Time Inconsistency and the Exchange Rate Channel of Monetary Policy?Kai LeitemoNorges Bank, NO-0107 Oslo, Norway kai.leitemobi.noistein RislandNorges Bank, NO-0107 Oslo, Norway ostein.roislandnorges-bank.noRagnar TorvikNorges Bank and Norwegian University of Science and Technology, NO-7491 Trondheim, Norway ragnar.torviksvt.ntnu.moAbstractThis paper analyses time-inconsistency problems related to the exchange rate channel of monetary policy. Within a simple open-economy macroeconomic model, where the exchange rate is the only forward-looking variable, we show that a difference emerges between optimal policy under discretion and under commitment. Moreover, the nature of the time-inconsistency problem resembles that resulting from standard New Keynesian models: when cost-push shocks occur, the exchange rate channel gives rise to excessive output stabilisation andinsufficient inertia in monetary policy under a discretionary policy.Keywords: Monetary policy; time inconsistency; exchange rateJEL classification: E42; E52; E61I. IntroductionTime-inconsistency problems in monetary policy have received considerable attention in economic theory. The earlier literature focused on time incon-sistency leading to the well-known inflationary bias and on means of overcoming policy imperfections. More recently, time-inconsistency issueshave attracted renewed attention due to the large influence of the New Keynesian theoretical framework.1It has been shown that there is a time- inconsistency problem regarding optimal stabilisation when supply shocks occur.Scand. J. of Economics 104(3), 391397, 2002# The editors of the Scandinavian Journal of Economics 2002. Published by Blackwell Publishers, 108 Cowley Road, Oxford OX4 1JF, UK and 350 Main Street, Malden, MA 02148, USA.?We would like to thank Richard Clarida, Henrik Jensen, Ricardo Mestre, Ulf So derstro m,Carl E. Walsh, and participants at the workshop on Macroeconometric Modelling at the ECB and the CFS Summer School for valuable comments. 1See the survey by Clarida, Gal and Gertler (1999).Central to this literature is the New Keynesian Phillips curve, whichstates that current inflation depends on the output gap (or some othermeasure of marginal costs) and expected future inflation. The New Key- nesian Phillips curve is clearly attractive on theoretical grounds, since it can be derived from optimising behaviour. The empirical evidence is somewhat mixed, however.2The aim of this paper is not to debate the realism of the assumptions underlying the New Keynesian monetary policy literature. The objective is rather to examine whether similar time-inconsistency problems may occur under alternative assumptions. As we will show, the conclusions are robust as long as the openness of the economy is taken into account. Despite disagreement about the degree to which price setting is forward- looking, it is widely accepted that asset prices, such as the exchange rate, are forward-looking. Here, we analyse time-inconsistency problems related tothe exchange rate channel of monetary policy. We find that the optimal policy is time inconsistent due to the forward-looking exchange rate channel, even though price and output determination is purely backward-looking. Although this is not surprising in itself, since the existence of forward- looking variables in general leads to time inconsistency, we show that the nature of the time-inconsistency problem is in many respects similar to that resulting from the standard New Keynesian model.II. The ModelIn order to focus on the time-inconsistency problem related to the exchange rate channel of monetary policy, we chose a model where the exchange rateis the only forward-looking variable. Specifically, we opted for the simple, but frequently cited, open-economy model of Ball (1999), where the adjust-ment mechanisms for output and inflation are purely backward-looking. However, while there are no forward-looking variables in the Ball model, we introduce forward-lookingness by imposing uncovered interest rate parity with rational expectations. The model can be summarised as follows:yt ryt?1? 1rt?1 2et?1 ?yt,(1)?t ?t?1 ?yt?1 (et?1? et?2) ?t,(2)2Gali, Gertler and Lo pez-Salido (2001), Sbordone (2002) and others have found that theforward-looking element in the Phillips curve is important. Fuhrer (1997) finds, however, thatthe forward-looking element is not significant for the US economy. Roberts (1997, 1998)argues that the New Keynesian Phillips curve does not fit well when rational expectations are imposed. Ball (1994), Mankiw (2001) and Mankiw and Reis (2001) argue that the New Keynesian Phillips curve yields theoretical implications at odds with reality.392K. Leitemo, . Risland and R. Torvik# The editors of the Scandinavian Journal of Economics 2002.et et1jt r?t? rt,(3)where ytis output, rtis the real interest rate, etis the real exchange rate, ?tis consumer price inflation and the ?s are white noise shocks. All varia