Andrea
all your random effect estimates (Wooldridge's auxiliary regression
included) are actually OLS estimates. This happens because in the first
stage of the GLS computation the estimate of var_u computed from within and
between residuals is negative and Stata replaces it with zero. This is
well documented in the [xt] Stata manual and may due to bad specification
or small sample problems. One solution may be to estimate the re model using
the -mle- option for -xtreg-.
The BP test is still informative because it uses OLS residuals
(it's a lagrange multiplier test and as such is carried out
under the null).
Giovanni
Scrive andrea fracasso <andrea.fracasso@gmail.com>:
> Hi.
> I am puzzled by the results I get from running Breusch Pagan and
> Hausman tests on my (unbalanced) panel data sample.
> The results of the tests are quite sensitive to the correction applied
> to the standard errors, and somehow weird (at least, to me).
> The regressors I use are a rate of growth (difa142), and two
> interaction terms, that is in2t=var*difa142 and in2t2=(var^2)*difa142
>
>
> I write some comments and questions between the results. I believe
> that these results exhibit a good deal of the problems discussed
> separately by listservers. However, being them all together, I am not
> sure how to interpret the results and how to procede.
>
> I estimate xtreg difa298 difa142 in2t in2t2, re cluster(co)
>
> Random-effects GLS regression Number of obs =
> 772
> Group variable (i): co Number of groups =
> 73
>
> R-sq: within = 0.3139 Obs per group: min =
> 7
> between = 0.6914 avg =
> 10.6
> overall = 0.3632 max =
> 11
>
> Random effects u_i ~ Gaussian Wald chi2(3) =
> 97.53
> corr(u_i, X) = 0 (assumed) Prob > chi2 =
> 0.0000
>
> (Std. Err. adjusted for 73 clusters in
> co)
> ------------------------------------------------------------------------------
> | Robust
> difa298 | Coef. Std. Err. z P>|z| [95% Conf.
> Interval]
> -------------+----------------------------------------------------------------
> difa142 | 1.010826 .1579594 6.40 0.000 .7012313
> 1.320421
> in2t | -4.775301 2.948644 -1.62 0.105 -10.55454
> 1.003935
> in2t2 | 24.42007 14.02081 1.74 0.082 -3.060215
> 51.90035
> _cons | -.0658962 .1802725 -0.37 0.715 -.4192238
> .2874315
> -------------+----------------------------------------------------------------
> sigma_u | 0
> sigma_e | 6.3054774
> rho | 0 (fraction of variance due to u_i)
> ------------------------------------------------------------------------------
>
> I run BP xttest0
>
> Breusch and Pagan Lagrangian multiplier test for random effects:
>
> difa298[co,t] = Xb + u[co] + e[co,t]
>
> Estimated results:
> | Var sd = sqrt(Var)
> ---------+-----------------------------
> difa298 | 60.12951 7.754322
> e | 39.75904 6.305477
> u | 0 0
>
> Test: Var(u) = 0
> chi2(1) = 5.04
> Prob > chi2 = 0.0248
> The BP test suggests the existence of an individual effect even if
> sigma_u is 0. Why?
> I believe that a RE with rho=0 is an OLS!
> (Btw, I checked for serial correlation with -xtserial- and serial
> autocorrelation is rejected)
>
> The Hausman test (i.e. hausman fixed random) does not produce proper
> results because the difference of the variances is not positive
> definite.
>
> Test: Ho: difference in coefficients not systematic
>
> chi2(3) = (b-B)'[(V_b-V_B)^(-1)](b-B)
> = -0.02 chi2<0 ==> model fitted on these
> data fails to meet the asymptotic
> assumptions of the Hausman test;
> see suest for a generalized test
>
> I follow Wooldridge's suggestion and calculate the Hausman test by hand.
> I add to the regressors the averages over time of the time-varying
> regressors and test their significance in a random effects model.
> In the following case, I use the standard errors corrected by means of
> the -cluster- option.
>
> xtreg difa298 difa142 in2t in2t2 adifa142 ain2t ain2t2, re cluster(co)
>
> Random-effects GLS regression Number of obs =
> 772
> Group variable (i): co Number of groups =
> 73
>
> R-sq: within = 0.3140 Obs per group: min =
> 7
> between = 0.7037 avg =
> 10.6
> overall = 0.3649 max =
> 11
>
> Random effects u_i ~ Gaussian Wald chi2(6) =
> 468.98
> corr(u_i, X) = 0 (assumed) Prob > chi2 =
> 0.0000
>
> (Std. Err. adjusted for 73 clusters in
> co)
> ------------------------------------------------------------------------------
> | Robust
> difa298 | Coef. Std. Err. z P>|z| [95% Conf.
> Interval]
> -------------+----------------------------------------------------------------
> difa142 | .9954723 .1916506 5.19 0.000 .6198441
> 1.3711
> in2t | -4.693986 3.283152 -1.43 0.153 -11.12884
> 1.740873
> in2t2 | 23.39439 14.53121 1.61 0.107 -5.086252
> 51.87504
> adifa142 | .0635942 .2096473 0.30 0.762 -.3473069
> .4744954
> ain2t | -2.534238 5.876584 -0.43 0.666 -14.05213
> 8.983655
> ain2t2 | 29.47941 31.16784 0.95 0.344 -31.60843
> 90.56725
> _cons | -.0055123 .181651 -0.03 0.976 -.3615417
> .3505171
> -------------+----------------------------------------------------------------
> sigma_u | 0
> sigma_e | 6.3054774
> rho | 0 (fraction of variance due to u_i)
> ------------------------------------------------------------------------------
>
> Individually, the averages adifa142, ain2t, ain2t2 are massively
> insignificant.
> However, the wald test below reject the hypothesis of them being jointly 0.
>
> testparm adifa142 ain2t ain2t2
>
> ( 1) adifa142 = 0
> ( 2) ain2t = 0
> ( 3) ain2t2 = 0
>
> chi2( 3) = 7.52
> Prob > chi2 = 0.0570
>
> This would be in favour of a fixed effect model (at almost 5% sig.lev.).
>
> If I run the same r.e. model correcting with robust instead of cluster, I
> get
>
> xtreg difa298 difa142 in2t in2t2 adifa142 ain2t ain2t2, re robust
>
> Random-effects GLS regression Number of obs =
> 772
> Group variable (i): co Number of groups =
> 73
>
> R-sq: within = 0.3140 Obs per group: min =
> 7
> between = 0.7037 avg =
> 10.6
> overall = 0.3649 max =
> 11
>
> Random effects u_i ~ Gaussian Wald chi2(6) =
> 214.91
> corr(u_i, X) = 0 (assumed) Prob > chi2 =
> 0.0000
>
> ------------------------------------------------------------------------------
> | Robust
> difa298 | Coef. Std. Err. z P>|z| [95% Conf.
> Interval]
> -------------+----------------------------------------------------------------
> difa142 | .9954723 .1559118 6.38 0.000 .6898907
> 1.301054
> in2t | -4.693986 3.173922 -1.48 0.139 -10.91476
> 1.526787
> in2t2 | 23.39439 13.06566 1.79 0.073 -2.213824
> 49.00261
> adifa142 | .0635942 .2219267 0.29 0.774 -.371374
> .4985625
> ain2t | -2.534238 7.728836 -0.33 0.743 -17.68248
> 12.614
> ain2t2 | 29.47941 62.91061 0.47 0.639 -93.82311
> 152.7819
> _cons | -.0055123 .2277465 -0.02 0.981 -.4518874
> .4408627
> -------------+----------------------------------------------------------------
> sigma_u | 0
> sigma_e | 6.3054774
> rho | 0 (fraction of variance due to u_i)
> ------------------------------------------------------------------------------
>
> Each of the three averages is individually insignificant and, this
> time, they are also jointly insignificant.
> ( 1) adifa142 = 0
> ( 2) ain2t = 0
> ( 3) ain2t2 = 0
>
> chi2( 3) = 0.39
> Prob > chi2 = 0.9418
>
> The result of this test are at odds with those reported above with the
> correction -cluster-.
>
> I reckon that in2t and in2t2 (and therefore their averages too) are
> very closely correlated. However I do not see why this should affect
> only the results of the wald tests after the -cluster- corrected
> standard errors regressions.
> Has it anything ro do with the fact that these variables are time
> invariant and the cluster option sucks up all the degrees of freedom
> at the group level?
>
> As I will show below, the within estimation would suggest a very low
> correlation between u_i and xb. Such findings seem to support a RE
> model. In addition, the RE and FE models produce very similar
> coefficients, as it can be seen below.
>
> xtreg difa298 difa142 in2t in2t2 adifa142 ain2t ain2t2, fe cluster(co)
>
> Fixed-effects (within) regression Number of obs =
> 728
> Group variable (i): co Number of groups =
> 69
>
> R-sq: within = 0.3705 Obs per group: min =
> 7
> between = 0.7088 avg =
> 10.6
> overall = 0.4242 max =
> 11
>
> F(3,68) =
> 32.44
> corr(u_i, Xb) = 0.0700 Prob > F =
> 0.0000
>
> (Std. Err. adjusted for 69 clusters in
> co)
> ------------------------------------------------------------------------------
> | Robust
> difa300 | Coef. Std. Err. t P>|t| [95% Conf.
> Interval]
> -------------+----------------------------------------------------------------
> difa142 | .9328421 .1833901 5.09 0.000 .5668929
> 1.298791
> in2t | -4.626382 3.230345 -1.43 0.157 -11.07244
> 1.819671
> in2t2 | 23.52781 14.22296 1.65 0.103 -4.853671
> 51.90928
> _cons | -.1133588 .0220161 -5.15 0.000 -.1572912
> -.0694264
> -------------+----------------------------------------------------------------
> sigma_u | 1.5468984
> sigma_e | 5.3383765
> rho | .07746212 (fraction of variance due to u_i)
> ------------------------------------------------------------------------------
>
>
> In this model the estimated sigma_u is 1.54, not 0 as with the RE.
> Should I use the FE measure of sigma_u and build the RE model by
> quasi-demeaning the series by hand (and hence run the Hausman test by
> adding the averages overt time as I have done before) ?
>
> I would be extremely grateful if anyone could help me out interpreting
> these results.
> I am stuck since I can't choose which results to consider.
>
> This is even worse when the BP test fails to reject the hypothesis of
> no-individual effect, yet the hausman test is strongly in favour of a
> within model.
>
> many many thanks,
> andrea
> *
> * 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/
>
--
Giovanni S.F. Bruno
http://ideas.repec.org/e/pbr136.html
Istituto di Economia Politica, Università Bocconi
Via U. Gobbi, 5, 20136 Milano
Italy
tel. + 02 5836 5411
fax. + 02 5836 5438
*
* 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/