 |
[Date Prev][Date Next][Thread Prev][Thread Next][Date index][Thread index]
st: Hausman test, panel data, fixed- and random-effects
Dear all,
I am estimating panel data models to study the effects of the policies
of air pollution (ifga, presprop) over the concentration of two
important pollutants (sulfur dioxide, so2, and nitrogen dioxide, no2)
in four Mexican cities in a period of more than ten years (note that
the panels are unbalanced), that is T>N.
I have reason to believe that some omitted variables may be constant
over time but vary between cases, and others may be fixed between
cases but vary over time, so I decided to use a panel data model with
random effects, most likely I would end up using a pcse specification,
due to the heteroskedasticity present in the data. However, I have had
problems when performing the Hausman test to decide between a
fixed-effects specification and a random-effects specification, the
output appears below (I have include both the fixed-effects,
random-effects, and the Hausman tests). Is part of the problem that I
have too few observations? As always, any suggestions would be very
much appreciated.
Laura
. summarize so2 no2 presprop vehiculos pbtdef ifga energia
Variable | Obs Mean Std. Dev. Min Max
-------------+--------------------------------------------------------
so2 | 46 .0113261 .0035966 .006 .02
no2 | 47 .0264255 .0095548 .011 .047
presprop | 45 16.41439 5.584965 6.650289 27.13052
vehiculos | 44 1372728 1450837 96795 4622148
pbtdef | 44 2.20e+08 1.80e+08 6.43e+07 5.63e+08
-------------+--------------------------------------------------------
ifga | 48 5.491667 2.288624 .6 8.7
energia | 32 3018.091 2470.169 329 8095.6
.
. **RANDOM EFFECTS**
. * so2
. xtreg so2 pbtdef energia presprop ifga, re
Random-effects GLS regression Number of obs = 25
Group variable (i): clave Number of groups = 4
R-sq: within = 0.1190 Obs per group: min = 5
between = 0.9060 avg = 6.3
overall = 0.6031 max = 7
Random effects u_i ~ Gaussian Wald chi2(4) = 13.58
corr(u_i, X) = 0 (assumed) Prob > chi2 =
0.0088
------------------------------------------------------------------------------
so2 | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
pbtdef | 7.66e-12 2.66e-12 2.88 0.004 2.44e-12 1.29e-11
energia | -6.63e-07 1.93e-07 -3.43 0.001 -1.04e-06 -2.84e-07
presprop | .0000842 .0000871 0.97 0.334 -.0000865 .0002549
ifga | -.0000724 .0001829 -0.40 0.692 -.0004308 .000286
_cons | .0105937 .0018532 5.72 0.000 .0069615 .0142258
-------------+----------------------------------------------------------------
sigma_u | 0
sigma_e | .00173762
rho | 0 (fraction of variance due to u_i)
------------------------------------------------------------------------------
. * no2
. xtreg no2 pbtdef vehiculos presprop ifga, re
Random-effects GLS regression Number of obs = 38
Group variable (i): clave Number of groups = 4
R-sq: within = 0.0011 Obs per group: min = 8
between = 0.8323 avg = 9.5
overall = 0.2759 max = 10
Random effects u_i ~ Gaussian Wald chi2(4) = 12.05
corr(u_i, X) = 0 (assumed) Prob > chi2 =
0.0170
------------------------------------------------------------------------------
no2 | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
pbtdef | -6.81e-11 2.76e-11 -2.47 0.014 -1.22e-10 -1.40e-11
vehiculos | 8.57e-09 3.44e-09 2.49 0.013 1.83e-09 1.53e-08
presprop | -.0004293 .0003159 -1.36 0.174 -.0010486 .0001899
ifga | -.0000494 .0006242 -0.08 0.937 -.0012727 .001174
_cons | .0357281 .0072433 4.93 0.000 .0215314 .0499248
-------------+----------------------------------------------------------------
sigma_u | 0
sigma_e | .00375932
rho | 0 (fraction of variance due to u_i)
------------------------------------------------------------------------------
. **FIXED EFFECTS**
. xtreg so2 pbtdef energia presprop ifga, fe
Fixed-effects (within) regression Number of obs = 25
Group variable (i): clave Number of groups = 4
R-sq: within = 0.3789 Obs per group: min = 5
between = 0.6553 avg = 6.3
overall = 0.2823 max = 7
F(4,17) = 2.59
corr(u_i, Xb) = -0.9710 Prob > F = 0.0737
------------------------------------------------------------------------------
so2 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
pbtdef | -3.71e-11 3.33e-11 -1.11 0.281 -1.07e-10 3.32e-11
energia | 2.81e-09 6.75e-07 0.00 0.997 -1.42e-06 1.43e-06
presprop | .0000724 .0000729 0.99 0.335 -.0000814 .0002262
ifga | -.0005388 .0002206 -2.44 0.026 -.0010042 -.0000735
_cons | .0202899 .0061256 3.31 0.004 .0073659 .0332138
-------------+----------------------------------------------------------------
sigma_u | .01084947
sigma_e | .00173762
rho | .97499118 (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(3, 17) = 4.02 Prob > F = 0.0249
. est store fixedso2ener
.
. * no2
. xtreg no2 pbtdef vehiculos presprop ifga, fe
Fixed-effects (within) regression Number of obs = 38
Group variable (i): clave Number of groups = 4
R-sq: within = 0.3340 Obs per group: min = 8
between = 0.0534 avg = 9.5
overall = 0.0221 max = 10
F(4,30) = 3.76
corr(u_i, Xb) = -0.9059 Prob > F =
0.0135
------------------------------------------------------------------------------
no2 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
pbtdef | -5.42e-11 3.90e-11 -1.39 0.175 -1.34e-10 2.54e-11
vehiculos | -6.49e-09 2.31e-09 -2.81 0.009 -1.12e-08 -1.78e-09
presprop | -.0002618 .000137 -1.91 0.066 -.0005415 .0000179
ifga | .0007199 .0004104 1.75 0.090 -.0001182 .001558
_cons | .0456466 .0097798 4.67 0.000 .0256735 .0656197
-------------+----------------------------------------------------------------
sigma_u | .02521944
sigma_e | .00375932
rho | .97826279 (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(3, 30) = 49.23 Prob > F
= 0.0000
. est store fixedno2
.
.
. **RANDOM EFFECTS - HAUSMAN**
.
. hausman fixedso2ener randomso2ener
Note: the rank of the differenced variance matrix (3) does not equal
the number of coefficients being tested (4); be sure this is what
you expect, or there may be problems computing the test.
Examine the output of your estimators for anything unexpected and
possibly consider scaling your variables so that the
coefficients are on a similar scale.
---- Coefficients ----
| (b) (B) (b-B) sqrt(diag(V_b-V_B))
| fixedso2ener randomso2e~r Difference S.E.
-------------+----------------------------------------------------------------
pbtdef | -3.71e-11 7.66e-12 -4.48e-11 3.32e-11
energia | 2.81e-09 -6.63e-07 6.66e-07 6.47e-07
presprop | .0000724 .0000842 -.0000118 .
ifga | -.0005388 -.0000724 -.0004665 .0001233
------------------------------------------------------------------------------
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(3) = (b-B)'[(V_b-V_B)^(-1)](b-B)
= 18.27
Prob>chi2 = 0.0004
(V_b-V_B is not positive definite)
. hausman fixedno2 randomno2
Note: the rank of the differenced variance matrix (2) does not equal
the number of coefficients being tested (4); be sure this is what
you expect, or there may be problems computing the test.
Examine the output of your estimators for anything unexpected and
possibly consider scaling your variables so that the
coefficients are on a similar scale.
---- Coefficients ----
| (b) (B) (b-B) sqrt(diag(V_b-V_B))
| fixedno2 randomno2 Difference S.E.
-------------+----------------------------------------------------------------
pbtdef | -5.42e-11 -6.81e-11 1.39e-11 2.76e-11
vehiculos | -6.49e-09 8.57e-09 -1.51e-08 .
presprop | -.0002618 -.0004293 .0001675 .
ifga | .0007199 -.0000494 .0007693 .
------------------------------------------------------------------------------
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(2) = (b-B)'[(V_b-V_B)^(-1)](b-B)
= -2.78 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/support/faqs/res/findit.html
* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/