How to extract market expectations from asset prices is a question of great interest to both market participants and central bankers. In a recent CEPR Discussion Paper, Carlo Favero, Francesco Giavazzi, Fabrizio Iacone and Guido Tabellini examine a specific example: how the term structure of interest rates can be used to estimate the probability the market attaches to a particular country – in this case, Italy – joining EMU on a given date.

The researchers observe that there are striking differences between the surveys regularly conducted among market participants (such as the Reuters Survey) and the probabilities estimated by financial houses (such as JP Morgan) using the term structure. For example, in the early months of 1997, the probability that Italy would join EMU on 1 January 1999 ranged between 7–17%, according to the Reuters Survey. During the same period, the JP Morgan ‘EMU calculator’, which is published regularly in the Financial Times, assigned Italy probabilities ranging between 51–70%.

Favero et al investigate the source of these large discrepancies. They find that the probabilities computed by EMU calculators are ‘upward biased’. This is because the calculations are based on average rather than instantaneous forward rates.

They also compute the ‘out’ spread between Italian and German short-term interest rates, that is, the spread that would prevail at some date, if, on that day, Italy was outside EMU. This allows separate identification of the two components of the total spread: one that is due to different economic fundamentals; and one that is due to the markets’ assessment of the probability that Italy will be in EMU in 1999.

Between March 1996 and March 1997, for example, there was a 214 basis points reduction in the spread between Italian and German forward rates with maturity in 1999. Of this, the team calculates, 149 basis points are attributable to the convergence of fundamentals, while only 65 basis points are attributable to a changed assessment of Italy’s likelihood of being in EMU in 1999.

In contrast, EMU calculators like JP Morgan’s compute the probability that a country will join EMU in 1999 by mapping average forward rates into probabilities. Three assumptions underpin their calculations:

• First, that currently observed forward interest rates with maturity in 1999, and settlement 3–10 years later, are a weighted average of: a) the spot rate differential between the country and Germany in the case of the country joining; and b) the spot rate differential in the case of the country not joining.
• Second, that the spot rate differential when the country joins is zero;
• Third, that if the country does not join, the spot rate differential has a specific value.

Probabilities are then calculated as the ratio of the observed average forward rate differential to the assumed spot rate differential if the country is left out of EMU. Leaving aside the issue of market inefficiencies, Favero et al argue that the second and third assumptions introduce two potential sources of bias. The first arises from the need to specify a value for the spot rate differential when the country is outside EMU. The second relates to the use of average rather than instantaneous forward rates.

Favero and his colleagues analyse these two sources of bias. The first step involves estimating the interest rate differential in the case of no entry in 1999, the ‘out’ spread. The technique they use estimates the responses of the Bank of Italy to changing economic circumstances, hence linking the interest rate spread between Italy and Germany to macroeconomic fundamentals. It is a different technique to the one used by JP Morgan, but essentially confirms their results. This finding suggests that the first potential source of bias is not important empirically.

The researchers then construct an EMU calculator based on instantaneous forward rates. The use of these rates is crucial because it provides an easy way to describe the complementary events, ‘Italy is in EMU’ and ‘Italy is out of EMU’, at a specific future point in time. With average (rather than instantaneous) forward rates, the estimate is the average of the probabilities of being inside EMU at all points in time during a given period. Since the probability of being inside EMU at a future date increases with the length of the specified period, this average of probabilities is greater than the probability of being inside EMU exactly at the start of the period.

To illustrate their analysis, Favero et al consider the situation in March 1997. In that month, the probability of Italy joining EMU in 1999, based on instantaneous forward rates, was 24%. The probability based on average two-year forward rates was 41%, while the probability according to the Reuters Survey was 12%.

The importance of this finding is indicated by the following ‘limit case’ example. If the markets are 100% sure that Italy will join EMU in 2001, then the probability that Italy will join in 1999 is zero. In this case, the Italian instantaneous forward rate for 1999 will lie on the ‘out’ curve, and a computation based on this rate will deliver the correct estimate of the probability of Italy joining in 1999 – namely zero.

But the three-year average forward rate will be lower than the ‘out’ forward rate because it is an average of: two years of ‘out’ Italian instantaneous forward rates; and one year of German instantaneous forward rates. Hence the probability of Italy entering EMU in 1999, computed using average forward rates (one minus the ratio of the average forward rate differential between Italy and Germany to the differential between the ‘out’ Italian rate and the German rate), will be positive. The upward bias of the EMU calculator in this case produces an inaccurate forecast.

Edited by: David Begg, Jürgen von Hagen, Charles Wyplosz and Klaus F Zimmermann

This volume explores life once Europe shares the same currency. Some of the best European and American economists use available theories and data, including historical evidence, to look at the operation of monetary and fiscal policy, at the effects of shocks and at the international role of the euro. The book will serve as the reference for understanding the early challenges of EMU.

Authors: Rudiger Dornbusch, Barry Eichengreen, Antonio Fatás, Carlo Favero, Marc Flandreau, Francesco Giavazzi, Jacques Le Cacheux, Maurice Obstfeld, Giovanni Peri, Richard Portes, Hélène Rey, Kenneth Rogoff, Charles Wyplosz, Frédéric Zumer.

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