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From |
"Shaw, Jim (NIH/NCI)" <shawjim@mail.nih.gov> |

To |
"Statalist (E-mail)" <statalist@hsphsun2.harvard.edu> |

Subject |
RE: st: 2SLS with nonlinear exogenous variables |

Date |
Fri, 18 Jul 2003 07:08:00 -0400 |

Thanks for the response. Yes, I mean to estimate the equations separately. My primary concern relates to discussions I have read (e.g., Davidson and MacKinnon 1993, pp. 224--226) about the application of the IV procedure to nonlinear regression models. My overall sense is that if the endogenous right-hand side variables are nonlinear (e.g., binary, squared), then 2SLS will be both inconsistent and inefficient. In the example I provided in my previous e-mail, it was the exogenous variables that were nonlinear. I was told that 2SLS will still be inefficient when one or more of the exogenous variables are nonlinear. However, I have been unable to find any literature that clearly discusses the issue. Thanks for the suggestion regarding ivreg2. I will definitely look into it. -- James Shaw Research Associate College of Pharmacy The University of Arizona -----Original Message----- From: Mark Schaffer [mailto:M.E.Schaffer@hw.ac.uk] Sent: Friday, July 18, 2003 5:13 AM To: statalist@hsphsun2.harvard.edu; Shaw, Jim (NIH/NCI) Cc: Mark Schaffer Subject: Re: st: 2SLS with nonlinear exogenous variables Jim, Quoting "Shaw, Jim (NIH/NCI)" <shawjim@mail.nih.gov>: > Dear Statalist: > > Is 2SLS (as implemented by ivreg) still efficient if dummy variables > or > polynomials are included as exogenous variables/instruments? For > example, > would 2SLS be efficient if applied to the following system of > equations: > > y1 = y2 + x1 + x1^2 + x2 + e1 > > y2 = y1 + X1 + x3 + x4 + e2 > > where y1, y2, and x1-x3 are continuous variables, and x4 is a > binary variable. I am not absolutely sure I understand what you mean here. 2SLS is a single- equation method of estimation. Strictly speaking, if you want to apply it to the example above, then your first question is whether 2SLS applied to the y1 equation would be efficient in the class of of single-equation estimates even if some of the exogenous variables were binary or polynomials. Your second question is the same question but regarding the y2 equation. Hopefully someone will correct me if I'm wrong, but my recollection is that applied equation-by-equation, 2SLS is efficient in the class of single equation estimators (assuming some other conditions hold - more on that shortly). You can get efficiency gains over 2SLS if you estimate your system *as a system*, e.g., 3SLS or FIML. > I believe that 2SLS would yield consistent estimates in > the above > scenario. However, if not efficient, then what method (Stata > command) would > one want to use? I am dealing with repeated measures on subjects > (i.e., my > data are clustered) Here is where you lose efficiency with 2SLS. Clustering means you lose the independence of observations assumption needed for efficiency. -xtivreg- is one alternative; another is our (me, Kit Baum, Steve Stillman) -ivreg2- with the -cluster- and -gmm- options. The former is an IV approach that models the intra-group correlation as a "fixed effect" or "random effect"; the latter is a GMM approach that allows for intra-group correlation of an arbitrary form and is also robust to heteroskedasticity. Hope this helps. --Mark >, so I would want to use a command that could > address > this concern. Thanks. > > -- > James Shaw > Research Associate > College of Pharmacy > The University of Arizona > * > * 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**:**RE: st: 2SLS with nonlinear exogenous variables***From:*Mark Schaffer <M.E.Schaffer@hw.ac.uk>

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