IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v143y2018icp81-85.html

Convexity of probit weights

Author

Listed:
  • Schumann, Martin
  • Tripathi, Gautam

Abstract

We demonstrate that the probit weight function is U-shaped on R, i.e., it is strictly decreasing on (−∞,0), strictly increasing on [0,∞), and strictly convex on R. Knowledge of the shape of the probit weight function can be useful in several contexts. For instance, it can resolve any confusion that may arise from a result in the classic paper of Sampford (1953). The shape of the probit weight function can also be used to justify why the computation of the probit maximum likelihood estimator (MLE) –in fact, in general, the computation of all two-step estimators whenever the first step involves estimating a probit model –may fail in the presence of outliers or unbounded parameter spaces.

Suggested Citation

  • Schumann, Martin & Tripathi, Gautam, 2018. "Convexity of probit weights," Statistics & Probability Letters, Elsevier, vol. 143(C), pages 81-85.
    • Handle: RePEc:eee:stapro:v:143:y:2018:i:c:p:81-85
    DOI: 10.1016/j.spl.2018.07.022
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715218302669
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2018.07.022?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    2. Mikhail Zhelonkin & Marc G. Genton & Elvezio Ronchetti, 2016. "Robust inference in sample selection models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(4), pages 805-827, September.
    3. 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.
    4. Zhelonkin, Mikhail & Genton, Marc G. & Ronchetti, Elvezio, 2012. "On the robustness of two-stage estimators," Statistics & Probability Letters, Elsevier, vol. 82(4), pages 726-732.
    5. Joon Y. Park & Peter C. B. Phillips, 2000. "Nonstationary Binary Choice," Econometrica, Econometric Society, vol. 68(5), pages 1249-1280, 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. Nathan Canen & Kristopher Ramsay, 2024. "Quantifying theory in politics: Identification, interpretation, and the role of structural methods," Journal of Theoretical Politics, , vol. 36(4), pages 301-327, October.
    2. Orazio Attanasio & Peter Levell & Hamish Low & Virginia Sánchez-Marcos, 2015. "Aggregating Elasticities: Intensive and Extensive Margins of Female Labour Supply," Cambridge Working Papers in Economics 1519, Faculty of Economics, University of Cambridge.
    3. Boswijk, H. Peter & Franses, Philip Hans & van Dijk, Dick, 2010. "Cointegration in a historical perspective," Journal of Econometrics, Elsevier, vol. 158(1), pages 156-159, September.
    4. 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.
    5. Heckman, James J. & Lochner, Lance J. & Todd, Petra E., 2006. "Earnings Functions, Rates of Return and Treatment Effects: The Mincer Equation and Beyond," Handbook of the Economics of Education, in: Erik Hanushek & F. Welch (ed.), Handbook of the Economics of Education, edition 1, volume 1, chapter 7, pages 307-458, Elsevier.
    6. Collet, Roger & de Lapparent, Matthieu & Hivert, Laurent, 2015. "Are French households car-use addicts? A microeconomic perspective," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 54(C), pages 86-94.
    7. Fay, Scott & Feng, Cong & Patel, Pankaj C., 2022. "Staying small, staying strong? Retail store underexpansion and retailer profitability," Journal of Business Research, Elsevier, vol. 144(C), pages 663-678.
    8. Goic, Marcel & Rojas, Andrea & Saavedra, Ignacio, 2021. "The Effectiveness of Triggered Email Marketing in Addressing Browse Abandonments," Journal of Interactive Marketing, Elsevier, vol. 55(C), pages 118-145.
    9. Ebrahim Ahmed Ali Assakaf & Ameen Qasem & Sumaia Ayesh Qaderi & Mohammad Zaid Alaskar, 2025. "Corporate Social Responsibility and Intellectual Capital: The Moderating Role of Institutional Ownership in an Emerging Market," Sustainability, MDPI, vol. 17(11), pages 1-26, May.
    10. Woodcock Simon D, 2010. "Heterogeneity and Learning in Labor Markets," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 10(1), pages 1-69, September.
    11. Papanikolaou, Nikolaos I. & Wolff, Christian C.P., 2014. "The role of on- and off-balance-sheet leverage of banks in the late 2000s crisis," Journal of Financial Stability, Elsevier, vol. 14(C), pages 3-22.
    12. Joachim Inkmann, 2010. "Estimating Firm Size Elasticities of Product and Process R&D," Economica, London School of Economics and Political Science, vol. 77(306), pages 384-402, April.
    13. Hunt, Richard A. & Song, Yue & Townsend, David M. & Stallkamp, Maximilian, 2021. "Internationalization of entrepreneurial firms: Leveraging real options reasoning through affordable loss logics," Journal of Business Research, Elsevier, vol. 133(C), pages 194-207.
    14. Siddique, Md Abubakar & Akhtaruzzaman, Md & Rashid, Afzalur & Hammami, Helmi, 2021. "Carbon disclosure, carbon performance and financial performance: International evidence," International Review of Financial Analysis, Elsevier, vol. 75(C).
    15. Wang, Kun Tracy & Kartika, Fiki & Wang, Wanbin Walter & Luo, Guqiang, 2021. "Corporate social responsibility, investor protection, and the cost of equity: Evidence from East Asia," Emerging Markets Review, Elsevier, vol. 47(C).
    16. Das, Jayoti & De Loach, Stephen B., 2011. "Mirror, mirror on the wall: The effect of time spent grooming on earnings," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 40(1), pages 26-34, February.
    17. Diestre, Luis, 2018. "Safety crises and R&D outsourcing alliances: Which governance mode minimizes negative spillovers?," Research Policy, Elsevier, vol. 47(10), pages 1904-1917.
    18. Jones A.M & Rice N, 2009. "Econometric Evaluation of Health Policies," Health, Econometrics and Data Group (HEDG) Working Papers 09/09, HEDG, c/o Department of Economics, University of York.
    19. Arthur Lewbel, 2007. "Estimation of Average Treatment Effects with Misclassification," Econometrica, Econometric Society, vol. 75(2), pages 537-551, March.
    20. Takahiro Hoshino & Ryosuke Igari, 2017. "Quasi-Bayesian Inference for Latent Variable Models with External Information: Application to generalized linear mixed models for biased data," Keio-IES Discussion Paper Series 2017-014, Institute for Economics Studies, Keio University.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    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:eee:stapro:v:143:y:2018:i:c:p:81-85. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.