中国经济增长的源泉，1952-99：纳入人力资本积累因素

POLICY RESEARCH WORKING PAPER 2650 Sources of China s Both productivity growth and factor accumulation figured Economic Growth, 1952-99 significantly in China's remarkable growth Incorporating Human Capital performance between 1978 and 1999, a period of reform. Accumulation Considering China's need for an innovation-based Yan Wang knowledge economy, the Yudong Yao recent declining rate of human capital accumulation -education-is a cause for concern. The World Bank World Bank Institute Economic Policy and Poverty Reduction Division July 2001  POLICY RESEARCH WORKING PAPER 2650 Summary findings China's performance in economic growth and poverty the population aged 15 to 64) was quite rapid and reduction has been remarkable. There is an ongoing contributed significantly to growth and welfare. debate about whether this growth is mainly driven by After incorporating human capital, they also find that productivity or factor accumulation. But few past studies the growth of total factor productivity still plays a had incorporated information on China's human capital positive and significant role during the reform period. In stock, and thus contained an omission bias. contrast, productivity growth was negative in the pre- Wang and Yao construct a measure of China's human reform period. The results are robust to changes in labor capital stock from 1952 to 1999 and, using a simple shares in GDP. growth accounting exercise, incorporate it in their The recent declining rate of human capital analysis of the sources of growth during the pre-reform accumulation is a cause for concern, if China is to sustain (1952-77) and the reform period (1978-99). its improvements in growth and welfare in the coming They find that the accumulation of human capital in decade. Funding for basic education is unevenly China (as measured by the average years of schooling for distributed and insufficient in some poor regions. This paper-a product of the Economic Policy and Poverty Reduction Division, World Bank Institute-is part of a larger effort in the institute to examine country experience on globalization and growth. Copies of the paper are available free from the World Bank, 1818 H Street NW, Washington, DC 20433. Please contact Agnes Datoloum, room J4-259, telephone 202-473-6334, fax 202-676-9810, email address adatoloum@worldbank.org. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The authors may be contacted at ywang2@worldbank.org or yyao@imf.org. July 2001. (24 pages) The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the view of the World Bank, its Executive Directors, or the countries they represent. Produced by the Policy Research Dissemination Center  Sources of China's Economic Growth, 1952-1999: Incorporating Human Capital Accumulation Yan Wang and Yudong Yao* The World Bank JEL Classification Code: 040, 015, 053 * Senior Economist, and consultant, The World Bank. This is a part of an effort to assess China's recent trends in growth and poverty reduction, for the purpose of training and capacity building. We thank Vinod Thomas for encouragement, and Deepak Bhattasali, Shaohua Chen, Aart Kraay, and Martin Ravallion for advice and comments. The views expressed here are entirely the authors' and should not be attributed to the World Bank. Comments should be sent to ywang2@worldbank.org and yyao@worldbank.org   Sources of China's Economic Growth, 1952-1999: Incorporating human capital accumulation Yan Wang and Yudong Yao The World Bank "Ask what has been the most stunning economic event of the past century, and many people might cite the case of China in the two decades since it opened up. In that time the economy has grown more than fivefold, incomes have quadrupled, and 270m Chinese have been lifted out of absolute poverty. Yet with a couple more decades' hindsight, that achievement might be superseded by what may now be about to happen in the world's most populous country . The coming two decades, on the other hand, offer the possibility of an even more extraordinary pace of economic change." The Economist, March I0h, 2001. p.23 1. Introduction Few would deny China's extraordinary growth performance, but the sources and sustainability of this growth have been the subject of heated debate. This paper contributes to this debate by investigating the determinants of China's growth during the period of 1952-1999 using a simple growth accounting framework which incorporates human capital stock. By constructing a measure of human capital stock and comparing the growth experiences of the pre-reform and reform period, we try to shed light on the relative importance of factor accumulation (physical capital, labor and human capital) versus the growth of total factor productivity (TFP). There is an on-going debate about whether China's rapid and sustained growth during the reform period after 1978 is mainly driven by productivity or factor accumulation.' On the one side, the literature (e.g. Chow, 1993; Borensztein and Ostry, 1996; Hu and Khan, 1Heated debate initiated by Young (1995) on the source of growth in East Asian economies has spurred a growing literature on this subject. The author contends that the so-called "East Asian Miracle" is a myth because the engine driving the spectacular growth was fueled essentially by capital accumulation instead of total factor productivity (TFP) growth. -1-  1997) has reached a consensus on the fundamental sources of China's rapid growth. In particular, Chow concludes2 that capital formation played a principle role in China's economic growth while there was nearly no technological progress from 1952 to 1980. However for the reform period since 1978, two growth accounting studies (Borensztein and Ostry, 1996; Hu and Khan, 1997) show that productivity has become the primary driving force of China's rapid economic growth. For example, Borensztein and Ostry (1996) find that the growth rate of total factor productivity (TFP), which was negative before reform, rose to an average 3.8 percent per year in the post-reform period when it accounted for more than one-third of the total increase in output. One the other side, Krugman (1994) has argued that, similar to the East Asian tigers, China will soon face a limit on growth since it depends heavily on a massive increase in inputs with only small improvement in productivity. Moreover, Young (2000) concludes that the productivity performance of China's non-agricultural economy during the reform period is respectable, but not outstanding. More specifically, he finds that systematic understatement of inflation by enterprises accounts for 2.5% growth per annum in the non-agricultural economy during the reform period (1978-1998). The usual suspects, i.e. rising participation rates, improvements in educational attainment, and the transfer of labor out of agriculture, account for most of the remainder. As such, it is possible to transform the recent growth experience of China from the "extraordinary" into the "mundane". This study takes a small step forward by (i) measuring the human capital more accurately, and (ii) taking advantage of improved China data in the recent years and estimate the sources of growth with less errors. First, we construct an annual variable of human capital stock for 1952-1999. The variable, educational attainment for population age 15-64, provides an annual measure of the human capital stock for the labor force during the pre-reform and the reform period. We build our human capital stock based on number of graduates at different schooling levels, rather than quinquenial data based on enrollment rates in Barro and Lee (2000) or Nehru, Swanson and Dubey (1995).3 By contrast, the studies of Chow (1993), Borensztein and Ostry (1996) and Hu and Khan (1997) do not incorporate human capital as an input in their aggregate production functions for the Chinese economy. Due to this reason, their measurements of productivity suffer from an omission bias and the estimated productivity as residual is exaggerated by the absence of human capital from the growth-accounting calculations. Moreover, Young's (2000) estimation of human capital growth has several notable shortcomings. In particular, he disaggregates the labor force into various categories based on infrequent census data of population. In addition, each type of worker is weighted by the wage of that type based on the Household Survey files over a sub-sample period 1986-1992. Therefore, the obtained human capital growth is not an annual growth rate Chow (1993) estimates production functions for China's aggregate economy and for five sectors: agriculture, industry, construction, transportation. and commerce--using annual data (some constructed by the author) from 1952 to 1980. 3Our method avoids the problems of over-estimation due to high dropout and repeat rates which are often unreliable or under-reported. Independently, Wang 2000 developed a human capital stock using a different method than ours. -2-  and also cannot cover his whole sample period 1978-1998. This runs the risk of out-of- sample bias in the aggregated human capital series. Second, the data used in this study is updated based on Hsueh and Li (1999) which is more reliable. A major issue of the previous studies relates to possible measurement error, including problems with the deflators used to measure real output and real investment. The main problem has to do with the possible underdeflation of industrial output in the collective sector and the lack of an investment price index. Fortunately, Hsueh and Li (1999) provide a modified national income account based on their comprehensive review of Chinese national income accounting methodology and price indexes. In particular, Hsueh and Li (1999) make a great effort to improve the GDP deflator and investment deflator. In addition, previous studies rely on the self-estimated labor share by combining wage and employment data. Hsueh and Li (1999) provide data on provincial level compensation of labor as a percentage of provincial GDP for the reform period 1978-1995. To derive the aggregate share of labor, we simply need to take the average of provincial labor shares. We find that first, the accumulation of human capital was quite rapid and it contributes significantly to growth and welfare. Second, after incorporating human capital, the growth of total factor productivity still plays a positive and significant role during the reform period 1978-1999, in contrast to the negative productivity growth during the pre- reform period 1952-1977. Regarding the on-going debate, this paper proposes a middle- road answer to the sources of growth, and that is, both productivity growth and factor accumulation are very significant in accounting for China's growth performance during the reform period. This paper will proceed as follows. Section 2 briefly introduces the growth accounting method. Section 3 is devoted to the data and measurement issues with a focus on how to construct the human capital stock. Section 4 details how we construct the human capital series. Section 5 discusses the results of growth accounting and also provides some sensitivity analysis on the results. Section 6 summarizes our findings and implications. 2. Methodology of Growth Accounting Growth accounting essentially divides output growth into a component that can be explained by input growth, and a 'residual' which captures changes in productivity. Consider the following aggregate production function for the Chinese economy: Y =A Kl-a(L H )a t t t t t (1) where Yt is real GDP, At is total factor productivity, Kt is the real capital stock, Lt is total employment, Ht is average schooling years of population age 14-65 and represents human -3-  capital stock. Hence LtHt is a skill-adjusted measure of labor input. Taking logs and differentiating totally both sides of equation (1) yields A A A a, = g , - (1 - ax) k , - at(l, +h, ) (2) where at is growth in Total Factor Productivity (TFP), gt is the growth rate of real GDP, the lowercase variables with a "hat" correspond to the growth rates of the uppercase variables described in equation (1). Equation (2) decomposes the growth rate of output into growth of TFP, and a weighted average of the growth rates of physical capital stock and skill-augmented labor. Under the assumption of constant returns to scale, these weights are given by the shares of these two inputs in aggregate output. TFP was called "measure of our ignorance" by Abramovitz (1956). It covers many components: innovation-based technology progress, imitation-led technology progress, institutional change, efficiency change, omitted variables and measurement errors. TFP should not be equated with innovation-based technology change, although it often is. It is important to note that the decomposition of equation (2) remains valid under more general functional forms of the production function such as the translog production function used by Hu and Khan (1997) and Young (2000)4. The interpretation of the weights assigned to physical capital and skill-augmented labor as their share in aggregate output requires only the assumption of constant returns to scale. The Cobb-Douglas production function is chosen for simplicity. According to equation (2), therefore, any errors in measuring the variables, errors due to omission of relevant inputs, will directly spill over into the measure of TFP. In addition, the production function parameters are central to the decomposition of output growth into contributions from physical capital, labor and productivity. If these sources of bias are successfully removed, the remaining portion of output growth unexplained by the combined rate of growth of all the inputs of production is the measure of "true" TFP. Despite all these possible flaws, this residual still is the work horse of empirical growth analysis. For example, the TFP residual is central to the recent debate on the "New Economy". A significant proportion of this paper, as we shall see in the following sections, is devoted to reducing these biases. The next section describes the series Yt, Kt, Lt and Ht. 3. Data and Measurement Issues During the pre-reform period of 1952-77, the Chinese statistical system adopted the system of material product balances (MPS). The making of MPS was tailored to meet the needs of the central planning economy. The main aggregate indicators were total output value of society5 and national income. National income is value-added and comparable with GDP in the system of national accounts (SNA) adopted by the market-economy 4It should also be clear that conventional growth accounting, imputing output elasticities based on market rewards, will not shed any light on the possible extent of externalities. 5This is obtained by summing up gross output values and suffers from the double-accounting problem. -4-  countries. But national income does not account for the value-added of the service sector. Since the adoption of the comprehensive reform policy in 1978, China's statistical system has had to follow the international norm. Starting in 1985, SSB has received financial aid from the World Bank and the Asian Development Bank for further developing the national income accounts system, particularly for the estimation of GDP and its components in SNA and to make up the deficiency of MPS. SNA was completely implemented in the whole nation in 1992. Previously, data on China's growth were usually compiled from three kinds of Chinese official statistics publications, (A) China Statistics Yearbook from 1981 to 1997 (issue 1982 is absent); (B) China Historical Statistics 1949-1989; and (C) Comprehensive Statistical Data and Materials on 50 Years of New China 1949-1998. However, three shortcomings of the above data have plagued the empirical work. First, there was no national GDP during the pre-reform period. As a result, the previous studies on China's national economy have used NI for the pre-reform period. Second, there was no national NI deflator to deflate NI for the pre-reform period 1952-77. Finally, there was no national investment deflator for the period 1952-1990. The SSB began to construct the fixed asset investment price index in 1991. With the support and cooperation of the SSB, Hsueh and Li (1999) have made significant progresses and published the most complete set of Chinese national income from 1952 to 1995 based on SNA in 1999 both at the national and provincial level. Their main contributions include the following. (1) Based on historical statistical data stored in SSB and existing NI data, they fill up the service sector omitted in MIPS of China and construct GDP data for the pre-reform period 1952-77, which are directly comparable with those of the reform period 1978-95; (2) They provide real GDP, the investment growth rate and the corresponding deflators for the period 1952-95. Output Our data set covers a 48-year period (1952-1999). National GDP data and implicit GDP deflator come from the Hsuech-Li (1999) data set, covering the period 1952-95. GDP data and implicit GDP deflator from 1996 to 1999 are drawn from China Statistics Yearbook 1997, 1998, 1999 and 2000. We take 1995 as the base year to generate real GDP. Capital Stock To estimate the real capital stock for the aggregate economy each year, the standard perpetual inventory approach is used. Hsuech-Li data set provides national investment from 1952 to 1995. Investment is referred to gross fixed capital formation at the current price. The calculation of gross fixed capital formation is based on the total social fixed asset investment6. Investment data from 1996 to 1999 is drawn from China Statistics Yearbook 1997, 1998, 1999 and 2000. 6 The ownership structure of investment is dramatically different between the pre-reform period and the reform period. For the pre-reform period, the investment is dominated by state-owned investment. During -5-  The lack of physical capital deflator is a major issue of Chinese statistics because the standard Chinese statistical sources do not report the price index of the fixed asset investment until 1991. The investment deflator used by Hu and Khan (1997) is drawn from three sources: For the pre-reform period 1952-1977, they use the implicit deflator for capital accumulation estimated by Chow (1993); for the period 1978-1990, they adopt the price series of building materials as a proxy; For the period 1991-1994, they use the official fixed asset investment index. A major shortcoming of Hu and Khan's investment deflator is that the building materials price is unlikely to be a good proxy for the fixed asset investment. Alternatively, Young (2000) construct an implicit fixed asset formation deflator as a residual between GDP deflator and the deflators of other components of GDP including private consumption, government consumption, inventories and import and export. However, the inherent risk of Young's complex method is that any measurement errors of the deflators of GDP, consumption, government consumption, inventories and import and export can pass on to Young's "residual" investment deflator. Fortunately, Hsueh and Li provide an implicit investment deflator for the period 1952- 1995. Hsueh and Li (1999) take the data from the Annual Report of Statistics on Investment in Fixed Assets. Prices of investment are determined by taking the weighted average of prices of machinery and equipment, and prices of construction and installation. The prices of investment have faced significant changes only after 1978. Within the pre-reform period 1952-1977, the prices of investment including construction materials for building houses and other buildings, and machinery and equipment, are basically controlled by the state, and there was no significant change. After 1978, as the pricing of production means was becoming decentralized, the prices of construction materials and machinery equipment increased significantly. SSB formally started compiling a price index for fixed asset investment in 1991. This price index has existed since 1991. Combining Hsueh and Li's index from 1952-1995 and SSB's index from 1996 to 1999, we can get real investment for the period 1952 to 1999. The investment deflator takes the prices of 1995 as 100%. To construct a time series of capital stock from 1952-1999, we need to know the average depreciation rate of capital and its initial level. According to the Perkins' (1988) method, the overall depreciation rate is 5%. An initial value of 175 billion Yuan is set for the aggregate capital stock in 1952 (at 1952 prices), the estimate used by Chow (1993) and Hu and Khan (1997)7. Quantity and Quality of Labor The sources of the Chinese labor statistics are annual administrative and survey-based 8 estimates and the infrequently conducted population censuses ,which are reported in the the reform period, however, investment includes investment of state-owned enterprises, investment of private firms and joint-ventures and Foreign Direct Investment. An alternative way to calculate the initial capital stock in is set to 3 times National Income in 1951, which can be drawn from Hsuech-Li-Liu (1993) data set. 8 China conducted its first population census in 1954, subsequently, censuses were conducted in 1964, 1982 and 1990. -6-  China Statistical Yearbook. The SSB, using departmental reports and surveys, collected data on the "Total Labor Force of Society". Referring to the working population, this series has a fairly stringent definition of employment requiring, for example, that young people in cities and towns with temporary employment earn, as a minimum, the wage level of local grade-one workers in order to be included in the series. In this paper, we use the data series on the Total Labor Force of Society to measure the labor input. Young (2000) shows that the overall growth of the working population is perfectly consistent with reasonable demographic and participation data. The Labor Force of Society data indicate a substantial movement of labor out of agriculture into the industrial and service sectors of the economy.9 For example, labor force growth substantially exceeds the growth of the population. While the Labor Force of Society data series provides a reasonable measure of the overall growth of the labor force, it does not contain any information on the quality of workers, that is, changes in human capital stock over time. In analyzing the contribution of changes in educational attainment to the quality of labor, there are two approaches to measure the quality of labor force. One approach is to disaggregate the labor forcc-by level of schooling, and often by other available characteristics such as age and gender. Changes in the number of employees at each level of schooling are then weiglhted by their marginal products, proxied by the mean income associated with each schooling level, to give the overall change in an index of 'effective' or quality-adjusted labor. This ultimately allows the researcher to quantify the proportion of output growth that can be directly attributed to increases in educational attainment.10 The calculation of the labor quality index assumes that differences in market rewards are interpreted as reflecting genuine differences in marginal products. The second approach is to use educational attainment as a proxy for the component of the human capital stock obtained at schools (Barro and Lee, 2000). A higher educational attainment indicates higher quality of workers. So far there have been a number of attempts to measure educational attainment across countries. Earlier empirical studies used school enrollment ratios or literacy rates. Mankiw, Romer, and Weil (1992) used the proportion of the adult population enrolled in secondary school as a proxy for human capital investment. Romer (1990) considers literacy a proxy for human capital stock and uses the change in the literacy rate. However, there are some conceptual difficulties with the use of school enrollment data for two reasons. First, these measures do not adequately measure the aggregate stock of human capital available contemporaneously as an input to production process". In addition, in many empirical growth papers, it is not clear whether 9 The migration of labor out of agriculture is an essential feature of economic development and modernization, both historically in developed countries and currently in developing ones. 10 A prominent example is Jorgenson, Gollop and Fraumeni's (1987) aggregate index of labor quality based on changes in the composition of total hours worked by age, sex, education, employment class and occupation. Due to the data availability limit, however, nearly all the studies which carry out a detailed disaggregation by level of schooling are restricted to the United States. Temple (2000) emphasizes on the vocational training as another important aspect of human capital. -7-  school enrollment rates are intended to represent a flow of investment in human capital, or its stock. It is incorrect to use enrollment as a stock variable. As far as the first approach is concerned, it is difficult to apply it in the Chinese economy to obtain an annual quality index of labor during the pre-reform period and reform period. One main reason is that the published data on the relative labor incomes of Chinese workers by worker characteristic are basically non-existent. However, some survey data of the SSB's Urban Household Survey and the Household Survey by the Chinese Academy of Social Sciences contains information on the characteristics and individual labor income of the members of the survey households for certain periods (see for example, Wang 1996). Young (2000) utilizes several household survey data of the SSB for the incomplete reform period 1986-1992 to arrive at a rough estimation of human capital growth during the whole reform period 1978-98 by using the re'lative wage estimates to weight the changing composition of the labor. He finds that the Chinese workers' wages rise with educational attainment at a slower rate than in the other economies. Nonetheless, the survey files of the SSB for the years 1986-1992 and the Household Survey conducted by the Chinese Academy of Social Science are by no m-ieans a balanced sample (e.g. some provinces are not represented, while the samples arc heavily biased towards better educated households). As a result, we adopt the second approach in the present study and use average schooling years of population aged between 15-65 as an approximation of the quality change of labor force for the entire period 1952-1999. The next section summarizes the main procedures -for constructing the human capital stock series. 4. Human Capital Stock of China Development of China's Education Education begins with kindergarten (ages 3-6) and continues with primary (ages 6-12) and secondary education (ages 12-18), which includes junior and senior secondary schools, specialized secondary schools, vocational schools, and technical training schools. Higher education, which includes universities and colleges as well as postgraduate programs, requires 4-5 years for a B.A. degree, 7-8 years for a Masters degree, and 10-11 years for a Ph.D. Around 70% of China's population were without formal schooling after World War II (1937-1945) and the civil war (1945-1949). In the 1950s, there was a widespread movement to eradicate illiteracy. In the 1960s, the implementation of an obligatory/mandatory nine-year education policy began. This policy called for six years in primary school and three years in junior secondary school. While the implementation of this policy has been consistent in urban areas, it did not materialize in rural regions in terms of financial assistance. The enrollment growth at the primary level is slow compared to other levels because the coverage at this level was already extensive for a long time. Slower growth in enrollment in primary education also stems from declines in birth rates since 1970s and a reduction in dropout and repetition rates that reduced the -8-  proportion of students in the primary school-age range. By the mid-1990s, China had achieved virtually universal enrollment in primary education, but the quality vary a great deal. Only two-thirds of primary school students currently complete their entire primary cycle. In some remote and poor regions, completion rates were as low as 30 percent. Nonetheless, the percentage of no schooling has declined from 51.8% in 1964 to 16% in 1995. At secondary level, gross enrollment rates rose progressively but both enrollment rates and growth at this and the tertiary level remained low, relative to those of other Asian countries. Although government policies during the Great Leap Forward period created better educational opportunities for working class and peasants, famine and social conflict in the early 1960s thwarted that momentum. During the Cultural Revolution, all universities were closed between 1966 and the early 1970s in favor of several short-term training courses. Regular enrollment was restored in 1976, but China had already lagged behind Korea, Malaysia, Thailand and other Asian countries in terms of age cohort participation rates in higher education. In addition, completion rates are particularly low among poor regions and female students at the secondary level, many families lack the incentive- to send their children in school, due largely to4-sboth economic and cultural factors. At the tertiary level, however, coverage is extremely low. China does lag behind other countries regarding some dimensions of educational progress. For instance, its rate of enrollmnent particularly in higher education is below both the average among all Asian countries and the rates found in some low-income countries. Methodology Using a perpetual inventory method, Barro and Lee (2000) construct a measure of human capital stock. Their data set comprises at least one observation for 142 economies, of which 107 have complete information at five-year intervals from 1960 to 2000. The percentage of the population who have successfully completed a given level of schooling-say secondary, tertiary, or post-primary schooling-is a straightforward way to show the population's attainment of skills and knowledge associated with a particular level of education.12 With these data they can construct measures of average years of schooling at all levels for each country, which is taken as the human capital stock series. Following Barro and Lee (2000), the perpetual inventory method is adopted in this paper. The subsequent question is how to choose flow variables to the human capital stock. The distribution data of educational attainment by age cohort in the aggregate Chinese population are only infrequently recorded in the 1990 censuses, the 1987, 1995 and 1999 1% Sample Population Surveys, and the 1997 Survey on Population Change. Thus, we use new school graduates as flows that are added to the human capital stocks annually. 12 In practice, however, each cycle of education has significant variation in duration across countries. They also take account of this variation by using information on the typical duration of each level of schooling within countries. -9-  The number of graduates reflects the inflows of new school graduates to existing educational stock more accurately than the enrollment ratios used by Barro and Lee (2000). In the construction of average years of schooling, we take account of changes of national school duration over time. The initial figure of human capital stock in 1951 is 0.84 years of schooling per person, which is estimated based on the following schooling distribution assumptions: in 1951, 72% of the population were illiterate, 16% had incomplete primary, 8.4% completed primary, 2.7% had incomplete secondary, 0.1% completed high school, the rest were for higher education, about 0.6%. These assumptions are based on India's education attainment distribution in 1960 from Barro and Lee data (1997, 2000). Given the population aged over 15-65 in 1951, we obtain the estimate of average schooling years in 1951. The data report educational attainments in the population in five categories: primary, junior secondary school, senior secondary school (high school), specialized secondary school (vocational school) and tertiary education. For these five categories, number of schooling years are 5, 8, 11, 12, 14.5, respectively.13 Dased on the perpetual inventory method, we construct current flo.w3 of adult popuilation that are added to the stocks of the previous year. The data of annual graduates form the six schooling levels comes from "Comprehensive Statistical Data and Materials on 50 Years of New China 1949-1998". The formulas for the varioIIs levels of schooling for the total population are as follows. H1, t = (I - S )HI,,-1 + (PRI, - JUNIOR,+3 ) ............................. . ........................... (3) H2t1 (1- S1 )H2,1-1 + (JUNIOR, - SENIOR,+3 - SPECIAL,12 ) . .(4) H3,1 = (1- St )H3,t- I + (SENIOR, - HIGH t+3 5 ) --.-..(5) H4,1 = (1-Se )H4,t-I + SPECIALt .. ............................ (6) H5,t =(1 -)H5,,-1 +HIGH . ........................................... (7) where Hjt is the number of graduates for whom j is the highest level of schooling attained; j=1 for primary, 2 for junior secondary school, 3 for senior secondary school, 4 for specialized secondary school and 5 for tertiary. If a person cannot complete the enrolled duration level and thus drops out from it, we take him as a graduate of the schooling level he had before. For example, a drop-out of the senior secondary school is 13 Tertiary education includes university and junior college education. Depending on different time periods, it usually takes a total of 15-16 years to complete a four-year university and takes 14-15 years to complete a three-year junior college. We take 14.5 as the number of schooling years for people who were reported as having completed tertiary education in China. 40  taken as a graduate of the junior secondary school. Since the national duration of different schooling levels are known, we can obtain the net number of graduates at each schooling level. The variable 8