Including firm fixed-effect makes the coefficient insignificant

[SaraYasar]

Hello,

I am running panel regression with period and firm fixed effect. I have modeled several panel regressions for my research considering what other researchers did in the past for analyzing similar data. I also used new model specifications for a robustness check. Including period and firm fixed effect in the main regression are somehow OK, since the coefficient on the variable of interest is still significant. However, when I include firm fixed effect the t-stat drops from 4.13 to almost 1.80.

For the robustness check, I used three other model specifications. The coefficient on the variable of interest is highly statistically significant (t-value is almost 7) when I only include period fixed-effect. However, when firm fixed effect is included, the coefficient is no longer significant. Generally speaking, what causes such a huge difference by including firm fixed-effect? In this case when there is a huge difference, is it OK to exclude firm fixed effect? Do you think that the reason might be due to the fact that a large fraction of the dependent variable is explained by firm fixed-effect, and that is why the coefficients on the independent variable is no longer significant.

I really appreciate it, if you could help. Thanks in advance!

BR
Sara

[startz]

When you include fixed effects, then the explanatory power comes only from variation within a firm. So it isn't surprising that you get the results you do. But no, that does not mean you can ignore the fixed effects. (The one thing you might check is whether the fixed effects are significant.)

[SaraYasar]

When you include fixed effects, then the explanatory power comes only from variation within a firm. So it isn't surprising that you get the results you do. But no, that does not mean you can ignore the fixed effects. (The one thing you might check is whether the fixed effects are significant.)

I just checked to see if the firm fixed effects are significant in the models I have for my research (the main regression+models for robustness check). And it turned out that almost all firm fixed effects are highly statistically significant in the model that I have for the robustness check, however, in the main model, it is not the case. I think that is why when I include firm fixed effects in robustness check models the coefficient on the variable of interest becomes insignificant. That might be an explanation, if I am not mistaken. I hope someone corrects me if I am wrong.

[SaraYasar]

When you include fixed effects, then the explanatory power comes only from variation within a firm. So it isn't surprising that you get the results you do. But no, that does not mean you can ignore the fixed effects. (The one thing you might check is whether the fixed effects are significant.)

If I check the fixed effect and it turns out that they are significant, does it mean that fixed effects explain most of the variation in a dependent variable and that is why the independent variable is not significant? And, I am also wondering if it means that fixed effects cause such a huge difference in t-stats? Thanks in advance!

BR
Sara

[startz]

When you include fixed effects, then the explanatory power comes only from variation within a firm. So it isn't surprising that you get the results you do. But no, that does not mean you can ignore the fixed effects. (The one thing you might check is whether the fixed effects are significant.)

If I check the fixed effect and it turns out that they are significant, does it mean that fixed effects explain most of the variation in a dependent variable and that is why the independent variable is not significant? And, I am also wondering if it means that fixed effects cause such a huge difference in t-stats? Thanks in advance!

BR
Sara

The fact that the fixed effects are significant does not necessarily mean they explain most of the variation. It does mean that that is more likely.