Say I have a regression model: Y = a + bX + cW + (error) Suppose I have a balanced panel data set for m populations over n time periods. I want to know if I can pool all the data into one single Constant Coefficients model (a, b and c are constant across populations), or whether I should allow for different intercepts with a Fixed Effects Model with intercept dummies (b and c are constant across populations), or whether I have to run separate unrelated regressions (b and c are not constant across populations). Is there a way to do a Chow test where the null hypothesis is just Ho: b and c constant across populations? (In other words, test only the stability of the SLOPE coefficients b and c across populations?)

Say I have a regression model:

$$ Y = a + bX + cW + e $$

Suppose I have a balanced panel data set for $m$ populations over $n$ time periods. I want to know if I can pool all the data into one single Constant Coefficients model ($a$, $b$ and $c$ are constant across populations), or whether I should allow for different intercepts with a Fixed Effects Model with intercept dummies ($b$ and $c$ are constant across populations), or whether I have to run separate unrelated regressions ($b$ and $c$ are not constant across populations). Is there a way to do a Chow test where the null hypothesis is just $H_{0}:$ $b$ and $c$ constant across populations? (In other words, test only the stability of the SLOPE coefficients $b$ and $c$ across populations?)