A1842
Title: Approximate Bayesian numerical method with product-Whittle-Matern-Yasuda kernel for Rosen's hedonic regression
Authors: Andrej Srakar - Institute for Economic Research Ljubljana (Slovenia) [presenting]
Abstract: Hedonic regression has featured an extensive amount of applications. It is estimated in a spatial equilibrium context in two stages which leads to a nonlinear partial differential equation framework. To date, its Bayesian extensions, while present, have still not adequately addressed features of its original proposal, which extends to many possible regression specifications. We develop an approximate Bayesian probabilistic numerical method with product-Whittle-Matern-Yasuda kernel, which extends existing literature in several aspects and is able to address different features of the original proposal: it is developed for nonlinear partial differential equations, is based on spatial kernels and a Gaussian process regression framework, and is applicable to any hedonic regression model specification. We develop a quasi-MC sampling algorithm and Bernstein-von Mises type asymptotic theorems to study the performance of the approach. Using Bayesian model comparison approaches, we compare its performance to several other parametric and nonparametric Bayesian priors (Zellner, Wasserstein, Dirichlet process and Dirichlet process mixtures, Bayesian additive regression trees, Bayesian causal forests) and apply it to simulated and real data examples from the areas of real estate and retail.