# European Capital Markets with a Single Currency

By Jean Dermine; Pierre Hillion | Go to book overview

Appendix: Formal Analysis

A.1. The model

We use a model of debt management which is adapted from Miller ( 1997) and expanded with a model of optimal default and an analysis of different exchange rate regimes, including EMU.

Miller's model is formulated in discrete time. This leads to a fairly complicated form of the government budget constraint, which is then simplified by a first-order Taylor approximation. Here, we avoid the Taylor approximation by expressing all flow variables, as well as all interest rates, inflation rates, and rates of appreciation, as instantaneous rates.

The model abstracts from fluctuations in money demand and assumes that the real money stock is kept constant. It also abstracts from the effects of economic growth and assumes that the government keeps a constant level of debt measured in real terms. A part of this debt will be denominated in domestic currency and a part of it in foreign currency. The foreign currency bonds could alternatively be interpreted as inflation- indexed bonds.

The central part of the model is the government's flow budget constraint:
x = g + b(i - π) + b* (i* - π*) - mπ,
where x is real tax revenues; g is real expenditures (excluding interest payments); b is the real value of home currency denominated debt; b* is the real value of foreign currency denominated debt; i is the nominal interest rate on home currency denominated debt; i* is the nominal interest rate on foreign currency denominated debt; and m is the real money stock.

To understand the logic behind this budget constraint, first note that there is no ambiguity in measuring both domestic and foreign debt in real terms, because we assume absolute purchasing power parity:
EP* = P,
where E is the exchange rate, the price of foreign currency in terms of home currency; P* is the foreign price level; and P is the domestic price level.

Because of purchasing power parity, the nominal foreign currency value of foreign currency denominated debt can be measured in real terms in two equivalent ways. It can be divided by the foreign price level P* or it can be translated into nominal home currency by multiplying by the exchange rate and then dividing by the home price level P.

The terms (i - π) and (i* - π*) are the real interest rates paid on domestic and foreign debt, respectively.

The budget constraint assumes that the government issues new money and new

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