TABLE B-7.--CHINA: GROSS VALUE OF TOTAL INDUSTRIAL OUTPUT, BY PRODUCER AND CONSUMER GOODS, 1957–74 1957: State Statistical Bureau, "Ten Great Years," Peking, 1960, p. 87. 1958: Derived as the sum of producer goods and consumer goods. 1959: Derived from the 1958 total and the reported increase of 39.3 percent. See "Press Communique on the Growth of China's National Economy in 1959," Peking, 1960, p. 1. 1964: Derived from the 1965 total and an estimated increase of 20 percent. This increase is consistent with data for 10 provinces. Most of the data are for less than the full year and many are above 20 percent. The increase is also consistent with the statement that the gross value of industrial output in 1974 was 190 percent over that of 1964. See Chou En-Lai, "Report on the Work of the Government," "Peking Review," Jan. 24, 1975, p. 22. 1965-66 and 1968-73: Robert Michael Field, Nicholas R. Lardy, and John Philip Emerson, "A Reconstruction of the Gross Value of Industrial Output by Province in the People's Republic of China: 1949-73," U.S. Department of Commerce, forthcoming. 1974: Derived from the 1973 total and an estimated increase of 5 percent. This increase is consistent with the provincial data presented in table 5 and with the statement in Chou En-lai's "Report on the Work of the Government." See the entry for 1964. Producer and consumer goods: 1957-58: State Statistical Bureaul Loc. cit. The reported figures for 1958 were converted from 1957 to 1952 yuan, 1965: The value of consumer goods was derived from the statement that "output value... has nearly doubled in the 9-year period starting from 1966 and the average increase during this period was double that for the previous 16 years" (See FBIS, Dec. 27, 1974, E8), and the assumption that increase from 1973 to 1974 was the same as the average increase from 1965-1974. If X stands for the value of output, then and Since X equals 10,290,000,000 yuan, and X3 equals 133,770,000,000 yuan, the solution of the equations yields These figures for 1965 and 1974 are consistent with the statement that the value of output nearly doubled. The value of producer goods was derived as the residual. 1970: Derived from the value of producer and consumer goods in 1949 (see Table B-4) and the statement that heavy and light industry in 1970 were 38 and 11 times 1949, respectively (see "T' an-t'an tseng-ch'an chieh-yueh," Shanghai, 1974, p. 7). The derived figures were forced to equal the total; as a result, the figures in the table are 38.4 and 11.1 times 1949, respectively. It is assumed that heavy and light industry refer to producer goods and consumer goods in this context. 1972: The value of consumer goods was derived from the 1973 total and the reported increase of 10 percent (see 1973: The value of consumer goods was derived from the 1949 total (see table B-4) and the statement that output TABLE B-8.-CHINA: REPORTED AND ESTIMATED GROSS VALUE OF INDUSTRIAL OUTPUT, BY REGION, 1952, 1957, Note: Components may not add to the total because of rounding. For those provinces for which the gross value of industrial production was not reported or could not be derived, estimates were made by the method described in the source cited. Source: Robert Michael Field, Nicholas R. Lardy, John Philip Emerson, "A Reconstruction of the Gross Value of Industrial Output by Province in the People's Republic of China: 1949-73," U.S. Department of Commerce, forthcoming. APPENDIX C THE CALCULATION OF INDEX NUMBERS FROM INCOMPLETE DATA 23 I. Introduction In economics, the measurement of changes in output over time on the basis of incomplete data is a nearly universal problem: observations from some series are almost always missing. Soviet economic data, for example, are more complete for the last year of a 5-year plan period than for other years; in the United States, data are more complete for years in which a census of manufactures has been taken; and in some less developed countries, data are published only sporadically. The problem is how to calculate index numbers that squeeze the most information out of the data that are available. 24 Procedures to calculate index numbers from incomplete data that were devised by Kaplan and Moorsteen in 1960 and by Field in 1974 are described in sections II and III, respectively. The Field index is a generalization of the KaplanMoorsteen method. To make the two procedures clear, indexes are calculated from the hypothetical data presented in table C-1. In their work on Soviet industry, Kaplan and Moorsteen devised an ingenious method for dealing with the problem of incomplete data. They defined three indexes, as follows: A benchmark index is a Laspeyres index calculated for all years in which output data are available for every commodity. In the sample problem, the benchmark index is calculated for years 1 and 5. 23 Reprinted from Robert Michael Field, Nicholas R. Lardy, and John Philip Emerson, A Reconstruction of the Gross Value of Industrial Output in the People's Republic of China: 1949-73, U.S. Department of Commerce, forthcoming. 24 Norman M. Kaplan and Richard H. Moorsteen, Indexes of Soviet Industrial Output, Santa Monica, 1960, pp. 61-68. An interpolating index is a Laspeyres index calculated for the years between benchmark years. It is based on those commodities for which output data are available in every year. A separate index is calculated between each successive pair of benchmark years. In the sample problem, the interpolating index is calculated from output series B, D, and E. An extrapolating index is a Laspeyres index calculated for the years after the last benchmark year. It is based on those commodities for which output data are available in every year. In the sample problem, the extrapolating index is calculated from output series D, E, and F. The Kaplan-Moorsteen index for the years between benchmark years is calculated recursively from these indexes according to the formula: where I is the interpolating index, and a and B are the average annual rates of growth of the benchmark and interpolating indexes, respectively. The procedure for extrapolation is analogous. Indexes calculated by the Kaplan-Moorsteen method from the sample data are presented in table C-2. The final index has two desirable properties: The year-toyear pattern of change is the same as that shown by the interpolating and extrapolating indexes, and the average annual rates of growth between benchmark years are the same as those shown by the benchmark index. However, the index does not make use of all the data that are available. The interpolated portion of the index does not make use of series A or F, and the extrapolated portion does not make use of series B or C. How can the information not used in the interpolating and extrapolating indexes be captured in an aggregate index? Recasting the form of the Kaplan-Moorsteen index gives an insight into the problem. If the index for the base year is KM 。, then the index for the jth year is: KM1 = (1+) (+)KM. and the relationship between the years j and i is: But the ratio 1,/1, is based only on those series that are complete and does not necessarily take full advantage of all the data that are available. The best statement of the relationship between output in the years j and i is the link relative: where P and Q are price and quantity, respectively, n is the number of output series, and ♪ is an indicator function. The function is defined as: The link relative r, is the ratio of the output of those commodities for which output data are available both in year i and in year j. The Field index is calcu lated between successive benchmark years from a complete set of link relatives. First, because the series for which output data are available may not be growing at the same rate as aggregate output, the link relatives are adjusted in a manner analogous to that used by Kaplan and Moorsteen to adjust their in terpolating i ndex. The adjusted link relative is: where a and Y are average annual rates of growth. Specifically, if years g and h are benchmark years, a is the rate of growth for all commodities between benchmark years g and h, and Y is the rate of growth of those commodities for which output data are available both in year i and in year j. a has to be calculated only once, but y, must be calculated separately for each link relative. Finally, the index Î, is estimated by least squares from the following equation: Taking the logarithms of both sides of the equation yields: The sum of the squares of log ;; is minimized, subject to the constraint that the estimated index equals the benchmark index in benchmark years. If years g and h are benchmark years, minimize subject to (log ΣΣ (10g 1,-1,-10g R;;)2 log Ŷ1 = log Y, log Ŷ=log Y where Y, and Y are the values of the benchmark index in years g and h. The partial derivatives of the objective function are a system of simultaneous linear equations whose solution is the Field index. The equations for estimating the Field index between years 1 and 5 of the sample problem are as follows: The procedure for extrapolation is analogous to that described above for interpolation. However, two points should be noted. First, if there are more than 2 years for which the data are complete, the selection of the benchmark years on which to base the adjustment of the link relatives offers a choice. It would seem logical that one benchmark should be the last complete year, but the selection of the other is arbitrary, and the year selected may affect the rate of growth shown by the index. Second, adding output data for a subsequent year may change the index numbers for the years since the last benchmark. Because the original estimate was based on incomplete data, and because the output data for the additional year give new information against which to judge performance in the earlier years, the result is reasonable. The Field index calculated from the sample data is presented in table C-3 and compared with the Kaplan-Moorsteen index. The Field index has several desirable properties in addition to using all of the data. First, if the data are complete, the index is the same as a Laspeyres index. Second, if some of the series are missing but the remaining series are complete, the index is the same as the KaplanMoorsteen index. Third, the index can be calculated even if there are no series that are complete. And last, the index can be calculated without complete data for benchmark years. If there are not 2 benchmark years, the index can be derived from the unadjusted link relatives. TABLE C-3-ALTERNATIVE INDEXES CALCULATED FROM HYPOTHETICAL DATA |