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).

Tabl

e 2. Unit root tests on inflation and steady-state inflation uncertainty

INFLATION

SS_UNC

Test

Lag

Test statistic

Det. Comp.

Test statistic

Det. Comp.

ADF

3

-6.80 **

C, T, SD

-4.45 **

C, T, SD

REC

-3.50 *(5)

C, T, SD

-4.45 ** (3)

C, T, SD

EXO_SB

3

-5.14**

C, T, SD
1998 M12

-2.74

C, T, SD
1998 M12

REC

-3.03 * (5)

C, T, SD
1998 M12

-1.58 (5)

C, T, SD
1998 M12

END_SB

3

-8.14 **

C, T, SD

2008 M5

-3.58 **

C, T, SD

2001 M3

REC

-1.52 (11)

C, T, SD

2008 M7

-3.58 ** (3)

C, T, SD

2001 M3

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

Test 1: includ

ed lags (levels): 3, trend and

intercept, seasonal dummies included

Coint rank

Test stat.

p val

90%

95%

99%

r0 = 0

91.11

0 .0000

23.32

25.73

30.67

r0 = 1

19.71

0.0020

10.68

12.45

16.22

Test 2: includ

ed lags (levels): 1, trend and

intercept, seasonal dummies included

r0 = 0

137.26

0.0000

23.32

25.73

30.67

r1 = 1

21.37

0.0009

10.68

12.45

16.22

Test 3: includ

ed lags (levels): 8, trend and

intercept, seasonal dummies included

r0 = 0

67.20

0.0000

23.32

25.73

30.67

r1 = 1

16.20

0.0101

10.68

12.45

16.22

13



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