Re: [Gretl-users] strange R^2 with TSLS

On Thu, 6 Dec 2007, Sven Schreiber wrote: >> On the original issue of R^2, I'll file the bug report soon. >> >> > "Delay that order"... Actually for my real-world cases it turns > out there isn't anything (obviously) wrong. However, I'm still > puzzled by the 3-liner results I posted earlier. The point > estimates are quite different between ols and tsls -- then how > come the correlation between fitted and observed is the same to > five or six digits of precision? Hm. > "Strange but true". It seems to be in the arithmetic for the case of one independent variable and one instrument. nulldata 50 genr x = normal() genr y = normal() genr z = normal() ols y 0 x ols x 0 z --quiet genr xhat = $coeff(const) + $coeff(z)*z ols y 0 xhat genr yhat = $coeff(const) + $coeff(xhat)*x R2 = corr(y, yhat)^2 "R2" is numerically identical to the R^2 from the first OLS. Left as an exercise: prove that this is always the case.