Inflation Inertia and the Optimal Hybrid Inflation/Price-Level Target

Røisland, Øistein Working Paper Inflation Inertia and the Optimal Hybrid Inflation/PriceLevel Target Working Paper, No. 2005/4 Provided in Cooperation with: Norges Bank, Oslo Suggested Citation: Røisland, Øistein (2005) : Inflation Inertia and the Optimal Hybrid Inflation/PriceLevel Target, Working Paper, No. 2005/4, ISBN 82-7553-301-5, Norges Bank, Oslo, https://hdl.handle.net/11250/2498437 This Version is available at: https://hdl.handle.net/10419/209851 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc-nd/4.0/deed.no ANO 2005/4 Oslo July 1, 2005 Working Paper Monetary Policy Department Inflation inertia and the optimal hybrid inflation/price-level target by Øistein Røisland ISSN 0801-2504 (printed) 1502-8143 (online) ISBN 82-7553-300-7 (printed), 82-7553-301-5 (online) Working papers from Norges Bank can be ordered by e-mail: [email protected] or from Norges Bank, Subscription service, P.O.Box. 1179 Sentrum N-0107Oslo, Norway. Tel. +47 22 31 63 83, Fax. +47 22 41 31 05 Working papers from 1999 onwards are available as pdf-files on the bank’s web site: www.norges-bank.no, under “Publications”. Norges Bank’s working papers present research projects and reports (not usually in their final form) and are intended inter alia to enable the author to benefit from the comments of colleagues and other interested parties. Views and conclusions expressed in working papers are the responsibility of the authors alone. Working papers fra Norges Bank kan bestilles over e-post: [email protected] eller ved henvendelse til: Norges Bank, Abonnementsservice Postboks 1179 Sentrum 0107 Oslo Telefon 22 31 63 83, Telefaks 22 41 31 05 Fra 1999 og senere er publikasjonene tilgjengelige som pdf-filer på www.norges-bank.no, under “Publikasjoner”. Working papers inneholder forskningsarbeider og utredninger som vanligvis ikke har fått sin endelige form. Hensikten er blant annet at forfatteren kan motta kommentarer fra kolleger og andre interesserte. Synspunkter og konklusjoner i arbeidene står for forfatternes regning. InflationInertiaandtheOptimalHybrid Inflation/Price-Level Target∗ Øistein Røisland† July 1, 2005 Abstract Ahybridinflation/price-level target combines elements of both inflation and price-level targets. The paper derives a hybrid target within a new Keynesian model with inflation persistence due to price indexation. The result generalizes a result by Vestin (2005) that the optimal policy could be implemented with a price-level targeting regime. We show that the optimal price-level drift in the hybrid target is equal to thedegreeofpriceindexation. Keywords: Price-level target, Inflation persistence, Commitment JEL codes:E52, E61, E63 1 Introduction John Maynard Keynes suggested that monetary policy should regulate the supply of money so that "the index number of prices will never move far from a fixed point."1Except for Sweden in the thirties,2no central banks have followed up Keynes’ idea and adopted price-level targeting, although inflation targeting has become a popular monetary regime. The difference between price-level and inflation targeting is that the former implies a stationary price level, while the latter implies complete price-level drift and thus a non-stationary price level. Price-level targeting has been subject of renewed interest in recent years due to theoretical results characterizing optimal policy under commitment. ∗A thank Sharon McCaw, Tommy Sveen, David Vestin and Tony Yates for useful comments and discussions. The usual disclaimer applies. †Norges Bank (Central Bank of Norway), P.O.Box 1179 Sentrum, 0107 Oslo, phone: +47 22 31 67 39, fax: +47 22 42 40 62, e-mail: oistein.roisl[email protected]. The views expressed are the author’s own and not necessarily those of Norges Bank. 1Keynes (1923), cited in King (1998). 2See Berg and Jonung (1998). 1 In the canonical forward-looking new Keynesian model, optimal monetary policy under commitment in the timeless perspective is characterized by a stationary price level, while discretionary policy gives rise to a unit root in the price-level.3In order to overcome the inefficiency from discretion, Vestin (forthcoming) showed that if the standard loss function was replaced by an appropriately specified loss function with a price-level target, the monetary policy under discretion would be identical to the optimal policy under commitment. The intuition for the result is that a price-level target requires aperiodofinflation below target after a positive cost-push shock. When inflation is expected to be low in the future, firms respond to the shock by increasing prices by less, such that the shock has less effect on inflation today. How advantageous price-level targeting is relative to inflation targeting hinges, however, on the degree of forward-lookingness in the Phillips curve. Batini and Yates (2003) introduced a new perspective on the analysis of price-level and inflation targets by considering a ’hybrid’ target, which is a weighted average of an inflation target and a price-level target. They did not, however, use a utility-based welfare loss function as an evaluation criterion, and did not derive an optimal hybrid targeting regime. Here, we extend the model by Vestin (2005) in two directions. First, we consider the more general new Keynesian model with inflation persistence introduced by Woodford (2003). Second, we adopt Batini and Yates’ (2003) hybrid inflation/price-level targeting regime, which embeds both inflation targeting and price-level targeting. By combining these extensions, we reach a simple generalization of Vestin’s results that yields some new insights to the debate on price-level versus inflation targeting. 2Themodel We consider the following new Keynesian model: xt=Etxt+1 −1 σ(it−Etπt+1 −rn t)(1) πt−γπt−1=β(Etπt+1 −γπt)+κxt+ut(2) Equation (1) can be derived from the Euler equation for the representative household’s consumption decision, where xtis the output gap, defined as the deviation of output from the flexible-price level of output, itis the nominal interest rate, πtis the rate of inflation, rn tis the flexible-price real interest rate, and utis a white noise mark-up (’cost-push’) shock. Equation (2) is a ’hybrid’ new Keynesian Phillips curve, which is derived by Woodford (2003) assuming that a fixedfractionofrandomlychosenfirms reset their prices in any given period, while the remaining firms index their prices to 3See Clarida et al. (1999) and Woodford (2003). 2 a fraction γof lagged inflation. A similar Phillips curve has been derived by Amato and Laubach (2003) and Steinsson (2003), where the existence of the backward-looking term was due to rule-of-thumb behavior among price setters. Woodford showed that under these assumptions, a secondorder approximation to consumers’ utility gives the following welfare loss function:4 E0(1 −β) ∞ X t=0 βt[(πt−γπt−1)2+λx2 t],(3) where the relative weight λon the output gap depends on the deep parameters of the model. Suppose that the central bank is not able to enforce a policy under commitment (in a timeless perspective). A large strand of the monetary policy literature focusses on specifying modified loss functions that gives the central bank incentives to conduct a policy that replicates the optimal policy under commitment.5In the pure forward-looking model, i.e., γ=0, Vestin (2005) showed that the optimal policy would be implemented if the government assigned the following loss function to the central bank: E0(1 −β) ∞ X t=0 βt[p2 t+˜ λx2 t],(4) where ˜ λdepends on the parameters in the model (in a non-closed-form way). We consider the more general hybrid price-level/inflation target suggested by Batini and Yates (2003) and assume that the government assigns the following loss function to the central bank: E0(1 −β) ∞ X t=0 βt[(pt−ηpt−1)2+ˆ λx2 t],(5) where ptis the price level (in logs), and ˆ λis a choice parameter for the government. The parameter η(0≤η≤1) specifies the degree of price-level drift. If η=1, there is full drift and the loss function collapses to an inflation target. If η=0, there is a (pure) price-level target. Batini and Yates also investigated the intermediate regimes, but did not derive an optimal degree of price-level drift. As noted by Woodford (2003), by defining πq t≡πt−γπt−1and inserting this into equations (2) and (3), and noting the xtcan be treated as the 4The welfare loss function under the rule-of-thumb assumptions of Amato and Laubach (2003) and Steinsson (2003) are similar, albeit not identical, to the welfare loss function under price indexation. 5See e.g., Jensen (2002), Walsh (2003), Söderström (forthcoming ), and Nessèn and Vestin (forthcoming). 3 control variable instead of it,weseethatthepolicyproblembecomesisomorphic to the standard forward-looking model. Based on this insight, we can generalize Vestin’s (2005) result. Since Vestin showed that πtshould be replaced by ptin the loss function, we apply the ’isomorphism result’ and replace πq tin equation (3) by the level variable qt≡pt−γpt−1.The optimal weight on the output gap term is then equal to the optimal weight in the forward-looking model, i.e., λ=˜ λ.The optimal policy can therefore be implemented by assigning the following loss function to the central bank: E0(1 −β) ∞ X t=0 βt[(pt−γpt−1)2+˜ λx2 t].(6) Thus, it is possible to achieve a policy that is identical to the optimal policy under commitment if the central bank minimizes a modified loss function with a Batini-Yates type of hybrid target, where the degree of price-level drift in the hybrid target is equal to the degree of price indexation, i.e., η=γ. While Vestin considered the extreme case with no indexation, it is interesting to consider the other extreme with complete indexation. By setting γ=1in (5), we have the interesting result that the optimal monetary regime is (flexible) inflation targeting. There is an ongoing discussion about whether inflation targeting central banks should aim for price stability in the more ambitious sense of price level targeting. The above result shows, however, that if there is full indexation, which Giannoni and Woodford (2003) argue fits US data best and is also assumed by Christiano et al. (2005), central banks should keep on targeting inflation and not aim for price-level level targeting. 3Conclusion We have derived an optimal hybrid inflation/price level target as proposed by Batini and Yates (2003) in a new Keynesian model with inflation persistence stemming from price indexation. Building on the results by Vestin (forthcoming), we showed that the optimal degree of price-level drift in the hybrid target is equal to the degree of price indexation. In the case of complete indexation, the optimal monetary regime is flexible inflation targeting. 4 References Amato, J., and T. Laubach (2003). "Rule-of-Thumb Behavior and Monetary Policy." European Economic Review, Vol 47 (5), 791-831. Batini. N. and A. Yates (2003). "Hybrid Inflation and Price-Level Targeting". Journal of Money, Credit, and Banking 35. Berg, C. and L. Jonung (1999). "Pioneering Price Level Targeting: The Swedish Experience 1931-1937." Journal of Monetary Economics 43(3), 525552. Christiano, L. J., M. S. Eichenbaum, and C. L. Evans (2005). "Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy". Journal of Political Economy, 113 (1), 1-45. Clarida, R., J. Galì and M. Gertler (1999). ”The Science of Monetary Policy: A New Keynesian Perspective”. Journal of Economic Literature 37, 1661-1707. Giannoni, M. and M. Woodford (2003). "Optimal Inflation Targeting Rules". In B. S. Bernanke and M. Woodford, eds, Inflation Targeting. University of Chicago Press, Chicago. Jensen, H. (2002). "Targeting Nominal Income Growth or Inflation?" American Economic Review 92, 928-956. King, M. (1998). "Mr King explores lessons from the UK labour market." BIS Review 1003/1998. Keynes, J. M. (1923). "Notes for the Lecture to the National Liberal Club", reprinted in Collected Writings of John Maynard Keynes,Vol.XIX, Macmillan, London, 1991. Nessèn, M. and D. Vestin (forthcoming). "Average Inflation Targeting". Journal of Money, Credit, and Banking. Steinsson, J. (2003). "Optimal Monetary Policy in an Economy with Inflation Presistence". Journal of Monetary Economics 50,1425-1456. Söderström, U. (2005). "Targeting Inflation with a Role for Money". Economica, forthcoming. Vestin, D. (2005). "Price-Level Targeting versus Inflation Targeting in a Forward-Looking Model." Journal of Monetary Economics, forthcoming. Walsh, C. (2003). "Speed Limit Policies: The Output Gap and Optimal Monetary Policy." American Economic Review, 93(1), 265-278 Woodford, M. (2003). Interest and Prices. Princeton University Press, Princeton. 5 6 WORKING PAPERS (ANO) FROM NORGES BANK 2002-2005 Working Papers were previously issued as Arbeidsnotater from Norges Bank, see Norges Bank’s website http://www.norges-bank.no 2002/1 Bache, Ida Wolden Empirical Modelling of Norwegian Import Prices Research Department 2002, 44p 2002/2 Bårdsen, Gunnar og Ragnar Nymoen Rente og inflasjon Forskningsavdelingen 2002, 24s 2002/3 Rakkestad, Ketil Johan Estimering av indikatorer for volatilitet Avdeling for Verdipapirer og internasjonal finans Norges Bank 33s 2002/4 Akram, Qaisar Farooq PPP in the medium run despite oil shocks: The case of Norway Research Department 2002, 34p 2002/5 Bårdsen, Gunnar, Eilev S. Jansen og Ragnar Nymoen Testing the New Keynesian Phillips curve Research Department 2002, 38p 2002/6 Lindquist, Kjersti-Gro The Effect of New Technology in Payment Services on Banks’Intermediation Research Department 2002, 28p 2002/7 Sparrman, Victoria Kan pengepolitikken påvirke koordineringsgraden i lønnsdannelsen? En empirisk analyse. Forskningsavdelingen 2002, 44s 2002/8 Holden, Steinar The costs of price stability - downward nominal wage rigidity in Europe Research Department 2002, 43p 2002/9 Leitemo, Kai and Ingunn Lønning Simple Monetary Policymaking without the Output Gap Research Department 2002, 29p 2002/10 Leitemo, Kai Inflation Targeting Rules: History-Dependent or Forward-Looking? Research Department 2002, 12p 2002/11 Claussen, Carl Andreas Persistent inefficient redistribution International Department 2002, 19p 2002/12 Næs, Randi and Johannes A. Skjeltorp Equity Trading by Institutional Investors: Evidence on Order Submission Strategies Research Department 2002, 51p 2002/13 Syrdal, Stig Arild A Study of Implied Risk-Neutral Density Functions in the Norwegian Option Market Securities Markets and International Finance Department 2002, 104p 2002/14 Holden, Steinar and John C. Driscoll A Note on Inflation Persistence Research Department 2002, 12p 2002/15 Driscoll, John C. and Steinar Holden Coordination, Fair Treatment and Inflation Persistence Research Department 2002, 40p 2003/1 Erlandsen, Solveig Age structure effects and consumption in Norway, 1968(3) – 1998(4) Research Department 2003, 27p 2003/2 Bakke, Bjørn og Asbjørn Enge Risiko i det norske betalingssystemet Avdeling for finansiell infrastruktur og betalingssystemer 2003, 15s 2003/3 Matsen, Egil and Ragnar Torvik