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Re: st: Panel Data-FIXED, RANDOM EFFECTS and Hausman Test
No, it is not difficult to understand and estimate these models. Look at these papers:
Nathaniel Beck and Jonathan N. Katz, “What To Do (and Not To Do)With Time-Series Cross-Section Data,” American Political Science Review 89.3 (Sept. 1995): 634-47.
_____, “Time-Series-Cross-Section Data: What Have We Learned in the Past Few Year,” Annual Review of Political Science 4 (2001):271-93.
The models can be estimated in Stata using the xtpcse keyword. - David Greenberg, Sociology Department, New York University
----- Original Message -----
From: Muhammad Billal Malik <[email protected]>
Date: Friday, February 27, 2009 7:54 am
Subject: Re: st: Panel Data-FIXED, RANDOM EFFECTS and Hausman Test
To: [email protected]
> I am sorry David, but I have not been taught that in my Basic
> Econometric course, will it be easy to understand and run?
>
> On Thu, Feb 26, 2009 at 9:26 PM, David Greenberg <[email protected]> wrote:
> > 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
> >>
> >> *
> >> * For searches and help try:
> >> * http://www.stata.com/help.cgi?search
> >> * http://www.stata.com/support/statalist/faq
> >> * http://www.ats.ucla.edu/stat/stata/
> > *
> > * For searches and help try:
> > * http://www.stata.com/help.cgi?search
> > * http://www.stata.com/support/statalist/faq
> > * http://www.ats.ucla.edu/stat/stata/
> >
>
>
>
> *
> * For searches and help try:
> * http://www.stata.com/help.cgi?search
> * http://www.stata.com/support/statalist/faq
> * http://www.ats.ucla.edu/stat/stata/
*
* For searches and help try:
* http://www.stata.com/help.cgi?search
* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/