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The Zero Lower Bound: Frequency, Duration, and Numerical Convergence

The B.E. Journal of Macroeconomics, Vol. 15, Issue 1, 2015

20 Pages Posted: 24 Dec 2013 Last revised: 29 Jun 2015

Alexander W. Richter

Federal Reserve Bank of Dallas

Nathaniel A. Throckmorton

College of William and Mary

Date Written: April 19, 2014

Abstract

When monetary policy faces a zero lower bound (ZLB) constraint on the nominal interest rate, a minimum state variable (MSV) solution may not exist even if the Taylor principle holds when the ZLB does not bind. This paper shows there is a clear tradeoff between the expected frequency and average duration of ZLB events along the boundary of the convergence region --- the region of the parameter space where our policy function iteration algorithm converges to an MSV solution. We show this tradeoff with two alternative stochastic processes: one where monetary policy follows a 2-state Markov chain, which exogenously governs whether the ZLB binds, and the other where ZLB events are endogenous due to discount factor or technology shocks. We also show that small changes in the parameters of the stochastic processes cause meaningful differences in the decision rules and where the ZLB binds in the state space.

Keywords: Monetary policy; zero lower bound; convergence; minimum state variable solution; policy function iteration

JEL Classification: E31, E42, E58

Suggested Citation

Richter, Alexander W. and Throckmorton, Nathaniel A., The Zero Lower Bound: Frequency, Duration, and Numerical Convergence (April 19, 2014). The B.E. Journal of Macroeconomics, Vol. 15, Issue 1, 2015. Available at SSRN: https://ssrn.com/abstract=2371722 or http://dx.doi.org/10.2139/ssrn.2371722

Alexander W. Richter (Contact Author)

Federal Reserve Bank of Dallas ( email )

2200 North Pearl Street
PO Box 655906
Dallas, TX 75265-5906
United States
214-922-5360 (Phone)

HOME PAGE: http://alexrichterecon.com

Nathaniel A. Throckmorton

College of William and Mary ( email )

P.O. Box 8795
Williamsburg, VA 23187
United States

HOME PAGE: http://nathrockmorton.people.wm.edu/

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