Why do standard errors slightly deviate between `PyFixest` and `fixest`?

[s3alfisc]

Why do standard errors slightly differ between PyFixest and fixest? The answer is "different small sample correction defaults".

In Python, we get

import pandas as pd
import numpy as np
from pyfixest.estimation import feols
from pyfixest.utils import get_data

data = get_data()
fml = "Y ~ X1 | f1"
fit = feols(fml, data = data)

fit.tidy()
#              Estimate  Std. Error    t value      Pr(>|t|)     2.5 %    97.5 %
# Coefficient                                                                   
# X1          -0.949441    0.068857 -13.788641  2.886580e-14 -1.090269 -0.808613

whereas in R, we have

library(fixest)
library(reticulate)

data = py$data
fml = as.formula(py$fml)
fit = feols(fml, data = data)
summary(fit)
# OLS estimation, Dep. Var.: Y
# Observations: 997 
# Fixed-effects: f1: 30
# Standard-errors: Clustered (f1) 
#     Estimate Std. Error  t value   Pr(>|t|)    
# X1 -0.949441   0.068891 -13.7817 2.9236e-14 ***
# ---
# Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# RMSE: 1.7297     Adj. R2: 0.419595
#                Within R2: 0.161418

fixest::feols() produces a standard error of 0.068891, but PyFixest.feols() reports a standard error of 0.068857.

To reproduce PyFixest results in fixest, you need to use fixest::ssc(fixef.K = "none") instead of its default "nested".

feols(fml, data = data, ssc = ssc(fixef.K = "none")) |> summary()
# OLS estimation, Dep. Var.: Y
# Observations: 997 
# Fixed-effects: f1: 30
# Standard-errors: Clustered (f1) 
#     Estimate Std. Error  t value   Pr(>|t|)    
# X1 -0.949441   0.068857 -13.7886 2.8867e-14 ***
# ---
# Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# RMSE: 1.7297     Adj. R2: 0.419595
#                Within R2: 0.161418

Now standard errors, t statistics, and p values match exactly between the two libraries.

See the fixest vignette on standard errors for details.

PyFixest implements all options that fixest::ssc() offers, with the exception of fixef.K = "nested". I will add this feature in the future. Please let me know if you think this is high priority - as of now, I do not consider it too important.