Neural networks and non-linear statistical methods: an application to the modelling of pricequality relationships
This paper examines the potential of a neural network (NN) approach to the analysis of hedonic regressions, in which price is dependent on quality characteristics. The aim of the regressions is to measure, using objective data, the valuation consumers place on these characteristics. A neural network approach is employed because of potential non-linearities in the hedonic functions, using the property of universal approximation. Our NN implementation goes beyond the now-orthodox approach in using the Polytope algorithm, which we compare with Backpropagation, and uses two hidden layers. The results obtained provide an improvement on linear formulations, but the improvement in this case is relatively marginal. We view NN modelling as a useful means of specification testing and hence our results imply some support for a linear formulation as an adequate approximation. From a managerial perspective, the linear model is more easily interpreted. NN modelling is potentially very time-consuming, especially with the Polytope algorithm, and requires a good deal of technical skill. The application area studied in the paper involves hedonic regressions, which is the term usually employed for regressions of prices on the characteristics of goods. These employ objective data rather than subjective evaluations of intent and as well as having predictive capacity they serve to indicate the valuation placed on characteristics by consumers. In the extensive literature on the subject there is extensive debate on the appropriate functional form for the regressions. We have employed neural networks (NNs) in order to cast some light on the issue, because of their property of universal approximation which, although in danger of being taken too literally means a capacity to mimic a wide variety of shapes. We specifically employ an NN model as a test of linearity for hedonic functions, using the Polytope algorithm as an alternative to the standard Backpropagation method. Our results indicate that only a marginal improvement in goodness of fit is obtained, despite various theoretical arguments against a linear formulation. The linear model is given some support in our work as an adequate working approximation.
neural network hedonic regression universal approximation polytope algorithm backpropagation non-linear regression