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WP/21/101
IMF Working Paper
Research Department
Parameterizing debt maturity
Prepared by Philip Barrett* and Christopher Johnsâ€
Authorized for distribution by Malhar Nabar
April 2021
IMF Working Papers describe research in progress by the author(s) and are published to elicit comments and to encourage debate. The views expressed in IMF Working Papers are those of the author(s) and do not necessarily represent the views of the IMF, its Executive Board, or IMF management.
Abstract
This paper examines ways to summarize the maturity structure of public debts using a small number of parameters. We compile a novel dataset of all promised future payments for US and UK government debt from every month since 1869, and more recently for Peru, Poland, Egypt, and Nigeria. We show that there is a unique parametric form which does not arbitrarily restrict debt issuance – portfolios of bonds with exponential coupons. Compared to the most popular alternative, this form 1) more accurately describes changes in debt maturity for these six countries and 2) gives a quite different interpretation of historical debt maturity. Our work can be applied not just to analyze past debt movements, but – because parameter estimates are relatively similar across countries – also for monitoring changes in debt maturity, including in countries where data are partial or incomplete.
JEL Classification Numbers: E62, F34, H63
Keywords: Public Debt, Debt Maturity
Author’s E-Mail Address: pbarrett@imf.org, cwj20@georgetown.edu
Contents
1 Introduction
2 Data
3 Conceptual framework
4 Empirical evidence: Summarizing changes in US and UK debt maturity
5 Extension to select emerging markets
6 Conclusion
Figure
Figure 1: United States Federal government debt obligations by decade, 1920–2020. Vertical line indicates average maturity.
Figure 2: United Kingdom government debt obligations by decade, 1920–2020. Vertical line indicates average maturity.
Figure 3: Number of debt assets outstanding, 1920–2020
Figure 4: Average debt maturity, 1920–2020
Figure 5: United States federal government debt density by decade, 1920–2020. Vertical line indicates average months to payment.
Figure 6: United Kingdom government debt density by decade, 1920–2020. Vertical line indicates average months to payment.
Figure 7: Weights on exponential-coupon bonds for M = 3, decadal mean and two-standard-deviation range (shaded areas), 1920–2020.
Figure 8: Akaike information criterion, dropping observations with maturity greater than s months, full sample estimation 1920–2020.
Figure 9: Average absolute error of fitted density up to each issuance horizon, average an maximum across monthly observations, 1920–2020.
Figure 10: Weights on constant-coupon bonds for M = 3, decadal mean and two-standard-deviation range (shaded areas), 1920–2020.
Figure 11: Poland government debt obligations by half-decade, 1995–2020. Vertical line indicates average maturity.
Figure 12: Monthly weights on bonds for M = 3, Poland, 1991–2020.
Figure 13: Face value of total and marketable debt outstanding, 1869–2020.
Figure 14: Imputed inflation forecast parameter estimates.
Figure 15: United Kingdom RPI inflation expectations, 1981–2020.
Figure 16: US Treasury Statement of the Public Debt, January 31, 1930.
Figure 17: Marketable debt; comparison to CRSP and headline data.
Figure 18: Imputed inflation expectations, 1920–2020.
Figure 19: Face value of total and marketable debt outstanding, emerging markets
Figure 20: Peru government debt obligations by half-decade, 2000–2020. Vertical line indicates average maturity.
Figure 21: Egypt government debt obligations by half-decade, 2000–2020. Vertical line indicates average maturity.
Figure 22: Nigeria government debt obligations by half-decade, 2005–2020. Vertical line indicates average maturity.
Table
Table 1: MLE Estimates, Exponentially decaying coupon 1920–2020
Table 2: MLE Estimates, Constant coupon 1920–2020
Table 3: MLE Estimates, Exponentially decaying coupon
Table 4: Stream of payments for an asset of residual maturity Mit.
Table 5: MLE Estimates, Exponentially decaying coupon 1960–2020
Table 6: MLE Estimates, Exponentially decaying coupon 1980–2020
Table 7: MLE Estimates, 1869–2020
Table 8: MLE Estimates, 1920–2020, Real units
Table 9: MLE Estimates, Exponentially decaying coupon 1920–2020, Callable assumption
Table 10: MLE Estimates, Constant coupon 1920–2020, Callable assumption
Table 11: MLE Estimates, Exponentially decaying coupon
Table 12: MLE Estimates, Constant coupon
Table 13: MLE Estimates, Constant coupon
International Monetary Fund. Email: pbarrett@imf.org
Department of Economics, Georgetown University. Email: cwj20@georgetown.edu