Exact tests of the stability of the Phillips curve: the Canadian case

Structural breaks are tested for the parameters of the Canadian Phillips curve equation accounting for the possibilities that: (1) breaks can be discrete, or continuous, and (2) available data samples may be too small to justify using asymptotically valid structural change tests. Recent test procedures that are valid in finite samples are used. Specifically: (i) a predictive test for discrete breaks is applied; (ii) an LR test statistic for continuous-type breaks is considered, and, to obtain its exact p-value, a Maximized Monte Carlo test method is applied. The latter, which is a simulation-based technique, accounts for all nuisance parameters, including those that are identified only under the alternative hypothesis. This proposed alternative is a Kalman-filter-based time-varying-parameter (TVP) specification with coefficients that follow random walks. While evidence is found for both linear and non-linear breaks (the latter being characterized by continuous and unpredictable-type shifts in the inflation lag coefficients and in the constant), out-of-sample forecasts obtained from models having each type of break suggest that the TVP specification is preferred.