# Solved – How to compare whether the coefficients of two independent variables statistically different from each other

If I have two independent variables and they are dummy variable along with other independent variables and I run a linear probability model, I want to compare whether the coefficients of two dummy variables are statistically different from each other. I do not know how to compare that. Could someone help me on that?

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I want to compare whether the coefficients of two dummy variables are statistically different from each other

I understand that you want to test the hypotheses \$\$H_0: A=B\$\$ \$\$H_1: Anot=B\$\$.

So we are performing inference on the quantity \$A-B\$ and evaluating whether it is sufficiently far from 0 relative to its standard error. Ordinarily, in the single-parameter case, we just compare, e.g., \$A\$ to its standard error. But we have two parameters here. So we have \$\$sqrt{frac{(A-B)^2}{text{var}(A)+text{var}(B)-2text{cov}(A,B)}}\$\$ as our test statistic, where \$text{cov}(A,B)\$ is the covaraince of \$A\$ and \$B\$. Now we compare the test statistic to a standard normal distribution.