IDEAS home Printed from https://ideas.repec.org/p/iza/izadps/dp2378.html
   My bibliography  Save this paper

Estimating a Class of Triangular Simultaneous Equations Models Without Exclusion Restrictions

Author

Listed:
  • Klein, Roger

    (Rutgers University)

  • Vella, Francis

    (Georgetown University)

Abstract

This paper provides a control function estimator to adjust for endogeneity in the triangular simultaneous equations model where there are no available exclusion restrictions to generate suitable instruments. Our approach is to exploit the dependence of the errors on exogenous variables (e.g. heteroscedasticity) to adjust the conventional control function estimator. The form of the error dependence on the exogenous variables is subject to restrictions, but is not parametrically specified. In addition to providing the estimator and deriving its large-sample properties, we present simulation evidence which indicates the estimator works well.

Suggested Citation

  • Klein, Roger & Vella, Francis, 2006. "Estimating a Class of Triangular Simultaneous Equations Models Without Exclusion Restrictions," IZA Discussion Papers 2378, Institute of Labor Economics (IZA).
    • Handle: RePEc:iza:izadps:dp2378
    as

    Download full text from publisher

    File URL: https://docs.iza.org/dp2378.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Roger Klein & Francis Vella, 2009. "A semiparametric model for binary response and continuous outcomes under index heteroscedasticity," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(5), pages 735-762.
    2. Sentana, Enrique & Fiorentini, Gabriele, 2001. "Identification, estimation and testing of conditionally heteroskedastic factor models," Journal of Econometrics, Elsevier, vol. 102(2), pages 143-164, June.
    3. Dagenais, Marcel G. & Dagenais, Denyse L., 1997. "Higher moment estimators for linear regression models with errors in the variables," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 193-221.
    4. Klein, Roger W & Spady, Richard H, 1993. "An Efficient Semiparametric Estimator for Binary Response Models," Econometrica, Econometric Society, vol. 61(2), pages 387-421, March.
    5. Rummery, Sarah & Vella, Francis & Verbeek, Marno, 1999. "Estimating the returns to education for Australian youth via rank-order instrumental variables," Labour Economics, Elsevier, vol. 6(4), pages 491-507, November.
    6. Whitney K. Newey & Fushing Hsieh & James M. Robins, 2004. "Twicing Kernels and a Small Bias Property of Semiparametric Estimators," Econometrica, Econometric Society, vol. 72(3), pages 947-962, May.
    7. Arthur Lewbel, 1997. "Constructing Instruments for Regressions with Measurement Error when no Additional Data are Available, with an Application to Patents and R&D," Econometrica, Econometric Society, vol. 65(5), pages 1201-1214, September.
    8. Newey, Whitney K. & McFadden, Daniel, 1986. "Large sample estimation and hypothesis testing," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 36, pages 2111-2245, Elsevier.
    9. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-1057, September.
    10. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    11. Klein, R.W., 1991. "Specification Tests for Binery Choice Models Based on Index Quantiles," Papers 71, Bell Communications - Economic Research Group.
    12. Roberto Rigobon, 2003. "Identification Through Heteroskedasticity," The Review of Economics and Statistics, MIT Press, vol. 85(4), pages 777-792, November.
    13. Powell, James L. & Stock, James H. & Stoker, Thomas M., 1986. "Semiparametric estimation of weighted average derivatives," Working papers 1793-86., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    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. Lewbel, Arthur, 2018. "Identification and estimation using heteroscedasticity without instruments: The binary endogenous regressor case," Economics Letters, Elsevier, vol. 165(C), pages 10-12.
    2. Tian, Jilin & Sim, Nicholas & Yan, Wenshou & Li, Yanyun, 2020. "Trade uncertainty, income, and democracy," Economic Modelling, Elsevier, vol. 90(C), pages 21-31.
    3. Armstrong, Christopher & Nicoletti, Allison & Zhou, Frank S., 2022. "Executive stock options and systemic risk," Journal of Financial Economics, Elsevier, vol. 146(1), pages 256-276.
    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. M. Shahe Emran & Forhad Shilpi, 2017. "Land Market Restrictions, Women's Labour Force Participation and Wages in a Rural Economy," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 79(5), pages 747-768, October.
    6. Saniter, Nils, 2012. "Estimating Heterogeneous Returns to Education in Germany via Conditional Heteroskedasticity," IZA Discussion Papers 6813, Institute of Labor Economics (IZA).
    7. Prono, Todd, 2015. "Market proxies as factors in linear asset pricing models: Still living with the roll critique," Journal of Empirical Finance, Elsevier, vol. 31(C), pages 36-53.
    8. Simon Gilchrist & Egon Zakrajšek, 2013. "The Impact of the Federal Reserve's Large‐Scale Asset Purchase Programs on Corporate Credit Risk," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 45(s2), pages 29-57, December.
    9. Fortin, Bernard & Ragued, Safa, 2017. "Does temporary interruption in postsecondary education induce a wage penalty? Evidence from Canada," Economics of Education Review, Elsevier, vol. 58(C), pages 108-122.
    10. Milunovich George & Yang Minxian, 2013. "On Identifying Structural VAR Models via ARCH Effects," Journal of Time Series Econometrics, De Gruyter, vol. 5(2), pages 117-131, May.
    11. Lütkepohl, Helmut & Milunovich, George & Yang, Minxian, 2020. "Inference in partially identified heteroskedastic simultaneous equations models," Journal of Econometrics, Elsevier, vol. 218(2), pages 317-345.
    12. Ben-Moshe, Dan & D’Haultfœuille, Xavier & Lewbel, Arthur, 2017. "Identification of additive and polynomial models of mismeasured regressors without instruments," Journal of Econometrics, Elsevier, vol. 200(2), pages 207-222.
    13. Lídia Farré & Roger Klein & Francis Vella, 2013. "A parametric control function approach to estimating the returns to schooling in the absence of exclusion restrictions: an application to the NLSY," Empirical Economics, Springer, vol. 44(1), pages 111-133, February.
    14. Dungey, Mardi & Milunovich, George & Thorp, Susan & Yang, Minxian, 2015. "Endogenous crisis dating and contagion using smooth transition structural GARCH," Journal of Banking & Finance, Elsevier, vol. 58(C), pages 71-79.
    15. Faqin Lin & Can Huang & Xiaobo He & Chao Zhang, 2013. "Do more highly educated entrepreneurs matter?," Asian-Pacific Economic Literature, The Crawford School, The Australian National University, vol. 27(2), pages 104-116, November.
    16. Faria, João Ricardo & Wang, Le & Wu, Zhongmin, 2012. "Debts on debts," The North American Journal of Economics and Finance, Elsevier, vol. 23(2), pages 203-219.
    17. Alex Klein & Guy Tchuente, 2017. "Spatial differencing for sample selection models," Studies in Economics 1701, School of Economics, University of Kent.
    18. Montes-Rojas, Gabriel & Galvao, Antonio F., 2014. "Bayesian endogeneity bias modeling," Economics Letters, Elsevier, vol. 122(1), pages 36-39.
    19. Aleksandr Grigoryan & Knar Khachatryan, 2018. "Remittances and Emigration Intentions: Evidence from Armenia," CERGE-EI Working Papers wp626, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
    20. Nikolay Arefiev, 2014. "A Theory Of Data-Oriented Identification With A Svar Application," HSE Working papers WP BRP 79/EC/2014, National Research University Higher School of Economics.
    21. D’Haultfœuille, Xavier & Hoderlein, Stefan & Sasaki, Yuya, 2024. "Testing and relaxing the exclusion restriction in the control function approach," Journal of Econometrics, Elsevier, vol. 240(2).
    22. 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.
    23. Lima, Ricardo Carvalho de Andrade & Silveira Neto, Raul da Mota, 2019. "Zoning ordinances and the housing market in developing countries: Evidence from Brazilian municipalities," Journal of Housing Economics, Elsevier, vol. 46(C).
    24. Wayne Yuan Gao & Rui Wang, 2023. "IV Regressions without Exclusion Restrictions," Papers 2304.00626, arXiv.org, revised Jul 2023.
    25. Christophe Bruneel-Zupanc, 2023. "Don't (fully) exclude me, it's not necessary! Identification with semi-IVs," Papers 2303.12667, arXiv.org, revised Jul 2023.

    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. Roger Klein & Francis Vella, 2009. "A semiparametric model for binary response and continuous outcomes under index heteroscedasticity," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(5), pages 735-762.
    2. Joseph J. Sabia, 2007. "Reading, Writing, And Sex: The Effect Of Losing Virginity On Academic Performance," Economic Inquiry, Western Economic Association International, vol. 45(4), pages 647-670, October.
    3. Joseph J. Sabia, 2007. "The Effect of Body Weight on Adolescent Academic Performance," Southern Economic Journal, John Wiley & Sons, vol. 73(4), pages 871-900, April.
    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. Todd Prono, 2008. "GARCH-based identification and estimation of triangular systems," Supervisory Research and Analysis Working Papers QAU08-4, Federal Reserve Bank of Boston.
    6. Joseph J. Sabia, 2007. "Early Adolescent Sex and Diminished School Attachment: Selection or Spillovers?," Southern Economic Journal, John Wiley & Sons, vol. 74(1), pages 239-268, July.
    7. Vincent Hogan & Roberto Rigobon, 2002. "Using Heteroscedasticity to Estimate the Returns to Education," NBER Working Papers 9145, National Bureau of Economic Research, Inc.
    8. 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.
    9. Daniel J. Lewis, 2022. "Robust Inference in Models Identified via Heteroskedasticity," The Review of Economics and Statistics, MIT Press, vol. 104(3), pages 510-524, May.
    10. David Welsch & David Zimmer, 2010. "The Effect of Health and Poverty on Early Childhood Cognitive Development," Atlantic Economic Journal, Springer;International Atlantic Economic Society, vol. 38(1), pages 37-49, March.
    11. Hidehiko Ichimura & Whitney K. Newey, 2022. "The influence function of semiparametric estimators," Quantitative Economics, Econometric Society, vol. 13(1), pages 29-61, January.
    12. Klein, Roger & Vella, Francis, 2006. "Estimating the Return to Endogenous Schooling Decisions for Australian Workers via Conditional Second Moments," IZA Discussion Papers 2407, Institute of Labor Economics (IZA).
    13. Ronald B. Davies & Rodolphe Desbordes, 2015. "Greenfield FDI and skill upgrading: A polarized issue," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 48(1), pages 207-244, February.
    14. Stock, J.H. & Watson, M.W., 2016. "Dynamic Factor Models, Factor-Augmented Vector Autoregressions, and Structural Vector Autoregressions in Macroeconomics," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 415-525, Elsevier.
    15. Klein, Roger & Shen, Chan & Vella, Francis, 2011. "Semiparametric Selection Models with Binary Outcomes," IZA Discussion Papers 6008, Institute of Labor Economics (IZA).
    16. Prono, Todd, 2011. "When A Factor Is Measured with Error: The Role of Conditional Heteroskedasticity in Identifying and Estimating Linear Factor Models," MPRA Paper 33593, University Library of Munich, Germany.
    17. 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.
    18. Daniel J Lewis, 2021. "Identifying Shocks via Time-Varying Volatility [First Order Autoregressive Processes and Strong Mixing]," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 88(6), pages 3086-3124.
    19. Susanne M. Schennach, 2012. "Measurement error in nonlinear models - a review," CeMMAP working papers 41/12, Institute for Fiscal Studies.
    20. Isaiah Andrews & Anna Mikusheva, 2016. "Conditional Inference With a Functional Nuisance Parameter," Econometrica, Econometric Society, vol. 84, pages 1571-1612, July.

    More about this item

    Keywords

    heteroskedasticity; control function; endogeneity;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General

    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:dp2378. 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.