A Time-Varying Threshold Star Model of Unemployment and the Natural Rate

Smooth-transition autoregressive (STAR) models have proven to be worthy competitors of Markov-switching models of regime shifts, but the assumption of a time-invariant threshold level does not seem realistic and it holds back this class of models from reaching their potential usefulness. Indeed, an estimate of a time-varying threshold level of unemployment, for example, might serve as a meaningful estimate of the natural rate of unemployment. More precisely, within a STAR framework, one might call the time-varying threshold the "tipping level" rate of unemployment, at which the mean and dynamics of the unemployment rate shift. In addition, once the threshold level is allowed to be time-varying, one can add an error correction term--between the lagged level of unemployment and the lagged threshold level--to the autoregressive terms in the STAR model. In this way, the time-varying latent threshold level serves dual roles: as a demarcation between regimes and as part of an error-correction term