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

To |
statalist@hsphsun2.harvard.edu |

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

Date |
Tue, 25 Jun 2002 19:03:01 -0400 |

Anirban and Mark, I concur that -reg, robust - and -xtreg, fe- will not yield the same coefficients, at least in my experience. And I'd be shocked if the results of - xtreg, re- were the same as well ... Thanks for all of your insights on this! John anirban basu wrote: > On Tue, 25 Jun 2002, Mark Schaffer wrote: > > > > > Not quite sure what you mean, so apologies if I'm off target. The > > coefficient estimates with -regress- won't be the same as with > > -xtreg, fe- (unless the former is estimating the same model by > > explicitly including the fixed effects as dummy vars). Both sets of > > coefficients will be different again from those produced by > > -xtreg, re-. > > > > --Mark > > You may be right about this. However, I did get the same coeff from > -regress-, xtreg, fe and xtreg, re using a simulated dataset with > exchangeable corr and no dummy vars. ALso, I got different coeffs by > running an exponential corr model as expected.. Here are the details. I > may have missed something here..Thanks for your input, > > Anirban > > . 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) > (obs 1000) > > . gen id=_n > > . reshape long y , i(id) j(time) > (note: j = 1 2 3 4) > > Data wide -> long > ----------------------------------------------------------------------------- > Number of obs. 1000 -> 4000 > Number of variables 5 -> 3 > j variable (4 values) -> time > xij variables: > y1 y2 ... y4 -> y > ----------------------------------------------------------------------------- > > . > . reg y time, cluster(id) > > Regression with robust standard errors Number of obs =4000 > F( 1,999) =42518.72 > Prob > F =0.0000 > R-squared =0.7897 > Number of clusters (id) = 1000 Root MSE =1.0946 > > ------------------------------------------------------------------------------ > | Robust > y | Coef. Std. Err. t P>|t| [95% Conf. Interval] > -------------+---------------------------------------------------------------- > time | 1.896646 .0091981 206.20 0.000 1.878596 1.914696 > _cons | -.9866896 .0358667 -27.51 0.000 -1.057072 -.916307 > ------------------------------------------------------------------------------ > > . > . tsset id time > panel variable: id, 1 to 1000 > time variable: time, 1 to 4 > . iis id > . tis time > > . xtreg y time, fe > > Fixed-effects (within) regression Number of obs =4000 > Group variable (i) : id Number of groups =1000 > > R-sq: within = 0.9027 Obs per group: min =4 > between = 0.0000 avg =4.0 > overall = 0.7897 max =4 > > F(1,2999) =27835.94 > corr(u_i, Xb) = -0.0000 Prob > F =0.0000 > > ------------------------------------------------------------------------------ > y | Coef. Std. Err. t P>|t| [95% > Conf. Interval] > -------------+---------------------------------------------------------------- > time | 1.896646 .011368 166.84 0.000 1.874356 1.918936 > _cons | -.9866896 .0311325 -31.69 0.000 -1.047733 -.9256464 > -------------+---------------------------------------------------------------- > sigma_u | .84490704 > sigma_e | .80383774 > rho | .52489398 (fraction of variance due to u_i) > ------------------------------------------------------------------------------ > F test that all u_i=0: F(999, 2999) = 4.42 Prob > F =0.0000 > > . xtreg y time, re > > Random-effects GLS regression Number of obs =4000 > Group variable (i) : id Number of groups =1000 > > R-sq: within = 0.9027 Obs per group: min =4 > between = 0.0000 avg =4.0 > overall = 0.7897 max =4 > > Random effects u_i ~ Gaussian Wald chi2(1) =27835.94 > corr(u_i, X) = 0 (assumed) Prob > chi2 =0.0000 > > ------------------------------------------------------------------------------ > y | Coef. Std. Err. z P>|z| [95% Conf. Interval] > -------------+---------------------------------------------------------------- > time | 1.896646 .011368 166.84 0.000 1.874365 1.918927 > _cons | -.9866896 .0390072 -25.30 0.000 -1.063142 -.9102369 > -------------+---------------------------------------------------------------- > sigma_u | .74318848 > sigma_e | .80383774 > rho | .46085639 (fraction of variance due to u_i) > ------------------------------------------------------------------------------ > > . prais y time > > Number of gaps in sample: 999 (gap count includes panel changes) > (note: computations for rho restarted at each gap) > > Iteration 0: rho = 0.0000 > Iteration 1: rho = 0.4034 > Iteration 2: rho = 0.4136 > Iteration 3: rho = 0.4140 > Iteration 4: rho = 0.4140 > Iteration 5: rho = 0.4140 > > Prais-Winsten AR(1) regression -- iterated estimates > > Source | SS df MS Number of obs =4000 > -------------+------------------------------ F( 1, 3998) =8914.61 > Model | 8913.21448 1 8913.21448 Prob > F =0.0000 > Residual | 3997.37575 3998 .999843859 R-squared =0.6904 > -------------+------------------------------ Adj R-squared =0.6903 > Total | 12910.5902 3999 3.22845467 Root MSE =.99992 > > ------------------------------------------------------------------------------ > y | Coef. Std. Err. t P>|t| [95%Conf. Interval] > -------------+---------------------------------------------------------------- > time | 1.953367 .0157109 124.33 0.000 1.922565 1.984169 > _cons | -1.061051 .0456138 -23.26 0.000 -1.15048 -.9716229 > -------------+---------------------------------------------------------------- > rho | .4140074 > ------------------------------------------------------------------------------ > Durbin-Watson statistic (original) 0.925711 > Durbin-Watson statistic (transformed) 1.672284 > > > > > > > > > > > > Anirban > > > > > > ______________________________________ > > > ANIRBAN BASU > > > Doctoral Student > > > Harris School of Public Policy Studies > > > University of Chicago > > > (312) 563 0907 (H) > > > ________________________________________________________________ > > > > > > > > > On Tue, 25 Jun 2002, Mark Schaffer wrote: > > > > > > > Hi everybody. > > > > > > > > Just a couple of clarifying details on -cluster- vs. -xtreg- > > > and > > > > Anirban's response to John. > > > > > > > > The -cluster- option for -regress- doesn't really impose a > > > particular > > > > within-cluster correlation structure on the data. If I > > > understand it > > > > correctly, what -cluster- does instead is loosen the usual > > > assumption > > > > of independence of observations to independence of clusters. > > > The > > > > correlation between observations within clusters can be > > > arbitrary. > > > > The way this works is basically by treating all the > > > observations in a > > > > cluster as a kind of "super-observation" and then applying > > > the robust > > > > ("sandwich") formula to these super-observations in order to > > > > > > > calculate the standard errors of the coefficients produced > > > by - > > > > regress-. See the manual entry for -regress-, p. 87. > > > > > > > > The estimated coefficients (the betas) produced by -regress- > > > are the > > > > same whether or not the -cluster- option is used; the only > > > thing that > > > > is different is the standard errors. > > > > > > > > With fixed effects, you _do_ impose a particular correlation > > > > > > > structure, namely all the observations within a cluster > > > share U(k) in > > > > Anirban's notation. If you use -xtreg- with -fe- to > > > estimate, Stata > > > > does not, however, use a first-difference estimator - it > > > uses a fixed > > > > effects estimator. In other words, it doesn't > > > first-difference to > > > > get rid of the fixed effects, it uses the mean-deviation > > > > transformation to get rid of them. > > > > > > > > Hope this helps. > > > > > > > > --Mark > > > > > > > > Quoting anirban basu <abasu@midway.uchicago.edu>: > > > > > > > > > Hi John, > > > > > > > > > > > > > > > With reg command and cluster option, one basically imposes > > > an > > > > > exchangeable > > > > > correlation structure on the data. i.e assume corr (y(i), > > > > > y(j)) = rho, > > > > > where i ne j and i,j are any two observation from the > > > same > > > > > cluster. Rho > > > > > is constant for every pair of observation within a > > > cluster. > > > > > So, one can > > > > > visuaize it in terms of a random effects model where : > > > > > > > > > > Y(k) = Xb + U(k) + e, where k represents clusters and U(k) > > > is > > > > > a > > > > > cluster-specific random effect that is common to all > > > > > observation in that > > > > > cluster. However, -reg- does not give estimates of this > > > random > > > > > effect. It > > > > > just estimates -betas- assuming this structure. > > > > > > > > > > However, this estimation is correct only if U(k) are > > > > > uncorrelated with > > > > > Xs. i.e. the unobserved characteristics of a cluster over > > > time > > > > > is > > > > > uncorrelated with the X over time. If not then fixed > > > effects > > > > > is useful. > > > > > > > > > > > > > > > With fixed effects, one evades the correlation problem by > > > > > taking > > > > > differences. i.e for any cluster k: > > > > > > > > > > Y(ik) - Y(1k) = [X(ik) - X(1k)]b + [e(ik) - e(1k)] > > > > > > > > > > Note that by taking the difference, the unobserved U(k) is > > > > > eliminated. > > > > > However, fixed effects assume the U(k) is fixed over time > > > for > > > > > any cluster > > > > > k. i.e. the unobserved characteristics of a cluster is not > > > > > changing over > > > > > time. Also, since we are taking a difference, fixed > > > effects > > > > > model cannot > > > > > estimate the betas for baseline covariates since they > > > cancel > > > > > out in the > > > > > difference. > > > > > > > > > > Hope this helps, > > > > > > > > > > Anirban > > > > > > > > > > > > > > > > > > > > ______________________________________ > > > > > ANIRBAN BASU > > > > > Doctoral Student > > > > > Harris School of Public Policy Studies > > > > > University of Chicago > > > > > (312) 563 0907 (H) > > > > > > > > ________________________________________________________________ > > > > > > > > > > > > > > > On Tue, 25 Jun 2002, John Neumann wrote: > > > > > > > > > > > Hello all, > > > > > > > > > > > > Since I frequently see panel data questions flying > > > around > > > > > the > > > > > > list, I'm thinking that some of you can provide me with > > > a > > > > > > very succinct answer to the following question, and in > > > so > > > > > > doing clarify conceptually for me the data-related > > > issue: > > > > > > > > > > > > I have data on investment products, by year. Not all > > > > > > products have data in each year. The dependent > > > > > > variable is scaled in such a way as to make time series > > > > > > variation in its levels of no concern. Here's the > > > question: > > > > > > > > > > > > What is the difference between using the reg command, > > > > > > with the robust and cluster option, vs. the xtreg > > > command > > > > > > fixed effects model? The cluster variable using reg > > > would > > > > > > naturally be the i( ) parameter for xtreg ... > > > > > > > > > > > > Thanks! > > > > > > > > > > > > John Neumann > > > > > > Boston University > > > > Prof. Mark Schaffer > > Director, CERT > > Department of Economics, School of Management > > 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.som.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/ * * 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>

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