Approved for Release:
Several problems preclude widespread use of double
deflation:
- It requires a great deal of data to implement. A full
I-O table is needed for a complete accounting of a
sector’s inputs. A surrogate method relying on a
price index of a sample of a sector’s inputs can be
used, but even this requires much data and will not
support timely estimates.
' Double deflation assumes that the inputs actually
used in year t by sector j would have been used even
with a different set of relative prices, an unlikely
occurrence. It is possible that value added calculat-
ed by the double deflation method could be negative
if the prices of some of the major inputs in year t in-
creased greatly between year 0 and year t.
- Because double deflation is the difference between
two values, it is subject to large fluctuations that
result from small fluctuations in the two other
values.”
” Hill investigated the conditions under which double deflation is
the best procedure for estimating value added (Measurement, ch.
2.) Let y be the ratio in constant prices of the inputs used by sector j
in year t compared to year 0:
y = 3P(ii0)q(iJ.l)/ZP(i»0)q(iJ.0)-
Let z be the gross output index of sector j:
I = P(i,0)Q(i.I)/P(.i.0)Q(i.0)-
Finally, let x equal the ratio of sector j’s inputs to its gross output:
x = >3P(i,0) y (gross output grows faster than inputs) and if
w—l > 0 (the base-year share of inputs is between 0 and 1), then:
v = z+(w—l)(z—y)
= :z+b, where b > 0, and v > z > y.
The reverse is also true: if z < y, then v < z < y. Therefore, if in-
dexes of gross output and current inputs are both available, the
gross output index is always a better indicator of value added unless
the errors associated with the gross output index are much larger
than those associated with the input index.
Approved for Release: 2019/07/19 C05210421