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st: Negative R-squared in IV estimation


From   "Lim, Elizabeth" <elim@utdallas.edu>
To   "'statalist@hsphsun2.harvard.edu'" <statalist@hsphsun2.harvard.edu>
Subject   st: Negative R-squared in IV estimation
Date   Fri, 21 Oct 2011 18:19:02 +0000

Hello,

I'm hoping someone might be able to shed some light on the following issues that I've been struggling with:-

(1) As Wooldridge (2006) mentioned in his textbook, "Unlike in the case of OLS, the R-squared from IV estimation can be negative because SSR for IV can actually be larger than SST. Although it does not really hurt to report the R-squared for IV estimation, it is not very useful, either" (p. 521).  How do I deal with negative R-squared in 2SLS?  If it's not "useful" to report R-squared, especially negative R-squareds, what model statistics should I report?  

(2) Wooldridge (2006) further explained that "R-squareds cannot be used in the usual way to compute F tests of joint restrictions" (p.521).   If I want to report model F values in lieu of R-squareds, how do I do compute F values based on R-squared values?  What formula do I use?

(3) My understanding is that Model F values in OLS should increase with the addition of more variables in the model, but I'm not sure if the same interpretation applies in 2SLS models.  If the Model F value in 2SLS models *decreases* after adding interaction terms, what would this suggest?  Is there any cause for concern?

(4) Suppose I run a 2SLS, and all the coefficients and standard errors for all the variables in the 2SLS model are less than 1, but the coefficient estimates and standard errors on the interaction terms are large (by large, I mean in excess of 1). Is this an indication of some statistical or econometrics problem?  What might have caused the large values in the estimates and standard errors of the interaction term?  What can I do to check whether I've run the 2SLS analysis correctly?

I've attached an example below.

Y=beta0 + beta1*X1 + beta2*X2 + beta3*X3 + beta4*X2*X3

Endogenous variable = X1
Independent variables=X2, X3
Interaction term=X2*X3

Variables	Coefficient	Standard error
X1		-0.022		0.126
X2		-0.730		0.519
X3		  0.164		0.118
X2*X3		  4.789		2.468

Helpful references related to any of the questions above are greatly appreciated.  Thank you in advance for your help.

Regards,
Elizabeth



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