INDEX NUMBER RELATIVITY

The period of the first Five-Year Plans and the rapid collectivization of Soviet agriculture, 1929–1937, witnessed rapid economic growth accompanied by radical changes in the structure of the Soviet economy—first, from a predominantly agricultural towards an industrial one, and second, within industry, from a predominantly smaller-scale economy of light and consumer industries, to heavy industry, machinery, construction, and transportation. The vast expansion and mass production of heavy manufacturing goods reduced their cost of production, relative to those of light industry and of agricultural products. This phenomenon of simultaneous changes in the structure of production and relative prices during periods of rapid economic growth in the Soviet context was discovered and analyzed by Alexander Gerschenkron when he estimated the rate of economic growth of Soviet manufacturing during this period. Growth of the national product (GNP) of a country is estimated by a quantity index, aggregating the growth of production of individual sectors by assigning to each sector a "weight" corresponding to the average price of the products of this sector at a certain point of time during the period under investigation. It has been demonstrated that when the relative prices of the expanding sector are declining, as in the Soviet Union during the 1930s, the index produces a much higher rate of growth when prices of the initial period are used as weights than the index that uses prices at the end of the period. The first is called a Laspeyres index and the second a Paasche index, both named after their developers. Under the Laspeyres index, relatively higher prices, and hence larger weights, are assigned to faster growing sectors, thus producing a higher aggregate rate of growth, and vice versa. Hence the term "index number relativity."

One commonly quoted calculation of the two indexes for the period 1928 to 1937 is Abram Bergson's: According to his estimates Soviet GNP grew over that period by 2.65 times according to the Laspeyres variant but only by 1.54 times according to the Paasche index (1961, Table 18, p. 93). The two measures apparently present two very different views on the achievements of the Soviet economy during this crucial period, as well as on the estimates of economic growth over the longer run. However, since both are "true," they must be telling the same story. One commonly used "solution" to dealing with this relativity was to use the (geometric) average of the two estimates. An alternative was to replace both measures by a Divisia index (also named after its developer) that calculates growth for every year separately using prices of that year as weights, and then add up all growth rates for the entire period. The outcome is usually not far away from the average of the Laspeyres and Paasche indexes. Subsequent estimates of Soviet GDP growth over this period offered a variety of amendments to the original ones; some among them narrowed the gap between the two indices. During the rest of the Soviet period, the second half of the twentieth century, index number relativity did not play an important role, mostly because the major structural changes were accomplished already before World War II.

See also: collectivization of agriculture; economic growth, soviet; five-year plans

bibliography

Bergson, Abram. (1961). The Real National Income of Soviet Russia since 1937. Cambridge, MA: Harvard University Press.

Gerschenkron, Alexander. (1947). "The Soviet Indexes of Industrial Production." Review of Economics and Statistics 29:217–226.

Gur Ofer