Macroeconomic Model and Monetary Policy

The Macroeconomic Model

This section delves into macroeconomic problems, particularly those arising from interest rate-based monetary policy rules.

1. Phillips Curve and Inflation Inertia

The Phillips curve is developed and inflation inertia is explained. Inflation is defined as the rate of change of prices, with the rate of inflation calculated as:

\Pi = \frac{P - P{-1}}{P{-1}}

where:

  • \Pi is the rate of inflation.

  • P is today's price level.

  • P_{-1} is last period's price level.

High inflation can be volatile, creating uncertainty and undermining price information. Reducing high inflation is costly, often increasing unemployment. Central banks use inflation-targeting regimes to manage this ([see Chapter 5]).

1.1. Inflation Inertia

Changes in output lead to changes in inflation. A standard model suggests inflation depends on:

  • Past inflation (\pi_{-1}).

  • The gap between current unemployment and the Equilibrium Rate of Unemployment (ERU).

Some models suggest inflation anticipates future output increases, but empirical evidence is weak.

Two interpretations of the past inflation term:

  1. Expectations: Wage setters expect current inflation to match last period's.

  2. Inertia: Reflects wage and price setting in a complex economy.

Adaptive expectations are represented as:

\pi^e = \pi^e{-1} + a(\pi{-1} - \pi^e_{-1})

where:

  • \pi^e is expected inflation.

  • a is a positive constant less than or equal to one.

Simple adaptive expectations:

\pi^e = \pi_{-1}

A more realistic view incorporates inertia, where wage setters include past inflation to maintain living standards. We assume wage setters cannot incorporate expected future inflation changes.

The standard model defines inflation inertia as \pi = \pi_{-1}.

The inertia-augmented Phillips curve is:

\pi = \pi{-1} + a(y - ye)

Where:

  • \pi = current inflation

  • \pi_{-1} = inflation inertia

  • a(y - y_e) = output gap

With adaptive expectations, the expectations-augmented Phillips curve is:

\pi = \pi^e + a(y - y_e)

1.2. Deriving Phillips Curves

At the ERU, the labor market is in equilibrium where WS and PS curves intersect. Both wage and price setters are content with the real wage.

Constant Inflation:

If inflation is constant at 4% and unemployment is at the ERU, money wages rise by 4% to match price increases. Firms raise prices by 4% to maintain profit margins.

Rising Inflation:

If employment is above equilibrium, money wages rise to cover past inflation plus an additional amount to reach the WS curve. Firms increase prices, leading to higher inflation.

Falling Inflation:

If unemployment is above the ERU, workers have less power, leading to smaller wage increases. Firms raise prices less, and inflation falls.

Phillips curves are plotted with inflation on the vertical axis and output on the horizontal axis, mirroring the WS/PS curves.

There isn't always a direct relationship between output and unemployment due to:

  • Labor hoarding

  • Changes in labor force participation

Okun's Law describes the empirical relationship between changes in output growth and unemployment.

An inertia-augmented Phillips curve represents feasible inflation and output pairs for a given rate of lagged inflation: PC(\pi' = 4%).

Each Phillips curve is defined by:

  1. The lagged inflation rate, which fixes the curve's height.

  2. The slope of the WS curve, which fixes its slope.

The equation form is:

\pi = \pi^e + a(y - y_e)

Where 'a' is a positive constant reflecting the WS curve's slope.

1.3 Phillips's Original Curve

When average inflation is zero, the economy experiences unpredictable shocks. Wage setters perceive price increases as temporary and don't incorporate past inflation into wage demands. This creates the original Phillips curve (A.W. Phillips, UK, 1861-1957), which is downward sloping when unemployment is on the horizontal axis.

1.4 Phillips's Original Curve May Exist But It Cannot Be Exploited

Governments cannot use policy to move the economy along the original Phillips curve. For example, increasing the money supply to lower unemployment leads to workers building expected inflation into wage claims. The Phillips curve shifts upwards, and the long-run trade-off disappears (vertical long-run Phillips curve or VPC).

The Lucas critique states that stable Phillips curves exist only when governments don't try to exploit them. If governments stop trying to run the economy below the ERU, the original Phillips curve may reappear.

1.5 Disinflation Is Costly

Reducing inflation requires a period of unemployment above the ERU. The Phillips curve equation shows this:

\pi = \pi{-1} + a(y - ye)

(\pi - \pi{-1}) = a(y - ye)

If (\pi - \pi{-1}) < 0, then a(y - ye) < 0 \Rightarrow y < y_e

If the past could be ignored, then disinflation can be costless and the economy would jump from point B to A.

1.6 Disinflation and Central Bank Preferences

Central banks aim to reach the ERU with an inflation rate of 2%. They can choose different points on the Phillips curve during disinflation. A more inflation-averse bank accepts a steeper rise in unemployment to reduce inflation faster.

Central bank preferences can be represented with indifference curves. Flatter curves indicate a higher inflation aversion. Each central bank guides the economy down a path (D to A or F to A), adjusting to point A.

1.7 Costless Disinflation and Rational Expectations

Assumptions to eliminate the cost of disinflation:

  • Inflation inertia is absent (no nominal rigidities).

  • Rational expectations hold.

\pi = \pi^e + a(y - y_e) + \epsilon

Where \epsilon is a random shock term.

When the central bank announces a low inflation target (\pi^T), it is believed by market participants (credible policy).

Rational expectations mean no systematic errors:

E\pi = E\pi^e = E(\pi^T + \epsilon) = \pi^T + E\epsilon = \pi^T

\therefore \pi = \pi^T

The Phillips curve with rational expectations is:

\pi = \pi^T + a(y - y_e) + \epsilon

The Lucas surprise supply equation is:

y = y_e + \frac{1}{a} (\pi - \pi^e)

Output deviates from equilibrium only with surprise inflation. Firms struggle to distinguish between economy-wide and relative price changes. Overall, some increased supply response will occur following an inflation 'surprise'.

Wage and price setters might doubt the credibility of the inflation target, leading to the government having to demonstrate its commitment by accepting higher unemployment.

In a world of rational expectations, no inflation inertia, and credible government commitment, only surprise inflation leads to output deviations. Systematic monetary policy is ineffective, and the economy returns to equilibrium without cost and this contrasts with inertia-augmented Phillips curves.

Deviation in output leads to a change in inflation relative to lagged inflation which is different than the Lucas surprise supply equation.

2. Monetary Rules and the 3-Equation IS-PC-MR Model

The 3-equation model includes:

  1. IS equation.

  2. Phillips curve equation.

  3. Monetary rule (MR).

This model helps analyze the trade-off between output and inflation. [Chapter 5] and [Chapter 15] explain more sophisticated versions.

2.1. The 3-Equation Model: IS-PC-MR

  • IS Equation: A simpler form is: y = A - ar, where A is exogenous demand and r is the real interest rate.

The stabilizing interest rate (rs) equates y to ye:

ye = A - ars

rs changes whenever A or ye changes. So:

y - ye = -a(r - rs)

The output gap reveals how much the interest rate deviates from the stabilizing rate. Central banks use interest rates to influence the output gap.

  • Phillips Curve (PC): The inertia-augmented Phillips curve is: \pi = \pi{-1} + a(y - ye).

  • Monetary Rule (MR): Derived from the central bank's output-inflation trade-off:

y - y_e = -b(\pi - \pi^T)

This equation shows the choice between combinations of output and inflation. A higher b is a more inflation-averse central bank.

The MR goes through y = y_e and \pi = \pi^T.

The MR guides the economy back to equilibrium by adjusting the interest rate. When shifted away from equilibrium, the monetary authority uses interest rates to get back on the MR line, adjusting until the economy returns to (y_e, \pi^T).

2.2. An Inflation Shock

Central banks raise the interest rate to achieve a point “C” on the Phillips curve. Following, the Phillips curve shifts down as a result of the fall in inflation. After which, the economy is guided down the MR line to the south-east as the central bank implements the monetary policy rule, with the frequent adjustments of the interest rate required by the monetary policy rule.

2.3. A Temporary Demand Shock

A temporary aggregate demand shock: the IS curve rises but only for one period. The increased output above the equilibrium makes inflation rise leading to the Central bank raising the interest rate in response to the temporary aggregate demand shock for its consequences for inflation.

2.4. A Permanent Demand Shock

A permanent demand shock: The IS curve shifts to IS' and stays there. Similar to the temporary example, output increases above equilibrium, the stabilizing interest rate rises. Overall: adjustment along MR and IS' takes place in the usual way and there is a shift in equilibrium to point Z.

2.5 The MR line and the real interest rate

The Central Bank does this by steering through the inflation, so it sets nominal interest rate to achieve one, particular real interest rate. Overall: The IS curve then shifts leading to adjustment along MR and IS'.

2.6 Sacrifice ratios and disinflation strategies

A more inflation-averse central bank raises interest rates by more to dampen output. 'Cold turkey' or 'shock therapy' vs. a gradualist approach. If Phillips curves are linear and parallel, cumulative unemployment is the same under both strategies. The sacrifice ratio is independent of the central bank's inflation aversion, such that: y - y_e = -b(\pi - \pi^T)

But, if a small increase in unemployment will affect inflation more, then the result does not hold, as seen in Figure 3.12.

3. Inflation at the Medium-Run Equilibrium

3.1. Two Monetary Policies
3.1.1. Interest Rate Rule (MR Approach)

With the interest rate rule: In the 3-equation model, at the medium-run equilibrium, the central bank seeks to stabilize around the ERU.

3.1.2. Money Supply Rule (LM Approach)

With the Money supply rule: The growth of the money supply determines medium-run inflation. The symbol y (called gamma) to denote 'growth rate', so M is the growth rate of the money supply.

\overline{Y}M\frac{M - M{-1}}{M_{-1}}

3.2 How the MR relates to the LM curve

Use depends on the type of monetary policy, for example:

  • Central bank has to ensure that the money market is in equilibrium.

  • LM curve -> has no role in fixing the position of the economy.

4. Inflation in the IS/LM Model

Unlike 3-quation IS-PC-MR model, the government/ central bank not modeled -> using monetary policy rule in the sense of reaction function.
The real interest rate changes because the result of the interaction between the central bank's fixed money supply growth and inflation.
There is also that A spiral-shaped adjustment path in the Phillips curve diagram being traced as the economy moves first to the north-east and then in a counter-clockwise spiral back to the equilibrium, due to the dependence on the central bank to step in and cut the interest rate.

5. Conclusions

This chapter presented a framework for systematically investigating shocks and policies affecting the economy. It expanded upon the elements from Chapter 2 (IS curve, LM curve, WS and PS curves, ERU) by incorporating Phillips curves and the monetary rule (MR).
The adjustment path is more protracted in the IS/LM model than with the interest rate-based monetary policy rule.