Optimal Monetary Policy without IS equation

fr3421 · March 31, 2024, 12:06pm

Hi Forum,

when dealing with optimal monetary policy, central banker does not consider IS equation both under discretion and commitment? In most cases I see the following form,

\min \; \pi_t^2 + \nu x_t^2 s.t. \pi_t = \beta \mathbb{E}_t \pi_{t+1} + \kappa x_t

but no IS equation. Can someone please explain why? thanks a lot.

jpfeifer · April 1, 2024, 2:37pm

Do you have an example? It’s not true for e.g.

github.com

JohannesPfeifer/DSGE_mod/blob/master/Gali_2015/Gali_2015_chapter_5_discretion.mod

/*
 * This file implements the optimal monetary policy under discretion exercise 
 * in Jordi Gal� (2015): Monetary Policy, Inflation, and the Business Cycle, 
 * Princeton University Press, Second Edition, Chapter 5.2.1
 *
 * It demonstrates how to use the discretionary_policy command of Dynare.
 *
 *  THIS MOD-FILE REQUIRES DYNARE 4.5 OR HIGHER
 *
 * Notes:
 *      - all model variables are expressed in deviations from steady state, i.e. 
 *        in contrast to to the chapter, both the nominal interest rate and 
 *        natural output are not in log-levels, but rather mean 0
 *      - discretionary policy computes the optimal interest rate under discretion; 
 *        the mod-file has the optimal analytical rule commented out as the last 
 *        equation. Commenting it in allows using stoch_simul to generate the same
 *        IRFs
 *      - This file replicates the IRFs reported in Figures 5.1 and 5.2
 *      - Note that the output response under discretion in Figures 5.1 and 5.2 in the 
 *          book is wrong, while the one computed by the mod-file is correct. This can be

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fr3421 · April 1, 2024, 2:51pm

I am referring to Gali’s textbook (2nd edition) example of 5.2.1 and 5.2.2. The optimal conditions are derived without IS equations as one of the constraints.

jpfeifer · April 1, 2024, 3:09pm

As documented in the book further down below, the DIS equation is an implementability constraint. It describes how agents react to interest rates with their consumption. In the basic planner’s problem, the planner simply chooses consumption. Hence, the DIS equation is not needed.

fr3421 · April 1, 2024, 3:47pm

Thank you very much Prof. Pfeifer