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# Federal Debt Maturity in PWBM’s Dynamic OLG Model

By Jon Huntley

According to USAFacts, in 2015, the federal government paid more than $220 billion in interest, which is six percent of the federal budget and more than one percent of GDP. Thus, federal interest payments are a major component of the federal budget and significantly impact on the U.S. economy. The maturity structure of federal debt--the sizes of, due dates of, and interest rates on federal debt--affects federal interest payments. Longer-term debt issued at higher interest rates increases interest payments but “locks in” those payments for a long time. Shorter-term, lower-interest debt lowers interest payments but increases the impact of changes on interest rates on the federal budget as federal debt is refinanced. Previously, we analyzed the maturity structure of federal debt back to 1953. Below, we describe how PWBM incorporates the maturity structure of federal debt into our dynamic overlapping-generations (OLG) model to make projections of interest paid on the federal debt. The Data In order to project federal borrowing and interest payments, we use projections of future interest rates, the existing maturity structure of federal debt and a rule that approximates the way the federal government structures its debt at different due dates. We use PWBM’s projections of interest rates on one-, two-, three-, five-, seven-, 10-, and 30-year Treasuries for our future interest rates. We also use the portfolio of marketable U.S. Treasury securities, drawn from the Monthly Statement of Public Debt, to determine how much debt is due and how much interest is paid on U.S. Treasury securities in each of 30 one-year intervals.1 A Rule for New Federal Debt We combine the interest rate projections and the maturity structure on federal debt with a rule about how the federal government will choose the due dates on new debt in our dynamic OLG model. We start by calculating the share of total debt that is due in: • less than one year, • more than one year, but less than or equal to two years, • more than two years, but less than or equal to three years, • more than three years, but less than or equal to five years, • more than five years, but less than or equal to seven years, • more than seven years, but less than or equal to 10 years, and • more than 10 years. As shown in PWBM’s earlier analysis of the maturity structure of the federal debt, the U.S. Treasury historically issued securities to keep those shares approximately constant during periods of time in which there was not a large, sudden increase in federal debt. To approximate the U.S. Treasury’s decision-making process, the federal government in our dynamic OLG model issues one-, two-, three-, five-, seven-, 10-, and 30-year debt to preserve those debt shares over time. Financing an Illustrative$500 Billion Deficit

Table 1 shows how the debt maturity structure evolves in the OLG model by applying this rule to an example $500 billion deficit in 2018. The second column in Table 1 lists the value of debt due in each of the next 30 years (2018 through 2047) in millions of dollars.2 During 2018, the federal government will have to pay back about$3.8 trillion, which accounts for 26.6 percent of all federal debt. Combining the $3.8 trillion that the federal government needs to repay in 2018 with the hypothetical$500 billion needed to finance 2018 deficits leads to total federal borrowing in 2018 of about $4.3 trillion. Years to Maturity Value of Debt as of Dec. 31, 2017 (millions of USD) Share of Total Debt as of Dec. 31, 2017 New Debt Issues in 2018 (millions of USD) Value of Debt as of Dec. 31, 2018 (millions of USD) Share of Total Debt as of Dec. 31, 2018 1$3,827,538 26.6% $2,020,009$3,960,649 26.6%
2 $1,940,640 13.5%$508,915 $2,008,130 13.5% 3$1,499,215 10.4% $276,413$1,551,353 10.4%
4 $1,274,940 17.1%$1,184,167 17.1%
5 $1,184,167$584,529 $1,360,461 6$775,932 10.2% $696,618 10.2% 7$696,618 $419,348$827,143
8 $407,795 8.4%$408,252 8.4%
9 $408,252$390,011
10 $390,011$383,009 $449,738 11$66,729 13.7% $68,043 13.7% 12$68,043 $17,043 13$17,043 $16,428 14$16,428 $6,966 15$6,966 $0 16$0 $0 17$0 $0 18$0 $26,397 19$26,397 $38,002 20$38,002 $48,025 21$48,025 $150,683 22$150,683 $191,806 23$191,806 $199,129 24$199,129 $200,375 25$200,375 $192,670 26$192,670 $192,376 27$192,376 $192,855 28$192,855 $188,126 29$188,126 $176,501 30$176,501 $135,315$135,315
Total $14,377,262$4,327,538 $14,877,262 Notes: Data taken from the Monthly Statement of the Public Debt, December 2017. https://www.treasurydirect.gov/govt/reports/pd/mspd/2017/2017_dec.htm. Data includes all marketable U.S. Treasury securities excluding those that have matured and those issued by the Federal Financing Bank. Debts and debt issues are denominated in millions of nominal U.S. dollars. In PWBM’s dynamic OLG model, the federal government uses its rule to apportion the$4.3 trillion among one-, two-, three-, five-, seven-, 10-, and 30-year securities, as shown in the fourth column of Table 1. Of the $4.3 trillion in new debt,$2 trillion is issued in new one-year securities. Combining the $2 trillion of new issues with the$1.9 trillion of 2018 two-year bonds leads to a total of $4.0 trillion due in 2019, shown in the fifth column. In both 2018 and 2019, one-year debt as a share of total debt remains at 26.6 percent. The interest rate on the$4.0 trillion in one-year debt in 2019 is going to be the weighted average of the interest rate on existing $1.9 trillion and the interest rate on the$2 trillion in new one-year debt.3

The same rule is applied to every other maturity year as well. For example, in 2018, the federal government owes about $67 billion in 11-year debt. And, at the end of 2018, that$67 billion in 11-year debt is now 10-year debt, and combined with nearly $383 billion in new debt issues leads to$450 billion in 10-year debt starting in 2019. In both 2018 and 2019, the sum of eight-, nine-, and 10-year debt is 8.4 percent of total federal federal debt. Using this approach to modeling federal debt in the dynamic OLG, PWBM is able to precisely estimate the interest paid on federal debt and the budgetary effects of changes in fiscal policy.

Deficits and Interest

Table 2 shows how changes in deficits can lead to changes in the composition of debt issued by the federal government. Changes in the composition of debt can lead to changes in interest payments. In the dynamic OLG model, a change in the 2018 deficit from $500 billion to$1 trillion leads the government to issue a larger share of long-term debt. For example, the federal government would issue $135 billion in 30-year bonds to support a$500 billion deficit, but would issue $200 billion in 30-year bonds to support a$1 trillion deficit. In this example, the 30-year bond grows from 3.1 percent of the new debt issue to 4.2 percent. Since there is not a large difference between short- and long-term interest rates in 2018, the effect on the rate of interest paid is about one basis point (0.01 percent). However, the effect on interest payments grows if short- and long-term projected rates move further apart.

Years to Maturity $500 billion deficit$1 trillion deficit
1 $2,020,009$2,153,120
2 $508,915$576,405
3 $276,413$328,552
5 $584,529$670,049
7 $419,348$470,559
10 $383,009$424,952
30 $135,315$203,901

Notes: Debt issues denominated denominated in millions of nominal U.S. dollars.

1. We base the shares on total unmatured, marketable securities excluding matured securities ($92 billion on December 31, 2017) and Federal Financing Bank debt (about$11 billion on December 31, 2017) as reported in the December, 2017 Monthly Statement of Public Debt.  ↩

2. The second column in Table 2 is based on marketable debt excluding Federal Financing Bank and matured securities as reported in the December, 2017 Monthly Statement of Public Debt.  ↩

3. Interest payments based on coupon rates for each maturity year that are computed from weighted averages of unmatured, marketable securities excluding matured securities, Federal Financing Bank debt, TIPS (about $1.3 trillion on December 31, 2017) and floating rate notes (about$343 billion on December 31, 2017).  ↩