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1 Introduction

The global financial crisis has led to a dramatic increase in public budget deficits across most advanced economies. In the United States, the federal budget deficit as a percentage of GDP increased from 1.2% in 2007 to 10.1% in 2009. Policymakers have offered a variety of budget plans that seek to reduce these deficits by cutting outlays through changes to federal spending programs, or increasing revenue through changes to the federal tax code. However, there is a third option for reducing budget deficits that has been largely ignored. The mechanism behind explosive debt-GDP ratios is a model of how net interest payments evolve over time. By determining the maturity structure of the United States debt portfolio, the Treasury Department has substantial control over the level and timing of these payments. The maturity structure of public debt is a major policy decision that directly affects long-run budget sustainability.

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How should we evaluate the Treasury’s previous debt management policy, and what should new policy be going forward? To answer this, I construct a model to simulate counterfactual debt management strategies. The two major debt management decisions faced by a government are the type and proportion of securities to offer. By altering issuance relative to a historical baseline, I approximate how different policy would have affected the evolution of debt and interest payments in the United States between 1948 and 2012. I then extend the model forward using forecasts from the Congressional Budget Office to estimate how changes in the maturity structure can be expected to influence debt management outcomes over the next 10 years.

2 Background

Behind headline debt numbers are a diverse set of securities, each with different properties and obligations. Table 1 shows the Monthly Statement of the Public Debt as reported by the Bureau of Public Debt for December 31, 2012. At that time, gross debt outstanding in the United States was slightly over $16.4 trillion. Gross treasury obligations can be divided into two categories: debt held by the public and intragovernmental holdings. Intragovernmental debt is debt one part of the government owes another and generally represents the assets of social insurance trust funds; these debts are essentially accounting mechanisms used by the Treasury to separate trust funds from general spending and have no net effect on borrowing. Debt held by the public is the sum of the face value of all outstanding securities held outside federal government accounts. The majority of debt held by the public is marketable debt, which is frequently traded in the secondary market. This consists of zero-coupon bills, coupon-paying notes and bonds, and as of 1997, Treasury Inflation-Protected Securities (TIPS) which are indexed to the Consumer Price Index (CPI); TIPS account for 7.7% of marketable public debt. About 4% of the public debt is made up of nonmarketable securities which are nontransferable debt instruments. These consist primarily of savings bonds, investments from state and local governments, civil service retirement savings plans, and a variety of other small obligations. I was unable to find data on the maturity structure of nonmarketable debt, so I exclude it from this analysis. 2

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Debt held on the balance sheet of the Federal Reserve is considered to be debt held by the public. Although some authors prefer to include these obligations with intragovernmental debt, this accounting is not appropriate for my exercise. Since the Fed is required to buy securities on the open market, debt held by the Fed is just as much an obligation of the Treasury as if it were held by a private investor. The Treasury and the Fed face different institutional incentives and there is no reason the Fed would permit the Treasury to default on this debt.

Policy decisions from the Fed affect Treasury financing in two ways: through open market operations that determine the interest rate the Treasury must offer and through remittances to the Treasury that affects the primary surplus. The Fed remits net income to the Treasury after expenses and dividends are paid out; the National Income Product Accounts (NIPA) treat these deposits as revenue, not negative spending on net interest. During normal times these profits account for only 1% of federal revenues and can be safely ignored in this analysis.

The Treasury faces a tradeoff when deciding whether to issue short-term or long-term securities. If the yield curve is upward sloping, favoring shorter maturities may be optimal. Since investors typically demand a term premium, the interest payments on short-term debt will be lower. Additionally, if interest rates fall, the government will be able to easily refinance the debt at a lower cost. On the other hand, favoring longer maturities may be optimal if the government is concerned about insuring against rollover risk. Long-term debt smooths fiscal shocks. By locking-in interest rates today, unanticipated changes to interest rates or primary budget balances will be less likely to affect borrowing. If interest rates rise in the future, the government will not be forced to refinance large quantities of debt at high rates.

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Given its importance to long-run fiscal sustainability, one might expect the maturity structure to adjust in response to changing interest rates and primary deficits. The Treasury has opted not to pursue this strategy and instead issues debt in a “regular and predictable pattern.” Figure 1 shows that the maturity structure over the past three decades has remained stable.

3 Literature Review

The research agenda on optimal debt management has been heavily influenced by the neoclassical literature on optimal fiscal policy. Barro (1979) and Angeletos (2002) focus on how long- term debt allows for tax-smoothing in a neoclassical, stochastic production economy. In a similar exercise with nominal debt, Calvo and Guidotti (1992) show it is possible for a government to pick a maturity structure such that each successive government facing similar preferences is provided the incentive to follow the strategy of the initial government. Other research such as Krishnamurthy and Vissing-Jorgensen (2012) and Greenwood et al. (2010) has focused on the monetary services. Cochrane (2001) shows that within a fiscal model of the price level long-term debt helps to smooth policy since it will generally produce the minimum variance of inflation.

Hall and Sargent (2011) is the only major empirical study of optimal debt management for the U.S. Treasury. They note that net interest payments as reported by the Treasury only measure accrued interest on zero-coupon bonds and cash disbursed for coupon payments. This fails to account for real capital gains (or losses) and so does not measure the true burden of servicing the debt. Their results indicate that properly measured interest payments are significantly more volatile, but lower on average than the Treasury-reported series.

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4 Model

Counterfactual simulations only have meaning relative to an appropriate baseline. One approach would be to design a stylized model of debt management and compare the model’s debt time series to the historically observed time series. However, funding the largest government in the world is a complicated business; any model will be a poor approximation of the Treasury’s complex accounting conventions, so comparing counterfactuals to the actual debt time series would be inconsistent. My approach, instead, is to create a model that replicates as closely as possible the major debt management decisions the Treasury makes, feeding these decisions in as an input, and using the output as the historical baseline. If the model time series is tightly correlated with the relevant historically observed time series, then we can be confident that the model correctly captures basic debt management dynamics. Furthermore, since we generate counterfactuals using the same model, we can be sure that any comparisons will be consistent.

The two major debt management decisions faced by a government are the type and proportion of securities to offer. The two security types offered are zero-coupon bills with a maturity of one year or less and coupon-paying notes and bonds with maturities greater than a year. 3 In 1997, the Treasury began offering TIPS, which have their principal and coupon payments indexed to the CPI. Although TIPS will likely be an important part of Treasury debt management in future years, they currently remain small relative to nominal obligations. In the interest of tractability, I exclude them from my model.

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Let (prin_^ ) and (coup_^ ) be, respectively, the existing principal and existing coupon payments due at time (t). Although the Treasury occasionally initiates open-market buyback programs to pay down old debt, existing obligations are almost always paid as promised. The total financing needs at (t) will be

begin

due_t=oldcash_t+coup_^ +coup_^+prin_^ +prin_^+def_t

with (def_t) denoting the government’s primary budget deficit. The primary deficit is revenues minus all expenditures other than net interest. The Treasury’s need for short-term cash is difficult to predict in any given period, so it will occasionally retain cash balances from previous periods which I denote as (oldcash_t). That is, if (due_t < 0), then (oldcash_ =due_t) and we replace with (due_t=0). Without this provision it would be necessary to assume either the Treasury would initiate very short-term buyback programs, or that it could invest cash in the private market, neither of which are practical.

4.1 A Simple Zero Coupon Model

Suppose the Treasury can only auction a single zero-coupon security that pays $1 in (k in K). Using the basic discount formula, the principal from each issue will come due at time (t+k) such that

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with (y_) being the relevant yield to maturity. Total debt outstanding is simply the sum of existing and new principal payments due. Note that after the Treasury decides which maturity to offer in the first period, it is constrained to offer only that same security in all other periods.

4.2 Zero-coupon and coupon-paying securities with time dependent issuance

Let (mathbf) be a vector of prices at time (t) with (p_ in mathbf) being the price of a security with maturity (k) at the time of its issue. The Treasury’s current procedure for determining the coupon rates on new offerings is to round the yield bids to the nearest multiple of 1/8 of a percent such that the security is auctioned below par. That is, for a security with maturity (k) and a par value of one dollar the coupon is

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with price

begin

p_

= frac< c_(1-(1+y_)^<-k>)>>+(1+y_)^<-k>

Let (i_

in mathbf) be the fraction of (k) maturity securities being auctioned at (t) out of all auctions that period. Since all securities are issued below par, we must define a scalar

Principal due at (t) associated with security (k) will be

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with (prin_ in mathbf). Total principal due from new auctions are (prin_^=mathbf 1> ). Total coupon payments due associated with any particular maturity (k) are defined as (coup_ in mathbf). Within a given maturity, coupon payments from different auctions can still become due at the same date so it is necessary to define (tau)

for all (t in <tau+6,tau + 12, ldots, tau + k>). Total coupons due from new auctions will be

begin coup_

= displaystylesum_<tau=1>^ coup_ end

and (coup_

^=mathbf 1>). The face value of all debt outstanding is the sum of all future principal obligations or

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Interest payments are currently calculated as period-by-period coupon payments plus the difference between par value and market value at sale for zero-coupon bonds. Thus interest payments at (t) associated with each maturity (k) are

As noted by Hall and Sargent (2010), the net interest series reported by the Treasury does not completely measure the burden of servicing the debt since it does not measure capital gains. In the context of the government budget constraint, their alternative measure is clearly favorable. 204_0.PNG /%However, given that the Treasury rarely repurchases debt before maturity, it is not obvious that mark-to-market accounting for liabilities is appropriate from the perspective of a government. A mark-to-market loss on the value of a government’s asset (e.g. the Grand Canyon, or the interstate highway system) would be similarly meaningless if the asset will never be sold. Since the Treasury is continuously auctioning securities at par, cash outlays to investors is an important measure for evaluating the cost of borrowing over time. Servicing a stock of debt requires a flow of payments. Net interest/GDP is the percentage of all national income devoted toward this flow of payments. Since interest payments must be financed through taxes which distort economic incentives, net interest/GDP is my primary measure of the burden of the national debt. Calculating net interest is also useful since it allows the cost of different debt management strategies to be compared with the cost of tax and spending proposals scored using conventional budget accounting.

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5 Data

5.1 Historical Data

My primary dataset is the Monthly U.S. Treasury Database from the Center for Research in Security Prices (CRSP). The CRSP data provides monthly market data such as prices, amount outstanding, yields, and durations on nominal, publicly traded Treasury securities since 1925. Existing principal and coupon obligations are taken from the December 31, 1947 CRSP observation and missing data is replaced using the Treasury’s official Monthly Statement of the Public Debt (MPSD) from the same date. Yield data is taken from the CRSP Fixed Term Index file which is available for maturities of 1, 2, 5, 7, 10, 20, and 30 years. For the remaining securities, I use CRSP yields from the month in which the security was auctioned. I interpolate data from missing months using the cubic splines method. An important assumption I make throughout is that the yield for each security does not depend on the quantity being issued.

It is easy to find (mathbf) using Treasury auction data. Unfortunately, this data is only publicly available going back to 1980, so it is necessary to estimate (mathbf) using alternate methods. CRSP data assigns a unique CUSIP number to each security outstanding, but because the Treasury frequently reopens securities, an individual CUSIP frequently represents several different auctions. Thus, a reopening appears in the data as an increase in the amount outstanding for an individual CUSIPs. I mark a new issue if the amount outstanding increases by more than 15%. This seems to be the level that excludes arbitrary small changes that appear in CRSP data, and also matches well with the post-1980 Treasury data. Since CRSP data is only given for the last day of the month, this procedure requires the assumption that the Treasury conducts all auctions on a single day each month. For this reason, interest rate movements within a given month are not captured.

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I take data on GDP and primary surpluses from the official NIPA tables. NIPA accounting includes payments made to military and civil service trust funds which are not part of the publicly held debt, so these are netted out using NIPA Table 3.18B, line 24. I assume that primary surpluses are evenly distributed throughout the calendar year.

5.2 Forecast Data

All forecast data comes from the February 2013 Budget and Economic Outlook prepared by the Congressional Budget Office (CBO). For interest rates, CBO provides quarterly projections of yields on the 3-month bill and the 10-year note for the next decade. Their model forecasts 10-year yields rising to 5.2% by 2017 and remaining steady thereafter. This is roughly consistent with projections prepared by the Fed and private forecasters, though the CBO model has rates rising the highest (Bernanke 2013).

6 Results

6.1 Historical Counterfactual

To summarize, the model baseline starts in January of 1948 with existing principal and coupon obligations as reported by CRSP and the Treasury’s MSPD. The quantity of debt to be auctioned is determined by these initial obligations and the size of primary deficits as reported in NIPA tables. Nominal GDP and primary deficits are held fixed at their historical levels. Auctions are conducted each month across each maturity according to the price and issuance data extracted from CRSP data. Figure 2 plots the model’s estimates of the face value of debt outstanding on the left axis and marketable debt as reported in the Treasury Bulletin on the right. Both are as a percent of GDP and the correlation between the two series is 0.98.

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The model successfully reproduces the major shifts in the debt/GDP time series: a persistent decline after WWII, an increase following the high interest rates and budget deficits of the 1980s, a decline due to large surpluses starting in the late 1990s, and a sharp spike up after the financial crisis in 2008. But the model does not accurately reproduce debt levels. The model series falls more quickly and reaches its minimum of 10.7% of GDP in 1975, a full 8% of GDP above the historical series. The faster rate of decline in the model is likely caused by the omission of nonmarketable debt. Because the Treasury relied heavily on savings bonds to finance WWII and the Korean War, interest on nonmarketable debt comprised a large fraction of net interest payments during the 1950s and 1960s. As the Treasury shifted away from nonmarketable debt, these obligations were rolled over into marketable issues. The model does not account for shifts in nonmarketable issuance even though nonmarketable interest payments are counted in the NIPA tables. Thus, the primary surplus inputs are artificially large and debt levels decline faster than expected. However, for my exercise, discrepancies in levels are not problematic. Since I run counterfactuals within the same model, matching the shape of the debt/GDP path is much more important. 4

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6.1.1 Historical Counterfactuals: Only Zero-Coupon Securities

Figures 3 and 4 show the evolution of debt/GDP and net interest/GDP, respectively, under a single, zero-coupon security. Because large interest payments come due up to ten years in the future, I extend the graph forward to include all promised interest payments as of December 2012. GDP projections come from the CBO. I report results for the sub-periods before and after 1980 since interest rates peak around that year. This allows us to draw some conclusions about what kind of maturity structure is favorable in an environment with interest rates generally falling or rising. The one-year zero coupon is an actual security that the Treasury has offered, while the 5- and 10-year securities are hypothetical. Prior to 1980, the ones-only series and the historical series remain close together, suggesting that shortening issuance maturity would not have affected debt financing by much. Net interest payments are only slightly lower than the historical baseline in this period. The series begin to diverge during Volcker disinflation of the 1980s with shorter-term issuance appearing more favorable.

The 5- and 10-year securities are sold at deep discounts, so they consistently result in higher debt outstanding. Interest payments are significantly more volatile since periods of primary surplus allow the Treasury to build up cash balances only to have them quickly depleted when large principal payments come due. In the pre-1980 period, average interest payments are lower than the historical baseline. This strategy becomes very costly when the long-term debt auctioned off during the high interest rates of the 1980s comes due through the 1990s. In the post-1980 period, average payments for the ten-year strategy are 0.18% higher than the baseline, though the five-year strategy beats the baseline by 0.09%.

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6.1.2 Historical Counterfactuals: Mixed Coupon and Zero- Coupon Securities

Figures 5 and 6 show the path of interest payments and debt when coupon securities are added to the model. These are the actual securities that the Treasury issues on a regular basis. I include securities ranging from the 3-month bill to the 30-year bond to capture the full range of auction strategies. Coupon payments are significantly less volatile than the zero-coupon model since they are distributed evenly over time. The absence of large balloon payments means it is sufficient to run the model to 2012.

Over the entire period, a strategy of auctioning only a 3-month bill results in both the lowest amount of debt outstanding and the lowest average interest payments. For the year of 1974, the total debt falls to zero and the Treasury holds excess cash until a new round of primary deficits require new auctions. In the pre-1980 period securities between 3 months and 10 year produce virtually the same path for net interest, though shorter maturities are more volatile. This is perhaps because the yield curve was flatter on average. 206_0.PNG /%The fact that the maturity structure of existing obligations in 1948 remains unchanged also means that changes in new issuance will take several years to have measurable effects. The 30-year bond does manage to beat the historical series resulting in payments that are 0.12% of GDP lower on average. This suggests that the Treasury could have reduced borrowing costs moderately by relying on more long- term issuance.

As in the zero-coupon model, the series begins to diverge around 1980 with shorter securities beating the historical series by a significant amount. The 3-month and 1-year securities drop to virtually zero by 2009. For the post-1980 period, 3- month only issuance would have resulted in interest payments that were, on average, 0.37% of GDP lower than the historical baseline, translating into a total of $2.3 trillion in savings over 31 years. The excess cost of exclusively 30-year bond issuance is an average of 0.35% of GDP, or a total of $3.5 trillion. These results strongly suggest that favoring short-term issuance during a period of falling interest rates results in large savings over time.

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6.2 Forecasts

Current projections suggest that high debt levels and rising interest rates will push net interest/GDP back to the peak levels of the 1980s. This model provides a rough measure of how changes in maturity issuance can be expected to affect the path of net interest payments over the next decade. The model baseline uses economic and budget forecasts from the CBO and assumes that the maturity structure of new issues is fixed at its 2012 average. Figure 7 compares the model’s baseline estimate for debt with the CBO model. Levels differ due to the omission of nonmarketable debt and TIPS, but the shape remains the same. Debt/GDP is projected to decline over the next 5 years as growing employment leads to more growth, less spending on automatic stabilizers, and increased tax revenue. Around 2018, debt/GDP begins to rise again as mandatory healthcare spending and higher interest payments push expenditures higher.

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6.2.1 Scenario 1: Revert to Current Issuance in 2015

Since the Treasury perceives there are advantages to the current structure of maturity issuance, I first explore scenarios in which there are immediate changes in issuance, and then a reversion to current policy at some later date. Specifically I model issuing only 5-, 10- and 30-year securities until 2015, and then returning to the current structure — a broad combination of securities with a weighted average maturity of slightly over two years. Figures 8 and 9 show the paths of debt and net interest, respectively. In all cases, debt peaks around mid-2014, declines until 2018, and then increases slowly into the future. For the 5- and 10-year strategies, there is a steep drop in debt outstanding as a large quantity of those securities come due and get refinanced into shorter maturities. The path of net interest is much smoother. Favoring long-term issuance in the present leads to higher interest payments now, but lower payments in the future since current rates are locked in. Conversely, favoring short-term issuance leads to steady or declining payments for several years, and then a sharp rise once interest rates return to historically normal levels.

6.2.2 Scenario 2: Minimizing Interest Payments and Diversification

An alternate exercise is to depart completely from the current structure and attempt to push total interest payments as low as possible. I find this optimal structure using a program that cycles through a variety of different combinations and picks the one which yields the minimum net interest payments over the 10-year budget window. The program finds that the optimal strategy is to issue 10-years until January 2014, 7-years until July 2014, 5-years until October 2016, 2-years until March 2017, and then 3-month bills thereafter. Over the period from 2013 to 2023, this leads to a total savings of $769 billion relative to the historical baseline. Clearly, this strategy is not realistic for actual policy. Because it requires that deficits at a given time be financed through a single type of security, it offers no diversification. Nevertheless, this estimate is useful since it provides an upper-bound to the savings that might be achieved through changes in the maturity structure.

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A more practical policy would be to allow large shifts in issuance for a particular maturity while still preserving some minimum level of issuance for all other maturities. In 2012, the security accounting for the smallest proportion of all new issues was the 30-year bond at 2.3%. I round up to 3% and use this level as a lower bound for issuance. Thus, under my diversified strategy, each security makes up 3% of total issuance with the exception of the primary security which makes up the remaining 73%. The maturity of the primary security is determined by the optimal strategy outlined above. That is, the diversified strategy issues 73% 10-years and 3% of each other security until January 2014, then 73% 7-years and 3% of each other security until July 2014, etc. Figures 10 and 11 compare the evolution of debt and interest under the optimal strategy, the diversified strategy, and the forecast baseline. The diversified strategy produces less savings than the optimal strategy, but still beats the baseline interest payments by an average of 0.15% of GDP, or $424 billion. Even when we set a lower bound for the percentage of each maturity at a level above current Treasury policy, it is still possible to realize large savings.

6.2.3 Scenario 3: Higher Interest Rates

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The challenge of debt management is to choose a maturity structure that minimizes cost relative to the current forecast while still allowing flexibility to shift policy when the forecast changes. Predicting the path of interest rates is notoriously difficult, so it is important that the chosen maturity structure remains cost-effective under different scenarios for future rates. From this risk management perspective, a longer average maturity would be optimal since it provides valuable insurance against unanticipated spikes in rates. In this higher rate simulation, I assume that all interest rates stabilize at a level 50% higher than the CBO forecasts. This means that the rate on the 10- year note reaches 7.8% in 2017 instead of 5.2%. I run the current issuance reversion strategy of Scenario 1 as well as the minimum interest and diversification strategy of Scenario 2. The percentages of each issue are exactly the same as described above, so the optimal title refers to optimal under the previous forecast assumptions. Figures 12 and 13 report the results for debt and interest, respectively.

As expected, the simulations indicate that the savings from favoring long-term issuance are magnified in the higher interest rate environment. All strategies beat the forecast baseline. Of the three strategies that revert back to current issuance in 2015, the 10- year is the least costly, just as in the normal rate environment. The gains from the minimum interest and diversification strategies of Scenario 2 are especially large. The more realistic diversification strategy beats the baseline interest payments by an average of 0.4% of GDP, or just over $1 trillion. One qualification is that the macroeconomic factors that would lead to rates stabilizing at these levels would likely affect a variety of other inputs to the model. I do not attempt to estimate these general equilibrium effects but instead hold nominal GDP and primary surpluses constant.

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6.2.4 Scenario 4: Low Interest Rates

Prudent risk management also requires considering a scenario in which rates rise less than forecast. In this lower rate simulation, I assume that all interest rates stabilize at a level 50% lower than the CBO forecasts. Here, the 10-year note reaches a maximum of only 2.6% in 2017. In an economy with lower rates, locking- in current rates is less advantageous and so long-term issuance is more costly. Figures 14 and 15 show the outcome of the simulation. Here, the forecast baseline preforms moderately well. The 5-year strategy results in savings, while the 10- and 30- year strategies do not. Notably, even in this extreme low-rate scenario the performance of the diversification strategy still results in savings, though they are trivial.

7 Conclusion

My results show that the maturity structure of debt can be a powerful tool for managing the U.S. government’s long-term fiscal outlook. In my preferred strategy with diversification, lengthening the maturity structure could save the Treasury $424 billion in interest payments over the next ten years. More importantly, this strategy would also provide valuable insurance against rolling over large quantities of debt at high interest rates. If interest rates rise more quickly than expected, savings relative to the current policy baseline would be much larger. The changes needed to realize these savings do not require an act of Congress and could be implemented unilaterally by the Treasury department. The path of future interest payments is a policy decision, and there is compelling evidence that it should not be treated as fixed.

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The Treasury’s current policy is heavily influenced by the Treasury Borrowing Authorizing Committee, which meets quarterly to issue new guidance. The membership of this committee is comprised of senior executives from the nation’s largest investment funds and banks. Given that many of these firms are the Treasury’s largest customers, mismatched incentives of committee members may explain some of the reluctance to change policy.

Some caveats are necessary. First, this model does not estimate how the prices of different securities would adjust to major changes in issuance. If price elasticities are high, savings would be lower. Estimating these price elasticities and incorporating them into this model would be a valuable extension. Secondly, this model does not account for the many services Treasury securities provide beyond financing government deficits. For example, Greenwood et al. (2012) note that favoring short-term debt has benefits since these securities offer many money-like properties. Lengthening the maturity structure could disrupt financial markets; however, the Fed has a variety of tools to minimize such risks. The Fed’s new authority to pay interest on excess reserves is one example. Many of the other financial services provided by short-term debt could be easily replaced by new products from the private sector.

Finally, I address the question of risk management only through simple changes to the levels of interest rate forecasts. The model omits interaction effects between interest rates and other inputs, as well as how the timing of rate changes might affect debt outcomes. Incorporating these two effects would give a much clearer picture of the risk involved in pursuing particular strategies.