3.1. Study Areas
In the paper, we investigate the influence of an airport on residential property prices. We try to assess the joint effect of (i) airport noise and (ii) land use restrictions (introduced via zoning plans and LLUAs). In this research, we analyse data on two out of twelve regional airports in Poland: the Katowice-Pyrzowice airport, and the Poznan-Lawica airport (
Table 3).
Both Katowice-Pyrzowice airport and the Poznan-Lawica airport are located in the western part of Poland. The basic selection criterion is based on their relative importance, that can be measured by the number of passengers served in recent years (based on which they are ranked as the 4th and the 7th airport in Poland respectively). While we can argue that both selected airports are relatively similar concerning the importance and geographic location, they differ significantly concerning an urban setting. Poznan-Lawica is located in the city of Poznan in a densely populated and heavily urbanised area. On the other hand, Katowice-Pyrzowice is located outside the urban area of Katowice in the less developed rural setting. This particular difference affects the activity on the housing market, measured by the number of sales in the study period. Another important difference is the date of the introduction of the LLUA. The LLUA around Poznan-Lawica was set up on 28 February 2012, whereas in the case of Katowice-Pyrzowice the LLUA was introduced on 15 September 2014. Due to the disparity in the dates of LLUA introduction the study uses different study periods for two selected airports: 2008–2014 for Poznan-Lawica and 2007–2016 for Katowice-Pyrzowice (longer study period needed to obtain a sufficient number of transactions). These study periods include the periods before and after LLUA introduction. A total number of 884 transactions were collected for Poznan Lawica (478 before and 406 after the introduction of LLUA). In the case of Katowice-Pyrzowice, the research was based on 109 transactions (87 before and 22 after the introduction of LLUA).
In both cases, the research is based on the data on house transactions (e.g., time of sale, sale price, information about buyer and seller) around the two selected airports and was obtained from notarial deeds gathered in the Real Estate Cadastre and the National Geodetic and Cartographic Resources. Additional information on house attributes (e.g., usable building area, lot area, technical condition of the building) was obtained by onsite scrutiny and additional spatial information available online. Transactions were geo-coded.
The comparison between the two airports can be interesting for two reasons. Firstly, the LLUAs in both cities have different introduction date and the extent of restrictions imposed. In the case of Katowice-Pyrzowice, inside the LLUA any conversion, extension, and refurbishment of residential buildings are restricted with regards to allowable building acoustic performance. As a result, sound absorption and noise reduction norms must be met in case of windows, as well as construction and materials for walls and ceilings. In the Poznan-Lawica case, the situation is more complex as two zones within the LLUA were created. In the inner LLUA zone restrictions regarding residential buildings are similar to those affecting properties around Katowice-Pyrzowice. No significant restrictions regarding residential buildings were imposed for properties located within the outer LLUA zone around Poznan-Lawica (
Figure 1).
Secondly, the activity reported on the market differs significantly due to location factors. As noted before, Katowice-Pyrzowice airport is located outside the major metropolitan area, and the residential property market around can be classified as inactive (thin). Out of 109 transactions during the study period, 89 were outside LLUA, and 20 inside LLUA. On the other hand, Poznan-Lawica airport is located more centrally within the city. The property market in the proximity is fairly active. Out of 884 recorded transactions, 824 were outside LLUA and 60 inside LLUA (18 in inner LLUA zone and 42 in outer LLUA zone). That resulted in a significant difference in sample size reported in each city (
Figure 1).
3.2. Econometric Approach
We use hedonic regression to assess the joint effect of airport noise and the introduction of an LLUA on sales prices. To investigate the impact of the introduction of an LLUA around the airport on property prices we modified standard hedonic approach and used: (1) hedonic regression with linear splines as a baseline model, and (2) the difference-in-differences hedonic regression approach. Many sources confirm that the results obtained using hedonics models strongly depend on the functional form used [
45], consideration of the temporal effect [
46] and segmentation of the market [
47]. In line with mainstream urban and housing research using hedonic models, the semi-log form was utilized. Although there are several advantages of more flexible and complex functional forms (like Box-Cox transformation), in the presence of omitted variables semi-log form is more robust and accurate [
48].
To take account of the spatial dependence found in the house sales data, aside from the standard hedonic regression model (OLS), we used spatial regression models that take account of spatial disturbances, assuming that such approach outperforms standard specifications of the hedonic price functions [
49]. Although there are at least two crucial questions related to the usefulness of such models: what kind of the model do we prefer and which estimation procedure is appropriate [
32]. Fixity in location makes real estate subject to the various spatial phenomenon. Firstly, there are salient neighbourhood effects and environmental externalities that manifest locally and affect property prices. Some of them can be explicitly treated in a hedonic model, but some are not directly observed, sometimes due to data limitations [
50]. The failure to account for unobserved factors induces omitted variable bias. The econometric model that explicitly addresses spatial heterogeneity, and can be used to correct for unobserved factors that affect property prices is spatial error model (SEM), and is given by [
51,
52]:
where the dependent variable P is the property price, X is a vector of attributes affecting prices (structural, location, neighbourhood), and β is a vector of regression coefficients. In a second equation, W is a spatial weight matrix, λ is a spatial coefficient related to the autocorrelation of the error term, and ξ is an error term subject to spatial autocorrelation (a function of pure error term ε).
To account for a different kind of spatial dependence or spatial spillover effects, we used the Spatial Autoregressive Model (SAR), sometimes referred to as the Spatial Lag Model, both of them being particular cases of Spatial Durbin Model [
53]. Spatial spillover is related to property prices being affected by the prices of properties in the neighbourhood (due to information flows, contagion effects). It requires a spatially lagged dependent variable to be included in the equation. Thus the hedonic model is given by [
51]:
where
ρ is the spatial lag coefficient for dependent variable and
WP is the spatially-lagged dependent variable
P.
The spatial weight matrix is a canonical concept of spatial econometrics used to define the spatial dependences between observations in the research sample. It represents an association between observations across space and is based on the intuition that distances between objects in an urban area are related to both similarity and propensity to influence one another [
54]. There is no theory on the appropriate shape on this matrix, while different specifications lead to different results [
13,
55].
In our research, the spatial weight matrix was based on the geographic location of houses sold in the study period. The spatial weight matrix can be defined in many ways, most of them theoretically discussed and experimentally tested in the literature [
56]. In our study, we used the inverse distance matrix W, commonly used in applied hedonic research. The choice of this particular distance is justified by the notion that property sales in proximity were significantly more related than ones further away.
Spline regression is a modification of standard regression that can be used to address structural change in the relationship between independent and dependent variables. It is a specific case of piecewise regression that does not allow for discontinuity. The methods were used within the hedonic regression framework by Smersh and Smith [
57] and Chernobai, Reibel, and Carney [
14]. We use a baseline spline regression model to check whether the house price dynamics changed significantly after the LLUA was introduced. Additionally, we investigate whether house price dynamics was similar within the area affected by airport noise (LLUA) and reference area outside. The spline regression approach appears to be more justified than piecewise regression since changes in house price dynamics should be gradual within the study period. The knots used in constructing splines are based on a date (month) of the introduction of the LLUAs in the Poznan-Lawica and Katowice-Pyrzowice airports relative to the beginning of the study period (January 2008 in case of Poznan and January 2007 in case of Katowice). For Katowice-Pyrzowice airport we applied the following hedonic model with linear splines:
In a regression equation, lnP is a dependent variable (natural logarithm of sale price), and Xi is the vector of control variables (salient real estate attributes that affect its price). TG (Treatment Group) is a dummy variable equal to 1 if a property is located within an LLUA and 0 otherwise. The month is a time variable related to the month the particular transaction took place (number of months since the beginning of the study). Spline is a time variable equal to 0 if the month is less than 93, and equal to month – 92 otherwise. Coefficient β captures the impact of selected property characteristics on property prices, while indicate the house price dynamics. Coefficient captures the price difference between the Treatment and Control groups at the beginning of the study period. The coefficients and of spline adjustment variables indicate the change in house price dynamics both in Control and Treatment group respectively, after LLUA introduction in September 2014.
The situation in Poznan was more complicated because two zones within the LLUA were formed. The inner zone was created based on the noise level equal to L
AeqD = 60 and L
AeqN = 50 dB, while the outer zone was based on the L
AeqD = 55 and L
AeqN = 45 dB noise levels. Due to multiple zones within the LLUA in Poznan, we modified our approach to reflect the possibility that house prices were not uniformly affected by different restrictions imposed in particular zones. To account for that we regressed natural logarithm sales price (P) on property characteristics X using the modified hedonic equation, with linear splines:
Compared to the previous case, TGinner and TGouter are the Treatment Group dummy variables equal to 1 if a property is located within particular LLUA zones (inner and outer). Spline is a time variable equal to 0 if month is less than 50, and equal to month – 49 otherwise. Coefficients indicate the difference between sale price of properties located in particular area in relation to control area outside the influence of the airport. Coefficients and capture the difference in price dynamics in both zones prior to the formal introduction of LLUA in February 2012 relative to the control area, and coefficients ω1 and ω2 capture the impact of the introduction of an LLUA on property price dynamics, separately for the inner and the outer LLUA zone.
As a robustness check, we applied the difference-in-differences approach. As noted before, LLUAs are not assigned randomly, which may result in the endogeneity problem when building a hedonic price model. As noted by Gibbons and Machin [
58] the traditional hedonic approach based on cross-sectional data does not account for the potential endogeneity problem, in our case mostly caused by unobserved noise level differences and other airport operation related risk. To address the problem of endogeneity, and to assess the causal effect of the introduction of an LLUA on house prices we use the difference-in-differences (DiD) approach. The method is based on a comparison of a before-after estimate of house prices in an LLUA (Treated Group, TG) to a comparable properties sales prices outside of this area (Control Group, CG).
Following the general guidelines of the difference-in-differences method based on individual data, for Katowice-Pyrzowice airport we applied the model:
In the regression equation Xi is the vector of control variables (salient real estate attributes), TG (Treatment Group) is a dummy variable equal to 1 if a property is located within an LLUA and 0 otherwise. Post is a dummy variable equal to 1 when the sale occurred after the introduction of an LLUA. Coefficient β captures the impact of selected property characteristics on property prices. Coefficient captures price difference between the Treatment and Control groups before the introduction of LLUAs around the airport. The latter can be interpreted as a difference caused by the externalities generated by the airport’s operation, mainly aircraft noise because the LLUA was defined based on future aircraft noise level (LAeqN = 50 dB in 2020, which closely corresponds to current noise levels during night). Coefficient τ depicts market related price changes in a control group. The role of θ is to capture the pure impact of the introduction of an LLUA on property prices.
As noted before, the situation in Poznan was more complicated, thus in the case of the Poznan-Lawica airport we regressed natural logarithm of the sale price (P) on property characteristics using the modified DiD estimator:
In this modified approach TGinner and TGouter are Treatment Group dummy variables equal to 1 if a property is located within particular LLUA zones (inner and outer). Other abbreviations as in previous equation. Coefficients γ1 and γ2 capture the noise effect, and coefficients θ1 and θ2 capture the impact of the introduction of an LLUA on property prices, separately for the inner and the outer LLUA zone.
In this paper we estimated three types of hedonic models (OLS, SAR, and SEM) using both the spline and DiD approach. After repeating the procedure for the two airports we finally obtained 12 models (three specifications, two approaches, and two airports). As discussed previously, as a robustness check the estimates obtained from DiD regression were compared to the baseline spline regression approach. We also compared the differences in the results between both airports.