zero means. Positive variances such as ση2 and στ2 , and uit , ηi , and τt are mutually
independent. First, we consider a fixed effects model for the specification of α using individual
and/or time dummy variables.
In this paper, we use two kinds of models in terms of variable transformation: a linear model
using all of the original variables and a log-linear model with logarithmic transformation of all
variables. The following is the procedure for the choice of lag length and model selection.
First, we assume four kinds of α in terms of their components: α with only the individual
dummy variable ηi , with only the time dummy variable τt , and with both/neither ηi and/nor τt .
We set the maximum lag length to five, and chose one model from both linear and log-linear
models where the SBIC was minimized. Next, we conducted nonnested tests (PE tests), as
proposed by MACKINNON et al., 1983, between these two models, and examined which model
the data better supported10. We have annual data for 26 years from 124 regions. As data from the
first five years was used only as explanatory variables to estimate lag length, 2,604 observations
were available for this survey (2,604=124*(26-5)).
In the first procedure, we chose the model that had only a time dummy and 0 lag in each case
of linear and log-linear models as “the selected model” (see Table 2). We also show the results of
nonnested tests between these selected models in Table 3. We then finally select the log-linear
model that has only a time dummy and 0 lag since the null hypothesis is rejected if we set the null
hypothesis that the true model is a linear model and the null hypothesis is not rejected if we set the
null hypothesis that the true model is a log-linear model, simultaneously.
The results of the selected log-linear model in Table 4 indicate that the estimated coefficient
of the tourism (per capita tourists) is not statistically significant. We then defined “the minimum
SBIC model” as the log-linear model that has only a time dummy and 0 lag estimated without a
tourism variable. Table 3 shows that we also selected the minimum SBIC model rather than the
selected linear model, as the null hypothesis is not rejected if we set the null hypothesis to be that
the minimum SBIC model is optimal.
Since we used panel data, we had to examine whether the random effects model could be
applied. In Table 5, we show the estimated results of the random effects model with time-variant
error components (τt )11. Although the value of SBIC of the random effects model is smaller than
that of the fixed effects model (see Tables 4 and 5), the Hausman specification test statistics are
significant, which indicates a correlation between the error term and the explanatory variables.
Then we conclude that the fixed effects model is preferred to the random effects model. We should
also note that there is little difference in any of the estimated coefficients, excluding the constant
term, between the fixed effects model and the random effects model. In the column “transformed”
in Table 5, we show the corresponding coefficients calculated from original estimates of the
random effects model.
Now, we examine the impacts of government expenditure and tourism in accordance with the