Fixed-effect `p-value` with clustered covariance differs from Stata

[spring-haru]

Fixed-effect `p-value` with clustered covariance differs from Stata

[bashtage]

Stata is choosing to use a student's t. Since there is no obvious justification aside from strong assumptions (gaussian residuals), I do not follow that practice. If you use an appropriate student's t to compute the p-value, you will get the same value.

[spring-haru]

It does not seem to be the problem of Student's t vs Gaussian residuals. Rather, the difference seems to be caused by degree of freedom.

Define the following:
N: number of observations
n: number of entities
k: number of parameters

In the example above, linearmodels uses Student's t with degree of freedom df_resid which is N-n-k, whereas Stata uses n-1 (I have not written n-k, see blelow). This is numerically confirmed by the following code:

(resc in the above code is used)

import numpy as np
from scipy.stats import t

pval_manual_calc = 2*t.cdf(resc.tstats['hrsemp'], resc.df_resid)
pval_auto_calc = resc.pvalues['hrsemp']

np.isclose(pval_auto_calc, pval_manual_calc)

which gives True.

To reproduce the Stata result

n_1 = int(resc.entity_info['total']-1)
2*t.cdf(resc.tstats['hrsemp'], n_1)

giving 0.007087663950431981, which is the value Stata returns.

See the following links for discussion on the use of n-1 (not n-k) for Stata.

https://www.statalist.org/forums/forum/general-stata-discussion/general/1479383-df-in-clustered-regression-linear-coefficient-test

https://www.statalist.org/forums/forum/general-stata-discussion/general/1576484-estimating-p-value-from-t-value-in-regression-with-cluster-robust-standard-errors