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Re: st: Computation of standard errors in an IV setting
From
Christopher Baum <[email protected]>
To
"[email protected]" <[email protected]>
Subject
Re: st: Computation of standard errors in an IV setting
Date
Mon, 22 Jul 2013 09:28:04 +0000
<>
On Jul 22, 2013, at 2:33 AM, Surithra wrote:
> The original equation of interest is:
>
> y1 = x1 + x2 + x3 + e, where x2 is defined as negative of the absolute
> value of (0.5 - x1).
>
> The independent variable, x1 is endogenous and hence, x2 is also endogenous.
>
> I have an instrument for x1 - say z1.
>
> Now I would like to estimate the original equation (y1 = x1 + x2 + x3
> + e) using the IV, z1. However, what makes it complicated relative to
> a standard IV application is that x2 is a non-linear function of x1.
> As a result, while z1 has a monotonic effect on x1, z1 has a
> non-monotonic effect on x2.
>
> As a result I am not sure how I can use Stata to obtain the correct
> standard errors in this case.
This logic is misguided. The fact that one endogenous variable is a nonlinear function of another will not have
any deleterious effect on the computation of IV estimates. This situation would arise, for example, if x2 = x1^2.
As long as you have enough instruments that satisfy the necessary conditions, IV (or IV-GMM, better yet) will
work fine. E.g., using Mark Schaffer's -xtivreg2- from SSC:
. webuse grunfeld, clear
. g mv2 = mvalue^2
. g ks2 = kstock^2
. xtivreg2 invest (mvalue mv2 = kstock ks2 time), gmm2s robust fe
FIXED EFFECTS ESTIMATION
------------------------
Number of groups = 10 Obs per group: min = 20
avg = 20.0
max = 20
2-Step GMM estimation
---------------------
Estimates efficient for arbitrary heteroskedasticity
Statistics robust to heteroskedasticity
Number of obs = 200
F( 2, 188) = 14.29
Prob > F = 0.0000
Total (centered) SS = 2244352.228 Centered R2 = -0.2833
Total (uncentered) SS = 2244352.228 Uncentered R2 = -0.2833
Residual SS = 2880270.244 Root MSE = 123.1
------------------------------------------------------------------------------
| Robust
invest | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
mvalue | .2998763 .1260421 2.38 0.017 .0528383 .5469142
mv2 | .0000222 .0000193 1.15 0.250 -.0000156 .0000601
------------------------------------------------------------------------------
Underidentification test (Kleibergen-Paap rk LM statistic): 20.011
Chi-sq(2) P-val = 0.0000
------------------------------------------------------------------------------
Weak identification test (Cragg-Donald Wald F statistic): 10.196
(Kleibergen-Paap rk Wald F statistic): 8.751
Stock-Yogo weak ID test critical values: 10% maximal IV size 13.43
15% maximal IV size 8.18
20% maximal IV size 6.40
25% maximal IV size 5.45
Source: Stock-Yogo (2005). Reproduced by permission.
NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.
------------------------------------------------------------------------------
Hansen J statistic (overidentification test of all instruments): 3.006
Chi-sq(1) P-val = 0.0830
------------------------------------------------------------------------------
Instrumented: mvalue mv2
Excluded instruments: kstock ks2 time
------------------------------------------------------------------------------
Kit
Kit Baum | Boston College Economics & DIW Berlin | http://ideas.repec.org/e/pba1.html
An Introduction to Stata Programming | http://www.stata-press.com/books/isp.html
An Introduction to Modern Econometrics Using Stata | http://www.stata-press.com/books/imeus.html
| http://www.crup.com.cn/Item/111779.aspx
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