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  • Ivreg2 and Control function regression

    @Wooldridge Hi Sir,
    When we have two endogenous variables and two instrumental variables, one for each endogenous variable. Which regression method will be ideal to use, ivreg2 or Control function approach manually? To run the control function approach manually, I use the following steps-

    My main model is
    y1 = b0 + b1*x1 +b2*x2+ b3*(other Controls) +ui.
    I assume xi and x2 are endogenous and I have z1 as an IV for x1 and z2 for x2.

    Following Wooldridge(2015) paper, i first run

    reg x1 z1 and other control variables, robust
    From this model, I predict the residual, e1

    I run the second equation
    reg x2 z2 and other control variables, robust
    From this model, i predict the residual e2

    I use both the residuals in the final equation as additional regressors

    The final equation is as follows
    reg y1 x1 x2 e1 e2 and other control variables, robust

    If the residuals turn out to be significant, then there is a problem of endogeneity. Are these steps correct ?

  • #2
    Significance of the residual indicated endogeneity.

    Comment


    • #3
      I answered this question via email. Here's what I wrote, for those facing a similar situation:

      "I did not suggest omitting exogenous variables in the first stages, as you have done. If you leave z2 out of the equation for x1 and leave z1 out of the equation for x2, you no longer reproduce 2SLS. You are making substantive restrictions on the reduced forms, and the CF estimator will be inconsistent if these assumptions fail.

      Unless you have a good reason not to, the first stages should include all exogenous variables."

      I can add that with exclusion restrictions in the first stages, or reduced forms, it is more efficient to estimate the three equations at once using GMM. In the old days, it would've been three stage least squares. But the improved efficiency comes at the price of non-robustness if the exclusion restrictions in the first stages fail.

      Assuming the exclusion restrictions in the equations for x1 and x2 are valid, the test for the null of exogeneity is a Wald (essentially F) test of exclusion of e1 and e2.

      Comment


      • #4
        Thank you so much, Professor Wooldridge.

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