A Multi-Level Panel Smooth Transition Autoregression for US Sectoral Production

Macroeconomic time series are often obtained as an aggregate across regions or economic sectors. Even when the ultimate goal is to forecast the aggregate series it may be beneficial to consider the underlying disaggregate series. This especially holds when the disaggregate series are generated by a non-linear process. The aggregate of such series follows a very complicated process. Aggregating a number of relatively simple models for individual regions or sectors to a model of the macro series may lead to a more accurate description than when a model for the aggregate is considered. We introduce a multi-level smooth transition model for a panel of time series variables, which can be used to examine the presence of common non-linear features across many such variables. The model is positioned in between a fully pooled model, which imposes such common features, and a fully heterogeneous model, which might render estimation problems for some of the panel members. To keep the model tractable, we introduce a second-stage model, which links the parameters in the transition functions with observable explanatory variables. We discuss representation, estimation by concentrated simulated maximum likelihood and inference. We illustrate our model for data on industrial production of 18 US manufacturing sectors, and document that there are subtle differences across sectors in leads and lags for business cycle recessions and expansions.