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# st: Different coefficient magnitudes in ols and 2sls estimation

 From Sukesh Patro To statalist@hsphsun2.harvard.edu Subject st: Different coefficient magnitudes in ols and 2sls estimation Date Thu, 22 Apr 2010 11:14:04 -0500

```Hi,
I am estimating the following prediction model:
Y1 = a0 + a1*Y2 + a2*X1 + a3*X2 + e
I have theoretical grounds to expect that Y2 could be endogenous and
jointly determined with Y1. Therefore, in addition to estimating the
above model using OLS, I also estimate the following system using 2SLS
(I use ivreg2).
Y1 = a0 + a1*Y2 + a2*X1 + a3*X2 +e
Y2 = b0 + b1*Y1 + b2*Z1 + b2*Z1 + b3*X2 + v
The main problem we have is that the coefficient on Y2 in OLS is
significantly smaller than the coefficient in 2SLS. The following are
coefficients on Y2 using the OLS and 2SLS.
Coefficient OLS 0.200  (t=3.00)
Coefficient 2SLS 2.000 (t=2.50)
I checked the distribution of Y2 and the predicted value of Y2 from
the Y2 model (Y2-hat), and noticed that while the mean value of Y2-hat
is very similar to the mean value of Y2, the variance of Y2-hat is
significantly smaller than the variance of Y2.
Y2 has a Mean 0.30 Median 0 Variance 0.200
Y2-hat has a Mean 0.30 Median 0.30 Variance 0.002
My question is about the implication of the larger coefficient on Y2 in 2SLS.
Does the smaller variance of Y2-hat explain the larger coefficient size?
Does the significantly smaller variance of Y2-hat, suggest a problem
of weak instrument variable?
Alternatively, does it suggest a problem associated with errors in the
raw variable, Y2? That is, the significantly smaller coefficient in
the OLS estimate is attributable to large errors in Y2?
Which estimation is more reliable, OLS or 2SLS?
I also estimated the two equations using a SUR regression found the
magnitude of the coefficient estimates under SUR to be closer to those
under OLS.

Thanks much for your help in gaining clarity on this problem.
SSKP
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