USSR: Measures of Economic Growth and Development, 1950-80

Approved for Release: 2019/07/19 C05210421
Mathematically, the unknown parts of the table are
estimated by minimizing the sum of squared differ-
ences between the corresponding entries of the 1972
and 1970 I-O tables. If x(i,j) is the value of the sales of
sector i to sector j in 1970 and y(i,j) is the same sales
in 1972, then the following is minimized:
I1 Tl
5 =_ E _E(X(i.i)—y(i,J'))’/y(i,j).
l=l j=1
subject to the constraints that:
(1) gJx(i,j)=C(j), and
i=l
(2) ;x(i,j)=R(i), where
j=l
C(j) is the column sum of sector j (gross output less
value added and other estimated purchases) and R(i) is
the row sum of sector i (gross output less final demand
and other estimated sales). The minimum value of S is
determined by the equations:
(3) X(i.j)=y(iJ)(1+>\(i)+#(J')), Where
)\(i) and p(i) are Lagrangian multipliers. Substituting
each equation (3) into equations (1) and (2) produces a
system of 2n-l linear equations in 2n-1 unknowns (the
Lagrangian multipliers), where n is the number of
sectors in the I-O table (19 in this case). The values of
the Lagrangian multipliers can then be substituted
back into each equation (3) to determine the actual
value of each cell in the 1970 I-O table. For a detailed
description of this and other methods of estimating
I-O tables see John Pitzer, An Analysis of Technical
Change in the Soviet Economy: An Application of
Soviet Input-Output Tables (Ph.D. dissertation,
American University, 1980).
167
Estimating GNP in Factor-Cost Prices
The preceding sections have described the estimation
of GNP in producers’ prices and a complete 1970
Soviet I-O table. In order to complete the conversion
to factor-cost prices, it is necessary to eliminate the
remaining elements of value added which do not
represent a payment to a factor of production, esti-
mate the capital stock of each sector, and replace
Soviet profits with a capital charge which provides an
equal rate of return in each sector. All of these
changes directly affect value added. The I-O table is
needed to compute the direct and indirect impact of
the value-added changes on end-use GNP.
In any I-O table, the sum of a sector’s material
purchases and value added equal its gross output, or:
n
()4) X(j)= Ex(i,j)+w(j)+d(j)+Z(j), where
i=1
X(j) is the gross output of sector j, w(j) is the labor
income earned in sector j, d(j) is the depreciation in
sector j, and Z(j) is all other value added in sector j.
As in previous estimates of Soviet GNP in factor-cost
prices, it is assumed that w(i) and d(j) adequately
represent their respective variables. It is desired to
compute a uniform rate of return on each sector’s
capital stock, r, and to reprice the output of all sectors
to accommodate this uniform return. Equation (4)
now becomes
(5) P(i)X(i)= §D(i)X(iJl'l'WU)+d(.l)+FK(.l).
i=l
where p(i) is the price change required in sector i, and
K_(i) is the capital stock of sector j.
We make two further refinements. First, the capital
stock of each sector is disaggregated to show how
much was produced by the machinery, construction,
Approved for Release: 2019/07/19 C05210421