Do the US and Canada have a common nonlinear cycle in unemployment?

To enable answering the question in the title, we introduce a bivariate censored latent effects autoregression, and discuss representation, parameter estimation, diagnostics and inference. We show that this bivariate nonlinear model is very useful for examining common nonlinearity. We apply the model to the monthly unemployment rate in the US and Canada to examine if these variables have common cyclical properties conditional on lagged explanatory variables such as industrial production, the oil price and interest spread. We find that US variables have explanatory value for Canadian unemployment, but that Canadian variables do not predict cyclical patterns in the US. Also, we find that recessionary shocks in Canada are more persistent than similar sized shocks in the US in the same period. Finally, we obtain some evidence for a common nonlinear business cycle.