Table 6: The estimates of the common stochastic trends
|
ɛpp |
⅛2 |
g∆p2 |
gðl |
⅞ |
ɛʤ____ |
⅛__ | |
|
The estimates of the first order stochastic trends |
!, «±1 | ||||||
|
«±1,1 |
0.02 |
-0.03 |
0.08 |
-0.14 |
-1.61 |
1.32 |
-0.17 |
|
[0.32] |
[-0.85] |
[1.01] |
[-0.53] |
[-7.89] |
[2.45] |
[-0.79] | |
|
«±1,2 |
-0.01 |
-0.00 |
0.04 |
-0.33 |
-1.29 |
0.57 |
-0.14 |
|
[-0.48] |
[-0.01] |
[0.88] |
[-1.75] |
[-8.50] |
[1.44] |
[-0.88] | |
|
The estimates of the second order stochastic trends, «±2 | |||||||
|
«±2,1 |
-0.00 |
0.01 |
-0.00 |
1.00 |
-0.47 |
-0.47 |
-0.00 |
|
[-0.13] |
[1.06] |
[-0.30] |
[≡] |
[-8.03] |
[-7.99] |
[≡] | |
|
«±2,2 |
0.01 |
0.00 |
-0.03 |
0.00 |
-0.12 |
-0.01 |
1.00 |
|
[0.29] |
[0.24] |
[-0.78] |
[≡] |
[-0.77] |
[-0.05] |
[≡] | |
reason: The estimated model is formulated in second differences, which for the interest
rates and U.S. inflation rate means over-differencing. Thus, the highly significant
coefficients in the last four rows are likely to compensate for this.
10 The driving forces
Table 6 reports the estimates of the common stochastic trends where «±1 and « 2 define
the first and second order stochastic trends as a linear function of the VAR residuals.
The two «±1vectors are determined by the chosen normalization of β±1, whereas « 2
has been normalized and just-identified by the choice of the two zero coefficients.
As discussed in Section 2, the estimates of the second order trends are more straight-
forward to interpret and we shall mostly focus on them. Based on the estimates in
Table 6, the first stochastic I(2) trend, «±2 1 ɪɪ ⅛ seems to be generated from the
twice cumulated shocks to the bond spread and to the German term spread with al-
most equal weights (roughly 0.5, 0.5), whereas the second trend, ^'22T ∑2⅛ seems
to have been generated from the twice cumulated shocks to the US short term interest
rate.
Even though the estimates of the I(I) stochastic trends are less straightforward
to interpret, it is quite interesting to note that only the interest rates coefficients are
significant. Since, cumulated shocks both to the long-term and short-term interest rates
are highly significant, it means that there are not just one stochastic trend driving the
term structure, but at least two.10
The coefficients to ∆p2 and the pp are completely insignificant as are the coefficients
to nominal exchange rates. The former result seems very plausible given the previous
finding that prices seem to be purely adjusting (see also Juselius and MacDonald, 2004
and 2006). But, the finding that exchange rate shocks are completely insignificant may
seem surprising, given that the nominal exchange rate was found to have no long-run
levels feed-back. On the other hand, the fact that it was found to significantly adjust
to the polynomial cointegration relations can explain the lack of significant effects in
10This is consistent with the findings in Johansen and Juselius (2001).
23