This paper estimates Taylor rules featuring instabilities in policy parameters and switches in policy shocks’ volatility for the post-World War II (WWII) U.S. economy. We contrast a rule embedding a fixed-inflation target with another featuring trend inflation, i.e., a time-varying inflation target. The rule embedding trend inflation turns out to be (a) empirically superior according to a marginal likelihood-based comparison and (b) more able to pin down some relevant episodes of the post-WWII U.S. monetary policy history. Estimates conducted with Greenbook data confirm the empirical superiority of the rule featuring a time-varying inflation target. A comparison with recently published estimates of trend inflation is also conducted.

In Francq and Zakoïan [4], we derived stationarity conditions forARMA(p,q) models subject to Markov switching. In this paper, weshow that, under appropriate moment conditions, the powers of thestationary solutions admit weak ARMA representations, which we areable to characterize in terms of p,q, the coefficients of themodel in each regime, and the transition probabilities of theMarkov chain. These representations are potentially useful forstatistical applications.