The political economy of public debt

ORI GIN AL PA PER

The political economy of public debt

Geoffrey Brennan

Published online: 29 June 2012

� Springer Science + Business Media, LLC 2012

Abstract Public debt (as opposed to current taxation) alters the inter-temporal

pattern of tax rates—it reduces current rates and increases future rates. Accordingly,

whether the share of the cost of a given public expenditure is reduced or increased

by debt for a given individual depends on the time profile of that individual’s

income (tax base) vis-a-vis others’ incomes. Therefore, given the age-profile of

income in virtually all Western countries, individuals will tend to be better off under

current taxes the younger they are. If (as most standard models of political economy

assume) individuals vote according to their economic interests, and if they are

tolerably well-informed, then the pattern of support for public debt will track age.

And increases in the median age of the population will lead to larger public debt. In

other words, public debt policy collapses to a kind of demographic politics. This

explanation may, however, be sensitive to assumptions about motives for bequest.

Specifically, if bequestors seek to leave positive bequests and are motivated

exclusively by the lifetime consumption of their heirs (as well as themselves) then

the aged may, under plausible assumptions about the age of their heirs, prefer

current taxes over debt.

Keywords Public debt � Age-income profile � Median voter theorem

Author is grateful to Michael Brooks and Alan Hamlin for comments on earlier drafts. Their comments

bore especially on a piece of ‘‘Mickey Mouse’’ econometrics that appeared in earlier versions and that I

refer to in Sect. 4, but which is now mercifully excised!

G. Brennan (&)

Political Science, Duke University, Durham, NC, USA

e-mail: [email protected]

G. Brennan

Philosophy, UNC-Chapel Hill, Chapel Hill, NC, USA

G. Brennan

Philosophy, Australian National University, Acton, ACT, Australia

123

Const Polit Econ (2012) 23:182–198

DOI 10.1007/s10602-012-9124-5

JEL Classification H63 � H68 � D72

1 Throat-clearing

It is stating the blindingly obvious that public debt is a hot topic in the popular press.

The market interest rates on new raisings of Italian and Spanish public debt have

recently been headline news; estimates of the long-run net indebtedness of the

Greek fisc (leaving out of account the market value of the Parthenon and similar

Greek ‘‘assets’’) are updated daily, even if most commentators have assigned Greece

to the ‘‘basket-case’’ category; battles within the US political system over debt

limits have reached often hysteric proportions (and not only within ‘‘tea-party’’

circles).

It is easy enough to understand the anxieties that all this coverage represents. The

Global Financial Crisis has meant that tax revenues are in decline just at the very

time when there is strong political pressure from many quarters for ‘‘recovery

packages’’ of various kinds. To maintain public spending even at pre-existing levels

would require either tax rate hikes (widely thought to be unthinkable on macro-

economic grounds) or increased debt. And in order to undertake fiscal stimulus in

order to offset the reduction in private demand—whether in part or whole and

whether implemented by tax reductions or expenditure increases—yet further debt

will need to be secured.

None of this would amount to ‘‘a crisis’’ if it were not for the fact that most fiscal

systems entered the GFC with already rather high levels of accumulated debt—

levels that in some cases (the Greek, say) proved unsustainable and whose

sustainability in other cases seems at least to be highly questionable. On this basis,

the interesting aspect of the current situation is not so much the ‘‘flow’’ question as

the ‘‘stock’’ question—not so much the fact that the GFC has had significant fiscal

implications but rather the puzzle that, over an extended period of relative

prosperity and healthy growth, public debt accumulated in so many Western

economies to such dangerous proportions. It is this ‘‘stock’’ issue with which I shall

here be concerned—the explanation of public debt levels under more or less

‘‘equilibrium’’ conditions.

Any such explanation is clearly an exercise in political economy. And here I want

to explore what would be at stake in applying the standard median voter apparatus

to the analysis of public debt. As it happens, I have deep conceptual misgivings

about the usefulness of that model—misgivings that I will mention briefly at the

beginning of Sect. 3. However, in this paper, I want to set such misgivings aside and

simply pursue the logic of that simple model as far as it can usefully go.

There are three basic steps in the discussion. The first is to establish the likely

distributional effects of debt financing. This is essentially a task in the ‘‘economics

of public debt’’ and it will occupy me in Sect. 2.1

1 Of course, there are reasons for interest in the ‘‘economics of public debt’’ that go beyond any

attempted explanation of its levels. For example, the distributional consequences of public debt are a

significant element in assessing debt’s normative implications—for example, the question of whether or

not debt serves to ‘‘pass on’’ to (non-enfranchised) future generations the cost of current public spending

The political economy of public debt 183

123

In the political application (Sect. 3) the main object is to incorporate into the

economic discussion certain simple generalizations about the age-distribution of

earnings; this serves, under standard median voter assumptions, to transform the

public debt incidence question into an issue about demographic politics. Sections 2

and 3 form the analytic core of the paper; but I include in Sect. 4 a brief discussion

of the empirical literature on this question. Section 5 draws some simple

conclusions and offers some speculations based on what the paper suggests.

2 The economics

2.1 A brief history of public debt doctrine

The history of doctrine about public debt makes an interesting study. I do not intend

here to do more than trace its basic lineaments (and this only because doing so is

broadly helpful for my purposes). But there is, I think, a broader message

concerning the role of the ‘‘history of thought’’ in economics and an implied lament

for the decline of its study in what passes for ‘‘serious’’ economic education.

For a start, the last 60 years have been something of a roller-coaster ride in terms

of the content of the prevailing professional consensus. The literature is littered with

confident utterances of the kind: ‘‘well, we now know …’’, or ‘‘the latest researchshows…’’—which turn out to be reversed by professional consensus in relatively

short order. A little awareness of that trajectory is a good antidote to excessive

confidence about where professional consensus happens to currently lie.

The story is also full of episodes2 in which insights of earlier scholars were

rediscovered (sometimes consciously, sometimes witlessly), wheels re-invented,

earlier mistakes repeated—episodes of a kind that have the effect of heartening

older scholars and buttressing us against the contempt of our younger colleagues!

In many cases, it is not exactly that what was taken as incontrovertible turned out to be

wrong—often enough, the scholars of the time provided the right answer to what was later

Footnote 1 continued

and (hence?) whether or not debt-financing leads to ‘‘excess’’ public spending. These same considerations

also bear on the question as to whether (and to what extent) debt-financed public expenditure increases

can be expansionary in a macro-economic sense. These issues are, needless to say, of considerable

interest. But they are not my primary concern here. I want to begin by laying out what I take to be the

‘‘best theory’’ of the economic effects of public debt and use the results as an input into a political

analysis of public debt, along entirely conventional ‘‘public choice’’ lines. One can (and I do) have serious

doubts about the empirical relevance of certain of the assumptions that are involved in this chain of

reasoning. But I share a prejudice widely shared in the economics profession that the best way of

exposing dubious assumptions is by being totally explicit about the assumptions being made.2 I hint at these episodes in the footnotes. Buchanan’s rediscovery of the ‘‘Italian view’’ arose as a result

of a serious effort in intellectual history. Barro’s ‘‘rediscovery’’ of the Ricardian equivalence theorem by

contrast seems to have been entirely accidental. The Barro/Ricardo episode does not of course show that

the study of the history of one’s own discipline in the best professional training is ‘‘optimal’’: that depends

on what alternative objects of study are forgone in the process. Still, these episodes raise questions about

the almost universal decline in ‘‘History of Economic Thought’’ in graduate programs—and certainly

about the widespread professional confidence that the heroes of the discipline’s past have little to teach

us.

184 G. Brennan

123

perceived to be the wrong question. And that fact too is instructive, because it reminds us

that identifying the right question is itself a significant intellectual accomplishment. (And

incidentally an awareness of what past economists have taken the ‘‘right questions’’ in the

discipline to be, seems important for practising professionals—even if we are now

confident that we now have the right quarry in our sights.)

The history divides itself conveniently into three phases, each of which can be

conveniently summarized in terms of several core propositions that that school of

thought took to be both valid and centrally relevant.

a. 1945–1960, the Keynesian heyday:

i. There is no real burden associated with (internal) public debt. The real

burden occurs at the time when the expenditure is made: it is at that time

that real resources are used up.

ii. Internal debt is ‘‘debt we owe to ourselves’’. It adds nothing to our real

resource base. External debt is different: it does add real resources to the

economy, and those resources will have to be repaid some time.

iii. Substituting public debt for current taxation has an immediate macro-

expansionary effect: an increase in public expenditure financed by a tax

increase is expansionary, but less expansionary than if that public

expenditure increase were debt-financed. Indeed, in macro terms, public

debt involves no contractionary force whatsoever—debt-financed public

spending is ‘‘free’’ in macroeconomic terms.

b. 1960–1974, the Buchanan ‘recovery of the Italian theory’3:

i. Debt involves a postponement of the burden of taxation to future

generations (future time-periods). There can be no burden at the time

when the expenditure is made because bond-purchasers act totally

voluntarily. The burden must be borne in the future when coercive

taxation is levied to service and redeem the debt.

ii. ‘‘We owe it to ourselves’’ is an exercise in false aggregation—the ‘‘we’’

who owe and the ‘‘us’’ who we owe it to are both in principle and in

practice different persons.

iii. Internal debt and external debt are the same in this respect: all debt has to

be repaid (or perpetually serviced if not repaid) whoever holds the debt

instruments.

iv. Because future taxpayers are not around to defend their interests, public

expenditure will be predictably higher under debt-financing. More

generally, debt-financing is a violation of basic democratic principle. It

off-loads the cost of current expenditures onto the shoulders of a

necessarily un-enfranchised future.4

3 Buchanan’s ‘‘conversion’’ to the Italian view, as he came down the stairs of the Hotel Angleterra, (after

some months of studying the Italian literature on the subject) makes a wonderful story. But his realisation

that the Italians were right and the Keynesian orthodoxy quite wrong reveals that up to that time he had

more or less endorsed the Keynesian view. On this and more generally see Buchanan (1958/1999).4 A nice collection of the literature up to that point is contained in Ferguson (1964). The literature is now

vast.


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c. 1975?: Barro’s rediscovery of Ricardian equivalence5:

i. Debt involves an inter-temporal shift in the timing of tax payments; but if

agents are rational, that inter-temporal shift will have no effect on their

behaviour. Each will fully capitalise the future tax liabilities she faces into

the present and spread the liability optimally across her total time-horizon

independently of when the liability falls.

ii. This result might be modified if agents have finite time horizons. But, the

present is attached to the future either because each member of the current

generation is one of the future taxpayers or because as a bequestor each

dollar’s worth of reduced consumption by heirs is equivalent at the margin

to a dollar’s worth of reduced own-consumption. Infinite horizons can

therefore be assumed.

iii. Any real effect (including macro-stimulation) arising from debt financing

(as distinct from tax financing) is a result of ‘debt-illusion’—and

rationality rules out any such illusion.

My sense is that the prevailing consensus is that Barro’s logic is basically right—

and that the debate revolves now around two questions:

First, whether and to what extent there is debt-illusion6;

Second, whether and to what extent the Barro analysis depends on specific

assumptions about individuals’ bequest motives (and how plausible these

assumptions are).

I shall have something to say about the second of these questions in Subsect. 2.3

below. My initial task, however, is to focus on Barro’s logic in the infinite horizon case,

and in abstraction from complications that arise from a specific treatment of bequests.

Basically, I believe that Barro approaches the question of public debt incidence

by the wrong question. The issue of debt incidence is not settled according to

whether government bonds represent real net wealth or not. I concede the Barro/

Ricardo observation concerning the effects on the inter-temporal net consumption

pattern of the timing of a given, fixed tax liability. A fully rational agent will

respond to a tax bill equal to the present value of $100 at some point later in her life

in the same way as she responds to a tax bill of $100 now. Or at least, so for present

purposes I shall assume.

However, what is significant about debt-financing is not that it alters the time

profile of tax payments: what is significant is that it alters the time profile of taxrates! And recognition of this simple fact makes obvious the inter-temporal

substitution effects to which debt-financing gives rise. Isolating those substitution

effects was the task Buchanan and I undertook in Brennan and Buchanan (1980). I

shall briefly rehearse the argument contained in that paper in what follows.

Before doing so, however, it is useful to emphasize the precise comparison that is

at stake. Throughout, the analytic framework involves assuming a given expenditure

5 See Barro (1974) and Ricardo (1820).6 Ricardo himself thought the equivalence theorem was ‘valid in theory’ but false in practice: in other

words, Ricardo believed in debt-illusion. Barro, I take it, does not.

186 G. Brennan

123

project and poses the question: what is the difference between financing that given

expenditure from debt as distinct from current taxes? This approach explicitly

finesses questions about the level of expenditures. It may be that public expenditure

levels are likely to be higher if debt-financing is used: but if so, that is a result that

will follow from the analysis. Specifically, if Ricardian equivalence prevails, then

tax financing and debt financing will produce identical public expenditure levels.

2.2 The Brennan-Buchanan model

Consider the following simple model.

There are two periods (present and future).

There is a given public expenditure, which is to be financed either by current

taxes or debt. In the debt case, the taxes will be paid in the future period. So

taxation means a tax rate profile [t*c, 0]; while debt means a tax rate profile

[0, t*f] where t*c and t*f raise the same present value of tax revenue.

The tax is a proportional income tax.

Initially assume that all taxpayers live across both periods (so that the question of

inter-temporal transfers is strictly an inter-temporal one. We shall examine the

inter-generational case briefly below.)

Begin by considering the incidence of the time-profile of tax rates; and do this by

focusing initially on just two individuals: the training architect, A; and the

professional boxer, B. A is currently a university student with low current income

but high expected future income. B has high current income, but boxers only have

an effective life of 10 years. B’s future income will be much lower than his current

income. If the tax is imposed currently, A will pay little tax and B will pay a lot. If

the expenditure is debt financed, A will pay a lot of tax; and B will pay a little.

More generally, the change in the time profile of tax rates alters the cost-sharing

arrangements for the public expenditure across persons according to the time profile

of their respective tax bases (in this case, their incomes).

If there is no debt illusion, all citizens will fully discount the future tax liabilities

they face (as in the Barro-Ricardo model). But notice that under debt financing, it

will be better for each individual to be more like B and less like A—better, that is,

for each individual to move income into the current period away from the future

period. This means that there are diminished incentives to acquire human capital.

And any reduction in human capital means that everyone in the future will tend to

be worse off than they would have been under the current tax option. Debt financing

affects the total capital stock, making that stock lower than it would have been if the

expenditure had been financed out of current taxation.

The same basic story could perhaps more tellingly be told for the case of a

proportional consumption tax. The ratio of current to future tax rates [tc/tf] is lower

under the debt option than under the current tax option: if the consumption tax rate

is lower now and higher in the future, that tax rate effect will encourage higher

consumption now and lower consumption in the future—not via some perceived

current ‘income effect’ (as might be associated with government bonds being


123

perceived to be net wealth) but via a totally non-illusory substitution effect towards

the present and away from the future.

2.3 The bequest motive?

To the extent that taxes to service and redeem the debt fall at a point beyond the

current generation’s death, the effects of debt financing will depend on bequest

motives. In that sense, the fact of finite lived agents transforms the debt question

from a purely inter-temporal matter into a genuinely inter-generational one.

There are three cases here to consider.

1. The current voter/taxpayer has no bequest motive at all: his object is simply to

maximize his own lifetime consumption. Such an agent will prefer debt to taxes;

and will prefer debt more strongly the closer to death he sees himself to be.

2. The lifetime consumption of heirs is an argument in the current voter/taxpayer’s

utility function. That is, the current voter/taxpayer has a utility function of the

form:

U ¼ f Ca;Ca0ð Þ ð1Þ

where Ca is own lifetime-consumption and Ca’ is heir’s lifetime-consumption.

If each successive generation has a utility function of this form, this formula-

tion is sufficient to give the current taxpayer an effectively infinite horizon. In

this case, the earlier analysis extends directly. There is no difference between

inter-temporal and inter-generational effects. Note that this formulation does

not require that the taxpayer cares for his heirs a great deal—the bequest in

question may be quite modest. The point is rather that in equilibrium a dollar’s

worth of heir-consumption (net of taxes) will be worth the same as a dollar’s

worth of net-of-tax own-consumption at the margin. If that is so, then the

substitution effects that previously had a purely temporal aspect can be

expressed in terms of bequest incentives. If [as debt financing implies], heirs’

consumption is more heavily taxed (and own consumption more lightly taxed)

than otherwise, then the rational agent will reduce her bequests and increase her

own lifetime consumption. Note however that these effects do not depend on a

desire on the part of the current generation to leave a negative estate. Even

agents who desire that their ‘‘kids have it better than we did’’ will rationally

respond to the inter-temporal substitution effects to which debt financing gives

rise.

3. The bequestor makes bequests from a desire to have his estate as large as

possible, ceteris paribus. The relevant utility function is:

U ¼ g Ca;Eð Þ

where Ca is as in (1) above and E is the size of the estate.

Here, debt financing allows E to be higher than it otherwise would be, but not

high enough to fully compensate for the future tax liability that is embodied in

the debt. This is because some of the current tax reduction is ‘spent’ by the

taxpayer in increasing his own lifetime consumption.

188 G. Brennan

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Arguably, the most plausible form of this third motive is in combination with 2.

The advantage of the melded version is that it shows us that observation of a

positive estate, distributed to specified recipients, does not allow us to induce

effectively infinite horizons. Put another way, the current agent does not need to

have zero bequest motives in order for tax payments beyond his death to have

less concern to him than tax payments within his life.7

In the Barro model, the assumption seems to be that bequest motives are

exclusively of type 2. And here again, I shall follow what I take to be the Barro

orthodoxy. My claim is that, within that framework, it is simply not the case that

debt and current taxes have identical effects. Debt involves imposing a tax liability

on individuals according to their relative income levels when the debt is serviced/

redeemed; current taxes impose a liability that reflects current relative income

levels. Fully rational and perfectly informed individuals will recognize this fact and

rationally respond by shifting income (or tax base, more generally) into the low tax-

rate period: in other words, there will be inter-temporal substitution effects in

response to the debt-tax substitution.

[Although it is incidental to my purposes here, those substitution effects seem to

be in a direction consistent with Keynesian presumptions—namely, debt encourages

higher current income and higher current consumption than current taxes would.

The ‘stimulus’ effects of debt financing may be rather smaller than the Keynesians

assume and arise from rather different sources—but there is certainly analytic space

for them within the general Barro framework (fully rational and fully informed

agents, with the relevant bequest motives).]

2.4 Debt illusion?

What the foregoing model serves to show is that whether there is debt illusion or

not, debt financing will involve reduced capital accumulation (and/or reduced net

7 It may seem that this kind of mixed case requires some psychological justification. Why would A desire

to make bequests if it was not (exclusively) for a concern to leave heirs better off, one might ask. One

response to this question is to simply deny its validity: utility functions, one might respond, are just a

device for imposing order on behavior and any attempt to rationalize them psychologically involves a

kind of mistake. I do not myself take this view and those who share my dissatisfaction with this

behaviourist line are invited to read on.

Consider J who has four children. J wants to divide his estate equally among them because J wants to

signal to his children that they are equally loved: J wants to avoid the possibility that any differences in

bequest might be interpreted as signs of differential affection or concern. But J recognizes that some of

his children are likely to do better financially than others. Or perhaps there is just uncertainty about how

they will fare. And he would like the ones who do less well to get more from the estate. Public debt allows

J to meet both ends. This is because any public debt (under say a proportional income tax) gives a

contingent liability to heirs—one that will reflect what their income levels are. So if he can bequeath a

larger estate in monetary terms plus public debt, he can give to each child the average of the tax liabilities

that each will face. The children that flourish financially will do less well (bequest minus taxes paid) out

of the estate than the children whose future income profile is lower. In other words, J would prefer a larger

estate plus larger public debt (with the associated income related liability) than a smaller estate with no

future income related liability. The ‘‘reduced form’’ of this motive is that he prefers a larger estate as if for

its own sake.


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bequests) and hence lower aggregate income in future periods compared with thetax alternative. In other words, debt illusion is not required for the proposition that

public debt leaves future generations worse off than they otherwise would have

been. Indeed, the effects of debt illusion are ambiguous: debt illusion weakens the

substitution effect as it creates a perceived income effect.

The analysis takes no stand on the question of whether debt illusion exists or

whether on balance greater debt illusion means that things are worse for the future

or better. My own guess is that the substitution effects are small compared with

the income effects—so that more debt illusion means greater fiscal impact and

worse outcomes for the future but as the B–B model shows, the effects are

ambiguous.

One might ask then: does debt illusion make any real difference? Perhaps not for

the lot of future generations; but it does seem to make a difference for the level of

public spending. Recall that in the analytics of the B–B model, the first-round

assumption is that spending is fixed. Question: do the effects of debt-financing in

that model have any implications for the perceived cost of public spending? Is there

any reason to think that public spending will be higher under debt than under

current taxation? In the B–B model (and the Barro model whose assumptions B–B

borrow), the answer seems clearly no. There are no grounds for thinking that debt-

financing will encourage extra public expenditure. After all, taxpayer/citizens fully

recognize the future tax liabilities embodied in debt-financing: they recognize that

more expenditure will mean a heavier burden for themselves or their heirs equal to

the cost of the expenditure in question. To secure the over-spending result, debt-

illusion (or negative bequest motives) seem to be required. In that sense, it seems

clear that the original Buchanan (1958) analysis—and the earlier Italian tradition

from which that treatment derives—did assume debt illusion, of considerable

magnitude. The B–B model of 1980 should be seen then not as Buchanan’s

preferred model of public debt incidence, but rather as an ‘‘even if’’ response to the

Barro/Ricardo approach. And I offer the following median voter extension of that

model in the same spirit. The idea is to take the full Barro model, with zero debt

illusion and bequests conceived in the ‘‘heir-consumption’’ model [(2) above], and

investigate the implications for the ‘‘political economy of public debt’’ on that

basis.

There is one observation that can be offered in partial defence of the zero illusion

assumption. It seems to me plausible to conjecture that the extent of debt illusion is

itself a function of the level of debt. In particular, in the current climate, with much

anxiety about the capacity of sovereign governments to meet the tax liabilities

embodied in existing debt (let alone in any debt expansions), there are probably few

persons who harbour the illusion that debt is somehow free in the long run! Indeed

to the extent that marginal debt increases have significant effects on the interest

rates that have to paid on debt re-financing, the costs of debt can become highly

salient in the quite short term. In this sense, debt illusion may be a thing of the past.

That said, in the long process by which present debt levels were accumulated—in

the more or less normal circumstances with which I am primarily concerned here—

debt-illusion may well have been much more widespread.

190 G. Brennan

123

3 The politics

It is an insight of conventional public choice theory that the information gathered

about the distributional consequences of policies can, under certain conditions, be

mobilised to explain their political success. The ‘‘under certain conditions’’ proviso

is worth emphasizing, because the conditions in question are in my view formidable.

Specifically:

There has to be enough structure in the choice context that electoral

equilibrium is well-defined (i.e the dimensionality of the political domain has

to be restricted to one, so that global cycling problems don’t arise);

The ‘principal-agent problem’ that characterizes all systems of representative

government has to resolve itself in favour of the citizen-principals. Otherwise,

it is the preferences/beliefs of the political agents that are the predominant

determinants of policy—voters’ preferences will play at best a subsidiary role;

The electoral preferences have to track individual interests sufficiently closely.

That is, the ‘‘expressive’’ challenge to the conventional public choice account

of electoral preference must be disposed of (or finessed). And rational

ignorance problems must not be so great as to undermine voters’ assessments

of where their interests lie.

It is no secret8 that I consider these conditions a very major challenge to much of

conventional public choice theory—particularly the part that deals with empirical

applications, where the median voter theorem is the primary mechanism for

deriving detailed hypotheses about specific policies. Still, how deep these

challenges bite is in some measure an empirical question. And the B–B model

admits of a relatively straightforward extension to median-voter analytics.

Accordingly, the aim of this section is to pursue that extension, bearing in mind

the restrictive assumptions of the original B–B model and the additional

considerations that bear on the ‘‘public choice’’ aspects specifically.

The feature of the world that makes the extension straightforward revolves

around the age distribution of earnings. That is, the age-profile of earnings (and

thereby of income) is a systematic feature of developed economies. Typically

earnings increase with age to a maximum at or shortly after age 50 and falling

slightly thereafter until retirement age at which point it is basically zero. The age

profile of income largely tracks that earnings profile over the earlier years, but of

course, as earnings and age increase, savings increase and so the income from assets

increases. Toal income (earnings plus income from assets) falls at retirement; but

not to zero. My understanding is that the variance around this age-profile of income

is quite small. Some very tiny proportion of the population at the very top income

levels depends hardly at all on labour income, but for present purposes this group

can be ignored. On this basis, I depict a stylised version of the standard age-

earnings-profile in Fig. 1. Total income rises reasonably steeply to age 53, increases

8 Brennan and Buchanan (1980a) deals with the second. Brennan and Lomasky (1993) deals with the

third.


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only slightly to retirement age (at around 65) and falls to a constant lower level at

that point.

For simplicity, I am going to treat the debt/tax choice as if debt were perpetual.

The assumption is that all public debt is continuously refinanced, so that the choice

between tax and debt is a choice between tax now and a revenue- equivalent

perpetual tax sufficient to service all future debt interest. We can, however, still

conceive of the basic choice of individual voters in terms of a two-period [present/

future] model, in which each agent is voting in terms of her ideal time-profile of tax

rates. Future income here is simply the average of income levels over the indefinite

future.

Suppose initially that all individuals were the same age and therefore had the

same time-profile of income. This would mean that their tax-cost-share in any

public expenditure would be independent of time. Note, however, that in that case,

individuals would not be indifferent as to when tax rates were imposed. All would

prefer to ‘‘tax smooth’’, reflecting the fact that the ‘‘excess burdens’’ (‘‘welfare

costs’’) of the tax system are a convex function of the tax rate.9

In fact of course, at any time the electorate is composed of persons of different

ages. And the tax burden each will face over her lifetime will be a function of the

time profile of tax rates. If tax rates are higher when my income is in its low phase,

then I will bear a smaller share of the total tax burden than if the tax is levied in my

high-income years. The share of individual j in the cost of the marginal expenditure

is Ycj /RYc if tax-financed and Yf

j/RYf if debt-financed. The ratio of debt burden to

Age

Income

RH D

Ave lifetime incomeMax Ave future income

Fig. 1 Lifetime age-income profile

9 The motivation for tax smoothing here is somewhat different from that canvassed in Barro (1979) and

Lucas and Stokey (1983). The approach taken in both these papers is an aggregative one; and at least in

the first instance, is within the standard normative framework of the ‘socialist-planner’/‘benevolent

despot’. Barro believes that the model might be extended to a long-run descriptive analysis of government

response to aggregate tax-base fluctuations. But to the extent that that could be so, it does not seem to

involve any appeal to the individual level phenomena that are my focus here. To underline the difference

note that in the Barro setting, the object is to keep tax rates constant, whereas in the B–B setting the

relation between desired tax rate and income is negative: when my income goes up I want a lower tax rate

ceteris paribus because that is how I minimize my individual life-time tax liability!

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tax burden is Yfj/Yc

j divided by the aggregate growth of income, RYf/RYc, which is

common across all individuals. Because my interest here is with age-specific effects

rather than common effects, it will be an appropriate simplification to abstract from

generic growth entirely. [I believe that this abstraction has no implications for the

comparative static propositions that are the ultimate product of the treatment here.]

Given zero aggregate growth, j will prefer a tax-rate mix such that tf [ tc if Yfj/

Ycj \ 1 and tf \ tc if Yf

j/Ycj [ 1. In short, the preferred ‘time tax profile’ for each age

will be a function of income now compared with average income over that agent’s

future (including heirs’ incomes).

Calculating the future average income is slightly tricky. It depends, of course,

both on own-age and the expected age of one’s heirs. Over own lifetime, average

future income rises with age to a point illustrated by age H in Fig. 1. At that point,

average income over the remainder of life is at its maximum. But only if the age of

one’s heirs is expected to be precisely H will heirs’ future lifetime income be the

same as own future lifetime income. If one’s heirs (at own death) are older than H

then their expected lifetime income will be below that at H; and if they are younger,

it will be below that at H. There is in short an age somewhat less than H at which

present income and effective average-indefinite-future income are equal. At that

age, the voter-taxpayer will be indifferent between current taxation and debt. Below

that age, the individual will prefer that future tax rates be lower than present ones.

Between the ages of H and R (retirement) the individual will prefer that the current

tax rate be lower than future. And over the age range from R to D (death), the

individual will prefer current tax rates to be higher than future tax rates, because

heir’s expected income is higher than own-income over this age range.

On this basis, we derive the ideal tax rate ratio, tc/tf, for each age group—as

indicated in Fig. 2. And we can illustrate the crucial role of the bequest assumption.

If agents have bequest motives of either types 1 or 3, then the desired tax-rate profile

will simply fall with age. In that case, the median debt-preference will correspond to

that of the median age of the voting population. The older is the median voter the

lower will be her desired (tc/tf)—the more she will prefer taxes to be postponed to

the future.

And this fact immediately gives rise to two comparative static propositions:

(i) as the median age of voter/taxpayers increases so does the electoral preference

for debt over tax financing ceteris paribus;

(ii) countries with a higher median age of the voting population will have a

higher preference for debt over tax financing, ceteris paribus.

But if bequest motives are of type 2, the situation is considerable more

complicated. Then there will be no one-to-one relation between the median age and

the median tax-profile preference. Instead, there will be a coalition between the

young and the old in favour of a higher balance of current taxes. In this case, as

median age increases, two effects are relevant. Within the working population, the

distribution of voters moves in favour of those who prefer debt; but as the

proportion of the population in retirement increases, the distribution of voters moves

in favour of those who prefer current taxation. As the age distribution changes there

will be predictable effects, but the precise proportions in the various age cohorts will

be crucial and no neat predictions about political preferences for debt (and changes


123

in the median preference specifically) can be induced without fine-grained

demographic analysis.

4 The empirical record

These two propositions are on the face of things hospitable to empirical

investigation. At the roughest level, we might observe that the general increase in

debt/gdp ratios over the last few decades has been associated with declining birth

rates—especially in some of the more recently troubled places (Italy, Spain and

Ireland to name some that spring to mind). But as Alesina and Perotti (1994)

observe of the period 1960–1994, the story is mixed—with lots of countries

substantially reducing their debt over the post-world-war II period, including the

UK and Australia (and the US until 1980). Australia, which has had comparatively

low debt/gdp ratios for the last three decades, has certainly experienced an increase

in median age—from 27.5 in 1971 to 37.7 in 2011. The increase in median age in

the US, where the debt/GDP ratio has risen considerably more, has been somewhat

slower [from 28 in 1971 to 36.9].

UK public debt had been stable and slightly declining from the 1970’s and was

still modest by world standards in mid-2008. Modest too by the UK’s own historical

record. For roughly half of the period from 1700 to the present, UK public debt

stood above 100 % of GDP—and it topped 200 % at the end of the Napoleonic

Wars and again after World War II. Indeed since 1750, public debt has fallen below

50 % of GDP only twice: once for several decades from 1880 to 1915 and again

between the early 1970’s and 2008. UK public debt is projected to run at about

70 % of GDP by 2015: high for peace-time perhaps, but clearly not unsustainable if

the last 300 years is any guide! Over this longer horizon, the standard explanation

for fluctuating debt/gdp ratios focuses on the role of war (and imperial expansion)

and the general presumption seems to be that large debt can be ‘‘justified’’ to lenders

and taxpayers alike in the case of war but to a much lesser degree otherwise. What

Age

Ideal tc /tf

R D

Barro bequest motives

‘Other’ bequest motives

Fig. 2 Preferred inter-temporal tax rates by age

194 G. Brennan

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grounds that presumption is somewhat unclear—but age distribution considerations

certainly do not figure.

An extended empirical analysis of public debt in OECD countries since WWII is

undertaken by Franzese and Robert (2001) and one of the hypotheses included

involves age distribution considerations. This inclusion is however rationalized on

the basis of arguments taken from Cukierman and Meltzer (1989) [following

Alesina and Perotti (1994)]—but these arguments focus on bequest motives, and

specifically on the presumed desire on the part of a significant proportion of the

elderly to leave negative estates. Franzese (2001) uses the ratio of persons over age

65 to persons aged 15 or less as his age distribution variable. As the foregoing

discussion suggests, however, this is a particularly unfortunate demographic feature

to focus on. At least within the Barro framework, a higher ratio of post-65-ers in the

age distribution suggests a lower rather than a higher demand for debt, other things

equal.

In any event, Franzese (2001) concludes on the basis of his rather large

econometric exercise that ‘‘while the evidence clearly rejects previous inter-intra-

generational transfer theories of debt determination, it equally clearly demonstrates

the substantive importance of age-demographics to… long-run debts’’. [p. 65]

Earlier, Franzese remarks that ‘‘the historical record gives little support to versions

of the intra/inter-generational transfers theory of debt that predict … young-

er…democracies will accumulate less debt.’’ [p 46].10

Of course, one of the prime virtues of pursuing empirical testing is that the

exercise raises questions about the specification of variables that often help clarify

conceptual analysis. In that spirit, although the scope of this paper does not extend

to pursuing independent econometric investigation, several points are worth noting.

1. Explicit and implicit public debt:

Should the measure of public debt for testing the foregoing hypotheses be

‘‘explicit’’ debt only or include ‘‘implicit debt’’—primarily, future tax

obligations embodied in quasi-contractual pension entitlements to current

citizens payable in the future? There are perhaps good practical reasons against

including ‘‘implicit debt’’. For one thing, measures are quite sensitive to a

number of parameters whose values have to be somewhat conjectural. In some

cases, plausible estimates of implicit debt may simply be unavailable. For

another, the extent to which the ‘‘quasi-contracts’’ can be altered is an open

question. Implicit debt involves a current commitment to make payments in the

future that are more like an electoral promise than they are like a financial

contract. Countries have changed their pension entitlements; and their doing so

seems to have been broadly acceptable. Electoral promises are normally seen as

statements of intention—which can be modified if conditions alter. Typically,

explicit debt obligations are not regarded in this light: debt-holders do not

10 In some earlier extremely simple one-line regression analysis of my own, involving regressing debt/

GDP ratios against just median age for a sample of 12 OECD countries, the coefficients were significant

and explained 44 % of the variance. But the explanatory power disappeared almost entirely once (high-

debt/old) Japan and (low-debt/young) Australia were removed from the sample. [I am indebted to Alan

Hamlin for bringing this latter fact to my attention.].


123

purchase debt instruments on the understanding that the terms can be changed

later if it suits the fisc to change them. Moreover, although the financing of

future pension commitments could be orchestrated via a current tax (creating a

sinking fund) that is not the normal mode. Future pension commitments seem

rather more like a future ‘balanced budget operation’ than like a current

expenditure financed by sale of bonds. There are, in short, conceptual as well as

practical reasons for treating implicit debt separately.

2. Tax rate expectations:

The foregoing analysis is focused on the equilibrium preferences of different

age groups in relation to alternative inter-temporal tax rate profiles. Achieving

the desired tax rate profile depends on expectations about tax rates in the future.

If taxpayers believe that future tax rates will be higher than present tax rates for

independent reasons, they will want lower explicit debt (other things equal).

Implicit debt may serve as one signal of higher future tax rates (or not); but it is

only one of a number of possible such factors. Another possible factor is of

course perceived location in the business cycle: Barro-like macro-‘‘smoothing’’

will also predictably emerge from the model at stake here. The more general

point is that the model requires a measure of expectations of future tax rates to

calculate the precise prediction about debt.

3. Demand and supply:

The desired quantity of debt is unlikely to be independent of price. It costs

something to transfer tax rates inter-temporally—and that cost can fluctuate

(not least by reference to expectations concerning default). More generally,

whether a particular debt/GDP ratio is ‘‘problematic’’ depends on the supply of

funds (something which can vary from country to country, given a tendency for

citizens to prefer domestic debt). So, for example, what may seem like a

dangerously high debt/GDP ratio in Greece may be mildly regarded in Japan

(where aggregate savings rates are much higher).

4. Net debt or gross?

Suppose the fiscal balance sheet consists of accumulated public debt and

various saleable assets. It should be clear that a change in the inter-temporal

profile of tax rates can be wrought by increasing debt or by selling assets (or

obversely by reducing debt or acquiring saleable assets). Equally, raising debt

to acquire a saleable public asset is in this sense tax profile neutral to the extent

that the asset can be sold to redeem the debt. Put another way, current sale of

public assets is equivalent to debt in the approach taken here: the opportunity

cost of selling the asset now is its sale forgone in the future. And this fact is

essentially independent of whether the rate of return earned on the asset in

government hands is larger or smaller than it would be if in private hands.

To be sure, there is some question as to which assets are indeed saleable and

which not—and what the relevant criteria are. It might be thought that all that is

required is the existence of a buyer; but though that is a necessary condition, it

need not be sufficient. Some assets which fit this category might nevertheless be

unsellable for other reasons—because such sale would be politically unthink-

able (i.e cost incumbent government office) for example. Greece might in

principle sell off the Parthenon to an oil sheik and solve its fiscal problems

196 G. Brennan

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thereby; but it is doubtful whether any such move is being seriously entertained

by any of those active in designing rescue packages for Greece—and for

obvious reasons of political viability!

The more general point however is that measures of public debt can be

misleading. Britain’s apparently exemplary debt performance of the Thatcher

years was largely accomplished by the sale of public assets. The independent

analyst might well regard that feat as an accounting trick; but it is an illusion

invited by measuring public debt in gross rather than net terms (and this is a

practice that as far as I can tell, most of the publicly available measures

indulge).

5 Conclusion

None of the immediately foregoing observations is a satisfactory substitute for

doing the hard econometric work that would be required to properly incorporate

demographic features into an empirical analysis of political equilibrium in debt

determination. Such relevant econometric work as has been done to date (Franzese

2001, most notably) is perhaps not uniformly encouraging. And in any case, the

model depends on many assumptions whose plausibility I think there are good

reasons to question: the absence of debt illusion; the specific details of bequest

motives; the uni-dimensionality of the political choice space; the irrelevance of

supply-side effects; the systematic interest-orientation of voter preferences. The

model’s role is, as I see it, the negative one of showing that the assumptions of

zero debt illusion, and full inter-generational connectivity, are not sufficient to

establish ‘‘debt neutrality’’. And the non-neutrality of debt financing under these

assumptions has a ‘‘political economy’’ counterpart, which translates into a

demographic model of democratic politics—though the translation exercise is far

from straightforward.

References

Alesina, A., & Perotti, R. (1994). The political economy of budget deficits. NBER working paper no.

4637.

Barro, R. (1974). Are government bonds net wealth? Journal of Political Economy, 82, 1095–1117.

Barro, R. (1979). On the determination of the public debt. Journal of Political Economy, 87, 940–947.

Brennan, G., & Buchanan, J. (1980a). The power to tax. New York: Cambridge University Press.

Brennan, G., & Buchanan, James. (1980b). The logic of the Ricardian equivalence theorem.

Finanzarchiv, 38, 4–16.

Brennan, G., & Lomasky, L. (1993). Democracy and decision. New York: Cambridge University Press.

Buchanan, J. (1958/1999). Public principles of public debt. In G. Brennan, H. Kliemt, & R. Tollison

(Eds.), The collected works of James M. Buchanan (Vol. 2). Indianapolis: Liberty Fund.

Cukierman, A., & Meltzer, A. (1989). A political theory of government debt and deficits in a non-

Ricardian framework. American Economic Review, 79, 713–733.

Feldstein, M. (1976). Perceived wealth in bonds and social security: A comment. Journal of PoliticalEconomy, 84, 331–336.

Ferguson, J. (1964). Public debt and future generations. Chapel Hill: UNC Press.


123

Franzese, R. (2001). The positive political economy of public debt: An empirical examination of theOECD postwar experience. Workshop on Political Economy, Tel Aviv University.

Lucas, R., & Stokey, N. (1983). Optimal fiscal and monetary policy in an economy without capital.

Journal of Monetary Economics, 12, 55–94.

Ricardo, D. (1820). Funding system. In P. Sraffa (Ed.) (1951) The works and correspondence of DavidRicardo (vol IV, pp. 143–200). Cambridge: Cambridge University Press.

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The political economy of public debt