Long and Variable

A Monetary Policy Game inspired by Cowen and Tabarrok’s Macroeconomics textbook

Year 1, Q1 16 quarters left
The Economic LedgerYear 1, Q1

Economy grows at a steady pace as new Fed chair takes office

Inflation is close to 2 percent and unemployment is near its natural rate. Markets wait for the new chair's first decision.

Inflation, unemployment and the federal funds rate

  • Inflation
  • Unemployment
  • Fed funds rate
  • Goals

Percent, annual rate. Shaded area is your term. Goals: inflation 2%, unemployment at its natural rate of 4.5%.

The AD–AS model this quarter

  • AD
  • SRAS
  • LRAS
  • Last quarter

The economy starts close to the goal point, where AD crosses LRAS at 2% inflation.

Data table

Every quarter, for note-taking
QuarterFed fundsInflationUnemploymentReal GDP growthExpected inflationReal rateSpending growth

Briefing for the new chair

Keep inflation near 2% and unemployment near its natural rate

Your tool

Each quarter you set the federal funds rate, the overnight rate banks charge each other. The Fed hits it with open market operations. Lower rates speed up money and spending growth (M̃ + ṽ) and shift aggregate demand right. Higher rates shift it left.

Your goals

Inflation of 2% and unemployment at its natural rate of 4.5%. Your term is 16 quarters. At the end, the President decides whether to reappoint you based on how close you stayed to both goals.

The catch

Rate changes take time to work through spending. About half of a change is felt in the first quarter. Somewhere in your term the economy will be hit by a shock. You won't be told what it is; read the news and the data. Some shocks shift AD, others shift LRAS.

Real rates matter

Spending responds to the real rate: the funds rate minus expected inflation. If inflation expectations rise and you leave the funds rate alone, policy gets looser. The neutral funds rate is about 4% when expected inflation is 2%.

You chair the Fed for one four-year term. The game's name comes from Milton Friedman, who warned that monetary policy works with “long and variable lags.”

Under the hood

A quarterly version of the Cowen–Tabarrok AD–AS model

The game uses the dynamic AD–AS diagram from Modern Principles: real GDP growth on the horizontal axis, inflation on the vertical. All rates are percent per year.

Aggregate demandπ + g = S

Spending growth S = M̃ + ṽ must be split between inflation π and real growth g. AD is a line with slope −1.

What sets spending growthS = E(π) + ḡ − α·m + γ·(u−1 − u*) + d

With the real rate at its neutral level, spending grows at expected inflation plus normal growth. A real rate above neutral lowers S (AD shifts left). d collects demand shocks: confidence, wealth, taxes, government spending, exports. The γ term is the economy's slow self-correction.

Policy lagm = (1−ωt)·m−1 + ωt·(i − E(π) − r*)

The real-rate gap reaches spending gradually, passing through k such stages; more stages give a longer, hump-shaped lag. With variable lags the speed ωt is random each quarter, so the same move can bite fast or slow.

Long-run aggregate supplyg* = ḡ + z

The Solow growth rate. Real shocks z (oil, technology, taxes, pandemics) move LRAS.

Short-run aggregate supplyπ = E(π) + κ·(g − g*) + φ·(u* − u−1) + c

Upward sloping because wages and prices are sticky. Each SRAS curve is drawn for a given expected inflation rate. While unemployment is below its natural rate, workers push for raises to catch up with prices, so SRAS keeps shifting up (the φ term); c captures cost shocks.

ExpectationsE(π)+1 = (1−a)·[E(π) + λ·(π − E(π))] + a·2%

People update expectations toward actual inflation. A credible Fed (high a) keeps them anchored near 2%. Credibility erodes when inflation stays far from target. Instructors can switch anchoring off, making expectations purely adaptive.

Okun's lawΔu = −β·(g − ḡ − θ·z) / 4

Unemployment rises when growth falls short of its normal pace. Part of a real shock changes output per worker rather than jobs.

Parameters

A longer write-up with classroom notes is at colinworeilly.com/long-and-variable/model/

Instructor settings

Set up a game

Starting a game with these settings resets the current game. Use the same seed and shock to give a whole class the same economy.

To give students this exact setup, add this to the end of the game's web address:

B

The President's decision

Reappointed

The shock in your term

How other policies would have done with the same shocks

Your policy Taylor rule Never change the rate

Distance from goals is the root-mean-square gap of inflation and unemployment from their goals over your term. Under 1.3 points earns reappointment. The Taylor rule sets the funds rate at r* + π + 0.5(π − 2) + 0.5×output gap, using the past year's inflation.