The Impact of Knowledge-Intensive Employment Centers on the Rent Structure
of RotterdamBy Lukas Braunschweig, 381788
Department of Applied Economics,
Erasmus School of Economics,
Supervisor:
Frank van Oort
June, 2016
AbstractThe proclamation of clusters is a popular way to attract investment into knowledge-intensive activities.
However, little research has been undertaken on their effects on the rent structure of a given city. This
thesis examines how rents behave with differing distance from knowledge-intensive employment
centers in the city of Rotterdam using a linear regression model while controlling for other relevant
factors. The results show that distance from clusters matters for rents albeit not always in the theorized
ways probably due to upwards-sloping bid-rent gradients. While moderately knowledge-intensive
clusters do exhibit negative rent gradients, very knowledge-intensive one either have insignificant or
even positive distance effects.
Table of Contents
Table of Contents.........................................................................................................................................2
I. Introduction..........................................................................................................................................3
II. A History of Bid-Rent Theory................................................................................................................5
III. Literature Review...........................................................................................................................11
IV. Hypotheses.....................................................................................................................................18
V. Methodology......................................................................................................................................19
VI. Data................................................................................................................................................20
VII. Results............................................................................................................................................25
VIII. Discussion.......................................................................................................................................33
IX. References......................................................................................................................................36
X. Appendix............................................................................................................................................39
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I. IntroductionArguably the most successful and famous cluster in the world is the agglomeration of technology firms
just South-East of San Francisco: Silicon Valley. Its achievements in fostering innovation have helped
America to claim a leading role in the digital revolution and brought significant wealth to the region.
Hence it is not surprising that clusters play an increasingly important role in economic policies on all
government-levels in the European Union, as well. The European Commission plans to foster SME’s with
the help of clusters in its Europe 2020-strategy (European Comission, 2010) and has set up the European
Cluster Observatory to aid bureaucrats in implementing cluster strategies. National governments in the
Netherlands and Denmark also have a long history of applying clusters in their economic policies (Holtz-
Eakin, 2000). And even regional and city governments have recognized the importance of agglomeration
economies for economic growth and knowledge creation (see for example Free and Hanseatic City of
Hamburg (2011) or Paris Region Enterprises (2016)) – an ever more important feature in today’s
globalized and highly competitive knowledge economy.
Alfred Marshall (1890, 1920) described three sources of agglomeration economies that lead to increased
productivity, more innovation and higher business formation rates. Knowledge spillovers, in the form of
an exchange of tacit (that is incomplete) information between employees, enable people in a cluster to
make better decisions and foster innovation through exchange of ideas between knowledge actors. The
second advantage of clusters are non-traded local inputs. In essence, this concept means that because of
the great market for inputs, supplier of inputs can specialize and deliver inputs more economically than
for a smaller market. Finally, the existence of a local skilled labor pool reduces the search and training
costs of specialized personnel.
Being host to a cluster consisting of a few big and many small firms from the same industry certainly
spells advantages for a city’s community. Various researchers have shown that large enterprises do not
only pay higher wages to their staff ( (Oi & Idson, 1999) and (Brown & Medoff, 1989)) but also attract
more productive (i.e. better educated) workers (Oi & Idson, 1999) which increases the human capital
stock of a region. Jobs at large firms are also safer and tend to fluctuate less with overall economic
conditions (Neumark, Wall, & Zhang, 2011). Finally, as McWilliams and Siegel theorized (2001) and
Udayasankar (2008) confirmed empirically, larger firms are more willing to spend on Corporate Social
Responsibility, part of which usually is spent in local projects. The community therefore profits from
amenities that have been financed by the local employer. An illustration of this behavior can be seen in
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Wolfsburg where Volkswagen finances museums, galleries and theatres among others and in Eindhoven
where Philips finances the museum and sport clubs (The Economist, 2016).
The presence of one or a few dominant industries also can have a negative impact on a city. Often cities’
growth depends on a small number of industries which does not only give them an out-sized influence
on municipal politics but also binds the city’s fate to the industry’s. This can be two-sided blade as the
demise of Detroit or spending cuts by Wolfsburg’s mayor, following Volkswagen’s involvement in an
emissions-scandal which negatively impacted share prices (The Economist, 2016), show.
But hosting a highly-productive cluster can also harm a city’s residents in other ways. The fact that
clusters concentrate many jobs in a small area means that roads around it will be congested and not
always are companies willing to contribute to the necessary infrastructure investments (Bowles, 2016).
And finally, if one follows a bid-rent framework, big firm campuses should also drive up rents in the
surrounding areas, as employees want to avoid the costs of commuting, driving up demand in a housing
market with slowly adapting supply. Intuitively this issue of clusters seems obvious. Research has shown
that rents in towns with a university campus, median rents are significantly higher than in towns without
academic institutions (Ogur, 1973). In a staff paper of the South Dakota State University, Langelett and
Chang even showed that the bid-rent gradient of a university campus can “overwrite” the Central
Business District’s gradient and be the determining factor of rents in college towns (Langelett & Chang,
2013).
However, besides McMillen (1996) who found that Chicago’s O’Hara airport, an important employment
center exhibits a bid-rent gradient, scientific literature has mainly focused on the effect of university
campuses on the local housing market and their bid-rent gradients and largely ignored the bid-rent
gradients of employment centers other than city centers. Therefore, this thesis aims to explore the
impact of these localized hotspots of qualitative employment on the local rental housing market in the
municipality of Rotterdam, Netherlands.
In the subsequent section a short history of bid-rent gradient theory will be provided, which is followed
by an investigation into the existing literature on bid-rent gradients. Using the insights from the history
and literature review this paper’s hypotheses will be developed. Section IV and Section V will introduce
the data and the methodology for the empirical part of this thesis, respectively. Then the result will be
presented and discussed. The paper will conclude with a discussion of the findings and their implications
for the applicability of bid-rent theory in modern cities.
4
II. A History of Bid-Rent TheoryThe Classical Beginnings of Rent Theory
Modern economic models usually assume away distance and stipulate an economy that takes place on
the famous “pinhead” (Isard, 1956). This of course, is a major oversimplification of the real world. The
ignorance towards distance (bar the extreme case of international trade) has a tradition that goes back
to the very roots of economic science. Although Adam Smith conceptualized rent as the difference
between the price of agricultural output and its production costs and recognized that the cost of
production can vary with the quality of land and therefore will influence rent, he did not consider
transport costs as a factor impacting rent (Smith, 1904).
It was David Ricardo who made Rent Theory his research focus and further advanced the discipline after
Smith’s death. In his magnus opus “On the Principles of Political Economy and Taxation”, Ricardo saw
rent as “that portion of the produce of the earth, which is paid to the landlord for the use of the original
and indestructible powers of the soil”, combined with capital and interest considerations (Ricardo, 1817).
The English-Portuguese economist made two important contributions to Rent Theory. First, he posited
that the most productive land is used first and less valuable areas are only cultivated later, as good land
becomes scarce. Secondly, he claimed that land is used in a way that maximizes economic output. This
latter argument suggests that a given plot of land will go to the highest bidder who can get most value
out of the land and therefore is able to pay the highest rent. This assumption is integral to bid-rent
theory. However, while Ricardo acknowledged the possible effect of certain cost or productive
advantages of a plot of land on rent, such as hedges, buildings or location, over an equally fertile one, he
did not explicitly include distance from a market and the associated transport costs in his considerations.
Ponsard attributes the engagement of the majority of classical economists in abstract analysis to
Ricardo’s reduction of differences in land to differences of fertility and his neglect of spatial
considerations (Ponsard, 1983, p. 11).
Rent and the Use of Land in the Von Thünen-model
This ignorance of space in economic analysis afflicted mainly Anglo-Saxon thinkers. Meanwhile, German
authors thought intensively about the spatial structure of cities and their hinterlands. It is therefore not
surprising that the next advancement of the thinking about rent (which thanks to its spatial
considerations is actually a new branch of Rent Theory) came from a German. In his 1826 book “The
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Isolated State”, Von Thünen, a rural land-owner from Mecklenburg, was the first to connect economic
geography and traditional Rent Theory laying the foundation for the bid-rent model. Specifically, he
developed a model in which rent paid by a leaseholder is determined by the market price for the
produced crops and the costs of production (McCann, 2001)1. Assuming that all land is equally fertile and
featureless, farmers sell the same produce and have the same production function, as well as absentee
landlords and free entry into the agricultural market, production costs only differ with respect to
transport costs that in turn differ linearly with distance to the central market in the nearest city. In this
world, the closer a farmer is to the market, the smaller his transport cost will be and therefore his profits
will be higher than for farmers further away from the town. As the other farmers observe this and entry
into the agricultural market is free, the rent for these better plots will be bid up, so that all farmers will
just earn enough to cover their costs and survive while the landlords extract a higher rent (as Smith
predicted). Therefore, while all farmers earn the same, the rents will decrease with increasing distance
from the market, forming a linearly declining land-rent gradient (see Figure 1).
To illustrate let us assume a market in which corn is
sold at $100, transporting corn costs $1 per
kilometer and non-land input costs are independent
of location and fixed at $50. A farmer living directly
adjacent to the market does not incur transport
costs and therefore reaps a profit of $50, while
farmers at the 20 kilometer and 50 kilometer mark,
will earn profits of $30 and 0$, respectively, after
paying for transport ($20 and $50). Since rent is
assumed to be the residual income of land (Smith,
1904) (thanks to the competitiveness of the
agricultural market and a perfectly inelastic supply
of land) the landlords will skim these extra profits
in the form of rent, meaning that all farmers earn
the same. Increasing transportation costs will
make the gradient steeper and increasing market prices will shift the gradient outwards.
1 In the logical order and conceptualization of following explanation of Thünen’s model I will rely mainly on Chapter 4 of McCann (2001)
Figure 1: Thünen land-rent gradient Source: Urban and Regional Economics (McCann, 2001)
6
Of the many assumptions the one that is most readily relaxed is the premise that all farmers grow the
same crop. One can easily allow for more than one crop as long as the other assumptions still hold for all
crop varieties (i.e. all variables are the same for all farmers growing the same crop while they can vary
between crops). In this case competition is not only between farmers but also crops which means that
the crop with the more expensive transport costs will be located closer to the town and farmers of that
crop will have to pay a higher rent (see Figure 2).
The effective land-rent gradient will then be the
envelope of both crops’ gradients.
In an example barley sells for $100 while wheat
only pays $50 per bushel. However, with transport
costs of $2 it is twice as expensive to move than
wheat. Both crops have fixed non-land input costs
of $50. We see that barley will be planted as far as
33 kilometers from the market while wheat only is
viable to grow beyond that mark. Nothing is grown
further than 50 kilometers from the town. We can
see that Von Thünen took up Ricardo’s
assumption that land will be allocated to the use
that pays the highest rents is reflected in this
model.
Despite its many assumptions that largely do not
hold up in the real world and its focus on only
agricultural rents, the Thünen-model is exceptional because it is the first account of an effort to explain
the spatial configuration of land use of cities and their hinterland in economies dominated by agriculture.
Nobel Prize-winning economist Paul Krugman notes that Thüenen’s model anticipates many concepts
that should become part of mainstream economics (Krugman, 1995). These include the idea of an
equilibrium (the pattern of concentric land-use rings around the town), a market value instead of an
inherent value of goods and factors (land gets its value through bidders competing for it), the
simultaneous pricing of goods and factor inputs (the maximum possible rent depends on the market
price of agricultural output), markets that achieve efficient outcomes (the highest bidder can use the
best land) and finally Von Thünen recognized the role prices play in incentivizing efficient behavior (the
more efficient a bidder is in his production, the higher he can bid).
Figure 2: Land Competition in the Thünen-model Source: Urban and Regional Economics (McCann, 2001)
7
The emergence of Modern Bid-Rent Theory
Maybe this foresight of ideas that later would become the heart of mainstream economics, explains why
it took almost 150 years until major contributions were made to Von Thünen’s theory. Although Alfred
Marshall anticipated one important prediction of modern Rent Theory, namely that higher prices will
lead to higher density (Marshall, 1890), he did not produce a spatial theory of rents. Other economists,
while interested in land-use patterns, did not build on Von Thünen’s work until William Alonso’s book
“Location and Land Use: Towards a General Theory of Land Rent” (Alonso, 1964). In this book Alonso
largely adopts Von Thüen’s assumptions but includes a small but important difference: in Alonso’s bid-
rent model the land to non-land input relationships required for production are not fixed anymore but
can differ. This means that land and non-land factors can be substituted for each other.
8
The important implication of this new
assumption is that rent is not a
residual anymore, as Smith, Ricardo
and Von Thünen assumed, but rather
one of many factors that are included
in the cost function of a firm. The cost
(dis-)advantages of a production
location therefore do not accrue to
the landlord anymore but to the
landholder. This landholder therefore
has an incentive to optimize his cost
function. To achieve efficiency, the
marginal costs (which in a competitive
economy, are equal to prices) of land
and non-land factors must be equal to each other. If this is not the case, a firm will substitute the more
expensive factors for more of the cheaper factors until balance is restored. For bid-rent theory this
means that, assuming non-land factor prices are independent of distance from the city center and the
price of land decreases with increasing distance, the costs of land fall relative to non-land costs.
Therefore, a profit maximizing firm will substitute non-land factors for more land. Conversely this
indicates that the closer a firm is to the city center the less land and the more non-land factors it will use
in its production (McCann, 2001). It is easy to see that this is exactly what Alfred Marshall predicted. The
result of this observation is a shape of the bid-rent-gradient in Alonso’s model that differs from Von
Thünen’s straight line: the gradient will be curved (see Figure 3). To see why, recall that while transport
costs t per kilometer are assumed to be fixed, the absolute land area used, increases with d from the city
center. The t per land area unit therefore decreases, which in turn decreases the rate with rent has to fall
in order to compensate for the higher t.
But what about land competition in bid-rent theory? After all it is aimed at explaining the spatial
structure of cities. Most generally we can say that the highest bidder will be closest to the city center.
Who that highest bidder is depends on the bidder’s production functions and the substitutability of land
with non-land factors and the importance of easy market access (i.e. distance to the center) in their
business models. Therefore, producers whose production is relatively land-intensive will be pushed to
the city’s outskirts, as other producers can just substitute non-land factors for less land and therefore
Figure 3: Bid-Rent Curve for an individual firm Source: Urban and Regional Economics (McCann, 2001)
9
Figure 4: Firm land competition in the Bid-Rent Curve Model Source: Urban and Regional Economics (McCann, 2001)
move closer to the center while this is option is not available to the land-intensive producers. This is one
of the reason why logistics centers or factories are seldom located in the middle of a city and why service
industries and specialized retail stores can often be found in the very center of cities. An example for
how activities could be distributed in a city can be found in Figure 4. The actual rent gradient for a city is
(similarly to Von Thünen’s model) not determined by any single firm’s but rather is composed of the
highest bidder’s at any given point. Thus, it is the envelope of all individual gradients. Finally, we can
determine the edge of the city as the point at which agricultural use is the highest bidder for land.
The reader might have noticed that all the
models discussed thus far have focused on the
location behavior of producers while this paper
is looking to investigate the effect of clusters on
rents for households and not firms. However,
extending the bid-rent framework to describe
consumer behavior seems like a natural
extension. Instead of optimizing profits,
households try to maximize utility given their
constraints. Instead of a market at the city
center, it is assumed that all employment
opportunities are located in the city center.
Commuting is increasingly costly in both
monetary and non-monetary terms with
increasing distance to the center. The exact estimation of these cost vary from $0.17 (Wilson & Frew,
2007) to $4.12 (Langelett & Chang, 2013) (in the author’s opinion the high estimate is an
overestimation). The conclusions of this household model are heavily dependent on the assumptions
one makes about the preferences of different groups of people. In most models these groups are formed
around household income. If we for example assume that transport costs are the same for each group
we will arrive at a bid-rent gradient for low income households that is very steep, as travel costs make up
a higher relative share of their income, they are less willing to move far away from the center, meaning
that the city center will be densely populated by low income individuals, while the income rises when
moving towards the city’s edge (see Figure 5). However, if we assume that because they can earn more
money per hour, the opportunity costs of commuting for high-income individuals are higher, the
conclusion turns around completely. Now the rich will have a steeper bid-rent gradient and therefore
10
occupy central locations while the poor are pushed away from employment opportunities towards the
periphery of the city (see Figure 6). Other variations of the underlying assumptions are also possible but
will not be further discussed here.
Now it is time to reflect on one implicit, underlying assumption of the household bid-rent model that has
not yet been discussed, although it is crucial for the correct empirical evaluation of the theory. Namely,
housing is seen as a homogenous commodity so that all units can be compared and utility derived from
them only varies with distance to the city center. It is not hard to see why this simplifying assumption is
highly problematic. It clearly ignores the important aspects of the real-world decision-making process
therefore distorting reality, as well as delivering faulty predictions. Maybe the most important of these
aspects is a housing unit’s environment. While an exact, generally agreed-upon definition of this term is
not yet established, the environment includes locational aspects of a housing unit that usually are
specific to that location. Locational aspects can either increase or decrease the utility derived from a
housing unit. Positive examples are amenities like good schools, parks or a variety of cafés while negative
ones can be pollution, a high crime rate or low social status of an area. One approach widely utilized to
account for environmental differences and circumvent the mentioned problems, was developed by
Sherwin Rosen (Rosen, 1974). He argues that housing is a composite commodity. A composite
commodity is a collection of goods whose relative prices do not change. Therefore, these goods can be
bundled and treated like one commodity (Oxford Reference, 2016). According to Rosen, households
choose a bundle of the individual attributes that maximizes their utility. In this point of view, one can
then isolate these single attributes and assess their individual impact on the valuation of a given housing
unit. Therefore, one can arrive at an estimation of the bid-rent gradient that is not confounded by
varying locational characteristics of housing bundles (Rosen, 1974).
Before the hypotheses for the empirical part of this thesis are developed in Section IV, the next passage
will present an overview over the literature regarding the bid-rent model.
III. Literature ReviewMost economists using the bid-rent framework follow a methodology developed by Sherwin Rosen in a
highly influential paper about hedonic prices and implicit markets (Rosen, 1974). Noting that “structural
interpretations of the hedonic method [were] not available”, Sherwin Rosen developed a methodology
that allows researchers to estimate a household’s willingness-to-pay for a given attribute of a composite
commodity and find the equilibrium in markets for composite goods. In a market for a composite
commodity and with utility-maximizing consumers, implicit prices for attributes can be estimated by
11
regressing the good’s price on its characteristics. In the next step the found prices are used to construct
an inverted demand curve. By integrating the demand curve from a lower to a higher value of the
attribute of interest one can determine the willingness-to-pay for said attribute. Although Rosen uses
this methodology to analyze the welfare implications of quality standard legislation, this approach can be
and in fact has been, widely applied to the housing market to obtain implicit prices of attributes by
academic articles several of which are also review hereafter.
In Rosen’s approach willingness-to-pay values are derived from the utility of an individual. Contrary to
that, Ellickson (1981) develops an alternative to this hedonic price modeling approach that allows a
direct and clear interpretation of results and does not need utility functions as connector of demand and
the price for an attribute of housing. Instead of inspecting the impact of housing attributes one at a time,
Ellickson proposes a multinomial logit model that can treat housing characteristics simultaneously. It also
does not focus only on hedonic price estimation but on how households actually react to these prices.
His model gives the probability of a house with certain characteristics being occupied by a consumer of a
given type. He uses data from the San Francisco Bay Area to test his model. The results clearly are in line
with bid-rent theory. All theorized factors that impact housing demand had the predicted effect. It is
interesting to note that the factors that showed the biggest differences in valuation by low- and high-
income households were the number of rooms, the median tract income and the hedonic residual. This
model is supplemented by Lerman and Kern (1983). They add a methodology that allows them to
determine the highest bidder’s willingness-to-pay for individual housing attributes that is missing in
Ellickson’s model (and exists in Rosen). However, they do not apply their model to empirical data. This in
turn was undertaken by David Gross (1988) using data from Bogota, Colombia. He furthermore compares
the findings of Ellickson’s model with the traditional hedonic price model by Rosen. Gross builds a model
with the help of seven housing attributes. These are the number of rooms, floor quality, total dwelling
area, roof quality, the mean neighborhood income, a measure of accessibility of employment centers
and the quality of sanitary facilities. Generally, the adapted Ellickson-model confirms the theory and
gives higher willingness-to-pay estimates than other models. These differences seem to be valid when
contrasting them with intuitive expectations of household preferences. The Ellickson-model’s predictive
power, however, does not instill confidence in the model with a low accurateness in predicting actual
rents. Gross attributes this to specification issues in the variables used and suggest further testing with
better data.
After this brief overview of the two most commonly used methodologies to test the bid-rent theory we
now turn to empirical studies of several cities, mainly in the United States but also in Europe and Asia.
12
Wilson and Frew (2007) examine not only whether rent gradients exist in Portland, Oregon but also how
they evolved between 1992 and 2002. Their choice of city is due to the very restrictive urban growth
legislation during that time which means that the supply of land in Portland did not markedly increase,
while demand for land did. They therefore hypothesize “[an] increase [in] rents overall with the highest
increases occurring in the city center [as a] result of increased congestion and higher
commuting costs”. Bid-rent theory predicts an increase in rents and a pushing out of the low bidders.
Next to three variables measuring the distance to the city center, to the next freeway ramp and to the
next freeway intersection, hedonic attributes were also included in their model. They find that rents
adjusted for inflation did in fact increase over the ten-year period with the increases being highest close
to the city center and going towards zero at the outskirts of the city. Apparently the Bid-Rent model does
hold in Portland, Oregon.
Instead of looking for a bid-rent gradient, Muto (2006) examines Tokyo to see whether the land-use
predictions of the bid-rent model are correct. In doing so he utilizes Full Information Maximum
Likelihood with one land usage and two land valuation functions. The study uses publicly announced,
yearly valuations of fixed points in the city generated by the Land Evaluation Committee. These
observations are combined with information about distance to the next public transport stops, land
usage and several other factors of interest. Since his research included both residential and commercial
land usage, instead of using housing attributes, Muto uses the distances to the next park, school, coast
and road as hedonic features of a location. He finds that bid-rent gradients are steeper for commercial
land uses than for residential one. Generally, the land-use predictions of his model confirm bid-rent
theory but close to the second CBD of Tokyo one can find deviations from the model. Muto explains this
with the relatively shorter time since the commercial development in this smaller center in combination
with residents that are slow at adapting to the highest-bidding land use. As mentioned before Muto’s
paper does not directly support this paper’s hypotheses but it does establish confidence in the bid-rent
model, even in complex land markets.
A similarly mixed result is found for Stockholm in Sweden (Söderberg & Janssen, 2001). In their study of
Stockholm from 2001 Söderberg and Janssen examine the effect of distance from the city center on the
transaction price, assessment price and rental income of over 300 houses traded between 1992-1994.
They find that a small number of variables, namely age, distance from the city center, size of the
property and received subsidies can explain these three value indicators very well. Interestingly, while a
price gradient can be established for Stockholm, this is not the case for the rental income regressions,
meaning that there is no rent gradient. Söderberg and Janssen attribute this finding to Gross
13
Capitalization Rates with which rent is discounted, that differ between properties due to differences in
hedonic factors (e.g. maintenance costs) and expectations of market participants with regards to the
rent controls in the city. Of course one cannot say with certainty that without these factors there would
be a bid-rent gradient, but the existence of a land price gradient does indicate at least the possibility of
such a gradient.
These findings instill confidence in the bid-rent model. However, in their paper “The Structure of Urban
Land Prices” Colwell and Munneke (1997) challenge these since most of them assume a linear
relationship between land price and area. They argue that land urban prices decrease, concavely instead
of linearly. This would lead to an overestimation of the bid-rent gradient slopes and therefore the impact
of employment or amenity centers on rents. To test their hypothesis, they use a dataset from the Real
Estate Data Inc. for the city of Chicago in the years 1986-1992. By comparing two models, one that does
not allow for non-linear land prices and one that does, they find that the former significantly
overestimates the bid-rent gradient’s slope. While their finding challenges commonly used
methodologies, it does not reject Alonso’s Bid-Rent theory altogether since they still find significant and
negative distance coefficients.
Colwell and Munneke are supported by other researchers who do not find significant rent gradients. One
city for which this is the case is San Francisco, California (Wheaton, 1977) which is also one of the first
empirical studies on this topic. Similar to Söderberg and his colleague, Wheaton finds that a small
number of housing variables and neighborhood income (as a proxy for local externalities) already have a
high prediction power of rents. He furthermore computes a value of time between $0.05 and $1.40 per
hour. However, his Accessibility-index that estimates closeness to commercial centers exhibit a negative
sign and therefore reduces rents. This clearly contradicts the predictions of bid-rent theory. The author
theorizes that negative externalities of being close to commercial centers like noise and congestion could
outweigh the benefits of closeness. Whatever the reason for the negative sign of accessibility, this raises
first doubts about the correctness of the Alonso-model.
These are further amplified by the findings of Dubin and Sung (1987). They start their paper with the
simple observations that many cities are not simply mono-centric as assumed by bid-rent theory which
they suggest could lead to another rent gradient than the strictly negatively sloped one predicted by
Alonso. They believe that the gradient will vary by direction depending on differing characteristics that
influence rents positively or negatively. The two researchers construct four 20°-rays emancipating
outwards from the city center of Baltimore, Maryland. They then analyze a subsample of observations
within each of these rays to develop rent gradients for each ray. Their findings call into question the
14
theory behind the bid-rent model. While amenity centers (such as the CBD but also sub-centers) do
exhibit negative rent gradients, their impact is locally very limited (to around 1.5 miles). The expected
dominance by the CBD on the rent gradient could not be established, since none of the rays have an
overall negative slope. Dubin and Sung conclude that the existence of non-CBD peaks may distort the
influence of CBD’s on rents in other studies. Finally, they make the model’s assumption of a homogenous
plain responsible for the empirical failure of bid-rent theory.
The previous three paragraphs call into question the validity of the Alonso-model. But this is not really
surprising after a short consideration of how much the world has changed since the early 1960’s when
the theory was developed. Transport and information technology have leapt forward and reduced the
importance of proximity for economic activity. Indeed, this reasoning is confirmed by a long-term study
of Chicago’s bid-rent gradients (McMillen, 1996). In his often quoted study McMillen uses nonparametric
estimators to investigate how the land gradients of Chicago, Illinois have changed in the more than 150
years between 1836 and 1990. Between 1836 and 1928 one can observe a distinct, negative gradient
that flattens out over time (1836: 60% rent reduction per mile, 1928: 20%). This is in line with a mono-
centric model that predicts flatter gradients for lower transport costs. In the Chicago case this was due to
the introduction of the light-rail network. The second observed period (1960-1990) is marked by a
decline of explanatory power of the strict mono-centric model. While the CBD still has the greatest
influence on rents, these 30 years also see the rise of O’Hara airport, a major employment center, as a
second peak in Chicago’s land-value landscape. The dilution of the mono-centric model is not surprising
considering the spatial expansion and sub-urbanization of Chicago in that time. Three conclusions of this
study matter for this thesis’s purposes. First, it calls into question the validity of the mono-centric model
in modern cities. Second, the study seems to supplement our theory that not the spatial center to a city
is what matters for bid-rent theory but the concentration of employment, as exemplified by O’Hara
airport. Finally, rents still can be explained by a small number of variables in modern times.
But while many empirical studies (especially historical ones) of bid-rent gradients have focused on
Chicago, McMillen’s findings are not unique to the Windy City. Atack and Margo (1998) were the first
ones providing a historical long-term study of the land prices in New York City. By using data obtained
from newspaper announcing location and sales price, as well as other important variables, of plots
located on the Manhattan-peninsula, they largely confirm findings from Chicago. At the start of the
observed period in 1835 a negative land rent gradient with City Hall as center can be clearly
distinguished. This gradient slowly flattens out over time and disappears after the American Civil War.
Similarly, the regression’s explanatory power using distance as the only explanatory variable decreases
15
dramatically from 60% in 1835 to almost zero in 1900 due to increasing land development and land
heterogeneity. These findings clearly show the impact of technology on travelling costs, as well as that
they are the determining variable for the spatial distribution of land values. The researchers intend to
enrich the currently available plot information and repeat the analysis.
From the studies examined thus far, emerges the impression that bid-rent theory is largely failing to
explain rents in modern, non-monocentric cities. Does that mean that we have to discard the Alonso-
model altogether? Not necessarily. While it is true that it is hard to justify an application of the model to
modern cities, due to overly strict assumptions that rarely are met in the real world, smaller sub-urban
clusters might exhibit rent gradients.
And indeed, empirical findings do suggest that this suspicion has some merit. One of the more famous
accounts of rent gradients of campuses was delivered by Coulson (1991). He tried to dispel doubts over
the monocentric model by arguing that previous studies trying to find the predicted negative bid-rent
gradients failed because of their use of data from housing markets that do not conform to the theory’s
assumptions. He uses a dataset from State College, Pennsylvania, a small, monocentric college town that
is home to Penn State University. The campus forms the center of the city and is immediately adjacent to
the Central Business District. Contrary to other studies, Coulson’s observation points encompass an
entire housing market (about 10- to 15-mile radius from the center) and all have a similar level of taxes
and service provision. The model used by Coulson accounts for several housing attributes and direction
relative to the CBD of the city. He finds that a negative bid-rent gradient exists in State College and even
more importantly this gradient falls with a similar rate (slightly more than $0.5 per mile) as the
transportation costs increase. Accumulating this per mile transport costs yields a decrease in
accumulated value of $2633.41 per mile from the city center. This study does not only confirm bid-rent
theory in an ideal setting but also indicates that campuses and therefore clusters of knowledge jobs, do
have rent gradients.
The proof that a campus can replace the CBD as the center of a city was delivered by Langelett and
Chang (2013). The two researchers examined Brookings, South Dakota, a city with several employers, the
second biggest of which is the South Dakota State University. However, more than 50% of the town’s
population are students. Their linear-regression model did not only contain two distance variables (one
for the campus, one for the CBD) but also controlled for housing attributes. Surprisingly the CBD-distance
variable is insignificant at the 10%-level while the campus variable is significant. On average, being one
mile further away from campus reduces monthly rent by about $4.12. These findings suggest that the
center of a mono-centric bid-rent model must not necessarily lie in the CBD but what matters for the
16
location of the center is the share of the local population commuting towards a given area. This is highly
relevant for this thesis since it strengthens the suspicion that campuses (and local clusters) can raise
rents in the surrounding neighborhoods. However, it remains to be seen whether this relationship also
holds for clusters that are the destination for a smaller share of a city’s population’s commuters.
A similar conclusion can be drawn from the student populations at Brigham Young and Utah State
university (Lewis & Kapp, 1994). The existence of a bid-rent gradient with the university campuses at the
respective center is confirmed by the two researchers. They believe that the Alonso-model’s
assumptions hold for this student sample better than for other populations thanks to the homogeneity
of the individuals and the importance of the campuses in the students’ everyday lives. In particular Lewis
and Kapp found a negative, non-linear rent gradient at both universities. Curiously, BYU students who
were perceived as richer, exhibited a less steep gradients and therefore lower opportunity costs of time.
Although the authors do not explain why this is the case, one could speculate that the flatter gradient
results from the availability of a campus shuttle bus at the BYU. It seems therefore that accessibility and
not distance is the important factor influencing rents.
Of course this seems obvious. Distance from the CBD or a cluster of knowledge-intensive jobs is not the
actual variable that one is interested in when looking for bid-rent gradients but rather it is a proxy for the
true variable of interest: transportation costs. The first one to fully conceptualize a framework with
transportation costs instead of distance was Youngsun Kwon. In his paper “Rent-Commuting Cost
Function versus Rent-Distance Function” (2002), Kwon develops an alternative to the distance rent
function: the Rent-Commuting Cost Function (RCC). As Yinger (1993) argued this is the more appropriate
explanatory variable for urban rent gradients since what matters for the utility derived from a housing
unit is not so much the distance from the CBD but rather the costs of transportation. According to Kwon
these two variables diverged in modern cities without dense hub-and-spoke commuting network thanks
to modern transport and information technologies. The advantage of the RCC is that it is independent of
the specification of the commuting cost function, contrary to the Rent-Distance function. This allows for
better insights into suburban settings. The RCC is an interesting concept as it is more closely orientated
towards the true explanatory variable of commuting costs (rather than distance which only serves as a
proxy). This makes the fact that Kwon did not suggest a way to feasibly implement his concept in
empirical studies even more regrettable.
Although Kwon was the first to develop a satisfying Rent-Commuting Cost Function, the importance of
transport costs was recognized long before him. In 1987 Coulson and Engle tried to estimate these
monetary and non-monetary commuting costs using a dataset of six major American cities in the years
17
1974-1979 (Coulson & Engle, Transportation Costs and the Rent Gradient, 1987). Common to these cities
was that they did not have an extensive rail system which could be used for commuting. The demand for
automobile commuting therefore was seen as largely inelastic in these cities. By observing house values
(seen as capitalized rents) they find that non-gasoline costs have correctly been capitalized while time
costs and gasoline costs have been overcapitalized. Despite their somewhat crude methodology this
study suggests that using transport costs instead of distance as determinants for the bid-rent gradient
confirms the theory better. However, the authors recommend further research with better data and a
more sophisticated methodology.
The existing empirical evidence paints a cautioning but not disheartening picture of the merits of bid-
rent theory. In the years before and shortly after World War II the Alonso-model did well in explaining
land use and rent gradients in cities like Chicago and New York. Over time, however, these rent gradients
flattened out (in New York earlier than in Chicago) or disappeared completely with new sub-centers
emerging as peaks of rents in the urban spatial structure. Albeit an untested suspicion, it seems like the
driving force behind this development is the advancement of transportation and information
technologies starting with the introduction of public transport services, continuing with the wide-spread
adoption of cars and telephones and coming to a temporary peak with the use of the internet in virtually
every aspect of life. However, this does not mean that we have to discard bid-rent theory as not useful
altogether. Various researchers found that employment and educational centers do exhibit significantly
negatively sloping rent gradients in many cities. This encourages a shift of focus from the urban
perspective to the intra-urban level of the city . Apparently, city centers have lost their overarching
economic importance and gave way to a more fractured distribution of economic activities within the
city. This arguably is a better depiction of today’s modern metropolises than the strictly mono-centric
model. Therefore, a fruitful field for research could lay in the application of bid-rent theory to small intra-
urban employment centers. Another effect of new ways of transporting goods and people, as well as
exchanging information is the erosion of the correlation of cost of commuting and its proxy distance,
prompting the need to augment the theory in order to capture this development but also to develop a
methodology that allows for a better estimation of actual commuting costs in empirical studies. Despite,
the overall mixed evidence regarding the Alonso-model, the existing literature instills confidence in this
thesis’s pursuit of finding rent gradients for knowledge-intensive employment clusters.
In the next section the hypotheses that this thesis is looking to test will be developed using the insights
gained from bid-rent theory and the literature review.
18
IV. HypothesesAfter looking at the bid-rent theory and examining empirical evidence regarding its validity, it is time to
formulate the hypotheses that will be used to assess the impact of employment centers in Rotterdam.
The clusters of knowledge-intensive jobs we examine replace the city center in the theoretical Alonso-
framework, laid out in the second section of this thesis. Accordingly, I expect to observe strictly negative
rent gradients and therefore the first, most fundamental hypothesis is:
H1: The observed clusters will exhibit negative rent gradients with increasing distance
However, assuming that every cluster has the same effect on its surrounding neighborhoods, would be a
dangerous oversimplification of the real world. Therefore, one further hypothesis that builds on the first
one, will be developed in the following. As mentioned earlier, the expected steepness of rent gradients
depends on the assumptions one makes about the target population. The example of high- and low-
income households was used to illustrate this phenomenon. Assuming that knowledge workers earn
more than less educated peers, this means a higher opportunity cost of commuting to them, as they
could earn more during the time spent travelling. Of course, commuting costs make up a smaller share of
their monthly budget and therefore less sensitive to commuting costs. However, here it is assumed that
due to their higher income and decreasing marginal returns, knowledge workers have a higher marginal
utility of time than of money and therefore will choose to locate close to their jobs. This leads to the
second hypothesis:
H2: The rent gradient of clusters with more knowledge-intensive jobs will exhibit a steeper slope than less
knowledge-intensive clusters
The next section outlines the methods applied to test these two hypotheses before moving on the data
being analyzed.
V. MethodologyTo test the hypotheses postulated in the preceding section, this paper will use an OLS-regression of an
appropriate specification which is to be determined in the following chapter. The dependent variable will
be the rent a given property yields to its owner. The measure of rents will be regressed on the distance
to the nearest cluster. This procedure allows the analysis of the effect of distance from a cluster on rents.
However, clearly distance from an employment center is not the only factor affecting the rent of a piece
of land. Following Rosen (Rosen, 1974) this thesis therefore will also develop a hedonic pricing model
(1)19
that decomposes the heterogeneous good housing into several attributes to isolate their effects and to
control for Omitted Variable Bias that exists when regressing rent only on distance. Equation (1) presents
the complete model that will be used for the analysis of the data.
Rent=β0Distance+β1 Ageof Unit+β2Typeof Owner+β3 Amenities of Unit+β4 Amenities∈Neighborhood+β5Riverside+β6¿Unit
All of these factors are assumed to play a role in the determination of a housing unit’s rent and therefore
are included in this paper’s model. The following paragraphs will outline the presumed effects of each of
these factors.
The age of a housing unit is thought to affect rent in two (at least partially) contradictory ways. First and
more obvious, a given house depreciates with increasing age, as its technology becomes outdated or
even obsolete and the substance deteriorates, necessitating renovations. Therefore, the first effect of
age is assumed to have a negative influence on rent. However, depending on the market and the wealth
of agents in it, units from different architectural periods command significant price premiums or discount
(Rehm, Filipova, & Stone , 2006). These are so-called “vintage effects”. Hence, no overall prediction for
the sign of age can be made.
Next, I suspect that the type of owner of a given dwelling does influence the rent it can command. This
happens through a differing willingness. An institutional real estate investor might be more willing to
spend on the upkeep of its real estate than an occupant owner in order to maintain its asset base. The
same could hold in reverse, since occupant owners are directly affected by the effects of depreciating
technology. Therefore, I do not make a prediction about the sign of the effect of ownership on a housing
unit’s rent.
Another factor influencing a unit’s rent are the private amenities that are attached to a given dwelling
and not necessarily shared with the neighborhood. These could include a garden for single family homes
or an elevator for multi-family homes. The more private amenities a dwelling possess, the higher its rent
is expected to be. The same holds for public amenities that are shared with the neighborhood such as
public parks, connections to the public transport system or good schools.
Riverside, is a factor that is included in the model to take into account a geographic characteristic of the
observed city. Rotterdam is divided into North and South by the river Maas. Due to the South’s history as
the main center of the port and the resulting amassing of low-skilled workers close to their jobs and
relative remoteness from the city center which is found in the North, the South is still seen as a less
20
desirable place to live. Therefore, dwellings located South of the river Maas are expected to command
smaller rents, holding all else constant.
Finally, the size of a unit is expected to have a positive effect on the rent a dwelling can command.
Sign of expected Effect Factors
+ Amenities of Unit, Amenities of Neighborhood, Size of Unit
- Riverside
+/- Age of Dwelling, Type of Owner
After introducing the model that will be utilized in this paper’s analysis, the attention turns to the
variables and data that will be used to populate the model.
VI. DataIn this chapter I will first discuss the definition of a knowledge-intensive clusters for the purpose of my
analysis and then introduce the housing data and explain which variables were used to asses which
component of the theoretical model outlines above.
So far this thesis has not given an unambiguous definition of what it means when it talks about
knowledge clusters. The answer to this question lies in a feature that arguably all high-technology
clusters share: a high concentration of knowledge-intensive jobs in a given area. Therefore, I will use this
criterion to determine clusters in the city of Rotterdam. This is done with the help of LISA-database
(establishment level data from 1996-2012, available for research at Erasmus University Rotterdam).
Among other variables, LISA collects information on the number of jobs in the different postcodes of the
Netherlands and assigns them to sectors based on the SBI, a standard industrial classification based on
the “International Standard Industrial Classification of all Economic Activities”.
By using the definition of knowledge-intensive sectors of the Dutch PBL Netherlands Environmental
Assessment Agency (Weterings, Raspe, & van den Berge, 2011) (see Appendix I), the share of knowledge-
intensive jobs relative to the total number of jobs for all four digit postcodes in Rotterdam for 2012 can
be obtained. Next, the Location Quotients (LQs) for knowledge-intensive jobs can be calculated for every
postcode in Rotterdam, by dividing the obtained shares by the Dutch average share of knowledge-
intensive jobs relative to total jobs (see Equation 2).
Figure 5: Summary of Expected Effects
21
Knowledge LocationQuotient=
Knowledge jobs∈givenZIPTotal jobs∈givenZIPKnowledge jobs∈NL
Total jobs∈NL¿
¿
A value of 1 or higher is considered more knowledge-intensive in jobs than the Dutch average and
therefore a potentially interesting cluster. In the analysis differing degrees of knowledge-intensity will be
considered.
Overall this procedure yielded 65 postcodes for which the LQ was not equal to zero (some postcodes are
reserved for post boxes and therefore do not contain any jobs, leading to numerator of zero in (2)). The
LQs had a mean of 1.085515, indicating that Rotterdam has slightly higher share of knowledge-intensive
jobs than the Netherlands overall. The values for the individual LQs ranged from a minimum of
0.3648455 to a maximum of 2.38057. When mapping the LQs one can observe that the most knowledge-
intensive postcodes are located centrally at Dijkzigt (LQ of 2.38) where the medical campus of Erasmus
University is located and on the north-western edge of Rotterdam (2.19) next to the Rotterdam-The
Hague Airport. The least knowledge intensive areas can be found in the west of Rotterdam in residential
areas with below-average incomes and in the very South of the city (see Appendix III).
This data on the LQs of the different postcodes was then combined with a dataset about the tax values
of homes and several important attributes of the housing units, collected by the city government of
Rotterdam in 2012 (available for research at the Erasmus University of Rotterdam). I am aware that tax
values are not the same as rents, however, data on rents in Rotterdam are currently not available.
Furthermore, it is a common practice in economics to see land values as the sum of all discounted cash
flows that would result from renting out a dwelling (see for example Muto, 2005 or Söderberg and
Janssen, 2000). The authorities estimated the tax values by taking the average of the transaction value of
three homes with similar attributes surrounding the object of interest and adjusting this average for
special characteristics of the observed home. A wide array of housing types was examined by the
authorities, ranging from one-room city center apartments to sub-urban villas with more than 9 rooms.
This procedure resulted in a dataset with 294586 observations. However, since for some of these
observations data on some of the control variables were missing, these were dropped so that 137002
observations for which the data was complete were considered. The mean tax value of observed
dwellings was 166203€ with a minimum of 16000€ and a maximum of 9270000€. A histogram of tax
values shows a strong right skew in the observations due to outliers in the form of expensive villas.
(2)
22
Figure 6: Histogram tax_value
01.
0e-0
62.
0e-0
63.
0e-0
64.
0e-0
6D
ensi
ty
0 2000000 4000000 6000000 8000000 10000000tax_value
Figure 7: Histogram lntax_value
0.2
.4.6
.81
Den
sity
10 12 14 16tax value
Therefore, the natural logarithm of the variable tax_values was obtained. This resulted in a much better
fit with the normal distribution (see Figures 6 and 7).
With the help of QGIS-software, the observations’ linear distances from their nearest postcode-centroid
were calculated. The resulting average distance from the nearest postcode-centroid for the Rotterdam
sample was approximately 517 meters but individual observations were located as close as less than a
meter or as far as more than 1800 meters from the next centroid.
Besides the tax value of dwellings, data on several other housing attributes was collected by the City of
Rotterdam. With the help of this information we can approximate the factors theorized to affect rent in
(1).
Age, the first component of (1) is approximated with two variables: y_constr and y_constr_cat. y_constr
is a continuous variable indicating the year of construction. With increasing age, a building is expected to
depreciate and therefore y_constr is expected to have a negative sign. However, due to vintage effects
houses from a certain period in time can be sought after for example for their appealing architecture.
Therefore, another time variable is included as a dummy: y_constr_cat, a categorical variable that takes
on the value 1 for houses built before 1945 and 8 for houses built after 2010.
The effect of ownership in (1) is captured by the categorical variable ownership which indicates whether
the owner is the Muncipality(=1), a Corporation(=2), an institutional investor(=3), a non-corporate
landlord with two to ten apartments(=4), a corporate owner with two to ten apartments(=5), a non-
corporate owner with a maximum of 100 dwellings(=6), a non-corporate owner with more than 100
units(=7), other non-corporate owner(=8) or an owner occupier(=9).
The variable apartment_type that categorizes dwellings Single Family Home(=1), Multiple Family Home
with elevator(=2), Multiple Family Home without elevator(=3) and other Multiple Family Home(=4) is
23
used to estimate the private amenities that a dwelling offers since these should be approximately the
same per type of housing. For example, many Single Family Homes have a garden or more than one
bathroom, while this is not the case Multiple Family Homes. The public amenities that accrue to all
homes in a given neighborhood can be estimated by environment, also a categorical variable. Its
categories include Center (=1), Center Edge(=2), Urban(=3), City(=4), Suburban(=5), Village(=6), Villas(=7)
and Industrial(=8). Again, neighborhoods in the same categories are expected to have similar amenities
while differing between types of environment.
The variable riverside describes on which side of the river Maas a given dwelling is located. This dummy
variable takes on the value 1 if a dwelling is located South of the river Maas.
Finally, the size of a housing unit is estimated by no less than four variables: plot_size, ground_m2,
sum_ground_m2 and rooms. plot_size measures the size of the plot a dwelling is built upon in square
meters, ground_m2 measures the Lettable Floor Area, a measure for the inhabitable floor space of a
dwelling, in accordance with the NEN2580-guideline, while sum_ground_m2 indicates the total
apartment ground space available for living and storage. The number of rooms of a dwelling is captured
by the categorical variable room.
Before moving to the analysis of the results, the relationships between the variables will be examined.
The correlation table (see Figure 8) several surprising findings can be worked out. The distance to the
nearest postcode centroid has a rather weak correlation with the tax value of a dwelling and even more
important it does have the (from this thesis’s theoretical point of view) unexpected sign. The scatterplot
of tax value and distance (see Figure 9) shows this low correlation and also suggest a linear functional
form for the linear regression in the next section. Another noteworthy fact is the low and negative
correlation between tax value and plot size. The rest of the correlations between the variables are either
low or of the expected high magnitude (e.g. room and ground_m2) and of the expected sign.
lntax_value dist_near_pc4 y_constr sum_ground_m2 plot_size ground_m2 riverside roomlntax_value 1dist_near_pc4 0.2290 1y_constr 0.2481 0.3296 1sum_ground_m2 0.8104 0.1539 0.0656 1plot_size -0.1763 -0.0145 0.1077 -0.1940 1ground_m2 0.7543 0.1132 0.1163 0.8483 -0.1679 1riverside -0.2883 0.0311 -0.0025 -0.1860 0.1070 -0.1568 1room 0.6688 0.1137 0.0923 0.7224 -0.1687 0.8061 -0.0595
Figure 8: Correlation Table
24
VII. ResultsWe now want to empirically assess the effect of distance from the nearest knowledge intensive cluster
on the rent a dwelling can command. First, no restrictions on the degree of knowledge-intensity of
clusters are applied (i.e. even clusters with a LQ below 1 are included in the regression) to find the most
appropriate model. After this step the degree of knowledge-intensity will be incremented in 0.25 steps
until a LQ of higher than 2 to see whether this affects the findings of the analysis.
Figure 9: Scatterplot Tax Value and Distance
25
First, the natural logarithm of tax values is regressed only on distance from the nearest centroid of a
postcode. This yields a very small, positive effect of distance which is nonetheless significant at the 1%-
level. The positive sign of distance is surprising but not yet worrying as the effect of distance probably is
entangled with effects of positive sign that grow with distance. For example, the number of rooms and
size of a dwelling tend to increase with distance from the densely populated urban centers. Because this
regression produced an adjusted R2 of slightly more than five percent and the mentioned suspicion of a
considerable Omitted Variable Bias, the control variables were added one at a time (see Figure 9).
When adding all (Regression 8 in Figure 10) controls the adjusted R2 does grow to 84.62%, suggesting a
good fit of the model with the sample. Furthermore, the influence of distance on tax values does
become negative while still being significant. On first glance the effect of distance from the nearest
postcode-centroid has an almost negligible coefficient (-0.0000316). However, one needs to keep in
mind that the depend variable is expressed as a natural logarithm and the unit of distance is one meter.
Therefore, if a house is one meter further away from the nearest postcode-centroid, its value decreases
by 0.00316%. Hence, for the average house price in Rotterdam of 166203€ this is an absolute decrease in
value of approximately 5,25€ with every meter further from the centroid, holding all else constant. The
variable y_constr has, as expected a significantly positive albeit small coefficient. The categorical variable
for age y_constr_cat interestingly changes sign between the categories for the 1970s (negative) and
1980s (positive). This indicates that while houses built after 1979 enjoy a premium, those built between
1945 and 1979 trade at a discount compared to the reference category of houses built before 1945. This
means that pre-war houses, which are a rarity in Rotterdam due to severe damages to the city, are
sought after and command a vintage premium. Houses from the reconstruction era on the other hand
are seen as less desirable. This “Reconstruction”-effect is compensated after 1979. This is presumably
due to better building standards and technology and less depreciation of these modern homes.
Looking at Model 8 also confirms the idea that ownership matters for tax values. Dwellings owned by
their owners have significantly higher tax values than for other kind of owners, safe for “other non-
corporate owners”. This difference is especially pronounced for housing units owned by the municipality,
corporations or institutional investors. As explained above, this might be due differing propensities to
maintain owned property but also self-selection of owners. For example, municipality owned social
housing commonly is found in areas in which housing prices are low.
When examining the categories for the apartment type one can observe that different types of housing
command differing premiums and discounts relative to the reference group of “other Multiple Family
Home”. Not surprisingly single family homes command a premium of almost 30 percent, presumably due
26
to their higher amenities like a garden, more privacy etc. and their location closer to the public amities
like parks or in the countryside. Multiple family homes with elevators trade at a price approximately five
percent above the reference category, while the ones without an elevator are offered with a four
percent discount. The variables capturing public amenities riverside and environment were also
significant. Dwellings South of the river are evaluated to have tax values that are almost 18 percent
lower than the same dwelling could catch if it were located in the North of Rotterdam. The environment
of a housing unit also matters for the price of a dwelling as the significance of the coefficients for the
different categories of the variable environment shows. All but one of categories fetch lower prices than
the reference category (City Center). Apparently, living in the city center still is valued highly, despite
growing evidence that bid-rent gradients do not apply to city centers anymore (see Literature Review).
lntax_value 1. 2. 3. 4.
dist_near_pc4 0.0003685*** 0.0003195*** 0.0000847*** -0.0000136***
y_constr 0.0031763*** 0.0008464*** -0.0016416***
dyconstr2 -0.2892519*** -0.1267003*** -0.0480948***
dyconstr3 -0.1923389*** -0.0464912*** 0.0499795***
dyconstr4 -0.1933317*** -0.0339419*** 0.1180881***
dyconstr5 -0.1996341*** 0.0078125 0.201817***
dyconstr6 0.0653171*** 0.1935215*** 0.3621011***
dyconstr7 0.388351*** 0.2872492*** 0.467399***
dyconstr8 0.12008958*** 0.2404492*** 0.4500744***
duownership1 -0.7799984*** -0.4227296***
duownership2 -0.7539254*** -0.4490501***
duownership3 -0.2217548** -0.1497487
duownership4 -0.546338*** -0.2283928***
duownership5 -0.6429055*** -0.300033***
duownership6 -0.6759013*** -0.3083084***
duownership7 -0.522231*** -0.282901***
duownership8 0.0087365 0.0418429***
dapartment1 0.4299973***
dapartment2 0.0311101***
dapartment3 -0.0196627***
sum_ground_m2
plot_size
ground_m2
riverside
denvironment2
27
denvironment3
denvironment4
denvironment5
denvironment6
denvironment7
denvironment8
droom1
droom2
droom3
droom4
droom5
droom6
droom7
_cons 11.66466*** 5.553396*** 10.688589*** 15.11657***adjusted R^2
0.0524 0.1787 0.5223 0.6010
lntax_value 5. 6. 7. 8.
dist_near_pc4 -0.0000087*** 0.0000143*** -0.0000319*** -0.0000316***
y_constr 0.0001878*** 0.0010388*** 0.0011412*** 0.0007868***
dyconstr2 -0.0376283*** -0.0542932 -0.0929008*** -0.0880623***
dyconstr3 -0.0058451 -0.0357572*** -0.0598174*** -0.0492377***
dyconstr4 0.005254 -0.0622717*** -0.0690143*** -0.0392366***
dyconstr5 0.0968842*** 0.0221005*** -0.0007518 0.0206707***
dyconstr6 0.1914574*** 0.1250314*** 0.1018385*** 0.1254819***
dyconstr7 0.2294296*** 0.1415406*** 0.1147561*** 0.1542823***
dyconstr8 0.2340732*** 0.1541298*** 0.1621016*** 0.2058816***
duownership1 -0.2311193*** -0.1750904*** -0.1697595*** -0.175518***
duownership2 -0.1940236*** -0.1530427*** -0.1503186*** -0.1573265***
duownership3 -0.1171759* -.1808374*** -0.1649379*** -0.1503938**
duownership4 -0.602424*** -0.0355651*** -0.0352114*** -0.0335152***
duownership5 -0.1146295*** -0.0858741*** -0.0866015*** -0.0796636***
duownership6 -0.086373*** -0.0719515*** -0.0734888*** -0.0688149***
duownership7 -0.0880013*** -0.0946747*** -0.1104321*** -0.1121625***
duownership8 0.0259143*** 0.021526*** 0.0165713*** 0.0157875***
dapartment1 0.2763413*** 0.3248878*** 0.297996*** 0.2944313***
dapartment2 0.072774*** 0.0680328*** 0.0470676*** 0.0484409***
dapartment3 -0.0364535*** -0.0302123*** -0.0335233*** -0.0419588***
sum_ground_m2 0.005069*** 0.0046697*** 0.0045412*** 0.0044176***
plot_size 0.0000032*** 0.0000040*** 0.0000030*** 0.0000028***
Figure 10: Regression Tables without Restrictions on Knowledge-intensity
***= significant at the 1%-level
** = significant at the 5%-level
* = significant at the 10%-level
28
ground_m2 0.0028934*** 0.0028352*** 0.0028024*** 0.0023927***
riverside -0.1864484*** -0.1771982*** -0.1799992***
denvironment2 -0.1739058*** -0.1782211***
denvironment3 -0.203413*** -0.2065619***
denvironment4 -0.1401866*** -0.1393492***
denvironment5 -0.1017802*** -0.1026468***
denvironment6 -0.1195294*** -0.1249651***
denvironment7 0.0724187*** 0.0817554***
denvironment8 -0.1010124*** -0.0816854***
droom1 -0.2414717***
droom2 -0.0961367***
droom3 -0.0392677***
droom4 -0.0367461***
droom5 -0.0565204***
droom6 0.0237725***
droom7 0.038894***
_cons 10.75367*** 9.180192*** 9.189156*** 9.976766***
adjusted R^2 0.8100 0.8375 0.8462 0.8499
The three variables sum_ground_m2, plot_size and ground_m2 measuring dwelling size all have the
expected positive sign and are significant. However, especially the coefficient of plot_size is almost
negligible. The last size variable room is a little more interesting and deserves further attention. While
apartments with one to five rooms fetched a lower price than the reference category of eight or more
rooms (coefficients between -0.2415 and -0.0368), dwellings with six or seven rooms were more
expensive, holding all else constant. This calls into question the economic notion of more is always
better. One can only speculate about the reason for this finding. I suspect that the marginal utility of an
additional room is outweighed by the marginal costs of maintaining another room which makes these big
homes less attractive.
So far the analysis of the results has focused on the full sample of 137002 homes and 65 centroids and
the effect of all units to the nearest centroid of a postcode. This was done to find the regression with the
best fit and minimal Omitted Variable Bias. As can be seen in Figure 10 this regression is Model 8.
However, the aim of this paper is to evaluate the effect of distance from knowledge-intensive clusters on
a dwelling’s value. Therefore, the next paragraphs will repeat Model 8 with increasingly restrictive
definitions of knowledge-intensity to see whether the effect of distance depends on the degree of
knowledge-intensity (see Figure 11, page 31).
At first the sample was restricted to homes whose nearest centroid had a LQ of at least one. This
regression used 34 centroids and explains 84.96% of the total variation of the natural logarithm of tax
29
value. The distance from the nearest centroid is significantly negative (at the 1%-level), although not very
high. Holding all else equal, tax values decrease by 0.00606% with every additional meter from the
centroid. The other variables largely stay the same, safe for a few categories of ownership, environment
and room changing signs. An interesting finding that should be explicitly noted is that the third category
of ownership is omitted automatically due to collinearity. However, this should not be a problem since
ownership is just a control variable and dist_nearest_pc4 does not have an extraordinarily high VIF (see
Appendix IV). According to Paul Allison one can safely ignore collinearity if those two conditions are met
(Allison, 2016).
The next regression further limited the sample used to homes whose nearest centroid had a LQ of 1.25
or higher (i.e. 19 centroids). This regression explained the variation in tax values slightly better (R 2 =
88.05%). The effect of distance was only about half as big as for the k>=1 regression but still significantly
negative at the 1%-level. The third category of ownership again was omitted but the VIF of distance again
was not worryingly large.
With an adjusted R2 of 88.33% the regression limiting the sample to the ten centroids with LQs higher
than 1.5 has the best explanatory power of all models examined in this thesis. The negative effect of
distance on tax value is slightly less than in the second regression (-0.0000244) but nonetheless
significant at all levels. The omission of the third ownership category due collinearity does not pose a
problem in this regression either.
The fourth regression (LQ higher or equal to 1.75) showed a lower, but still high adjusted R2 than the
previous one (86.40%). Curiously, distance now has an insignificant effect on tax values which is directly
contradictory to the hypotheses developed in Section IV. Furthermore, next to the third category of
ownership, the fifth and the seventh category of environment were omitted due to collinearity. But the
two conditions for ignoring this, are met again.
Finally, the regression restricting the sample to two centroids with LQs higher than 2 and 343 dwellings
shows a very curious finding. Distance has a significantly positive effect on the tax values of homes. This
is against bid-rent theory and questions the hypotheses of this thesis. However, caution is necessary
when interpreting these findings. Firstly, the sample size of two centroids is very limited, meaning that
the external validity is questionable at best. Secondly, the VIFs of this regression show a high collinearity
of distance, leading to potentially biased estimators. A potential explanation for the sign of the effect of
distance could be that one of the two centroids (postcode: 3046) is located directly next to the
Rotterdam-The Hague Airport and a major highway linking Rotterdam with Delft. This hardly is a pleasant
30
area to live in. Therefore, people should be willing to pay more for living further away from this centroid.
But when running the same regressions for each of the two centroids separately one can see that the
3046-centroid (0.0002253) actually has a less steep (and insignificant) gradient than the seemingly more
attractive 3015-centroid (0.0006061) which is in the center of Rotterdam next to amenities like museums
and good public transport accessibility. A last note on the many omitted categorical variables shall be
made here. The primary reason for omission here, was the fact that there were simply no observations
relating to the omitted categories.
After presenting these findings, this thesis will conclude with a discussion and conclusion about the
effect of knowledge-intensive clusters on rents in Rotterdam.
lntax_valuek>=1 k>=1.25 k>=1.5 k>=1.75
dist_near_pc4 -0.0000606*** -0.0000289*** -0.0000244*** -0.0000013
y_constr 0.0011908*** 0.001491*** 0.0023255*** 0.0022152***
dyconstr2 -0.0412048*** -0.0524683*** 0.1181875*** -0.019215
dyconstr3 -0.0652561*** -0.1286271*** -0.2263896*** -0.1630647***
dyconstr4 -0.0320055*** -0.11609*** -0.1737266*** -0.2037045***
dyconstr5 0.0110428* 0.0367814*** -0.0301773*** -0.0661864***
dyconstr6 0.0861825*** 0.05833371*** -0.0264361** -0.0174679***
dyconstr7 0.1186978*** 0.0721456*** 0.0308603** 0.0309742**
dyconstr8 0.1328276*** 0.0827074*** 0.1428488*** 0.0624175**
duownership1 -0.149063*** -0.0607364*** 0.1141728*** -0.1923162***
duownership2 -0.1772638*** -0.1441764*** -0.1334286*** -0.089958***
duownership3 0 (omitted) 0 (omitted) 0 (omitted) 0 (omitted)
duownership4 -0.0498645*** -0.0070905 0.0412503*** 0.0281216**
duownership5 -0.0919179*** -0.0483708*** -0.0441373** -0.0140326
duownership6 -0.0886258*** -0.0443189*** 0.045316*** 0.0044404
duownership7 -0.1708318*** -0.1861158*** -0.1336861*** -0.0995685***
duownership8 -0.0114313*** -0.197992** 0.052848*** 0.012941
dapartment1 0.3181974*** 0.3430796*** 0.327683*** 0.3646274***
dapartment2 0.0414126*** 0.0349353*** 0.019628*** 0.0576776***
dapartment3 -0.038341*** -0.026041*** -0.303017*** -0.0757103***
sum_ground_m2 0.0042631*** 0.0033254*** 0.0028292*** 0.001595***
plot_size 0.0000017*** 0.0000002 0.0000033*** 0.0000011***
ground_m2 0.0024612*** 0.0030986*** 0.0038589*** 0.0040338***
riverside -0.1908576*** -0.191606*** -0.2766607*** -0.6045056***
denvironment2 -0.3610923*** -0.1234366*** -0.0735269*** -0.1364981***
denvironment3 -0.4001172*** -0.1198175*** -0.1489159*** 0.0607601
denvironment4 -0.2675589*** 0.0121255 0.1359702*** 0.373466***
31
denvironment5 -0.2385027*** 0.0162464 0.0182966 0 (omitted)
denvironment6 -0.256082*** -0.0235732 0.0506407* 0.2700543***
denvironment7 -0.0006791 0.3416255*** 1.09735*** 0 (omitted)
denvironment8 -0.2728962*** 0.0383364 0.0796857** 0.137553***
droom1 -0.1926041*** -0.1716144*** -0.0406069 -0.0071746
droom2 -0.0309875*** -0.00014 0.1473815*** 0.2380516***
droom3 0.0129498 0.0285744* 0.1794369*** 0.2713711***
droom4 0.0061724 0.0279441* 0.1694286*** 0.2640565***
droom5 -0.0027606 0.0163113 0.164025*** 0.2250236***
droom6 0.0756637*** 0.382606*** 0.2325924*** 0.2530362***
droom7 0.1157993*** 0.0853812*** 0.2786105*** 0.4153534***
_cons 9.352747*** 8.509706*** 6.749644*** 7.003961***
adj. R^2 0.8496 0.8805 0.8833 0.8640
Figure 11: Regression Tables with Restrictions on Knowledge-intensity
32
lntax_valuek>=2 Only 3015 Only 3046
dist_near_pc4 0.0003822*** 0.0006061*** 0.0002253
y_constr 0.003843*** 0.0053318*** 0.0124691
dyconstr2 -0.2992539** -0.4187808*** 0 (omitted)
dyconstr3 -0.1933095 0.5131276** -0.8623801
dyconstr4 0.2496645 0 (omitted) -0.520663
dyconstr5 0.0734633 0.3708953** -1.1175265
dyconstr6 -1.239897*** 0 (omitted) -1.949331
dyconstr7 -0.1372672 0.1459356 -1.216097
dyconstr8 0 (omitted) 0 (omitted) 0 (omitted)
duownership1 1.000993*** 0 (omitted) 0.7301033
duownership2 -0.4690373*** -0.542688*** 0 (omitted)
duownership3 0 (omitted) 0 (omitted) 0 (omitted)
duownership4 -0.0481216 -0.1418146** 0.1519459
duownership5 -0.1696528** -0.280471*** 0 (omitted)
duownership6 -0.0976562 -0.1740088*** 0 (omitted)
duownership7 0 (omitted) 0 (omitted) 0 (omitted)
duownership8 -0.4100074** 0 (omitted) -0.2119704
dapartment1 0.8625005*** 0.4244441*** 0 (omitted)
dapartment2 0.0110917 0.0119607 0 (omitted)
dapartment3 0.0021564 0.0299371 0 (omitted)
sum_ground_m2 0.0000643 0.0017315*** 0.0000108
plot_size 0.0000107 -0.0001866*** 0.0000247**
ground_m2 0.0038233*** 0.0027989*** 0.0010431
riverside 0 (omitted) 0 (omitted) 0 (omitted)
denvironment2 -0.2684563*** -0.2470764*** 0 (omitted)
denvironment3 0 (omitted) 0 (omitted) 0 (omitted)
denvironment4 0 (omitted) 0 (omitted) 0 (omitted)
denvironment5 0 (omitted) 0 (omitted) 0 (omitted)
denvironment6 0 (omitted) 0 (omitted) 0 (omitted)
denvironment7 0 (omitted) 0 (omitted) 0 (omitted)
denvironment8 -0.831523*** 0 (omitted) 0 (omitted)
droom1 -0.3146396*** -0.2646323** -0.4918073
droom2 0.1569341 0.2149585* -0.5570457
droom3 0.2197384** 0.2718141** -0.3417601
droom4 0.3282782*** 0.3768*** -0.2603551
droom5 0.410431*** 0.504768*** 0.1990015
droom6 0.4644084*** 0.4907834*** 0.054926
droom7 0.6919235*** 0.7534334*** 0 (omitted)
_cons 4.180003 1.212693 -11.0815
adj. R^2 0.8714 0.8556 0.7471
VIII. DiscussionFinally, the question that remains is what the above findings mean for the general applicability of the
bid-rent framework in modern, polycentric cities. Bid-rent theory is a child of the early 19 th-century when
transportation was slow and expensive and urbanization just started to set in. The rapid growth of cities
sparked the interest in their spatial structures. However, as this growth accelerated and cities became
too big to have a single center, the validity of the bid-rent theory using a single city center as a reference
point was questioned both by theorists and empirical findings. Today, the search continues for a
replacement of the city center or even a completely new framework of thinking. Literature offered
airports (e.g. in Chicago), University Campuses (e.g. in Collegetown) or multi-centric models as
alternative to the Alonso-model.
This thesis tests whether knowledge-intensive employment centers can be a viable alternative to the
(single) city center in a mono-centric model as suggested by Joel Garreau in his book “Edge City” (1991).
It tried to establish whether the distance from knowledge-intensive clusters has a significant impact on
the rent a housing unit can fetch on the market holding all other relevant factors constant. A linear
regression model with tax values as dependent variable and distance from the nearest centroid of a
postcode as variable of interest was developed Furthermore, controls for various factors were added to
eliminate Omitted Variable Bias and increase the precision of the estimators. This model was applied to
data collected by the city of Rotterdam.
***= significant at the 1%-level
** = significant at the 5%-level
* = significant at the 10%-level
33
The results are mixed. While distance seems to have the predicted significantly negative effect on house
values in four out of the six regressions run, for one the effect was insignificant and for the last one
distance had the opposite of the predicted effect. Therefore, the first hypothesis cannot be rejected,
meaning that knowledge-intensive clusters generally do exhibit negative bid-rent gradients. However,
the second hypothesis must be rejected. It is not the case that a higher knowledge-intensity always leads
to steeper gradients. In fact, as can be seen from Figure 11, the gradients become steeper with a higher k
until k reaches 1.75, after which they become flatter again. This suggests that the relationship between
the effect of distance from a cluster on rents and the degree of knowledge-intensity is not linear but
rather U-shaped. The reason for this shape is unclear. But it might be due to different commuter group
profiles. As explained above differing assumptions about a population group lead to differing bid-rent
gradients. In this case for example, the primary group of people working in the two clusters might have
upward sloping rent gradients due to some shared characteristic. For example, both employment centers
are located close to highways, making them easily accessible by car. As argued in McCann (2001). High-
income groups often have upwards sloping bid-rent gradients and prefer to live on the outskirts of a city
commuting to work by car. However, further research has to confirm the upward slope for cities other
than Rotterdam and the provided explanation.
0.997
0.9975
0.998
0.9985
0.999
0.9995
1
1.0005
1.001
Without Restrictionsk>=1k>=1.5k>=1.25k>=1.75k>=2
Distance
Val
ue
Figure 11: Rent Gradients of all Regressions
34
This leads us to the limitations of this study. Not only, was the sample restricted to one city, and as a
result some regressions had as little as two clusters to observe. The next logical step would be to use the
same definition for knowledge-intensive clusters and to collect similar housing data for the whole of the
Netherlands to test the robustness of the findings in this thesis. Additionally, a more sophisticated
regression model should be developed and different specifications of the distance-rent relationship
should be tested and a better proxy for transport costs than distance should be incorporated. Doing this
unfortunately was beyond the scope of this paper. The last limitation that should be addressed by
further research is the exclusion of distance effects other than the nearest postcode centroid. Ideally,
one would run a regression controlling for the effect of clusters located further away than the next one
but that still potentially have an impact on rent. Imagine for example a house that is situated between
two clusters but is one meter closer to one of them. This thesis’ methodology completely ignores the
effect on rent of the cluster that is further away, although there is little reason to believe that this effect
vanishes with one additional meter of distance.
Overall, one can say that this paper suggests that knowledge-intensive clusters matter for the rent
structure of modern cities. However, the results are not clear enough to present clear-cut policy
recommendations. For moderately knowledge-intensive employment clusters there seem to be negative
externalities to residents in the form of higher rents. These should be taken into consideration when
designing cluster policies. For very knowledge-intensive employment centers on the other hand, these
externalities are positive. Governments should therefore try to locate clusters in areas where the
accumulated effects of these externalities are minimized. This would mean placing them in industrial and
not in residential areas.
Hopefully, this thesis is a starting point for further research in the exact nature of the influence of high-
tech clusters on the rent structure of cities and its robustness in different settings.
35
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38
X. Appendix
Appendix I: List of Knowledge-intensive Industries (taken from Weterings et. al. (2011), page 104)
39
40
ZIP CodeLocation Quotient ZIP Code
Location Quotient ZIP Code
Location Quotient ZIP Code
Location Quotient
3000 - 3031 0,786112 3062 1,417001 3093 -
3001 - 3032 1,567105 3063 1,133249 3094 -
3002 - 3033 1,64225 3064 0,9693574 3095 -
3003 - 3034 1,524731 3065 1,702389 3096 -
3004 - 3035 1,147953 3066 1,500552 3097 -
3005 - 3036 0,8574769 3067 0,7728564 3098 -
3006 - 3037 1,035812 3068 0,943135 3099 -
3007 - 3038 0,9503129 3069 0,5863227
3008 - 3039 1,256072 3070 -
3009 - 3040 - 3071 0,9623153 Observations 65
3010 - 3041 0,4530251 3072 1,745873 Minimum 0,7501127
3011 1,234389 3042 0,6270131 3073 0,6464555 Mean 1,16261414
3012 0,7501127 3043 0,7547053 3074 0,9256984 Std. Dev. 0,64463975
3013 0,8850687 3044 0,7040626 3075 1,778433
3014 1,194715 3045 1,331951 3076 1,3553628
3015 2,38057 3046 2,193705 3077 1,089
3016 1,000873 3047 0,6616901 3078 0,7154721
3017 - 3048 - 3079 1,942365
3018 - 3049 - 3080 -
3019 - 3050 - 3081 1,174206
3020 - 3051 0,9638782 3082 1,31047
3021 1,001869 3052 1,329921 3083 1,381862
3022 1,141769 3053 0,8398102 3084 0,8522414
3023 0,9989169 3054 0,7915879 3085 0,6418592
3024 1,289741 3055 1,212155 3086 0,6652775
3025 0,7585588 3056 1,288567 3087 0,4563027
3026 1,190727 3057 - 3088 0,3689086
3027 1,207223 3058 - 3089 0,3648455
3028 1,223328 3059 0,8792165 3090 -
3029 1,181351 3060 - 3091 -
3030 - 3061 0,9183446 3092 -Appendix II: List of all Rotterdam ZIP-Codes with corresponding Location Quotients
41
Appendix III: Map of Rotterdam with ZIPs and their Location Quotients
42
Variable k>=1 k>=1.25 k>=1.5 k>=1.75 k>=2
dist_near_pc4 7.28 1.27 1.32 1.72 7.28
y_constr 37.60 16.38 21.48 20.89 37.60
dyconstr2 1.47 1.93 1.10 1.06 1.47
dyconstr3 1.91 7.93 9.02 10.97 1.91
dyconstr4 2.44 4.63 5.18 8.92 2.44
dyconstr5 35.31 8.36 10.67 7.96 35.31
dyconstr6 3.17 13.82 20.46 12.36 3.17
dyconstr7 26.81 6.43 5.56 8.65 26.81
dyconstr8 - 1.35 1.49 1.33 -
duownership1 2.42 1.36 1.06 1.03 2.42
duownership2 11.63 3.19 3.24 2.75 11.63
duownership3 - - - - -
duownership4 3.73 1.30 1.23 1.17 3.73
duownership5 1.74 1.05 1.07 1.14 1.74
duownership6 4.88 1.54 1.33 1.34 4.88
duownership7 - 1.31 1.25 1.28 -
duownership8 1.60 1.05 1.04 1.04 1.60
dapartment1 12.45 4.73 5.41 4.82 12.45
dapartment2 5.05 2.84 3.10 3.07 5.05
dapartment3 1.53 2.26 2.16 3.03 1.53
sum_ground_m2 2.79 3.92 3.57 2.66 2.79
plot_size 2.99 1.49 1.59 1.74 2.99
ground_m2 5.84 5.73 5.55 5.31 5.84
riverside - 1.81 5.39 95.91 -
denvironment2 5.32 109.16 85.25 9.67 5.32
denvironment3 - 141.09 53.21 17.94 -
denvironment4 - 215.79 97.71 637.11 -
denvironment5 - 150.11 116.53 - -
denvironment6 - 115.43 107.39 642.57 -
denvironment7 - 14.40 1.04 - -
denvironment8 16.01 1.97 1.99 2.31 16.01
droom1 - 6.31 10.44 15.23 -
droom2 27.23 37.33 57.43 96.16 27.23
droom3 16.17 60.34 117.55 192.19 16.17
droom4 4.99 52.28 101.56 199.26 4.99
droom5 9.24 35.93 69.76 106.78 9.24
droom6 2.73 6.01 9.20 10.38 2.73
droom7 1.98 2.51 2.61 192.19 1.98Appendix IV: VIFs for Regressions with Restrictions on Knowledge-intensity
43