Producer Price Index Manual: Theory and Practice ... - METAC

7. Treatment of Quality Change
Table 7.2. Example of Overlap Method of Quality Adjustment
(a) General Illustration
Product Type Item January February March April
A 1 1
p
1
2 1
p
2
2
p
1
2
p
2
3 3
p
3
4 2
p
4
B 5 1
p
5
6 1
p
6
2
p
5
2
p
6
7 3
p
7
8 1
p
8
2
p
8
3
p
1
3
p
4
3
p
5
3
p
8
4
p
1
4
p
3
4
p
4
4
p
5
4
p
7
4
p
8
(b) Numerical Illustration
Product Type Item January February March
A 1 4.00 5.00 6.00
2 5.00 6.00
2. overlap 6.90
2. imputation 6.56
2. targeted imputation 7.20
2. comparable replacement 6.50
3 6.50
4 7.50 8.00
B 5 10.00 11.00 12.00
6 12.00 12.00
6. imputation 13.13
6. targeted imputation 12.53
7 14.00
8 10.00 10.00 10.00
7.83 The method is only as good as the validity
of its underlying assumptions. Consider
i = 1 ... m products where p t m
is the price of
t 1
product m in period t, p + n
is the price of a replacement
product n in period t + 1, and there are
overlap prices for both products in period t. Now
item n replaces m but is of a different quality. So
let A(z) be the quality adjustment to
t 1
p +
n
which
equates its quality to
t 1
p +
m
* t+ 1 t+ 1 t+
1
m
n
such that the qualityadjusted
price ( )
p = A z p . Put simply,
the index for the product in question over the period
t – 1 to t + 1 is
t− 1, t+ 1 t t− 1 t+
1 t
(7.2) I = ( pm / pm ) × ( pn / pn)
p p
= × .
p p
t+
1
n
t−1
m
t
m
t
n
158