## wpiea2024005-print-pdf — Introduction and selected sections

## Source details

**Canonical URL:** [wpiea2024005-print-pdf — Introduction and selected sections](https://www.imf.org/-/media/files/publications/wp/2024/english/wpiea2024005-print-pdf.pdf)

## Other formats

- [Markdown version](/-/media/files/publications/wp/2024/english/wpiea2024005-print-pdf.pdf.md)
- [Structured JSON version](/-/media/files/publications/wp/2024/english/wpiea2024005-print-pdf.pdf.json)

---

### Overview and research question
- Asks whether a high level of national debt imposes a burden on future generations who must pay it off.
- Notes claims that when r < g governments can roll over debt without raising taxes and the debt/GDP ratio will fall (references: Blanchard 2019; Furman and Summers 2020).
- Highlights the U.S. historical episode: public debt/GDP rose from 42% in fiscal year 1941 to 106% in 1946 and then fell to 23% in fiscal year 1974; this experience is often attributed to growth exceeding interest rates.
- Presents competing perspectives:
  - Hall and Sargent (2011) and Eichengreen and Esteves (2022): part of World War II debt paydown came via primary surpluses.
  - Reinhart and Sbrancia (2015): interest rates were held down relative to growth by policies (financial repression, Fed pegging) and unexpected inflation.

### Key empirical findings (Introduction summary)
- Counterfactual excluding primary surpluses and interest-rate distortions:
  - Debt/GDP falls from 106% in 1946 to 74% in 1974 (versus actual fall to 23%).
  - Natural erosion of debt from economic growth was considerably smaller than often suggested over the three decades after World War II.
- Extended counterfactual to 2022:
  - Counterfactual debt/GDP starts rising again in 1980 and is 84% in 2022.
  - The 2022 counterfactual level is 22 percentage points below the 1946 level of 106% (i.e., 84% vs. 106%).
  - The rise reflects that, on average since 1980, the economy’s growth rate has averaged less than the undistorted real interest rate on debt.

### Factors materially influencing the debt/GDP path
- Primary surpluses and deficits:
  - Sharp fall in government spending after World War II produced primary surpluses of 3.6% of GDP in 1947 and 6.3% of GDP in 1948.
  - From 1947 through 1974, the primary surplus averaged 1.1% of GDP; annual values ranged between 3.4% and -1.5% of GDP through 1974.
  - After 1974, primary deficits predominated, with especially large deficits around 2008 and the COVID pandemic.
- Federal Reserve interest-rate peg (financial repression):
  - April 1942–1951: Fed capped yields from 0.375% for Treasury bills to 2.5% for 30-year bonds and stood ready to buy any quantity of bonds.
  - Price-control elimination June 1946 led to CPI inflation in fiscal years 1947–1951 ranging from -0.7 percent to 18.3 percent with an average of 7.1 percent.
  - The March 1951 “Accord” ended the peg; large portions of debt issued during the peg had ten- to thirty-year maturities transmitting low rates well after 1951.
- Surprise inflation:
  - Unexpected inflation reduces debt/GDP by lowering ex-post real interest rates relative to ex-ante real rates; the relevant inflation concept is the GDP deflator.
  - Inflation surprises were large in the 1960s–1970s, especially for ten-year-ahead expectations, eroding real returns on long-term securities and contributing to the decrease in debt/GDP through 1974.
  - From the 1980s under the Volcker regime, actual inflation was usually lower than expected inflation, pushing ex-post real interest rates above ex-ante rates and contributing to rising debt/GDP.
  - The sharp increase in inflation in 2021–2022 again made unexpected inflation a factor reducing the debt/GDP ratio.

### Methodological approach for counterfactuals
- Core debt identity (nominal par values, fiscal-year frequency):
  - Dt = (1 + it) Dt−1 − Pt
    - Dt: par value of the debt at end of fiscal year t.
    - it: average interest rate on the debt (total interest payments in fiscal year t divided by Dt−1).
    - Pt: primary surplus in fiscal year t.
- Counterfactual construction:
  - Set Pt = 0 for all t to simulate no primary surpluses.
  - Replace actual nominal interest rates it with undistorted rates ˆit that remove effects of the pre-Accord peg and surprise inflation.
    - For debt issued before 1952: estimate ex-ante real rate that would have prevailed without the peg by inferring from ex-ante real rates after the peg.
    - To remove surprise inflation: add the unexpected component of inflation (measured using surveys of expectations) to actual nominal interest rates so ex-post real rates equal ex-ante real rates (equivalently, as if debt were fully inflation-indexed).
- Maintain actual nominal GDP in all counterfactuals (abstracts from general-equilibrium crowding-out effects); counterfactual debt/GDP paths are lower bounds on full general-equilibrium outcomes.
- Reverse maturity structure held fixed at historical weights in counterfactuals.

### Reverse maturity structure and aggregation of counterfactual interest rates
- Reverse maturity notation:
  - Dt−1 = sum_{j=0}^M D^j_{t−1}; w^j_{t−1} ≡ D^j_{t−1} / Dt−1.
  - i^{j+1}_t is the actual average interest rate in year t on debt issued in t−1−j.
  - Aggregate it = sum_{j=0}^M w^j_{t−1} i^{j+1}_t.
- Counterfactual aggregate ˆit formed by adjusting each maturity-specific rate to ˆi^{j+1}_t while holding w^j_{t−1} fixed:
  - x^{j+1}_t = ˆi^{j+1}_t − i^{j+1}_t, then ˆit = it + sum_{j=0}^M w^j_{t−1} x^{j+1}_t ≡ it + x_t.
- Data sources and practical steps:
  - Reverse maturity from Hall, Payne, and Sargent (2018) before 1960 and CRSP thereafter.
  - Term structure of inflation expectations from surveys of short- and long-term expectations to estimate surprise-inflation effects.
  - Estimate peg effects by comparing pegged rates by maturity to market rates during 1952–1960.

### The adjustments to interest rates (definitions and implementation)
- Adjustment formula by issuance vintage (x_{j+1}^t):
  - x_{j+1}^t = 0 for t−1−j ≤ 1942.
  - x_{j+1}^t = r⋆_{j+1}^t − (i_{j+1}^t − π_t) for 1943 ≤ t−1−j ≤ 1951 (peg period).
  - x_{j+1}^t = π_t − E_{t−1−j}[π_t] for t−1−j ≥ 1952 (post-peg surprise inflation).
- Interpretation:
  - Post-1952 vintages: adjust ex-post rates to eliminate unexpected inflation (π_t − E_{t−1−j}[π_t]) where expectations come from surveys.
  - 1943–1951 vintages: adjust by the difference between ex-post real rate and estimated undistorted real rate r⋆_{j+1}^t; r⋆_{j+1}^t estimated from ex-ante real rates in 1952–1961.
  - Pre-1943 vintages: baseline x = 0 due to lack of long-term expectation measures; authors conjecture inclusion would increase the role of surprise inflation.
- Two complications handled conservatively:
  - Treasury bills: assume surprise inflation has no effect on real returns on T-bills (most commonly 90 days).
  - TIPS (since 1997): inflation surprises do not erode these securities; adjustments exclude TIPS.
- Data timing:
  - Fiscal-year timing uses July–June early sample, shifts to October–September starting fiscal year 1977 with a Transitional Quarter (third quarter 1976) treated separately.

### Constructing counterfactual undistorted real rates for the peg period
- Baseline for r⋆_{j+1}^t:
  - For a given maturity at issuance, the counterfactual undistorted real rate equals the average of ex-ante real rates on securities with that maturity issued over fiscal years 1952–1961.
  - Ex-ante real rates by maturity for 1952–1961 calculated from nominal rates (Global Financial Database) and the term structure of inflation expectations.
  - Resulting baseline term structure: 1.7% at one year, 2.2% at five years, 2.5% at ten years, 2.7% at thirty years.
- Robustness checks:
  - Add/subtract 0.5% or 1% to entire term structure for securities issued before the Accord; combined-counterfactual debt/GDP in 1974 ranges 67% (−1%) to 81% (+1%) and in 2022 ranges 77.7% (−1%) to 91.0% (+1%).

### Results: simulations of debt/GDP starting in 1946 (three counterfactuals)
- Simulation start: 1946 debt/GDP = actual 106%.
- Scenarios compared:
  - Primary balance scenario: Pt = 0 in all years; interest rates historical.
  - Adjusted interest-rate scenario: apply x_{j+1}^t adjustments; primary surpluses historical.
  - Combined scenario: Pt = 0 and interest rates adjusted (both distortions removed).
- Key outcomes 1946–1974:
  - Actual debt/GDP: 106% in 1946 → 23% in 1974 (decline of 83 percentage points).
  - Counterfactual 1974 debt/GDP:
    - Primary Balance scenario: 40%
    - Adjusted Interest Rate scenario: 51%
    - Combined scenario: 74%
  - In the combined scenario the ratio falls by 32 points (106 to 74 percent).
  - Decomposition of the actual 83-point fall:
    - 17 points explained by primary surpluses alone.
    - 28 points explained by interest-rate distortions alone.
    - 6 points from interaction of the two factors.
- Dynamics of aggregate interest-rate adjustment x_t (1947–1974):
  - x_t large early: 13 percentage points in 1947 and 8 points in 1951.
  - By 1951, actual debt/GDP had diverged by more than 20 percentage points from the rate-adjusted scenario.
  - x_t mostly small until late 1960s; over 4 percentage points in 1974 and remains high through the rest of the 1970s.

### The Debt Buildup, 1975–2022 (Section 5.2)
- Actual debt/GDP:
  - Started to rise in 1975, with a dip in the late 1990s; in 2022 it stood at 97%.
- Principal drivers:
  - Biggest factor: shift from primary surpluses to primary deficits (tax cuts notably in early 1980s; deficits ballooned after 2008 and the 2020 pandemic).
  - Secondary factor: on average r⋆ > g since 1980.
- Combined counterfactual path:
  - Debt/GDP falls from 74% in 1974 to 70% in 1979, then rises to 84% in 2022.
- Average rates:
  - Average r⋆: 2.3% over 1947-1979; 2.8% over 1980-2022.
  - Average g: 3.5% over 1947-1979; 2.6% over 1980-2022.
- Quantified long-run counterfactual:
  - Over 1946-2022, economic growth without primary surpluses or interest-rate distortions would have reduced debt/GDP by only 22 percentage points, from 106% to 84%.
- Comparison of counterfactual rises since 1979:
  - Primary-balance counterfactual rise: 19 percentage points (from 34% to 53%).
  - Combined counterfactual rise: 14 percentage points.
  - Reason: average negative inflation surprises since 1979 increased ex-post real rates and debt/GDP.

### Key statistics (selected debt/GDP values from Table 1)
- Debt/GDP ratio (%) — Actual and Counterfactuals:
  - 1946: Actual 106.1, Primary Balance 106.1, Adjusted Interest Rate 106.1, Combined 106.1
  - 1974: Actual 23.2, Primary Balance 39.9, Adjusted Interest Rate 50.9, Combined 73.8
  - 2022: Actual 97.0, Primary Balance 53.3, Adjusted Interest Rate 122.8, Combined 84.1

### Contributions to change in Debt/GDP (1946–1974) — Table summaries
- Table 2A — ∆(Debt/GDP) contributions:
  - r−g: -82.9
  - surpluses: -48.1
  - (residual): -29.6
- Table 2B — decomposition of r−g:
  - r − g: -82.9
  - r − r⋆ : -11.7
  - surpluses: -36.3
  - (residual): -29.6

### The role of the residual εt and robustness
- Exact debt evolution with residual:
  - Dt = (1 + it) Dt−1 − Pt + εt.
- Residual εt arises from factors beyond interest and primary balance (Treasury cash, interest on government assets, stimulus flows).
- Residual behavior and simulation sensitivity:
  - Combined counterfactual with ε = 0: debt/GDP falls to 78% in 1974 (vs. 74% with historical ε).
  - Combined counterfactual with ε = 0: debt/GDP reaches 77% in 2022 (vs. 84% with historical ε).
  - Residual averages:
    - -0.19 percent of GDP over 1947-1974.
    - 0.25 percent of GDP over 1975- (series truncated in source).
- Treatment of T-bills and TIPS:
  - Surprise-inflation adjustments applied only to debt not T-bills or TIPS; adjustments incorporate s_{t−1} (T-bill fraction) and z_{j t−1} (TIPS fraction).

### Comparison to Blanchard (2019) and treatment of taxes/crowding out
- Measurement differences:
  - This paper uses government interest payments on outstanding debt (rates paid when debt was issued); Blanchard uses market yields (typically lower) and after-tax rates in some analysis.
- Taxation and crowding out:
  - Blanchard: taxes on interest reduce debt burden.
  - Counterpoint: bond issuance crowds out capital and reduces tax revenue on lost capital income; net effect ambiguous.
  - Baseline assumption here: debt has no net effect on tax revenue; evolution determined by pre-tax interest rate.

### Conclusions and policy implications
- Up to 1974, the fall in debt/GDP was driven mostly by primary surpluses and interest-rate distortions.
  - Absent those factors, debt/GDP would have fallen from 106% in 1946 to only 74% in 1974.
- Since 1974, the main driver of the debt increase is large primary deficits; a secondary factor is that r⋆ has on average exceeded g.
  - With primary balance and undistorted interest rates, debt/GDP would have grown from 74% in 1974 to 84% in 2022.
- Historical experience suggests a limited tendency for the economy to “grow out of” a high debt level without primary surpluses or interest-rate distortions.
- Interest-rate distortions that aided postwar debt reduction are unlikely to recur (wartime pegs unlikely; Fed commitment to low inflation; shorter average debt maturity reduces effects of surprise inflation).
- Implication: substantial reduction in the debt/GDP ratio will probably require primary budget surpluses.
  - Under current policy, Congressional Budget Office projections indicate large primary deficits over the next three decades, which would likely push debt/GDP higher absent major fiscal consolidation.

*Source: wpiea2024005-print-pdf — Did the U.S. Really Grow Out of Its World War II Debt? (Working Paper No. WP/2024/005).*

### Introduction ...........................................................................................................

### wpiea2024005-print-pdf - Introduction

### Overview and research question
- Asks whether a high level of national debt imposes a burden on future generations who must pay it off.
- Notes recent claims (Blanchard 2019; Furman and Summers 2020) that when r < g (the real interest rate is below the growth rate of the economy) governments can roll over debt without raising taxes and the debt/GDP ratio will fall.
- Observes the influential historical episode: U.S. public debt/GDP rose from 42% in fiscal year 1941 to 106% in 1946 and then fell to 23% in fiscal year 1974, an experience often attributed to growth exceeding interest rates.
- Presents competing perspectives:
  - Hall and Sargent (2011) and Eichengreen and Esteves (2022): the U.S. paid down part of World War II debt via primary surpluses (taxes in excess of current spending).
  - Reinhart and Sbrancia (2015): interest rates were held down relative to growth by policies (financial repression, Fed pegging) and unexpected inflation, which may not be repeatable.

### Key empirical findings (from the Introduction)
- Counterfactual excluding primary surpluses and interest-rate distortions:
  - Debt/GDP falls from 106% in 1946 to 74% in 1974 (versus actual fall to 23%).
  - The natural erosion of debt from economic growth was considerably smaller than often suggested over the three decades after World War II.
- Extended counterfactual to 2022:
  - Counterfactual debt/GDP starts rising again in 1980 and is 84% in 2022.
  - The 2022 counterfactual level is 22 percentage points below the 1946 level of 106% (i.e., 84% vs. 106%).
  - The rise reflects that, on average since 1980, the economy’s growth rate has averaged less than the undistorted real interest rate on debt.

### Factors identified as materially influencing the debt/GDP path
- Primary surpluses and deficits
  - Sharp fall in government spending after World War II produced primary surpluses of 3.6% of GDP in 1947 and 6.3% of GDP in 1948.
  - From 1947 through 1974, the primary surplus averaged 1.1% of GDP; annual values ranged between 3.4% and -1.5% of GDP through 1974.
  - After 1974, primary deficits predominated (negative primary balances except late 1990s), contributing to rising debt/GDP; deficits were especially high around 2008 and the COVID pandemic.
- Federal Reserve interest-rate peg (financial repression)
  - April 1942–1951: Fed capped yields at levels ranging from 0.375% for Treasury bills to 2.5% for 30-year bonds, standing ready to buy any quantity of bonds.
  - Peg made it impossible to adjust rates to control inflation; price controls eliminated June 1946 led to volatile CPI inflation in fiscal years 1947–1951, which ranged from -0.7 percent to 18.3 percent with an average of 7.1 percent.
  - The March 1951 “Accord” ended the peg.
  - The peg affected debt dynamics because large portions of debt issued during the peg had maturities of ten to thirty years, transmitting low rates well after 1951.
  - The pre-Accord peg is treated as the clearest case of financial repression in the postwar U.S.; other repressive measures (e.g., Regulation Q) are mentioned but not quantified here.
- Surprise inflation
  - Unexpected inflation reduces the debt/GDP ratio by lowering ex-post real interest rates relative to ex-ante real rates; the relevant inflation concept is the GDP deflator.
  - Inflation surprises (actual inflation minus expectations measured one year earlier and ten years earlier) were large in the 1960s–1970s, often exceeding expectations—especially ten-year-ahead expectations—eroding real returns on long-term securities and contributing to the decrease in debt/GDP through 1974.
  - From the 1980s under the Volcker regime, actual inflation was usually lower than expected inflation, pushing ex-post real interest rates above ex-ante rates and contributing to rising debt/GDP, though the effect was smaller because average debt maturity was shorter.
  - The sharp increase in inflation in 2021–2022 again made unexpected inflation a factor reducing the debt/GDP ratio.

### Methodological approach for counterfactuals
- Core debt evolution identity (nominal par values, fiscal-year frequency):
  - Dt = (1 + it) Dt−1 − Pt
    - Dt: par value of the debt at end of fiscal year t.
    - it: average interest rate on the debt (total interest payments in fiscal year t divided by Dt−1).
    - Pt: primary surplus in fiscal year t.
- Counterfactuals constructed by:
  - Setting Pt = 0 for all t to simulate no primary surpluses.
  - Replacing actual nominal interest rates it with undistorted rates ˆit that remove effects of the pre-Accord peg and surprise inflation.
    - For debt issued before 1952: estimate the ex-ante real rate that would have prevailed without the peg, inferred from ex-ante real rates observed after the peg.
    - To remove surprise inflation: add the unexpected component of inflation (measured using surveys of expectations) to actual nominal interest rates so ex-post real rates equal ex-ante real rates (equivalently, as if debt were fully inflation-indexed).
- Maintain actual nominal GDP in all counterfactuals (i.e., assume counterfactuals do not change nominal GDP or undistorted real interest rates and thus abstract from general-equilibrium crowding-out effects that would likely worsen debt/GDP outcomes).
  - Authors note this makes their counterfactual debt/GDP paths lower bounds on what full general-equilibrium analysis would imply.

### Reverse maturity structure and aggregation of counterfactual interest rates
- Introduces the “reverse maturity structure”: the distribution across past issuance years of the debt outstanding in a given year.
  - Notation:
    - Dt−1 = sum_{j=0}^M D^j_{t−1}, where D^j_{t−1} is debt outstanding at end t−1 issued in year t−1−j.
    - w^j_{t−1} ≡ D^j_{t−1} / Dt−1 are the weights (reverse maturity shares).
    - i^{j+1}_t is the actual average interest rate in year t on debt issued in t−1−j.
    - Aggregate it = sum_{j=0}^M w^j_{t−1} i^{j+1}_t.
- Counterfactual aggregate interest rate ˆit is formed by adjusting each i^{j+1}_t to ˆi^{j+1}_t (removing peg and surprise-inflation distortions) while holding w^j_{t−1} fixed at historical values:
  - Define adjustments x^{j+1}_t = ˆi^{j+1}_t − i^{j+1}_t, then
    - ˆit = it + sum_{j=0}^M w^j_{t−1} x^{j+1}_t ≡ it + x_t.
- Practical data steps (summarized in the Introduction):
  - Measure reverse maturity structure using granular Treasury-security data from Hall, Payne, and Sargent (2018) before 1960 and CRSP thereafter.
  - Construct a term structure of inflation expectations from surveys of short- and long-term expectations to estimate surprise-inflation effects on real returns for securities issued in different years.
  - Estimate the effects of the pre-1952 interest-rate peg by comparing pegged rates by maturity to market rates during 1952–1960.
- Robustness:
  - Simulations require assumptions about unobserved variables, but results are reported as not greatly changed by varying these assumptions in reasonable ways.
  - The analysis holds reverse-maturity weights w^j_{t−1} fixed in counterfactuals (i.e., assumes counterfactual increases in aggregate debt do not change the reverse maturity structure), noted as an approximation and left for future refinement.

### Interpretation and limitations emphasized
- The counterfactual without surpluses or interest-rate distortions isolates the “natural tendency” of the economy to grow out of debt (the “negative snowball” or “melting” effect).
- Because simulations hold undistorted real rates and real GDP equal to historical values (i.e., omit crowding-out effects), the counterfactual debt/GDP paths should be interpreted as lower bounds on what a full general-equilibrium model would generate.
- The analysis focuses on par values of debt (as policy-relevant), noting that market-value approaches (Hall and Sargent 2011) would complicate analysis without materially changing results given close par and market-value paths.

*wpiea2024005-print-pdf - Introduction*

### 3.3    The Adjustments to Interest Rates

### 3.3    The Adjustments to Interest Rates

### Definition and formula
- The adjustment x_{j+1}^t applies to the interest rate paid on debt issued at t−1−j and depends on whether t−1−j is before, during, or after the peg. The expressions for x_{j+1}^t are:
  - 0 for t−1−j ≤ 1942
  - r⋆_{j+1}^t − (i_{j+1}^t − π_t) for 1943 ≤ t−1−j ≤ 1951
  - π_t − E_{t−1−j}[π_t] for t−1−j ≥ 1952
- r⋆_{j+1}^t is the undistorted real interest rate on the outstanding debt at t that was issued at t−1−j.
- E_{t−1−j}[π_t] is the expectation at t−1−j of the inflation rate at t.

### Interpretation by issuance period (reverse chronological review)
- For t−1−j ≥ 1952:
  - x_{j+1}^t adjusts ex-post rates to eliminate the effect of unexpected inflation.
  - The relevant inflation surprise is π_t − E_{t−1−j}[π_t].
  - Expectations are derived from surveys (described in next sections).
- For 1943 ≤ t−1−j ≤ 1951 (peg period):
  - x_{j+1}^t is the difference between the ex-post real interest rate and the undistorted real rate r⋆_{j+1}^t.
  - Ex-post real rate = average nominal interest rate on outstanding debt issued at t−j−1 minus π_t.
  - r⋆_{j+1}^t is not observed and must be estimated using ex-ante real rates in years after the peg.
- For t−1−j ≤ 1942 (issued before the peg):
  - x_{j+1}^t = 0 in the baseline because measures of long-term expectations before 1943 do not exist.
  - The authors conjecture that long-term expectations before 1943 would show positive inflation surprises, implying an even larger role for surprise inflation in reducing the debt/GDP ratio if those expectations were available.

- Peg dating note:
  - The peg was adopted in April 1942 and ended in March 1951. The paper dates the peg as fiscal years 1943-1951 (July 1942 through June 1951) to match fiscal-year data.

### Two complications (overview; handled in Appendix and simulations)
- Treasury Bills:
  - A substantial fraction of debt consists of Treasury bills (most commonly 90 days).
  - Equation (6) assumes all debt outstanding at the end of year t−1 is eroded by surprise inflation over year t, but many bills roll over within the year at rates that adjust to inflation news.
  - To be conservative, the authors assume surprise inflation has no effect on real returns on Treasury bills and modify equation (6) accordingly.
- Inflation-Indexed Debt:
  - Starting in 1997, part of the debt is Treasury Inflation-Protected Securities whose nominal rates adjust so ex-post real rates equal ex-ante rates.
  - Inflation surprises do not erode these securities; equation (6) is adjusted accordingly.
- Additional measurement caveats:
  - Some long-term bonds mature within year t, so returns are not eroded by the full inflation surprise over t (potential overstatement).
  - Securities are issued throughout each year while expectations are measured at year-end (potential understatement).
  - Authors judge these biases unlikely to be important but note future research could use higher-frequency data.

### Data and counterfactual specification (selected points relevant to rate adjustments)
- Timing:
  - Unit of time is fiscal year. Early sample fiscal year runs July (t−1)–June t; starting fiscal year 1977 timing shifts to October (t−1)–September t, creating a transitional quarter (third quarter 1976) treated separately.
- Reverse maturity structure:
  - Constructed from Hall et al. (2018) for 1942–1960 and CRSP Monthly U.S. Treasury Database for 1961–2022.
  - Use final month of each fiscal year to construct D_j^t (amount outstanding at end of year t that was issued in year t−j) and weights w_j^t = D_j^t / D_t.
  - Post-1960 CRSP lacks non-marketable debt (e.g., savings bonds); authors assume reverse maturity structure of non-marketable debt remains constant after 1960.
  - Historical facts: share of debt with reverse maturities above five years peaked at 48 percent in 1951; from 1975–2022 it fluctuated between 10 and 25 percent. Average reverse maturity fell from 4.4 years in 1951 to 2.2 years in 2022.
- Aggregate interest rates:
  - i_t defined as total interest payments during year t divided by total debt outstanding at end of t−1, excluding intragovernmental holdings.
  - Interest payment series from OMB Historical Data. Starting 1962, subtract intragovernmental payments; before 1962, net interest is available but understates payments. Empirically, the desired series is approximately ten percent higher in years with both measures; before 1962 authors multiply net interest by 1.1.

### Constructing counterfactual undistorted real rates for the peg period
- Actual interest rates under the peg:
  - For each Treasury issue Hall et al. (2018) reports issue date, quantity, maturity, and usually coupon rate; coupon is used as the relevant interest rate.
  - Missing coupon rates are filled with interest rates by maturity under the peg reported by Friedman and Schwartz (1963).
  - i_{j+1}^t is the average interest rate on outstanding securities at t that were issued at t−j−1.
- Counterfactual real rates r⋆_{j+1}^t:
  - No direct evidence of ex-ante real rates during the pre-Accord period if the Fed had not pegged rates.
  - Baseline assumption: for any security of a given maturity (at issuance), the counterfactual rate equals the average of ex-ante real rates on securities with that maturity issued over the decade after the peg ended (fiscal years 1952–1961).
  - r⋆_{j+1}^t is the average of assumed rates across maturities weighted by the term structure of securities issued at t−1−j and outstanding at t.
  - Ex-ante real rates by maturity for 1952–1961 are calculated from nominal rates on debt issued during that period (Global Financial Database) and the term structure of inflation expectations.
  - Resulting term structure of undistorted real interest rates: 1.7% at the one-year horizon, 2.2% at five years, 2.5% at ten years, and 2.7% at thirty years.

### Results: simulations of debt/GDP starting in 1946
- Simulation setup:
  - All simulations begin in 1946 with debt/GDP at its actual level of 106%.
  - Compare actual path after 1946 to three counterfactual scenarios:
    - Primary balance scenario: set primary surplus to zero in all years; interest rates remain historical.
    - Adjusted interest rate scenario: apply adjustments x_{j+1}^t to eliminate effects of both surprise inflation and the pre-Accord peg; primary surpluses remain historical.
    - Combined scenario: set primary surplus to zero and also adjust interest rates.
  - In the combined scenario the path of debt/GDP is determined by r⋆ − g (undistorted real interest rate minus growth rate of output).
- Key outcomes (1946–1974, postwar erosion period):
  - Actual debt/GDP fell from 106% in 1946 to 23% in 1974 (a decline of 83 percentage points).
  - Counterfactual 1974 debt/GDP:
    - 40% in the primary balance scenario
    - 51% in the adjusted interest rate scenario
    - 74% in the combined scenario
  - In the combined scenario the ratio falls by 32 points (from 106 to 74 percent).
  - Therefore, of the actual 83-point fall, 51 points are explained by the combination of primary surpluses and interest rate distortions.
    - Decomposition: 17 points explained by primary surpluses alone; 28 points explained by interest rate distortions alone; 6 points from interaction of the two factors (adjusting primary balance raises the level of debt, magnifying interest-rate-adjustment effects).
- Dynamics of aggregate interest-rate adjustment x_t (1947–1974):
  - Large early adjustments: 13 percentage points in 1947 and 8 points in 1951, when surges in inflation with pegged nominal rates produced deeply negative real rates.
  - By 1951, the actual debt/GDP ratio had already diverged by more than 20 percentage points from the rate-adjusted scenario.
  - After early episodes, x_t is mostly small until the late 1960s when unexpected inflation pushes it up; x_t is over 4 percentage points in 1974.
  - x_t remains high through the rest of the 1970s, somewhat dampening the rise in the debt/GDP ratio in that later period.

*Source: wpiea2024005-print-pdf — 3.3 The Adjustments to Interest Rates*

### 5.2    The Debt Buildup, 1975-2022

### 5.2    The Debt Buildup, 1975-2022

### Evolution and principal drivers
- The actual debt/GDP ratio:
  - Started to rise in 1975, with a dip in the late 1990s.
  - In 2022 it stood at 97%.
- The biggest factor behind the increase was a shift from primary surpluses to primary deficits.
  - Persistent deficits emerged following tax cuts at several points, most notably the Reagan tax cuts of the early 1980s, and the deficit ballooned after the 2008 financial crisis and the 2020 pandemic.
- Counterfactual (combined: primary balance and undistorted real interest rates):
  - Debt/GDP falls from 74% in 1974 to 70% in 1979, then rises to 84% in 2022.
- The trajectory in the combined counterfactual depends on r⋆−g (the difference between the undistorted real interest rate and the growth rate).
  - Average r⋆ rose from 2.3% over 1947-1979 to 2.8% over 1980-2022.
  - Average g fell from 3.5% over 1947-1979 to 2.6% over 1980-2022.
  - The increase in debt/GDP from 1979 to 2022 reflects that on average r⋆ > g during that period, reversing the earlier r⋆ < g over 1947-1979.

### Quantified counterfactual and historical comparisons
- Over 1946-2022, economic growth without primary surpluses or interest-rate distortions would have reduced debt/GDP by only 22 percentage points, from 106% to 84%.
- Post-1979 rise in debt/GDP is larger in the primary-balance counterfactual (which keeps real interest rates at actual ex-post levels) than in the combined counterfactual:
  - Primary-balance counterfactual rise: 19 percentage points (from 34% to 53%).
  - Combined counterfactual rise: 14 percentage points.
  - This reflects average negative inflation surprises since 1979, which increased ex-post real rates and debt/GDP.
- The actual real interest rate r has exceeded the growth rate g since 1979 in the data used.

### Measurement differences and relation to other literature
- Differences from Blanchard (2019) stem from measurement choices:
  - This paper uses the government’s interest payments on outstanding debt; Blanchard uses market yields on debt (which have been lower).
  - This paper uses pre-tax interest rates; Blanchard uses after-tax rates.
  - The Appendix (in the source) details and defends these measurement choices.
- Comparison to Hall and Sargent (2011):
  - Following Hall and Sargent’s framework for 1946-1974, change in D/Y can be decomposed into contributions from r−g (term a) and primary surpluses (term b).
  - Reported contributions 1946–1974 (Table 2A in source):
    - Contribution of r−g: -48 percentage points.
    - Contribution of primary surpluses: -30 percentage points.
  - Decomposing r−g into r⋆−g and −x (distortions) (equation (10) and Table 2B in source):
    - Of the -48 percentage point contribution of r−g, -12 points are attributed to r⋆−g and -36 points to distortions in interest rates (inflation surprises and the pre-Accord peg).
  - These results imply that distortions and surpluses were crucial to the large post-war decline in debt/GDP.

### Conclusions and policy implications
- Up to 1974, the fall in debt/GDP was driven mostly by primary surpluses and interest-rate distortions.
  - Absent those, and with the path determined entirely by r⋆−g, debt/GDP would have fallen from 106% in 1946 to only 74% in 1974, not to the actual trough of 23%.
- Since 1974, the main driver of the debt increase is large primary deficits; a secondary factor is that r⋆ has on average exceeded g.
  - With primary balance and undistorted interest rates, debt/GDP would have grown from 74% in 1974 to 84% in 2022.
- The historical experience suggests a limited tendency for the economy to “grow out of” a high debt level without primary surpluses or interest-rate distortions.
- Interest-rate distortions that aided debt reduction after World War II are unlikely to recur:
  - Policymakers are unlikely to return to wartime interest-rate pegs with price controls.
  - The Federal Reserve appears committed to returning inflation to low levels, reducing scope for debt erosion via surprise inflation.
  - Any future inflation surprises will have smaller effects because the average maturity of the debt is shorter.
- Implication: Substantial reduction in the debt/GDP ratio will probably require primary budget surpluses.
  - Under current policy, Congressional Budget Office projections indicate large primary deficits over the next three decades, which would likely push debt/GDP higher absent major fiscal consolidation.

### Key statistics and counterfactual table (from source)
- Selected values of debt/GDP ratio (%) — Actual and Counterfactuals (Table 1 in source):
  - 1946: Actual 106.1, Primary Balance 106.1, Adjusted Interest Rate 106.1, Combined 106.1
  - 1974: Actual 23.2, Primary Balance 39.9, Adjusted Interest Rate 50.9, Combined 73.8
  - 2022: Actual 97.0, Primary Balance 53.3, Adjusted Interest Rate 122.8, Combined 84.1

*Source: wpiea2024005-print-pdf - 5.2    The Debt Buildup, 1975-2022 (IMF).*

### 2022.  Source:  OMB, authors’ calculations.

### wpiea2024005-print-pdf - 2022. Source: OMB, authors’ calculations.

### Contributions to Change in Debt/GDP (1946–1974)
- Table 2A — ∆(Debt/GDP) contributions:
  - r−g: -82.9
  - surpluses: -48.1
  - (residual) -29.6
- Table 2B — ∆(Debt/GDP) contributions decomposing r−g:
  - r
    * −g: -82.9
  - r−r
    * : -11.7
  - surpluses: -36.3
  - (residual) -29.6
- Note: Table 2A shows contributions of r−g (term a in equation 9) and primary surpluses (term b). Table 2B divides r−g into contributions of r
  * −g (term a1 in equation 10) and the interest rate distortion r−r
  * (term a2).

### Key Figures (descriptions)
- Figure 1: Federal Debt Held by the Public as a Percent of GDP — line represents the ratio of federal debt held by the public to GDP. Source: OMB.
- Figure 2: Primary Surplus as a Percent of GDP — line represents primary budget surplus to GDP; primary surplus = total fiscal surplus + interest payments on debt held by the public. Sources: OMB, authors’ calculations.
- Figure 3: Actual and Expected Inflation — lines represent GDP deflator inflation rate and forecasts made one year and ten years in the past. Source: Authors’ calculations.
- Figure 4: Reverse Maturity Structure of Public Debt — reverse maturity structure by issuance vintage; lighter shades indicate longer reverse maturities. Source: Authors’ calculations.
- Figure 5: Short- and Long-Term Inflation Expectations — Sources: Livingston Survey, Survey of Professional Forecasters, Federal Reserve FRB/US Model, authors’ calculations.
- Figure 6: Term Structure of Inflation Expectations — each line indicates expectations formed one year prior for the following ten years. Sources as above.
- Figure 7: Debt/GDP Paths - Counterfactual Scenarios — lines show actual history and counterfactual debt-GDP ratio paths. Source: Authors’ calculations.
- Figure 8: Aggregate Interest Rate Adjustments, 1947-1974 — line represents x
  t, the difference between the aggregate interest rate in adjusted-rate scenario and the actual interest rate. Source: Authors’ calculations.

### Aggregate debt dynamics and residuals
- Exact debt evolution (equation A.1):
  - D
    t = (1 + i
    t) D
    t−1 − P
    t + ε
    t.
- Residual ε
  t arises from factors beyond interest and primary balance (e.g., Treasury operating cash, interest on government assets).
- In counterfactuals, when i
  t and P
  t are adjusted, the path of ε
  t is held constant.
- Series for ε
  t (as a share of GDP) is generally small, but sizable in 1947 and some years since 2008.
- Large residuals explained by changes in Treasury cash holdings and by stimulus payments (2008–2009, COVID).
- Residual averages:
  - -0.19 percent of GDP over 1947-1974
  - 0.25 percent of GDP over 1975- (text truncated)

### Accounting for T-bills and TIPS in interest-rate adjustments
- Interest-rate adjustment x
  j+1
  t is modified so surprise-inflation adjustments apply only to debt not T-bills or TIPS.
- Equation (A.2) defines piecewise x
  j+1
  t across vintage and date ranges, incorporating:
  - s
    t−1 : fraction of debt outstanding at end of t−1 issued during t−1 that is T-bills
  - z
    j
    t−1 : fraction of debt outstanding at end of t−1 issued during t−1−j that is TIPS
  - ̃i
    j+1
    t : average interest on securities other than T-bills outstanding at end of t−1 issued during t−1−j
- Adjustments for T-bills relevant for j = 0; adjustments for TIPS relevant starting in 1997.

### Transitional Quarter (TQ) treatment
- Transitional Quarter is the third quarter of calendar year 1976 (between fiscal years 1976 and 1977).
- Debt dynamics equation (A.1) holds for TQ with i
  t and P
  t measured as non-annualized rates; π
  t in TQ measured as non-annualized inflation.
- TQ complicates measurement of inflation expectations in adjacent periods; handled explicitly in term-structure procedures.

### Measurement of fiscal variables and aggregate interest rates
- Debt held by the public at end of each fiscal year: OMB database; debt/GDP uses OMB nominal GDP by fiscal year.
- Primary balance P
  t = total fiscal surplus + total interest payments (interest on debt held by the public).
- Aggregate interest rate i
  t = total interest payments during t divided by stock of debt at end of t−1 (debt held by the public). Interest payments exclude intragovernmental payments.
- For t ≥ 1962: interest payments = gross interest − intragovernmental interest payments from OMB historical database.
- For t < 1962: OMB reports net interest understating interest on debt held by the public. Empirical correction:
  - For 1962–2022, ratio of correct interest payments to net interest reported by OMB averages 1.1.
  - Therefore, for t < 1962, estimate interest payments by multiplying net interest by 1.1 and dividing by debt at end of t−1.
- Sensitivity: using unadjusted net interest for t < 1962 would yield debt/GDP in combined counterfactual 73% in 1974 (vs 74% baseline) and 83% in 2022 (vs 84% baseline).

### Reverse maturity structure construction (1942–2022)
- Pre-1961 (Hall et al. (2018) dataset):
  - weights w
    j
    t−1 = D
    j
    t−1 / D
    t−1 (equation A.3) — sums exactly to one.
- 1961–2022 (CRSP Monthly U.S. Treasury Database) limitations:
  - Excludes non-marketable debt and Treasury bills.
- Procedure:
  - Split total debt D
    t into Treasury bills, marketable debt excluding T-bills, and non-marketable debt using MSPD and Hall and Sargent (2022).
  - Compute reverse maturity for marketable debt w
    j,m
    t−1 = D
    j,m
    t−1 / D
    m
    t−1 (equation A.4).
  - For non-marketable debt after 1960, assume reverse maturity structure is fixed at 1960 pattern:
    - w
      j,nm
      t−1 = w
      j,nm
      1960 ∀ t > 1961 and ∀ j ≥ 0 (equation A.5).
    - Rationale: non-marketable debt declined from 23% of total debt in 1960 to 3% in 2022 (Figure A.4).
  - Aggregate weights: w
    j
    t−1 = w
    j,m
    t−1 m
    t−1 + w
    j,nm
    t−1 (1 − m
    t−1) (equation A.6), where m
    t−1 is marketable share of total debt.
- T-bills share s
  t−1 computed as s
  t−1 = D
  bills
  t−1 / D
  0
  t−1 (equation A.7) using MSPD.
- TIPS share z
  j
  t−1 computed as z
  j
  t−1 = D
  j,tips
  t−1 / D
  j
  t−1 (equation A.8), using CRSP securities (and T-bills for j = 0) in numerator and denominator; denominator includes non-marketable debt.

### Measuring inflation and inflation expectations
- Actual inflation:
  - GDP-deflator inflation rate in fiscal year t measured as growth in GDP deflator from last quarter of t−1 to last quarter of t (NIPA).
  - CPI inflation before 1970 measured from last month of t−1 to last month of t (June-to-June), using BLS CPI.
- One-year expectations:
  - For t ≥ 1970: E
    t
    [π
    t+1] = median SPF forecast of inflation over next four quarters for last quarter of fiscal year t.
  - For t < 1970: proxy GDP-deflator expectation from Livingston survey forecasts of CPI; use method akin to Carlson (1977) and FRB Philadelphia conversion (June surveys), treating expectation errors for GDP deflator and CPI as equal.
- Ten-year expectations:
  - For t ≥ 1968: E
    t
    [π
    10] measured using long-term expected inflation from Fed FRB/US Model (PTR variable), PCE deflator forecasts used as proxy for GDP deflator inflation.
  - For t < 1968: construct proxy from relationship between one-year and ten-year expectations:
    - Smooth one-year expectations via HP filter with λ = 100.
    - Regress difference between ten-year and smoothed one-year on change in smoothed one-year for 1968–1997 (Table A.1) to capture lag behavior; fitted values extended back to 1952 as proxy.
- Term structure assumptions (except 1972–1976):
  - E
    t
    [π
    t+j] = E
    t
    [π
    t+1] + (j − 1) k
    t for 2 ≤ j ≤ 5 (equation A.9).
  - E
    t
    [π
    t+j] = E
    t
    [π
    t+5] for j > 5 (equation A.10).
  - Long-term expectation equals ten-year average: E
    t
    [π
    10] = (1/10) Σ_{j=1}^{10} E
    t
    [π
    t+j] (equation A.11).
  - Solve for k
    t: k
    t = (E
    t
    [π
    10] − E
    t
    [π
    t+1]) / 3 (equation A.12).
- Special procedure for 1972–1976 (Transitional Quarter proximity):
  - Use quarterly SPF forecasts to build quarterly term structure.
  - Assume linear change from τ+4 through τ+20 and then constant (equations A.13–A.14).
  - Long-term quarterly expectation E
    τ
    [π
    40] equals average over next 40 quarters (equation A.15); solve k
    τ via equation A.16.
  - Fiscal-year expectations for 1972–1976 computed from quarterly series via geometric aggregation (equation A.17).
  - Non-annualized expected inflation in TQ computed from quarterly annualized expectation via equation A.18.

### Counterfactual real interest rates under the pre-Accord peg and robustness
- Baseline assumption for undistorted real rates on securities issued pre-Accord:
  - Rate for a given maturity equals average of ex-ante real rates on securities of that maturity issued over the decade after the peg ended.
  - Baseline term structure ranges from 1.7% at a one-year horizon to 2.7% at thirty years.
- Sensitivity checks:
  - Add/subtract 0.5% or 1% to entire term structure for securities issued before the Accord.
  - Table A.2 results for combined counterfactual:
    - Baseline debt/GDP in 1974 = 74%; varying undistorted rates yields 67% (−1%) to 81% (+1%).
    - Baseline debt/GDP in 2022 = 84%; sensitivity range 78% (−1%) to 91% (+1%).

### The role of the debt-dynamics residual in simulations
- The residual ε
  t is measured using equation (A.1) and series for D
  t, i
  t, and P
  t.
- In simulations/counterfactuals, ε
  t is held constant when i
  t and P
  t are adjusted.
- Notable residual behavior:
  - Large negative residual in 1947 due to run-down of military cash balances.
  - Large positive/negative residuals since 2008 reflect changes in Treasury cash management around debt ceiling incidents and stimulus flows (2008–2009, COVID).

*Source:  OMB, authors’ calculations.*

### 2022.  Therefore, the residual contributed somewhat to both the decline in debt/GDP in the

### Did the U.S. Really Grow Out of Its World War II Debt?

### Role of the residual (ε) in historical debt dynamics
- The analysis constructs a counterfactual in which ε is set to zero in all years while keeping interest rates and primary surpluses at their historical levels to assess ε’s importance.
- In the combined counterfactual with ε = 0, debt/GDP falls only to 78 percent in 1974.
- In the combined counterfactual with historical ε’s, debt/GDP is 74 percent in 1974.
- In the combined counterfactual with ε = 0, debt/GDP reaches only 77 percent in 2022.
- In the combined counterfactual with historical ε’s, debt/GDP is 84 percent in 2022.
- The counterfactual with ε = 0 isolates the path of debt/GDP driven solely by r* − g, the difference between the undistorted real interest rate and the growth rate.

### Comparison to Blanchard (2019) — measurement differences and implications
- Finding in this paper: the real interest rate has exceeded the growth rate on average since 1979, either with or without adjustments to the real rate for surprise inflation.
- Blanchard (2019) reports that real rates have consistently been lower than growth rates; the differing results are explained by measurement choices:
  - This paper measures the interest rate as the government’s interest payments divided by outstanding debt, which yields the interest rates set when the debt was issued.
  - Blanchard uses current market yields on debt, specifically a weighted average of the one-year and ten-year Treasury rates; since 1979, these yields have usually been lower than the interest rates paid by the government because interest rates have trended downward.
  - This paper ignores the taxation of interest income; Blanchard examines after-tax interest rates calculated from estimates of the relevant tax rates in some of his analysis.
- Figure A.11 scenarios (debt/GDP normalized to 100 in 1979) with zero primary surplus and ε = 0:
  - Using this paper’s measure of interest rates, debt/GDP rises from 1979 to 2022 because r usually exceeds g over this period.
  - Using Blanchard’s measure of pre-tax market yields, the ratio rises until 2002 and then falls, leaving it close to its 1979 level in the last few years.
  - Using Blanchard’s after-tax interest rates, the ratio falls significantly from 1979 to 2022 because r is usually less than g.
- For the paper’s analysis, the relevant interest rates are the rates paid by the government—the rates for which the debt dynamics equation holds in the data.

### Treatment of taxes on interest and economic crowding out
- Blanchard’s point: taxes collected on interest on government bonds reduce the debt.
- Counterpoint in this paper: issuance of government bonds crowds out capital, and the government loses the taxes it would have collected on the lost capital income.
- The relative sizes of the gain (tax on bond interest) and the loss (foregone tax on capital income) are ambiguous:
  - Crowding out of capital by debt is likely to be less than one-for-one.
  - Returns on capital are higher on average than the interest rate on debt (because of risk), so a dollar of capital produces more tax revenue than a dollar of debt.
- The authors’ baseline assumption: debt has no net effect on tax revenue; therefore, the evolution of debt is determined by the pre-tax interest rate.

### Key quantitative results from appendices and robustness checks
- Table A.1 (regression of difference between ten-year and smoothed one-year inflation expectations on change in smoothed one-year expectations, 1968-1997):
  - Coefficient: -1.549 [0.217]
  - Observations: 30
  - R-squared: 0.637
- Table A.2 (Robustness check — alternative assumptions about undistorted real interest rates under the peg; Debt/GDP (%), combined counterfactual values):
  - Column order: Year | Actual | Combined Counterfactual Baseline | Robustness (-1%) | Robustness (-0.5%) | Robustness (+0.5%) | Robustness (+1%)
  - 1974: 23.2 | 73.8 | 67.4 | 70.6 | 77.2 | 80.8
  - 2022: 97.0 | 84.1 | 77.7 | 80.8 | 87.5 | 91.0
- Figure notes and data construction:
  - Aggregate interest rate is computed from gross interest payments minus intra-governmental payments for 1962-2022; for 1947-1961 it is computed as 1.1 times the rate based on net interest.
  - Debt/GDP paths in Figure A.10 compare actual history and combined counterfactual scenarios with ε equal to either its actual value or zero.
  - Figure A.11 shows debt/GDP paths with primary balance and εt set to zero, with each line using a different interest rate measure and debt/GDP normalized to 100 in 1979.

*Did the U.S. Really Grow Out of Its World War II Debt? — Working Paper No. WP/2024/005*

---


_Source: https://www.imf.org/-/media/files/publications/wp/2024/english/wpiea2024005-print-pdf.pdf_