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Re: st: Negative R-squared in IV estimation


From   Yuval Arbel <yuval.arbel@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Negative R-squared in IV estimation
Date   Fri, 21 Oct 2011 20:57:13 +0200

here are my answers to some of your questions

On Fri, Oct 21, 2011 at 8:19 PM, Lim, Elizabeth <elim@utdallas.edu> wrote:
> 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?
>

Yuval: In many situations (particularly in non-linear models like
probit) It is not rare to get negative adjusted R-square or low
R-squares. Moreover, in many of these cases STATA's output does not
report at all R-squares. Usually, you can report the log-likelihood of
the procedure. You also have substitutes to the R-Square, such as,
Akaike and Schwartz criterion, which are obtained by applying
restrictions to the log-likelihood function. I personally only report
the log-likelihood

> (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?
>
Yuval: Again, this problem will be solved authomatically when you run
the STATA model. STATA will usually report in the output LR statistic
for the regression significance

> (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?
>
Yuval: Just be sure that supplementing these interaction terms does
not make the equation unidentified. But it seems to me the principle
is the same

> (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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>



-- 
Dr. Yuval Arbel
School of Business
Carmel Academic Center
4 Shaar Palmer Street, Haifa, Israel
e-mail: yuval.arbel@gmail.com

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