municipality. When crossing water, kilometres are not an appropriate measure because there
would usually be higher costs connected with crossing water. Therefore the kilometres are
transformed into Danish kroner using the assumption that one kilometre on land equals one
krone. When crossing water the price of a ferry ticket is applied instead of kilometres. The
distances are from 1996. The distances could be defined in other ways taking other factors
into account such as congestion, speed limits, time values, etc., but more accurate distances
will not be used in this paper.
3.4 The effects of urban externalities
First, a real wage model with gender, education, sector, and unemployment as explanatory
variables is set up and compared with a model which also includes municipalities as fixed
effects. An F-test1 cannot reject that the constant terms are all equal and therefore fixed
effects are left out. In the fixed effects model with time dummies, unemployment is
insignificant which corresponds to the results in Albæk et al. (1999).
Three measures of the centre are applied now in a model with gender, time, education,
sector, and unemployment as explanatory variables. Fundamentally, more than one measure
could enter into the model, but here it is assumed that there is only one type of centre in which
one positive externality is present. The logarithmic transformation of all three measures
describes the data better. Distance to the commuting centre is the worst measure comparing
with the two others because the adjusted is smallest comparing the three models which only
differ with respect to the distance measure. It might be because a definition of 35 commuting
centres is chosen where some of the centres are small islands where no positive externality in
production would be expected. The second best measure is the distance to Copenhagen. Given
the geography of Denmark one would expect that it could be difficult to identify some
distances because of the many belts, seas, sounds, and straits.
Table A.1 in appendix A contains the variable »distance5« this being the best of the three
proposed measures. »Distance5« is the distance to five university towns: Copenhagen, Ârhus,
Odense, Aalborg, and Esbjerg. Whether or not to interpret it as distance to an economic centre
or distance to a university city is a matter of choice.
The test described regarding heteroscedasticity2 rejects the hypothesis that there is no
heteroscedasticity in all three models with the explanatory variables of table A.1 in appendix
A. The results of the FGLS regression are preferred to WLS and OLS because the t-value of β
is numerically smaller in the heteroscedasticity test.
Because both the average wage and distances are in logarithmic form the estimated
parameters are elasticities. However, the elasticity is small: -0.04. If an improvement in
infrastructure could be interpreted as a shorter distance then a10% improvement in
infrastructure would result in a 0.4% higher wage. In the context of the theoretical setup of
this paper it is also a welfare gain because the higher wages are due to a positive externality.
Even though the elasticity is small the total welfare gain is worth calculating. In 1999 1.5
million workers had a place of work outside the 5 centres and their average wage was 260,000
DKK. If all distances outside the centres were improved by 10% there would on average per
worker be a welfare gain of 1040 DKK. The total welfare gain would be 1.5 million workers
times 1040 DKK; a total of 1.560 billion DKK.
1 See appendix B, I).
2 See appendix C, I).
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