IDEAS home Printed from https://ideas.repec.org/p/iza/izadps/dp14008.html
   My bibliography  Save this paper

Informational Content of Factor Structures in Simultaneous Binary Response Models

Author

Listed:
  • Khan, Shakeeb

    (Boston College)

  • Maurel, Arnaud

    (Duke University)

  • Zhang, Yichong

    (Singapore Management University)

Abstract

We study the informational content of factor structures in discrete triangular systems. Factor structures have been employed in a variety of settings in cross sectional and panel data models, and in this paper we formally quantify their identifying power in a bivariate system often employed in the treatment effects literature. Our main findings are that imposing a factor structure yields point identification of parameters of interest, such as the coefficient associated with the endogenous regressor in the outcome equation, under weaker assumptions than usually required in these models. In particular, we show that a "non-standard" exclusion restriction that requires an explanatory variable in the outcome equation to be excluded from the treatment equation is no longer necessary for identification, even in cases where all of the regressors from the outcome equation are discrete. We also establish identification of the coefficient of the endogenous regressor in models with more general factor structures, in situations where one has access to at least two continuous measurements of the common factor.

Suggested Citation

  • Khan, Shakeeb & Maurel, Arnaud & Zhang, Yichong, 2020. "Informational Content of Factor Structures in Simultaneous Binary Response Models," IZA Discussion Papers 14008, Institute of Labor Economics (IZA).
  • Handle: RePEc:iza:izadps:dp14008
    as

    Download full text from publisher

    File URL: https://docs.iza.org/dp14008.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Gouriéroux, Christian & Monfort, Alain & Renne, Jean-Paul, 2017. "Statistical inference for independent component analysis: Application to structural VAR models," Journal of Econometrics, Elsevier, vol. 196(1), pages 111-126.
    2. Sukjin Han & Sungwon Lee, 2019. "Estimation in a generalization of bivariate probit models with dummy endogenous regressors," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(6), pages 994-1015, September.
    3. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    4. Pedro Carneiro & Karsten T. Hansen & James J. Heckman, 2003. "Estimating Distributions of Treatment Effects with an Application to the Returns to Schooling and Measurement of the Effects of Uncertainty on College," NBER Working Papers 9546, National Bureau of Economic Research, Inc.
    5. Koen Jochmans, 2013. "Pairwise‐comparison estimation with non‐parametric controls," Econometrics Journal, Royal Economic Society, vol. 16(3), pages 340-372, October.
    6. James J. Heckman & Edward Vytlacil, 2005. "Structural Equations, Treatment Effects, and Econometric Policy Evaluation," Econometrica, Econometric Society, vol. 73(3), pages 669-738, May.
    7. Heckman, James J. & Navarro, Salvador, 2007. "Dynamic discrete choice and dynamic treatment effects," Journal of Econometrics, Elsevier, vol. 136(2), pages 341-396, February.
    8. James J. Heckman & John Eric Humphries & Gregory Veramendi, 2018. "Returns to Education: The Causal Effects of Education on Earnings, Health, and Smoking," Journal of Political Economy, University of Chicago Press, vol. 126(S1), pages 197-246.
    9. Carneiro, Pedro & Hansen, Karsten T. & Heckman, James J., 2003. "Estimating Distributions of Treatment Effects with an Application to the Returns to Schooling and Measurement of the Effects of Uncertainty on College Choice," IZA Discussion Papers 767, Institute of Labor Economics (IZA).
    10. Yingyao Hu & Susanne M. Schennach, 2008. "Instrumental Variable Treatment of Nonclassical Measurement Error Models," Econometrica, Econometric Society, vol. 76(1), pages 195-216, January.
    11. Pedro Carneiro & Karsten T. Hansen & James J. Heckman, 2003. "2001 Lawrence R. Klein Lecture Estimating Distributions of Treatment Effects with an Application to the Returns to Schooling and Measurement of the Effects of Uncertainty on College Choice," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 44(2), pages 361-422, May.
    12. Flavio Cunha & James J. Heckman & Susanne M. Schennach, 2010. "Estimating the Technology of Cognitive and Noncognitive Skill Formation," Econometrica, Econometric Society, vol. 78(3), pages 883-931, May.
    13. Shakeeb Khan & Denis Nekipelov, 2018. "Information structure and statistical information in discrete response models," Quantitative Economics, Econometric Society, vol. 9(2), pages 995-1017, July.
    14. Andrew Chesher, 2005. "Nonparametric Identification under Discrete Variation," Econometrica, Econometric Society, vol. 73(5), pages 1525-1550, September.
    15. Newey, Whitney K., 1994. "Kernel Estimation of Partial Means and a General Variance Estimator," Econometric Theory, Cambridge University Press, vol. 10(2), pages 1-21, June.
    16. Jason Abrevaya & Jerry A. Hausman & Shakeeb Khan, 2010. "Testing for Causal Effects in a Generalized Regression Model With Endogenous Regressors," Econometrica, Econometric Society, vol. 78(6), pages 2043-2061, November.
    17. Stéphane Bonhomme & Jean-Marc Robin, 2010. "Generalized Non-Parametric Deconvolution with an Application to Earnings Dynamics," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 77(2), pages 491-533.
    18. Bierens, Herman J. & Hartog, Joop, 1988. "Non-linear regression with discrete explanatory variables, with an application to the earnings function," Journal of Econometrics, Elsevier, vol. 38(3), pages 269-299, July.
    19. Klein, Roger & Shen, Chan & Vella, Francis, 2015. "Estimation of marginal effects in semiparametric selection models with binary outcomes," Journal of Econometrics, Elsevier, vol. 185(1), pages 82-94.
    20. Chiburis, Richard C., 2010. "Semiparametric bounds on treatment effects," Journal of Econometrics, Elsevier, vol. 159(2), pages 267-275, December.
    21. Carneiro, Pedro & Lee, Sokbae, 2009. "Estimating distributions of potential outcomes using local instrumental variables with an application to changes in college enrollment and wage inequality," Journal of Econometrics, Elsevier, vol. 149(2), pages 191-208, April.
    22. Elie Tamer, 2003. "Incomplete Simultaneous Discrete Response Model with Multiple Equilibria," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 70(1), pages 147-165.
    23. Chen, Songnian & Khan, Shakeeb & Tang, Xun, 2016. "Informational content of special regressors in heteroskedastic binary response models," Journal of Econometrics, Elsevier, vol. 193(1), pages 162-182.
    24. Jared Ashworth & V. Joseph Hotz & Arnaud Maurel & Tyler Ransom, 2021. "Changes across Cohorts in Wage Returns to Schooling and Early Work Experiences," Journal of Labor Economics, University of Chicago Press, vol. 39(4), pages 931-964.
    25. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-1430, November.
    26. Abowd, John M & Card, David, 1989. "On the Covariance Structure of Earnings and Hours Changes," Econometrica, Econometric Society, vol. 57(2), pages 411-445, March.
    27. Sherman, Robert P, 1993. "The Limiting Distribution of the Maximum Rank Correlation Estimator," Econometrica, Econometric Society, vol. 61(1), pages 123-137, January.
    28. 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.
    29. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    30. S. M. Schennach & Yingyao Hu, 2013. "Nonparametric Identification and Semiparametric Estimation of Classical Measurement Error Models Without Side Information," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(501), pages 177-186, March.
    31. Azeem M. Shaikh & Edward J. Vytlacil, 2011. "Partial Identification in Triangular Systems of Equations With Binary Dependent Variables," Econometrica, Econometric Society, vol. 79(3), pages 949-955, May.
    32. Shakeeb Khan & Elie Tamer, 2010. "Irregular Identification, Support Conditions, and Inverse Weight Estimation," Econometrica, Econometric Society, vol. 78(6), pages 2021-2042, November.
    33. Lewbel, Arthur, 2000. "Semiparametric qualitative response model estimation with unknown heteroscedasticity or instrumental variables," Journal of Econometrics, Elsevier, vol. 97(1), pages 145-177, July.
    34. repec:hal:spmain:info:hdl:2441/dambferfb7dfprc9m01h6f4h2 is not listed on IDEAS
    35. Alessio Moneta & Doris Entner & Patrik O. Hoyer & Alex Coad, 2013. "Causal Inference by Independent Component Analysis: Theory and Applications," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 75(5), pages 705-730, October.
    36. Khan, Shakeeb, 2001. "Two-stage rank estimation of quantile index models," Journal of Econometrics, Elsevier, vol. 100(2), pages 319-355, February.
    37. Han, Aaron K., 1987. "Non-parametric analysis of a generalized regression model : The maximum rank correlation estimator," Journal of Econometrics, Elsevier, vol. 35(2-3), pages 303-316, July.
    38. Edward Vytlacil & Nese Yildiz, 2007. "Dummy Endogenous Variables in Weakly Separable Models," Econometrica, Econometric Society, vol. 75(3), pages 757-779, May.
    39. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-531, May.
    40. Henderson, Daniel J. & Li, Qi & Parmeter, Christopher F. & Yao, Shuang, 2015. "Gradient-based smoothing parameter selection for nonparametric regression estimation," Journal of Econometrics, Elsevier, vol. 184(2), pages 233-241.
    41. repec:hal:wpspec:info:hdl:2441/dambferfb7dfprc9m01h6f4h2 is not listed on IDEAS
    42. Donald, S. G. & Newey, W. K., 1994. "Series Estimation of Semilinear Models," Journal of Multivariate Analysis, Elsevier, vol. 50(1), pages 30-40, July.
    43. Quang Vuong & Haiqing Xu, 2017. "Counterfactual mapping and individual treatment effects in nonseparable models with binary endogeneity," Quantitative Economics, Econometric Society, vol. 8(2), pages 589-610, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Gu, Jiaying & Russell, Thomas M., 2023. "Partial identification in nonseparable binary response models with endogenous regressors," Journal of Econometrics, Elsevier, vol. 235(2), pages 528-562.
    2. Benjamin Williams, 2018. "Identification of the Linear Factor Model," Working Papers 2018-002, The George Washington University, Department of Economics, H. O. Stekler Research Program on Forecasting.
    3. Songnian Chen & Shakeeb Khan & Xun Tang, 2020. "Dummy Endogenous Variables in Weakly Separable Multiple Index Models without Monotonicity," Boston College Working Papers in Economics 996, Boston College Department of Economics.
    4. Songnian Chen & Shakeeb Khan & Xun Tang, 2020. "Identification and Estimation of Weakly Separable Models Without Monotonicity," Papers 2003.04337, arXiv.org, revised Apr 2020.

    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. Aradillas-Lopez, Andres, 2010. "Semiparametric estimation of a simultaneous game with incomplete information," Journal of Econometrics, Elsevier, vol. 157(2), pages 409-431, August.
    2. 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.
    3. Heckman, James J. & Humphries, John Eric & Veramendi, Gregory, 2016. "Dynamic treatment effects," Journal of Econometrics, Elsevier, vol. 191(2), pages 276-292.
    4. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
    5. Yingying Dong & Arthur Lewbel, 2015. "A Simple Estimator for Binary Choice Models with Endogenous Regressors," Econometric Reviews, Taylor & Francis Journals, vol. 34(1-2), pages 82-105, February.
    6. Lewbel, Arthur, 2007. "Endogenous selection or treatment model estimation," Journal of Econometrics, Elsevier, vol. 141(2), pages 777-806, December.
    7. Balat, Jorge F. & Han, Sukjin, 2023. "Multiple treatments with strategic substitutes," Journal of Econometrics, Elsevier, vol. 234(2), pages 732-757.
    8. Lina Zhang & David T. Frazier & D. S. Poskitt & Xueyan Zhao, 2020. "Decomposing Identification Gains and Evaluating Instrument Identification Power for Partially Identified Average Treatment Effects," Papers 2009.02642, arXiv.org, revised Sep 2022.
    9. James J. Heckman, 2008. "The Principles Underlying Evaluation Estimators with an Application to Matching," Annals of Economics and Statistics, GENES, issue 91-92, pages 9-73.
    10. Jane Cooley Fruehwirth & Salvador Navarro & Yuya Takahashi, 2016. "How the Timing of Grade Retention Affects Outcomes: Identification and Estimation of Time-Varying Treatment Effects," Journal of Labor Economics, University of Chicago Press, vol. 34(4), pages 979-1021.
    11. Philipp Eisenhauer & James J. Heckman & Edward Vytlacil, 2015. "The Generalized Roy Model and the Cost-Benefit Analysis of Social Programs," Journal of Political Economy, University of Chicago Press, vol. 123(2), pages 413-443.
    12. Jorge Rodríguez & Fernando Saltiel & Sergio Urzúa, 2022. "Dynamic treatment effects of job training," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(2), pages 242-269, March.
    13. Tatiana Komarova & William Matcham, 2022. "Multivariate ordered discrete response models," Papers 2205.05779, arXiv.org, revised Mar 2023.
    14. Magnac, Thierry & Pistolesi, Nicolas & Roux, Sébastien, 2013. "Post schooling human capital investments and the life cycle variance of earnings," IDEI Working Papers 765, Institut d'Économie Industrielle (IDEI), Toulouse.
    15. James J. Heckman, 2008. "Econometric Causality," International Statistical Review, International Statistical Institute, vol. 76(1), pages 1-27, April.
    16. Heckman, James J. & Navarro, Salvador, 2007. "Dynamic discrete choice and dynamic treatment effects," Journal of Econometrics, Elsevier, vol. 136(2), pages 341-396, February.
    17. Mohitosh Kejriwal & Xiaoxiao Li & Evan Totty, 2020. "Multidimensional skills and the returns to schooling: Evidence from an interactive fixed‐effects approach and a linked survey‐administrative data set," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(5), pages 548-566, August.
    18. Carneiro, Pedro & Lee, Sokbae, 2009. "Estimating distributions of potential outcomes using local instrumental variables with an application to changes in college enrollment and wage inequality," Journal of Econometrics, Elsevier, vol. 149(2), pages 191-208, April.
    19. Mohitosh Kejriwal & Xiaoxiao Li & Linh Nguyen & Evan Totty, 2024. "The efficacy of ability proxies for estimating the returns to schooling: A factor model‐based evaluation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 39(1), pages 3-21, January.
    20. Jaap Abbring & James Heckman, 2008. "Dynamic policy analysis," CeMMAP working papers CWP05/08, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

    More about this item

    Keywords

    discrete choice; factor structures; causal effects;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions

    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:iza:izadps:dp14008. See general information about how to correct material in RePEc.

    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: Holger Hinte (email available below). General contact details of provider: https://edirc.repec.org/data/izaaade.html .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.