Topic: Contributions in panel data econometrics Title: An oblique projection approach to consumer price level prediction Authors:  Christian Heinze - University Bielefeld (Germany) [presenting]
Abstract: Consumer price index data suitable for spatial comparison at a high resolution is scarce in many countries but of great interest to regional economists. We focus on German countries and present predictions of suitable consumer price indexes for the years 1993-2012. For this case, the available price index data comprise a small cross-section for 1993 and annual inflation rates for a subset of the German states. In a first step, we construct an auxiliary panel of pseudo price indexes in form of predictions from a low-complexity regression model. Therein, parameter estimates are based on the above mentioned data and corresponding covariate observations. Secondly, the pseudo index panel is used to estimate a VAR transition matrix - using nuclear norm regularization to enforce a low rank - alongside an innovation covariance matrix. Finally, the implied spatio-temporal covariance structure allows Kridge-type prediction - implemented as Kalman filtering - of the missing price indexes based on the available price indexes. This approach amounts to replacing the covariances of an (almost) unobserved process by those of a related and observed (pseudo-)process. This has an interpretation as an oblique projection. Therefore, the angles between certain subspaces characterize its inferiority to the corresponding orthogonal projection. We also present an expression in terms of the two processes.