An Assessment of China’s Fertility Level Using the Variable-r Method

Abstract

The fertility level in China is a matter of uncertainty and controversy. This paper applies Preston and Coale’s (1982) variable-r method to assess the fertility level in China. By using data from China’s 1990 and 2000 censuses as well as annual population change surveys, the variable-r method confirms that Chinese fertility has reached a level well below replacement.

The current fertility level in China is a matter of considerable controversy (Guo and Chen 2007; Lavely 2001; Retherford et al. 2005; Scharping 2007; Zhang and Zhao 2006). The reported total fertility rate (TFR) was 2.3 in China’s 1990 census and dropped below replacement level in the early 1990s (Feeney and Yuan 1994; Zeng 1996).1 Since then, the TFR has remained at about 1.5, with a low of 1.22 reported in the 2000 census, according to the age-specific fertility rates published in the China Population Statistical Yearbook (National Bureau of Statistics of China [NBS] 1991–2006). A TFR of 1.5 is not only well below replacement but it is also among the lowest national rates in the world. Many believe that China’s reported fertility level is too low to be accurate and attribute this rate to the deterioration of the Chinese statistical system, claiming that a large number of births—particularly out-of-plan births (births without an official quota)—are underreported in official enumerations (e.g., Liang 2003; National Population and Family Planning Commission of China [NPFPC] 2007; Zhang and Cui 2003). Others maintain that fertility in China is indeed well below replacement level (e.g., Guo 2004; Retherford et al. 2005; Zhang 2004).

This paper applies Preston and Coale’s (1982) variable-r method to assess China’s fertility level. The variable-r method offers a simple and robust estimate of the net reproduction rate (NRR). Unlike traditional fertility-estimation methods, which often require detailed birth records, the variable-r method requires only the relative age distribution in two enumerations and the proportional birth distribution, both of which are readily available for China.

I begin with a brief review of the debate over the current fertility level in China, followed by a discussion of the variable-r method. Because the application of the variable-r method requires that the data from two enumerations have the same completeness of coverage, I assess whether major changes in enumeration coverage occurred between the 1990 and the 2000 censuses. Comparison of census and population sample survey data suggests that the 1990 and 2000 census data are comparable in coverage, which justifies the usage of variable-r method. This research confirms that Chinese fertility has reached a level well below replacement.

ASSESSING THE CURRENT FERTILITY LEVEL IN CHINA

A government-prescribed fertility transition in China began in the early 1970s. Observed TFR dropped by more than half in 10 years, from 5.8 in 1970 to 2.7 in 1979 (Coale and Chen 1987; Yao 1995), a great success of China’s “later, sparser, and fewer” program (Scharping 2003) that urged couples to marry later, to increase the length of birth intervals, and to have no more than three children. In the 1980s, even with a much more restrictive one-child policy, observed TFR oscillated around 2.5 (Feeney and Wang 1993). The early 1990s brought a sudden drop in TFR, dropping to 1.65 in 1991 and then lower to 1.52 in 1992 (Yao 1995). These lower numbers represented a great departure from the TFR of 2.3 reported in the 1990 census. The observed fertility level stayed around 1.5 through the 1990s, and the 2000 census recorded a new low of 1.22. The 2004 and 2005 annual population surveys reported slightly higher TFRs of 1.45 and 1.34, respectively. The fertility trend in China from 1970 to 2005 is portrayed in Figure 1.

Figure 1.

Reported Total Fertility Rate: China 1970–2005, Unadjusted

Sources: Guo (2004); NBS (1995–2006); Yao (1995).

Notes: Data for 1970–1992 are from Yao’s (1995) compilation: 1970–1981 data are based on the 1982 National One-per-thousand Population Sampling Survey on Fertility; 1982–1987 data are based on the 1988 National Two-per-thousand Population Sampling Survey on Fertility and Contraceptives; 1988–1992 data are based on the 1992 Fertility Sampling Survey in China; 1993 data are from Guo (2004), which is based on the 1997 National Survey on Fertility and Reproductive Health; 1994–2005 are from China Population Statistical Yearbook (NBS 1995–2006).

Both the sharp drop in fertility and the very low level observed after 1990 raised suspicions of underreporting (Feeney and Yuan 1994; Goodkind 2004; Liang 2003; Zeng 1996). The suspicions were grounded on four significant circumstances.

First, data evaluations indicate that a considerable proportion of births and children go uncounted in Chinese censuses and surveys. For example, Feeney and Yuan (1994) found that the 1992 fertility survey missed between 10% and 20% of births. Zeng (1996) estimated an underreporting rate of between 25% and 28%. A comparison of 1990 census and 2000 census data yields an estimate that 13.68% of infants (age 0) were not enumerated in the 1990 census (Zhang and Cui 2003).

Second, the reported fertility level is close to or even lower than the level implied by policy. Birth-planning policy is fragmented by local administrations and tailored to local conditions (Greenhalgh 1986; Peng 1991; Short and Zhai 1998). Gu et al. (2007) estimated that the literal implementation of these local policies would imply a national TFR of around 1.47. Fertility at or below this level implies a perfect execution of the policy, which contradicts the general impression of difficulties in policy implementation and numerous reports of local resistance and policy breaches.

Third, the low fertility rates reported in China seems to be at odds with Chinese traditions. Although the socioeconomic transformation of the post-Mao era greatly improved living standards, China is still largely a developing county with very limited social welfare programs. It is thus expected that the Chinese, particularly those living in rural areas, would continue to have at least moderate fertility demands in order to continue the family line and to secure old-age support.

Fourth, after consistently observing a TFR of 1.6 or lower for 15 years (1991–2005), the Chinese government still cites a total fertility rate of 1.8, which is below replacement level but higher than that observed (NPFPC 2007). Official estimates are presumably backed by data yet to be disclosed, if not based on political considerations.

Virtually every demographer agrees that underreporting exists in China’s population and fertility data. Underreporting is neither a new nor a uniquely Chinese phenomenon (Anderson 2004). The debate concerns the level of underreporting and how reported fertility should be adjusted. Efforts to estimate fertility level in China have concentrated on “recovering” uncounted births with various techniques, such as reverse-projection by using aggregate data, birth history reconstruction by using household records, and estimating birth cohort size based on school enrollment (e.g., Ding 2003; Guo 2004; Retherford et al. 2005; Zhang 2004; Zhang and Cui 2003). Preston and Coale’s (1982) variable-r method provides an alternative.

THE VARIABLE-r METHOD

As an application of the Generalized Population Model (Lahiri 2004; Preston and Coale 1982), the period net reproduction rate (NRR) can be expressed as a function of age-specific growth rates and the proportionate age distribution of mothers at childbirth. In Eq. (1), υ(a) denotes the proportionate age distribution of mothers at childbirth; r(x) denotes the agespecific growth rate; and α and β specify the beginning and end of women’s reproductive age range, which is assumed to be 15 and 49, respectively. Estimation of NRR in this way constitutes the variable-r method:

$$NRR={\int }_{\alpha }^{\beta }\upsilon (a)e^{{\int }_0^{a}r(x) dx}da.$$ (1)

The beauty of the variable-r method is its simplicity and robustness. It captures the NRR “without any reference to underlying fertility or mortality” (Preston, Heuveline, and Guillot 2001:176). Both υ(a) and r(x) can be easily estimated from censuses and surveys. Applications of this method yield very robust results. For example, estimates using Swedish data from 1973 to 1977 produced an error of less than 1% in each year compared with the NRR computed from age-specific fertility and mortality rates (Preston and Coale 1982). Using Japanese data between 1995 and 2000, the variable-r method produced exactly the same value of NRR as the traditional method (Preston et al. 2001).

Apart from its simplicity and robustness, an attractive feature of the variable-r method is its relaxed data requirements. The success of using traditional methods for fertility estimation relies on the accuracy of enumeration (or adjustment) of births and of women of reproductive age. The variable-r method relaxes data requirements in several respects. First, the population age structure required by the variable-r method is the relative age distribution—that is, the age-specific growth rate. Even in the event of substantial underreporting, if two enumerations have similar characteristics of underreporting, the fertility estimate yielded by the variable-r method would closely resemble the results derived from a complete enumeration. Second, instead of focusing on one birth cohort, the variable-r method makes use of the full age distribution from birth to the end of reproduction, thus providing a more stable measure of fertility. This more stable measurement occurs not only because using full age distribution smoothes out irregularities in individual ages but also because data quality is generally better in ages beyond the infant and child ages, particularly in Chinese census data. Third, the variable-r method uses the age structure of females only. Enumeration of females is less sensitive to the accounting of the military population, which is a significant problem in Chinese census data (Coale 1984).

In addition, using the variable-r method produces a reproductive measure that is central to the concept of replacement fertility. NRR measures the number of daughters that a hypothetical cohort of newborn baby girls would bear during their lifetime. An NRR of 1.0 means that a female population subjected to set fertility and mortality schedules would exactly reproduce/replace itself. The NRR is thus essential to the idea of replacement-level fertility. By contrast, the evaluation of replacement-level fertility using the TFR needs to take both mortality level and sex ratio at birth explicitly into account. This would be a particular problem in the Chinese context, in which elevated sex ratios at birth and gender-biased mortality (Cai and Lavely 2003) make the comparison of fertility to the replacement level sensitive to assumptions about mortality and sex-selective behaviors.

NRR is the sum of the product of the maternity function m(a) and the survival function p(a) (Eq. (2)). The maternity function m(a) is the age-specific fertility rate of female births. NRR can be converted to TFR by using a well-known approximation shown in Eq. (3), in which SRB is the sex ratio at birth (males per one female) and p m (m̄) is the probability of surviving to the mean age of the maternity function (Preston and Coale 1982). I use Eq. (3) to compare NRR with the more commonly used TFR.

$$NRR={\int }_{\alpha }^{\beta }m(a)p(a)da$$ (2)

$$TFR=\frac{(1+SRB) · NRR}{p(\overline{m})}$$ (3)

Like any other demographic method, even with its more relaxed data requirements, the variable-r method is still sensitive to data quality, particularly the data quality for young ages. Although the growth rate is calculated for each age group, the growth rates for younger age groups have a disproportional effect on the fertility estimate because the effect of growth is cumulative. As Preston and Coale (1982:248) noted, the variable-r method is mainly subject to two kinds of reporting errors: from changes in the patterns of age misreporting, and from differences in completeness of coverage. Age misreporting is less a problem for the Chinese data, as has been shown by various demographic exercises (Banister and Hill 2004; Coale 1984; Coale and Banister 1994). I consider in detail whether a difference in coverage exists across Chinese censuses.

The data required for estimating NRR by the variable-r method are readily available from Chinese censuses and surveys: the National Bureau of Statistics of China (NBS) publishes population age structure and age-specific fertility data in annual volumes of the China Population Statistical Yearbook, which is based upon censuses and annual population change surveys. Following the steps laid out in Preston et al. (2001), I approximate the integration in Eq. (1) by summation of variables calculated for five-year age groups, as shown in Table 1.

Table 1.

Computing NRR Using the Variable-r Method, China 1990–2000

Age x	5Px (1990) million (1)	5Px (2000) million (2)	5Bx million (3)	5rx (4)	eSx (5)	5νx (6)	5νx · eSx (7)
	0	55.4	31.3		−0.0551	0.8712
5	47.7	41.8		−0.0127	0.7354
10	47.0	60.1		0.0236	0.7558
15	58.5	50.2	3.7	−0.0149	0.7724	0.0222	0.017
20	61.5	46.6	74.5	−0.0268	0.6959	0.4502	0.313
25	50.8	57.4	69.2	0.0119	0.6703	0.4185	0.281
30	40.2	62.0	14.4	0.0419	0.7668	0.0868	0.067
35	41.8	53.0	2.8	0.0230	0.9020	0.0171	0.015
40	30.4	39.0	0.6	0.0242	1.0151	0.0039	0.004
45	23.2	41.6	0.2	0.0563	1.2414	0.0012	0.001
Sum			165.4			1.0000
NRR							0.698

Sources: NBS (1991–2001); Yao (1995).

Notes: ₅P_x is the female population in five-year age groups; ₅B_x is the number of births to women in five-year age groups; ₅r_x = ln(₅P_x ²⁰⁰⁰/₅P_x ¹⁹⁹⁰) / 10.33 – growth rate in each five-year age group; S_x is the cumulation of ₅r_x to the midpoint of the interval; ₅ν_x = ₅B_x/(Σ₅B_x); and NRR = Σ₅ν_x ·e^Sx. Population age structures are taken directly from the two censuses. The age distribution of birth is calculated from pooled birth data from 1990 to 2000: 1990 and 2000 are from the 1990 and 2000 censuses, 1994–1999 are from the annual population surveys, and 1991–1993 are derived from the age structure of women from the annual population surveys and the age-specific fertility data from the 1992 fertility survey.

The variable-r method produces an estimate of NRR of 0.698 between the 1990 and 2000 censuses, which is 30% below the replacement level. This calculation assumes that the 1990 and 2000 censuses have similar coverage. In light of the suspected problem of underenumeration, this assumption needs to be critically evaluated.

UNDERREPORTING IN THE 1990 AND 2000 CENSUSES

Population data from China were once praised for their high quality (Coale 1984). Data accuracy benefited from the fact that the Chinese have good knowledge of their date of birth, from the tightly controlled household-registration system, and from a relatively immobile population. Some of the conditions favorable for accurate enumeration have faded with the rise of migration and the pressure to meet birth-planning quotas (Lavely 2001). Nevertheless, Banister and Hill’s (2004:68) close examination of Chinese censuses data found that census coverage for adults (older than age 15) “is generally good” and that “census coverage is estimated to have improved gradually from each census to the next.”

Figure 2 shows the intercensal survival ratios of female cohorts from the 1982 census to the 1990 and 2000 censuses as well as corresponding life table survival ratios. Except for few age groups, most noticeably the age 0–4 cohort in the 1982 census, the three enumerations accord well with the mortality schedules.2 This correspondence confirms the good quality of the 1982 and 1990 census data, relieving some concerns about the quality of the 2000 census data.

Figure 2.

Intercensal Female Cohort Survival Ratios: China 1982, 1990, and 2000

Sources: NBS (1992, 2002); Banister and Hill (2004)

Notes: The life table survival ratios between 1982 and 1990 are based on Banister and Hill’s (2004) adjusted female life table of 1982–1990. The life table survival ratios between 1982 and 2000 are based on Banister and Hill’s adjusted female life table of 1990–2000. Huang and Liu’s (1995) single-year mortality age pattern derived from the 1982 and 1990 censuses are used to convert Banister and Hill’s abridged tables to single-year tables. The 1982 and 1990 censuses had a standard time of July 1; the 2000 census’ standard time was November 1. Linear interpolation is used to line up birth cohorts and to calculate survival ratio of fraction years between 1982 and 2000.

As indicated in Figure 2, the youngest cohorts were underenumerated in the 1982 census. The same was repeated in the 1990 census, and very likely in the 2000 census as well. This is precisely why many suspect that fertility rates were underreported. As is often noted, the main reason behind the underenumeration of infants and children in China is the pressure from the birth-planning policy (Goodkind 2004). Births, particularly out-of-plan births, are underreported not only because parents seek to avoid penalties or to retain the possibility of having another child but also because of strong incentives embedded in China’s bureaucratic institutions. Local government officials are routinely evaluated based on a set of population-control targets, such as birth rate and the one-child rate, as well as economic performance indices that are based on population size (e.g., per capita gross domestic product, or GDP). Meanwhile, population enumeration in China is still largely founded on the household registration system. The link between birth quotas and permission for household registration creates a major obstacle to accurate enumeration because persons lacking official registration are often missed by enumerators. Migration further complicates the enumeration process because a large proportion of migration is not recorded in the household-registration system.

The general assumption is that underenumeration is more severe for young ages because small children are more easily hidden from public observation. As children grow up and become more integrated into society, however, they are more likely to be registered and also more likely to be visible to enumerators. Given that there were no major changes in the motives for underreporting in China—namely, the concealment of out-of-plan births—there is no reason to expect that the underreporting pattern of 2000 would differ dramatically from that of 1990. A thorough evaluation of the completeness of the 2000 census data must await the 2010 census. In lieu of that, I use age-structure data from the 1995 and 2005 1% population sample surveys (mini-censuses) to examine whether major changes in the pattern of underenumeration are observed.

In addition to censuses, China conducts 1% population sample surveys in years ending in 5, and one-per-thousand sample surveys in other years. The questionnaires used in those surveys are very similar to the ones used in the censuses. NBS provides survey results, such as population age structure and age-specific fertility, as well as overall sample proportion in its annual publication of China Population Statistical Yearbook.

To assess the underenumeration pattern of infants and children across enumerations, I compare the five-year survival ratios for ages 0–9 in the 1990 and 2000 censuses with their following 1% surveys (Figure 3).3 The enumeration patterns for ages 2–9 in the two censuses are clearly similar. Compared with the 1990 census, the 2000 census has better coverage for age 0 but worse coverage for age 1. Their effects cancel each other when data are pooled into five-year age groups. When the age groups 0–4 and 5–9 in the two censuses are compared with the same cohorts in the following 1% surveys, they have very similar underreporting rates. In other words, I find no major change in the pattern of underenumeration between the two censuses that would affect the application of the variable-r method.4

Figure 3.

Survival Ratios of Females Aged 0–9 From Census to the Following 1% Survey (Mini-Census): 1990–1995 and 2000–2005

Sources: NBS (1992, 1996, 2002, 2006); Banister and Hill (2004).

Notes: The cohort sizes of 1995 and 2005 are adjusted with the adjusted sample proportion described in Footnote 1 (1.101% and 1.538%, respectively). The cohort size of 2000 is adjusted by relative completeness of the 1990 and the 2000 censuses provided in Banister and Hill (2004). The 1990 census used a standard time of July 1; the 1995 survey’s standard time was October 1; the 2000 census and the 2005 survey had a standard time of November 1. Linear interpolation is used to line up birth cohorts and to calculate exact five-year survival ratio between July 1990 and July 1995.

To summarize, Banister and Hill’s (2004) research suggested that the Chinese census data are of reasonable quality and that the 1990 and 2000 censuses have a similar coverage for age 15 and older. My data evaluation confirms the existence of underreporting of infants and children in Chinese census data but finds no major change of underreporting pattern between the two censuses. Given the consistency of Chinese census data, the variable-r method can be appropriately applied to estimate Chinese fertility.

RESULTS

Using unadjusted population data from the 1990 and 2000 censuses, the variable-r method yields an intercensal NRR of 0.698. If I use Banister and Hill’s (2004) estimate of the relative completeness of the two censuses, the NRR decreases to 0.671. The difference between these two estimates is minuscule, and both estimates indicate that fertility in China was more than 30% below replacement level in the 1990s.

To compare the estimated fertility level against the more commonly used TFR, I use Eq. (3) to approximate TFR from the estimated NRR. The approximation can be affected by the assumed values of SRB and the probability for surviving to the mean age of reproduction (p(m̄)). Between 1990 and 2000, the mean age of childbearing fluctuated around 26 years (Guo and Chen 2007). Given China’s current mortality level, the small fluctuation of the mean age at reproduction has only minimal effect on the approximation. The probability of a female surviving from birth to the mean age of childbearing is about 94.1%, according to Banister and Hill’s (2004) adjusted female life table of 1990–2000.

The approximation is more sensitive to the assumption of sex ratio at birth. The observed sex ratio at birth in China increased from 1.113 (boys per 1 girl) in 1989 to 1.169 in 2000, although some proportion of the elevated sex ratio is attributable to sex-selective underreporting (Cai and Lavely 2003; Goodkind and West 2005; Zeng et al. 1993). The approximated TFR corresponding to the unadjusted NRR (= 0.698) is 1.52 if I take the frequently cited normal sex ratio at birth of 1.05, and 1.63 if I take the highest reported sex ratio at birth of 1.20.5 The approximated TFR corresponding to the adjusted NRR (= 0.671) is 1.46 if I take sex ratio at birth of 1.05, and 1.57 if I take the highest reported sex ratio at birth of 1.20. Even at a high level of sex ratio at birth, the TFR in China was still well below replacement. The true sex ratio at birth in China in the 1990s is likely below 1.20 when sex-selective underreporting is taken into consideration;6 thus, the true TFR is likely to fall within the narrow range of 1.5–1.6.

The variable-r estimate of fertility in China between the 1990 and 2000 censuses is in line with the estimates presented by Guo (2004), Retherford et al. (2005), and Zhang (2004), but lower than the officially acknowledged rate. The fact that estimates based on different data and methods produce similar results supports the conclusion that fertility in China has indeed reached a level well below replacement.

Many are now calling on the Chinese government to relax its fertility policy (e.g., Caldwell and Zhao 2007; Yi 2007; Wang 2005).7 One source of resistance to policy change has been the fear that the fertility rate in China is significantly underreported (Jiang 2006). An accumulation of evidence now permits me to conclude with considerable confidence that China’s fertility is indeed at a level well below replacement. Thus, uncertainty about the fertility level should no longer be an impediment to the return of reproductive freedom to China’s citizens.