閤 Are Government Bonds Net Wealth? OR。 Robert J. barro The Journal of political Economy, Vol. 82, No 6.(Nov -Dec, 1974), pp. 1095-1117 Stable url: http://inks.jstororg/sici?sici0022-3808%28197411%2f12%2982%3a6%3c1095%3aagbnw%3e2.0.co%3b2-1 The Journal of political Economy is currently published by The University of Chicago Press Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/about/terms.htmlJstOr'sTermsandConditionsofUseprovidesinpartthatunlessyouhaveobtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the jsTOR archive only for your personal, non-commercial use Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.istor.org/iournals/ucpress.html Each copy of any part of a JSTOR transmission must contain the same copyright notice that ap on the screen or printed page of such transmission STOR is an independent not-for-profit organization dedicated to and preserving a digital archive of scholarly journals. For more information regarding JSTOR, please contact support @jstor. org Thu mar1522:34:002007
Are Government Bonds Net Wealth? Robert J. Barro The Journal of Political Economy, Vol. 82, No. 6. (Nov. - Dec., 1974), pp. 1095-1117. Stable URL: http://links.jstor.org/sici?sici=0022-3808%28197411%2F12%2982%3A6%3C1095%3AAGBNW%3E2.0.CO%3B2-1 The Journal of Political Economy is currently published by The University of Chicago Press. Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/about/terms.html. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/journals/ucpress.html. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is an independent not-for-profit organization dedicated to and preserving a digital archive of scholarly journals. For more information regarding JSTOR, please contact support@jstor.org. http://www.jstor.org Thu Mar 15 22:34:00 2007
Are Government Bonds Net wealth? Robert Barro The assumption that government bonds are perceived as net wealth by the private sector is crucial in demonstrating real effects of shifts in the tock of public debt. In particular, the standard effects of exp fiscal policy on aggregate demand hinge on this assumption. Government bonds will be perceived as net wealth only if their value exceeds the cap- alized value of the implied stream of future tax liabilities. This paper onsiders the effects on bond values and tax capitalization of finite lives, imperfect private capital markets, a government monopoly in the production of bond"liquidity services, and uncertainty about future x obligations. It is shown within the context of an overlapping generations model that finite lives will not be relevant to the capitalia tion of future tax liabilities so long as current generations are nected to future generations by a chain of operative intergenerational transfers(either in the direction from old to young or in the direction from young to old ). Applications of this result to social security and to other types of imposed intergenerational transfer scheme noted In the presence of imperfect private capital markets, government debt issue will increase net wealth if the government is more efficient at the margin, than the private market in carrying out the loan process Similarly, if the government has monopoly power in the production of bond"liquidity services, "then public debt issue will raise net wealth. Finally, the existence of uncertainty with respect to individual future tax liabilities implies that public debt issue may increase the overall risk contained in household balance sheets and thereby effectively re- duce household wealth The assumption that government bonds are perceived as net wealth by the private sector plays an important role in theoretical analyses of monetary and fiscal effects. This assumption appears, explicitly or im- plicitly, in demonstrating real effects of a shift in the stock of public debt I have benefited from comments on earlier drafts by Gary Becker, Benjamin Eden, Milton Friedman, Merton Miller, Jose Scheinkman, Jeremy Siegel, and Charles Upton. The National Science Foundation has su dgz bf The univesity of Chicag ain ri his reserved 095
JOURNAL OF POLITICAL ECONOMY (see, e.g., Modigliani 1961, sec. IV; Mundell 1971; and Tobin 1971 chap. 5),and in establishing nonneutrality of changes in the stock of money(Metzler 1951, sec. VI). More generally, the assumption tha government debt issue leads, at least in part, to an increase in the typical household,s conception of its net wealth is crucial for demonstrating a ositive effect on aggregate demand of"expansionary"fiscal policy, which is defined here as a substitution of debt for tax finance for a given level of government expenditure(see, e.g., Patinkin 1964, sec. XII. 4; and blinder and Solow 1973, pp. 324-25). The basic type of argument in a full- mployment model is, following Modigliani(1961), that an increase in government debt implies an increase in perceived household wealth ence, an increase in desired consumption(a component of aggregate finally, a decline in the fraction of output which goes to capital accumu g demand) relative to saving; hence, an increase in interest rates; an tion. However, this line of reasoning hinges on the assumption that the ncrease in government debt leads to an increase in perceived household lon-full employment context it remains true that the effect of bublic debt issue on aggregate demand(and, hence, on output and employment) hinges on the assumed increase in perceived household wealth It has been recognized for some time that the future taxes needed to finance government interest payments would imply an offset to the direct positive wealth effect. For example, in a paper originally published in 1952, Tobin(1971, p. 91)notes: How is it possible that society merel by the device of incurring a debt to itself can deceive itself into believing that it is wealthier? Do not the additional taxes which are necessary to carry the interest charges reduce the value of other components of private ley( 1962, pp 75-77)has gone somewhat further by arguing It is possible that households regard deficit financing as equivalent to taxation. The issue of a bond by the government to finance expenditures involves a liability for future interest payments and possible ultimate repayment of principal, and thus implies future taxes that would not be if th ditures were financed by current taxation If future tax liabilities implicit in deficit financing are accurately foreseen the level at which total tax receipts are set is immaterial; the behavior of the community will be exactly the same as if the get were continuousl There seem to be two major lines of argument that have been offered to defend the position that the offset of the future tax liabilities will be only partial. One type of argument, based on finite lives, supposes that Of course, most analyses of government debt effects do not offer a specific defense for this position. For example, Blinder and Solow(1973, p. 325, n 8)say: This [analysis ncludes government bonds as a net asset to the public. We are aware of. but not rsuaded by, the arguments which hold that such bonds are not seen as net worth by ndividuals because of the implied future tax liability
GOVERNMENT BONDS the relevant horizon for the future taxes(which might correspond to the remaining average lifetimes of the current taxpayers) will be shorter than that for the interest payments. 2 Accordingly, a stream of equal values for interest payments and taxes will have a net positive present value. This argument has been used explicitly by Thompson(1967, p. 1200). The ally based on imperfect tal markets, supposes that the relevant discount rate for tax liabilities will be higher than that for the interest payments. Hence, even with an infinite horizon for tax liabilities, a stream of equal values for interest payments and taxes will have a net positive present value. This argument has been used by Mundell(1971). 3 The first part of this paper deals with the effect of government bond issue on the calculus of individual wealth in an overlapping-generations economy with physical capital where individuals have finite lives. No elements of"capital market imperfections "are introduced into this model The key result here is that, so long as there is an operative intergenerational transfer(in the sense of an interior solution for the amount of bequest or ft across generations), there will be no net-wealth effect and, he effect on aggregate demand or on interest rates of a marginal change in government debt. This result does not hinge on current generations' weighing the consumption or utility of future generations in any sense on an equal basis with own consumption, nor does it depend on current generations' placing any direct weight at all on the consumption or utility f any future generation other than the immediate descendant. Current generations act effectively as though they were infinite-lived when they re connected to future generations by a chain of operative inter generational transfers The analysis then shows that social security payments are analogous to anges in government debt. Marginal changes in this type ( or other types)of imposed intergenerational transfers have no real effects when current and future generations are already connected by a chain of opera tive discretionary transfers, The effects of inheritance taxes and of transaction costs"for government bond issue and tax collections are also considered. It is shown that inheritance taxes do not affect the basic the net-wcalth effect of government bonds would actually be negaliathat results, but that the presence of government transaction costs implies The second part of the deals with the existence of imperfect private capital markets. It is shown that, to the extent that public debt This type of argument applies taxes or to taxes based on wage income, but not to taxes which are based on the of nonhuman assets. This distinction has been made by Mundell(1971, pp. 9, 10) a different line of argument that leads to a similar conclusion is that cts like a monopolist in the ion of the liquidity services yielded by its liabilities. I discuss this argument in part Ill, below
JOURNAL OF POLITICAL ECONOMY issue entails a loan from low-discount-rate to high-discount- rate individ- uals, a positive net-wealth effect results if the government is more efficient th e private market carrying out this sort of loan. If the government is more efficient only over a certain range, and if the public choice process determines the amount of government debt issue in accord with efficiency criteria, it is again true at the margin that the net-wealth effect of government bond issue is nil The third part of the paper discusses government debt as a bearer of nonpecuniary"liquidity services. It is shown that if the government acts like a competitive producer of these services, as would be dictated by a public choice process which reflects efficiency criteria, then the net wealth effect of government bond issue would be zero on this count. More generally, the net-wealth effect would be positive if the government acts like a monopolist and would be negative if the government is an overproducer of liquidity The last part of the paper deals with the risk characteristics of govern- ment debt and of the tax liabilities associated with the interest payments on this debt. It is argued that if relative tax liabilities are known, a change in government debt will not alter the overall risk contained in household balance sheets, When relative tax liabilities are uncertain, the effect of government debt issue on the overall risk may be positive or negative depending on the nature of the tax system and on the transaction costs associated with private insurance arrangement I. The Effect of Finite Lives-a Model with Overlapping Gener use here a version of the Samuelson(1958)-Diamond(1965)over lapping-generations model with physical capital. Each individual lives two periods, which will be distinguished by the superscripts y(young) and o(old). Generations are numbered consecutively beginning with the generation which is currently old(subscript 1); followed by its descendant which is currently young(subscript 2); followed by its descendant; and so on. I assume here that there are the same number of people, N, in each generation, and that all individuals are identical in terms of tastes and productivity. I also abstract from any technological change over time The members of each generation work(a fixed amount of time set equal to one unit)only while young and receive an amount of wage income we Expectations on w for future periods(i. e, for future generations)are ssumed to be static at the current value. Asset holdings(4)take the form of equity capital (K). Subsequently, government bonds are introduced as an additional form in which assets can be held. The rate of return on assets
GOVERNMENT BONDS denoted by r and is assumed to be paid out once per period. Expectations on r for future periods are assumed to be static at the current value. A member of the ith generation holds the amount of assets ay while young nd the amount a while old The asset holding while old constitutes the provision of a bequest, which is assumed to go to the immediate descen ant, a member of generation i 1. Since the focus of the analysis concerns shifts in tax liabilities and government debt for a given level of government expenditure, it is assumed for convenience that the govern ment neither demands commodities nor provides public services. In this section,it is also assumed that the amounts of government debt and taxes are zero. Using the letter c to denote consumption, and assuming that consumption and receipt of interest income both occur at the start of the period, the budget equation for a member of generation l, who is currently old, is A+A48=c+(1-r)A The total resources available are the assets held while young, Ai, plus the bequest from the previous generation, Ao. The total expenditure is con- sumption while old, ci, plus the bequest provision, Ai, which goes to a member of generation 2, less interest earnings at rate r on this asset holding The budget equation for members of generation 2(and, more generally, for members of any generation i 22) is, assuming that wage payments occur at the start of the young period =C+(1-r)A2 and, for the old period A2+A2=c2+(1-r)A2 a portion of the lifetime resources of a member of generation i goes to a bequest provision, Ai, which I assume is motivated by a concern for a member of generation i 1. This concern could be modeled by intro- ducing either the(anticipated)consumption levels or attainable utility of a member of generation i I into the utility function for a member of the ith generation. For the purpose of the present analysis, the crucial condition is that this utility depend on the endowment of a member of +I rather than, per se, on the gros distinction between the gross bequest and the net bequest, which deter- mines the endowment of i l, will be discussed below. So long as a member of generation i can transfer resources to a member of generation l only through the transfer of unrestricted purchasing power(which rules out the"merit good"case discussed in n 8 below), the two types of models of interdependent preferences--concern with consumption levels and concern with attainable utility-will be equivalent in the sense of
IIOP JOURNAL OF POLITICAL ECONOMY indirectly implying a concern for the endowment of a member of generation i+ I For present purposes, it is convenient to assume that the utility of a member of generation i depends solely on own two-period consumption cI and ci, and on the attainable utility of his immediate descendant, Ui+ I The asterisk denotes the maximum value of utility, conditional on giver values of endowment and prices. Hence, the utility function for a member f the ith generation has the form U;=U4(c,cU*1) Subsequently, I consider the implications of entering the attainable utility of a member of the previous generation, Ui-I, as an additional ent Each member of generation I determines his allocation of resources to maximize U,, subject to equations (1)-(4)and to the inequality conditions,(ci, ca, 4920 for all i. The key restriction here is that the bequest to the member of the next generation cannot be negative. The choice of bequest, subject to this restriction, takes o v1, and the chain of Ai on generation 2's resources, the impact of U> or dependence of U2 on U3, of U3 on U4, etc. The solution to this problem will take the general for c"=c(A+A8,,r) (A1+A8-c)=A(4+A8,c,r) Similarly, for members of generation 2(and, more generally, for members of any generation i 22), the solution would take the form c2= c2(A1, w,r), Ai c=c(42+AB,c,r), (A2+A-c2)=A2(4 A member of get with the at generation i can attach a ce of his descendant. further it indiffer pposed that hich makes it comparable to cl and f in terms of generating U, in the form of ca rface dependent preferences in Becker(1974, sec. 3.A I have not imposed the condition, A120, so that young individuals are allowed issue interest-bearing debt on themselves. Ifissued, these debts are assumed to be perfec substitutes for equity capital. These debts correspond to the consumption loans which have been discussed by Samuelson (1958)
GOVERNMENT BONDS The model can be closed, as in Diamond(1965, pp. 1130-35), b specifying a constant-returns-to-scale production function that depend of capital and labor the products of capital and labor to r and w, respectively. The value of r for the current period would then be determined in order to equate the supply of assets to the demand-that is K where K(r, w) is such as to equate the marginal product of capital to r The current demand for assets, A1+ A,, depends, from equations (5 and(6), on r, w, and the previous periods value of K, which is equal to A1+ Ao. Since the number of people in each generation is assumed to equal a fixed number N, it is not necessary to enter this number explicitly into the aggregate asset demand in equation (7). Similarly, N is omitted from the aggregate formulations below. Since N is constant and technical change is not considered, the current and previous periods'values of K would be equal in a steady state With the marginal product of labor equated to we and with constant returns to scale, output is given by y=rk+w Equations(2),(3),(7), and(8) imply a commodity market clearing where Ak denotes the change in capital stock from the previous to the current period. The value of AK would be zero in a steady state, but the present analysis is not restricted to steady-state situations Suppose now that the government issues an amount of debt, B, which can be thought of as taking the form of one-period, real-valued bonds. These bonds pay the specified amount of real interest, rB, in the current period and the specified real principal, B, in the next period. It supposed that asset holders regard equity and government bonds perfect substitutes. It can be assumed, for simplicity, that the government bond issue takes the form of a helicopter drop to currently old (generation 1)households. Equivalently, it could be assumed that the bonds were sold on a competitive capital market, with the proceeds from this sale used to effect a lump-sum transfer payment to generation I households amount of bond issue would be limited by the government's collateral, in the ense of its taxing capacity to finance the interest and principal payments(see n. 12
I IO2 JOURNAL OF POLITICAL ECONOMY Allowing some portion of the proceeds to go to generation 2 households would not alter any of the basic conclusions The future interest payments on the government debt must be financed in some manner. Further, the principal may eventually be paid off- that is, the government may not reissue the bonds when they come due in the next period. I assume, provisionally, that the current periods interest payments are financed by a lump-sum tax levy on generation 2 householdswhile young), and that the principal is paid off at the begin- ning of the next period by an additional lump-sum tax levy on generation 2 households (while old ). In this setup there is no direct effect of the overnment debt issue and its financing on generation 3 and later gene.o tions. I examine, subsequently, the implications of imposing some part the taxes on generations of the more distant future. The generation 1 budget constraint is now A1+A8+B=c"+(1-)AB, where B represents the lump-sum transfer payment, which is assumed to occur at the beginning of the period, For generation 2, the current budget constraint is now =+(1-)A2+rB where rB represents the tax levy for the government interest payments The next periods budget constraint for generation 2 is now A2+A=c+(1-r)A+B, where B represents the tax levy for repayment of principal. The two constraints on generation 2 can be combined into a single two-period x+(1-r)A-B=C+(1-n)2+(1-r)2A2.(12) The form of equation(12)implies that the utility attainable by a member generation 2 can be written in the indirect form U/=f2*[(1-r)4-B,t,r], (13) hat is,the“ net bequest,”(1-n)A-B, determines the“ endowment for members of generation 2 From equation(10), it is also clear that ci varies inversely with (1-r)Ai-B for a given value of Ai+ Ao. Hence, given the pre- determined value of ci, and using equations (4),(10), and (13),U,can be written in the form f1[(1-n)4-B;c},A+48, For given values of ci, Ai+ Ao, w, and r, the choice problem for members of generation 1 amounts to the optimal selection of the net bequest
GOVERNMENT BONDS IIO (1-r)Ai-B, subject to the constraint that the gross bequest, Ai,be nonnegative. In particular, if the solution to this problem is associated with a value of Ai in the interior--that is, if the constraint, Ai 20,is not binding-any marginal change in B would be met solely by a change in Ai that maintains the value of the net bequest,(1-r)Ai-B. Thi response in Ai will keep unchanged the values of co, c2, c2, and A2 ence, the utility levels attained by members of generations 1, 2, etc. ill be unaffected by the shift in B In terms of the effect on r, the current asset market clearing condition of equation (7)would now be modified to The increase in B implies a one-to-one increase in the asset supply on the left-hand side of equation(14). However, Ai rises by 1/(1-r) times the change in B in order to maintain the size of the net bequest, (1-r)Ai-B Further, with c2 fixed, the increase in rB(taxes)in equation(11) implies that Al falls by r/(1-r) times the change in B. On net, total asset demand on the right-hand side of equation(14)rises one-to-one with B, so that no change in r is required to clear the asset market. Equivalently, he commodity market clearing condition, as expressed in equation(9) continues to hold at the initial value of r because the bond issue has no impact on aggregate demand Essentially, a positive value of B, financed by a tax levy on the next generation, enables a member of the old generation to"go out''insolvent by leaving a debt for his descendant. However, if, prior to the government bond issue, a member of the old generation had already selected a positive bequest, it is clear that this individual already had the option of shifting resources from his descendant to himself but he had determined that such shifting, at the margin, was nonoptimal. Since the change in B does not alter the relevant opportunity set in this sense, it follows that--through the appropriate adjustment of the bequest--the values of current and future consumption and attained utility will be unaffected. On the other hand, if a member of generation I were initially at a corner where Ai=0-in particular, if Ai<0 would have been chosen had it been permissible-then an increase in B creates a relevant new opportunit In this situation a generation I household would react by increasing ci along with B, as long as the corner solution for Ai still applied. The upward shift in B would then correspond to an excess of earning-asset upply over demand (even after taking account of a shift in A2), which would tend to raise the value of r. This increase in r would induce a drop in capital formation, which constitutes the real effect of government debt issue which has been described by Modigliani( 1961). However, the main point is that the existence of this government debt effect hinges on a non-
