University of Amsterdam
Faculty of Economics and Business
Msc Finance, Real Estate Finance
MASTER THESIS
Vacation Rental Houses in the Czech
Republic: Hedonic Analysis of the Effect
of Air Pollution on the Rental Price
Author: Romana Plach´a
Supervisor: dr. F. P. W. Schilder Academic Year: 2016/2017
This document is written by Romana Plach´a, who declares to take full respon-sibility for the contents of this document. I declare that the text and the work presented in this document is 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.
Acknowledgments
I take this opportunity to express gratitude to my supervisor, dr. F. P. W. Schilder, for valuable advice and useful suggestions. I am also grateful to my parents and friends for the unceasin support during my studies.
The core of this thesis is to analyse the effect of air pollution on the rental prices of holiday rental houses in the Czech Republic. Vacation houses are a real phenomenom in the country: from about 25 000 in 1970s, the number increased to around 400 000 in 2012. Nevertheless, even though the demand for recreation is so high and air pollution is one of the key environmental problems in the country, there is no study explaining the effect of air pollution on the rental price of a vacation house.
For analysing the effect, there is used the hedonic pricing model, estimated by the means of OLS. It was necessary to control for house characteristics, location variables, air pollution variables, and seasonality.
The results indicate that in the studied sample of 597 vacation houses from the Czech Republic there is a negative and significant effect of the three anal-ysed air pollutants, PM10, PM2,5, and SO2, on the rental price of a vacation
house.
Contents
List of Tables vii
List of Figures viii
1 Introduction 1
2 Literature review 4
2.1 Vacation houses and determinants of the rental price . . . 5
2.2 Effect of air pollution on the house prices . . . 6
2.2.1 Literature . . . 6
2.2.2 Discussion of the issues . . . 8
2.2.3 Consequences for the thesis . . . 9
3 Methodology 11 4 Data and descriptive statistics 16 4.1 Data . . . 16
4.2 Correction for outliers . . . 17
4.3 Description of variables . . . 19
4.4 Descriptive statistics . . . 22
5 Assumptions and results 25 5.1 Assumptions . . . 25
5.2 Results . . . 27
5.3 Postestimation test . . . 32
6 Robustness checks 33 6.1 Log-log model . . . 33
6.2 Log-log model with interaction terms . . . 36
References 46
List of Tables
4.1 Summary statistics of the variables of interest . . . 17
4.2 Summary statistics . . . 23
5.1 Log-linear model . . . 28
6.1 Log-log model . . . 34
6.2 Marginal willingness to pay for air quality . . . 36
6.3 Log-log model with interaction terms . . . 37 A.1 Thermal power stations with installed capacity above 200 MW . I A.2 Summary statistics with minima and maxima . . . II A.3 Log-linear model, Breusch-Pagan test . . . II
4.1 Scatter plot of PM10 and ln(Price) (EUR) . . . 18 4.2 Scatter plot of PM2,5 and ln(Price) (EUR) . . . 18 4.3 Scatter plot of SO2 and ln(Price) (EUR) . . . 18
5.1 Histogram of rental prices (EUR) with the normal density . . . 26 5.2 Normal probability plot . . . 26
Chapter 1
Introduction
Vacation houses are a real phenomenon in the Czech Republic. From about 25 000 of holiday houses in 1970s, the number increased to around 400 000 in 2012, when the population of the country was 10.5 million. ( ˇCesk´y statistick´y ´
uˇrad 2017) In that year, the Czech Republic was ranked as the second country in the world with the most holiday homes per capita. (Vavroˇn 2012) Nowadays, it is still at the top of the ranking together with the Scandinavian countries, Spain, and France. (Matˇejka 2016) The popularity of the holiday houses caused that many private owners started to rent their properties, when they are not using them.
In the recent years, there is also a continuing rise in the environmental at-tention, which has led to a rise in the demand for particular characteristics related to housing, such as air quality, water quality, or noise level. Never-theless, air pollution is one of the key environmental problems in the Czech Republic.
When decision makers are forming environmental policy, it is convenient to know as much as possible about the demand for and supply of the relevant environmental goods. However, for revealing the demand curves, it is necessary to be familiar with the prices that consumers are able and willing to pay. For marketed goods, it does not impose any difficulties as the prices are observable. Nevertheless, as environmental goods are non-marketed, there must be used other techniques, such as hedonic pricing model, to obtain the prices. Hedonic pricing model is based on the idea that, when a consumer buys some marketed good, such as a house, he is implicitly buying, apart from the house and its neighbourhood, also some environmental good. Then, it is possible to obtain the contribution of the environmental good to the price of the marketed good
by regressing the characteristics of the purchased good on the observed price. (Boyle & Kiel 2001)
Even though the demand for recreation is so high in the Czech Republic, there is no study explaining the effect of environmental problems, such as the air pollution, on the rental price of the vacation houses. Vlˇcek (2012) found that PM10 concentration higher by 1 µg/m3 reduces the value of a regular house in the Czech Republic by 0.74 %. Nevertheless, the expected effect of air pollution on the rental price of vacation rental houses is different. The author supposes that the demand for a first house is less elastic and the demand for a holiday house is more sensitive, thus the effect on the rental price is expected to be stronger.
Therefore, the aim of the thesis is to analyse the effect of the quality of environment, particularly air pollution, on the rental prices of vacation rental houses in the Czech Republic, and in addition to find out, what are the sig-nificant determinants influencing the rental price of a vacation house in the Czech Republic. Firstly, the data for the rental prices and other characteris-tics of the vacation houses were taken from a website www.ubytovani.chata.cz, where are offered cheap but also more expensive vacation houses, apartments, timbers, and huts for rent by private owners from all over the Czech Republic and Slovakia. Secondly, the data about air pollution in the individual re-gions were taken from the website of Czech Hydrometeorological Institute, http://portal.chmi.cz. As the measures of air pollution, there are included the air pollutants PM2,5, PM10, and SO2, as these are the most problematic
ones in the country, and affect human health directly. There is used the he-donic pricing model estimated by ordinary least squares (OLS). Based on the existing literature, because of high correlation among the air pollutants, there are performed separate regressions for each of them.
The results support the existing literature and show that an increase in the concentrations of the studied air pollutants in the air by 1 % (PM10, PM2,5, and SO2) decreases the rental price per person per night by 0.35 – 1.36 %. As
air quality is a public good, the analysis will not have a meaning only for house owners and tenants, but also policy makers and public can benefit from it as well. For example, local government can assess the air tourism policies adopted in past and consider future strategies. (Garriga & Sal´o 2011)
Structure of the thesis is as follows: In Chapter 2, there is stated all the rel-evant existing literature related to the research question, divided into 2 parts. The first part analyses the determinants of the rental price of vacation houses
1. Introduction 3
by the hedonic pricing model, whereas the second part focuses on the effect of air pollution on the house prices, including a short review on air pollution, mentioning different types of air pollutants, the chosen pollutants for this the-sis, and also certain issues from existing literature. In Chapter 3, there is introduced the used methodology and stated literature explaining the logic be-hind the hedonic pricing model. Moreover, there are mentioned the analysed hypotheses. In Chapter 4, there is introduced the studied sample, provided data description with descriptive statistics, and also correction for outliers. In Chapter 5, there are firstly checked the OLS assumptions, and secondly, there are provided the results of the log-linear specifications. Moreover, in Chapter 6, there are presented robustness checks, including analysing log-log specifications and models with interaction terms. Consequently, the results are summarized and discussed in Chapter 7. There are also provided implications and possible extensions.
Literature review
The existing literature on this research question is scarce. As far as the author knows, there is not any study about the effect of air pollution or another environmental externality on the rental prices of holiday houses. Largely, there exist only studies analysing the impact of air pollution levels on the house prices. Nevertheless, based on the theory of elasticity of demand, the expected effect of air pollution on the rental prices of vacation rental houses is different. Firstly, the demand for holiday houses is generally not as high as the demand for the first houses. As it is a kind of “luxury”, individuals usually do not hurry with buying a holiday house. Also, as it is a holiday house, where people plan to spend their free time, they are willing to pay more for the quality, which includes also clean air. People are not restricted by work, therefore not determined just to one location, so they are able to easily switch among different holiday houses in different regions, depending for example also on the quality of air. Thus, it is supposed that the demand curve for the first house is less elastic than the one for the second house. In other words, the demand for the second, holiday house is more sensitive and therefore the expected effect of air pollution on the price, and thus also on the rental price, is stronger.
The literature review is divided into two sections. The first part analyses the determinants of the rental price of vacation houses by the hedonic pricing model, whereas the second part focuses on the effect of air pollution on the house prices, including a short review on air pollution, mentioning different types of air pollutants, the chosen pollutants for this thesis, and also certain issues from existing literature. Lastly, there are mentioned implications for the thesis.
2. Literature review 5
2.1
Vacation houses and determinants of the rental
price
There are not many studies about the phenomenon of vacation houses in the tourism economics literature. Nevertheless, in some countries, the residential tourism creates more than 50 % of the housing in the tourist areas. (Garriga & Sal´o 2011)
The only study I found about the impact of environmental amenities, such as forestlands, or permanent grasslands, on the recreational-housing rental price is a study from Mollard et al. (2007) and it is applied to France. For the rental prices, it uses catalogue data for two regions for year 2002, which are distributed at the beginning of the calendar year. Therefore, the rental rates are derived from the assumptions about household’s preferences. To get the actual price, it would be needed to adjust the catalogue price according to the regions’ filling rates. Nevertheless, in this study, they focused only on the peak season (from 15th July to 15th August), when they expect the filling rates to be 100 %, because usually the demand is even higher.
Nelson (2010) estimated hedonic prices for summer and winter vacation houses in rural western Maryland, the United States. The dependent variable is the weekly rent and the independent variables are size of the house, quality, and location characteristics such as reachability of a lake, or accessibility of a ski slope. The results show an importance of the access to the recreation site for the rental offers. On average, a vacation houses located at a lakefront exhibit a premium from $1.100 up to $1.200 per week, and the properties with easy access to a ski slope command a premium between $500 and $600 per week. This implies an importance of including the location into the hedonic pricing models.
Article by W¨ustemann (2014) analyses the amenity values related to dif-ferent land uses by the means of the hedonic pricing model in Germany. Fur-thermore, there is investigated the effect of the distance to the closest major city on the rental prices. The results show that the land variables have high positive effect on the price variable and yield an inverse relation between rental prices and high shares of pastures and forestland.
Third study about the hedonic price modelling of holiday rental houses in the Europe is written by Garriga & Sal´o (2011). The article analyses the market value of the factors that explain the overall price of a representative sample of
holiday houses in Spain. Included explanatory variables are characteristics of a vacation house (number of rooms, size, swimming pool, type of the house, sea view), location (distance to the beach), and seasonality. Thus, this article is useful for providing tools to help the decision making process of the stakeholders and policy makers, the main included agents.
Last study I would like to mention in this part is a study by Hamilton (2007), where are analysed the determinants for the prices of tourist accommodation in a coastal area. When compared to other literature, it takes into account also the impact of climate change on tourism demand. As climate is correlated to seasonality, which highly affects the holiday housing, it suggests that including the seasonality variable into the regression will improve the model.
2.2
Effect of air pollution on the house prices
Air, especially in inhabited areas, is contaminated with air pollutants, which, among other, come also from human activity. These substances have un-favourable effects on human health and the whole environment. (V´agnerov´a 2015) There are six common air pollutants, so called “criteria pollutants”, which The Clean Air Act requires Environmental Protection Agency (EPA) to set emission standards and regulations for. These were demonstrated to have adverse consequences for human health, the environment, and moreover cause property damage. The 6 air pollutants are ground-level ozone (O3),
car-bon monoxide (CO ), sulfur dioxide (SO2), particulate matter (PM ), lead (Pb),
and nitrogen dioxide (N O2). (EPA 2017)
2.2.1
Literature
Rosen (1974) introduced a general theory for using the hedonic pricing model to examine the supply of and demand for attributes for heterogeneous or dif-ferentiated goods, which is also housing. He suggested a two-step method for the estimation of marginal willingness to pay and also of the supply curve. Consequently, Freeman & Myrick (1974) presented how this framework can be used to interpret studies about the relationship between the house value and air pollution. However, the very first use of the environmental hedonic pricing model was done in the United States in 1967 by Ridker & Henning (1967). The aim of the study was to determine the damaging impact of air pollution on the residential property values. There were used two measures of air pollution: the
2. Literature review 7
sulfation levels and levels of suspended particulates. In both cases, there were used the annual geometric averages as the measures of central tendency in the regressions. Nevertheless, the second measure was finally dropped out of the model because of statistically unsatisfactory results. The final finding of this analysis was that there is a significant impact of air pollution on the residential property values. Reduction in the sulfation level by 0.25 mg/day assumes rise in the house price by at least $83 and more likely closer to $245.
In the next years, there were two major empirical studies. The first one was by Harrison & Rubinfeld (1978), who analysed the impact of N O2
concentra-tion, in the squared form, on median property prices in the Boston metropolitan area. This specification was chosen based on estimations with several possi-ble exponents to find the best fit. The results showed a statistically signif-icant negative effect. The second empirical research was realized by Nelson (1978) and was conducted explicitly on the hedonic price framework. In these studies, there were used two different groups of independent variables. The first one included property characteristics, such as location, size, or structural characteristics, whereas the second one focused on the characteristics of the neighbourhood, involving population, availability of public services (schools, police), or accessibility to parks. Harrison & Rubinfeld (1978) had more than one variable related to air pollution in their data set, however, they did not include all of them because of high correlation. On the other hand, Nelson (1978) included two measures of air pollution, nevertheless, did not state the correlation between them.
Palmquist (1982), in a study, where he analysed 20 metropolitan areas in the United States, included four variables related to air pollution. Because of the problems with multicollinearity in case of Harrison & Rubinfeld (1978), he tested for the possibility of multicollinearity among the different measures, however, did not reveal any problems. Nevertheless, his results showed mix of different signs and different significance. Palmquist (1982) explained that it can be caused by omitted locational variables. Two years later, Palmquist (1984) also pointed out the importance of choosing the correct type, potentially types, of air pollution, when analysing the effect of air pollution on the house price. In the study, air pollution was measured by annual average concentrations of suspended particulate matters. Moreover, he also emphasized special attention to the number of square meters of the living space.
In a more recent article by Komarova (2009), there are estimated two models for analysing the effect of CO2, NO, SO2, and also PM on the house prices,
and it is based on the sample of 20 000 of flats in Moscow, covering all areas of the city. In the study, there are analysed two models. The results show small, however, significant negative effect of air pollution of the house prices. Particularly, when the concentration of PM in the air increases by 1 %, the house price decreases by 0.03 %. Also, the results support the assumption that households take into account the level of air pollution in the area, when choosing a house. Nevertheless, in this study there are certain limitations and shortcomings: similarly to other articles, there are used the offer prices and not the transaction prices because of the unavailability of the data. Also, it was not possible to include the age of the building, and noise level and crime data. The only study about the effect of air pollution on the house prices in the Czech Republic is a thesis by Vlˇcek (2012). As a pollutant was chosen PM10. Vlˇcek (2012) analysed 6 cities in the Czech Republic and found that if the level of PM10 in the air increases by 1 µg/m3, then the price of as house drops by 0.74 %.
2.2.2
Discussion of the issues
The analysis of air pollution effect on house values in the existing literature raised some substantial, already mentioned, issues. The ones that provide implications for the thesis will be shortly discussed.
Correlation among air pollutants Harrison & Rubinfeld (1978) used the variable NOX, which represented a concentration of nitrogen oxides. This variable was used in the study as a proxy for air quality, since it was not pos-sible to include also variable PART (concentration of particulates) because of high correlation of 96 %. The high correlation would cause specifying their independent impacts on housing values extremely difficult. Based on this, Ko-marova (2009) also proceeded with separate regressions for each air pollutants variables – TSP, SO2, CO, NOx, and HxCx.
Log-log model Komarova (2009) included two models into the analysis. First model was a simple linear model, nevertheless, she found out that the more appropriate one is the log-log model, including the dependent variable as well as the main independent variables in the logarithmic forms.
Size of the house Palmquist (1982) emphasized special attention to the number of square meters of the living space. It is assumed that the number
2. Literature review 9
of square meters does not have a linear effect on the house price. When the number of square meters rises, construction costs do not rise proportionally. Therefore, it is generally known that the price per square meter differs with the size of the house. To allow for this nonlinear relationship, Palmquist (1982) included the square of the size of the living area into his model.
2.2.3
Consequences for the thesis
In this thesis, there are used three of the EPA’s “criteria pollutants”: partic-ulate matters (PM2,5 and PM10 ), and sulfur dioxide (SO2). The pollutants
PM2,5 and PM10 are involved, as nowadays they are considered as the biggest problem in the Czech Republic. SO2 was the main air pollutant especially in
the end of the last century in the country. (V´agnerov´a 2015) Moreover, all these three air pollutants affect the human health directly. More about PM2,5, PM10, and SO2, and their effects on health can be found in Section 4.3.
Based on the raised issues and relatively high correlation in the used air pollutants, there are performed separate regressions for each air pollutant. As well as in a study by Komarova (2009), there is performed also log–log model in the robustness checks to see how much the coefficients change with different functional form. Unfortunately, the data about the size of vacation houses in square meters were not available, therefore this is one of the shortcomings of the analysis. Instead, there is used a maximum capacity of persons for each vacation house as a proxy variable.
As mentioned, data about the size of the vacation house in square meters and also about the age of the building, number of bedrooms and bathrooms were not available. Thus, as house characteristics, apart from the proxy for the size, there are used dummy variables indicating whether a vacation house has a Wi-Fi, sauna, whirlpool, swimming pool, inner fireplace, and terrace, as these are considered to be important for choosing a vacation house. There is not included a distance to the city centre, but there is used distance to the closest shop, restaurant, bus station, and train station, expressed in kilometres. Based on the studies that involve the distance to the cause of air pollution, such as industrial zones or power plants into their analysis (Brasington & Hite 2005), there are chosen the largest sources of air pollution in the country and there is indicated, in which regions they are located.
The thesis adds to the existing literature in several ways. Firstly, the ex-isting studies have examined only the effect of air pollution on house prices,
or the determinants of the rental price of a vacation house. Secondly, there is only one study about the effect of air pollution on residential house prices in the Czech Republic and no study about the effect on the rental prices of vaca-tion houses, even though the demand is high and vacavaca-tion houses are popular. Thirdly, despite having a smaller sample than in some other studies, there are used different variables and interaction terms, such as popularity of a region among foreigners, or effect of levels of air pollution in different seasons.
Chapter 3
Methodology
House is a physical, long-term durable asset with a unique set of characteris-tics, such as size, quality, and location, which affects the value. Homebuyers value these individual characteristics of each house in different ways, accord-ing to their unique utility functions. Therefore, a certain house can be valued differently by different homebuyers. This implies that housing is a heteroge-neous good with heterogeheteroge-neous consumers, which makes the valuation difficult. The typical method, which deals with this problem and explains the value of housing by breaking down the total expenditure into the values of individual characteristics, is the hedonic pricing model. (Sirmans et al. 2005)
The intuition behind the model is that the utility coming from the con-sumption of housing, differentiated product, is identified by the utility coming from the characteristics of the housing. As an explicit market for clean air does not exist, the hedonic pricing model is also generally exploited for estimating the economic value of the clean air, a nonmarket amenity, to individuals. The theory anticipates that air pollution, which is an economic bad, is negatively correlated with the housing values, when controlling for all the other charac-teristics of the property. (Chay & Greenstone 2005)
As mentioned earlier, the first study about the relationship between the house prices and air pollution was published in 1970s. (Ridker & Henning 1967) Nevertheless, the economic interpretation of this correlation was first provided by Rosen (1974), who introduced a model for a differentiated good that can be represented by a vector of its characteristics, X = (x1, x2, . . . , xn).
In relation to a house, there can be involved structural characteristics, public services in the neighbourhood, or local amenities, such as air pollution. In the price of housing, there is also included a statistical error of estimation, ui.
(Komarova 2009)
Therefore, the price of a house can be expressed:
Pi = P (x1i, x2i, . . . , xni, ui)
The willingness to pay or the marginal implicit price is determined by the value an individual pays for improvements in extra unit of an attribute, such as air quality. It is the partial derivative of P(·) with respect to the nth char-acteristic ∂P
∂xn. (Chay & Greenstone (2005), Komarova (2009))
It is also necessary to analyse the factors that determine the house price for studying the possible effect of environmental factors. The equilibrium hedo-nic price is dependent on the interactions between the consumers’ bid functions and suppliers’ offer functions. The derivative of the implicit price function with respect to air pollution reveals the equilibrium differential, which distributes the households into locations and offsets for the ones that confront higher lev-els of air pollution. As it is expected that the locations with high levlev-els of air pollution have lower prices of the house, then at each point on the hedonic price schedule, “the marginal price of a housing characteristic is equal to an individual consumer’s marginal willingness to pay for that characteristic and an individual supplier’s marginal cost of producing it”. (Chay & Greenstone 2005) As the hedonic price model exposes the marginal willingness to pay, it is useful to derive the welfare effects of a marginal change in a characteristic. (Rosen (1974), Chay & Greenstone (2005)) When analysing the effect of air pollution, it is necessary to keep in mind that the hedonic pricing model can be used only when the households know about the presence of the environ-mental externalities, and are able to choose a house in an alternative market. (Komarova 2009)
Halvorsen & Pollakowski (1981) advise to use flexible functional forms of the hedonic pricing model, when estimating the prices, such as the Box-Cox forms. Nevertheless, Cassel & Mendelsohn (1985) state that simpler forms, such as semi-log form, are more solid for the estimation of coefficients of environmental variables, such as air pollution, as the environmental factors do not explain much of the variation in house prices, and moreover, there can be encountered many problems with using the Box-Cox form.
Furthermore, as Sirmans et al. (2005) state, a problem in the hedonic pricing model is that the estimates of the implicit price of each independent variable
3. Methodology 13
are not assumed to be the same for all rental ranges of individual houses. Also, there are many independent variables that can be involved in the model and high correlation among some of these can cause an estimation problem. Many studies focused on this problem and the results show that the semi-log form of the model, where the dependent variable is in the form of natural logarithm, has certain benefits over the linear form. “Firstly, it allows for a degree of non-linearity in the price equation, secondly, the coefficients can be easily interpreted as the percentage change in the price given a one-unit change in the characteristic, and lastly, the model helps to minimize the problem of heteroscedasticity.” (Sirmans et al. (2005), Mollard et al. (2007)) Because of these reasons, the dependent variable of the rental price is included in the employed model in the form of natural logarithm.
Therefore, to analyse the effect of air pollution on the rental price of a vacation house, there is used the hedonic price model in a semi-log form. The model estimated by OLS regression is following:
ln(rentprice)it = β0+ N X i=1 αiDchari + N X i=1 βiDloci + N X i=1 γiDitseas+ N X i=1 δiDairit +θiD f or it +uit i = 1, . . . , N t = 1, . . . , T
, where i identifies each house and t is the holiday period according to the seasonality variable. The dependent variable is the natural logarithm of the rental price of a vacation house per person per night. (Taylor & Smith (2000), Mollard et al. (2007), Nelson (2010)) PN
i=1αiD char
i represents the
characteris-tics of the house (size in terms of number of persons, terrace, grill, whirlpool, sauna, swimming pool, parking), PN
i=1βiDiloc represents the location variables
(region, distance to the nearest train and bus station, restaurant, shop, pres-ence of a source of air pollution in a given region),PN
i=1γiDseasit represents time
variable (seasonality: summer season, winter season, other season),PN
i=1δiDitair
represents the level of air pollution (exact levels of PM2,5, PM10, or SO2 in
different seasons), Df orit is a dummy variable for a popular location among foreigners, and uit is the error term.
variable equal 1 when the region, in which a vacation house is located, is popular among foreigners and 0 otherwise. There does not exist any study including this variable in the employed models, however, there is expected to be a significant effect on the rental price. More foreigners means higher demand, which pushes the rental prices up. Moreover, this variable can be also used as a proxy for attractiveness of the location, as foreigners usually choose “the better” locations for their recreation.
By the equation, there will be examined the impact of air pollution on the rental prices of vacation houses in the Czech Republic, and moreover found out, what are the significant determinants influencing the rental price of a vacation house in the country. Based on the previously mentioned literature, the hypotheses are:
Hypothesis 1: Air pollution has a significant effect on the rental price of a vacation rental house.
Hypothesis 2: Involving variable related to the levels of air pollution improves the model.
Hypothesis 3: The effect of air pollution on rental price is however smaller than the effect of the house characteristics.
Before performing the analysis, it will be necessary to check the validity of the OLS assumptions. Firstly, there will be checked for linearity between the dependent and independent variables by observing the normality of the distribution of variables and by observing, whether the cumulative probabil-ity significantly differs from the OLS line. Secondly, there will be identified highly correlated variables and consequently omitted some of them to avoid multicollinearity.
After running the regressions, there will be used useful postestimation test, test for heteroscedasticity. It is necessary to check for heteroscedasticity, as homoscedasticity is one of the OLS assumptions. Even though heteroscedas-ticity does not cause bias or inconsistency in the OLS estimators, it causes the estimators of the variance to be biased. As a consequence, the OLS standard errors, as they are based directly on the variances, are not valid for the con-struction of the confidence intervals and t-statistics. There are two generally used tests for the heteroscedasticity, the Breusch-Pagan test and the White test. (Wooldridge 2013) As the White test adds the squares and cross products of all the independent variable into the model to test for various types of het-eroscedasticity, it is more general, nevertheless, including all of these terms can
3. Methodology 15
cause the White test less likely to produce a significant result than a less gen-eral test would. (Williams 2015) As the complete specification of the employed model includes 25 independent variables, there will be used the Breusch-Pagan test.
After the section presenting the results, there will be a part including robust-ness checks. Based on the study by Komarova (2009), there will be performed a log-log model, where not only the dependent variable of the rental price is in the logarithmic form, but also the variables of interest, PM2,5, PM10, and SO2. Moreover, there will be also included interaction terms and checked for
Data and descriptive statistics
In this part, there are provided the sources of the data, correction of the data set for outliers, description of the analysed data and included variables, and lastly presented a table with descriptive statistics.
4.1
Data
Firstly, the data for the rental prices and other characteristics of the vacation houses were taken from a website www.ubytovani.chata.cz, where are offered cheap but also more expensive vacation houses, apartments, timbers, and huts for rent by private owners from all over the Czech Republic and Slovakia. There can be found information about the rental price, location, distance to a train station and a bus station, amenities such as restaurants, supermarkets, shops, possibility of sport activities in the close vicinity, or details about the equipment of the house. The rental prices and data are representative for the year 2016.
The studied sample contains 1 791 observations, which means rental prices for 597 unique holiday houses from all the 13 regions of the Czech Republic in three different seasons (winter, summer, other).
Secondly, the data about air pollution in the individual regions were taken from the website of Czech Hydrometeorological Institute, http://portal.chmi.cz, which provides information about the quality of air in each region of the Czech Republic together with the precise amount of pollutants. In the thesis, as the measures of air pollution, there are used the pollutants PM2,5, PM10, and SO2, as these are the most problematic ones in the country, and affect human
4. Data and descriptive statistics 17
in every region, there were calculated the average levels of these pollutants for every region and every season.
4.2
Correction for outliers
For the estimates of the coefficients to be unbiased and consistent, it is neces-sary to check the data set for outliers. To get a better understanding about the observations, there is provided Table 4.1 with summary statistics (mean, standard deviation, minimum, and maximum) of the continuous variables of interest.
Table 4.1: Summary statistics of the variables of interest
Variable Mean Std. Dev. Min. Max.
Price (EUR) 10.9 6 1.5 99.8
PM10 22.4 6.3 11.3 38.6
PM2,5 17.9 7.2 7.3 36.9
SO2 3.9 2.5 0 13.2
N 1791
By analysing the presented numbers, there are no clear outliers. The average price per person per night is 10.9 EUR (299.4 CZK), but ranges from 1.5 EUR (42 CZK) to 99.8 EUR (2 744.8 CZK). The average annual level of PM10 in the air is 22.4 µg/m3, varying from 11.3 µg/m3 to 38.6 µg/m3. For the pollutant PM2,5, the average annual level is 17.9 µg/m3 with minimum of 7.3 µg/m3 and
maximum of 36.9 µg/m3. For the third included pollutant, SO
2, the annual
level ranges from 0 to 13.2 µg/m3, with the average level of 3.9 µg/m3.
Further analysis by the means of scatter plots will determine if there are any other outliers in the data set, which needs to be corrected for. This is done by plotting the dependent variable in the logarithmic form, lPriceEUR, against the independent variables of interest, PM10, PM2,5 and SO2, as can be seen
in Figure 4.2, Figure 4.1, and Figure 4.3. These three variables are corrected for outliers by command winsorize in Stata, which replaces the largest and smallest values with the largest and smallest values within a 95 % confidence interval. Following this method of correction for outliers, there is no need to exclude any observation from the data set and simultaneously the estimates of the coefficients are less sensitive to the outlying values.
0 1 2 3 4 5 10 20 30 40 PM10 95% CI Fitted values ln(Price_EUR)
Figure 4.1: Scatter plot of PM10 and ln(Price) (EUR)
0 1 2 3 4 5 0 10 20 30 40 PM2,5 95% CI Fitted values ln(Price_EUR)
Figure 4.2: Scatter plot of PM2,5 and ln(Price) (EUR)
0 1 2 3 4 5 0 5 10 15 SO2 95% CI Fitted values ln(Price_EUR)
4. Data and descriptive statistics 19
4.3
Description of variables
Dependent variable
Ln(Price): Natural logarithm of the rental price per one person per one night in a given season, expressed in euros. The exchange rate is 1 EUR = 27 CZK, based on the average for year 2016. (kurzy.cz 2017) The price excludes recre-ation fees for the municipality.
Independent variables House characteristics:
Size: Maximum number of persons in the house.
Pool : Dummy variable equalled to 1 if a house has a swimming pool, 0 otherwise.
Sauna: Dummy variable equalled to 1 if a house has a sauna, 0 otherwise. Grill : Dummy variable equalled to 1 if a house has a grill, 0 otherwise. Terrace: Dummy variable equalled to 1 if a house has a terrace, 0 otherwise. Whirlpool : Dummy variable equalled to 1 if a house has a whirlpool, 0 otherwise.
Fireplace: Dummy variable equalled to 1 if a house has an indoor fireplace, 0 otherwise.
The expected signs of the coefficients of the dummy variables representing the house characteristics are positive. These house attributes provide more comfort and rise the utility for potential renters, therefore increase the value of the vacation house, and thus increase the rents. The only difference is for the variable Size, where the expected sign of the coefficient is negative. The larger is the capacity of the holiday house, the lower the price per person per night is expected to be.
Location:
Bus: Distance to the closest bus station, measured in kilometres. Train: Distance to the closest train station, measured in kilometres. Restaurant : Distance to the closest restaurant, measured in kilometres. Shop: Distance to the closest shop, measured in kilometres.
The expected signs of the coefficients of the distance variables are negative. The locations nearby train stations or bus stations can be more easily reached by the potential renters of the vacation houses, therefore, being close to the stations of public transport is expected to increase the rent. Similarly, the
locations nearby a restaurant or a shop are more convenient and provide more comfort for potential renters, therefore, being close to them is also expected to increase the rent level.
Lastly, there are 13 dummy variables representing 13 regions of the Czech Republic (Stˇredoˇcesk´y, ´Usteck´y, Plzeˇnsk´y, Karlovarsk´y, Jihoˇcesk´y, Vysoˇcina, Pardubick´y, Libereck´y, Kr´alov´ehradeck´y, Olomouck´y, Zl´ınsk´y, Jihoˇcesk´y, Mo-ravskoslezsk´y). These variables do not have any expected signs.
Air pollution:
PM is a widespread air pollutant, which is created by solid and liquid parti-cles suspended in air. The most relevant pollutants related to health problems are PM10 (particles with a diameter of less than 10 µm) and PM2,5 (particles with a diameter of less than 2.5 µm). PM2,5 is commonly called PM and it generates 50-70 % of PM10. These pollutants include inhalable particles that can penetrate the respiratory system. The effects on health can be short term but also long term. It involves respiratory and cardiovascular morbidity (asthma, respiratory symptoms), mortality from these diseases, and also mor-tality from lung cancer. Even though the short-term exposure to PM10 causes serious respiratory health problems, the stronger risk factor for mortality, no-tably in the long-term, is PM2,5. The most vulnerable groups are the ones with pre-existing heart or lung disease, elderly people, and children. The exact level of PM10, which causes health problems, is not determined, as it varies among population. Nevertheless, the first problems are usually observed in case of average levels lower than 30 µg/m3, which is not unusual in the Czech
Republic. (WHO 2013) Third included pollutant is sulfur dioxide, SO2, which
primarily causes breathing difficulties, especially for people who suffer from asthma. Moreover, when SO2 reacts with water and other chemicals in the air,
it produces acid rain. This rain, or acid fog, damages building materials and kills vegetation. (Bajari et al. 2010)
The biggest sources of air pollution in the Czech Republic are large ther-mal power stations, companies emitting air pollutants, and road transport. ( ˇCervinka 2017) Firstly, let’s focus on the thermal power stations. For sim-plicity, there are not included exact distances between every holiday house and the closest power station. However, there are chosen thermal power stations in the Czech Republic with installed capacity above 200 MW to create a dummy variable, indicating whether a holiday house is located in the same region as one of the thermal power stations or not. The list of the chosen power
sta-4. Data and descriptive statistics 21
tions with their location can be found in Table A.1. Secondly, there needs to be stated also companies, which significantly contribute to the levels of air pollution in individual regions. In Moravskoslezsk´y region, it is ArcelorMittal Ostrava a.s., which is the biggest metallurgical enterprise in the country. As the company often burns fossil fuels for producing steel, it emits air pollutants PM and CO2. ArcelorMittal Ostrava a.s. together with 2 thermal power
sta-tions (Dˇetmarovice, Kunˇcice) cause that people in the Moravskoslezsk´y region breathe the most polluted air in the Europe. (FrankBold 2017) In ´Usteck´y re-gion, apart from thermal power plants burning brown coal, there is a chemical refinery Chemopetrol Litv´ınov and Lovochemie Lovosice. These three compa-nies are the ones, which the most increase the level of air pollution in the Czech Republic. Third factor contributing to the air pollution is road transport, which represents a problem especially in Prague and the whole Stˇredoˇcesk´y region. It causes high levels of PM.
Based on this information, there are indicated the most polluted regions in the Czech Republic and there is created a dummy variable indicating whether a holiday house is located in one of the polluted regions or not.
PM10 : Average level of PM10 in a given season in a given region, expressed in µg/m3.
PM2,5 : Average level of PM2,5 in a given season in a given region, ex-pressed in µg/m3.
SO2: Average level of SO2 in a given season in a given region, expressed in
µg/m3.
Source: Dummy variable indicating whether a holiday house is located in one of the regions, where are present the most significant sources of air pollution in the Czech Republic.
The expected signs of the coefficients related to air pollution are negative. Higher air pollution levels represent worse living environment, therefore the expected effect on the rental price is negative.
Seasonality:
Winter, Summer, Other : Dummy variables, indicating whether the price is applicable to winter, summer, or other seasons. The winter season is from 1st December to 28th February, the summer season is from 1st June to 31st August, and the other seasons are from 1st March to 31st May and from 1st September to 30th November.
the omitted category is Other, which denotes the non-peak seasons. It implies that the variable Other is a base group. There is proceeded this way in order to avoid the dummy variable trap.
Popularity of regions:
Foreigners: Dummy variable equalled to 1 if the region is popular among foreigners, 0 otherwise. There were chosen 7 regions (Jihoˇcesk´y, Jihomoravsk´y, Karlovarsk´y, Kr´alov´ehradeck´y, Libereck´y, Zl´ınsk´y, Stˇredoˇcesk´y) as popular re-gions among foreigners for recreation in the Czech Republic. (Bouˇsov´a 2007)
The expected sign of the corresponding coefficient is positive. More foreign-ers represents higher demand, which pushes the rents up.
4.4
Descriptive statistics
The summary statistics of all the variables is presented in Table 4.2 and the summary statistics including also minima and maxima is in Table A.2
The average price per person per night is 10.9 EUR (299.4 CZK), with the minimum value of 1.5 EUR (42 CZK) and maximum of 99.8 EUR (2 744.8 CZK). The average price per person per night in the winter season is 12.35 EUR (339.7 CZK), whereas in the summer season it is slightly more, 12.42 EUR (341.4 CZK). Outside the peak seasons, the average price per person per night is 7.9 EUR (217.1 CZK). If a vacation house is located in the same region as one of the largest sources of air pollution in the Czech Republic, then the price per person per night is on average by 1.10 EUR (30.2 CZK) lower than if there is no large power station in the region. Moreover, the price per person per night is higher by 1.6 EUR (44.8 CZK) in case the region is popular among foreigners than when it is not.
The average holiday house has a maximum capacity of 9 persons, neverthe-less, the value ranges from 2 persons to 40 persons. Most of the holiday houses have a terrace (88.8 %), and grill (73.0 %). Approximately one third of them has a swimming pool (31.2 %) and even more has an inner fireplace (37.4 %). Nevertheless, only 10.7 % have a sauna and 3.7 % have a whirlpool. More than half of the holiday houses has Wi-Fi (52.4 %).
The holiday houses in the sample are located in the 13 regions of the Czech Republic. Most of them (16.1 %) is located in the South Moravia, a region close to the boarder with Austria and Slovakia, typical for its vineyards and biking and swimming possibilities. 12.1 % of the houses are located in the
4. Data and descriptive statistics 23
Table 4.2: Summary statistics
Variable Mean Std. Dev.
Price (EUR) 10.9 6.0 Price (CZK) 299.4 165.6 Size 9.2 4.9 Wifi 0.524 0.5 Pool 0.312 0.463 Sauna 0.107 0.309 Fireplace 0.374 0.484 Terrace 0.888 0.316 Grill 0.73 0.444 Whirlpool 0.037 0.188 Jihocesky 0.121 0.326 Jihomoravsky 0.161 0.367 Karlovarsky 0.028 0.166 Kralovehradecky 0.114 0.318 Liberecky 0.109 0.312 Moravskoslezsky 0.065 0.247 Olomoucky 0.092 0.289 Pardubicky 0.044 0.204 Plzensky 0.025 0.157 Stredocesky 0.05 0.219 Ustecky 0.03 0.171 Vysocina 0.07 0.256 Zlinsky 0.09 0.287 Bus 0.74 0.94 Train 3.05 2.55 Restaurant 1.14 1.48 Shop 1.37 1.56 PM10 22.38 6.25 PM2,5 17.91 7.23 SO2 3.87 2.52 Source 0.409 0.492 Foreigners 0.673 0.469 N 1791
South Bohemia, a region with mountains ˇSumava, the largest dam reservoir Lipno in the country, and a town registered in the UNESCO World heritage site, ˇCesk´y Krumlov. And 11.4 % of the holiday houses are located in the region of Hradec Kr´alov´e with the highest mountains in the Czech Republic, Krkonoˇse, therefore this area provides good skiing opportunities. Interesting fact is that only 5 % of the vacation houses are located in the capital of Prague and its surroundings.
The closest bus station is on average located 0.74 km from the vacation house, however, the closest train station is on average farther away, 3.05 km. The closest shop and restaurant is on average 1.37 km, respectively 1.14 km. Most of the vacation houses (67.3 %) are located in the regions popular among foreigners for recreation.
The average level of PM10 is 22.38 µg/m3 and of PM2,5 it is 17.91 µg/m3.
For the pollutant PM10, the average level in the winter season is 28.66 µg/m3 with maximum value of 38.64 µg/m3, in the summer season it is 16.63 µg/m3 with maximum value of 21.02 µg/m3, and in the other seasons the average level is 21.83 µg/m3 with maximum value of 29.89 µg/m3. The exact level of PM10, which causes health problems, is not determined, as it varies among population. Nevertheless, the first problems are usually observed in case of average levels lower than 30 µg/m3, which is not unusual in the Czech Republic.
For the second pollutant, PM2,5, the average level in the winter season is 25.20 µg/m3 with maximum value of 36.94 µg/m3, in the summer season it is
10.91 µg/m3 with maximum value of 14.64 µg/m3, and in the other seasons the average level is 17.62 µg/m3 with maximum value of 25.38 µg/m3. For the last pollutant, SO2, the average level is 3.77 µg/m3. In winter season, the
average is 4.49 µg/m3 with maximum of 13.15 µg/m3, in summer season the average is 3.42 µg/m3 with maximum of 6.71 µg/m3, and in the other seasons
it is 3.71 µg/m3 with maximum of 8.96 µg/m3. Moreover, 41 % of the holiday
houses in the sample are located in the same region as one of the largest sources of air pollution in the country.
Chapter 5
Assumptions and results
In this part of the thesis, there are firstly checked the assumptions for the use of OLS estimation. It is essential to check the linear relationship between the dependent and independent variables and correlation among the independent variables. After, there are presented and interpreted the results of the final models. For the homoscedasticity will be tested after the regressions.
5.1
Assumptions
Linearity In order to be able to use the OLS for the statistical analysis, there needs to be a linear relationship between the dependent and independent ables. Thus, it is necessary to check the normality of distribution of the vari-ables. In Figure 5.1, there is plotted the histogram of the variable PriceEUR together with the normal density. It is obvious that the distribution of the data slightly differs from a normal distribution. The distribution is right-skewed, nevertheless, this does not indicate a problem of a violation of linearity. More-over, in the Figure 5.2 can be seen that the cumulative probabilities are not significantly different from the OLS line.
Multicollinearity It is also necessary to avoid multicollinearity in the model. Because of this reason, some of the variables related to regions, which were highly correlated, were excluded (Plzeˇnsk´y, Zl´ınsk´y). For the air pollu-tants, there is a high correlation of 97.49 % between PM10 and PM2,5. This is caused by the fact that PM2,5 creates around 70 % of the PM10. Therefore, based on the article by Komarova (2009), there was proceeded with separate regression for each of the pollutants. In this way, the related coefficient is over-estimated, nevertheless, majority of studies related to negative environmental
0 .02 .04 .06 .08 Density 0 20 40 60 80 100 Price (EUR)
Figure 5.1: Histogram of rental prices (EUR) with the normal density
0.00
0.25
0.50
0.75
1.00
Expected cumulative probabilities
0.00 0.25 0.50 0.75 1.00 Observed cumulative probabilities
5. Assumptions and results 27
externalities use only a single variable representing air pollution. Based on the correlation matrix, the rest of the independent variables was left in the model, as there are no correlation coefficients that would be unexpectedly high.
5.2
Results
The final model specification was found by detecting all the highly correlated independent variables causing multicollinearity problems, excluding them, and moreover by omitting the insignificant independent variables. Nevertheless, because of the importance of location, dummy variables indicating regions of the Czech Republic were left in the regression, even if not significant. The final specification includes 25 variables.
The results of the estimations of the different specifications of the final model are presented in the Table 5.1. There are provided the coefficients with corresponding significance level and standard errors in the parentheses. More-over, there is also shown the adjusted R-squared. As mentioned before, because of high correlation among the air pollutants (PM10, PM2,5, and SO2), there
are three separate regressions, each including one of the air pollutants. For the estimation, the statistical software Stata was used, and for the interpreta-tion of the results there was generally used 1 % significance level, if not stated differently.
As the model is in the semi-log form, the interpretation of the resulting coefficients is following:
%∆rentalprice = (100 ∗ βi)∆xi
, where 100 ∗ βi is sometimes called the semi-elasticity of rental price with
Table 5.1: Log-linear model
This table looks at the determinants of logarithm of the rental price per person per night in EUR, lPriceEUR. There are presented 4 different specifications: column (1) does not include any air pollutants, column (2) includes PM10, column (3) includes PM2,5, and column (4) includes SO2. The air pollutants are the variables of interest and are included as average levels per season per region. For definitions of all variables see Section 4.3. The table also reports number of observations and adjusted R-squared for each specification. Regions as well as constants were included in the regressions but are not reported. Standard errors are reported in parentheses. *, **, and *** indicate significance at 10%, 5%, and 1%, respectively.
(1) (2) (3) (4)
lPrice (EUR) lPrice (EUR) lPrice (EUR) lPrice (EUR)
Size -0.0228∗∗∗ -0.0224∗∗∗ -0.0226∗∗∗ -0.0227∗∗∗ (0.00209) (0.00207) (0.00208) (0.00209) WiFi 0.145∗∗∗ 0.142∗∗∗ 0.144∗∗∗ 0.144∗∗∗ (0.0196) (0.0195) (0.0196) (0.0196) Sauna 0.0592∗ 0.0587∗ 0.0590∗ 0.0590∗ (0.0335) (0.0333) (0.0334) (0.0335) Fireplace 0.0873∗∗∗ 0.0881∗∗∗ 0.0877∗∗∗ 0.0868∗∗∗ (0.0203) (0.0201) (0.0202) (0.0202) Whirlpool 0.467∗∗∗ 0.453∗∗∗ 0.462∗∗∗ 0.464∗∗∗ (0.0543) (0.0539) (0.0542) (0.0542) Winter 0.444∗∗∗ 0.673∗∗∗ 0.561∗∗∗ 0.473∗∗∗ (0.0228) (0.0462) (0.0414) (0.0245) Summer 0.448∗∗∗ 0.274∗∗∗ 0.345∗∗∗ 0.437∗∗∗ (0.0228) (0.0381) (0.0381) (0.0230) Bus 0.0521∗∗∗ 0.0510∗∗∗ 0.0517∗∗∗ 0.0518∗∗∗ (0.0114) (0.0113) (0.0113) (0.0113) Train -0.0104∗∗∗ -0.0102∗∗∗ -0.0103∗∗∗ -0.0103∗∗∗ (0.00377) (0.00374) (0.00376) (0.00376) Restaurant -0.0145∗∗ -0.0143∗∗ -0.0144∗∗ -0.0144∗∗
5. Assumptions and results 29 (0.00716) (0.00709) (0.00714) (0.00714) Shop 0.0147∗∗ 0.0145∗∗ 0.0146∗∗ 0.0145∗∗ (0.00727) (0.00721) (0.00725) (0.00725) Source -0.00449 -0.149∗∗ -0.0619 -0.0651 (0.0529) (0.0583) (0.0554) (0.0560) Foreigners 0.117∗ 0.276∗∗∗ 0.167∗∗ 0.154∗∗ (0.0673) (0.0723) (0.0687) (0.0680) PM10 -0.0335∗∗∗ (0.00590) PM2,5 -0.0155∗∗∗ (0.00457) SO2 -0.0379∗∗∗ (0.0117) N 1791 1791 1791 1791 adj. R2 0.336 0.347 0.340 0.339
Standard errors in parentheses ∗p < .10,∗∗ p < .05,∗∗∗ p < .01
Model without air pollutants (column (1)): House characteristics:
The coefficient for the house size, which is represented by the maximum capacity of the house in persons, is negative (-0.0228) and significant. This implies that if the capacity is higher by 1 person, then the rental price per person is lower by 2.28 %. Also, all the included house characteristics are statistically significant at 1 % significance level, only the variable Sauna is statistically significant at 10 % significance level. Moreover, all the coefficients have the expected sign. A WiFi in a house adds to the rental price 14.5 %. The presence of a sauna increases on average the rental price by 5.92 %, an inner fireplace by 8.73 %, and a whirlpool even by 46.7 %.
Seasons:
In summer season (June – August), the rental prices per night per person are on average by 44.8 % higher than in the other seasons (March – May and
September – October). In case of winter season (December – February), the prices are higher by 44.4 % than in the other seasons.
Location characteristics:
The variable Train has the expected negative sign (-0.0104) and it is signif-icant. This implies that distancing from a train station by 1 km represents a loss in the rental value by 1 %. Similarly, the distance to the closest restaurant has the expected sign: additional kilometre of the distance between a holiday house and a restaurant decreases the rental price by 1.45 %. Nevertheless, the coefficient of the variable Bus is positive (0.0521) and statistically significant. This means that one kilometre further from a bus station increases the rental value by 5.21 %. Similarly for the variable Shop: additional kilometre to the closest shop increases the rent by 1.47 %. The explanation for this can be that the potential renters of the houses use cars, therefore they do not care about the distance to the shop. Moreover, they can on average prefer travelling by a train, thus they are not interested in the distance to the closest bus station.
The coefficient for the source of air pollution is negative (-0.00449), however, not statistically significant. The last coefficient, the coefficient for Foreigners, is positive and statistically significant. It implies that when a holiday house is located in a region popular among foreigners, then the rental price is on average higher by 11.7 %.
The adjusted R-squared of this specification is 33.6 %. Model with PM10 (column (2)):
When including the level of air pollutant PM10 in the air into the model, most of the coefficients of the independent variables do not change. Neverthe-less, the coefficient of variable Winter increases from 0.444 to 0.673, indicating that on average the rental price per person per night is higher by 67.3 % in the winter than in the other seasons. On the contrary, the coefficient for the variable Summer dropped from 0.448 to 0.274, meaning that on average the rental price per person per night is higher by 27.4 % in the summer than in the other seasons. Other two coefficients that changed are Source and Foreigners. After inclusion of the variable PM10, the variable Source became negative and statistically significant. It means that when a holiday house is located in a region, where also one of the largest sources of air pollution in the Czech Re-public is located, then the rental price is on average lower by 14.9 %. On the other hand, when a holiday house is located in a region, which is considered as popular among foreigners, then the rental price is on average higher by 27.6 %.
5. Assumptions and results 31
The coefficient of the variable of interest, PM10, is -0.0335 and it is statis-tically significant. This means that an increase in the average level of PM10 by 1 µg/m3 , decreases the rental price by 3.35 %.
The adjusted R-squared of this specification is 34.7 %, which is still rela-tively low in comparison to other comparable studies (70 % on average), but higher than in the specification without the inclusion of air pollutants. (Ko-marova 2009)
Model with PM2,5 (column (3)):
When substituting PM10 by PM2,5 in the regression, the same coefficients change again. The average rental prices in summer are higher by 34.5 % and by 56.1 % in winter than in the other seasons. The difference is also in the coefficient related to the source of air pollution. Even though the coefficient is negative, it is not statistically significant. Last but not least, there is also a difference in the coefficient of variable Foreigners. The difference in the rental prices between the popular regions among foreigners and the ones, which are not so popular, is 16.7 %.
The coefficient of interest, for PM2,5, is -0.0155, which means that on aver-age an increase in the PM2,5 by 1 µg/m3 decreases the rental price per person
by 1.55 %.
The adjusted R-squared of this specification is 34.0 %.
Model with SO2 (column (4)): The estimation of the last specification
including SO2 as air pollutant again changed the coefficients for the already
mentioned variables. Difference between the rental price in winter and in other seasons is on average 47.3 %, and in summer it is 43.7 %. As in previous spec-ification, coefficient of the variable Source is negative, however, not significant. And lastly, when a holiday house is located in a region, which is popular among foreigners, then the price is higher by 15.4 %.
The coefficient of interest, for SO2, is -0.0379, which means that on average
an increase in the SO2 by 1 µg/m3 decreases the rental price per person by
3.79 %.
The adjusted R-squared of this specification is 33.9 %.
Adjusted R-squared increases if and only if the new added variables im-prove the model more than would be expected by chance. (Wooldridge 2013) Therefore, it implies that controlling for level of air pollution, as it increases the adjusted R-squared in all three specifications, improves the model. Moreover,
the variable of interest is always significant. It is obvious that after controlling for each type of air pollution, only coefficients and significance of four variables were changing: Summer, Winter, Source, and Foreigners. It implies that before the inclusion of air pollution, there was an omitted variable bias in the model and that air pollution is correlated with the mentioned variables.
5.3
Postestimation test
Homoscedasticity
The results in the Table A.3 show that the null hypothesis of homoscedas-ticity cannot be rejected in all the presented estimations. The semi-log form of the equation indeed eliminated heteroscedasticity, as in the case of linear-linear form, heteroscedasticity would be present, with chi2(1) of 848.08. Nevertheless, in the case of semi-log form, there is no need to use the heteroscedastic robust standard errors, neither the GLS estimation as Harrison & Rubinfeld (1978), or Palmquist (1982) did.
Chapter 6
Robustness checks
In this part, there will be presented robustness checks and additional results by verifying different functional form of the employed model and by adding interaction terms.
6.1
Log-log model
Based on the article by Komarova (2009), there is proceeded with log-log model. In this specification, not only the dependent variable is in the form of natu-ral logarithm, but also the main independent variables: PM10, PM2,5, and SO2. In this case, the interpretation of resulting coefficients is based on
elas-ticity. This means that 1 % change in an independent variable transformed to a logarithmic form causes a change of β% in the rental price of a holiday house. Nevertheless, the interpretation of the coefficients of variables that are not transformed is still the same: 1 unit change in a variable causes (β ∗ 100)% change in the rental price.
As in the previous part, it was started with the most general model and gradually there were removed insignificant variables while checking for the ad-justed R-squared.
The results of the log-log specification are provided in Table 6.1. When comparing the coefficients to the semi-log specifications, there are not signif-icant differences for most of the variables. The only differences can be found in the coefficients for variable Summer, Winter, Source, and Foreigners. In the specification including PM10 (column (2)), the coefficient of -0.597 implies that when a holiday house is located in one of the regions where is also located one of the largest sources of air pollution, then the price is lower by 59.7 %,
whereas in the semi-log model it was only 27.6 %. In case of PM2,5 (column (3)), the difference is even bigger. In the log-log model it decreases the rental value by 66.2 %, whereas in the semi-log model only by 6.19 %. Big differ-ence is also in the specification with SO2 (column (4)): -33.2 %, respectively
-6.51 %. In this log-log form, the coefficients for the variable Source are sig-nificant. Another difference is in the coefficients for the variable Foreigners: in case of log-log model the effect is stronger. The percentage differences in the rental prices between regions popular among foreigners and the ones not so popular are 38.1 % in the model including PM10 (column (2)), 30.1 % for model with PM2,5 (column (3)), and 19.2 % for model with SO2 (column (4)).
Nevertheless, in the semi-log model the percentages are 27.6 %, respectively 16.7 %, and 15.4 % (Table 5.1). In case of PM10, the rental price is on average higher by 80.6 % in the winter than in the other seasons, and by 7.92 % in the summer than in the other seasons. In case of PM2,5, the differences are similar: 82.4 % for winter, but -7.59 % for summer. In the last specification, with SO2, the differences are 50 % for winter, and 42.7 % for summer.
Table 6.1: Log-log model
This table looks also at the determinants of logarithm of the rental price per person per night in EUR, lPriceEUR, however, now the variables of interest (PM10, PM2,5, and SO2) are in the logarithmic form. There are presented 4 different specifications: column (1) does not include any air pollutants, column (2) includes PM10, column (3) includes PM2,5, and column (4) includes SO2. For definitions of all variables see Section 4.3. The table also reports number of observations and adjusted R-squared for each specification. Regions as well as constants were included in the regressions but are not reported. Standard errors are reported in parentheses. *, **, and *** indicate significance at 10%, 5%, and 1%, respectively.
(1) (2) (3) (4)
lPrice (EUR) lPrice (EUR) lPrice (EUR) lPrice (EUR)
Size -0.0228∗∗∗ -0.0222∗∗∗ -0.0223∗∗∗ -0.0219∗∗∗ (0.00209) (0.00206) (0.00206) (0.00243) WiFi 0.145∗∗∗ 0.139∗∗∗ 0.140∗∗∗ 0.149∗∗∗ (0.0196) (0.0193) (0.0194) (0.0205) Sauna 0.0592∗ 0.0573∗ 0.0577∗ 0.0512 (0.0335) (0.0330) (0.0331) (0.0360) Fireplace 0.0873∗∗∗ 0.0890∗∗∗ 0.0887∗∗∗ 0.0890∗∗∗
6. Robustness checks 35 (0.0203) (0.0199) (0.0200) (0.0211) Whirlpool 0.467∗∗∗ 0.442∗∗∗ 0.447∗∗∗ 0.482∗∗∗ (0.0543) (0.0535) (0.0536) (0.0567) Winter 0.444∗∗∗ 0.806∗∗∗ 0.824∗∗∗ 0.500∗∗∗ (0.0228) (0.0512) (0.0581) (0.0264) Summer 0.448∗∗∗ 0.0792 -0.0759 0.427∗∗∗ (0.0228) (0.0520) (0.0772) (0.0242) Bus 0.0521∗∗∗ 0.0500∗∗∗ 0.0504∗∗∗ 0.0514∗∗∗ (0.0114) (0.0112) (0.0112) (0.0116) Train -0.0104∗∗∗ -0.0101∗∗∗ -0.0102∗∗∗ -0.0110∗∗∗ (0.00377) (0.00371) (0.00372) (0.00396) Restaurant -0.0145∗∗ -0.0141∗∗ -0.0142∗∗ -0.0141∗ (0.00716) (0.00704) (0.00706) (0.00722) Shop 0.0147∗∗ 0.0145∗∗ 0.0145∗∗ 0.0124 (0.00727) (0.00715) (0.00717) (0.00784) Source -0.0550 -0.597∗∗∗ -0.662∗∗∗ -0.332∗∗∗ (0.0420) (0.0803) (0.0951) (0.0710) Foreigners 0.117∗ 0.381∗∗∗ 0.301∗∗∗ 0.192∗∗∗ (0.0673) (0.0742) (0.0712) (0.0683) lPM10 -1.358∗∗∗ (0.173) lPM2,5 -1.105∗∗∗ (0.156) lSO2 -0.353∗∗∗ (0.0726) N 1791 1791 1791 1587 adj. R2 0.336 0.358 0.354 0.351
∗p < .10,∗∗ p < .05,∗∗∗ p < .01
The coefficient for PM10 implies that 1 % increase in the level of PM10 in the air decreases the rental price by 1.358 %. For the pollutant PM2,5 the decrease is 1.105 %, and for SO2 the effect is the smallest, 0.353 %. When
comparing the adjusted R-squared of the semi-log and log-log model, it is higher in all the specifications of the log-log model (35.80 %, 35.39 %, and 35.15 %), which means that the used variables and theirs forms explain more of the variation in the dependent variable, the rental price, in case of the log-log model.
The adjusted R-squared in the specification without any air pollutant is still 33.59 %, therefore inclusion of the levels of air pollution improves the model. In addition, the Breusch-Pagan test proved that there is no problem of heteroscedasticity.
Moreover, by the estimation of log-linear and log-log models, it is possible to recover the marginal willingness to pay. The average price per person per night is 10.89 EUR, therefore the marginal willingness to pay to decrease the concentration of PM10 in air by 1 % equals 0.15 EUR. The results of the rest of the equations are provided in Table 6.2.
Table 6.2: Marginal willingness to pay for air quality
Pollution variables MWTP per 1 unit
change (EUR)
MWTP per 1 % change (EUR) Log-linear model Log-log model
PM10 0.37 0.15
PM2,5 0.17 0.12
SO2 0.41 0.04
6.2
Log-log model with interaction terms
Secondly, it was needed to take into account the possibility of heterogeneous effects by including interaction terms into the model. It was checked for the effects of the levels of each air pollutant in different seasons of the year. The results for each air pollutant are presented in Table 6.3.
6. Robustness checks 37
Table 6.3: Log-log model with interaction terms
This table looks also at the determinants of logarithm of the rental price per per-son per night in EUR, lPriceEUR, with the variables of interest (PM10, PM2,5, and SO2) in the logarithmic form. Moreover, there are included interaction terms among air pollutants and seasonality. There are presented 3 different specifica-tions: column (1) includes PM10, column (2) includes PM2,5, and column (3) includes SO2. For definitions of all variables see Section 4.3. The table also reports number of observations and adjusted R-squared for each specification. Regions as well as constants were included in the regressions but are not re-ported. Standard errors are reported in parentheses. *, **, and *** indicate significance at 10%, 5%, and 1%, respectively.
(1) (2) (3)
lPrice (EUR) lPrice (EUR) lPrice (EUR)
Size -0.0221∗∗∗ -0.0219∗∗∗ -0.0218∗∗∗ (0.00205) (0.00204) (0.00243) Wifi 0.139∗∗∗ 0.137∗∗∗ 0.149∗∗∗ (0.0193) (0.0192) (0.0205) Sauna 0.0571∗ 0.0563∗ 0.0511 (0.0329) (0.0327) (0.0360) Fireplace 0.0892∗∗∗ 0.0898∗∗∗ 0.0888∗∗∗ (0.0199) (0.0198) (0.0211) Whirlpool 0.439∗∗∗ 0.431∗∗∗ 0.481∗∗∗ (0.0534) (0.0531) (0.0566) Winter -0.374 -0.581∗ 0.447∗∗∗ (0.448) (0.316) (0.0736) Summer -0.257 0.214 0.531∗∗∗ (0.459) (0.319) (0.0770) Bus 0.0497∗∗∗ 0.0491∗∗∗ 0.0513∗∗∗ (0.0112) (0.0111) (0.0116) Train -0.0101∗∗∗ -0.0100∗∗∗ -0.0110∗∗∗ (0.00370) (0.00368) (0.00396) Restaurant -0.0141∗∗ -0.0140∗∗ -0.0141∗
(0.00703) (0.00698) (0.00721) Shop 0.0144∗∗ 0.0143∗∗ 0.0123 (0.00714) (0.00709) (0.00783) Source -0.240∗∗∗ -0.270∗∗∗ -0.181∗∗∗ (0.0594) (0.0587) (0.0624) Foreigners 0.409∗∗∗ 0.443∗∗∗ 0.215∗∗∗ (0.0747) (0.0737) (0.0691) lPM10 -1.680∗∗∗ (0.218) lPM10 x Winter 0.379∗∗∗ (0.144) lPM10 x Summer 0.0887 (0.154) lPM2,5 -2.033∗∗∗ (0.220) lPM2,5 x Winter 0.540∗∗∗ (0.113) lPM2,5 x Summer -0.307∗∗ (0.125) lSO2 -0.392∗∗∗ (0.0843) lSO2 x Winter 0.0402 (0.0507) lSO2 x Summer -0.0834 (0.0567) N 1791 1791 1587 adj. R2 0.360 0.368 0.353
