# Comparison between coefficients of two fixed effects models with same sample

I have a problem. I have two models of OLS regressions with time and group fixed effects of a crosscountry paneldata analysis:

$$Y_i = b_1 X_i + b_2 D_1 Z_i + b_3 D_2 Z_i\tag 1$$

and

$$Y_i = b_1 X_i + b_2 D_1 Z_i + b_3 D_2 Z_i + b_4 G_i\tag2$$

$$i$$ is the index of my country, $$D_1$$ and $$D_2$$ are two Dummies and $$G$$ is a control variable. I want to compare $$b_2$$ and $$b_3$$ between my two models (1) and (2). I don't think that a Wald Test is possible because of my fixed effects and I can't use the z-test of Clogg and Petkova because my samples aren't independent and i don't compare between different groups. Is there any possibility to compare if the coefficients differ significantly between my models.

Thanks and best regards

• A simple approach assuming you have sufficient countries is to resample at the country level and use the standard deviation of the difference across bootstrap samples as the standard error. You can then conduct a Wald test. – Heteroskedastic Jim Dec 25 '18 at 16:53