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A Regularization Approach to Biased Two-Stage Least Squares Estimation

Listed author(s):
  • Nam-Hyun Kim

    ()

    (Department of Economics, University of Konstanz, Germany)

  • Winfried Pohlmeier

    ()

    (Department of Economics, University of Konstanz, Germany; The Rimini Centre for Economic Analysis, Italy)

We propose to apply –norm regularization to address the problem of weak and/or many instruments. We observe that the presence of weak instruments, or weak and many instruments is translated into a nearly singular problem in a control function representation. Hence, we show that mean squares error-optimal -norm regularization with a small sample size reduces the bias and variance of the regularized 2SLS estimators with the presence of weak and/or many instruments. A number of different strategies for choosing a regularization parameter are introduced and compared in a Monte Carlo study.

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File URL: http://www.rcfea.org/RePEc/pdf/wp15-22.pdf
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Paper provided by The Rimini Centre for Economic Analysis in its series Working Paper Series with number 15-22.

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Date of creation: Jun 2015
Handle: RePEc:rim:rimwps:15-22
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  1. Carrasco, Marine, 2012. "A regularization approach to the many instruments problem," Journal of Econometrics, Elsevier, vol. 170(2), pages 383-398.
  2. Hahn, Jinyong & Hausman, Jerry, 2002. "Notes on bias in estimators for simultaneous equation models," Economics Letters, Elsevier, vol. 75(2), pages 237-241, April.
  3. Blomquist, Soren & Dahlberg, Matz, 1999. "Small Sample Properties of LIML and Jackknife IV Estimators: Experiments with Weak Instruments," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(1), pages 69-88, Jan.-Feb..
  4. Arel-Bundock, Vincent, 2013. "A solution to the weak instrument bias in 2SLS estimation: Indirect inference with stochastic approximation," Economics Letters, Elsevier, vol. 120(3), pages 495-498.
  5. Jeffrey M Wooldridge, 2010. "Econometric Analysis of Cross Section and Panel Data," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262232588, July.
  6. Luiz M. Cruz & Marcelo J. Moreira, 2005. "On the Validity of Econometric Techniques with Weak Instruments: Inference on Returns to Education Using Compulsory School Attendance Laws," Journal of Human Resources, University of Wisconsin Press, vol. 40(2).
  7. Stock, James H & Wright, Jonathan H & Yogo, Motohiro, 2002. "A Survey of Weak Instruments and Weak Identification in Generalized Method of Moments," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(4), pages 518-529, October.
  8. Bun, Maurice J.G. & Windmeijer, Frank, 2011. "A comparison of bias approximations for the two-stage least squares (2SLS) estimator," Economics Letters, Elsevier, vol. 113(1), pages 76-79, October.
  9. Hahn, Jinyong & Kuersteiner, Guido, 2002. "Discontinuities of weak instrument limiting distributions," Economics Letters, Elsevier, vol. 75(3), pages 325-331, May.
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