ADBI Working Paper 904
Y. Dosmagambet et al.
14
3.3 Structural VAR Estimates
The decomposition of the forecast error variance in Tables 3 and 4 allows us to assess
the impact of structural shocks in the crude oil market on the variability of the KASE
index, the impact of structural shocks in the crude oil market on the exchange rate
volatility, and the impact of volatility from structural shocks in
the crude oil market on the
exchange rate volatility, respectively. Although, in the short term, the
effects of the three
structural shocks in the crude oil market (crude oil supply shocks, aggregate demand for
industrial commodities related
to the business cycle, and specific demand shocks in the
crude oil market) are insignificant.
We base the structural VAR estimates on Kilian (2009):
𝐵𝐵𝑧𝑧
𝑡𝑡
= 𝛾𝛾 + ∑
𝑟𝑟
𝑖𝑖
𝑝𝑝
𝑖𝑖−1
𝑧𝑧
𝑡𝑡−𝑖𝑖
+ 𝜀𝜀
𝑡𝑡
(1)
where y is a parameter vector, C
i
and B denote the lagged and contemporaneous
coefficient matrices, respectively, and e
t
is a vector of mutually and serially uncorrelated
structural innovations.
Assuming that B
−1
exists, the reduced-form representation of Eq. (1) is:
𝑧𝑧
𝑡𝑡
= 𝛼𝛼 + ∑
𝐴𝐴
𝑖𝑖
𝑝𝑝
𝑖𝑖−1
𝑧𝑧
𝑡𝑡−𝑖𝑖
+ 𝑒𝑒
𝑡𝑡
(2)
where
a
=
B
−1
c
,
Ai
=
B
−1C
i
, and the reduced-form innovations,
et
, are
linear
combinations of the structural shocks,
e
t
,
e
t
=
B
−1
e
t
.
We estimate the reduced-form Eq. (2) and recover the structural shocks,
et
, by imposing
zero (exclusion) restrictions on the elements of
B
. We use the structural moving-average
representation to infer the impulse responses. We follow Kilian (2009) to impose a block
recursive structure on the contemporaneous link between the reduced-form VAR
innovations and the underlying structural disturbances. In particular, we
assume that
B
−1
has a recursive structure such that we can decompose the reduced-form innovations,
e
t
,
according to
et
=
B
−1
e
t
, as follows:
𝑒𝑒
𝑡𝑡
=
⎝
⎜
⎛
𝑒𝑒
𝑡𝑡
∆𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝
𝑒𝑒
𝑡𝑡
𝑝𝑝𝑟𝑟𝑟𝑟
𝑒𝑒
𝑡𝑡
𝑟𝑟𝑝𝑝𝑟𝑟
𝑒𝑒
𝑡𝑡
𝑟𝑟𝑝𝑝𝑟𝑟
⎠
⎟
⎞
=
𝑏𝑏
11
𝑏𝑏
21
𝑏𝑏
31
𝑏𝑏
41
0
𝑏𝑏
22
𝑏𝑏
32
𝑏𝑏
42
0
0
𝑏𝑏
33
𝑏𝑏
43
0
0
0
𝑏𝑏
44
=
�
𝜀𝜀
𝑡𝑡 𝑝𝑝𝑜𝑜𝑜𝑜 𝑠𝑠𝑠𝑠𝑝𝑝𝑝𝑝𝑜𝑜𝑠𝑠 𝑠𝑠ℎ𝑝𝑝𝑜𝑜𝑜𝑜
𝜀𝜀
𝑡𝑡
𝑎𝑎𝑟𝑟𝑟𝑟𝑟𝑟𝑒𝑒𝑟𝑟𝑎𝑎𝑡𝑡𝑒𝑒 𝑑𝑑𝑒𝑒𝑑𝑑𝑎𝑎𝑑𝑑𝑑𝑑 𝑠𝑠ℎ𝑟𝑟𝑜𝑜𝑜𝑜
𝜀𝜀
𝑡𝑡
𝑟𝑟𝑖𝑖𝑜𝑜−𝑠𝑠𝑝𝑝𝑒𝑒𝑜𝑜𝑖𝑖𝑠𝑠𝑖𝑖𝑜𝑜 𝑑𝑑𝑒𝑒𝑑𝑑𝑎𝑎𝑑𝑑𝑑𝑑 𝑠𝑠ℎ𝑟𝑟𝑜𝑜𝑜𝑜
𝜀𝜀
𝑡𝑡
𝑟𝑟𝑒𝑒𝑎𝑎𝑜𝑜 𝑒𝑒𝑒𝑒𝑜𝑜ℎ𝑎𝑎𝑑𝑑𝑟𝑟𝑒𝑒 𝑟𝑟𝑎𝑎𝑡𝑡𝑒𝑒
�
In fact, the results in Table 3 show that, in the first month, the impact of shocks in the oil
market on the stock index is close to zero. As the horizon increases, the effect of shocks
of the real price of oil, the
aggregate demand, and the real exchange rate gain a little
more importance, while the impact of supply shocks is negligible throughout the period
under review. For example, the total power of explanation of these shocks for the impact
is less than 14% of the variance in the real price of the oil market on the variability of the
KASE index, less than 3% of the variance in the real price of the oil market on the volatility
of the exchange rate, and 16% of the variance of volatility in the oil market in the volatility
of the exchange rate, but the power of explanation increases as the forecast horizon
increases. With the 15-month horizon, we see 19% of real oil price shocks, and
aggregate demand shocks explain only 12% of the stock index volatility. With a horizon
longer than 15 months, the impact of real oil price shocks on the stock index is about
61%, followed by a real exchange rate of about 33%.
