Appendix: Interest Rate- and Exchange Rate-Induced Changes in Budget Balance

Ahsan Mansur, Richard Haas, and Peter Heller
Published Date:
May 1986
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This section contains a short theoretical exposition of how the budget balance might be adjusted for changes in interest and exchange rates, consistent with purchasing-power-accrual accounting.

Adjustments for interest rate-induced changes allow for a distinction between the “nominal” and “market” values of outstanding debt. Most of the discussion on national debt refers to “nominal” value, which is the amount of money the government will repay to holders of conventional stocks and securities when they are redeemed. The “market” value of any stock—the price at which it can currently be bought—may be more or less than the nominal value, depending on movements in the interest rate. If the government issues a certain amount of debt D in the form of long-term bonds yielding a nominal coupon i0, and the current market (consol) rate of interest is i, the real market value of the debt would be (Di0)/(Pi). The change in the real market value of the debt is ∆ VP,i.

Thus, if the accounting is done in real terms, allowing for interest rate- and inflation-induced changes, one should subtract both the rate of inflation times the real long-term debt outstanding, and the change in the real value of outstanding debt owing to changing market rates of interest.52 The adjustments in nominal terms would equal

One simple way to convert the nominal values of outstanding government debt to market values is to examine the difference between the nominal and market values of both private and official holdings of government debt. This information may be readily obtained from stock exchange statistics. Adjustments for inflation may then be done on the basis of the methods suggested in the first subsection of Section V, and using the market value of outstanding debt.

The above discussion assumes that all government debt is denominated in domestic currency and does not consider the implications of foreign-currency-denominated debt. This closed-economy modeling may be appropriate for some of the major industrial countries like the United States, but for others, like Canada and France, foreign debt represents a significant proportion of outstanding public debt. Governments can borrow and lend domestically and abroad in an open economy. The real values of assets denominated in foreign currency, like those of domestic-currency-denominated assets, are changed by variations in inflation and interest rates. But unlike its domestic counterpart, outstanding public debt denominated in foreign currency tends to increase (decrease) in value, in domestic-currency terms, as the exchange rate depreciates (appreciates).

Let BH and BF denote the public debt denominated in domestic currency and in foreign currency, respectively, and assume that both types of bonds may be held by domestic residents as well as by foreigners. Simultaneous inflation- and exchange rate-induced changes in real public sector debt outstanding (∆VP,e) are given by

The expression for adjustment to the budget deficit becomes more complicated when one simultaneously takes into account the induced effects owing to inflation, interest rate, and exchange rate changes (∆VP,i,e) on the value of outstanding domestic-currency- and foreign-currency-denominated debt.

where E* denotes the amount of net foreign reserves held by the government.

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