st: STATA module grstest

["Markus Ibert" <markibert@web.de>]

Dear statalist users,
 
I think I might have found an error in the user-written stata module 'grstest' (http://ideas.repec.org/c/boc/bocode/s457069.html). The module implements the Gibbons, Ross, Shanken test which is a common tool in finance to assess model performance. For example, if there are n stocks and we have the time-series of returns, we run time-series regressions of excess returns (returns in excess of the risk-free rate) on a factor (for example the market return). Using popular models, for example the CAPM, the hypothesis is that the n intercepts from these n time-series regressions jointly equal zero. The resulting GRS test to test this hypothesis is a F-test.

But if we set n=1, then there is only one regression and we can simply obtain the t-statistic for the hypothesis that the intercept is zero from the usual stata 'reg' command. In the case with n=1 the F-statistic is the square of the t-statistic and reported p-values should be same. But the module 'grstest' gives very different, unplausible p-values and F-statistics (the data is, as requested by the module, in wide-format). So I wrote my own module for the test and compared the results with the 'grstest' module. It seems like the 'grstest' in many cases gives false results (in some cases it is correct though). I tried to contact the author some months ago but he did not reply which is why I am now posting this to make people who use the module aware of the possible error. Correct me if my reasoning is wrong.


All the best,
Markus

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