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Blanchard, Olivier; Gali, Jordi

Working Paper A new Keynesian model with unemployment

NBB Working Paper, No. 92

Provided in Cooperation with: National Bank of Belgium, Brussels

Suggested Citation: Blanchard, Olivier; Gali, Jordi (2006) : A new Keynesian model with unemployment, NBB Working Paper, No. 92, National Bank of Belgium, Brussels

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A new Keynesian model with unemployment

Olivier Blanchard Jordi Gali NATIONAL BANK OF BELGIUM

WORKING PAPERS - RESEARCH SERIES

A NEW KEYNESIAN MODEL WITH UNEMPLOYMENT

______

Olivier Blanchard (*) Jordi Gali (**)

We thank Ricardo Caballero, Peter Ireland, Julio Rotemberg, and participants in seminars at ITAM, MIT, Wharton, Boston Fed, and at the UQAM conference on "Frontiers of Macroeconomics" for helpful comments. We also thank Dan Cao for valuable research assistance.

______(*) MIT and NBER. (**) CREI, UPF, CEPR and NBER.

NBB WORKING PAPER No. 92 - OCTOBER 2006 Editorial Director

Jan Smets, Member of the Board of Directors of the National Bank of Belgium

Statement of purpose:

The purpose of these working papers is to promote the circulation of research results (Research Series) and analytical studies (Documents Series) made within the National Bank of Belgium or presented by external economists in seminars, conferences and conventions organised by the Bank. The aim is therefore to provide a platform for discussion. The opinions expressed are strictly those of the authors and do not necessarily reflect the views of the National Bank of Belgium.

The Working Papers are available on the website of the Bank: http://www.nbb.be

Individual copies are also available on request to: NATIONAL BANK OF BELGIUM Documentation Service boulevard de Berlaimont 14 BE - 1000 Brussels

Imprint: Responsibility according to the Belgian law: Jean Hilgers, Member of the Board of Directors, National Bank of Belgium. Copyright © fotostockdirect - goodshoot gettyimages - digitalvision gettyimages - photodisc National Bank of Belgium Reproduction for educational and non-commercial purposes is permitted provided that the source is acknowledged. ISSN: 1375-680X

NBB WORKING PAPER No. 92 - OCTOBER 2006 Editorial

On October 12-13, 2006 the National Bank of Belgium hosted a Conference on "Price and Wage Rigidities in an Open Economy". Papers presented at this conference are made available to a broader audience in the NBB Working Paper Series (www.nbb.be).

The views expressed in this paper are those of the authors and do not necessarily reflect the views of the National Bank of Belgium.

Abstract

We develop a utility based model of fluctuations, with nominal rigidities, and unemployment. In doing so, we combine two strands of research: the New Keynesian model with its focus on nominal rigidities, and the Diamond-Mortensen-Pissarides model, with its focus on labor market frictions and unemployment. In developing this model, we proceed in two steps. We first leave nominal rigidities aside. We show that, under a standard utility specification, productivity shocks have no effect on unemployment in the constrained efficient allocation. We then focus on the implications of alternative real wage setting mechanisms for fluctuations in unemployment. We then introduce nominal rigidities in the form of staggered price setting by firms. We derive the relation between inflation and unemployment and discuss how it is influenced by the presence of real wage rigidities. We show the nature of the tradeoff between inflation and unemployment stabilization, and we draw the implications for optimal monetary policy.

JEL-code : E32, E50.

Keywords: new Keynesian model, labor market frictions, search model, unemployment, sticky prices, real wage rigidities.

NBB WORKING PAPER No. 92 - OCTOBER 2006 TABLE OF CONTENTS

1. Introduction...... 1

2. A Simple Framework ...... 5 2.1 Assumptions ...... 5 2.2 The Constrained Efficient Allocation...... 8

3. Equilibrium under Flexible Prices...... 11 3.1 Value Maximization by Firms...... 11 3.2 Equilibrium with Nash Bargained Wages ...... 13 3.3 Equilibrium under Real Wage Rigidities ...... 20

4. Introducing Sticky Prices...... 21 4.1 Log-linearized Equilibrium Dynamics ...... 22 4.2 Approximate Log-linearized Dynamics ...... 24

5. Monetary Policy, Sticky Prices and Real Wage Rigidities...... 26 5.1 Two Extreme Policies ...... 26 5.2 Optimal Monetary Policy...... 28

6. Calibration and Quantitative Analysis...... 30 6.1 The Dynamic Effects of Productivity Shocks ...... 31

7. Relation to the Literature ...... 37

8. Conclusions ...... 39

Appendixes...... 40 References ...... 47 National Bank of Belgium Working Paper Series...... 49

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30 GSRWMWXIRX [MXL 97 IZMHIRGI -R SYV FEWIPMRI GEPMFVEXMSR [I WIX Y XS  [LMGL MW GSRWMWXIRX [MXL XLI EZIVEKI YRIQTPS]QIRX VEXI MR XLI 97 +MZIR \ ERH Y [I GER HIXIVQMRI XLI WITEVEXMSR VEXI YWMRK XLI VIPEXMSR • ! Y\!  Y  \  8LMW ]MIPHW E ZEPYI JSV • VSYKLP] IUYEP XS 

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2SXI XLEX XLI EFSZI GEPMFVEXIH TEVEQIXIVW GSQFMRIH [MXL XLI EWWYQTXMSR SJER I•GMIRX WXIEH] WXEXI EPPS[ YW XS TMR HS[R ¦ 7TIGM“GEPP]  MQTPMIW ¦  YRHIV XLI SYV FEWIPMRI97GEPMFVEXMSR ERH ¦  YRHIV XLI )YVSTIER SRI

 8LI (]REQMG )’IGXW SJ 4VSHYGXMZMX] 7LSGOW

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TSPMGMIW -R *MKYVI  [I EWWYQI E TYVIP] XVERWMXSV] WLSGO ¡E !   [LMGL EPPS[W YW XS MWSPEXI XLI QSHIP W MRXVMRWMG TIVWMWXIRGI [LIVIEW MR *MKYVI  [I EWWYQI

¡E ! E QSVI VIEPMWXMG HIKVII SJ TIVWMWXIRGI -R FSXL “KYVIW [I HMWTPE] XLI VIWTSRWIW JSV FSXL XLI 97 ERH )YVSTIER PEFSV QEVOIX GEPMFVEXMSRW -R EPP GEWIW [I VITSVX VIWTSRWIW XS E SRI TIVGIRX HIGPMRI MR TVSHYGXMZMX] ERH I\TVIWWIHMR TIVGIRX XIVQW

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31 Figure 4. Dynamic Responses to Transitory Productivity Shock

32 Figure 5. Dynamic Responses to a Persistent Productivity Shock

33 Figure 6. Taylor-type Rule vs. Optimal Policy

34 ;I FIKMR F] HMWGYWWMRK XLI GEWI SJ E XVERWMXSV] WLSGO %W WLS[R MR *MKYVI  ERH MQTPMIH F] XLI EREP]WMW EFSZI YRHIV E TSPMG] XLEX WXEFMPM^IW YRIQTPS]QIRX E XVERWMXSV] WLSGO XS TVSHYGXMZMX] LEW E ZIV] PMQMXIH MQTEGX SR MR”EXMSR [LMGL VMWIW PIWW XLER XIR FEWMW TSMRXW YRHIV FSXL GEPMFVEXMSRW ERH HMWTPE]W RS TIVWMWXIRGI 8LI WM^I SJ XLI I’IGX MW EPQSWX MHIRXMGEP JSV FSXL GEPMFVEXMSRW

9RHIV MR”EXMSR WXEFMPM^EXMSR SR XLI SXLIV LERH YRIQTPS]QIRX VMWIW F] EFSYX  FEWMW TSMRXW SR MQTEGX MR XLI 97 GEPMFVEXMSR  FEWMW TSMRXW MR XLI )YVSTIER SRI 1SWX MRXIVIWXMRKP] ERH EW HMWGYWWIH EFSZI YRIQTPS]QIRX VIQEMRW EFSZI MXW MRMXMEP ZEPYI [IPP EJXIV XLI WLSGO LEW ZERMWLIH [MXL XLI TIVWMWXIRGI FIMRK WMKRM“GERXP] KVIEXIV YRHIV XLI )YVSTIER GEPMFVEXMSR 8LI HM’IVIRGI MR TIVWMWXIRGI MW E GSRWIUYIRGI SJ FSXL E PS[IV NSF “RHMRK VEXI ERH E WQEPPIV WITEVEXMSR VEXIMR )YVSTI

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35 “VQIH F] SYV VIWYPXW [LMGL TSMRX XS ER MRGVIEWI SJ  TIVGIRXEKI TSMRXW  MR XLI YRIQTPS]QIRX VEXI YRHIV XLI 97 GEPMFVEXMSR -RXIVIWXMRKP] XLI YRIQTPS] QIRX MRGVIEWI YRHIV XLI )YVSTIER GEPMFVEXMSR MW WMKRM“GERXP] WQEPPIV XLSYKL WXMPP LYKI   TIVGIRXEKI TSMRXW -R FSXL GEWIW YRIQTPS]QIRX MW LMKLP] TIVWMWXIRX [MXL MXW VIWTSRWI HMWTPE]MRK E TVSQMRIRX LYQTWLETIH TEXXIVR 8LI HIKVII SJ TIVWMWXIRGI MW VIQEVOEFP] PEVKIV YRHIV XLI )YVSTIER GEPMFVEXMSR JSV XLI WEQI VIEWSRW HMWGYWWIH IEVPMIV

9RHIV XLI STXMQEP TSPMG] XLI MRGVIEWI MR YRIQTPS]QIRX SR MQTEGX MW EFSYX  TIVGIRXEKI TSMRX YRHIV XLI 97 GEPMFVEXMSR LEPJ XLEX WM^I YRHIV XLI )YVSTIER SRI 2SXI XLEX XLI WM^I SJ WYGL VIWTSRWIW MW WIZIVEP XMQIW WQEPPIV XLER YRHIV MR”EXMSR XEVKIXMRK 8LI TVMGI JSV LEZMRK E WQSSXLIV YRIQTPS]QIRX TEXL MW TIV WMWXIRXP] LMKLIV MR”EXMSR [MXL XLI PEXXIV ZEVMEFPI MRGVIEWMRK F] EFSYX  FEWMW TSMRXW YRHIV FSXL GEPMFVEXMSRW

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48 NATIONAL BANK OF BELGIUM - WORKING PAPERS SERIES

1. "Model-based inflation forecasts and monetary policy rules" by M. Dombrecht and R. Wouters, Research Series, February 2000. 2. "The use of robust estimators as measures of core inflation" by L. Aucremanne, Research Series, February 2000. 3. "Performances économiques des Etats-Unis dans les années nonante" by A. Nyssens, P. Butzen, P. Bisciari, Document Series, March 2000. 4. "A model with explicit expectations for Belgium" by P. Jeanfils, Research Series, March 2000. 5. "Growth in an open economy: some recent developments" by S. Turnovsky, Research Series, May 2000. 6. "Knowledge, technology and economic growth: an OECD perspective" by I. Visco, A. Bassanini, S. Scarpetta, Research Series, May 2000. 7. "Fiscal policy and growth in the context of European integration" by P. Masson, Research Series, May 2000. 8. "Economic growth and the labour market: Europe's challenge" by C. Wyplosz, Research Series, May 2000. 9. "The role of the exchange rate in economic growth: a euro-zone perspective" by R. MacDonald, Research Series, May 2000. 10. "Monetary union and economic growth" by J. Vickers, Research Series, May 2000. 11. "Politique monétaire et prix des actifs: le cas des Etats-Unis" by Q. Wibaut, Document Series, August 2000. 12. "The Belgian industrial confidence indicator: leading indicator of economic activity in the euro area?" by J.J. Vanhaelen, L. Dresse, J. De Mulder, Document Series, November 2000. 13. "Le financement des entreprises par capital-risque" by C. Rigo, Document Series, February 2001. 14. "La nouvelle économie" by P. Bisciari, Document Series, March 2001. 15. "De kostprijs van bankkredieten" by A. Bruggeman and R. Wouters, Document Series, April 2001. 16. "A guided tour of the world of rational expectations models and optimal policies" by Ph. Jeanfils, Research Series, May 2001. 17. "Attractive Prices and Euro - Rounding effects on inflation" by L. Aucremanne and D. Cornille, Documents Series, November 2001. 18. "The interest rate and credit channels in Belgium: an investigation with micro-level firm data" by P. Butzen, C. Fuss and Ph. Vermeulen, Research series, December 2001. 19 "Openness, imperfect exchange rate pass-through and monetary policy" by F. Smets and R. Wouters, Research series, March 2002. 20. "Inflation, relative prices and nominal rigidities" by L. Aucremanne, G. Brys, M. Hubert, P. J. Rousseeuw and A. Struyf, Research series, April 2002. 21. "Lifting the burden: fundamental tax reform and economic growth" by D. Jorgenson, Research series, May 2002. 22. "What do we know about investment under uncertainty?" by L. Trigeorgis, Research series, May 2002. 23. "Investment, uncertainty and irreversibility: evidence from Belgian accounting data" by D. Cassimon, P.-J. Engelen, H. Meersman, M. Van Wouwe, Research series, May 2002. 24. "The impact of uncertainty on investment plans" by P. Butzen, C. Fuss, Ph. Vermeulen, Research series, May 2002. 25. "Investment, protection, ownership, and the cost of capital" by Ch. P. Himmelberg, R. G. Hubbard, I. Love, Research series, May 2002. 26. "Finance, uncertainty and investment: assessing the gains and losses of a generalised non-linear structural approach using Belgian panel data", by M. Gérard, F. Verschueren, Research series, May 2002. 27. "Capital structure, firm liquidity and growth" by R. Anderson, Research series, May 2002. 28. "Structural modelling of investment and financial constraints: where do we stand?" by J.- B. Chatelain, Research series, May 2002. 29. "Financing and investment interdependencies in unquoted Belgian companies: the role of venture capital" by S. Manigart, K. Baeyens, I. Verschueren, Research series, May 2002. 30. "Development path and capital structure of Belgian biotechnology firms" by V. Bastin, A. Corhay, G. Hübner, P.-A. Michel, Research series, May 2002. 31. "Governance as a source of managerial discipline" by J. Franks, Research series, May 2002.

NBB WORKING PAPER No. 92 - OCTOBER 2006 49 32. "Financing constraints, fixed capital and R&D investment decisions of Belgian firms" by M. Cincera, Research series, May 2002. 33. "Investment, R&D and liquidity constraints: a corporate governance approach to the Belgian evidence" by P. Van Cayseele, Research series, May 2002. 34. "On the Origins of the Franco-German EMU Controversies" by I. Maes, Research series, July 2002. 35. "An estimated dynamic stochastic general equilibrium model of the Euro Area", by F. Smets and R. Wouters, Research series, October 2002. 36. "The labour market and fiscal impact of labour tax reductions: The case of reduction of employers' social security contributions under a wage norm regime with automatic price indexing of wages", by K. Burggraeve and Ph. Du Caju, Research series, March 2003. 37. "Scope of asymmetries in the Euro Area", by S. Ide and Ph. Moës, Document series, March 2003. 38. "De autonijverheid in België: Het belang van het toeleveringsnetwerk rond de assemblage van personenauto's", by F. Coppens and G. van Gastel, Document series, June 2003. 39. "La consommation privée en Belgique", by B. Eugène, Ph. Jeanfils and B. Robert, Document series, June 2003. 40. "The process of European monetary integration: a comparison of the Belgian and Italian approaches", by I. Maes and L. Quaglia, Research series, August 2003. 41. "Stock market valuation in the United States", by P. Bisciari, A. Durré and A. Nyssens, Document series, November 2003. 42. "Modeling the Term Structure of Interest Rates: Where Do We Stand?, by K. Maes, Research series, February 2004. 43. Interbank Exposures: An Empirical Examination of System Risk in the Belgian Banking System, by H. Degryse and G. Nguyen, Research series, March 2004. 44. "How Frequently do Prices change? Evidence Based on the Micro Data Underlying the Belgian CPI", by L. Aucremanne and E. Dhyne, Research series, April 2004. 45. "Firms' investment decisions in response to demand and price uncertainty", by C. Fuss and Ph. Vermeulen, Research series, April 2004. 46. "SMEs and Bank Lending Relationships: the Impact of Mergers", by H. Degryse, N. Masschelein and J. Mitchell, Research series, May 2004. 47. "The Determinants of Pass-Through of Market Conditions to Bank Retail Interest Rates in Belgium", by F. De Graeve, O. De Jonghe and R. Vander Vennet, Research series, May 2004. 48. "Sectoral vs. country diversification benefits and downside risk", by M. Emiris, Research series, May 2004. 49. "How does liquidity react to stress periods in a limit order market?", by H. Beltran, A. Durré and P. Giot, Research series, May 2004. 50. "Financial consolidation and liquidity: prudential regulation and/or competition policy?", by P. Van Cayseele, Research series, May 2004. 51. "Basel II and Operational Risk: Implications for risk measurement and management in the financial sector", by A. Chapelle, Y. Crama, G. Hübner and J.-P. Peters, Research series, May 2004. 52. "The Efficiency and Stability of Banks and Markets", by F. Allen, Research series, May 2004. 53. "Does Financial Liberalization Spur Growth?" by G. Bekaert, C.R. Harvey and C. Lundblad, Research series, May 2004. 54. "Regulating Financial Conglomerates", by X. Freixas, G. Lóránth, A.D. Morrison and H.S. Shin, Research series, May 2004. 55. "Liquidity and Financial Market Stability", by M. O'Hara, Research series, May 2004. 56. "Economisch belang van de Vlaamse zeehavens: verslag 2002", by F. Lagneaux, Document series, June 2004. 57. "Determinants of Euro Term Structure of Credit Spreads", by A. Van Landschoot, Research series, July 2004. 58. "Macroeconomic and Monetary Policy-Making at the European Commission, from the Rome Treaties to the Hague Summit", by I. Maes, Research series, July 2004. 59. "Liberalisation of Network Industries: Is Electricity an Exception to the Rule?", by F. Coppens and D. Vivet, Document series, September 2004. 60. "Forecasting with a Bayesian DSGE model: an application to the euro area", by F. Smets and R. Wouters, Research series, September 2004. 61. "Comparing shocks and frictions in US and Euro Area Business Cycle: a Bayesian DSGE approach", by F. Smets and R. Wouters, Research series, October 2004.

50 NBB WORKING PAPER No. 92 - OCTOBER 2006 62. "Voting on Pensions: A Survey", by G. de Walque, Research series, October 2004. 63. "Asymmetric Growth and Inflation Developments in the Acceding Countries: A New Assessment", by S. Ide and P. Moës, Research series, October 2004. 64. "Importance économique du Port Autonome de Liège: rapport 2002", by F. Lagneaux, Document series, November 2004. 65. "Price-setting behaviour in Belgium: what can be learned from an ad hoc survey", by L. Aucremanne and M. Druant, Research series, March 2005. 66. "Time-dependent versus State-dependent Pricing: A Panel Data Approach to the Determinants of Belgian Consumer Price Changes", by L. Aucremanne and E. Dhyne, Research series, April 2005. 67. "Indirect effects – A formal definition and degrees of dependency as an alternative to technical coefficients", by F. Coppens, Research series, May 2005. 68. "Noname – A new quarterly model for Belgium", by Ph. Jeanfils and K. Burggraeve, Research series, May 2005. 69. "Economic importance of the Flemish maritime ports: report 2003", F. Lagneaux, Document series, May 2005. 70. "Measuring inflation persistence: a structural time series approach", M. Dossche and G. Everaert, Research series, June 2005. 71. "Financial intermediation theory and implications for the sources of value in structured finance markets", J. Mitchell, Document series, July 2005. 72. "Liquidity risk in securities settlement", J. Devriese and J. Mitchell, Research series, July 2005. 73. "An international analysis of earnings, stock prices and bond yields", A. Durré and P. Giot, Research series, September 2005. 74. "Price setting in the euro area: Some stylized facts from Individual Consumer Price Data", E. Dhyne, L. J. Álvarez, H. Le Bihan, G. Veronese, D. Dias, J. Hoffmann, N. Jonker, P. Lünnemann, F. Rumler and J. Vilmunen, Research series, September 2005. 75. "Importance économique du Port Autonome de Liège: rapport 2003", by F. Lagneaux, Document series, October 2005. 76. "The pricing behaviour of firms in the euro area: new survey evidence, by S. Fabiani, M. Druant, I. Hernando, C. Kwapil, B. Landau, C. Loupias, F. Martins, T. Mathä, R. Sabbatini, H. Stahl and A. Stokman, Research series, November 2005. 77. "Income uncertainty and aggregate consumption, by L. Pozzi, Research series, November 2005. 78. "Crédits aux particuliers - Analyse des données de la Centrale des Crédits aux Particuliers", by H. De Doncker, Document series, January 2006. 79. "Is there a difference between solicited and unsolicited bank ratings and, if so, why?" by P. Van Roy, Research series, February 2006. 80. "A generalised dynamic factor model for the Belgian economy - Useful business cycle indicators and GDP growth forecasts", by Ch. Van Nieuwenhuyze, Research series, February 2006. 81. "Réduction linéaire de cotisations patronales à la sécurité sociale et financement alternatif" by Ph. Jeanfils, L. Van Meensel, Ph. Du Caju, Y. Saks, K. Buysse and K. Van Cauter, Document series, March 2006. 82. "The patterns and determinants of price setting in the Belgian industry" by D. Cornille and M. Dossche, Research series, May 2006. 83. "A multi-factor model for the valuation and risk management of demand deposits" by H. Dewachter, M. Lyrio and K. Maes, Research series, May 2006. 84. "The single European electricity market: A long road to convergence", by F. Coppens and D. Vivet, Document series, May 2006. 85. "Firm-specific production factors in a DSGE model with Taylor price setting", by G. de Walque, F. Smets and R. Wouters, Research series, June 2006. 86. "Economic importance of the Belgian ports: Flemish maritime ports and Liège port complex - report 2004", by F. Lagneaux, Document series, June 2006. 87. "The response of firms' investment and financing to adverse cash flow shocks: the role of bank relationships", by C. Fuss and Ph. Vermeulen, Research series, July 2006. 88. "The term structure of interest rates in a DSGE model", by M. Emiris, Research series, July 2006. 89. "The production function approach to the Belgian output gap, Estimation of a Multivariate Structural Time Series Model", by Ph. Moës, Research series, September 2006. 90. "Industry Wage Differentials, Unobserved Ability, and Rent-Sharing: Evidence from Matched Worker- Firm Data, 1995-2002", by R. Plasman, F. Rycx and I. Tojerow, Research series, October 2006.

NBB WORKING PAPER No. 92 - OCTOBER 2006 51 91. "The dynamics of trade and competition", by N. Chen, J. Imbs and A. Scott, Research series, October 2006. 92. "A New Keynesian Model with Unemployment", by O. Blanchard and J. Gali, Research series, October 2006.

52 NBB WORKING PAPER No. 92 - OCTOBER 2006