IDEAS home Printed from https://ideas.repec.org/p/bri/uobdis/17-683.html
   My bibliography  Save this paper

Two-Stage Least Squares as Minimum Distance

Author

Listed:
  • Frank Windmeijer

Abstract

The Two-Stage Least Squares instrumental variables (IV) estimator for the parameters in linear models with a single endogenous variable is shown to be identical to an optimal Minimum Distance (MD) estimator based on the individual instrument specific IV estimators. The 2SLS estimator is a linear combination of the individual estimators, with the weights determined by their variances and covariances under conditional homoskedasticity. It is further shown that the Sargan test statistic for overidentifying restrictions is the same as the MD criterion test statistic. This provides an intuitive interpretation of the Sargan test. The equivalence results also apply to the efficient two-step GMM and robust optimal MD estimators and criterion functions, allowing for general forms of heteroskedasticity. It is further shown how these results extend to the linear overidentified IV model with multiple endogenous variables.

Suggested Citation

  • Frank Windmeijer, 2017. "Two-Stage Least Squares as Minimum Distance," Bristol Economics Discussion Papers 17/683, School of Economics, University of Bristol, UK, revised 13 Jun 2018.
    • Handle: RePEc:bri:uobdis:17/683
    as

    Download full text from publisher

    File URL: http://www.bristol.ac.uk/efm/media/workingpapers/working_papers/pdffiles/dp17683.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Frank Windmeijer, 2018. "Testing Over- and Underidentification in Linear Models, with Applications to Dynamic Panel Data and Asset-Pricing Models," Bristol Economics Discussion Papers 18/696, School of Economics, University of Bristol, UK.
    2. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    3. Goldberger, Arthur S & Olkin, Ingram, 1971. "A Minimum-Distance Interpretation of Limited-Information Estimation," Econometrica, Econometric Society, vol. 39(3), pages 635-639, May.
    4. Chen, Xiaohong & Jacho-Chávez, David T. & Linton, Oliver, 2016. "Averaging Of An Increasing Number Of Moment Condition Estimators," Econometric Theory, Cambridge University Press, vol. 32(1), pages 30-70, February.
    5. Parente, Paulo M.D.C. & Santos Silva, J.M.C., 2012. "A cautionary note on tests of overidentifying restrictions," Economics Letters, Elsevier, vol. 115(2), pages 314-317.
    6. Joshua D. Angrist & Jörn-Steffen Pischke, 2009. "Mostly Harmless Econometrics: An Empiricist's Companion," Economics Books, Princeton University Press, edition 1, number 8769.
    7. Joshua D. Angrist, 1988. "Grouped Data Estimation and Testing in Simple Labor Supply Models," Working Papers 614, Princeton University, Department of Economics, Industrial Relations Section..
    8. Angrist, Joshua D., 1991. "Grouped-data estimation and testing in simple labor-supply models," Journal of Econometrics, Elsevier, vol. 47(2-3), pages 243-266, February.
    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. Kiviet, Jan F., 2020. "Testing the impossible: Identifying exclusion restrictions," Journal of Econometrics, Elsevier, vol. 218(2), pages 294-316.
    2. Windmeijer, Frank, 2025. "The robust F-statistic as a test for weak instruments," Journal of Econometrics, Elsevier, vol. 247(C).
    3. Nicolas Apfel & Frank Windmeijer, 2022. "The Falsification Adaptive Set in Linear Models with Instrumental Variables that Violate the Exclusion or Conditional Exogeneity Restriction," Papers 2212.04814, arXiv.org, revised Apr 2024.
    4. Frank Windmeijer & Xiaoran Liang & Fernando P. Hartwig & Jack Bowden, 2021. "The confidence interval method for selecting valid instrumental variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(4), pages 752-776, September.
    5. David T. Frazier & Eric Renault & Lina Zhang & Xueyan Zhao, 2020. "Weak Identification in Discrete Choice Models," Papers 2011.06753, arXiv.org, revised Jan 2021.
    6. Frank Windmeijer, 2019. "Weak Instruments, First-Stage Heteroskedasticity and the Robust F-test," Bristol Economics Discussion Papers 19/708, School of Economics, University of Bristol, UK.
    7. Domguia, Edmond Noubissi & Ngounou, Borice Augustin & Pondie, Thierry Messie & Bitoto, Fabrice Ewolo, 2024. "Environmental tax and energy poverty: An economic approach for an environmental and social solution," Energy, Elsevier, vol. 308(C).
    8. Gibbons, Stephen & Heblich, Stephan & Pinchbeck, Edward W., 2024. "The spatial impacts of a massive rail disinvestment program: the Beeching axe," LSE Research Online Documents on Economics 124531, London School of Economics and Political Science, LSE Library.
    9. Gibbons, Stephen & Heblich, Stephan & Pinchbeck, Edward W., 2024. "The spatial impacts of a massive rail disinvestment program: The Beeching Axe," Journal of Urban Economics, Elsevier, vol. 143(C).
    10. Frank Windmeijer, 2022. "Weak Instruments, First-Stage Heteroskedasticity, the Robust F-Test and a GMM Estimator with the Weight Matrix Based on First-Stage Residuals," Papers 2208.01967, arXiv.org.

    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. Paul A. Bekker & Jan van der Ploeg, 2000. "Instrumental Variable Estimation Based on Grouped Data," Econometric Society World Congress 2000 Contributed Papers 1862, Econometric Society.
    2. Cornelissen, Thomas & Dustmann, Christian & Raute, Anna & Schönberg, Uta, 2016. "From LATE to MTE: Alternative methods for the evaluation of policy interventions," Labour Economics, Elsevier, vol. 41(C), pages 47-60.
    3. Jang-Ok Cho & Merrigan, Philip & Phaneuf, Louis, 1998. "Weekly employee hours, weeks worked and intertemporal substitution," Journal of Monetary Economics, Elsevier, vol. 41(1), pages 185-199, February.
    4. Peter Siminski & Simon Ville & Alexander Paull, 2016. "Does the military turn men into criminals? New evidence from Australia’s conscription lotteries," Journal of Population Economics, Springer;European Society for Population Economics, vol. 29(1), pages 197-218, January.
    5. Inoue, Atsushi, 2008. "Efficient estimation and inference in linear pseudo-panel data models," Journal of Econometrics, Elsevier, vol. 142(1), pages 449-466, January.
    6. Goodman-Bacon, Andrew, 2021. "Difference-in-differences with variation in treatment timing," Journal of Econometrics, Elsevier, vol. 225(2), pages 254-277.
    7. Atila Abdulkadiroğlu & Joshua D. Angrist & Susan M. Dynarski & Thomas J. Kane & Parag A. Pathak, 2011. "Accountability and Flexibility in Public Schools: Evidence from Boston's Charters And Pilots," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 126(2), pages 699-748.
    8. Bruno T. Rocha & Patrícia C. Melo & Nuno Afonso & João de Abreu e Silva, 2021. "Motorways, urban growth, and suburbanisation:evidence from three decades of motorway construction in Portugal," Working Papers REM 2021/0174, ISEG - Lisbon School of Economics and Management, REM, Universidade de Lisboa.
    9. de Laiglesia, Juan R., 2005. "Investment and credit effects of land titling and registration:," Proceedings of the German Development Economics Conference, Kiel 2005 10, Verein für Socialpolitik, Research Committee Development Economics.
    10. Frank Windmeijer, 2022. "Weak Instruments, First-Stage Heteroskedasticity, the Robust F-Test and a GMM Estimator with the Weight Matrix Based on First-Stage Residuals," Papers 2208.01967, arXiv.org.
    11. Frank Windmeijer, 2019. "Weak Instruments, First-Stage Heteroskedasticity and the Robust F-test," Bristol Economics Discussion Papers 19/708, School of Economics, University of Bristol, UK.
    12. Valeria Bejarano-Salcedo & William Iván Moreno-Jimenez & Juan Manuel Julio-Román, 2020. "La Magnitud y Duración del Efecto de la Intervención por Subastas sobre el Mercado Cambiario: El caso Colombiano," Borradores de Economia 1142, Banco de la Republica de Colombia.
    13. Cao, Lihong & Du, Yan & Hansen, Jens Ørding, 2017. "Foreign institutional investors and dividend policy: Evidence from China," International Business Review, Elsevier, vol. 26(5), pages 816-827.
    14. Juan M. Contreras & Sven H. Sinclair, 2008. "The Labor Supply Response in Macroeconomic Models: Working Paper 2008-07," Working Papers 20141, Congressional Budget Office.
    15. Verbeek, Marno & Vella, Francis, 2005. "Estimating dynamic models from repeated cross-sections," Journal of Econometrics, Elsevier, vol. 127(1), pages 83-102, July.
    16. Manuela Jr., Wilfred S. & Friesen, Mark, 2025. "Determinants of car parking revenues: An econometric analysis of large European airports," Journal of Air Transport Management, Elsevier, vol. 122(C).
    17. Felici, Marco & Kenny, Geoff & Friz, Roberta, 2023. "Consumer savings behaviour at low and negative interest rates," European Economic Review, Elsevier, vol. 157(C).
    18. Raphael, Steven & Rice, Lorien, 2002. "Car ownership, employment, and earnings," Journal of Urban Economics, Elsevier, vol. 52(1), pages 109-130, July.
    19. Brockhaus, Jan & Kalkuhl, Matthias & Kozicka, Marta, 2016. "What Drives India’s Rice Stocks? Empirical Evidence," 2016 Annual Meeting, July 31-August 2, Boston, Massachusetts 235659, Agricultural and Applied Economics Association.
    20. James P. Vere, 2004. "Dragon Children: Identifying the Causal Effect of the First Child on Female Labor Supply with the Chinese Lunar Calendar," Labor and Demography 0407003, University Library of Munich, Germany, revised 18 Oct 2004.

    More about this item

    Keywords

    Instrumental Variables; Two-Stage Least Squares; Minimum Distance; Overidentification Test.;
    All these keywords.

    JEL classification:

    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: 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:bri:uobdis:17/683. 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: Vicky Jackson (email available below). General contact details of provider: https://edirc.repec.org/data/sebriuk.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.