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From |
Stas Kolenikov <skolenik@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

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

Date |
Sat, 5 Jun 2010 09:27:42 -0500 |

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/

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

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

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