DENNIS FOK, DICK VAN DIJK* AND PHILIP HANS FRANSES

SUMMARY
We introduce a multi-level smooth transition model for a panel of time series, which can be used to examine
the presence of common nonlinear business cycle features across many variables. The model is positioned
in between a fully pooled model, which imposes such common features, and a fully heterogeneous model,
which allows for unrestricted nonlinearity. We introduce a second-stage model linking the parameters that
determine the timing of the switches between business cycle regimes to observable explanatory variables,
thereby allowing for lead–lag relationships across panel members. We discuss representation, estimation by
concentrated simulated maximum likelihood and inference. We illustrate our model using quarterly industrial
production in 19 US manufacturing sectors, and document that there are subtle differences across sectors
in leads and lags for switches between business cycle recessions and expansions. Copyright  2005 John
Wiley & Sons, Ltd.