Doubt about Lagrange Multiplier Statistics for q exclusions restrictions

Reply Mon 15 Nov, 2021 04:25 pm
For obtaining the Lagrange Multiplier Statistics I follow this steps (Wooldridge 2019, Introductory Econometrics):

1. Regress 𝑦 on the restricted set of independent variables and consider the residuals 𝑒̃;
2. Regress 𝑒̃ on all of the independent variables and obtain the R-squared 𝑅^2_𝑒
3. Compute 𝐿𝑀=𝑛⋅𝑅^2_𝑒
4. Compare 𝐿𝑀 to the appropriate critical value, 𝑐, in a πœ’^2_π‘ž distribution: if 𝐿𝑀>𝑐 the null hypothesis is rejected and all the coefficients.

My doubt is about point 2., I don't understand if I should include an intercept in regressing the 𝑒̃ on the independent variables or not. If I do include the intercept the resulting 𝑅^2_𝑒 is the same as the one from the unrestricted regression.
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