Markets: A Rigorous Course
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M11 · Problem 9 ★★★

Taylor principle with lagged inflation

Suppose expectations are adaptive, πte=πt−1\pi^e_t=\pi_{t-1}, and the economy is

πt=πt−1+κxt,xt=−σ(it−πt−1−r∗),\pi_t=\pi_{t-1}+\kappa x_t,\qquad x_t=-\sigma(i_t-\pi_{t-1}-r^*),

with policy it=r∗+πt−1+a(πt−1−π∗)i_t = r^*+\pi_{t-1}+a(\pi_{t-1}-\pi^*). (a) Derive the law of motion for π^t=πt−π∗\hat\pi_t=\pi_t-\pi^*. (b) Find the set of aa for which inflation converges, and the subset for which convergence is monotone. (c) Interpret the upper bound. What does it say about a central bank that reacts too aggressively to lagged data?

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