Heterogeneous Impact of Soil Contamination on Farmland Prices in the Belgian Campine Region: Evidence from Unconditional Quantile Regressions

Abstract

We estimate a hedonic-pricing model using geo-coded farmland-transaction data from the Campine region, situated in the north-east of Belgium. Unlike previous hedonic studies, we use the method of unconditional quantile regression (Firpo et al., in Econometrica 77(3):953–973, 2009). An important advantage of this new method over the traditional conditional quantile regression (Koenker and Bassett, in Econometrica 46(1):33–50, 1978) is that it allows for the estimation of potentially heterogeneous effects of cadmium pollution along the entire (unconditional) distribution of farmland prices. Using a threshold specification of the hedonic-pricing model, we find evidence of a U-shaped valuation pattern, where cadmium pollution of the soil has a negative and significant impact on prices only in the middle range of the distribution, insofar as cadmium concentrations are above the regulatory standard of 2 parts per million for agricultural land. Results obtained from a probit model to classify land plots into different price segments further suggest that the heterogeneous impact of soil pollution on price can be directly related to the variety of amenities that farmland provides.

Appendices

Appendix 1: Differences Between CQR and UQR—Illustrative Simulation Example

This appendix presents a simple simulation example (borrowed with some modifications) from McMillen (2013) to illustrate the differences between traditional CQR and new UQR, and to point to potential problems that may arise when interpreting the estimates returned by CQR.

Consider a single explanatory variable, X, which is limited to take integer values from 1 to 10. Each integer value occurs 200 times in the simulated data set, leading to a total of 2000 observations. The regression equation is specified as ${Y}=10-{0.5X}+\varepsilon .$ To ensure an $R^{2}$ of approximately 0.8 for the OLS (mean) regression, we specify $\varepsilon \sim \hbox {N}\left[ {0,\sigma _\varepsilon \left( {X}\right) } \right] ,$ where $\upsigma _{\varepsilon }^{2}\left( {X}\right) = \frac{0.2\sigma _{X}^{2}}{{X}}.$ This variance function for $\varepsilon$ implies that the quantiles of the conditional distribution of Y given X converge; that is, the dispersion (variance) of the conditional distribution of Y decreases with higher values of X.

The results from OLS, CQR, and UQR are summarized in Table 6. Selected CQR regression lines, representing the 10th, 50th, and 90th percentiles of the conditional distribution of Y given X, are shown in Fig. 6. The OLS regression line represents the conditional mean of Y.

Table 6 Simulation results for OLS, CQR, and UQR—estimated coefficients on X

Fig. 6

Predicted CQR and OLS regression lines. The blue lines represent the 10th, 50th, and 90th percentile-regression lines returned by CQR, whose slopes are equal to $-0.390$, $-0.507$, and $-0.597$, respectively. The red line represents the mean-regression line obtained using OLS, which practically coincides with the 50th-percentile regression line. The variance of the conditional distribution of Y given X decreases from 1.8 for $X = 1$, to 0.2 for $X = 10$

The points a and b in Fig. 6 show why standard CQR results may be misinterpreted. Point a is associated with a high value of X on the 90th-percentile regression line, whereas point b represents a low value of X on the 10th-percentile regression line. The value of the dependent variable Y at point a is lower than its value at point b, where the former is positioned at the bottom end of the unconditional distribution of Y. Therefore, it is not the case that an increase in X leads to a greater decline in Y whenever Y is unconditionally high. The steeper slope at the 90th percentile merely indicates that an increasing X leads to greater declines in Y along the 90th percentile of Y than at its 10th percentile, conditional on the values of X.

Another way to illustrate the differences between the estimated effects of X on Y using either CQR or UQR is to look at the quantile plots presented in Fig. 7. Specifically, they show the CQR and UQR estimates (along with their 95 % confidence bands) of the effects of X at nine different quantiles (from the 10th to 90th percentile). It can immediately be seen that the estimated effect obtained using UQR is highly non-monotonic, exhibiting a pronounced U-shaped pattern, whereas the effect obtained using standard CQR declines monotonically. It is interesting to see that the pattern displayed by the quantile coefficients obtained using UQR is close to a “mirror image” of the inverse U-shaped pattern shown in FFL (2009, their Fig. 1, p. 965).

Fig. 7

Quantile plots for OLS, CQR, and UQR. The vertical axis measures the mean and quantile effects at different quantiles; i.e., the estimated coefficients on X at different quantiles of the conditional and unconditional distributions of Y for CQR and UQR, respectively. The shaded areas represent the 95 % confidence intervals for the CQR estimates (light grey) and UQR estimates (dark grey)

The quantile coefficients obtained using CQR are the estimated slopes of the regression lines in Fig. 6, which show how the quantiles of the conditional distribution of Y given X are affected by a 1-unit change in X. Thus, CQR and UQR estimate two different things, where CQR focuses on the unobserved heterogeneity of Y reflected by the distribution of Y for a given value of X, $\hbox {F(Y|X)}=\hbox {F}\left( \varepsilon \right)$, while UQR centers on the observed distribution of Y for the entire population, $\hbox {F}\left( {Y}\right)$. Yet it is curious to see that in many empirical applications of CQR, results are often erroneously interpreted as if they were UQR results.

Appendix 2: Within- and Between-Municipality Covariances among Farmland Prices

This appendix provides simple descriptive measures of the covariance (or correlation) patterns among observed prices as a function of the distances between the farmland plots.

Following Barrios et al. (2012), we calculated the within- and between-municipality covariances for pairs of prices of farmland plots whose (straight-line) distance in km is within some bandwidth h of a given distance d; that is,

$$\begin{aligned} \widehat{C_{W}\left( d\right) } =\frac{\sum \nolimits _{i<j} \mathbf{1}_{m_{i}=m_{j}} \cdot \mathbf{1}_{\left| {d_{ij} -d} \right| \le h} \cdot \tilde{p}_{i}\cdot \tilde{p}_{j}}{\mathop \sum \nolimits _{i<j} \mathbf{1}_{m_{i}=m_{j}} \cdot \mathbf{1}_{\left| {d_{ij} -d} \right| \le h}} \end{aligned}$$

(11)

and

$$\begin{aligned} \widehat{C_{B}\left( d\right) } =\frac{\sum \nolimits _{i<j} \mathbf{1}_{m_{i}\ne m_{j}} \cdot \mathbf{1}_{\left| {d_{ij} -d} \right| \le h} \cdot \tilde{p}_{i}\cdot \tilde{p}_{j}}{\sum \nolimits _{i<j} \mathbf{1}_{m_{i}\ne m_{j}} \cdot \mathbf{1}_{\left| {d_{ij} -d} \right| \le h}} \end{aligned}$$

(12)

where $\tilde{p}_{i}$, $\tilde{p}_{j}$ are the “demeaned” sales prices (measured as deviations from the overall sample mean). The symbols $m_{i}$ and $m_{j}$ denote the municipalities in which the plots i and j are located. Specifically, $m_{i}=m_{j}$ $(m_{i}\ne m_{j})$ means that farmland plots i and j are (not) located in the same municipality. Note that all farmland plots have been ordered, and the condition $i<j$ just takes account of the symmetry of the variance-covariance matrix.

The panels in Fig. 8 show the covariance functions for bandwidth h going from 1 to 4 or the within- and between-municipality covariances. For example, with bandwidth $h=1$, we look at the prices of all plots j located at a distance between 0 and 2 km from plot i for $d=1$, between 1 and 3 km for $d=2$, between 2 and 4 km for $d=3$, and so on.

Fig. 8

Within- and between-municipality price covariances

The main conclusions from the graphs presented in Fig. 8 are that the covariances decrease with distance, and that the between-municipality covariances are of a magnitude much smaller than the within-municipality covariances. Therefore, the results provide some empirical support for (i) the importance of using simple inverse distances, and (ii) the land-market segmentation along municipal boundaries. In a certain way, the latter can be interpreted as a manifestation of “home biases” along municipal boundaries, due to higher transaction or information-search costs associated with the prices prevailing “on the other side of the fence”. Admittedly, this is just our conjecture, which has not been further tested here. Based on the findings from the covariance analysis, our empirical application in the main text uses only the within-municipality prices of farmland in constructing the spatiotemporal lag of the dependent price variable.