Inflation and Inflation Uncertainty in the Euro Area

4. The Relationship between Inflation and Steady-State Inflation Uncertainty in
a Bivariate VAR Framework

Next, we estimate a bivariate VAR for inflation and steady-state inflation uncertainty
to test for causality and for the presence of structural breaks related to EMU. As a first
step, the order of integration of the variables needs to be established. Standard ADF
tests reject the null hypothesis of a unit root in levels in both cases. We then carry out
the unit root tests proposed by Saikkonen and Lütkepohl (2002) and Lanne et al.
(2002). These are based on first estimating the deterministic term by a generalized
least squares (GLS) procedure under the unit root null hypothesis and subtracting it
from the original series. Then an ADF-type test is performed on the adjusted series
which also includes terms to correct for estimation errors in the parameters of the
deterministic part. As in the case of the ADF statistic, the asymptotic null distribution
is non-standard. Critical values are tabulated in Lanne et al. (2002). The test results
when allowing for exogenous breaks indicate that steady-state uncertainty might not
be stationary, but those including endogenously determined breaks again support
stationarity of both series (see Table 2).

Table 3. Johansen Trace Test for: [infl, infl ss var]

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