Elias Dinas from EUI asks: In section 4.6.1 you explain very clearly the problems from the straightforward use of the 2SLS logic in binary choice and/orendogenous treatment models. You also provide a simple ‘linearized’ alternative but this is useful at the cost of introducing back-door identifying information. It so happens that I have a continuous Y a binary D, instrumented with two Zs (one binary the other continuous). I guess that if Y was also a dummy, MLE could provide consistent estimates for the average effect (following wooldridge 2003:478). However, in this case, I think I am left with two alternatives: 2-stage probit least squares (the cdsimeq command in stata) whose second stage however seems to belong in the fobidden regressions family, and the ‘linearized’ 2-Stage solution you suggest in the book. So my question is should I prefer one over the other or even consider a third option? Thank you very much for your help and looking forward for your reply. Elias Dinas
Thanks for your question Elias.
Section 4.6.1 discusses two approaches to 2SLS with a dummy endogenous variable, forbidden (plug-in) regression and the use nonlinear fitted values as instruments, neither of which we really like. Rather, as suggested by our discussion of nonlinear models with endogenous regressors in Section 6.4.3 (LDV reprise), we think you should use garden-variety 2SLS (IV) for dummy endogenous variables (as always; of course you can try fancier methods in the privacy of your own home, but this is what we like to see in published papers). With a single Bernoulli instrument IV gives you LATE; with two Bernoulli instruments, you get a weighted average of the two underlying LATEs. When one instrument is continuous, the weighting is a little trickier (see, e.g., the “fish paper”). But my experience is that the marginal effects from nonlinear structural models will be close to 2SLS (that’s how you can tell the structural model MFX were done correctly), and with 2SLS you might even get the standard errors right!
Is 2SLS really OK?
Elias Dinas from EUI asks: In section 4.6.1 you explain very clearly the problems from the straightforward use of the 2SLS logic in binary choice and/orendogenous treatment models. You also provide a simple ‘linearized’ alternative but this is useful at the cost of introducing back-door identifying information. It so happens that I have a continuous Y a binary D, instrumented with two Zs (one binary the other continuous). I guess that if Y was also a dummy, MLE could provide consistent estimates for the average effect (following wooldridge 2003:478). However, in this case, I think I am left with two alternatives: 2-stage probit least squares (the cdsimeq command in stata) whose second stage however seems to belong in the fobidden regressions family, and the ‘linearized’ 2-Stage solution you suggest in the book. So my question is should I prefer one over the other or even consider a third option? Thank you very much for your help and looking forward for your reply. Elias Dinas
Thanks for your question Elias.
Section 4.6.1 discusses two approaches to 2SLS with a dummy endogenous variable, forbidden (plug-in) regression and the use nonlinear fitted values as instruments, neither of which we really like. Rather, as suggested by our discussion of nonlinear models with endogenous regressors in Section 6.4.3 (LDV reprise), we think you should use garden-variety 2SLS (IV) for dummy endogenous variables (as always; of course you can try fancier methods in the privacy of your own home, but this is what we like to see in published papers). With a single Bernoulli instrument IV gives you LATE; with two Bernoulli instruments, you get a weighted average of the two underlying LATEs. When one instrument is continuous, the weighting is a little trickier (see, e.g., the “fish paper”). But my experience is that the marginal effects from nonlinear structural models will be close to 2SLS (that’s how you can tell the structural model MFX were done correctly), and with 2SLS you might even get the standard errors right!
–JA