Reexamining,China’s,Demographic,Transition,and,Age,Structure|China and sex

　　Abstract: This paper discusses the shortcomings of Western theories on demographic transition by comparing transitions in demographic structure for Europe and China. This paper further proposes several criteria for judging the direction of demographic transition and whether or not it has finished. Apart from establishing new theories of demographic transition and the trasition of demographic structure, this paper differentiates the concepts of “relative surplus population” and “relative suitable population,” and “relative insufficient population” and identifies key demographic differences along the way. In doing so, this paper argues that China’s demographic structure is undergoing a process of rebalancing.
　　Key words: relative surplus population, demographic transition, trasition of demographic structure, unstable population, quasi-stationary population
　　JEL Classifications: J11, J78
　　China has seen a reduction of over 300 million births and a remarkable improvement in its demographic structure since the adoption of the family planning policy. In development terms, the policy has accelerated the transition of China’s demographic structure to one more in sync with its socioeconomic development. In various demographic studies, however, non-systematic use of age structure indicators has led to conflicting conclusions. For example, one study used China’s increasing proportion of the elderly and dependents to conclude that China’s existing demographic structure indicates a growing imbalance. The Economist went so far as to write that “China’s population problem has become its fatal weak point.”
　　Demographic structure is defined as the integrated distribution of individuals within each major age group in the total population in an administrative area at a given point of time.
　　The trend for demographic development in most developed countries shows that an initially high fertility rate will decrease to replacement level or much lower after undergoing a significant decrease in population. This occurs regardless of whether the decrease is a “natural” and slow passive decline, due to socioeconomic development, or an “unnatural,” sharp drop due to human intervention. In a few countries with relative population scarcity, the fertility rate will increase for a certain period of time, but as demonstrated by the cases of other countries historically, the rate will eventually fall to the replacement level and then remain stable, resulting in a quasi-stationary population of a suitable size (on the condition that the population is in harmony with socioeconomic development trends). 　　In this paper, we use the term “quasi-stationary population of a suitable size” to mean a population with a quasi-stable age structure and a quasi-stable size. The development of quasi-stable age structure is not only a simultaneous development of a quasi-stable population but is also a process of said population adapting to economic, social, and civil development. In this paper, “demographic transition” is defined as the transition of an unstable population to a quasi-stationary population of a suitable size. It can also be defined as the process of births replacing the age structure of the existing unstable population year by year at relevant fertility rates.
　　In a closed population, i.e., ignorable international migration, age structure is consistent with births over a given period of time (namely, the population of surviving zero-year-old individuals at a given period) at relevant fertility levels. The total population of individuals within each age group depending on birth rate is the population size over the years. In short, the fluctuation of population size and age structure is a simultaneously integrated process which is the product of relevant fertility and mortality levels.
　　Like any population with a long history, the dynamic fluctuation of China’s existing age structure not only speaks volumes about its current developmental stage, but it also reflects the cycle of replacement and development in a population whose generations have varied life spans. Like the rings of a tree, China’s age structure is an integrated whole that embodies rich historical data. What does it imply, then, that China will see a large aging population and a long period of low fertility in the near future? What are the prospects for and implications of these demographic changes? How will the forces of a large aging population affect quality of life for the elderly? Is there a sufficient supply of labor? Is the current family planning policy responsible for China’s “demographic dividend,” which has lasted only forty years, and its subsequent long-term negative growth? Or did the policy result in an ever-increasing demographic bonus that constantly approaches peak value? In summary, this paper attempts to bring some nuance to China’s population question by exploring the following three questions: what the effects of these demographic issues are given China’s socialist economy, how we can better understand the law of demographic transition when dealing with a large population size, and what the relationship is between age structure and sustainable socioeconomic development. 　　1. Understanding China’s Unique Demographic Transition: Part 1
　　In 1934, Adolphe Landry was among the first to study how nations undergo “demographic transitions” as a result of economic development. In 1947, C.P. Blacker divided the demographic transition into five stages. Warren Thompson (1948) and Frank Notestein (1950) condensed Blacker’s divisions into three stages, which became the well-known law of demographic transition: that is, the transition from the first stage (characterized by high fertility, high mortality, and low growth) to the second stage (characterized by high fertility, low mortality, and high growth) to of the third stage (characterized by low fertility, low mortality, and low growth).
　　Before the economic reforms of the late 1970s and early 1980s, China"s economy relied on relatively primitive technology, including within the agricultural sector, and relied exclusively on increasing labor to increase the material goods production. Accordingly, reproduction was unstable. Long influenced by a culture that encouraged multiple offspring, China had seen a relative surplus population for many years. Births in China increased from over 19 million in 1949 to over 27 million in 1970. In order to solve corresponding problems, such as the decreased quality of life and long-term unemployment, birth control policy that advocates “late, spaced and few” two-child policy (late marriage, the two births should be separated by three or four years, and no more than two children are allowed) was carried out nationwide in urban and rural areas beginning in 1970. In 1971, China"s demographic structure began to move from the second stage of demographic transition – marked by high fertility, low mortality, and high growth – to the initial period of the third stage, marked by low fertility, low mortality, and low growth. In fewer than ten years, China"s total fertility rate, which reflects the average number of children a woman of child-bearing age gives birth to in a lifetime (on the condition that China"s unstable population supposed to be a stable one), decreased from 5.81 in 1970 to 2.28 in 1980. The result not only indicates the successful control of rapid population growth but also reflects the transition to the low fertility, low mortality, and low growth stage of the demographic transition. In fact, one could argue that this demographic transition and its effects created a positive environment for the 1978 Third Plenary Session of the 11th Central Committee, which created a modern economic strategy for China driven by economic development. 　　In the early 1980s, as a result of birth control policy that permitted only one child for each urban and rural family, China’s total fertility rate rebounded sharply to 2.63 and 2.85 in 1981 and 1982, respectively. In mid 1984, the national birth control policy was adjusted, and the total fertility rate fluctuated above 2.28. In the late 1990s, the fertility rate dropped below the replacement level and remained stable as a result of socioeconomic development’s becoming the dominant factor for the decrease in fertility rate. This fundamentally altered the historical trend of an ever-growing population and laid a sound foundation for solving the corresponding problems. Implementation of the birth control policies over the past 40 years has resulted in huge changes to the total fertility rate, which provides both a vivid empirical example as well as a living textbook for promoting reform and development policies and for understanding the basic principles of public policymaking.
　　China’s birth control policies in the 20th century were characterized by a sharp drop in fertility rate that actively facilitated demographic transition and resulted in a noticeable change to age structure. In contrast, the demographic transition that took place first in northern and western Europe, in southern and then in eastern Europe was facilitated mainly by socioeconomic development. In other words, in Europe’s demographic transition, socioeconomic development preceded declining birth rates, and the transition took roughly 50 to 100 years. As a result of this slower, more organic transition, there are smaller disparities among age structures and almost no significant fluctuations between generations. Because of the unique nature of China’s demographic transition, the indicators developed by Western demographers may not be universally applicable. While these indicators can be applied in most developed countries, they are not applicable to the existing and near-future demographic structure of a country like China.
　　While China’s birth control policies have undoubtedly solved many social issues, the real effects of such policies are often clouded by the use of age structure as the primary indicator. This study aims to examine China’s population more holistically and within the context of its unique demographic history.
　　In examining China’s relative surplus population, our objective is to facilitate sustainable socioeconomic development. Specifically, in aiming to help solve relative surplus population, we aim to promote harmony between generations and socioeconomic development. Sustainable socioeconomic development, then, is a process by which the age structure of the relative surplus population accelerates society’s transition to a stable age structure of a suitable population size. 　　We should not draw conclusions about China’s ideal population size by calculating the so-called “bearing capability” of the population based on various natural resources in the absence of a definite prerequisite. Studies on population and socioeconomic development in European and American countries reveal that the so-called multi-state model that simulates multiple cases of demographic development lacks scientific evidence.
　　The mechanism of “active” demographic transition is the basic way in which developing countries can solve the problem of relative surplus population. If we analyze China’s ongoing demographic transition based on the indicators of age structure, we will mistake the positive effects of a demographic structure in transition for negative effects. As stated earlier, age structures are relics of different fertility rates over different periods of time, which show China’s fertility rates before the transition of its demographic structure. As an indicator, age structure reveals only the early effects of reducing relative surplus population (for example, the sharp drop of proportions in children as of the overall population). In other words, the indicators reflect only superficially the slowing growth rate of China’s relative surplus population and cannot be used to determine the direction of overall population growth, as residual growth momentum keeps expanding the size of the relative surplus population slowly.
　　Using age structure as a primary indicator, moreover, scholars have assumed that China’s demographic bonus will soon disappear and be followed by a long period of negative demographic dividend, which implies that China’s demographic structure will become increasingly unbalanced and demographic problems will worsen. China’s working-age population has undergone a transition from a slowing growth rate to zero or even negative growth, which eases employment pressure while improving labor productivity. This, consequently, creates more economic and social benefits. All of these factors must be taken into account when conducting a study of China’s demography.
　　Likewise, certain scholars object to maintaining a low fertility rate in China in the 21st century by arguing that it will inevitably result in an extremely unbalanced demographic structure. While most scholars would agree that it is crucial to maintain a low fertility rate, however, few solutions to the resulting problem of an “unbalanced” demographic structure are presented. Maintaining a low fertility rate over a certain period will automatically generate a correspondingly unbalanced age structures in the whole demographic structure. Even taking into account global migration, we can agree that such demands are self-contradictory. 　　To date, domestic and foreign studies on demographic structure have simply based their conclusions on the fluctuation margin of age structures over different periods. However, the seemingly “universal” indicators of age structure contain many idiosyncrasies and may not be applicable to all societies. Population fluctuation and demographic transition are not two isolated processes but are closely related to the different stages of socioeconomic development. Given their differences in goals for suitable population size, differences in productivity levels, differences in the pace of the third-stage demographic transition with or without human intervention, and the length of said transition, not only the value of the indicators but the indicators themselves will vary between developing and developed countries.
　　In 1911, Lotka and Sharpe proved the proposition of a stable population, in which he took a stationary population as a standard population and solved the theoretical defect of making population structure irrelevant to the actual fertility rate when standardizing an unstable population (Sharpe et al., 1911). In 1948, Mill (1917) proposed in his Principles of Political Economy that only developing countries should use increasing production as a central goal, whereas most developed countries should take the more equitable distribution of wealth and resources and population control are central goals. According to Mill, if technology continues to advance and capital continues to increase, there will be room for a growing population. Mill predicted that human development would eventually reach a quasi-stationary state of a suitable population size no matter whether the population had been increasing or decreasing as a result of objective demand. The demographic development in most contemporary developed countries has proved this to be the dominant trend. Lotka (1925) first proved using mathematical demography that a closed population with fixed fertility and mortality rates for each age group will eventually reach a stable state with a fixed growth rate. Coale (1957) greatly simplified Lotka’s methodology for calculating the intrinsic growth rate of a stable population.
　　That China’s unstable population will eventually reach a quasi-stationary state requires us to modify existing theories. In terms of the relevant demographic transition at present and at a certain time in the future, we offer new calculation methodologies, indicators, and standards of a balanced demographic structure in order to have a clear understanding of the annual replacement level for demographic structure, as well as its overall level. 　　2. Understanding China’s Unique Demographic Transition: Part 2
　　When comparing the problem of current relative surplus population in capitalist societies to that of previous periods, Marx pointed out that “the current surplus population is not a result of the insufficient productivity at all. On the contrary, it is the increase of productivity that requires the reduction of population and elimination of surplus population by means of starvation or migration. Today, it is not the case that the population puts pressure on productivity, but that productivity puts pressure on population.” 1 In other words, the relative surplus population does not result only from low levels of industrial technology, primitive agricultural practices, and insufficient productivity but also would result from advanced technology and improved productivity. At any level of technological development, in other words, population and productivity can be compatible or conflicting, with the former putting pressure on the latter and vice versa.
　　The three-stage demographic transition theory has been held up by some scholars and international institutes as the universal law of demographic transition. However, can we conclude that the third stage is indeed the final stage of demographic transition? What criteria should we use to determine whether the demographic transition is complete? Here, we argue that the key criterion is whether or not the population has reached a quasi-stationary one and suitable size that matches its productivity. Most European countries underwent a period of exploration and colonization, which absorbed some of the relative surplus population. Thus, after finishing the third-stage demographic transition, these countries generally saw an quasi-stationary one and suitable population size that matched their productivity, which then gave birth to the theory of demographic transition. In subsequent decades, these countries’ population and demographic structure fluctuated within a small margin, which also proved that the demographic transition was complete.
　　However, the case is completely different for countries like China. Take China’s population during the period slightly before the third stage and in the third stage. Relative surplus population had been a problem in China for many years, as a result of low industrial technology and primitive agriculture. Moreover, the period of large-scale global migration had ended, so China was forced to implement its birth control policy to solve the problem of relative surplus population. Thanks to advances in technology and improvements in productivity, employment pressures eased to some extent after China finished entering the third stage of demographic transition. With the update of products and the transformation of production modes, population pressure resurfaced, which resulted in the commingling of previous and new surplus populations. 　　Therefore, it is crucial for China to maintain a low fertility rate for a long period before its population begins to approach quasi-stationary one. The population within the period is expected to enter the time of fast shrinkage after reaching its peak of around 1.4 billion before the year of 2050. Eventually, China"s population will reach quasi-stationary one with suitable size that meets objective demand. Such a population size would not only create sustainable socioeconomic development but would also help to maintain China’s position within the global power structure. As we can see, the traditional theory of demographic transition is not completely applicable to China. In order to solve the problem of relative surplus population in a society like China, the society must undergo a “fourth-stage demographic transition” to reach a relative suitable population size. We term this the “initial quasi-stationary population.”
　　During China’s fourth-stage demographic transition, despite a slow decline due to low mortality, population fluctuation is mainly determined by the regressive replacement level, which sees a decrease of the fertility rate to a low level. In terms of China’s unstable population, only when fertility rate is confirmed to equal replacement level does the intrinsic growth rate of the population equal zero. At such a fertility rate, the population will keep growing due to the impact of the growth potential energy that has accumulated in the age structure. Once the fertility rate drops to and stays at a low level, the population will see negative growth, and the negative growth potential will accumulate in the age structure. After a period of negative growth, the fertility rate will return to the replacement level, whereas the population will keep shrinking and eventually reach a growth rate of approximately zero, resulting in a fixed demographic structure and a quasi-stationary population.
　　Given an unstable population with no international migration and an even sex ratio, we assume that population reaches a stable state when the population undergoes more than one life cycle at fixed fertility and mortality rates. As we see here, the precondition of a stable population is the fixed fertility rate and mortality rate of each age, whose development is also the development of a stable population.
　　If the intrinsic fertility and mortality rates of a stable population fluctuate, its intrinsic growth rate will fluctuate accordingly. The fixed state is a special case of a stable population: that is a stationary population. If we ignore international migration, the life cycle of a population would be treated as a birth cohort of a year which undergoes a decrease followed with year by year in each age-specific mortality rate. A simple calculation method for the assumed queue life cycle is the life table. The assumed queue population is also called the life table population or stationary population, from which we will observe several relevant indicators of an age-based functional relationship. 　　The age structure of a stable population is determined by the intrinsic fertility rate and mortality rate and is therefore called the intrinsic age structure. The factor of age structure is steady whereas the population fluctuates within the same margin of growth and shrinkage. If the intrinsic growth rate is , we get the formula of the distribution of the age group in the age structure of a stable population by taking into account the characteristics of the population. If we assume that is the distribution of age group in the age structure of a stable population, then its formula is:
　　(1)
　　Formula (1) shows that we can calculate the distribution of the age group in a stable population based on the functions of intrinsic growth rate and life table . Given that the age distribution is usually calculated separately, we can divide the population into five equidistant age groups from one year old to five years old by applying the conventional grouping method. So the numerator of the formula that shows the distribution of one year-old population is , of which is the median value that represents the age of each group, whereas is the average life span of each age group. The product of these two is the numerator expression of the formula. The denominator of the formula is the sum of numerators that represent each age group, namely,
　　. Similarly, we can calculate the numerator of the expression that shows the distribution of the five-year-old population. The numerator is and the denominator is
　　.
　　If we exclude both sex-selective abortion and the practice of assuming the gender of unborn children based on the birth and gender order of children born to the same mother, we can calculate the proportion of males and females in the total population based on a sex ratio of 1.06 in the five-year-old population. We can then calculate the distribution of male (m) and female (f) in the total five year-old population by applying the following formula:
　　(2)
　　The result of can be precisely calculated by applying Formula (2) or calculated more generally by applying a simple formula:
　　.
　　A stationary population is the final state of demographic transition, whereas its age structure is the final age structure of an unstable population. Before the transition can be completed, significant differences between the age structure will occur. A stationary population is a special type of stable population. As the formula of the distribution of each age in a stable population shows, a stationary population is the ultimate form of the age structure of an unstable population after a long period of transition, as well as a final direction of the demographic transition of an unstable population. 　　With rapid economic and social development in China, there has been increased industrialization and urbanization, along with a rising demand trend for various services, which, by means of integration and development, gives birth to various industries that gradually replace certain household functions. Meanwhile, bearing children has become voluntary, and bearing fewer children has become a new trend. Low fertility rates over a long period will help to solve the problem of relative surplus population (which to date has impeded socioeconomic development and increased survival pressure), thus accelerating the transition to a suitable population size in harmony with socioeconomic development: namely, the transition to a quasi-stationary population.
　　3. Integrated Population Fluctuation
　　The interval of the 40 age groups of the demographic structure that has formed over the 40 years of China’s implementation of its birth control policy, along with the interval of other age groups of the demographic structure formed in the period of high fertility before the implementation of the policies, combine to form a unique demographic structure that presents with different micropopulations and fertility rates in 2010. In some sense, China’s existing demographic structure is characterized by the survival rate, fertility rate, and over or below replacement levels of each micropopulation.
　　To study China"s demographic structure (we usually combine relative indicators with its corresponding absolute numbers (namely, the demographic structure of each age beyond human intervention), to observe the fluctuations of each demographic proportion. In other words, we can observe and study the “fluctuation” of proportions based on the distribution of the “relatively fixed” population in the demographic structure. Given that none of the indicators represents the whole demographic structure, the results cannot accurately reflect the whole reality, even if standardization method is applied.
　　In one sense, the proper trend of population fluctuation as the objective demand of a certain level of socioeconomic development is reflected in the proper trend of demographic transition. If we assume that population fluctuation is a macro indicator, then demographic transition is the relevant micro indicator of the macro fluctuation and trend. Population fluctuation is both a specific embodiment and a brief summary of demographic transition. If we exclude international migration, the population fluctuation and development at a certain fertility rate is determined by the fluctuation of fertility and mortality. The annual births are made up of the live-born zero-year-old population, whereas annual deaths are made up of the total deaths of each age. If births exceed deaths, the total population grows; if births equal deaths, the total population sees zero growth; and if births are fewer than deaths, the total population sees negative growth. 　　Since the 1970s, the sharp drop in births as a result of China’s birth control policies, and the subsequent sustained low fertility rate, has inevitably resulted in a decline of the zero-to-14-year-old population (namely, people aged 0-14 defined as child population) as a proportion of the total population. This has subsequently grown into a working population 15 years later, which has resulted in a sharp decrease in the working-age population as a percentage of the overall population. The working population from 15 to 64 years old is made up of 50 age groups and usually accounts for the largest proportion of the total population thanks to a low mortality rate for each age. However, as the shrinking child population matures into a working-age population, the latter will subsequently see a noticeable declining growth rate and even zero or negative growth, and it will eventually stabilize at a certain rate. Affected by the dual decreases of the two age-interval structures, the population of elderly people (65 years old and above) will inevitably see passive growth and a fast growth rate within the overall population. In short, population reproduction sees “active” and “passive” fluctuation of proportions as a result of the fluctuation of births. Moreover, we emphasize “active” and “passive” fluctuation to prove that the only controllable factor in the transition of a relative surplus population to a quasi-stationary population is births over the years, while all other age interval of the demographic structure are beyond policy control.
　　4. “Balancing” China’s Demographic Structure
　　Within a nation’s demographic structure, growth momentum will accumulate in a period during which the fertility rate is much higher than the replacement level. Such growth momentum will weaken considerably in a period during which the fertility rate drops sharply from a much higher level to the replacement level. Negative growth momentum, on the other hand, will accumulate when the fertility rate is lower or significantly lower than the replacement level. This concept of growth or negative growth momentum is useful in characterizing the demographic structure of a society.
　　As of 2010, China’s birth control policies had been in place for 40 years. The interval of the 40 age groups of the demographic structure shows that the more than ten age groups formed at a low fertility rate had been accumulating negative growth momentum since the late 1990s. However, given that growth momentum of the previous interval of the demographic structure outweighed such negative growth momentum, China’s population is still in a period of growth. 　　The relative weight of these two momenta are likely to trade places in the coming years. Thanks to the interaction of these two “potentials” which have different impacts on population fluctuation, the population will see a short period of fluctuation before entering a period of negative growth. At a low fertility rate, China’s existing demographic structure is not only exhausting the growth momentum accumulated in the interval of the older age groups of the demographic structure, but it is also accumulating negative growth momentum. In this sense, China’s existing demographic structure is undergoing a dramatic transition.
　　Because these indicators are time-sensitive, it is necessary to set a unit of time suitable to studying China’s demographic structure. Ideally, this unit will match the time it takes to replace the demographic structure of a population, i.e., the life cycle of a population. Using this method, we discover that the demographic transition of China’s population at a stable low fertility rate has been a process of annual births at low fertility rates gradually replacing the original demographic structures.
　　We can, therefore, attempt to solve the issue of relative surplus population by calculating the necessary adjustment for each age structure that will replace its corollary in the previous generation.
　　We use the population replacement methodology for our calculations below.
　　If we assume to be the indicator of the average life expectancy of a population, then:
　　The life cycle of a population=the time span to replace demographic structure≈ .
　　In populations with an average life expectancy of 40 years and one with an average life expectancy of 80 years, then their respective life cycles (namely, the unit of time needed to replace the demographic structure) are:
　　Time needed to replace the demographic structure(1)≈40 years;
　　Time needed to replace the demographic structure(2)≈80 years.
　　We then calculate the approximate value of the annual replacement level based on the life table:
　　? The birth rate of the population in the life table= death rate
　　? When = 40 years old, the annual replacement level of the demographic structure is:
　　
　　Meaning that the annual replacement level of the demographic structure is 2.5 percent. Similarly, when =80 years old, the annual replacement level of the demographic structure is:
　　Meaning that the annual replacement level of the demographic structure is 1.25 percent. 　　The mathematical analysis of demography shows that the shorter the life expectancy is, the higher the birth and death rates, and the larger the proportion of births and deaths in the total population. The replacement rate of demographic structure is, therefore, much faster. On the other hand, the longer the life expectancy is, the lower the birth and death rates, and the smaller the proportion of births and deaths in the total population. The replacement rate is, therefore, much slower.
　　Given a stable mortality rate, we should first include population size and fertility rate in our analysis of the demographic structure; second, given advancements in productivity thanks to advanced technologies and improved overall health of the population, we can analyze whether a population may be considered relative surplus, suitable or insufficient for sustainable socioeconomic development, use of resources, and environmental protection. Maintaining population growth that is higher than the replacement level is the development goal for countries or regions with insufficient populations. The practices of the countries with insufficient populations like Australia and New Zealand have shown that it is feasible to increase the population. Thirdly, we set the unit of time as the life cycle of a population to measure demographic structure and establish the calculation methods for the overall demographic transition and the annual average demographic transition. Fourth, we define the prerequisites for applying the indicators of demographic structure. Fifth, we judge whether the existing demographic structure may be considered “balanced” based on whether the direction of the demographic transition is in sync with the nature of population development. The above five points are the rational basic principles for evaluating a nation’s demographic transition.
　　Using this methodology, we can understand not only the advent of an aging population in China but also recognize the positive role of effective control on the socioeconomic development of a fast-growing population. At the same time, the interaction between a population’s size and its level of socioeconomic development reduces the fertility rate and keeps it low. In the process of resolving a relative surplus population, the faster the transition to a quasi-stationary population, the faster the population is aging. The aging population in China reflects not only a declining fertility rate and the transition of its corresponding age structure but also the natural resolution of its relative surplus population. Thus, arguments that “demographic dividend” will soon disappear in China deviate from the preconditions of this relative surplus population. With the transition of China’s relative surplus population to a suitable size and eventually to the fixed state that characterizes the quasi-stationary population, China’s demographic bonus will continue to trend upwards before it reaches its peak.
　　References
　　[1] Blacker, C. P. 1947. “Stages in Population Growth.” Eugenics Review 39 (3): 88-101.
　　[2] Coale, A. J. 1957. “A New Method for Calculating Lotka’s - the Intrinsic Rate of Growth in a Stable Population. Population Studies 11(1): 92-94.
　　[3] Landry, A. 1934. La Revolution Demographique. Paris: Bordeaux [J. Bie?re].
　　[4] Ma, Yingtong. 2007. “Family Planning Brings China Demographic Bonus.” China Economist 2 (4):78-87.
　　[5] Mill, J. S. 1917. Principles of Political Economy with Some of their Applications to Social Philosophy. London: W. J. Ashley.
　　[6] Notestein, F. W. 1950. “The Population of the World in the Year 2000.” Journal of the American Statistical Association 45 (251): 335-349
　　[7] Sharpe, F. R., and A. J. Lotka. 1911. “A Problem in Age Distribution.” Philosophical Magazine 12(124): 435–438.
　　[8] Thompson, W. S. 1944. Plenty of People. New York: The Jaques Cattell Press.

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