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Re: st: Panel Data-FIXED, RANDOM EFFECTS and Hausman Test
With a small number of nations and more years than nations you may be better off using panel-corrected standard errors than the approach you are taking. David Greenberg, Sociology Department, New York University
----- Original Message -----
From: Muhammad Billal Malik <[email protected]>
Date: Thursday, February 26, 2009 2:20 pm
Subject: st: Panel Data-FIXED, RANDOM EFFECTS and Hausman Test
To: [email protected]
> I am having some problems with my econometrics based dissertation. I
> doing a panel data on 12 sub-saharan african nations, with 6 variables
> over a 17 year time period.
>
> I am using a simple log log model to test to see if one of my
> variables lx2 (tourism receipts) has a positive affect on GDP. I have
> run a pooled regression, then fixed effects between and within, and
> finally a random effects. I have then carried out a Hausman test and
> achieved a negative value, which has confused me more. I was wondering
> what do I do, as in what model shall I choose? I have attached my
> STATA output so you can see if I have gone through the right steps.
>
> I will really appreciate if you can help me,
>
> Kind Regards,
>
> Mohammud
>
>
> Carrying out a pooled data regression
> . regress ly lx1 lx2 lx3 lx4 lx5 lx6
>
> Source | SS df MS Number of obs =
> 57
> -------------+------------------------------ F( 6, 50) =
> 52.04
> Model | 59.1406489 6 9.85677481 Prob > F =
> 0.0000
> Residual | 9.47031674 50 .189406335 R-squared =
> 0.8620
> -------------+------------------------------ Adj R-squared =
> 0.8454
> Total | 68.6109656 56 1.22519581 Root MSE =
> .43521
>
> ------------------------------------------------------------------------------
> ly | Coef. Std. Err. t P>|t| [95% Conf. Interval]
> -------------+----------------------------------------------------------------
> lx1 | .173204 .0545574 3.17 0.003 .0636223
> .2827857
> lx2 | .0816157 .0737985 1.11 0.274 -.0666129
> .2298442
> lx3 | 1.207415 .7336368 1.65 0.106 -.2661382
> 2.680968
> lx4 | .8167941 .0985049 8.29 0.000 .6189412
> 1.014647
> lx5 | 4.014936 1.263028 3.18 0.003 1.478069
> 6.551803
> lx6 | .2619006 .2371792 1.10 0.275 -.2144879
> .738289
> _cons | -20.5465 5.498655 -3.74 0.000 -31.59087 -9.502123
> ------------------------------------------------------------------------------
>
> . gen country = region
> Setting up a panel
> . tsset country year, yearly
> panel variable: country (strongly balanced)
> time variable: year, 1990 to 2006
>
> Carrying out a fixed effects within regression on panel data
> . xtreg ly lx1 lx2 lx3 lx4 lx5 lx6, fe
>
> Fixed-effects (within) regression Number of obs =
> 57
> Group variable (i): country Number of groups =
> 10
>
> R-sq: within = 0.7640 Obs per group: min =
> 2
> between = 0.5507 avg =
> 5.7
> overall = 0.5374 max =
> 8
>
> F(6,41) =
> 22.12
> corr(u_i, Xb) = 0.5835 Prob > F =
> 0.0000
>
> ------------------------------------------------------------------------------
> ly | Coef. Std. Err. t P>|t| [95% Conf. Interval]
> -------------+----------------------------------------------------------------
> lx1 | -.0075411 .0061342 -1.23 0.226 -.0199293
> .0048472
> lx2 | .1397473 .0208394 6.71 0.000 .0976612
> .1818334
> lx3 | -.0471179 .0766965 -0.61 0.542 -.2020095
> .1077738
> lx4 | .0883038 .0510516 1.73 0.091 -.0147971
> .1914046
> lx5 | .4423916 .1609951 2.75 0.009 .1172554
> .7675278
> lx6 | -.0635172 .0380633 -1.67 0.103 -.1403876
> .0133532
> _cons | 2.404044 .8235133 2.92 0.006 .7409252
> 4.067163
> -------------+----------------------------------------------------------------
> sigma_u | .95115353
> sigma_e | .03719725
> rho | .99847294 (fraction of variance due to u_i)
> ------------------------------------------------------------------------------
> F test that all u_i=0: F(9, 41) = 755.95 Prob > F
> = 0.0000
>
> . xtreg ly lx1 lx2 lx3 lx4 lx5 lx6, be
>
> Carrying out a fixed effects between regression on panel data
>
>
> Between regression (regression on group means) Number of obs =
> 57
> Group variable (i): country Number of groups =
> 10
>
> R-sq: within = 0.0790 Obs per group: min =
> 2
> between = 0.9488 avg =
> 5.7
> overall = 0.7682 max =
> 8
>
> F(6,3) =
> 9.26
> sd(u_i + avg(e_i.))= .4441503 Prob > F =
> 0.0477
>
> ------------------------------------------------------------------------------
> ly | Coef. Std. Err. t P>|t| [95% Conf. Interval]
> -------------+----------------------------------------------------------------
> lx1 | .5188441 .2315068 2.24 0.111 -.2179138
> 1.255602
> lx2 | -.0061883 .4172493 -0.01 0.989 -1.334062
> 1.321685
> lx3 | .1313838 4.684306 0.03 0.979 -14.77617
> 15.03894
> lx4 | .9508895 .2441334 3.89 0.030 .173948
> 1.727831
> lx5 | 7.621178 7.059213 1.08 0.359 -14.84439
> 30.08674
> lx6 | -.672947 1.417266 -0.47 0.667 -5.183319
> 3.837425
> _cons | -26.37744 19.85242 -1.33 0.276 -89.5567
> 36.80181
> ------------------------------------------------------------------------------
>
> . xtreg ly lx1 lx2 lx3 lx4 lx5 lx6, re
>
> Carrying out a random effects regression on panel data
>
>
> Random-effects GLS regression Number of obs =
> 57
> Group variable (i): country Number of groups =
> 10
>
> R-sq: within = 0.7556 Obs per group: min =
> 2
> between = 0.6683 avg =
> 5.7
> overall = 0.6327 max =
> 8
>
> Random effects u_i ~ Gaussian Wald chi2(6) =
> 94.90
> corr(u_i, X) = 0 (assumed) Prob > chi2 =
> 0.0000
>
> ------------------------------------------------------------------------------
> ly | Coef. Std. Err. z P>|z| [95% Conf. Interval]
> -------------+----------------------------------------------------------------
> lx1 | -.0065896 .0077505 -0.85 0.395 -.0217803
> .0086011
> lx2 | .1253869 .0257565 4.87 0.000 .0749051
> .1758687
> lx3 | -.0363082 .0969763 -0.37 0.708 -.2263783
> .1537619
> lx4 | .1554292 .061983 2.51 0.012 .0339448
> .2769135
> lx5 | .4387479 .2031582 2.16 0.031 .0405652
> .8369306
> lx6 | -.0456517 .0477556 -0.96 0.339 -.1392509
> .0479475
> _cons | 2.241371 1.053202 2.13 0.033 .1771336
> 4.305609
> -------------+----------------------------------------------------------------
> sigma_u | .44383293
> sigma_e | .03719725
> rho | .99302502 (fraction of variance due to u_i)
> ------------------------------------------------------------------------------
> Fixed-effects (within) regression Number of obs =
> 57
> Group variable (i): country Number of groups =
> 10
>
> R-sq: within = 0.7640 Obs per group: min =
> 2
> between = 0.5507 avg =
> 5.7
> overall = 0.5374 max =
> 8
>
> F(6,41) =
> 22.12
> corr(u_i, Xb) = 0.5835 Prob > F =
> 0.0000
>
> ------------------------------------------------------------------------------
> ly | Coef. Std. Err. t P>|t| [95% Conf. Interval]
> -------------+----------------------------------------------------------------
> lx1 | -.0075411 .0061342 -1.23 0.226 -.0199293
> .0048472
> lx2 | .1397473 .0208394 6.71 0.000 .0976612
> .1818334
> lx3 | -.0471179 .0766965 -0.61 0.542 -.2020095
> .1077738
> lx4 | .0883038 .0510516 1.73 0.091 -.0147971
> .1914046
> lx5 | .4423916 .1609951 2.75 0.009 .1172554
> .7675278
> lx6 | -.0635172 .0380633 -1.67 0.103 -.1403876
> .0133532
> _cons | 2.404044 .8235133 2.92 0.006 .7409252
> 4.067163
> -------------+----------------------------------------------------------------
> sigma_u | .95115353
> sigma_e | .03719725
> rho | .99847294 (fraction of variance due to u_i)
> ------------------------------------------------------------------------------
> F test that all u_i=0: F(9, 41) = 755.95 Prob > F
> = 0.0000
>
> . estimates store fixed
>
> . xtreg ly lx1 lx2 lx3 lx4 lx5 lx6, re
>
> Random-effects GLS regression Number of obs =
> 57
> Group variable (i): country Number of groups =
> 10
>
> R-sq: within = 0.7556 Obs per group: min =
> 2
> between = 0.6683 avg =
> 5.7
> overall = 0.6327 max =
> 8
>
> Random effects u_i ~ Gaussian Wald chi2(6) =
> 94.90
> corr(u_i, X) = 0 (assumed) Prob > chi2 =
> 0.0000
>
> ------------------------------------------------------------------------------
> ly | Coef. Std. Err. z P>|z| [95% Conf. Interval]
> -------------+----------------------------------------------------------------
> lx1 | -.0065896 .0077505 -0.85 0.395 -.0217803
> .0086011
> lx2 | .1253869 .0257565 4.87 0.000 .0749051
> .1758687
> lx3 | -.0363082 .0969763 -0.37 0.708 -.2263783
> .1537619
> lx4 | .1554292 .061983 2.51 0.012 .0339448
> .2769135
> lx5 | .4387479 .2031582 2.16 0.031 .0405652
> .8369306
> lx6 | -.0456517 .0477556 -0.96 0.339 -.1392509
> .0479475
> _cons | 2.241371 1.053202 2.13 0.033 .1771336
> 4.305609
> -------------+----------------------------------------------------------------
> sigma_u | .44383293
> sigma_e | .03719725
> rho | .99302502 (fraction of variance due to u_i)
> ------------------------------------------------------------------------------
>
> . estimates store random
>
> Carrying out a HAUSMAN TEST
>
> . hausman fixed random
>
> ---- Coefficients ----
> | (b) (B) (b-B) sqrt(diag(V_b-V_B))
> | fixed random Difference S.E.
> -------------+----------------------------------------------------------------
> lx1 | -.0075411 -.0065896 -.0009515
> .
> lx2 | .1397473 .1253869 .0143604
> .
> lx3 | -.0471179 -.0363082 -.0108097
> .
> lx4 | .0883038 .1554292 -.0671254
> .
> lx5 | .4423916 .4387479 .0036437
> .
> lx6 | -.0635172 -.0456517 -.0178655
> .
> ------------------------------------------------------------------------------
> 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(6) = (b-B)'[(V_b-V_B)^(-1)](b-B)
> = -4.12 chi2<0 ==> model fitted on these
> data fails to meet the asymptotic
> assumptions of the Hausman test;
> see suest for a generalized test
>
> *
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*
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