Constrained interest rates and changing dynamics at the zero lower bound

Gregor Bäurle, Daniel KaufmannORCID iD:, Sylvia Kaufmann and Rodney Strachan


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.

    • Supplementary Material
  • 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.

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

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

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

  • 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.

  • 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.

  • 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.

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

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

  • 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.

  • 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.

  • 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.

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

  • 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.

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

  • 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.

  • 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.

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

  • 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.

  • 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.

  • 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.

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

  • 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.

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

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

  • 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.

  • 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.

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

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

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

  • 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.

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

  • 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.

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

  • 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.

  • 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.

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

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

  • 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.

  • 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.

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

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

  • 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.

  • 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.

Purchase article
Get instant unlimited access to the article.
Price including VAT
Log in
Already have access? Please log in.

Journal + Issues

SNDE recognizes that advances in statistics and dynamical systems theory can increase our understanding of economic and financial markets. The journal seeks both theoretical and applied papers that characterize and motivate nonlinear phenomena. Researchers are required to assist replication of empirical results by providing copies of data and programs online. Algorithms and rapid communications are also published.