Say I estimate the following multivariate linear regression $$ y = \beta_0 +\beta_1 x_1 +\beta_2 x_2+\beta_3x_3+\beta_4x_4 + \epsilon$$ How can I test that $\beta_1=\beta_2=\beta_3$?
I know that to test if $\beta_1=\beta_2$ you can simply construct a $Z$ test with $$ Z = \frac{\beta_1-\beta_2}{\sqrt{se_{\beta_1}^2+se_{\beta_2}^2}}$$
Is there an analogue for multiple coefficient estimates?