Accounting for China s Long-term Growth: How Important is Demographic Change?

Accounting for China s Long-term Growth: How Important is Demographic Change? Minchung Hsu, Pei-Ju Liao, and Min Zhao This version: February 2011 Abstract This paper studies factors that account for China s growth from 1957 to 2007. We particularly aim to explore the role of demographic changes. A general equilibrium overlapping generations model with endogenous fertility and factor accumulations is employed. The main findings are (1) in the pre-reform period (1957-1982), the demographic change was the main engine of China s per capita output growth (accounting for around 71% of the simulated growth); technological progress and efficiency improvement alone could not sustain a positive growth; (2) in the post-reform period (1982-2007), technological progress and efficiency improvement played an important role for China s growth (around 68% of the growth); the effects of the demographic change was minor. JEL Classification: O11, O53, O20. Keywords: China, fertility, growth, demographic transition. National Graduate Institute for Policy Studies (GRIPS), Tokyo, Japan. Corresponding author. Email: pjliao@econ.sinica.edu.tw. Institute of Economics, Academia Sinica, Taipei, Taiwan. The World Bank Beijing Office, Beijing, China. We would like to thank the participants at 2010 Taipei International Conference on Growth, Trade and Dynamics, the 10th SAET Conference on Current Trends in Economics at Singapore, the 2011 annual meeting of American Economic Association (CEANA session), and seminar participants at National Chi Nan University and Feng Chia University. 1

1 Introduction China has experienced a rapid economic growth in the past three decades, particularly after its market-oriented economic reform in the early 1980s. Its annual growth rate of per capita GDP on average was as high as 9 percent in the post-reform period, while the average growth rate in 1957-2007 was around 6 percent. Therefore, several studies have attempted to explain the sources of China s growth. The existing literature focuses on the importance of total factor productivity growth (TFP) or factor accumulations, for example, Chow (1993) and Young (2003). As a complement to the literature, this paper explores the role of demographic changes in China s fast growth. China s high economic growth has been associated with a sharp decline in fertility. As Figure 1 shows, the total fertility rate in the 1950s and the 1960s was above 6 (discarding the drought period from 1959-65). It rapidly declined to less than 3 at the beginning of the implementation of the one-child policy; and stayed between 1 and 2 after 1990. Therefore, in addition to TFP growth and factor accumulations, it is natural to ask: how important is demographic change for China s growth? A few empirical studies link demographic changes to China s growth. Li and Zhang (2007) find that a decline in the birth rate by 0.1 percent will increase economic growth by 0.9 percent in a year in China s post-reform period. Bloom et al. (2010) suggest that an increase in life expectancy and a rise in the share of working-age population are important for China s growth experience. This paper undertakes a structural approach. We develop a general equilibrium overlapping generations model with endogenous factor accumulations and fertility for analysis. 1 In the model, demographic change affects growth not only through demographic dividends (i.e. a rising share of working-age population) but also through accumulating physical capital and human capital. Lower fertility allows parents to transfer their resources from raising children to savings and/or to provide education to the fewer children. Therefore, physical capital and human capital may be accumulated during demographic transition. Demographic dividends, physical-capital accumulation, and the formation of human capital contribute to economic growth. In the model, parents choose fertility and children s education; allocate their time between raising children and working; and allocate their income between consumption, savings, and the expenditure on children. Human capital is discrete, either skilled or unskilled. On the production side, there is a representative firm using skilled labor, unskilled labor, and 1 The model follows the main spirit of Doepke (2004) and Liao (2010). 2

physical capital as inputs. We further incorporate the institutional distortions in the model to capture the possible productivity inefficiency, price distortions, and the effects of population policies in China, especially in the pre-reform period of China which was a command economy. Endogenous fertility is essential to our analysis. First, fertility choice is combined with the decision of education investment. Therefore, there is a quantity-quality trade-off of children. Second, technological progress may have feedback effects on fertility. If fertility is exogenous in the model, the contribution of demographic change to growth may be overestimated. In the numerical analysis, the pre-reform period (1957-1982) and the post-reform period (1982-2007) are both investigated. As a benchmark, the model is calibrated to represent the three stages of China s development. The first stage denotes a command economy with high fertility (above 6). The data of 1957 is applied to represent the first stage. In the second stage, the total fertility rate in China was around 3 and China was in the beginning of its economic reform (to become a market economy). Therefore, we choose 1982 for the second stage. The last stage represents a market-oriented economy with low fertility (about 1.5). The data in 2007 is applied. Each stage is solved as a steady state. Based on the benchmark, we do counterfactual experiments to study the impacts of growth factors on growth. Specifically, we focus on two types of growth sources: (1) technological progress and efficiency improvement; (2) demographic change. Technological progress and efficiency improvement refer to TFP growth (efficiency improvement is included) and changes in factor weights in the production. Demographic change consists of changes in four parameters: survival rates for children and youth, the cost of raising a child (the effects of the one-child policy are included), and the education time cost. Our results suggest that demographic change made a positive contribution to China s growth, especially in the early stage of development. In the pre-reform period, demographic change alone generated a per capita output growth of 2.7 percent per year. With an overall annual growth of 3.8 percent, demographic change explained about 71 percent (2.7/3.8) of the simulated growth. We also find that in the pre-reform period, technological progress and efficiency improvement could not sustain a positive growth. However, their roles reversed in the post-reform period. The contributions of technological progress and efficiency improvement with relation to growth were crucial (accounting for 68 percent of the simulated growth), while demographic change had only minor effects on growth. We also find that the price distortion on investment led to an over-accumulation of physical capital in early periods. Removing the price distortion could make the growth 3

rate even higher in later periods. Cheng (2003) chooses the year 2000 as the initial condition in his calibration. He finds that demographic structures had a small effect on economic growth. Instead, we extend to 1957 and our results suggest that demographic change made an important contribution to economic growth in 1957-1982. After the 1980s, the decline in fertility was relatively small. Therefore, its effect was minimal. Furthermore, the importance of productivity improvement for growth in our results is consistent with the literature. The growth accounting literature generally attributes the rapid growth of China in the post-reform period to TFP growth and a high rate of physical capital accumulation. 2 In the pre-reform period, they had minor or negative effects. The rest of this paper is organized as follows. The next section briefly reviews China s population policies. Section 3 provides the OLG model. Section 4 describes the parameters and the calibrated results. Section 5 discusses the contribution of each factor to growth. In Section 6, a sensitivity test of production parameters is provided. Finally, Section 7 concludes this paper. 2 Population Policies in China Figure 2 provides total fertility rates and per capita GDP across countries in 2007. One hollow circle represents one country. China is denoted by the solid circle. Among countries with the similar level of per capita GDP, China has achieved a relatively low fertility rate due to its birth-control policies. China s family planning program consists of two main campaigns. In 1971, the targets of population growth (natural increase 1.5 percent in rural areas and 1 percent in cities) were integrated into the five-year plan for 1971-75. To achieve the targets, the policy wan, xi, shao was implemented. 3 The most strict rules were applied in the cities where couples were encouraged to delay marriage until age 25 for women and 28 for men and to have no more than two children. In the countryside, the requirements for marriage were set at 23 and 25 years for women and men, respectively. The maximum family size was set at three children. In addition, urban and rural couples were both encouraged to have a longer intervals (four to five years) between births. 2 For example, Borensztein and Ostry (1996); Chow (1993); Hu and Khan (1997); and Wang and Yao (2003). 3 China already had birth-planning activities before the 1970s. Basically, the activities were restricted to educational works, such as offering contraceptive counseling, rendering abortions, and sterilizations. The work were only confined to big coastal cities and a few areas in the hinterland. See Scharping (2003). 4

In the first phase, all rules in general were not compulsory. Instead, economic subsidies and easy access to contraception practices were provided. In 1971-1982, the total fertility rate fell from above 6 to around 2.9, a 53 percent decline within a decade. The fraction of working-age population as a percentage of total population increased from 56 percent to 64 percent. 4 However, the first campaign still failed to match the official targets of population growth. Therefore, in 1979, the government moved to target the number of children per family directly and the one-child policy was formalized. At this stage, controlling births became a constitutional duty each couple, in both rural and urban areas, was allowed to have only one child. Single-child families obtain benefits and financial rewards, such as a child allowance, priority access to schools, employment, health care, larger land, and housing. On the other hand, a large fine is imposed on the above-quota births. Non-financial punishments are also included. For example, parents working in government sectors will be demoted or not eligible for promotion. With the implementation of the one-child policy, the fertility rate was further lowered from 2.9 of 1982 to 1.5 of 2007. 5 The percentage of working-age population increased to 71 percent in 2007. 6 In 1970-2007, 69 percent of the decline in total fertility rates (3.1/4.5) occurred in the first phase, while only 31 percent was in the second period. One possible explanation is the relaxation of the one-child policy after 1984 a second child is permitted under special conditions. For example, couples in the urban areas of Shanghai are allowed to have a second birth if one spouse or both spouses are single children. In Beijing, parents are allowed to have the second child if the first is disabled or dead. Furthermore, there are exceptions for allowing a third and even a fourth child. In Xinjiang, minorities can have as many as four children. In rural areas of Tibet, there are no restrictions on the number of children that ethnic minority families can have. 7 4 Development Data Platform, the World Bank. 5 In this paper, the total fertility rates are from Chinese Statistical Yearbook (CSY). After 2003, the official total fertility rates are not available. Therefore, the birth rates reported in CSY are used to calculate the total fertility rates. 6 Development Data Platform, the World Bank. 7 See Scharping (2003) and Li, Zhang, and Zhu (2005). 5

3 The Model Following Liao (2010), a three-period overlapping generations model with endogenous fertility is constructed. 8 It is basically a neo-classical type market-oriented model. However, China was a command economy before the economic reform in 1980. To characterize the pre-reform periods of China, we consider production inefficiency and institutional price distortions in our model. 3.1 Demographics Current population (N) consists of three generations: children (N c ), young adults (N y ), and old adults (N o ): N = N c + N y + N o. Human capital is discrete. A young adult is either skilled or unskilled, which was determined by his parents. Therefore, the population of young adults is given by: N y = N y s + N y u. Assume young adults give birth at the beginning of the period. Fertility is denoted as n i j, which represents the number of j-type children that an i-type young adult has, (i, j) {s,u}. 9 A young adult can have both skilled and unskilled children. The population of children is then given by: N c = (n ss + n su )N y s +(n us + n uu )N y u. Children survive to young adulthood with the probability π c. In addition, young adults will be alive with the probability π y in the old adulthood period. Therefore, the evolution of population in this economy is given by: N y = π c N c ; N o = π y N y ; where N y is the population of young adults in the next period and N o is the population of old adults in the next period. 8 Doepke (2004) provides a related model. However, Doepke (2004) abstracts from mortality, old generation, and physical-capital accumulation, which are the key elements in our model. 9 In this paper, we use i to denote the type of a young adult and j to represent the type of his children. 6

3.2 Production There exists one representative firm, using skilled labor L s, unskilled labor L u, and physical capital K as inputs. The firm uses a CES technology, and the production function is given by: Y = Aχ{µL α u +(1 µ)[θkρ +(1 θ)l ρ s ] α ρ } 1 α, (1) where Y denotes aggregate output; µ is the factor weight on unskilled labor; θ is the factor weight on physical capital; α determines the elasticity of substitution between L u and K and ρ determines the elasticity of substitution between L s and K. In this setting, the elasticity of substitution between unskilled labor and physical capital is equal to the elasticity of substitution between unskilled labor and skilled labor. Capital-skill complementarity requires α > ρ. 10 A denotes total factor productivity. χ represents aggregate inefficiency to capture the lack of incentives in a command economy. A lower χ will proportionally reduce total factor productivity as well as aggregate output level. In addition, marginal products of skilled labor, unskilled labor, and physical capital are all influenced by the aggregate inefficiency. Equation (1) is a constant-return-to-scale function. Therefore, output per capita (y pc ) is given by: L u y pc = L N Aχ[µlα u +(1 µ)(θk ρ +(1 θ)l ρ s ) α ρ ] 1 α, where l u = L s +L u, l s = 1 l u, and k = L K s +L u. Demographic change (a decline in fertility) results in changes in labor-population ratio, the fraction of skilled labor as a percentage of total labor, and physical capital per labor; therefore, it contributes to output growth. 3.3 Representative Agent s Problem Assume children cannot work and depend on their parents for support. Old adults retire from the labor market and consume their own savings. Only young adults can supply labor and make decisions on consumption at young adulthood (c i ), asset holdings (a i ), and the number of children for each type. The maximization problem of an i-type young adult can be expressed by the Bellman equation: V i = max {c i,a i,n is,n iu } { } ci 1 σ c 1 σ i + β πy 1 σ 1 σ + ψ[πc (n is + n iu )] ε [π c n is V s + π c n iu V u], 10 The hypothesis of capital-skill complementarity is also used in the demographic literature, such as Fernández-Villaverde (2001). Empirical studies find evidence to support this hypothesis. See Griliches (1969) and Papageorgiou and Chmelarova (2005). 7

subject to c i + π y a i = [1 ηφ(n is + n iu )]w i φ s n is w s ; c i = (1+r )(1+d)a i τ i ; where c i denotes the young adult s consumption at old age; w i represents his wage income; β is the subjective discount factor; σ is risk aversion; ψ is an altruism coefficient, which represents how much the young adult loves his children; ε is the elasticity of altruism; V s is the utility that a child will get when he becomes a skilled young adult; and V u is the utility that a child will get when he becomes an unskilled young adult. V s and V u are both foreseeable for the young adult when he is making decisions. Assume each young adult has one unit of time. φ is the time cost of raising a child. η denotes the distortion of population policies (i.e the one-child policy). A tighter population policy is represented by a larger η, which increases the cost of raising a child and affects the young adult s fertility choices. φ s is the education time cost. We assume that only skilled young adults can teach. Therefore, if a young adult, skilled or unskilled, wants to provide education to his children, he needs to send his children to school and pay the education costs φ s w s for a child. 11 There is a perfect competitive annuity market that allows a young adult to contribute π y a i at young adulthood and receive this annuity after retiring. An old adult consumes his own savings with the asset return, (1+r )(1+d)a i. r is the interest rate in the next period. We use d to represent the price distortion on the return of investment that is used to capture the heavy-industry-oriented policy in China (see more discussion in section 3.4). A positive d encourages capital accumulation. To finance this policy, the government collects a typespecific lump-sum tax, τ i, from old adults. This distortion/tax mechanism in the model is designed so that there is only distortion on price and no wealth effect. In our model, the distorted capital return specifically benefits old adults, and the type-specific lump-sum tax exactly removes the distorted capital gain to prevent the unrealistic subsidies that only benefit old adults. However, the price distortion still affects an individual s saving choices (a ) and the equilibrium interest rate r. A recursive competitive equilibrium of this model is provided in the appendix A. 11 The wage rate for being a teacher is equal to the skilled wage rate, so that in equilibrium a skilled adult is indifferent between working in the production sector and being a teacher. In this model, the contribution of teachers is not counted to aggregate output. 8

3.4 Market vs. Command Economies Because our analysis includes the pre-reform period when China was a planning economy, we should discuss the appropriateness of using the above model to characterize China s economy before proceeding to the calibration of the model. In the literature, Scotese and Wang (1995) employed a neoclassical-type market model to characterize Chinese economy by introducing some costs to capture the effects of the planning element. Chow (1985) also used a market model to study Chinese output, consumption and investment paths, and suggested that the market model was a decent characterization of how the economy would evolve without political interference 12 In this paper, we carefully specify some distortions/costs to capture the important features in the planning period. The first feature that we would like to capture is the heavyindustry-oriented policy. In the 1950s, having a developed heavy-industry sector represented a nation s power and economic achievement. Therefore, after recovering from the war, the Chinese government adopted a heavy-industry-oriented development strategy to the planned economy of China. In other words, constructing a heavy industry was the priority for economic development. Heavy industry is a capital-intensive sector. However, in the early 1950s, China was a capital-scarce agricultural economy. Capital was limited and the Chinese economy, which had little foreign exchange, was unable to import capital from more advanced economies. Therefore, distortion policies were introduced in order to develop heavy industry, such as a policy of distorting interest rates, overvalued exchange rates, low input prices, and a planning allocation mechanism. 13 The Great Leap Forward was an extreme case of these policies to encourage capital accumulation. In our model, the distortion policy on capital accumulation is captured by the price distortion of investment, d. It changes the return of assets proportionally which encourages investment. In addition, as discussed in Section 2, the one-child policy was implemented in 1979 to control the rapid population growth in China. Incentives and punishments included in the policy would change parents cost of raising a child. This part is captured by η in the model, which increases the child-raising cost. The distortions in the planning economy were accompanied by low economic efficiency 12 He used the residuals from the estimated model as indicators for periods of political importance. He found that, except some periods with special government policies, e.g. the Great Leap Forward and the Cultural Revolution, the residuals were not large. 13 See Lin, Cai, and Li (2009) for the detail. 9

allocation inefficiency and technical inefficiency in China. 14 For those not captured by the above distortions, we use an aggregate inefficiency factor, χ, to capture other inefficiencies under the planning economy. It alters total factor productivity, and so lowers marginal products of capital and labor and the level of output. 3.5 Characteristics in Equilibrium Following Doepke (2004) and Liao (2010), two characteristics can be shown in equilibrium. First of all, only corner solutions exist. The intuition is that children within one family are identical, except education. Therefore, parents will send either all children or none of them to school. Skilled and unskilled children will not live in the same family. The second characteristic is indifference conditions. A young adult will be indifferent between having skilled children and unskilled children if the following condition holds: V s V u = ( pis p iu ) 1 ε, (2) where p is = ηφw i + φ s w s and p iu = ηφw i. The right-hand side of (2) represents the relative cost of a skilled child to an unskilled child for an i-type adult. Since the relative costs are different between skilled adults and unskilled adults, only one type will satisfy the indifference condition in equilibrium. The proofs of the two characteristics are shown in the appendix B. The maximization problem thus can be rewritten as: { } ci 1 σ c 1 σ i max + β πy {c i,a i,n i j} 1 σ 1 σ + ψ(πc n i j ) 1 ε V j, (3) subject to c i + π y a i = (1 ηφn i j)w i 1{ j = s}φ s n i j w s ; (4) c i = (1+r )(1+d)a i τ i ; (5) where (i, j) {s,u}; 1{ j = s} is an indicator function: 1{ j = s} = 1 if j = s and 0 otherwise. The first order conditions are given by: n ε i j p i j = ψ(1 ε)π c1 ε V j[w i π y a i p i j n i j ] σ ; (6) c i c i = [β(1+d)(1+r )] 1/σ. (7) where p i j = ηφw i + 1{ j = s}φ s w s, representing the total cost of a j-type child for an i-type adult. 14 See Lin, Cai, and Li (2009). 10

An individual s fertility decisions follow equation (6). Fertility is positively affected by the survival rate of children; but negatively influenced by longevity (the survival rate of young adults). In addition, fertility increases as income goes up. Therefore, children are normal goods in our model. However, an increase in income pushes the total cost of child-raising up, thereby lowering fertility. In the model, a lower fertility rate contributes to growth through the following mechanism. First, a lower fertility rate means fewer children and more time for work. Second, a lower fertility rate implies more resources for parents savings. Hence, physical-capital is accumulated. Finally, parents may be willing to invest more in the fewer children, which leads to human-capital formation. The three channels then affect aggregate output. Based on these two characteristics, only the following case is possible along a balanced growth path: (i, j) {(s,s),(u,s),(u,u)}. 15 In other words, skilled parents always choose skilled children, some unskilled parents choose skilled children, and others choose unskilled children along a balanced growth path. We focus on this case in the quantitative analysis. The evolution of population of unskilled young adults is given by: N y u = π c n uu λ uu N y u, where λ uu denotes the proportion of unskilled parents having unskilled children. The growth rate of the population of unskilled young adults is: g N y u = N y u /Ny u = πc n uu λ uu. (8) Along a balanced growth path, the population of each group grows at the rate of (8). In addition, the production side also grows at the same rate. All variables are transformed into per capita terms. Therefore, the de-trended model is stationary along a balanced growth path. 16 4 Calibration The benchmark is calibrated to the data of China in 1957, 1982 and 2007 to represent the three stages of China s demographic and economic development. In the first stage, the total fertility rate in the economy was high and economic growth was low. In the second stage, the total fertility rate fell to 2.87 and the economy was at the beginning of economic reform 15 See the discussion in Liao (2010). 16 In our quantitative analysis, exogenous TFP growth and technological progress are considered. Therefore, the growth rate along the balanced growth path is different from (8). 11

and openness. The last stage represents the current China: low fertility and high growth. Each is solved as a steady state. 1982 is selected for three reasons. First, it is at the beginning of China s economic reform. Second, China s one-child policy was made compulsory in 1982 though it was initiated in 1979. Third, a population census was held in 1982. Therefore, we chose 1982 to be the middle stage and selected a twenty-five-year interval, i.e. 1957 and 2007 were selected to be the first and the third stages. 4.1 Parameters Table 1 summarizes the parameters in each steady state. The time period in the economy is equal to twenty-five years. Death rates in China Statistical Yearbook are reported by every age year cohort. 17 To obtain the survival rates for our calibration, we first calculate survival rates (π age ) for each age by the death rates in China Statistical Yearbook. Then, we construct one sequence of the survival rate for children (π c ) and another for young adults (π y ) using conditional probabilities, π c = π y = 24 π age ; age=0 49 π age. age=25 The survival rate for children represents the survival rate from age 0 to age 24; and the one for young adults is at the age between 25 and 49. The constructed sequences are plotted in Figure 3. The survival rate for young adults increased from 87 percent in 1957 to 94 percent in 1982 and to 96 percent in 2007. The survival rate for children increased from 80 percent in 1957 to 93 percent in 1982 and to 98 percent in 2007, which was a faster improvement than the survival rate for young adults. The education time cost is chosen so as to match the ratio of skilled workers as a percentage of total workers. Skilled workers refers to people who have graduated from senior high school or above. In 1957, the fraction of skilled workers was about 3.12 percent. 18 In 1982, it was equal to 11.4 percent. 19 The ratio of skilled labor rose to 18.8 percent in 2007. 20 Therefore, we set φ s to be 0.003, 0.017, and 0.076 for the three steady states, respectively. 17 Source: China Statistical Yearbook, various issues, National Bureau of Statistics. 18 Source: The Second Population Census, 1964. 19 Source: The Third Population Census, 1982. 20 Source: China Statistical Yearbook, National Bureau of Statistics. 12

The one-child policy provides economic incentives for parents to give just one birth. It will affect the cost of raising a child. However, the economic incentives consist of both financial and non-financial benefits and punishment. Some may last for many years, not just a one-time treatment. Therefore, it is not easy to measure the effects of the one-child policy on child raising costs. In our calibration, we choose the distortion (η) and the cost of raising a child (φ) together to match a half of the total fertility rates in data. In other words, we do not distinguish the distortion by the one-child policy and the child raising cost in the calibration. The total fertility rate was 6.4, 2.87 and 1.45 in 1957, 1982 and 2007 respectively. 21 Therefore, the cost of raising a child is equivalent to 8.1, 17 and 26.3 percent of a worker s wage in the three steady states, respectively. Seven parameters are assumed to remain unchanged in a relatively short period of time: four preference parameters (annual discount factor, risk aversion, elasticity of altruism, and altruism coefficient) and three parameters that relate to the production (the elasticity of substitution between skilled labor and physical capital, the elasticity of substitution between unskilled labor and physical capital, and the annual depreciation rate). The annual discount factor of the third steady state is calibrated to match the average (physical) capital-output ratio 3.15 in 2002-2006. 22 Thus, the annual discount factor in the third steady state is 0.943. We also assume that the annual discount factor does not change across time. In other words, the annual discount factors in the first and second steady states are equal to 0.943. Empirical evidence shows that preference parameters vary across countries and a country s culture is an important determinant (for example, Hammel (1990)) 23. Since the remaining three preference parameters of China are not available in data or in the literature, our strategy is to borrow these parameters from a country which has similar culture to China. Taiwan is a useful substitute because China and Taiwan share a similar culture. Therefore, following Liao (2010), the elasticity of altruism is equal to 0.5, altruism coefficient is 0.238, and the risk aversion is 0.5 for all steady states. We follow Chow (1993) in setting the annual depreciation rate in China at 0.05 and 21 The model is measured in an individual level, so we match a half of the total fertility rates. 22 There is no direct information of China s capital stock, so We follow Chow (1993) to estimate the sequence of capital stock in 1952-2006 using the law of motion of capital. Following Chow (1993), the depreciation rate is 0.05 in our estimation and the initial value of capital stock at the end of 1952 (including land values) is about 2.7 times of the output of 1952. To prevent the effects of initial values, our estimation starts with 1952. We find that the estimated capital-output ratios in the 2000s are not sensitive to the initial capital stock, because the investment before 1978 was relatively small. 23 Also see Cook et al. (2005); Weber and Hsee (1998); and Hull (1983) 13

convert into 25 years. According to the estimate in Krusell et. al. (2000), we set the elasticity of substitution between unskilled labor and physical capital at 1.67 and the elasticity of substitution between skilled labor and physical capital at 0.67. Their estimate implies that α is equal to 0.401 and ρ is 0.493. α is greater than ρ, so capital-skill complementarity is guaranteed in our calibration. 24 Total factor productivity (Aχ) in the third steady state is normalized to become 100. In the first and second steady states, TFP is calibrated so that the annual growth rate of per capita output in 1957-1982 and 1982-2007 matches 3.8% and 9%, respectively. 25 Thus, TFP is equal to 16.5 for the first steady state and 31.53 for the second steady state. According to our setting, the annual TFP growth is equal to 1.1% in 1957-1982, 6.3% in 1982-2007, and 3.7% in 1957-2007. 26 The large TFP growth from the second steady state to the third steady state reflects an improvement in productivity as well as in production efficiency in the post-reform period of China. The distortion on the price of physical capital d is set as follows. First, it is set to become 0 in the third steady state. Then, we choose d to match the capital-output ratio 2.3 (average of 1953-1957) and 2.89 (average of 1978-1982) for the first and second steady states, respectively. Hu and Khan (1997) compute the income share of total labor for China. However, the time series data is computed until 1994. Following their methods and data sources, we extend the income share of total labor to 2007. 27 The income share of physical capital in the first steady state is 0.664, which is the average of 1953-1957; 0.604 in the second steady state, which represents the average of 1978-1982; and 0.49 in the third steady state, the average of 2003-2007. To compute the income share of unskilled labor, skill premium and the fraction of skilled workers are required. In 1957, the fraction of skilled workers was about 3.12 percent. In 1982, it was 11.4 percent. However, the survey of wage rates by education are not available in 1957 and 1982. We thus chose the average wage in the public sector to be a proxy of skilled wage rate and the average wage in manufacturing sector to be a proxy of unskilled 24 Krusell et. al. (2000) use the U.S. data to estimate the elasticity of substitution. It may not be suitable to apply to a developing country, such as China. Therefore, a sensitivity test for the setting of the elasticity of substitution is provided in the later section. 25 Source: China Statistical Yearbook, National Bureau of Statistics. 26 In comparison, Hu and Khan (1997) estimate that the TFP growth was 1.1% in 1953-1978, 3.9% in 1979-1994, and 2.1% in 1953-1994. On the other hand, Borensztein and Ostry (1996) estimate that it was -0.7% in 1953-78 and 3.8% in 1979-1994. 27 Source: China Statistic Yearbook, National Bureau of Statistics, 2008. 14

wage rate. 28 In addition, as reported in China Statistical Yearbook 1983, the wage in the public sector is adjusted to represent the additional benefits rather than cash income. The adjustment was 1.179 and 1.217 in 1957 and 1982, respectively. The corresponding skill premium was equal to 1.078 and 1.165. 29 Therefore, the ratio of unskilled labor income to total labor income is 0.966 and 0.870 for the first and second steady state, respectively. The 2006 household survey reported that the skill premium was 1.528 in 2005. 30 The skilled labor ratio rose to 18.8 percent in 2007. These two values bring the income share of unskilled labor down to 0.739 in the third steady state. The last two production parameters are the factor weights, µ and θ. In the process of solving a steady state, we used the income share of physical capital and unskilled labor to pin down the two weights. 31 Therefore, µ and θ are equal to 0.4223 and 0.9985 for the first steady state; 0.5202 and 0.9903 for the second one; and 0.7330 and 0.9876 for the third one. 4.2 Solutions to the Steady States Three steady states are independently solved. The main features of the three steady states are summarized in Table 2. In the first steady state, only 0.3 percent of unskilled parents are willing to send their children to school. Although the education cost becomes more expensive, this ratio increases to 2.3 percent in the second steady state and rises again to 9.8 percent in the third steady state (not reported in tables). Therefore, in 2007, the fraction of skilled labor increases to 18.8 percent. Table 3 provides an individual s time allocation for each steady state by types. 32 First of all, although the cost of raising a child increases over time, all parents spend less time raising children at home. This is mainly due to the large decline in fertility. Second, skilled adults spend more time teaching due to the popularity of sending children to school. Third, 28 Source: China Statistical Yearbook, various issues, National Bureau of Statistics. 29 In 1957, the wage in manufacturing was 690 Yuan and 631 Yuan in public sector. Thus, skill premium is obtained by 631 690 1.179 = 1.078. In 1982, skill premium is computed by 827 864 1.217 = 1.165. 30 Source: National Bureau of Statistics, unpublished data. 31 They are given by the following equations: K(r+ δ) Y w u L u w s L s + w u L u = = (1 µ)(θkρ +(1 θ)ls ρ ) α ρ 1 θk ρ µlu α +(1 µ)(θk ρ +(1 θ)ls ρ ; (9) ) α ρ 1 1 µ µ (θkρ +(1 θ)ls ρ ) α ρ 1 (1 θ)ls ρ lu α + 1. (10) 32 The time spent on raising children is computed by φn i j. The time spend on teaching is given by φ s n ss + φ s n us λ us N y u N y s. 15

as the fertility declines, parents spend more time working. Abundant labor force contributes to economic growth. 5 Accounting for China s Growth 5.1 Sources of Economic Growth In this section, China s economic growth is separated into two periods: the pre-reform period 1957-1982 and the post-reform period 1982-2007. Counterfactual experiments are provided to explore the sources of economic growth. Specifically, we focus on two types of sources. One is technological progress and efficiency improvement. Another is demographic change. The former is represented by changes in three production parameters: Aχ, µ, and θ. Demographic change includes four demographic parameters: π c, π y, ηφ, and φ s. The results are summarized in Table 4. These results are the one under an environment with price distortion of physical capital. The benchmark presents the annual growth rate of per capita output from one steady state to another, as discussed in the last section. Therefore, the growth rate of per capital output in the benchmark is exactly equal to the growth rate in data. In the pre-reform period, the annual growth rate of per capita output is 3.8%. Demographic change alone generated a growth rate of 2.7%, which is about 71 percent of simulated growth (2.7/3.8). On the other hand, the contributions of technological progress and efficiency improvement were negative. Therefore, in the early stage of China s economic development, demographic change (a sharp decline in fertility) was the main engine. However, the story is different in the post-reform period. In 1982-2007, technological progress and economic improvement resulted in an annual growth of 6%, while demographic change only accounted for 0.4%. Therefore, in the later stage of China s economic development, the rapid growth was mainly due to technological progress and efficiency improvement. Demographic change had minor effects on growth. Table 5 further reports the sources of growth by channels: labor-population ratio, the fraction of skilled labor, and physical capital per young adult. The last channel is reported as annual percentage changes. Others are the level of corresponding ratios. For example, the labor-population ratio in the benchmark (in 1982) is 24%; the fraction of skilled labor is 11%; and the annual growth of physical capital per young adult is 3%. We find that technological progress and efficiency improvement are the main reasons for human-capital accumulation. Under the environment with technological progress and efficiency improvement alone, the fraction of skilled labor increases to 5% in the pre-reform 16

period; it increases to 14% in the post-reform period. Demographic change has minor effects on the formation of human capital. In addition, in the pre-reform period, the effects of demographic change on physicalcapital accumulation is larger than the effects of technological progress and efficiency improvement. However, in the post-reform period, their roles are reversed. In the second stage, technological progress and efficiency improvement generate an annual growth of 5% of the accumulation of physical capital, while the contribution of demographic change is low. 5.2 Removing the Price Distortion We remove the price distortion of physical capital and repeat the previous quantitative analysis. In other words, d = 0 in all steady states. Other parameters remain unchanged. The steady-state results without price distortion are summarized in Table 6. We find that without the price distortion fertility is higher; but the fraction of skilled labor and capital-output ratio are much lower than the benchmark. The encouragement for physical-capital accumulation by the price distortion reflects the heavy-industry-oriented policies in the Great Leap Forward in the 1950s of China. The contributions of growth sources without price distortion are reported in Table 7. Although removing price distortion increases the annual growth rate of per capita output, we still find that demographic change is the most important factor in the pre-reform period and technological progress and efficiency improvement become more important in the postreform period. 6 Sensitivity Tests Production parameters In the calibration, we follow Krusell et al. (2000) to adopt α = 0.401 and ρ = 0.493. They are the mean values of the estimate for the U.S., which may not be suitable to the calibration of China. To test if our results are sensitive to α and ρ, we repeat the counterfactual experiments using the values within the 95% confidence interval. The factor weights, µ and θ will change accordingly. Others remain unchanged. Both periods are tested. The 95% confidence interval of the estimated α stands between -0.067 and 0.869. Therefore, we test -0.067, 0.167, 0.401, 0.635, and 0.869 for α. The 95% confidence interval of ρ stands between -0.591 and -0.399. Therefore, -0.591, -0.543, -0.493, -0.447, -0.399 are tested. 17

The results are summarized in Table 8. Only the pre-reform period is reported. The results show that the assumption of α and ρ does not have significant impacts on our main conclusions. The contribution of demographic change in the pre-reform period was about 2.5%-3% per year regardless of the setting of α and ρ. 7 Conclusions This paper investigates China s economic growth in 1957-2007 with endogenous factor accumulations and fertility choice. A three-period general equilibrium overlapping generations model is constructed to measure the impacts of demographic change on growth. The literature argues the important role of TFP growth or factor accumulations in explaining economic growth. As a complement to the literature, we find that demographic change made a positive and outstanding contribution to China s growth, especially in the early stage of its development. In 1957-2007, the demographic change generated about 1.5% per year of per capita output growth. In the pre-reform period, the contribution of demographic change was larger, around 71% of the simulated growth. In the post-reform period, technological progress and efficiency improvement accounted for 6% percentage points out of 9 percent annual growth rate of per capita output. Our findings about the role of productivity improvement in explaining growth are consistent with the literature (for example, Young, 2003; and Hu and Khan, 1997). Appendix A: Recursive Competitive Equilibrium The representative firm employs skilled labor, unskilled labor, and physical capital as inputs to maximize its profit: where Y is defined by (1). 33 max Y w s (x)ls f w u (x)lu f r(x)k f, (11) Ls f,lu,k f f 33 The equilibrium wage rates and the rate of return of capital are given by: w u = Aχ{µLu α +(1 µ)[θk ρ +(1 θ)ls ρ ] α ρ } 1 α α µl α 1 u ; w s = Aχ{µLu α +(1 µ)[θk ρ +(1 θ)ls ρ ] α ρ } 1 α α (1 µ)[θk ρ +(1 θ)ls ρ ] α ρ ρ (1 θ)l ρ 1 s ; r+ δ = Aχ{µLu α +(1 µ)[θkρ +(1 θ)ls ρ ] α ρ } 1 α α (1 µ)[θk ρ +(1 θ)ls ρ ] α ρ ρ (θ)k ρ 1. 18

The maximization problem of a representative agent is given by: V(x) = max {c,a,n s,n u } subject to the budget constraint: { c 1 σ } c 1 σ + β πy 1 σ 1 σ + ψ[πc (n s + n u )] ε [π c n s V s (x )+π c n u V u (x )], (12) c+π y a = [1 ηφ(n s + n u )]w(x) φ s n s w s (x); (13) c = (1+r (x ))(1+d)a τ ; (14) and a law of motion of the state vector x = G(x), where the state vector x {N y s,n y u,k,a}. Define λ i j as the fraction of i-type young adults having j-type children. Since only corner solutions exist in equilibrium, the following conditions should be satisfied: λ ss (x)+λ su (x) = 1; (15) λ us (x)+λ uu (x) = 1. (16) By assumption, a skilled adult allocates his time between raising children, working, and teaching. Thus, the supply of the skilled labor in the market is given by: L s (x) = [1 (φ + φ s )n ss (x)λ ss (x) φn su (x)λ su (x)]n y s φ sn us (x)λ us (x)n y u, The supply of skilled labor is equal to the total amount of skilled labor minus skilled labor spent on raising children and teaching. On the other hand, unskilled parents allocate their time between working and raising children. The supply of unskilled labor is given by: L u (x) = [1 φn us (x)]λ us (x)n y u +[1 φn uu(x)]λ uu (x)n y u. Assume that skilled young adults can work as either skilled or unskilled workers, while unskilled young adults only work as unskilled workers. Therefore, the market clearing conditions for the labor market are: L f s (x) L s (x), (17) Lu f (x) = L u(x)+[l s (x) Ls f (x)]. (18) The equality of the skilled labor market holds if w s (x) > w u (x). Aggregate supply of physical capital tomorrow is given by: K (x) = π y (a sn y s + a un y u). (19) 19

The market clearing condition requires that aggregate demand of physical capital (K f (x)) equals aggregate supply of physical capital K. Therefore, K f (x) = K. (20) To keep balanced budget, the lump-sum tax of old adults is given by: Finally, the law of motion of young adults is given by: τ s (x) = (1+r(x))da s ; (21) τ u (x) = (1+r(x))da u. (22) Ns y = π c [n ss (x)λ ss (x)ns y + n us(x)λ us (x)nu y ]; (23) N y u = π c [n su (x)λ su (x)n y s + n uu (x)λ uu (x)n y u]. (24) Now we have all elements to define a recursive competitive equilibrium. A recursive competitive equilibrium of this model consists of the value functions V s (x) and V u (x), pricing functions w s (x), w u (x), and r(x), mobility functions λ ss (x), λ su (x), λ us (x), and λ uu (x), policy functions n ss (x), n su (x), n us (x), n uu (x), a s (x), and a u (x), decision functions of the firm K f (x), L f s (x), and L f u(x), a law of motion of state variables x = G(x), and the government tax policy τ s (x) and τ u (x), such that: 1. Given the pricing functions and the law of motion of state variables, the value functions and policy functions solve the young adult s dynamic programming problem. 2. If λ i j (x) > 0, where (i, j) {s,u}, n i j (x) maximizes the young adult s problem. 3. The mobility functions (15) and (16) are satisfied. 4. Given the pricing functions, the decision functions of the firm maximize its profit. 5. The market-clearing conditions (17), (18), and (20) are satisfied. 6. The law of motion G for the state variable x is given by (19), (23), and (24). 7. The government tax policy keeps balanced budget, i.e., (21) and (22) are satisfied. Appendix B: Corner Solutions and Indifference Conditions The decision process can be broken down into two stages. First of all, a young adult with type i, i {s,u}, allocates his resources between consumption at young adulthood (c i ), asset holdings (a i ) and the total expenditure of children (E i). Then, the young adult allocates the total expenditure of children between raising skilled and unskilled children. Assume he 20

spends a fraction f i on his skilled children and the rest on his unskilled children. The number of skilled and unskilled children he has is given by: n is = f ie i p is ; n iu = (1 f i)e i p iu, where p is and p iu are defined in Section 3.5. Different from Liao (2010), a distortion for the cost of a child η is included in our model. It will only affect the content of p is and p iu. Others are similar. Therefore, following the argument in Liao (2010): since 0 < ε < 1, the life-time utility is convex in f i, which implies only corner solutions exist in equilibrium. Given the results of corner solutions, the number of children a young adult has becomes n i j = E i p i j. A young adult s maximization problem can be re-written to obtain (3). Substitute the number of children a young adult has into (3) and realize that only the third part of the life-time utility depends on children s type. Therefore, a young adult will be indifferent between having a skilled child and an unskilled child if the condition (2) holds. Since the distortion for the cost of a child applies to both skilled and unskilled children. The argument of Liao (2010) still holds in our model. We conclude that in equilibrium only one type of young adult will satisfy the indifference condition. The details for the proof can be found in Liao (2010). References Bloom, D.E., D. Canning, L. Hu, Y. Liu, A. Mahal, and W. Yip. 2010. The Contribution of Population Health and Demographic Change to Economic Growth in China and India, Journal of Comparative Economics 38, pp.17-33. Borensztein, E. and D.J. Ostry. 1996. Accounting for China s Growth Performance, American Economic Review, Vol. 86, No. 2, pp. 224-228. Cheng, K.C. 2003. Economic Implications of China s Demographics in the 21st Century, the IMF working paper, wp/03/29. Chow, G. 1985, A Model of Chinese National Income Determination, Journal of Political Economy, Vol.93(4), pp.782-792. Chow, G. 1993. Capital Formation and Economic Growth in China, Quarterly Journal of Economics,108(3), PP. 809-842. Cook, K.S., T. Yamagishi, C. Cheshire, R. Cooper, M. Matsuda, and R. Mashima. 2005. Trust Building via Risk Taking: A Cross-Societal Experiment, Social Psychology Quarterly 2005, Vol. 68, No. 2, pp. 121-142. 21