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A Calibration of the Shadow Rate to the Euro Area Using Genetic Algorithms 6 ISBN 2443-8022 (online) A Calibration of the Shadow Rate to the Euro Area Using Genetic Algorithms Eric McCoy and Ulrich Clemens DISCUSSION PAPER 051 | JULY 2017 EUROPEAN ECONOMY Economic and EUROPEAN Financial Affairs ECONOMY European Economy Discussion Papers are written by the staff of the European Commission’s Directorate-General for Economic and Financial Affairs, or by experts working in association with them, to inform discussion on economic policy and to stimulate debate. The views expressed in this document are solely those of the author(s) and do not necessarily represent the official views of the European Commission. Authorised for publication by Lucio Pench, Director for Fiscal Policy and Policy Mix. LEGAL NOTICE Neither the European Commission nor any person acting on its behalf may be held responsible for the use which may be made of the information contained in this publication, or for any errors which, despite careful preparation and checking, may appear. This paper exists in English only and can be downloaded from https://ec.europa.eu/info/publications/economic-and-financial-affairs-publications_en. Europe Direct is a service to help you find answers to your questions about the European Union. Freephone number (*): 00 800 6 7 8 9 10 11 (*) The information given is free, as are most calls (though some operators, phone boxes or hotels may charge you). More information on the European Union is available on http://europa.eu. Luxembourg: Publications Office of the European Union, 2017 KC-BD-17-051-EN-N (online) KC-BD-17-051-EN-C (print) ISBN 978-92-79- 64893-9 (online) ISBN 978-92-79-64894-6 (print) doi:10.2765/457704 (online) doi:10.2765/505287 (print) © European Union, 2017 Reproduction is authorised provided the source is acknowledged. For any use or reproduction of photos or other material that is not under the EU copyright, permission must be sought directly from the copyright holders. European Commission Directorate-General for Economic and Financial Affairs A Calibration of the Shadow Rate to the Euro Area Using Genetic Algorithms Eric McCoy, Ulrich Clemens Abstract In the face of the lower bound on interest rates, central banks have relied on unconventional policy tools such as large-scale asset purchases and forward guidance to try to affect long-term interest rates and provide monetary stimulus to the economy. Assessing the impact of these measures and summarising the overall stance of monetary policy in this new environment has proven to be a challenge for academics and central banks. As a result, researchers have worked on modifying current term structure models and have adapted them to the current situation of close to zero or even negative interest rates. The paper begins by providing a non-technical overview of Leo Krippner's two-factor shadow rate model (K-ANSM2), explaining the underlying mechanics of the model through an illustrative example. Thereafter, the paper presents the results obtained from calibrating Krippner's K- ANSM2 shadow rate model to the euro area using genetic algorithms and discusses the pros and the cons of using genetic algorithms as an alternative to the optimisation method currently used (Nelder- Mead optimisation routine). Finally, the paper ends by analysing the strengths and weaknesses of using the shadow short rate as a tool to illustrate the stance and the dynamics of monetary policy. JEL Classification: E43, E44, E52, E58. Keywords: Monetary Policy, Shadow Rates, Genetic Algorithms, Zero Lower Bound. Acknowledgements: We would like to thank Eric Ruscher, Luis Sebastian Fau, Paul Kutos, Anton Jevcak and Lucian Briciu for their helpful comments and feedback on the paper. In addition, we are very grateful to Leo Krippner for the help he provided in answering various technical questions. Contact: Eric McCoy, European Commission, Directorate-General for Economic and Financial Affairs, [email protected], Ulrich Clemens, European Commission, Directorate-General for Economic and Financial Affairs, [email protected]. EUROPEAN ECONOMY Discussion Paper 051 CONTENTS 1. Introduction ..................................................................................................................................... 3 2. A non-technical overview of the shadow rate ......................................................................... 5 3. Calibrating the shadow rate model .......................................................................................... 12 3.1 The calibration dataset 12 3.2 The calibration algorithm 13 4. Empirical results for the Euro Area.............................................................................................. 16 5. The shadow rate as a measure of the monetary policy stance........................................... 20 6. Conclusion .................................................................................................................................... 24 7. Technical annex ........................................................................................................................... 24 7.1 A term structure-based shadow rate 24 7.2 Calibrating shadow rate models 26 7.3 The optimisation algorithm 28 8. REFERENCES ................................................................................................................................... 29 2 1. INTRODUCTION Traditionally, the most important indicator for a central bank's monetary policy stance is the policy rate. As such, it can be assessed against historical or normative benchmarks such as the Taylor rule to gauge the appropriateness of the level of monetary policy accommodation. The convergence of policy rates towards a lower bound that is assumed to be close to zero or even in negative territory in combination with the adoption of unconventional measures targeting the longer end of the yield curve (e.g. large scale asset purchases or various forms of forward guidance on the expected policy rate path), however, have impaired the function of policy rates as a summary indicator of a central bank's monetary policy stance. In light of this, alternative measures of the central bank's policy stance that can help quantify those monetary stimulus measures that go beyond steering the policy rates have been proposed. For example, the size of the central bank balance sheet should reflect quantitative easing measures, but cannot capture policy measures that are targeted at influencing markets' expectations regarding future policy rates and announcement effects.1 By contrast, measures built on financial market prices can capture those expectation effects. To capture the monetary policy induced flattening of the yield curve, for instance one can simply look at the spread between long- and short-term market rates. Nevertheless, this rather rough measure does not provide a continuous stance measure that reflects monetary policy in both a conventional and unconventional environment. Alternatively, monetary conditions indices (MCI), which typically combine information on real interest rates and exchange rates, can be calculated. However, the inclusion of variables such as the exchange rate implies that the MCI can be substantially driven by factors outside the control of the central bank, for example foreign central banks' monetary policies. Lastly, and most prominently, term structure-based shadow short rate (SSR) models such as the one presented here have been proposed to capture monetary policy at the lower bound.2 The advantages and disadvantages of this particular measure of the monetary policy stance are discussed in the following sections. Term structure modelling used to be rather straightforward in the non-zero lower bound (ZLB) economic context that prevailed before the global financial crisis. In fact, Gaussian affine term structure models (GATSMs), including the popular subclass of arbitrage-free Nelson and Siegel models (ANSM), were widely favoured by many academics, researchers, central bankers and private- sector practitioners. Notwithstanding their popularity and widespread use, GATSMs have one well- acknowledged downside which was deemed small relative to their benefits in the pre-crisis period. That is, the mathematical specifications underlying the stochastic process for the short rate imply non- zero probabilities of interest rates of any maturity evolving to negative values. However, allowing for interest rates to evolve to negative levels in a GATSM model becomes untenable in a ZLB environment as the model would no longer fit the observed market yield curve (which is constrained by the ZLB). Therefore, the market-calibrated GATSM cannot provide anymore a valid representation of the term structure and its dynamics. Recently developed models for the shadow rate offer a solution in the sense that on the one hand the Gaussian diffusion process for the “shadow” short rate can freely adopt negative values, while on the other hand the “ZLB” short rate diffusion process will remain constrained by the “lower bound”. These academic developments are essential, as there is no longer a misspecification of the model relative to the data being modeled (i.e. the observed market yield curve) and at the same time by virtue of the fact that the SSR can take on negative values, the dynamics of the shadow short rate can now reflect the effects of non-standard monetary policy measures (like the asset purchase programmes as well as 1 Furthermore, the mapping from the central banks' balance sheet size to market prices and interest rates is uncertain
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