This paper studies whether the relationship between monetary policy shocks of different size and output is better described by threshold autoregressive (TAR) or smooth transition autoregressive (STAR) dynamics. Using a Bayesian framework, a TAR process and a STAR process are formally compared within an unobserved components model of output, augmented with a monetary policy variable. The Bayesian model comparison favors the notion that the dynamics are nonlinear and better described by a smooth transition between regimes, which suggests that aggregation plays a role in the dynamics between monetary policy and output. This evidence is further supported by the results of a model that uses output data at the sectoral level: when more disaggregated data are employed, the transition between regimes is more abrupt. Moreover, the results show that, when the transition between regimes is smooth, large monetary policy shocks identified as the residuals of a VAR are neutral, consistent with the implications of menu-costs models.
This paper uses Monte Carlo simulations to investigate the effects of outlier observations on the properties of linearity tests against threshold autoregressive (TAR) processes. By considering different specifications and levels of persistence for the data-generating processes, we find that additive outliers distort the size of the test and that the distortion increases with the level of persistence. In addition, we also find that larger additive outliers can help to improve the power of the test in the case of persistent TAR processes.
Within the context of threshold regressions, we show that asymptotically-valid likelihood-ratio-based confidence intervals for threshold parameters perform poorly in finite samples when the threshold effect is large. A large threshold effect leads to a poor approximation of the profile likelihood in finite samples such that the conventional approach to constructing confidence intervals excludes the true threshold parameter value too often, resulting in low coverage rates. We propose a conservative modification to the standard likelihood-ratio-based confidence interval that has coverage rates at least as high as the nominal level, while still being informative in the sense of including relatively few observations of the threshold variable. An application to thresholds for US industrial production growth at a disaggregated level shows the empirical relevance of applying the proposed approach.