# Chow tests for "poolability" with panel data

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?)

• what's chows test?
– user46925
Jul 27, 2016 at 12:35
• Seems an econometrics question, consider adding the [econometrics] tag for more visibility. Nov 27, 2016 at 18:48
• You might want to have a look at the function (or its documentation) pooltest from the R package plm which seems to do what you want. Jan 30, 2017 at 13:07

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.

A test of the null hypothesis that some coefficients are zero vs. some alternative being non-significant will not tell you that you can pool. It just suggests absence of strong evidence for these coefficients being non-zero.

Model building by hypothesis testing in this manner is problematic (unless your inference from your final model accounts for it, e.g. by bootstrapping the whole model building process). For suitable approaches see e.g. Frank Harrell's "Regression Modelling Strategies" book.

I would suggest to compare your model with your model + a dummy variable P representing your population + 2 interactions terms (P:X and P:W).

The reasoning is that if a,b and c stable across populations, then these new degree of freedom does not yield a much better model. A Chi-squared test would then allow to check if this augmented model is significantly better than your first model.

As I am not an expert, I would advise you to wait for more peers on this question.