## Yet Another Note on Benefits of Nominal GDP Targeting

At lunch today Christina Romer reminded me of--or rather drove into my thick head a point that I had missed during the seminar, even though he was standing only six feet in front of me at the time--Ivan Werning's point that level nominal GDP targeting is a good policy in a liquidity trap not just or not primarily because it promises future inflation but also and (for his parameter values) primarily because it promises a future boom. In the IS-LM framework with the long-term real interest rate on the vertical axis, the liquidity trap maintains itself both because the LM curve is shifted upwards (because fear of deflation raises the expected real returns to holding cash) and because the IS curve has been shifted to the left (because fear of continued depression makes business calculate that investment is unprofitable). Raising expected inflation can unlock only the first half of the trap. Level nominal GDP targeting can unlock both halves.

Ivan Werning: Managing a Liquidity Trap: Monetary and Fiscal Policy: As first argued by Krugman (1998), optimal monetary policy can improve on this dire outcome by committing to future policy in a way that affects current expectations favor- ably. In particular, I show that, it is optimal to promote future inflation and stimulate a boom in output. I establish that optimal inflation may be positive throughout the episode, so that deflation is completely avoided. Thus, the absence of deflation, far from being at odds with a liquidity trap, actually may be evidence of an optimal response to such a situ- ation. I show that output starts below its efficient level, but rises above it towards the end of the trap. Indeed, the boom in output is larger than that stimulated by the inflationary promise.

There are a number of ways monetary policy can promote inflation and stimulate output. Monetary easing does not necessarily imply a low equilibrium interest rate path. Indeed, as in most monetary models, the nominal interest rate path does not uniquely determine an equilibrium. Indeed, an interest rate of zero during the trap that becomes positive immediately after the trap is consistent with positive inflation and output after the trap. I show, however, that the optimal policy with commitment involves keeping the interest rate down at zero longer. The continuous time formulation helps here because it avoids time aggregation issues that may otherwise obscure the result.

Some of my results echo findings from prior work based on simulations for a Poisson specification of the natural rate of interest. Christiano et al. (2011) reports that, when the central bank follows a Taylor rule, price stickiness increases the decline in output during a liquidity trap. Eggertsson and Woodford (2003), Jung et al. (2005) and Adam and Billi (2006) find that the optimal interest rate path may keep it at zero after the natural rate of interest becomes positive. To the best of my knowledge this paper provides the first formal results explaining these findings for inflation, output and interest rates. An implication of my result is that the interest rate should jump discretely upon exit- ing the zero bound—a property that can only be appreciated in continuous time. Thus, even when fundamentals vary continuously, optimal policy calls for a discontinuous interest rate path…

Level nominal GDP targeting also has very nice properties in an economy buffeted by either positive or negative commodity-price supply shocks. The principal case in which it appears inferior to inflation targeting is one in which the economy is subject to shocks to the persistent rate of productivity growth.

Level