In 2018, prices in Venezuela rose about 650-fold in a single year

65,374% Venezuela’s inflation rate in 2018

U.S. prices took 66 years, from 1959 to 2025, to rise about 11-fold. What makes prices rise, and why do some governments let inflation explode?

Open with the number. It comes from the notebook’s Fig. 7 key numbers: 65,374 percent in 2018, followed by 19,906 percent in 2019. An inflation rate of 65,374 percent means the price level ends the year 654.7 times higher than it started it: something that cost one bolívar in January cost about 650 by December.

The contrast is the U.S. price level of Fig. 1: 100 in 1959 and about 1,105 in 2025, so prices rose about 11-fold over 66 years.

Ask the room: what would you do with your wages if prices rose that fast? (Spend them the same day; switch to dollars; buy goods that keep their value.) Those are the costs of inflation we come back to in Act III.

This chapter is the last long-run chapter. Chapters 3 to 7 explained real variables: income, capital, ideas, wages, employment. Now we explain a nominal one, the price level, and its growth rate.

Today: three questions

• How do we measure inflation? The growth rate of a price index, U.S. inflation since 1960, prices across the years, and the world.
• Where does inflation come from? The quantity theory of money, neutrality, and two tests with U.S. history and 165 economies.
• What does inflation do, and why do governments allow it? Real and nominal interest rates, who gains and who loses, the inflation tax and hyperinflations.

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

The headline result: in the long run, inflation is money growth beyond the growth of real GDP; nominal interest rates carry inflation with them; and very high inflation comes from governments that pay their bills by printing money.

Two famous one-liners frame the chapter. Milton Friedman: inflation is a monetary phenomenon. Thomas Sargent: persistent high inflation is a fiscal one. By the end of the deck students should see why both are right.

Measuring inflation

Act I

Inflation is the growth rate of the price level

\[\pi_t = \frac{P_{t+1} - P_t}{P_t} \qquad\Longrightarrow\qquad P_T = P_0\,(1+\pi)^T\]

• \(P_t\) is a price index: the cost of a basket of goods, set to 100 in a base year. The CPI uses a household’s basket; the GDP deflator uses all of GDP.
• When \(\pi_t < 0\), prices fall: deflation.
• Small rates add up. By the rule of 70, at 2% a year prices double in about 35 years.

Inflation is about the change in prices, not their level.

The left equation is the definition. Multiplying by P_t and adding P_t gives P_{t+1} = (1 + π_t)P_t; chaining the years gives the right equation when the rate is constant. Fig. 1 builds the U.S. price level in exactly this way from the inflation rates.

Rule of 70: set P_T/P_0 = 2 and take logs, T ln(1 + π) = ln 2, and ln 2 is about 0.70. So the doubling time is about 70 divided by inflation in percent. The notebook’s Check 1 confirms it: a price index growing at 2 percent for 35 years ends at 200.

The same algebra gives average inflation over many years: π̄ = (P_T/P_0)^{1/T} − 1, the formula Fig. 3 uses for decades.

Ask: a pension of 1,000 dollars a year that is never raised: what does it buy after 35 years at 2 percent? (What 500 dollars bought when it started.)

U.S. inflation since 1960

U.S. prices rise every year, but how fast has varied a lot. When was inflation highest, and has it ever been negative?

Let students guess before the reveal. Most know about the 2021–2022 burst; fewer know the 1970s. Ask the older students, or anyone whose parents talk about mortgage rates in 1980.

Ask also: did U.S. prices ever fall from one year to the next?

The Great Inflation of the 1970s, two calm decades, and a Covid burst

Data: U.S. Bureau of Labor Statistics, CPI for All Urban Consumers (CPIAUCSL), via FRED, annual averages; World Bank, WDI (FP.CPI.TOTL.ZG) and Global Inflation Database for the other G20 economies. Inspired by Fig. 8.1 in Jones (2024), Macroeconomics, 6th ed.

How to read it: the annual inflation rate of the U.S. consumer price index, in percent, since 1960. The button at the top switches to the price level, on a ratio scale, starting at 100 in 1959.

Do live:

1. Hover over 1980: the peak, 13.5 percent. Then 2009: slightly negative, deflation. Then 2022: 8.0 percent.
2. Click “price level”: prices are about 11 times their 1959 level. On a ratio scale a steeper line means faster inflation: the steepest stretch is the 1970s.
3. Back on “inflation rate”, click Germany and Japan in the legend. Germany peaked at only 7.0 percent in 1973, Japan at 23.2 percent in 1974. In the price-level view Japan’s line is almost flat from the mid-1990s to 2021: prices fell in 15 of those 27 years.

Data caveat: the series is the annual average of the monthly CPI, so the peaks are lower than the monthly twelve-month rates reported in the news at the time.

Inflation rose for fifteen years, fell fast, and stayed near 2% for two decades

United States	Inflation
average 1960–1964	1.26%
peak, 1980	13.50%
average 2000–2019	2.17%
2009	−0.32%
2022	7.99%
2025	2.63%

• The Great Inflation built up from the late 1960s to 1980, then ended in a few years.
• From 1992 to 2020 inflation stayed below 4%.
• The Great Inflation hit the whole rich world, but not equally: Germany peaked at 7.0%, Japan at 23.2%.

Inflation can stay low for decades and still come back.

All numbers come from the notebook’s key numbers for Fig. 1.

The end of the Great Inflation is the story of Paul Volcker’s Federal Reserve after 1979, which the short-run chapters model. Here we only need the fact that inflation is not fixed by nature: it rose and fell with policy.

The Covid burst of 2021–2022 is the reminder. After almost three decades below 4 percent, many people assumed high inflation was a thing of the past.

Ask: Germany and Japan faced the same oil shocks as the United States in the 1970s. Why did their inflation differ so much? (Keep the question open: the money-growth tests of Act II and the interest-rate figure of Act III return to it.)

Inflation is not the same as high prices

Prices are high today, so inflation must be high.

The U.S. price level in 2025 was the highest ever, about 4 times its 1980 level. But inflation was 2.63% in 2025, against 13.50% in 1980. Inflation measures how fast prices change.

The myth mixes up a level and a growth rate, the distinction of Chapter 3. In the CPI of Table 8.1, rescaled to 2025 = 100, the price level of 1980 is 25.59: a quarter of today’s. So prices are far higher now, but they are rising much more slowly.

When people say “prices are still high” after an inflation burst, they are right about the level. When inflation falls back to 2 percent, prices keep rising, only more slowly. They do not fall back, unless there is deflation, and the 2009 episode shows that deflation is rare and small.

For the policy students: a government that promises to “bring prices down” after a burst is promising deflation, which central banks avoid. What it can promise is lower inflation.

A price index moves a price from one year into the dollars of another

Year	CPI, 2022 = 100	CPI, 2025 = 100
1900	2.78	2.53
1950	8.23	7.48
1970	13.27	12.06
1980	28.15	25.59
2000	58.84	53.49
2022	100.00	90.91
2025	110.00	100.00

\[X_b = X_a \times \frac{P_b}{P_a}\]

• Gasoline at 27¢ in 1950 cost $3.28 in 2022 dollars, and $3.61 in 2025 dollars.
• A pension of $10,000 fixed in 1970 bought in 1983 what $3,900 bought in 1970: it lost 61% of its value.

The table is the textbook’s Table 8.1, from the MeasuringWorth CPI, with a column added for the latest base year. Every cell of the textbook’s version is reproduced in the notebook.

The formula: multiply by the ratio of the two price levels. For gasoline: 0.27 × 100/8.23 = 3.28. The “1950 dollars” cancel, like units in a conversion. Only the ratio matters, so the base year makes no difference: the 2025 column gives the same answer in 2025 dollars.

So gasoline was only a little cheaper in 1950 than in 2022, although the sticker price was thirteen times lower.

The pension example is the textbook’s retiree. The notebook finds a loss of 61 percent by 1983; the textbook rounds it to 60 percent and 4,000 dollars. It returns in Act III: anyone with an income fixed in dollars loses when inflation is higher than expected.

Ask: what were 100 dollars of 1900 worth in 2025 dollars? (100 × 100/2.53, about 3,950 dollars.)

High inflation around the world

Count the countries with inflation above 25% a year. Was the U.S. Great Inflation part of a world wave, and is high inflation more or less common today?

The threshold of 25 percent is the textbook’s definition of high inflation for this figure. Ask the students to sketch the share of countries over time before the reveal: when was it highest?

Ask also: with a threshold of 10 percent instead, would the chart look very different?

High inflation peaked in the early 1990s and has been rare since 2000

Data: World Bank, World Development Indicators, Inflation, consumer prices (FP.CPI.TOTL.ZG); World Bank regions and OECD membership. Inspired by Fig. 8.2 in Jones (2024), Macroeconomics, 6th ed.

How to read it: for each year, the percentage of economies whose inflation was above the threshold on the slider. The default is 25 percent.

Do live:

1. At 25 percent: small in the 1960s, a jump in 1974, high through the 1980s, a peak of 31.1 percent in 1994, then a collapse.
2. Move the slider to 10 percent: in 1974 most countries had double-digit inflation. Move it to 100 percent: inflation that high never hit more than about one country in nine, with a peak in the early 1990s.
3. Click the regions in the legend. Latin America & Caribbean reached 41 percent in 1974 and 39 percent in 1991; Europe & Central Asia peaked at 40.5 percent in 1993, after the Soviet Union broke up; Sub-Saharan Africa jumped to 55.6 percent in 1994, when the CFA franc was devalued by half.

Data caveat: the number of economies with data more than doubles over the period, so the early shares rest on fewer countries. Hover over a line to see how many.

High inflation came in waves, and the last wave ended in the 1990s

Inflation above 25%	Share of countries
1960s, highest	5.6%
peak, 1994	31.1%
2002–2025, highest (2023)	7.9%
2025	3.0%

• The waves had regional causes: Latin America in the 1970s and 1980s, the former Soviet Union after 1991, West and Central Africa in 1994.
• Countries with data rose from 63 in 1960 to 192 at most.
• The Covid years brought a small rise, then a fall.

What changed after the 1990s? Act III points to how governments pay their bills and who controls the printing press.

The numbers come from the notebook’s key numbers for Fig. 2. The textbook’s description holds: below 6 percent in the 1960s, almost one country in three in 1994, below 5 percent in every year from 2002 to 2021.

The decline since the mid-1990s is one of the big changes in the world economy. Several explanations compete: more independent central banks, governments with better access to borrowing, the end of the transition from planned economies, and inflation targets. The policy slide on central bank independence comes back to it.

Ask: a country with 25 percent inflation, is that a hyperinflation? (No. The usual definition is above about 500 percent a year: Figs. 6 and 7.)

Money and prices

Act II

Money comes in several measures, from currency to savings deposits

Billions of dollars	January 2023	August 2026
currency	2,299	2,476
monetary base: currency + bank reserves	5,329	5,412
M1: + checking accounts	19,597	19,991
M2: + savings and money market accounts	21,274	23,343

• Broader measures add accounts that are harder to turn into cash.
• M1 jumped from 4,856 to 16,313 between April and May 2020: the Fed redefined M1.
• A series break makes growth rates across it meaningless, so the tests use M2.

The table is the textbook’s Table 8.2 from the Federal Reserve’s H.6 release; January 2023 reproduces it within rounding. The notebook adds the latest month.

Currency is the narrowest measure: paper money and coins. The monetary base adds the reserves banks keep at the central bank. M1 adds checking accounts, and M2 adds savings and money market accounts.

The data-hygiene lesson: M1 more than triples in one month in 2020. Nobody printed 11 trillion dollars. In May 2020 the Federal Reserve moved savings deposits into M1. Always check a jump against the definitions before you interpret it.

Today’s money is not backed by gold: it is fiat money, valued because others accept it. Digital payment apps move existing money between accounts; they do not create new money.

The quantity equation: money times velocity equals nominal GDP

\[M_t\,V_t = P_t\,Y_t\]

• \(V_t\), the velocity of money, counts how many times a year each dollar is spent.
• Nominal GDP, \(P_tY_t\), is all the spending on final goods in a year.
• Example: money of 100 and nominal GDP of 200 mean each dollar changes hands twice a year, \(V = 2\).

On its own this is almost a definition of \(V\). It becomes a theory once we add three assumptions.

The example is the chapter’s illustrative economy: money 100, velocity 2, real GDP 200, so the price level is 1.

The equation holds by construction if we measure V as PY/M. The content of the quantity theory lies in the extra equations of the next slide, above all the assumption that V and Y do not respond to M.

Ask: when you pay by card instead of cash, does velocity change? (It can: the same money supports more spending. That is why velocity drifts slowly with payment habits and technology.)

Four equations pin down money, velocity, prices and output

Equation	Name	What it takes as given
\(M_tV_t = P_tY_t\)	quantity equation	nothing
\(Y_t = \bar{Y}_t\)	classical dichotomy	real GDP, from the growth models of Chapters 4 to 6
\(V_t = \bar{V}\)	constant velocity	payment habits and technology
\(M_t = \bar{M}_t\)	money supply	the central bank’s choice

The classical dichotomy: in the long run, real GDP is set by real forces alone. Money and prices do not enter the growth models.

As everywhere in the book, a bar marks a variable taken as given from outside the model. Three of the four equations simply set a variable equal to something given; the fourth links them.

The classical dichotomy is an assumption we have been making all along. The Solow and Romer models determine output from capital, labor, ideas and productivity. There is no price level in them.

Constant velocity is the shakiest assumption, and Fig. 3’s velocity chart tests it. The money supply as a choice of the central bank is a simplification: Chapter 12 models how central banks decide.

Solving the model: the price level and inflation

\[P^*_t = \frac{\bar{M}_t\,\bar{V}}{\bar{Y}_t}\]

• The spending power of money over the goods there are to buy.
• With \(\bar{M} = 100\), \(\bar{V} = 2\), \(\bar{Y} = 200\): \(P^* = 1\).

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

• Money that grows as fast as real GDP only keeps up with the extra goods.
• With \(\bar{g}_M = 5\%\) and \(\bar{g}_Y = 3\%\): \(\pi^* = 2\%\) (exactly 1.94%).

Inflation is money growth beyond the growth of real GDP: “too much money chasing too few goods”.

Left: substitute the three given variables into the quantity equation and divide by Ȳ.

Right: take logs of the quantity equation in two consecutive years and subtract. Each change in a log is approximately a growth rate, so g_M + g_V = g_P + g_Y. With constant velocity g_V = 0, and π = g_P.

The exact discrete-time version is π = (1 + g_M)/(1 + g_Y) − 1 = 1.05/1.03 − 1 = 1.94 percent. The notebook’s Check 3 simulates the economy year by year and gets 1.942 percent in every year. For the moderate rates of Figs. 1 to 5 the shortcut is close; for hyperinflations it is not (with 100 percent money growth: 94 percent exact, 97 by the shortcut), but the message is the same.

Changes in levels move prices once; changes in growth rates move inflation

A change in …	the price level \(P^*\)	inflation \(\pi^*\)
money \(\bar{M}\), up 1% once	+1%	no lasting change
velocity \(\bar{V}\), up 1% once	+1%	no lasting change
real GDP \(\bar{Y}\), up 1% once	−1%	no lasting change
money growth \(\bar{g}_M\), up 1 point	rises faster every year	+1 point
real GDP growth \(\bar{g}_Y\), up 1 point	rises more slowly	−1 point

Real GDP growth stays within a few percent; money growth can be anything. So big, lasting differences in inflation must come from money growth.

Taking logs of P* = MV/Y gives ln P* = ln M + ln V − ln Y: every elasticity is one in size. The notebook’s Check 2 confirms it: 1 percent more money or velocity raises P* by 1.000 percent; 1 percent more real GDP lowers it by 0.990 percent (1/1.01, an elasticity describes small changes).

The bottom rows are the key prediction. Growth models keep real GDP growth in a narrow band, a few percent a year. Money growth is a policy choice and has ranged from 2 percent to thousands of percent. Figs. 3 and 4 test exactly this.

Ask: an oil shock raises prices for a year. Is that inflation in this model? (It is a one-time jump in the price level if it lowers Ȳ once; only lasting money growth keeps inflation high.)

Money is neutral in the long run

\[\frac{\lambda\,p_{\text{bread}}}{\lambda\,p_{\text{book}}} = \frac{p_{\text{bread}}}{p_{\text{book}}} \qquad\qquad \frac{\lambda W}{\lambda P} = \frac{W}{P}\]

• Multiply money by \(\lambda\), say 2: the price level doubles, from 1 to 2.
• If every price and wage doubles, every relative price and the real wage stay put: still 10 loaves for an hour of work.
• Nobody has a reason to work, buy or produce differently: real GDP stays at \(\bar{Y}\).

Neutrality holds in the long run. In the short run, prices and wages adjust slowly, and money can move real GDP: Chapters 9 to 13.

The numbers are from the notebook’s Check 2: doubling money doubles P*, and a real wage of 10 loaves an hour stays at 10 loaves.

Relative prices and the real wage are the signals people act on. If money changes all nominal values in proportion, the signals are unchanged. A currency reform that replaces every old note with λ new ones is the same experiment, and countries that have done it saw no change in real output from the reform itself.

Why only the long run? If some prices are slow to adjust, a burst of money first changes relative prices, and firms produce more for a while. The short-run model is built around this idea.

Printing money does not make a country richer

If the government printed more money, everyone could buy more.

Doubling the money supply doubles the price level, from 1 to 2. The real wage stays at 10 loaves an hour, and real GDP stays where the growth models put it. Only more goods make a country richer.

The myth treats money as wealth. For one person it is: a person who finds a hundred-dollar bill is richer. For a whole country, more money with the same goods only raises the prices of the goods.

The argument is the neutrality slide: with V and Y given, P rises in proportion to M. Venezuela and the hyperinflations of Act III are the extreme proof: money grew by thousands of percent, and real GDP fell.

The subtle point for the policy students: printing money does transfer resources, from the people who hold money to the government that spends it. That is the inflation tax of Act III. It does not create resources.

Testing the theory with U.S. history

Each point will be one U.S. decade since 1870: average money growth across, average inflation up. If velocity were constant and real GDP never grew, points would lie on the 45° line \(\pi = g_M\). Where do you expect them, and why?

Collect predictions. The strong form says: on the 45-degree line. The quantity theory with growth says: below it, by about the growth rate of real GDP minus the growth of velocity.

Ask for a number: if real GDP grows about 3 percent a year and velocity is roughly flat, how far below the line? (About 3 points.) Then reveal.

U.S. decades line up with money growth, about 4 points below the 45° line

Data: Jordà–Schularick–Taylor Macrohistory Database (broad money, CPI), 18 economies, 1870–2020; Federal Reserve, M2 (M2NS), via FRED; MeasuringWorth CPI. Inspired by Fig. 8.3 in Jones (2024), Macroeconomics, 6th ed.

How to read it: each point is one U.S. period. Across, the average annual growth of broad money (M2 after 1959); up, average annual CPI inflation. The upper line is the 45-degree line; the lower one is shifted down by the average gap in the data.

Do live:

1. At 10-year periods: the 1910s and the 1970s have the fastest inflation and fast money growth; the 1920s and 1930s had slow money growth and deflation. The title reports the U.S. correlation, 0.76, and the average gap, 4.0 points.
2. Move the slider to 5 years: the cloud is wider, because wars and the Great Depression move prices a lot over a few years. Move it to 20 years: only 8 points, all with money growth between 5 and 9 percent.
3. Back at 10 years, click Japan, Italy and France: their 1940s sit far up and to the right (Japan: money growth 45 percent, inflation 65 percent a year), on the same band. Germany’s 1920s are listed in a note: money grew 1,139 percent a year, prices 1,210 percent.

Data caveat: the last U.S. point covers only 2020–2025. The other countries stop in 2020, and some have gaps.

Fast-money decades were high-inflation decades

U.S. decade	Money growth	Inflation
1980s	7.66%	4.72%
1990s	4.05%	2.80%
2000s	6.08%	2.39%
2010s	7.43%	1.73%
2020–2025	4.41%	4.46%

• The gap \(g_M - \pi\) is about 4 points, close to real GDP growth minus velocity growth.
• All 18 rich economies: correlation 0.86, the same gap of 4.0 points.
• The fit is best over long periods: the theory is about the long run.

The table shows the five most recent rows of the decade table; the earlier decades are in the live chart. The correlation and the average gap for all 18 countries are in the notebook’s notes to Fig. 3.

Why is the gap about 4 points and not 3? The quantity theory says π = g_M + g_V − g_Y. Real GDP growth is part of it; falling velocity adds to it. The next figure shows that U.S. velocity was not constant.

Look at the 2010s: money grew 7.4 percent and inflation was only 1.7 percent. The gap of almost 6 points is much larger than average. The 2020s reversed it. Hold that thought for the velocity chart.

Is velocity really constant?

The theory assumed a constant velocity. We can measure it: \(V = PY/M\). How do you think U.S. M2 velocity behaved since 1960?

Ask students to sketch it. A flat line is the textbook’s assumption. Some will guess that card payments and online banking raised velocity.

Hint for the discussion: velocity is the ratio of nominal GDP to money. If people hold more money for the same spending, velocity falls.

Velocity was steady for 30 years, then rose and fell

Data: U.S. Bureau of Economic Analysis, GDP (GDPA); Federal Reserve, M2 (M2SL), via FRED, calendar-year averages. Our chart; the textbook discusses velocity in Chapter 8 of Jones (2024), Macroeconomics, 6th ed., without a figure.

How to read it: nominal GDP divided by M2, one point per year.

Do live: hover over 1960 and 1990 (about 1.8 both), 1997 (2.18, the peak), 2021 (1.16, the trough) and 2025 (1.41).

Why did it move? In the 1990s, money flowed out of savings deposits into mutual funds that are not part of M2, so M2 grew slowly relative to spending. After 2008 and again in 2020, interest rates on deposits were near zero and households piled up savings in bank accounts, so M2 grew much faster than spending.

When velocity falls, money can grow faster without more inflation

Year	M2 velocity
1960	1.78
1970	1.78
1980	1.86
1990	1.85
1997	2.18
2007	1.98
2021	1.16
2025	1.41

\[\pi = \bar{g}_M + g_V - \bar{g}_Y\]

• From 1960 to 1990, velocity was close to the textbook’s assumption.
• With \(g_V < 0\), as after 1997, the gap \(g_M - \pi\) is larger than real growth.
• In 2021–2025 velocity rose again, and inflation came back.

All values come from the notebook’s velocity cell.

Velocity explains two things we saw. First, why the U.S. gap in Fig. 3 is about 4 points rather than the 3 points of real growth: velocity fell on average. Second, why the 2010s had fast money growth and low inflation: velocity was falling fast.

The notebook’s Check 3 also simulates a velocity that falls 1 percent a year: with 5 percent money growth and 3 percent real growth, inflation drops from 2 to 1 percent.

This is the main objection to the quantity theory, and the Devil’s-advocate slide at the end takes it on.

Testing the theory across the world

Now each point will be one of 165 economies, with average money growth and inflation over 1990–2025, on ratio scales. Do fast-money countries have high inflation? With real growth of 3%, how many lie above the line \(\pi = g_M - g_Y\)?

Collect predictions for both questions. For the second, remind students what “above the line” means: inflation higher than money growth minus 3 percent. If the quantity theory with constant velocity were exact and every country grew 3 percent a year, every point would sit on the line.

Ask them also to name a country they expect at the top right.

Across 165 economies, faster money growth means higher inflation

Data: World Bank, World Development Indicators, broad money growth (FM.LBL.BMNY.ZG) and CPI inflation (FP.CPI.TOTL.ZG), with gaps from the Global Inflation Database. Inspired by Fig. 8.4 in Jones (2024), Macroeconomics, 6th ed.

How to read it: one point per economy, average annual broad-money growth across, average inflation up, both on ratio scales. The line is the quantity theory, π = g_M − g_Y, for the growth rate on the slider. The buttons switch between the textbook’s period, 1990–2021, and 1990–2025.

Do live:

1. At g_Y = 3 percent: 42 of 165 economies lie above the line. Brazil, Angola and the Democratic Republic of the Congo sit at the top right, with both rates in the hundreds of percent.
2. Move the slider to 0: the line becomes the 45-degree line, and most economies lie below it, because real GDP grows.
3. Note the bend: on a ratio scale, subtracting g_Y bends the line down a lot at low money growth and hardly at all at high money growth.
4. Hover over Georgia and Venezuela, far above the band: their money averages cover fewer years than their inflation averages (Georgia’s money starts after its hyperinflation; Venezuela’s stops before it). Not a fair test.

The economies line up along a rising band

1990–2021	Money growth	Inflation
Switzerland	4.8%	1.0%
Denmark	4.2%	1.8%
Turkiye	46.8%	35.3%
Argentina	63.6%	92.6%

• Correlation of the logs: 0.85 in both periods.
• The middle half of economies: money growth 9.4–20.8%, inflation 3.2–17.8%.
• The median gap \(g_M - \pi\) is 5.6–5.8 points: larger than real growth, so velocity fell in many economies.

Across time and across countries, the quantity theory gets the big picture right.

The four rows are the textbook’s examples; they hold in the 1990–2021 averages. The correlation, the middle half and the median gap are from the notebook’s key numbers. The World Bank now spells Turkey “Turkiye”.

The fit is about the big differences: between 1 percent and 1,000 percent. Within the dense cloud at the lower left, money growth explains much less. Other things matter there: velocity, real growth, and the period chosen.

Exercise from the notebook: which value of g_Y puts about half of the economies above the line? It should be close to the median gap.

Interest rates and deficits

Act III

The Fisher equation: the nominal rate pays the real return plus inflation

\[1 + R = \frac{1+i}{1+\pi}\]

\[i \approx R + \pi \qquad R = i - \pi\]

• \(i\) is paid in dollars, \(R\) in goods.
• \(R = 2\%\) and \(\pi = 2\%\) give \(i = 4\%\) (exactly 4.04%).
• In the long run \(R\) is the marginal product of capital, so \(i^* = R + \bar{g}_M - \bar{g}_Y\): one more point of money growth adds one point to \(i\).

The real rate cannot be looked up: we compute it from the nominal rate and inflation.

The derivation follows one dollar. Today it buys 1/P_t goods. Saved, it returns 1 + i dollars next year, which buy (1 + i)/P_{t+1} goods. The ratio is the return in goods, 1 + R = (1 + i)/(1 + π). Multiplying out, 1 + i = 1 + R + π + Rπ, and dropping the tiny product Rπ gives the Fisher equation.

The long-run version combines it with the quantity theory: with R = 2 percent and 3 percent real growth, money growth of 5 percent gives i* = 4 percent, and 6 percent gives 5 percent (notebook Check 4).

When inflation is high the shortcut fails: the exact formula is R = (1 + i)/(1 + π) − 1. We see a case on the myth slide.

Real interest rates in the United States

In the 1970s the U.S. nominal interest rate rose to record highs. Was the real interest rate, \(i - \pi\), high too? And in 2021–2022?

Collect predictions. Many students assume that high nominal rates mean high returns. Others will remember that inflation was high too.

Ask: what sign do you expect for the real rate in 2022, when inflation was 8 percent and the Fed was just starting to raise rates?

The real rate was negative in the 1970s and in most years since 2008

Data: Federal Reserve, 3-month Treasury bill rate (TB3MS), and BLS CPI (CPIAUCSL), via FRED; OECD 3-month rates (IRS, IR3TIB) and World Bank inflation for the other economies. Inspired by Fig. 8.5 in Jones (2024), Macroeconomics, 6th ed.

How to read it: the nominal rate is the return on 3-month U.S. Treasury bills, averaged over each year; the real rate is the nominal rate minus CPI inflation. Inflation is hidden at first: click it in the legend. The menu at the top left switches countries.

Do live:

1. The nominal rate peaks at just over 14 percent in 1981, a year after inflation peaked. Ask why a year later (the short-run chapters answer it).
2. The real rate is negative from 1974 to 1980 and sharply negative in 2021–2022: −5.97 percent in 2022.
3. Show inflation in 2009: it was negative, so the real rate was above the nominal rate.
4. Choose Germany: in 1974 its real rate was +2.9 percent, against −3.2 percent in the United States. Choose Turkey: in 2022 a short rate of 14 percent with 72 percent inflation.

Data caveat: for other countries the rate is an interbank rate from the OECD, which in the United States has been 0.6 points above the Treasury-bill rate on average.

The real rate swings around zero, and it was negative in 23 of 66 years

United States
highest nominal rate, 1981	14.0%
2009: real rate above nominal	0.47% > 0.15%
lowest real rate, 2022	−5.97%
real rate, 2025	1.43%
average real rate, 1960–2022	0.59%
average real rate, 1960–2007	1.31%

• Negative real rates: 1974–1980, 2003–2005, 2008, 2010–2018 and 2020–2022.
• The marginal product of capital is positive, so long-lasting negative real rates point to the short run.
• High inflation, high nominal rates: as Fisher predicts.

All numbers come from the notebook’s key numbers for Fig. 5.

One textbook statement does not hold in our data: the textbook says the real rate averages “about 1.5 percent” over the period, but the plotted series averages 0.59 percent over 1960–2022, and 1.31 percent before 2008. Since 2023 the real rate has been positive again.

The second bullet is the textbook’s argument. In the long run the real rate equals the marginal product of capital, which cannot be negative. A negative real rate for years means something else is going on: the central bank holding the nominal rate down, or inflation surprising lenders. Both are short-run stories.

A high interest rate is not a high return

A savings account paying 14% a year is a great deal.

It depends on inflation. In Turkey in 2022, a 14% rate with 72% inflation was a real return of −34%: savers lost a third of their purchasing power. And taxes on nominal interest make it worse.

The Turkey numbers are from Fig. 5 and the notebook’s Check 4. The shortcut R = i − π gives −58 percent; at rates this high it is poor. The exact formula, (1 + i)/(1 + π) − 1 = 1.14/1.72 − 1, gives −33.7 percent.

The U.S. nominal peak of 14 percent in 1981 is the same lesson in milder form: inflation was also high, so the real return was modest.

The tax point is on the next slide: a tax on nominal interest also taxes the part that only makes up for inflation.

For the policy students: an interest rate is only informative next to the inflation rate. The same holds for wage growth, pension growth or a budget that grows “by 5 percent”.

Surprise inflation and nominal taxes move wealth around

A surprise

\[R = R^e - (\pi - \pi^e)\]

• A loan is set at 4%, expecting 2% inflation.
• Inflation turns out 8%: the lender earns −4% in real terms; the borrower gains.

A tax on nominal interest

\[(1-\tau)\,i - \pi = (1-\tau)R - \tau\pi\]

• \(\tau = 25\%\), \(R = 2\%\): at 2% inflation the after-tax real return is +1.00%; at 8% it is −0.50%.
• The effective tax rate rises from 50% to 125%.

Left: lender and borrower set i = R^e + π^e. Once the rate is fixed, the realized real rate is i − π. Every point of unexpected inflation takes a point of real return from the lender and gives it to the borrower. Unexpected disinflation does the opposite. The numbers are from the notebook’s Check 5.

Right: the tax applies to all of i, including the part that only compensates for inflation. The after-tax real return is (1 − τ)R − τπ. As a share of the real return, the tax paid is τ(1 + π/R): 50 percent at 2 percent inflation, 125 percent at 8 percent. Even fully expected inflation then lowers the return to saving.

These are two of the textbook’s costs of inflation, made into numbers. Martin Feldstein argued that the interaction of inflation with taxes discouraged investment in the 1970s.

Inflation does not hit everyone equally

Inflation is a general rise in prices, so it hurts everyone the same way.

Surprise inflation moves wealth from lenders, savers and fixed pensions (the $10,000 pension of 1970 lost 61% by 1983) to borrowers. And the inflation tax falls on holders of cash, not on owners of land, houses or shares.

The myth looks only at prices. Inflation is also a change in the real value of every contract written in dollars. Whoever owes dollars gains when they lose value; whoever is owed dollars loses.

Who holds cash? Disproportionately poorer households, who have no bank account or few other assets. So the inflation tax is often regressive.

Who gains? Borrowers with fixed-rate debt: homeowners with fixed mortgages, and governments with debt in their own currency.

For the policy students: the distribution of the costs depends on how contracts are written. The next policy slides ask whether contracts and taxes should be indexed, and whether controls on prices can help.

The costs of inflation come from surprises and from rules written in dollars

When inflation is a surprise

• Wealth moves from lenders to borrowers.
• Fixed incomes and fixed-rate contracts lose value.
• Banks that borrow short and lend long at fixed rates can fail.

Even when it is expected

• Taxes on nominal returns discourage saving and investment.
• Prices that adjust at different speeds distort relative prices.
• Shoe-leather costs of holding less cash; menu costs of changing prices.

If inflation were steady, known and built into every contract and tax, it would be little more than a nuisance.

This is the textbook’s list in two columns. The left column needs a surprise; the right column does not.

The bank example: a bank that pays market rates on deposits but holds old fixed-rate loans sees its costs rise with inflation while its income does not. This is the U.S. savings-and-loan problem of the late 1970s and 1980s.

Relative prices matter because they tell people what to produce. If some prices adjust every week and others once a year, inflation makes the slow ones look cheap for a while, and resources go to the wrong uses.

Shoe-leather and menu costs are small at low inflation and large at high inflation: in a hyperinflation people spend hours a day getting rid of cash.

The takeaway leads to the policy question of the next slide: why not index everything?

Should contracts and taxes be indexed to inflation?

Indexing ties payments to the price level: pensions, wages, bonds and tax brackets rise with inflation. Should governments index more of them?

For indexing

• It removes the redistribution of surprise inflation.
• Taxing real, not nominal, interest ends the tax on saving.
• Indexed bonds reveal the inflation markets expect.

Against, or with care

• Indexed wages pass a supply shock on to all prices.
• Wide indexing can lock in inertia and make disinflation harder.
• Tax rules in real terms are complex to run.

Left column. Feldstein (1976, American Economic Review) shows how taxing nominal interest raises the effective tax on capital income when inflation rises, and argues for indexing the tax base. Shiller (1997, Brookings Papers on Economic Activity) documents how little indexation people choose for themselves and calls it a puzzle. Campbell and Shiller (1996, NBER Macroeconomics Annual) score the case for inflation-indexed government bonds: they protect savers and let economists read expected inflation from the gap between nominal and indexed yields. The U.S. Treasury now issues such bonds (TIPS), and Social Security benefits rise automatically with the CPI.

Right column. Gray (1976, Journal of Monetary Economics) shows that wage indexation shields the economy from monetary shocks but amplifies real shocks such as an oil-price rise. Economies with near-universal indexing, such as Brazil and Israel before their stabilizations, found that indexing kept yesterday’s inflation in today’s prices and made it hard to stop.

Ask the policy students: which payments in your country are indexed? Pensions? The minimum wage? Tax brackets? Who loses from the ones that are not?

Can price controls stop inflation?

In August 1971, President Nixon froze U.S. wages and prices to break a “wage-price spiral”. Can a government stop inflation by forbidding prices to rise?

What happened

• Inflation slowed while the freeze lasted.
• Controls came back in 1973; shortages and gasoline lines followed.
• Prices jumped when the controls ended in 1974.

The lesson of the model

• Controls treat a symptom: with \(\pi^* = \bar{g}_M - \bar{g}_Y\), the cause is money growth.
• Pent-up inflation returns when controls end.
• Meanwhile, frozen prices stop signalling scarcity.

The story is the textbook’s case study. Blinder and Newton (1981, Journal of Monetary Economics) estimate that the 1971–1974 controls held the price level down while they were in force and that the effect was largely undone after decontrol. Rockoff (1984, Drastic Measures, Cambridge University Press) reviews the history of U.S. wage and price controls, including the two world wars, and finds the same pattern of temporary success when the underlying money growth is not addressed.

The stabilization plans of the 1980s in Argentina (the Austral plan) and Brazil (the Cruzado plan) froze prices without fixing the budget, and inflation soon came back. Israel’s plan of the same decade also used temporary controls, but together with a large cut in the deficit, and it lasted. The difference is the subject of the budget-constraint slides next.

For the policy students: today’s version of the question is price caps on energy or rents. The same trade-off applies: a cap can protect households from a spike, but it blunts the price signal that brings new supply.

The government budget constraint: spending is paid by taxes, borrowing or new money

\[\underset{\text{uses}}{G} \;=\; \underset{\text{taxes}}{T} \;+\; \underset{\text{new debt}}{\Delta B} \;+\; \underset{\text{new money}}{\Delta M}\]

• Spending 25% of GDP, taxes 20%, new borrowing 2%: new money must be 3% of GDP.
• If lenders stop lending: 5% of GDP.
• The revenue from new money is seigniorage, the inflation tax: it is paid by everyone who holds money.

A government that cannot tax or borrow has one source left: the printing press.

The numbers come from the notebook’s budget-constraint cell. Solving for the new money: ΔM = G − T − ΔB.

Why is new money a tax? When the government doubles the money supply and spends the new half, the price level doubles. The currency people already held now buys half as much. They paid for the government’s spending through the fall in the value of their cash. A 200-dollar holding buys what 100 dollars bought before.

Who escapes it? People who hold their wealth in land, houses or shares: those prices rise with the others.

This is Sargent’s point: if the root cause of high inflation is money growth, the root cause of fast money growth is usually a government budget that cannot be balanced any other way.

The printing press raises little, and it has a ceiling

\[\frac{\Delta M}{PY} = \frac{\bar{g}_M}{(1+\bar{g}_M)\,\bar{V}} \approx \frac{\pi^* + \bar{g}_Y}{\bar{V}}\]

Money growth	Seigniorage, % of GDP
5%	0.40
100%	4.17
1,000%	7.58
10,000%	8.25
ceiling \(1/\bar{V}\)	8.33

• Velocity of currency \(\bar{V} = 12\): with 2% inflation and 3% growth, new money pays for about 0.4% of GDP.
• A deficit of 5% of GDP needs money growth of 150% and inflation of about 143%.
• U.S. new currency: 0.40% of GDP in 1975, 0.96% at most, in 2020.

The formula divides new money by nominal GDP and uses the quantity equation, M = PY/V. Here money means currency, the money the government itself issues; for the United States its velocity is about 12.

The table is the notebook’s Check 7. Even 10,000 percent money growth raises less than the ceiling of 1/V = 8.33 percent of GDP, because g/(1 + g) is always below 1. In practice the ceiling is lower: in a hyperinflation people flee from money, velocity rises, and the base of the tax shrinks.

The deficit row solves the formula for g_M: σV/(1 − σV) with σ = 5 percent and V = 12 gives 0.6/0.4 = 150 percent money growth. A deficit close to the ceiling needs explosive money growth: that is the arithmetic of hyperinflation.

The U.S. numbers are new currency each year as a share of GDP, from the notebook (1975: 0.40, 1980: 0.38, 2000: 0.34, 2020: 0.96, 2025: 0.15). Even the Great Inflation raised very little, which is why the textbook says the fiscal story does not explain the U.S. 1970s.

Hyperinflations

A hyperinflation is inflation above about 500% a year. How high can it go, and once it starts, does it fade slowly over decades or end within a few years?

Ask students to guess the highest annual rate they think a country has had since 1960, and how long a hyperinflation typically lasts.

Remind them of the arithmetic: a deficit close to the seigniorage ceiling needs ever faster money growth.

Hyperinflations reach thousands of percent, and they end within a few years

Data: World Bank, WDI CPI inflation, via FRED (FPCPITOTLZGARG, FPCPITOTLZGBRA, FPCPITOTLZGRUS); World Bank Global Inflation Database (Ha, Kose and Ohnsorge 2023). Inspired by Fig. 8.6 in Jones (2024), Macroeconomics, 6th ed.

How to read it: annual CPI inflation in percent for Argentina, Brazil and Russia. The dashed line marks 500 percent, the usual threshold of a hyperinflation. The buttons switch between a linear and a ratio scale.

Do live:

1. Linear scale: Argentina peaks at 3,080 percent in 1989, Brazil at 2,948 percent in 1990 and again in 1993–1994. Russia’s series starts at 874 percent in 1993.
2. Each ended within a few years: Argentina was below 25 percent by 1992 and below 5 percent by 1994; Brazil below 5 percent by 1998.
3. Switch to the ratio scale: Argentina’s inflation climbed again in the 2010s and 2020s, to 220 percent in 2024.
4. Click Ukraine in the legend: 4,735 percent in 1993, below 25 percent by 1997. Bolivia: 11,750 percent in 1985.

Data caveat: the ratio scale cannot show zero or negative rates, so Argentina’s deflation of 2001 leaves a gap. Zimbabwe’s official numbers for 2001–2008 are unusable (they show prices falling 73 percent in 2007), and the notebook drops them.

Hyperinflations end fast, but high inflation tends to come back

Country	Peak	Year
Nicaragua	13,110%	1987
Bolivia	11,750%	1985
Peru	7,482%	1990
Ukraine	4,735%	1993
Argentina	3,080%	1989
Brazil	2,948%	1990
Russia	874%	1993

• 31 economies had at least one year above 500% since 1960: mostly in Latin America and the former Soviet bloc.
• They ended when money growth fell, which needs a budget fix.
• Ending one also needs every price setter to believe it will end.

Peaks are from the chart’s data. The count of 31 economies is from the notebook’s cleaned panel.

The quantity theory says a hyperinflation ends when money growth falls. The budget constraint says money growth can fall only if spending falls, taxes rise or lending resumes. Sargent (1982, “The Ends of Four Big Inflations”) studied Austria, Hungary, Poland and Germany after World War I: each ended abruptly once a credible fiscal reform and an independent central bank were in place.

The second difficulty is coordination. If everyone expects high inflation, firms raise prices and workers demand raises in anticipation, and inflation continues. Everyone has to be convinced at once that it will stop.

Both difficulties explain why high inflation recurs: Argentina had high inflation for decades.

Venezuela’s inflation

Venezuela’s inflation was 255% in 2016, very high but not yet a hyperinflation. What came next?

The textbook’s chart ended in 2016, when its author wrote that reports suggested a hyperinflation was under way. Ask students to guess the peak.

Ask also: Mexico and Nigeria had high inflation too. Did they ever reach 500 percent?

Venezuela’s inflation exploded after 2016

Data: World Bank, WDI CPI inflation, via FRED (FPCPITOTLZGMEX, FPCPITOTLZGNGA, FPCPITOTLZGVEN); Venezuela after 2016 from the World Bank Global Inflation Database. Inspired by Fig. 8.7 in Jones (2024), Macroeconomics, 6th ed.

How to read it: annual inflation of Mexico, Nigeria and Venezuela, starting on a ratio scale because Venezuela’s peak would flatten the others on a linear one. The dashed line is 500 percent.

Do live:

1. Venezuela crosses 500 percent in 2018 and stays above it until 2021: 65,374 percent in 2018, 19,906 in 2019, 2,355 in 2020, 1,589 in 2021. By 2024 it was down to 49 percent.
2. Mexico peaked at 132 percent in 1987, Nigeria at 73 percent in 1995: high inflation, never a hyperinflation, and both came down within a few years.
3. Click Turkey: above 25 percent in most years from the late 1970s to 2003, a peak of 105 percent in 1994, and never a hyperinflation.

Data caveat: Nigeria’s few years of falling prices (1963, 1967 and 1968) cannot be drawn on a ratio scale and leave gaps.

Venezuela had a hyperinflation from 2018 to 2021

Venezuela	Inflation
2016	255%
2017	438%
2018	65,374%
2019	19,906%
2020	2,355%
2021	1,589%
2022	201%
2024	49%

• Four years above 500%, then a fall that has not reached normal rates.
• Mexico (132% in 1987) and Nigeria (73% in 1995) had high inflation, not a hyperinflation.
• Unlike Venezuela’s GDP figures of earlier chapters, these numbers are real.

All numbers come from the notebook’s key numbers for Fig. 7.

The textbook was right that a hyperinflation was under way. The fiscal story fits: a government that depended on oil revenue lost much of it, could not borrow abroad, and financed its spending by printing money.

The comparison with Mexico and Nigeria: high inflation is common, hyperinflation rare. What separates them is whether the government keeps some access to taxes and borrowing.

High inflation without a hyperinflation

How many economies have had inflation of more than 100% in some year but never crossed 500%?

Ask for a guess, then reveal the bar chart. Ask students to name any country they expect on it.

22 economies had peaks between 100% and 500%

Data: World Bank, WDI CPI inflation (FP.CPI.TOTL.ZG) and Global Inflation Database, 1960–2025 (Zimbabwe 2001–2008 dropped). Our chart, from the data behind Fig. 8.7 in Jones (2024), Macroeconomics, 6th ed.

How to read it: one bar per economy, the highest annual inflation rate it reached since 1960, for the economies whose peak lies between 100 and 500 percent.

Do live: hover over Lebanon (487 percent, the highest), Viet Nam (454), Iraq (449), Israel (373), Mexico (132) and Turkey (105, the second lowest).

Ask: what do these countries have in common? Wars (Iraq, South Sudan), transitions from planned economies (Viet Nam, Laos, Mongolia, Romania, Albania), debt crises (Mexico, Uruguay, Ghana), and financial collapse (Lebanon). Most also had large budget deficits at the time.

High inflation can last for decades without exploding

Economy	Highest inflation
Lebanon	487%
Viet Nam	454%
Iraq	449%
Israel	373%
Mexico	132%
Turkey	105%

• Turkey stayed above 25% in most years from the late 1970s to 2003, with a peak of 105% in 1994.
• Israel’s peak was followed by a stabilization that combined a budget cut with a new monetary policy.
• High inflation is common; hyperinflation needs a budget that has run out of other options.

Peaks are from the chart’s data; Turkey’s history from the notebook’s notes to Fig. 7.

The difference between high inflation and hyperinflation is a matter of degree, not of kind. The quantity theory works the same way at 100 and at 10,000 percent. What makes the extreme cases explode is the seigniorage ceiling: as people hold less money, the government needs ever faster money growth for the same revenue.

Israel is the counterexample to the “controls never work” lesson: its stabilization plan used temporary price controls together with a large fiscal adjustment and a fixed exchange rate, and inflation stayed down.

Should central banks be independent of the government?

Every government is tempted to print money to pay its bills. Should the central bank be shielded from the treasury, and can that shield hold when the budget breaks?

The case for independence

• It closes the printing-press option before a crisis.
• A bank that cannot be ordered to print makes low inflation credible.
• More independence has gone with lower inflation.

Its limits

• The bank is still part of the state; politicians appoint its head.
• If deficits persist, pressure on the central bank builds.
• Independence asks who holds unelected officials to account.

Left column. Kydland and Prescott (1977, Journal of Political Economy) and Barro and Gordon (1983, Journal of Monetary Economics) show why a policymaker with discretion ends up with too much inflation: the time-inconsistency problem. Rogoff (1985, Quarterly Journal of Economics) proposes delegating policy to a “conservative” central banker. Alesina and Summers (1993, Journal of Money, Credit and Banking) find that rich countries with more independent central banks had lower and more stable inflation, with no cost in growth. Cukierman, Webb and Neyapti (1992, World Bank Economic Review) build an index of legal independence and find that in developing countries the turnover of central bank governors matters more than the law on paper.

Right column. Sargent and Wallace (1981, Federal Reserve Bank of Minneapolis Quarterly Review) show that if the fiscal authority does not adjust, a tight central bank only postpones inflation: “some unpleasant monetarist arithmetic”. Posen (1995, NBER Macroeconomics Annual) argues that the link between independence and low inflation partly reflects the political support for low inflation that produces both.

In the euro area the separation is sharper still: national governments tax and spend, and a multinational central bank sets monetary policy.

Ask the policy students: what should a central bank do if the government it depends on cannot pay its debts?

“Velocity is not constant, so the quantity theory is useless”

A skeptic says: “U.S. M2 velocity rose from 1.85 in 1990 to 2.18 in 1997 and fell to 1.16 in 2021. In the 2010s money grew 7.4% a year and inflation was 1.7%. A theory built on constant velocity cannot guide policy.”

Reply: velocity drifts by a few percent a year; money growth differs by hundreds of percent. Over decades and across 165 economies the band holds (correlation 0.85), and in every hyperinflation money growth came first. Velocity explains the gap, not the slope.

Take the objection seriously: it is right about low-inflation economies in the short and medium run. Central banks stopped targeting money growth in the 1980s and 1990s for exactly this reason, and today they set interest rates instead (Chapter 12).

The reply in three parts. First, scale: the quantity theory is a theory of large and lasting differences, and those are dominated by money growth. Lucas (1980, American Economic Review) shows that once short-run noise is filtered out, U.S. inflation moves one for one with money growth. McCandless and Weber (1995, Federal Reserve Bank of Minneapolis Quarterly Review) find a correlation close to one between long-run money growth and inflation across a large sample of countries. Second, the gap: velocity changes shift the points off the line by roughly the same amount, as the 4-point U.S. gap shows; they do not remove the slope. Third, the limits: Teles, Uhlig and Valle e Azevedo (2016, Economic Journal) find that the one-for-one relation is strong in high-inflation periods and weaker when inflation is low and stable, which is what the theory with drifting velocity predicts.

Ask: in which countries would you trust the quantity theory most for a forecast? (Those with high and variable money growth.)

What to remember from this chapter

• Inflation is the growth rate of the price level. A price index moves prices across years: \(X_b = X_a\,P_b/P_a\).
• The quantity theory: \(P^* = \bar{M}\bar{V}/\bar{Y}\) and \(\pi^* = \bar{g}_M - \bar{g}_Y\). In the long run money is neutral, and U.S. decades and 165 economies line up as predicted.
• Velocity is not constant: it explains the gap between money growth and inflation, not the link.
• The Fisher equation, \(i = R + \pi\): real rates are often negative, surprise inflation helps borrowers, and nominal taxes tax saving.
• \(G = T + \Delta B + \Delta M\): very high inflation comes from governments that cannot tax or borrow. Hyperinflations end with a fiscal fix.

Ask each student to write one sentence answering the opening question: what makes prices rise, and why do some countries let inflation explode? A good answer: in the long run prices rise when money grows faster than output, and governments let money grow fast when they cannot pay their bills any other way.

For the policy students, three habits: compare every interest rate and growth rate with inflation; ask who holds the contracts written in dollars; and ask how a government pays for its spending.

Walk the three branches of the mind map in about a minute each: measuring inflation (cyan), money and prices (lavender), interest rates and deficits (green). Click the image to zoom in.

Inflation is money growth beyond real growth, and very high inflation is a budget problem

Next: Chapter 9, An Introduction to the Short Run

This chapter completes the long run. Chapters 3 to 7 explained real variables; this one added the price level and showed that, in the long run, money changes only nominal values.

Chapter 9 starts the short run, where prices adjust slowly, money is no longer neutral, and the negative real rates and the Great Inflation of this chapter get their explanation.

Sources: data and models

• Figs. 1 and 2, inflation in the United States and the world. U.S. Bureau of Labor Statistics, CPIAUCSL, via FRED; World Bank, World Development Indicators (FP.CPI.TOTL.ZG); World Bank Global Inflation Database (Ha, J., M. A. Kose and F. Ohnsorge (2023), Journal of International Money and Finance 137); World Bank country groups; OECD members. Table 8.1: MeasuringWorth, Officer and Williamson. Inspired by Figs. 8.1 and 8.2 and Table 8.1 in Jones (2024).
• Figs. 3 and 4, money and inflation; velocity; Table 8.2. Jordà–Schularick–Taylor Macrohistory Database, release 6 (Jordà, Ò., M. Schularick and A. M. Taylor (2017), NBER Macroeconomics Annual 31); Federal Reserve, M2NS, M2SL and the H.6 release; BEA, GDPA; World Bank, broad money growth (FM.LBL.BMNY.ZG). Inspired by Figs. 8.3 and 8.4 and Table 8.2 in Jones (2024).
• Fig. 5, interest rates. Federal Reserve, TB3MS, via FRED; OECD Data Explorer, short-term interest rates (IRS, IR3TIB). Inspired by Fig. 8.5 in Jones (2024).
• Figs. 6 and 7, high inflation and hyperinflation. World Bank WDI via FRED (FPCPITOTLZGARG, FPCPITOTLZGBRA, FPCPITOTLZGRUS, FPCPITOTLZGMEX, FPCPITOTLZGNGA, FPCPITOTLZGVEN) and the Global Inflation Database. Inspired by Figs. 8.6 and 8.7 in Jones (2024).
• Models. The quantity theory, the Fisher equation, the costs of inflation and the government budget constraint follow Sections 8.2 to 8.5 of Jones (2024); the who-gains block and the seigniorage formulas are the book chapter’s own.
• 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 8.

Sources: research cited

• The quantity theory and velocity. Friedman, M. (1968), Dollars and Deficits, Prentice Hall; Lucas, R. E. (1980), American Economic Review 70(5); McCandless, G. and W. Weber (1995), Federal Reserve Bank of Minneapolis Quarterly Review 19(3); Teles, P., H. Uhlig and J. Valle e Azevedo (2016), Economic Journal 126(591).
• Costs of inflation and indexing. Feldstein, M. (1976), American Economic Review 66(5); Gray, J. A. (1976), Journal of Monetary Economics 2(2); Campbell, J. and R. Shiller (1996), NBER Macroeconomics Annual 11; Shiller, R. (1997), Brookings Papers on Economic Activity 1997(1).
• Price controls. Blinder, A. and W. Newton (1981), Journal of Monetary Economics 8(1); Rockoff, H. (1984), Drastic Measures: A History of Wage and Price Controls in the United States, Cambridge University Press.
• Fiscal causes, hyperinflation and central banks. Sargent, T. (1982), “The Ends of Four Big Inflations”, in R. Hall (ed.), Inflation: Causes and Effects, University of Chicago Press; Sargent, T. and N. Wallace (1981), Federal Reserve Bank of Minneapolis Quarterly Review 5(3); Kydland, F. and E. Prescott (1977), Journal of Political Economy 85(3); Barro, R. and D. Gordon (1983), Journal of Monetary Economics 12(1); Rogoff, K. (1985), Quarterly Journal of Economics 100(4); Cukierman, A., S. Webb and B. Neyapti (1992), World Bank Economic Review 6(3); Alesina, A. and L. Summers (1993), Journal of Money, Credit and Banking 25(2); Posen, A. (1995), NBER Macroeconomics Annual 10.