If I have a model with Y$\in${0,1}, and am estimating y= $\beta$x+$\eta$

My understanding is if I use a probit model say, I am imposing structure on the DGP by assuming Y|x=$\eta$ is distributed normally, which should achieve the cramer-rao lower bound.

So is it the case that estimating the equation by ols vs probit, the latter (or even a logit?) should yield lower standard errors?

  • $\begingroup$ Why is the conditional variable distributed normally? $\endgroup$ – Dave May 6 at 4:52
  • $\begingroup$ I was just saying for a probit specification, you can interpret it as the error being normally distributed, which is the same as the condtional variable being normal? or is that incorrect $\endgroup$ – Steve May 6 at 15:11
  • $\begingroup$ Probit is for when the response variable is binomial. $\endgroup$ – Dave May 6 at 16:28
  • $\begingroup$ yes the reponse is binomial, but then the error is normal, no? $\endgroup$ – Steve May 6 at 17:36
  • $\begingroup$ No, that’s not how it works. How would you end up with a residual of 2, for instance? $\endgroup$ – Dave May 7 at 2:08

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