1
$\begingroup$

I am conducting IV Regression and to make sure that my instrument is not weak, I want to use Montiel Olea & Pflueger (2013) robustness test. (see: Paper by Montiel Olea & Plueger (2013) ). To do so, you need their stata ado "weakivtest", which is an post-regression command. However, in their paper they specify 4 steps how to conduct this test (without stata ado). The first steps says the following: If there are additional exogenous regressors, replace all variables by their projection residuals onto those exogenous regressors. Normalize instruments to be orthonormal. (see Montiel Olea & Pflueger, 2013: p.360).

How do I do that? Do I have to run a regression and simply use the residuals? Which regression to run: first stage or second stage or...? Or don't I need to do any of this because the stata ado takes care about it? (note that normalizing my instrument is not a problem).

Thank you very much!

$\endgroup$

1 Answer 1

1
$\begingroup$

Let $X_1$ be the $(n \times k_1)$ matrix for the endogenous variables and $X_2$ the exogenous $(n \times k_2)$ matrix for the additional exogenous variables.

Then the residuals from regressing $X_1$ on $X_2$ is given by: $$ M_{X_2} X_1, $$ where $$ M_{X_2} = (I - X_2(X_2'X_2)^{-1}X_2')) $$ Where $I$ is the identity matrix.

So you replace $X_1$ by $M_{X_2}X_1$ in the regression.

Alternatively, you can regress every variable in $X_1$ on all the variables in $X_2$ (i.e. running $k_1$ regressions). Then take the residuals of these regressions in the second stage.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.