“…where π is the steady state inflation, and ϵ π t ∼ N (0, σ 2 π ) is an independently and identically distributed shock to inflation target (Ireland, 2007;Cogley et al, 2010;Justiniano et al, 2013). It has been documented in the literature that inflation contains very low frequency variation (Coibion and Gorodnichenko, 2011), which also has important implications for asset pricing dynamics (Cieslak and Povala, 2015;Davis et al, 2019;Bauer and Rudebusch, 2020). Equation ( 41) is one way to incorporate low frequency variation in inflation by incorporating stochastic target inflation.…”