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Estimating the economic value of the Dutch National
Opera using the Travel Cost Method
Author: Felix Welsink University of Amsterdam 10539468
Thesis supervisor: Andrej Woerner January 30, 2018
Abstract
In times of lower amounts of public funding, cultural institutions have to prove their worth in economic terms. So does the Dutch National Opera (DNO). In this thesis we estimate the economic value of DNO for the year of 2014. In 2014 52,248 individual bookings were made at the DNO, with an average of 2.68 tickets per booking. To calculate the economic value of DNO we use the Zonal Travel Cost Method, a non-use valuation method that calculates the Consumer Surplus (CS), in which the amount of tickets bought per person in a certain postal code zone is compared with the travel costs made. We determine a demand function, in which tickets per person is a function of travel costs (negative relation), the average monthly fiscal income (positive relation), the percentage of people older than 65 (positive relation) and the percentage of non-western immigrants (negative relation). The consumer surplus we find is 363.3 million euros. DNO has a cost-benefit ratio of 13.9 in 2014. Comparing the CS to the amount of public funding in 2014 (24.2 million euros), the economic value of DNO is higher than the amount of public funding, meaning that a higher amount of subsidies could be given to DNO. We also determine a demand function that corrects for nonlinearity. Although this functional form has a better fit, the estimation of the Consumer Surplus appears to be unreliable.
2 Table of contents
Introduction ... 3
2. Literature review ... 5
2.1 Travel Cost Method (TCM) ... 5
2.2 Research on valuations of cultural institutions ... 6
3. Data sources and variables ... 9
3.1 Dataset DNO ... 9
3.2 Dataset CBS ... 10
3.3 Further transformation of data and choice of variables ... 11
3.4 Travel costs ... 13
4. Results ... 14
4.1 OLS regression 1 ... 14
Test on normal distribution of the error term ... 18
4.2 OLS regression 2 ... 21
4.3 Calculation of Consumer Surplus ... 25
5. Conclusion and discussion ... 27
5.1 Conclusion ... 27
5.2 Discussion ... 28
5.3 Recommendations ... 29
References ... 30
Appendix 1: Additional graph on total number of tickets per postal code zone versus distance ... 32
Appendix 2: Table with Adjusted R2 of relation census dataset 2004-2010 ... 33
Appendix 3: Robustness check – extrapolating the 2004-2010 relationship to 2014 ... 34
Appendix 4: Checks on outliers of regression results in Table 4.1 ... 35
Appendix 5: Checks on OLS assumptions Equation 4.1 ... 37
Appendix 6: Graphs and table for interpretation of Equation 4.2 ... 39
Appendix 7: Checks on OLS assumptions Equation 4.2 ... 41
Appendix 8: Calculating the Consumer Surplus using another functional form ... 42
Statement of Originality
This document is written by Student Felix Welsink who declares to take full responsibility for the contents of this document.
I declare that the text and the work presented in this document are original and that no sources other than those mentioned in the text and its references have been used in creating it.
The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.
I would like to thank the following persons for giving me advice and helping my write my thesis:
Andrej Woerner (thesis supervisor, University of Amsterdam), Sandra Eikelenboom (Head of Marketing, Sales and Communication at the Dutch National Opera), Eline Danker (Head of Fundraising and Relationship Management at the Dutch National Opera), Mattijn Hallers (data manager marketing at the Dutch National Opera) Martin van der Beek (ICT Consultant at Object Vision), Jaap Boter (associate professor at VU University), Ger Janssen, Marjon Kok, Margaux Simmons and Quirien Reijtenbagh
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Introduction
In 2011 the Dutch government – under the lead of Secretary of State Halbe Zijlstra at that time – published a new vision on cultural policy. This renewed vision came together with large cutbacks in subsidies to cultural institutions of 200 million Euros per year (more than 20% of the total budget). In this new vision the government put more emphasis on entrepreneurship: cultural institutions should obtain a higher percentage of own income and should look for connections with the financial sector in the form of advice and sponsorships to maintain their public funding (Rijksoverheid, 2011, p. 11-12).
Aside from using financial measures as a criterion for public support, the renewed vision of the Dutch government also identifies the need for an economic meaning of culture (Rijksoverheid, 2011, p. 32). Since 2011 the government annually publishes a report called Cultuur in Beeld, which throws light on the cultural industries from a more quantitative point of view. In this report an economic value of the cultural sector is calculated.
Unfortunately, the economic value is calculated on a sector-level only. No economic valuations on the lower level of individual institutions are generated. Economic valuations of individual cultural institutions could be very useful for a government to assess which institutions need to get subsidized and how much. Economic analysis of cultural institutions could be a valuable addition to the quantitative apparatus governments use.
Where economic valuation can be used by governments as a tool of analysis on the one hand, it can be used by cultural institutions as an argument for subsidies on the other hand. Economist Don Fullerton argues that economists used to have problems to find economic compelling arguments for public supports of the arts (1991, p. 67). In his article On justifications for public support of the arts Fullerton gives several economic arguments for subsidies, but he discards the given economic arguments, when the capitalistic economic framework is used (1991, p. 79). Although, Fullerton did not discuss the Travel Cost Method, which we use in this thesis. Using this method for the calculation of an economic value of cultural institutions was not usual at that time.
Economic arguments on subsidies are often given on a basis of merit goods: the government understands what is good for society (Fullerton, 1991, p. 73). A second argument concerns positive externalities. Art could be perceived as a form of national pride, could have educational effects, be good to attract tourists and be important for future generations (Forrest, et al., 2000, p. 381; Fullerton, 1991, pp. 74–75). Measuring the consumer surplus is an economic tool, which may contribute to justification of government subsidies. Measuring
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consumer surplus can also be used as an argument for more public funding and it can be applied by the government in assessing how to spend their subsidies.
This bachelor thesis contributes to the need of more economic valuations by providing a valuation of the Dutch National Opera (DNO) in the year of 2014.1 DNO is the Dutch national opera company, which is situated at Waterloo Square in Amsterdam. DNO brings about ten opera productions each season and celebrates a high international profile. In 2016 DNO was rewarded as Opera Company of the Year (Leeuwerink, 2016).2
The economic value of DNO will be calculated through the Travel Cost Method (TCM). A theatre attendance function will be derived by estimating the relationship between the number of opera tickets per person in a certain four-digit postal code zone and his/her travel costs. Average monthly fiscal income per postal code, percentage of people older than 65 per postal code and the percentage of non-western immigrants are included in the regression equation to control for socio-economic background. After estimating the zonal theatre attendance function, the consumer surplus (CS) is calculated. CS is the measure for economic value and is compared to the amount of subsidies DNO received in 2014.3
We estimate that DNO had a CS of 363.3 million euros in 2014. This economic value is higher than the amount of subsidies. This gives DNO a cost-benefit ratio of 13.9 in 2014, and provides the organization with a good argument on public funding.
This thesis is organized in five sections. Chapter 2 gives a review of literature about economic valuation of cultural institutions. Different methods of economic valuation are described, focusing on the TCM. Chapter 3 provides information about the datasets and variables used in this thesis. Chapter 4 explains the different methods that were used to model the tickets per person and estimates the CS. It also checks the validity of the empirical approach and discusses the results of different methods. At last, chapter 5 discusses the findings and concludes.
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In the year 2014 DNO produced 12 productions, which are the following: Der Ring des Nibelungen (a cyclus of four operas: Das Rheingold, Die Walküre, Siegfried and Götterdämmerung), Lucia di Lammermoor, Arabella, Faust, Laika, Falstaff, Kopernicus, Gurre-Lieder, Orfeo, L’étoile, Lohengrin and La Bohème.
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The Opera Company of the Year award is a worldwide opera-award to recognise and reward success in opera.
3 According to DNO’s annual report the opera house received 24.289 million euros of subsidies from the
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2. Literature review
In this chapter the Travel Cost Method (TCM) will be explained in more detail. Thereafter, the TCM will be compared with other economic valuation methods which are used to evaluate cultural institutions. Finally, former research will be described, as this thesis is a further study on this research.
2.1 Travel Cost Method (TCM)
The TCM is an economic valuation method, often used for the estimation of national parks (Throsby, 2001, p. 81). The TCM and associated valuation methods estimate an economic value for an externality or public good by estimating a demand function (Throsby, 2001, p. 25). The TCM is based on the proposition that consumers’ valuations of such facilities are indicated by how much travel costs they were willing to incur to visit it
A strength of the TCM is that it uses actual costs to estimate the Willingness To Pay (WTP), which makes it non-hypothetical. The TCM uses revealed preference methods to calculate the economic value (Voltaire, Lévi, Alban, & Boncoeur, 2017, p. 1594). Revealed preference methods assess the value of something by looking at actual behavior (such as booking data), which makes it non-hypothetical. Stated preference methods, the counterpart of revealed preference methods, are regarded less reliable, because they are hypothetical. Stated preference methods use remarks from respondents, mostly via open-ended surveys (Armbrecht, 2014, pp. 141–142).
A weakness of the TCM is that it does not account for multi-purposes trips. This thesis assumes that a visit to DNO is the single trip purpose for Dutch visitors, on which will be elaborated later. Another weakness is that the TCM does not examine non-use values, because it does not take people into account who do not visit the theatre but still value its existence (Yung et al. , 2013, p. 340).
There are two versions of the TCM. There is a distinction between the Zonal Travel Cost Method (ZTCM) and the Individual Travel Cost Method (ITCM). The ZTCM which is used in this paper was established by Marion Clawson and Jack Knetsch. It measures as demand the number of trips relative to a population as an equation of the costs of making a trip to the site. The ITCM however measures the number of visits made by an individual in a certain amount of time to a site/theatre (K. G. Willis, J.D. Snowball, 2012, pp. 92–93).
Other economic valuation methods are the contingent valuation method (CVM) and the hedonic pricing method (Throsby, 2001, pp. 81–83). The CVM asks people about their
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Willingness To Pay mostly by means of surveys and calculates the use-value as well as the non-use value. This means that the CVM calculates a more total value, because it also includes the non-use value (Hansen, 1997, p. 6). A difference between the TCM and the CVM is that the TCM is a revealed preference method, while the CVM is a stated preference method. The CVM therefore has a hypothetical nature, while the TCM has a non-hypothetical nature. Another downside to the CVM is the free-rider problem: people have an incentive to not state their true preferences for a public good, because they know they cannot be refused from using its benefits (Throsby, 2001, p. 82). In the case of cultural institutions this incentive could be the following: if the amount of public funding depends on the Willingness To Pay of the public via e.g. a questionnaire, a frequent user of that cultural institution could overestimate the value he or she assigns to that institute, knowing that this will lead to higher estimation results and might bring the amount of public funding up.
The hedonic pricing valuation method also uses revealed preferences to make economic valuations. Hedonic pricing valuations are used – as the TCM and the CVM are – to give a monetary value of non-market goods (Lazrak, et al., 2009, pp. 1–2). This approach uses market data as a proxy to estimate the non-market effect which is studied (Throsby, 2001, p. 126). It estimates prices of goods on the basis of its characteristics. Implicit prices for these characteristics can be estimated by regressing on these characteristics and reveal the marginal Willingness To Pay. In the hedonic pricing model there is a high chance of Omitted Variable Bias, because usually goods have a lot of characteristics. This method has been applied to cultural heritage projects4 a few times, and is not yet used to assess the economic value of cultural institutions.
2.2 Research on valuations of cultural institutions
Economic valuations of cultural institutions are limited. Australian economist David Throsby argues that estimating the demand for public goods is difficult due to deficiencies and leanings in the estimation methods. He also states that the normal conditions for price formation in competitive markets are not necessarily met in markets for cultural goods, because the characteristics of cultural goods are different from economic goods (Throsby, 2001, pp. 24–25). Where economic valuations of cultural institutions are scarce, economic
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Cultural heritage is a term for the legacy of artifacts inherited from a former civilization. Cultural heritage projects are carefully saved in the present time and maintained for future generations.
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impact analyses of the short-term economic effects of cultural activities are applied a lot (Hansen, 1997, p. 2).
We First shortly discuss these economic impact analyses. After this, the only two papers that apply the TCM to a theatre are discussed. As the art forms theatre and opera are both performing arts they are quite similar, so that we use these two papers as basis for this thesis and henceforth discuss them below. We also discuss a Contingent Valuation of the Royal Theatre in Copenhagen. Furthermore, another research of interest is a comparison between competing museums on travel time by Boter et al. (2005), as discussed below. Frequently the government uses economic impact analyses to calculate the economic effects of cultural activities. Examples of these economic impact analyses are: direct revenue impacts of cultural activities on the local economy, indirect spending effects on the incomes of related businesses and individuals such as restaurants and transport services, employment effects (direct and indirect) and wider economic implications for urban revitalization (Throsby, 2001, pp. 124–125). Trine Bille Hansen, on the other hand, argues that these are short-term economic effects and cannot be used as an argument for public funding to the arts, because the positive effects may be not bigger than if other public supported activities had been started (1997, p. 2). To provide for arguments for public funding, economic valuations need to be done.
The first research about consumer surplus in performing arts was written by Forrest et al. (2000). They use a survey to collect booking data from The Royal Exchange Theatre in Manchester during the season 1992-1993 to calculate a demand function and the consumer surplus. They use the Zonal Travel Cost Model and run an OLS regression. Finally, they compare consumer surplus to the amount of state subsidies and find that the amount of subsidies was justifiable with a benefit/cost ratio of 1.33. This research is very similar to our research: we also use real booking data, do an OLS regression on continuous data and calculate the consumer surplus.
Willis et al. (2012) analyze different motives for theatre attendance for The Northern Theatre in Newcastle, England, and estimated theatre attendance and consumer surplus. They use booking data from 29 productions performed by The Northern Theatre in Newcastle together with socio-economic data from the UK population census. In order to estimate a value for The Northern Theatre they use the Individual Travel Cost Method via both a Poisson regression and negative binomial models. Their finding is that education is one of the most important determinants of theatre attendance; unfortunately, this variable is missing in the datasets we use. Furthermore, they compared consumer surplus with the amount of
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government subsidies and conclude that consumer surplus was higher than the amount of subsidy.
Hansen used the CVM to calculate the estimated aggregated willingness-to-pay for the Royal Theatre in Copenhagen (1997). Hansen took 1,843 telephone-interviews as a sample of the complete population of Denmark (users and non-users of the Royal Theatre) and asked the respondents about their willingness to pay for the Royal Theatre. She took measures to prevent the CVM of overstatement (Hansen, 1997, p. 13). She gives a legitimation for public subsidies for this theatre, because the population is willing to pay an option price for the opportunity of being able to go to the Royal Theatre. She concludes that the CVM cannot be used as a policy tool, because the research is too expansive and there is a big uncertainty in the results (Hansen, 1997, p. 22).
A different method is used by Boter et al. (2005) by comparing the use value of multiple Dutch museums based on travel time. Using a dataset of the Dutch Museum Association, they had access to the booking data of more than 80 thousand Museum Cardholders. A latent class logit model was used to examine the characteristics that have an influence on the probability of a museum visit. An advantage of the latent class method is that it accounts for multi purposed trips. Consumers are assumed to be heterogeneous, through the use of a number of segments of consumers with different preferences. (Boter et al., 2005, pp. 26–29). Boter et al. created four segments in which consumers have another willingness to travel and estimated a top 10 museums per segment. They found that each of the four segments have another top 10 museums, which depends on the willingness to travel, the percentage of youth cardholders and the sort of collection visited (Boter et al., 2005, pp. 28–29).
It seems that the TCM is the most suitable method for this research and provides the most space for further research. Although this method does not account for multi-purposed trips and the non-use value, it is the only method that uses revealed preferences instead of stated preferences, and is therefore relatively cheap and easy applicable. Using an economic impact assessment would not be a good measure, as it only accounts for short-term effects. Using the CVM to calculate the economic value would also be a good method, because it also takes into consideration the non-use value, but this method is more expensive due to the use of a questionnaire instead of booking data and less realistic due to stated preferences instead of revealed preferences. The hedonic pricing method would not be suitable as well, because it is mostly used to evaluate cultural heritage projects.
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3. Data sources and variables
This chapter provides a description on the datasets used in this thesis. Firstly, we will describe the dataset of the Dutch National Opera. Secondly, we provide a description on the dataset of the CBS. Section 3.3 shows details about the included variables and in section 3.4 we will discuss the calculation of the travel costs.
3.1 Dataset DNO
The booking data we use in this thesis comes from the Dutch National Opera (DNO). DNO is the biggest opera company of the Netherlands. Together with the Dutch Travel Opera Company (located in Enschede) and Opera Zuid (located in Maastricht) DNO comprises the Dutch opera “market”. As the Dutch Travel Opera Company and Opera Zuid are relatively small companies and offer few performances a year, while DNO offers big performances on a frequent schedule, we expect the performances of the two smaller opera companies not possible to be seen as a substitute for a performance of DNO. Because opera is a niche-product (it requires interest in theatre and classical music), we expect opera performances and theatre performances to be substitutable to a low degree, which makes a DNO-production even less substitutable.
We extracted the booking data from Audience View, the customer relationship management (CRM) system of DNO. This dataset consists of all individual bookings made in 2014. Audience View has been used by DNO since 2014. The information extracted regarding individual bookings is: customer number, order number postal code, country and number of tickets in the booking.
We included solely operas which were shown in 2014 in the theatre building of Dutch National Opera & Ballet (in Amsterdam at Waterloo square) in the dataset. The production Laika, which was shown in the Stadsschouwburg Amsterdam in June 2014, was therefore not included. The production Kopernikus, which was performed in the Boekmanzaal – a smaller auditorium in the building of Dutch National Opera & Ballet – in April 2014, was included. In total 52.248 bookings in 2014 could be assigned to a customer number.
Subsequently, we dropped all bookings which were not made by a Dutch customer, as this would lead to noise in the data. This is because for most foreigners a visit to DNO is part of a multi-purposed trip, for which the TCM does not account. This left 49.400 bookings (in total 94,5 % of all bookings were made by people from the Netherlands). After that, all bookings without a postal code were dropped, which left 47.788 bookings. Subsequently, we
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dropped some outliers; it appeared that there were three customers in the dataset who visited DNO respectively 167, 119 and 336 times in 2014, which did not look plausible. Finally, 47.165 bookings were left (which is 90,2% of the total bookings), spread over 17.623 different customers. The average number of tickets per booking was 2.68.
Graph 3.1 below pictures the tickets per person per postal code zone. It can be seen that the further the postal code zone is located, fewer tickets per person per postal code have been booked. An extra graph that pictures the total amount of tickets per postal code zone is added in Appendix 1.
Graph 3.1 Tickets per person versus distance
3.2 Dataset CBS
We extracted the census data for both years from the website of the CBS. It consisted of three files: two files on 2010 and one file on 2004. We merged the two files on 2010, leaving us with one dataset of 2010 and one dataset of 2004.
There is however one restriction on the combination of datasets. The CBS only had census data from 2010 or 2004 available – the use of datasets with current data were not freely available. Matching the census data with booking data out of one of these years was impossible, because Audience View only had data from September 2010 on. In order to assess possible trends, which might have an effect on future year data, we compared the
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census datasets of 2004 and 2010 with each other to see whether the socio-economic variables differed significantly between the two years. In total, 416.245 individual postal codes could be compared with each other, which were compared with each other. As the Netherlands consists of approximately 440.000 different postal codes, our dataset consists of socio-economic variables of 94,6 % of the population.
The datasets with socioeconomic data seemed to correspond to a high degree, which can be seen in Table 3.1 below. The correlation coefficient takes a value between -1 and 1, in which 1 is the strongest positive relation. As Table 3.1 below shows, the correlation coefficients for our control variables are above 0.8, so there is a strong relationship between the values of the socio-economic variables in 2004 and the values in 2010. This seems very logical as socio-economic variables in a certain postal code are not expected to change that much over a six-year period. Therefore, we assumed that a similar relation exists for 2010-2014. The census dataset of 2010 is used in combination with booking data of 2010-2014. Table 3.1 shows the correlation coefficients for each of the variables.5 In Appendix 2 the same table can be found with the Adjusted R2 between the variables of the two years.
Table 3.1 Relation 2004-2010
Variable name
Correlation coefficient Average monthly fiscal income 0.8139
Percentage 65+ 0.8544
Percentage non-western
immigrants 0.8137
The census dataset of 2010 used for this thesis consisted of the following variables: percentage 65 years and older, average fiscal monthly income and the percentage of non-western immigrants. The CBS included social security payments, retirement payments and wages in the variable average fiscal monthly income.
3.3 Further transformation of data and choice of variables
Firstly, we transformed the DNO-dataset, which included data on customer-level, to data on a four-digit postal code level. In this way we obtained the following information per postal code zone: number of customers, number of DNO visits and number of DNO tickets. Afterwards, we checked which four-digit postal codes were missing. We included the missing
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A robustness check is done where the effect from 2004 to 2010 is extrapolated to 2014. The regressions of Chapter 4 are done again (included in Appendix 3) to see whether this makes a difference to the results. It appeared that it did not make any difference.
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postal codes as well, with zero values for the variables number of customers, number of DNO visits and number of DNO tickets. Subsequently, we calculated the travel costs to DNO – on which more details will be given in the next section – on a four-digit level. Finally, the socio-economic variables were added. Those variables needed to be transformed from a six-digit level to a four-digit level to get one coherent dataset.
We used the percentage of people older than 65, the percentage of non-western immigrants and the average monthly fiscal income as control variables. Below, in Table 3.2, we added the summary statistics of the included variables. The research of Forrest et al. (2000, p. 390) showed that only the proportion of the zone’s 18-and-over population educated to tertiary standard and the proportion of people over retirement-age (as a percentage of the population, including people older than 15) had a significant effect on the visitor rate of the Royal Exchange Theatre in Manchester (2000, pp. 387–388). Because we were not able to include a measurement of education, as this was absent in the dataset of the CBS, average monthly fiscal income was included instead as an expected approximate to education (Carnevale, Rose, & Cheah, 2011, p. 1). We also included the variable percentage non-western immigrants as control variable, due to a literature research done by Willis and Snowball. They expected that white people would attend western art forms more often than other groups, but did not have empirical evidence for this statement (2012, pp. 100–101).
Instead of using count variables, as Willis and Snowball did in their research, on theatre attendance, this research uses tickets per person in a certain postal code zone as dependent variable, which is a continuous variable greater than zero. This is the total number of tickets in a certain four-digit postal code zone divided by the population of that postal code zone. As we describe below the distance between four-digit postal code zones and DNO was calculated. The Netherlands have 4,782 different four-digit postal code zones. We needed to drop some of those due to missing values. There were some postal code zones with no inhabitants, some postal codes of which no census data was available and some postal codes which appeared to be Post Box Numbers (belonging to companies). We dropped these postal codes. Finally, 4,001 unique four-digit postal codes stayed in the dataset.
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Variable Obs Mean Std. Dev. Min Max
Tickets per person 4,001 0.0055096 0.0369075 0 1.433333
Travel Costs 4,001 21.71722 10.70667 0.019 48.013
Average monthly fiscal income 4,001 1977.505 618.2309 0 6169
Percentage of population older than
65 4,001 14.63779 6.018231 0 83.7
Percentage of population
non-western immigrants 4,001 6.29836 10.26082 0.001 85.6
3.4 Travel costs
The travel costs from each four-digit postal code in the Netherlands to DNO were calculated. To calculate the travel distance, we used a table from Object Vision, which consisted of the distance between all the different postal codes in the Netherlands on a four-digit level. In this way we calculated the travel distance per postal code to DNO via the fastest route by car in kilometers.
Travel costs exist of the actual costs of travelling by car (or another way of transportation) plus the opportunity cost of the travel time (K. G. Willis, J.D. Snowball, 2012, p. 101). Because the bookings data of DNO does not contain data on the way people travelled to the theatre, we used a simple value of €0.19 per kilometer. This number is the maximum tax free refund of travel expenses per kilometer in the Netherlands. Comparing this to average price of petrol in the Netherlands in 2017, which was €1.552 shared by the average number of kilometers per liter of petrol, which was 1 on 14, travelling one kilometer costs around €0.11. €0.19 might be a good proxy, because it also includes parking costs and delay costs, and should be a proxy of all ways in which people travel. The opportunity costs of the travel time are put at 0, as Willis and Snowball argue, because it is relatively difficult to calculate them (2012, p. 102). Therefore, our value per kilometer is rather conservative.
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4. Results
To estimate whether there is a relation between tickets per person and travel costs two Ordinary Least Squares (OLS) models are used (Stock & Watson, 2011, p. 468). To check whether OLS provides good estimators the OLS assumptions are checked in the regression models. The OLS assumption of independently and identically distributed (i.d.d.) variables seems to hold in both cross-sectional regressions. This is because this thesis uses the whole population by using all bookings made by an individual for tickets to a Dutch National Opera performance in 2014 and because the thesis includes census data on all individual postal codes in the Netherlands. The other OLS assumptions are tested in the different regressions.
First an OLS model is used, in which all variables are assumed to follow a linear relationship. Consequently, an OLS model in which some variables have a logistic and a quadratic relation with the dependent variable is used in order to see whether this improves the fit of the model.
4.1 OLS regression 1
To examine the relationship between theatre attendance and travel costs, first it is tested if there exists a negative relationship between those two variables. A linear regression with multiple regressors is performed as in Equation 4.1
Equation 4.1
(4.1) TXTSppi = β0+ β1TCi+ β2 AVmfii+ β3 Elderlyi+ β4 NWIi+ ui
𝐓𝐗𝐓𝐒𝐩𝐩𝐢: Tickets per person: total amount of tickets bought in a four-digit postal code zone divided by the population in that postal code zone.
𝐓𝐂𝐢: Travel costs in euros from a four-digit postal code to DNO.
𝐀𝐕𝐦𝐟𝐢𝐢: Average monthly fiscal income in a four-digit postal code zone.
𝐄𝐥𝐝𝐞𝐫𝐥𝐲𝐢: People who are 65 or older as the percentage of the population in a four-digit postal code.
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Table 4.1 Results of running regressions Dependent variable TXTSpp Independent variables (1) (2) (3) (4) TC -0.000577*** -0.000625*** -0.000426*** -0.000280*** (0.0000941) (0.000181) (0.0000355) (0.0000279) AVmfi -0.000000449 0.00000693*** (0.00000378) (0.00000101) Elderly -0.000190 0.000107** (0.000149) (0.0000430) NWI -0.000138** -0.0000390*** (0.0000553) (0.0000143) _constant 0.0180*** 0.0236* 0.0139*** -0.00452** (0.00260) (0.0141) (0.000972) (0.00202) n 4001 4001 3957 3957 R-squared 0.028 0.030 0.087 0.148
Robust standard errors in parentheses. Stars denote the following significance levels *p<0.1, **p<0.05, ***p<0.01.
At first we tested the individual effect of TCi on TXTSppi . After this we performed a regression with TCi and the control variables on TXTSppi . The results of these regressions can be found in part 1 and 2 of Table 4.1.
Regression 1 shows that TCi is highly significant and has a R2 of 0.028. This means that a change in TXTSppi can be explained by TCi for a small amount. TCi has a negative effect on TXTSppi, as was expected.
Regression 2 explains that the effects of TCi, AVmfii and NWIi are highly significant and that the effects of Elderlyi are significant at a 5% level. By adding the control variables the adjusted R2 increased from 0.028 to 0.030, which is a low increase.
Although all the effects of the independent variables are significant to a high level, not all the relations are as we expected. The effect of TCi on TXTSppi is negative, as expected. The effect of AVmfii is negative, which means that an increase in average monthly fiscal income will lead to a decrease in tickets per person. This is not the effect we expected.
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The effect of Elderlyi is negative, which is unexpected: an increase in the percentage of people older than 65 leads to a decrease in tickets per person. This is not what we expected: an increase in the percentage of elderly should lead to more tickets per person, as older people have more time to visit DNO. The effect of NWIi is negative, as expected. An increase in the percentage of non-western immigrants results in less tickets per person, because it is expected that westerners will attend more than other groups (K. G. Willis, J.D. Snowball, 2012, pp. 100–101).
Checking on outliers
Before checking the other OLS assumptions, tests on outliers and points of influence have been done. Looking at the summary statistics it can be seen that there could be some outliers in our dependent variable. TXTSppi has a mean of .0551 and has a high standard deviation of 0.0369. The lowest value is of TXTSppi is 0 and the highest value is 1.4333. There is a chance of having some really high outliers in our dataset, which have a great influence on the regression output.
Another remarkable finding is that the lowest value of AVmfii is 0. The dataset shows that there are 43 postal codes zone with an average monthly fiscal income of 0. This is impossible, because in the Netherlands the least people get is a social security payment, which was in 2014 at a maximum of €677.27 for singles (De Belastingdienst, 2014, p. 1).
After looking at the summary statistics, a closer look at the dataset was necessary in order to identify deficiencies. A matrix graph and two scatterplots on the relation between TCi and TXTSppi and the relation between Elderlyi and TXTSppi were used to determine outliers. These can be found in Appendix 1. The matrix graph and scatterplots show that there are three data points with a much bigger value of TXTSppi than the others. These were the postal code zones 1101 (Amsterdam Zuid-Oost), 1043 (Amsterdam) and 3541 (Utrecht). The average amount of tickets per person were respectively 1.4333, 1.33 and 1. Comparing those postal code zones to the zones around them, showed these values to be outliers.
After this studentized residuals were created. 6 Attention should be paid at studentized residuals that are greater than 2 or -2. 27 studentized residuals appeared to be greater than two. A list of those values is included in Appendix 1. The list included the outlier postal codes 1101, 1043 and 3541, as well as four postal codes that had an average monthly
6 A studentized residual is the quotient resulting from the division of a residual by an estimate of its standard
17
fiscal income of zero. Is also consisted of 20 other data points; these points showed to have different values, which are not unlikely to happen.
Following these tests the postal codes 1101, 1043 and 3541 were dropped out of the dataset. Also the postal codes with an average monthly fiscal income of zero were dropped. Regression 3 and 4 in Table 4.1 show the same regressions as regression 1 and 2, but without the outliers.
Regression 3 shows that TCi is highly significant and the R2 increased from 0.028 to 0.087. TCi still has a negative effect on TXTSppi, as was expected. Regression 4 has an R2 of 0.148, which is high compared to the R2 of 0.030 of regression 2. We can see that all the variables we included have the expected direction. TCi has a negative effect of 0.000280 and is highly significant. An increase in TCi by one kilometer will decrease the tickets per person by 0.000280. AVmfii has a positive effect of 0.0000693 and is highly significant as well. An increase in average monthly fiscal income by one euro will increase the number of tickets per person by 0.0000693. The effect of Elderlyi is positive (0.000107), significant and can be interpreted as following: an increase of one percentage point in the percentage elderly in a certain postal code zone will increase the number of tickets per person in that postal code zone with 0.000107. The effect of NWIi is negative (-0.0000390) and significant as well. The effect of NWIi can be interpreted as following: an increase of one percentage point in the percentage non-western immigrants in a certain postal code zone will decrease the number of tickets per person in that postal code zone with 0.0000390. The impact of the variables is quite severe, comparing it to the mean of TXTSppi (.0055096): it can be seen that a distance of 200 kilometers from DNO decreases the tickets per person by 0.0560 and an increase in the percentage of elderly of ten percent increases the tickets per person by 0.00107.
Comparing the regression without the outliers to the regression including the outliers, we can see an improvement in the fit of the model and the expected effects. To check whether the results are appropriate estimators, the OLS assumptions for a multiple regression model should be checked.
Checking the OLS assumptions
The four assumptions described above will be checked for the regression results described in Table 4.2. Assumption 2 is discussed in the introduction of this chapter and assumption 3 is checked on the results of the regression in Table 4.1. Therefore, checks on those assumptions will be left out. After checking assumption one and four, the results will be checked on linearity as well and a test on model specification will be done.
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There are four least squares assumptions in a multiple regression model (Stock & Watson, 2011, pp. 245–247). These are the following:
1. 𝜀𝑖~Ν(0, 𝜎2)
a. The error term is homoscedastic b. The error term is normally distributed
c. The error term has a conditional mean of zero
2. All variables are independently and identically distributed (i.i.d.) 3. Large outliers are unlikely
4. No perfect multicollinearity
Test on homoscedasticity of the error term
The regressions in Table 4.1 are tested on the presence of homoscedasticity in the error term. If heteroscedasticity would be present, robust standard errors should be used in the regression (Stock & Watson, 2011, p. 375). We used White’s test to check whether the null hypothesis (the variance of the residuals is homogenous) needs to be rejected or not. If Prob > Chi-squared is smaller than 0.05 H0 will be rejected and a regression with robust standard errors is done. We show the results of these tests in Appendix 4.
The table in Appendix 5 shows that the standard errors of regressions (1), (2), (3) and (4) are heteroscedastic. Therefore, the regressions in Table 4.1 are done with robust standard errors.
Test on normal distribution of the error term
A kernel density plot was created to check whether the residuals follow a normal distribution. Such a plot shows the distribution of data. Figure 4.1 shows the distribution of the residuals of regression (5). Comparing the kernel density estimate to the normal density we note excess kurtosis in the residuals of the error term which thus do not follow a normal distribution. Because of the non-normality of the error term, the estimated coefficients cannot be called Best Linear Unbiased Estimators (BLUE).
19 Figure 4.1 Kernel density estimate residuals
Test on perfect multicollinearity
To check whether the regressions has multicollinearity7 a variance inflation factor (VIF) is used. If the VIF value of a regression is greater than 10, multicollinearity might be present. According to the VIF values shown in Appendix 5 no multicollinearity is present in our regression.
Test on linearity
In Equation 4.1 linearity we assume linearity. This means that the effect of an independent variable on the dependent variable does not depend on the value of the independent variable (Stock & Watson, 2011, pp. 302–303). To check for nonlinearity we created augmented partial residual plots (APR-plots) for each of the independent variables. These plots are included in Appendix 5.
Looking at the plots we can conclude that AVmfii may have a nonlinear effect on TXTSppi. Also TCi might be nonlinear. NWIi and Elderlyi seem to have a linear effect. In the next model we will investigate whether there is a better fit, if the relations are nonlinear.
Test for model misspecification
A model specification error may occur if one or more important variables are left out of the regression. If there is a model specification error, omitted variable bias (OVB) is apparent in the model. We used a regression specification error test (RESET) for omitted variables to check for omitted variable bias. The null hypothesis is that the model has no omitted variables. Looking at the results in Appendix 5, it shows us that our model clearly has omitted variable bias (F-value of 322.84). Variables that might be off influence are education
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and nurture: when someone has been taken to the opera by her or his parents a lot in her or his childhood, there is a higher chance of more DNO-visits when she or he is a grown-up. A higher level of education also can influence the number of DNO-visits: the higher the level of education, the higher the number of DNO-visits. Forrest et al. found education to have a high significant effect on the visitor rate (Ziemer et al., 1980, p. 136).
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4.2 OLS regression 2
As the tests on outliers showed in section 4.1, the variables AVmfii and TCi might be nonlinear. Therefore, we checked which transformation of the variables suits the model the best. For TCi we made a quadratic, logarithmic and a square root transformation. For AVmfii we checked whether a quadratic relationship significantly improves the model. We furthermore tested whether Elderlyi and NWIi have a quadratic effect. Firstly the individual effects of the independent variables on TXTSppi were checked. After this three new models were built, which were compared individually with Equation 4.1. The results of these regressions are included in Appendix 6.
Looking at the individual effects of the independent variables on TXTSppi in Appendix 6 we see that the predictive power of TCi increases in each of the transformations. The linear relation had a R2 of 0.087. A quadratic transformation gives an R2 of 0.156, a logarithmic transformation gives a R2 of 0.207 and a square root transformation gives a R2 of 0.127. AVmfii shows the best fit when it is quadratic (R2 = 0.207). For Elderlyi a quadratic relation seems to have the same R2 as a linear relationship. NWIi also shows a better fit, when taken quadratic in the regression (R2 = 0.013).
Although the square root transformation of TCi is not the best transformation in terms of the highest R2, this transformation seems to be the most logic one: the closer someone lives to DNO, the higher one euro extra travel costs weigh. The farther away someone lives, the less value one extra euro travel costs weigh. This seems logically: as people live very far away, one euro extra travel costs do not seem to matter that much, as DNO is already very far. When people live closer to DNO, one euro extra travel costs has a relatively higher effect. The square root transformation is also good useable in calculating the CS in the way Forrest et al. did it.
For AVmfii we included the quadratic term, as it has a much better fit than the linear term. NWIi and Elderlyi were kept linear, as they did not increase the fit (very much) and there is no logical explanation for a quadratic term.
This resulted in the following equation 4.2:
(4.2) TXTSppi = β0+ β1√TCi+ β2 AVmfii+ β3 (AVmfii)2+ β4 Elderlyi+ +β6 NWIi+ ui
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The graph in Figure 4.2 below shows the quadratic relationship between the independent variables AVmfii and TXTSppi to make the relationship between the variables more convenient to interpret. Table 4.2 shows the results of the regression on TXTSppi after we included a square root term of TCi and a quadratic term of AVmfii .
Figure 4.2 Graph of the quadratic relationship of AVmfii with TXTSppi
Table 4.2 Regression on model specification Equation 4.2 Dependent variable TXTSpp Independent variables (1) sqTC -0.00314*** (0.000372) AVmfi -0.0000201*** (0.00000451) AVmfi2 6.09e-09*** (1.24e-09) Elderly 0.000178*** (0.0000403) NWI -0.0000434** (0.0000169) Constant 0.0301*** (0.00408) n 3957 R-squared 0.259
Robust standard errors in parentheses. Stars denote the following significance levels *p<0.1, **p<0.05, ***p<0.01.
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The results can be interpreted as follows: the higher the square root of the travel costs, the higher the number of tickets per person. A change in average monthly fiscal income will lead in general to an increase in tickets per person; although for the very low incomes a positive change in average monthly fiscal income will lead to a decrease in tickets per person. A change in percentage of people older than 65 in a postal code zone will lead to an increase in tickets per person. Finally, a positive change in percentage of nonwestern immigrants will at first lead to an decrease in tickets per person.
Checking the OLS assumptions
The four OLS assumptions will be checked for the regression results of Equation 4.2. Checks on assumption 2 and 3 will be left out. A test on linearity is not necessary as well, because of nonlinearity in the function. At last the RESET test for omitted variable bias is done.
Homoscedasticity of the error term
The regression of Equation 4.2 was tested on the presence of homoscedasticity in the error term by White’s test. Heteroscedasticity seemed to be apparent, with a Chi-squared value of 606.44 and a p-value of 0.000. Therefore, the regression results presented in Table 4.2 have robust standard errors. We included the results of White’s test in Appendix 7.
Test on normal distribution of the error term
A kernel density plot was created to check whether the residuals follow a normal distribution. Comparing the line to a normal distribution gives us the conclusion that the error term is still not normally distributed. Comparing the graph to the kernel density plot of the error term shows that the distribution of the error term is closer to a normal distribution, but still not completely normal.
Figure 4.3 Kernel density estimate results
0 2 0 4 0 6 0 D e n s it y -.1 0 .1 .2 .3 Residuals Kernel density estimate Normal density
kernel = epanechnikov, bandwidth = 0.0008
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Test on perfect multicollinearity
Again a VIF test was done on multicollinearity. According to the VIF values shown in Appendix 7 multicollinearity may be apparent in the variables AVmfiiand (AVmfii)2, because the VIF value exceeds 10. Multicollinearity between these two variables is an issue that cannot be ignored. Although, as we cannot do anything about this, we used the variables in our model, knowing that there is multicollinearity between AVmfii and (AVmfii)2.
Test for modelspecification
Again we used the regression specification error test (RESET) for omitted variables to check for omitted variable bias. Looking at the results in Appendix 7 shows us that our model clearly has omitted variable bias (F-value of 200.82), although there seems to be less omitted variable bias than in model specification 1 (F-value of 322.84). Again, variables that might be off influence are education and nurture, as we explained in Section 4.1.
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4.3 Calculation of Consumer Surplus
To calculate the economic value of DNO, we need to calculate the CS. For both the model specifications in this thesis a CS is calculated, because a change in the functional form of a demand function results in a change in CS (Ziemer et al., 1980, p. 137). CS is calculated in the same way as Forrest et al. did in their research. As they did, this thesis calculates CS per postal code zone.
Forrest et al. used a Box-Cox regression model to estimate the visitor rate, in which they estimated a maximum likelihood estimate of λ. The demand function of Forrest et al. looked as follows:
VRi = a0+ β1Diλ+ β2 EDUCi+ β3 OLDi+ ui 𝐕𝐑𝐢: Visitor rate in a certain concentric circle around the theatre. 𝐄𝐃𝐔𝐂𝐢: Average educational level in concentric circle.
𝐎𝐋𝐃𝐢: People who are 65 or older as the percentage of the population in a four-digit postal code.
As we did an OLS regression with no estimation of λ, λ is one. To calculate consumer surplus per zone, Forrest et al. used the following below. As Forrest et al. also used continuous booking data and the functional form of their demand function is almost the same as ours, it should be possible to calculate the consumer surplus of our dataset in the same way.
CSi = λb1 −1/λ 1 + λ [Ki 1+λ λ − (K i− TXTSppoi) 1+λ λ ] − TCiTXTSppoi TXTSppoi = TXTSppi∗ POPi
ki = bo+ b2AVmfii+ b3Elderlyi+ b4NWIi Ki = ki∗ POPi
𝐓𝐗𝐓𝐒𝐩𝐩𝐨𝐢: Tickets per postal code: total amount of tickets bought in a four-digit postal code zone.
𝐂𝐒𝐢: Consumer Surplus for a four-digit postal code zone. 𝐤𝐢: Demand function minus β1TCi
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As λ is one, the equation will look as following:
CSi = 1 2b1[Ki
2− (K
i− TXTSppoi)2] − TCiTXTSppoi
The total value of Consumer Surplus in 2014 for the linear demand curve was €363,169,400.
In OLS regression two λ is 0.5, as we took the square root of the travel costs. In this functional form, the equation for calculating CS will look as following:
CSi = 1
3b12[Ki3− (Ki− TXTSppoi)3] − TCiTXTSppoi
Calculating CS in 2014 for the functional form transformation of TCi to sqTCi gives a CS of 3.25299E+14. Such a high value does not make sense and is therefore not reliable as an economic valuation of DNO.
We also tried to calculate the CS on the basis of another functional form, in which the travel costs are the square root of the distance (to correct for non-linearity). Although this functional form also increased the fit of the model, the value of the CS did not seem reliable as well. We included the results of this calculation in Appendix 8. It seems that the results differ a lot depending on the specification of the functional form.
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5. Conclusion and discussion 5.1 Conclusion
This thesis calculates the economic value of the Dutch National Opera through calculating the consumer surplus. It is important to calculate this economic valuation, because cultural policymakers do not use tools to calculate the long-term economic value of cultural institutions yet. The Travel Cost Method is used to measure the CS of DNO. It is a relatively cheap measure, because it uses bookings data and census datasets. A demand function was drawn up to estimate the tickets per person in a certain postal code zone. Also the socio-economic variables average monthly fiscal income, % people older than 65 and % non-western immigrants were included. The demand function was estimated in two different functional forms: a linear functional form and a functional form, that included the square root of the travel costs and a quadratic term for average monthly fiscal income. The latter functional form appeared to have the best fit.
For both functional forms we calculated the consumer surplus. The public funding DNO got in 2014 (24.289 million euros) was less than the CS of DNO in 2014. The CS calculated via a linear functional form appears to be 363.3 million euros, with a cost-benefit ratio8 of 13.9, and the CS calculated via a functional form with a square root and quadratic term appears to be 3.25299E+14 euros. Although the functional form that included the square root and quadratic term has a better fit than the linear functional form, the CS calculated for this functional form is extremely high and therefore not reliable. Checking for different functional forms that correct for a non-linear effect (included in Appendix 8), we obtained very different values of the CS using different specifications. Although the different values using different functional forms, the economic value of 363.3 million euros seems to be a realistic valuation.
This economic valuation could be useful for theatre managers, because it gives them an extra argument for public funding. It also gives them insight in the effects of travel costs and socio-economic variables on theatre attendance. This can be of importance to assess where marketing campaigns should be located and what areas include many potential visitors. However, the economic value of DNO should be calculated for more years and more cultural institutions to be able to use it as an analysis tool for the government to assess how to spread public funding.
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5.2 Discussion
It is good to question whether this thesis made a realistic assessment of the economic value of DNO. During this thesis a few assumptions were made, which have an impact on the economic valuation which are worthwhile discussing.
At first it is important to note that the dataset could have been more up-to-date. The dataset of the CBS comes from 2010 and the dataset of DNO comes from 2014. Because providing census data does not belong to the main tasks of the CBS, newer datasets are expensive to use. For this reason, we used an older dataset that was free to use. If the CBS provided more recent census data, a more actual economic valuation of DNO could have been provided. The papers of Willis et al. and Forrest et al. both were able to use more up-to-date datasets, because the Office for National Statistics of Great Britain collects census data on a regular basis. Although this may have an effect on the reliability of our research, we did a robustness check which extrapolated the relation between the datasets of 2004 and 2010 to 2014. This extrapolation did not make a big difference, so we can assume that the our less actual dataset is suitable for this research. We sum up the results of this robustness check in Appendix 3.
Secondly, during the analysis a lot of data got lost, due to incompleteness in both the datasets. At first, opera-visitors who did not come from the Netherlands were dropped, because no census data on their foreign postal codes was provided (and a visit to DNO was probably part of a multi-purposed visit). We also dropped bookings which did not include a postal code. We also needed to drop some postal codes in the census datasets, because two different sets of 2010 needed to be merged. In the final analysis we used 3,957 of the 4,782 different four-digit postal codes in the Netherland (= 82.7%), because some of postal codes which did not conclude any data, the exclusion of Postal Box Numbers (companies) and the dropping of some outliers.
Thirdly, both RESET tests in the OLS regressions concluded that omitted variable bias is apparent in the models. We were not able to give a solution for this problem. In both the papers of Willis et al. and Forrest et al. education had a significant impact on theatre attendance. Because opera is quite a niche art form – usually more difficult than plays that are shown in a regional theatre –, education could be one of the omitted variables. Due to a lack of data about educational level, this effect could not be tested. Although, we expect a higher educational level to result in a higher amount of tickets per person.
Also nurture could be one of those omitted variables; it is often said that the probability of attendance to more difficult art forms is dependent on whether your parents
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took you there as a child. Unfortunately, this effect also could not be tested. Nevertheless, we expect that if parents bring their children to opera performances, they is a higher chance of them returning to an opera performance when they are older.
Fourthly, a value of €0.19 was assumed to be the average travel costs per kilometer. This number is the maximum tax free refund of travel expenses per kilometer in the Netherlands. Because we left the opportunity costs of travel and extra costs for e.g. parking out, this is quite a conservative proxy and the economic value of DNO might have been estimated lower than it really is.
Fifthly, high substitution effects may adjust the travel costs. We assume that the substitution effects on a visit to DNO are limited, because DNO is the only big player in the Dutch opera market, as is argued in Chapter 3. Substituting an opera performance for a theatre performance (or any other genre) seems implausible, as opera is a very specific genre with a very specific audience.
Sixth, we assumed that DNO is the major and single destination of a trip for people in the Netherlands. Due to the high ticket prices, this could be quite realistic. Although it can also make the estimation of the economic value too high, because not all the travel costs could be assigned to a DNO visit.
Finally, in Section 5.1 it seemed that the economic value by calculating the CS differed a lot using a different model specification. Further research needs to be done to adapt the functional form or the way in which the CS was calculated.
5.3 Recommendations
The information provided by this thesis can be important to theatre managers, because it provides them with an extra argument for public funding. I strongly recommend cultural institutions to intensify their toolkit on calculating their economic value.
Nowadays economic valuation on individual cultural institutions is not part of the analysis the Dutch Culture Council makes in advising the government which cultural institutions need to be subsidized by what amount. The TCM is an appropriate and easy way to calculate these individual economic values, because it is an analysis of booking data.
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Appendix 1: Additional graph on total number of tickets per postal code zone versus distance 0 500 1000 1500 2000 2500 3000 3500 0 31 60 91 121 152 182 213 244 N u m b e r o f D N O ticke ts # of kilometers
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Appendix 2: Table with Adjusted R2 of relation census dataset 2004-2010
Variable name Adj. R-squared Average monthly fiscal income 0.6624
Percentage 65+ 0.729
Percentage non-western
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Appendix 3: Robustness check – extrapolating the 2004-2010 relationship to 2014
Dependent variable TXTSpp Independent variables (1) (2) TC -0.000430*** -0.000316*** (0.0000356) (0.0000308) 14_AVmfi 0.00000439*** (0.000000896) 14_Elderly 0.0000883** (0.0000408) 14_NWI -0.0000363*** (0.00000945) Constant 0.0139*** 0.00137 (0.000977) (0.00195) n 3998 3924 R-squared 0.085 0.132
Robust standard errors in parentheses. Stars denote the following significance levels *p<0.1, **p<0.05, ***p<0.01.
Comparing regression 2 in the table above shows that an extrapolation of the 2004-2010 relationship to 2014 does not make a significant difference. The regression coefficients are as significant as in regression 2 of Table 4.1. The R2 of regression 2 is a bit lower than the R2 in regression 2 of Table 4.1 (0.148).
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Appendix 4: Checks on outliers of regression results in Table 4.1
Graph Matrix graph
The matrix graph above shows scatterplots between all the included variables. In this way it helps finding outliers more easily.
36
Table Studentized residuals of Equation 4.1
The table above shows the studentized residuals of Equation 4.1. Values greater than two (which can be seen in the first column) need further research. If the extremely high or low values cannot be explained, the datapoint might be an outlier and might be dropped.
. 3519. 3.925277 9886 Saaksum .14 35.435 1675 16.6 0 3440. 2.200812 9496 Bunne .07804878 34.371 1667 17.4 0 2861. 2.557491 8389 Zandhuizen .09552239 28.576 1362 12.7 .9 1208. 2.127313 4062 Zennewijnen .08888889 14.991 2167 4.6 5.8 949. 3.982448 8222 Lelystad .15263158 12.616 4089 23.1 8.6 816. 3.47625 2514 Den Haag .1373913 11.191 3177 14 9.5 647. 2.246304 2254 Voorschoten .09433962 9.671 2144 18.8 2.3 570. 5.031933 1627 Hoorn (NH) .2 8.854 0 0 0 511. 2.063572 2334 Leiden .08846154 8.265 2927 10.2 12.4 498. 4.916101 1476 Schardam .19047619 8.189 3967 21.6 .9 368. 29.92065 3541 Utrecht 1 6.707 0 0 0 195. 3.601372 2111 Aerdenhout .144 4.769 4893 22.7 3.7 141. 8.178495 2019 Haarlem .31111111 3.819 4200 7.5 8.5 111. 2.813659 1145 Katwoude .11818182 3.192 2870 20.8 2.6 105. 2.136486 1154 Uitdam .0962963 3.116 2283 9.3 1.4 79. 2.141382 1184 Amstelveen .09473684 2.033 3153 16.8 5.7 77. 2.193519 1151 Broek in Waterland .0970339 2.014 2794 17.5 3.1 67. 49.48796 1101 Amsterdam Zuidoost 1.4333333 1.748 0 0 13.5 52. 37.8816 1043 Amsterdam 1.2 1.33 0 0 4 35. 6.339822 1077 Amsterdam .24535519 .874 4812 16.5 8.8 34. 2.233342 1075 Amsterdam .09840479 .855 3629 10.4 15.6 19. 6.31862 1071 Amsterdam .24562102 .646 4511 13.7 8 12. 2.883719 1015 Amsterdam .12317157 .551 3095 10.2 10.6 10. 2.317514 1019 Amsterdam .10216963 .532 3068 4.3 22.1 5. 3.757915 1016 Amsterdam .15461465 .418 3193 11.1 11 4. 4.914291 1017 Amsterdam .19652462 .323 3452 10.1 10.3 1. 8.333417 1011 Amsterdam .31927438 .019 2400 10.1 11.7 e Postal~e Municipality Txtsper~n TC Avmont~e Q NWI . list e Postalcode Municipality Txtsperperson TC Avmonthlyfiscalincome Q NWI if abs(e) > 2
