The mental map of Dutch entrepreneurs. Changes in the subjective rating of locations in the Netherlands, 1983-1993-2003

worse, and it has spread to other areas. Relative scarcity of land also is not limited to the
Randstad any more. The provinces of Gelderland and North Brabant have to deal with
these problems to an increasing extent.

Distance and rating

The general preference of entrepreneurs for their own environment has been mentioned
above as one of the main elements determining the rating of potential locations. A
comparison of the Figures 1a and 1b shows that one of the most important changes in
the rating pattern during the last two decades is that the difference in rating between the
center and the periphery has become smaller. An obvious question, then, is whether this
change is related to changes in the degree of locational self-preference. It is conceivable
that firms in the Randstad area are less satisfied with their locational environment than
they were in the past. Another possibility is that Dutch firms generally show a stronger
locational self-preference, which would also result in a flattening of the rating pattern.

To gain insight into this matter, we need to quantify locational self-preference. In other
words, the relationship between distance and the rating given to locations should be
expressed in the form of a mathematical function. For this purpose, a new file was
created for each of the surveys, in which every single combination of respondent and
rated location represents a case. These files contain only two variables: the rating given
to the location by the respondent, and the distance between the respondent’s actual
location and the rated location, calculated from their map coordinates.

Several types of function have been examined. The modified exponential, a function
which has been applied in time series analysis (Croxton et al. 1969), was chosen
because it describes the relationship between distance and rating very well. It explains a
large proportion of the variance in the ratings, and graphically, it closely approximates
the observed values (Meester 2000, 2004). Typical of the modified exponential is its
horizontal asymptote or base level (Figure 3). In our analysis, the base level coincides
with the average rating that is given to places that are far away. The function can be
written as k+a.b^d, where d stands for distance. The three coefficients of the model, k, a,
and b, can be determined by nonlinear regression, in an iterative process.

The function coefficients of the modified exponential and the corresponding function
curves can be used to examine whether or not changes in the relation between distance
and rating actually have occurred. Figure 3 and Table 1 show the results. Clearly,

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