Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Studies in Nonlinear Dynamics & Econometrics

Ed. by Mizrach, Bruce

IMPACT FACTOR 2018: 0.448
5-years IMPACT FACTOR: 0.877

CiteScore 2018: 0.85

SCImago Journal Rank (SJR) 2018: 0.552
Source Normalized Impact per Paper (SNIP) 2018: 0.561

Mathematical Citation Quotient (MCQ) 2018: 0.07

See all formats and pricing
More options …
Ahead of print


Volume 24 (2020)

Constrained interest rates and changing dynamics at the zero lower bound

Gregor Bäurle / Daniel KaufmannORCID iD: https://orcid.org/0000-0003-3260-0660 / Sylvia Kaufmann / Rodney Strachan
Published Online: 2019-06-28 | DOI: https://doi.org/10.1515/snde-2017-0098


The interaction of macroeconomic variables may change as nominal short-term interest rates approach zero. In this paper, we propose to capture these changing dynamics with a state-switching parameter model which explicitly takes into account that the interest rate might be constrained near the zero lower bound by using a Tobit model. The probability of state transitions is affected by the lagged level of the interest rate. The endogenous specification of the state indicator permits dynamic conditional forecasts of the state and the system variables. We use Bayesian methods to estimate the model and to derive the forecast densities. In an application to Swiss data, we evaluate state-dependent impulse-responses to a risk premium shock identified with sign-restrictions. We provide an estimate of the latent rate, i.e. the rate lower than the constraint on the interest rate level which would be state- and model-consistent. Additionally, we discuss scenario-based forecasts and evaluate the probability of exiting the ZLB region. In terms of log predictive scores and the Bayesian information criterion, the model outperforms a model substituting switching with stochastic volatility and another including intercept switching only combined with stochastic volatility.

This article offers supplementary material which is provided at the end of the article.

Keywords: constrained variable; regime switching; stochastic volatility; time-varying probability; Tobit model

JEL Classification: C3; E3


  • Arias, J. E., J. F. Rubio-Ramírez, and D. F. Waggoner. 2018. “Inference Based on Structural Vector Autoregressions Identified with Sign and Zero Restrictions: Theory and Applications.” Econometrica 86: 685–720.CrossrefWeb of ScienceGoogle Scholar

  • Auerbach, A. J., and M. Obstfeld. 2005. “The Case for Open-Market Purchases in a Liquidity Trap.” The American Economic Review 95: 110–137.CrossrefGoogle Scholar

  • Auerbach, A. J., and Y. Gorodnichenko. 2012. “Measuring the Output Responses to Fiscal Policy.” American Economic Journal: Economic Policy 4: 1–27.Web of ScienceGoogle Scholar

  • Bańbura, M., D. Giannone, and L. Reichlin. 2010. “Large Bayesian Vector Auto Regressions.” Journal of Applied Econometrics 25: 71–92.Web of ScienceCrossrefGoogle Scholar

  • Bauer, M. D., and G. D. Rudebusch. 2016. “Monetary Policy Expectations at the Zero Lower Bound.” Journal of Money, Credit and Banking 48: 1439–1465.CrossrefWeb of ScienceGoogle Scholar

  • Baumeister, C., and L. Benati. 2013. “Unconventional Monetary Policy and the Great Recession: Estimating the Macroeconomic Effects of a Spread Compression at the Zero Lower Bound.” International Journal of Central Banking 9: 165–212.Google Scholar

  • Bäurle, G., and D. Kaufmann. 2018. “Measuring Exchange Rate, Price, and Output Dynamics at the Effective Lower Bound.” Oxford Bulletin of Economics and Statistics 80: 1243–1266.CrossrefWeb of ScienceGoogle Scholar

  • Belmonte, M., G. Koop, and D. Korobilis. 2014. “Hierarchical Shrinkage in Time-Varying Parameter Models.” Journal of Forecasting 33: 80–94.Web of ScienceCrossrefGoogle Scholar

  • Benhabib, J., S. Schmitt-Grohe, and M. Uribe. 2002. “Avoiding Liquidity Traps.” Journal of Political Economy 110: 535–563.CrossrefGoogle Scholar

  • Botev, Z. 2017. “The Normal Law Under Linear Restrictions: Simulation and Estimation via Minimax Tilting.” Journal of the Royal Statistical Society, Series B 79: 125–148.Web of ScienceCrossrefGoogle Scholar

  • Caggiano, G., E. Castelnuovo, and G. Pellegrino. 2017. “Estimating the Real Effects of Uncertainty Shocks at the Zero Lower Bound.” European Economic Review 100: 257–272.CrossrefWeb of ScienceGoogle Scholar

  • Chan, J. C. C., and E. Eisenstat. 2018. “Bayesian Model Comparison for Time-Varying Parameter VARs with Stochastic Volatility.” Journal of Applied Econometrics 33: 509–532.CrossrefWeb of ScienceGoogle Scholar

  • Chib, S. 1992. “Bayesian Analysis in the Tobit Censored Regression Model.” Journal of Econometrics 51: 79–99.CrossrefGoogle Scholar

  • Christensen, J. H., and G. D. Rudebusch. 2016. “Modeling Yields at the Zero Lower Bound: Are Shadow Rates the Solution?” In Dynamic Factor Models (Advances in Econometrics), edited by E. Hillebrand and S. J. Koopman, Vol. 35, 75–125. Howard House, Wagon Lane, Bingley BD16 1WA, UK: Emerald Group Publishing Limited.Google Scholar

  • Clark, T. E. 2011. “Real-Time Density Forecasts from Bayesian Vector Autoregressions with Stochastic Volatility.” Journal of Business & Economic Statistics 29: 327–341.Web of ScienceCrossrefGoogle Scholar

  • Debortoli, D., J. Galí, and L. Gambetti. 2018. “On the Empirical (Ir)relevance of the Zero Lower Bound Constraint.” Economics Working Papers 1594, Department of Economics and Business, Universitat Pompeu Fabra.Google Scholar

  • Diebold, F. X., F. Schorfheide, and M. Shin. 2017. “Real-Time Forecast Evaluation of DSGE Models with Stochastic Volatility.” In Theoretical and Financial Econometrics: Essays in Honor of C. Gourieroux, edited by S. Darolles, E. Renault, and A. Monfort, 322–332. Journal of Econometrics 201, Special issue.Google Scholar

  • Doan, T., R. Litterman, and C. A. Sims. 1984. “Forecasting and Conditional Projection Using Realistic Prior Distributions.” Econometric Reviews 3: 1–100.CrossrefGoogle Scholar

  • Eggertsson, G. B., and M. Woodford. 2003. “The Zero Bound on Interest Rates and Optimal Monetary Policy.” Brookings Papers on Economic Activity 34: 139–235.Google Scholar

  • Eggertsson, G. B., M. Woodford, T. Einarsson, and E. M. Leeper. 2004. “Optimal Monetary and Fiscal Policy in a Liquidity Trap (with Comments).” NBER International Seminar on Macroeconomics 1: 75–144.Google Scholar

  • Frühwirth-Schnatter, S., and R. Frühwirth. 2010. “Data Augmentation and MCMC for Binary and Multinomial Logit Models.” In Statistical Modelling and Regression Structures – Festschrift in Honour of Ludwig Fahrmeir, edited by T. Kneib and G. Tutz, 111–132. Heidelberg: Physica-Verlag.Google Scholar

  • Galí, J. and T. Monacelli. 2005. “Monetary Policy and Exchange Rate Volatility in a Small Open Economy.” Review of Economic Studies 72: 707–734.CrossrefGoogle Scholar

  • Gust, C. J., J. D. Lopez-Salido, M. E. Smith, and E. Herbst. 2017. “The Empirical Implications of the Interest-Rate Lower Bound.” American Economic Review 107: 1971–2006.Web of ScienceCrossrefGoogle Scholar

  • Iwata, S., and S. Wu. 2006. “Estimating Monetary Policy Effects when Interest Rates are Close to Zero.” Journal of Monetary Economics 53: 1395–1408.CrossrefGoogle Scholar

  • Jordan, T. 2009. “Die Geldpolitik der Schweizerischen Nationalbank in stürmischen Zeiten.” Speech on 19 March, Swiss National Bank.Google Scholar

  • Kaufmann, S. 2015. “K-state Switching Models with Time-Varying Transition Distributions – Does Loan Growth Signal Stronger Effects of Variables on Inflation?” Journal of Econometrics 187: 82–94.Web of ScienceGoogle Scholar

  • Kimura, T., and J. Nakajima. 2016. “Identifying Conventional and Unconventional Monetary Policy Shocks: A Latent Threshold Approach.” The B.E. Journal of Macroeconomics 16: 277–300.Google Scholar

  • Krippner, L. 2015. Zero Lower Bound Term Structure Modeling. New York: Palgrave Macmillan.Google Scholar

  • Lopes, H. F., and E. Salazar. 2005. “Bayesian Model Uncertainty in Smooth Transition Autoregressions.” Journal of Time Series Analysis 27: 99–117.Google Scholar

  • Miyao, R. 2002. “The Effects of Monetary Policy in Japan.” Journal of Money Credit and Banking 34: 376–392.CrossrefGoogle Scholar

  • Nakajima, J. 2011. “Monetary Policy Transmission Under Zero Interest Rates: An Extended Time-Varying Parameter Vector Autoregression Approach.” The B.E. Journal of Macroeconomics 11: 1–24.Google Scholar

  • Plante, M., A. W. Richter, and N. A. Throckmorton. 2018. “The Zero Lower Bound and Endogenous Uncertainty.” The Economic Journal 128: 1730–1757.CrossrefGoogle Scholar

  • Reifschneider, D., and J. C. Williams. 2000. “Three Lessons for Monetary Policy in a Low-Inflation Era.” Journal of Money, Credit and Banking 32: 936–966.CrossrefGoogle Scholar

  • Robert, C. P. 2009. “Simulation of Truncated Normal Variables.” arxiv:0907.4010v1 [stat.co], LSTA, Université Pierre et Marie Curie, Paris.Google Scholar

  • Schenkelberg, H., and S. Watzka. 2013. “Real Effects of Quantitative Easing at the Zero Lower Bound: Structural VAR-Based Evidence from Japan.” Journal of International Money and Finance 33: 327–357.CrossrefWeb of ScienceGoogle Scholar

  • SNB. 2003. “Swiss National Bank Lowers the Target Range for the Three-Month Libor Rate by 0.5 Percentage Points to 0%–0.75%.” Press release on 6 March, Swiss National Bank.Google Scholar

  • SNB. 2009. “Swiss National Bank Takes Decisive Action to Forcefully Relax Monetary Conditions.” Monetary policy assessment on 12 March, Swiss National Bank.Google Scholar

  • SNB. 2011. “Die Nationalbank Trifft Massnahmen Gegen den Starken Franken.” Press release on 3 August, Swiss National Bank.Google Scholar

  • Swanson, E. T., and J. C. Williams. 2014a. “Measuring the Effect of the Zero Lower Bound on Medium- and Longer-Term Interest Rates.” The American Economic Review 104: 3154–3185.CrossrefGoogle Scholar

  • Swanson, E. T., and J. C. Williams. 2014b. “Measuring the Effect of the Zero Lower Bound on Yields and Exchange Rates in the U.K. and Germany.” Journal of International Economics 92: S2–S21.CrossrefWeb of ScienceGoogle Scholar

  • Teräsvirta, T., and H. M. Anderson. 1992. “Characterizing Nonlinearities in Business Cycles Using Smooth Transition Autoregressive Models.” Journal of Applied Econometrics 7: S119–S136.CrossrefGoogle Scholar

  • Woodford, M. 2003. Interest and Prices: Foundations of a Theory of Monetary Policy. Princeton: Princeton University Press.Google Scholar

  • Wright, J. H. 2012. “What does Monetary Policy do to Long-Term Interest Rates at the Zero Lower Bound?” The Economic Journal 122: F447–F466.Web of ScienceGoogle Scholar

  • Wu, J. S., and F. D. Xia. 2016. “Measuring the Macroeconomic Impact of Monetary Policy at the Zero Lower Bound.” Journal of Money Credit and Banking 48: 253–291.CrossrefWeb of ScienceGoogle Scholar

About the article

Published Online: 2019-06-28

Citation Information: Studies in Nonlinear Dynamics & Econometrics, 20170098, ISSN (Online) 1558-3708, DOI: https://doi.org/10.1515/snde-2017-0098.

Export Citation

© 2019 Walter de Gruyter GmbH, Berlin/Boston.Get Permission

Supplementary Article Materials

Comments (0)

Please log in or register to comment.
Log in