A new semiparametric spatial model for panel time series

Abstract

This paper presents a semiparametric model for large-dimension vector time series whose elements correspond to economic agents. Dependence between agents’ variables is characterized using a spatial model. Functions of agents’ economic distances provide restrictions that enable estimation of a vector autoregressive specification. We present sufficient conditions for our model to generate stationary, β-mixing series with finite higher-order moments. We estimate the model using a simple two-step sieve least-squares procedure, where the sieve estimators are constructed to preserve shape restrictions on the functions of economic distance, e.g., positive definiteness of a covariance function. We provide rates of convergence for the sieve estimators, T limiting distributions for the model's finite-dimensional parameters, and a bootstrap method for inference. In an illustrative application, we use this model to characterize how the comovement in output growth across US industrial sectors depends on the similarity of sectors’ technologies. We also present a small Monte Carlo evaluation of our estimators.