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Re: st: Fixed Effect Estimation Results


From   "Rodrigo Alfaro" <ralfaro76@hotmail.com>
To   <statalist@hsphsun2.harvard.edu>
Subject   Re: st: Fixed Effect Estimation Results
Date   Tue, 4 Apr 2006 14:22:39 -0400

Joana

I have some questions about your problem: (1) how do you get u_i? I think that you are using "\hat u_i"... in this case (2) did you create this fixed-effects measures using fe or re model?, in any case \hat u_i = y_i - x_i*\hat b, where \hat b is fe or re coefficient. (3) Finally as you can see \hat u_i is correlated with x_i*\hat b (by construction!!). Indeed the correlation is -1, why did you get -0.9899? I think the reason is because you did the correlation in total variation instead to use the between variation, which is one way to get the correlation of u_i versus other variable.

Rodrigo.

----- Original Message ----- From: "Joana Quina" <joana.statalist@gmail.com>
To: <statalist@hsphsun2.harvard.edu>
Sent: Tuesday, April 04, 2006 12:13 PM
Subject: Re: st: Fixed Effect Estimation Results



Dear William,

Firstly, I apologise for not having reported my results.  The ones you
quote are the ones obtained by Sam, who initiated this thread.

My results are shown below.  The corr is very high (-0.9899) and the
within R2 is 0.4587.  There are *no* extra variables in the
random-effects estimation.  A similar model specification has been
used in the literature.

Also, I found that it is the "lpop" variable that is driving the high
correlation result - omitting it surprisingly *reduces* the
correlation.

I have re-run my regressions several times and always obtain the same
results. I regularly check updates (a while ago there was a problem
with xtreg, which was corrected).

Joana

. xtreg lbeda_pc lpop lgdp_pc_ppp elrsacw polity_n pts_s_n corrupt
milm_j us_un_fr
iend japan_un_friend uk_un_friend france_un_friend  indep, re
Random-effects GLS regression Number of obs = 96
Group variable (i): id Number of groups = 27

R-sq: within = 0.4093 Obs per group: min = 2
between = 0.6133 avg = 3.6
overall = 0.5911 max = 4

Random effects u_i ~ Gaussian Wald chi2(12) = 73.52
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000

------------------------------------------------------------------------------
lbeda_pc | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lpop | -.6168131 .1338557 -4.61 0.000 -.8791654 -.3544608
lgdp_pc_ppp | -.2690165 .1925044 -1.40 0.162 -.6463181 .1082851
elrsacw | .1004888 .1544715 0.65 0.515 -.2022697 .4032473
polity_n | .0293785 .0180981 1.62 0.105 -.0060931 .0648501
pts_s_n | .0405079 .0644439 0.63 0.530 -.0857998 .1668155
corrupt | -.1543259 .0422096 -3.66 0.000 -.2370552 -.0715967
milm_j | -.0010754 .0014974 -0.72 0.473 -.0040103 .0018594
us_un_friend | -.0329801 .0127515 -2.59 0.010 -.0579725 -.0079877
japan_un_f~d | .0455285 .0226189 2.01 0.044 .0011962 .0898608
uk_un_friend | .0178181 .0290755 0.61 0.540 -.0391689 .0748052
france_un_~d | .0135801 .0212409 0.64 0.523 -.0280514 .0552116
indep | -.0052071 .009476 -0.55 0.583 -.0237797 .0133656
_cons | 1.744271 2.436455 0.72 0.474 -3.031092 6.519634
-------------+----------------------------------------------------------------
sigma_u | .68013164
sigma_e | .29411034
rho | .84246212 (fraction of variance due to u_i)
------------------------------------------------------------------------------

. est store random2

. xtreg lbeda_pc lpop lgdp_pc_ppp elrsacw polity_n pts_s_n corrupt
milm_j us_un_fr

iend japan_un_friend uk_un_friend france_un_friend  indep, fe
Fixed-effects (within) regression Number of obs = 96
Group variable (i): id Number of groups = 27

R-sq: within = 0.4587 Obs per group: min = 2
between = 0.5312 avg = 3.6
overall = 0.5104 max = 4

F(12,57) = 4.03
corr(u_i, Xb) = -0.9899 Prob > F = 0.0002

------------------------------------------------------------------------------
lbeda_pc | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lpop | -4.848811 2.22036 -2.18 0.033 -9.295005 -.4026177
lgdp_pc_ppp | -.2184703 .3257575 -0.67 0.505 -.8707884 .4338478
elrsacw | .3184507 .1787963 1.78 0.080 -.0395826 .6764841
polity_n | .0598919 .0217173 2.76 0.008 .0164037 .1033801
pts_s_n | .1013231 .074363 1.36 0.178 -.0475863 .2502325
corrupt | -.1579303 .0489601 -3.23 0.002 -.2559712 -.0598893
milm_j | -.0005835 .0016394 -0.36 0.723 -.0038663 .0026994
us_un_friend | -.0261931 .0134911 -1.94 0.057 -.0532086 .0008224
japan_un_f~d | .0407745 .0305656 1.33 0.188 -.0204322 .1019811
uk_un_friend | .0328692 .0323695 1.02 0.314 -.0319497 .0976881
france_un_~d | -.0031448 .0282499 -0.11 0.912 -.0597143 .0534247
indep | .1052638 .0703668 1.50 0.140 -.0356432 .2461709
_cons | 6.981901 4.983844 1.40 0.167 -2.998075 16.96188
-------------+----------------------------------------------------------------
sigma_u | 4.8302321
sigma_e | .29411034
rho | .99630617 (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(26, 57) = 13.71 Prob > F = 0.0000

. est store fixed2

. hausman fixed2 random2

---- Coefficients ----
| (b) (B) (b-B) sqrt(diag(V_b-V_B))
| fixed2 random2 Difference S.E.
-------------+----------------------------------------------------------------
lpop | -4.848811 -.6168131 -4.231998 2.216321
lgdp_pc_ppp | -.2184703 -.2690165 .0505462 .2627927
elrsacw | .3184507 .1004888 .2179619 .0900371
polity_n | .0598919 .0293785 .0305134 .0120043
pts_s_n | .1013231 .0405079 .0608153 .0371059
corrupt | -.1579303 -.1543259 -.0036043 .0248082
milm_j | -.0005835 -.0010754 .000492 .0006674
us_un_friend | -.0261931 -.0329801 .006787 .0044057
japan_un_f~d | .0407745 .0455285 -.004754 .0205583
uk_un_friend | .0328692 .0178181 .0150511 .0142267
france_un_~d | -.0031448 .0135801 -.0167249 .0186247
indep | .1052638 -.0052071 .1104709 .0697258
------------------------------------------------------------------------------
b = consistent under Ho and Ha; obtained from xtreg
B = inconsistent under Ha, efficient under Ho; obtained from xtreg

Test: Ho: difference in coefficients not systematic

chi2(12) = (b-B)'[(V_b-V_B)^(-1)](b-B)
= 9.04
Prob>chi2 = 0.6999

On 04/04/06, William Gould, Stata <wgould@stata.com> wrote:

Joana Quina <joana.statalist@gmail.com> reports,

1. She has estimated the parameters of a model using -xtreg, fe- and
that the reported correlation between u_i and X_ij*b is .9249.

2. She has estimated the parameters of the same same model on
the same data. She then performs a Hausman test that fails to
reject random effects.

She writes,

> It seems counter-intuitive. Any suggestions would be much appreciated.

It certainly does seem counterintuitive. My first reaction is to suggest
Joana check her work.

Let's first understand just how counterintuitive this is. The correlation
between u_i and X_ij*b is .9249. Now let's use an estimation method that
constrains that correlation to be 0. X_ij is fixed, so the only thing that
can give is b. The estimated b has got to change. The Hausman tests basis
its calculation on the change in b, and it reports that the change is small,
relative to variance.

That could could mean is that the variance is large, so large as to suggest
that the model, estimated either way, is not worth much. But Joana showed us
(1) and the within R^2 was .6385, so let's dimiss that.

However, X_ij is *NOT* necessarily fixed. Joana could have included extra
variables in the random-effects estimation, variables whose coefficients could
not be estimated by the fixed-effects estimation. In that case, the result is
not counterintuitive at all. Omit those variables, as done in the
fixed-effects estimation, and u_i is correlated. Include them, and the
correlation vanishes. Said differently, the subset of the b's estimated by
both estimators did not change, and the extra b's estimated by the
random-effects estimator eliminated the correlation. This is exactly what one
hopes will happen if one has a well-specified model.

Is that what happened?

-- Bill
wgould@stata.com
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