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Re: st: Same results OLS and Random Effects


From   John Antonakis <john.antonakis@unil.ch>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Same results OLS and Random Effects
Date   Sat, 19 Jun 2010 21:07:44 +0200

Well, it seems that you have a high ratio of within to between variation, which is why rho = 0 (rho is another term for Intraclass Correlation Coefficient). Try running the following to see what it gives you (for rho and the confidence interval):

loneway y zid

To better grasp the implication of ICC = 0, one formula to calculate the ICC is (after estimating a basic ANOVA):

(MSb - MSw) / ((MSb + (k-1)*MSw))

Note: k = average group size; MS=mean square; b=between; w=within.

The rho in xtreg is calculated in a slightly different way.

Also, after running xtreg, what do you get when you run -xttest0-? Next, after estimating the random-effects estimator ideally with cluster-robust SE, what does -xtoverid- give you?. If the test is significant, you must use fixed-effects (in the context of xtreg, fe or with OLS and explicit dummies; and it would be best to also use a cluster correction for the standard errors, because even if you don't have between-group variation nor random effects, within cluster-disturbances may still be correlated).
HTH,
John.

____________________________________________________

Prof. John Antonakis, Associate Dean Faculty of Business and Economics
Department of Organizational Behavior
University of Lausanne
Internef #618
CH-1015 Lausanne-Dorigny
Switzerland

Tel ++41 (0)21 692-3438
Fax ++41 (0)21 692-3305

Faculty page:
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Personal page:
http://www.hec.unil.ch/jantonakis
____________________________________________________



On 19.06.2010 19:18, Pelkowski, Jodi wrote:
Nature of problem:

In running xtreg with random effects,  sigma_u and rho are reports as “0”.   I obtain the exact same coefficients and standard errors when OLS is run.   (So basically Stata is defaulting to OLS).  There is no problem using fixed effects.     When the same regression is estimated using the Limdep regression package, sigma_u and rho are both >0 and the coefficients  and standard errors differ from OLS.

Why is Stata defaulting to OLS.   Whom do I believe Stata or Limdep?

Note:  I checked to see if there was anything strange with the regressors or the id variable.   There isn’t.  For example if I switch the dependent variable with a regressor, Stata works fine.
The original dependent variable takes on integer values between 1 and 255 with lots of variation.  The sample size is 931 and there are 108 groups.


Below is a simplified version of regression that was run:


. xtset zid
       panel variable:  zid (unbalanced)

. xtreg y x stars,  re

Random-effects GLS regression                   Number of obs      =       931
Group variable: zid                             Number of groups   =       108

R-sq:  within  = 0.0193                         Obs per group: min =         1
       between = 0.1555                                        avg =       8.6
       overall = 0.0534                                        max =        37

Random effects u_i ~ Gaussian                   Wald chi2(2)       =     52.36
corr(u_i, X)       = 0 (assumed)                Prob > chi2        =    0.0000

------------------------------------------------------------------------------
           y |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
           x |  -.5014859   .2454555    -2.04   0.041    -.9825698    -.020402
       stars |  -14.90484   2.827657    -5.27   0.000    -20.44694    -9.36273
       _cons |   207.6687   17.41683    11.92   0.000     173.5324    241.8051
-------------+----------------------------------------------------------------
     sigma_u |          0
     sigma_e |  73.292219
         rho |          0   (fraction of variance due to u_i)


 . sum y x stars zid

    Variable |       Obs        Mean    Std. Dev.       Min        Max
-------------+--------------------------------------------------------
           y |       931    120.6498    74.36455          1        255
           x |       931    78.77133    10.84436      44.01     106.93
       stars |       931     3.18797    .9413473          1          5
         zid |       931    57.77336    32.22844          1        114
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