Zero lower bound

mmalmi · February 2, 2021, 3:25pm

Hi everyone,
I am trying to run a Zero Lower Bound constraint in a new keynesian model and I have found so many versions and algorithms that I do not know what ZLB code is more appropriate for a normal NK model in dynare.
Thank you very much for your help.
María

Max1 · February 2, 2021, 5:09pm

Hi mmalmi,

there are two different approaches to implement the ZLB in the literature.

Some papers implement it as a perfect foresight simulation.
Other papers implement it as an occasionally binding constraint (OccBin).

For the OccBin approach there are two algorithms which are more popular.
One is from Tom Holden and the other is from Guerrieri & Iacoviello (2015).
The latter is simpler and more useful for beginners, but less powerful.

mmalmi · February 2, 2021, 5:32pm

Thank you Max1 for your reply. And could you provide any example of papers or codes that implement it as a perfect foresight simulation.
Thanks once more for you help!

Max1 · February 2, 2021, 7:09pm

You should have a look at Johannes homepage and GitHub page.

There you can find examples like this one:

github.com

JohannesPfeifer/DSGE_mod/blob/master/Gali_2015/Gali_2015_chapter_5_commitment_ZLB.mod

/*
 * This file implements the optimal monetary policy at the ZLB under commitment exercise 
 * in Jordi Gal� (2015): Monetary Policy, Inflation, and the Business Cycle, 
 * Princeton University Press, Second Edition, Chapter 5.4.2
 *
 * THIS MOD-FILE REQUIRES DYNARE 4.5 OR HIGHER
 *
 * Notes:
 *  - This mod-file makes use of the Levenberg-Marquardt mixed complementarity problem (lmmcp)
 *      approach to deal with the ZLB constraint. For this purpose, the Lagrangian is written to 
 *      include the instrument i (in contrast to Gali's setup where he uses a inequality constraint obtained 
 *      by substituting out i). I.e. we have
 *      \[
 *          L = \sum\limits_{t = 0}^\infty \beta ^t \left[ \frac{1}{2}\left(\pi_t^2 + \theta x_t^2 \right) + \xi_{1,t}\left(\pi_t - \kappa x_t - \beta \pi_{t+1} \right) 
 *              + \xi_{2,t}\left(x_t - x_{t+1} + \frac{1}{\sigma}\left(i_t - \pi_{t+1} - r_t^n} \right) \right) \right] 
 *      \]
 *      which gives rise to the FOC
 *      \[
 *          \xi_{2,t}\frac{1}{\sigma} = 0
 *      \]

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