Credibility in Economic Policy: Rules vs. Discretion - Notes

Credibility in Economic Policy: Rules vs. Discretion

Introduction

• Lucas Critique: Policymakers must recognize that policy changes alter agents' behavior.

• Agents anticipate policymakers' actions when forming expectations.

• This interaction is modeled as a game between policymakers and agents.

• This approach helps understand how one player (agents) reacts to changes in the other player's (policymaker) behavior.

Example: Capital Taxation (Kydland and Prescott, 1977)

• The government announces a 20% reduction in capital taxation starting next year.

• If agents believe this, they'll invest more, increasing capital at the start of next year.

• However, once the capital is installed, the government is incentivized to break the announcement and raise capital taxation.

• Rational agents understand the economic environment and the government's incentive to renege.

• Therefore, agents won't believe the announcement, potentially nullifying the policy's effect.

Example: Monetary Policy

• Lucas' Aggregate Supply: $y = \bar{y} + \alpha(\pi - \pi^e) + \epsilon$

  • Where:

    • $y$ = actual output

    • $\bar{y}$ = natural level of output

    • $\alpha$ = sensitivity of output to unexpected inflation

    • $\pi$ = actual inflation

    • $\pi^e$ = expected inflation

    • $\epsilon$ = aggregate supply shock

• Social Loss Function: $\Omega = \frac{1}{2}(y - y^*)^2 + \frac{\beta}{2}\pi^2$

  • Where:

    • $\Omega$ = social loss

    • $y^<em>$ = target output level (y^ > \bar{y})

    • $\beta$ = weight on inflation in the loss function

• The policymaker aims to minimize deviations of real output from the target and cares about inflation.

Game Theoretic Approach

Four Stages:

1. Policymaker decides whether to announce a policy.

2. Agents react (or not) based on the announcement.

3. Aggregate supply shock is revealed.

4. Policymaker decides whether to implement the announcement.

Three Options for the Policymaker:

1. Discretionary: No announcement.

2. Policy Rule: Announce and stick to the policy.

3. Cheat: Announce but do something else.

Discretionary Policy

• The policymaker makes no announcement.

• This policy is suboptimal because another policy exists that results in a lower value of the loss function.

Policy Rule

• The policymaker announces an inflation target of $\pi = 0$ and commits to it.

• Initially, assume agents believe the announcement.

• However, this policy rule is time-inconsistent.

• The policymaker is incentivized to break the announcement and cheat.

Cheating Policy

• The policymaker announces an inflation target of $\pi = 0$.

• Initially, assume agents believe the announcement.

• After agents form their expectations, the policymaker chooses to cheat by aiming for a high level of output, leading to a high level of inflation.

• If agents genuinely believed the announcement, it would result in the best outcome (loss function minimized).

• However, agents understand the model and realize the policymaker's incentive to deviate from the announced rule.

• This lack of credibility undermines the announcement.

Solutions to the Time Inconsistency Problem

• Reputation:

  • The previous example was a one-shot game.

  • In a dynamic environment, policymakers may want to build a reputation for commitment.

• Independent Central Bank:

  • Separate the goals of output maximization (government) and low inflation (central bank) to avoid conflicts of interest.

• Appoint central bankers for long terms

  • This ensures their independence from the government.

Examples of Monetary Policy Rules

• Constant money growth rate.

• Target growth rate of nominal GDP.

• Target the inflation rate.

• Taylor Rule: $i = \pi + 2 + 0.5(\pi - 2) + 0.5(GDP \ Gap)$

  • Where:

    • $i$ = nominal interest rate

    • $\pi$ = inflation rate

    • $GDP \ Gap$ = percentage deviation of actual GDP from potential GDP

1. Introduction

   • Lucas Critique: Policymakers must recognize that policy changes alter agents' behavior.

   • The interaction as a game between policymakers and agents.

2. Example: Capital Taxation (Kydland and Prescott, 1977)

   • Government announcement of capital taxation changes and agent responses.

3. Example: Monetary Policy

   • Lucas' Aggregate Supply equation.

   • Social Loss Function and the objectives of policymakers.

4. Game Theoretic Approach

   • Stages of policymaker and agent interactions.

   • Policymaker options: Discretionary, Policy Rule, Cheating.

5. Discretionary Policy

   • Characteristics and implications of discretionary policy.

6. Policy Rule

   • Commitment to an inflation target and its time-inconsistency issues.

7. Cheating Policy

   • Consequences of announcing targets but deviating from them.

8. Solutions to the Time Inconsistency Problem

   • Building reputation, independent central banks, long-term appointments for central bankers.

9. Examples of Monetary Policy Rules

   • Various rules including constant money growth rates, targeting nominal GDP and inflation, and the Taylor Rule.