Are Central Bankers Inflation Nutters? An MCMC Estimator of the Long-Memory Parameter in a State Space Model

Inflation targeting is a common monetary policy regime. Inflation targets are often flexible in the sense that the central bank allows inflation to temporarily deviate from the target to avoid causing unnecessary volatility in the real economy. In this paper, we propose modeling the degree of flexibility using an autoregressive fractionally integrated moving average (ARFIMA) model. Assuming that the central bank controls the long-run inflation rate, the fractional integration order becomes a measure of how flexible the inflation target is. A higher integration order implies that inflation deviates from the target for longer periods of time and consequently, that the target is flexible. Several estimators of the fractional integration order have been proposed in the literature. Grassi and Magistris (2014) show that a state-based maximum likelihood estimator is superior to other estimators, but our simulations show that their finding is over-biased for a nearly non-stationary time series. To resolve this issue, we first proposed a Bayesian Monte Carlo Markov Chain (MCMC) estimator for fractional integration parameters. This estimator resolves the problem of over-bias. We estimate the fractional integration order for 6 countries for the period 1993M1 to 2017M9. We found that inflation was integrated to an order of 0.8 to 0.9 indicating that the inflation targets are implemented with a high degree of flexibility.