Lund makes two key identifying assumptions. First, he explicitly rules out the “doubledecay” process of Jegadeesh and Pennacchi (1996) on the grounds of parsimony, and assumes that the “risk premium” state variable Vt does not affect the actual AR(1) process (25) followed by the instantaneous spread. This assumption appears empirically reasonable for the 1990-98 period considered, as will be discussed below. However, one advantage of the more general model, as recognized in Andersen and Lund (1996), is that the second state variable can capture structural shifts in the nominal interest spread processes resulting, e.g., from shifts in inflation targets.
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Second, the model implies yield spreads from bonds maturing prior to January 1, 1999 are unaffected by shifts in the EMU probability state variable 0t. This is critical, because the “market price of risk” Vt is also a free state variable that captures some movements in the shape of the term structure unjustified by the AR(1) process (25) estimated for the instantaneous spread st. However, Vt affects all maturities, whereas 0t affects only post-1999 maturities. 0t is inferred in essence by the difference between the observed post-1999 portion of the yield curve, and the post-1999 “local yield curve” predicted by extrapolating the pre-1999 yield curve for estimated state variables (s, Vt). Thus, Lund’s EMU probability assessments are essentially assuming that the non-EMU scenario for interest rate differentials is largely identified by the estimated 2-factor behavior of the term structure of yield spreads over 1990-98 for pre-1999 maturities.

Judging from Figure 1, Lund’s model appears to estimate generally lower Italian-German interest differentials conditional upon EMU not occurring, and consequently higher non-EMU probabilities (lower EMU probabilities) than other models. Despite the low standard errors of Lund’s structural parameter estimates, however, it is not really possible to say whether Lund’s inferred non-EMU scenarios are better or worse than the Morgan and Favero etal approaches.

The problem is that structural parameters are inferred partly from the time series behavior of the term structure of yield spreads, and partly from what is needed to match the cross-sectional patterns of yield spreads on individual weeks. The appropriate statistical theory for assessing the latter informational source has not really been developed. The typical null hypothesis also used here is that market participants know the true, time-invariant deep structural parameters and the state variable realizations with certainty when pricing bonds, and that observed and actual bond prices deviate only by independent, homoskedastic measurement error. Under this strong null hypothesis and given abundant cross-sectional data, inferred parameters tend to have low estimated standard errors.

Lund’s estimates are best viewed as a model-specific description of a non-EMU scenario consistent with term structures of yield spreads observed over 1990-98. Term structures observed over the 1980’s might yield different estimates of the non-EMU scenario.