U.S. federal debt is back where it stood at the end of World War II

99.5% Federal debt held by the public, as a share of GDP, at the end of fiscal year 2025

In 1946 the ratio was 106.1%. By 1974 it was down to 23.2%, and yet the government never paid the war debt back. How can a debt shrink without being repaid, and could it happen again?

Open with the number. It is the last point of the notebook’s Fig. 2: debt held by the public (bonds owned outside the federal government) was 99.5 percent of GDP in FY2025, close to the record of 106.1 percent in FY1946.

The puzzle that runs through the deck: from 1946 to 1974 the debt ratio fell by more than 80 points, while the budget was close to balance in most years. Act II solves it with one line of algebra: when nominal GDP grows faster than the interest rate on the debt, the ratio falls on its own.

Ask the room: how big is 99.5 percent of GDP? (About one year of everything the U.S. economy produces.) Is that a lot? Compared with what: a household mortgage, Japan, the U.K. in 1946?

The epigraph of the textbook chapter jokes that federal deficits have overtaken the number of stars in the galaxy. The chapter’s job is to say when such numbers are a problem and when they are not.

Today: three questions

• How big are government budgets and debts? U.S. spending, revenue and debt since the 1930s, and other rich countries.
• What rules tie deficits to debt? The flow and intertemporal budget constraints, the debt-GDP ratio and crowding out.
• Why is the future the problem? Entitlements, health spending and the debt projections, and the policy choices they force.

These are the three acts of the deck and the three branches of the mind map on the title slide: the facts, the framework, and its uses.

This chapter has no behavioral model to solve for an equilibrium. It rests on accounting relations that hold every year, in every country, whatever voters and politicians decide. That makes them powerful: every policy proposal has to satisfy them.

The headline result: a government’s budget must balance in present value. When GDP grows faster than the interest rate, the debt ratio falls without repayment; rising health spending is the problem that growth will not solve.

Spending, taxes and debt

Act I

The federal budget

How large is the U.S. federal government, and has it always been this size?

Ask the room first: what share of GDP does the federal government spend today? Ten percent, twenty, forty? And in the 1930s, before World War II? Collect two or three guesses before showing the chart.

The war made the federal government big, and spending has outrun revenue since 1970

Data: Office of Management and Budget, Historical Tables of the FY2027 Budget, Table 1.2 (receipts and outlays, % of GDP). Chart inspired by Fig. 18.1 in Jones (2024), Macroeconomics, 6th ed.

How to read it: federal outlays (spending) and receipts (revenue) as a percentage of GDP, by fiscal year. The U.S. fiscal year 2025 ran from October 2024 to September 2025. The slider picks a period; its averages appear as dotted lines and in the title. The dashed lines at 18 and 20 percent are the textbook’s reference levels.

Do live:

1. “FY1934–1939”: a small federal government; revenue averaged 5.9 percent of GDP.
2. Point at the war: spending peaked at 42.7 percent of GDP in FY1944.
3. “FY1950–1969”: spending 17.6 and revenue 17.0 percent, roughly balanced.
4. “FY1998–2001”: the only surpluses since 1969 (revenue 19.4, spending 18.0).
5. “FY1975–2024”: spending 21.1 percent, revenue only 17.3 percent.

Point at the two spikes of spending: FY2009 (the Great Recession) and FY2020 (the pandemic).

A gap of about four points of GDP has opened between spending and revenue

• From FY1975 to FY2024 spending averaged 21.1% of GDP and revenue 17.3%. The textbook’s “about 20 percent for both” hides that gap.
• Revenue reached 20% of GDP only twice: FY1944 and FY2000.
• In FY2025: spending 23.1%, revenue 17.3%. The difference is the deficit that Fig. 2 adds to the debt.

Revenue has a ceiling near 20% of GDP; spending has no such ceiling.

Numbers: the notebook’s Fig. 1 key numbers. The textbook says spending peaked “just under 44 percent” and revenue was “nearly 21 percent” in 1944; today’s OMB tables give 42.7 and 20.5 percent, because 1940s GDP has since been revised up. A good reminder that historical shares change when the denominator is remeasured.

Beyond the federal budget (fig. 1b in the book chapter): the U.S. general government, federal plus state and local, spent 39.6 percent of GDP in 2024 and collected 31.5 percent. That is the measure we use to compare countries in Fig. 3. In the same chart, Norway runs surpluses in 30 of 31 years thanks to oil revenue, and Ireland’s spending jumps to 65.0 percent of GDP in 2010, when it rescued its banks.

Health, Social Security and interest take most of each federal dollar

FY2025, federal budget	% of GDP	dollars per person
Total spending	23.1	20,500
Health (including Medicare)	6.5	5,800
Social Security	5.2	4,600
Net interest	3.2	2,800
National defense	3.0	2,700
Income security, other	5.2	4,600
Total revenue (income taxes 8.8, payroll 5.8)	17.3	15,300
Budget balance	−5.9	−5,200

Interest on the debt now costs more than national defense.

This is our version of Table 18.1, built in the notebook from OMB’s tables. Income security (2.3 percent) and other spending (2.9 percent) are merged into one row here; corporate taxes (1.5) and other revenues (1.3) complete the revenue side.

The textbook’s table shows OMB’s March 2023 estimate for FY2023, written before that year was over. The actual numbers came in lower: spending 22.4 instead of 24.2 percent, revenue 16.2 instead of 18.2 percent. Same lesson as in Chapter 2: check the vintage.

The deficit of 5.9 percent of GDP is the same share as in the textbook’s table, but net interest has grown from 2.5 to 3.2 percent of GDP. Dollars per person turn abstract shares into something students can picture: about 20,500 dollars of federal spending per resident, 15,300 dollars of taxes.

Ask: which lines would you cut to close a gap of 5,200 dollars per person? Students quickly find that the big lines are health, Social Security and interest, and that interest cannot be cut by a vote.

Deficits and the debt

Each deficit adds to the debt. How high did U.S. debt go after World War II, and how did it come down?

Ask the room: after the war, did the U.S. government pay back its debt? Most students answer yes. Hold the answer until Act II.

The war debt melted away; recessions and the pandemic rebuilt it

Data: Office of Management and Budget, Historical Tables of the FY2027 Budget, Tables 1.2 (surplus or deficit) and 7.1 (federal debt held by the public), % of GDP. Chart inspired by Fig. 18.2 in Jones (2024), Macroeconomics, 6th ed.

How to read it: two series with two vertical axes. The budget balance (surplus +, deficit −) is on the left axis; the debt held by the public is on the right axis. The two zeros are aligned, so the dashed line marks zero on both. OMB’s debt table starts in FY1940.

Point at three episodes:

1. The war: deficits of up to 29.6 percent of GDP (FY1943), and the debt at 106.1 percent in FY1946.
2. The long fall: to 23.2 percent by FY1974, with the budget close to balance in most years.
3. The rise since the late 1970s: 47.9 percent by FY1993, down to 31.5 percent after the surpluses of FY1998–2001, then up with the deficits of FY2009 (9.8 percent) and FY2020 (14.5 percent), to 99.5 percent in FY2025.

Hover over a year to read both series.

The ratio fell by 83 points after 1946 while the budget was roughly balanced

• From 106.1% in FY1946 to 23.2% in FY1974. The deficits of those years were small, so something other than repayment did the work.
• The rise since 1980 matches the deficits: the late 1970s and 1980s, the Great Recession and the pandemic.
• The FY1998–2001 surpluses cut the ratio to 31.5%.

A falling debt ratio does not require a shrinking debt. Act II shows why.

106.1 − 23.2 = 82.9 points. This is the puzzle of the hook. The answer, in Act II: nominal GDP grew faster than the interest rate on the debt, so the debt shrank relative to the economy even though its dollar amount did not fall much.

The textbook’s figure has one more debt point, for 1939, from an older edition of OMB’s table; our line starts in FY1940.

Debt held by the public excludes bonds held by government trust funds such as Social Security’s. It is the measure that matters for financial markets.

Two centuries of debt

Are U.S. debt levels unusual in history and across countries?

Ask: which rich country has had the highest debt ratio you can think of? When? Collect guesses: Japan today, the U.K. after the wars, Greece.

Britain carried debts above 250% of GDP twice and grew out of both

Data: International Monetary Fund, Public Finances in Modern History, general government gross debt (d), % of GDP; Mauro, Romeu, Binder and Zaman (2015), Journal of Monetary Economics. Chart inspired by Fig. 18.2 in Jones (2024), Macroeconomics, 6th ed.

How to read it: gross government debt in percent of GDP, for 48 countries, some back to 1800. Gross debt counts all government bonds and loans, also those held by other parts of the government, and all levels of government where the data allow. So the U.S. line lies above Fig. 2’s debt held by the public: by 15.1 points in 1946 and 24.9 points in 2024.

Click a country in the legend to add or remove it; the buttons show groups (the textbook’s countries, the G7, regions, all).

Do live:

1. Add the United Kingdom: 260 percent of GDP after the Napoleonic wars (1821), 270 percent after World War II (1946), and down to 43 percent by 2007.
2. Add Japan: 258 percent in 2020, 237 percent in 2024, the highest of any rich country.
3. Add Germany: no values for 1914–1924 and 1939–1949, the wars and the hyperinflation. Plotly joins the points on either side with a straight line, so the gap looks smooth. Look at your data.

Wars build debts; growth and time bring them down

• The U.K. went from 270% of GDP in 1946 to 43% in 2007, mostly through growth, as in the United States.
• Japan’s gross debt reached 258% in 2020 without a crisis. In 2024 Italy (135%) and Greece (155%) were also above the U.S. (122%).
• The series start in different years and have holes; comparisons need the same measure.

There is no single debt ratio at which trouble starts.

Numbers: the notebook’s “two centuries of government debt” section. All 2024 values are IMF gross debt.

The data come from Mauro, Romeu, Binder and Zaman (2015), “A modern history of fiscal prudence and profligacy”, Journal of Monetary Economics. The IMF asks users to cite it.

The textbook’s point: what lenders accept depends on growth prospects, the ability to collect taxes and the credibility of the government and the central bank. Britain in 1821 and 1946 had a long record of repaying; that credibility let it carry very high debts. Countries without that record have defaulted at much lower ratios (the textbook cites Latin America in the 1980s, Russia in 1998, Greece in 2011 and Argentina in 2020).

Big or small government?

Rich countries tax and spend very different shares of GDP. Where does the U.S. stand?

Rank six rich countries by government spending in 2019 (all levels of government): France, Japan, South Korea, Sweden, the U.K. and the U.S. Is the U.S. near the top, in the middle, or near the bottom?

Let students write down a ranking before showing the chart. A common guess, because the U.S. budget is so large in dollars, is that the U.S. government is among the biggest. Shares of GDP tell a different story.

The U.S. government is among the smallest of the rich countries

Data: OECD, Government at a Glance, general government expenditure, % of GDP (DSD_GOV@DF_GOV_PF_YU, measure GE), via the OECD Data Explorer. Chart inspired by Fig. 18.3 in Jones (2024), Macroeconomics, 6th ed.

How to read it: general government spending (central, state and local together) as a percent of GDP, for six countries, in 2019 (the last year before the pandemic, as in the textbook) and 2024 (the latest year with data for all six). Each bar shows its value. Hover for the exact number.

Point at the order in 2019: South Korea 31.9, Japan 37.8, the U.S. 38.2, the U.K. 40.5, Sweden 49.8, France 55.3 percent.

Then at 2024: spending was higher in all six countries, by 0.6 points in Sweden up to 5.7 points in the U.K. (46.2 percent).

The prediction: near the bottom, the 11th lowest of 38 OECD countries

• In 2019 the U.S. spent 38.2% of GDP, France 55.3%. Only Korea and Japan were lower among the six.
• The four large euro-area countries averaged 47.8% in 2019 and 50.6% in 2024.
• Data are revised: Korea’s 2019 figure is now 2.0 points lower than in the textbook, and Japan has dropped below the U.S.

Big budgets in dollars can be small budgets relative to the economy.

Numbers: the notebook’s Fig. 3 key numbers and its data-revision check. The 2023 edition of the OECD data, which the textbook used, reproduces all six printed bars within 0.1 point; today’s data differ by up to 2.0 points (Korea) and 1.1 points (Japan).

The animation of all 38 OECD countries from 2007 to 2024 (fig. 3b in the book chapter) shows the two recessions: in 2009 and 2020 spending jumped almost everywhere, while GDP fell.

The difference between the U.S. and Europe is mostly health and pensions paid through the government. In the U.S. much health spending is private (Fig. 8 counts both), so a smaller government does not mean a smaller health bill.

Debt around the world

Which rich countries owe the most once we subtract what their governments own?

Ask: is a government with large debts but also a large oil fund or pension fund really in debt? This introduces net debt: liabilities minus financial assets.

Net debt rose almost everywhere after 2007, and fell back after 2021

Data: OECD government financial balance sheets, general government net financial worth (BF90, DSD_NASEC20@DF_T720GOV_A), divided by GDP (DSD_NAMAIN10@DF_TABLE1_EXPENDITURE), via the OECD Data Explorer. Chart inspired by Fig. 18.4 in Jones (2024), Macroeconomics, 6th ed.

How to read it: net debt, the debt of all levels of government minus the financial assets they own, in percent of GDP, from 1995, for 39 countries. It starts with the textbook’s five countries in the textbook’s colors (Italy, Japan, the U.S., the U.K., Germany). Click names in the legend, or a button for a group. The vertical axis widens when a country leaves the default scale.

Do live:

1. The five: Japan from 18 percent in 1995 (the Economic Outlook series) to a peak of 124 percent in 2020; Italy peaks at 152 percent and the U.S. at 122 percent; Germany falls after 2011, to 22 percent in 2025.
2. Add Norway: −414 percent of GDP in 2024. Its oil fund is worth more than four years of GDP.
3. Add Canada: from 96.5 percent in 1996 to 15.8 percent in 2025.

In 2024 the U.S. had the third-highest net debt of 36 countries

• U.S. 109.5% of GDP, after Italy (122.8%) and Greece (121.9%).
• The U.K.’s ratio fell from 101% to 68% between 2021 and 2022. Assets and bonds are valued at market prices: when rates jumped, old low-rate bonds lost value, and inflation raised nominal GDP.
• Japan’s net debt was 93.7% of GDP in 2023, not the “more than 140 percent” printed in the textbook.

A debt ratio moves with interest rates, inflation and asset prices, not only with deficits.

Numbers: the notebook’s Fig. 4 key numbers and data check. The textbook gives two numbers for Japan in two places: “more than 126 percent in 2021” and “more than 140 percent in 2023”. Neither series reaches 140 percent; the gross debt, before subtracting the government’s assets, is much higher, which may explain the second number. When two numbers in a text disagree, check them in the data.

The fall of 2022 is not an austerity story. Higher interest rates lowered the market value of long-term bonds issued at low rates, and high inflation raised nominal GDP, the denominator. Both effects lowered measured ratios, most likely more than any change in deficits. Act II’s inflation slide explains why surprise inflation erodes debt.

Japan’s column in the main figure starts in 2005 for the balance sheets; 1995–2005 come from a similar OECD Economic Outlook series (dotted in the book’s Fig. 4). The two differ by 3.4 points in 2005.

The budget arithmetic

Act II

Every year, what the government uses must equal what it raises

\[\underset{\text{uses}}{G_t + Tr_t + iB_t} \;=\; \underset{\text{sources}}{T_t + \Delta B_{t+1} + \Delta M_{t+1}}\]

Set \(\Delta M_{t+1} = 0\) and fold transfers into \(G_t\):

\[B_{t+1} = (1+i)\,B_t + \underset{\text{primary deficit}}{G_t - T_t}\]

Deficit measure	formula	counts interest?
primary	\(G_t - T_t\)	no
total (the headline)	\(G_t + iB_t - T_t\)	yes

The debt rolls forward like a credit-card balance: last year’s balance plus interest plus this year’s overspending.

The flow budget constraint, equations (1) and (2) of the book chapter’s Model overview. \(B_t\) is the debt at the start of year t; \(\Delta B_{t+1} = B_{t+1} - B_t\) is new borrowing; \(\Delta M_{t+1}\) is new money. The U.S. Treasury does not pay its bills by printing money (the fiscal side of inflation was Chapter 8), so we drop it.

Derivation in two steps: borrowing covers the total deficit, \(\Delta B_{t+1} = G_t + iB_t - T_t\); then add \(B_t\) to both sides and group \(B_t + iB_t = (1+i)B_t\).

Dividing by \(B_t\): the debt grows at the rate \(i + (G_t - T_t)/B_t\). A balanced primary budget means the debt grows at the rate i; a balanced total budget means it stays put; to hold the dollar debt constant, the primary surplus must equal the interest bill.

U.S. numbers (notebook, Fig. 2 key numbers): in FY1999 the total surplus was 1.3 percent of GDP but the primary surplus 3.8 percent, because 2.5 percent went to interest. In FY2025 the total deficit of 5.9 percent was 3.3 percent interest and only 2.6 percent primary deficit.

A balanced primary budget still lets the debt grow at the interest rate

Debt $5 tn, GDP $20 tn, \(i = 5\%\), \(g = 4\%\)	year 1	year 2	year 3
(a) primary balance, \(T = G\): debt ($ tn)	5.250	5.512	5.788
(a) debt-GDP ratio (%)	25.24	25.48	25.73
(b) total balance, \(T = G + iB\): debt ($ tn)	5.000	5.000	5.000
(b) debt-GDP ratio (%)	24.04	23.11	22.22

• In (a) the government borrows to pay the interest: the debt grows 5% a year and the ratio about 1% a year (\(i - g\)).
• In (b) a primary surplus of $0.25 tn pays the interest: the debt is fixed and the ratio shrinks about 4% a year (\(g\)).

The notebook’s Check 1, based on Exercise 5 of the textbook: a government that owes 5 trillion dollars at 5 percent interest, with GDP of 20 trillion growing at 4 percent a year.

Case (a), primary budget balanced: the total deficit equals the interest bill, 0.250, then 0.263, then 0.276 trillion. The ratio grows by 0.96 percent a year, exactly 1.05/1.04 − 1.

Case (b), total budget balanced: taxes pay spending and interest, a primary surplus of 0.25 trillion. The ratio falls by 3.85 percent a year, about the growth rate of GDP.

Ask: which of the two would a politician call “a balanced budget”? Both, which is why the next slide matters.

“Balanced” depends on whether interest is counted

If the government balances its budget, its debt stops growing.

Only if the total budget balances. With a balanced primary budget the debt still grows at the interest rate, because the interest is borrowed. In FY2025 the U.S. primary deficit was 2.6% of GDP; the total deficit, with interest, was 5.9%.

A common confusion in news coverage and in student answers. Fiscal plans often target the primary balance because it measures what current policy adds; the interest bill is the cost of past borrowing.

The distinction becomes more important as the debt grows: at a debt of 100 percent of GDP, every point of interest is a point of GDP in the total deficit. In FY2025 net interest (3.2 percent of GDP in Table 18.1) exceeded national defense (3.0 percent).

Over time, the budget must balance in present value

\[\underset{\text{pdv of spending}}{G_1 + \frac{G_2}{1+i}} \;+\; \underset{\text{initial debt}}{(1+i)B_1} \;=\; \underset{\text{pdv of taxes}}{T_1 + \frac{T_2}{1+i}}\]

A one-dollar rise in …	changes \(T_2\) by	why
\(T_1\) (a tax cut is a fall)	\(-(1+i)\)	borrowed today, repaid with interest
\(G_1\)	\(+(1+i)\)	the same: financed by borrowing
\(G_2\)	\(+1\)	paid in the same period
the initial debt \(B_1\)	\(+(1+i)^2\)	interest accumulates for two periods

With \(i = 5\%\), a tax cut of 100 today means 105 of extra taxes tomorrow.

The intertemporal budget constraint, equation (3). Derivation: write equation (2) for periods 1 and 2; nobody lends after period 2, so \(B_3 = 0\); solve the period-2 constraint for \(B_2 = (T_2 - G_2)/(1+i)\) and substitute into the period-1 constraint. With more periods each extra term is discounted once more. The full derivation is in the book chapter’s Model overview.

Equivalent form, equation (4): the present value of the budget balances equals \((1+i)B_1\). A deficit in one period must be matched by a surplus of equal present value in another, and a government that starts in debt needs surpluses large enough to pay it.

The notebook’s Check 2: initial debt 25 trillion, spending 7 trillion in each period, taxes 5 trillion in period 1. Then \(B_2\) = 28.25 trillion and period-2 taxes must be 36.66 trillion: both sides of equation (3) equal 39.917. Check 3: cutting period-1 taxes by 1 trillion raises period-2 taxes by 1.05 trillion.

“Period 2” can stand for the whole future. The constraint does not say when, only that the present values must add up.

The timing of taxes can change; their present value cannot

• Once spending and the initial debt are set, the constraint fixes the present value of all taxes. A tax cut today is a tax rise later.
• Ricardian equivalence: households that see the later taxes save the whole tax cut, so their consumption does not move (Chapter 16).
• Generational accounting: when “later” is decades away, the people who pay are not the people who benefited.

Debt moves burdens across time and generations. Whether that is fair depends on who gains from the spending.

Ricardian equivalence goes back to Barro (1974, Journal of Political Economy). It needs households that look far ahead, can borrow and lend freely, and care about the heirs who will pay the later taxes. Most evidence finds that private saving offsets only part of a deficit; the textbook says at most about half. We test it with Fig. 5.

Generational accounting is due to Auerbach, Gokhale and Kotlikoff (1994, Journal of Economic Perspectives). It computes the lifetime net taxes that current policy implies for each birth cohort, and the extra taxes future cohorts would need to satisfy the intertemporal constraint.

The textbook’s example of a fair transfer: World War II. The generation that fought it bore the casualties and the rationing; borrowing let later generations, who also benefited from the victory, share the cost.

Ask: is borrowing to fight climate change more like the war, or more like borrowing for current consumption?

What matters is the debt relative to GDP

\[b_t = \frac{1+i}{1+g}\,b_{t-1} + d_t \qquad\Longrightarrow\qquad b_t - b_{t-1} \;\approx\; (i-g)\,b_{t-1} + d_t\]

• \(b_t\) is the debt-GDP ratio, \(d_t\) the primary deficit in % of GDP, \(g\) the growth of nominal GDP.
• Two forces: new primary deficits add to the ratio; old debt grows with interest at \(i\) while GDP grows at \(g\).
• When \(g > i\), the economy outgrows its debt, even with a balanced primary budget.

GDP is the tax base: a debt that grows more slowly than GDP becomes easier to carry every year.

Equations (5) and (6). Derivation: divide equation (2) by \(Y_t\); write \(B_t/Y_t = b_{t-1}/(1+g)\); subtract \(b_{t-1}\) and use \((1+i)/(1+g) - 1 = (i-g)/(1+g)\). The approximation drops the division by 1 + g, close to 1 when g is a few percent.

The same result from the growth rules: with a balanced primary budget the debt grows at i and GDP at g, so the ratio grows at about i − g. With a balanced total budget the debt is constant, so the ratio shrinks at about g. That is Check 1 again: +0.96 percent and −3.85 percent a year.

Both i and g are nominal: both include inflation. The textbook’s analogy: lenders lend more to someone whose income is high and rising.

Notation reminder: the statistical tables report the ratio as end-of-year debt over that year’s GDP, which is why \(b_t = B_{t+1}/Y_t\) in the book chapter.

At a debt near 100% of GDP, a point of interest weighs as much as a point of deficit

A one-point rise in …	changes \(b_t - b_{t-1}\) by about	at \(b_{t-1} = 99.5\%\)
the primary deficit \(d_t\)	\(+1\) point	\(+1\) point
the interest rate \(i\)	\(+b_{t-1}/100\) points	+1 point
nominal GDP growth \(g\)	\(-b_{t-1}/100\) points	−1 point

The higher the debt, the more the ratio reacts to interest rates and growth, and the less it is under the control of current policy.

Comparative statics of equation (6), holding last year’s ratio fixed. The notebook’s Check 6: one point more interest at a ratio of 99.5 percent raises the yearly change by 0.957 points, that is \(b/(1+g)/100\), about \(b/100\).

The policy meaning: a government with a debt of 100 percent of GDP is exposed to the bond market. If interest rates rise by two points, the deficit would have to fall by about two points of GDP just to keep the ratio on its old path. When the U.S. debt was 30 percent of GDP, the same rise in rates mattered a third as much.

Whether a debt is sustainable depends on \(i\) versus \(g\)

\[-d = \frac{i-g}{1+g}\,b \qquad\qquad b_t = b^* + \left(\frac{1+i}{1+g}\right)^{t}(b_0 - b^*), \quad b^* = \frac{1+g}{g-i}\,d\]

Case	what happens to the ratio	example, \(b_0 = 99.5\%\), \(g = 4\%\)
\(i < g\)	converges to \(b^*\) from any start, even with permanent deficits	\(i = 3\%\), \(d = 2\%\): \(b^* = 208\%\)
\(i = g\)	adds up all primary deficits	no surplus needed to hold 99.5%
\(i > g\)	\(b^*\) is a tipping point; only surpluses hold the ratio	\(i = 5\%\): surplus 0.96% a year

When \(i > g\), a government needs a primary surplus just to stand still, and the surplus grows with the debt.

Equation (7) is the primary surplus that holds the ratio constant; equation (8) is the closed-form path for a constant primary deficit d, with \(a = (1+i)/(1+g)\). Each year the gap to \(b^*\) is multiplied by a.

The notebook’s Check 5:

• i = 5, g = 4: the stabilizing surplus is 0.957 percent of GDP; with it the ratio stays at 99.50 percent for 31 years.
• i = 3, d = 2: \(b^*\) = 208 percent, reached only slowly: after 31 years the ratio is 127.58 percent (simulated and closed form agree). The gap shrinks by about 1 percent a year.
• i = 5 with a primary surplus of 1 percent: the tipping point is 104.0 percent. Starting at 99.5 percent the ratio drifts down to 97.9 after 31 years; starting at 108.5 it climbs to 110.1.

Confidence and default: if lenders start to doubt repayment, they ask for a higher i, which raises a and the required surplus, and can tip a stable ratio into an explosive one. The fear can fulfill itself.

Growth, not repayment, paid for most of the war debt

Change in the U.S. debt ratio (points of GDP)	total	from primary deficits	from interest minus growth
FY1950–1974	−55.4	−14.1	−41.3
FY1981–1993	+22.7	+14.6	+8.1
FY2001–2008	+7.7	+6.0	+1.7
FY2007–2025	+64.3	+80.5	−16.2

After the war, three quarters of the fall came from GDP growing faster than the interest rate. Since 2007, primary deficits did the work, in the other direction.

The notebook’s debt_change_parts: the change in the ratio minus the sum of primary deficits is the term \((i-g)\,b/(1+g)\) of equation (6), summed over the years. Primary balances come from revenue and spending excluding interest, available from FY1950.

FY1950–1974: the ratio fell by 55.4 points; primary surpluses paid for 14.1 of them, and 41.3 came from growth (plus inflation) outpacing the interest rate. FY2007–2025: primary deficits added 80.5 points, but low interest rates and the inflation of 2021–23 offset 16.2 of them.

Hall and Sargent (2011, American Economic Journal: Macroeconomics) do a finer decomposition of the post-war decline into growth, inflation and the returns paid to bondholders, and reach the same conclusion: the U.S. grew and inflated its way out of most of the war debt.

The textbook calls growth one of the “magic elixirs” of budget problems.

The U.S. did not repay its war debt

After World War II, the U.S. paid down its debt with years of budget surpluses.

From FY1950 to FY1974 the dollar debt was rolled over, not repaid. The ratio fell 55.4 points, and primary surpluses explain only 14.1 of them; the rest came from GDP outgrowing the interest rate.

The myth is attractive because it fits the household analogy: a family that borrowed in bad times pays it back in good times. The government did run modest primary surpluses after the war, but the decisive force was the denominator.

Ask: why did nominal GDP grow faster than the interest rate in those years? Strong real growth (the golden age of the 1950s and 1960s), inflation at times above what bondholders expected, and interest rates on government debt kept low by regulation and, until 1951, by the Federal Reserve.

That last point links to the next slide: only unexpected inflation helps.

Only surprise inflation erodes the debt

Inflation shrinks the debt ratio, so a heavily indebted government can just let prices rise.

Expected inflation is already in the interest rate: \(\frac{1+i}{1+g} = \frac{1+r}{1+g_{real}}\). With \(r = 1\%\) and real growth 2%, the ratio after 10 years is 99.735% whether inflation is 0% or 4%. Only inflation that surprises lenders after they bought the bonds lowers the real burden.

The Fisher equation (Chapter 8): \(1 + i = (1+r)(1+\pi)\) and \(1 + g = (1+g_{real})(1+\pi)\). The inflation factor cancels in the ratio that drives equation (5).

The notebook’s Check 6: with π = 0, i = 1.00 and g = 2.00 percent; with π = 4 percent, i = 5.04 and g = 6.08 percent. The debt ratio after 10 years is 99.735 percent in both cases.

The surprise inflation of 2021–23 is part of the −16.2 points of the previous table, and part of the fall in measured net debt in 2022 (Fig. 4). But a government cannot surprise lenders forever: once they expect inflation, they demand a higher i. This is why very high debts raise fears of inflation, and why central bank independence matters (Chapter 8).

Somebody’s saving must pay for every machine and building

\[\underset{\text{private saving}}{(Y-T-C)} + \underset{\text{government saving}}{(T-G)} + \underset{\text{foreign saving}}{(IM-EX)} = I\]

\[\Delta I = -(1-\theta-\phi)\,\Delta \quad\text{when the deficit rises by }\Delta\]

Other saving responds by …	\(\theta\)	\(\phi\)	change in investment
nothing: full crowding out	0	0	\(-\Delta\)
Ricardian: households save the tax cut	1	0	0
private saving offsets half	0.5	0	\(-0.5\Delta\)
half private, half foreign	0.5	0.5	0

Equation (9), from the national income identity of Chapter 2: subtract C, G and EX − IM from both sides of Y = C + I + G + EX − IM, then add and subtract T. Here G is government purchases only.

Equation (10): θ is the share of the deficit that private saving makes up, φ the share that foreign saving makes up.

The notebook’s Check 7, in percent of GDP: C 67, I 18, G 20, EX 11, IM 16, T 17. Private saving 16 + government saving −3 + foreign saving 5 = 18 = I. A deficit one point larger with θ = 0.5 and φ = 0 lowers investment to 17.5.

The textbook’s reading of the evidence: private saving rises by no more than about 50 cents per dollar of deficit, so without foreign saving at least half of a deficit comes out of investment. Fig. 5 shows what happened in the U.S.

Crowding out

Have the larger deficits since 1980 pushed down U.S. private investment?

Government saving averaged −2.2% of GDP in 1960–1979 and −4.1% in 1980–2025. Predict the investment rate after 1980: lower, the same, or higher than before?

Let students commit. The identity of the previous slide says a deficit must come out of investment unless private or foreign saving rises. Which happened?

Deficits nearly doubled after 1980, yet the investment rate did not fall

Data: U.S. Bureau of Economic Analysis via FRED: gross private domestic investment (GPDI), net federal government saving (FGDEF), GDP. Chart inspired by Fig. 18.5 in Jones (2024), Macroeconomics, 6th ed.

How to read it: gross private domestic investment and federal government saving (the federal budget balance from the national accounts), both in percent of GDP, by calendar year. The slider picks 1960–1979 or 1980–2025; the averages appear as dotted lines and in the title. A third series, private plus foreign saving, is hidden: click its name in the legend. By equation (9) it is the gap between the two lines.

Do live:

1. Move between the two periods: investment 17.3 then 17.7 percent; government saving −2.2 then −4.1 percent.
2. Point at the 1990s: government saving rose from −5.1 percent (1992) to +1.6 percent (2000), investment from 15.3 percent (1991) to 19.9 percent.
3. Show the hidden series: it rose when deficits grew, to 31.4 percent of GDP in 2020.

The prediction: about the same. Other saving filled the gap

• Investment averaged 17.3% of GDP before 1980 and 17.7% after, although deficits were about twice as large.
• Private plus foreign saving rose by 2.4 points of GDP and covered the larger deficits.
• Year to year, the two lines move together: the correlation of the yearly changes is 0.55, that of the levels only 0.29.

Over decades, private and foreign saving absorbed the deficits; in the short run, deficits and investment moved together.

Numbers: the notebook’s Fig. 5 key numbers. Private + foreign saving averaged 19.44 percent of GDP in 1960–1979 and 21.86 percent in 1980–2025.

Foreign saving, the current account deficit, is the topic of Chapter 19. The U.S. has borrowed from the rest of the world since the 1980s; that is one reason crowding out has been smaller than the identity alone would suggest.

The textbook’s summary: the U.S. debt ratio is not especially large by international standards, and foreign saving has kept investment close to its post-war average. The worry is the future (Act III).

A correlation between deficits and investment does not prove crowding out

Deficits and investment fall together, so deficits must be crowding out investment.

In a recession investment falls, tax revenue falls and spending rises: both lines drop for the same reason. The correlation of the yearly changes is positive in all 36 OECD countries with data (median 0.41), from 0.01 in Colombia to 0.75 in Japan.

Numbers: the notebook’s cross-country version of Fig. 5 (fig. 5b in the book chapter), with the general government budget balance (net lending) and private investment from the OECD. The U.S. correlation with this measure is 0.62, close to the 0.55 of the federal measure.

A third variable, the business cycle, drives both series. To measure crowding out we would need changes in deficits that are not caused by the cycle, for example tax laws passed for long-run reasons. This is the identification problem every policy student meets again in empirical work.

Ireland, in the same chart: the budget balance fell to −32.2 percent of GDP in 2010, when the government rescued its banks; investment jumped to 51.5 percent of GDP in 2019 for an accounting reason (multinationals moving intellectual property, Chapter 17).

The fiscal problem ahead

Act III

Entitlements

What has driven the growth of federal spending since 1950, and what do official projections expect?

Ask: name the three biggest federal programs. Students usually name defense first. The chart shows Social Security, Medicare and Medicaid.

Entitlements grew from almost nothing to more than half of non-interest spending

Data: Office of Management and Budget, Historical Tables (FY2027 Budget), Tables 1.2, 3.1 and 8.5; Congressional Budget Office, The Long-Term Budget Outlook: 2026 to 2056. Chart inspired by Fig. 18.6 in Jones (2024), Macroeconomics, 6th ed.

How to read it: three series in percent of GDP: revenue, federal spending excluding interest, and the three big entitlement programs (Social Security, Medicare and Medicaid, with CHIP and the health insurance tax credits as CBO counts them). Solid lines are actual data (OMB, to FY2025); dashed lines are CBO’s projections of February 2026, to 2056. The markers are the textbook’s CBO projections of 2002, read every ten years from its figure; click “CBO 2002 (textbook)” in the legend to hide them.

Point at:

1. Entitlements: 0.3 percent of GDP in 1950, 7.1 percent in 2000, 11.2 percent in 2025, 14.1 percent projected for 2056.
2. Revenue: between 14 and 20 percent of GDP for 75 years; CBO projects 17.5 to 18.8 percent.
3. The 2002 markers: much steeper than the new projection, but actual spending since 2002 was far above the old projection in 2009–12 and 2020–21.

Under current policy, spending stays about 2 points above revenue every year

• CBO’s 2056: revenue 18.8%, spending excluding interest 21.0%, entitlements 14.1% of GDP.
• The primary deficit averages 2.09% of GDP over FY2026–2056, 64.7 points in total.
• The 2002 projection was steeper: 24.5% non-interest spending for 2056. But the direction is the same.

A permanent primary deficit is the arithmetic of the “fiscal problem”: the debt ratio keeps rising unless \(g\) is well above \(i\).

Numbers: the notebook’s Fig. 6 key numbers. CBO projections assume current law: today’s tax rules and benefit formulas continue. They are not forecasts of what Congress will do.

The textbook’s CBO 2002 projections had entitlements at 21.1 percent of GDP and total spending near 40 percent by 2075. The new projections end in 2056 and are lower, mainly because health cost growth slowed after 2010 compared with the 2002 assumptions.

Why the numbers matter for Act II: with d near 2 percent and i = g, equation (5) says the ratio rises by about 2 points a year. The next figure turns that into a debt path.

Debt in 2056

What happens to the debt ratio under CBO’s projected deficits, and what would it take to hold it at today’s level?

With \(i = g = 4\%\) and primary deficits averaging about 2% of GDP, predict the debt ratio in 2056 (it is 99.5% today). Then guess how large a yearly deficit cut would keep it near 99.5%.

Let students use Act II: with i = g the ratio is the starting ratio plus the sum of all later primary deficits (the middle row of the sustainability table). The sum is 64.7 points. Some students will get close to the answer with that alone.

Cutting the primary deficit by 2 points of GDP every year holds the ratio near today’s level

Data: Office of Management and Budget, Historical Tables, Table 7.1; Congressional Budget Office, The Long-Term Budget Outlook: 2026 to 2056 (primary deficits). Projection with equation (5). Chart inspired by the discussion of Fig. 18.6 in Jones (2024), Macroeconomics, 6th ed.

How to read it: debt held by the public in percent of GDP. Actual to FY2025, then a projection that runs CBO’s primary deficits through equation (5), with i = g = 4 percent. The shaded band is the projection period; the dotted line marks the FY2025 level, 99.5 percent. The slider cuts the primary deficit in every year from FY2026 by 0 to 3 points of GDP, by raising taxes or cutting spending, the textbook’s two “possible solutions”. The title gives the FY2056 ratio.

Do live:

1. Cut 0.0: the ratio reaches 164.2 percent in FY2056.
2. Move to 1.0: 133.2 percent. Then 2.0: 102.2 percent, almost flat.
3. Move to 3.0: 71.2 percent, a primary surplus of about 0.9 percent a year.

The Colab version also has sliders for i and g; the website version fixes i = g.

The prediction: about 164%, and a cut of about 2 points stabilizes it

• With \(i = g\), the ratio adds up the deficits: 99.5 + 64.7 ≈ 164% in FY2056.
• One point of \(i\) above \(g\) (\(i = 5\%\)) gives 209%; one point below (\(i = 3\%\)) gives 130%.
• A cut of 2 points of GDP every year, the size of the average primary deficit, keeps the ratio near 102%.

The same deficits can end in 130% or 209% of GDP: the gap between interest and growth matters as much as policy.

Numbers: the notebook’s “What the projection means for the debt” (cell outputs: 129.9, 164.2 and 208.8 percent for i = 3, 4 and 5 percent with g = 4 percent).

Two points of GDP is a large number. In FY2025 dollars per person it is about 1,800 dollars a year (2 points out of 23.1 points of spending ≈ 20,500 dollars), or roughly one third of all federal health spending per person in Table 18.1.

Your turn in the book: with i = 4.5 and g = 3.5 percent, how large must the yearly cut be to hold the FY2056 ratio near today’s? (Use the Colab widget.)

Components of spending

Which part of federal spending is projected to grow: Social Security, health, or everything else?

Ask: the population is aging, so pensions must be the problem. True or false? Collect answers before the chart.

Health is the part of the budget that keeps growing

Data: Office of Management and Budget, Historical Tables (FY2027 Budget), Tables 1.2, 3.1 and 8.5; Congressional Budget Office, The Long-Term Budget Outlook: 2026 to 2056. Chart inspired by Fig. 18.7 in Jones (2024), Macroeconomics, 6th ed.

How to read it: Fig. 6’s spending excluding interest, split into three parts, in percent of GDP: Social Security; Medicare and Medicaid; all other spending (defense, income security, education, roads and everything else). Solid lines are actual data, dashed lines CBO projections; the three add up to non-interest spending.

Point at:

1. All other spending: about 13–14 percent of GDP before 1980, 8.4 percent in 2000, a jump to 17.7 percent in 2020, and 6.9 percent projected for 2056.
2. Social Security: about 4 percent by 1980, 5.2 percent today, leveling off near 6 percent.
3. Medicare and Medicaid: from the mid-1960s, 3.1 percent in 2000, 6.0 percent in 2025, 8.1 percent in 2056. The crossing with all other spending: 2041.

Pensions level off; health spending does not

• Social Security: 4.0% of GDP in 2000, 5.6% in 2030, 6.0% in 2056, then flat. Some mix of higher payroll taxes and lower benefits must cover it.
• Medicare and Medicaid: 3.1% in 2000, 6.0% in 2030, 8.1% in 2056, still rising when pensions have stopped.
• Everything else, defense included, shrinks as a share of GDP.

Aging explains the rise of pensions; health costs rise for an additional reason.

Numbers: the notebook’s Fig. 7 key numbers. The textbook’s case study on Social Security: spending rises “from about 4.2 percent of GDP to about 6 percent”. The new data: 4.0 → 5.6 → 6.0 percent, close to it.

Social Security is pay-as-you-go: current workers’ payroll taxes, split between workers and employers, pay current retirees. As the ratio of workers to retirees falls, either the tax rate rises or benefits fall. Once the baby boom has retired, the ratio stabilizes, and so does spending.

Health is different: the 2002 projection had health at 7.7 percent of GDP by 2030 and 14.9 percent by 2075. The new projection is slower (6.0 percent in 2030), but still rising. The next slide splits the reasons.

Aging and costs that outpace income both raise the health share

\[h = \frac{H}{Y} = \frac{N_r}{N}\times\frac{c}{y} \qquad\Longrightarrow\qquad g_h = \underset{\text{aging}}{g_{N_r/N}} + \underset{\text{excess cost growth}}{(g_c - g_y)}\]

• If the cost per recipient grows 3% a year and income per person 2%, the share grows about 1% a year and doubles in about 70 years.
• Add 1% a year of aging and it doubles in about 35 years.
• With revenue at a fixed share of GDP, a rising \(h\) raises \(d_t\) every year, and the debt ratio has no resting point.

Taxes must rise or spending must fall: the arithmetic leaves no third option.

Equation (11). Health spending H is the number of recipients \(N_r\) times the cost per recipient c; GDP is the population N times GDP per person y. The growth rate of a product is the sum of the growth rates; that of a ratio is the difference.

The notebook’s Check 8: with costs growing 3 percent and income 2 percent a year, the share after 70 years is 9.90 percent of GDP, 1.98 times its start; the exact yearly growth is 0.980 percent. The rule of 70 at work.

The textbook notes that CBO’s long-run projections assume costs per recipient grow one point faster than GDP per person, slower than in recent decades.

Why might costs grow faster than income? New medical technology (Newhouse 1992, Journal of Economic Perspectives), and the value of life itself (next figure and the policy slide).

Health spending everywhere

Is the rise of health spending an American problem, or a rich-country one?

Ask: the U.S. health system is famously expensive. Do countries with public health systems avoid the rise? Collect answers.

Health takes a rising share of GDP in almost every rich country

Data: OECD Health Statistics, System of Health Accounts, current health expenditure, % of GDP (DSD_SHA@DF_SHA), via the OECD Data Explorer. Chart inspired by Fig. 18.8 in Jones (2024), Macroeconomics, 6th ed.

How to read it: total current health spending, public and private, as a percent of GDP, from 1970, for 45 countries. It starts with the textbook’s five countries in the textbook’s colors (the U.S., Germany, France, Japan, the U.K.). Click names in the legend, or a group button. The 2025 values are provisional estimates; the OECD’s current data start in 1970, so the textbook’s 1960 and 1965 points cannot be drawn.

Do live:

1. The five: the U.S. from 6.2 percent in 1970 to 17.6 percent in 2025; the U.S. pulls away in the 1980s.
2. Point at 2020: a spike (U.S. 18.7, U.K. 12.0 percent): health spending rose and GDP fell at once.
3. Add South Korea: 2.6 percent in 1970, 8.4 percent in 2023, as it grew rich and aged. Then India (3.3) and Indonesia (2.7).

The share grew 1.4% to 1.9% a year in each of the five countries

• U.S. health spending nearly tripled as a share of GDP, from 6.2% in 1970 to 17.6% in 2025. The other four rose from about 4.8% to 11–12%.
• Of 43 countries with data for both years, 38 spent a larger share in 2023 than in 2000.
• In 2023 the U.S. spent 16.9% of GDP, against 11.6% in Germany, the next highest.

Health spending grows faster than income nearly everywhere, whoever pays for it.

Numbers: the notebook’s Fig. 8 key numbers: average yearly growth of the share from 1970 to 2025 of 1.90 percent (U.S.), 1.47 (Germany), 1.42 (France), 1.62 (Japan) and 1.93 (U.K.).

Since 2010 the U.S. share has stayed near 16–18 percent, while Japan and the U.K., the lowest spenders until 2010, came close to Germany and France.

This figure counts public and private spending. In most European countries the government pays most of it, so a rising health share shows up directly in the budget. In the U.S. the government’s share (Medicare, Medicaid, insurance subsidies) is also rising, as Fig. 7 showed.

Should a law cap government debt?

The EU’s rules set reference values of 3% of GDP for deficits and 60% for debt. Should countries tie their hands with debt limits?

What the framework says

• No ratio is dangerous on its own: the U.K. carried 270% in 1946.
• What matters is \(i - g\), the debt and the primary balance.
• A rule on \(d\) is clearer than a rule on \(b\).

What is debated

• Is there a growth “cliff” near 90% of GDP?
• The cliff shrank once errors were fixed.
• Strict rules can force cuts in a slump.

The left column is Act II. Equation (7) says the surplus needed to hold the ratio depends on (i − g) b; equation (8) says that with i < g the ratio converges whatever its start. So a single ceiling for every country and every interest rate has no basis in the arithmetic. A rule on the primary balance, or on spending growth, targets the variable the government controls.

The research. Reinhart and Rogoff (2010, “Growth in a Time of Debt”, American Economic Review Papers and Proceedings) reported that growth falls sharply in countries whose debt exceeds about 90 percent of GDP. Herndon, Ash and Pollin (2014, Cambridge Journal of Economics) replicated the study, found a spreadsheet error and debatable weighting choices, and found no sharp threshold. Debt and growth are negatively correlated, but causality runs both ways: slow growth also raises debt ratios. Contested.

The EU’s reference values date from the Maastricht Treaty of 1992 and the Stability and Growth Pact. They were often broken and were reformed in 2024 toward country-specific paths for net spending.

Ask the policy students: should a debt rule be suspended in a recession or a pandemic? Who decides when the emergency is over?

Raise taxes or cut spending?

Closing a primary deficit of about 2% of GDP holds the U.S. debt ratio near today’s level. Should it be done with taxes, spending cuts, or both?

What the accounting says

• Either works for the debt: a point is a point.
• Revenue has stayed between 14% and 20% of GDP.
• Health and pensions are most of the spending.

What is debated

• Spending cuts may cost less output than tax rises.
• That finding depends on how plans are measured.
• Timing: a cut in a slump deepens it.

The left column: equation (5) does not care whether d falls because T rises or G falls. Fig. 6b: a cut of 2 points of GDP every year keeps the ratio near 102 percent. Table 18.1: health, Social Security and interest take 14.9 of the 23.1 points of spending; interest cannot be cut directly.

The research. Alesina, Favero and Giavazzi (2019, Austerity: When It Works and When It Doesn’t, Princeton University Press) study fiscal plans in 16 OECD countries and find that consolidations based on spending cuts cost much less output than those based on tax increases. Guajardo, Leigh and Pescatori (2014, Journal of the European Economic Association), using IMF narrative data on consolidations, find that consolidations are contractionary on average, and that earlier evidence of “expansionary austerity” came partly from how fiscal changes were measured. The size of the difference between tax- and spending-based plans is contested.

Timing links to the short-run model of Chapters 11–13: a consolidation in a recession lowers demand when output is already below potential.

Ask the policy students: which would you cut first, and which group would bear the cost?

Who should pay for rising health spending?

If richer people rationally want to spend more of their income on health, how should a government pay for it?

The case it is optimal

• Extra consumption adds less as we get richer.
• An extra year of life does not lose value.
• New treatments drive costs; people want them.

The case for restraint

• U.S. regions spend very differently, with similar results.
• Higher taxes have their own costs.
• Each generation’s bill is set by the last.

The left column is the textbook’s argument, from Hall and Jones (2007, “The Value of Life and the Rise in Health Spending”, Quarterly Journal of Economics): because the marginal utility of consumption falls as income rises while the value of an extra year of life does not, the optimal health share rises with income. Their simulations suggest the optimal U.S. share could exceed 30 percent by mid-century. Newhouse (1992, Journal of Economic Perspectives) found that new medical technology, not aging or insurance alone, explains most of the long-run rise in costs.

The right column. Fisher and coauthors (2003, Annals of Internal Medicine) found that U.S. regions with much higher Medicare spending per person did not deliver better quality or survival, evidence that part of U.S. spending is waste. Financing a rising share through taxes raises tax rates, with their own effects on work and saving. Generational accounting (Auerbach, Gokhale and Kotlikoff 1994) shows how current policy shifts the bill to later cohorts.

Options the textbook mentions besides taxes: private insurance and mandated health-saving accounts, each with its own problems.

Ask the policy students: should the government pay for every new treatment that works, whatever it costs?

“The debt never has to be repaid”

A skeptic says: “The U.S. has never repaid its debt; it just rolls it over. Japan’s debt is above 230% of GDP and it borrows cheaply. The budget constraint is a textbook fiction.”

Reply: rolling over is fine, and the arithmetic shows when. If \(i < g\), the ratio settles even with deficits; that is how the war debt shrank. But the constraint binds in present value: if \(i\) rises above \(g\), only primary surpluses hold the ratio, and interest already costs more than defense.

Take the objection seriously. The skeptic is right that governments almost never repay debt in the household sense, and that Japan (gross debt 237 percent of GDP in 2024) has not had a crisis. Blanchard (2019, “Public Debt and Low Interest Rates”, American Economic Review) argued that when the safe interest rate is below the growth rate, as it was for most of U.S. history, debt may have no fiscal cost and a limited welfare cost. Mian, Straub and Sufi (2022, “A Goldilocks Theory of Fiscal Deficits”, NBER Working Paper 29707) model how the room for deficits depends on how much interest rates rise as debt grows.

The reply uses Act II. Equation (8): with i < g the ratio converges to b, even with a permanent primary deficit (i = 3, g = 4, d = 2 gives b = 208 percent). With i > g, b* becomes a tipping point and equation (7) asks for a surplus proportional to the debt (0.96 percent of GDP at i = 5, g = 4). Fig. 6b: one point of i above g turns 164 percent into 209 percent in 2056.

Since 2022, interest rates have risen: U.S. net interest was 3.2 percent of GDP in FY2025, more than defense (3.0). And a higher debt makes i itself sensitive to lenders’ confidence.

Ask: what would have to be true for the U.S. to keep rolling over forever?

What to remember from this chapter

• The U.S. federal government spends about 23% of GDP and collects about 17%; its debt, 99.5% of GDP, is back near the 1946 record.
• Each year, the debt rolls forward with interest plus the primary deficit; over time, the budget must balance in present value.
• What matters is debt over GDP: when \(g > i\) it falls without repayment, as after World War II; when \(i > g\), only primary surpluses hold it.
• Deficits must be financed by private or foreign saving, or they crowd out investment.
• The fiscal problem of this century is health spending, rising faster than income in almost every rich country.

Ask each student to write one sentence answering the opening question: how much can a government borrow, and why does growth matter more than repayment? A good answer: as much as lenders believe it can service out of future taxes; what matters is the debt relative to GDP, which falls on its own when GDP grows faster than the interest rate, and rises unless the primary balance is in surplus when it does not.

For the policy students, three habits: ask whether a deficit is primary or total; compare i with g before judging a debt; and look at the projections, not only today’s numbers.

Walk the three branches of the mind map in about a minute each: spending, taxes and debt (cyan), the budget arithmetic (lavender), the fiscal problem ahead (green). Click the image to zoom in.

A budget must balance in present value: growth can shrink a debt, but it will not pay for rising health spending

Next: Chapter 19, International Trade

This chapter used accounting relations, not a behavioral model, and they hold whatever governments decide. Chapter 19 turns to the international economy, including the foreign saving that has financed much of the U.S. deficit, the third term of the saving-investment identity.

Sources: data and figures

• Figs. 1 and 2, U.S. budget and debt; Table 18.1. Office of Management and Budget, Historical Tables of the FY2027 Budget, Tables 1.2, 3.1, 7.1 and 8.5. Inspired by Figs. 18.1 and 18.2 and Table 18.1 in Jones (2024).
• Two centuries of debt. International Monetary Fund, Public Finances in Modern History, gross debt; Mauro, P., R. Romeu, A. Binder and A. Zaman (2015), Journal of Monetary Economics 76. Inspired by Fig. 18.2 in Jones (2024).
• Figs. 3 and 4, spending and net debt. OECD, Government at a Glance (DSD_GOV@DF_GOV_PF_YU), government balance sheets (DSD_NASEC20@DF_T720GOV_A), national accounts (DSD_NASEC10@DF_TABLE12, DSD_NAMAIN10@DF_TABLE1_EXPENDITURE), via the OECD Data Explorer. Inspired by Figs. 18.3 and 18.4 in Jones (2024).
• Fig. 5, investment and deficits. BEA via FRED: GPDI, FGDEF, GDP; OECD national accounts for 36 countries. Inspired by Fig. 18.5 in Jones (2024).
• Figs. 6 and 7, projections. OMB Historical Tables; Congressional Budget Office, The Long-Term Budget Outlook: 2026 to 2056 (February 2026); CBO (2002), Long-Range Fiscal Policy Brief No. 1, projections for 1950–2075 (the textbook’s markers). Inspired by Figs. 18.6 and 18.7 in Jones (2024).
• Fig. 8, health spending. OECD Health Statistics, System of Health Accounts (DSD_SHA@DF_SHA), via the OECD Data Explorer. Inspired by Fig. 18.8 in Jones (2024).
• Textbook. Jones, C. I. (2024). Macroeconomics, 6th ed. W. W. Norton. Book chapter, with the data, code and derivations: Data Science and Macroeconomic Models, Chapter 18.

Sources: research cited

• Debt and taxes over time. Barro, R. J. (1974), Journal of Political Economy 82(6); Auerbach, A. J., J. Gokhale and L. J. Kotlikoff (1994), “Generational Accounting: A Meaningful Way to Evaluate Fiscal Policy”, Journal of Economic Perspectives 8(1); Hall, G. J. and T. J. Sargent (2011), American Economic Journal: Macroeconomics 3(3).
• Debt limits and low interest rates. Reinhart, C. M. and K. S. Rogoff (2010), “Growth in a Time of Debt”, American Economic Review 100(2); Herndon, T., M. Ash and R. Pollin (2014), Cambridge Journal of Economics 38(2); Blanchard, O. (2019), “Public Debt and Low Interest Rates”, American Economic Review 109(4); Mian, A., L. Straub and A. Sufi (2022), “A Goldilocks Theory of Fiscal Deficits”, NBER Working Paper 29707.
• Fiscal consolidation. Alesina, A., C. Favero and F. Giavazzi (2019), Austerity: When It Works and When It Doesn’t, Princeton University Press; Guajardo, J., D. Leigh and A. Pescatori (2014), “Expansionary Austerity? International Evidence”, Journal of the European Economic Association 12(4).
• Health spending. Hall, R. E. and C. I. Jones (2007), “The Value of Life and the Rise in Health Spending”, Quarterly Journal of Economics 122(1); Newhouse, J. P. (1992), “Medical Care Costs: How Much Welfare Loss?”, Journal of Economic Perspectives 6(3); Fisher, E. S. et al. (2003), “The Implications of Regional Variations in Medicare Spending”, Annals of Internal Medicine 138(4).