IDEAS home Printed from https://ideas.repec.org/a/bla/istatr/v76y2008i2p214-227.html
   My bibliography  Save this article

Parametric and Nonparametric Regression in the Presence of Endogenous Control Variables

Author

Listed:
  • Markus Frölich

Abstract

The aim of this paper is to convey to a wider audience of applied statisticians that nonparametric (matching) estimation methods can be a very convenient tool to overcome problems with endogenous control variables. In empirical research one is often interested in the causal effect of a variable X on some outcome variable Y. With observational data, i.e. in the absence of random assignment, the correlation between X and Y generally does not reflect the treatment effect but is confounded by differences in observed and unobserved characteristics. Econometricians often use two different approaches to overcome this problem of confounding by other characteristics. First, controlling for observed characteristics, often referred to as selection on observables, or instrumental variables regression, usually with additional control variables. Instrumental variables estimation is probably the most important estimator in applied work. In many applications, these control variables are themselves correlated with the error term, making ordinary least squares and two‐stage least squares inconsistent. The usual solution is to search for additional instrumental variables for these endogenous control variables, which is often difficult. We argue that nonparametric methods help to reduce the number of instruments needed. In fact, we need only one instrument whereas with conventional approaches one may need two, three or even more instruments for consistency. Nonparametric matching estimators permit consistent estimation without the need for (additional) instrumental variables and permit arbitrary functional forms and treatment effect heterogeneity. Cet article démontre que l'estimation non paramétrique peut être utile pour résoudre le problème lié aux variables de contrôle endogènes. L'objectif de nombreux travaux empiriques est d'identifier l'effet causal d'une variable X sur une variable dépendante Y. La corrélation entre X et Y qui est observée dans les données ne reflète généralement pas l'effet du traitement car celui‐ci est masqué par les différences dans les caractéristiques (observables ou non) des deux groupes. Les économètres résolvent souvent ce problème d'une des deux façons suivantes: (1) en contrôlant pour la sélection qui est liée aux caractéristiques observées ou (2) en utilisant des instruments, qui ne sont fréquemment valides que conditionnellement à d'autres variables de contrôle. L'estimation basée sur des instruments (IV) est probablement la méthode la plus importante dans la recherche appliquée. Dans beaucoup d'applications ces variables de contrôle sont elles‐mêmes suspectées d'endogénéité ce qui rendrait OLS et 2SLS inconsistants. La solution habituelle est de chercher des instruments supplémentaires pour ces variables de contrôle endogènes, mais cette approche est très difficile en pratique. Nous montrons dans cet article qu'utiliser une méthode instrumentale non paramétrique réduit le nombre des instruments nécessaires. En effet, nous n'avons besoin dans ce cas que d'un seul instrument alors que les méthodes conventionnelles nécessitent deux, trois ou plus encore d'instruments pour garantir leur consistance. Il existe des estimateurs non paramétriques basés sur le matching qui convergent à la vitesse racine de n sans exiger des instruments supplémentaires et qui ne restreignent ni la forme fonctionnelle ni l'hétérogénéité de l'effet du traitement.

Suggested Citation

  • Markus Frölich, 2008. "Parametric and Nonparametric Regression in the Presence of Endogenous Control Variables," International Statistical Review, International Statistical Institute, vol. 76(2), pages 214-227, August.
  • Handle: RePEc:bla:istatr:v:76:y:2008:i:2:p:214-227
    DOI: 10.1111/j.1751-5823.2008.00045.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1751-5823.2008.00045.x
    Download Restriction: no

    References listed on IDEAS

    as
    1. Andrew Chesher, 2003. "Identification in Nonseparable Models," Econometrica, Econometric Society, vol. 71(5), pages 1405-1441, September.
    2. Michael Lechner, 2002. "Some practical issues in the evaluation of heterogeneous labour market programmes by matching methods," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 165(1), pages 59-82, February.
    3. A. Smith, Jeffrey & E. Todd, Petra, 2005. "Does matching overcome LaLonde's critique of nonexperimental estimators?," Journal of Econometrics, Elsevier, vol. 125(1-2), pages 305-353.
    4. Daron Acemoglu & Simon Johnson & James A. Robinson, 2001. "The Colonial Origins of Comparative Development: An Empirical Investigation," American Economic Review, American Economic Association, vol. 91(5), pages 1369-1401, December.
    5. Black, Dan A. & Smith, J.A.Jeffrey A., 2004. "How robust is the evidence on the effects of college quality? Evidence from matching," Journal of Econometrics, Elsevier, vol. 121(1-2), pages 99-124.
    6. James J. Heckman, 2008. "Econometric Causality," International Statistical Review, International Statistical Institute, vol. 76(1), pages 1-27, April.
    7. Victor Chernozhukov & Christian Hansen, 2005. "An IV Model of Quantile Treatment Effects," Econometrica, Econometric Society, vol. 73(1), pages 245-261, January.
    8. Racine, Jeff & Li, Qi, 2004. "Nonparametric estimation of regression functions with both categorical and continuous data," Journal of Econometrics, Elsevier, vol. 119(1), pages 99-130, March.
    9. James Heckman & Hidehiko Ichimura & Jeffrey Smith & Petra Todd, 1998. "Characterizing Selection Bias Using Experimental Data," Econometrica, Econometric Society, vol. 66(5), pages 1017-1098, September.
    10. Chamberlain, Gary, 1982. "The General Equivalence of Granger and Sims Causality," Econometrica, Econometric Society, vol. 50(3), pages 569-581, May.
    11. Lechner, Michael, 2008. "A note on endogenous control variables in causal studies," Statistics & Probability Letters, Elsevier, vol. 78(2), pages 190-195, February.
    12. Das, M., 2005. "Instrumental variables estimators of nonparametric models with discrete endogenous regressors," Journal of Econometrics, Elsevier, vol. 124(2), pages 335-361, February.
    13. Granger, C W J, 1969. "Investigating Causal Relations by Econometric Models and Cross-Spectral Methods," Econometrica, Econometric Society, vol. 37(3), pages 424-438, July.
    14. Andrew Chesher, 2005. "Nonparametric Identification under Discrete Variation," Econometrica, Econometric Society, vol. 73(5), pages 1525-1550, September.
    15. James J. Heckman & Jeffrey A. Smith, 1999. "The Pre-Program Earnings Dip and the Determinants of Participation in a Social Program: Implications for Simple Program Evaluation Strategies," NBER Working Papers 6983, National Bureau of Economic Research, Inc.
    16. Dustmann, Christian & van Soest, Arthur, 1998. "Public and private sector wages of male workers in Germany," European Economic Review, Elsevier, vol. 42(8), pages 1417-1441, September.
    17. Carl-Johan Dalgaard & Henrik Hansen & Finn Tarp, 2004. "On The Empirics of Foreign Aid and Growth," Economic Journal, Royal Economic Society, vol. 114(496), pages 191-216, June.
    18. Guido W. Imbens, 2004. "Nonparametric Estimation of Average Treatment Effects Under Exogeneity: A Review," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 4-29, February.
    19. Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, vol. 71(5), pages 1565-1578, September.
    20. Sims, Christopher A, 1972. "Money, Income, and Causality," American Economic Review, American Economic Association, vol. 62(4), pages 540-552, September.
    21. Hanushek, Eric A, 1986. "The Economics of Schooling: Production and Efficiency in Public Schools," Journal of Economic Literature, American Economic Association, vol. 24(3), pages 1141-1177, September.
    22. Heckman, James J & Smith, Jeffrey A, 1999. "The Pre-programme Earnings Dip and the Determinants of Participation in a Social Programme. Implications for Simple Programme Evaluation Strategies," Economic Journal, Royal Economic Society, vol. 109(457), pages 313-348, 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. Alberto Alesina & Johann Harnoss & Hillel Rapoport, 2016. "Birthplace diversity and economic prosperity," Journal of Economic Growth, Springer, vol. 21(2), pages 101-138, June.
    2. Manthos Delis & Maria Iosifidi & Efthymios G. Tsionas, 2014. "On the Estimation of Marginal Cost," Operations Research, INFORMS, vol. 62(3), pages 543-556, June.
    3. Jiti Gao & Maxwell King, 2011. "A New Test in Parametric Linear Models against Nonparametric Autoregressive Errors," Monash Econometrics and Business Statistics Working Papers 20/11, Monash University, Department of Econometrics and Business Statistics.
    4. Maimaiti, Yasheng & Siebert, W. Stanley, 2010. "Wage Work for Women: The Menstrual Cycle and the Power of Water," IZA Discussion Papers 4776, Institute of Labor Economics (IZA).
    5. Michael Lechner & Markus Froelich, 2010. "Combining Matching and Nonparametric IV Estimation: Theory and an Application to the Evaluation of Active Labour Market Policies," University of St. Gallen Department of Economics working paper series 2010 2010-21, Department of Economics, University of St. Gallen.
    6. Tamini, Lota D., 2011. "A nonparametric analysis of the impact of agri-environmental advisory activities on best management practice adoption: A case study of Québec," Ecological Economics, Elsevier, vol. 70(7), pages 1363-1374, May.
    7. Kornelius Kraft & Julia Lang, 2013. "Profit Sharing and Training," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 75(6), pages 940-961, December.
    8. Joeri Smits & Jeffrey S. Racine, 2013. "Testing Exclusion Restrictions in Nonseparable Triangular Models," Department of Economics Working Papers 2013-02, McMaster University.
    9. Krishnan, Pramila & Krutikova, Sofya, 2013. "Non-cognitive skill formation in poor neighbourhoods of urban India," Labour Economics, Elsevier, vol. 24(C), pages 68-85.
    10. Gounopoulos, Dimitrios & Kallias, Konstantinos & Newton, David & Tzeremes, Nickolaos, 2016. "Political connections and IPO underpricing: An efficiency problem," MPRA Paper 69427, University Library of Munich, Germany.

    More about this item

    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:bla:istatr:v:76:y:2008:i:2:p:214-227. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wiley Content Delivery). General contact details of provider: http://edirc.repec.org/data/isiiinl.html .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.