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From |
John Neumann <neumannj@bu.edu> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Cross-Sectional Time Series |

Date |
Thu, 27 Jun 2002 12:29:33 -0400 |

Since I started the trouble :), I must enthusiastically make it a trio! Thanks all! John Mark Schaffer wrote: > Seconded. That was very instructive. Thanks! > > --Mark > > Quoting anirban basu <abasu@midway.uchicago.edu>: > > > Hi David and Vince, > > > > Thanks for your insights and helpful comments. This was a good > > learning > > experience.. > > > > Anirban > > > > ______________________________________ > > ANIRBAN BASU > > Doctoral Student > > Harris School of Public Policy Studies > > University of Chicago > > (312) 563 0907 (H) > > ________________________________________________________________ > > > > > > On Wed, 26 Jun 2002, Vince Wiggins, StataCorp wrote: > > > > > I have one additional comment in the continuing thread > > comparing the results > > > of -regress-, -xtreg, fe-, and -xtreg , re-. > > > > > > While I agree with the comparisons between the models > > presented by Mark > > > Schaffer <M.E.Schaffer@hw.ac.uk> and David Drukker > > <ddrukker@stata.com>, there > > > is a more mundane reason why the example presented by > > Anirban Basu > > > <abasu@midway.uchicago.edu> elicits virtually identical > > estimates from > > > -regress-, -xtreg, fe-, and -xtreg, re-. The short answer > > is they have to be > > > identical, at least to machine precision of the > > computations. > > > > > > Anirban Basu asks us to generate data in the following > > manner, > > > > > > . mat C= (1, 0.6, 0.6, 0.6 \ 0.6, 1, 0.6, 0.6 \ 0.6, > > 0.6, 1, 0.6 \ /* > > > */ 0.6, 0.6, 0.6, 1) > > > . drawnorm y1 y2 y3 y4, n(1000) means(1 3 4 7) corr(C) > > > . gen id=_n > > > . reshape long y , i(id) j(time) > > > > > > Anirban is using -drawnorm- to create 4 correlated variables > > and then > > > -reshape- to turn these into a panel data with 4 values for > > a single y. This > > > is a fine way to create data with a random effect. Here are > > the first three > > > panels: > > > > > > . list in 1/12 > > > > > > id time y > > > 1. 1 1 -.0939699 > > > 2. 1 2 2.265574 > > > 3. 1 3 2.323656 > > > 4. 1 4 6.053069 > > > 5. 2 1 1.367081 > > > 6. 2 2 3.062155 > > > 7. 2 3 4.830178 > > > 8. 2 4 7.105754 > > > 9. 3 1 1.145398 > > > 10. 3 2 4.087784 > > > 11. 3 3 3.99791 > > > 12. 3 4 6.942679 > > > > > > > > > Anirban, the asks us to try the OLS, fixed-effects, and > > random-effects > > > estimators on this data by typing, > > > > > > . regress y time > > > > > > . xtreg y time , i(id) fe > > > and, > > > . xtreg y time , i(id) re > > > > > > What is unusual about this model is that we are including > > -time- as a > > > regressor. Note that we have perfectly balanced panels of 4 > > observations > > > each, and that the variable -time- exactly repeats itself -- > > counting 1, 2, 3, > > > 4 in each panel. > > > > > > What does this mean for the fixed-effects (FE) > > transformation? The FE > > > transformation just subtracts the panel mean for each > > variable (dependent and > > > independent) from each value. The panel mean for time is > > 2.5 in every panel. > > > This means the the FE transformation just subtracts a > > constant value from > > > -time-. Subtracting a constant from a regressor does not > > have any effect on > > > its estimated coefficient. > > > > > > But wait, we also subtracted the panel means from the > > dependent variable y and > > > those means were not the same for each panel. As it turns > > out, when panels > > > are balanced, the FE transformation of any variable produces > > a variable that > > > has a regression coefficient of exactly 1 when regressed > > against the > > > untransformed variable. Thus, the relationship with a > > variable that has not > > > been transformed (like -time-, that had only a constant > > subtracted) remains > > > exactly the same. > > > > > > So, with only a single independent variable that repeats > > exactly in each > > > balanced panel, OLS and fixed-effects regression will > > produce the same > > > estimate of the coefficient on the regressor (within machine > > tolerance of the > > > different computations performed). > > > > > > Side-note: While I was aware of the behaviour of variables > > that repeat within > > > panel for balanced panels, I hadn't previously considered > > why the FE > > > transformation of the dependent variable has no effect. A > > little scribbling > > > on the white board from Bobby Gutierrez > > <rgutierrez@stata.com> shows that when > > > the FE transformation is expressed in matrix form it is > > idempotent for balanced > > > panels. That causes the transformation to essentially fall > > out of regression > > > of y on y-transformed leaving a coefficient of 1. > > > > > > What about the random-effects (RE) estimator? The GLS > > random-effects > > > estimator is just a matrix-weighted combination of the FE > > estimator and the > > > between-effects (BE) estimator. The BE estimator is a > > regression of the > > > panel-level mean of each variable (again, dependent and > > independent). As we > > > saw above, the panel-level mean for -time- is a constant 2.5 > > in every panel > > > and thus is collinear with the constant. This means that > > the between > > > estimator cannot estimate B_time and provides no additional > > information for > > > this coefficient. It has no contribution to the RE > > estimator. So, the RE > > > estimator must be identical to the FE estimator in a model > > with a single > > > covariate that repeats exactly within each balanced panel. > > > > > ________________________________________________________________ > > 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/ * * 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/

**References**:**Re: st: Cross-Sectional Time Series***From:*anirban basu <abasu@midway.uchicago.edu>

**Re: st: Cross-Sectional Time Series***From:*Mark Schaffer <M.E.Schaffer@hw.ac.uk>

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