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From |
anirban basu <abasu@midway.uchicago.edu> |

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

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

Date |
Tue, 25 Jun 2002 17:36:48 -0500 (CDT) |

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

**Re: st: Cross-Sectional Time Series***From:*John Neumann <neumannj@bu.edu>

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

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