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From |
Nir Regev <regev.nir@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Another method of squaring an instrumental variable |

Date |
Sat, 5 Jun 2010 17:50:35 +0300 |

Hi Stas, Thank you for your answer. I know I have a case of under-identification. I wish I had another instrument but I don't. The question is, maybe there is someway I can fix for the standard errors of my forced "second stage". What I am thinking is using the Variance of x, meaning, Var(x) = E(x^2) - (E(x))^2, since I have two of the three, maybe I can derive the right SE for x_hat^2 (This is just a hunch) Alas, Econometrics is not my strongest point and I am looking for a reference on this matter. By the way, I ran the procedure I thought of and technically, it works. It is not a case of perfect collinearity since squaring is non-linear. Nir On Sat, Jun 5, 2010 at 5:27 PM, Stas Kolenikov <skolenik@gmail.com> wrote: > I don't think this is the right approach. Recall that E[x^2] is not > equal to ( E[x] )^2 (Jensen's inequality). You need to have E[ > regressor | instrument ] in the RHS, so you should've run two > regressions of x and x^2 on your instrument(s). But since you have > only one, that would create perfect collinearity between your > instrumented variables in the main regression -- in other words, you > don't have enough instruments for your endogenous variables x and x^2. > > On Sat, Jun 5, 2010 at 7:47 AM, Nir Regev <regev.nir@gmail.com> wrote: >> I am trying to estimate an equation of y = x + x^2+u >> x is endogenous (which makes x^2 endogenous too) and I have only one >> instrumental variable z, which is a dummy. >> >> On a regular case, I would square z and let z and z^2 be the >> instrumentals, however, since z is a dummy this is irrelevant. >> >> I believe it is possible to run the first stage of 2SLS where: >> x=z+u, >> predict x_hat, >> square x_hat >> and run the second stage both on x_hat and x_hat^2. >> >> I think this is a consistent estimate but my standard errors and >> hypothesis tests will no doubt be miscalculated. >> >> Has anyone ever heard of such a method and knows how to fix the standart errors? >> > > -- > Stas Kolenikov, also found at http://stas.kolenikov.name > Small print: I use this email account for mailing lists only. > > * > * For searches and help try: > * http://www.stata.com/help.cgi?search > * http://www.stata.com/support/statalist/faq > * http://www.ats.ucla.edu/stat/stata/ > * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: Another method of squaring an instrumental variable***From:*Stas Kolenikov <skolenik@gmail.com>

**References**:**st: Another method of squaring an instrumental variable***From:*Nir Regev <regev.nir@gmail.com>

**Re: st: Another method of squaring an instrumental variable***From:*Stas Kolenikov <skolenik@gmail.com>

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