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I have a large panel with 4 time periods and 10,000 observations per year. First I do OLS regressions for each year, and they all look fine. Then I run the FE model for the entire period, and one fairly important variable changes sign. This is odd, but what worries me most is that R2 is very small (0.058), and the adjusted R2 is negative (-0.277). Note that I have 9 independent variables, not counting the dummies for years, and the coefficients for 6 of them are statistically significant. How could this be? I'd be grateful for any suggestions.

Mikhail
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  • What are your variables? What is your goal? Why are you using dummies for years? How many years have you got? What are all these observations? – Peter Flom Oct 25 '23 at 18:49
  • @Peter I study the composition of workforce in the 19th century and my dependent variable is a share of resident workers. My 9 independent variables describe the factors that may have influenced it, such as a distance to a rail station, % of paupers, availability of alternative employment etc. I use dummies for years to account for the general trend towards reduction of the number of workers of this type. – Mikhail Oct 26 '23 at 20:37
  • Why dummies for years? Leave it numeric and use a spline to look at nonlinearity. – Peter Flom Oct 26 '23 at 23:43

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The goal of regression is to decrease the variability. What $R^2_{adj}<0$ means is that your estimated variance (a measure of variability) after performing the regression exceeds that of the variance before you do the regression. That is, you have made it worse.

It is possible to get individual coefficients to be significant in this situation, however, because the tests of individual coefficients are different from the overall test and overall adjusted $R^2$, but I would be weary to take them seriously. I like a comment in the linked question.

perforce you will conclude the entire regression is not significant and you (obviously!) wouldn't conduct further testing of the individual coefficients

Dave
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  • Thank you, you have answered the first part of my question and confirmed that the FE regression does not work. But why does it fail? What could cause this problem? – Mikhail Oct 25 '23 at 15:56
  • @Mikhail How many parameters do you have in your model, and how do you calculate adjusted $R^2?$ – Dave Oct 25 '23 at 15:59
  • I have 9 parameters plus 3 year dummies. I use plm to run panel data regression, and take R2 from its output. – Mikhail Oct 26 '23 at 13:31