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From |
Austin Nichols <austinnichols@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: RE: Robust instrumental variable regression |

Date |
Mon, 17 Jan 2011 17:59:45 -0500 |

Jorge Eduardo Pérez Pérez <perez.jorge@ur.edu.co>: The reference cited elliptically in http://www.stata.com/statalist/archive/2003-09/msg00585.html http://www.stata.com/statalist/archive/2006-06/msg00472.html etc. is Amemiya (1982) and is given below--that paper proves consistency of the 2SLAD model for the structural parameter \beta which determines the conditional mean of the outcome given X. That's the conditional mean, not median. If distributional assumptions imply that the conditional mean is also the median, fine, but that is not the same approach due to Koenker (2005 etc.) that most people think of when they reach for -qreg-. On 2SLAD, see also Powell (1983,1986), Chen (1988), Portnoy and Chen (1996), and Arias, Hallock and Sosa-Escudero (2001). For comparisons, see the 2007 NBER lecture at http://www.nber.org/WNE/lect_14_quantile.pdf Chernozhukov and Hansen (2006) not only recommend a more general method, but in their footnote 1 on page 493, they clarify that 2SLAD will produce inconsistent estimates when the effects of the endogenous variables vary across quantiles: "We do not use the term ‘‘two stage quantile regression’’ (2SQR) because it is already used to name the procedure proposed by Portnoy and Chen (1996) as an analog of the two stage LAD (2SLAD) of Amemiya (1982) and Powell (1983). This procedure has been widely used to estimate quantile effects under endogeneity. When the QTE vary across quantiles, the 2SQR does not solve (1.4) and thus is inconsistent relative to the treatment parameter of interest. Note that 2SLAD and 2SQR are still excellent strategies for estimating constant treatment effect models." Amemiya, Takeshi. (1982). "Two stage least absolute deviations estimators." Econometrica 50(3):689-711. http://www.jstor.org/stable/1912608 Arias, Hallock & Sosa-Escudero (2001). "Individual heterogeneity in the returns to schooling: Instrumental variables quantile regression using twins data." Empirical Economics 26(1): 7-40. Chen. (1988). "Regression Quantiles and Trimmed Least Squares Estimators for Structural Equations and Non-Linear Regression Models." Unpublished Ph.D. dissertation, University of Illinois at Urbana-Champaign. Chernozhukov and Hansen. (2006). "Instrumental quantile regression inference for structural and treatment effect models." Journal of Econometrics, 73, 245-261. Koenker, R. (2005). Quantile regression. Cambridge: Cambridge University Press. Portnoy, S. and Chen, L. (1996). "Two-stage regression quantiles and two-stage trimmed least squares estimators for structural equation models." Communication in Statistics, Theory Methods, 25(5):1005-1032. Powell, J. (1983). "The Asymptotic Normality of Two-Stage Least Absolute Deviations Estimators." Econometrica 51(5):1569-1575. Powell, J. (1986). "Censored Regression Quantiles." Journal of Econometrics, 32(1):143-155. 2011/1/14 Jorge Eduardo Pérez Pérez <perez.jorge@ur.edu.co>: > Median regression is more robust to outliers than linear regression. > Median regression with instrumental variables can be performed with > the procedure described in this post (which includes a relevant > reference): > > http://www.stata.com/statalist/archive/2003-09/msg00585.html * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**st: RE: Robust instrumental variable regression***From:*Jan Bryla <JBR@finansraadet.dk>

**Re: st: RE: Robust instrumental variable regression***From:*Maarten buis <maartenbuis@yahoo.co.uk>

**RE: st: RE: Robust instrumental variable regression***From:*Nick Cox <n.j.cox@durham.ac.uk>

**RE: st: RE: Robust instrumental variable regression***From:*"Feiveson, Alan H. (JSC-SK311)" <alan.h.feiveson@nasa.gov>

**RE: st: RE: Robust instrumental variable regression***From:*Nick Cox <n.j.cox@durham.ac.uk>

**Re: st: RE: Robust instrumental variable regression***From:*Jorge Eduardo Pérez Pérez <perez.jorge@ur.edu.co>

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