A further potential bias originates in numeraire issues when considering the forward expectations hypotheses underlying EMU probability calculators. The “risk-neutral” expectational operators that incorporate the assorted risk premia by changing the probability measure do depend upon which currency is used when assessing investments. Consequently, forward rates from Italian and German swap rates cannot be compared without first expressing the underlying investments in a common currency.

where Et is the risk-adjusted expectations operator relevant to the domestic investor when assessing future speculations, given the domestic discount factor used in (15). From (5) above, ftT 9 E**(rt+T). However, the same is not true for the relationship between the foreign forward interest rate and future spot rate from the domestic investor’s perspective. The zero-profit equilibrium condition on contracting to borrow foreign currency at the forward interest rate and subsequently investing at the spot interest rate is

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I know of no EMU probability calculator that considers this potential source of bias. Papers that test or use the intra-European uncovered interest parity hypothesis at maturities of less than a year typically rule out a substantial effect from numeraire issues from the fact that intra-European exchange rate volatilities are small. However, the maturities in (17) and (18) are substantially longer, creating the possibility of a greater impact.

Estimating the non-EMU scenario

One of the most critical issues in identifying the probability of two countries joining in a currency union is estimation of the relevant forecast conditional upon EMU not occurring. As this scenario represents a counterfactual hypothesis, the merits of the forecasts cannot directly be tested, but can only be judged by the overall merits of the methodologies. Three quite different approaches will be discussed here: J.P. Morgan’s “kitchen sink” regression, Favero et a/s central bank reaction function, and Lund’s term structure model. A fourth approach used by De Grauwe (1996) and Credito Italiano employs the average spreads from a period with low EMU prospects. De Grauwe uses 1990 average spreads, while Credito Italiano uses 1993. Other banks have also created EMU calculators, but Morgan’s is one of the few to publicly document its methodology.

J.P. Morgan’s EMU calculator identifies non-EMU forward rate spreads by regressing daily 10-year swap spreads (the difference, e.g., between Italian and German swap rates) on a set of non-European interest rate variables intended to capture “international factors relating to investors appetite for risk or the supply of liquidity.” Non-European variables were used for exogeneity reasons, and the regression interval 1988-1992 was selected as a period in which expectations of future currency union were plausibly not affecting intra-European interest differentials. Regressions were only run through December 1991 for those countries that experienced currency devaluations in the fall of 1992.

Various regressors are considered; the analysis concludes “[w]e are principally left with using the average of the U.S.-Canada and Japan-Australia 10yr bond spread and the U.S. and Japanese 10yr-2yr yield spread.” The estimated “non-EMU” 10-year swap spread is then transformed into an estimate of the post-1998 forward swap spread by using the observed pre-1999 swap spread and the average slope of the swap spread curve over 1988-92.