Dear all,
I have a panel data set consisting of 58 counties in California and 19 years from 1980 to 1998. I am interested in using the various xt commands to estimate the impact of population growth on the level of auto tort filings in the courts, with automobile accidents (measured as # of persons injured) and other variables as controls. My question is which one of the many models provides the most reliable (or reasonable) estimate. Shown at the bottom are results from 4 models: (1) fixed effects (xtreg, fe); (2) fixed effects with AR(1) (xtregar, fe); (3) xtgls with AR1 and heteroskedastic; and lastly as an experiment, (4) fixed effects with time dummies.
The coef. for population in the first model is .13; it dropped to .04 (along with a significant drop in t-score) in the xtregar model. In the xtgls model the coef. increased to .49, which is quite close to the result from the last model with fixed effects and time dummies (.45).
I'm inclined to accept the results from the xtgls estimate and xtreg with time dummies as more reasonable in capturing the underlying relationship between population growth and tort filings. As a background, over the 19-year time frame auto tort filings in California rose initially for a few years and have declined since late 1980s, whereas population growth has shown a steady upward trend throughout the entire period. It appears a fixed- effects model (either xtreg or xtregar) would be inappropriate for fitting a linear population trend to a curvilinear filings trend. Theoretically I consider the xtgls model and xtreg fixed effects with time dummies as kind of veering away from the time-series within estimate and thus the results less subject to the year-to-year fluctuations. Am I correct in my interpretation? Any comments will be greatly appreciated.
Thanks,
Ron
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Ron Pi
Senior Research Analyst
Office of Court Research
Judicial Council of California - Administrative Office of the Courts
455 Golden Gate Avenue
San Francisco, CA 94102-3688
415-865-7652, Fax 415-865-4330, [email protected]
www.courtinfo.ca.gov <http://www.courtinfo.ca.gov/
"Serving the courts for the benefit of all Californians"
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(1)
. xtreg lg_auto lg_pop lg_persinj, fe
Fixed-effects (within) regression Number of obs = 1102
Group variable (i): cnty_id Number of groups = 58
R-sq: within = 0.1669 Obs per group: min = 19
between = 0.9775 avg = 19.0
overall = 0.9537 max = 19
F(2,1042) = 104.36
corr(u_i, Xb) = 0.2423 Prob > F = 0.0000
------------------------------------------------------------------------------
lg_auto | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lg_pop | .1301814 .0691205 1.88 0.060 -.0054498 .2658126
lg_persinj | 1.070011 .0780321 13.71 0.000 .9168932 1.223129
_cons | -4.280112 .9003019 -4.75 0.000 -6.046724 -2.513501
-------------+----------------------------------------------------------------
sigma_u | .31447197
sigma_e | .32886923
rho | .47763231 (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(57, 1042) = 15.86 Prob > F = 0.0000
(2)
. xtregar lg_auto lg_pop lg_persinj, fe
FE (within) regression with AR(1) disturbances Number of obs = 1044
Group variable (i): cnty_id Number of groups = 58
R-sq: within = 0.0607 Obs per group: min = 18
between = 0.9771 avg = 18.0
overall = 0.9537 max = 18
F(2,984) = 31.81
corr(u_i, Xb) = 0.9297 Prob > F = 0.0000
------------------------------------------------------------------------------
lg_auto | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lg_pop | .0422914 .1162172 0.36 0.716 -.1857707 .2703535
lg_persinj | .7162647 .0906067 7.91 0.000 .5384602 .8940692
_cons | -.6454783 .8010065 -0.81 0.421 -2.217356 .9263991
-------------+----------------------------------------------------------------
rho_ar | .4537742
sigma_u | .85230185
sigma_e | .30011025
rho_fov | .88969031 (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(57,984) = 5.74 Prob > F = 0.0000
(3)
. xtgls lg_auto lg_pop lg_persinj, pan(correlate hetero) corr(ar1)
Cross-sectional time-series FGLS regression
Coefficients: generalized least squares
Panels: heteroskedastic with cross-sectional correlation
Correlation: common AR(1) coefficient for all panels (0.6745)
Estimated covariances = 1711 Number of obs = 1102
Estimated autocorrelations = 1 Number of groups = 58
Estimated coefficients = 3 Time periods = 19
Wald chi2(2) = 26360.56
Log likelihood = . Prob > chi2 = 0.0000
------------------------------------------------------------------------------
lg_auto | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lg_pop | .4957223 .0509799 9.72 0.000 .3958035 .595641
lg_persinj | .707074 .0547812 12.91 0.000 .5997049 .8144432
_cons | -5.911482 .2030015 -29.12 0.000 -6.309357 -5.513606
------------------------------------------------------------------------------
(4)
. xi: xtreg lg_auto lg_pop lg_persinj i.year, fe
i.year _Iyear_1980-2000 (naturally coded; _Iyear_1980 omitted)
Fixed-effects (within) regression Number of obs = 1102
Group variable (i): cnty_id Number of groups = 58
R-sq: within = 0.2870 Obs per group: min = 19
between = 0.9783 avg = 19.0
overall = 0.9578 max = 19
F(20,1024) = 20.61
corr(u_i, Xb) = 0.6570 Prob > F = 0.0000
------------------------------------------------------------------------------
lg_auto | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lg_pop | .4521733 .1189174 3.80 0.000 .2188237 .6855228
lg_persinj | .5979279 .0857454 6.97 0.000 .4296712 .7661847
_Iyear_1981 | -.0087351 .0570119 -0.15 0.878 -.1206086 .1031384
_Iyear_1982 | -.0120469 .0576697 -0.21 0.835 -.1252111 .1011173
_Iyear_1983 | -.0932685 .0574431 -1.62 0.105 -.2059881 .019451
_Iyear_1984 | .0697582 .0576145 1.21 0.226 -.0432977 .1828141
...additional years deleted here...
_cons | -4.653511 1.289873 -3.61 0.000 -7.184607 -2.122415
-------------+----------------------------------------------------------------
sigma_u | .39874337
sigma_e | .30689493
rho | .62799507 (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(57, 1024) = 18.02 Prob > F = 0.0000
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