Springer Texts in Business and Economics
Empirical Example
Baltagi and Griffin (1983) considered the following gasoline demand equation:
log Car = a + в ilog 7Ф + e2log ppMO + в 3log Cf + U (12.40)
where Gas/Car is motor gasoline consumption per auto, Y/N is real income per capita, PMO/ PGdp is real motor gasoline price and Car/N denotes the stock of cars per capita. This panel consists of annual observations across eighteen OECD countries, covering the period 1960-1978. The data for this example are provided on the Springer web site as GASOLINE. DAT. Table 12.1
gives the Stata output for the Within estimator using xtreg, fe. This is the regression described in (12.5) and computed as in (12.9). The Within estimator gives a low price elasticity for gasoline demand of -.322. The F-statistic for the significance of the country effects described in (12.14) yields an observed value of 83.96. This is distributed under the null as an F(17,321) and is statistically significant. This F-statistic is printed by Stata below the fixed effects output. In EViews, one invokes the test for redundant effects after running the fixed effects regression.
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Table 12.1 Fixed Effects Estimator - Gasoline Demand Data
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Table 12.2 gives the Stata output for the Between estimator using xtreg, be. This is based on the regression given in (12.24). The Between estimator yields a high price elasticity of gasoline demand of -.964. These results were also verified using TSP.
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Table 12.2 Between Estimator - Gasoline Demand Data
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Table 12.3 gives the Stata output for the random effect model using xtreg, re. This is the Swamy and Arora (1972) estimator which yields a price elasticity of -.420. This is closer to the Within estimator than the Between estimator.
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Table 12.3 Random Effects Estimator - Gasoline Demand Data
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Table 12.4 Gasoline Demand Data. One-way Error Component Results
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ві |
в2 |
вз |
P |
|
|
OLS |
0.890 |
-0.892 |
-0.763 |
0 |
|
(0.036)* |
(0.030)* |
(0.019)* |
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|
WALHUS |
0.545 |
-0.447 |
-0.605 |
0.75 |
|
(0.066) |
(0.046) |
(0.029) |
||
|
AMEMIYA |
0.602 |
-0.366 |
-0.621 |
0.93 |
|
(0.066) |
(0.042) |
(0.029) |
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|
SWAR |
0.555 |
-0.402 |
-0.607 |
0.82 |
|
(0.059) |
(0.042) |
(0.026) |
||
|
IMLE |
0.588 |
-0.378 |
-0.616 |
0.91 |
|
(0.066) |
(0.046) |
(0.029) |
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* These are biased standard errors when the true model has error component disturbances (see Moulton, 1986). Source: Baltagi and Griffin (1983). Reproduced by permission of Elsevier Science Publishers B. V. (North-Holland). Table 12.5 Gasoline Demand Data. Wallace and Hussain (1969) Estimator |
Dependent Variable: GAS
Method: Panel EGLS (Cross-section random effects)
Sample: 1960 1978
Periods included: 19
Cross-sections included: 18
Total panel (balanced) observations: 342
Wallace and Hussain estimator of component variances
|
Coefficient |
Std. Error |
t-Statistic |
Prob. |
|
|
1.938318 |
0.201817 |
9.604333 |
0.0000 |
|
|
log(Y/N) |
0.545202 |
0.065555 |
8.316682 |
0.0000 |
|
log(PMG/PGDP ) |
-0.447490 |
0.045763 |
-9.778438 |
0.0000 |
|
log(Car/N) |
-0.605086 |
0.028838 |
-20.98191 |
0.0000 |
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Effects Specification |
||||
|
S. D. |
Rho |
|||
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Cross-section random |
0.196715 |
0.7508 |
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Idiosyncratic random |
0.113320 |
0.2492 |
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Table 12.4 gives the parameter estimates for OLS and three feasible GLS estimates of the slope coefficients along with their standard errors, and the corresponding estimate of p defined in (12.16). These were obtained using EViews by invoking the random effects estimation on the individual effects and choosing the estimation method from the options menu. Breusch’s (1987) iterative maximum likelihood was computed using Stata(xtreg, mle) and TSP. Table 12.5 gives the EViews output for the Wallace and Hussain (1969) random effects estimator, while Table 12.6 gives the EViews output for the Amemiya (1971) random effects estimator. Note that EViews calls the Amemiya estimator Wansbeek and Kapteyn (1989) since the latter paper generalizes this method to deal with unbalanced panels with missing observations, see Baltagi (2008) for details. Table 12.6 gives the Stata maximum likelihood output. |
Table 12.6 Gasoline Demand Data. Wansbeek and Kapteyn (1989) Estimator
Dependent Variable: GAS
Method: Panel EGLS (Cross-section random effects)
Sample: 1960 1978
Periods included: 19
Cross-sections included: 18
Total panel (balanced) observations: 342
Wallace and Hussain estimator of component variances
|
Coefficient |
Std. Error |
t-Statistic |
Prob. |
|
|
C |
2.188322 |
0.216372 |
10.11372 |
0.0000 |
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log(Y/N) |
0.601969 |
0.065876 |
9.137941 |
0.0000 |
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log(PMG/PGDP ) |
-0.365500 |
0.041620 |
-8.781832 |
0.0000 |
|
log(Car/N) |
-0.620725 |
0.027356 |
-22.69053 |
0.0000 |
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Effects Specification |
||||
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S. D. |
Rho |
|||
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Cross-section random |
0.343826 |
0.9327 |
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Idiosyncratic random |
0.092330 |
0.0673 |
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Table 12.7 Gasoline Demand Data. Random Effects Maximum Likelihood Estimator . xtreg c y p car, mle
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|
c |
Coef. |
Std. Err. |
z |
P> |z| |
[95% Conf. Interval] |
|
|
log(Y/N) |
.5881334 |
.0659581 |
8.92 |
0.000 |
.4588578 |
.717409 |
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log(PMG/PGDP ) |
-.3780466 |
.0440663 |
-8.58 |
0.000 |
-.464415 |
-.2916782 |
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log(Car/N) |
-.6163722 |
.0272054 |
-22.66 |
0.000 |
-.6696938 |
-.5630506 |
|
cons |
2.136168 |
.2156039 |
9.91 |
0.000 |
1.713593 |
2.558744 |
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sigma u |
.2922939 |
.0545496 |
.2027512 |
.4213821 |
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sigma e |
.0922537 |
.0036482 |
.0853734 |
.0996885 |
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rho |
.9094086 |
.0317608 |
.8303747 |
.9571561 |
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Likelihood-ratio test of sigma u = 0: chibar2(01)= 463.97 Prob >= chibar2 = 0.000 |
