMM with nearly-weak instruments," Econometrics Journal, Royal Economic Society, vol. 12(s1), pages 135-171, January.
    17. 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.
    18. Leandro M. Magnusson, 2010. "Inference in limited dependent variable models robust to weak identification," Econometrics Journal, Royal Economic Society, vol. 13(3), pages 56-79, October.
    19. Hausman, Jerry, 2015. "Specification tests in econometrics," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 38(2), pages 112-134.
    20. Daiji Kawaguchi & Yukitoshi Matsushita & Hisahiro Naito, 2017. "Moment Estimation of the Probit Model with an Endogenous Continuous Regressor," The Japanese Economic Review, Springer, vol. 68(1), pages 48-62, March.
    21. Terza, Joseph V. & Basu, Anirban & Rathouz, Paul J., 2008. "Two-stage residual inclusion estimation: Addressing endogeneity in health econometric modeling," Journal of Health Economics, Elsevier, vol. 27(3), pages 531-543, May.
    22. Frank Windmeijer, 2019. "Two-stage least squares as minimum distance," Econometrics Journal, Royal Economic Society, vol. 22(1), pages 1-9.
    23. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    24. Isaiah Andrews, 2018. "Valid Two-Step Identification-Robust Confidence Sets for GMM," The Review of Economics and Statistics, MIT Press, vol. 100(2), pages 337-348, May.
    25. Frank Kleibergen, 2005. "Testing Parameters in GMM Without Assuming that They Are Identified," Econometrica, Econometric Society, vol. 73(4), pages 1103-1123, July.
    26. Cawley, John & Meyerhoefer, Chad, 2012. "The medical care costs of obesity: An instrumental variables approach," Journal of Health Economics, Elsevier, vol. 31(1), pages 219-230.
    27. Andrews, Donald W.K. & Cheng, Xu, 2014. "Gmm Estimation And Uniform Subvector Inference With Possible Identification Failure," Econometric Theory, Cambridge University Press, vol. 30(2), pages 287-333, April.
    28. 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.
    29. David McKenzie & Hillel Rapoport, 2011. "Can migration reduce educational attainment? Evidence from Mexico," Journal of Population Economics, Springer;European Society for Population Economics, vol. 24(4), pages 1331-1358, October.
    30. Kinda, Tidiane, 2010. "Investment Climate and FDI in Developing Countries: Firm-Level Evidence," World Development, Elsevier, vol. 38(4), pages 498-513, April.
    31. James H. Stock & Jonathan Wright, 2000. "GMM with Weak Identification," Econometrica, Econometric Society, vol. 68(5), pages 1055-1096, September.
    32. Edward Miguel & Shanker Satyanath & Ernest Sergenti, 2004. "Economic Shocks and Civil Conflict: An Instrumental Variables Approach," Journal of Political Economy, University of Chicago Press, vol. 112(4), pages 725-753, August.
    33. Wooldridge, Jeffrey M., 2014. "Quasi-maximum likelihood estimation and testing for nonlinear models with endogenous explanatory variables," Journal of Econometrics, Elsevier, vol. 182(1), pages 226-234.
    34. Hahn, Jinyong & Kuersteiner, Guido, 2002. "Discontinuities of weak instrument limiting distributions," Economics Letters, Elsevier, vol. 75(3), pages 325-331, May.
    35. Rivers, Douglas & Vuong, Quang H., 1988. "Limited information estimators and exogeneity tests for simultaneous probit models," Journal of Econometrics, Elsevier, vol. 39(3), pages 347-366, November.
    36. José Luis Montiel Olea & Carolin Pflueger, 2013. "A Robust Test for Weak Instruments," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(3), pages 358-369, July.
    37. Powell, Lisa M. & Tauras, John A. & Ross, Hana, 2005. "The importance of peer effects, cigarette prices and tobacco control policies for youth smoking behavior," Journal of Health Economics, Elsevier, vol. 24(5), pages 950-968, September.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Frazier, David T. & Renault, Eric & Zhang, Lina & Zhao, Xueyan, 2021. "Weak Identification in Discrete Choice Models," The Warwick Economics Research Paper Series (TWERPS) 1336, University of Warwick, Department of Economics.
    2. Wang, Wenjie, 2021. "Wild Bootstrap for Instrumental Variables Regression with Weak Instruments and Few Clusters," MPRA Paper 106227, University Library of Munich, Germany.
    3. Antoine, Bertille & Renault, Eric, 2020. "Testing identification strength," Journal of Econometrics, Elsevier, vol. 218(2), pages 271-293.
    4. Mardi Dungey & Vitali Alexeev & Jing Tian & Alastair R. Hall, 2015. "Econometricians Have Their Moments: GMM at 32," The Economic Record, The Economic Society of Australia, vol. 91, pages 1-24, June.
    5. Alastair R. Hall, 2015. "Econometricians Have Their Moments: GMM at 32," The Economic Record, The Economic Society of Australia, vol. 91(S1), pages 1-24, June.
    6. Gregory Cox, 2020. "Weak Identification with Bounds in a Class of Minimum Distance Models," Papers 2012.11222, arXiv.org.
    7. Cheng, Xu, 2015. "Robust inference in nonlinear models with mixed identification strength," Journal of Econometrics, Elsevier, vol. 189(1), pages 207-228.
    8. Wooldridge, Jeffrey M., 2014. "Quasi-maximum likelihood estimation and testing for nonlinear models with endogenous explanatory variables," Journal of Econometrics, Elsevier, vol. 182(1), pages 226-234.
    9. Bertille Antoine & Otilia Boldea, 2015. "Efficient Inference with Time-Varying Information and the New Keynesian Phillips Curve," Discussion Papers dp15-04, Department of Economics, Simon Fraser University, revised 25 Aug 2016.
    10. Chernozhukov, Victor & Fernández-Val, Iván & Kowalski, Amanda E., 2015. "Quantile regression with censoring and endogeneity," Journal of Econometrics, Elsevier, vol. 186(1), pages 201-221.
    11. Bertille Antoine & Otilia Boldea, 2014. "Efficient Inference with Time-Varying Identification Strength," Discussion Papers dp14-03, Department of Economics, Simon Fraser University.
    12. Murray Michael P., 2017. "Linear Model IV Estimation When Instruments Are Many or Weak," Journal of Econometric Methods, De Gruyter, vol. 6(1), pages 1-22, January.
    13. Antoine, Bertille & Renault, Eric, 2012. "Efficient minimum distance estimation with multiple rates of convergence," Journal of Econometrics, Elsevier, vol. 170(2), pages 350-367.
    14. Richard Bluhm & Denis de Crombrugghe & Adam Szirmai, 2016. "Poverty Accounting. A fractional response approach to poverty decomposition," Working Papers 413, ECINEQ, Society for the Study of Economic Inequality.
    15. Lippi Bruni, Matteo & Mammi, Irene & Ugolini, Cristina, 2016. "Does the extension of primary care practice opening hours reduce the use of emergency services?," Journal of Health Economics, Elsevier, vol. 50(C), pages 144-155.
    16. Isaiah Andrews & Anna Mikusheva, 2016. "Conditional Inference With a Functional Nuisance Parameter," Econometrica, Econometric Society, vol. 84, pages 1571-1612, July.
    17. Jun, Sung Jae, 2008. "Weak identification robust tests in an instrumental quantile model," Journal of Econometrics, Elsevier, vol. 144(1), pages 118-138, May.
    18. Maurice J. G. Bun & Frank Windmeijer, 2010. "The weak instrument problem of the system GMM estimator in dynamic panel data models," Econometrics Journal, Royal Economic Society, vol. 13(1), pages 95-126, February.
    19. Caroline Krafft, 2020. "Why is fertility on the rise in Egypt? The role of women’s employment opportunities," Journal of Population Economics, Springer;European Society for Population Economics, vol. 33(4), pages 1173-1218, October.
    20. Balsmeier, Benjamin & Buchwald, Achim & Peters, Heiko, 2011. "Outside board memberships of CEOs: Expertise or entrenchment?," DICE Discussion Papers 26, Heinrich Heine University Düsseldorf, Düsseldorf Institute for Competition Economics (DICE).

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2011.06753. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: http://arxiv.org/ .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.