Standard errors of the estimators when IV2SLS is used as OLS

[spring-haru]

I compared the results of Wages of Married Women at this page, using linearmodels, statsmodels and R. Naturally, all of them give the same estimates of the const and educ. However, the standard errors of the estimators in linearmodels are (slightly) differenit from those in statsmodels and R, which give basically the identical values (after rounding). I also "manually" calculated them in each case of linearmodels and statsmodels. The results are identical, and basically the same as in statsmodels. It seems to suggest that there is something "funny" in the standard errors of the estimators linearmodels. I wonder if you can help me in understanding those results.

Standard Errors of const
linearmodels: 0.184793
statsmodelss: 0.185226
R: 0.18522590

Standard Errors of educ
linearmodels: 0.014366
statsmodelss: 0.014400
R: 0.01439985

Python Code

import numpy as np
from linearmodels.iv import IV2SLS
from linearmodels.datasets import mroz
from statsmodels.formula.api import ols
from statsmodels.api import add_constant

data = mroz.load().dropna()
data = add_constant(data, has_constant='add')

# linearmodels -------
formula_lm = 'np.log(wage) ~ 1+ educ'
result_lm = IV2SLS.from_formula(formula_lm, data).fit(cov_type='unadjusted')
print(result_lm.std_errors)

# Statsmodels -------
formula_sm = 'np.log(wage) ~ educ'
result_sm = ols(formula_sm, data).fit()
print(result_sm.bse)

Manual Calculations

# linearmodels -------------------------------------
# no of observations
n_lm = result_lm.nobs

# residuals
resid_lm = result_lm.resids

# Standard Erros of Regression
SER_lm = np.std(resid_lm, ddof=1) * np.sqrt((n_lm - 1) / (n_lm - 2))

# Standard Errors of Intercept
SE_const_lm = SER_lm / np.std(data.educ, ddof=1) / \
    np.sqrt(n_lm - 1) * np.sqrt(np.mean(data.educ**2))
print(SE_const_lm)

# Standard Errors of educ
SE_educ_lm = SER_lm / np.std(data.educ, ddof=1) / np.sqrt(n_lm - 1)
print(SE_educ_lm)

# statsmodels -------------------------------------
# no of observations
n_sm = result_sm.nobs

# residuals
resid_sm = result_sm.resid

# Standard Erros of Regression
SER_sm = np.std(resid_sm, ddof=1) * np.sqrt((n_sm - 1) / (n_sm - 2))

# Standard Errors of Intercept
SE_const_sm = SER_sm / np.std(data.educ, ddof=1) / \
    np.sqrt(n_sm - 1) * np.sqrt(np.mean(data.educ**2))
print(SE_const_sm)

# Standard Errors of educ
SE_educ_sm = SER_sm / np.std(data.educ, ddof=1) / np.sqrt(n_sm - 1)
print(SE_educ_sm)

[bashtage]

There is no bug.

In [13]: formula_lm = 'np.log(wage) ~ 1+ educ'
    ...: result_lm = IV2SLS.from_formula(formula_lm, data).fit(cov_type='unadjusted', debiased=True)
    ...: print(result_lm.std_errors)
    ...:
Intercept    0.185226
educ         0.014400
Name: stderr, dtype: float64

[spring-haru]

Thanks.
It would be great if the manual is updated to reflect your comment on the debiased option of fit(), like that of PanelOLS. It would also be useful to make debiased=True a default option like PanelOLS. In any case, linearmodels is extremely useful!

[bashtage]

It would also be useful to make debiased=True a default option like PanelOLS

I prefer to not change the defaults since this would change any existing code. I have added some additional documentation and included debiased as a kwarg since it is supported by all covariance estimators.

[eande12345]

I am trying to follow your code but python returns

TypeError: fit() got an unexpected keyword argument 'cov_type'
on this line
result_lm = IV2SLS.from_formula(formula_lm, data).fit(cov_type='unadjusted')

[bashtage]

@eande12345 Can you post the formula you are using?

[bashtage]

This works as expected

from linearmodels.datasets import wage
from linearmodels.iv import IV2SLS
data = wage.load()
formula = 'np.log(wage) ~ 1 + exper + exper ** 2 + brthord + [educ ~ sibs]'
IV2SLS.from_formula(formula, data).fit(cov_type="unadjusted")