(26) L(T) LT-1))了 ceL I HT-1) Since data on capital utilization are rare, it is customary to assume that the flow of capital services is proportional to the measured capital stock( denoted by A (T)), with K (T)=xxA: (T) Ko) Σ6x A() 2.7) K-1) A(T-1) measuring Factor Supplies My analysis focuses on two aggregate inputs, capital and labour, subdivided into finer sub-input categories. In general, I divide capital input into five categories: residential buildings non-residential buildings, other durable structures, transport equipment and machinery. with the exception of my analysis of Singaporean manufacturing, I do not include land input, which is difficult to measure. To minimize any error, I focus my analysis of Taiwan and Korea on the non-agricultural economy, where land input accounts for only a small percentage of total payments to factors of production. "Labour is distinguished on the basis of sex(two categories), age(nine to eleven categories, depending upon the country and time period under consideration), and education(two to seven categories). The stock of each capital input is measured using the perpetual inventory method with land For example, Kim& Park(1985, table 5-13)estimate that during the 1960s and 1970s 'i also do not include inventories. i have found that the "changes in stocks"series published by most of the NICS are cither(i)outright gross fabrications used to conceal large discrepancies between the production and expenditure accounts; and/or(i)based upon the flimsiest of data. In Young(1992)I made use of unpublished stocks data provided to me by the Singaporean and Hong Kong govemments. Problems with the existence of accurate stocks data for the other economies, combined with a growing suspicion as to the accuracy of the Hong ong numbers, have led to me to drop consideration of stocks from the analysis
geometric depreciation, where I initialize the capital stock by assuming that the growth rate ivestment in the first five years of the investment series is representative of the growth of investment prior to the beginning of the series . 0 Given positive rates of depreciation and a sufficiently long investment series prior to the first date of the analysis, the perpetual inventory approach is fairly insensitive to the level of capital used to initialize the series. For Hong Kong, che published investment series begins in 1961. I use my own estimates of capital formation which mimic the methodology of the Hong Kong govermment, to extend the series on all asset types back to 1947. For Singapore the published investment series begins in 1960. I use data on the construction of one-family equivalent residential units and retained imports of cement"to extend the residential and non-residential durable structures investment series back to 1947. For depreciation rates for detailed asset types. I derive the depreciation rate for each of the five broad asset types used in my analysis as the unweighted average of the depreciation rates of the detailed asset types likely to be found in each industry. This approach is crude, but the results re, in any case, not sensitive to moderate adjustments in the depreciation rates(see, for example, Young 1992) ° Specifically K=∑-1(1-6)=l(81+5) where 16 is the first year of investment data for asset j,8 is the depreciation rate for asset j, and 8 is the average growth of investment in asset j in the first five years of the investment series. con..1o An exception is Singaporean manufacturing, where, because of a lack of lengthy(and Production to initialize the capital stock in 1969 1] The estimates using retained imports of cement are, admittedly, rather crude. These data, however, suggest a large surge in construction activity in the mid- 1950s(which I have not been able to corroborate), with the real value of investment in durable structures in the mid-1950s exceeding the levels recorded in the early-1960s. Although I feel these data are suspect, I make use of them in order to bias the results in favour of Singapore
Taiwan the published investment series begins in 1951 and for South Korea in 1953. In general, I focus my analysis on the post-1966 period, allowing each economy 13 or more years of investment data to establish the capital stock. Tuming now to the measurement of labour inputs, my task is to estimate the working population, cross-classified by up to seven attributes, i c, industry, sex, age, education, income, hours of work, and class of worker. Census and survey data frequently contain information on row and column sums in lower dimensions. Under the assumption that there are no interaction across attributes other than those present in the available sub-dimensional tables, I derive an approximation of the maximum likelihood estimate of each cell using the iterative proportional fitting technique suggested by Bishop. Fienberg and Holland(1975). In general, I make use of the information provided by additional worker characteristics, e.g. occupation, which, in their cross-tabulation with attributes of interest to me provide additional information. Thus, for example, I actually estimate the 1990 Singaporean working population cross-classified by dustry x occupation x class of worker x sex x age x education x income, using all available census tabulations. For my TFP estimates, I then sum across occupational categories to derive a reduced six-dimensional table of the variables of interest to me. All four economies conduct occasional censuses and on a more regular annual basis, Pi have found extensive Japanese data on pre-war investment in Korea and Taiwan. I have yet to find, however, an appropriate deflator with which to link the pre and post-war series, as well as a means of adjusting for wartime damage in Korea. ITo analyze the sensitivity of the results to the value of capital used to initialize the series, I also tried initial values of (i zero capital and (i double the capital implied by the procedure described above. The impact of these(substantial)adjustments on average total factor Taiwan, (1%,+2%)per annum in Singapore, and (-4%, + 3%) per annum in Korea (where e o productivity growth during the 1966-1990 period was (- 1%,+ 1%)per annum in Hong Kong an pre-1966 investment series is shorter) Hours of work data are drawn from other, non-Census, sources
surveys of labour force conditions. The labour force surveys are, however, subject to an enormous margin of error. Thus, for example, the 1989 Singaporean Labour Force Survey estimated the working population at 1. 277, 254, with 51. 2% having completed a secondary education or more. The 1990 Census, however, found that the actual working population numbered 1,537,011 (i.e 20% more than reported in the previous survey), with 66.3% having completed a secondary education or more. Similarly, the 1980 Korean Economically Active Population Survey estimated the non-agricultural working population at 9, 048,000, whereas the 1980 Census put the number at 7, 887,308, or 13% less. Aside from their small sample sizes, the principal problem underlying the inaccuracy of the labour force surveys is the fact that their scaling factors are drawn from the previous census. Since these economi rapid transformation, these scaling factors tend to be grossly inaccurate. As the surveys are updated with the new census scaling factors, their estimates become consistent with the most recent census results. Thus, for example, the 1991 Singaporean Labour Force Survey estimated the working population at 1, 524, 315. In the estimates below, I confine myself to census years treating the census results as the appropriate measure of the"population "and the survey results as a"sample", making use of these, when they contain cross-tabulations which are unavailable in the census, by conforming the survey row and column totals to those given by the census. Since over the long run, the labour force surveys track(with large variance)the census, the long-term average rates of productivity growth reported below are not dependent on this choice of N6 For example 25000 housing units in the case of the 1989 Singaporean labour force survey and less than 15000 households in the case of the 1980 Korean economically active population survey