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A non-parametric CAE approach to office rents: Identification of Helsinki metropolitan area submarkets
Expert Systems with Applications 39 (2012) 460–471
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Expert Systems with Applications journal homepage: www.elsevier.com/locate/eswa
A non-parametric CAE approach to office rents: Identification of Helsinki metropolitan area submarkets Marjan Cˇeh a,⇑, Kauko Viitanen b, Iztok Peruš a a b
Faculty of Civil and Geodetic Engineering, University of Ljubljana, Jamova 2, SI-1000 Ljubljana, Slovenia Institute of Real Estate Studies, Helsinki University of Technology TKK, P.O. Box 1200, FI-02015 TKK, Finland
a r t i c l e
i n f o
Keywords: CAE non-parametric empirical method Submarkets Office rents Accessibility Agglomeration GIS-created variables
a b s t r a c t The study attempts to identify and estimate the office rents of submarkets in the Helsinki metropolitan area. We applied a non-parametric empirical approach called the CAE method to identify six parameters: highway APD (access point distance), car traffic density, light rail APD, main retail distance, office building density and effective age. Our results suggest that car traffic density is the single most influential parameter. Office rent decreases with effective age and increases with the density of office buildings. Longer distances to highway access points and to the main retail centres decrease office rents, while shorter distances to the light rail access points increase office rents in general and particularly for locations close to highway access points. We identified local peaks by inspecting multiple graphs. The local peaks were considered evidence for the existence of commercial office submarkets within the Helsinki metropolitan area. We identified seven submarkets at different rent levels. Interpreting submarkets from the CAE graphs allowed us to recognise particular business districts in the Helsinki metropolitan area. In addition, it is of great significance that the roles of the given and estimated variables can be exchanged. The method is directly applicable in real estate studies using adapted database and prescribed smoothing parameters. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction In the domain of commercial office space, firms consider the advantages and disadvantages of office building quality, neighbourhood development and location according to their customers’ and employees’ needs and perceptions. Among these, location comprises a complex phenomenon depending on various factors detectable by market players. Researchers have tried to detect the location factors, to predict their value using various approaches and to determine their different levels of influence using scientific approaches. In examining the relationship between a city’s spatial impact and its market for office space, pre-existing geography is an inertial force in creating a path dependency for the location of office-based services. The establishment of a large market for office space can create agglomeration economies (Lizieri, 2009). Early (Clapp, Kim, & Gelfand, 2002; Clapp, Pollakowski, & Lynford, 1992), and recent (Brounen and Jennen, 2008) studies suggest that spatial patterns are strongly related to market dynamics. Brounen and Jennen (2009) created a measure of growth potential that allows for the
⇑ Corresponding author. ˇ eh). E-mail addresses: [email protected], [email protected] (M. C 0957-4174/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2011.07.037
evaluation of office agglomerations over time. Nappi-Choulet and Maury (2009) proposed a Bayesian STAR model to control for heteroskedasticity in the market for office space in Paris. Hysom and Crawford (1997) concluded that location is an amalgam of several factors which, when combined, impart a specific value to a location. Intra-metropolitan location was found to depend on agglomeration economics, which consist of localised economies that accrue to firms of the same sector. Agglomeration economies are represented by the density of office buildings. Profit maximisation could be enhanced by agglomeration, especially when office or commercial retail space is highly dense and in locations where there is potential for increasing the ratio of future rents to land, labour and transport costs (Jennen & Brounen, 2009; Margulis, 2007). Several researchers have suggested that commercial firms value access to service centres (Bruinsma, 1997; Koppels, 2006; Ryan, 2005; Sivitanidou, 1995,1996). A similar explanation and identification was reported earlier by Bruinsma (1997), who stated that the centrality and the accessibility of an office best explain why firms tend to value cities as location sites. Trevillion, Wang, and Withall (2006) reported on the shift of offices away from traditional central business districts (CBDs) and into new business locations, citing difficulties in fulfilling long-term demand requirements in the market for office space in Edinburgh. Koppels
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(2006) proposed an analysis of rent variations within metropolitan boundaries at a single moment in time, an approach by which the added value of office property attributes and site-specific characteristics can be assessed. Research by Jakobson and Onsager (2005) considered head offices as flow nodes and emphasised their geographical concentrations. Ryan (2005) and Ghebreegziabiher and Jasper (2008) examined the importance of access to light rail transit and highway systems in estimating office and industrial property rents. Hedonic price analysis was applied to properties in the San Diego metropolitan area and Amsterdam’s South Axis area. The results indicated that access to highways and access to light rail are significant factors in estimating office property rents. A different approach was proposed by Mourouzi-Sivitanidou (1999). She explored adjustments in metropolitan office rental rates towards their implicit equilibrium levels. Sing, Ooi, Wong, and Lum (2006) presented results on the office space preferences of occupants of Suntec City. Based on mean scores, they revealed that prestige of an office location and accessibility by public transport are the two factors most highly ranked by firms. Recent studies have analysed and identified office submarkets. Dunse, Leishman, and Watkins (2001, 2002) argued that there are sound theoretical and technical arguments for segmenting office markets into distinct submarkets. They suggested that office submarkets should be derived empirically, rather than according to the prior knowledge of agents or researchers, by applying principal components and cluster analysis. Among the attributes they tested were age of the real estate, distances to key points of accessibility and location quality indicators. More recently, Archer and Smith (2003) explained office clustering (i.e., office submarkets) using the nature of office functions, related industry economies of scale, and office location in the context of modern urban theory and communication requirements. McMillen and Smith (2003) claimed that large metropolitan areas with high congestion levels are virtually certain to have at least one sub-centre and that the number of sub-centres rises with population and commuting costs. These two variables account for nearly 80% of the variation in the number of sub-centres across urban areas. Many studies of property markets use Geographic Information Systems (GIS), which can enable one to better locate business clusters (i.e., Jennen & Brounen, 2009; Rodriguez, Sirmans, & Marks, 1995; Thrall, 1998; Weber, 2001). Karakozova (2004) is, to our knowledge, the only study published of the market for Helsinki office space. She investigated the variation in office capital growth over a 30-year period, from 1971 to 2001, using three alternative models: a regression model, an error correction model (ECM), and an integrated autoregressivemoving average model with exogenous explanatory variables (ARIMAX). This paper relies on a new approach to identifying submarkets and estimating commercial office properties, dealing simultaneously with six influential parameters without any a priori assumptions. We describe and apply a non-parametric empirical approach called the CAE method. We also discuss the input variables that are most influential in determining office rents. Our important results are shown in graphs, enabling analysis of the influence of the input variables on the office rents and the identification of submarkets. This study is part of a research project conducted at the Institute of Real Estate Studies, Helsinki University of Technology TKK. 2. The CAE method The CAE method is based on a special type of multi-dimensional, non-parametric regression and represents a kind of probabilistic neural network. Developed by Grabec and Sachse (1991,1997), it enables relatively simple empirical modelling of different phenom-
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ena. The method has already been used in the field of structural engineering to model attenuation relationships (Fajfar & Peruš, 1997) and, more recently, to model the force–displacement envelope of dynamically loaded RC columns (Peruš and Fajfar, 2007). In addition, an application in the field of metallurgy (i.e., prediction of tool wear in hot forging and modelling hot flow curves) was also successful (Tercˇelj, Peruš, & Turk, 2003, 2004; Tercˇelj, Turk, Kugler, & Peruš, 2008). A detailed description of the CAE method can be found elsewhere (see Peruš, Poljanšek, & Fajfar, 2006). However, the description in this paper enables a very simple and efficient application of the CAE method in real estate studies. Office rent, denoted as r, is characterised by a sample of observations of N offices. The mathematical description of an observation of a single office is called a model vector. Consequently, the whole phenomenon can be described by a finite set of model vectors
fX1 ; . . . ; Xn ; . . . ; XN g
ð1Þ
We assume that the observation of a particular office can be described by a number of variables, where the variables are treated as components of a model vector
Xn ¼ fqn1 ; qn2 ; . . . ; qnD ; r n1 ; . . . ; r nk ; . . . ; r nM g
ð2Þ
The vector Xn can be further decomposed into two truncated vectors, Qn and Rn:
Q n ¼ fqn1 ; qn2 ; . . . ; qnD g and Rn ¼ fr n1 ; . . . ; rnk ; . . . ; r nM g
ð3aÞ
Vector Qn is complementary to vector Rn, implying that their concatenation yields the complete data model vector Xn. The prediction vector, too, is composed of two truncated vectors, i.e., the given b truncated vector Q and the unknown complementary vector R:
b ¼ f^r1 ; . . . ; ^r k ; . . . ; ^r M g Q ¼ fq1 ; q2 ; . . . ; qD g and R
ð3bÞ
b can be The problem is how the unknown complementary vector R estimated from a given truncated vector Q and the model vectors {X1, . . . , Xn, ... , XN}, i.e., how the office rent r can be estimated from known input parameters and the data in the database. Using the conditional probability density function, the optimal estimator can be expressed as
^rk ¼
N X
An r nk
ð4Þ
n¼1
where
an An ¼ P N
ð5Þ
i¼1 ai
The Gaussian density function with width w is chosen as a weight function. It is centred at each nth model vector in order to determine the influence of the nth model vector at the point of the prediction vector
"
D X ðql qnl Þ2 an ¼ exp D=2 D 2w2 ð2pÞ w l¼1
1
# ð6Þ
^rk is the estimate of the kth output variable, rnk is the same output variable corresponding to the nth model vector in the database, N is the number of model vectors in the database, qnl is the lth input variable of the nth model vector in the database, and ql is the lth input variable corresponding to the prediction vector. D is the number of input variables and defines the dimension of the sample space. Note that Eq. (6) requires the input parameters to be normalised or in the range of 0–1. This allows us to use the same width w of the Gaussian function for all of the input variables (dimensions). The Gaussian function is used to smooth interpolation between the points of the model vectors. In this context, the width w is the
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‘‘smoothing’’ parameter. It determines how quickly the influence of the data in the sample space decreases with increasing distance from the point whose coordinates are determined by the input variables of the prediction vector. In some applications, a nonconstant value of w yields more reasonable results than does a constant value. The width w can (a) vary with the input variables (dimensions); (b) be determined for each prediction point; or (c) be determined for each test specimen in the database. The last option was selected for use in the present study. For this case, the formula for an (from Eq. (6)) can be rewritten as
"
D X ðql qnl Þ2 an ¼ exp 2w2l ð2pÞD=2 w1 w2 wl l¼1
1
# ð7Þ
where different values of wl correspond to different components of the model vectors. In principle, a proper value of w is related to the distance between data points in the database. However, in practice, the optimal value of the smoothing parameter has to be determined through trial and error. For small values of w, the influence of different test samples decreases rapidly with the increasing difference between the values of the input parameters of the test samples and those of the predicted office rent. In such a case, only samples with very similar characteristics influence the prediction. On the other hand, a large value of w causes an averaging effect since the prediction is substantially influenced by a larger number of test samples, including those with quite different characteristics from the prediction sample. The optimal w value should yield reasonably smooth results and a reasonably small average error, measured in terms of E1 (from Eq. (8)). A general application of the method does not include any prior information about the phenomenon. Eqs. (4) and (5) suggest that the estimate of an output variable is computed as a linear combination of truncated vectors Rn, while the coefficients An are nonlinear functions of all input variables (Qn) in the database. Thus, this approach can model a non-linear phenomenon. The weights An depend on the similarity between the input variables of the prediction vector, as well as on the corresponding input variables pertinent to the model vectors stored in the database. Consequently, the unknown output variable is determined in such a way that the computed vector, composed of given and estimated data, is consistent with the model vectors in the database. The average prediction error Ek for the kth output variable can be determined using the ‘‘leave one out cross validation method’’, which predicts every test specimen based on all other test specimens. By averaging the absolute errors of predictions for all N test specimens, Ek is calculated as:
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u N 1u 1 X Ek ¼ t ð^r nk r nk Þ2 r k N n¼1
q^ ¼
N 1X an N n¼1
ð10Þ
This is a legitimate density function because it is non-negative and the area under this function is always equal to one, which is assured by choosing the Gaussian density function as a weight function (see Eq. (6). It is defined for each point of the sample space and is known for each prediction point. It represents a measure of how the influence of the test specimens (offices) is spread over the sample space and strongly depends on the smoothing parameter w. In addition, it helps to detect less accurate predictions due to the data distribution in the database as well as local extrapola^ value is, the greater tion outside the data range. The higher the q the number of offices (relative to the total number of offices in the database) with input parameters similar to the input parameters of the prediction vector that exist in the database. In this context, less accurate predictions are indicated by the darker area – i.e., the ‘‘grey zone’’. Fig. 1 shows an example of the influence of w. The office rent was determined with different constant w values. The results in Fig. 1a show large fluctuations for wmin = 0.01, wmax = 0.05 and relatively smooth results for wmin = 0.07, wmax = 0.15. Fig. 1b shows a comparison of the predicted and experimental results. The average error E1 is indicated and plotted as a function of w in Fig. 1b. The results indicate that the error measure first decreases and then increases with increases in w. Smooth solutions, which are physically realistic, are subject to an averaging effect (known in the literature as the ‘‘boundary effect’’), which most noticeably influences small and large values of office rent. Small values are typically overestimated, while large values are typically underestimated. By a trial-and-error procedure, where wmin and wmax were varied by accounting for the trapezoid rule (Peruš, Poljanšek, & Fajfar, 2006), the optimal values for the smoothness parameter were found to be wmin = 0.035 and wmax = 0.09. However, as can be seen from Fig. 1a, the corresponding solution is highly nonlinear. Therefore, it is hard to recognise clear and logical relationships between the variables of the observed phenomenon. For this reason, values larger than the optimal values of wmin and wmax (wmin = 0.07 and wmax = 0.15) were used throughout the paper (unless indicated otherwise). However, the reader should be aware that this choice implies averaged results and that the prediction error is higher than it would be given the optimal solution. 3. Database
ð8Þ
where r k is the average of the kth known outputs of all of the model vectors rnk, ^r nk is the prediction of the measured value rnk of the kth output of the nth model vector, and N is the number of model vectors in the sample space. In order to check the dispersion of the predicted kth output variable ^r k given by Eq. (4), we use the so-called ‘‘local standard deviation’’ b E rk :
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u N uX b E rk ¼ t An ð^rk r nk Þ2
An intermediate result in the computational process is the esti^ of the known input variables: mated probability density function q
ð9Þ
n¼1
The expression for local standard deviation b E rk is constructed in the same way as an estimation for output parameters ^r k according to Eqs. (4)–(7), whereas the local coefficient of variation (CoV) is defined as the ratio of b E rk and ^rk .
The database consists of 660 records from various sources. As described in Section 1, different variables have been identified by various researchers as the most influential for determining office rent. However, in order to keep the study manageable (and to facilitate practical and graphical presentation of the results), we sought to keep the number of input parameters as low as possible. (Note that this is not a limitation of the CAE method.) After trial and error and intensive discussions, we identified six input variables/parameters as the most important for the estimation of office rent. Many of these were adapted for the purposes of the GIS and DBMS tools. The chosen input parameters for the CAE method were:
Highway access point distance (APD). Car traffic density. Light rail access point distance (APD). Main retail distance. Office building density. Effective age.
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Fig. 1. Office rent for different w values: (a) presentation with isolines (highway APD = 500, main retail distance = 500, light rail APD = 500, office building density = 10) and (b) comparison of experimental and estimated values using six input parameters.
All input parameters are directly or indirectly related to many input variables identified by other researchers (see Section 1). The first five input parameters for the proposed CAE method are the so-called GIS-created variables. The sixth, effective age, is a non-GIS-created variable. A more detailed description of the input parameters is given below: Highway access point distance (APD): The data on the highway attributes and locations were provided by the Helsinki Metropolitan Area Council (YTV). The highway network was extracted from the roads layer based on the road type attribute. The entrances to the highways were used to find the access points to the network. For each office building in the database, we calculated and recorded the Euclidian distance to the closest highway access point. Car traffic density: We calculated the density of the car traffic for each office building location. The calculation was based on the main street network spatial model and the corresponding number of passing vehicles counted in 24-hour periods on working days in September 2005 on specific segments of the road network. The vehicle counts were carried out by the Helsinki City Planning Department and the Finnish Road Administration. Car density is expressed as the number of cars per square kilometre. Light rail access point distance (APD): The Helsinki Metropolitan Area Council (YTV) provided the network data. City train stops and metro stops in a light rail network were used as the access points to the network. For each office building in the sample, we calculated and recorded the Euclidian distance to the closest light rail access point. Main retail distance: Retail service centres are the nodes of retail agglomeration and indicate commercial centrality in an urban framework. We limited the selection of nodes to shopping centres with total incomes above 150 million Euros per year. Data on the location and total income of shopping centres were based on the report of the Finish Council of Shopping Centres for 2006. For each office building in the sample, we calculated and recorded the Euclidian distance to the closest retail agglomeration node.
Office building density: The data layer for the office buildings was selected from the building registry, where the building use attribute was set as ‘‘office space’’. The density of office buildings was calculated for the entire Helsinki metropolitan area and expressed as the number of buildings per square kilometre. Effective age: The effective ages of the office buildings (in years) as of 2007 were calculated from the building date and, if applicable, the renovation date. This parameter contains elements of dynamics. The output variable is office rent. For this purpose, we adapt the office rental benchmarking data to the year 2006. Office rent is expressed as rent value in Euros per square metre of office space. The basic characteristics of the database are presented in Fig. 2 as frequency distributions for each of the six input parameters. Except for the case of car traffic density, the distributions are closer to a logarithmic distribution or to some sort of extreme distribution than to the normal distribution. Since the CAE method is general in its concept, it is not limited to certain parameter distributions or to the input parameter, which may or may not be correlated. In the CAE method proposed, normalised (non-dimensional) parameters are used. The input parameters were normalised by using the equation:
i ¼ q
qi qi;min qi;max qi;min
ð11Þ
i is the ith normalised input parameter, qi is the ith input where q parameter under consideration, and qi,max and qi,min are the selected upper and lower bounds of the same input parameter, respectively. For the sake of simplicity, qi,max and qi,min were taken as the minimum and maximum values of the corresponding ith input parameter. 4. Results, discussion of the estimated office rent, and identification of submarkets 4.1. General trends In this chapter, we present and discuss influences on estimated office rents as quantified by the input parameters. Office rent was
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Fig. 2. Distributions of the input parameters.
estimated as a function of two different input parameters (Fig. 3) as well as all six input parameters at the same time (Figs. 4–7). In the latter case, more than one graph is needed to observe the behaviour of functions in 6+1-dimensional sample space. The two input parameters are presented as continuous values on the abscissa and ordinate, whereas the other four input parameters are fixed at discrete, chosen values. In this way, the sections can be easily observed through a multidimensional sample space. The results are presented in terms of isolines, which connect points of equal estimated office rents. In the background, we plot isolines of the esti^ (Eq. (10)) using thinner lines mated probability density function q ^ is suitable for visualising the distribution of and smaller fonts. q the influence of all data from the database over the sample space where the regression functions are calculated. Larger values indicate more reliable results, and vice versa for smaller values. In addition, the less reliable predictions are shaded (‘‘grey zone’’) for better visualisation. Fig. 3 shows the results of the analysis as a function of two input parameters. The graphs clearly indicate that office rent decreases with effective age and increases with office building density. Effective age is a more important parameter than office building density, especially at an effective age of 20 years or less. Similar conclusions can be drawn from Fig. 3b. The highway APD and office building density parameters exhibit similar influences. However, their general influence is smaller than that depicted in Fig. 3a (note the absolute difference between the maximum and minimum values of the isolines). In addition, we cannot conclude that one of the parameters prevails, as
^ Fig. 3. Office rent estimated as a function of pairs of input parameters. The q isolines are also shown (thin lines).
is the case in Fig. 3a. The influence of highway APD is large in Fig. 3c, while the influence of main retail distance is relatively small. The
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^ isolines Fig. 4. Office rent (bold lines) estimated as a function of six input parameters. Four input parameters are fixed (main retail distance = 250, light rail APD = 300). The q are also shown (thin lines).
result seems to be contradictory at first sight; however, it can be explained by the presence of downtown business centres with high office rents, which typically have large values of highway APD. The results are assembled into submarkets by data clustering (Ceh & Kivilahti, 2007), which is beyond the scope of this study and will be
discussed in a follow-up paper. Office building density is much more influential than main retail distance, as shown in Fig. 3d. In Figs. 4–7, the office rent is shown as a function of all six input parameters. Car traffic density and effective age are plotted on the abscissa and ordinate of the two-dimensional graph, respectively.
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^ Fig. 5. Office rent (bold lines) estimated as a function of six input parameters. Four input parameters are fixed (main retail distance = 1100, light rail APD = 300). The q isolines are also shown (thin lines).
The other four input parameters are fixed at discrete, chosen values. Figs. 4 and 5 show the results for fixed light rail APD (300) and for variation in main retail distance (250 and 1100), while Figs. 6 and 7 show the results for fixed light rail APD (1000), and Figs. 4 and 5 show the same variation of main retail distance. At first sight,
the relationships appear far more nonlinear than those presented in Fig. 3. High nonlinearity indicates that linear regression and different sorts of simple non-linear regression schemes may not work well for estimating office rents. This may also explain why different researchers have arrived at different conclusions.
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^ Fig. 6. Office rent (bold lines) estimated as a function of six input parameters. Four input parameters are fixed (main retail distance = 250, light rail APD = 1000). The q isolines are also shown (thin lines).
Figs. 4 and 5 show office rent at light rail APD of 300 m (very close to a metro station). Main retail distance varies from 250 m in Fig. 4 (very close to a shopping centre) to 1100 m in Fig. 5. Office rent increases with car traffic density and decreases with effective age. It also increases with office building density and
decreases with higher values of highway APD. A comparison of Figs. 4 and 5 indicates that higher values of main retail distance, in general, decrease office rent. The influences of different input parameters are mutually interdependent. For example, effective age significantly influences office rent given low office building
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^ Fig. 7. Office rent (bold lines) estimated as a function of six input parameters. Four input parameters are fixed (main retail distance = 1100, light rail APD = 1000). The q isolines are also shown (thin lines).
density (i.e., 5) and small values of highway APD (i.e., 200), while it becomes irrelevant at higher values of highway APD (i.e., 2500). Note the larger grey zones for higher values of highway APD (i.e., 2500), implying less densely spaced data and less reliable predictions.
Figs. 6 and 7 show the office rent at light rail APD of 1000 m (a larger distance from a metro station). Main retail distance varies from 250 m in Fig. 6 (very close to a shopping centre) to 1100 m in Fig. 7 (a larger distance from a shopping centre), as in Figs. 4 and 5. The predictions are qualitatively similar to those in Figs. 4
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and 5. In general, office rent increases with increases in light rail APD, but only for small values of highway APD (i.e., 200). The result seems logical: convenient access to light rail is preferred over convenient access to a highway. We can conclude from Figs. 4 to 7 that car traffic density has an important influence on office rents. The greater the value of car traffic density, the higher the rent is in a given location. Effective age also influences office rents at small values of highway APD, although its influence vanishes at larger highway APD values. Office building density increases office rents, while highway APD and main retail distance decrease office rents. The conclusions are similar to those obtained from Fig. 3. The local standard deviation b E r (Eq. (9)) provides an estimate of the dispersion of the results. Fig. 8 shows the local standard deviations b E r for office rents (the results are comparable to some of those shown in Figs. 4, 5 and 7). b E r amounts to 3–4.5, which corresponds to a coefficient of variation (CoV) of 0.28–0.36. In general, the CoV is around 0.3. Note again that by using the optimal values of w, CoVs could be made (significantly) smaller, though the results would be less clear. 4.2. Identification of submarkets Some researchers have argued that there are sound theoretical and technical arguments for segmenting office markets into distinct submarkets (Dunse & Colin, 2002; Dunse et al. 2001). Submarkets should be derived empirically, rather than using the prior knowledge of agents or researchers. A step toward this goal is presented in this section. The existence of office space submarkets can be recognised by thorough analysis of the graphs in Fig. 4–7. This allows interpretation of submarkets’ characteristics given the six parameters. We identified seven submarkets in different rent intervals (from 7.5 EUR/m2 to 17 EUR/m2). The smooth solutions in Fig. 4–7 obtained using CAE are, in spite of relatively small values of smoothing (wmin = 0.04, wmax = 0.10), subject to small averaging effects. Small values of office rents are typically overestimated and large values underestimated. Therefore, one should bear in mind that office rents below 7 EUR/m2 belong to the office rent class Submarket 1 and office rents above 17 EUR/m2 belong to Submarkets 5 and 6. A detailed description of all seven submarkets is given below. 4.3. Submarket 1 (7–9 EUR/m2) This submarket has the lowest rent level. Other characteristics include large distance to highway AP, very low car traffic density, very low office building density, uncorrelated with main retail distance and
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light rail APD. The rent is exclusively dependant on the effective age, which captures the quality of the office building (Figs. 4–7). 4.4. Submarket 2 (9–11 EUR/m2) The main characteristics of this rather low-rent submarket are high effective age and old buildings (between 40 and 60 years). Highway APD is between 200 and 1500 m, and car traffic density expands to around 3000 104, both of which represent middle values on the scale. This submarket is independent of office building density, main retail locations and light rail AP (Figs. 4–6). 4.5. Submarket 3 (11–13 EUR/m2) The offices of this submarket are located close to shopping centres (main retail distance is low, at 250 m) and close to light rail stations (access point distance is 300 m), a pattern characteristic of commuting and trading hubs. This submarket exhibits values of highway APD from 200 to 2500 m, implying that it is independent of car traffic density. This is confirmed by rather low scores for car traffic density (around 2000–3000 104). The submarket is almost independent of office building density, but the effective age is limited to buildings up to 30 years old (Fig. 4). 4.6. Submarket 4 (13–15 EUR/m2) This submarket contains old office buildings (effective age between 50 and 60 years) along roads with extremely high car traffic density (5000 104). It is independent of office building density, and buildings belonging to this submarket are located away from highway APs (1500–2500 m). This market is located far from shopping centres (main retail distance is high) and far from any light rail AP. It may represent part of the office space in the relative vicinity of the central business district (CBD) (Fig. 7). 4.7. Submarket 5 (13–14 EUR/m2) This submarket is located close to shopping centres (main retail distance is low), but can be far from metro stations (light rail APD is between 300 m and 1000 m). On the other hand, the car traffic density must be very high (4500 104 to 5000 104) for office space to belong to this particular submarket (typical for CBD). Highway APD is between 1500 m and 2500 m (typical of office space located outside of the city centre towards the highway). Office building density is rather loosely defined (5–25 offices per square km). The rent tends to depend on effective age. In that sense, Submarket 5 is similar to Submarket 1. We observe a local maximum in the rent (14 EUR/m2), which is limited by the effective age of the building
^ isolines are also shown (thin Fig. 8. Standard deviation (bold lines) of office rent estimated as a function of six input parameters for some of the cases presented above. The q lines).
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(from 40 to 55 years). We conclude that Submarket 5 presents rent levels for older office buildings in CBD. Newer buildings in CBD are captured by Submarket 6 (Fig. 6). 4.8. Submarket 6 (13–16 EUR/m2): CBD and main alternative to CBD Almost all attributes of Submarket 6 are the same as in Submarket 5. An exception is effective age, which is limited to newer buildings (up to 10 years old) in Submarket 6. Interestingly, Submarkets 5 and 6 amalgamate at an office building density of 25, which means that the difference in building age becomes obsolete at the highest office building densities (typically in CBD, with prices between 19 and 25 EUR/m2). Submarket 6 also encompasses developing business districts west of the city centre (the main alternative to CBD) around Lake Laajalahti (the geographical limit to the growth of CBD is the sea coast to the south and to the east), namely the subcentral region within Espoo municipality and its business districts of Leppavaara, Tapiola, Otaniemi, Keilanemi and Munkkiniemi, where rent levels are 13–15 EUR/m2 (see Fig. 7), with average office rents per BD between 17 EUR/m2 and 20 EUR/m2. 2
4.9. Submarket 7 (14–17 EUR/m ) This submarket is very specific due to its limited effective age (only new buildings), its narrow car traffic density gap (around 4000 104) and its highway APD (200 m2), all of which are necessary for inclusion in this submarket. In this domain, office building density is not important, nor are main retail distance (1100 m) or light rail APD (above 1000 m). This submarket can be found in the newly developed Keilanemi business district. 4.10. Additional applications 4.10.1. Using graphs for the estimation of office rent The use of linear interpolation by means of the graphs from Fig. 4–7 allows simple estimation of office rents. For example, suppose we would like to estimate the office rent for a commercial property with the following characteristics:
Car traffic density = 23,000. Effective age = 17. Office building density = 15. Highway APD = 1500. Main retail distance = 750 and Light rail APD = 300. The estimation can be summarised as follows:
Fig. 4b2
Fig. 5b2
Main retail dist. = 250 Office building density = 15 Highway APD = 1500 Light rail APD = 300 Main retail dist. = 1100
From the graphs, the estimated office rent is approximately 10.8, while the ‘‘exact’’ value calculated by the CAE amounts to 11.2. The difference is 3.3%. However, note that interpolation
Fig. 9. Car Traffic Density estimated as a function of Highway APD and Effective Age at fixed office rent, Office Building Density, Main Retail Distance and Light Rail APD.
may be more difficult if more input variables fall outside of the fixed values defined in Figs. 4–7. 4.10.2. Determination of the office’s properties in the case of decision support for investment It is rather important that the roles of given and estimated variables can be exchanged by posing the following question: what office properties will achieve some prescribed rent? In this case, the same model described in Chapter 2 is applicable. Only the selection of the given data and estimated variables is changed. In order to demonstrate this ability of the CAE method, we present the following example. Let us assume an office rent of 11.5 EUR/m2. What are the expected values of car traffic density of such offices as a function of highway APD and effective age if the office building density amounts to 20, main retail distance to 500 and light rail APD to 750? As can be seen from Fig. 9, car traffic density decreases with higher values of highway APD. Effective age first decreases up to the range of 20–40 years, then decreases. 5. Conclusions By interpreting CAE graphs, it is possible to recognise particular business districts in the Helsinki metropolitan area as office submarket areas, which coincide with the parametric descriptions of the submarkets. An office submarket is defined as a group of offices where, although the characteristics of each office are different, offices serve as substitutes for one another. Using multiple graphs, we
? reading: 11.3
? linear interpolation: 10:5 þ 1100750 1100250 ð11:3 10:5Þ ¼ 10:8
? reading: 10.5
identified local peaks, which were considered evidence for the existence of commercial office submarkets in the Helsinki metropolitan area. Seven submarkets were identified at rent levels from
M. Cˇeh et al. / Expert Systems with Applications 39 (2012) 460–471
7.5 EUR/m2 to 17 EUR/m2. The differentiation of submarkets by rent levels revealed different combinations of parameters. It should be noted that submarkets were not identified based on prior knowledge of agents, but were estimated empirically as advised by some recent studies (Dunse & Colin, 2002). CAE graphs are also used for the estimation of office rent, particularly for the determination of an office’s rent if decision support is required for investment deals, if the given and estimated variables are reversed. This allows for simple estimation of input parameters at prescribed office rents. The CAE method has proven to be a powerful tool in research, especially when there is little prior knowledge of the investigated phenomena and when the phenomena are highly non-linear and uncertain. This is also the case for estimation of office rent. The CAE approach requires an appropriate database and numerical analysis for each estimate. Its advantage is its lack of flexibility. There are no fixed functional relationships between the input and output parameters. Any number of input parameters (which are contained in the database) can be used, and different databases or different subsets of a database can be employed. Note that the CAE method, in the form presented in this paper, enables simple and straightforward application in real estate studies. 5.1. Summary This paper deals with a non-parametric approach to office rents in the Helsinki metropolitan area. We identified submarkets and estimated office rents using the CAE method by relying on six parameters: Highway access point distance (APD), car traffic density, light rail APD, main retail distance, office building density and effective age. Our results suggest that car traffic density is the single most influential parameter. Office rent decreases with effective age and increases with the density of office buildings. Longer distances to highway access points and to main retail centres decrease office rents, while shorter distances to light rail access points increase office rents in general and particularly for locations close to highway access points. Acknowledgements The authors wish to acknowledge the National Technology Agency of Finland (Project 40079/06) for financial support. References Archer, W. R., & Smith, M. T. (2003). Explaining location patterns of suburban offices. Real Estate Economics, 31(2), 139–164. Brounen, D., & Jennen, M. (2009). Local office rent dynamics: A tale of ten cities. The Journal of Real Estate Finance and Economics. doi:10.1007/s11146-008-9118-2. Bruinsma, F. R. (1997). The impact of accessibility on the valuation of cities as location for firms, Faculteit der Economische Waenschppen en Econometrie, Vrije Universiteit Amsterdam. Research Memorandum, 6, 1–23. Ceh, M. & Kivilahti, A. (2007). The spatial submarkets of Helsinki Metropolitan Area office markets. In 14th annual European real estate society conference, London. Clapp, J., Kim, H., & Gelfand, A. (2002). Predicting spatial patterns of house prices using LPR and Bayesian smoothing. Real Estate Economics, 30, 505–532. Clapp, J., Pollakowski, H., & Lynford, L. (1992). Intrametropolitan location and office market dynamics. Journal of the American Real Estate and Urban Economics Association, 20(1), 229–257.
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Dunse, N., & Colin, J. (2002). The existence of office submarkets in cites. Journal of Property Research, 19(2), 159–182. Dunse, N., Leishman, C., & Watkins, C. (2001). Classifying office submarkets. Journal of Property Investment and Finance, 19(3), 236–250. Fajfar, P., & Peruš, I. (1997). A non-parametric approach to attenuation relations. Journal of Earthquake Engineering, 1(2), 319–340. Ghebreegziabiher, D., & Jasper, W. (2008). The effect of railway stations on office space rent levels: The implication of HSL South in station Amsterdam South Axis in Railway. In F. Bruinsma, E. Pels, P. Rietveld, H. Priemus, & B. Van Wee (Eds.), Development impacts on urban dynamics (pp. 65–293). HD: PhysicaVerlag. Grabec, I., & Sachse, W. (1991). Automatic modelling of physical phenomena: Application to ultrasonic data. Journal of Applied Physics, 69, 6233–6244. Grabec, I., & Sachse, W. (1997). Synergetics of measurement. Prediction and control. Berlin, Heidelberg: Springer-Verlag. Hysom, J. L., & Crawford, P. J. (1997). The evolution of office building research. Journal of Real Estate Literature. American Real Estate Society, 5, 145–157. Jakobson, A. E., & Onsager, K. (2005). Head office location: Agglomeration, clusters or flow nodes? Urban Studies, 42(9), 1517–1535. Jennen, M. G., & Brounen, D. (2009). The effect of clustering on office rents: Evidence from the Amsterdam market. Real Estate Economics, 37(2), 185–208. Karakozova, O. (2004). Modelling and forecasting office returns in the Helsinki area. Journal of Property Research, 21(1), 51–73. Koppels, P. W. (2006). The market value of office features. In 13th annual European real estate society conference (book of papers) (pp. 554–561). Lizieri, C. (2009). Towers of capital: Office markets & international financial services. New York: Wiley. Margulis, H. L. (2007). Commercial sub-markets in suburban Cuyahoga County, Ohio. Urban Studies, 44, 249–274. McMillen, D. P., & Smith, S. C. (2003). The number of subcenters in large urban areas. Journal of Urban Economics, 53, 321–338. Mourouzi-Sivitanidou, R. (1999). Office rent process: The case of US Metropolitan Markets. Real Estate Economics, 30(2), 317–344. Nappi-Choulet, I., & Maury, T. P. (2009). A spatiotemporal autoregressive price index for the Paris office property market. Real Estate Economics, 37(2), 305–340. Peruš, I., & Fajfar, P. (2007). Prediction of the force - drift envelope for RC columns in flexure by CAE method. Earthquake Engineering and Structural Dynamic, [Print ed], 36(15), 2345–2363. Peruš, I., Poljanšek, K., & Fajfar, P. (2006). Flexural deformation capacity of rectangular RC columns determined by the CAE method. Earthquake Engineering and Structural Dynamic, 35(1), 1453–1470. Rodriguez, M., Sirmans, C. F., & Marks, A. P. (1995). Using geographic information systems to improve real estate analyses. Journal of Real Estate Research, 10(2), 163–174. Ryan, S. (2005). The value of access to highways and light rail transit: Evidence for industrial and office firms. Urban Studies, 42(4), 751–764. Sing, T., Ooi, J., Wong, A., & Lum, P. (2006). Network connectivity and office occupiers space decision: The case of Suntec City. Journal of Property Investment & Finance, 24(3), 221–238. Sivitanidou, R. (1995). Urban spatial variations in office – Commercial rents: The role of spatial amenities and commercial zoning. Journal of Urban Economics, 38, 23–49. Sivitanidou, R. (1996). Do office-commercial firms value access to service employment centres? A hedonic value analysis within polycentric Los Angeles. Journal of Urban Economics, 40, 125–149. Tercˇelj, M., Peruš, I., & Turk, R. (2003). Suitability of CAE neural network and FEM for predicting of wear on die radii in hot forging. Tribology International, 36, 573–583. Tercˇelj, M., Turk, R., Kugler, G., & Peruš, I. (2008). Neural network analysis of the influence of chemical composition on surface cracking during hot rolling of AISI D2 tool steel. Computational Materials Science, 42(4), 625–637. Thrall, G. I. (1998). GIS applications in real estate and related industries. Journal of Housing Research, 9(1), 33–59. Trevillion, E., Wang, L., & Withall, T. (2006). Recent trends in the Edinburgh and Glasgow office markets. In 13th annual European real estate society conference, Weimar (book of papers) (pp. 562–577). Turk, R., Peruš, I., & Tercˇelj, M. (2004). New starting points for prediction of tool wear in hot forging. International Journal of Machine Tools & Manufacture, 44(12– 13), 1319–1331. Weber, B. (2001). The use of GIS & OLAP for accurate valuation of developable land. Journal of Real Estate Portfolio Management, 7(3), 253–280.
Contents lists available at ScienceDirect
Expert Systems with Applications journal homepage: www.elsevier.com/locate/eswa
A non-parametric CAE approach to office rents: Identification of Helsinki metropolitan area submarkets Marjan Cˇeh a,⇑, Kauko Viitanen b, Iztok Peruš a a b
Faculty of Civil and Geodetic Engineering, University of Ljubljana, Jamova 2, SI-1000 Ljubljana, Slovenia Institute of Real Estate Studies, Helsinki University of Technology TKK, P.O. Box 1200, FI-02015 TKK, Finland
a r t i c l e
i n f o
Keywords: CAE non-parametric empirical method Submarkets Office rents Accessibility Agglomeration GIS-created variables
a b s t r a c t The study attempts to identify and estimate the office rents of submarkets in the Helsinki metropolitan area. We applied a non-parametric empirical approach called the CAE method to identify six parameters: highway APD (access point distance), car traffic density, light rail APD, main retail distance, office building density and effective age. Our results suggest that car traffic density is the single most influential parameter. Office rent decreases with effective age and increases with the density of office buildings. Longer distances to highway access points and to the main retail centres decrease office rents, while shorter distances to the light rail access points increase office rents in general and particularly for locations close to highway access points. We identified local peaks by inspecting multiple graphs. The local peaks were considered evidence for the existence of commercial office submarkets within the Helsinki metropolitan area. We identified seven submarkets at different rent levels. Interpreting submarkets from the CAE graphs allowed us to recognise particular business districts in the Helsinki metropolitan area. In addition, it is of great significance that the roles of the given and estimated variables can be exchanged. The method is directly applicable in real estate studies using adapted database and prescribed smoothing parameters. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction In the domain of commercial office space, firms consider the advantages and disadvantages of office building quality, neighbourhood development and location according to their customers’ and employees’ needs and perceptions. Among these, location comprises a complex phenomenon depending on various factors detectable by market players. Researchers have tried to detect the location factors, to predict their value using various approaches and to determine their different levels of influence using scientific approaches. In examining the relationship between a city’s spatial impact and its market for office space, pre-existing geography is an inertial force in creating a path dependency for the location of office-based services. The establishment of a large market for office space can create agglomeration economies (Lizieri, 2009). Early (Clapp, Kim, & Gelfand, 2002; Clapp, Pollakowski, & Lynford, 1992), and recent (Brounen and Jennen, 2008) studies suggest that spatial patterns are strongly related to market dynamics. Brounen and Jennen (2009) created a measure of growth potential that allows for the
⇑ Corresponding author. ˇ eh). E-mail addresses: [email protected], [email protected] (M. C 0957-4174/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2011.07.037
evaluation of office agglomerations over time. Nappi-Choulet and Maury (2009) proposed a Bayesian STAR model to control for heteroskedasticity in the market for office space in Paris. Hysom and Crawford (1997) concluded that location is an amalgam of several factors which, when combined, impart a specific value to a location. Intra-metropolitan location was found to depend on agglomeration economics, which consist of localised economies that accrue to firms of the same sector. Agglomeration economies are represented by the density of office buildings. Profit maximisation could be enhanced by agglomeration, especially when office or commercial retail space is highly dense and in locations where there is potential for increasing the ratio of future rents to land, labour and transport costs (Jennen & Brounen, 2009; Margulis, 2007). Several researchers have suggested that commercial firms value access to service centres (Bruinsma, 1997; Koppels, 2006; Ryan, 2005; Sivitanidou, 1995,1996). A similar explanation and identification was reported earlier by Bruinsma (1997), who stated that the centrality and the accessibility of an office best explain why firms tend to value cities as location sites. Trevillion, Wang, and Withall (2006) reported on the shift of offices away from traditional central business districts (CBDs) and into new business locations, citing difficulties in fulfilling long-term demand requirements in the market for office space in Edinburgh. Koppels
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(2006) proposed an analysis of rent variations within metropolitan boundaries at a single moment in time, an approach by which the added value of office property attributes and site-specific characteristics can be assessed. Research by Jakobson and Onsager (2005) considered head offices as flow nodes and emphasised their geographical concentrations. Ryan (2005) and Ghebreegziabiher and Jasper (2008) examined the importance of access to light rail transit and highway systems in estimating office and industrial property rents. Hedonic price analysis was applied to properties in the San Diego metropolitan area and Amsterdam’s South Axis area. The results indicated that access to highways and access to light rail are significant factors in estimating office property rents. A different approach was proposed by Mourouzi-Sivitanidou (1999). She explored adjustments in metropolitan office rental rates towards their implicit equilibrium levels. Sing, Ooi, Wong, and Lum (2006) presented results on the office space preferences of occupants of Suntec City. Based on mean scores, they revealed that prestige of an office location and accessibility by public transport are the two factors most highly ranked by firms. Recent studies have analysed and identified office submarkets. Dunse, Leishman, and Watkins (2001, 2002) argued that there are sound theoretical and technical arguments for segmenting office markets into distinct submarkets. They suggested that office submarkets should be derived empirically, rather than according to the prior knowledge of agents or researchers, by applying principal components and cluster analysis. Among the attributes they tested were age of the real estate, distances to key points of accessibility and location quality indicators. More recently, Archer and Smith (2003) explained office clustering (i.e., office submarkets) using the nature of office functions, related industry economies of scale, and office location in the context of modern urban theory and communication requirements. McMillen and Smith (2003) claimed that large metropolitan areas with high congestion levels are virtually certain to have at least one sub-centre and that the number of sub-centres rises with population and commuting costs. These two variables account for nearly 80% of the variation in the number of sub-centres across urban areas. Many studies of property markets use Geographic Information Systems (GIS), which can enable one to better locate business clusters (i.e., Jennen & Brounen, 2009; Rodriguez, Sirmans, & Marks, 1995; Thrall, 1998; Weber, 2001). Karakozova (2004) is, to our knowledge, the only study published of the market for Helsinki office space. She investigated the variation in office capital growth over a 30-year period, from 1971 to 2001, using three alternative models: a regression model, an error correction model (ECM), and an integrated autoregressivemoving average model with exogenous explanatory variables (ARIMAX). This paper relies on a new approach to identifying submarkets and estimating commercial office properties, dealing simultaneously with six influential parameters without any a priori assumptions. We describe and apply a non-parametric empirical approach called the CAE method. We also discuss the input variables that are most influential in determining office rents. Our important results are shown in graphs, enabling analysis of the influence of the input variables on the office rents and the identification of submarkets. This study is part of a research project conducted at the Institute of Real Estate Studies, Helsinki University of Technology TKK. 2. The CAE method The CAE method is based on a special type of multi-dimensional, non-parametric regression and represents a kind of probabilistic neural network. Developed by Grabec and Sachse (1991,1997), it enables relatively simple empirical modelling of different phenom-
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ena. The method has already been used in the field of structural engineering to model attenuation relationships (Fajfar & Peruš, 1997) and, more recently, to model the force–displacement envelope of dynamically loaded RC columns (Peruš and Fajfar, 2007). In addition, an application in the field of metallurgy (i.e., prediction of tool wear in hot forging and modelling hot flow curves) was also successful (Tercˇelj, Peruš, & Turk, 2003, 2004; Tercˇelj, Turk, Kugler, & Peruš, 2008). A detailed description of the CAE method can be found elsewhere (see Peruš, Poljanšek, & Fajfar, 2006). However, the description in this paper enables a very simple and efficient application of the CAE method in real estate studies. Office rent, denoted as r, is characterised by a sample of observations of N offices. The mathematical description of an observation of a single office is called a model vector. Consequently, the whole phenomenon can be described by a finite set of model vectors
fX1 ; . . . ; Xn ; . . . ; XN g
ð1Þ
We assume that the observation of a particular office can be described by a number of variables, where the variables are treated as components of a model vector
Xn ¼ fqn1 ; qn2 ; . . . ; qnD ; r n1 ; . . . ; r nk ; . . . ; r nM g
ð2Þ
The vector Xn can be further decomposed into two truncated vectors, Qn and Rn:
Q n ¼ fqn1 ; qn2 ; . . . ; qnD g and Rn ¼ fr n1 ; . . . ; rnk ; . . . ; r nM g
ð3aÞ
Vector Qn is complementary to vector Rn, implying that their concatenation yields the complete data model vector Xn. The prediction vector, too, is composed of two truncated vectors, i.e., the given b truncated vector Q and the unknown complementary vector R:
b ¼ f^r1 ; . . . ; ^r k ; . . . ; ^r M g Q ¼ fq1 ; q2 ; . . . ; qD g and R
ð3bÞ
b can be The problem is how the unknown complementary vector R estimated from a given truncated vector Q and the model vectors {X1, . . . , Xn, ... , XN}, i.e., how the office rent r can be estimated from known input parameters and the data in the database. Using the conditional probability density function, the optimal estimator can be expressed as
^rk ¼
N X
An r nk
ð4Þ
n¼1
where
an An ¼ P N
ð5Þ
i¼1 ai
The Gaussian density function with width w is chosen as a weight function. It is centred at each nth model vector in order to determine the influence of the nth model vector at the point of the prediction vector
"
D X ðql qnl Þ2 an ¼ exp D=2 D 2w2 ð2pÞ w l¼1
1
# ð6Þ
^rk is the estimate of the kth output variable, rnk is the same output variable corresponding to the nth model vector in the database, N is the number of model vectors in the database, qnl is the lth input variable of the nth model vector in the database, and ql is the lth input variable corresponding to the prediction vector. D is the number of input variables and defines the dimension of the sample space. Note that Eq. (6) requires the input parameters to be normalised or in the range of 0–1. This allows us to use the same width w of the Gaussian function for all of the input variables (dimensions). The Gaussian function is used to smooth interpolation between the points of the model vectors. In this context, the width w is the
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‘‘smoothing’’ parameter. It determines how quickly the influence of the data in the sample space decreases with increasing distance from the point whose coordinates are determined by the input variables of the prediction vector. In some applications, a nonconstant value of w yields more reasonable results than does a constant value. The width w can (a) vary with the input variables (dimensions); (b) be determined for each prediction point; or (c) be determined for each test specimen in the database. The last option was selected for use in the present study. For this case, the formula for an (from Eq. (6)) can be rewritten as
"
D X ðql qnl Þ2 an ¼ exp 2w2l ð2pÞD=2 w1 w2 wl l¼1
1
# ð7Þ
where different values of wl correspond to different components of the model vectors. In principle, a proper value of w is related to the distance between data points in the database. However, in practice, the optimal value of the smoothing parameter has to be determined through trial and error. For small values of w, the influence of different test samples decreases rapidly with the increasing difference between the values of the input parameters of the test samples and those of the predicted office rent. In such a case, only samples with very similar characteristics influence the prediction. On the other hand, a large value of w causes an averaging effect since the prediction is substantially influenced by a larger number of test samples, including those with quite different characteristics from the prediction sample. The optimal w value should yield reasonably smooth results and a reasonably small average error, measured in terms of E1 (from Eq. (8)). A general application of the method does not include any prior information about the phenomenon. Eqs. (4) and (5) suggest that the estimate of an output variable is computed as a linear combination of truncated vectors Rn, while the coefficients An are nonlinear functions of all input variables (Qn) in the database. Thus, this approach can model a non-linear phenomenon. The weights An depend on the similarity between the input variables of the prediction vector, as well as on the corresponding input variables pertinent to the model vectors stored in the database. Consequently, the unknown output variable is determined in such a way that the computed vector, composed of given and estimated data, is consistent with the model vectors in the database. The average prediction error Ek for the kth output variable can be determined using the ‘‘leave one out cross validation method’’, which predicts every test specimen based on all other test specimens. By averaging the absolute errors of predictions for all N test specimens, Ek is calculated as:
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u N 1u 1 X Ek ¼ t ð^r nk r nk Þ2 r k N n¼1
q^ ¼
N 1X an N n¼1
ð10Þ
This is a legitimate density function because it is non-negative and the area under this function is always equal to one, which is assured by choosing the Gaussian density function as a weight function (see Eq. (6). It is defined for each point of the sample space and is known for each prediction point. It represents a measure of how the influence of the test specimens (offices) is spread over the sample space and strongly depends on the smoothing parameter w. In addition, it helps to detect less accurate predictions due to the data distribution in the database as well as local extrapola^ value is, the greater tion outside the data range. The higher the q the number of offices (relative to the total number of offices in the database) with input parameters similar to the input parameters of the prediction vector that exist in the database. In this context, less accurate predictions are indicated by the darker area – i.e., the ‘‘grey zone’’. Fig. 1 shows an example of the influence of w. The office rent was determined with different constant w values. The results in Fig. 1a show large fluctuations for wmin = 0.01, wmax = 0.05 and relatively smooth results for wmin = 0.07, wmax = 0.15. Fig. 1b shows a comparison of the predicted and experimental results. The average error E1 is indicated and plotted as a function of w in Fig. 1b. The results indicate that the error measure first decreases and then increases with increases in w. Smooth solutions, which are physically realistic, are subject to an averaging effect (known in the literature as the ‘‘boundary effect’’), which most noticeably influences small and large values of office rent. Small values are typically overestimated, while large values are typically underestimated. By a trial-and-error procedure, where wmin and wmax were varied by accounting for the trapezoid rule (Peruš, Poljanšek, & Fajfar, 2006), the optimal values for the smoothness parameter were found to be wmin = 0.035 and wmax = 0.09. However, as can be seen from Fig. 1a, the corresponding solution is highly nonlinear. Therefore, it is hard to recognise clear and logical relationships between the variables of the observed phenomenon. For this reason, values larger than the optimal values of wmin and wmax (wmin = 0.07 and wmax = 0.15) were used throughout the paper (unless indicated otherwise). However, the reader should be aware that this choice implies averaged results and that the prediction error is higher than it would be given the optimal solution. 3. Database
ð8Þ
where r k is the average of the kth known outputs of all of the model vectors rnk, ^r nk is the prediction of the measured value rnk of the kth output of the nth model vector, and N is the number of model vectors in the sample space. In order to check the dispersion of the predicted kth output variable ^r k given by Eq. (4), we use the so-called ‘‘local standard deviation’’ b E rk :
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u N uX b E rk ¼ t An ð^rk r nk Þ2
An intermediate result in the computational process is the esti^ of the known input variables: mated probability density function q
ð9Þ
n¼1
The expression for local standard deviation b E rk is constructed in the same way as an estimation for output parameters ^r k according to Eqs. (4)–(7), whereas the local coefficient of variation (CoV) is defined as the ratio of b E rk and ^rk .
The database consists of 660 records from various sources. As described in Section 1, different variables have been identified by various researchers as the most influential for determining office rent. However, in order to keep the study manageable (and to facilitate practical and graphical presentation of the results), we sought to keep the number of input parameters as low as possible. (Note that this is not a limitation of the CAE method.) After trial and error and intensive discussions, we identified six input variables/parameters as the most important for the estimation of office rent. Many of these were adapted for the purposes of the GIS and DBMS tools. The chosen input parameters for the CAE method were:
Highway access point distance (APD). Car traffic density. Light rail access point distance (APD). Main retail distance. Office building density. Effective age.
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Fig. 1. Office rent for different w values: (a) presentation with isolines (highway APD = 500, main retail distance = 500, light rail APD = 500, office building density = 10) and (b) comparison of experimental and estimated values using six input parameters.
All input parameters are directly or indirectly related to many input variables identified by other researchers (see Section 1). The first five input parameters for the proposed CAE method are the so-called GIS-created variables. The sixth, effective age, is a non-GIS-created variable. A more detailed description of the input parameters is given below: Highway access point distance (APD): The data on the highway attributes and locations were provided by the Helsinki Metropolitan Area Council (YTV). The highway network was extracted from the roads layer based on the road type attribute. The entrances to the highways were used to find the access points to the network. For each office building in the database, we calculated and recorded the Euclidian distance to the closest highway access point. Car traffic density: We calculated the density of the car traffic for each office building location. The calculation was based on the main street network spatial model and the corresponding number of passing vehicles counted in 24-hour periods on working days in September 2005 on specific segments of the road network. The vehicle counts were carried out by the Helsinki City Planning Department and the Finnish Road Administration. Car density is expressed as the number of cars per square kilometre. Light rail access point distance (APD): The Helsinki Metropolitan Area Council (YTV) provided the network data. City train stops and metro stops in a light rail network were used as the access points to the network. For each office building in the sample, we calculated and recorded the Euclidian distance to the closest light rail access point. Main retail distance: Retail service centres are the nodes of retail agglomeration and indicate commercial centrality in an urban framework. We limited the selection of nodes to shopping centres with total incomes above 150 million Euros per year. Data on the location and total income of shopping centres were based on the report of the Finish Council of Shopping Centres for 2006. For each office building in the sample, we calculated and recorded the Euclidian distance to the closest retail agglomeration node.
Office building density: The data layer for the office buildings was selected from the building registry, where the building use attribute was set as ‘‘office space’’. The density of office buildings was calculated for the entire Helsinki metropolitan area and expressed as the number of buildings per square kilometre. Effective age: The effective ages of the office buildings (in years) as of 2007 were calculated from the building date and, if applicable, the renovation date. This parameter contains elements of dynamics. The output variable is office rent. For this purpose, we adapt the office rental benchmarking data to the year 2006. Office rent is expressed as rent value in Euros per square metre of office space. The basic characteristics of the database are presented in Fig. 2 as frequency distributions for each of the six input parameters. Except for the case of car traffic density, the distributions are closer to a logarithmic distribution or to some sort of extreme distribution than to the normal distribution. Since the CAE method is general in its concept, it is not limited to certain parameter distributions or to the input parameter, which may or may not be correlated. In the CAE method proposed, normalised (non-dimensional) parameters are used. The input parameters were normalised by using the equation:
i ¼ q
qi qi;min qi;max qi;min
ð11Þ
i is the ith normalised input parameter, qi is the ith input where q parameter under consideration, and qi,max and qi,min are the selected upper and lower bounds of the same input parameter, respectively. For the sake of simplicity, qi,max and qi,min were taken as the minimum and maximum values of the corresponding ith input parameter. 4. Results, discussion of the estimated office rent, and identification of submarkets 4.1. General trends In this chapter, we present and discuss influences on estimated office rents as quantified by the input parameters. Office rent was
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Fig. 2. Distributions of the input parameters.
estimated as a function of two different input parameters (Fig. 3) as well as all six input parameters at the same time (Figs. 4–7). In the latter case, more than one graph is needed to observe the behaviour of functions in 6+1-dimensional sample space. The two input parameters are presented as continuous values on the abscissa and ordinate, whereas the other four input parameters are fixed at discrete, chosen values. In this way, the sections can be easily observed through a multidimensional sample space. The results are presented in terms of isolines, which connect points of equal estimated office rents. In the background, we plot isolines of the esti^ (Eq. (10)) using thinner lines mated probability density function q ^ is suitable for visualising the distribution of and smaller fonts. q the influence of all data from the database over the sample space where the regression functions are calculated. Larger values indicate more reliable results, and vice versa for smaller values. In addition, the less reliable predictions are shaded (‘‘grey zone’’) for better visualisation. Fig. 3 shows the results of the analysis as a function of two input parameters. The graphs clearly indicate that office rent decreases with effective age and increases with office building density. Effective age is a more important parameter than office building density, especially at an effective age of 20 years or less. Similar conclusions can be drawn from Fig. 3b. The highway APD and office building density parameters exhibit similar influences. However, their general influence is smaller than that depicted in Fig. 3a (note the absolute difference between the maximum and minimum values of the isolines). In addition, we cannot conclude that one of the parameters prevails, as
^ Fig. 3. Office rent estimated as a function of pairs of input parameters. The q isolines are also shown (thin lines).
is the case in Fig. 3a. The influence of highway APD is large in Fig. 3c, while the influence of main retail distance is relatively small. The
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^ isolines Fig. 4. Office rent (bold lines) estimated as a function of six input parameters. Four input parameters are fixed (main retail distance = 250, light rail APD = 300). The q are also shown (thin lines).
result seems to be contradictory at first sight; however, it can be explained by the presence of downtown business centres with high office rents, which typically have large values of highway APD. The results are assembled into submarkets by data clustering (Ceh & Kivilahti, 2007), which is beyond the scope of this study and will be
discussed in a follow-up paper. Office building density is much more influential than main retail distance, as shown in Fig. 3d. In Figs. 4–7, the office rent is shown as a function of all six input parameters. Car traffic density and effective age are plotted on the abscissa and ordinate of the two-dimensional graph, respectively.
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^ Fig. 5. Office rent (bold lines) estimated as a function of six input parameters. Four input parameters are fixed (main retail distance = 1100, light rail APD = 300). The q isolines are also shown (thin lines).
The other four input parameters are fixed at discrete, chosen values. Figs. 4 and 5 show the results for fixed light rail APD (300) and for variation in main retail distance (250 and 1100), while Figs. 6 and 7 show the results for fixed light rail APD (1000), and Figs. 4 and 5 show the same variation of main retail distance. At first sight,
the relationships appear far more nonlinear than those presented in Fig. 3. High nonlinearity indicates that linear regression and different sorts of simple non-linear regression schemes may not work well for estimating office rents. This may also explain why different researchers have arrived at different conclusions.
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^ Fig. 6. Office rent (bold lines) estimated as a function of six input parameters. Four input parameters are fixed (main retail distance = 250, light rail APD = 1000). The q isolines are also shown (thin lines).
Figs. 4 and 5 show office rent at light rail APD of 300 m (very close to a metro station). Main retail distance varies from 250 m in Fig. 4 (very close to a shopping centre) to 1100 m in Fig. 5. Office rent increases with car traffic density and decreases with effective age. It also increases with office building density and
decreases with higher values of highway APD. A comparison of Figs. 4 and 5 indicates that higher values of main retail distance, in general, decrease office rent. The influences of different input parameters are mutually interdependent. For example, effective age significantly influences office rent given low office building
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^ Fig. 7. Office rent (bold lines) estimated as a function of six input parameters. Four input parameters are fixed (main retail distance = 1100, light rail APD = 1000). The q isolines are also shown (thin lines).
density (i.e., 5) and small values of highway APD (i.e., 200), while it becomes irrelevant at higher values of highway APD (i.e., 2500). Note the larger grey zones for higher values of highway APD (i.e., 2500), implying less densely spaced data and less reliable predictions.
Figs. 6 and 7 show the office rent at light rail APD of 1000 m (a larger distance from a metro station). Main retail distance varies from 250 m in Fig. 6 (very close to a shopping centre) to 1100 m in Fig. 7 (a larger distance from a shopping centre), as in Figs. 4 and 5. The predictions are qualitatively similar to those in Figs. 4
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and 5. In general, office rent increases with increases in light rail APD, but only for small values of highway APD (i.e., 200). The result seems logical: convenient access to light rail is preferred over convenient access to a highway. We can conclude from Figs. 4 to 7 that car traffic density has an important influence on office rents. The greater the value of car traffic density, the higher the rent is in a given location. Effective age also influences office rents at small values of highway APD, although its influence vanishes at larger highway APD values. Office building density increases office rents, while highway APD and main retail distance decrease office rents. The conclusions are similar to those obtained from Fig. 3. The local standard deviation b E r (Eq. (9)) provides an estimate of the dispersion of the results. Fig. 8 shows the local standard deviations b E r for office rents (the results are comparable to some of those shown in Figs. 4, 5 and 7). b E r amounts to 3–4.5, which corresponds to a coefficient of variation (CoV) of 0.28–0.36. In general, the CoV is around 0.3. Note again that by using the optimal values of w, CoVs could be made (significantly) smaller, though the results would be less clear. 4.2. Identification of submarkets Some researchers have argued that there are sound theoretical and technical arguments for segmenting office markets into distinct submarkets (Dunse & Colin, 2002; Dunse et al. 2001). Submarkets should be derived empirically, rather than using the prior knowledge of agents or researchers. A step toward this goal is presented in this section. The existence of office space submarkets can be recognised by thorough analysis of the graphs in Fig. 4–7. This allows interpretation of submarkets’ characteristics given the six parameters. We identified seven submarkets in different rent intervals (from 7.5 EUR/m2 to 17 EUR/m2). The smooth solutions in Fig. 4–7 obtained using CAE are, in spite of relatively small values of smoothing (wmin = 0.04, wmax = 0.10), subject to small averaging effects. Small values of office rents are typically overestimated and large values underestimated. Therefore, one should bear in mind that office rents below 7 EUR/m2 belong to the office rent class Submarket 1 and office rents above 17 EUR/m2 belong to Submarkets 5 and 6. A detailed description of all seven submarkets is given below. 4.3. Submarket 1 (7–9 EUR/m2) This submarket has the lowest rent level. Other characteristics include large distance to highway AP, very low car traffic density, very low office building density, uncorrelated with main retail distance and
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light rail APD. The rent is exclusively dependant on the effective age, which captures the quality of the office building (Figs. 4–7). 4.4. Submarket 2 (9–11 EUR/m2) The main characteristics of this rather low-rent submarket are high effective age and old buildings (between 40 and 60 years). Highway APD is between 200 and 1500 m, and car traffic density expands to around 3000 104, both of which represent middle values on the scale. This submarket is independent of office building density, main retail locations and light rail AP (Figs. 4–6). 4.5. Submarket 3 (11–13 EUR/m2) The offices of this submarket are located close to shopping centres (main retail distance is low, at 250 m) and close to light rail stations (access point distance is 300 m), a pattern characteristic of commuting and trading hubs. This submarket exhibits values of highway APD from 200 to 2500 m, implying that it is independent of car traffic density. This is confirmed by rather low scores for car traffic density (around 2000–3000 104). The submarket is almost independent of office building density, but the effective age is limited to buildings up to 30 years old (Fig. 4). 4.6. Submarket 4 (13–15 EUR/m2) This submarket contains old office buildings (effective age between 50 and 60 years) along roads with extremely high car traffic density (5000 104). It is independent of office building density, and buildings belonging to this submarket are located away from highway APs (1500–2500 m). This market is located far from shopping centres (main retail distance is high) and far from any light rail AP. It may represent part of the office space in the relative vicinity of the central business district (CBD) (Fig. 7). 4.7. Submarket 5 (13–14 EUR/m2) This submarket is located close to shopping centres (main retail distance is low), but can be far from metro stations (light rail APD is between 300 m and 1000 m). On the other hand, the car traffic density must be very high (4500 104 to 5000 104) for office space to belong to this particular submarket (typical for CBD). Highway APD is between 1500 m and 2500 m (typical of office space located outside of the city centre towards the highway). Office building density is rather loosely defined (5–25 offices per square km). The rent tends to depend on effective age. In that sense, Submarket 5 is similar to Submarket 1. We observe a local maximum in the rent (14 EUR/m2), which is limited by the effective age of the building
^ isolines are also shown (thin Fig. 8. Standard deviation (bold lines) of office rent estimated as a function of six input parameters for some of the cases presented above. The q lines).
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(from 40 to 55 years). We conclude that Submarket 5 presents rent levels for older office buildings in CBD. Newer buildings in CBD are captured by Submarket 6 (Fig. 6). 4.8. Submarket 6 (13–16 EUR/m2): CBD and main alternative to CBD Almost all attributes of Submarket 6 are the same as in Submarket 5. An exception is effective age, which is limited to newer buildings (up to 10 years old) in Submarket 6. Interestingly, Submarkets 5 and 6 amalgamate at an office building density of 25, which means that the difference in building age becomes obsolete at the highest office building densities (typically in CBD, with prices between 19 and 25 EUR/m2). Submarket 6 also encompasses developing business districts west of the city centre (the main alternative to CBD) around Lake Laajalahti (the geographical limit to the growth of CBD is the sea coast to the south and to the east), namely the subcentral region within Espoo municipality and its business districts of Leppavaara, Tapiola, Otaniemi, Keilanemi and Munkkiniemi, where rent levels are 13–15 EUR/m2 (see Fig. 7), with average office rents per BD between 17 EUR/m2 and 20 EUR/m2. 2
4.9. Submarket 7 (14–17 EUR/m ) This submarket is very specific due to its limited effective age (only new buildings), its narrow car traffic density gap (around 4000 104) and its highway APD (200 m2), all of which are necessary for inclusion in this submarket. In this domain, office building density is not important, nor are main retail distance (1100 m) or light rail APD (above 1000 m). This submarket can be found in the newly developed Keilanemi business district. 4.10. Additional applications 4.10.1. Using graphs for the estimation of office rent The use of linear interpolation by means of the graphs from Fig. 4–7 allows simple estimation of office rents. For example, suppose we would like to estimate the office rent for a commercial property with the following characteristics:
Car traffic density = 23,000. Effective age = 17. Office building density = 15. Highway APD = 1500. Main retail distance = 750 and Light rail APD = 300. The estimation can be summarised as follows:
Fig. 4b2
Fig. 5b2
Main retail dist. = 250 Office building density = 15 Highway APD = 1500 Light rail APD = 300 Main retail dist. = 1100
From the graphs, the estimated office rent is approximately 10.8, while the ‘‘exact’’ value calculated by the CAE amounts to 11.2. The difference is 3.3%. However, note that interpolation
Fig. 9. Car Traffic Density estimated as a function of Highway APD and Effective Age at fixed office rent, Office Building Density, Main Retail Distance and Light Rail APD.
may be more difficult if more input variables fall outside of the fixed values defined in Figs. 4–7. 4.10.2. Determination of the office’s properties in the case of decision support for investment It is rather important that the roles of given and estimated variables can be exchanged by posing the following question: what office properties will achieve some prescribed rent? In this case, the same model described in Chapter 2 is applicable. Only the selection of the given data and estimated variables is changed. In order to demonstrate this ability of the CAE method, we present the following example. Let us assume an office rent of 11.5 EUR/m2. What are the expected values of car traffic density of such offices as a function of highway APD and effective age if the office building density amounts to 20, main retail distance to 500 and light rail APD to 750? As can be seen from Fig. 9, car traffic density decreases with higher values of highway APD. Effective age first decreases up to the range of 20–40 years, then decreases. 5. Conclusions By interpreting CAE graphs, it is possible to recognise particular business districts in the Helsinki metropolitan area as office submarket areas, which coincide with the parametric descriptions of the submarkets. An office submarket is defined as a group of offices where, although the characteristics of each office are different, offices serve as substitutes for one another. Using multiple graphs, we
? reading: 11.3
? linear interpolation: 10:5 þ 1100750 1100250 ð11:3 10:5Þ ¼ 10:8
? reading: 10.5
identified local peaks, which were considered evidence for the existence of commercial office submarkets in the Helsinki metropolitan area. Seven submarkets were identified at rent levels from
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7.5 EUR/m2 to 17 EUR/m2. The differentiation of submarkets by rent levels revealed different combinations of parameters. It should be noted that submarkets were not identified based on prior knowledge of agents, but were estimated empirically as advised by some recent studies (Dunse & Colin, 2002). CAE graphs are also used for the estimation of office rent, particularly for the determination of an office’s rent if decision support is required for investment deals, if the given and estimated variables are reversed. This allows for simple estimation of input parameters at prescribed office rents. The CAE method has proven to be a powerful tool in research, especially when there is little prior knowledge of the investigated phenomena and when the phenomena are highly non-linear and uncertain. This is also the case for estimation of office rent. The CAE approach requires an appropriate database and numerical analysis for each estimate. Its advantage is its lack of flexibility. There are no fixed functional relationships between the input and output parameters. Any number of input parameters (which are contained in the database) can be used, and different databases or different subsets of a database can be employed. Note that the CAE method, in the form presented in this paper, enables simple and straightforward application in real estate studies. 5.1. Summary This paper deals with a non-parametric approach to office rents in the Helsinki metropolitan area. We identified submarkets and estimated office rents using the CAE method by relying on six parameters: Highway access point distance (APD), car traffic density, light rail APD, main retail distance, office building density and effective age. Our results suggest that car traffic density is the single most influential parameter. Office rent decreases with effective age and increases with the density of office buildings. Longer distances to highway access points and to main retail centres decrease office rents, while shorter distances to light rail access points increase office rents in general and particularly for locations close to highway access points. Acknowledgements The authors wish to acknowledge the National Technology Agency of Finland (Project 40079/06) for financial support. References Archer, W. R., & Smith, M. T. (2003). Explaining location patterns of suburban offices. Real Estate Economics, 31(2), 139–164. Brounen, D., & Jennen, M. (2009). Local office rent dynamics: A tale of ten cities. The Journal of Real Estate Finance and Economics. doi:10.1007/s11146-008-9118-2. Bruinsma, F. R. (1997). The impact of accessibility on the valuation of cities as location for firms, Faculteit der Economische Waenschppen en Econometrie, Vrije Universiteit Amsterdam. Research Memorandum, 6, 1–23. Ceh, M. & Kivilahti, A. (2007). The spatial submarkets of Helsinki Metropolitan Area office markets. In 14th annual European real estate society conference, London. Clapp, J., Kim, H., & Gelfand, A. (2002). Predicting spatial patterns of house prices using LPR and Bayesian smoothing. Real Estate Economics, 30, 505–532. Clapp, J., Pollakowski, H., & Lynford, L. (1992). Intrametropolitan location and office market dynamics. Journal of the American Real Estate and Urban Economics Association, 20(1), 229–257.
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