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Should We be Afraid of Friedman's Rule?

Should one think of zero nominal interest rates as an undesirable liquidity trap or as the desirable Friedman rule? I use three different frameworks to discuss this issue. First, I restate Cole and Kocherlakota's (1998) analysis of Friedman's rule: short run increases in the money stock - whether through issuing spending coupons, open market operations or foreign exchange intervention - change nothing as long as the money stock shrinks in the long run. Second, two simple ‘Keynesian’ models of the inflationary process with a zero lower bound on nominal interest rates imply either that deflationary spirals should be common or that a policy close to the Friedman rule and thus some deflation is optimal. Finally, a formal ‘baby-sitting coop’ model implies multiple equilibria, but does not support the injection of liquidity to restore the good equilibrium, in contrast to Krugman (1998).