A History Of U.S. Debt Limits

Over some long periods of time, yes. Over other long periods of time, no; it wasambiguous in terms of gold versus silver or gold and silver versus greenbacks.77. How is the debt limit measured? Is it “marked to market” or expressed in terms of “facevalue”?It has been measured in terms of face values ever since Alexander Hamilton startedreporting Treasury accounts in 1790. Fluctuating interest rates have driven market values away from face values.8 Market interest rates have occasionally includedpremia for default risk and exchange rate risk.92Accounting SystemsThe Congress and Treasury measure government debt and interest payments differently than domacroeconomists. In a nutshell, the official accounts measure government debt by the total parvalue of outstanding promises, while the macroeconomist’s budget constraint is cast in terms ofmarket values. Official accounts aren’t marked to market, while macroeconomists’ are.To understand how the Treasury’s measure of government debt is related to the market value ofdebt, we bring in information about bonds’ coupons and prices of (presumably risk-free) promisestto future dollars. Let the market price qt jbe the number of dollars at time t that it takes tobuy a risk-free claim to a dollar at time t j. Thus, the superscript t denotes the date at whichthe price is quoted, while the subscript t j refers to which the date at which a promise is to bet }nt , where n is the maximum horizonfulfilled. At any date t, let there be a list of prices {qt jtj 1tover which the government has promised payments.10 The price qt jis linked to the yield tomaturity ρjt for j-period risk-free zero-coupon bonds bytqt j 1.(1 ρjt )j7Footnote 3 of Garber and Grilli (1986) notes that “The U.S. government never circulated bonds payable only ingold in the 19th century.” Except during and after the War of 1812 and the Civil War, bonds were usually payablein “coin” that could mean either gold or silver. Before 1871 when France and other European countries abandonedbimetallism, the exchange rate between gold and silver fluctuated within narrow bonds. After the 1870s, silverdepreciated significantly, putting ambiguity into whether U.S. bonds were payable in gold or silver. Before 1900,Secretaries of Treasury had an option to pay in silver that they chose not to exercise.8Gaps between market and par values of both directions have attracted Congresses attention. Prior to theintroduction of zero-coupon Treasury Bills in 1929, Congress prohibited the Treasury from selling securities for lessthan their par values. Recent experiences in which market values of bonds issued during the Mexican War wereabove par values prompted the Congress to make the famous 5-20’s issued during the Civil War callable at parvalues at the government’s discretion after 5 years.9For the period after 1945, Hall and Sargent (2011) present measures of the marketable U.S. Treasury markedto market and in terms of face value. We have extended these series back to 1776.10When the government has issued perpetual consols, nt .7

At time t the government promises to pay stt j dollars at times t j, j 1, 2, . . . , nt . Promisedpayments consist of coupons ctt j and principal repayments (also known as par values) btt j :stt j ctt j btt j .(1)These are sums of the corresponding components associated with each bond.The market value of government debt at time t isntXtqt jstt j ,(2)j 1which states that the total value of government debt is the sum of a collection of prices timesquantities.The US Congress and Treasury define the total government debt at time t as the outstandingtotal par valuentXbtt j ,(3)j 1which differs from the market value of government debtntXj 1tqt jstt j ntXtqt j(ctt j btt j )j 1for two reasons: It neglects the government’s outstanding promises to pay coupons that are economicallyindistinguishable from promises to pay principalntXctt j ;(4)j 1and The book value given by equation (3) fails to discount future payments of principal btt j byt .multiplying them by the market prices, or “discount factors”, qt jThe first omission causes the official Treasury concept (3) to understate the market value ofdebt, while the second omission tends to make it overstate it. This means that it is possible forP t tthe official government debt nj 1bt j either to exceed or to fall short of the market value ofPn t t tgovernment debt j 1 qt j st j . In figure 5, we plot the par value of the debt in blue and marketvalue of the debt in red from 1776 to 2014. In figure 6 we plot the ratio of market value to the8

140market valuepar value120World War II percent of GDP100G.W.Bush/Obama 806040 Reagan 1790Civil War 20World War I War of 1812 Revolutionary gure 5: Market and Par Value of Gross Debt, as a Share of GDPpar value. As is apparent in these two graphs, inequalities in both directions have occurred in theU.S. data.Figure 7 plots the sum of the future promised principal payments,Pn ttj 1 bt j ,in blue. Thisis just the par or face value of the debt. In red the same figure plots the sum of the promisedP t tP t tcoupon and principal payments nj 1bt j nj 1ct j .2.1Macroeconomists’ government budget constraintAn instance of the government budget constraint appearing in macroeconomic models (for exampleequation (3) of Hall and Sargent (2011))11 isntXj 1nt 1tqt jstt j Xttqt j 1st 1t j 1 σt ,(5)j 1where Gtt are net-of-interest government purchases at t, Ttt are taxes net of transfers at t, andσtt Ttt Gtt is the government’s net of interest surplus at t.12 The left side of (5) is the value11This version ignores the TIPS that Hall and Sargent (2011) include. It also in nominal terms and ignores theprice level and inflation adjustments that can convert it to real terms. See Hall and Sargent (2011).12In subsection 2.4, we will make use of the following notation and vision. At each date t, we will think of thegovernment as having a fiscal plan consisting of a pair of sequences, namely, a sequence {Gtt j } j 0 of governmenttpurchases planned at t for period t j and a sequence {Tt j} oftaxcollectionsnetoftransfersplanned at tj 0tfor period t j. These two sequences imply an associated net-of-interest surpluse sequence {σt j} j 0 whose jthtcomponent equals Tt j Gtt j .9

120110100100 market value/par 950197520002025Figure 6: Ratio of Market Value to Par Value of Debt150promised principal paymentspromised principal coupon payments125percent of GDP10075502501800182018401860Figure 7: Total Principal1880Pn ttj 1 bt j19001920 Coupons101940Pn ttj 1 ct j196019802000as Share of GDP

of government debt in period t, while the first term on the right side is the value of promisedt .future payments that the government had made at time t 1 evaluated at time time t prices qt jEquation (5) states that the value of the government debt changes between times t and t 1becauset 1t1. Prices of time t j promises st 1t j to time t j dollars change from qt j to qt j .2. The government alters its promised payments so that stt j 6 st 1t j for some j’s.3. The government runs a deficit or surplus at date t.It is enlightening to rewrite equation (5) asntXnt 1tqt jstt j j 1tqt j 1Xt 1qt j 1j 1nt 1 X!t 1tqt j 1st 1t j 1 σtnt 1t 1qt j 1st 1t j 1 wheretqt j 1t 1qt j 1 jt 1trt 1,tqt j 1st 1t j 1 σt(6)j 1j 1 Xj (1 rt 1,t) is the one period gross nominal rate of return on a j-period purejdiscount bond and rt 1,tis the net nominal rate of return. The second term on the right side ofthe second line of equation (6) measures time t nominal interest rate payments on the time t 1nominal government debt:ntXj 1 {z}sum overmaturitiesjrt 1,t {z }netreturns t 1qt j 1st 1t j 1 {z}(7)valuesSo equation (6) expresses the nominal value of government debt in period t as the sum of the valueof government debt yesterday, net interest payments on last period’s debt, and the governmentdeficit σtt .2.2Interest reported by the governmentThe nominal interest payments defined in expression (7) are not what the US government reportsnow or has ever reported. Instead, the government reports a different notion of interest on thegovernment debt, namely:1. Before 1929:ct 1t11

40353025percent20151050 5 2020Figure 8: Nominal Holding Period Returns (thin black) and Official Net Interest Payments (thickblue) as a Percentage of the Debt, Annual by Fiscal Year2. After 1929:1ct 1 rt 1,tbt 1t1,twhere bt 11,t is the par value of pure discount one-period treasury bills issued at t 1. Sowhat the government reports as interest payments consists of coupon payments on longermaturity bonds plus the net yield on one-period zero-coupon Treasury bills (these haveexisted only since 1929).To understand how the government’s post 1929 definition of nominal interest payments ongovernment debt relates to the theoretical concepts underlying a standard macroeconomic fort 1t 1mulation like (5), first introduce the decomposition bt 1 bt 1t1,t b 1,t where b 1,t is the par (orprincipal) values of bonds with initial maturities exceeding one period falling due at time t. (Herewe follow game theorists in using the subscript 1 to mean “not 1” meaning “not a treasury bill”.)Then note that qtt 1 and rewrite the standard macroeconomic government budget constraint(6) asntXj 1nt 1tqt jstt j ct 1t bt 1t Xj 2tqt j 1t 1qt j 1nt 1t 1 ct 1 bt 1t1,t b 1,t Xj 212!t 1tqt j 1st 1t j 1 σtjt 1t(1 rt 1,t)qt j 1st 1t j 1 σt .(8)

The second and third terms on the second line of the right side of equation (8) decompose principalpayments into those attributable to maturing one-period pure discount bonds bt 1and to maturingPnt 1 t 1 1,t t 1t 1longer term bonds b 1,t . Rewrite the right side of equation (8) as j 2 qt j 1 st j 1 plusnt 1ct 1t 1rt 1,tbt 11,t{zofficial}interest Xjt 1t 1t 11trt 1,tqt j 1st 1t j 1 (1 rt 1,t )b1,t b 1,t σt {z}j 2 {z}capital gainscash to payprincipalThe first term is what the government records as interest payments. The second term measurescapital gains or losses of holders of longer term government debt held from t 1 to t. These capitalgains are included in the macroeconomic concept of interest earnings on the government debt butare neglected in the official concept. The third term constitutes repayments of principal at timet. We can interpret the sum of the first and third components of the above sum as expressingcash t that the government must come up with at time t in order to “service” its debt, meaningpay coupons plus principal that fall due at time t.13Figure 8 reports (in thin black) the nominal one-period holding period return paid by thegovernment debt, namely,14Pnt 1jt 1t 1j 1 rt 1,t qt j 1 st j 1Pnt 1 t 1 t 1j 1 qt j 1 st j 1and (in blue) official net interest payments as a percentage of the debt, namely, before 1929and after 1929ct 1Pnt 1t t 1j 1 bt j 11 rt 1,tbt 1ct 1t1,t.Pnt 1 t 1bj 1 t j 1The official nominal interest payments series is much less volatile than is the macroeconomist’sdefinition of nominal interest. This reflects volatility in capital gains on the government debtPnt 1jt 1t 1j 2 (1 rt 1,t )qt j 1 st j 1 .13Tables 1.5 and 1.7 of International Monetary Fund (2014) report what they call Gross Financing Needs of allmember countries for the coming years. This is the sum of our first and third terms.14To avoid big spikes in years where the debt increases dramatically (e.g. 1917, 1940), we actually plotted121ct 1 rt 1,tbt 1t1,tPnt 1 t 1Pnt 1 t1j 1 bt j 1 2j 1 bt j 1, using interest payments reported by the government as the numerator. These areclose to what we calculate by summing coupon payments.13

2.3Market versus par valuesThe official debt limit after 1939 and the one that we infer before 1939 both apply to the governP t tP t tment’s measure of total debt, nj 1bt j , rather than the market value of the debt, nj 1qt j (btt j ctt j ). It is easy to devise debt management operations that can raise or lower the government’smeasure of outstanding debt while leaving its market value unaltered: just raise or lower btt j andaccompany it with an offsetting change in ctt j .A practical illustration of such an operation involves the U.S. Treasury’s STRIPS Program.15Since 1985, Treasury notes and bonds with a maturity of 10 years or longer are eligible to be“stripped”, meaning that the Treasury can unbundle coupon and principal payments and thenallow them to be bought and sold as separate securities. For example, a 20 year Treasury bondcomprises a single principal payment, due at maturity, bundled together with 40 coupon payments,one every six months over the intervening 20 years. When this bond is converted to STRIPS form,the components, (i.e., the 40 interest payments and the principal payment) becomes separate“zero-coupon” securities.Of course, since the price of the original bond is just the sum of the prices of the 41 individualzero coupon securities, unbundling should have no impact on the market value of the bundle ofpromises that comprise the bond. From an economic standpoint, each of these 41 securities isjust a promise to pay a dollar at a date in the future, and thus the labels “coupon payment” and“principal payment” are irrelevant from the standpoint of what the government owes its creditors.However, from the perspective of the statutory debt limit, these labels matter. Promises labeledprincipal payments count against the debt limit. Promises labeled coupon or interest paymentsdo not. The U.S. Treasury can lower the par value of outstanding debt by replacing bonds withlower coupons with other bonds having larger coupons.162.4Reinterpretation of the flow budget constraintAn implication of the “flow” government budget constraint (5) or its equivalent form (6) is aninter-temporal budget constraint constructed by integrating flow constraints forward in time andimposing a boundary condition on government debt “at infinity”. Thus, at each t, an intertemporal version of the government budget constraint isXjtqt jstt j Xttqt j(Tt j Gtt j )j15STRIPS is an acronym for Separate Trading of Registered Interest and Principal of Securities.Some state governments engage in this practice. As noted by The Volcker Alliance (2015), in 2011 and 2012the State of New Jersey sold securities bearing coupons above market levels. The State recorded the increase indebt at the par value and the premium above par as revenue.1614

orXtqt jstt j Xttqt jσt j(9)jjtwhere Gtt j are government purchases planned at t for period t j, Tt jare tax collections net oftt Gttransfers planned at t for period t j, and σt j Tt jt j is the net-of-interest governmentsurplus at t j planned at t.17 Equation (9) asserts that the market value of government debt att on the left side equals the present value of government surpluses at t on the right side. Largegovernment debts signal large prospective net-of-interest surpluses.In light of the equality (9), the government budget constraint (6) can also be writtenntXj 1nt 1ttqt jσt j Xnt 1t 1t 1qt j 1σt j 1 j 1Xjt 1t 1rt 1,tqt j 1σt j 1 σtt(10)j 1Equation (10) is the other side of the coin of equation (6). It says that the present value of thegovernment surplus at t is equal to the present value of the government surplus at time t 1 plusa time t capital gain on the present value of the time t 1 surplus plus the time t net-of-interestdeficit σtt .We shall eventually use equation (10) to interpret the fiscal consequences of various alterationst 1tof Federal tax and expenditure policies that, by setting Gtt j 6 Gt 1t j and Tt j 6 Tt j , oftenaltered present value of government surpluses and therefore market values of government debt.3Delegation and ReassertionWe have constructed a new time series, an implied pre-1939 aggregate debt limit (i.e., the red linesin figures 1-3). In this section, we describe notable movements in this time series and an associatedpar value of the debt subject to the aggregate limit depicted in the blue lines in figures 1-3. Astory emerges about a process of slow and uneven concessions of Congressional authority over debtmanagement to the Treasury. In the process of telling this story, we answer the question posedin section 1: why had earlier Congresses rejected advice from Mellon’s predecessors to delegatesecurity design and debt management authority to the Treasury?Laws authorizing debt by the Continental Congress and then by the US Congress resembledearlier British laws regulating borrowing by the Crown and by the American colonies. After theGlorious Revolution of 1688, Parliament placed issue-by-issue limits on sovereign borrowing.18The power to issue (or really, power to not issue) debt meant Parliament must approve bigprojects like wars. Because the framers of the Constitution liked this division of authority, theyassigned Congress power to issue and manage the debt.1718Please see footnote 12 above.For example, see William III (1697-8).15

3.1The American RevolutionUS debt limits are nearly as old as the Declaration of Independence. The Continental Congress’sfirst authorizations to borrow at the start of the War of Independence included debt limits.However those early debt limits did not bind. For example, although in 1779 the ContinentalCongress authorized its representatives to borrow 10 million from France, France eventually lentonly 1.8 million.The Continental Congress ran up a large debt to finance the war. Despite Article VI ofthe US constitution,19 the U.S. eventually defaulted on much of this debt and did so in waysthat discriminated heavily across different classes of U.S. government creditors. Hall and Sargent(2014) document this in detail. For many years, bitter memories of those discriminatory defaultsmotivated successive Congresses strictly to limit the Treasury’s authority to issue debts thatresembled currency.Between 1775 and 1781, the Continental Government spent 85 million Spanish dollars. It collected 7 million in taxes, raised 40 million Spanish dollars by issuing over 200 million Continentaldollars that promised to pay Spanish dollars, and incurred 41 million in interest bearing debtand unpaid interest. The Continental Congress placed limits on most types of borrowing, but thecredit of the United States was so poor that these limits were rarely binding.On October 3, 1776 the Continental Congress authorized its first issue of interest-bearingbonds, called Loan Office Certificates. These promised to pay 4 percent per annum. Congressinitially authorized up to 5 million of these. The Congress soon authorized an additional 15million to be issued and raised the coupon rate to 6 percent.20 When the Continental Congressauthorized Benjamin Franklin and Silas Deane to negotiate its first foreign loan from the FarmersGeneral of France, on December 23, 1776, it limited the amount the two could borrow:21Resolved that the commissioners of Congress at the court of France be authorizedto borrow, on the faith of the thirteen United States, a sum not exceedingtwo million sterling, for a term not less than ten years.In addition to Loan Office Certificates, the Continental Congress authorized a second domesticcla

Brandeis University 415 South Street Waltham, MA 02453 ghall@brandeis.edu Thomas J. Sargent Department of Economics New York University 19 W. 4th Street, 6th Floor . Congress did not resume control after World War I or World War II. 2. Has the debt limit been an upper bound on total debt to be anticipated over medium to