S.G.B. Henry 933successfully upheld. Then, estimates of the structural disturbances for the model
for which the VECM (18.19) is the reduced form could be obtained, as shown by
Wickens and Motto (2001). That is, the responses of unemployment to structural
shocks, that is,et, defined asB−^1 εt, whereBis the matrix of contemporaneous
coefficients in the structural model underlying (18.19), could be estimated.^26 In
the light of the earlier results on weak exogeneity, such overidentifying restrictions
on the loading matrix, in particular, are unlikely to hold.
Hence the status of single-equation estimates of (18.18), such as those given
in Nickell (1998), for example, and repeated as the first equation in Table 18.1
above, is then unclear. It is hard to treat it simply as “the” long-run unemployment
equation as claimed. Rather, it appears to be part of a fuller dynamic system which
involves equations which could be interpreted as determining the real interest rate,
movements in skill shortages and the union–non-union wage markup, amongst
other things.
The purpose of this last exercise is not to suggest estimation of the full system
underlying (18.19) as the way ahead to resolve this issue. Instead, it highlights the
dangers of using large sets of potentiallyI( 1 ), and possibly jointly endogenous,
variables if the intention is to estimate a single equation for long-run unemploy-
ment. Thus, one important conclusion from this exercise is to emphasize the
importance of the approach by Davidson (1998) of determining an irreducible co-
integrating (IC) equation. He recommends minimal cointegrating sets of variables
as contenders for structural (that is, behavioral) long-run relations.
In what follows, a simpler alternative is proposed which places emphasis on
external factors in accounting for the changes in unemployment over the last 25
years.
18.4.2.2 The price push variables
The long-run, or equilibrium, pricing equation which underlies most recent studies
on the NKPC is:
Pt=μtMCt, (18.22)where:
MCt=( 1 /α)(WtNt/Yt).In this equationMCtis nominal marginal cost,Wtis wages,Ntis employment
andYtis real output. Assuming a Cobb–Douglas (CD) technology and a constant
elasticity demand function, real marginal cost is (in logs):
mct−pt=−lnα+sLt, (18.23)wheresLtis the labor share. An extension is where technology is not restricted to
be CD, and it may be shown that real marginal cost is then affected by the real price
of imports (RPM) (see Bentolila and Saint-Paul, 1999). In turn, a long-run “equi-
librium” price can de defined asPt∗, wherePt∗=μ∗tMCtandMCis nominal (not
real) marginal cost, and this equilibrium markup is likely to be time-varying (see
Batini, Jackson and Nickell, 2005). Potential determinants of this varying markup