Chapter

X. Interest Payments

Editor(s):
Ke-young Chu, and Richard Hemming
Published Date:
September 1991
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What is the impact of inflation on interest payments and the fiscal deficit?

Which concept of the fiscal deficit best reflects shifts in fiscal stance in an inflationary environment?

How is the growth of public debt determined? Under what conditions does an economy fall into a debt trap?

What determines a sustainable level of public debt? What does this imply for the fiscal deficit?

Expenditure on interest payments has been the focus of much recent attention. Since interest payments are usually linked to market interest rates, the level of such expenditures can be dramatically affected by the rate of inflation. Through its impact on the level of nominal interest expenditures, inflation complicates the interpretation of the fiscal deficit and of the sustainability of the government’s fiscal stance. The purpose of this note is to trace through the link between interest payments, inflation, fiscal deficits, and public debt, and to discuss some issues related to assessing the sustainable level of public debt.

Interest Payments, Inflation, and the Fiscal Deficit: An Example

Consider a country whose outstanding stock of public debt is $100 million, held by the private sector in the form of short-term floating-interest domestic bonds. The government pays 7.1 percent interest on this debt, reflecting an expected rate of inflation of 4 percent and a 3 percent real return to bondholders. For simplicity it is assumed that real GDP is constant, the budget is initially in balance—with both revenue and expenditure also equal to $100 million—and revenue and noninterest expenditure grow in line with inflation, thus maintaining their ratio to nominal GDP. If the expected rate of inflation were to rise to 7 percent, the government would then have to pay bondholders 10.2 percent, equivalent to $10.2 million, resulting in a deficit, in the conventional sense, of $2.9 million. This reflects an increase in interest expenditure of 10.2 - 7.1 = 3.1 less 0.2 which represents the excess of increased revenue over increased noninterest expenditure owing to higher inflation. The increase in interest expenditure, however, merely compensates bondholders for a drop in the real value of the bonds they hold. In other words, part of the return to the bondholder—the inflationary component of the yield—is a return of capital (as opposed to a return on capital). This return of capital represents an implicit amortization of the outstanding stock of debt, although in an accounting sense it is a payment of interest.

From the government’s point of view, any return of capital during the year is exactly counterbalanced by a reduction in the real value of the stock of public debt at the end of the year. Thus, although the conventional deficit has increased as a result of higher interest payments, the real stock of public debt by the end of the year is the same as when inflation was assumed to be 4 percent and the budget was in balance. Table 1 illustrates a number of scenarios that are identical in real terms (the preceding paragraph describes the transition between scenarios B and C), but which, because of alternative inflation assumptions and levels of nominal interest payments, yield markedly different conventionally measured fiscal deficits. This raises questions about the usefulness of the conventional measure of the deficit as an indicator of fiscal policy stance.

Table 1.Inflation, Interest Payments, and the Fiscal Deficit
ABCDE
Assumptions
Inflation rate (in percent)0.04.07.020.0100.0
Nominal interest rate (in percent)3.07.110.223.6106.0
Fiscal balance
Revenue96.2100.0102.9115.4192.3
Expenditure92.3100.0105.8130.8284.6
Non interest89.392.995.6107.2178.6
Interest3.07.110.223.6106.0
Of which: Real interest3.03.03.03.03.0
Deficit measures (- deficit)
Conventional3.90.0-2.9-15.4-92.3
Primary6.97.17.38.213.7
Operational3.94.14.35.210.7
Debt
Nominal debt, beginning of year100.0100.0100.0100.0100.0
Flow (- conventional deficit)-3.90.02.915.492.3
Nominal debt, end of year96.1100.0102.9115.4192.3
Real debt, end of year96.196.196.196.196.1

Three Concepts of the Fiscal Deficit

Given that interest payments and the fiscal deficit are affected by the rate of inflation, alternative approaches to measuring the real impact of budgetary policy are needed. Three alternative concepts of the fiscal deficit, each of which treats the interest expenditure component of public expenditures in a different manner, have been proposed in recent years. The choice between these alternatives, however, depends on the purpose at hand.

To measure the net claim on financial resources by the public sector, the conventional deficit should be used. The conventional deficit, or the public sector borrowing requirement (PSBR), is the standard measure of the fiscal deficit used by the Fund. Defined on a cash basis, it measures the difference between total government cash outlays, including interest outlays but excluding amortization payments on the outstanding stock of public debt, and total cash receipts, including tax revenue, nontax revenue, and grants. Since interest paid on the stock of debt in a particular year is chiefly the result of past deficits rather than current behavior, a measure of the current fiscal policy stance might exclude all interest payments. The primary deficit, that is, the noninterest component of the conventional fiscal deficit, measures how the current fiscal policy stance improves or worsens the net indebtedness of the public sector, thus providing important information on the sustainability of the fiscal policy stance. The link between the primary deficit, interest payments, and public debt is further discussed below.

The third concept of the deficit is a hybrid of the conventional and primary deficit concepts. The operational deficit—or the inflation-corrected deficit—is defined as the conventional deficit less the inflationary component of current interest payments or, alternatively, as the sum of the primary deficit and the real component of interest payments. This indicates whether fiscal policy affects the real public debt. In an inflationary environment, the time path of real debt can provide a different perspective on the sustainability of fiscal policy than the prospective evolution of nominal debt (this is also discussed below).

Table 1 shows how these different concepts of the fiscal deficit behave under the various hypothetical scenarios. While the conventional deficit widens (from an initial surplus) by $96.2 million as the inflation rate increases from 0 to 100 percent, both the primary and the operational surpluses increase by only $6.8 million.

Debt and Interest Rates

When public debt is held in the form of floating-interest domestic bonds, as is assumed above, the growth rate of nominal interest payments will exceed the inflation rate with a positive real interest rate if real GDP is constant. This will in turn push up the conventional deficit relative to GDP. In the case where the stock of public debt is either denominated in foreign currency or is index-linked, however, interest payments will tend to rise at the same rate as prices. The intuition behind this result is as follows. Assuming that the exchange rate is adjusted to reflect the evolution of domestic prices, the domestic value of external debt will rise in proportion to the increase in the price level. Since interest rates on external debt will not be affected by domestic inflation, interest payments will rise in proportion to the increase in the domestic value of external debt. When both GDP and noninterest expenditure are assumed to increase in line with inflation, the conventional deficit as a proportion of GDP will be unaffected. The behavior of interest payments with domestic indexed debt is similar, provided that the adjustment of principal is treated as amortization. Interest payments are affected because a nominal fixed interest rate is applied to the principal after adjustment for inflation. Thus, nominal interest payments on such debt grow in line with the price level, and under earlier assumptions, the conventional deficit as a proportion of GDP is unaffected by domestic inflation. In cases where the adjustment of principal is not treated as amortization, but rather as a monetary correction classified as an interest expenditure, the evolution of interest payments is exactly the same as with floating-rate domestic debt. The conventional deficit can, however, fall relative to GDP if nominal interest payments do not adjust in line with inflation. If the government has issued significant quantities of long-term debt, this could happen up to the point where inflation leaves creditors willing to hold only short-term bonds. It would also be the case where the government manipulates the interest rate on its debt instruments to artificially lower its debt service costs. However, it is argued in the note on Public Expenditure and Sustainable Fiscal Policy that such a practice is likely to be self-defeating.

Interest Payments and Public Debt Dynamics

The preceding sections illustrate how interest payments and fiscal deficits are influenced by inflation. To determine how the sustainability of the government’s fiscal stance is affected, the implications for public debt have to be determined. The following framework describes the link between the overall fiscal balance, the primary balance, and debt accumulation.

Public debt at the end of period t can be written as

where Dt-1 is the debt outstanding at the end of period t-1 and Dt is the overall deficit in period t. The overall deficit can be expressed as

where pt is the primary deficit, r is the real interest rate on government debt, π is the inflation rate, and [(1+r)(1+π)1]Dt1 are interest payments. Substituting (2) into (1) yields

As a proportion of GDP, (3) can be expressed as

where denotes a ratio to nominal GDP, and g is the growth rate of real GDP. Subtracting Dt-1 from both sides of (4) yields

from which it follows that for p^

t = 0:

Since nominal GDP can be written Yt=(1+g)(1+π)Yt1, (5) can be expressed as

from which it follows that for p^

t = 0:

Conditions (6) and (8) have a straightforward interpretation. The nominal interest rate, r(1 + π) + π, is the growth rate of the debt resulting from expenditure on interest payments while pt/Dt-1 is the growth rate of debt attributable to the noninterest component of the deficit. These combine to give the overall growth rate of the debt. The debt-to-GDP ratio will increase indefinitely if the growth rate of nominal GDP, g(1 + π, is smaller than the growth rate of the debt. If the primary deficit is zero, then this outcome requires only that the real (or nominal) rate of interest exceed the real (or nominal) growth rate of the economy. This is often referred to as a domestic debt trap. However, the built-in tendency for the debt-to-GDP ratio to increase can be offset if there is a primary surplus. By the same token, while the interest rate may be less than the growth rate, a sufficiently large primary deficit will lead to an increase in the debt-to-GDP ratio.

Sustanablity

The sustainability of public debt can be assessed according to a variety of criteria. However, by analogy with the way such judgements are made in the private sector, the prospect of insolvency and debt default probably provides the clearest indication of unsustainability. But how is the solvency of the government or the public sector judged? The private sector analogy points to the need to reflect all current and future assets and liabilities in a comprehensive balance sheet and then ensure that assets are sufficient to cover liabilities, in which case public spending plans are sustainable. It has been argued that this should be the government’s guiding principle in assessing its fiscal policy stance. But while assessing sustainability in terms of government or public sector solvency has considerable intuitive appeal, its information requirements are enormous. Indeed, in the few industrial countries where there has been an attempt to construct a public sector balance sheet, only limited success has been achieved. The prospects of much progress in developing countries are slight. An informationally less demanding approach is required.

One alternative is to judge sustainability using simple rules that describe the time path of the debt. For example, condition (8) can yield a rule to ensure that the debt-to-GDP ratio does not increase. For projected paths of the real interest rate and output growth, this rule specifies a benchmark primary balance consistent with an unchanged debt ratio. Fiscal policy is sustainable if the primary balance exceeds the benchmark. A problem with this rule is that it is not sufficiently forward looking, in that it takes no account of the impact of future changes in fiscal policy, and in particular known expenditure demands. A number of rules have been proposed that assess sustainability in the light of projected noninterest expenditure. Such rules gauge sustainability relative to the tax ratio consistent with unchanged debt ratio. However, their ease of interpretation and implementation notwithstanding, the attraction of these simple rules is deceptive. Major limitations remain. The absence of any feedback effects from the fiscal deficit to the real interest rate and output growth deprives the rules of an important policy dimension. Moreover, targeting an unchanged debt ratio is arbitrary. Just as there are good reasons why governments should under certain circumstances run deficits, so it is also reasonable to expect an often prolonged increase in government debt relative to GDP. The question is what the upper limit to the debt-to-GDP ratio should be. This question, however, does not lend itself to a clear-cut answer without reference to the issue of solvency.

Lastly, it should be noted that these rules focus on nominal debt, which in an inflationary environment can be misleading, at least in the short term. While nominal debt is increasing, the government can effectively amortize unindexed debt through an unanticipated increase in inflation, thus reducing real debt. But such a response to a high or rising level of debt does not offer a permanent solution to a sustainability problem. First, the burden of the debt is shifted from future taxpayers to current bondholders and other holders of money. Bondholders are likely to respond by requiring higher rates of return to reflect the inflation risk associated with nominal assets and will demand shorter maturity bonds. Ultimately, the pressure for indexation will be irresistible, in which case the distinction between nominal and real debt will disappear. Second, high rates of inflation themselves have implications that may be harder to tolerate than the action required to bring debt under control.

Country Illustration

Fiscal adjustment in Brazil

Inflation rates in Brazil during the mid-1980s were high and variable, which had implications for the design of fiscal policy in the context of broad stabilization objectives. As Table 2 indicates, the conventional fiscal deficit more than doubled to nearly 50 percent of GDP between 1984 and 1988. However, virtually the entire deficit reflected a monetary correction to compensate bondholders for the impact of inflation. The operational deficit was only modest, and there was a primary surplus in all but one year. In the adjustment program followed during 1988/89 (which was supported by the Fund), both the conventional and operational deficits were thus targeted. The primary deficit, however, was not targeted, because accurate data on interest payments were not available on a timely basis given Brazil’s federal structure. Data on debt were more reliable, making it easier to compute the operational deficit, although lags in the availability of price data presented some problems in making a quick assessment of the monetary correction.

Table 2.Brazil: Conventional, Operational, and Primary Balances
19841985198619871988
(In percent of GDP)
Conventional fiscal balance-23.6-28.0-11.1-31.4-48.5
Of which: Monetary correction-21.1-23.7-7.5-25.9-44.3
Operational fiscal balance-2.5-4.3-3.6-5.5-4.3
Of which: Interest payments
(non inflationary component)-6.9-6.4-4.5-4.8-5.6
Primary balance4.42.10.9-0.71.3
(In percent)
Inflation rate (annual)195.8220.0136.0224.8638.7
Source: International Monetary Fund.
Source: International Monetary Fund.
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