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From |
Mark Schaffer <M.E.Schaffer@hw.ac.uk> |

To |
statalist@hsphsun2.harvard.edu, "Morris, Stephen" <s.morris@imperial.ac.uk> |

Subject |
Re: st: 2SLS with quadratic RHS endogenous vars |

Date |
Fri, 28 Nov 2003 14:33:40 +0000 (GMT) |

Steve, The answer to your questions is very nicely and succinctly discussed in Wooldridge (2000), Econometric Analysis of Cross Section and Panel Data, section 9.5, esp. pp. 236-7. The short answer is that you need to go down the route of your Option 1 and include xsquared as a second endogenous regressor. If you do this, you may need additional instruments. One source of additional instruments would be squares of some of the other exogenous variables. A quite clever idea is suggested by Wooldridge on p. 237. It's similar to your Option 2 but with an important difference: instead of using xhatsquared as a regressor in your second stage equation, use it as an *instrument*, i.e., estimate ivreg2 y q (x xsquared = z xhatsquared) In effect this adds a nonlinear function of your exogenous variables to your instrument set. Your Option 2 is apparently a trap worthy of a special term, namely "forbidden regression". In Wooldridge's words, the mistake behind "is in thinking that the linear projection of the square is the square of the linear projection". See the book for a detailed discussion. Cheers, Mark Quoting "Morris, Stephen" <s.morris@imperial.ac.uk>: > Hi, > > Does anyone know of a way to run a 2SLS model in Stata where the > endogenous RHS variable would ideally appear in a quadratic form? > > I am using -ivreg2- to find the effect of an independent variable x > on a dependent variable y, where I believe that x and y will be > simultaneously determined. I have what I think are a set of > non-weak, orthogonal instruments for x, namely z. So, the command I > use is: > > ivreg2 y q (x = z) > > q is a set of exogenous variables also thought to influence y. > > I have reason to believe that the true impact of x on y is > non-linear, and I would ideally like to estimate a model including x > and x squared. Given that x is simultaneously determined with y I am > not sure how to proceed. > > Option 1: > > One approach would be to run â€“ivreg2- as normal and instrument > both x and x squared. That is, to run: > > ivreg2 y q (x xsquared = z) > > This produces a set of results, but the sign and magnitude of the > coefficients on x and x squared are counterintuitive. I think this > might be because unless my first stage model is able to predict > perfectly x and x squared (which it is not) I will not actually be > modelling a quadratic form (i.e. the predicted value of x squared > from the first stage regressions does not equal the square of the > predicted value of x). > > Option 2: > > So, the other thing I thought to do was to estimate the first stage > equation for x and compute the linear prediction (call this xhat). > Then square these predictions (call this xhatsquared) and use these > to measure the effects of x squared in my second stage: > > reg y q xhat xhatsquared > > The results appear to be more sensible, but I am not sure if the > approach is valid. > > Any thoughts on which option to use, if either, would be greatly > appreciated. I am using Stata version 8.2. I have previously > searched the FAQ and the Statalist archives, and the question I pose > is similar to one posted by Jim Shaw on 18 July, but with respect to > non-linear RHS endogenous variables rather than non-linear RHS > exogenous variables. > > Thanks very much. > > Steve > > > > * > * For searches and help try: > * http://www.stata.com/support/faqs/res/findit.html > * http://www.stata.com/support/statalist/faq > * http://www.ats.ucla.edu/stat/stata/ > Prof. Mark Schaffer Director, CERT Department of Economics School of Management & Languages Heriot-Watt University, Edinburgh EH14 4AS tel +44-131-451-3494 / fax +44-131-451-3008 email: m.e.schaffer@hw.ac.uk web: http://www.sml.hw.ac.uk/ecomes ________________________________________________________________ DISCLAIMER: This e-mail and any files transmitted with it are confidential and intended solely for the use of the individual or entity to whom it is addressed. If you are not the intended recipient you are prohibited from using any of the information contained in this e-mail. In such a case, please destroy all copies in your possession and notify the sender by reply e-mail. Heriot Watt University does not accept liability or responsibility for changes made to this e-mail after it was sent, or for viruses transmitted through this e-mail. Opinions, comments, conclusions and other information in this e-mail that do not relate to the official business of Heriot Watt University are not endorsed by it. ________________________________________________________________ * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**st: -ivreg- in PolSci***From:*"Clive Nicholas" <Clive.Nicholas@newcastle.ac.uk>

**References**:**st: 2SLS with quadratic RHS endogenous vars***From:*"Morris, Stephen" <s.morris@imperial.ac.uk>

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