Say I have the following regression model:
$\ln\left(\dfrac{y_i}{x_{2i}}\right)=\alpha_1+\alpha_2\ln(x_{2i}) + \alpha_3\ln(x_{3i}) +e_i$
where I know the values of the regression coefficients and standard errors.
Now, I can rewrite the model as:
$\ln(y_i)=\beta_1+\beta_2\ln(x_{2i}) + \beta_3\ln(x_{3i}) +e_i$
where $\beta_1=\alpha_1$, $\beta_2=\alpha_2+1$, and $\beta_3=\alpha_3$.
How do I compute the standard errors for the new model, given that I know what they are for the original model? I believe they are just the same? But I am not sure... if someone could explain to me that would be greatly appreciated.