i run 2stage least-squares regression with instrumental variables.
i got negative R-squared value of -23.416 which does not make any sense in interpretation.
However, the f-statistic of the regression is signficant. what was the problem with the regression analysis.
I am enclosing output and also the data file ( i run the regression in eviews)
thanks in advance
R-squared is meaningful (as a measure of your model's predicting power) only when you estimate your model by OLS (i.e. with Gauss-Markov Theorem assumptions satisfied) . However, if the error term is correlated with any of the regressors (which must be your case otherwise you would not have used TSLS) then the decomposition TSS=RSS+ESS is no longer valid and the whole idea behind the coefficient of determination breaks apart.
R-squared is meaningful (as a measure of your model's predicting power) only when you estimate your model by OLS (i.e. with Gauss-Markov Theorem assumptions satisfied) . However, if the error term is correlated with any of the regressors (which must be your case otherwise you would not have used TSLS) then the decomposition TSS=RSS+ESS is no longer valid and the whole idea behind the coefficient of determination breaks apart.
R squared may be negative when RSS > TSS. This condition is possible in 2SLS/IV model. It is explained at this link below:
https://www.stata.com/support/faqs/statistics/two-stage-least-squares/
The following quotation is relevant:
" For two-stage least squares, some of the regressors enter the model as instruments when the parameters are estimated. However, since our goal is to estimate the structural model, the actual values, not the instruments for the endogenous right-hand-side variables, are used to determine the model sum of squares (MSS). The model’s residuals are computed over a set of regressors different from those used to fit the model. This means a constant-only model of the dependent variable is not nested within the two-stage least-squares model, even though the two-stage model estimates an intercept, and the residual sum of squares (RSS) is no longer constrained to be smaller than the total sum of squares (TSS). When RSS exceeds TSS, the MSS and the R2 will be negative. " See https://www.stata.com/support/faqs/statistics/two-stage-least-squares/
Some practical discussion is found at the link below why R squared may be negative in two stage regression:
https://stats.stackexchange.com/questions/139782/why-report-r-squared-in-instrumental-variables-estimation
Srikanth Potharla Sir you can also have a look on https://stats.stackexchange.com/questions/12900/when-is-r-squared-negative.
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