Supplementary Materials for

Fertility Matters and Provincial Differences: Revisiting China's Demographic Futures

This PDF file includes:

1 Population Projection Model2 Data of Base Year 20103 Assumptions on Total Fertility Rate (TFR) during the Period 2011-21004 Assumptions of Mortality Rate during the Period 2011-21005 Assumptions on sex ratio at birth during the period 2011-2100Figs. S1 to S7Table S1References

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1 Population Projection ModelThis paper estimates the number of male and females in 31 Chinese provinces1 taking into

account provincial-specific birth and mortality rates, and boy/girl birth ratios. The projection is conducted annually for each of 101 1-year age groups (from new born to centenarians) during the period 2010-2100, using 31 cohort-component models and data from different sources as explained below. The provincial projections are aggregated to obtain a national projection.

Cohort-component ModelA cohort-component model simultaneously applies fertility and mortality rates to a base

population in order to estimate the subsequent population in each cohort. Hence, the size of groups of women or men in the same age cohort per unit of time, is projected as the combined effect of rates of inflows (births or aging of survivors from population groups in the previous age cohorts) and outflows (deaths and aging). A graph of the cohort-component model implemented in the software Stella (inc., 2017) is shown in Figure S1.

Inputs of the Cohort-component ModelThe cohort-component model takes four inputs for each of the 31 Chinese provinces: 1)

number of male and females in each of 101 age groups for the base year 2010; 2) age and sex specific mortality rate for each year in the period 2010 to 2100; 3) age-specific fertility rate for women 15-49 years old for each year in the period 2010 to 2100 and 4) ratio of boys/girls among all births for each year in the period 2010 to 2100.

We assume that both the net interprovincial and foreign migration rates are zero for all years.

EquationsEstimates of population in each age cohort are calculated based on assumptions regarding

births and deaths as follows:(1) Population of New born babies. The number of births of males Pm, it (0 ) and females Pf ,it

(0 ) taking place in province i in a given year t are estimated as a function of age-specific fertility rates and infant mortality rates for that year. These numbers of births are expressed in equations (1) and (2) as functions of bm ,it and b f , it which are the number of births of males and females from women 15-49 years old, in province i at a given year t ; and IMRm,it and IMRf , it, the sex-specific infant mortality rates in province i at a given year t .

In turn, bm,it and b f , it are functions of: a) the size of the female population of child bearing age (x years old, with 15 ≤ x ≤ 49) in province i during that year t , Pf ,it

( x ); b) the age-specific fertility rate (i.e., fertility rate for females x years old, in province i for year t), FRit

(x ); and c) the percentage of boys among all births in province i for year t , Rit

.Pm , it (0 )=bm ,it

× (1−IMRm , it )=[ P f , it (15 ) FRit(15 )+P f ,it

(16 ) FRit(16 )+…+Pf ,it

(48 ) FRit( 48 )+Pf ,it

(49 ) FRit( 49 ) ] × Rit

× (1−IMRm,it ) (1)Pf ,it

(0 )=bf ,it× (1−IMR f ,it )=[ Pf ,it

(15 ) FRit(15 )+Pf ,it

(16 ) FRit(16 )+…+P f , it

( 48 ) FRit(48 )+P f , it ( 49 ) FRit

(49 ) ]× (1−Rit )× (1−IMRf ,it ) (2)

1 The special Administrative Regions (SAR) of Hong Kong and Macao, and the province of Taiwan are not represented in this model.

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(2) Population in one-year age groups, ages 1 to 99 years old. The number of males of age x (with 1 ≤ x ≤99) in province i at year t Pm, it ( x ) is equal to the number of survivors now entering this age group, calculated based on the population size and mortality rate for males one year younger (age x−1 ) in year t−1 denoted as MDRm, it−1

( x−1 )):Pm, it ( x )=Pm, it−1

( x−1 ) × [1−MDRm,it−1(x−1 ) ] (3)

The female population of age x, in province i at year t is projected similarly as:Pf ,it

( x )=Pf , it−1( x−1 ) × [1−MDRf , it−1

( x−1 ) ] (4)(3) Population ages 100 and older. The number of males 100 years old and older, in province i

for year t Pm , it ¿ is projected as a function of a) the population in that same age group during the previous time period Pm, it −1

¿; b) the mortality rate for that age group in year t−1, MDRm, it−1¿; and

c) the number of males who were 99 years old during the previous year and are now entering this group – calculated based on the corresponding mortality rate for that particular year MDRm, it−1

(99 )):Pm, it ¿ (5)

The population of females 100 years old and older, in province i during year t , is calculated as:Pf ,it

¿ (6)

2 Data of Base Year 2010Data for the base year 2010 is taken from the Sixth National Population Census conducted in

each of the 31 provinces (NBS, 2011) by the National Bureau of Statistics (NBS). These data is deemed to be of higher quality than the data collected by the Ministry of Public Security (MPS), and the National Population and Family Planning Commission (NPFPC) (Attane & Minglei, 1999). The data taken from the Sixth National Population Census includes:

1) Provincial population of 101 age groups (0, 1, 2… 99, 100+) by sex (male and female);2) Provincial age-specific fertility rate for women aged 15 to 49 years old;3) Provincial mortality rate of 101 age groups (0, 1, 2… 99, 100+) by sex (male and female);4) Provincial sex ratio at birth (#boys/#girls).Total population size for each province in year 2010 is shown in Figure S2.

3 Assumptions on Total Fertility Rate (TFR) during the Period 2011-2100The recent transition from a one-child to a two-child family planning policy, together with the

possibility of more lax limits on family size, and other socio-economic changes add uncertainty to the total fertility rate (TFR) that will be observed in China in this century. To represent this uncertainty, this paper considers five scenarios that differ in assumptions about TFR. These scenarios assume TFR values within the range of the assumptions of similar studies published in the literature (Bank, 2018; Chai & Xu, 2016; N. B. o. S. o. China, 2013; Guo, 2012).

Five ScenariosTable S1 summarizes the assumptions of the five scenarios of national TFR used to project the

annual population during the period 2011-2100. The rationale for these scenarios follows:

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(1) Scenario 1 (Low): the TFR remains constant at 1.18 during the whole projection period. This scenario reflects the continuation of the fertility rate observed in 2010, which is from the Sixth National Population Census (NBS, 2011).

(2) Scenario 2 (Low to Mid-high): the TFR rises linearly from 1.18 in 2010 to 1.80 in 2020; and then remains at 1.80 during 2020-2100. A TFR of 1.8 is consistent with projections from the State Council of the People's Republic of China (S. C. o. t. P. s. R. o. China, 2016).

(3) Scenario 3 (Middle): the TFR stays constant at 1.60 for the whole projection period. A TFR of 1.6 corresponds to the World Bank estimate of the fertility rate observed in 2010 2 (Bank, 2018).

(4) Scenario 4 (Middle to Mid-high): the TFR rises linearly from 1.60 in 2010 to 1.80 in 2020; and then remains at 1.80 during 2020-2100.

(5) Scenario 5 (High): The TFR rises to 2.10 in year 2011 and stays at this level during the whole projection period. A TFR of 2.10 corresponds to the level required for population replacement (Wilson, 2004). An increase in the TFR of this magnitude is considered plausible given the current two-child policy and the prospects of a future policy that lifts restrictions on family size. This TFR is likely to be an upper bound given a growing trend in postponement of marriage and parenthood (Badkar, 2012; Howden & Zhou, 2015).

Data processing from National TFR to Provincial Age-specific Fertility RateThe five scenarios of national TFR are used to estimate five scenarios of age-specific fertility

rate for women between ages 15 to 49 years old, in each province. These provinces and age-specific TFRs are obtained by combining the assumed national TFR under a scenario, with information on 1) provincial age-specific fertility rate for women ages 15-49 years old in the base year 2010 and 2) provincial TFR in the base year 2010 and 3) changes in national age-specific fertility patterns for 2010-2100 estimated by the United Nations (United Nations, 2017b).(1) From national TFR to provincial TFR

The projection of provincial TFR for each year takes into account the provincial differences observed in year 2010 and the changes in national TFR assumed under each scenario. The TFR in province i for year t TFRitis a function of the national TFR for that year TFRt, and the ratio of the provincial TFR to the national TFR in year 2010 TFRi2010

/TFR2010:

TFRit=

TFRi2010

TFR2010× TFRt (7)

Figure S3 shows the provincial TFR for years 2010 and 2100 under each of the five scenarios considered.(2) From provincial TFR to provincial age-specific fertility rates

Estimates of the age-specific fertility rates for women ages 15 to 49 years old are obtained by taking into consideration assumptions on changes in age-specific fertility due to the postponement of marriage and parenthood. Hence, age-specific fertility rates during 2010-2100 are estimated as a function of three factors: 1) provincial TFR during 2010-2100, 2) provincial

2 The 2010 fertility rate reported by the Chinese National Bureau of Statistics in the Sixth National Population Census (3) is lower than the one reported by the World Bank (7). Some observers argue that the NBS number is lower because of underreporting (Times, 2013).

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age-specific fertility rate for women 15-49 years old in year 2010, and 3) changes in the national age-specific fertility during 2010-2100, as explained below. a. National changes in age-specific fertility during 2010-2100

The United Nations (2017b) estimate future changes in fertility rates of Chinese women for five age groups (i.e. 15-19, 20-24, 25-29, 30-34, 35-39, 40-44 and 45-49 years old) and for each of five-year periods (2005-2010, 2010-2015, …, 2095-2100). We use the projections corresponding to the UN medium-variant scenario (14) which indicate that while during the period 2005-2010 fertility was highest among women aged 20-24 years old, in the year 2095-2100 those aged 30-34 will be most fertile.

From the UN estimates we obtain a normalized national fertility rate of women aged x years old in year t β t ( x ) by dividing the UN estimated age-specific fertility rate for such age-group by the sum of UN fertility rates for all groups as follows:

β t ( x )=FR tUN

( x )

∑y=15

49

FRt UN( y )

(8)

Where x=15 ,16 ,…, 49. FRtUN(x ) is the national age-specific fertility rate of the women

population in age x for year t from the UN estimates.China’s normalized fertility rates during 2010-2100 are shown in Figure S4.

b. Provincial fertility patterns during 2010-2100We assume that changes in age-specific fertility observed in each province will be the same as

those projected at the national level for 2010-2100. This means the change of normalized age-specific fertility rate in each province i will be the same as the change in normalized age-specific fertility rate at a national level. Based on this assumption, the normalized age-specific fertility rate in province i for women of age x years old for year t is:

α it( x )=

β t ( x )β2010 ( x ) (9)

Where β2010 ( x ) and β t ( x ) are the national normalized age-specific fertility rates for women of age x for years 2010 and t . x=15 , 16 , …, 49.

The normalized age-specific fertility rate in province i for women aged x years old, at year t is:

β it( x )=

β i2010( x )× α it

( x )

∑y=15

49

(β i2010( y ) × αit

( y ) )=

FRi2010( x )

∑y=15

49

(FRi2010( y ) )

×α it(x )

∑y=15

49

( FRi2010( y )

∑y=15

49

( FRi2010( y ) )

× α it( y ))

(10)

Where β i2010( x ) is the normalized age-specific fertility rate in province i in age x for year 2010;

FRi2010( x ) is the age-specific fertility rate for women of age x in province i for year 2010.

x=15 ,16 ,…, 49.c. Provincial age-specific fertility rate for women between 15 and 49 years old considering the

fertility pattern changeThe age-specific fertility rate (for women ages x=15 , 16 , …, 49) in province i at year t is

obtained by multiplying provincial TFR and the provincial normalized age-specific fertility rate:

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FRit(x )=TFRit × β it

( x ) (11)

4 Assumptions of Mortality Rate during the Period 2011-2100We assume an increase in life expectancy as estimated by the United Nations (United Nations,

2017b), and hence adjust the provincial age-specific mortality rates for males and females accordingly. The age and sex specific mortality rates for years 2011-2100 are estimated by combining information on 1) age and sex specific provincial mortality rate in the base year 2010, and 2) changes in national mortality rates for 2010-2100 estimated by the UN. The method is as follows:

Changes in national and provincial mortality rates during 2010-2100The United Nations (2017b) estimate future China’s age-specific mortality rates for each of

five-year periods (2005-2010, 2010-2015, …, 2095-2100). We use the projections corresponding to the UN medium-variant scenario (United Nations, 2017a) as shown in Figs. S5-S6.

Based on these estimates we calculate the expected changes in national age-specific mortality rate for each year in the period 2011-2100. The change in the mortality rate for Chinese males aged x years old, occurring between year 2010 and year t is:

γmt( x )=

MDRmt UN ( x )MDR m2010UN ( x )

(12)

Where MDRm2010 UN ( x ) is the national mortality rate for males of age x years old, observe in year 2010 from the UN estimates and MDRmt UN ( x ) is the UN estimate for year t .

We assume that future changes in mortality rates in each province will be the same as those projected at the national level for the period 2010-2100. Therefore, the change in mortality rate for males of age x years old, in province i occurring between year 2010 and year t is:γm, it ( x )=γmt

( x ) (13)

Provincial age-specific mortality rate considering the increase in life expectancyThe provincial age-specific mortality rate for year t is obtained by multiplying the change in

provincial age-specific mortality rate expected for year t and the provincial age-specific mortality rate in the base year. Hence, the mortality rate for males aged x years old, in province i at year t is:MDRm, it

( x )=γm, it( x ) × MDRm , i2010

( x ) (14)Where MDRm, i2010

( x ) is the age-specific mortality rate for males aged x years old, observed in province i during the year 2010.

The provincial age-specific mortality rate for females during each year in the period 2010-2100 is calculated in the same way.

5 Assumptions on sex ratio at birth during the period 2011-2100Assumptions on national boy/girl birth ratio

China’s ratio of males to females at birth was 1.21 in 2010 (NBS, 2011), significantly higher than the world’s average level. Changes in family planning policy (Howden & Zhou, 2015) and other socio economic factors suggest this ratio will gradually approach a number closer to 1.07 in

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2030, which is the anticipated goal of sex ratio at birth (State Council of the People's Republic of China, 2016).

We assume that the national birth ratio will linearly decrease from its current levels to 1.07 in year 2030, and remain constant thereafter. Estimates of the sex ratio at birth for 2010-2100 for each province are obtained as a function of 1) provincial sex ratio at birth in the base year 2010, and 2) the estimated national sex ratio at birth for years 2010-2100.

Obtaining provincial boy/girl birth ratios from national estimatesWe assume the provincial sex ratio at birth will trend towards the value of 1 at a speed that

depends on the ratio observed in year 2010, relative to the overall ratio for China. Therefore, provinces that had in 2010 a sex ratio equal to the Chinese level of 1.21, will reach a ratio of 1.07 in 2030 (i.e., equal to the Chinese level for that year). Provinces with current ratios closer to 1, will approach 1 in 2030. In other words, the relationship between the provincial ratio of males to females at birth in year M i2010 and that ratio in year 2030, M i2030 is:Mi2010

−11.21−1

=M i2030

−11.07−1

(15)

This is equivalent to

M i2030=1+

(M i2010−1 )×(1.07−1)1.21−1

(16)

The ratio of males to females at birth in province i for years t=2011 ,2012 ,... , 2029 is

M it=M i2010

+(M i2030

−M i2010)×( t−2010)

2030−2010 (17)

The ratio of males to females at birth in province i for years t=2031,2032 , …,2100 will be the same as the ratio in year 2030:M it

=M i2030 (18)The provincial ratio of males to females at birth in years 2010 and 2100 is shown in Figure S7.Finally, the percentage of boys among all births in province i for year t during the period

2010-2100 can be expressed in terms of the projection of ratio of males to females:

Rit=

M it

1+M it

(19)

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Fig. S1. Graph of the cohort-component model used to estimate population change.

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Fig. S2. Total population in 31 Chinese provinces at the end of year 2010 (data from the 6 th

National Population Census NBS).

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Fig. S3. Provincial TFR in years 2010 and 2100 under five scenarios.

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15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 490

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09 2005-2010

2010-2015

2015-2020

2020-2025

2025-2030

2030-2035

2035-2040

2040-2045

2045-2050

2050-2055

2055-2060

2060-2065

2065-2070

2070-2075

2075-2080

2080-2085

2085-2090

2090-2095

2095-2100Age

Fig. S4. China’s normalized fertility rates during 2010-2100 projected by the UN medium-variant scenario.

1

1 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100+

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9 2005-20102010-20152015-20202020-20252025-20302030-20352035-20402040-20452045-20502050-20552055-20602060-20652065-20702070-20752075-20802080-20852085-20902090-20952095-2100Age

Fig. S5. China’s mortality rate pattern of male during 2010-2100.

1

1 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100+

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9 2005-20102010-20152015-20202020-20252025-20302030-20352035-20402040-20452045-20502050-20552055-20602060-20652065-20702070-20752075-20802080-20852085-20902090-20952095-2100Age

Fig. S6. China’s mortality rate pattern of female during 2010-2100.

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Fig. S7. Boy/girl birth ratio in Chinese provinces for years 2010 and 2100.

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Table S1. Generation of different scenarios of national TFR.Scenario National TFR

1. Low 1.18 during 2011-2100. Equal to the current TFR as reported in the 6th Population Census (NBS, 2011)

2. Low to Mid-high

Linearly increasing from 1.18 in 2010 to 1.80 in 2020; and then remaining at 1.80 during 2020-2100. 1.8 corresponds to the projections from the State Council of the People's Republic of China (S. C. o. t. P. s. R. o. China, 2016)

3. Middle 1.60 during 2011-2100. Equal to the current TFR as estimated by the World Bank (Bank, 2018)

4. Middle to Mid-high Linear increasing from 1.60 in 2010 to 1.80 in 2020; and then remaining at 1.80 during 2020-2100

5. High 2.10 during 2011-2100. A TFR of 2.1 corresponds to the replacement rate

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ReferencesAttane, I., & Minglei, S. (1999). Birth rates and fertility in China. How credible are recent data? Population: An

English Selection, 11, 251-260. Badkar, M. (2012). Ending one-child policy is China's priority. Retrieved from https://www.pri.org/stories/2012-

11-16/ending-one-child-policy-chinas-priorityBank, W. (2018). Total Fertility Rate. https://data.worldbank.org/indicator/SP.DYN.TFRT.IN?locations=CNChai, L., & Xu, Z. (2016). Forecast of China Population under Different Fertility Policy. Open Journal of Social

Sciences, 4(07), 213. China, N. B. o. S. o. (2013). 2010 Population Census. http://www.stats.gov.cn/english/Statisticaldata/CensusData/China, S. C. o. t. P. s. R. o. (2016). Plan for China’s population development (2016-2030). Retrieved from

http://www.gov.cn/zhengce/content/2017-01/25/content_5163309.htm.Guo, Z. (2012). The low fertility rate is the major demographic risk in China. China Economic Journal, 5(2-3), 65-

84. Howden, D., & Zhou, Y. (2015). Why Did China's Population Grow so Quickly? The Independent Review, 20(2),

227-248. inc., i. s. (2017). Stella. Retrieved from https://www.iseesystems.com/store/products/stella-architect.aspxNBS. (2011). 6th Population Census of the People’s Republic of China. Retrieved from: http://www.stats.gov.cnState Council of the People's Republic of China (2016). National Population Development Plan in China (2016-

2030). http://www.gov.cn/zhengce/content/2017-01/25/content_5163309.htm. In Chinese.Times, N. Y. (2013). Adjusting the data from the Chinese census (挤干中国人口普查数据中的水分). Retrieved

from https://cn.nytimes.com/opinion/20130306/cc06population/United Nations, D. o. E. a. S. A., Population Division. (2017a). 2017 Revision of World Population Prospects.

Available from United Nations, Department of Economic and Social Affairs, Population Division 2017 Revision of World Population Prospects https://esa.un.org/unpd/wpp/

United Nations, D. o. E. a. S. A., Population Division. (2017b). World Population Prospects: The 2017 Revision, DVD Edition. Retrieved from

Wilson, C. (2004). Fertility below replacement level. Science, 304(5668), 207-209.

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