American Economic Association

On the Limitations of Government Borrowing: A Framework for Empirical Testing Author(s): James D. Hamilton and Marjorie A. Flavin Source: The American Economic Review, Vol. 76, No. 4 (Sep., 1986), pp. 808-819 Published by: American Economic Association Stable URL: http://www.jstor.org/stable/1806077 Accessed: 21/08/2009 14:21

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http://www.jstor.org On the Limitations of Government Borrowing: A Frameworkfor EmpiricalTesting

By JAMES D. HAMILTON AND MARJORIE A. FLAVIN*

How long can governmentbudget deficits interest payments) is infeasible;(though, as continueunchecked? This questionraises two we shall see below, a permanentdeficit when separate issues. First, are perpetualdeficits interest payments are counted as part of the desirable-are the effects on inflation, in- deficit may still be feasible).The questionof vestment, and the balance of paymentsones feasibility of a permanentdeficit (exclusive that we can live with? Second, are perpetual of interest payments)holds profoundimpli- deficits feasible-even if the government cations for macroeconomictheory and prac- wanted to run a budget deficitforever, is this tice. If governments intend to raise the somethingit reallycould do? needed revenues with future tax increases, If we were talkingabout the budget plans then government deficits may have no of a private household, clearly the question stimulativeeffect on aggregatedemand,' but of feasibility would be paramount,for we can have significantdistortionary effects on entertainlittle doubt that householdswould private incentives if the future tax increases like to run a permanentdeficit if they could are large (see Robert Barro,1984b). On the get away with it, continually rolling over other hand, if the revenuesare to be raised debt without having to pay anything back implicitly through money creation, budget and enjoying the associatedfree lunch. We deficits can be a principalcause of inflation, presume that households do not generally as suggested by Thomas Sargent(1982) and engage in such behavior primarily for the Sargentand Neil Wallace(1981). reason of feasibility-no one would be will- Whethergovernments can continuallyrun ing to continue lending money to such a a budget deficit remains an unsettled theo- household.For this reason,we usuallyspecify retical question. If the governmentborrows that householdsare subjectto the borrowing at an interest rate that equals or exceeds the constraintthat the expectedpresent value of economy's growth rate, then a continuing expenditures(exclusive of interestpayments) unpaid deficit implies that the debt must not exceed the expected present value of receipts. The question we pose in this paper is whether governmentsare subjectto an anal- ogous constraint-when a governmentruns 1If government spending (G,), taxes (T,) and debt a deficit, is it making an implicit promiseto (B,) are related by creditors that it will run offsettingsurpluses 00 00 in the future?If governmentsare subjectto B, + , (1 + r)'jG,+j , (1+r)+jT,+j this constraint,which we will term the pres- j-1 j-l ent-valueborrowing constraint, the policy of then any proposal that changes taxes but leaves spend- running a permanent deficit (exclusive of ing the same must be such that the right-hand side of the above expression remains constant. Thus, permanent income defined by

* Department of Economics, University of Virginia, x Charlottesville, VA 22901. This paper was written while ?, (1+ r) j ( W,+jL+j- Tt+j) we were visiting at the University of California-San j-1 Diego. We are indebted to Charles Engel, Ron Michener, and John Taylor for helpful comments. Research sup- would be completely unaffected by any such tax policy. port from the National Science Foundation under grant See Robert Barro (1974, 1984a) and Olivier Blanchard SES-8420434 is gratefully acknowledged. (1985) for further discussion. 808 VOL. 76 NO. 4 HAMILTON AND FLA VIN: GOVERNMENT BORROWING 809 grow to become an infinitemultiple of GNP.2 At first glance, a test of the present-value Equilibriummodels in whichinvestors would borrowingconstraint might seem straightfor- continue to buy governmentdebt undersuch ward enough. The U.S. government,for ex- circumstances have proven difficult to de- ample, has run more or less a chronic def- velop; see Bennett McCallum(1984) for a icit since 1930, suggesting that permanent clear discussion of the issues. If the real deficits are quite feasible and practical. interest rate is less than the growthrate, by However, this simple argumentignores the contrast, deficits could continue forever potential role of debt retirement through without an increase in the ratio of debt to monetization and likewise ignores capital GNP. Theoreticalmodels that seem to allow gains on bonds or tangible assets through this possibility have been explored by Wil- inflation. Moreover,the official government lem Buiter (1979), Jonathan Eaton (1981), deficit includes interest payments, whereas and JeffreyCarmichael (1982), though these we will argue below that the correctmagni- results have not gone unchallenged(see, for tude for purposesof testingthe present-value example,John Burbidge,1983). borrowing constraint should exclude such In any case, it seems desirableto supple- payments. Finally, a formal test of whether ment these theoretical considerationswith historical deficits were rationallyanticipated empirical evidence. David Aschauer (1985) and allowance for what might rationallybe and John Seater and Roberto Mariano expected to happen out of sample seems (1985), among others, have tested the hy- necessary to evaluate this hypothesis ade- pothesis that the government'sreceipts must quately. equal its expendituresin present-valueterms In this paper we propose an empirical jointly with a permanentincome hypothesis, frameworkfor testing the practicallimits to and accepted. Paul Evans (1985) docu- public borrowing which addresses these mented the absence of statisticalcorrelation criticisms.We show that the propositionthat between U.S. budget deficits and interest the government can accumulateever-grow- rates, which he interpretedas evidence in ing debt through perpetualdeficit financing support of this same joint hypothesis.Barro has a mathematicalparallel in the proposi- (1984b) tested the hypothesis that the gov- tio-n that prices can rise continually in a ernment is subject to the present-valuebor- self-fulfilling speculativebubble. Thus, em- rowing constraint jointly with the assump- pirical tests that have been developedfor the tion that taxation and deficit policies have latter hypothesis may also be fruitfullyap- historically been optimal, and again ac- plied to study the limits of govemmentbor- cepted. However,to our knowledgethere has rowing. been no direct empiricaltest of the present- The conclusions we draw from these tests value borrowingconstraint itself. complement those of Barro (1984a) and Robert Eisner and Paul Pieper (1984), who have noted that while the officialbudget has registereda chronic deficit, the real value of 2Again we are referring to the government deficit exclusive of interest payments. To take a simple exam- government debt fell substantially in the ple, let output Q(t) grow at the rate q(Q(t) = Qoeq,), postwar period, suggestingthat the official and let spending gQ(t) and taxes xQ(t) be fixed multi- accounts have grossly misstatedthe true fis- ples of GNP. If r is the cost of borrowing and B(t) is cal posture of the government.Once an eco- the debt, then debt accumulates according to nomically reasonable definition of the gov- dB/dt = (g- x)Q(t)+ rB(t) ernment budget deficit is adopted, the data seem fully compatiblewith the assertionthat implying B(t) = { Bo + tQ(g-x)} eqt if q = r the governmentbudget historicallyhas been balanced in expected present-valueterms. = {(g- x)/(q- r)}QO(eqt - ert)+Boer, otherwise, Our tests show this conclusion to be rea- sonably robust with respect to specification which explodes relative to Qoeqt whenever g > x and of the information on which creditorswere q < r. basing their forecasts of future surpluses. 810 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 1986

Past deficits have been followed by increases denote real tax revenues,Gt real government in revenues which covered the government's purchases of goods (excludinginterest pay- interest obligations, though the implicit "in- ments on the debt), and R, the dollarflow of flation tax" has historically made an im- nominal interest paymentsmade to the pub- portant contribution. lic divided by the price level. Thus, the offi- Section I provides a formal statement of cial deficit in constantdollars is measuredby the present-value borrowing constraint to be tested. Section II briefly discusses some is- (2) Gt+Rt-Tt sues of data and measurement. In Section III we present the results of alternative em- and new debt must be issued in this amount pirical tests of whether the postwar record of during the year. Changes in the stock of budget deficits in the United States could be high-poweredmoney (Mt) likewiseretire an consistent with the present-value borrowing amount of debt whose marketvalue is3 constraint under rational expectations, with brief conclusions offered in Section IV. (3) (M,-M1t-)/P.t

1. The Present-ValueGovernment Finally, let Bt denote the real marketvalue BorrowingConstraint of debt held by the public (Bt=t=Pt). Ejdj From (1)-(3), its value is given by Suppose we collected all government debt of a given coupon and maturity into group j. (4) Bt=(1 + r)B,- -EOjO,/P, +Evjt Let dy t denote the nominal market value of i i such debt at the end of period t and O0, the total nominal coupon payments between + Gt + Rt -Tt -(Mt -Mt-,)Ipt + Ul t. dates t - 1 and t. We further let P, denote an aggregate price index of goods in the In principle, equation (4) might be thought economy and r the ex post real interest rate of as an accountingidentity. In practice,we that is earned on one-period government must append the errorterm U1, since bond bonds during an average year. purchasesor sales towardsthe beginningof Suppose no new bonds of type j are is- the period would have taken place at market sued or redeemed during period t. Then prices closer to those characterizingBt, 1 changes in the market value of group j debt rather than Bt, and since measurementsof can be evaluated using a simple term-struc- the real market value of net government ture argument. Define V to be the real indebtedness are necessarilyimperfect (see excess one-period holding yield of j bonds Section II below). Again abstractingfrom relative to the average earned on a compara- this issue of intraperiodtiming, note further ble investment in one-period bonds: that Ej1j ,/Pt + U2 t = Rt. Thus

(5) Bt=(1 + r)B,tI-St + Vt, (1) V;,- ' + 0t, (1 ?r)dj,t1 vi'tt t- where + If real interest rates were white noise (or (6) St-Tt-lMt+)+Pti-+Gt (Mt constant) and if the expectations theory of + + the term structure held, then Et_ v would Vt--Evj,t U1,t U2,t- equal zero. In general, positive values of vj,, mean bondholders have made a capital gain on long-term government debt, or that short-term rates are higher than average. 3We are formally modelling assets held by the government as negative values of dj,,, so that foreign The market value of outstanding govern- exchange transactions by the Federal Reserve are also ment debt will also change due to operations included in (3). Details of the variables used in the of the Treasury and Federal Reserve. Let T, empirical analysis are provided in Section II. VOL. 76 NO. 4 HAMILTON AND FLA VIN: GOVERNMENT BORROWING 811

The key points to note about (5) are: (a) it tained forever, for example, we see from (5) describes the market rather than the par that BN=Nk + BO and limNo,BN/(l + value of government debt, since open mar- r)N = 0. Thus a policy of keeping the interest ket operations by the Federal Reserve retire component of the deficit from rising will debt at market value; (b) the measure of the ultimately force the government to pay off surplus S, excludes interest payments from its debts in present-value terms. On the other government spending; and (c) money sei- hand, a permanent deficit exclusive of inter- gniorage (Mt - M, 1)/P, is added to taxes est payments - S, + V, = k is not consistent Tt as a source of revenue for retiring out- with (8), for then BN= k[(l + r)N_ll/r + standing government debt. (1 + r)NB0 and limN OBN/(1+ r) N= k/r By recursive substitution forwards, equa- + Bo. Recall McCallum's demonstration that tion (5) is seen to imply a permanent deficit inclusive of interest payments could be consistent with optimizing N (Si- v) (1+ r)'BN behavior by bondholders (and would satisfy (7) Bt,= F, +N our condition (8), whereas a permanent def- i=t+1 (1+ r)'' (1+r) icit exclusive of interest payments is not consistent with optimizing behavior in his Equation (5) and its implication (7) cannot model (and would violate (8)). Finally, we be a point of serious controversy, for they do note that condition (8) does not imply that little more than summarize the definitions of the national debt must eventually be paid monetary and fiscal policy. What is of eco- off. In fact, (8) is consistent with a con- nomic interest (and subject in principle to stantly increasing stock of debt, as long as empirical refutation) is what creditors expect the rate of increase is less than the govern- to happen to the second term in (7) as N ment's borrowing rate. Rather, the question gets large. Indeed, letting Et denote the ex- we pose is whether interest on this debt is to pectations of creditors based on information be paid with future tax increases or instead available at date t, it is clear from (7) that with continual issue of new debt. the hypothesis that the government is subject If (8) represents the null hypothesis that to the present-value borrowing constraint, the government budget must be intertempor- ally balanced, how may we usefully frame 00 (Si-VI) the alternative possibility that government (8a) Ho: Bt Eti I (I+r)' deficits (i.e., negative values of S,) need not be balanced with future surpluses? One in- is mathematically equivalent to the restric- teresting class of alternative hypotheses is tion that the real supply of bonds held by obtained by assuming that the public is expected to grow no faster on average than the rate of interest: E, lim FBN/(1+r)N]=AO>O. N -oo

(8b) Ho: Et lim BN = 0. Thus, we allow the possibility that a certain N - oo (I1+r)N annual amount of real government expenditures r(AO- BO)need never be paid for with Using the equivalence between (8a) and taxes. From equation (7) we then obtain (8b), we are now in a position to comment in more detail on the precise nature of the present-value borrowing constraint. Note (9) B = L (I ) r)t first that condition (8) can be consistent with i=t?1 (1? r)' a permanent government deficit as conven- tionally measured, that is, inclusive of inter- as a general class of solutions to (5). The est rates. If a constant (interest inclusive) hypothesis Ho that the government bud- deficit of - S, + V, + rBt -1 = k were main- get must be balanced in present-value 812 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 1986

TABLE 1-ILLUSTRATIVE SUMMARY OF ADJUSTMENTS TO OFFICIALLY REPORTED SURPLUS FOR FISCAL YEAR 1974 AND FOR DEBT AT END OF FISCAL YEAR 1974 (Millions of current dollars)

Surplus: Officially Reported Surplus -3,460 Plus: interest + 28,072 Minus: interest paid to government trust funds - 6,583 Minus: deposit of Fed earnings -4,845 Plus: change in agency securities + 903 Equals: Measure of surplus in which interest payments are excluded + 14,087 Plus: net capital gains on gold stock + 3,250 Plus: money seigniorage + 11,331 Equals: true surplus (current dollars) + 28,668 Divided by: consumer price index -1.469 Equals: true surplus (1967 dollars) + 19,515 Debt: Officially Reported Debt 474,235 Minus: investments in government accounts - 140,194 Equals: par value of Treasury debt 334,041 Multiplied by: market-par ratio 0.951 Equals: market value of Treasury debt 317,740 Minus: currency in circulation - 73,833 Minus: member bank reserves - 30,086 Equals: market value of net interest-bearing debt held by public 213,821 Minus: Treasury operating balance - 9,159 Minus: market value of gold holdings - 39,951 Equals: adjusted government debt (current dollars) 164,711 Divided by: consumer price index -1.469 Equals: adjusted government debt (1967 dollars) 112,124

termsholds true if and only if A0 = 0 in equa- A. Interest Payments tion (9). Equation (9) is mathematicallyequivalent The theoretical measure of government to the models of self-fulfillingfads or specu- spending (G,) in the above derivation ex- lative bubbles firstexplored by RobertFlood cludes outlays for interest payments. Cor- and Peter Garber (1980). We accordingly recting the officially reportedsurplus (T,- propose that such tests might also be fruit- G,) to exclude interest payments from G, fully applied to understandingthe limits of requiresthree steps. 1) Add to (T, - G,) total governmentborrowing. The next section dis- interest paid by the government.2) For data cusses the data on which such tests might prior to the accountingchange in 1982, avoid be based, while Section III summarizesour double countingby subtractingback out that results. part of this Treasuryinterest that was paid directly into governmenttrust funds such as II. Issues of Data andMeasurement Social Security. 3) Likewisesubtract the deposit of Federal Reserveearnings which are This section, inspired in part by Barro already included in T, under miscellaneous (1984a) and Eisner and Pieper, briefly dis- receipts. Sample calculationsfor corrections cusses how the theoretical magnitudes ap- to the deficit and debt are provided in Ta- pearingin our equation(9) are relatedto the ble 1; the actual series used in our empirical budget figuresactually reported in the United work are reportedin Table2. States. Complete details are provided in a Some debt is issued by various federal data appendix availablefrom the authorson agencies in addition to that issued by the request. Treasury. Outlays for the service of such VOL. 76 NO. 4 HAMILTON AND FLA VIN: GOVERNMENT BORROWING 813

TABLE 2-ADJUSTED VALUES FOR SURPLUS AND DEBT B. TrustFunds (Millions of 1967 dollars)

Fiscal Adjusted Surplus Adjusted Debt for Some might arguethat trustfund holdings Year for Fiscal Year End of Fiscal Year are to be used against the government'slia- bilities implied by futureSocial Securityben- 1960 + 8,533 167,954 1961 + 921 170,826 efit payments. It seems to us that this is an 1962 + 2,117 176,187 inaccurateinterpretation. Such programsare 1963 + 3,697 177,944 not a currentliability in the sense that they 1964 + 3,968 176,036 can be associatedwith any concretenumber. 1965 + 9,604 173,319 1966 + 11,514 160,103 Rather, they represent the outcome of an 1967 + 7,997 157,441 uncertain political process, and the correct 1968 - 3,262 162,227 way to represent this "liability" is by the 1969 + 14,142 144,302 discounted cash flow of an entry on current 1970 + 6,529 136,877 account rather than any dubiousimputation 1971 - 3,631 145,977 1972 + 1,812 151,836 to capital account. For this reason,we follow 1973 + 13,451 136,272 the official accounts in registeringnet Social 1974 + 19,515 112,124 Security inflows or outflows on the deficit 1975 - 13,152 134,673 account, but differ from the officialaccounts 1976 a -35,480 185,230 1977 - 4,162 191,707 on the debt account. The correct measure 1978 + 3,022 183,956 subtracts that money which is owed from 1979 + 28,211 148,641 one branch of governmentto another. 1980 + 20,506 121,432 1981 - 27,747 145,895 C. Items 1982 - 22,147 209,445 Off-Budget 1983 - 38,336 265,164 1984 - 28,675 303,205 Starting in 1971, the activities of certain

a agencies such as the Postal ServiceFund and Data for fiscal year 1976 include the transition Rural Electrificationand TelephoneRevolv- quarter (July 1, 1976 through September 30, 1976). ing Fund are characterizedas "off-budget." Any deficits of such operationsrequire the issue of Treasurybonds, thoughthey do not debt are presently included as expenditures count in the officially measureddeficits of of that agency, and should be subtracted the U.S. government. from G, to arrive at our measure of G,. Suppose that these fundswere indeed used Unfortunately, such data are not readily primarily to issue market-interestloans to available. Since agency debt is small (for the private sector. Imagine the agency issu- example, $12 B in 1974 comparedwith $475 ing a $1 loan financedthrough a $1 sale of B in Treasury debt), little harm can come Treasury bonds, and so running an off- from assuming that the present-valuerela- budget $1 deficit for that year. In the follow- tion holds for agency debt, in which case we ing year, the agency receives $r as interest could approximatethe presentvalue of later payments from the private sector, but the agency interest payments by the current Treasurypays $r back to the public as inter- marketvalue of new agencydebt issue. Thus, est on the T bond. For this year, the official we subtract new issue of agency securities budget and off-budgetitems would accord- from G,, and do not count the marketvalue ingly sum to a zero net deficit. Thus, the of agency securitiesin our measureof public holdings of governmentdebt, B,.4

ingly higher by $r. In the accounts as actually reported, this policy would be associated with a $1 deficit in year 4To take a simple example, suppose that in year 1 1 and no surplus in subsequent years. In our proposed spending exceeds taxes by $1, with the shortfall made measure, by contrast, the deficit is zero in all years; i.e., up by $1 issue of new agency debt. In all subsequent agency debt has no effect on the present-value calcula- years, interest spending is $r and taxes are correspond- tion for Treasury debt, as it should not in this case. 814 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 1986

present-value budget across the two years (Au -Au,+1 > 0) at price ptA u and uses the would register a deficit if one combined the proceeds to retire debt, then next period's official budget and off-budget items into a debt will be given by single account, whereas the operation itself is clearly fiscally neutral- the government Dt+1 = (I + it) Dt -PtSt issued a $1 Treasury bond but acquired a $1 - - private bond, and has simply swapped like -( AuA-Ut+ Au 1) AuP4Pt+ assets with the public. A correct measure would be obtained in this case if we adopt which can be written as our convention of excluding Treasury interest payments from G, and simply ignore the (Dt+l( _pAu- Pt+lAut+i)=D1PAA~ lAu +) = (I + it)(Dt,-ptAuAUt) off-budget surplus or deficit altogether. Of _ - course, these programs are not pure + ( 7T, )AP uAU PtS market loans but in fact have a substantial subsidy aspect. Our only justification for where 7A U (PtAu - PtA u )/ptA u. Thus, if we ignoring this is that it is difficult to quantify define true government indebtedness as the and presumably small relative to the com- stock of Treasury debt held by the public plete budget. less the current market value of the government's gold holdings (i.e., as D,- PtAuAut), D. Net GovernmentIndebtedness the equation governing the evolution of true government indebtedness is obtained by sub-

Eisner and Pieper have begun the difficult tracting (it - r7tAu)ptA uAut from the officially task of quantifying the market value of vari- measured surplus (Tt - Gt). ous tangible assets owned by the govern- For fiscal year 1974, gold prices increased ment. The question for purposes of the pres- by 17.16 percent, whereas the nominal inter- ent study is, do government bondholders est rate on one-year government bonds was believe that future interest payments will 7.56 percent. Based on a market value of the really be met through sale of such assets, government's gold holdings of $33.8 B, a rather than by more conventional means such sum of (.1716 -.0756)(33.8) = $3.2 B should as tax revenues or monetization? Our own be added to the surplus for fiscal year 1974 view is that, for the vast majority of these to represent capital gains from gold. assets, the promise of substantial liquidation We also need to subtract liquid assets held of government tangible assets is not a politi- by the Federal Reserve from our measure of cally credible backing for U.S. Treasury debt. the government debt (see fn. 3). Since these One important exception is the govern- are all carried on the books at par value, the ment's gold holdings. There is abundant his- simplest way to construct the correct mea- torical evidence that governments willingly sure of the market value of these assets is draw down or deplete these stocks in the from the liabilities side, namely, by sub- wake of fiscal crises; this indeed is presum- tracting high-powered money from out- ably the primary purpose of holding such standing government debt to get a measure stocks in the first place. Let Aut denote the of net interest-bearing debt held by the pub- government's gold holdings in ounces, ptAu lic. The Treasury operating cash balance the price per ounce of gold, and Dt the must also be subtracted to arrive at the nominal value of debt, all measured at the figure Bt appearing in equation (5). beginning of period t. Let PtSt denote the Painstaking calculations of the true market correctly measured surplus during period t value of government debt based on actual (excluding interest payments from spending market quotations of outstanding securities but making no correction for gold flows), have been updated by W. Michael Cox and let it be the one-period interest rate, (1985). At the end of fiscal year 1974, out- which for simplicity we assume is the same standing government debt was trading at a for all bonds. If at the end of period t the market value of only 95 percent of its par government sells off some amount of gold value. VOL. 76 NO. 4 HAMILTON AND FLA VIN: GOVERNMENT BORROWING 815

E. Money Seigniorage plicitly imposes strong restrictions on the variables used by agents in forming expecta- When the Federal Reserve acquires a tions E, and on the dynamics allowed for n,. Treasury bond, future interest payments on Behzad Diba and Herschel Grossman (1984) that bond accrue to the Fed and are counted and Hamilton and Whiteman suggested that as part of tax revenues under "Miscella- a more general test should first be consid- neous Receipts" in the official budget. Since ered which is more robust with respect to the present value of this tax benefit is equal such restrictions. In particular, for any sta- to the Fed's initial cost of the bond, seignior- tionary process for (n,, E,EJ1(1 + +), age is in this sense theoretically already in- when AO= 0, B, will be stationary, whereas cluded in the budget. In practice, however, for Ao > 0, B, will not be stationary. We any finite-sample estimate of the discounted accordingly initially examine two simple value of these miscellaneous receipts must be tests. less than the discounted value of M,,i - M,+i_,, because open market purchases to- A. Dickey-Fuller Testfor Unit Roots wards the end of the sample period have not yet been amortized. For this reason, we David Dickey and Wayne Fuller (1979, exclude deposits of Fed interest from our p. 431) suggested the following test of the measure of T, and include the seigniorage null hypothesis that a series z, is nonsta- measure (M, - M, -), where M, denotes tionary with unit roots. Estimate high-powered money (the sum of currency in circulation plus reserves of member banks). Z, - z, = Jo+ 4lzt-l

III. EmpiricalTests + 42(Zt-I1 t-z 2) + ez,

We are interested in the question of by ordinary least squares, and calculate whether the U.S. government's creditors a1/o where a1 is the OLS standard error could rationally expect that the government for 'P. The null hypothesis (nonstationarity) budget would be balanced in present-value says this statistic should be zero; the alterna- terms. In the light of the discussion of Sec- tive (stationarity) says less than zero. tion I, we state this hypothesis as the restric- Using the data in Table 2 we estimated tion Ao = 0 in the formulation the following equation by OLS for t = 1962 to 1984 (standard errors in parentheses): (10) B,=AO(1+r)' 00 S, - S,_1 = -0.53 - 0.70S,1 +Et E (I+r) JS,+j+n, (3.27) (0.24) j=1 + 0.38(S,1- St-2)+ est where B, and S, are the adjusted debt and (0.24) surplus series reported in Table 2 and n, is a regression disturbance term reflecting ex- B1- B,1= 79.63 - 0.48B,1 pected changes in real short-term interest (28.13) (0.17) rates, the term structure of long rates, and measurement error. The operator E, denotes +1.02(B,1 -Bt-2)+ B, t the expectations of creditors, which we as- (0.22) sume are formed rationally. Equation (10) is mathematically equivalent The Dickey-Fuller test statistics are - 2.92 to the model proposed by Flood and Garber in the case of the surplus and - 2.82 in the for studying self-fulfilling hyperinflations. case of debt, to be compared with a 5 per- However, Hamilton and Charles Whiteman cent critical value of - 3.00 and 10 percent (1985) expanded on the caveat stated by value of -2.63 reported in Fuller (1976, Flood and Garber that their technique im- Table 8.5.2, p. 373). The data thus favor 816 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 1986 rejection of the null hypothesis of non- We took r = 0.0112, the average ex post stationarity in both cases; that is, the data real rate over 1960-84. This equation clearly seem fully compatible with the assertion that yields no indication that government debt investors rationally expected the budget to tends to be growing at rate r; the coefficient be balanced in present-value terms. Ao is statistically insignificant, and, if anything, negative in sign. B. Generalized Flood-GarberTest While the two tests employed above are more general than most of those appearing If expectations of future surpluses are con- in the literature on speculative price bubbles, ditioned in part on past surpluses and if we the motivating assumption that { E,t4 =I(1 include lagged debt to eliminate the serial + r )-jS, j } follows a stationary process is correlation of the resulting error term, then still not completely general. In particular, if equation (10) takes the form one admits the possibility of out-of-sample changes in regime, the parameter Ao in (11) B,=cO+AO(1+r)t+c1Bt_ equation (10) would be unidentified (see Hamilton, forthcoming, and the references + ... +cpB,_p+boS,+bis,- therein). One might further want to admit the possibility of a change in regime in which + ... + bp-,St-p+l + et the government budget had been expected to be balanced in present-value terms up until (Here t is the residual from a projection some date t and only after that date was a of [E,tEj=1(1+ r)'St? + n,] on [St,S,, permanent deficit introduced, in which case ... 9S,p+19 Bt-1, Bt- 2 ,... B,_p, and a the corresponding "bubble" term would be constant].) If one were willing to impose zero up until date t and A,(1 + r)T-' for stronger restrictions on the dynamics of n, T > t. and on the information set used by creditors, One obvious candidate for a possible then one would want to estimate (11) jointly change in regime in both the { St } series and with cross-equation restrictions on the pro- the bubble term AO(1+ r)t is the inaugura- cess followed by S,, as in Flood and Garber's tion of Ronald Reagan as president in 1981. study of money demand. In the absence of As a general test of this possibility, one can such restrictions, Hamilton and Whiteman imagine allowing all of the parameters in showed that the coefficients cj, bj are un- (11) to take on different values before and restricted, and a more general test of Ho is after 1981, and seeing whether the post-1981 obtained by simple OLS estimation5 of (11): Ao is still zero. Unfortunately, there are in- sufficient degrees of freedom to carry out B, = 48.41 - 22.68 (1+ r) t+ 0.69 B such a test; if one believes that a change in (26.40) (21.29) (0.21) regime occurred in 1981, it is impossible to determine statistically whether the change + 0.20 B,2- 1.30 S,- 063 St_1E. represents a new time series process for { S, } (0.24) (0.13) (0.31) that is still consistent with (8), or instead represents a change to a nonzero value for the bubble term AO. Distinguishing between these possibilities must await additional data. 5Flood and Garber note in their fn. 18 (p. 754) that What one can say, however, is that the cas- caution must be exercised in interpreting the usual t-test ual impression afforded by the official deficit in this application. An added complication for our application is that under some specifications of the series-that the government has been run- alternative hypothesis Ao could be regarded as a ran- ning a permanent deficit for 25 years in dom variable. A related issue arises in interpreting complete disregard of the present-value bor- Flood and Garber's results if it were thought that some rowing constraint-is not supported by a random economic event set off the speculative bubble. closer inspection of the data. For the sample Our Dickey-Fuller test is likewise not without prob- lems; if (8) fails, the nonstationary root is not unity as taken as a whole, the data appear quite the Dickey-Fuller tests assume but rather (1 + r). consistent with the assertion that the govern- VOL. 76 NO. 4 HAMILTON AND FLA VIN: GOVERNMENT BORROWING 817 ment has historically operated subject to the TABLE 3-ESTIMATES OF PARAMETERS constraint that expenditures not exceed re- IN EQUATIONS (13) AND (15) ceipts in expected present-value terms. Parameter Estimate Standard Error

C. Restricted Flood-GarberTest AO -61.52 (58.20) k1 241.51 (68.87) k2 0.90 (3.83) The test actually used by Flood and a, 0.15 (0.19) Garber (1980) would be valid for our appli- a2 -0.47 (0.22) cation only under the further restrictions a3 -0.51 (0.20) that nt follows a white-noise process

(12) n= k + elt where Et(Y) E(YISI, St-1, St-2,...) and and that creditors' expectations of future b 1/(1 + r). Substituting (12) and (14) into surpluses are based solely on realizations of (10) yields past surpluses.6 A straightforward manipula- tion of the formula derived by Lars Hansen (15) Bt=AO(l+r)t+kl and Sargent (1981, p. 99) yields that for (alb + a2b2 + a3b3)S1 (13) St= k2 + a,St-I + a2St-2 (1-alb-a2b2 - a3b3) + a3St-3 + 2t' (a2b + a3b2)St-, then (- alb - a2b2 - a3b3) 00 (14) EA, b'St+j (a3b)St-2 j-1 - a2b2 - a3b3) elft bk2 (1- alb (1- b)(1- a1b-a2b2-a3b3) We estimated equations (13) and (15) jointly by nonlinear least squares for t = 1963 to 1984. Parameter estimates and standard er- (a1b + a2b2 + a3b3)St rors are summarized in Table 3. (1-a1b - a2b2 - a3b3) As in the less restrictive tests above, we note that there seems to be no role whatever (a2b + a3b2)St- I for the bubble term; Ao is statistically insignificant, and, if anything, negative. The a1b - a2b2 - a3b3) (1- assumption that bondholders rationally expected the debt to be paid back in present- (a3b)SS2 value terms fits the data better than the (1- a1b - a2b2-a3b3) assumption that debt has simply accu- mulated with an ever-growing interest load. Moreover, for these parameter estimates, equation (15) has an R2 of 0.53; that is, 6The second assumption in particular is admittedly more than half of the observed variance in unrealistic. Indeed, it can be shown that expectations the market value of real government debt must be based on additional information besides S, (namely, on the exogenous shocks to which the endoge- nous policy variable S, responds) if equation (8) is to hold, because the forecast errors (E, - E, 1)S,,j cannot be fundamental for S,. It nevertheless seems of forecasts of creditors (E,S,,j) and our econometric interest to see how good an approximation one gets to forecasts (ES,+j) based on a univariate autoregression the data by ignoring this difference between the true for S,. 818 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 1986 could be explained from a rational expecta- the government must promise creditors that tions forecast of the discounted value of it will balance the budget in expected pres- future surpluses. Note such high explanatory ent-value terms seems largely consistent with power is achieved despite the fact that all of postwar U.S. data. the other parameters that characterize the This result might seem surprising since the dynamics of outstanding debt in equation official budget accounts register essentially (15) are tied down by the univariate process uninterrupted deficits for the United States for surpluses (13), and such parameters ap- from 1960 to 1981. However, the real value pear in (15) only to the extent that they of government debt held by the public actu- could characterize rational expectations fore- ally fell during this period, indicating that casts of future surpluses. The high R2 is also the continuing reported deficits grossly mis- achieved despite the omission of all of the stated the true fiscal posture of the govern- additional variables besides past surpluses ment. We suggested an alternative measure that would be used by agents to forecast of the government deficit that takes into future surpluses. account revenues from monetization and Of course, to achieve such a fit to the data, capital gains on gold but excludes interest the regression is forced to fit strongly nega- payments. From the time-series properties of tive coefficients in the autoregressive process the adjusted deficit series, one can construct for surpluses at two- and three-year lags, as a rational expectations forecast of the pres- the values in Table 3 indicate. Bondholders ent value of future government budget sur- must assume that big deficits typically only pluses. Such a forecast series can account for last a year or two, and will later be balanced 53 percent of the observed variance of real out with surpluses. There is indeed moderate government debt under the assumption that support for this position in a completely the government budget must be balanced in unconstrained OLS estimate of the latter present-value terms. regression: If our conclusion on the limitations of government borrowing is correct, then the St=-0.30 + 0.62St1 prevailing sentiment in Washington that cur- (3.51) (0.23) rent deficits can continue forever is wrong; the adjusted deficit series must soon turn to -0.3OSt 2- 0.2OSt 3 ?2t+ surplus. One policy change that could turn (0.28) (0.27) the adjusted series to surplus would be a resurgence of money growth. The restricted rational expectations estimates of Table 3 simply exaggerate this fea- ture in the data. Overall, then, the present- REFERENCES value hypothesis seems to hold up quite well. Aschauer, David A., "Fiscal Policy and Ag- IV. Conclusions gregate Demand," American Economic Re- view, March 1985, 75, 117-27. 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