IDEAS home Printed from https://ideas.repec.org/p/boc/bocoec/587.html

Using Heteroskedasticity to Identify and Estimate Mismeasured and Endogenous Regressor Models

Author

Listed:
  • Arthur Lewbel

    (Boston College)

Abstract

This paper proposes a new method of obtaining identification in mismeasured regressor models, triangular systems, and simultaneous equation systems. The method may be used in applications where other sources of identification such as instrumental variables or repeated measurements are not available. Associated estimators take the form of two stage least squares or generalized method of moments. Identification comes from a heteroskedastic covariance restriction that is shown to be a feature of many models of endogeneity or mismeasurement. Identification is also obtained for semiparametric partly linear models, and associated estimators are provided. Set identification bounds are derived for cases where point identifying assumptions fail to hold. An empirical application estimating Engel curves is provided.

Suggested Citation

  • Arthur Lewbel, 2003. "Using Heteroskedasticity to Identify and Estimate Mismeasured and Endogenous Regressor Models," Boston College Working Papers in Economics 587, Boston College Department of Economics, revised 15 Dec 2010.
    • Handle: RePEc:boc:bocoec:587
    Note: Previously circulated as "Identification of Heteroskedastic Endogenous or Mismeasured Regressor Models."
    as

    Download full text from publisher

    File URL: http://fmwww.bc.edu/EC-P/wp587.pdf
    File Function: main text
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Cragg, John G. & Donald, Stephen G., 1997. "Inferring the rank of a matrix," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 223-250.
    2. Heckman, James J, 1974. "Shadow Prices, Market Wages, and Labor Supply," Econometrica, Econometric Society, vol. 42(4), pages 679-694, July.
    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. Klein, Roger & Vella, Francis, 2010. "Estimating a class of triangular simultaneous equations models without exclusion restrictions," Journal of Econometrics, Elsevier, vol. 154(2), pages 154-164, February.
    5. 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.
    6. Roberto Rigobon, 2003. "Identification Through Heteroskedasticity," The Review of Economics and Statistics, MIT Press, vol. 85(4), pages 777-792, November.
    7. Blanchard, Olivier Jean & Quah, Danny, 1989. "The Dynamic Effects of Aggregate Demand and Supply Disturbances," American Economic Review, American Economic Association, vol. 79(4), pages 655-673, September.
    8. Chamberlain, Gary, 1987. "Asymptotic efficiency in estimation with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 34(3), pages 305-334, March.
    9. Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, vol. 71(5), pages 1565-1578, September.
    10. 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.
    11. Otsu, Taisuke, 2011. "Empirical Likelihood Estimation Of Conditional Moment Restriction Models With Unknown Functions," Econometric Theory, Cambridge University Press, vol. 27(1), pages 8-46, February.
    12. James Heckman, 2013. "Sample selection bias as a specification error," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 31(3), pages 129-137.
    13. 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.
    14. 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.
    15. Rigobon, Roberto, 2002. "The curse of non-investment grade countries," Journal of Development Economics, Elsevier, vol. 69(2), pages 423-449, December.
    16. Breusch, T S & Pagan, A R, 1979. "A Simple Test for Heteroscedasticity and Random Coefficient Variation," Econometrica, Econometric Society, vol. 47(5), pages 1287-1294, September.
    17. Todd Prono, 2008. "GARCH-based identification and estimation of triangular systems," Supervisory Research and Analysis Working Papers QAU08-4, Federal Reserve Bank of Boston.
    18. Erickson, Timothy & Whited, Toni M., 2002. "Two-Step Gmm Estimation Of The Errors-In-Variables Model Using High-Order Moments," Econometric Theory, Cambridge University Press, vol. 18(3), pages 776-799, June.
    19. David Card, 1993. "Using Geographic Variation in College Proximity to Estimate the Return to Schooling," Working Papers 696, Princeton University, Department of Economics, Industrial Relations Section..
    20. Hausman, Jerry A., 1983. "Specification and estimation of simultaneous equation models," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 1, chapter 7, pages 391-448, Elsevier.
    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. 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.
    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. Schennach, Susanne M., 2020. "Mismeasured and unobserved variables," Handbook of Econometrics, in: Steven N. Durlauf & Lars Peter Hansen & James J. Heckman & Rosa L. Matzkin (ed.), Handbook of Econometrics, edition 1, volume 7, chapter 0, pages 487-565, Elsevier.
    4. Hu, Yingyao & Schennach, Susanne & Shiu, Ji-Liang, 2022. "Identification of nonparametric monotonic regression models with continuous nonclassical measurement errors," Journal of Econometrics, Elsevier, vol. 226(2), pages 269-294.
    5. Christopher F Baum & Arthur Lewbel, 2019. "Advice on using heteroskedasticity-based identification," Stata Journal, StataCorp LLC, vol. 19(4), pages 757-767, December.
    6. Arthur Lewbel, 2007. "Estimation of Average Treatment Effects with Misclassification," Econometrica, Econometric Society, vol. 75(2), pages 537-551, March.
    7. Todd Prono, 2008. "GARCH-based identification and estimation of triangular systems," Supervisory Research and Analysis Working Papers QAU08-4, Federal Reserve Bank of Boston.
    8. Lewbel, Arthur, 2018. "Identification and estimation using heteroscedasticity without instruments: The binary endogenous regressor case," Economics Letters, Elsevier, vol. 165(C), pages 10-12.
    9. Jin Li & Ye Luo & Zigan Wang & Xiaowei Zhang, 2021. "Asymptotic Theory for IV-Based Reinforcement Learning with Potential Endogeneity," Papers 2103.04021, arXiv.org, revised Dec 2024.
    10. Bonhomme, Stphane & Robin, Jean-Marc, 2009. "Consistent noisy independent component analysis," Journal of Econometrics, Elsevier, vol. 149(1), pages 12-25, April.
    11. Klein, Roger & Vella, Francis, 2010. "Estimating a class of triangular simultaneous equations models without exclusion restrictions," Journal of Econometrics, Elsevier, vol. 154(2), pages 154-164, February.
    12. Breunig, Christoph & Mammen, Enno & Simoni, Anna, 2018. "Nonparametric estimation in case of endogenous selection," Journal of Econometrics, Elsevier, vol. 202(2), pages 268-285.
    13. Guilhem Bascle, 2008. "Controlling for endogeneity with instrumental variables in strategic management research," Post-Print hal-00576795, HAL.
    14. Hall, George & Rust, John, 2021. "Estimation of endogenously sampled time series: The case of commodity price speculation in the steel market," Journal of Econometrics, Elsevier, vol. 222(1), pages 219-243.
    15. Xiaohong Chen & Yingyao Hu & Arthur Lewbel, 2007. "Nonparametric Identification and Estimation of Nonclassical Errors-in-Variables Models Without Additional Information," Boston College Working Papers in Economics 676, Boston College Department of Economics.
    16. Yu, Ping & Phillips, Peter C.B., 2018. "Threshold regression with endogeneity," Journal of Econometrics, Elsevier, vol. 203(1), pages 50-68.
    17. 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.
    18. Ai, Chunrong & Chen, Xiaohong, 2012. "The semiparametric efficiency bound for models of sequential moment restrictions containing unknown functions," Journal of Econometrics, Elsevier, vol. 170(2), pages 442-457.
    19. Gayle, George-Levi & Viauroux, Christelle, 2007. "Root-N consistent semiparametric estimators of a dynamic panel-sample-selection model," Journal of Econometrics, Elsevier, vol. 141(1), pages 179-212, November.
    20. 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.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;

    JEL classification:

    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • D12 - Microeconomics - - Household Behavior - - - Consumer Economics: Empirical Analysis

    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:boc:bocoec:587. 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: Christopher F Baum (email available below). General contact details of provider: https://edirc.repec.org/data/debocus.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.