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Parametric and Nonparametric Regression in the Presence of Endogenous Control Variables

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  • 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. Copyright (c) 2008 The Author. Journal compilation (c) 2008 International Statistical Institute.

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
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    References listed on IDEAS

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    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 for the Study of Labor (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.

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