Re-Thinking Debt Burden: Going with the Flow?


This paper provides an empirical framework for computing a flow measure of public debt called the debt-to-duration ratio. A ratio of this measure to GDP (DD-to-GDP) is a unit-free measure of debt burden interpreted as the percentage of income for debt service or repayment. Using monthly US Treasury data (1997–2018), we compare this measure to the debt-to-GDP ratio. The DD-to-GDP ratio is an alternative for use in discussions about sustainability of current levels of debt. An empirical test of the relationship between rising debt ratios and growth shows that duration has an important counteracting relationship with higher debt lowering growth but longer duration being associated with higher growth in the medium term.

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  1. 1.

    For example: All links accessed on August 1, 2018.

  2. 2.

    The focus of this paper is solely on public debt, with a particular focus on the US Treasury debt. Overall marketable US Treasury debt was approximately $14.8 trillion at the end of our sample in April 2018, about 20% of $68.6 trillion in total private and public debt (including household, corporate, and financial debt:, accessed August 1, 2018. While these other debt levels or their changes may exhibit macroeconomic effects, we focus here on the appropriate measurement of public debt.

  3. 3.

    An economy’s public debt might be considered sustainable if predicted government deficits do not grow without bound at a rate that exceeds the growth rate of national income. At the limit, an unsustainable debt would entail all non-bondholders paying a 100% tax rate to service the debt (Domar 1944). The debt burden as used here in the DD-to-GDP ratio is represented as an estimate of the percentage of income that would have to be borrowed, reborrowed, or printed in order to avoid a default. Domar (1944) defined the debt burden as “the tax rate (or rates) which must be imposed to finance the service charges. Thus, our measure includes not only interest charges, but also estimates the portion of the debt that must be refinanced, borrowed, or printed.

  4. 4.

    Duration is used instead of maturity, since the latter only represents the time until the bond expires. The duration of a bond accounts for the coupon payments as well as the variation of interest rates during the lifetime of a bond.

  5. 5.

    Throughout this paper, and in this case, we are only considering the marketable debt issued by the Treasury (, Table III accessed August 1, 2018. Official reports of publicly held debt-to-GDP ratios were 75.0% at the end of 2017, however this includes an amount of non-marketable debt (, accessed August 1, 2018). Further adjustments are described in detail in the text.

  6. 6.

    Shiller (2011) makes this argument more explicitly in accessed August 1, 2018.

  7. 7.

    Cochrane (2012) is among several economists suggesting that the recent low interest rate environment, along with rising debts would be an optimal time to significantly extend the maturity of U.S. public debt.

  8. 8.

    Our data on maturity and debt-to-GDP show that this correlation is 0.40 for our sample period (1997–2018). Interestingly, such a correlation was virtually non-existent prior to 2008 and became highly significant in the post-2008 period with a correlation coefficient of − 0.02 for 1997–2008 and 0.98 between 2009 and 2018.

  9. 9.

    Maturity of the marketable Treasury debt is frequently updated by the Treasury Department in their quarterly Treasury Presentation to TBAC (Final),, accessed August 1, 2018.

  10. 10.

    As noted by both Elmendorf and Mankiw (1999) and Panizza and Presbitero (2013), for deficits to have a short-run stimulative effect on the economy, it must be assumed that Ricardian Equivalence does not hold allowing debt to affect real variables. In both Elmendorf and Mankiw, and Panizza and Presbitero, the authors assume fixed spending with temporary tax cuts. Thus, the decline in public savings is not fully offset by an increase in private savings, allowing for short-run aggregate demand effects.

  11. 11.

    The meaning of “high” debt levels is arguably arbitrary. Generally, debt-to-GDP ratios of around 100% are considered high.

  12. 12.

    There is vigorous debate on the validity of the estimated thresholds for the debt-to-GDP ratio in the literature. Reinhart and Rogoff (2010) was one of the first to estimate a threshold of 90% for the debt-to-GDP ratio using data for a large number of countries over a long period of time. Their findings have been subsequently challenged by Herndon et al. (2014). For a non-technical summary of this debate please refer to: (accessed August 1, 2018).

  13. 13.

    This is not to say that there is not a level of “unsustainable” fiscal deficits. As noted by Domar (1944) “… it is doubtful, nevertheless, whether an economy with an ever-rising tax rate levied for the sole purpose of paying interest on the debt will be able to escape serious economic and social difficulties which may possibly lead to a repudiation of the debt.”

  14. 14. accessed August 1, 2018.

  15. 15.

    In the case of bills, notes, and bonds, this calculation is relatively straightforward. For Treasury Inflation-Protected Securities (TIPS) and Floating-Rate Notes (FRNs), the calculation entails some additional calculations. In calculating the duration of TIPS, we use the ten-year breakeven inflation rate (T10YIE from, accessed August 1, 2018 to adjust expected coupon payments at future dates. See Rudolph-Shabinsky and Trainer (1999) and Jacoby and Shiller (2008) for guidance. The duration of FRNs is determined as the time until the next interest rate reset.

  16. 16.

    The assumption we make regarding duration is that it is a measure of debt burden. A sovereign DD-to-GDP ratio of 0.10 implies that this proportion of income is a reasonable estimate of how much debt must be rolled over or printed in a given period of time. To roll debt implies the sovereign must go to market, and thus they are not guaranteed to place that debt.

  17. 17. accessed August 1 2018. Data prior to 1997 are not available in the easy to use digital format but can be accessed as a pdf file. As a result, it has to be manually entered for each month prior to 1997. At present, we are in the process of digitizing these data and we hope to maintain an updated database of our measure in the near future.

  18. 18. accessed August 1, 2018.

  19. 19. accessed August 1, 2018.

  20. 20.

    Treasury bills (i.e., T-bills or money-market instruments) mature in one year or less, while Treasury notes have maturities of 2, 3, 5, 7, and 10 years. Treasury bonds have maturities between 10 and 30 years. Treasury Inflation-Protected Securities (TIPS) have maturities of 5, 10, or 20 years, and pay a fixed interest rate on a principal that adjusts according to increases in the Consumer Price Index (CPI). In 2014, the Treasury began selling Floating-Rate Notes (FRN) which have maturities of two years. Interest rates are set to be equal to the 13-week T-bill and reset prior to each payment.

  21. 21.

    We also carried out the analysis presented in the next section using maturity to compute the DD. The results of this exercise are not reported here for brevity and are available upon request.

  22. 22.

    Note that all measures of DD, marketable debt, and GDP are not adjusted for inflation.

  23. 23.

    We make a slight adjustment to the projected debt held by the public in order to make it comparable to our dataset. The dataset constructed here only includes marketable debt held by the public. The adjustment uses recent measures of non-marketable debt from Table FD-2 from Bureau of the Fiscal Service, US Department of Treasury (2018), Non-marketable debt is 3.35% of all debt held by the public over this period, and therefore, CBO projections of debt are adjusted downward by this amount.

  24. 24.

    These numbers differ somewhat from Summary Table 2 in Congressional Budget Office (2018) due to the aforementioned adjustment. There is only a “nine-year” projection here due to the fact that the Office of Debt Management, US Department of Treasury (2018) no longer provides sufficient information to make maturity projections at the 10-year horizon.

  25. 25.

    Office of Debt Management, US Department of Treasury (2017) was the last TBAC presentation that provided even a visual projection of future maturities. For several years projected maturities were provided in each TBAC presentation, but ceased in 2018 ( accessed August 1, 2018.

  26. 26.

    Based on the Office of Debt Management, US Department of Treasury (2017) Q3 presentation, we use 70.8 months of debt maturity at the end of 6/2017, and a visual approximation of 83.5 months at what is likely the end of 2027 to estimate an annual maturity growth rate of maturity of 1.664%. Some details about maturity projections are provided in the 2017: Q3 TBAC presentation.

  27. 27.

    Over our sample period, the regression coefficients on \({\text{LMLD}}_{t} = \beta_{0} + \beta_{1} {\text{tenyear}}_{t} + \epsilon_{t}\) are: \(\beta_{0} = 0.136 \, \& \, \beta_{1} = 0.065\) with each significant at the 1% level and an overall \(R^{2} = 0.793\).

  28. 28.

    We use 2027 here to remain consistent with the end of the plot of expected maturities provided in the TBAC presentation of 2017:Q3.

  29. 29.

    For comparison, the average DM-to-GDP ratio in our dataset from April 1997 to December 2010 was 6.9%. The DD-to-GDP ratio over this same period in our data was 10.5%.

  30. 30.

    There are few differences between our empirical exercise and the analysis conducted in Cecchetti et al. (2011). First, because at present our measure of debt burden, DD-GDP ratio, only goes back to 1997, we are forced to use data from 1997 through first quarter of 2018. To have sufficient sample size, we conduct our analysis at quarterly frequency unlike Cecchetti et al. (2011) who used annual data for their sample of countries. Second, data on schooling attainment, one of the independent variables in the specification estimated by Cecchetti et al. (2011) is not available at quarterly frequency and hence we do not control for this variable. Finally, we ignore the dummy variable indicating banking crises that did not factor into their conclusion that rising public debt impacted growth.

  31. 31.

    For the sake of interpretation, we provide an example for comparing debt-to-GDP with DD-to-GDP coefficients (Columns (1) & (2)). Starting at estimation sample mean values of debt-to-GDP (66.1), duration (3.4), DD-to-GDP of 19.4, and GDP (12.6 trillion), we imply a 10-percentage point increase in debt-to-GDP raises total debt from 8.3 trillion to 9.6 trillion. This is an increase in the DD-to-GDP ratio from 19.4 to 22.4. Thus, an approximate 3-percentage point increase in DD-to-GDP would be associated with a 30-basis point decline in growth, similar to the 28-basis point decline. The ratio of these effects depends on the magnitude of duration.


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The authors wish to thank Adam Diehl for his helpful assistance.

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Correspondence to Andre R. Neveu.

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Bhatt, V., Neveu, A.R. Re-Thinking Debt Burden: Going with the Flow?. Eastern Econ J 45, 179–203 (2019).

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  • Debt
  • Fiscal policy
  • Duration
  • Interest rate
  • Debt management

JEL Classification

  • E62
  • E66
  • E6