Did the US Really Grow Out of Its World War II Debt?
What this paper finds — and why it matters
Layer 1: Overview
Research question and motivation. The fall in the US federal debt-held-by-the-public/GDP ratio from a postwar peak of 106% in fiscal year 1946 to a trough of 23% in 1974 is widely cited (Elmendorf-Mankiw, Krugman) as evidence that an economy “grows out of” debt because the GDP growth rate exceeds the interest rate on government debt (r < g). That narrative underpins the modern view (Blanchard 2019; Furman-Summers 2020) that high public debt “may have no fiscal cost.” Acalin and Ball ask how much of the postwar debt decline was genuinely due to growth exceeding undistorted real interest rates, versus three other factors: primary budget surpluses, the Fed’s 1942-1951 interest-rate peg before the Fed-Treasury Accord, and surprise inflation.
Method and data. The authors simulate counterfactual debt/GDP paths from the standard debt-dynamics identity D_t = (1+i_t)D_{t-1} - P_t, starting from the actual 1946 debt level and holding nominal GDP fixed at its historical path. They build three counterfactuals: (i) “primary balance” (set primary surplus to zero each year); (ii) “adjusted interest rate” (remove distortions from both the peg and surprise inflation); and (iii) “combined” (both), whose path is driven purely by r* - g, the undistorted real rate minus growth. A key innovation is measuring the “reverse maturity structure” — the fractions of currently outstanding debt issued in each past year — using Hall-Payne-Sargent (2018) data for 1942-1960 and CRSP thereafter. They construct a term structure of inflation expectations from one-year (Livingston, SPF) and ten-year (FRB/US) survey data, and estimate undistorted peg-era real rates from ex-ante real rates on securities issued in 1952-1961. T-bills and TIPS are assumed unaffected by inflation surprises (conservative). Debt is par value, held by the public, by fiscal year.
Main quantitative findings. In the combined counterfactual, debt/GDP falls only to 74% in 1974 (vs. 23% actual); the individual counterfactuals give 40% (primary balance) and 51% (adjusted rate) in 1974. Of the actual 83-point fall (106 to 23), 51 points are explained by surpluses plus rate distortions, decomposed as 17 points from surpluses alone, 28 from rate distortions alone, and 6 from their interaction; only 32 points (the fall to 74%) reflect growth net of undistorted rates. Extending to the present, the combined counterfactual ratio starts rising in 1980, dipping to 70% in 1979 before climbing to 84% in 2022 — only 22 points below the 1946 level of 106. Over the full 76 years, undistorted growth alone would have cut debt/GDP by just 22 points. The post-1979 reversal reflects a sign change in r* - g: average r* rose from 2.3% (1947-1979) to 2.8% (1980-2022) while average g fell from 3.5% to 2.6%. The estimated undistorted real-rate term structure is 1.7% (1yr), 2.2% (5yr), 2.5% (10yr), 2.7% (30yr).
Mechanisms and implications. Primary surpluses averaged 1.1% of GDP over 1947-1974 (peaking at 6.3% in 1948), then turned to persistent deficits. The peg (caps of 0.375% on bills to 2.5% on 30-year bonds) combined with post-1946 inflation surges (CPI averaging 7.1% in FY1947-1951) produced deeply negative ex-post real rates; the aggregate interest-rate adjustment x_t reached 13 points in 1947 and 8 points in 1951. Policy implication: the distortions are unlikely to recur (no peg/price controls planned, Fed committed to low inflation, shorter average maturity — down from 4.4 years in 1951 to 2.2 years in 2022 — blunts inflation’s effect), so substantially reducing today’s 97% (FY2022) ratio will likely require primary surpluses, which CBO projections suggest are not forthcoming.
Layer 2: Deep Dive
What is the identification/counterfactual strategy and what are its main threats?
There is no causal identification in the econometric sense; the strategy is an accounting simulation of the debt-dynamics identity under counterfactual interest rates and primary balances, holding nominal GDP (and real GDP and undistorted real rates) fixed at historical values. Threats: (1) the undistorted peg-era real rates are unobserved and must be guessed from 1952-1961 ex-ante real rates; (2) the reverse maturity structure (weights w) is held at historical levels even though higher counterfactual debt would alter issuance; (3) general-equilibrium feedback is ignored — higher counterfactual debt would raise real rates and crowd out capital, lowering GDP, both of which would push debt/GDP even higher, so the authors interpret their paths as LOWER BOUNDS; (4) pre-1943 debt is not adjusted for surprise inflation because long-term expectations data do not exist before 1943, which the authors argue biases against finding a large inflation role.
How are the effects of the peg and surprise inflation distinguished, and can they be separated?
The adjusted-interest-rate scenario removes both jointly. The authors state it would be difficult to separate them cleanly because that requires measures of expected inflation during the peg period (1942-1951), and there are no data on long-term inflation expectations before 1951 or short-term expectations before 1947 (start of Livingston). For post-1952 debt, the surprise-inflation adjustment is pi_t minus the expectation formed when the security was issued; for peg-era debt the adjustment is the gap between the ex-post real rate and the assumed undistorted real rate.
What is the decomposition relative to Hall and Sargent (2011)?
Hall-Sargent decompose the 1946-1974 debt/GDP change into r-g and primary surpluses but do not ask how interest-rate distortions shape r-g. Replicating their approach (Table 2A), the authors attribute -48.1 points to r-g and -29.6 points to primary surpluses (the terms sum to -78 points, less than the actual -82.9 because of the debt-dynamics residual). The paper’s extension (Table 2B) splits the -48.1 r-g contribution into only -11.7 points from r*-g (undistorted) and -36.3 points from the distortion r-r*, with surpluses still -29.6. So most of the apparent ‘growth out of debt’ was actually interest-rate distortion.
Why do the Table 2 surplus contributions differ from the Table 1 scenario differences?
In Table 2 surpluses contribute -29.6 points, larger than the 17-point effect implied by the Table 1 difference between actual 1974 debt/GDP and the primary-balance scenario. The reason is an interaction: eliminating surpluses raises the debt path d_{t-1}, which magnifies the r-g term, so additional debt is partly eroded by r-g. The authors call the Figure 7 / Table 1 scenario paths the more precise representation.
How do the findings reconcile with Blanchard’s (2019) claim that r < g since 1979?
The authors find r > g on average since 1979 (even in the primary-balance counterfactual with actual ex-post rates), so debt/GDP would rise. The difference from Blanchard is purely measurement: (1) they use the government’s interest payments on outstanding debt — the rates set at issuance — whereas Blanchard uses current market yields (a weighted average of 1- and 10-year Treasury rates), which since 1979 have been lower because rates trended down; (2) the authors use pre-tax rates while Blanchard uses after-tax rates. Figure A.11 confirms: with the authors’ measure debt/GDP rises 1979-2022; with Blanchard’s pre-tax market yields it rises then falls back near its 1979 level; with his after-tax rates it falls significantly. The authors argue the rate paid by the government is the relevant one for the debt-dynamics identity, and that a natural baseline assumes debt has no net effect on tax revenue (so pre-tax rates apply).
What is a notable nuance about the post-1979 period in the primary-balance counterfactual?
The post-1979 rise in debt/GDP is LARGER in the primary-balance counterfactual (19 points, from 34% to 53%) than in the combined counterfactual (14 points). This is because inflation surprises since 1979 have on average been negative (post-Volcker disinflation, actual below expected), raising ex-post real rates and thus debt/GDP. It confirms that actual r has exceeded g since 1979.
What robustness checks are run?
(1) Undistorted peg-era real rates shifted by +/-0.5% and +/-1% across the whole term structure: 1974 combined debt/GDP ranges from 67% (-1%) to 81% (+1%) around the 74% baseline; 2022 ranges from 78% to 91% around 84% (Table A.2). (2) Pre-1962 interest measured by net interest times 1.1; using net interest directly gives 73% in 1974 and 83% in 2022 vs. 74% and 84% baseline. (3) The debt-dynamics residual epsilon (mainly Treasury cash balances) is held at historical values; setting it to zero gives a combined counterfactual of 78% in 1974 and 77% in 2022, showing the residual contributed -0.19% GDP/year on average over 1947-1974 and +0.25% over 1975-2022. (4) Term-structure shape assumptions and the GDP-deflator-vs-CPI expectation-error approximation are checked in the Appendix as reasonable.
What heterogeneity across the debt structure matters?
The reverse maturity structure is central: the share of debt with reverse maturities above five years peaked at 48% in 1951 (long-term WWII bonds), then fell, fluctuating between 10% and 25% from 1975-2022; average reverse maturity fell from 4.4 years in 1951 to 2.2 years in 2022. Shorter maturity means inflation surprises erode less debt — a reason later inflation surprises had smaller effects than the 1940s-1970s ones. T-bills (assumed unaffected by surprise inflation since rolled over at adjusting rates) and TIPS (post-1997, indexed) are excluded from the inflation-surprise adjustment. Non-marketable debt fell from 23% of total in 1960 to 3% in 2022; its reverse maturity structure is assumed constant after 1960.
What are the timing/measurement complications?
Unit is fiscal year (July-June before FY1977, October-September after), creating a ‘Transitional Quarter’ in Q3 1976 requiring special handling. Inflation is GDP-deflator growth. Pre-1970 deflator expectations are proxied from Livingston CPI forecasts assuming equal expectation errors for CPI and deflator. Ten-year expectations before 1968 are fitted from one-year expectations via a regression (1968-1997) with a negative coefficient (-1.549) on the change in smoothed one-year expectations, capturing long-term expectations lagging short-term moves.
What are the policy implications and their scope conditions?
Because the postwar debt reduction came largely from one-off distortions (the peg with price controls, and surprise inflation) unlikely to recur — and the Fed is committed to low inflation while shorter average maturity weakens inflation’s erosive power — economic growth alone is unlikely to resolve the current ~97% (FY2022) ratio. Substantial reduction will probably require primary surpluses, which CBO projects will not occur under current policy (large primary deficits forecast for three decades). Scope conditions: results are lower bounds (GE crowding-out omitted); they depend on the assumed undistorted real-rate term structure; the 2021-2022 inflation surge is again temporarily reducing debt/GDP.