Solved – Chow tests for “poolability” with panel data

Question

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?)

Answer 1

The plm package in R provides a a function for the poolability test in just three steps:

# 1. Run a normal OLS model with fixed effects (model="within")
plm_model<- plm(y ~ x, data= dataset, model= "within")

# 2. Run a variable coefficients model with fixed effects (model="within")
pvcm_model<- pvcm(y ~ x, data= dataset, model= "within")

# Run the poolability test
pooltest(plm_model, pvcm_model)

The null hypothesis is that the dataset is poolable (i.e. individuals have the same slope coefficients), so if p<0.05 you reject the null and you need a variable coefficients model.