VIF calculation in python statsmodel

Question

The code for calculating VIF in statsmodel is below:

k_vars = exog.shape[1]
x_i = exog[:, exog_idx]
mask = np.arange(k_vars) != exog_idx
x_noti = exog[:, mask]
r_squared_i = OLS(x_i, x_noti).fit().rsquared   ## NO INTERCEPT
vif = 1. / (1. - r_squared_i)

When fitting, it does not include an intercept. It seems intercept should be included according to "Introductory Econometrics (6ed)" by Wooldridge: "... R-squared from regressing Xj on all other independent variables ( and including an intercept )."

Is statmodels wrong? Is there another package I can cross check? Thanks.

Answer 1

When using statsmodels, always be mindful of adding constant (which is necessary in this case); quoting from the docs :

An intercept is not included by default and should be added by the user. See statsmodels.tools.add_constant .

Reference from MATLAB: https://www.mathworks.com/help/econ/examples/time-series-regression-ii-collinearity-and-estimator-variance.html

Answer 2

In a traditional matrix formulation of the linear regression, the X-matrix always has a column vector of 1's in the first position - without this, we would get a regression through the origin, ie without an intercept term. I came across this question while looking for VIFs in statsmodels.