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

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.     

A new bounded log-linear regression model

In this paper we introduce a new regression model in which the response variable is bounded by two unknown parameters. A special case is a bounded alternative to the four parameter logistic model. The four parameter model which has unbounded responses is widely used, for instance, in bioassays, nutrition, genetics, calibration and agriculture. In reality, the responses are often bounded although the bounds may be unknown, and in that situation, our model reflects the data-generating mechanism better. Complications arise for the new model, however, because the likelihood function is unbounded, and the global maximizers are not consistent estimators of unknown parameters. Although the two sample extremes, the smallest and the largest observations, are consistent estimators for the two unknown boundaries, they have a slow convergence rate and are asymptotically biased. Improved estimators are developed by correcting for the asymptotic biases of the two sample extremes in the one sample case; but even these consistent estimators do not obtain the optimal convergence rate. To obtain efficient estimation, we suggest using the local maximizers of the likelihood function, i.e., the solution to the likelihood equations. We prove that, with probability approaching one as the sample size goes to infinity, there exists a solution to the likelihood equation that is consistent at the rate of the square root of the sample size and it is asymptotically normally distributed.