Inflation, indexing and economic development

World Development, Vol. 15, No. 8, pp. 1119-1130,1987. Printed in Great Britain.

0

0305-750x/87 1987 Pergamon

$3.00 + 0.00 Journals Ltd.

Inflation, Indexing and Economic Development LARRY SAMUELSON* Pennsylvania State University, University Park University of Illinois, Urbana Summary. - Recent analyses have established that there are significant costs as well as benefits to issuing indexed bonds. An assessment of the desirability of indexing has proven to be elusive, perhaps because of the complexity involved in formulating the (presumably government) preferences by which indexing is to be evaluated and in ascertaining the optimal government policy with which to accompany indexing. This paper develops a general framework for examining indexed bonds. The envelope theorem is exploited to derive a convenient representation of the effects of indexing. The crucial elements in evaluating indexed bonds are the relative desirabilities of transferring purchasing power to the government and reducing consumer liquidity. The greater is the relative importance placed on the former, the more likely are the effects of indexed bonds to be favorably evaluated.

government can achieve more preferred economic outcomes by issuing indexed bonds than it can without issuing such bonds. The complexity of the effects of indexed bonds has hitherto prevented a comprehensive and definitive treatment of this question, though valuable progress has been made. This paper does not answer the question, but develops a method of addressing the question that should simplify the examination and assessment of indexing. We begin in the following section by reviewing the basic issues raised by indexing. This review is facilitated by a number of insightful examinations of the Brazilian indexing experiment. These studies have identified both benefits and undesirable side effects of indexing. Unfortunately, the diversity and ambiguity of the potential effects of indexing make it difficult to assess indexing’s net impact. Section 2 closes with the conclusion that a framework for assessing indexing is required, and identifies several properties which such a construction must exhibit. Section 3 develops a general framework for evaluating indexing and provides an application of that framework. The envelope theorem is exploited to derive an exceptionally convenient representation of the costs and benefits of

1. INTRODUCTION The recent economic experience of the developed countries has exerted a significant impact on economic thought and practice. Since its appearance in the United States in the 1970s the word stagflation has become common. The coexistence of high unemployment and inflation rates has challenged the conventional Keynesian wisdom. Individual behavior has adjusted to the persistence of inflation. Finally, it is occasionally suggested that if inflation cannot be eliminated, perhaps it can be more easily tolerated with the help of government-issued indexed bonds. In its most optimistic form, this suggestion offers the promise of “inflation without tears.“’ Indexed bonds appear to be an even more attractive recourse in less developed countries (LDCs). The fragility of less developed economies makes it especially difficult to control inflation. At the same time, LDCs appear to be especially burdened by the distortions of inflation. In particular, one effect of inflation is to discourage saving and hence hinder capital formation. The accumulation of capital is likely to be an important component of a development strategy, and inflation-induced savings reductions are accordingly likely to be a serious threat to development. Since one of the benefits of indexed bonds is their ability to mobilize savings, indexed bonds may have an important role to play in economic development. This paper examines the role of indexing in development.* The basic question is whether a

*I am grateful to the participants of the conference on “The Resurgence of Inflation in Latin America,” 4-5 April 1986 at the University of Illinois, especially the discussants of this paper, for valuable comments and suggestions. Financial support from the National Science Foundation is gratefully acknowledged.

1119

1120

WORLD

DEVELOPMENT

indexing. We find that the crucial elements in evaluating indexing include the relative desirabilities of transferring purchasing power to the government and reducing consumer liquidity. The greater is the relative importance placed on the former, the more likely are the effects of indexed bonds to be favorably evaluated. Section 4 discusses the analsysis and results. Attention is drawn to policies which may provide attractive alternatives to indexing. In particular, our identification of the transfer of purchasing power to the government as a primary benefit of indexing suggests that an evaluation of indexing might be regarded as an assessment of the excess burden of using indexed bonds to finance government expenditures. This immediately directs attention to other, more direct methods of financing such expenditures. Section 4 also identifies some potentially important issues which arise in connection with indexing but which generally do not appear in economic models, and identifies areas in which further work is required. These include the ability to examine the costs of government policy and distributional issues. The latter are likely to be especially important when considering indexing and inflation, since inflation accomplishes potentially important alterations in the distribution of income. Our model allows us to examine issues concerning the distribution of resources between the government and the private sector, but additional work is required before the distribution of resources within the private sector can be addressed. The result of our analysis is not a verdict on the desirability of indexing, but a framework for organizing assessments of indexing. It is hoped that this methodological exercise will provide useful techniques for evaluating indexing.

2. INDEXING AND ECONOMIC DEVELOPMENT (a) A control-theoretic urpment A useful point of departure in examining indexing is provided by the control theory literature.’ Let an economy’s endogenous variables, such as the rate of inflation, interest rate, income, be employment level, and national referred to as state variables. Let the policy variables which are set by the government, such as spending, borrowing, and taxation levels, be referred to as control variables. A dynamic economy can then be represented by a collection of difference or differential equations which describe the evolution over time of the economy’s state variables given a time-path of control

variables. The problem is to choose the control variables so as to achieve a desirable realization of the state variables. A subset of the economy’s state variables is said to be controllable if, for any arbitrarily chosen time-path of these variables, a choice of control variables exists which causes that time-path to be realized. An interesting question then concerns how many of an economy’s state variables can be controlled. The larger is this number, the more effectively can the government influence economic outcomes. The basic result to emerge from the control theory literature is that the government can control as many state variables as it has control variables at its disposal.’ In light of this. it appears as if indexing must always make a government better off. Indexing allows the government to acquire an extra control variable, the rate of return on indexed bonds. (Notice that nominal bonds might still be offered, so that the rate of return on nominal bonds is retained as a control variable.) This should permit the government to control an additional state variable, and therefore enhance the effectiveness of government policy. Arguments in favor of indexing in LDCs often cite the ability of indexing to affect saving, an approach consistent with a vision of indexing as allowing control of an additional state variable. If this conception of indexing is accurate, governments would never fail to seize the opportunity to index. Two comments on this argument are in order. First, the relationship between indexing and the effectiveness of government policy has been examined in somewhat different settings. In 1963, Tobin argued that the presence of indexed bonds could be expected to make monetary policy more efficient (see Tobin, 1975). This argument was subsequently examined by Beckerman (1980), who concludes that it cannot be determined on theoretical grounds whether indexing will make monetary policy more or less efficient. How can this be reconciled with our contention that indexing should enhance policy effectiveness? The key to this quandary lies in identifying what is meant by the effectiveness of government policy. For Tobin and Beckerman, policy is said to become more efficient if a given policy variable adjustment yields a larger shift in the aggregate demand curve. In the control-theoretic argument, policy is said to become more efficient if the number of state variables which the government can control increases. For example, a shift from a case in which only output can be controlled to a case in which output and the price level can be controlled would be described as an increase in policy effectiveness. Considerations

INFLATION,

INDEXING,

AND

of whether the government must exercise more or less vigorous policy variations in order to control the state variables in question do not arise. We shall return to this difference in Section 4. Second, an initial assessment of the Brazilian indexing experiment suggests that a controltheoretic analysis may be applicable. Indexing in Brazil was successful in mobilizing savings.- It thus appears as if exploiting the ability to set the rate of return on indexed bonds did allow the government to control the economy’s savings. This enhanced the government’s control over a particularly important economic activity. (b) Indexing-induced

economic distortions

Further consideration reveals that this theoretical argument and the interpretation of the Brazilian indexing experience are incomplete. Consider the theoretical argument. The rate of return on indexed bonds does provide the government with an additional control. However, there is no assurance that the optimal level of this control will be high enough to induce individuals to hold indexed bonds. Instead, optimality may entail a rate of return on indexed bonds sufficiently low that such bonds are not held. The controllability argument then allows the possibility that an optimal indexing policy will entail no purchases of indexed bonds. Equivalently, we can say that control-theoretic arguments can be invoked to ensure that the government will consider issuing indexed bonds, but not that they will actually be issued. A further examination of the Brazilian indexing experience reveals that several adverse side effects of indexing appeared. The presence of these side effects suggests that the optimal rate of return on indexed bonds may well be low enough to preclude such bonds from being held. In order to assess the desirability of indexing, the nature and extent of these side effects must be examined. We begin with two preliminary points, the first of which is made by Baer and Beckerman (1980) (see also Beckerman, 1987). Indexing is a device which potentially mitigates the adverse effects of an uncertain rate of inflation, but not of a high rate of inflation. If the rate of inflation were known, nominal rates of return on assets would adjust to compensate for the inflation rate. Higher rates of inflation would simply prompt higher nominal rates of return. Indexing would be redundant. Indexed and non-indexed bonds would have to carry identical nominal (and hence real) rates of return if both were to exist, and would be indistinguishable.

ECONOMIC

DEVELOPMENT

1121

If the rate of inflation is uncertain, nominal rates of return can increase to compensate for the expected rate of inflation, but cannot remove the risk associated with the uncertainty of inflation. Risk averse agents would be willing to sacrifice some of an asset’s expected rate of return in order to avoid this risk. Indexed bonds remove this risk, and are accordingly no longer identical to nominal bonds. Indexed bonds now have a potentially important role to play. The important implication of this distinction is that the effects of indexing stem primarily from considerations involving the riskiness and not the level of inflation.’ This leads to our second point. Indexing can relieve bondholders of risk, but cannot remove risk from the economy. Instead, this risk must reappear in other forms. Hence, indexing cannot eliminate the economic distortions which accompany inflation. It can only either shift their burden or alter their form.7 The new configuration of economic distortions may be either more or less burdensome than the original state. We can now consider the adverse side effects of indexing. The relationship between indexing and the rate of inflation has generated particular interest. The relevant question can be posed in two ways. Does the introduction of indexed bonds exacerbate inflation? More subtly, does the presence of indexed bonds strengthen the inflation-feedback mechanism, so that an inflationary shock has more severe and more persistent effects? Baer and Beckerman (1980) suggest that the answer to the first question is affirmative, stressing an indexing-induced increase in the money supply. Bomberger and Makinen (1980) suggest a similar conclusion, though for somewhat different reasons. Beckerman (1979) suggests an affirmative answer to the second question. The usual intepretation that accompanies these conclusions is that the aggravation of inflation poses a challenge to the desirability of indexing. The relationship. between indexing and inflation involves a number of factors. First, indexing encourages savings by reducing the risk which accompanies saving. This allows the government to finance its expenditures in less inflationary ways, thus dampening inflation. Notice that in this regard, indexing has apparently desirable effects on inflation. However, this increase in savings reduces consumption and hence exerts downward pressure on national income and employment. The benefits of lower inflation are then achieved only at the cost of recessionary pressures (assuming that indexing is used to more conveniently finance a given government expenditure level rather than to increase spending).

1122

WORLD

DEVELOPMENT

The government is always faced with the choice of reducing inflation via a recession, and it is not clear that an indexing-induced shift from inflation into recession will be preferred by a government that presumably declines to implement a recessionary policy in the no-indexing case. We can next observe that indexing renders the holding of money balances less attractive, and consumers reduce these balances in favor of holding government-issued indexed bonds. This exacerbates the flight from money associated with inflation. If the government is committed to the financing through an inflation tax of a given time-path of government deficits, then an indexing-induced reduction in desired money balances is equivalent to a reduction in the tax base. This reduced tax base forces the government to increase tax rates in order to maintain revenue collections. with these increased tax rates taking the form of higher inflation rates.” Here, we find that indexing aggravates inflation. However, it is important to observe that an indexing-induced decrease in money balances is accompanied by an increase in purchases of government-issued indexed bonds. The latter provide financing to the government, and hence potentially mitigate the inflationary pressure of reduced money balances. The net implications for inflation are ambiguous. Indexing also potentially creates liquidity problems for financial institutions, as balances of nominal assets held in such institutions are reduced. The government may then be forced to protect such institutions by providing liquidity, which will apparently fuel inflation. Baer (1987) notes that this mechanism has been particularly important in Brazil. Again, however, a counterforce appears. This inflationary provision of liquidity to the financial system occurs only because indexing prompts consumers to take the deflationary action of reducing money balances and holdings of non-indexed bonds. The net effect on total financial system liquidity and inflation is unclear. The government increase in liquidity may either exceed or fall short of the private reductions in liquidity. Similar factors arise in assessing whether indexing makes the inflation-feedback mechanism more severe. Consider an increase in inflationary expectations or an inflationary shock. Consumers will again be prompted to shift their asset holdings out of money. The availability of indexed bonds enhances the attractiveness of alternatives to money, and the shift out of money may accordingly be more pronounced if indexed bonds are available. The adjustment which arises in response to this more pronounced shift may entail heightened inflation.

This argument captures only the most obvious effect of indexing on the inflation-feedback mechanism, and other effects potentially arise. Beckerman (1979) constructs a more sophisticated analysis of this relationship. He argues that indexing has aggravated the inflation-feedback mechanism in Brazil. However, he finds that the net effect is in general ambiguous, and cannot be determined on theoretical grounds. Baer (1987) and Beckerman (1987) provide an intuitive discussion of these issues, and McNelis (1987) conducts an empirical investigation of indexing and the inflation-feedback mechanism. These observations prompt us to conclude the following. Indexing may have an adverse effect on the rate of inflation. However, relationships between indexing and inflation arise in a number of ways, each of which has an ambiguous net effect. An assessment of indexing must be flexible enough to capture these diverse forces. In particular, an analysis which focuses on only one of these forces may be illuminating, but cannot provide an assessment of indexing. Attention is accordingly directed to the construction of a framework within which these forces can be assessed. Before considering such a framework, a diversion is in order to observe that similar considerations arise in connection with other side effects of indexing. Space limitations restrict us to simply mentioning these effects. Baer and Beckerman (1980) o:‘fer a more complete discussion. These side effects include difficulties arising out of the fact that in issuing indexed bonds, the government assumes an obligation subject to some uncertainty. This uncertainty presumably reappears in the government’s budget in the form of an uncertain monetary or fiscal policy. The government can accordingly shift the inflation risk away from bondholders, but cannot remove it from the economy. The effects of the risk reallocation must be examined in assessing indexing. In addition, the introduction of indexed bonds causes two units of account to coexist, one nominal and one real. As inflationary conditions and expectations change, the relative desirabilities of these two units vary, and potentially volatile shifts from one unit to the other may arise. This introduces instabilities into financial markets and foreign exchange markets. (See Beckerman (1987) for further discussion of this issue in a slightly different context.)

(c) The evaluation of indexing We would like to construct a framework for assessing the desirability of indexed bonds. In

INFLATION,

INDEXING,

AND

light of our previous discussion, four basic requirements for this framework can be identified. First, it must be comprehensive enough to encompass the important costs and benefits of indexing. An essential first step in this direction has been taken by studies which have identified the major effects of indexing, such as the ability to mobilize savings or aggravate inflation. It is now necessary to integrate these factors into a single model so that their relative importance can be assessed. Second, the model must allow a general equilibrium analysis. We have seen that indexing involves potentially conflicting forces and has ambiguous net effects. This is not surprising in light of our observation that indexing can shift but not eliminate inflationary distortions. An assessment of indexing must adopt a general equilibrium approach to capture the transformed nature of these distortions. Third, the effects of indexed bonds depend upon the nature of the policy that the government pursues in connection with indexing. For example, choices of the government’s policy variables are likely to exist which yield either higher or lower inflation rates than the noindexing case. It is accordingly not meaningful to ask simply whether indexing worsens the inflation rate. As a first pass, it could be asked whether indexing yields a higher inflation rate given a setting of the government’s other policy variables. A more important question would be whether indexing would aggravate inflation given that the government chooses an optimal policy for its remaining variables. These first three observations are fairly standard exhortations to conduct a careful and thorough analysis of indexing. The fourth point is more fundamental. The link between the effects of indexing and the settings of the government’s other policy variables makes it difficult to assess such phenomena as the effects of indexing on inflation. Suppose it is discovered that if indexing is practiced and if the government sets its other instruments optimally, then the rate of inflation will increase. How is this to be evaluated? The inflation rate is higher, but the government has presumably optimally chosen it to be higher. It is then not obvious that the higher rate of inflation is to be considered an adverse effect of indexing. The appropriate standard by which the effects of indexing, including a variation in the inflation rate, should be judged is the preferences by which the government chooses its policies. The government’s preferences over economic outcomes must then be modeled. The relevant question is accordingly whether indexing allows the government to achieve outcomes which are

ECONOMIC

1123

DEVELOPMENT

preferred to those which are achievable without indexing. This is a very difficult question. First, it is not clear that the government’s preferences remain constant as indexing is introduced. For example, the ability of indexing to mitigate some of the adverse effects of inflation may make the government more willing to endure inflation if it indexes. More seriously, it is not immediately clear what arguments should enter government preferences. Initially, it appears as if the rate of inflation should enter these preferences. However, it could also be argued that the rate of inflation is only an intermediate consideration, with the arguments of the government’s preferences actually being the well-being of the present and future agents in the economy. If this is the case, current assessments of indexing which concentrate on such factors as the inflationary implications of indexing are examining factors which do not enter government preferences. An assessment of indexing cannot be constructed by such methods. What is required is an approach which simultaneously considers the structure of the economy, government preferences, and the effects of indexing. The following section develops such a framework.’ 3. A FRAMEWORK FOR EVALUATING INDEXING (a) Governmentpolicy

instruments

We begin by identifying the policy variables which the government has at its disposal in period t. These include: real quantity of government expenditures on domestic goods and services real quantity of government expenditures on imported goods and services real quantity of borrowing in period real tax revenues sum taxes

government

t

raised from lump-

real quantity of non-linked bonds purchased by the government from the financial sector in period t at rate (.) nominal

return

on such bonds

real rate of return on linked bonds issued by the government to consumers real quantity of linked bonds issued by the government to consumers.

1124

WORLD

DEVELOPMENT

Linked and non-linked bonds can be taken to have a price of unity, and to promise to pay one plus a real or nominal rate of interest in period t + 1. We assume that indexed bonds are not issued privately. The government sets the real rate of interest on linked bonds r,, and sells the quantity bf which is demanded by consumers. The government chooses not only !Y:, or its purchases of bonds from financial institutions, but also the rate on such bonds. This market accordingly may not clear, so that financial institutions may be rationed in their attempts to sell such bonds. The effect of such bond sales is to provide liquidity to financial institutions. We retain the option that the government may purchase bonds from the financial system at more than one rate of interest. These assumptions appear to best approximate the policy options open to a government. We have not included the money supply in the government’s list of policy variables. The government is faced with a budget constraint (see Christ, lY79). It can arbitrarily choose levels of all but one of the variables entering its constraint, but the final variable must adjust to preserve the constraint. It again appears most realistic to assume that the government explicitly chooses borrowing and lending levels and that the money supply adjusts to preserve the constraint. Notice that this allows our model to capture any considerations which arise because of an effectively endogenous money supply. The government thus has at least seven policy instruments at its disposal (g,, g:, z,, i :‘, t$, s,, and r,), and may have more if it issues bonds to the financial system at varying rates of interest. Notice that the quantity of indexed bonds does not appear in this list, because we assume that this quantity is determined by the demand for such bonds once the rate of return is set. The assumption that the government may ration the liquidity it provides to the financial system causes both the quantity of such bonds and their return to appear as instruments.

(b) Government utility We would like to know whether the rate of return on indexed bonds which appears in the government’s optimal policy is sufficiently high to induce consumers to purchase indexed bonds (the indexing case), or whether it is set so low as to preclude such purchases (the no-indexing case). We might pursue this question in four steps. First, a model of the economy could be constructed. Second, the government’s preferences over economic outcomes could be mod-

eled. Next, these preferences could be used to choose an optimal outcome subject to the constraint posed by the structure of the economy. Finally, this outcome could be examined to ascertain whether it involves indexing. This approach has two disadvantages. First, it is difficult. It is quite likely that the solution to the constrained optimization problem cannot be made explicit enough to permit inferences concerning the presence of indexing. In addition, each step of the modeling process involves potentially arbitrary assumptions concerning the structure of the economy or government preferences. We would like to avoid reliance on arbitrary assumptions whenever possible. We adopt an alternative approach to the question of whether indexed bonds are part of an optimal policy. This alternative will require significantly weaker assumptions concerning the economy and government’s preferences. The key to this approach is the envelope theorem. We begin by assuming that the government’s preferences over economic outcomes can bc represented by a differentiable utility function, which presumably represents the policymaker’s preferences. We designate this function by U(.), and postpone consideration of its arguments. From this function, an indirect utility function V can be derived which has the government’s policy instruments as its arguments, or V(g,,g:,z,,i:,b~,s,.r,). We assume that each of these functions is differentiable.“’ Let the period I rate on indexed bonds r, be set arbitrarily, and let the values of the government’s remaining policy variables be chosen to maximize the government’s utility given the arbitrarily set rate on indexed bonds. Let the resulting utility level be denoted v(r,) = V(gXr,),g:*(r,).8(r,),i I;‘*(Tt),b~(r,),.~(:(r,),r,), where gT(r,) is a function identifying the optimal level of g, given that the rate r, on indexed bonds is set, and the remaining terms in V(.) are analogous. Hence, v(r,) identifies the maximum utility available to the government given that the period t rate on indexed bonds is given by r,. The question of interest now concerns the derivative of the function v(rJ, or dl/(r,)ldr,. If we can establish conditions under which it is positive or negative for various values of r,, the question of the optimality of indexing can be resolved. In particular, if dl/(r,)ldr, < 0 for those r, high enough to induce indexed bond purchases, then indexing will not be part of an optimal policy. (c) The envelope theorem Determining

the

sign of av(r,)/ar,

is still a

INFLATION,

INDEXING,

AND

formidable task. We are now in a position to exploit the envelope theorem in simplifying this task. Consider a rate of return on indexed bonds given by i,, and consider a government policy which has the following properties: s,(i,) = Gti,)

(1)

g@,) = g:*(i,)

(2)

G(i,) = zX?(it)

(3)

i ‘;‘(i,) = i ‘;:*(P,)

(4)

tiv,,

= ti*ct,,

(5)

&(f,) = St?,).

(6)

Then

we have:

V(g,(F,)&,),i v(@,),g:*(i,).i

~(i,).~(i,),z,(i,),s,(F,).i,)

=

(7)

:‘*(~~),~*(i,),~(i,),sy(i,),F,)

and V(g,(r,)&(r,).i

~(r,),d;(rI).ZI(rr),S,(r,),rr)

c

(8)

V(~(r,),g:*(r,),i’;(r,),~(r,),zT(r,),sT(r,),r,). Equation (7) indicates that at rate f,, a policy satisfying (l)-(6) gives the same utility level as the optimal policy. This is no surprise, since the two policies coincide at rate ?,. Equation (8) indicates that at other rates, a policy satisfying (l)-(6) can yield no higher utility than the optimal policy. This follows immediately from the definition of an optimal policy. We now let W(r,) = V(s,(r,) .&(r,) &r,)

,i i;(rJ &Xr,) ,sI(rr) ,r,) 7

where the policy in question Then we have the following tionship: dv((i,)

dW(i,)

dr,

dr,

satisfies (l)-(6).” fundamental rela-

(9)

’

Equation (9) holds because v(r,) and W(r,) are equal at r, = ft, with li(r,) equalling or exceeding W(r,) for any other r,. If both functions are differentiable, as assumed, then this can occur only if v(r,) and W(r,) are tangent at f,. They must then have the same slope at F,, yielding (9). This argument is a straightforward application of the envelope theorem. It allows an important simplification in our analysis. In evaluating the effect of a change in the rate of return on indexed bonds, we need not compute and examine the corresponding variations in optimal policy. Instead, we may examine arbitrarily chosen changes in the government’s other policy vari-

ECONOMIC

DEVELOPMENT

112s

ables. In particular, these other changes can be chosen so as to yield an especially convenient calculation.

We now employ (9) to examine indexing. We begin by making explicit our assumptions concerning the economy: The economy consists of a government, Al. consumer and a a representative representative financial institution. Consumers purchase indexed bonds from the government and non-indexed bonds from the financial institution. The government purchases non-indexed bonds from the financial institution. Consumer period t utility can be exA2. pressed as a function of the real quantity of domestic goods and services consumed in period t, the real quantity of imported goods and services consumed in period t, the real money balance held in period t, and real disposable incomes and prices in future periods. Only the total consumption of domestic A3. (imported) goods and services affects the magnitudes of the economy’s remaining state variables, and not the distribution of this consumption between consumers and the government. Only the total of assets held in the A4. financial system at each rate of interest affects the magnitudes of the economy’s remaining variables, and not the distribution of these holdings between consumers and the government. The government’s period t utility funcA5. tion potentially includes the period t and future utilities of the consumer and financial institution as well as any state variables which do not appear in the period t component of consumer utility functions. In addition, the government may derive utility from its expenditures on either domestic or imported goods and services. Assumption Al identifies the agents and assets in the economy. We have chosen a rather sparse economic model to simplify the presentation. Additional types of agents, such as (potentially bond-holding) firms, could be introduced without affecting the results. Additional markets, such as a capital market, could also be easily accommodated. The device of a representative consumer is both standard and convenient, but has substantive implications which will be discussed in Section 4.

1126

WORLD

DEVELOPMENT

Assumption A2 partitions the consumer utility function in a convenient way. Consumer utility presumably depends upon current and future economic events. We choose a direct utility representation for the former, but an indirect utility representation for the latter. The consumer’s period t holdings of linked or non-linked bonds do not enter the period t utility function. Instead, their effect on utility arises through their effect on future disposable income. We do allow the possibility that money enters the consumer utility function. This captures the fact that consumers may value liquidity, and arises out of the necessity of money as a medium of exchange. l2 Assumptions A3 and A4 commonly appear in macroeconomic models. National income, for example, is commonly written as the sum of investment, consumer expenditures on goods and services, and government expenditures. As long as the sum of the latter two remains constant, national income is unaffected by variations in the composition of this sum. Assumption A5 identifies the arguments of the government utility function. We would like to impose as few restrictions here as possible. An initial intuition is that the government’s utility should be a function of the utilities of the agents in the economy, and the latter are accordingly included in the government utility function. A “benevolent servant” model of government might not admit any further arguments in the utility function. However, additional factors may concern the government. For example, governments may attach a significance to such variables as the foreign exchange rate or expected inflation rate which goes beyond the effect of these variables on agents’ utilities.13 We accordingly allow the economy’s state variables to enter the government utility function. To avoid repetition, those variables which enter the period t component of the consumer’s utility function are not also independently entered into the utility function, though this could easily be relaxed. Policy variables might be excluded on the grounds that they are merely means of controlling state variables, so that the inclusion of the latter makes the former unnecessary. However, an important exception arises. Governments may value the ability to purchase goods and services, and we accordingly include government spending in the utility function. This may be an especially important factor in LDCs, where government spending is likely to be an integral component of a development strategy. Consider now an existing rate on indexed bonds given by t,, and consider the effect on government utility of a marginal departure from

this rate, or dV(i,)ldr,. Let the government adopt the following variations in its other policy variables: (10.1) The government purchases an additional quantity of bonds bearing a nominal return of zero from the financial system equal to the amount by which consumers reduce money balances held in such institutions. (10.2) The government purchases an additional quantity of bonds bearing a nominal return equal to the nominal interest rate (the return on nonlinked bonds) from the financial system equal to the amount by which consumers reduce holdings of nonlinked bonds. (10.3) The government purchases an additional quantity of domestic (imported) goods and services equal to the amount by which consumer purchases of goods and services have decreased. The government increases period (10.4) t + 1 taxes so as to preserve consumer period t + 1 disposable income. The effects of this policy are readily discerned. None of the economy’s aggregate magnitudes are affected. Total consumption of domestic and imported goods and services is unchanged, as are total balances in the financial system at each rate of return. Given assumptions A3-A4. this allows the equilibrium value of the economy’s state variables, including national income, the price level, the rate of interest, and investment but excluding the composition (but not aggregates) of consumption and asset holdings, to remain unchanged. The policy in question satisfies (l)-(6). It accordingly gives rise to a function W(r,) that satisfies (9). We then need only compute dW(?,)l dr, to ascertain whether an increase or decrease in the rate of return on indexed bonds will increase government utility. To perform this computation, we observe that W(r,) is an indirect utility function which identifies the government’s utility given that rate r, is set on indexed bonds and given that the policy described in (lO.l)(10.4) is followed. To calculate dW(?,)ldr,, it is then sufficient to calculate the effect on the government’s direct utility function of a variation in r, from i, given policy (lO.l)-( 10.4). This is easily accomplished. The policy in question affects government utility in the following ways: (11.1) Government purchases of goods and services are adjusted. (11.2) Consumer utilities are affected. This

INFLATION,

INDEXING,

AND

is caused by the adjustment in purchases of domestic (imported) goods and services and an adjustment in money balances. The remaining arguments of the consumer’s utility function and the economy’s remaining state variables remain unchanged, so that we must contend only with these two effects. We can accordingly represent the effect on the government direct utility function as (deleting time subscripts):

au ay acl au ay arll +aYaclar +aYZF au _ auay _&

as C

z

ay .ac

I II 1

_$&y] +g [ au

au ay a irl + TPdnldr

[_>,

<

DEVELOPMENT

1127

evaluation of any anticipated inflation, with or without indexing. The government will then find indexing a desirable policy, or dli(r,)ldr, > 0, if the advantages of increased government purchasing power offset the reductions in consumer purchasing power and liquidity. Notice that we do not claim that the government actually will follow the policy satisfying (l)-(6) when adjusting its rate on indexed bonds. Instead, this policy provides a convenient analytical device. It allows us to reduce the consideration of indexing to a pair of opposing forces. Notice in particular that we have removed the rate of inflation from consideration. The evaluation of indexing then requires governments to carefully weigh the relative merits of increased purchasing power and reduced consumer utility.

4. CONCLUSION

(10)

where dclar, dc’ldr. and dmldr are the variations in private consumption of domestic goods and services, private consumption of imported goods and services, and private money balances induced by the variation in the government policy, and Y is the consumer utility function. The negative signs in (10) are achieved by noting that ag/& = dg’l&’ = - 1. Standard consumer theory leads us to expect aclar,< 0, ac’lar,< 0, dmlar,

ECONOMIC

0.

(e) Assessment We can now interpret (10) and identify the issues in assessing indexing. Indexing transfers purchasing power from consumers to the government. ’ The first two terms in (10) capture this transfer for the case of domestic and imported purchases. These terms will be positive if and only if the government values the purchasing power enough to offset the resulting decrease in consumer utility. As we have mentioned, purchasing goods and services may be an important objective for LDC governments, so that these terms can be expected to be positive. The third term identifies the cost associated with indexing, given by the consumer utility effects of a decrease in consumer liquidity. This third term is then negative. Notice that the welfare effects of decrease in liquidity are at the heart of the

Six points warrant mention. First, our search for a framework within which to assess indexing was prompted by the fact that the observed effects of indexing are complex, and their evaluation involves delicate questions concerning the nature of the government utility function. Assessing these effects is then not only quite difficult, but requires a number of arbitrary and strict assumptions concerning the structure of the economy and the government’s preferences (though see note 9). The method developed above exploits the envelope theorem to find an equivalent (in utility terms) but simpler policy to accompany indexing than the optimal policy, and hence an equivalent but simpler set of indexing implications. This reduces the complexity of the task of assessing indexing and reduces the number and severity of the assumptions we must make concerning the economy and the government’s preferences. The result is a straightforward method for assessing indexing. In particular, we have reduced the assessment of indexing to a comparison of two forces. Second, we can observe that the basic advantage of indexing in our system is its ability to transfer purchasing power from consumers to the government. For many governments in LDCs, this may be an important consideration. However, the question naturally arises as to whether more direct means of obtaining purchasing power might not be preferable. It may especially be the case that more direct means of raising purchasing power may avoid some of the adverse effects of indexing. This point can be reformulated. The hypothetical policy which we have constructed to accompany indexing (for examination purposes)

1128

WORLD

DEVELOPMENT

presumes that the government will tax consumers’ future incomes from bonds. Why does the government not simply increase present taxes and eschew indexing? These queries serve as a reminder that a central issue in the assessment of indexing is the evaluation of the excess burden of using indexed bonds to finance government expenditures. We now turn to a consideration of the assumptions which have entered our analysis. We have assumed that the consumer’s period t utility is a function of period t events and of future disposable incomes and prices. The latter presumption initially appears to be an obvious application of an indirect utility function. On further examination, however, this is a strict assumption. Its implication is that the level of government debt has no effect on the economy, since higher levels of government debt can be countered in the future by simply increasing taxes. A considerable literature considers whether this type of relationship, often referred to as “Ricardian equivalence,” is likely to hold. Ricardian equivalence readily appears in models with representative agents, lump-sum taxes, perfect foresight, and an infinite horizon. Whether it holds in more realistic constructions as well as in actual economies remains an open question. Further work is clearly required to examine the robustness of our findings to alternative formulations which may not exhibit this property.15 Our use of representative agents raises another difficulty. We have mentioned that indexing can shift or alter the uncertainty effects of inflation, but cannot eliminate them. It is accordingly apparent that the effects of indexing will be primarily distributive in nature. Our results are consistent with this, since we have found an important effect of indexing to be the alteration

of the distribution of purchasing power between the government and consumers. However, our use of a representative consumer prevents us from examining the effects of indexing on distribution among consumers or other private agents in the economy. These effects may be important, and further work is again required to construct models which can address distribution issues in more detail. This will require some advances in macroeconomic modeling, which currently relies heavily on representative agent models. The fifth point brings us back to the discussion of policy effectiveness in Section 2. The policy we have examined calls for the government to intervene in financial markets by replacing any decreases in consumer assets with assets of its own. Indexing then apparently calls for a vigorous government financial-market policy. In our model, the vigor of this policy imposes no disutility on the government. In reality, the costs of a vigorous policy may be significant. I6 To capture this, new models are required which can explicitly capture the costs of policy. Such models have a potentially important role to play in analyses of government policy and perhaps economics in general, and this is clearly an important area for further work. Finally, this analysis has not attempted to produce a verdict on the desirability of indexing. Instead, we have developed a method by which the diverse effects of indexing can be organized in a manageable structure which is relatively free of arbitrary assumptions concerning government utility. Whereas considerable work remains to be done to ascertain the robustness of the analysis and to expand the purview of the model, the general technique should provide a useful method for focusing indexing discussions.

NOTES

1. This phrase is borrowed from the title of Fishlow (1974). Fischer (1975) contains references which advocate indexing and discuss recent indexing expcriences. See also Fischer (19X3). Peled (1980) offers an excellent rigorous treatment of indexed bonds.

4. This statement is imprecise. but intuition of the result. It is analogous to that a system of equations has a unique numbers of endogenous variables and equal.

2. The focus of our inquiry is government-issued indexed bonds. Sachs (1980). Kaour (1982). and Flood and Marion (1982) examine other types of indexing. Liviatan and Levhari (1977) explain why indexed bonds are not likely to be privately issued. We shall use the term indexing to refer to the government issue of indexed bonds, and will often refer to the latter as simply indexed bonds.

5. Accounts of the Brazilian indexing given by Baer and Beckerman (1974. (1974), Simonsen (1983) and Macedo

3. A guide to basic control-theoretic given by Aoki (1976).

principles

is

6. For example, inflation cause it increases the risk Indexing encourages saving saving instrument. Implicit indexing is the presumption inflation are also less certain

captures the the statement solution if the equations are

cxperiencc are 1980). Fishlow (1983).

discourages savings beassociated with saving. by providing a risk-free in most discussions of that higher rates of rates of inflation.

INFLATION.

INDEXING,

AND

7. Indexed bonds may allow inflation risk to be eliminated from the economy if risk-sharing or diversification is achieved as a result of indexing. This requires that inflation have independent effects on bondholders. This is unlikely to be the case in general. and we can accordingly assume that indexing does not eliminate inflation risk. 8. Bomberger and Makinen (19X0) obervc that in the cast of the Hungarian hyperinflation, the indexinginduced tax base reduction was sufficient to prompt significant increases in the inflation rate. Y.

For an alternative

approach,

see Peled

(1980).

IO. The assumption of diffcrentiablc utility functions does not drive the results, but it does make the analysis substantially simpler. In particular. it allows us to present our arguments in terms of calculus rather than set theory. 11. The diffcrcnce between the functions li(r,) and W(r,) is that the former presumes an optimal setting of the government’s remaining policy variables given r,, while the latter assumes only that these variables are set so as to satisfy (l)-(6). 12. Considerable disagreement persists on how money is best modeled. It is clear that the ability of money to serve as a medium of exchange is important. since otherwise money would be forsaken in favor of non-linked bonds. It has been common to capture this

ECONOMIC

DEVELOPMENT

1129

liquidity-provision aspect of money in macroeconomic models based on optimizing behavior by including money in the consumer utility function. A recent alternative involves incorporating explicit cash-inadvance constraints into the consumer’s problem. 13. For example, many governments under fixed exchange rate regimes appeared to attach a disutility to devaluation higher than could be justified by an appeal to the utilities of the economy’s agents. 14. This is initially somewhat surprising, since indexing is often described as returning the inflation tax to consumers. The transfer of resources to the govcrnment is a result of the government policy which accompanies indexing. 15. Stiglitz (19X3) discusses the implications of neutrality propositions for the effects of indexed bonds. See also Fischer (1983). 16. Indexing may reduce the costs of government policy. A potential difficulty is that consumers may not believe government announcements of anti-inflation policies, and the government may find it costly to make such announcements credible. By forcing the government to repay its obligations in real rather than nominal units. indexing may increase the cost to the government of inflation. This may allow the government to credibly commit to a policy featuring a lower inflation rate, and hence may reduce the costs of fighting inflation.

REFERENCES Aoki, M., Optimal Control and System Theory in Dynamic Economic Analysis (Amsterdam: North Holland 1976). Baer, Werner, “The resurgence of inflation in Brazil: World Development, Vol. 15, No. 8 197486,” (1987). Baer, Werner, and Paul Beckerman, “Indexing in Brazil,” World Development, Vol. 2, No. 1 (1974), pp. 3547. Baer, Werner, and Paul Beckerman, “The trouble with index-linking; Reflections on the recent Brazilian World Development, Vol. 8 (1980), pp. experience,” 677-703. Beckerman, Paul, “Index-linked financial assets and the Brazilian ‘Inflation-feedback’ mechanism,” Mimeo (Urbana-Champaign: University of Illinois, 1979). government bonds Beckerman, Paul, “Index-linked and the efficiency of monetary policy,” Journal of Macroeconomics, Vol. 2 (1980). pp. 307-331. Beckerman, Paul, “Inflation and dollar accounts in Peru’s banking system, 1978-83,” World Development, Vol. 15, No. 8 (1987). Bomberger, W. A., and G. E. Makinen, “Indexation, inflationary finance, and hyperinflation: The 19451946 Hungarian experience,” Journal of Political Economy, Vol. 88 (1980), pp. 550-560. Christ, Carl F., “On fiscal and monetary policies and

the government budget restraint,” American Economic Review, Vol. 69 (1979), pp. 526-538. Dornbusch, R., and M. H. Simonsen (Eds), Inflation, Debt, and Zndexation (Cambridge, MA: MIT Press, 1983). “The demand for index bonds,” Fischer, Stanley, Journal of Political Economy, Vol. 83 (1975), pp. 509-534. Fischer, Stanley, “Welfare aspects of government issue of indexed bonds,” in Dornbusch and Simonsen (1983), pp. 223-246. Fishlow, Albert, “Indexing Brazilian style: Inflation without tears?” The. Brookings Papers on Economic Activity, No. 1 (1974) pp. 261-282. Flood, Robert P., and Nancy Peregrim Marion, “The transmission of disturbances under alternative exchange-rate regimes with optimal indexing,” Quarterly Journal of Economics, Vol. 97 (1982), pp. 43-66. Kapur, Basant K., “Problems of indexation in financially liberalized less developed economies,” World Development, Vol. 10 (1982). pp. 199209. Liviatan, Nissan, and David Levhari, “Risk and the theory of indexed bonds,” American Economic Review, Vol. 67 (1977), pp. 366-375. Macedo, Roberto, “Wage indexation and inflation: The recent Brazilian experience,” in Dornbusch and Simonsen (1983), pp. 133-159.

1130

WORLD

DEVELOPMENT

McNelis, Paul D., “Indexing, exchange rate policy, and inflationary feedback effects in Latin America.” World De;elopment, Vol. 15, No. 8 (1987). Peled, D., “Government issued indexed bonds - Do they improve matters?” PhD Dissertation (University of Minnesota, 1980). Sachs, J., “Wage indexation, flexible exchange rates, and macroeconomic policy,” Quarterly Journal of Economics, Vol. 94 (1980), pp. 731-748. Simonsen, Mario Henrique, “Indexation: Current

theory and the Brazilian experience,” in Dornbusch and Simonsen (1983), pp. 99132. Stiglitz, J. E., “On the relevance or irrelevance of public financial policy: Indexation, price rigidities, and optimal monetary policies,” in Dornbusch and Simonsen (1983), pp. 18>222. Tobin, James, “An essay on the principles of debt management,” in James Tobin (Ed.). Essavs in Economics, Volume I: Macroecohom& (Amsterdam: North Holland, 1975).