where variables Wjt include wages, diesel oil, and plastic price variables and ωfr, ωllt are brand and
retailer specific effects. Actually, it is likely that labor cost, plastic price (which is the major com-
ponent of bottles and packaging) and oil prices (which affect transportation costs) are important
determinants of variable costs. Also, the relatively important variations of all these price indices
over time suggests a potentially good identification of our cost equations. Table 5 presents the
results of these cost equations estimated by OLS for the 7 different models.
|
Model |
(1) |
(2) |
(3) |
(4) |
(5) |
(6) |
(7) |
|
Wage |
2.09 |
-1.02 |
-1.90 |
-4.48 |
3.02 |
1.90 |
2.07 |
|
(Std. err.) |
(0.72) |
(0.73) |
(0.75) |
(0.75) |
(0.78) |
(0.74) |
(0.64) |
|
Plastic |
0.03 |
2.77 |
3.95 |
5.10 |
-0.48 |
0.25 |
0.04 |
|
(Std. err.) |
(0.69) |
(0.70) |
(0.72) |
(0.72) |
(0.74) |
(0.70) |
(0.64) |
|
Diesel oil |
0.58 |
0.12 |
-0.18 |
-0.09 |
0.71 |
0.64 |
0.63 |
|
(Std. err.) |
(0.33) |
(0.34) |
(0.35) |
(0.35) |
(0.36) |
(0.34) |
(0.30) |
|
ω^,ωn not shown |
796.57 |
646.20 |
554.26 |
471.66 |
872.82 |
773.86 |
962.38 |
|
(p val.) |
(0.00) |
(0.00) |
(0.00) |
(0.00) |
(0.00) |
(0.00) |
(0.00) |
|
F test {ω(l = θ} |
10.32 |
6.44 |
7.21 |
8.43 |
6.36 |
3.00 |
6.69 |
|
(p val.) |
(0.00) |
(0.00) |
(0.00) |
(0.00) |
(0.00) |
(0.01) |
(0.00) |
Table 5 : Cost Equations for the Random Coefficients Logit Model
These cost equations are useful mostly in order to test which model fits best the data. We thus
performed the non nested test of Rivers and Vuong (2002) which gives the same inference as the
Vuong (1989) test. Results of the tests are provided in Table 6. Each matrix element gives the test
statistic of testing the hypothesis //1 in column in favor of the hypothesis H2 in row. When the
test statistic is negative and below the critical value chosen (-1.64 for a 5% test), it means that
we reject Hi in favor of H2. When the test statistic is positive and above the critical value chosen
(1.64 for a 5% test), it means that we reject H2 in favor of Hi. When the test statistic is between
the two critical values (-1.64,1.64), it means that we cannot distinguish statistically Hi from H2.
|
Tn → N(0,1)_______________________________ | ||||||
|
∖ |
H2______________________________ | |||||
|
H |
2 |
3 |
4 |
5 |
6 |
7 |
|
1 |
0.86 |
2.39 |
2.21 |
3.68 |
1.22 |
-2.54 |
|
2^ |
3.00 |
3.57 |
4.33 |
0.05 |
-2.10 | |
|
3^ |
0.36 |
2.50 |
-0.99 |
-2.66 | ||
|
F |
1.68 |
-1.11 |
-2.68 | |||
|
5^ |
-2.05 |
-3.02 | ||||
|
β^ |
-2.76 | |||||
Table 6 : Non Nested Tests Across Models
31