Re: st: RE: Robust instrumental variable regression

[Austin Nichols <austinnichols@gmail.com>]

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Unpublished Ph.D. dissertation, University of Illinois at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

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