FINANCIAL MARKETS’ ASSESSMENT: Term structure-based EMU 7

It seems likely that the reaction function estimated by Favero et al is partly capturing Italian monetary policy over 1987-1996. Achieving the Maastricht criteria certainly would create concern about inflation differentials, while the pre-1993 Exchange Rate Mechanism implies German interest rates were relevant over that period. However, whether forecasts based on this reaction function are relevant conditional upon Italy failing to enter EMU in 1999 is open to question. other

While the objective of qualifying by 2002 or later would plausibly prompt retention of the same reaction function, an alternate hypothesis is that the Bank of Italy might revert to its policies of the 1980’s. The Bank of Italy reaction function estimated by Clarida, Gall, and Gertler (1997) over 1981:6 through 1989:12 is quite different from that in Favero et al; in particular, higher steady-state real interest rates, and lower long-run sensitivity to Italian inflation, Italian output, and German interest rates. If this were used instead as the non-EMU scenario, inferred EMU probabilities would be quite different.

Bond pricing models

Lund (1998) provides a good example of the application of current bond pricing models to the issue of inferring EMU probabilities. Lund models, e.g., Italian instantaneous interest rates as the sum of the German rate and the Italian-German spread:
w6874-16

implying yield differentials between Italian and German discount bonds depend upon the expected future evolution of instantaneous spot rate differentials:
w6874-17
If the two currencies join together in a currency union, the instantaneous spread drops instantly to zero. Rather than modeling this as only occurring on January 1, 1999, however, Lund posits a post-January 1999 hazard rate that allows for delayed entry. The current assessment 0t of that hazard rate determines the current EMU probability assessment [ 1 – exp(-0tt)] of a country joining Germany in a currency union within t years after 1/1/99. Combined with assumed independent Ornstein-Uhlenbeck (or AR(1)) processes for the instantaneous spread st conditional upon no unification and the market price Vt of spread risk, Lund develops a 3-factor model of yield spreads. In continuous time, the pre-EMU “risk-neutral” processes used in pricing spreads via (22) are
w6874-18
prior to January 1, 1999.

Lund estimates the parameters in (12) and the state variable realizations via nonlinear Kalman filtration, using two data sources: weekly 1-, 2-, 3-, 6-, and 12-month Eurorate differentials, and 1-10 year yield differentials inferred from swap rates. The broadest data interval was January 1990 through August 12, 1998, although subsets of that interval were used for specific countries either because of data unavailability, or because of deliberate data exclusion.

First, short-maturity interest rates were excluded for currencies affected by speculative attacks prior to September 1993, so that the impact of a fourth underlying state variable (currency crises) could plausibly be ignored. Second, post-1999 maturities were not considered prior to 1995, because of lack of confidence in the inferred EMU hazard rates. The vector of yield spreads for different maturities provided crosssectional evidence each period regarding parameter values and state variable realizations, while the time series evolution of those yield differentials provided further evidence regarding parameter values.