[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/p/zbw/imfswp/146.html
   My bibliography  Save this paper

Dynamics and synchronization of global equilibrium interest rates

Author

Listed:
  • Beyer, Robert
  • Milivojevic, Lazar
Abstract
With the COVID-19 pandemic, the intense debate about secular stagnation will become even more important. Empirical estimates of equilibrium real interest rates are so far mostly limited to advanced economies, since no statistical procedure suitable for a large set of countries is available. This is surprising, as equilibrium rates have strong policy implications in emerging markets and developing economies as well; current estimates of the global equilibrium rate rely on only a few countries; and estimates for a more diverse set of countries can improve understanding of the drivers. This paper proposes a model and estimation strategy that decompose ex ante real interest rates into a permanent and transitory component even with short samples and high volatility. This is done with an unobserved component local level stochastic volatility model, which is used to estimate equilibrium rates for 50 countries with Bayesian methods. Equilibrium rates were lower in emerging markets and developing economies than in advanced economies in the 1980s, similar in the 1990s, and have been higher since 2000. In line with economic integration and rising global capital markets, synchronization has been rising over time and is higher among advanced economies. Equilibrium rates of countries with stronger trade linkages and similar demographic and economic trends are more synchronized.

Suggested Citation

  • Beyer, Robert & Milivojevic, Lazar, 2021. "Dynamics and synchronization of global equilibrium interest rates," IMFS Working Paper Series 146, Goethe University Frankfurt, Institute for Monetary and Financial Stability (IMFS).
    • Handle: RePEc:zbw:imfswp:146
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/228630/1/1744660344.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Frankel, Jeffrey A & Rose, Andrew K, 1998. "The Endogeneity of the Optimum Currency Area Criteria," Economic Journal, Royal Economic Society, vol. 108(449), pages 1009-1025, July.
    2. Cukierman, Alex, 2016. "Reflections on the natural rate of interest, its measurement, monetary policy and the zero lower bound," CEPR Discussion Papers 11467, C.E.P.R. Discussion Papers.
    3. Del Negro, Marco & Giannone, Domenico & Giannoni, Marc P. & Tambalotti, Andrea, 2019. "Global trends in interest rates," Journal of International Economics, Elsevier, vol. 118(C), pages 248-262.
    4. Mengheng Li & Siem Jan (S.J.) Koopman, 2018. "Unobserved Components with Stochastic Volatility in U.S. Inflation: Estimation and Signal Extraction," Tinbergen Institute Discussion Papers 18-027/III, Tinbergen Institute.
    5. Mikael Juselius & Claudio Borio & Piti Disyatat & Mathias Drehmann, 2017. "Monetary Policy, the Financial Cycle, and Ultra-Low Interest Rates," International Journal of Central Banking, International Journal of Central Banking, vol. 13(3), pages 55-89, September.
    6. Krueger, Dirk & Ludwig, Alexander, 2007. "On the consequences of demographic change for rates of returns to capital, and the distribution of wealth and welfare," Journal of Monetary Economics, Elsevier, vol. 54(1), pages 49-87, January.
    7. Gauti B. Eggertsson & Neil R. Mehrotra, 2014. "A Model of Secular Stagnation," NBER Working Papers 20574, National Bureau of Economic Research, Inc.
    8. Kalemli-Ozcan, Sebnem & Papaioannou, Elias & Peydró, José-Luis, 2013. "Financial regulation, financial globalization, and the synchronization of economic activity," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 68(3), pages 1179-1228.
    9. Sébastien Fries & Jean‐Stéphane Mésonnier & Sarah Mouabbi & Jean‐Paul Renne, 2018. "National natural rates of interest and the single monetary policy in the euro area," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(6), pages 763-779, September.
    10. Danielsson, Jon, 1994. "Stochastic volatility in asset prices estimation with simulated maximum likelihood," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 375-400.
    11. Holston, Kathryn & Laubach, Thomas & Williams, John C., 2017. "Measuring the natural rate of interest: International trends and determinants," Journal of International Economics, Elsevier, vol. 108(S1), pages 59-75.
    12. Potjagailo, Galina & Wolters, Maik H., 2023. "Global financial cycles since 1880," Journal of International Money and Finance, Elsevier, vol. 131(C).
    13. Andrew Blake & Haroon Mumtaz, 2015. "Applied Bayesian Econometrics for central bankers," Handbooks, Centre for Central Banking Studies, Bank of England, number 36, April.
    14. Carvalho, Carlos & Ferrero, Andrea & Nechio, Fernanda, 2016. "Demographics and real interest rates: Inspecting the mechanism," European Economic Review, Elsevier, vol. 88(C), pages 208-226.
    15. Burstein, Ariel & Kurz, Christopher & Tesar, Linda, 2008. "Trade, production sharing, and the international transmission of business cycles," Journal of Monetary Economics, Elsevier, vol. 55(4), pages 775-795, May.
    16. Lukasz Rachel & Thomas Smith, 2015. "Secular Drivers of the Global Real Interest Rate," Discussion Papers 1605, Centre for Macroeconomics (CFM).
    17. Domenico Giannone & Michele Lenza & Lucrezia Reichlin, 2010. "Business Cycles in the Euro Area," NBER Chapters, in: Europe and the Euro, pages 141-167, National Bureau of Economic Research, Inc.
    18. Cesa-Bianchi, Ambrogio & Imbs, Jean & Saleheen, Jumana, 2019. "Finance and synchronization," Journal of International Economics, Elsevier, vol. 116(C), pages 74-87.
    19. Julian di Giovanni & Andrei A. Levchenko, 2010. "Putting the Parts Together: Trade, Vertical Linkages, and Business Cycle Comovement," American Economic Journal: Macroeconomics, American Economic Association, vol. 2(2), pages 95-124, April.
    20. Michael T. Kiley, 2020. "What Can the Data Tell Us about the Equilibrium Real Interest Rate?," International Journal of Central Banking, International Journal of Central Banking, vol. 16(3), pages 181-209, June.
    21. Mark A. Wynne & Ren Zhang, 2018. "Measuring The World Natural Rate Of Interest," Economic Inquiry, Western Economic Association International, vol. 56(1), pages 530-544, January.
    22. Donald Morgan & Bertrand Rime & Philip Strahan, 2003. "Bank Integration and State Business Cycles," NBER Working Papers 9704, National Bureau of Economic Research, Inc.
    23. Clark, Todd E. & van Wincoop, Eric, 2001. "Borders and business cycles," Journal of International Economics, Elsevier, vol. 55(1), pages 59-85, October.
    24. Pierre-Olivier Gourinchas & Hélène Rey, 2019. "Global real rates: a secular approach," BIS Working Papers 793, Bank for International Settlements.
    25. Meller, Barbara & Metiu, Norbert, 2017. "The synchronization of credit cycles," Journal of Banking & Finance, Elsevier, vol. 82(C), pages 98-111.
    26. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(3), pages 361-393.
    27. Carlo A. Favero & Arie E. Gozluklu & Haoxi Yang, 2016. "Demographics and the Behavior of Interest Rates," IMF Economic Review, Palgrave Macmillan;International Monetary Fund, vol. 64(4), pages 732-776, November.
    28. John B. Taylor & Volker Wieland, 2016. "Finding the Equilibrium Real Interest Rate in a Fog of Policy Deviations," Business Economics, Palgrave Macmillan;National Association for Business Economics, vol. 51(3), pages 147-154, July.
    29. repec:zbw:bofrdp:2016_024 is not listed on IDEAS
    30. Thomas Laubach & John C. Williams, 2003. "Measuring the Natural Rate of Interest," The Review of Economics and Statistics, MIT Press, vol. 85(4), pages 1063-1070, November.
    31. Grassi Stefano & Proietti Tommaso, 2010. "Has the Volatility of U.S. Inflation Changed and How?," Journal of Time Series Econometrics, De Gruyter, vol. 2(1), pages 1-22, September.
    32. Mervyn King & David Low, 2014. "Measuring the ''World'' Real Interest Rate," NBER Working Papers 19887, National Bureau of Economic Research, Inc.
    33. Corsetti, Giancarlo & Pericoli, Marcello & Sbracia, Massimo, 2005. "'Some contagion, some interdependence': More pitfalls in tests of financial contagion," Journal of International Money and Finance, Elsevier, vol. 24(8), pages 1177-1199, December.
    34. Yunus Aksoy & Henrique S. Basso & Ron P. Smith & Tobias Grasl, 2019. "Demographic Structure and Macroeconomic Trends," American Economic Journal: Macroeconomics, American Economic Association, vol. 11(1), pages 193-222, January.
    35. Etienne Gagnon & Benjamin K. Johannsen & David López-Salido, 2021. "Understanding the New Normal: The Role of Demographics," IMF Economic Review, Palgrave Macmillan;International Monetary Fund, vol. 69(2), pages 357-390, June.
    36. Gabriele Fiorentini & Alessandro Galesi & Gabriel Pérez-Quirós & Enrique Sentana, 2018. "The rise and fall of the natural interest rate," Working Papers 1822, Banco de España.
    37. James C. Morley & Charles R. Nelson & Eric Zivot, 2003. "Why Are the Beveridge-Nelson and Unobserved-Components Decompositions of GDP So Different?," The Review of Economics and Statistics, MIT Press, vol. 85(2), pages 235-243, May.
    38. Kurt G. Lunsford & Kenneth D. West, 2019. "Some Evidence on Secular Drivers of US Safe Real Rates," American Economic Journal: Macroeconomics, American Economic Association, vol. 11(4), pages 113-139, October.
    39. Ansgar Belke & Jens Klose, 2017. "Equilibrium Real Interest Rates and Secular Stagnation: An Empirical Analysis for Euro Area Member Countries," Journal of Common Market Studies, Wiley Blackwell, vol. 55(6), pages 1221-1238, November.
    40. Hsieh, David A, 1991. "Chaos and Nonlinear Dynamics: Application to Financial Markets," Journal of Finance, American Finance Association, vol. 46(5), pages 1839-1877, December.
    41. Kara, Engin & von Thadden, Leopold, 2016. "Interest Rate Effects Of Demographic Changes In A New Keynesian Life-Cycle Framework," Macroeconomic Dynamics, Cambridge University Press, vol. 20(1), pages 120-164, January.
    42. Marco Del Negro & Domenico Giannone & Marc P. Giannoni & Andrea Tambalotti, 2017. "Safety, Liquidity, and the Natural Rate of Interest," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 48(1 (Spring), pages 235-316.
    43. Neely, Christopher J. & Rapach, David E., 2011. "International comovements in inflation rates and country characteristics," Journal of International Money and Finance, Elsevier, vol. 30(7), pages 1471-1490.
    44. Tibor Hledik & Jan Vlcek, 2018. "Quantifying the Natural Rate of Interest in a Small Open Economy - The Czech Case," Working Papers 2018/7, Czech National Bank.
    45. Krustev, Georgi, 2019. "The natural rate of interest and the financial cycle," Journal of Economic Behavior & Organization, Elsevier, vol. 162(C), pages 193-210.
    46. James D. Hamilton & Ethan S. Harris & Jan Hatzius & Kenneth D. West, 2016. "The Equilibrium Real Funds Rate: Past, Present, and Future," IMF Economic Review, Palgrave Macmillan;International Monetary Fund, vol. 64(4), pages 660-707, November.
    47. Enrico Sergio Levrero, 2021. "Estimates of the Natural Rate of Interest and the Stance of Monetary Policies: A Critical Assessment," International Journal of Political Economy, Taylor & Francis Journals, vol. 50(1), pages 5-27, February.
    48. Alan S. Blinder, 1999. "Central Banking in Theory and Practice," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262522608, April.
    49. Baxter, Marianne & Kouparitsas, Michael A., 2005. "Determinants of business cycle comovement: a robust analysis," Journal of Monetary Economics, Elsevier, vol. 52(1), pages 113-157, January.
    50. Giuseppe Ferrero & Marco Gross & Stefano Neri, 2019. "On secular stagnation and low interest rates: Demography matters," International Finance, Wiley Blackwell, vol. 22(3), pages 262-278, December.
    51. Roberto S. Mariano & Yasutomo Murasawa, 2003. "A new coincident index of business cycles based on monthly and quarterly series," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(4), pages 427-443.
    52. Klose, Jens, 2020. "Equilibrium real interest rates for the BRICS countries," The Journal of Economic Asymmetries, Elsevier, vol. 21(C).
    53. Jotikasthira, Chotibhak & Le, Anh & Lundblad, Christian, 2015. "Why do term structures in different currencies co-move?," Journal of Financial Economics, Elsevier, vol. 115(1), pages 58-83.
    54. Oscar Jorda & Sanjay R. Singh & Alan M. Taylor, 2022. "Longer-Run Economic Consequences of Pandemics," The Review of Economics and Statistics, MIT Press, vol. 104(1), pages 166-175, March.
    55. Thomas Laubach & John C. Williams, 2015. "Measuring the natural rate of interest redux," Working Paper Series 2015-16, Federal Reserve Bank of San Francisco.
    56. Clark, Todd E. & Kozicki, Sharon, 2005. "Estimating equilibrium real interest rates in real time," The North American Journal of Economics and Finance, Elsevier, vol. 16(3), pages 395-413, December.
    57. Jonathan H. Wright, 2011. "Term Premia and Inflation Uncertainty: Empirical Evidence from an International Panel Dataset," American Economic Review, American Economic Association, vol. 101(4), pages 1514-1534, June.
    58. Rhys R. Mendes, 2014. "The Neutral Rate of Interest in Canada," Discussion Papers 14-5, Bank of Canada.
    59. Probst, Julius, 2019. "Global real interest rate dynamics from the late 19th century to today," International Review of Economics & Finance, Elsevier, vol. 59(C), pages 522-547.
    60. Blonigen, Bruce A. & Piger, Jeremy & Sly, Nicholas, 2014. "Comovement in GDP trends and cycles among trading partners," Journal of International Economics, Elsevier, vol. 94(2), pages 239-247.
    61. Dahlquist, Magnus & Hasseltoft, Henrik, 2013. "International Bond Risk Premia," Journal of International Economics, Elsevier, vol. 90(1), pages 17-32.
    62. Beyer, Robert C.M. & Wieland, Volker, 2019. "Instability, imprecision and inconsistent use of equilibrium real interest rate estimates," Journal of International Money and Finance, Elsevier, vol. 94(C), pages 1-14.
    63. FUJITA Shigeru & FUJIWARA Ippei, 2015. "Declining Trends in the Real Interest Rate and Inflation: Role of aging," Discussion papers 15140, Research Institute of Economy, Trade and Industry (RIETI).
    64. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-856, July.
    65. Chan, Joshua C.C. & Grant, Angelia L., 2016. "Modeling energy price dynamics: GARCH versus stochastic volatility," Energy Economics, Elsevier, vol. 54(C), pages 182-189.
    66. Kulish, Mariano & Rees, Daniel, 2011. "The yield curve in a small open economy," Journal of International Economics, Elsevier, vol. 85(2), pages 268-279.
    67. Jens H. E. Christensen & Glenn D. Rudebusch, 2017. "New Evidence for a Lower New Normal in Interest Rates," FRBSF Economic Letter, Federal Reserve Bank of San Francisco.
    68. Julien Garnier & Bjørn-Roger Wilhelmsen, 2009. "The natural rate of interest and the output gap in the euro area: a joint estimation," Empirical Economics, Springer, vol. 36(2), pages 297-319, May.
    69. Donald P. Morgan & Bertrand Rime & Philip E. Strahan, 2004. "Bank Integration and State Business Cycles," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 119(4), pages 1555-1584.
    70. Jacquier, Eric & Polson, Nicholas G. & Rossi, P.E.Peter E., 2004. "Bayesian analysis of stochastic volatility models with fat-tails and correlated errors," Journal of Econometrics, Elsevier, vol. 122(1), pages 185-212, September.
    71. Brand, Claus & Bielecki, Marcin & Penalver, Adrian, 2018. "The natural rate of interest: estimates, drivers, and challenges to monetary policy JEL Classification: E52, E43," Occasional Paper Series 217, European Central Bank.
    72. Lawrence H Summers, 2014. "U.S. Economic Prospects: Secular Stagnation, Hysteresis, and the Zero Lower Bound," Business Economics, Palgrave Macmillan;National Association for Business Economics, vol. 49(2), pages 65-73, April.
    73. J. Bradford DeLong & Lawrence H. Summers, 2012. "Fiscal Policy in a Depressed Economy," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 43(1 (Spring), pages 233-297.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. repec:zbw:bofrdp:2022_007 is not listed on IDEAS
    2. Ambrocio, Gene & Ferrero, Andrea & Jokivuolle, Esa & Ristolainen, Kim, 2022. "What Should the Inflation Target Be? Views from 600 Economists," CEPR Discussion Papers 17289, C.E.P.R. Discussion Papers.
    3. Ruch,Franz Ulrich, 2021. "Neutral Real Interest Rates in Inflation Targeting Emerging and Developing Economies," Policy Research Working Paper Series 9711, The World Bank.
    4. Yudai Hatayama & Yuto Iwasaki & Kyoko Nakagami & Tatsuyoshi Okimoto, 2024. "Globalization and Its Growing Impact on the Natural Rates of Interest in Developed Economies," Bank of Japan Working Paper Series 24-E-13, Bank of Japan.
    5. Ambrocio, Gene & Ferrero, Andrea & Jokivuolle, Esa & Ristolainen, Kim, 2022. "What Should the Inflation Target Be? Views from 600 Economists," CEPR Discussion Papers 17289, C.E.P.R. Discussion Papers.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Brand, Claus & Bielecki, Marcin & Penalver, Adrian, 2018. "The natural rate of interest: estimates, drivers, and challenges to monetary policy JEL Classification: E52, E43," Occasional Paper Series 217, European Central Bank.
    2. Gabriele Fiorentini & Alessandro Galesi & Gabriel Pérez-Quirós & Enrique Sentana, 2018. "The rise and fall of the natural interest rate," Working Papers 1822, Banco de España.
    3. Del Negro, Marco & Giannone, Domenico & Giannoni, Marc P. & Tambalotti, Andrea, 2019. "Global trends in interest rates," Journal of International Economics, Elsevier, vol. 118(C), pages 248-262.
    4. Jens H. E. Christensen & Glenn D. Rudebusch, 2019. "A New Normal for Interest Rates? Evidence from Inflation-Indexed Debt," The Review of Economics and Statistics, MIT Press, vol. 101(5), pages 933-949, December.
    5. Marx, Magali & Mojon, Benoît & Velde, François R., 2021. "Why have interest rates fallen far below the return on capital?," Journal of Monetary Economics, Elsevier, vol. 124(S), pages 57-76.
    6. Zhang, Ren & Martínez-García, Enrique & Wynne, Mark A. & Grossman, Valerie, 2021. "Ties that bind: Estimating the natural rate of interest for small open economies," Journal of International Money and Finance, Elsevier, vol. 113(C).
    7. Fiedler, Salomon & Gern, Klaus-Jürgen & Jannsen, Nils & Wolters, Maik H., 2019. "Growth prospects, the natural interest rate, and monetary policy," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 13, pages 1-34.
    8. COMUNALE Mariarosaria & STRIAUKAS Jonas, 2017. "Unconventional monetary olicy: interest rates and low inflation. A review of literature and methods," LIDAM Discussion Papers CORE 2017026, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    9. Michael D. Bauer & Glenn D. Rudebusch, 2020. "Interest Rates under Falling Stars," American Economic Review, American Economic Association, vol. 110(5), pages 1316-1354, May.
    10. Holston, Kathryn & Laubach, Thomas & Williams, John C., 2017. "Measuring the natural rate of interest: International trends and determinants," Journal of International Economics, Elsevier, vol. 108(S1), pages 59-75.
    11. Guihai Zhao, 2020. "Learning, Equilibrium Trend, Cycle, and Spread in Bond Yields," Staff Working Papers 20-14, Bank of Canada.
    12. Brand, Claus & Goy, Gavin W & Lemke, Wolfgang, 2020. "Natural rate chimera and bond pricing reality," VfS Annual Conference 2020 (Virtual Conference): Gender Economics 224546, Verein für Socialpolitik / German Economic Association.
    13. Michael D. Bauer & Glenn D. Rudebusch, 2023. "The Rising Cost of Climate Change: Evidence from the Bond Market," The Review of Economics and Statistics, MIT Press, vol. 105(5), pages 1255-1270, September.
    14. Marco Del Negro & Domenico Giannone & Marc P. Giannoni & Andrea Tambalotti, 2017. "Safety, Liquidity, and the Natural Rate of Interest," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 48(1 (Spring), pages 235-316.
    15. Kurt G. Lunsford & Kenneth D. West, 2019. "Some Evidence on Secular Drivers of US Safe Real Rates," American Economic Journal: Macroeconomics, American Economic Association, vol. 11(4), pages 113-139, October.
    16. Krustev, Georgi, 2019. "The natural rate of interest and the financial cycle," Journal of Economic Behavior & Organization, Elsevier, vol. 162(C), pages 193-210.
    17. Claudio Borio & Piti Disyatat & Phurichai Rungcharoenkitkul, 2018. "What Anchors for the Natural Rate of Interest?," PIER Discussion Papers 98, Puey Ungphakorn Institute for Economic Research.
    18. Belke, Ansgar & Klose, Jens, 2020. "Equilibrium real interest rates and the financial cycle: Empirical evidence for Euro area member countries," Economic Modelling, Elsevier, vol. 84(C), pages 357-366.
    19. Bielecki, Marcin & Brzoza-Brzezina, Michał & Kolasa, Marcin, 2020. "Demographics and the natural interest rate in the euro area," European Economic Review, Elsevier, vol. 129(C).
    20. Brand, Claus & Goy, Gavin W & Lemke, Wolfgang, 2020. "Natural rate chimera and bond pricing reality," VfS Annual Conference 2020 (Virtual Conference): Gender Economics 224546, Verein für Socialpolitik / German Economic Association.

    More about this item

    Keywords

    equilibrium interest rate; stochastic volatility; Bayesian inference; synchronization;
    All these keywords.

    JEL classification:

    • E52 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Monetary Policy
    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:zbw:imfswp:146. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ZBW - Leibniz Information Centre for Economics (email available below). General contact details of provider: https://edirc.repec.org/data/hoffmde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.