## Abstract

The paper first addresses the question of the sustainability of debt growth by examining the behavior of taxation implied by fiscal rules that respect a government’s intertemporal budget constraint. Sustainable debt growth may require the tax burden to rise above some socially acceptable level. In this case, whereas drastic remedies may prove ineffective, a more relevant choice concerns the degree of monetary financing of the deficit (as distinct from monetization of the debt), which affects the dynamics of taxation implied by the constraint. Monetary financing is then introduced into a model by Blanchard, and the effects of monetary financing on the interest rate and capital intensity are examined. Finally, some policy implications are considered.

**T**he parting shot with which Willem Buiter (1985) concludes his guide to public sector debt and deficits is that “probably more uninformed statements have been made on the issue of public sector debt and deficits than over any other topic in macroeconomics.” It may be an extreme statement, but it certainly rests on the great variety of professional and nonprofessional views about the issue. These views, in turn, may find some justification in the no less remarkable variety of historical experiences.

In the United Kingdom, the ratio of public debt to gross domestic product (GDP) exceeded unity for nearly a century, declining to lower levels only after 1860. The debt ratio reached very high levels in many countries after the two world wars. There was then a generalized increase in the 1930s, in connection with the Great Depression. The past decade has been another period of fast growth of debt almost everywhere: between 1972 and 1983 the debt ratio increased by over 70 points in Denmark and Ireland, by over 44 points in Belgium, by 40 points in Japan, and by 35 points in Italy. The growth continues unabated in Italy, where the ratio is nearing 100 percent, and is now fast in the United States. The remarkable feature of these recent experiences is that they have occurred in peacetime, though during a period of severe supply shocks and of decline in the trend growth rate.

Past experiences of debt accumulation are varied in their eventual outcomes.^{1} There are important cases of painless re-entry to a more normal situation, mostly in Anglo-Saxon countries; cases in which the overhang of a high debt stock became a primary cause of financial instability, leading eventually to inflation, which in turn provided a drastic remedy to the original problem by curtailing the real value of the outstanding debt, as in France in the 1920s; cases in which a high debt stock was one of many factors producing conditions of hyperinflation, as in the Republic of Germany and other countries after the first world war; cases of forced loans, wealth taxes, or forced consolidation, as in Piedmont in the early nineteenth century or in Mussolini’s Italy in the 1920s. The one safe lesson one can draw from both facts and theory is that it is meaningless to look for a critical value of the ratio of debt to GDP beyond which the system breaks down and traumatic solutions become necessary: after all, the ratio was lower in France in the 1920s than in the United Kingdom between 1790 and 1840.

As far as the economic theory of public debt is concerned, much was said in old strands of the literature that has subsequently been rediscovered in quite modern contributions, and much has been added since.^{2} But a large and growing body of literature offers few certainties about many crucial issues regarding the short- and medium-run effects of debt; the most crucial is perhaps the one about which there is least certainty—how fast and how far can debt grow before causing a change of regime in one of the forms experienced in history.

This paper has no ambition to fill such a gap; its purposes are more modest. I shall first consider the widest notion of sustainability of debt growth: the one requiring that a transversality condition or intertemporal budget constraint be respected by the government. I shall introduce a notion of fiscal rule and examine when a fiscal rule causing a permanent deficit fulfills this condition (Section I). The constraint does not require that debt growth be bounded; even if it is, the debt ratio may rise to very high levels. The taxonomy of fiscal rules is more interesting if the implied behavior of the tax burden is considered; this is done in Section II. Those implications may be irrelevant as long as the analysis is kept at a very high level of abstraction—not so if allowance is made for the distributional effects of the concomitant rise in interest payments and taxes. As pointed out with force by Keynes (1971) in his 1923 *A Tract on Monetary Reform*, the ability or the willingness of a government to collect a rising amount of taxes is likely to set a limit to sustainable debt growth. Keynes’s “two remedies”—a capital levy or monetization for the purpose of reducing the real value of debt—are examined, to show that their success depends on quite stringent conditions, unlikely to be met in present-day cases. A sharp distinction is then drawn between what is usually referred to as monetization and different degrees of monetary financing of the deficit. In Section III, I examine how the dynamics of debt and taxation are affected by monetary financing and argue that, when there are perceived limits to the enforceable level of the tax burden, lax fiscal rules, even though they are not of necessity directly responsible for inflation, are bound to be associated with a higher propensity toward inflation. The long-run effects of monetary financing on the real interest rate strengthen this conclusion, and I examine such effects by explicitly introducing money creation in a well-known model by Olivier Blanchard (1984, 1985). I offer some conclusions in Section IV.

## I. Fiscal Rules and the Intertemporal Budget Constraint

The analysis may start with the budget identity, which, considering ratios to GDP, is

where a dot above a variable denotes changes over time, *M* is the stock of high-powered money issued for the treasury; *y* is nominal GDP; *b* and *f* are, respectively, the stock of one-period bonds issued at par and the government’s borrowing requirement as ratios to GDP; *n* is the (constant) real growth rate of GDP; and *p* is the rate of inflation. The borrowing requirement is given by

where *g* and τ are the ratios to GDP of, respectively, public expenditure (net of transfers and interest payments) and taxes (net of transfers), and *i* is the nominal rate of interest on bonds.

Let *i*_{t} − *p*_{t}=*r*, the real rate of interest, which for the moment is supposed to be constant. It is also assumed that monetary financing of the deficit is the only source of increase of base money, which is considered to grow at the rate τ_{t} = *n* + *p*_{t}, the sum of the real growth rate and the inflation rate. Hence Ṁ/*Y* = λ_{t}*m*_{t} (*p*_{t}), where *m*_{t} (*p*_{t}) is the ratio of base money to nominal GDP, a decreasing function of the inflation rate. One can then rewrite the budget identity as

Equation (3) describes how the ratio of the stock of debt to GDP grows over time. Note that ḃ_{t} + Ṁ_{t}/*Y*_{t} is the deficit ratio after corrections for inflationary losses on the stock of bonds and for the effects of real growth.^{3}

The widest notion of sustainability of debt growth is one setting a limit not on the level of the debt ratio but on its long-run growth rate. Whether the limit imposes a constraint on the fiscal and borrowing behavior of the government depends on whether the interest rate exceeds or falls short of the growth rate of the system. In the latter case, with *n* > *r*, the debt ratio will grow at a declining rate, as can be seen from equation (3), and will eventually approach a stationary value even when the government runs a constant primary deficit and services its growing debt by further borrowing. Governments in this case are allowed to conduct what Buiter (1985) calls “honest Ponzi games.”

The limit becomes operational and constrains government’s behavior over time when the interest rate exceeds the growth rate, as shall be assumed in most of what follows. Not only are there sound theoretical and, in the current period, empirical reasons for concentrating on this case. When *n* > *r*, the debt ratio can conceivably rise to very high levels: even with the possible effects on the interest rate, dealt with in the last section of this paper, if an external shock lowers the growth rate or raises the interest rate, the “honest Ponzi games” conducted in the past may suddenly become quite expensive.

From integration of equation (3) one obtains

which expresses the intertemporal budget identity over an infinite horizon and in terms of present discounted values. The intertemporal budget constraint is a condition of sustainability imposing that in the long run the rate of debt accumulation should be less than the interest rate.^{4} Debt, in other words, should not be serviced indefinitely by borrowing. When this condition is fulfilled,

and the intertemporal constraint is expressed by

The economic meaning of equation (6) is evident. If one starts with a positive stock of debt, the condition that government should not borrow indefinitely to service its debt and that debt therefore should grow at a rate lower than the interest rate requires that, sooner or later, debt must be serviced by an excess of tax revenues and monetary financing over noninterest expenditure. Note that monetary financing and a positive inflation rate, although not affecting equation (5), affect the revenue side of equation (6).

To examine further the problem of sustainability of debt growth in terms of the intertemporal budget constraint, suppose that the fiscal authority follows a fiscal rule, constant over time, that causes a permanent deficit. The whole set of such possible fiscal rules is described by

where 0 ≦ α ≦ *i*. If α = 0, the deficit ratio will remain constant over time, whereas the primary deficit (net of interest payments) will shrink and eventually become a surplus as interest payments rise; if α > 0, the deficit ratio will grow over time.

With the set of fiscal rules described by expression (7), the growth of the debt ratio will be given by

The (uninteresting) case in which the debt ratio is already stationary at the outset—because *a* − λ_{0}*m*_{0} = (α − λ_{0})*b*_{0}—will be ignored, and only the implications of the intertemporal constraint when debt is growing will be considered.

Respect of condition (5) and of the intertemporal constraint (6) does not imply, as noted by McCallum (1984), that the growth of debt is bounded and that there exists a finite stationary value for *b*. If such a value exists, the condition is certainly satisfied; but it can also be satisfied by *b* growing indefinitely.

Thus, consider first the case in which *n* = *p* = 0, so that there is neither growth nor inflation. The constraint here requires that α. < *r*. Even with α = 0 and a constant positive deficit, however, debt grows indefinitely over time. With *a* > 0 and 0 < α < *r*, the constraint is satisfied, while not only the debt ratio but also the deficit grow forever. Only with *a* < 0 and α > 0 is debt growth bounded. With α = *r*, the constraint is not respected even if a < 0, so that the government runs a constant primary surplus: the constraint requires a *growing* primary surplus, even when, or rather because, debt grows forever.

Consider now a more general case, in which the real growth rate of the economy can be positive and part of the deficit may be financed by the issue of monetary base.

If the real interest rate exceeds the real growth rate, fulfillment of the intertemporal budget constraint by the set of fiscal rules given in equation (7) now requires that α − *p* < *r* = *i* − *p*, a less stringent requirement than in the previous case: the growth rate of debt implied by the given fiscal rule must not exceed the nominal (rather than the real) interest rate. Further, positive real growth or monetary financing (or both) of the deficit sets a limit to the growth of debt for a wide variety of fiscal rules for which growth was unbounded, with *n* = *p* = 0. In general, as can be seen from equations (5) and (8), the intertemporal budget constraint is met, but growth is unbounded, if λ < α < *i*; debt growth is instead bounded if α < λ < *i*.

If α = *i*, the constraint is not satisfied. When the fiscal rule is so lax that α equals the nominal interest rate, monetary financing can help to satisfy the constraint only if it takes place at a growing rate, hence with accelerating inflation. In this case a constant share of the total deficit must be financed with base money; but as the total deficit grows over time at a rate *r* − *n*, *pm* (*p*) must also grow at the same rate, and *p* will have to grow faster if *m* falls as inflation accelerates. In this undesirable (but perhaps not implausible) case, there may also exist, at least on paper, a steady-state value for *b*.^{5}

This brief survey of fiscal rules in view of their compatibility with the intertemporal budget constraint shows that the constraint provides a very weak criterion of sustainability of protracted deficits and debt growth. Its fulfillment is ensured also by rules that make the debt, and possibly the borrowing, requirement grow forever; even when the growth of debt is bounded, the limit may be quite high and debt may grow at very high rates for a long time.

The taxonomy of sustainable and unsustainable fiscal rules according to the criterion of the intertemporal budget constraint, and, among sustainable rules, to the existence of limiting steady-state values, is thus by itself not very interesting either for theory or for policy. Its implications for the taxing or spending behavior of the government are, however, more relevant.

Let us suppose that *g*, the ratio to GDP of government expenditure net of transfers, is given. It will still be assumed that the real rate of interest is constant (an attempt to remove this assumption will be made later). With a constant rate of inflation, *i* = *r* + *p*, and one obtains from equations (2), (7), and (8) the taxing behavior of the government implied by each fiscal rule:

Fulfillment of the intertemporal budget constraint requires that α < *i*.^{6} Hence it also requires that the tax burden (net of transfers other than interest payments) must grow together with the stock of debt: without limit if the growth of the debt stock is unbounded, or, if it is bounded, toward a limit that can conceivably be quite high. Is a situation of unlimited or very fast growth of the tax burden admissible? In principle it is, if the analysis is kept at an abstract level.

Consider a situation with a fiscal rule such as to cause growing debt, according to equation (8): debt growth may be without bounds or may be tending toward a limit, depending on whether α exceeds or falls short of λ. The alternative is to change the fiscal rule now so as to stop further debt growth. If *g*, the noninterest expenditure, is given, the choice is between raising taxation now (keeping it at a constant level from now on) and letting taxation rise with debt over time.^{7}

If the (constant) growth rate exceeds the (constant) interest rate, a problem of choice does not even arise. If α = *i* < λ, as debt grows the tax burden will remain constant at the initial level, as appears from equation (9) (remember that there is no constraint in this case). If α < *i* < λ, with an unchanged fiscal rule taxes would rise with debt and would approach a steady-state level, corresponding to the stationary level of debt *b** = (*a* − λ*m*)/(λ − α). It is easily shown, however, that in the case of *n* > *r*, with an unchanged fiscal rule, the tax burden although rising would never reach the level required to stop further debt growth immediately.^{8} Thus, with *n* > *r* there is no reason that debt growth should be stopped by raising taxes now.

When the interest rate exceeds the growth rate, in contrast, all fiscal rules satisfying equation (6) are equivalent, irrespective of the speed of debt growth (hence of the time profile of taxation) implied by each of them. As McCallum (1984) has shown, all fiscal rules that meet the intertemporal budget constraint are compatible with optimal equilibrium in a model of rational agents with perfect foresight and infinite horizons, even if the rules cause unbounded growth of debt and, hence, of taxation. If the initial stock of debt *g* and λ*m* are the same, any two discounted flows of taxes satisfying equation (6) must be equal, whatever the time profile of the tax burden: the constraint is respected if the tax burden is increased now and then kept constant or if it is allowed to rise with the stock of debt.

In addition, agents are indifferent about the time profile of taxation as long as they have infinite horizons and the rate at which they discount future taxes is the same as that used in the intertemporal budget constraint (a known proposition).^{9} If because of myopic preferences the agents’ rate of discount instead exceeds *r* − *n* by some factor π, while the rate of discount used in equation (6) remains the same, higher future taxes, even if the tax burden must grow forever, are always preferred to a tax increase now that would keep the debt ratio, hence the tax burden, constant in the future.^{10} As will be seen later, however, if one introduces myopic preferences, one must allow for the effects of debt on the real interest rate.

## II. Sustainability and Taxation

Can it really be presumed that fulfillment of the intertemporal budget constraint is all that is needed to establish the sustainability of the growth of debt caused by a given fiscal rule? More precisely, if one starts with a given fiscal rule that meets the constraint (hence, with α < *i*), can one presume that the associated behavior of the fiscal burden, as given by equation (9), is always sustainable? Such presumption requires that there are no limits to the levels of taxation that society is ready to accept: if there are, a fiscal rule initially meeting the constraint may become unsustainable in the longer run. There are at least two conditions needed to rule out the existence of a limit to the sustainable level of taxation. First, a continuously rising tax burden must be without consequences for the individuals’ incentive to work and for the tax base. Second and more important, the individual distribution of income must not be affected by the simultaneous rise in the tax burden and in interest payments on the growing debt: if it is, as will be the case unless very restrictive assumptions on the initial distribution of income and wealth hold, the required increase in taxation may become unsustainable because of the social and political reactions that it raises.

The problem of the distributional effects arising from the need to service a growing stock of debt was well understood by De Viti de Marco and especially by Keynes.^{11} In *A Tract on Monetary Reform*, Keynes stated with the greatest clarity the political problem arising “when the State’s contractual liabilities … have reached an excessive proportion of the national income. The active and working elements in no community, ancient or modern, will consent to hand over to the *rentier* or bond-holding class more than a certain proportion of the fruits of their work” (Keynes (1971, p. 54)).

Considering the French situation in the early 1920s, Keynes (1971, p. 58) observed that in that country “the service of debt will shortly absorb … almost the entire yield of taxation” and concluded that “France must come in due course to some compromise between increasing taxation, and diminishing expenditure, and reducing what they owe their *rentiers*” (p. 59). What Keynes had in mind was the sustain-ability of the behavior of taxation implicit in a fiscal rule respecting the intertemporal budget constraint: when “the claims of the bond holder are more than the taxpayer can support” (p. 55), further growth of the debt service, hence of debt, becomes impossible, and some relief must be sought elsewhere.

For a situation in which such limit has been reached and “the piled-up debt demands more than a tolerable proportion” (p. 54) of income, Keynes, ruling out debt repudiation, considered two possible remedies. He favored a capital levy as “the scientific … expedient … the rational, the deliberate method,” but he doubted that it was feasible because “it is difficult to explain, and it provokes violent prejudice by coming into conflict with the deep instincts by which the love of money protects itself (p. 55). The other remedy was “currency depreciation.”

In the conditions of debt accumulation prevailing today in many countries, Keynes would perhaps place less faith in a capital levy as the decisive and sufficient remedy. Such conditions are not those of a debt overhang from a succession of past deficits incurred during war, in which the growth of debt is only a heritage of the past and is no longer due to primary deficits. When, as is often the case nowadays, the fiscal rules that started the process of debt accumulation are still being followed by the authorities, a capital tax levied with the purpose of retiring part of the outstanding debt may be worse than useless unless the rule is changed. Thus, suppose that (*a* − λ*m*) is positive and exceeds (λ − α)*b*, so that debt is growing. If the rule is not altered, a reduction in the stock of outstanding debt obtained by means of a capital levy would not affect the long-run dynamics of the debt; the reduced stock would grow at a higher rate until the previous value is reached again.

This is, of course, an extreme assumption because it does not allow for a reduction of the deficit from lower interest payments on the smaller stock (although the temptation to use the reduction in interest payments to make more room for other expenditures may be strong). But even if the deficit is allowed to decline by the full amount of the reduction of interest payments, the capital levy and the ensuing reduction of the stock of debt will not stop further debt growth unless there is already (or unless the authorities take measures to enforce) a primary surplus net of monetary financing. From the budget identity, debt grows as long as (*g* − λ_{t} − λ*m*) > (λ − *i*)*b*; with *i* > λ, constancy of the debt ratio at a lower level of the debt stock requires that the first term be negative. If the fiscal rule is not, or is not made, consistent with the constancy of the debt ratio at the lower level attained after the capital levy, placement of the new debt may become difficult or impossible as a result of a crisis in confidence. Thus a capital levy becomes a useful remedy only after conditions of fiscal virtue, in terms of the budget net of interest payments, have been established.

But what about “currency depreciation,” which Keynes considered the only feasible remedy for the French plight? “If we look ahead,” he wrote, “the level of the franc is going to be settled in the long run … by the proportion of his earned income which the French taxpayer will permit to be taken from him to pay the claims of the French *rentier*” and “will continue to fall until the commodity value of the francs due to the *rentier* has fallen to a proportion of the national income which accords with the habit and mentality of the country” (Keynes (1971, pp. 59–60)). In his open letter to the French Minister of Finance in 1926, Keynes reiterated his view that there was “one exit only—a rise of internal prices,” observing that “*if internal prices had risen as fast as the exchange has fallen, the real burden of the national debt service would be reduced by at least a third*” (Keynes (1932, pp. 107 and 109).

What Keynes meant by currency depreciation was not a permanent rise of a steady rate of inflation, but a once-and-for-all operation of increase in the price level, which would be tantamount to a capital levy for its effects on debt. Although the wealth tax implicit in a sudden price rise is more unfairly distributed than a capital levy, it is a fact that the “owners of small savings suffer quietly … these enormous depredations, when they would have thrown down a government which had taken from them a fraction of the amount by more deliberate but juster instruments…. It is, so to speak, nature’s remedy, which comes into silent operation when the body politic has shrunk from curing itself (Keynes (1971, pp. 54–55)).

The conditions for the success of Keynes’s second remedy in taking care of a debt problem are at least two. Remember that the problem in this context does not arise from the formal requirements of intertemporal sustainability, which are assumed to be initially respected, but from the fact that the increase in taxation required to meet rising interest payments proves to be politically unsustainable beyond a certain level—whence the need to cut interest payments somehow so as to respect the intertemporal constraint. The first condition is the same as that necessary for the success of a capital levy: a reduction in the real stock of debt obtained by means of a once-and-for-all price rise will succeed in preventing further debt growth only if revenues already exceed expenditures net of interest payments and monetary financing; only, that is, if the stage has already been reached at which interest payments are the sole remaining cause of the debt problem, and a “sound” budget situation has otherwise been re-established. The second condition is that a large share of the outstanding debt consists of fixed-coupon long-term bonds, so that real interest payments can fall roughly in proportion with the real value of the stock of debt. Both conditions were verified in the French situation with which Keynes was concerned; either or both are lacking in present-day cases. Because in most recent experiences the acceleration of debt growth has followed closely a period of high (and initially unexpected) inflation, savers have sought protection from further real losses by requiring shorter-term instruments (as shown by the decrease in the average life of debt in all countries) or formal indexation to prices or to short-term interest rates.^{12} This feature is explicitly introduced in the earlier presentation, since it was assumed that all bonds issued are one-period bonds and the real interest rate has so far been taken as given. Without those two conditions, a sudden rise in the price level, as recommended by Keynes for France, would have no effect whatever on debt growth and on the rise in taxation required to meet the intertemporal budget constraint. Even worse, if the deliberate operation of curtailing the real value of the debt outstanding fails its purpose of arresting further debt growth, there would arise conditions of financial instability because savers would learn from experience, and new bonds could be placed only at much higher real rates.

## III. Monetary Financing

One must at this stage draw a sharp distinction between a sudden jump in the price level necessary for a once-and-for-all reduction of the real value of the debt outstanding, which was the “second remedy” considered by Keynes and is usually referred to as “monetization of the debt,” and the choice between different degrees of monetary financing of the deficit and, hence, between different steady rates of inflation. Keynes’s remedy is in the nature of a surgical operation, the success of which depends on the existence of healthy conditions of the primary budget and on the possibility of removing the abscess that causes the pathology by inflicting real losses on the bond holders. Instead, no assumptions are made in the following with respect to the state of the primary budget, while it is explicitly assumed that bond holders are immune from inflationary losses. Thus, a choice as to the degree of monetary financing of the deficit and the rate of inflation cannot affect the real value of the outstanding debt and has therefore nothing in common with monetization in the Keynesian sense. What such a choice does affect, however, for any given fiscal rule respecting the intertemporal constraint, is the dynamics of debt and its steady-state level, if any; hence, the dynamics of the tax burden and its steady-state level, if any. The latter will be affected, on the one hand, by the different debt dynamics associated with different degrees of monetary financing and, on the other, by the different nominal interest rates associated with different rates of inflation. The choice arises and acquires relevance when there is a limit to the level of the tax burden that is socially or politically acceptable and when the authorities embark upon a fiscal rule that would drive taxation beyond that limit. Conditions under which drastic surgery is both possible and feasible are indeed less frequent than cases in which remedies allowing the patient to survive with a chronic illness are sought.^{13}

How are debt growth and taxation affected if the degree of monetary financing, and hence *pm*, is allowed to vary? At first the real interest rate will be taken as given; monetary financing will then be added to a recent model by Blanchard (1984, 1985) to examine its effects on the real interest rate.

The way in which the financing of the deficit through money creation affects the dynamics of interest-bearing debt is readily seen from equation (8): for plausible values of the price elasticity of demand for money,^{14} both the growth and the level of debt diminish unambiguously. A higher rate of inflation has two opposite effects on the level of debt service and hence of taxation, which, in the sustainable case, must grow with debt service: on the one hand, higher inflation lowers the level of the interest-bearing debt; on the other hand, it raises the nominal interest rate, which, under the assumption made here, fully reflects the rate of inflation. Suppose, however, that α < λ, so that there exists a steady-state level *b** of *b* and an associated value of τ, τ* = *g* = *a* + (*i* − α)*b* *. One then has

which again is negative for reasonable values of the price elasticity of demand for money—in particular, since λ*m* = (*i* − *r* + *n*)*m*, with a unitary elasticity of the demand for money with respect to the nominal interest rate, *d*(λ*m*)/*dp* = −(*r* − *n*)*dm*/*dp* > 0.

To see how different rates of monetary financing affect the flows of future taxes that are compatible with the intertemporal budget constraint, consider for the same initial values of the debt ratio, *b*_{0}, and of the ratio to income of expenditure net of interest payments, *g*, and for the same real growth rate, *n*, two different rates of creation of base money: λ = *n* +*p* and λ′ = *n* + *p*′ > λ. The monetary financing of the deficit as a ratio to income will be in the two cases, respectively, λ*m* and λ′*m*′, with *m*′ < *m*. Let the two streams of taxes associated with λ*m* and λ′*m*′ be, respectively, τ_{s} and τ′_{s} Then, from equation (6), one has

To a higher rate of money creation there will correspond a lower discounted flow of future taxes, if *r* > *n* and provided that λ′*m*′ > λ*m*. This last condition is observed if the price elasticity of demand for money is less than *p*/(*p* + *n*). If the interest elasticity of demand for money is unity, this is always the case: the difference between the two discounted streams of taxes associated to different rates of inflation then becomes simply *m* − *m*′ > 0.

To derive the same result in another way, suppose that at *t* = 0 debt is growing because, with a rate of money creation λ (and a rate of inflation *p*), *a* = λ*m* > (λ = α)*b*_{0}. The rate of money creation necessary to keep the level of debt constant at *b*_{0} with an unchanged fiscal rule will be λ′, such that *a* − ′*m*′ = (λ′ − α)*b*_{0}. With a rate of inflation *p*, taxes would have grown with *b*_{t}, according to equations (8) and (9). With the new rate of inflation *p*′, they will rise initially to τ′_{0} = *g* − *a* + (*i*′ − α)*b*_{0} and then remain at that level forever. The difference between the two streams of taxes discounted at the rate *r* − *n* will be

which will be equal to (λ′*m*′ − λ*m*)/(*r* − *n*).^{15}

Although to different rates of money creation there correspond different levels of the tax burden, different rates of inflation also entail a different cost of holding base money. If this cost is measured by the rate of inflation times the amount of money held—*pm* and *p*′*m*′ in the two cases—the difference between the discounted flows, including both the taxes collected by the fiscal authorities and the tax silently enforced by the monetary authorities, becomes, as can be easily verified, *n*(*m*′ − *m*)/(*r* − *n*) < 0 as long as *r* > *n*. Thus the discounted stream of taxes plus the inflation tax is higher for a higher rate of inflation. If, however, the cost of holding money at different inflation rates is more correctly measured by the nominal interest forgone because money rather than an interest-bearing asset is being held, one is back to the previous result: if one adds to τ and to τ′, respectively, *im* and *i*′*m*′, the difference between the two discounted flows is *m* − *m*′ > 0.

Whatever the correct measure of the cost of inflation, a continuous rise of taxation is likely to meet more vociferous objections than a steadily higher inflation tax as measured by a higher rate of inflation. To bring out this point, let us explicitly consider the existence of a limit to the amount of resources that “the active and working elements” of the community “will consent to hand over to the … bond-holding class” (Keynes (1971, p. 54)). In this case, if the authorities are unable or unwilling to cut expenditures, the choice is not to have a higher inflation rate but when and to what extent to step up monetary financing of the deficit.

Suppose that there is a limit, ¯τ, to the tax burden that citizens are ready to bear or that the government is able to impose without political risk. Suppose that, with a given sustainable fiscal rule and a rate of money creation λ, such limit is reached at *t* = *T*, when the level of debt *b*_{T} is such that τ_{T} = ¯τ. With that fiscal rule and that rate of money creation, debt would increase further after *T*; but because taxes cannot be increased above τ_{T}, debt growth must be stopped at *T* to prevent a further increase of interest payments that would now be incompatible with the intertemporal constraint. Hence, unless noninterest expenditures are cut, the monetary financing of the deficit, and with it the inflation rate, must be increased by an amount sufficient to keep *b* constant at *b*_{T} and τ constant at τ_{T} = ¯τ, with allowance made for the increase in nominal interest payments attributable to the higher inflation rate.

The new rate of money creation, λ^{+}, must then be such that the associated ratio of the monetary financing of the deficit to income, λ^{+}*m*^{+}, fulfills the condition λ^{+}*m*^{+} = *g* + *i*^{+}*b*_{T} − τ_{T} − λ^{+}*b*_{T} = *a* − (*i* − α)*b*_{T} + (*i*^{+} − λ^{+})*b*_{t}, where *i* = *r* + *p* and *i*^{+} = *r* + *p*^{+} are the nominal interest rates associated, respectively, with rates of money creation λ and λ^{+}. Thus, λ^{+}*m* ^{+} = *a* − (λ − α)*b*_{T}

The required jump in the rate of inflation may be considerable if the fiscal rule is lax, or when the limit to a further increase in taxation is met at a low level of *b*. It is further unlikely that the jump to higher inflation may occur precisely when it becomes impossible to collect more taxes or without affecting the confidence of the financial markets. If the government is aware of the limit to the rise in the tax burden and the market anticipates its decision, the rate of inflation will start rising immediately.^{16} If instead the government realizes too late its inability to service the additional debt by raising more taxes, the markets may be quicker to perceive a situation of unease. An expectation that the budget constraint will not be respected may cause fears of repudiation—as in a model by Masson (1985)—and make the public unwilling even to renew the debt coming due for redemption, except perhaps at much higher interest rates. The outcome may be a financial crisis and, eventually, a much higher rate of inflation than the one required on paper to stop the growth of debt at *T*.

What are the alternatives? Given the fiscal rule, they are of the Sargent and Wallace (1981) variety: except that, whereas in Sargent and Wallace’s exposition the intertemporal constraint is not respected from the very beginning and the limit to debt growth is set by the maximum amount of government bonds that agents are ready to hold in their portfolios, here the constraint is respected initially, but there is a limit to the required increase in taxation. The authorities may choose not to wait for *T* to increase monetary financing, but to increase monetary financing at *t* = 0, such that the maximum permissible level of taxation, ¯τ, instead of being reached at *T*, becomes the limiting (steady-state) value of a bounded process of debt growth. One then must have τ* = *g* − *a* + (*i*′ − α)*b** = *g* − *a* + (*i* − α)*b*_{T} = ¯τ and λ′*m*′ = *a* − (λ′ − α)*b**, where *b** and τ* are the steady-state levels of taxation and debt, λ′ is the new rate of money creation associated with those levels and the given fiscal rule, and *i*− = *r* + *p*′ is the corresponding nominal interest rate. From the first condition, constraining the level of taxation, one obtains the value of *b** as a function of *b*_{T}; from the second, one obtains the level of monetary financing compatible with *b**.

It is easily checked that λ′*m*′ is higher than λ*m*, which cannot, however, be sustained after *T*. But λ′*m*′ is lower than λ^{+}*m*^{+}, the rate that would otherwise prevail after *T*.^{17} The choice of λ′*m*′ as from now is then one of a rate of inflation higher from now until *T*, but lower thereafter. Taxes would be higher at the beginning, because of the higher nominal debt service, but would then become lower than under the first possibility, because they would never reach ¯τ, the critical value. This latter fact may make the choice attractive to the authorities because it would remove the dangers of instability.^{18} Alternative time profiles of inflation and taxation can, of course, be imagined that answer the same requirement of allowing the intertemporal constraint to be respected without approaching an unenforceable level of taxation.

When one considers the limits to the taxing ability of a government, it is thus not surprising that lax fiscal rules, even if not directly responsible for inflation, are associated with a higher propensity to inflation. This conclusion is strengthened if the analysis is extended to consider the effects on the real interest rate of the level of debt on the one hand and of monetary financing on the other. This will now be undertaken by introducing monetary financing in a model by Olivier Blanchard.

Blanchard (1984, 1985), following Yaari (1965), modeled individual and aggregate consumer behavior in a framework of uncertain lifetimes.^{19} Consumption, as derived from utility maximization subject to a budget constraint, is proportional to human and nonhuman wealth. Uncertainty about lifetime affects the rates at which future consumption and the stream of future earned income net of taxes are discounted. If π is the individuals’ probability of death, individuals will discount future consumption at the rate θ + π, where θ is the rate of time preference. Future incomes net of taxes will be discounted at the rate *r* + π. In the government’s intertemporal budget constraint, future expenditures and taxes are, however, discounted at the rate *r*. It follows, as shown by Blanchard, that, with given output, the size of public debt affects *r*, the real interest rate, which is higher than the debt. If the model is completed with a production function, it is also shown dynamically that the size of debt affects capital intensity and the long-run level of consumption.

Blanchard’s model only has interest-bearing debt and does not allow for any monetary financing of the deficit. Monetary financing is easily introduced. Buiter claims that, in this case, “if all non-money assets are index-linked, money is a veil” and “real interest rates are unaffected by monetary policy.” ^{20} It can instead be shown that the degree of monetary financing of the deficit, by affecting the growth and the level of debt (hence the associated level of taxation), does indeed have those real effects denied by Buiter.

For reasons of simplicity, in what follows it shall be assumed that the economy is stationary, so that *n* = 0 and λ = *p*; the results are, however, easily extended to the case of a steady positive real growth rate. It shall also be assumed that the fiscal rule is such that α = 0, so that there exists a steady-state level of interest-bearing debt (*a*/*p*) − *m*, with *a*/*p* being the level of total monetary and nonmonetary debt. All variables are expressed in real per capita terms. The symbols that have so far been used to denote ratios to income will be written with a circumflex to show that they are real per capita magnitudes; thus the per capita level of real interest-bearing debt will be ^b = *b*ŷ, where ŷ is per capita income.

Money finds its place in the utility function because of the liquidity services it yields to agents. An instantaneous utility function of Cobb-Douglas form is assumed:

where *c* is per capita consumption. Each agent maximizes

subject to the budget constraint. The solution for the aggregate is ^{21}

In equations (13)–(15), *w* is nonhuman wealth, composed of physical capital *k*, bonds, and money, and *h* is human capital, defined as the stream of future labor income net of taxes discounted at the rate *r* + π:

where *z* is earned income. Further, from the income-expenditure equality one has

The accumulation of real per capita nonhuman wealth equals disposable income net of the inflationary losses on assets:

In the steady state, · ^b = k̇ = ·^m = ·h = 0. Hence the steady-state levels of *w* and *h*, *w** and *h**, are

where the steady-state level of taxation is that obtained from equation (9) above. By using equations (14) and (17), one obtains

Substitution of equations (13) and (17) yields finally

Thus, given capital per person *k* and per capita output ŷ, the real interest rate, which exceeds the rate of time discount if π > 0, depends on the steady-state level of total public debt. Because that level depends on the rate of money creation, the real rate of interest also comes to depend on the rate of money creation. Given the fiscal rule, the higher is the degree of monetary financing of the deficit, the lower is the stock of debt, and the lower is the steady-state real interest rate.

The intuition behind this result is the following. With given per capita output and per capita expenditure, per capita consumption also is given. Hence total human and nonhuman wealth, on which consumption depends, also must be given. To a different degree of monetary financing (and a different rate of inflation) there does, however, correspond a different composition of total wealth: the higher is the rate of money creation, the lower is nonhuman wealth, because of a lower public debt, and the higher is human wealth, because of lower taxation. The rate of interest must move so as to ensure that these two changes offset each other and that the total remains unchanged.

Because a lower rate of money creation corresponds not only to a higher stock of interest-bearing debt but also to a higher real interest rate, the inverse relationship between the level of taxation and the rate of money creation is strengthened. To exemplify in the simple case with *n*–0 and α = 0, compare the two steady-state levels of taxation corresponding to two rates of money creation, *p* and *p*′ > *p*. With a unitary elasticity of the demand for money with respect to the nominal interest rate, as in equation (14), the difference between the two levels will be (â/*p*)[*r*(*p*′ − *p*)/*p*′] if *r* is constant. If, however, to the two different levels of total debt (â/*p*) and (â/*p*′) there correspond two different real interest rates, *r* and *r*′ < *r*, the difference between the two levels of taxation will be (â/*p*)[(*rp*′ − *r*′*p*)/*p*′], greater than in the previous case. Further, if there is a critical level beyond which taxation cannot be increased, such a limit will now correspond to a level of interest-bearing debt lower than in the case of a constant real interest rate—whence an additional attraction for stepping up monetary financing, therefore inflation, at an earlier date.

If one now removes the assumption of given capital and output per person, one can, again following Blanchard, examine the effects of different degrees of monetary financing on capital intensity and the steady-state level of consumption. Suppose that (in a one-commodity world) ŷ = *f*(*k*), with *f*′ > 0, *f*″ < 0. Then equation (17) becomes

if k̇ = 0,

From equation (13) one has

Differentiation of equation (16) yields

By using equations (13), (14), (18), (23), and (24), one obtains

Consumption thus reaches a stationary level, with ċ = 0, when

for the steady-state value of the debt. The locus k̇ = 0 is given by equation (22), the traditional production function diminished by *g*. The locus ċ = 0 is given by equation (26) and is a function of *k* and of total debt. On the *c-k* plane, it is thus an increasing function of *k*, tending to infinity for that value of *k* that is chosen when *r* = θ. The two loci will normally intersect at values of *k* corresponding to a real interest rate such that 0 < *r* < θ, and their intersection determines the steady-state values of per capita consumption and capital per person.

The position of the ċ = 0 locus depends on the size of total debt, which in turn depends on the rate of monetary financing: the lower is the latter, the higher is the size of the debt, the higher is the level of *c* corresponding to any given level of *k* on the locus (because total nonhuman wealth is higher), and the greater therefore is the slope of the locus. For a greater slope of the ċ = 0 locus, however, the intersection with the k̇ = 0 locus occurs at a lower steady-state level of both per capita capital and consumption. Thus, consider two economies with the same fiscal rule and the same level of government spending: the one with the lower level of monetary financing will have a higher level of debt, a higher real interest rate, and lower levels of steady-state consumption and capital, A reduction in the rate of monetary financing will increase consumption in the short run, but higher consumption at the initial level of output will cause capital decumulation and a reduction in the steady-state level of capital stock and consumption.

These possible long-run effects of debt growth on capital intensity and consumption may lend additional attraction to higher rates of monetary financing and of inflation when governments are unable or unwilling to modify their lax fiscal rules and wish at the same time to avoid the damaging consequences of fast debt growth.

## IV. Conclusions

The notion that a fiscal rule is sustainable if it respects the government’s intertemporal budget constraint provides an unsafe criterion for assessing the financial situation of the public sector.

First, even if there are no limits to the tax burden that the community is ready to bear for servicing the debt, or if such limits are neglected, the constraint is not sufficient to establish a condition of sustainability when the size of the debt affects the real interest rate in the medium run. When it does, as is probable in the case of finite horizons, a given fiscal rule may become less sustainable with time and may eventually turn out to be unsustainable even in the widest sense of the budget constraint. This outcome becomes more likely if the perception of approaching unsus-tainability causes a risk premium to be demanded on state bonds. It follows that, even when initially the real growth rate exceeds the real interest rate, so that a problem of sustainability does not even arise, it would be unwise to rely on an indefinite perpetuation of this favorable situation to justify fiscal rules causing debt to grow to high levels. Exogenous shocks may lower the trend growth rate, raise the real cost of debt, or both. Fiscal rules, moreover, are not easily reversible, so that it may prove difficult and painful to adapt a formerly acceptable rule to changing circumstances.

Second, given the fiscal rule, respect of the intertemporal budget constraint determines the behavior of taxation. The existence of a limit to the tax burden may make the rule unsustainable after a certain time because from that point onward the rule cannot be followed nor the constraint be respected. It is difficult to define in principle and to perceive in practice the maximum level of the fiscal burden a government can enforce on society without causing strong political opposition, damaging growth prospects, or both: such a level depends on several economic and noneconomic factors, among which the distribution of income, wealth, and the tax burden is of paramount importance. Again, a change of external conditions may set the behavior of the tax burden required by the constraint onto an unsustainable path.

Consideration of these two points may help to explain both the painless re-entry from a situation of very high levels of debt and the more recent experiences of the past decade in some countries. The former is associated with periods of fast growth of output and of the tax base, with relatively low real interest rates. The latter finds some explanation in the sudden transition from a period in which the excess of the growth rate over the interest rate made primary deficits compatible with stationary or slowly growing debt ratios to a period, still persisting, of much lower growth and much higher interest rates. Fiscal rules that have caused no problems in good times later become the source of present or future troubles because they now imply a much faster growth of interest payments, and of the tax burden, if the government’s intertemporal budget constraint is to be respected.

If one starts with a potentially lax fiscal rule, when an unfavorable change of conditions has occurred and debt has started growing fast, an orthodox path to re-entry may prove extremely difficult. The analysis in the paper has neglected any effect of changes in the fiscal rule on real growth. There may be no such effects in the long run. It is, however, difficult to accept that such changes have no consequences for demand and output in the short run, especially if the economy is below full employment. If there occurs an unfavorable change in the external conditions that depresses growth or raises interest rates, an attempt to curb debt growth by means of drastic cuts in expenditure or tax increases will prove unattractive—for the justified fear that what is gained by changing the fiscal rule is lost by lowering growth.

Thus one comes to a third reason that the intertemporal budget constraint is unable to provide a well-defined criterion for policy. Respect of the constraint for a given fiscal rule and the tax implications of a rule that respects the constraint both depend on the degree of monetary financing of the deficit and thus on a choice of the inflation rate. I have argued that capital levies and monetization are not likely to be successful shortcuts for the solution of a debt problem. A choice regarding the degree of monetary financing is different from these two remedies in its nature and its effects. Although not a solution to the basic fiscal problem, it may become the only way out if the authorities allow themselves to be trapped in the impossible alternative between raising taxes above the socially acceptable level and financial instability from unsustainable debt growth.

One may, however, look at the degree of freedom allowed by the choice as to the extent of monetary financing of the deficit in a less negative way. When a less favorable external situation causes a sudden acceleration of debt growth and originates a debt problem, monetary financing may become a policy variable to be used to make a re-entry plan more feasible (because more gradual) and to cushion the possible negative effects on demand and growth. The alternative between “bonds only” and “money only” in the financing of the deficit neglects intermediate and less dramatic combinations, leaving an impossible choice between hyperinflation and unsustainable debt growth.

In the situation of a high debt stock inherited from the past, it is perhaps a paradox that the legislature, by deciding on current fiscal policy, actually determines the future inflation tax, which, in principle, falls outside its competence, whereas the decisions by the monetary authorities with regard to the current inflation tax affect the future tax burden beyond the decisions of the legislature. Unfortunately, legislatures do not care very much about the future inflation tax, whereas monetary authorities care little about the future tax burden. This causes the risk of a conflict with potentially dangerous outcomes, a conflict that would best be avoided by some mutual concession on both parts.

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(Amsterdam) Vol. 16 (July 1985), pp. 19–44.*Journal of Monetary Economics*Barro, Robert, “Are Government Bonds Net Wealth?”

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(Amsterdam), Vol. 4 (August 1978), pp. 569–81.*Journal of Monetary Economics*Blanchard, Olivier J., “Current and Anticipated Deficits, Interest Rates and Economic Activity,”

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(Chicago), Vol. 93 (April 1985), pp. 223–47.*Journal of Political Economy*Blanchard, Olivier J., and Lawrence H. Summers, “Perspectives on High World Real Interest Rates,”

: 2 (1984), The Brookings Institution (Washington), pp. 273–324.*Brookings Papers on Economic Activity*Blanchard, Olivier J., Rudiger Dornbusch, and Willem Buiter,

*Public Debt and Fiscal Responsibility*, Paper 22 (Brussels: Centre for European Policy Studies, 1985).Bresciani-Turroni, Costantino, “Le vicende del Marco Tedesco,”

, Vol. 7 (Milano: Universita Bocconi, 1931).*Annali di Economia*Bresciani-Turroni, Costantino,

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*Public Principles of Public Debt*(Homewood, Illinois: R.D. Irwin, 1958).Buiter, Willem, “Fiscal Policy in Open, Interdependent Economies,” Discussion Paper Series, No. 28 (London: Centre for Economic Policy Research, 1984).

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*L’indebitamento pubblico in Italia*(Rome: Camera dei Deputati, 1985).Cukierman, Alex, and Jorgen Mortensen,

, Economic Papers, No. 15 (Brussels: Commission of the European Communities, June 1983).*Monetary Assets and Inflation Induced Distortions of the National Accounts—Conceptual Issues and Corrections of Sectoral Income Flows in Five EEC Countries*de Larosière, Jacques, “The Growth of Public Debt and the Need for Fiscal Discipline” (Washington: International Monetary Fund, 1984),

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(Geneva, 1946).*The Course and Control of Inflation*Organization for Economic Cooperation and Development,

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^{}*

Mr. Spaventa is Professor of Economics at the University of Rome. He was visiting scholar in the Fiscal Affairs Department of the Fund during fall 1984. In that year he also chaired a commission appointed by the Italian Chamber of Deputies to report on the growth of public debt in Italy.

^{}1

On past experiences see, among others, Kindleberger (1984, Chapter 9 and Part Four), Nurkse (1946), Bresciani-Turroni (1931), and Marconi (1981). Surveys of recent experiences are in Organization for Economic Cooperation and Development (1984 and 1986), de Larostère (1984), Tanzi (1985); on the recent Italian experience, see Spaventa (1984) and Camera dei Deputati (1985).

^{}2

The obvious reference is to Ricardo (1951); the less obvious one is to De Viti de Marco ((1953); first edition (1934)) and in general to the Italian School of Public Finance in the 1930s. For Buchanan (1958, p. 116), who gives an exhaustive account of the Italian debate, “the basic Ricardian proposition concerning the fundamental equivalence between extraordinary taxes and public loans … has been discussed to such greater length in Italian works that it may properly be said to belong to the Italian rather than to the English tradition,” It may perhaps be added that the Italian debate may display less analytical elegance than modern contributions that have redebated the same issues, but it often shows a far greater sense of reality.

^{}3

The literature on inflation correction has grown apace with the growth of deficits and debt. See, for instance, Miller (1982), Miller and Babbs (1983), Cukierman and Mortensen (1983), and Eisner and Pieper (1984). Objections to inflation accounting, especially from official agencies, often stem from the belief that higher nominal figures help to keep up the pressure for fiscal adjustment. This argument can be easily turned on its head: when inflation declines, nominal interest payments as a ratio to GDP fall even if the real interest rate, and hence real interest payments, rise, as often happens. In this case, it is not inflation accounting but the lack of it that may delude the authorities into thinking that their budget problem is on the way to being solved, while instead there has been no deceleration of debt growth.

^{}4

See Blanchard (1984, 1985); Buiter (1984, 1985); and Blanchard, Dornbusch, and Buiter (1985). McCallum (1984) shows that the boundedness of debt growth, as also shown below, is not necessary to meet the intertemporal constraint. The government’s intertemporal constraint is the necessary counterpart of a transversality condition for rational agents with infinite horizons.

^{}5

Thus, suppose that α = *i* but that a constant share μ of the (growing) borrowing requirement is financed with money creation. Debt growth is, in this case, given by ḃ_{t} = (*a* + *i*_{t})(1 − μ) − λ_{t}*b*_{t}, with the nominal interest rate and the nominal growth rate rising together with the rate of inflation and the rate of money creation. The intertemporal budget constraint is now met, and there may exist a steady-state value for *b*.

^{}6

When α = *i* one has a “polar Ricardi an regime” because the growth in debt service is entirely backed by the growth in taxation; see Aiyagari and Gertler (1985).

^{}7

The increase in taxes necessary to ensure constancy of the debt ratio at *t* = 0 is *a* − λ*m* + (α − λ)*b*_{0}, and taxes would rise from τ_{0} = *g* − *a* + (*i* − α)*b*_{0} to τ′ = *g* + (*r* − *n*)*b*_{0} − λ*m*.

^{}8

If the steady-state level of τ is τ* = *g* − a + (*i* − α)*b** and τ′ is the level of taxation required to stop debt growth immediately, τ* − τ = (*n* − *r*)(*b*_{0} − *b**) < 0 for *n* < *r*.

^{}10

The difference between the two flows—τ′, a level of taxation higher now but constant in the future, and τ_{s}, the growing level of taxes implied by the given fiscal rule, with both discounted at the rate (*r* − *n* + π)—is always positive.

^{}11

In what follows, I will be quoting from Keynes’s *A Tract on Monetary Reform* (1923; in Keynes (1971)). But De Viti de Marco had perceived the problem with equal clarity when he considered the increase in taxation that the state has to impose to pay the interests on a loan: “The State is unaffected by this transaction, but the economic budget of the community is not…. The community is not a homogeneous entity, which pays 50 million worth of taxes and perceives 50 million worth of interests; the State receives 50 million of taxes from *some*, and pays 50 million of interests to *others*” (De Viti de Marco (1953, p. 402; 1961 reprint)).

^{}12

On the relevance of the average maturity of the debt for the success of monetization and on the shortening of that maturity in recent times, see Blanchard, Dornbusch, and Buiter (1985). Among the industrial countries, Italy provides perhaps an extreme example of the impossibility of solving the debt problem through monetization in the Keynesian sense. In Italy the average maturity of the interest-bearing debt on the market is less than four years. Further, and more important, at the end of 1984 treasury bills (with a maximum duration of one year) accounted for almost 40 percent of total public debt, whereas more than 45 percent was in the form of treasury certificates, with a yield indexed on that of the six-month or (for a smaller fraction) of the one-year treasury bills. Finally, Italy still has a large primary deficit, and interest payments have reached about the level of the revenues from the personal income tax.

^{}13

The case of “normal” monetary financing, as distinguished from drastic and sudden monetization intended to reduce the real value of debt, was explicitly considered by Keynes (1971, p. 43): the “conveniences of using money in daily life are so great that the public are prepared, rather than forgo them, to pay the inflationary tax, provided it is not raised to a prohibitive level. Like other conveniences of life the use of money is taxable, and … a government can get resources by a *continuous* practice of inflation, even when this is foreseen by the public generally, unless the sums they seek to raise in this way are grossly excessive.”

^{}15

*b*

_{0}to remain stationary, λ′ must be such that (

*a*− λ′

*m*′)/(λ′ −

*a*) =

*b*

_{0}, so that

^{}16

As in Sargent and Wallace (1981) and in a model by Nicoletti (1986).

^{}17

The difference between the two rates of monetary financing is λ^{+}*m*^{+} − λ′*m*′ = *b*_{t}(λ′*i* − λ*i*′)/(*i*′ − α) = *b*_{t}(*r* − *n*)(*p*′ − *p*)/(*i*′ − α).

^{}18

This point seems to be disregarded in the criticisms by Blanchard, Dornbusch, and Buiter (1985, p. 17) against the plausibility of a Sargent and Wallace (1981) outcome.

^{}19

See also Blanchard and Summers (1984) and Buiter (1984).

^{}20

See Buiter (1984, p. 60). Another model in which “contrary to what a superficial reader of Barro might be led to infer, the money-bonds mixture ‘matters’” can be found in Calvo (1985).

^{}21

It is crucial for aggregation and for the results that “whereas individual wealth accumulates, for those alive, at rate *r* + π, aggregate wealth accumulates at rate *r*” (Blanchard (1985, p. 229)). This depends on the Yaari assumption that agents contract to return their wealth to life insurance companies when they die: because insurance companies pay *w* to the agents who are alive, π*w* is only a transfer.