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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 13:27:24 -0500 |

Yes, it will give some coefficients and standard errors, but squaring the predicted value won't give you a good estimate of the square of the variable. You would still want to think about x and x^2 as separate variables, and by any account you would have to agree that you don't have enough instruments. On Sat, Jun 5, 2010 at 9:50 AM, Nir Regev <regev.nir@gmail.com> wrote: > 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/ > -- 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/

**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>

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

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