I. Basic Model

This section sets up the basic analytical framework of the paper by integrating Gray’s (1976) analysis of wage indexation and Calvo and Guidotti’s (1990) analysis of debt indexation. Emphasis is placed on the interaction between the degree of wage indexation and government fiscal and monetary decisions.

II. Wage and Debt Indexation

In order to maintain analytical tractability, the government budget constraint in equation (12) and the interest parity condition in equation (13) are linearized. (This keeps the analysis closely comparable to Calvo and Guidotti.) Assuming—without loss of generality—that hereafter the international interest rate, i*, is equal to zero and taking the first-order terms of a Taylor series expansion of equations (12) and (13) around the point $i=\pi =i^{*}=0,$it follows that¹²

where kπ is the seigniorage on cash balances, k is a constant, and

Let us now solve government l’s optimization problem. Government 1 chooses the pair of functions $\left\{E_{1}x\left(g\right),\mu \left(g\right)\right\}$ in order to minimize

subject to equation (10) and budget constraint (16), taking it π^e and i as predetermined; recall that π^e is part of the wage contract. Note that since the government cannot fully control inflation—because of the unobservable shocks, ϵ and u —it cannot fully control taxes once inflation is realized. Government 1, however, can specify a function E₁x(g) to indicate what taxes are expected to be—given the information available to government 1—as a function of government spending.

The above minimization problem yields the following first-order condition:

The left-hand side of equation (19) is the expected cost (as of period 1) of an increase in inflation triggered by a higher rate of monetary expansion, μ The expected cost of inflation is composed of a direct cost—the first term on the left-hand side of equation (19)—and a cost in terms of the expected deviation (as of period 1) of output from its optimal level— the second term on the left-hand side of the equation.¹³ The expected output deviation depends directly on the degree of wage indexation chosen by the private sector. With full wage indexation—when η = 1— the output deviation expected at time 1 is zero, independent of the inflation rate. The right-hand side of equation (19) equals the marginal cost reduction associated with government l’s expected conventional-tax saving obtained from higher inflation: higher inflation reduces the real value of government debt (in addition to raising seigniorage on cash balances), which is why the stock of nominal debt, θb, appears as part of the inflation tax in equation (19).

Calvo and Guidotti (1990) have shown that in equilibrium inflation, on average, produces no revenue from the stock of nominal debt. However, the inflation tax on nominal debt generates revenue on a state-by-state basis, so that it can he used to smooth conventional taxes across states of nature. This property is at the heart of Calvo and Guidotti’s (1989, 1990) concept of flexibility, which provides a role for nominal government debt.

In equilibrium, equations (11) and (17) hold. Using them (also see the Appendix details), the policy reaction functions of government 1 are obtained

and

Equation (20), the state-contingent policy for the rate of monetary expansion, shows that shocks to government expenditure are partly financed by government 1 with the inflation tax. The inflation-tax base that applies to unanticipated inflation includes the stock of nominal debt. Equation (21) shows that shocks to government expenditure are also partly financed by conventional taxes.¹⁴ Equation (22) shows that because of the presence of time inconsistency on the part of the government, expected inflation depends directly on the stock of nominal public debt. However, on average the inflation tax collects no revenue on the public debt (equation (23)).

As in the Appendix, equations (10), (12), (20), and (21) yield the following expressions for taxes and inflation:

In period 0. government 0 chooses the optimal degree of debt indexation—by choosing θ—while the private sector chooses the optimal degree of wage indexation, η. Both take into account the behavior of government 1 as described by equations (20)-(25). Formally, the resulting pair (θ, η) is a Nash equilibrium.

Using equations (20)-(25) and assuming that ϵ u, and g are uncorrelated, government 0’s loss function is given by

Similarly, the loss function of wage setters is given by

where

The loss function given in equation (27) looks exactly the same as that given in equation (14) in Gray’s (1976) paper. The difference between the two loss functions is that, in the present framework, the variance of monetary shocks, ${\sigma }_M^2,$ is endogenous since it is obtained from the government’s optimization problem. In particular, the variance of monetary shocks equals the sum of the variance of the exogenous money demand shock ϵ${\sigma }_{ϵ}^2,$ and the variance of the rate of monetary growth, ${\sigma }_{\mu }^2\mathrm{.}$ The variance of the rate of monetary growth, in turn, is a function of both θ and η, as well as the variance of government expenditure, ${\sigma }_g^2\mathrm{.}$

Now the paper turns to the determination of equilibrium wage and debt indexation. To follow on intuition, the paper focuses on special cases that illuminate the essential elements driving the choice of θ and η. During the ensuing discussion, θ will be restricted to the interval (0, 1).¹⁵

CASE I: A = = a. If A = 0, then conventional taxes are not distortionary, implying no time-inconsistency problem in government behavior. It is easy to verify that in this case the government will finance government expenditure only by raising conventional taxes. Hence, the rate of monetary growth, μ, will be set equal to zero; the degree of debt indexation, θ, is irrelevant since it does not affect inflation (although it does affect the variability of conventional taxes). Since μ = 0, the variance of ${\sigma }_M^2$ equals ${\sigma }_{ϵ}^2\mathrm{.}$

The degree of wage indexation, η, follows from minimizing loss function (27), the exact problem studied by Gray (1976). It is well known that in the presence of both monetary and real shocks it is optimal to have partial wage indexation, $0<{\eta }^0<1,$where superscript o stands for “optimal.” Moreover, the optimal degree of wage indexation depends positively on the variance of monetary shocks, ${\sigma }_M^2,$ and negatively on the variance of real shocks, ${\sigma }_u^2\mathrm{.}$ It can also be shown that η^ο is positively related to the labor supply elasticity, h, and negatively to the labor demand elasticity,$1/(1-\alpha )\mathrm{.}$

The intuition behind the choice of wage indexation follows from Gray (1976). In the presence of shocks to productivity, it is optimal to have real wage flexibility. Indeed, if the variance ${\sigma }_M^2$ equals zero, Gray shows that the optimal degree of wage indexation, η^ο, equals $h/(1+h),$which is nonnegative and less than one. This degree of wage indexation achieves the optimal response of the real wage to real shocks. At the other extreme, if the only shocks are monetary—if ${\sigma }_u^2=0$—then it is optimal to index wages fully—η^ο = 0. This prescription reflects the fact that in the absence of shocks to productivity it is not optimal to have real wage variability.

CASE II: B = o. In this case the government carries out its monetary and fiscal policy without taking output deviations into account in its objective function.

Government 0 chooses θ to minimize

Loss function (29) is comparable to the government loss function given in equation (20) in Calvo and Guidotti (1990). In fact, both are equal when ${\sigma }_{ϵ}^2={\sigma }_u^2=0.$ A new term appears in equation (29), relative to the government loss function of Calvo and Guidotti: the second term on the right-hand side of the equation, which contains the variances of ϵ and u and the expression $[1+\alpha \beta (1-\eta )]\mathrm{.}$The latter, in particular, makes the government’s choice of 0 dependent on the degree of wage indexation set by the private sector.

These differences notwithstanding, it is shown in the Appendix that the choice of the optimal degree of debt indexation maintains the qualitative properties discussed by Calvo and Guidotti. In particular, it is shown that, for appropriate parameter values, optimal θ, θ^ο, is greater than zero and less than one. Moreover, the optimal degree of debt indexation, 1 — θ^ο, decreases with the variance of government expenditure, ${\sigma }_g^2,$ and increases with the expected value of government expenditure, $\overline{g}$ and the level of public debt, b.

The intuition behind these results follows from considering the tradeoff faced by government 0. On the one hand, a higher level of nominal debt—less debt indexation—creates incentives for government 1 to generate a suboptimally high inflation rate because of the time-inconsistency problem. On the other hand, a higher level of nominal debt enlarges the unanticipated portion of the inflation tax base. (Recall that, since the nominal interest rate reflects the expected inflation rate point-for-point, no inflation tax can be collected on average on the nominal debt.) Since inflation is costly, a higher inflation tax base makes the inflation tax more efficient for smoothing out conventional taxes: it raises the amount of government revenue that can he generated under a given level of inflation distortion. Moreover, since nominal bonds are a part of the inflation tax base that corresponds to unanticipated inflation, the gains from the nominal debt accrue only to the extent that there is variability in the budget constraint. Thus, a higher variance of g increases the scope for nominal debt. Conversely, because of the time-inconsistency problem, a higher $\overline{g}$ and a higher b increase the incentives to raise average inflation, thus inducing a reduction in θ^ο.

It is apparent from equation (29) that the level of wage indexation, as well as the variances of shocks ϵ and u, affects the optimal degree of debt indexation. In particular, the Appendix shows that optimal debt indexation, 1 — θ^ο, is positively related to η, as well as to the variances of ϵ and u.

The relation between θ^ο and the variances of those shocks derives from the following considerations. The variability of unobservable shocks e and u induces output variability which, in turn, generates—through money market equilibrium—an inflation variability that cannot be controlled by the policymaker. This element of inflation variability is costly and plays no useful role in smoothing conventional taxes. In fact, since unanticipated inflation generates revenue fluctuations, it results in unwanted tax variability, which is uncorrelated with government expenditure. Since this effect is magnified by the presence of nominal debt, it follows that the higher the uncontrollable portion of inflation the larger the share of the public debt that should be indexed.

The presence of partial wage indexation implies that output variability reflects the variance of real wages, in addition to the variance of the technological shock, u. By equation (24) it can be observed that the higher the degree of wage indexation, the higher the variability of inflation, all other things equal. This relation reflects the fact that unexpected inflation is associated with an expansion of output—and hence an expansion of money demand. By equation (20), however, it can be observed that the variance of the rate of monetary growth, μ, takes into account the role of wage indexation: $[1+\alpha \beta (1-\eta )]$appears in the numerator of the second term in the equation. Hence, the relationship between the variance of government expenditure and the variance of inflation is independent of the degree of wage indexation.

This amplification caused by wage indexation, however, applies to the uncontrollable—and, hence, unwanted—portion of inflation variability. The higher is the degree of wage indexation, the higher is the unwanted variability of inflation, for given ${\sigma }_{ϵ}^2$ and ${\sigma }_u^2\mathrm{.}$ This explains why there is a positive relationship between the degrees of wage and debt indexation in the government’s optimization problem. More wage indexation generates higher unwanted inflation variability, thereby inducing the government to index more of the public debt. Thus, the government’s reaction function, with θ^ο as a function of η, is downward sloping in the (η, θ) plane, as depicted by schedule G in Figure 1. Interestingly, the fact that higher wage indexation induces the government to choose higher debt indexation implies that higher wage indexation leads to a more anti- inflationary policy stance, which follows from the fact that higher debt indexation reduces government 1’s incentive to promote inflation.

Consider now the private sector’s choice of wage indexation. Wage setters choose η to minimize loss function (27), where ${\sigma }_M^2$ is now given by

The full characterization of wage indexation is provided in the Appendix; the basic insights of Gray (1976) are shown to remain valid in this case. Equation (30) illustrates that the variance of the rate of monetary growth is a nonmonotonic function of θ. In particular, it is easy to show that ${\sigma }_M^2$ increases with low values of θ and decreases with high values of θ. This nonmonotonicity reflects two factors. At low values of θ, an increase in θ makes the inflation tax more efficient: thus, it induces a substitution away from conventional taxes toward the inflation tax. For sufficiently high levels of θ, additional nominal debt decreases the variability of both conventional taxes and the inflation tax by enlarging the tax base for unanticipated inflation. Thus, a substitution effect dominates at low levels of θ, while a scale effect dominates at high levels of θ.

The nonmonotonicity of ${\sigma }_M^2$ as a function of θ implies that the reaction of wage setters is nonmonotonic as well, as illustrated by schedule W in Figure 1. At low values of θ, an increase in θ increases the variance of monetary shocks, and hence increases the optimal degree of wage indexation, η^ο At high levels of θ, an increase in θ decreases the variance of monetary shocks, and hence decreases η^ο.

The intersection of schedules G and W provides the Nash equilibrium (η^ο, θ^ο). Depending on the parameter values, schedule G can intersect schedule W to the left of maximum η (shown in Figure 1.) or to its right.¹⁶

To study the effects of changes in various exogenous parameters on the equilibrium levels of wage and debt indexation, consider first an increase in the variance of government expenditure, ${\sigma }_g^2\mathrm{.}$¹⁷ A rise in ${\sigma }_g^2$ shifts schedule G to the right, while it shifts schedule W upwards. Schedule G shifts to the right because, by previous considerations, a rise in ${\sigma }_g^2$ increases the tax-smoothing role of nominal debt. Schedule W shifts up because an increase in ${\sigma }_g^2$ increases the variance of monetary shocks, thus inducing the private sector to choose a higher degree of wage indexation. In the case where schedule G intersects schedule Won its upward-sloping segment, a rise in ${\sigma }_g^2$ results in an increase in η^ο an increase in wage indexation—but has an ambiguous effect on the degree of debt indexation, $1-{\theta }^0\mathrm{.}$This ambiguous effect responds to two opposing elements. On the one hand, for a given degree of wage indexation the government will reduce debt indexation when government expenditure becomes more volatile. On the other hand, higher volatility of government expenditure increases the variance of monetary shocks and induces more wage indexation. Higher wage indexation, by previous arguments, induces more debt indexation.

Wage and Public Debt Indexation

Citation: IMF Staff Papers 1993, 001; 10.5089/9781451947137.024.A001

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Wage and Public Debt Indexation

Citation: IMF Staff Papers 1993, 001; 10.5089/9781451947137.024.A001

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Wage and Public Debt Indexation

Citation: IMF Staff Papers 1993, 001; 10.5089/9781451947137.024.A001

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When schedule G intersects schedule W on its downward-sloping part, an increase in ${\sigma }_g^2$ has an ambiguous effect on both wage and debt indexation. The ambiguity with respect to η^ο comes from two opposing effects. On the one hand, an increase in ${\sigma }_g^2$ increases the variance of monetary shocks, other things being equal. On the other hand, the reduction in the equilibrium degree of debt indexation tends to reduce the variance of monetary shocks. This provides an example in which government policy regarding debt indexation dampens the private sector’s incentive to increase wage indexation. The rise in ${\sigma }_g^2$ increases the variability of inflation and tends to reinforce the incentive to increase wage indexation. The government response to the rise in ${\sigma }_g^2$ —indexing more of the public debt—reduces inflation volatility, and hence dampens the private sector’s incentive to raise wage indexation. This example shows that more debt indexation can reduce wage indexation.

Consider the effects of an increase in expected government expenditure, $\overline{g}\mathrm{.}$ An increase in $\overline{g}$ has no effect on schedule W and shifts schedule G to the left. Schedule G shifts to the left because an increase in expected government expenditure tends to raise expected inflation. Hence, it is optimal for government 0 to reduce the amount of outstanding nominal debt to reduce government l’s incentives to generate inflation. Thus, an increase in $\overline{g}$ induces a fall in both η^ο and θ^ο if the initial equilibrium is on the upward-sloping portion of schedule W; it induces an increase in η^ο and a fall in θ^ο if the initial equilibrium is on the downward-sloping portion of schedule W. The change in η^ο reflects the different effects that less debt indexation may have on the variance of monetary shocks affecting wage contracts.

Consider the effects of an increase in ${\sigma }_{ϵ}^2\mathrm{.}$ From the government’s point of view, an increase in ${\sigma }_{ϵ}^2$ raises the optimal degree of debt indexation for any given level of wage indexation. More debt indexation is optimal because a higher ${\sigma }_{ϵ}^2$ implies that the policymaker has less control over the variability of inflation. This implies that an increase in ${\sigma }_{ϵ}^2$ shifts schedule G to the left. Similarly, other things being equal, a higher ${\sigma }_{ϵ}^2$ increases the variance of monetary shocks, and hence shifts schedule W upward. As a result, a higher ${\sigma }_{ϵ}^2$ reduces θ^ο but has an ambiguous effect on η^ο if the initial equilibrium is on the upward-sloping portion of schedule W. It induces an increase in η^73x03bf; and a fall in θ^73x03bf; if the initial equilibrium is on the downward-sloping portion of schedule W.

Comparing the effects of an increase in ${\sigma }_g^2$ with those of an increase in ${\sigma }_{ϵ}^2$ illustrates how important the policy response is to the equilibrium relation between wage and public debt indexation. For wage setters, an increase in both variances would increase monetary volatility, thereby resulting in higher wage indexation, which is why schedule W is affected in the same way in both cases. For the government, however, increases in ${\sigma }_g^2$ and ${\sigma }_{ϵ}^2$ yield opposite policy responses—causing schedule G to shift in opposite directions. The higher volatility of government expenditure induces it to reduce debt indexation, but the higher volatility in the demand for money induces the government to increase debt indexation. Thus, exogenous changes that would have similar effects in the absence of a government response may have opposite equilibrium effects because of the different policy responses they induce.

Consider the effects of an increase in the variance of the technological shock, ${\sigma }_u^2\mathrm{.}$ A rise in ${\sigma }_u^2$ shifts schedule G to the left and shifts schedule W down. The shift of schedule G reflects the fact that higher ${\sigma }_u^2$ increases the portion of inflation variability that cannot be controlled by the government. Schedule W shifts down because, other things being equal, an increase in the variance of real shocks makes it optimal for wage setters to reduce wage indexation. Hence, when schedule G intersects schedule W on its upward-sloping portion, an increase in ${\sigma }_u^2$ results in a fall of η^ο but has an ambiguous effect on θ^ο. When schedule G intersects schedule W in its downward-sloping section, an increase in ${\sigma }_u^2$ has ambiguous effects on both η^ο and θ^ο.

Consider the effects of an increase in the level of debt, b. Higher public debt shifts schedule G to the left since it induces the government to increase debt indexation. Schedule W shifts to the left: for given low levels of θ, wage setters choose a higher η and for given high levels of θ they choose a lower η. This reflects the different effects that an increase in b will exert on the variance of monetary shocks if an economy is situated on either the upward- or downward-sloping part of schedule W. As a result, an increase in b reduces θ^ο but has an ambiguous effect on η^ο if the initial equilibrium was on the upward-sloping part of schedule W, and has an ambiguous effect on both θ^ο and η^ο if the initial equilibrium was on the downward-sloping part of schedule W.

Finally, consider the effects of a change in the elasticity of the labor supply. An increase in labor supply elasticity, h has no effect on schedule G and shifts schedule W up. This implies that an increase in h results in higher indexation of both wages and debt.

The above analysis shows that, depending on the type of exogenous disturbance, wage and debt indexation may move in the same or in opposite directions. In Gray (1976), the effects on wage indexation are clearly classified by the source of shocks, but the present framework presents a less clear relationship between the source of shocks and the degrees of wage and debt indexation. There are two reasons for this. First, government policy responses are introduced into the analysis. Second, the effect of changes in debt indexation on the variance of the rate of monetary growth is shown to be nonmonotonic.

CASE III: THE GENERAL CASE.¹⁸ In addition to the effects considered in Case II, this final case incorporates the deviations of output from a perfect-information level in the government objective function.

Consider first the effect of introducing output deviations into the government’s loss function—that is, letting B be greater than zero. In particular, this case focuses on the effects of an increase in B from an initial equilibrium where B = 0. As indicated from equations (20)—(25), inflation and tax variability reflect the variability of shocks ϵ and u. and the government’s choice of the rate of monetary growth responds to shocks in government expenditure. More specifically, since the rate of monetary growth is uncorrelated with the technological shock, u. its variance adds to output variability. Thus, introducing output deviations into the government’s loss function leads the policymakers to reduce the optimal variance of the rate of monetary growth. By equations (20) and (21), it can be observed that an increase in B reduces the variance of monetary growth but increases the variance of conventional taxes, reflecting a substitution away from unanticipated inflation toward conventional taxes as means of financing shocks to government expenditure.

What is the effect on the optimal degree of debt indexation? Increasing B may be thought to make inflation variability more costly to the policy- maker. Thus, one would expect that debt indexation would move to reduce inflation variability. Indeed, the Appendix shows that, for a given η and for low initial values of θ^ο, optimal debt indexation increases as B increases. For high values of η^ο and a given η, optimal debt indexation declines following an increase in B. This implies that for low initial values of θ^ο an increase in B shifts schedule G to the left and for high initial values of θ^ο shifts schedule G to the right. The Appendix shows that a low initial value of θ^ο refers to values of θ at which ${\partial \sigma }_M^2/\partial \theta >0,$implying that schedule W is upward sloping. Similarly, a high initial value of θ^ο refers to values of θ at which${\partial \sigma }_M^2/\partial \theta <0,$for which schedule W is downward sloping.

Consider next the effects on η of letting B be greater than zero. Since, by previous considerations, an increase in B results in lower inflation variability, it should also reduce the optimal degree of wage indexation for a given θ^ο. The Appendix shows that, starting from B = 0, an increase in B does lead wage setters to choose lower wage indexation, implying that an increase in B shifts schedule W down. The above considerations imply that if the initial equilibrium is on the upward-sloping portion of schedule W, then a higher B induces a fall in optimal wage indexation but has an ambiguous effect on debt indexation. If the initial equilibrium is on the downward-sloping portion of schedule W, then a higher B induces a fall in η^ο and an increase in θ^ο.

III. Wage and Debt Indexation Under Policy Precommitment

In this section the model is modified by allowing government 0 to precommit credibly to the policies of government 1. Calvo and Guidotti (1990) show that under full precommitment the flexibility of nominal debt becomes the dominant element in deciding the optimal degree of debt indexation. In their model, the absence of time-inconsistency costs implies that optimal policy calls for expanding the nominal public debt until, in the limit, both inflation and conventional taxes are completely smoothed out. In fact, in Calvo and Guidotti (1990), swapping an unboundedly large nominal stock of debt for an unboundedly large stock of indexed assets—note that net public debt is unaffected by such swap— attains, in the limit, the complete-markets solution.

It turns out that this remarkable result does not necessarily apply to the present framework. The reason is that in the present model there are unobservable shocks that impart unwanted volatility to inflation and conventional taxes. As long as this uncontrollability exists, a swap of nominal debt for indexed assets of the type described above would magnify the unwanted variability of inflation and taxes by enlarging without bound the tax base of the unexpected inflation. Hence, in the present framework, the optimal share of nominal debt, θ^ο, will remain bounded as long as either ${\sigma }_{ϵ}^2$ or ${\sigma }_u^2$ is positive.

As in Calvo and Guidotti (1990), it can be shown that optimal government policies under precommitment differ from those without precommitment only insofar as they concern the expected levels of monetary growth and taxes. The state-contingent part of the policy is the same with or without precommitment. The optimal policy regarding taxes and the rate of monetary growth under precommitment is given by equations (20), (21), (22), (24), and (25), where E1(.) is interpreted as the expectation over ϵ and u, and Eμ, is given by

Equation (31) shows that if government 0 can precommit to policies, then the optimal policy calls for expected inflation to be independent of the stock of nominal debt. This reflects the fact that, on average, the inflation tax collects no revenue on nominal debt because the nominal interest rate incorporates any expected inflation point-for-point.

In order to fix ideas, think of Case II, where B = 0. The government loss function under precommitment is given by

Equation (32) is the precommitment analog of equation (29). As indi- cated earlier, the only difference between the two loss functions involves expected inflation and taxes.¹⁹ If ${\sigma }_{ϵ}^2$and${\sigma }_u^2$ equal zero, then the minimization of equation (32) with respect to 0 reproduces the result of Calvo and Guidotti (1990): θ should be set unboundedly large. If either ${\sigma }_{ϵ}^2$or ${\sigma }_u^2$is positive, then optimal $\theta <\infty \mathrm{.}$Moreover, if $({\sigma }_{ϵ}^2+{\beta \sigma }_u^2)/[1+\alpha \beta {(1-\eta )]}^2<{\sigma }_g^2,$then optimal $\theta >0.$It is henceforth assumed that this condition holds.²⁰

It is easy to verify that the optimal degree of debt indexation is obtained from the following first-order condition:

In accordance with intuition it can be shown that, other things being equal, optimal 0 is higher—optimal debt indexation is lower—in the presence of precommitment than in its absence.²¹ Furthermore, equation (33) shows that, as in the no-precommitment case, the government reaction function is negatively sloped in the $(\eta ,\theta )$ plane. The Nash equilibrium with no policy precommitment $({\theta }^0,{\eta }^0)$is determined by equation (33) and the solution to the wage indexation problem in the previous section that is, the minimization over η of equation (27) where${\sigma }_M^2$ is given by equation (30). The fact that the optimal degree of debt indexation is smaller in the presence of precommitment implies that, for given parameter values, the precommitment equilibrium $({\theta }^0,{\eta }^0)$is more likely to be situated on the downward-sloping portion of schedule W than the no-precommitment equilibrium is likely to be.

It can be shown that several comparative statics exercises yield the same qualitative (although not quantitative) results under policy precommitment as under no policy precommitment. This is the case for the effects of an increase in ${\sigma }_g^2$ or ${\sigma }_u^2$ on $({\theta }^0,{\eta }^0)$. Other comparative statics exercises, however, yield different qualitative results depending on whether government 0 can precommit to its policies. Consider, for instance, the effects of an increase in expected government expenditure. $\overline{g}\mathrm{.}$ Without precommitment, an increase in $\overline{g}$ shifts schedule G to the left, because expected inflation is a function of debt indexation owing to the time-inconsistency problem. Under precommitment, however, expected inflation is independent of debt indexation because policymakers realize that, on average, the inflation tax collects no revenue on the stock of nominal debt. Thus, under precommitment, schedule G is independent of θ, and changes in $\overline{g}$ have no effect on the equilibrium ${\theta }^0,{\eta }^0$.

IV. Conclusions

This paper has explored the possible connections between government policy regarding the indexation of the public debt and the private sector’s choice of wage indexation. The analysis has been carried out in a framework where incomplete markets and policy incentives play central roles. The analysis has relied on existing theories of wage and public debt indexation. The insights obtained should be viewed as a first step toward understanding the macroeconomic interactions of different forms of indexation. Further analysis could be directed at exploring in greater depth the microfoundations of the problem, as well as the nature of wage contracts.

The analysis suggests that the relationship between wage and public debt indexation may be quite complex. As far as the government is concerned, the optimal degree of debt indexation is positively related to the degree of wage indexation chosen by the private sector. As far as wage setters are concerned, the relationship between the optimal degree of wage indexation and the level of debt indexation is nonmonotonic because of the different effects that debt indexation may have on inflation variability.

Wage and public debt indexation are determined as a Nash equilibrium. Whether equilibrium wage and debt indexation are positively or negatively related in response to changes in exogenous parameters depends on the nature of the changes, as well as on some characteristics of the initial equilibrium. It also may depend on whether or not the government has the ability to precommit to future policies. Hence, the analysis does not support the presumption that equilibrium wage and debt indexation move in the same direction. Moreover, the analysis provides examples in which more wage indexation may lead the government to adopt a more anti-inflationary policy stance. Therefore, the results of the analysis weaken the presumption that indexation encourages policymakers to tolerate inflation. Finally, this paper has shown that the uncontrollability of inflation as a tax instrument is an additional element that favors indexing the public debt. Introducing output fluctuations in the government objective function, however, does not have a clear-cut effect on optimal public debt indexation.