Abstract
We build a nonlinear dynamic model with currency, demand deposits and bank reserves. Monetary base is controlled by central bank, while money supply is determined by the interactions between central bank, commercial banks and public. In economic crises when banks cut loans, monetary policy following a Taylor rule is not efficient. Negative interest on reserves or forward guidance is effective, but deflation is still likely to be persistent. If central bank simultaneously targets both interest rate and money supply by a Taylor rule and a Friedman's k-percent rule, inflation and output are stabilized. An interest rate rule policy is just a subset of a more general monetary policy framework in which central bank can move interest rate and money supply in every direction.
Highlights
In the Great Recession and the recent COVID-19 crisis, the federal funds rate and the ECB policy rate have been near zero or even negative for a long time
The last two tools can directly change money supply; they cannot be a daily tool like an interest rate targeting policy in the standard monetary policy framework
This paper shows that central bank can add a Friedman’s k-percent rule into the current standard framework to hit the inflation target in economic crises
Summary
In the Great Recession and the recent COVID-19 crisis, the federal funds rate and the ECB policy rate have been near zero or even negative for a long time. ZMDs have the same unit of account as currency When holding these deposits, households earn a gross nominal interest rate Rmt which is determined by the perfectly competitive banking market. The banker can adjust the level of his deposits and reserves after households and firms pay each other or when households withdraw currency from bank account. We will relax the assumption and examine the situation when the banking system is awash of excess reserves and central bank controls the interbank rate by adjusting Rnt. Definition: A perfect foresight equilibrium is a sequence of bankers’ decision choice {ct, ci,t, nt, bht , st, mt, bft , dt}, household’s choice f~ct; ~ci;t; b~ht ; ~st; m~ t; xt; lt; ymt g, the firms’ choice {yt}, central bank’ choice {τt, Rnt }, and the market price fqlt; Rft ; pt; pmt g such that: 1. Definition: A perfect foresight equilibrium is a sequence of bankers’ decision choice {ct, ci,t, nt, bht , st, mt, bft , dt}, household’s choice f~ct; ~ci;t; b~ht ; ~st; m~ t; xt; lt; ymt g, the firms’ choice {yt}, central bank’ choice {τt, Rnt }, and the market price fqlt; Rft ; pt; pmt g such that: 1. Given the market price, the initial conditions and central bank’s choices, banker’s choices solve the banker’s problem, household’s choices solve the household’s problem, firm’s choice solves the firm’s problem
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