## Abstract

The sterilization of capital inflows at the start of a price stabilization program may give rise to future pressures to discontinue the program as a result of the unduly high debt-service burden that the sterilization policy may generate.

**C**apital inflows often accompany the first stages of stabilization programs based on exchange rates. This is, in principle, a welcome development, since these inflows contribute to the accumulation of reserves at the central bank. However, the monetary authorities are often reluctant to let money supply grow by the amount corresponding to the accumulation of reserves. They fear that such monetary expansion— which may actually be sizable in the aftermath of hyperinflation—is taken by the private sector as a clear signal that the stabilization program is beginning to falter. Consequently, it is not unusual for the monetary authorities to decide to sterilize some of the capital inflows by, in effect, acquiring some of the additional reserves through the sale of domestic government debt.

Sterilization of capital inflows has the obvious advantage of keeping money supply under control. However, it will be argued in this note that if the associated open market operation is carried out by expanding the stock of nominal domestic debt, forces may be set in motion that could also jeopardize the credibility—and, hence, sustainability—of the anti-inflationary effort.

### I. A Simple Example

This is a two-period example. Let the “present” be period 0, and the “future” be period 1. Distorting taxes in period 1 in real terms, *x*, are given by the following period 1 government budget constraint:

where g is noninterest real government expenditure, and *P* is the price level in period 1; *B* is the stock of nominal bonds outstanding at the end of period 0, and *i* is the nominal interest rate from period 0 to period 1; finally, *R* is the stock of interest-bearing reserves at the end of period 0, and *r** is the international interest rate.^{1} In other words, future taxes, *x*, equal government expenditure plus the cost of servicing present debt (interest plus amortization), minus gross revenue from international reserves.

It is assumed that the government dislikes taxes, *x*, and inflation, π (where π is the rate of inflation between periods 0 and 1). More specifically. the future government's loss function is assumed to take the following form:

where *A* is a positive number.

A basic assumption of this example is that the present government cannot tie the hands of the future government. In formal terms, this means that the future government will try to minimize its loss function by resorting to any admissible policy in period 1.

The example will focus on the case in which the future government is free to choose the rate of inflation, π, in order to minimize its loss (equation (2)), subject to its budget constraint (equation (1)). This implies. in particular, that the future government will honor any previous debt commitment, and it is, thus, not allowed to confiscate *B* or to change its contractual interest rate, *i*.

Assuming that the present price level is equal to unity, it follows that *P* = 1 + π. Consequently, equation (1) can be expressed as

Hence, optimal inflation from the point of view of the future government will be the one that minimizes equation (2) with respect to π, subject to (3). The first-order condition for this problem is

The private sector is assumed to know the government's objective function. Hence, given that there is no uncertainty in this model and perfect capital mobility is assumed, at equilibrium, domestic bonds must exhibit the same rate of return as international assets. Thus, the following Fisher equation holds:

Substituting equations (3) and (5) into (4) yields

which is a central analytical result. Thus, assuming that, at equilibrium, distorting taxes and the stock of nominal bonds are positive, it follows from equation (6) that inflation will also be positive. Moreover, inflation is an increasing function of the domestic nominal public debt. This captures one of the effects mentioned in the introduction. More intuitively, a larger nominal debt requires, other things being equal, raising more distorting taxes. This gives the future government greater incentives to use inflation instead of distorting taxes, which explains the ex post positive association between nominal public debt and inflation. It should be noted, however, that given the rationality assumption (equation (5)), *in equilibrium distorting taxes are independent of the inflation rate*, since the public anticipates inflation and incorporates it in t, as implied by equation (5). Consequently, in this model inflation is just a pure negative externality, which would disappear if there were no public nominal debt, *B* (recall equation (6)).^{2}

Let us now go back to the sterilization issue. Let *M* stand for the demand for money to be held from period 0 to period 1, and let *M*_{o} denote the stock of money in the hands of the public at the beginning of period 0. Hence, assuming, for the sake of concreteness, that at the beginning of period 0 there are no domestic bonds or reserves at the central bank, one has (recalling that the price level in period 0 is assumed to be equal to unity)

In other words, the accumulation of reserves at the central bank results from an increase in the demand for money, *M* — *M*_{o}, and from the issuance of central bank debt, *B*.

It is assumed that individuals expect that the government will be ready to exchange *M* for goods in period 1. Thus, they expect to get *M/P* units of output in period 1. Consequently, the opportunity cost of holding money from period 0 to period 1 is, as in standard models, the nominal interest rate, *i*. Hence

Furthermore, it is assumed that the output required to buy up *M/P* in the future is obtained through nondistorting taxes.^{3}

Suppose that it is possible to launch a credible stabilization program that substantially lowers *i* and, hence, increases the demand for money by a sizable amount. This generates, by equation (7), the problem of capital inflows cited earlier. One option is to expand the money supply accordingly. Since, by assumption, the initial stock of bonds is zero, then, in the absence of capital inflow sterilization, one has *B* = 0, and thus, by equation (6), equilibrium inflation is equal to zero. In other words, recalling equation (2), in the present model, full accommodation of money supply implies that optimal inflation (π = 0) is attained. Under the present circumstances, distorting taxes are, by equations (3), (5), and (7)

Consider now the policy of full sterilization of capital inflows. This requires being able to keep the interest rate, *i*, such that *M* − *M*_{o} = 0, which, by equation (7), implies *R* — *B* (that is, reserves are bought entirely through the issuance of central bank debt). Let i be defined as the interest rate that discourages any change in the demand for money:

Naturally, given that the economy comes from experiencing high inflation, it is assumed that ¯*i*>*r**. The last step will be to show that a positive level of *B* exists that generates ¯*i* and, hence, that full sterilization is possible.

By equation (5), there is a positive level of inflation associated with ¯*i*, which is denoted ¯π Therefore, by equation (6), and recalling that full sterilization requires *R* — *B*, one gets

Therefore, there is a sufficiently high stock of central bank debt and reserves to generate the rate of inflation consistent with full sterilization. What has been achieved? Well, nothing good, really. Inflation is now positive, not the optimal zero level as before, while distorting taxes are, by equation (3), recalling that *R* − *B*

which exceeds the level needed under no sterilization (equation (9)). Hence, in this example sterilization is definitely worse than full monetary accommodation. Furthermore, inflation could be very large, given that initial real monetary balances, *M*_{o}, are inherited from a high-inflation episode—destroying the credibility of the stabilization program.

### II. Conclusions

This note gives an example in which a stabilization program could run into serious credibility problems as a result of a sterilization—partial or total—of capital inflows. The note examines the effect of sterilization through the issuance of nominal debt. The Achilles' heel of such a policy was shown to be the additional debt itself. To keep money at the initial preprogram level, for example, the nominal interest rate must be kept high, which requires equally high inflationary expectations. In the example, this can come about only if the public thinks inflation will be high. The policymaker—unwittingly, one hopes—generates those expectations by buying a large stock of reserves in exchange for new public debt. The larger public debt induces people to expect high inflation, because sticking to a stable price level, for example, would make servicing the public debt excessively costly from a social and political point of view,^{4}

## REFERENCES

Calvo, Guillermo A., and Pablo E. Guidottì,

*“Indexation and Maturity of Government Bonds: An Exploratory Model,” in*, ed. by Rudiger Dornbusch and Mario Draghi (New York; Cambridge: Cambridge University Press, 1990).*Government Debts and Capital Markets*Fernandez, Roque B., “What Have Populists Learned from Hyperinflation?” (unpublished; Washington: International Monetary Fund, January 1990).

Guillermo A. Calvo is Senior Advisor in the Research Department.

The author would like to thank José Fajgenbaum and Pablo Guidoni for their helpful comments.

^{1}

International prices are constant and equal to unity.

^{2}

Thus, in the present model optimal inflation would be achieved if public debt were fully (and credibly) indexed to the price level. This result—which is not stressed in this note—is not robust to realistic extensions of the model (see Calvo and Guidotti (1990)), and does not necessarily hold if open debt confiscation is allowed.

^{3}

In an infinite-horizon model, the public also expects to be able to exchange *M*/*P* for goods, as in the present setup, and there is no need to assume that the government stands ready to implement the exchange itself. The somewhat contrived assumptions here—that the government buys up the whole of *M*/*P* in the future, and that the funds required for the transaction involve nondistorting taxes—should be seen as an attempt to capture the flavor of more realistic models without having to pay the high price of dealing with much more complex analytical structures. It should be noted, however, that it is straightforward to extend the model to the case in which, in period 1, money is absorbed through distorting taxes.

^{4}

To a large extent, the failure of the July 1989 stabilization program in Argentina appears to be linked to issues discussed in the present note. See Fernandez (1990) for a fascinating account of that and several other related episodes in Argentina during the last 15 years.