Can Univariate Time Series Models of Inflation Help Discriminate Between Alternative Sources of Inflation Persistence

When it comes to measuring inflation persistence, a common practice in empirical research is to estimate univariate autoregressive moving average (ARMA) time series models and measure persistence as the sum of the estimated AR coefficients. We examine four potential sources of lag dynamics in inflation: the evolution of policymakers? willingness to stabilize output, shifts in the mean inflation rate, imperfect credibility and learning and unemployment persistence. We show that the reduced-form solution for inflation in all these models have an ARMA(p,q) representation. By implication estimating a reduced-form for inflation will not be able to distinguish among these alternative hypotheses. We illustrate this using US and UK data.