Stepping on a Rake: Replication and Diagnosis

Pegging the Interest Rate on Bank Reserves

“…To derive the key equation summarizing global equilibrium dynamics, we first use (8), ( 10), (14), (16) holding with equality, and (19), to express loans t as a function of employment h t :…”

“…When prices are set one period in advance, firm i chooses its price P t (i) at date t−1 to maximize E t−1 P t (i)y t (i) − βλ t+1 I t L t (i) λ t Π t+1 subject to the production function (14), the demand schedule (15), and the borrowing constraint (16). The first-order condition of this optimization problem implies…”

“…Since our central bank pegs its policy instruments, it does not react to deviations from equilibrium; we do not need, therefore, to worry about the feasibility of its off-equilibrium reaction (Bassetto, 2005;Loisel, 2016). 14 Because it delivers determinacy under a permanent (IOR-rate) peg, our model solves the two puzzles and the paradox: the effects of a temporary (IOR-rate) peg do not grow explosively as its duration becomes infinite or as prices become perfectly flexible, but instead converge towards the finite effects of a permanent peg or the finite flexible-price effects; and fiscal interventions in the vanishingly distant future have vanishingly small effects, instead of unboundedly large effects, on current outcomes.…”