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

Producer Price Index Manual
riod t value of all N artificial commodities is just
equal to minus period t commodity tax revenue.
Define the period t price and quantity vectors for
the artificial commodities in the usual way; that is,
p At ≡ [p 1 At ,...,p N At ] and q At ≡ [q 1 At ,...,q N At ] = f t , t =
0,1. The extra price vector p At is now added to the
old period t price vector p f t that was used in the final-demand
deflator, and the extra quantity vector
q At is added to the initial period t quantity vector f t
that was used in the final-demand deflator, that is,
define the augmented final-demand price and
quantity vectors, p t * and f t *, as follows:
(18.75) p f t * ≡ [p f t ,p At ] ; f t * ≡ [f t ,q At ] ; t = 0,1.
Using the augmented price and quantity vectors
defined above, a new tax-adjusted final-demand
deflator is calculated using the chosen index number
formula, P(p f 0 *,p f 1 *,f 0 *,f 1 *), and the question
asked is whether it will equal our initial national
value-added deflator (that did not make any tax
adjustments for commodity taxes on final demands),
P(p 0 ,p 1 ,q 0 ,q 1 ); that is, ask whether the following
equality holds:
(18.76) P(p f 0 *,p f 1 *,f 0 *,f 1 *) = P(p 0 ,p 1 ,q 0 ,q 1 ).
18.79 Under the assumption that all establishments
face the same prices, it can be shown that
the tax-adjusted final-demand deflator will exactly
equal the national value-added deflator, provided
that the index number formula in equation (18.76)
is chosen to be the Laspeyres, Paasche, or Fisher
formulas, P L , P P, or P F . In general, equation
(18.76) will not hold as an exact equality if the
Törnqvist-Theil formula, P T , is used. However, if
the commodity tax rates are equal in periods 0 and
1, so that assumptions equation (18.73) hold in addition
to assumptions equation (18.67), then it can
be shown that equation (18.76) will hold as an exact
equality when P is set equal to P T , the Törnqvist-Theil
formula. These results are of some
practical importance for the following reason.
Most countries do not have adequate surveys that
will support a complete system of value-added
price indices for each sector of the economy. 24
Adequate information is generally available that
will enable the statistical agency to calculate the
final-demand deflator. However, for measuring the
productivity of the economy using the economic
approach to index number theory, the national
value-added deflator is the preferred deflator. 25
The results that have just been stated show how the
final-demand deflator can be modified to give a
close approximation to the national value-added
deflator under certain conditions.
18.80 It has always been a bit of a mystery how
tax payments should be decomposed into price and
quantity components in national accounting theory.
The results presented in this section may be helpful
in suggesting reasonable decompositions under
certain conditions.
24 In particular, information on the prices and quantities of
intermediate inputs used by sector are generally lacking.
These data deficiencies were noted by Fabricant (1938, pp.
566–70) many years ago, and he indicated some useful
methods that are still used today in attempts to overcome
these data deficiencies.
25 See Schreyer (2001) for more explanation.
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