Fiscal inconsistencies and high inflation

sense: it is meant here to come to understand the

D. Heymann and P. Sanguinetti,

A-

91

Fiscal inconsistencies and high inflation

1--7--r----r

“p

P

lnflatlon(p)

lH(p)--R(P) 1

Fig. 1

possibility that, given private sector expectations, to produce surprise inflation. We can rewrite (8) in the following way:

the government

would

try

or alternatively,

where the above condition implicitly defines a relationship between the the discrepancy inflation rate and a ‘target’ deficit d*, which measures between desired spending and the maximum (at zero inflation) yield of standard taxes. Now, the expression R(p) = (m(p) - h,)p/( 1 + p) measures inflationary tax revenues net of the losses produced by the fiscal lag effect; given the assumptions about the demand for money, it is a single-peaked function which has a maximum at p = 6 and reaches zero at p =0 and p =@.‘I The second term in the right-hand side of (9), H(p), is an increasing, convex function, which tends to infinity as p tends to p. Fig. 1 shows the graph of each term separately; fig. 2a depicts the determination of the equilibrium level of inflation resulting from the intersection of the curve G(p)=R(p)+H(p) with the level of fiscal pressures d* [eq. “Due to the fiscal-lag effect, the ‘net inflation revenue’ reaches which is lower than that which maximizes the inflation tax.

a maximum

at a value for p

92

D. Heymann and P. Sanguinetti, Fiscal inconsistencies and high inflation 2a. Alpha large

lnflatlon (p)

P’

E

2b. Alpha small

P’

lnflatlon (p)

P' b

Fig. 2

increases (9)]. In the case shown in this figure, the rate of inflation monotonically with d*, and tends to the limit p as d* grows large. On the other hand, for a small enough value of c(, the possibility exists that the G(p) curve displays a non-monotonic behavior. This case is illustrated in lig. 2b, where now the relationship between inflation and fiscal pressures is not up the possibility for uniquely determined for all values of d*, opening multiple equilibria. Though this latter case is probably not too relevant in practice (cf. section 3 below), its qualitative results are interesting, since it points to the existence of four ‘regimes’, associated with different types of behavior of fiscal policies and inflation.

2.3. Fiscal pressures These four regions

and inji’ation

- whose qualitative

features,

except for the case where a

93

D. Heymann and P. Sanguinetti, Fiscal inconsistencies and high inflation

PC

Pb inflation

[-

G(P)

(p)

R(P)

’

Fig. 3

multiplicity of equilibria arises, are also illustrative of the solutions when c( is ‘large’ - are indicated in fig. 3. The figure shows the graph for the equilibrium relationship d* =G(p) (for a small) together with a plot for the inflation-tax revenue curve R(p). Four cases are clearly distinguished: (i) g* 5 h, + h, (or d* SO). In this case there is no ‘pressure’ to spend beyond the taxing potential. As a consequence, inflation (due to a fiscal impulse) is zero, and the tax system operates with ‘excess capacity’. The desired deficit is zero; the target level of expenditures can be financed by setting taxes below the maximum feasible value; for d * =O, p* =0 is the unique solution to (9) if tl # 0. (ii) O
above

1

~ R’(p) + H’(p)

expression

> 0.

is positive

since

the

economy

is located

on

the

D. Heymann and P. Sanguinetti, Fiscal inconsistencies and high inflation

94

increasing branch of the inflationary tax revenue curve: R’(p) >O (see fig. 3) and H’(p) is always positive. In summary, this case would correspond qualitatively to a moderate inflation regime, where fiscal pressures are partially accommodated by the government by raising the inflation tax. There is a unique discretionary equilibrium p* for each value of the ‘fiscal overhang’ d*, so that ‘inflationary traps’ are ruled out. (iii) d* d*. Here, the behavior of the government resembles that of a revenue maximizer. The discrepancy between the level of spending which would ‘pacify’ political demands (g*) and the limited ability to tax (h,+h,) is so big that the target level of deficit is now beyond the maximum level of inflationary tax revenues R(p”) (see fig. 3). Thus, the strong incentives for the government to inflate imply that private expectations are going to be validated only at a very high level of inflation; as a consequence, the equilibrium is located on the wrong side of the revenue curve. Inflation rises with fiscal pressures, but realized expenditures decline with g*:

ap

-= ag*

1

->o, R’(P) + H’(P)

and

-aK=R'(p) $ <0, ag* since R’(p) ~0 and H’(p) > 1R’(p) 1. Thus, a curious effect appears, because

increases

‘2Recall that this region does not exist if a is large. 13Total revenues can be expressed as g=(m(p)-h,)L+h,+h,=R(P)+h,+h,, l+P

since Rh)S

R(P,), then gb)

Sg(P.).

in fiscal pressures

produce

D. Heymann and P. Sanguinetti, Fiscal inconsistencies and high inflation

95

a fall in actual spending. This result bears an analogy with the observed behavior in hyperinflations, where public expenditures typically shrink while prices increase very rapidly. Also, from fig. 3 it can be seen that in this region, the equilibrium is again unique and determined only by d *. In other words, no expectations-driven inflationary traps are possible here. In the limit, as the value of d* keeps increasing, p becomes close to p, where even an ‘unexpected increase in inflation would cause a revenue loss through the fiscal-lag effect which nearly offsets the increase in seigniorage. At this point, the government has clearly lost control over its fiscal policies: it is hardpressed to spend, but cannot deliver even by bearing higher inflationary costs, and it ends up losing both because of the high level of inflation and the low level of realized expenditures.

2.4. High inflation

with low deficits

The equilibrium in this fourth region of very high inflation has other interesting properties. As d* keeps increasing, total revenues approach h,, + h,, that is, the revenue from regular taxes in the absence of the fiscal-lag effect. Therefore, actual expenditures are similar to those which the government could sustain at zero inflation. This corresponds to the intuitive idea that, when inflation reaches extremely high levels ‘it serves no purpose’ as a revenue raising devise. In such conditions, it may seem that the government could actually ‘do without inflation’. Thus, in principle, it could be argued that, if expectations were somehow brought down, regular taxes would automatically compensate for the loss of inflationary revenues, and the economy would stabilize without any further action needed. But this statement would be misleading. In this type of very high inflation, the government is ‘forced’ to contract spending; if by any chance inflationary expectations were to go to zero, the pressures on fiscal policies would come to the open so that, given its unchanged incentives, the government would again rely on the inflation tax. In other words, the zero-inflation policy is not time-consistent. A corollary of this argument would be that a sustained disinflation requires a shift in the parameters of the problem and, in particular, an increase in the taxing capacity and/or a drop in g*. That is, government incentives would have to be changed permanently.

2.5. The effects

I$ tax indexing

Another implication of the model has to do with the effect of policies such as the indexation of the tax system (i.e. a reduction of h, for a given fiscal ‘capacity’ h,+ h,). It is found that the effects of such a policy would be

96

D. Heymann and P. Sanguinetti, Fiscal inconsistencies and high inflation

substantially different depending on the type of fiscal and inflationary regime.r4 Applying the implicit function theorem to eq. (9) we obtain

Consider first the case where the economy is in the low inflation regime (d* d), the inverse result holds. Although the denominator is still positive [cf. point (iv) above], the value of the numerator will now be negative. To see this, recall that as d* keeps increasing, m(p) -h, goes to zero implying that actual expenditures (g) tend to h,+h,, and that the expression between brackets in (10) tends to -d* which is, of course, negative. As a consequence, inflation and h, are negatively associated in this region. The intuition is straightforward: in this case, the fiscal lag acts as a disincentive against producing surprise inflation. If this brake operates with less strength, the government’s ‘scramble for revenues’ would make it accelerate inflation even further. Thus, when the government is subject to strong pressures, not only public expenditures may fall because of the revenue-constraint, but also, measures that in other contexts would have helped to reduce inflation, could in fact accelerate inflation even further. There is an analogy between tax indexation

14Thisconclusion is independent of whether a is small or large. Fischer and Summers (1989) have analyzed a policy game where tax indexing is taken as a measure that reduces the marginal cost of inflation; they find that the equilibrium inflation rate always increases when the tax system is less exposed to the fiscal-lag effect. Our result is different, since we model directly the effect of tax indexing on revenues - and thus on ‘spending opportunities’ ~ without modifying the parameters of the loss function. In this case, reducing the fiscal lag effect lowers the steadystate inflation when fiscal pressures are low, but may have the opposite effect when d* is large. 15A formal proof is omitted. However, note that as d* tends to zero R(p) tends to d* so that 2R(p)>d*.

D. Heymann and P. Sanguinetti, Fiscal inconsistencies and high inflation

91

and other policies traditionally used to reduce the distortions produced by high inflation, such as the issue of ‘inflation-proof financial assets: such policies may tend to accelerate the inflationary process and, under certain circumstances, may not be welfare improving [cf. Fischer and Summers (1989)].

3. Some simulation exercises Although the model is not designed to produce quantitatively precise results, it seems useful to make it subject to numerical simulations, in order to get a feeling of what kind of outcomes it generates, and check whether they bear any resemblance with actual experience. In order to do so, it is of course necessary to impose values to the parameters and to specify the functional form of money demand. We will work with a standard Cagan-type function;16 accordingly, the model has one ‘driving variable’, d* and four parameters: the zero-inflation level of money demand A, the semi-elasticity of the demand for real balances fl, the value of the tax base subject to the fiscal lag effect h,, and CI,the ‘inflation cost’ parameter in the government’s loss function. The time unit is defined as one month. Therefore, inflation will be measured as a monthly rate, and (since we shall use a GDP scaling throughout), real money balances shall be measured as a portion of monthly GDP. The analysis will be carried out using basic values for the parameters reminiscent to that of the Argentine case. A money demand function with A = 1, /?= 3 implies a level of real balances of around 8% of annual GDP at low inflation and a fraction over 3 points of GDP at 30% per month inflation. The value of 3 for the semi-elasticity fi is similar to that estimated by Kiguel and Neumayer (1990) and Rodriguez (1991). This implies a maximum ‘gross’ inflation tax revenue (i.e. before subtracting losses through the fiscal-lag effect) of 9.5% of GDP, at an inflation rate near 25% pr month. Moreover, we shall assume a ‘tax capacity’ (h,+h,) of 20% of GDP, with h, =0.12, that is, a little more than half of the tax base is subject to a one-month collection lag. The results of the simulations for different values of the parameter a are depicted in fig. 4. They indicate that: (i) Multiple equilibria are indeed identified in some cases. However, given the monetary-fiscal parameters used in the exercise, steady-state high inflation traps appear only for very low values of a. 16We shall be using this specification as if it was valid for the whole range of possible inflation rates. However, the empirical evidence suggests that the semi-elasticity B may fall with the rate of inflation. See, for example, Easterly and Schmidt-Hebbel (1991).

D. Heymann and P. Sanguinetti,

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Fiscal inconsistencies

and high inflation

4a. Beta=3 hl=O.12 0.90

0.800.70b

o.EG-

5

0.50

2 $J

0.400.300.x)-

o.mc 0.00

l-

kr

.“.-=+-

O.lO0.10

’ 0.33

0.40

Monthly

Inflation (p)

0.20

alpha=O.CCKE -

alpha=O.Ol

0.50

0.60

0.70

..~~~*..~ alpha=O.B

0.80

1

4b. Beta=3 hl=O.12 1 .m0.93 0.80-

0.00

0.10

0.M

0.30

Monthly

I-

alpha=O.l

-

0.40

0.50

0.60

Inflation (p)

alpha=0.5

Fig. 4. Simulations.

*‘*~~*~*~ alpha=1

1

D. Heymann and P. Sanguinetti, Fiscal inconsistencies and high inflation

99

(ii) The inflation rate that solves the model seems not too sensitive to the parameter a when fiscal pressures are low (in the ‘moderate inflation’ range); by contrast, the behavior at large d * varies considerably with a. (iii) The model generates high inflation solutions for large, but not implausible levels of d* when a takes ‘intermediate’ values. For example, with a=O.l, a ‘target’ zero inflation deficit of 15% of GDP would be associated with an inflation rate over 20% per month; the same d* would induce a 30% inflation with a = 0.05.” (iv) Inflation rates in the ‘hyperinflation’ range (say, over 50% per month) are not obtained as solution except for very low levels of a or extremely large fiscal pressures. In other words, while high inflations appear in the model as possible steady states for not extraordinary parameter values, hyperinflations look like aberrant states. In a way, this may suggest that the model does not account well for hyperinflations, but it also reinforces the impression of those episodes as extreme cases where the collapse of fiscal policies leaves little room to contemplate other policy objectives - and as phenomena of a transitory nature, which ‘burn themselves out’ in a relatively short interval of time.

4. Fiscal pressures and the public debt The argument presented in the previous sections relied on the assumption that money creation is the only source of government finance. A closer look at the behavior of public debt in high and hyper-inflations shows a rather complex picture of old debts not punctually serviced or refinanced with great difficulties, new bond issues of limited sizes with very high promised yields and very short maturities - that the market sometimes willingly absorbs even when outstanding assets remain unpaid - more or less ‘forced’ sales of bonds to the financial sector or to suppliers, arrears in the pre-commited payments and the like. That is, by some means or other, governments do engage in debt financing, and the existing debt is not homogeneous regarding the public’s perceptions of the actual default risk. By and large, however, the image of a credit constrained government appears appropriate in those instances: not only does the ‘monetarist arithmetic’ [in terms of Sargent and Wallace (1981)] operate at high speed, but also the perspective of an outright default (which sometimes materializes) is present in agents’ expectations, so that the government’s access to the loan market is severely restricted. This section sketches a simple extension of the previous model, incorporating government debt. The exercise is set up so as to stay as close as possible

“It may be useful to recall that the measured, actual deficit has a maximum near 9.5”/” of GDP. The solution with p = 0.30 is just above the rate which maximizes the ‘gross’ inflation tax.

100

D. Heymann

and P. Sanguinetti,

Fiscal inconsistencies

and high injation

to the one-period analysis done before; for that purpose and for general tractability reasons, several simplifying assumptions have to be imposed. The problem we study is a variant of one discussed in recent literature [cf. Calvo and Guidotti (1990a, b)]. The government is supposed to have ‘inherited’ a certain volume of debt, of size b, a portion of which is (perfectly) indexed to the price level. All bonds have a one-period maturity and they become due at the end of period t- 1, after that period’s markets have ‘closed’ and before they open in t. At this moment, the government must refinance the debt, or it can choose to repudiate its obligations. If it does default, we assume that no new debt is issued in the following periods. When the default option is not taken, the government may sell either perfectly indexed bonds (i.e. with returns contingent on the price level at maturity) or nominal bonds. In period t, the government taxes, spends and sets the inflation rate; its expenditures now include (in the non-default case) the service of the debt. As before, the decision-maker cares about the level of inflation and the discrepancy between the level of ‘primary’ spending (i.e excluding debt services) and a ‘desired’ level. In this setting, the government has two ways of trying to reduce the real value of its debt burden: by inflating away its nominal liabilities or by explicitly declaring its bankruptcy, in which case we assume that it bears a cost, which is represented by adding a fixed term to the loss function.” The formulation corresponds to the view that explicit default is more of an ‘eventful’ decision than a choice at the margin; including the costs in the loss function suggests an interpretation as the ‘voice’ of bond-holders, which somehow hurts the government. The willingness to hold government bonds can be expected to vary with the level of the debt and with d*, ‘the primary fiscal pressures’. When fiscal pressures are large, the government is bearing high costs due to inflation and to the expenditure gap: in those circumstances, the authorities could be tempted to default on the debt, in order to soften a very tight budget constraint, even if that means incurring a direct cost. If that reaction is incorporated into the public’s expectations, a rise of d* above a certain critical value may trigger a collapse in the demand for government debt. This is indeed what the model indicates.” It is intuitively clear why such a threshold value for d* should exist. For small primary fiscal pressures, the resulting inflation is also low, so that the government can ‘afford’ to increase it slightly in order to collect enough “Default costs have been treated in various ways in the literature. Calve (1988) introduces them in the government’s budget constraint, so that their effect is to reduce spending. Prati (1991) assimilates default costs to a sort of distortionary tax by including them in the budget constraint of the representative agent. The approach we follow here is similar to that presented in Alesina et al. (1990). 19A proof is outlined in a longer version of the paper.

D. Heymann and P. Sanguinetti, Fiscal inconsistencies and high inflation

101

seigniorage revenues to meet the interest payments and still be able to partially accommodate the (small) pressures for deficit spending. Clearly, this alternative is cheaper compared to the case in which the government decides not to service the debt and bears the fixed cost of default. By contrast, if d * is large, and consequently the inflation rate is also high, the costs of servicing the debt rise considerably both in terms of an increasing inflation and of lower levels of primary expenditures. In those circumstances, the government may find it preferable to pay the cost of repudiation in order to be relieved of its debt burden. The critical value d^ is of course a function of the parameters of the problem. Increases in debt services reduce 2: for a given primary fiscal pressure, there is - ceteris paribus - a maximum sustainable debt; this falls as d* grows larger. In other words, a ‘hard-pressed government finds itself credit-constrained even at low levels of debt. In addition, it can be verified that d^grows with the proportion of the debt which is indexed to the price level. Thus, according to the model, the existence of nominal debt stengthens the incentive for explicit default: when the debt consists mainly of indexed bonds, the government gains less from inflationary surprises; this, in turn, reduces the equilibrium inflation rate for a given d* and, therefore, lowers the losses in the debt-servicing case. It would then seem that, in a literal interpretation of the previous result, the ‘optimal’ mix of indexed and nominal debt would be located at the corner solution, where the government does not issue nominal liabilities at all. However, the assumptions of the exercise are clearly biased towards this conclusion. First, we have worked under the hypothesis that it is feasible to have perfect contemporaneous indexing when, in fact, the definition of an appropriate basket to use in indexation clauses is non-trivial, and there are built-in lags in measuring and reporting price indices. This problem becomes of great importance when inflation grows high. In addition, our analysis has disregarded the possibility of random shocks. Recent literature has stressed that nominal debt can be a low-cost instrument to absorb those shocks [cf. Bohn (1988)]. We conjecture that an analysis similar to that sketched here, but allowing, say, for disturbances in fiscal pressures, may result in a positive level of nominal debt in the ‘preferred’ mix of government liabilities, and also would suggest that the share of nominal debt should vary negatively with fiscal pressures. The qualitative reasoning behind this conjecture is as follows. For low levels of d*, the incentives to generate unexpected inflation are weak, since the government does not face a large spending gap; inflation is also low. In those conditions, the gains from being able to smooth out shocks in d * would offset with excess the losses from a higher equilibrium inflation. On the contrary, with a large d*, the existence of a sizeable volume of nominal debt has strong effects on equilibrium inflation and the ‘marginal cost’ of inflation is high: this would

102

D. Heymann

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Fiscal inconsistencies

and high inj7ation

imply a preference for issuing indexed bonds - as long as d * remains lower than the critical value -, even if it means giving up an option to accommodate fluctuations in desired spending.

5. Concluding

remarks

We have developed a very simple model of inflationary finance. In its formal aspects, this model represents a slight departure from the existing literature. Its result, however, seem to capture some of the features of different inflationary regimes. We would like to stress three types of results. First, the measured deficit may not be a good indicator of the government’s incentives to engage in inflationary financing. A low deficit can mean either that the government ‘lives comfortably within its means’ or, alternatively, that it is subject to very strong pressures, but is unable to finance more than a limited volume of spending at a very high inflation rate. Beyond an initial transitional period, a sustainable stabilization would require diminishing the pressures on fiscal policies. Second, multiple equilibria are typical features of models of high inflation. They do arise in our model, but as a property of certain particular cases. Our analysis suggests that moderate inflation regimes are immune to (at least some type of) multiple equilibria problems; very high inflations, on the other hand, do not appear here as expectational ‘traps’. Third, some policy measures, i.e. tax indexation, may have quite different effects depending on the inflationary regime, since they may act in quite different ways on the incentives of the government and of the groups that influence fiscal policy. The main conclusions of the model depend on a particular specification of the policy-maker preferences. The choice of the loss function allows us to incorporate in a single analysis different types of fiscal behavior. It is clear, however, that there is a considerable degree of arbitrariness in the specitication of government preferences. Ideally, a model like this one should be embedded in a more comprehensive description incorporating the distributional games which determine both the capacity of the tax system and the demand for public spending. An analysis of this kind, most probably, would emphasize the importance of fiscal institutions such as those governing the budget process and the asymmetries in the power to influence fiscal policies given by such institutions and by the relative strength of competing social groups. From the point of view of a narrowly economic description of the inflation process, our model produces steady-state outcomes which do not represent accurately the volatile behavior observed in high inflation episodes. We have down-played informational considerations and issues of price dynamics in order to highlight what we believe are some interesting aspects of the high

D. Heymann

and P. Sanguinetti,

inflation problem; a full account themes in a prominent place.

Fiscal inconsistencies

of the matter

should

and high inflation

certainly

include

103

those

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Persson, T. and G. Tabellini, 1991, Macroeconomic policy, credibility and politics (Harwood Academic Publishers, London). Prati, A., 1991, Self-fulfilling debt runs and debt management, Mimeo. (UCLA, Los Angeles, CA). Rodriguez, C., 1991, The macroeconomics of the public sector deficits: The case of Argentina, WPS 632 (World Bank. Washington. DC) March. Rogoff, K., 1989, Reputation, coo;dination’ and monetary policy, in: R. Barro, ed., Modern business cycle theory (Harvard University Press, Cambridge, MA). Sanguinetti, P., 1992, The politics of intergovernmental transfers and local government deficits: Theory and evidence, Mimeo. (UCLA, Los Angeles, CA). Sargent, T. and N. Wallace, 1986, Some unpleasant monetarist arithmetic, in: T. Sargent, Rational expectations and inflation (Harper & Row, New York).