I am running two regressions that I thought would yield identical results and I’m wondering whether anyone can explain why they are different. One is with statsmodels OLS and the other is with linearmodels PanelOLS.

A minimum working example is shown below. The coefficients are similar, but definitely not the same (0.1167 and 0.3514 from statsmodels, 0.1101 and 0.3100 from linearmodels). And the R-squared is quite different too (0.953 vs 0.767).

import statsmodels.formula.api as smf
from linearmodels import PanelOLS
from statsmodels.datasets import grunfeld

data = grunfeld.load_pandas().data

#   Define formula and run statsmodels OLS regression
ols_formula = 'invest ~ value + capital + C(firm) + C(year) -1'
ols_fit   = smf.ols(ols_formula,data).fit()

#   Set multiindex and run PanelOLS regression
data = data.set_index(['firm','year'])
panel_fit = PanelOLS(data.invest,data[['value','capital']],entity_effects=True).fit()

#   Look at results
ols_fit.summary()
panel_fit

Any insight appreciated!