A one-line formula tracks the Fed’s interest rate with a correlation of 0.75

0.75 Correlation between the fed funds rate and the rule \(i = 1 + 1.5\,\pi\), 1960–2023

Could a robot chair the Federal Reserve? A recipe that looks only at inflation follows the Fed’s big swings. Yet in 2021–22 the Fed set its rate 6.7 points below that recipe. When is a rule good enough, and when does judgment matter?

Open with the number. It comes from the notebook’s Fig. 16 check: the correlation of the actual fed funds rate with John Taylor’s simple rule, quarterly, from 1960Q1 to 2023Q1, is 0.75. The rule uses only one input, core PCE inflation, and three numbers that are all 2: r̄ = 2, m̄ = 1/2, π̄ = 2. Then i = 1 + 1.5π.

The textbook opens with a provocative question: could we replace the chair of the Fed with a robot? Nobody proposes it seriously, but the question is useful. If one line of algebra describes decades of policy, what are the hundreds of economists at the Fed doing? And what goes wrong when the Fed departs from the line, as in the 1970s or in 2021–22?

Ask the room: who sets interest rates where you live? Do they follow a formula? Would you trust one?

Today: three questions

• What does a policy rule do to the short-run model? It turns the IS and Phillips curves into one AS/AD diagram.
• How does the economy react to shocks under the rule? An inflation shock, a disinflation and a demand boom, period by period.
• Does the rule describe real central banks, and what makes low inflation cheap? The Taylor rule, inflation-output loops, forecasts, credibility and three centuries of inflation.

These are the three acts of the deck and the three branches of the mind map on the title slide.

The headline: a central bank that follows a rule turns the short-run model into one diagram. Because expectations are sticky, every shock fades only slowly and lowering inflation costs a recession; a credible target is what makes low inflation cheap.

Chapters 11 and 12 built the pieces: the IS curve and the Phillips curve, with the central bank choosing the real interest rate case by case. Here the bank follows a fixed recipe.

A rule and one diagram

Act I

The short-run model so far has three pieces

\[\text{IS:}\quad \widetilde{Y}\!_t = \bar{a} - \bar{b}\,(R_t - \bar{r})\]

\[\text{Phillips:}\quad \Delta\pi_t = \bar{\nu}\,\widetilde{Y}\!_t + \bar{o}\]

• In Chapter 12 the central bank picked \(R_t\) for each shock, one at a time.
• Now it commits to a rule: a fixed recipe from what it sees to the rate it sets.
• \(\widetilde{Y}\!_t\): output’s percent gap from potential. Bars mark parameters.

A rule replaces many case-by-case decisions with one equation.

The IS curve (Chapter 11): spending falls below normal when the real interest rate R is above the marginal product of capital r̄; ā is the aggregate demand shock and b̄ the interest sensitivity. The Phillips curve (Chapter 12): inflation rises when output is above potential, plus any inflation shock ō, such as an oil price jump.

Notation of the book chapter: a bar marks a parameter (ā, b̄, m̄, ν̄, ō, r̄, π̄), a tilde marks short-run output, the subscript t counts years.

The baseline numbers used in every figure: target π̄ = 2 percent, Taylor’s policy response m̄ = 1/2, interest sensitivity b̄ = 2 (Chapter 11’s example), Phillips-curve slope ν̄ = 1. The shocks: ō = 2 for one period, ā = 2 for nine periods, and a cut in the target from 4 to 2 percent.

Ask: what does the central bank actually observe each month? (Inflation, quickly; the output gap, only roughly and with revisions. Act III comes back to this.)

The aggregate demand curve

What happens to output when inflation rises, if the central bank follows a rule?

The rule sets the real rate \(\bar{m} = 1/2\) point above \(\bar{r}\) for each point of inflation above the 2% target, and \(\bar{b} = 2\). Inflation is 3%. What is output? Now add a demand shock \(\bar{a} = 2\): which way does the curve move?

Ask for numbers. A good answer: the real rate rises by 0.5 × (3 − 2) = 0.5 points, the IS curve turns that into 2 × 0.5 = 1 point of lost output, so Ỹ = −1 percent. A demand shock moves the curve to the right by 2 points.

Common wrong answer: “output does not depend on inflation”. Ask students to follow the chain: inflation → the rule → the interest rate → spending.

Higher inflation means lower output, because the central bank raises rates

Model figure: the AD curve \(\widetilde{Y}\!_t = \bar{a} - \bar{b}\bar{m}(\pi_t - \bar{\pi})\) with \(\bar{b}\bar{m} = 1\) and \(\bar{\pi} = 2\). Adapted from Fig. 13.1 in Jones (2024), Macroeconomics, 6th ed.

How to read it: output Ỹ (percent from potential) on the horizontal axis, inflation π on the vertical axis, as for the IS curve. The dot marks inflation on target. The title writes the equation with the current numbers. The slider sets the demand shock ā; the baseline curve stays behind as a dashed gray line.

Do live:

1. At ā = 0 the dot is at (0, 2): inflation on target, output at potential.
2. Read the curve at π = 3: output is −1 percent. Each point of inflation above target costs b̄m̄ = 1 point of output.
3. Move ā to +2: the whole line shifts 2 points to the right, and the dot moves to (2, 2). Move to −2: it shifts left.

Point out that a change in inflation itself is a movement along the line, not a shift.

The AD curve describes the central bank, not shoppers

• The answer: at 3% inflation the rule adds 0.5 points to the real rate, and output falls to −1%. Each point of inflation costs \(\bar{b}\bar{m} = 1\) point of output.
• A demand shock \(\bar{a}\) shifts AD right; a higher target \(\bar{\pi}\) shifts it up. The dot always sits at \((\bar{a}, \bar{\pi})\).
• \(\bar{b}\) and \(\bar{m}\) enter only as a product: a tougher bank and a more rate-sensitive economy draw the same curve.

AD slopes down because the bank leans against inflation with the interest rate.

Numbers: the Model overview’s chain for 3 percent inflation, 0.5 × (3 − 2) = 0.5 and 0 − 2 × 0.5 = −1, and the Fig. 1 readout. The notebook’s key numbers: inflation 2 points above target raises the real rate by 1 point and costs b̄ × 1 = 2 points of output (the textbook’s example); at π = 4 the AD curve gives Ỹ = −2 percent.

Second fact from the Model overview: when inflation is on target and there is no demand shock, the bank wants output at potential, whatever m̄ is.

The comparative statics table of the book chapter: a rise in π is a movement along AD; ā shifts it right by one point per point; π̄ shifts it up by one point per point.

Two equations make the AD curve

\[\text{IS:}\ \ \widetilde{Y}\!_t = \bar{a} - \bar{b}\,(R_t - \bar{r}) \qquad \text{rule:}\ \ R_t - \bar{r} = \bar{m}\,(\pi_t - \bar{\pi})\]

\[\text{AD:}\quad \widetilde{Y}\!_t = \bar{a} - \bar{b}\bar{m}\,(\pi_t - \bar{\pi})\]

\[\text{in the diagram:}\quad \pi_t = \bar{\pi} + \frac{\bar{a} - \widetilde{Y}\!_t}{\bar{b}\bar{m}} \qquad \text{slope } -\frac{1}{\bar{b}\bar{m}}\]

The interest rate drops out: AD links the two outcomes, output and inflation.

The rule gives exactly the interest-rate gap R − r̄ that appears in the IS curve, so substitute it. The result has no interest rate in it: AD is a relation between two endogenous variables.

Because inflation goes on the vertical axis, solve for π: move the inflation term left and Ỹ right, divide by b̄m̄. The line passes through (ā, π̄) with slope −1/(b̄m̄); in the baseline b̄m̄ = 2 × 0.5 = 1, so the slope is −1.

Full derivation: the book chapter’s Model overview, “The policy rule and the AD curve”.

The AD curve is not a demand curve for goods

The AD curve slopes down because people buy less when prices are high.

The vertical axis is the inflation rate, not the price level. AD slopes down because the central bank raises the real interest rate when inflation is above target, and spending falls. With a different rule, the curve would have a different slope.

The textbook’s review question: how is the AS/AD graph like a supply-and-demand diagram, and how is it different? Like one: two curves, one sloping down and one up, crossing at an equilibrium; shocks shift them. Different: the axes are output relative to potential and the inflation rate; AD summarizes the central bank’s reaction plus the IS curve; AS is the Phillips curve, firms’ pricing.

Later in the act: a rule that does not raise the real rate with inflation (m̄ < 0) would make AD slope up, and the economy would be unstable.

An aggressive central bank

What changes when the central bank reacts more strongly to inflation?

Inflation rises from 2% to 3%. With \(\bar{m} = 1/2\), output fell 1%. The bank now uses \(\bar{m} = 1\). How far does output fall? Is the new AD curve steeper or flatter?

Collect answers. Many students guess “steeper”, because a tougher bank sounds like a steeper line. Ask them to think in the diagram: a small change in inflation now brings a large change in output, so the line is flatter.

A tougher rule flattens the AD curve and deepens the recession

Model figure: the AD curve with policy response \(\bar{m}\); the dashed line is \(\bar{m} = 0.5\). Adapted from Fig. 13.3 in Jones (2024), Macroeconomics, 6th ed.

How to read it: the same axes. A is the steady state (0, 2); B is where the economy lands when inflation is 3 percent. The dashed gray line is the baseline AD curve with m̄ = 0.5. The title follows the chain: inflation, then the rise in the real rate R − r̄, then output. The slider sets m̄.

Do live:

1. Start at m̄ = 1: R − r̄ = 1.00 and output falls to −2.00 percent.
2. Move to 0.5: the baseline case of the textbook’s Fig. 13.2, R − r̄ = 0.50 and Ỹ = −1.00. (This is why the deck skips that figure.)
3. Move to 0.25: the curve is steep, and the bank barely reacts: −0.50 percent.
4. Move to 1.75: −3.50 percent.

Both curves pass through A, whatever m̄.

A flatter AD curve means a bank that fights inflation harder

• The answer: with \(\bar{m} = 1\) the same 1-point rise in inflation lowers output by 2% instead of 1%. The curve is flatter.
• At \(\bar{m} = 0.25\) the fall is only 0.5%: a steep AD curve is a bank that barely reacts.
• Every curve passes through \(A\): with inflation on target and no shock, the bank wants output at potential.

The slope of AD is a policy choice: it measures how much output the bank will give up per point of inflation.

Numbers: the Fig. 3 readouts for m̄ = 0.25, 0.5, 1 and 1.75 (output −0.50, −1.00, −2.00, −3.50 percent at π = 3).

The slope of the line in the diagram is −1/(b̄m̄): with b̄ = 2, it is −1 at m̄ = 0.5 and −0.5 at m̄ = 1.

Act II will show the trade-off: a flatter AD curve means a deeper but shorter recession after a shock, and, surprisingly, the same total loss of output.

The Phillips curve becomes the aggregate supply curve

\[\text{AS:}\quad \pi_t = \pi_{t-1} + \bar{\nu}\,\widetilde{Y}\!_t + \bar{o}\]

• Firms expect last year’s inflation, \(\pi^e_t = \pi_{t-1}\), which is known when the year starts.
• In a boom they pay overtime and run machines harder, so prices rise faster than expected: AS slopes up with slope \(\bar{\nu}\).
• AS crosses \(\widetilde{Y} = 0\) at \(\pi_{t-1} + \bar{o}\): whenever inflation changes, next year’s AS curve moves.

The AS curve carries expectations into the diagram. That is the engine of every event in Act II.

Write out Δπ = π_t − π_(t−1) and add π_(t−1) to both sides of the Phillips curve. With adaptive expectations the same line reads π_t = π^e_t + ν̄Ỹ_t + ō: inflation is what firms expected, plus a push from a hot economy, plus any shock.

The book chapter’s AS table: Ỹ up one point raises π by ν̄ (a movement along); last year’s inflation up one point shifts AS up one point; a shock ō shifts it up while it lasts; a larger ν̄ turns it steeper.

The notebook has a separate AS figure (Fig. 4, with a slider for last year’s inflation). We skip it: the next figure has the same AS curve and the same slider, now called expected inflation.

A check from the notebook: with π_(t−1) = 2 and ν̄ = 1, inflation reaches 3.5 percent when output is 1.5 percent above potential.

The AS/AD diagram

Where do the two curves cross, and is that point a resting place?

Expected inflation equals the 2% target. Where do AS and AD cross? Now firms expect 4% instead: what happens to inflation and output this year? Will the economy stay there?

Ask for the crossing point in both cases. Good answers: at (0, 2) when expectations are on target; with 4 percent expected inflation the AS curve shifts up, inflation rises and output falls. Whether the economy stays there is the key question; most students say yes.

AS and AD cross at potential output and the target, when expectations agree

Model figure: AS \(\pi_t = \pi^e_t + \bar{\nu}\widetilde{Y}\!_t\) and AD with \(\bar{m} = 0.5\), \(\bar{b} = 2\), \(\bar{\nu} = 1\), \(\bar{\pi} = 2\). Adapted from Fig. 13.5 in Jones (2024), Macroeconomics, 6th ed.

How to read it: AS (rising) and AD (falling) on the same axes. The slider sets expected inflation, which is last year’s inflation. The title says where the curves cross and whether that point is a steady state.

Do live:

1. At 2 percent: the curves cross at Ỹ = 0.00, π = 2.00, “the steady state”.
2. Move to 4 percent: the crossing moves to Ỹ = −1.00, π = 3.00, “not a steady state”.
3. Move to 1 percent: Ỹ = +0.50, π = 1.50, again not a steady state.

Ask: in the 4 percent case, inflation turned out to be 3 percent. What will firms expect next year? (3 percent: the AS curve moves again.)

Only on target is the crossing a steady state

• The answer: with expectations at the target the curves cross at \(\widetilde{Y} = 0\), \(\pi = 2\%\).
• With 4% expected: \(\pi = 3\%\), \(\widetilde{Y} = -1\%\). Inflation differs from what firms expected, so next year’s AS curve shifts.
• A steady state needs \(\pi_t = \pi_{t-1}\): the AS curve then forces \(\widetilde{Y}^* = 0\), and AD then forces \(\pi^* = \bar{\pi}\).

In the long run output is at potential and the bank’s target becomes the economy’s inflation rate.

Numbers: the Fig. 5 readouts and the notebook’s steady-state check: for (m̄, ν̄) = (0.25, 0.5), (0.5, 1) and (2, 2), the solution with expected inflation at the target is Ỹ = 0.00 percent and π = 2.00 percent every time, equation (4).

Derivation, step 1 of the Model overview: no shocks and π_t = π_(t−1) in AS give ν̄Ỹ* = 0, so Ỹ* = 0; then AD with ā = 0 gives π* = π̄.

The inputs of the diagram are the parameters (π̄, m̄, ν̄, b̄) and expected inflation; the outcomes are this year’s output and inflation.

Solving AS and AD gives this year’s output and inflation

\[\widetilde{Y}\!_t = \frac{\bar{a} - \bar{b}\bar{m}\,(\pi_{t-1} - \bar{\pi} + \bar{o})}{1 + \bar{b}\bar{m}\bar{\nu}}\]

\[\pi_t - \bar{\pi} = \lambda\left[(\pi_{t-1} - \bar{\pi}) + \bar{o} + \bar{\nu}\bar{a}\right], \qquad \lambda \equiv \frac{1}{1 + \bar{b}\bar{m}\bar{\nu}}\]

• The bracket is the inflation pressure. Only the share \(\lambda\) reaches inflation; the rule removes the rest by holding output down.
• Baseline: \(\bar{b}\bar{m}\bar{\nu} = 1\), so \(\lambda = 1/2\).

Half of every inflation push reaches inflation; the other half is paid for in output.

Step 2 of the Model overview: substitute AS for π_t in AD, collect the Ỹ_t terms, (1 + b̄m̄ν̄)Ỹ_t, and divide. For inflation, subtract π̄ from AS and insert the result; the bracket simplifies to 1/(1 + b̄m̄ν̄).

The bracket is the inflation pressure that reaches the economy in period t: the gap inherited from last period, plus the inflation shock, plus the push from a demand shock.

λ is the book chapter’s shorthand, not the textbook’s. It lies between 0 and 1 and falls when m̄ or ν̄ rises.

The notebook checks the formula: with ō = 2 hitting the steady state, the solution gives Ỹ = −1.00 percent and π = 3.00 percent, and the share of the gap left each period is 1/(1 + b̄m̄ν̄) = 0.50.

Three events

Act II

Event 1: an inflation shock

An oil price jump pushes inflation up for one year. What does the central bank’s rule do to output?

The economy is in its steady state at 2% inflation. A shock \(\bar{o} = 2\) hits for one year only. Where do inflation and output land this year: does inflation reach 4%?

Ask students to draw it: the AS curve shifts up by 2 points. If output stayed at potential, inflation would rise to 4 percent. Does it? Use the solution of the last slide: λō = 1.

Ask also for the sign of output. Some students expect output to rise “because prices rise”.

The shock raises inflation and lowers output at the same time

Model figure: inflation shock \(\bar{o}\) in period 1 only, baseline \(\bar{m} = 0.5\), \(\bar{b} = 2\), \(\bar{\nu} = 1\). Adapted from Fig. 13.6 in Jones (2024), Macroeconomics, 6th ed.

How to read it: AS is the original curve, AS₁ the curve shifted up by the shock, AD the unchanged policy curve. A is the old steady state, B the economy in period 1. The slider sets the size of the shock; the title gives period-1 inflation and output.

Do live:

1. At ō = 2: B is at π = 3.00, Ỹ = −1.00.
2. Move to 4: π = 4.00, Ỹ = −2.00. Half the shock, again.
3. Move to 0.5: π = 2.25, Ỹ = −0.25.

The economy slides down AD from A to B: the bank fights the higher inflation with a higher interest rate.

A price shock brings stagflation: higher inflation and a recession

• The answer: inflation rises only to 3%, not 4%, because output falls to −1%.
• Half of the shock shows up as inflation, half as recession, since \(\bar{b}\bar{m}\bar{\nu} = 1\).
• A tougher bank (higher \(\bar{m}\)) gets less inflation and a deeper recession; a fall in oil prices gives the mirror image.

Stagflation, the U.S. experience after the oil shocks of the 1970s, is what a rule does with a price shock.

Numbers: the notebook’s check (ō = 2: Ỹ = −1.00, π = 3.00) and the Fig. 6 readouts. Formulas: π₁ − π̄ = λō = 1 and Ỹ₁ = −b̄m̄λō = −1.

Why a recession? The rule sees inflation above target and raises the real rate. That is the bank’s choice: it accepts lower output to keep inflation from rising one for one.

A notebook exercise: with ō = 3, B is at π = 3.50, Ỹ = −1.50 (the Fig. 6 slider); with m̄ = 1, inflation rises less and output falls more.

After the shock

The shock is over in year 2. Does the AS curve jump back to where it started?

In year 2 the shock is gone, \(\bar{o} = 0\). Firms now expect last year’s 3% inflation. Where are inflation and output in year 2, and in year 3?

Most students say the AS curve returns to its old position because the shock is gone. Push back: what do firms expect in year 2? Students who use the formula get π₂ − 2 = ½ × 1 = 0.5 and Ỹ₂ = −0.5.

Expectations keep the AS curve high, so the economy returns only step by step

Model figure: the path after a one-period shock \(\bar{o} = 2\), baseline parameters. Adapted from Figs. 13.7 and 13.8 in Jones (2024), Macroeconomics, 6th ed.

How to read it: the slider picks the period t. Earlier AS curves are drawn in light teal, the current one in full color; the path so far carries the textbook’s letters B, C, D for periods 1, 2 and 3. AD never moves.

Do live:

1. t = 1: B, π = 3.00, Ỹ = −1.00.
2. t = 2: C, π = 2.50, Ỹ = −0.50. AS₂ sits between the original AS and AS₁, because firms expect 3 percent.
3. t = 3: D, π = 2.25, Ỹ = −0.25.
4. Step to 6 and 8: π = 2.03 and 2.01. The AS curve creeps back toward its original position.

This slider replaces the textbook’s Fig. 13.7 (period 2), which the notebook also draws as Fig. 7 with two panels.

The inflation gap and the recession halve every year

Year	\(\pi\)	\(\widetilde{Y}\)
1	3.00	−1.00
2	2.50	−0.50
3	2.25	−0.25
4	2.125	−0.125
5	2.0625	−0.0625

• The answer: no jump back. Year 2 has \(\pi = 2.5\%\), \(\widetilde{Y} = -0.5\%\).
• With no shocks, \(\pi_t - \bar{\pi} = \lambda(\pi_{t-1} - \bar{\pi})\): each gap shrinks by the factor \(\lambda = 1/2\).
• The steps get shorter: the economy moves fastest when it is farthest from home.

Sticky expectations keep inflation high, and the same stickiness keeps the economy in a slump.

Numbers: the notebook’s simulation table (period 1 to 5) and its formula check: 3.0000, 2.5000, 2.2500, 2.1250, 2.0625 percent; output −1, −0.5, −0.25, −0.125, −0.0625. From period 2 on, the ratio of successive gaps is exactly 0.5.

Equation (7) of the Model overview is a difference equation: applied again and again, the gap after s periods is λ^s times the starting gap. Because λ < 1, the gap always dies out.

The fall in the gap from one year to the next is (1 − λ) times the gap, proportional to the gap: the principle of transition dynamics from the Solow model (Chapter 5) holds here too.

The notebook asks: how many periods until inflation is within 0.1 point of the target? (Period 5: 2.0625.)

The whole episode

How long does the stagflation last, and how much output does it cost in total?

The shock added 2 points to inflation once. Add up the output lost over all the years that follow. Then make prices less responsive to the slump (a flatter AS curve, smaller \(\bar{\nu}\)): is the total loss larger or smaller?

Ask for a number for the total. Some students will add −1 − 0.5 − 0.25 − … and get −2. Ask them to guess the effect of a flatter AS curve before the reveal: does it spread the same loss over more years, or raise the loss?

A one-year shock leaves a recession that lasts many years

Model figure: the inflation shock \(\bar{o} = 2\) in period 1, with AS slope \(\bar{\nu}\); panel (b), the time paths, is the book’s addition. Adapted from Fig. 13.9 in Jones (2024), Macroeconomics, 6th ed.

How to read it: panel (a) is the textbook’s summary in the AS/AD diagram, the jump from A to B and the slow return along AD. Panel (b) shows the same path as two time series, inflation and output, against the 2 percent target. The slider sets the slope ν̄ of the AS curve; the title gives the inflation peak and the sum of output.

Do live:

1. ν̄ = 1: inflation peaks at 3.00 percent; sum of Ỹ = −2.00.
2. ν̄ = 0.5: peak 3.33, sum −4.00. ν̄ = 0.25: peak 3.60, sum −7.91 (the 20 periods drawn do not quite finish the episode).
3. ν̄ = 2: peak 2.67, sum −1.00.

Point at panel (b): the shock lasts one period, but inflation stays above target, and output below potential, for years.

The total cost of the shock is \(\bar{o}/\bar{\nu}\), whatever the bank does

• The answer: the losses add up to 2% of a year’s output with \(\bar{\nu} = 1\).
• A flatter AS curve makes it costlier: \(\bar{\nu} = 0.5\) doubles the loss to 4%; \(\bar{\nu} = 2\) halves it to 1%.
• Prices that react little to a slump need a longer slump to come down.

Price shocks are costly twice: once in inflation, then in the recession needed to bring it down.

Numbers: the notebook’s total-cost check (equation 8): inflation shock ō = 2 with ν̄ = 0.5, 1 and 2 gives sums of −4.0000, −2.0000 and −1.0000, exactly as the formula says.

Why the shock costs more than one period: it raised expected inflation. The AS curve of the next year starts from the higher inflation, and only a slump brings it down.

The Model overview’s prediction “shocks to prices hurt twice”.

A one-time shock to prices has lasting effects

An oil shock lasts a year, so it raises inflation for a year.

The shock raises inflation in year 1, firms then expect higher inflation, and the AS curve stays up. Inflation is still 2.25% in year 3, and the slump needed to undo the shock adds up to 2% of a year’s output.

Numbers: the Fig. 8 path (π₃ = 2.25 percent) and the total cost of −2.00 from the notebook.

This is the textbook’s point that price shocks are insidious. It is also why central banks watch measures of expected inflation so closely: if a shock does not move expectations, the AS curve can return at once and the slump is not needed (Fig. 20 in Act III).

Adding up the AS curve gives the cost of any episode

\[\pi_T - \pi_0 = \bar{\nu}\textstyle\sum_t \widetilde{Y}\!_t + \sum_t \bar{o}_t\]

\[\sum_{t=1}^{T}\widetilde{Y}\!_t = \frac{(\pi_T - \pi_0) - \sum_t \bar{o}_t}{\bar{\nu}}\]

• Only the move in inflation, the shocks and \(\bar{\nu}\) matter. The policy response \(\bar{m}\) is not in it.
• Each point of disinflation costs \(1/\bar{\nu}\) points of a year’s output: the sacrifice ratio.

A tougher bank changes the shape of the slump, not its total size.

Step 4 of the Model overview. Add the AS curve, π_t − π_(t−1) = ν̄Ỹ_t + ō_t, over the periods 1 to T. On the left every middle term cancels (a telescoping sum), leaving π_T − π₀. Take T large enough for the economy to be back in a steady state.

Inflation shock: π_T − π₀ = 0 and the shocks add up to 2, so the sum is −2/ν̄. Disinflation from 4 to 2: π_T − π₀ = −2 with no shocks, so the sum is −2/ν̄ again. Demand boom: inflation starts and ends at 2 with no inflation shocks, so the sum is 0.

Chapter 9 measured the U.S. Phillips curve slope at about 1/3; the baseline ν̄ = 1 here is illustrative.

Event 2: a disinflation

The central bank lowers its target from 4% to 2%. Does a tougher bank make the disinflation cheaper?

Inflation has been 4% for years, and firms expect 4%. The bank cuts its target to 2%. Where is inflation in year 1? Then compare a gentle bank (\(\bar{m} = 0.25\)) with a tough one (\(\bar{m} = 2\)): which loses less output in total?

This is Paul Volcker’s Fed in the 1980s, in the textbook’s numbers. Ask for the year-1 inflation rate and for the comparison. Most students expect the tough bank to finish the job faster and so to lose less. Keep the guesses on the board for the reveal.

Lowering the target costs a recession while expectations catch up

Model figure: target cut from 4% to 2% in period 1, with policy response \(\bar{m}\). Adapted from Figs. 13.10 and 13.11 in Jones (2024), Macroeconomics, 6th ed.

How to read it: panel (a) shows the old AD curve and the new one, AD₁, shifted down by 2 points because the target appears only in AD. The economy jumps from A to B in period 1, then slides down AD₁ to the new steady state C as the AS curve shifts down period by period (AS₂₀ is the last one drawn). Panel (b) shows inflation and output over 20 periods. The slider sets m̄; the title gives the output lost over 20 periods.

Do live:

1. m̄ = 0.5: B is at π = 3, Ỹ = −1 (the textbook’s Fig. 13.10, which this figure includes as its first period). Output lost: 2.00 percent.
2. m̄ = 2: in panel (b) the slump is much deeper at first and much shorter. The title still says 2.00.
3. m̄ = 0.25: a shallow, long slump. Still 2.00.

The total cost of the disinflation is 2% of a year’s output, whatever the bank does

• The answer: in year 1 inflation falls only to 3%, halfway to the new target, and output to −1%.
• Then the economy slides down the new AD curve to \(C\): 2% inflation, output at potential.
• Gentle or tough, the bank loses 2.00% of a year’s output. Only \(\bar{\nu}\) changes it: \((\bar{\pi} - \bar{\pi}')/\bar{\nu}\).

A recession is needed only because firms keep expecting the old inflation. Act III asks what happens if they believe the new target.

Numbers: the notebook’s total-cost check, target 4 → 2 with m̄ = 0.25, 0.5 and 2.00: −2.0000 each time; the Fig. 11 readouts (2.00 percent for every m̄); and the formulas π₁ − π̄′ = λ(π₀ − π̄′) = 1 and Ỹ₁ = −b̄m̄(π₁ − π̄′) = −1.

Why does the cut shift AD down? At any inflation rate, the new rule sees more “excess” inflation and sets a higher real rate. Four percent is now too high.

A notebook exercise asks for the total loss with ν̄ = 0.5, 1 and 2; equation (8) gives 2/ν̄ = 4, 2 and 1.

A tougher central bank does not make a disinflation cheaper

A tough central bank gets inflation down at a lower cost.

With sticky expectations, a tough bank (\(\bar{m} = 2\)) makes the slump deeper and shorter, a gentle one (\(\bar{m} = 0.25\)) shallower and longer. Both lose 2.00% of a year’s output. What lowers the cost is credibility, which moves expectations themselves.

Numbers: the notebook’s check of equation (8) for m̄ = 0.25, 0.50 and 2.00.

The two readings of “tough” need to be kept apart. In the model with adaptive expectations, toughness (m̄) changes only the timing. In the real world, a reputation for toughness may lower expected inflation directly, which is a change in how expectations form, not in m̄. That is the subject of Fig. 20 and the Lucas critique.

Event 3: a demand boom

A boom abroad raises demand for U.S. exports. What do output and inflation do?

A demand shock \(\bar{a} = 2\) starts in year 1 and lasts nine years. How much of it shows up in output, and how much in inflation, in year 1?

The textbook’s example: a boom in Europe raises the demand for U.S. exports. Ask for the split between output and inflation. Students who remember λ = 1/2 get half and half: Ỹ = λā = 1, π − 2 = λν̄ā = 1.

A demand boom moves the economy up the AS curve

Model figure: demand shock \(\bar{a}\) in periods 1–9, baseline parameters. Adapted from Fig. 13.12 in Jones (2024), Macroeconomics, 6th ed.

How to read it: AD shifts out to AD₁, by ā points at every inflation rate. Firms see the extra demand and raise prices, so the economy moves up the unchanged AS curve from A to B. The slider sets ā; the title gives period-1 inflation and output.

Do live:

1. ā = 2: B at π = 3.00, Ỹ = 1.00.
2. ā = 4: π = 4.00, Ỹ = 2.00.
3. ā = −2, a fall in demand: π = 1.00, Ỹ = −1.00. Both fall.

Half of the boom goes into output, half into inflation

• The answer: output rises 1% and inflation 1 point, to 3%. Again half and half, because \(\lambda = 1/2\).
• A fall in demand is the mirror image: output and inflation both fall.
• The economy cannot stay at \(B\): inflation is above what firms expected, so the AS curve will shift.

Demand shocks move output and inflation in the same direction; price shocks move them in opposite directions.

Numbers: the Fig. 12 readouts and the first-period table of the Model overview (Ỹ₁ = λā, π₁ − π̄ = λν̄ā).

The takeaway is a practical diagnostic for policymakers: if inflation and output rise together, think demand; if inflation rises while output falls, think supply or prices. It is the same distinction the textbook uses to read the 1970s.

A notebook exercise: with ν̄ = 2 (prices react strongly), more of the shock goes into inflation and less into output.

While the boom lasts

The boom continues. Does the economy drift back to \(A\), or somewhere else?

The shock \(\bar{a} = 2\) stays in place for nine years. Firms keep updating their expectations. Where do inflation and output head? Hint: at the resting point output is at potential.

Most students expect the economy to return to A, as after the inflation shock. Ask them: with ā still positive, can inflation be at the target with output at potential? (No: the shifted AD curve gives output above potential at the target.)

As the boom persists, inflation climbs toward a higher resting point

Model figure: the path while \(\bar{a} = 2\) lasts, periods 1–9, baseline parameters. Adapted from Fig. 13.13 in Jones (2024), Macroeconomics, 6th ed.

How to read it: the slider picks the period. Inflation at B is above the 2 percent firms expected, so next year’s AS curve shifts up, and the economy climbs AD₁ from B toward C.

Do live:

1. t = 1: B, π = 3.00, Ỹ = 1.00.
2. t = 2: π = 3.50, Ỹ = 0.50. t = 3: 3.75 and 0.25.
3. t = 8: π = 3.99, Ỹ = 0.01: point C, the textbook’s period 8. t = 9: 4.00 and 0.00.

The same gap-halving as before, now toward C instead of A.

The boom ends at potential output with inflation of 4%

\[\text{at } C:\ \ \widetilde{Y} = 0 \text{ on AD}_1 \quad\Longrightarrow\quad \pi^c = \bar{\pi} + \frac{\bar{a}}{\bar{b}\bar{m}} = 2 + \frac{2}{1} = 4\%\]

• The answer: output falls back to potential while inflation rises toward \(\pi^c = 4\%\).
• \(C\) looks like a resting point, but it is not the steady state: inflation is above target, and the boom will end.
• A tougher bank keeps \(C\) closer to the target: with \(\bar{m} = 1\), \(\pi^c = 3\%\).

A rule that reacts only to inflation lets a lasting boom raise inflation for good.

Equation (9). At C the AS curve gives π_t = π_(t−1) (output at potential, so inflation is stable) and the shifted AD curve gives 0 = ā − b̄m̄(π^c − π̄).

Numbers: the notebook’s key numbers, π_c = 4.000 percent; simulated inflation in period 8 of 3.992 percent and output of 0.008 percent. The textbook’s label “eight periods” is arbitrary: the economy gets close to C and never quite reaches it. The notebook’s long simulations: after 60 periods π = 4.0000 with m̄ = 0.5 and π = 3.0000 with m̄ = 1.0, as the formula says.

The Model overview’s fifth prediction: the rule reacts to a demand shock only after it has raised inflation. A bank that could see ā directly could offset it with the interest rate (Chapter 12’s housing-bubble example). Act III shows why seeing it in real time is hard.

The whole boom

What happens when the boom ends, and what does the whole episode look like in the diagram?

The boom ends after year 9 and AD returns to where it started. Sketch the path from \(A\) through \(B\) and \(C\): where does the economy go next, and in which direction does the loop turn?

Give students 30 seconds to sketch. The key step: when ā returns to zero, the economy is at C with inflation near 4 and expectations near 4, so it jumps to a point with high inflation and output below potential. Ask for the direction of the loop: clockwise or counterclockwise?

A boom and its unwinding trace a counterclockwise loop

Model figure: demand shock \(\bar{a} = 2\) ending in the period set by the slider; panel (b) shows the time paths. Adapted from Figs. 13.14 and 13.15 in Jones (2024), Macroeconomics, 6th ed.

How to read it: panel (a) is the loop in the AS/AD diagram, A → B → C → D → A. The slider sets the last period of the shock; C and D mark that period and the next one. Panel (b) shows inflation and output over 20 periods. The title gives the inflation peak and the sum of output.

Do live:

1. Last period 9 (the textbook): inflation peaks at 4.00 percent; sum of Ỹ = 0.00. D is at π = 3, Ỹ = −1, the textbook’s point after the shock ends (its Fig. 13.14, period 10).
2. Move to 2: peak 3.50, sum still 0.00. Move to 3: peak 3.75. The loop is smaller.
3. Move to 12: peak 4.00, sum 0.01 (20 periods do not quite finish the slump).

Trace the loop with the pointer: right and up, up and left, down and left, back. Counterclockwise.

Booms are paid for with recessions

• The answer: when the boom ends, the economy drops to \(D\): inflation 3%, output −1%. Then both gaps halve each year back to \(A\).
• The path turns counterclockwise: up and right, up and left, down and left, back.
• Over the episode output adds up to 0.00: the boom and the slump cancel. What remains is years of high inflation.

A temporary boom is not free: the inflation it leaves behind is removed only by a later slump.

Numbers: the Fig. 15 readouts and the Model overview’s event 3: π₁₀ − π̄ = λ(π₉ − π̄) ≈ 1, so inflation is about 3 percent and output about −1 percent at D. The textbook’s label π₁ = π₁₀ holds here because b̄m̄ν̄ = 1; the notebook asks whether it still holds with ν̄ = 2.

Equation (8): inflation starts and ends at 2 percent with no inflation shocks, so the sum of output is zero.

Why central banks try to keep output at potential: the boom brings no net gain in output, only a long spell of high inflation and then a recession. A notebook exercise: for a shock that lasts 3 periods, inflation peaks at 3.75 percent.

The loops are the model’s testable prediction: Fig. 17 looks for them in U.S. data.

The policy response sets the shape of a slump; the AS slope sets its size

A higher …	recession on impact	speed of return \(1-\lambda\)	total output cost	inflation at \(C\)
policy response \(\bar{m}\)	deeper	faster	unchanged	closer to target
AS slope \(\bar{\nu}\)	milder	faster	smaller, \(1/\bar{\nu}\) per point	unchanged

Event (baseline)	output in year 1	inflation in year 1	total output
inflation shock \(\bar{o} = 2\)	−1%	3%	−2
target cut 4% → 2%	−1%	3%	−2
demand boom \(\bar{a} = 2\), 9 years	+1%	3%	0

One diagram, three shocks, one rule: the halving of the gap drives every path back home.

The first table is the book chapter’s “role of the parameters”, from equations (5) to (9) with λ = 1/(1 + b̄m̄ν̄), which falls when m̄ or ν̄ rises. The second table collects the baseline results of the three events.

Ask: which parameter would a central banker most like to change? (ν̄, or better, expectations themselves. The bank chooses m̄, but m̄ only reshapes the slump.)

Rules meet the data

Act III

Central banks set a nominal rate, which must rise more than one for one

\[i_t = \bar{r} + \pi_t + \bar{m}\,(\pi_t - \bar{\pi})\]

\[\text{Taylor:}\ \ i_t = 1 + 1.5\,\pi_t\]

Fisher equation \(i_t = R_t + \pi_t\); Taylor’s numbers \(\bar{r} = 2\), \(\bar{m} = 1/2\), \(\bar{\pi} = 2\).

inflation \(\pi\)	nominal \(i\)	real \(i - \pi\)
0.5%	1.75%	1.25%
2.0%	4.00%	2.00%
4.0%	7.00%	3.00%
6.0%	10.00%	4.00%

Each point of inflation lifts the nominal rate 1.5 points, so the real rate rises too.

Add π_t to both sides of the rule R_t − r̄ = m̄(π_t − π̄); the left side becomes R_t + π_t = i_t, by the Fisher equation of Chapter 8. Collect the π terms: i_t = (r̄ − m̄π̄) + (1 + m̄)π_t. With Taylor’s numbers, 2 − 1 = 1 and 1 + 0.5 = 1.5.

Numbers: the notebook’s check of equation (10) for π = 0.5, 2, 4 and 6 percent. At the 2 percent target the rule gives 4 percent, which is r̄ + π̄.

A limit: the rule asks for a negative nominal rate when inflation falls below −2/3 percent, which banks can hardly set. Chapter 14 returns to this zero lower bound.

The full Taylor rule also reacts to output, R − r̄ = m̄(π − π̄) + x̄Ỹ. Substituted into IS, it gives an AD curve of the same shape, steeper; with b̄ = 2 and x̄ = 1/2 the bank cancels half of a demand shock at once (notebook check: Ỹ = 1.00 instead of 2.00 for ā = 2 at the target).

A nominal rate that rises less than inflation makes inflation explode

When inflation rises, raising the interest rate a bit is enough to fight it.

If the nominal rate rises by less than inflation, the real rate falls (\(\bar{m} < 0\)), AD slopes up, and the gap grows each year. With \(\bar{m} = -1/4\) the inflation gap goes 2, 4, 8, 16 points. A stable rule raises the nominal rate more than one for one.

Numbers: the notebook’s check with m̄ = −0.25 in the baseline: b̄m̄ν̄ = −1/2, λ = 1/(1 − 0.5) = 2, and the inflation gap is 2.00, 4.00, 8.00 and 16.00 points in periods 1 to 4.

This is often called the Taylor principle. Clarida, Galí and Gertler (2000) estimate that the Fed’s response to inflation was below one for one before 1979 and well above one afterwards, one explanation for the high and unstable inflation of the 1970s (Fig. 16 shows the actual rate far below the rule then).

The fed funds rate and the rule

Does a one-line rule predict the Federal Reserve’s interest rate?

Ask the room: in which decades do you expect the Fed to have been below the rule (too loose), and when above it? Collect two or three guesses (the 1970s, after 2008, after Covid-19).

The simple rule follows the Fed’s big swings, with large gaps in three periods

Data: Board of Governors of the Federal Reserve System, effective fed funds rate (FEDFUNDS); U.S. Bureau of Economic Analysis, core PCE price index (JCXFE), via FRED. Chart inspired by Fig. 13.16 in Jones (2024), Macroeconomics, 6th ed.

How to read it: quarterly, in percent. The actual fed funds rate against the rule i = r̄ + π + m̄(π − π̄) with m̄ = 1/2 and π̄ = 2, using core PCE inflation over the last four quarters (prices of consumer spending without food and energy, the measure that reproduces the textbook’s line). The slider sets r̄; the title gives the average gap, actual minus rule, since 2009.

Do live:

1. r̄ = 2 (Taylor): point at the rise in the 1970s, the peak around 1980, the long decline. The highest rule rate is 16.15 percent in 1975Q1.
2. Point at 1967–1980: the actual rate is well below the rule.
3. Point at 2009–2020 and 2021–2022: far below again.
4. Lower r̄ to 0: the gap since 2009 shrinks from −2.89 to −0.89 points. Many economists now think the neutral real rate fell, but 2021–22 is still far off.

The book chapter also has the same test for 33 economies (BIS policy rates, OECD core CPI): the euro area, the U.K. and Canada were also below the rule after 2009, by 2.2, 3.3 and 2.6 points on average, and by 4.7, 5.9 and 5.5 points in 2021–2022.

The rule describes the Fed well, except in the 1970s, after 2008 and in 2021–22

• The two lines move together: correlation 0.75, 1960–2023.
• Actual minus rule: −2.3 points in 1967–80, policy was too loose and inflation rose; −2.7 in 2009–20; −6.7 in 2021–22.
• In recessions the Fed went below the rule; the full Taylor rule, which also reacts to output, explains part of that.

A rule is a useful yardstick: big departures from it are worth explaining.

Numbers: the notebook’s key numbers. Average gap (actual minus rule): 1967–1980, −2.29 points; 1990–1993, −0.94; 2001–2004, −1.67; 2009–2020, −2.71; 2021–2022, −6.74. Correlation 0.75 from 1960Q1 to 2023Q1.

Interpretation, with care. After 2008 the Fed was at the zero lower bound: the rule asked for rates the Fed could not set below zero, and it used other tools (Chapter 14). In 2021–22 the Fed raised rates late after the pandemic; the debate is whether it misread the inflation as temporary.

Latest data in the file: fed funds 3.67 percent in 2026Q3; core inflation 3.10 percent in 2026Q2.

Should the Fed follow a rule?

Congress gives the Fed its goals, not its methods. Should the Fed commit to a formula like Taylor’s, or keep full discretion?

What the model says

• A rule is predictable, so it anchors expectations.
• The rule must raise rates more than one for one.
• Taylor’s line tracks decades of policy.

What it leaves out

• New shocks: 2008, 2020.
• \(\bar{r}\) is unknown, and it moves.
• Inflation and the gap are revised later.

The left column is Act I and the Fig. 16 test. The right column: no rule could have foreseen the financial crisis or the pandemic, when the Fed’s discretion (emergency lending, asset purchases) mattered a lot; the rule’s answer depends on r̄, as the Fig. 16 slider shows (a 2-point change in r̄ moves the rule by 2 points every quarter); and real-time data get revised (Fig. 17).

The research. Taylor (1993, Carnegie-Rochester Conference Series on Public Policy) proposed the rule as a description and a guide, not as a formula to follow mechanically. Kydland and Prescott (1977, Journal of Political Economy) show why commitment can beat discretion: a bank free to surprise the public with inflation ends up with higher inflation and no gain in output (the time consistency problem; Nobel Prize 2004). Barro and Gordon (1983, Journal of Monetary Economics) add that reputation can do part of a rule’s work. The Fed’s Monetary Policy Report to Congress has compared its rate with several simple rules since 2017.

The textbook’s answer: no robot, but rules as guidelines. Bernanke calls the middle ground “constrained discretion”: flexibility in the short run, a firm commitment to the inflation target over the long run.

Ask the policy students: if a rule is published, who gains from it: the central bank, markets or voters?

Inflation and output in U.S. data

Does the U.S. economy move in the counterclockwise loops the model predicts?

Remind the room of Fig. 15: a boom raises inflation, high inflation leads the bank to cause a recession, the recession brings inflation down. Ask which decades should show the biggest loops.

U.S. years trace counterclockwise loops, largest before 1985

Data: BEA real GDP (GDPC1); CBO potential GDP (GDPPOT); BLS CPI (CPIAUCSL), via FRED; the textbook’s data vintage of 30 March 2023 from ALFRED. Chart inspired by Fig. 13.17 in Jones (2024), Macroeconomics, 6th ed.

How to read it: each point is one year, connected in order. Horizontal: the output gap, actual GDP relative to the CBO’s estimate of potential, in percent. Vertical: CPI inflation. A few key years are labeled; hover shows the rest. The buttons pick the period and the data vintage.

Do live:

1. “1960–1985”: the boom of the late 1960s raises inflation; the high inflation of 1974–75 and 1979–80 is followed by deep recessions (1975, 1982), and inflation falls. Counterclockwise.
2. “1985–2025”: smaller loops, the Great Moderation. The exceptions: 2009–2011, when inflation rose despite the slump, and the jump to 8 percent in 2022.
3. “1985–2022, textbook data”: the whole cloud moves left by about 1 point. Same shape, different level.

The loops are there, but the size of the gap depends on the data vintage

• Before 1985 the loops turn counterclockwise, as the model predicts. After 1985 they shrink.
• The textbook says output in 2009 was “more than 5 percent” below potential: −5.20% in its data, −4.66% in today’s.
• 2021 was a slump of −1.3% in the 2023 vintage and a small boom of +0.8% today, because potential output was revised down.

Potential output cannot be observed. Every output gap is an estimate, and estimates get revised.

Numbers: the notebook’s key numbers. 2009 gap: −5.20 percent (textbook vintage), −4.66 (current); 2021: −1.29 vs +0.81; 2022: −1.04 vs +0.92. Current minus textbook gap, 1985–2022: 1.03 points on average, 2.10 at most. Inflation rose from −0.32 percent in 2009 to 3.14 percent in 2011, partly because of energy and commodity prices: an inflation shock during a slump.

Other countries (fig. 17b in the book chapter, OECD gaps for 40 economies): the U.K. shows a textbook loop. The boom of 1987–89 (output 5.7 percent above potential in 1988) raised inflation to 8.0 percent in 1990; the slump that followed (−4.1 percent in 1993) brought it down to 2.6 percent. Japan from 1995 to 2013: inflation between −1.4 and +1.8 percent whatever the gap did, as if ν̄ were close to zero. The OECD’s U.S. gap for 2009 is −3.98 percent: another model, another number.

For the policy students: a rule that reacts to the output gap inherits all of these revisions.

Forecasting the Great Recession

Did professional forecasters see the collapse in jobs of 2008–09 coming?

Ask: if the Fed could forecast demand shocks well, it could offset them before they raise inflation (the end of Act II). How good are forecasts? Let students guess how far off the one-year-ahead forecasts were in 2008.

Forecast after forecast expected a mild slowdown while jobs collapsed

Data: Federal Reserve Bank of Philadelphia, Survey of Professional Forecasters, median forecasts of payroll employment (EMP); BLS payroll employment (PAYEMS), via FRED; after Stock and Watson (2017). Chart inspired by Fig. 13.18 in Jones (2024), Macroeconomics, 6th ed.

How to read it: the thick line is actual U.S. nonfarm payroll employment, in millions. Each thin line is the median forecast made in one quarter, from 2007Q4 to 2009Q4, for that quarter and the next four. Click legend entries to show or hide single forecasts.

Do live:

1. Show only the 2007Q4 and 2008Q1 forecasts: employment was expected to keep growing or hold steady.
2. Add 2008Q4, made after the panic of October 2008: a far milder fall than what happened.
3. Add the 2009 forecasts: only from mid-2009, near the trough, do they catch up.

James Stock and Mark Watson called this the “mother of all forecast errors”. The survey covers only the U.S.

Forecasters missed the collapse by millions of jobs

• Every one-year-ahead forecast from 2007Q4 to 2009Q4 was too high, by up to 7.2 million jobs (the survey of 2008Q3).
• Each new forecast was revised down, and was still too high. The errors fell to about 1 million only in mid-2009.
• A central bank that cannot see a demand shock coming can react only once it shows up in the data.

This is one reason rules respond to inflation, which is observed, rather than to shocks, which are seen too late.

Numbers: the notebook’s forecast errors, four quarters ahead: 2007Q4 survey 4.25 million jobs too high; 2008Q1 6.18; 2008Q2 6.83; 2008Q3 7.24; 2008Q4 5.86; 2009Q1 3.04; 2009Q2 0.90; 2009Q3 1.27; 2009Q4 0.95.

The link to the model: the textbook’s “further thoughts on demand shocks”. In principle the bank could set the interest rate to offset ā exactly and skip the whole boom-bust loop of Fig. 15. In practice ā is seen late and imperfectly, even by professionals. A rule that reacts to inflation reacts to the shock indirectly, through the AS curve.

Inflation in rich economies

Was the fall of inflation since the 1980s a U.S. achievement?

U.S. Fed chairs Volcker, Greenspan, Bernanke and Yellen get much credit for low inflation. Ask: did inflation fall just as much elsewhere? If so, what does that say about the credit?

Inflation was high everywhere in the 1970s and low almost everywhere after the 1980s

Data: OECD consumer price indices (DSD_PRICES@DF_PRICES_ALL), via the OECD Data Explorer; World Bank, World Development Indicators (FP.CPI.TOTL.ZG) for the euro area and other economies. Chart inspired by Fig. 13.19 in Jones (2024), Macroeconomics, 6th ed.

How to read it: annual CPI inflation, in percent. The buttons list a group of countries in the legend (“Textbook” = the U.S., the U.K., the euro area and Japan); a click on a country in the legend adds or removes it.

Do live:

1. “Textbook”: the 1970s peaks, the U.K. 24.2 percent in 1975, Japan 23.2 percent in 1974. Then low and stable from the 1990s; Japan near zero or below for almost two decades.
2. 2021–2022: inflation returns in the U.S., the U.K. and the euro area, then falls back in 2023–2024. Japan later, from 2022, still about 3 percent in 2025.
3. Add Germany and Switzerland: 1970s peaks of only 7.0 and 9.8 percent.

Data note: the textbook’s U.S. line ends at about 6.3 percent in 2022, but the full-year value is 8.0 percent; the textbook probably used an early partial-year number.

The taming of inflation was global

Average	U.S.	U.K.	Euro area	Japan
1970s	7.09	12.64	8.54	9.00
1990s	3.00	3.62	3.79	1.21
2010s	1.77	2.07	1.34	0.47

• 1970s peaks: U.K. 24.2%, Japan 23.2%, euro area 14.7%, U.S. 11.3%.
• In the 2010s all four averaged below 2.1%.
• Germany and Switzerland, with banks known for fighting inflation, peaked at only 7.0% and 9.8%.

If inflation fell everywhere, either good policy spread everywhere or everyone got lucky.

Numbers: the notebook’s inflation by decade and peaks in 1970–1979 (U.S. 11.25, U.K. 24.21, euro area 14.66, Japan 23.20 percent); Germany and Switzerland from the Fig. 19 notes.

Latest values: 2025 inflation, U.S. 2.69, U.K. 3.9, euro area 2.47, Japan 3.17 percent.

The textbook: a precise accounting of the taming of inflation is not available. The next slide is the debate.

Good policy or good luck?

Inflation and output became far more stable after the mid-1980s. Did central banks earn the credit?

Better policy

• Stronger responses to inflation after 1979.
• Germany, Switzerland: low peaks.
• Independent banks with explicit targets.

Good luck

• Smaller shocks: no repeat of the 1970s oil shocks.
• Volatility fell in many series.
• Luck ran out in 2008 and in 2021–22.

The left column: Clarida, Galí and Gertler (2000, Quarterly Journal of Economics) estimate policy rules before and after Volcker; the Fed’s response to inflation rose from below one for one to well above it. Romer and Romer (2004, Journal of Economic Perspectives), a case study in the textbook, argue that Fed chairs who understood the costs of inflation and the limits of policy did much better, and that their views were visible before they were appointed. The Bundesbank and the Swiss National Bank peaked low in the 1970s (Fig. 19).

The right column: Stock and Watson (2002, NBER Macroeconomics Annual) attribute much of the fall in U.S. output volatility after the mid-1980s to smaller shocks, with improved policy a smaller part. The answer is contested; most estimates leave a role for both.

The model gives a way to think about it: a smaller ō and ā give smaller loops (good luck); credibility and a well-chosen m̄ make shocks fade faster and cost less (good policy).

Ask: what evidence would separate the two? (Compare countries with different policies but similar shocks, or periods with similar shocks and different policies.)

When expectations look ahead, the AS curve moves with the target

\[\text{AS:}\quad \pi_t = \pi^e_t + \bar{\nu}\,\widetilde{Y}\!_t + \bar{o}\]

\[\pi^e = c\,\bar{\pi}' + (1-c)\,\bar{\pi} \quad\Longrightarrow\quad \widetilde{Y}\!_1 = -\bar{b}\bar{m}\lambda\,(1-c)(\bar{\pi} - \bar{\pi}')\]

• Rational expectations: firms use all their information, including the target the bank announces.
• \(c\) is the credibility of the announcement, between 0 (adaptive) and 1 (fully believed).

The recession of a disinflation shrinks in proportion to \(1-c\).

Equation (11) keeps expected inflation in the AS curve instead of last year’s inflation. Robert Lucas developed the idea of rational expectations (Nobel Prize 1995).

The credibility share c is the book chapter’s addition, not the textbook’s: after a cut in the target from π̄ to π̄′, firms build the share c of the cut into their expectations. The algebra of step 2 goes through with π^e in place of π_(t−1); expected inflation is above the new target by (1 − c)(π̄ − π̄′).

The notebook’s check: c = 0 gives Ỹ₁ = −1.00 and π₁ = 3.00 (Event 2), c = 1/2 gives −0.50 and 2.50, c = 1 gives 0.00 and 2.00.

A credible disinflation

Can a central bank lower inflation without a recession?

The bank announces a cut in its target from 4% to 2%. If firms fully believe it and expect 2% at once, what happens to output? And if only half believe it?

Ask students to draw both curves moving. Under adaptive expectations only AD moved. If firms believe the new target, the AS curve moves too. Ask what happens to the recession in each case.

If firms believe the new target, inflation falls with no recession

Model figure: target cut from 4% to 2%, with expected inflation \(c\cdot 2 + (1-c)\cdot 4\); the credibility slider is the book’s addition. Adapted from Fig. 13.20 in Jones (2024), Macroeconomics, 6th ed.

How to read it: AD and AS are the old curves through A (0, 4); AD′ is the new policy curve, shifted down by 2 points; AS′ is the AS curve with the expectations set by the slider. B is the economy in period 1. The title gives expected inflation, inflation and output.

Do live:

1. Credibility 1.00: expected 2.00, π = 2.00, Ỹ = 0.00. Both curves move down together; A to B at potential output. The textbook’s figure.
2. Credibility 0.50: expected 3.00, π = 2.50, Ỹ = −0.50.
3. Credibility 0: expected 4.00, π = 3.00, Ỹ = −1.00, the adaptive case of Event 2.

Every bit of credibility saves output

credibility \(c\)	\(\pi^e\)	\(\pi_1\)	\(\widetilde{Y}\!_1\)
0	4.0%	3.00%	−1.00%
0.5	3.0%	2.50%	−0.50%
1	2.0%	2.00%	0.00%

• The answer: a fully believed target is a free disinflation. Half credibility halves the slump.
• Adaptive: the whole path costs 2% of a year’s output. Fully credible: nothing.
• A bank tempted to surprise the public cannot be fully believed: the time consistency problem.

Managing expectations is one of the main tools of modern monetary policy.

Numbers: the notebook’s credibility check (c = 0, 0.5, 1) and the cost comparison: under adaptive expectations, output lost over 20 periods = 2.00 percent of potential output; with a fully credible target, period-1 output = 0.00 percent and inflation = 2.00 percent.

The time consistency problem (Kydland and Prescott): once firms and workers have set prices and wages on the basis of low expected inflation, a central bank is tempted to stimulate for a quick boom. Firms anticipate the temptation and build it into their prices: high inflation, no gain in output. A commitment, like Ulysses tied to the mast so as not to steer toward the Sirens, can be worth more than discretion.

The Lucas critique: a model with fixed expectations gives wrong answers about a new policy, because people change their expectations when the policy changes.

Can a central bank make a disinflation cheap?

A central bank must bring inflation down. Can announcements, targets and reputation do part of the work of a recession?

What the model says

• The slump shrinks with \(1-c\).
• Full credibility: no slump at all.
• Targets anchor what firms expect.

What the evidence adds

• Credibility must be earned first.
• Regime changes ended hyperinflations fast.
• Targeting’s own gains are debated.

The left column is Fig. 20. The right column: in practice credibility is earned, and disinflations have rarely been free.

The research. Goodfriend and King (2005, Journal of Monetary Economics), “The incredible Volcker disinflation”, argue that the 1979–84 disinflation was costly because the public did not believe the Fed at first; expected inflation, measured in long-term interest rates, stayed high for years. Sargent (1982, “The ends of four big inflations”, in Hall, ed., Inflation: Causes and Effects, University of Chicago Press) shows that the hyperinflations of the 1920s in Austria, Hungary, Poland and Germany stopped abruptly when fiscal and monetary regimes changed, with smaller output costs than the adaptive model predicts. Ball (1994, “What determines the sacrifice ratio?”, in Mankiw, ed., Monetary Policy, University of Chicago Press) finds that quick disinflations cost less output per point than slow ones. On inflation targeting itself, Ball and Sheridan (2005, in Bernanke and Woodford, eds., The Inflation-Targeting Debate) find that OECD countries that adopted targets did not perform much better than those that did not, once other factors are accounted for; others find larger gains in emerging economies. Name it as contested.

The U.S. adopted an explicit 2 percent target in 2012, Japan in 2013. Bernanke calls it “constrained discretion”.

Ask the policy students: would you rather have a central bank with a published target and less discretion, or a trusted chair with more?

Three centuries of U.K. inflation

Which period of U.K. history came closest to low and stable inflation?

Explain the goal first: a central bank wants inflation of about 2 percent, every year, with as little variation as possible. Ask students to guess which period of the last 300 years came closest: the gold standard, the postwar decades, or the age of inflation targets.

Only 1997–2016 came close to low and stable inflation

Data: Bank of England, A millennium of macroeconomic data for the UK (Thomas and Dimsdale, version 3.1), CPI inflation to 2016, research datasets; ONS CPI index (D7BT) from 2017; after Reis (2022). Chart inspired by Fig. 13.21 in Jones (2024), Macroeconomics, 6th ed.

How to read it: each point is a 20-year window of U.K. history since 1737. Horizontal: average yearly inflation in the window. Vertical: its volatility, the standard deviation of the yearly rates. The goal is the point (2, 0): 2 percent inflation with no variation. The last window, 2017–2025, has only 9 years and is marked differently. Hover over a point to see its distance to the goal.

Point at:

1. The war years, 1797–1816 and 1917–1936: low average inflation but huge volatility.
2. Deflation in much of the 19th century, and high inflation from 1937 to 1996.
3. 1997–2016, the years of Bank of England independence and inflation targeting: 1.9 percent on average with a volatility of 1.1.
4. 2017–2025 drifting away, pulled by the burst of 2021–2023.

Independence and a target delivered the best two decades in 300 years

• 1997–2016: average 1.92%, volatility 1.06, a distance of 1.07 from the goal.
• The next-best full window, 1877–1896, is at 3.48, with deflation of about 1% a year.
• The partial window 2017–2025 sits at 3.16: the inflation burst of 2021–23 pulled it away.

Low and stable inflation is a recent and hard-won achievement, and it can slip.

Numbers: the notebook’s key numbers. Distances to the goal (2, 0): 1997–2016, 1.07; 2017–2025 (9 years, average 3.63, volatility 2.70), 3.16; 1877–1896 (average −1.02, volatility 1.73), 3.48; 1897–1916, 4.67; 1857–1876, 4.85. 1977–1996: average 6.34, volatility 4.07.

Other countries (fig. 21b in the book chapter, the Jordà–Schularick–Taylor Macrohistory Database for 17 more countries since 1870): in 16 of the 18 countries, the window closest to the goal is 1997–2016. Canada’s is even closer than the U.K.’s (1.86 percent, volatility 0.68). In Japan and Switzerland, where inflation averaged close to zero in 1997–2016, the partial window 2017–2025 comes closest. Germany’s 1917–1936 window holds the hyperinflation of 1923, so the chart leaves it out.

The textbook’s conclusion: the Great Moderation was a great accomplishment of monetary policy, but the name seems quaint after 2008, the pandemic and 2021–22.

“Real people are not that naive”

A skeptic says: “This whole model assumes firms simply expect last year’s inflation. Real price setters read the news and listen to the central bank. With rational expectations, the adaptive AS/AD model is just wrong: that is the Lucas critique.”

Reply: the model needs only that expectations move slowly, and the data agree. Disinflations have cost real recessions, and the U.S. loops turn as the model says. Fig. 20 spans the range from adaptive to fully credible, and the lesson holds either way: the more the public believes the target, the cheaper low inflation is.

Take the objection seriously. Lucas (1976, Carnegie-Rochester Conference Series on Public Policy) showed that a model with fixed expectations can give wrong answers about a new policy, and modern models build rational expectations in. The textbook itself presents rational expectations as a second benchmark.

The reply. First, sticky expectations are an empirical fact more than a theory: the Volcker disinflation cost a deep recession (Goodfriend and King 2005 attribute it to low credibility), and the counterclockwise loops of Fig. 17 appear only if inflation adjusts slowly. Second, the textbook’s case study raises the question whether people can compute the implications of a policy change, and whether the cost of doing so keeps inflation sticky; research continues. Third, the two benchmarks bracket reality: the credibility slider of Fig. 20 is a way to reason between them.

Ask: what measure of expected inflation would you watch if you were a central banker? (Surveys of households and firms, professional forecasts, the gap between nominal and inflation-protected bond yields.)

What to remember from this chapter

• A policy rule turns the IS curve into a downward AD curve; the Phillips curve is the upward AS curve. In the steady state \(\widetilde{Y}^* = 0\) and \(\pi^* = \bar{\pi}\).
• Sticky expectations make every shock fade slowly: the gap halves each year in the baseline.
• Price shocks bring stagflation; disinflation costs \(1/\bar{\nu}\) per point whatever \(\bar{m}\); booms are paid for with slumps, in counterclockwise loops.
• Taylor’s rule tracks the Fed (0.75), with big gaps in the 1970s, after 2008 and in 2021–22.
• Credibility makes low inflation cheap: targets, independence and reputation.

Ask each student to write one sentence answering the opening question: what happens to output and inflation when the central bank follows a rule? A good answer: the rule makes AD slope down, the economy always returns to the target with output at potential, but because expectations are sticky the return is slow and costs output; a credible target makes it cheaper.

For the policy students, three habits: ask whether a shock is to prices or to demand (opposite or same signs); judge a disinflation by its total cost, not its depth; and ask how much the public believes the central bank.

Walk the three branches of the mind map in about a minute each: a rule and one diagram (cyan), three events (lavender), rules meet the data (green). Click the image to zoom in.

A rule makes the short-run model one diagram; credibility makes low inflation cheap

Next: Chapter 14, Financial Crises and the Short-Run Model

This chapter gave the central bank a rule and put the short-run model into one diagram. Chapter 14 adds financial crises: what happens when the interest rate the bank sets is not the rate firms and households pay, and when the rule asks for a rate below zero.

Sources: data and models

• Figs. 1, 3, 5, 6, 8, 9, 11, 12, 13, 15 and 20, the AS/AD model. The book chapter’s own simulations with the baseline \(\bar{\pi} = 2\), \(\bar{m} = 1/2\), \(\bar{b} = 2\), \(\bar{\nu} = 1\). Adapted from Figs. 13.1, 13.3, 13.5–13.15 and 13.20 in Jones (2024); the credibility slider and the time-path panels are the book’s additions.
• Fig. 16, the policy rule. Federal Reserve Board, FEDFUNDS; BEA, JCXFE, via FRED; other economies: BIS policy rates (WS_CBPOL), OECD CPI excluding food and energy. Inspired by Fig. 13.16 in Jones (2024).
• Fig. 17, inflation-output loops. BEA GDPC1; CBO GDPPOT; BLS CPIAUCSL, via FRED and ALFRED; OECD Economic Outlook No. 119 output gaps. Inspired by Fig. 13.17 in Jones (2024).
• Fig. 18, forecasts. Federal Reserve Bank of Philadelphia, Survey of Professional Forecasters (EMP); BLS PAYEMS, via FRED; Stock, J. and M. Watson (2017), Journal of Economic Perspectives 31(2). Inspired by Fig. 13.18 in Jones (2024).
• Fig. 19, OECD inflation. OECD consumer price indices (DSD_PRICES@DF_PRICES_ALL); World Bank WDI (FP.CPI.TOTL.ZG). Inspired by Fig. 13.19 in Jones (2024).
• Fig. 21, U.K. inflation since 1737. Bank of England, A millennium of macroeconomic data for the UK (Thomas and Dimsdale, v3.1); ONS D7BT; Jordà–Schularick–Taylor Macrohistory Database; Reis, R. (2022), LSE working paper. Inspired by Fig. 13.21 in Jones (2024).
• Textbook. Jones, C. I. (2024). Macroeconomics, 6th ed. W. W. Norton. Book chapter, with the data, code and every figure: Data Science and Macroeconomic Models, Chapter 13.

Sources: research cited

• Rules and commitment. Taylor, J. B. (1993), Carnegie-Rochester Conference Series on Public Policy 39; Kydland, F. and E. Prescott (1977), Journal of Political Economy 85(3); Barro, R. and D. Gordon (1983), Journal of Monetary Economics 12(1); Bernanke, B. (2003), “Constrained discretion” and monetary policy, speech, Federal Reserve Board; Board of Governors of the Federal Reserve System, Monetary Policy Report (semiannual); Clarida, R., J. Galí and M. Gertler (2000), Quarterly Journal of Economics 115(1).
• Expectations and disinflation. Lucas, R. E. (1976), Carnegie-Rochester Conference Series on Public Policy 1; Goodfriend, M. and R. King (2005), Journal of Monetary Economics 52(5); Sargent, T. (1982), in R. Hall (ed.), Inflation: Causes and Effects, University of Chicago Press; Ball, L. (1994), in N. G. Mankiw (ed.), Monetary Policy, University of Chicago Press.
• Inflation targeting and the Great Moderation. Ball, L. and N. Sheridan (2005), in B. Bernanke and M. Woodford (eds.), The Inflation-Targeting Debate, University of Chicago Press; Stock, J. and M. Watson (2002), NBER Macroeconomics Annual 17; Romer, C. and D. Romer (2004), Journal of Economic Perspectives 18(1).