and applies the ordinary least squares method. The OLS estimates of the standard errors may be
highly inaccurate if the data exhibits heteroskedasticity and/or cross-sectional and serial
correlation. The panel data models increase precision of estimates and allow us to control for an
unobservable individual region’s heterogeneity and temporal effects without aggregation bias.
The Hausman test for misspecification (Greene 2003, p. 301) is employed to help us select from
two principal types of panel data models: the fixed effect model and the random effect model.
Under the null hypothesis, the random effects estimator is consistent and efficient, while under
the alternative, it is inconsistent. The random effect model is chosen if we fail to reject the null
hypothesis. In the case of relative gasoline price (3:2:1 crack spread), the χ2 test statistic was
calculated at 26.92 (48.99) and significant at the 5% (1%) significance level. This suggests that
the fixed effect estimator is consistent and asymptotically efficient in both cases.
Different specification tests are applied on the data set to better specify the panel data model.
Applying the Wooldridge test for autocorrelation in panel data for the relative gasoline price (or
crack spread) (Wooldridge 2002, p. 282), we get an F-test statistic of 917 (1,708), which is
highly significant, and the null hypothesis of no first-order autocorrelation is rejected. Tests
developed by Pesaran (2004) and Frees (1995) of cross-sectional independence are applied and
both null hypotheses are rejected; this confirms the existence of cross-sectional correlation across
regions.
Based on these diagnostic results, we used a fixed effect panel data model with correction for
first-order serial correlation. We also estimated a feasible generalized least squares (FGLS)
model with generalized error structure to allow for the presence of AR(1) autocorrelation within
panels, as well as for heteroskedasticity and cross-sectional correlation across panels. By using
three alternative model specifications we hope to provide information on the robustness of the
results.
The fixed effect model is specified as
(2) πit =αi+Xi'tβ+εit i =1,...,N;t =1,...T.