I would like to understand, precisely, why you can have a negative $R^2$ with a 2SLS estimation, such as you have in commands like ivreg2 in Stata. There is reference for such an occurrence for ivregress here: http://tinyurl.com/qbb9o9s. It states the residuals are calculated with the endogenous variables of the structural model, but it also states that the estimation does not have a nested constant-only version of the model -- this last detail is probably what makes possible the $R^2$ to be negative, I guess. I know that an estimation without the constant can produce a negative R-squared (I understand this), but I cannot say for sure if not having a nested constant-only version of the model is in any way similar. Could someone help me understand how the residuals are calculated?
1 Answer
First of all, ask yourself whether your instruments are actually strong enough to warrant the usage of TSLS. As you perhaps know from Bound et al. (1995), your estimates can be badly biased and inconsistent with 2SLS, see for example here. Moreover, you should do an F test for the first stage and check whether it's about ten.
Even better, use robust test statistics. Ivreg2 and condivreg have some available but only for one endogenous regressor under conditional homoskedasticity. The R square value is usually useless for inference. Check whether your coefficients are statistically significant, first using a t-test and then Anderson-Rubin confidence intervals as given by condivreg.
These intervals may be infinitely large which will then correspond to your instrument strength.
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$\begingroup$ I understand that R-squared as stated in
ivreg2andivregressis a bit useless. But it still a mystery to me how those residuals are calculated from the structural equation with the endogenous variables. That is what I want to understand. $\endgroup$– John DoeCommented Mar 2, 2015 at 20:15 -
$\begingroup$ If it's just about the residuals then see this excellent answer by Dimitriy here stats.stackexchange.com/questions/126313/… $\endgroup$– AndyCommented Mar 2, 2015 at 20:23
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$\begingroup$ Thank you, Andy. So in the version of Stata you estimate the residuals with the $\beta_{IV}$ and the original $X$ with the endogenous variables? Now I think I see more clearly how the residuals are calculated. $\endgroup$– John DoeCommented Mar 2, 2015 at 20:45
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1$\begingroup$ I told you this several times in the other thread that you use the original endogenous variable and not the fitted values for the calculation of the standard errors ;-) $\endgroup$– AndyCommented Mar 2, 2015 at 20:48