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From |
"Reardon, Sean F." <sreardon@stanford.edu> |

To |
<statalist@hsphsun2.harvard.edu> |

Subject |
st: RE: RE: OLS, FE xtreg and the i() option |

Date |
Wed, 2 Mar 2005 14:20:15 -0800 |

robert -- in a fixed effects regression, if x is uncorrelated with the grouping variable (if mean(x) is the same across groups), the OLS and the fixed effects estimator will give the same coefficient estimate (but different standard errors). so if your x variable does not vary across years (mean(x) is constant over time), then -reg- and -xtreg- will give the same estimates. so from your results i would guess that your x-variable varies across countries, but not across years -- hence your year fixed effects will not be much different than your OLS estimates, but your country fixed effects estimates will be. note: a constant value of mean(x) across groups is sufficient, but not necessary for OLS and the fixed effects estimator to give the same coefficient estimates: to see this, let i index observations, let j be a grouping variable, and Xj_bar be the mean of X in group j) fiting the following model using OLS yields the same point estimate for the coefficient of X as the fixed effects estimator Yij = b0 + b1(Xj_bar) + b2(Xij - Xj_bar) = b0 + (b1 - b2)(Xj_bar) + b2(Xij) note that if Xj_bar is the same for all j, then the (b1 - b2)(Xj_bar) term will be absorbed in the intercept and this will be the same as fitting Yij = b0 + b2(Xij) using OLS. likewise, if b1=b2, then the (b1 - b2)(Xj_bar) term will drop out and this will be the same as fitting Yij = b0 + b2(Xij) using OLS. so OLS will give the same estimates as the fixed effects estimator if either a) Xj_bar is constant across groups or b) the between-group slope is the same as the within-group slope (i.e., b1=b2). sean. _____________________________ sean f. reardon associate professor of education and (by courtesy) sociology school of education 485 lasuen mall, #315 stanford university stanford, ca 94305-3096 650.736.8517 (office phone) 650.725.7412 (office fax) sean.reardon@stanford.edu _____________________________ -----Original Message----- From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Gustavo Sanchez Sent: Wednesday, March 02, 2005 10:34 AM To: statalist@hsphsun2.harvard.edu Subject: st: RE: OLS, FE xtreg and the i() option Robert [robboh@gmail.com] asked: >I have been working on a panel dataset, looking at the relationship >between inflation and openness, but am slightly confused at to the >results I have been finding. When running OLS and Fixed-Effects (FE) >estimations completely different results are found. However, when the >i() option for the FE estimation is set to the year (which it >shouldn't be; it should be the country code), the panel data results >are almost exactly equal to OLS. >Am I making an error in my use of Stata, or is this a kind of >'pooling' (when setting i() to the year), implying that the 'correct' >value is as found by the 'correct' FE estimation. I have not been >able to find any direct information on this in the Stata documentation >or the net in general - any comments that you can give will be much >appreciated. * * 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/ * * 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/

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