Background

It is increasingly common to find econometric studies using the hedonistic price method for the study of environmental problems, and in our case, for noise pollution in the real-estate market (^{Nelson 2004}, ^{Jasper and Straaten 2009}).

^{Marmolejo and Romano (2009)} took a step forward to explain that behind the willingness to pay, in the case of the Prat airport’s residential environment (Barcelona), there underlie different characteristic elements of real estate prices (proximity, type of housing, rent, etc.) through the aforementioned hedonic price method.

Adjusting hedonic price models to the case of housing has been a common exercise but has not been free from difficulties either due to data restriction or because of market heterogeneity. In the literature it is common to find cross-sectional studies in various markets (^{Schnare and Struyk 1976}, ^{Goodman 1988} or ^{Hanley and Spash 1993}). In the case of Spain, ^{Bilbao (2000)} or ^{Bover and Velilla (2001)}, represent interesting examples.

Data collection

One feature of this analysis is that all impacts are measured in monetary units finally updated to 2012. That is, the prices of the houses studied correspond to the sale prices of that year (including taxes), using the methodology of cross-sectional data collection.

This study has been based on the strategic noise map drawn up in 2005 with data provided by the Gando Air Base itself and prepared by the National Institute of Aerospace Techniques Esteban Terradas (INTA).

The mapping used was obtained from the Air Force Centre for Mapping and Photogrammetry (CECAF). Additionally, we used the Electronic Office of the Directorate General of Land Registry to verify the different surface areas constructed and conservation status of affected households in the study area.

With respect to economic data regarding the market price of homes in the sample, information from various real estate websites (segundaman.com, fotocasa.es, elidealista.es and the Professional Association of Valuation Companies) and evaluations were obtained.

Furthermore, we used data gathered from the Noise Map Report for Major Spanish Airports for the civilian airport of Gran Canaria, which shares runways with military facilities (^{MINISFOM and AENA 2007}).

The results of several relevant studies were used in assessing noise to calculate depreciation in the real estate market in the area (^{Commission on the Third London Airport and Roskill 1971}, ^{Rosen 1974}), as well as a contrast study of the US Orange County Health Department regarding the reactions of the population to noise depending on perceived decibels (^{Randall 2001}).

In these studies a series of datatables, transposed to Gran Canaria Airport data were used, and therefore the Gando Air Base by the similarities of both airports. Finally, for the econometric evidence of the different models of hedonic functions, the GRELT (Gnu Regressión, Econometric and Time Series) computer free program was used.

The sources considered in the face of computer modeling, pertain only to landing and takeoff operations of the Fockker 27 and the EF-18 Hornet with origin or destination in Gando Air Base because these two types of aircraft operate on the Air Base permanently and are the most responsible for acoustic pollution.

The INM (Integrated Noise Model) was used to calculate noise levels (^{FAA 1999}). Previous considerations:

Based on the input data and the methodology described, the noise levels in the Air Base environment have been calculated for the two selected indices (L_night and L_den). The results of sound impact, and in the absence of legislation that establishes the admissible limits of sound emmission, are shown by means of noise maps that represent noise levels caused by isophones of a sound level from 60 decibels (A) for L _den, and from 50 decibels (A) for L_night (Table I, Fig. 2 and Fig. 3).

Fig. 2 L den affected area, distribution of isophones by colors 

Fig. 3 L night affected area, distributed by isophones in colors 

The following tables II and III, summarize the data obtained in relation to the sample studied.

Econometric estimation of the hedonic pricing function

Geographical limitation

For obtaining the simple random sample that we used on a study population of 6447 homes, we have made a division of two phases: assigning a number to each home and through random numbers generated by a computer, we chose as many subjects as necessary to complete the sample size³. Applying the selected data our sample size was 175 homes.

Model approach

Our econometric model has five initial environmental variables (Cocu1,…,5) depending on decibels perceived by each home. Economic theory does not clearly specify what is the best functional method (^{Freeman et al. 2014}).

Furthermore, the selection of regressors takes evidence from multiple alternatives and comparisons. We should not forget that, if the chosen subject deals with a specific economic theory, it could help us to specify the model. Economic literature has established criteria for chooosing models.

The most commonly used criteria and implemented in this study are: maximization criterion adjusted determination coefficient (R²); Schwarz, Akaike and Hannan-Quinn Information Criteria; along with Ramsey Reset test to validate the functional form of the models shortlisted.

One of the simplest and most popular procedures, implemented in this study, is the stepwise backward regression consisting of a step-by-step selection of variables in the regression, based on a battery of sequential contrasts to decide procedure on regressors, one by one through a backward elimination of explanatory variables or regression, depending on the level of significance set to determine the region of acceptance or rejection of the null hypothesis.

This procedure excluded, one by one, on the basis of variables in the statistical model values of t-student. Finaly, we established five initial models proposed as a starting point the study. From these, different regression models and tests of global significance and information criteria were made (Table V).

After analyzing the previous five models, we decided to choose model 5 as the most complete and the best fit, with the largest number of significant regressors (14) and which showed the best goodness of fit with correct flexible and functional form. Our model presents an endogenous variable logarithm, (20) constant linear variables including, (6) regressors in logarithms, (6) quadratically.

The model is overall significant because the result of the value p (f-statistic) is 9.52 e-73, well below 5 % so the null hypothesis is a generally accepted significant model. Regarding the coefficient of determination, it shows a very acceptable level and higher than previous models, that is, the value shows that exogenous variables explain 94.75 % of the dispersion of the endogenous variable so, initially, the goodness of fit is optimal.

The corrected determination coefficient with 93.42 % has the same interpretation. Finally, the Reset Ramsey test reports that the functional form is correct, the null hypothesis is always true considering a significance level of 5 %. The results of the values of endogenous squared and cubed are 0.156 and 0.146, respectively.

Model estimation and validation

Outliers

To detect the existence of outliers or influential observations in the model, we must make the contrast of standardized residuals (Fig. 4). Then, we can compare them with the critical reference interval of a distribution N (0,1), considered in this case in an interval (2,-2).

Fig. 4 Residuals model estimated for the sale price of the homes of the sample in logarithm.175 Observations 

Depending on the interval chosen, there is no significant presence of outliers. There are a number of points of leverage, observations 4, 19, 36, 45, 46, 47, 78, 102, 105, 108, 109 and 123. These atypical individuals whose errors are abnormally high may have a potential or actual influence to substantially modify the regression plane, that is, the estimated model parameters. To check this, observations 4, 102, 105 and 123, would have a potential risk but not a certain influence.

Normality of disturbances

Specifically, we will analyze the graph of the frequency distribution (histogram) of the values of residuals (Fig. 5). At this point we compare the shape of this distribution that theoretically has the normal distribution, which would be unimodal, symmetrical and certainly flared.

Fig. 5 Statistical contrast to normal.Residual plot. 

To study the normality of the residuals of the estimated model, at first, we might consider the normal statistic that GRELT gives us by default, and this is the approach proposed by ^{Doornik-Hansen (2008)}, contrast with a Chi-square with 2 degrees of freedom. We note a probability of 0.1194 for a Chi-square with 2 degrees of freedom (5.99) of 4.251, being in the region of acceptance, so we accept the null hypothesis, that is to say, disturbances are distributed normally.

Another interesting statistic is the statistic normality ^{Jarque Bera (1980)}, based on the coefficients of skewness and kurtosis of the residuals of the regression, where the asymmetry coefficient (- 0.358) and kurtosis (0.424) approach 0 and 3 respectively, the probability of normality of the residuals by the result of lower index value Jarque Bera increases. With a value of 5.056 for a Chi-square with 2 degrees of freedom (5.99) and a probability p of 0.080, we would accept the null hypothesis of normality of residuals, reinforcing the idea that there is statistically significant evidence to reject the normality of residuals.

Heteroscedasticity and autocorrelation

First we graphically analyze of residuals (Fig. 6), representing absolute errors in the ordinate axis on endogenous on the abscissa and on the other hand, the squared errors in the ordinate axis on the explanatory nondichotomous variables of our model (Scon, logSsue, sqAntg and sqDist) on the horizontal axis.

Fig. 6 Absolute values of errors versus endogenous adjusted 

In figure 6 we can see a linear fit between residuals and endogenous variable as we increase the price of housing. In addition, a number of outliers can be seen in the graph because they are far from the average values. Using the graph to check squared residuals against each of the exogenous values, none of the graphs show a clear relationship between the exogenous variables and squared residuals and between the endogenous variable and residues in absolute values.

But we can not rely only on a graphical analysis to find out whether the model is not homoscedastic. We have to carry out several analytical tests. Breusch-Pagan test (^{Greene 1998}) uses the residuals obtained from the original regression, squaring and presents against independent variables. It is distributed as a Chi-square with p-1 degrees of freedom where p is the number of regressors in the auxiliary regression, which in our case is 13 without the constant. Its statistic would be the sum of the squared residuals, 31.343, between two, resulting in 15.671, with a p value of 0.267. The test statistic yields a value lower than the Chi-squared value with 13 degrees of freedom, which is 22.4. Thus we would accept the null hypothesis so that the result tells us that our model is homoscedastic.

RESULTS AND CONCLUSIONS

The estimated parameters of the hedonic price model are important to inform policy makers. Based on statistical tests shown above, it may be concluded that the hedonic price model proposed reasonably explains the behavior of the endogenous variable and therefore may be used to make predictions regarding the performance of this variable.

In estimating the model, the parameter values represent an indicator of significant importance in explaining the issue under study because on this basis, the form and degree of influence of each explanatory variable is determined.

According to the results of the estimates and considering the rest of the coefficients of the variables under ceteris paribus study, we will highlight the environmental variables, where the coefficient β ₁₇₀₂ indicates that for households that are affected by noise pollution from 55-60 decibels, their value is 16.11 % higher than other homes suffering other levels of noise pollution.

The β ₁₇₀₃ tells us that for households affected by noise pollution from between 60 to 65 decibels, their value is 36.65 % higher than other homes suffering other levels of noise pollution. And lastly, the coefficient β ₁₇₀₄ tells us that for households affected by noise pollution from 65-70 decibels, their value is 31.76 % higher than other homes suffering other levels of noise pollution.

The price of homes that are affected by a noise level between 55 and 60 decibels is 14.9 % more expensive than noise free and the highest noise level (more than 70 decibels). The price of homes that support a noise level between 60 and 65 decibels is 31.2 % higher than noise free and the highest noise level and 16.3 % higher than those seen affected by a noise level between 55 and 60 decibels.

The price of homes that withstand a noise level between 65 and 70 decibels is 27.9 % higher than noise free and the highest noise level, 13 % higher than those that are are affected by a noise level between 55 and 60 decibels and 3.3 % lower than those that support a noise level between 60 and 65 decibels.

A plausible explanation for these data is that if they suffer high decibel rates, the value of housing increases, because they are the most luxurious, nearest to the airport, in addition to large green areas and good communication, access and security of public transport.

Another way of applying the model is to obtain how much you can vary the endogenous variable if, for example, we had a house of 100 m² built; 150 m²; 10 years old; with a garage; 2 rooms/bedrooms; located in the municipality of Ingenio; a middling state of preservation; at 1250 m from the airport and undergoing 65 to 70 decibels, leaving the rest of exogenous variables ceteris paribus.

The result would be a value equal to 11.614 logPvc_i (the sale price of homes in logarithms), that is, the sale price of homes in this case, is 110 697.05 euros.

We should mention that proper adjustment was achieved between prices and attributes of the dwellings. We obtained the really explanatory variables of price differences between properties and, their implicit marginal prices.

The choice of the appropriate functional form in our hedonic regression estimate was reduced to an empirical question, as there were no contributions in previous studies that demonstrate categorically that a particular functional form is the most suitable. Therefore, we must choose the one that best fits the data of the sample and the selected regressors.

In our case, the methodology of multiple regression by ordinary least squares concludes that the best approach is the semilog hedonic price model, using the price of as endogenous and in housing in logarithmic terms and as regressors: built surface; very poor state, poor or regular maintenance; the existence of a garage; number of rooms/bedrooms; noise pollution from 55 to 60, 60 to 65 and 65 to 70 decibels; logarithm of land surface; age squared; and distance to noise focus squared.

This result leads us to think that the studio isolated variable noise pollution, as the only relevant factor for our endogenous conclusions, is not conclusive and we need to add other explanatory variables that have a significant influence.

The fact that a property is near a noise source is not in itself conclusive evidence of a loss of real estate value. Therefore, the analyst must find and use valid methods to accurately measure the loss of the property at market value.

Consequently, airport noise pollution generated by Gando Air Base does not constitute a negative attribute for homes in the area, except in the case of noise levels above 70 decibels.

The prices of housing in the area have not been affected by this problem or by the distance to the noise source, which may explain why no housing or environmental policy measures have been taken either by the affected municipalities or by the Cabildo Insular de Gran Canaria or by the Government of the Canary Islands due to the noise of military aircraft.

If this can become a problem in the future, it will be a question of research that can be carried out with more recent data on prices and housing characteristics. Of course, our model is not able to answer if noise pollution is a factor influencing other dimensions of human welfare, wich could recommend the introduction of policies. This is, of course, out of the scope of our research.