A Stochastic Model with Penalized Coefficients for Spatial Price Comparisons: An Application to Regional Price Indexes in Italy

This paper focuses on a new strand of research that uses stochastic approach for making spatial price comparisons. We propose a novel method to account for the presence of spatial dependencies in consumer prices and consequently in price indexes by imposing penalization conditions on the estimation of traditional CPD models leading to the spatially-penalized country-product-dummy (SP-CPD) model. The paper proposes an appropriate estimation strategy, which enables us to simultaneously estimate all the parameters in the model, including the smoothing parameter of the penalization term instead of determining it externally. In order to estimate spatial price indexes for areas lacking in price data, we suggest applying the kriging methodology to the price indexes obtained from the SP-CPD model. This new approach is applied to official Italian CPI data for constructing regional spatial price indexes for 2014. The results show that price levels are higher in the Northern-Central regions than in the South.