After twenty chapters, the widest income gap is still the one we explain least

2% GDP per person of the ten poorest of 110 countries, relative to the U.S., 2023

Their capital alone would put them at 24% of U.S. income. What keeps them at 2%? That is still an open question.

Open the last lecture with the number that best sums up what macroeconomics knows and does not know. The notebook’s Lesson 1: across 110 countries in the Penn World Table, the ten poorest earn on average 0.023 of U.S. GDP per person in 2023. If they had their own capital per person but U.S. productivity, the production model predicts 0.244.

So we know where the gap is: in total factor productivity, which averages 0.094 for these ten countries, less than a tenth of the U.S. level. We do not know why TFP is so low. Hold that question: it is the first open question in Act III.

Frame the lecture: this chapter builds no new model. It puts twenty chapters side by side as five lessons, two from growth, one about money, two about the short run, and then turns to what is still unknown.

Today: three questions

• The long run. What sets living standards, why do some countries grow faster for decades, and what drives inflation?
• The short run. Why can a central bank move output, and why does being believed make that cheaper?
• The frontier. Which big questions are still open, and how would we measure the answers?

These are the three branches of the mind map on the title slide. Act I covers the book’s Lessons 1 to 3 (Chapters 3 to 8), Act II Lessons 4 and 5 (Chapters 9 to 14), Act III the open questions, with Chapters 16 to 20 behind the policy slides.

The deck has two live charts, both from the chapter notebook: Japan’s catch-up with a menu of country groups, and the U.S. Phillips curve. Every other number on the slides is recomputed in the notebook from data files you already met.

The long run

Act I

The book’s long-run models fit in one table

Model (chapter)	Key result	What it says
Production (4)	\(y^* = \bar{A}\bar{k}^{1/3}\)	capital has strongly diminishing returns
Solow (5)	\(y^* = \left(\bar{s}/\bar{d}\right)^{1/2}\bar{A}^{3/2}\)	investment sets the level, not the growth rate
Romer and Solow–Romer (6)	\(g_y^* = \gamma\bar{n}\), \(\;\tfrac{3}{2}\gamma\bar{n}\)	new ideas set the long-run growth rate
Labor market (7)	\(u^* = \bar{s}/(\bar{s}+\bar{f})\)	job flows set unemployment
Quantity theory (8)	\(\pi^* = \bar{g}_M - \bar{g}_Y\)	money growth sets inflation

Real forces set output and unemployment; money sets prices.

Walk the rows top to bottom; each is one chapter’s headline result, collected in the notebook’s Model overview, where each is derived step by step (equations 1, 3, 6, 7, 10 and 11 there).

• Production: an exponent of 1/3 on capital means that to be ten times richer through capital alone, a country would need a thousand times more capital per person.
• Solow: in logs, a 1 percent rise in the investment rate raises y* by 0.5 percent, a 1 percent rise in TFP by 1.5 percent. Capital accumulation alone cannot sustain growth.
• Romer: ideas are nonrival, so income per person depends on the total stock of knowledge; with capital, growth is 3/2 times faster because part of the extra output is invested.
• Labor market: s̄ here is the job-separation rate (the same letter as the investment rate in Solow, as in the book). Institutions such as hiring and firing costs and unemployment insurance work through s̄ and f̄.
• Quantity theory: with constant velocity, one more point of money growth means one more point of inflation.

The notebook’s “model in code” checks every row by simulation, e.g. a Solow economy simulated for 300 years lands on y* = 2.236, the formula’s value.

Lesson 1: living standards

How much of the income gap between the poorest countries and the U.S. can their lack of capital explain?

Ask the room for a share before showing the table. Remind them of the tool: development accounting from Chapter 4. Measured income relative to the U.S. is split into two factors, the part that capital per person predicts (k^(1/3)) and the residual, TFP.

Capital alone would put the poorest at a quarter of U.S. income; low TFP takes them to 2%

\[\frac{y_1^*}{y_{US}^*} = \frac{\bar{A}_1}{\bar{A}_{US}}\times\left(\frac{\bar{k}_1}{\bar{k}_{US}}\right)^{1/3}\]

U.S. = 1, in 2023	Actual income	From capital alone	TFP
Ten poorest countries (average)	0.023	0.244	0.094
China	0.298	0.707	0.422

The puzzle is less “why so little capital?” than “why so little TFP?”

The notebook’s Lesson 1, Penn World Table data for 110 countries (Venezuela is dropped: hyperinflation broke its 2023 price data). Actual income is the product of the two factors: for China, 0.298 = 0.422 × 0.707. With its own capital and U.S. TFP, China would be at 71 percent of U.S. income instead of 30.

For the ten poorest, capital alone predicts about a quarter of U.S. income; actual income is about 2 percent. The other factor of ten is TFP.

Caveat: TFP is measured as a residual, the part of income that capital does not explain. Lesson 1 of the textbook also names skills and hours worked; with human capital in the accounting, the residual shrinks but stays large. A residual is a measure of our ignorance, which is why Act III starts here.

Your turn from the notebook: look up India and decide whether its gap is mostly a capital gap or a TFP gap.

Lesson 2: transition dynamics

Japan earned a fifth of U.S. income per person in 1950. What happened next?

Sketch Japan’s income relative to the U.S. from 1950 to 2022. Does it catch up fully, overtake, or stop short? When does the gap stop closing?

Give students a minute to sketch. The principle they should use: an economy below its steady state grows faster than the world frontier, and the further below, the faster; growth slows as the gap closes. The textbook’s guess for Japan’s steady state is about 0.75 of U.S. income.

Collect a few sketches: some will draw full convergence to 1, some an overshoot.

Japan closed most of the gap by 1991, then slipped back

Data: Groningen Growth and Development Centre, Maddison Project Database 2023 (gdppc, 2022 dollars; Bolt and van Zanden 2024). Chart inspired by the discussion in Chapter 21 of Jones (2024), Macroeconomics, 6th ed.

How to read it: each line is one economy’s GDP per person divided by U.S. GDP per person in the same year, so the U.S. is the line at 1 (not drawn). The menu shows one group at a time: the textbook’s case (Japan), two groups from the discussion (“Catching up”, “Falling behind”), then one per Maddison region. The dashed line at 0.75 is the textbook’s guess for Japan’s steady state. Hover to read a value; click a name in the legend to hide it.

Do live:

1. “Textbook: Japan”: point at 1950 (0.20), the steep climb, the peak of 0.85 in 1991 and the drift down to 0.65 in 2022.
2. “Catching up”: South Korea from 0.07 to 0.71, Taiwan from 0.10 to 0.91, and China’s late but steep rise.
3. “Falling behind”: Argentina from 0.52 to 0.31, Venezuela from 0.56 to 0.09. Keep this for the next slide but one.
4. Pick a region, e.g. East Asia or Latin America, and ask which economies look like Japan.

In Colab the notebook has a picker for any of the 168 economies.

Fast growth far below the steady state, slower growth as the gap closes

• The answer: Japan rose from 0.20 of U.S. income in 1950 to a peak of 0.85 in 1991, then fell to 0.65 in 2022.
• From 1950 to 2000 Japan grew 4.8% a year, the U.S. 2.2%.
• South Korea went from 0.07 to 0.71 and Taiwan from 0.10 to 0.91.

\[g_{k,t} = \bar{d}\left[\left(\frac{k^*}{k_t}\right)^{2/3} - 1\right]\]

The further an economy is below its own steady state, the faster it grows.

Reveal the sketches. Most students draw convergence; few draw the slide back after 1991. Japan’s ratio is now a little below the textbook’s 0.75; the model has no reason to stop at the peak, because the peak was above where Japan’s policies put its steady state.

The equation is the Solow version of transition dynamics (equation 4 of the notebook’s Model overview): capital per person grows at a rate set only by the distance to the steady state; output per person grows about a third as fast. The combined Solow–Romer model gives the same message around a balanced growth path (equation 9).

Data lesson: over 1870–2022 the Maddison data give 1.6 percent a year for the U.S. and 1.2 for the U.K.; the textbook quotes 2.0 and 1.5, and Chapter 3’s U.S. series gives 1.9. Data sets disagree about the 19th century; the gap between the two countries survives. For Japan and the U.S. after 1950 the data reproduce the textbook’s 4.8 and 2.2 exactly.

The same logic predicts that China’s fast growth will slow as it nears its own steady state.

Catch-up is toward a country’s own steady state, not toward the U.S.

Transition dynamics says poor countries grow faster, so they all catch up with the rich.

Only economies below their own steady state grow fast. Policies and institutions can move that steady state down: Argentina fell from 0.52 of U.S. income in 1950 to 0.31 in 2022, Venezuela from 0.56 to 0.09.

Numbers: the notebook’s Fig. 1 “What to notice” (Maddison data). Show the “Falling behind” group on the previous chart if you have not yet.

The point is the word “own”. In the Solow model the steady state depends on the investment rate, depreciation and TFP; in the combined model also on the research share. Countries with high investment and improving institutions (South Korea, Taiwan) had a steady state far above where they started, so they grew fast. Argentina and Venezuela started rich, but their steady states fell, so they grew more slowly than the U.S. for decades: transition dynamics in reverse.

This is conditional convergence: among countries with similar steady states (the OECD of Chapter 5), the poor grow faster; across the whole world, there is little sign that the poor grow faster.

Lesson 3: the classical dichotomy

Suppose a country’s money supply grows ten points a year faster, for decades. What happens to its inflation? To its real GDP?

Let students answer both halves. The trap: many think more money must mean more output, at least a little. The long-run answer of Chapter 8 is that money growth shows up in prices, one for one, and real GDP is set by the real forces of Lessons 1 and 2.

Where money grows fast, prices rise fast: a correlation of 0.85 across 165 economies

1990–2025, % a year	Japan	Switzerland	U.S.	Türkiye	Argentina	Brazil
Broad money growth	2.1	4.8	5.8	47.3	68.0	216.0
Inflation	0.7	1.1	2.7	37.5	96.8	238.7

\[\pi^* = \bar{g}_M - \bar{g}_Y\]

In the long run, money sets inflation and real forces set output: the classical dichotomy.

The notebook’s Lesson 3, World Bank data (Chapter 8’s file): average annual growth of broad money and average CPI inflation, 1990–2025. Inflation runs from under 1 to over 200 percent, so the notebook measures the fit with the correlation of the logarithms: 0.85.

A gap to explain: in the median economy, money grew 13.9 percent a year and prices 6.8 percent, about 7 points apart. With constant velocity the gap would be real GDP growth; it is larger because velocity fell in many economies as their financial systems deepened (Chapter 8).

Where does fast money growth come from? The government’s budget: ΔM = G − T − ΔB. A government with a large deficit that cannot borrow prints money. And long-run unemployment is a separate problem with separate causes: the job-losing and job-finding rates of u* = s̄/(s̄ + f̄), set by labor-market institutions, not by money.

The short run

Act II

In the short run, the central bank moves output through a chain of curves

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

\[\text{Phillips: } \Delta\pi_t = \bar{\nu}\,\widetilde{Y}\!_t + \bar{o} \qquad\qquad \text{Okun: } u_t - \bar{u} = -\tfrac{1}{2}\widetilde{Y}\!_t\]

With a policy rule \(R_t - \bar{r} = \bar{m}(\pi_t - \bar{\pi})\), the IS curve becomes aggregate demand:

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

Sticky inflation is the hinge: because \(\pi_t\) barely moves, a higher \(i_t\) raises the real rate \(R_t\).

The notebook’s Model overview, equations (12) to (15), Chapters 9 and 11 to 13.

Read the chain left to right: the central bank raises the nominal rate i; inflation is sticky, so the real rate R rises (MP, from the Fisher equation); investment, and in an open economy net exports, fall, so short-run output Ỹ falls (IS); a slump slows inflation (Phillips); and unemployment rises by half a point per point of lost output (Okun).

The AD curve replaces the central bank’s case-by-case choice with a rule: when inflation is above target, raise the real rate. It slopes down in (Ỹ, π). With the Phillips curve as aggregate supply, the AS/AD framework of Chapter 13.

A toy number from the notebook’s IS check: with b̄ = 2 and r̄ = 2 percent, a real rate of 1 percent puts output 2 percent above potential and a rate of 5 percent 6 percent below.

Lesson 4: the short-run trade-off

When U.S. output runs above potential for a year, how much does inflation pick up?

Predict the slope: does inflation rise by about 0, about 1/3 or about 1 point per percent of output above potential? How closely will the U.S. years since 1961 follow that rule?

Students met this estimate in Chapter 9. Ask who remembers the number; then ask whether they expect a tight line or a cloud. Write two or three guesses on the board.

U.S. inflation speeds up in booms and slows in slumps

Data: BEA, real GDP (GDPC1); CBO, real potential GDP (GDPPOT); BLS, CPI for all urban consumers (CPIAUCSL), via FRED. Chart inspired by the discussion in Chapter 21 of Jones (2024), Macroeconomics, 6th ed.

How to read it: each dot is one U.S. year from 1961 to 2025. Across: short-run output Ỹ, the percent gap between real GDP and the CBO’s potential. Up: the change in CPI inflation from the year before, in percentage points. The line is the least-squares fit; its slope is in the title. Hover over a dot to see its year.

Do live:

1. Point at the fitted line: it rises.
2. Hover over the outliers far above the line: the oil-shock years of the 1970s and 2021–2022. Those are price shocks ō, not booms.
3. Hover over a deep slump on the left, e.g. 2009 or 2020: inflation fell.

The chart is U.S.-only: the output gap needs an estimate of potential output, and this book’s data files have the CBO’s for the U.S. only (the OECD and the IMF publish gaps for other countries).

The slope is about a third, as in Chapter 9, but shocks scatter the points

• The answer: a slope of 0.35 from 65 years (1961–2025), close to the “about 1/3” of Chapter 9.
• The intercept is 0.10: with output at potential, inflation barely changes.
• Price shocks \(\bar{o}\), the 1970s oil shocks and 2021–2022, push years far off the line.

A boom buys output today at the price of faster inflation tomorrow.

Numbers: the notebook’s Lesson 4, np.polyfit of Δπ on Ỹ. Reveal the predictions: most students remember a third.

What the slope means: keeping output 1 percent above potential for one year raises inflation by about a third of a point, and the next year by another third, because the curve is in the change of inflation. A boom that lasts keeps pushing inflation up.

Why the cloud: the Phillips curve has a price-shock term ō, and the expected inflation behind it may not equal last year’s inflation. Both move points off the line.

Your turn from the notebook: has the curve become flatter? Fit 1961–1999 and 2000–2025 separately. A flatter curve since the 1990s is one of the debates of Chapter 12.

Money is neutral in the long run, not in the short run

If money is neutral in the long run, the central bank cannot change real output.

Because inflation is sticky, raising the nominal rate \(i_t\) raises the real rate \(R_t\), which cuts investment and net exports. Output falls below potential, and the classical dichotomy returns only as inflation adjusts.

This myth mixes Lessons 3 and 4. Lesson 3 is about decades: money growth shows up in prices, and output is set by real forces. Lesson 4 is about the next year or two: with inflation stuck near last year’s rate, the central bank’s nominal rate is in effect a real rate.

In an open economy, the higher real rate also attracts foreign funds, the currency appreciates and net exports fall (Chapter 20, Fig. 4), a second channel to lower output.

Ask: what would have to be true for a change in the nominal rate to have no real effect even in the short run? (Inflation would have to jump at once by the same amount, so the real rate would not change. That is what perfectly flexible prices and expectations would do.)

Lesson 5: credibility

In 1980 U.S. inflation was 13.5%. By 1985 it was 3.5%. How much output did the U.S. give up to get there?

Paul Volcker became Fed chair in August 1979 and raised interest rates sharply. Ask for a guess in percent of a year’s GDP: 2? 5? 15? Then introduce the measure: the sacrifice ratio, the output lost in total (the sum of the negative output gaps) per point of lower inflation.

Volcker’s disinflation cost 16.4% of a year’s GDP: 1.6% for each point

U.S., 1980–1985
Fall in CPI inflation	13.5% → 3.5%, 10.0 points
Output lost: the sum of the negative \(\widetilde{Y}\!_t\)	16.4% of a year’s potential GDP
Sacrifice ratio	1.6% of output per point

\[\pi_{\text{start}} - \bar{\pi} = -\bar{\nu}\sum_t \widetilde{Y}\!_t \quad\Longrightarrow\quad \text{sacrifice ratio} = \frac{1}{\bar{\nu}}\]

With adaptive expectations, the slope of the Phillips curve fixes the total slump, however fast the central bank moves.

The notebook’s Lesson 5, from the same U.S. file as Fig. 2: over the six years 1980–1985 the output gaps below zero add up to 16.4 percent of a year’s potential GDP, for a fall in inflation of 10.0 points.

The equation: add up the Phillips curve over every year of the adjustment; the changes in inflation sum to the total fall, so the output lost per point is 1/ν̄ (the notebook’s Model overview, after equation 16). Its Check 7 simulates a disinflation from 6 to 2 percent with ν̄ = 0.5 and finds exactly 2.0 = 1/ν̄, whatever the central bank’s reaction m̄.

Our arithmetic, not the notebook’s: with the measured slope of 0.35, adaptive expectations would predict about 1/0.35 ≈ 2.9 per point, more than the measured 1.6. One reading: expectations fell faster than last year’s inflation, a sign of partial credibility. A second: the ratio is sensitive to the years chosen (the notebook’s Your turn compares 1980–1983 and 1981–1986).

A central bank that is believed can disinflate with a smaller slump

\[\text{Adaptive: } \pi_t^e = \pi_{t-1} \quad\Longrightarrow\quad \text{inflation falls only through a slump}\]

\[\text{Credible: } \pi_t^e = \bar{\pi} \quad\Longrightarrow\quad \pi_t = \bar{\pi} \text{ with } \widetilde{Y}\!_t = 0\]

After credibility was rebuilt, U.S. inflation averaged 2.3% in 1993–2019, against 6.3% in 1970–1989.

Being believed is a policy tool: it moves expectations so that output does not have to move.

The Phillips curve is π_t = π_t^e + ν̄Ỹ_t + ō. If price setters expect last year’s inflation, the only way to bring inflation down is Ỹ < 0. If they believe the new target and set π_t^e = π̄, inflation can fall to the target with output at potential: the costless disinflation of Chapter 13, Fig. 20.

The paradox in the textbook’s fifth lesson: a central bank known to be tough on inflation needs fewer recessions, so credibility stabilizes output too.

The averages are the notebook’s Lesson 5 numbers. Caveat: low inflation after 1993 also reflects good luck (fewer oil shocks) and globalization; credibility is one of several explanations.

Should central banks announce explicit inflation targets?

Since 1990, from New Zealand to the Fed in 2012, many central banks have announced a numerical inflation target. Does a number build credibility?

What the model says

• A believed target lowers \(\pi^e\).
• A smaller slump is needed.
• A rule ties the bank’s hands.

What is debated

• Targets, or just good luck?
• Rigid when supply shocks hit.
• Credible at the zero bound?

The model: the credibility slide. Kydland and Prescott (1977, Journal of Political Economy) showed why discretion leads to inflation: once expectations are set, a central bank is tempted to inflate to raise output, people anticipate it, and the economy gets the inflation without the output. A public commitment, a rule, removes the temptation.

The evidence is contested. Bernanke, Laubach, Mishkin and Posen (1999, Inflation Targeting: Lessons from the International Experience, Princeton University Press) argue that targets anchor expectations and make policy transparent. Ball and Sheridan (2005, in Bernanke and Woodford, eds., The Inflation-Targeting Debate, University of Chicago Press) compare OECD countries that adopted targets with those that did not, and find that the adopters’ gains mostly reflect regression to the mean: inflation fell everywhere. Ball (1994, in Mankiw, ed., Monetary Policy, University of Chicago Press) finds that fast disinflations had smaller sacrifice ratios.

Ask the policy students: after the inflation of 2021–2022 (Chapter 10), should central banks keep a target of 2 percent, raise it, or switch to a target for the price level?

The frontier

Act III

Five big questions are still open

• Low TFP. Why do poor countries invest so little and use their inputs so poorly?
• Institutions. Which ones work best for new ideas, for sharing the gains from trade, for money?
• Potential output. How do we tell a slower trend from a recession, in real time?
• Bubbles. Why do they form, and what should policy do about them?
• Aging. How will governments pay for pensions and rising health spending?

The five questions of the textbook’s last section, in our words, each with a chapter behind it:

1. Low TFP: Lesson 1. Weak property rights and rule of law lower the return to investing, but why are they weak? (policy slide ahead)
2. Institutions: patents, prizes and research funding for ideas (Chapter 6); sharing the gains from trade, which create winners and losers (Chapter 19); currency boards, a single currency and capital controls, and the policy trilemma (Chapter 20, Figs. 7 and 8).
3. Potential output: it cannot be measured directly. Mistaking a slowdown in potential for a recession leads to too much stimulus (Chapter 12, Fig. 13). Next slides.
4. Bubbles: the standard model explains the slump after spreads rose in 2008, but not why the housing bubble formed or why banks became so leveraged (Chapters 10 and 14).
5. Aging: long-run budget projections and rising health spending (Chapter 18, Figs. 6 and 8). Policy slide ahead.

Potential output in real time

Since 2003, has U.S. productivity growth sped up, held steady or slowed down?

Ask the room: smartphones, cloud computing, AI. Most students expect faster productivity growth. The answer is on the next slide.

U.S. productivity growth fell by almost half after 2003

U.S. private business, % a year	1995–2003	2003–2025
Output per hour	3.2	1.8
Total factor productivity	1.5	0.8

A gap of 1.4 points a year for 22 years adds up to about a third less output per hour.

A pause or a new normal? The answer decides what counts as potential output, and so what counts as a recession.

The notebook’s open-questions section, from the BLS growth-accounting indexes of Chapter 6 (private business sector, release of March 2026), with the growth_rate function of Lesson 2.

Why it matters for policy: if potential output slows and the central bank reads the slower growth as a negative output gap, it stimulates too much and inflation rises. That is the textbook’s reading of the 1970s productivity slowdown. Orphanides (2003, Journal of Monetary Economics) shows that the Fed’s real-time estimates of the output gap in the 1970s were far too negative. The reverse happened in the late 1990s: the Fed under Greenspan judged that faster growth was a rise in potential, and did not raise rates as much.

The research on the slowdown is unsettled. Gordon (2016, The Rise and Fall of American Growth, Princeton University Press) argues that today’s inventions matter less than electricity or the engine. Byrne, Fernald and Reinsdorf (2016, Brookings Papers on Economic Activity) and Syverson (2017, Journal of Economic Perspectives) find that mismeasurement of digital goods explains little of it.

Your turn from the notebook: compute the same rates for 1948–1973 and 1973–1995. Which earlier period does 2003–2025 resemble?

Can policy raise TFP in poor countries?

TFP explains most of the gap between rich and poor countries. Which reforms would raise it, and how sure are we?

What the models say

• Investors who cannot keep their returns invest little.
• Ideas are nonrival: adopting existing ones is cheap.
• So the gap points to the rules, not to a lack of ideas.

What is debated

• Institutions, geography or skills: which comes first?
• Rich countries may build good institutions, not the reverse.
• Which reforms, in which order, for which country?

The left column: Lesson 1 and Chapter 4. TFP of 0.094 for the ten poorest countries; since ideas are nonrival and mostly available worldwide, low TFP must come from how inputs are used, which the textbook links to property rights and the rule of law.

The evidence. Hall and Jones (1999, Quarterly Journal of Economics) do development accounting across countries and find that output per worker is closely related to “social infrastructure”, the institutions and government policies that shape incentives. Acemoglu, Johnson and Robinson (2001, American Economic Review) use the mortality of early European settlers as a source of variation in institutions and find large effects of institutions on income today.

Contested. Glaeser, La Porta, Lopez-de-Silanes and Shleifer (2004, Journal of Economic Growth) argue that human capital comes first, and that institution measures partly reflect income. Albouy (2012, American Economic Review) questions the settler-mortality data. Nobody has a recipe; the textbook’s question is still the right one: why are property rights weak where they are weak?

Ask the policy students: if you advised a development bank, would you fund schools, courts or roads first?

Can growth keep the debt of aging societies in check?

Pensions and health care will cost more as populations age. Can governments grow their way through, or must taxes rise or spending fall?

\[b^* = \frac{(G-T)/Y}{g_Y - i}\qquad \text{if } g_Y > i\]

What the model says

• Deficit 2% of GDP, \(g_Y = 5\%\), \(i = 3\%\): \(b^* =\) 100%.
• If \(i > g_Y\), no limit.

What is debated

• How long will \(i < g_Y\) last?
• Aging: bigger deficits, slower growth.

The equation: the debt-GDP ratio of the notebook’s Model overview (Chapter 18). Divide the debt equation B_(t+1) = (1 + i)B_t + G_t − T_t by nominal GDP; when nominal growth g_Y exceeds the interest rate i and the deficit is a constant share of GDP, the ratio settles at b. The notebook’s Check 9 simulates 400 years with the slide’s illustrative numbers and lands on b = 1.000, 100 percent of GDP.

The research. Blanchard (2019, American Economic Review, “Public Debt and Low Interest Rates”) argues that with interest rates below growth for most of U.S. history, debt has lower fiscal costs than often thought. Mauro and Zhou (2021, IMF Economic Review) find that r − g < 0 is common across countries and centuries, but can turn positive suddenly, just before debt crises. The Congressional Budget Office’s long-term budget outlooks project rising U.S. debt, driven by health care, Social Security and interest costs.

The textbook’s frame: either taxes rise substantially, or spending on retirement and especially health falls relative to trends. As people get richer, they want to spend more on health, so the health share of GDP will likely keep rising (Chapter 18, Fig. 8).

Ask the policy students: which would you choose, and who would bear the cost?

“Macroeconomics failed: it missed 2008 and cannot say why poor countries are poor”

A skeptic says: “Twenty chapters of models, and the profession did not see the financial crisis coming, cannot explain the productivity slowdown, and calls the biggest gap of all a residual.”

Reply: the models say where the ignorance is, and what to measure. They put the poor-country gap in TFP (0.094), not in capital. They predicted Japan’s slowdown, the money–inflation link (0.85) and the cost of disinflation (1.6 per point). Naming what we do not know is how a science moves forward.

Take the objection seriously: it is partly right. The textbook itself says the standard model explains the fall in activity once spreads rose in 2008, but not why the housing bubble formed or why banks became so leveraged. And TFP is, by construction, the part of income our inputs do not explain.

The reply: a model is a tool for organizing the data. Every number in the reply was recomputed in this chapter’s notebook from data the models told us to collect. Without development accounting we would not know that the poor-country gap is mostly TFP; without transition dynamics Japan’s slowdown would look like failure, not arithmetic; without the Phillips curve we could not price a disinflation.

The textbook’s closing thought, in our words: research and learning both live in confusion before understanding. The open questions of this act are the invitation.

Ask: which open question would you most like to see answered, and what data would you collect first?

What to remember from this book

• Levels: capital, skills, hours, ideas and TFP set living standards; TFP explains most of the gap.
• Growth: new ideas sustain it; economies far below their own steady state grow fast, then slow.
• Long run: money sets inflation (0.85 across 165 economies); real forces set output.
• Short run: sticky inflation gives a Phillips trade-off (slope 0.35) and lets policy move output.
• Credibility: a believed central bank lowers inflation with a smaller slump.

Ask each student to write one sentence for the opening question: what has macroeconomics learned, and what does it still not know? A good answer names one lesson and one open question, e.g. “Inflation is a monetary phenomenon in the long run, but we still don’t know why TFP is so low in poor countries.”

The notebook’s Model overview collects the twenty key results in one place, with links back to the chapter where each model was built.

Walk the three branches of the mind map in about a minute each: the long run (cyan), the short run (lavender), the frontier (green). Click the image to zoom in.

Five lessons explain growth, inflation and the cycle; the deepest questions are still open

The end of the book

This is the last chapter. Reopen any notebook, change a parameter and ask your own question. Every notebook in the book has live figures and parameters you can change; the data files are public and the code reads them from GitHub. The best way to keep learning macroeconomics is to pick a question from Act III and start measuring.

Sources: data and figures

• Fig. 1, income relative to the U.S. Groningen Growth and Development Centre, Maddison Project Database 2023 (doi:10.34894/INZBF2; Bolt and van Zanden 2024), gdppc in 2022 dollars. Inspired by the discussion in Chapter 21 of Jones (2024).
• Fig. 2, the U.S. Phillips curve, and the 1980–85 disinflation. BEA GDPC1; CBO GDPPOT; BLS CPIAUCSL, via FRED. Inspired by the discussion in Chapter 21 of Jones (2024).
• Development accounting. Penn World Table 11.0, with capital per person by perpetual inventory (the book’s Chapter 4 files).
• Money and inflation. World Bank WDI FM.LBL.BMNY.ZG and FP.CPI.TOTL.ZG, gaps filled from the World Bank’s Global Inflation Database (Ha, Kose and Ohnsorge) (the book’s Chapter 8 file).
• Productivity. BLS, Total factor productivity and related measures for major industries, release of March 19, 2026 (the book’s Chapter 6 file).
• Textbook. Jones, C. I. (2024). Macroeconomics, 6th ed. W. W. Norton. Book chapter, with the data, code, every figure and the twenty key results: Data Science and Macroeconomic Models, Chapter 21.

Sources: research cited

• Credibility and inflation targets. Kydland, F. and E. Prescott (1977), “Rules Rather than Discretion: The Inconsistency of Optimal Plans”, Journal of Political Economy 85(3); Bernanke, B., T. Laubach, F. Mishkin and A. Posen (1999), Inflation Targeting: Lessons from the International Experience, Princeton University Press; Ball, L. (1994), “What Determines the Sacrifice Ratio?”, in N. G. Mankiw (ed.), Monetary Policy, University of Chicago Press; Ball, L. and N. Sheridan (2005), “Does Inflation Targeting Matter?”, in B. Bernanke and M. Woodford (eds.), The Inflation-Targeting Debate, University of Chicago Press.
• Potential output and the slowdown. Orphanides, A. (2003), Journal of Monetary Economics 50(3); Gordon, R. J. (2016), The Rise and Fall of American Growth, Princeton University Press; Byrne, D., J. Fernald and M. Reinsdorf (2016), Brookings Papers on Economic Activity, Spring; Syverson, C. (2017), Journal of Economic Perspectives 31(2).
• Institutions and TFP. Hall, R. E. and C. I. Jones (1999), Quarterly Journal of Economics 114(1); Acemoglu, D., S. Johnson and J. Robinson (2001), American Economic Review 91(5); Glaeser, E., R. La Porta, F. Lopez-de-Silanes and A. Shleifer (2004), “Do Institutions Cause Growth?”, Journal of Economic Growth 9(3); Albouy, D. (2012), American Economic Review 102(6).
• Debt and aging. Blanchard, O. (2019), “Public Debt and Low Interest Rates”, American Economic Review 109(4); Mauro, P. and J. Zhou (2021), IMF Economic Review 69(1); Congressional Budget Office, The Long-Term Budget Outlook (annual).