New Keynesian Model: Optimal Policy in Dynare
Channel: Willi Mutschler
Date: 2021-06-18

This video is part of a series on the baseline New Keynesian model and its implementation in Dynare. In this video I focus on Optimal Policy and discuss concepts like the Divine Coincidence, Indeterminacy, Taylor Principle, Optimal Policy under Commitment, Optimal Policy under Discretion, Simple Implementable Rules and how to compare different policy regimes. Even though this video provides some insight on the theory behind these concepts, I try to not get caught up in the details, but focus mainly on the implementation aspects in Dynare.

Slides, notes and codes: https://mutschler.eu/dynare/optimal-policy/nk_video_optimal_policy/

**Timestamps**

*Optimal Policy in Baseline New Keynesian Model*
01:42 - Why are DSGE models useful to think about optimal policy?
02:43 - Two sources of distortions in canonical New Keynesian Model
05:05 - Definitions: Efficient vs natural output
05:59 - Characterization of Optimal Policy
08:16 - Divine Coincidence

*Implementing Optimal Policy in Baseline New Keynesian Model with simple rules*
09:36 - Exogenous one-for-one rule yields indeterminacy
10:30 - Dynare Implementation: Setting up optimal rules
12:46 - Dynare Implementation: One-For-One rule with indeterminacy
13:52 - Optimal rule with feedback to target variables
14:20 - Taylor Principle
15:05 - Dynare Implementation: Optimal simple rule with feedback to target variables
17:37 Dynare Implementation: Visualizing Taylor principle determinacy region using `dynare_sensitivity`
22:15 - Summary Optimal Simple Rules and Divine Coincidence

*Policy Trade-Offs and Breaking Divine Coincidence*
22:46 - Policy Trade-Offs, Commitment vs Discretion
24:55 - Farewell Divine Coincidence: combining real frictions with nominal rigidities
25:48 - Adding cost-push shock to Basic New Keynesian Model
28:18 - Ramsey Optimal Policy

*Optimal Policy Under Commitment*
30:12 - Theory
31:11 - Dynare Commands
34:59 - Dynare Implementation: Adding cost-push shock to baseline New Keynesian Model
37:46 - Dynare Implementation: Prepare optimal Policy under Commitment
38:01 - Dynare Implementation: Response to transitory cost-push shock
38:27 - Dynare Implementation: `planner_objective`
38:55 - Dynare Implementation: update parameters of objective function in `steady_state_model` block
39:36 - Dynare Implementation: `ramsey_model`
39:59 - Dynare Implementation: `evaluate_planner_objective`
40:33 - Dynare Implementation: Response to persistent cost-push shock under commitment

*Optimal Policy Under Discretion*
41:04 - Theory
42:34 - Dynare Commands
42:48 - Linear-Quadratic Problem
43:26 - Dynare Implementation: Response to transitory cost-push shock under discretion
43:46 - Dynare Implementation: `planner_objective`
43:51 - Dynare Implementation: `discretionary_policy`
44:23 - Dynare Implementation: Response to persistent cost-push shock under discretion

*Comparison of Optimal Policy*
44:37 - Comparing responses to cost-push shock under Commitment and Discretion

*Simple Implementable Rules*
47:57 - How to communicate optimal rules or optimal policy?
49:03 - Simple Implementable Rules
49:58 - Comparing Policy Regimes: Conditional Welfare, Unconditional Welfare Mean, Loss function
51:28 - Steady-State Consumption Equivalent

*Optimal Simple Implementable Rules*
52:51 - Theory
53:34 - Dynare Command `osr`
55:04 - Dynare Implementation: computing optimal simple rules that minimize variance of inflation and output gap

*Outro & References*
56:51 - Outro
56:56 - References

**Hints & Corrections**
- Don't save you mod files on cloud storage or network drives

Checkout https://mutschler.eu/dynare for more stuff on DSGE models and Dynare.