University of Groningen Groningen Growth and Development Centre ...

T u(u)
weighted with the total industry output at own prices: o
jk
. The UVRs from the other
industries (belonging to J k (b)) are weighted only by the output value of the matched products
in the industry:
o
M u(u)
jk
I j
∑
u u
= uv q . Hence the weights are given by
i=1
ij
ij
w
w
u(u)
jk
u(u)
jk
= o
= o
T u(u)
jk
M u(u)
jk
/ o
/ o
M u(u)
k
M u(u)
k
=
∀j∈
J
I j
∑
i=1
uv
u
ij
k
u
ij
(a)
q / o
M u(u)
k
∀j∈
J
k
(b)
(8)
with
o
M u(u)
k
=
T u(u)
∑ o
jk
+
J k (a)
∑
Jk
(b)
o
M u(u)
jk
To arrive at the Paasche index, the US weights are replaced by the Brazilian or Mexican output valued
at US prices:
UVR
xu( x)
1
k
=
J k
x(
x)
⎛UV
⎟ ⎟ ⎞
j
⎜
u(
x)
× w
jk
⎜ u(
u)
= 1⎝UVj
⎠
∑
j
(9)
with
w
w
u(x)
jk
u(x)
jk
= o
= o
T u(x)
jk
M u(x)
jk
/ o
/ o
M u(x)
k
M u(x)
k
I j
∑
i=1
∀j∈
J
uv
u
ij
x
ij
k
q / o
(a)
M u(x)
k
∀j∈
J
k
(b)
(10)
with
o
M u(x)
k
=
T u(x)
∑ o
jk
+
J k (a)
∑
Jk
(a )
o
M u(x)
jk
The split in the industry set is based on an assessment of the reliability of the industry UVRs.
Given the homogeneous character of the products belonging to an industry, it is expected that
product UVRs in an industry do not differ much. Hence, if the variation of the product UVRs
is high, this is an indication of unreliability. Also, reliability increases the higher the
percentage of industry output covered by matched products. Therefore the coverage ratio is
also taken into account when assessing the industry UVR reliability. The following decision
rule is used: when the coefficient of variation is less than 0.1, the industry is assigned to J k (a),
other wise to J k (b):
if
otherwise
[ ]
cv UVR
j
< 0.1
then
j∈
J
j∈
J
The coefficient of variation of industry j (cv j ) is measured as follows:
[ UVR ]
j
k
k
(a)
(b)
(11)
var
j
cv [ UVR ]
j
= (12)
UVR
The variance of the industry UVRs is given by the mean of the weighted deviations of the product
UVRs around the industry UVR (see Selvanathan, 1991):
8