Too Early Or Too Late: What Do We Learn from a 30-Year Two-Child Policy Experiment

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Too Early or Too Late: What Do We Learn from a 30-Year Two-child Policy Experiment

Preliminary Version: Sep 24, 2015

Yu Qin [email protected] Department of Real Estate National University of Singapore

Fei Wang [email protected] School of Labor and Human Resources Renmin University of China

Abstract There have been heated debates as to whether China should replace One Child Policy with two-child policy to push up the fertility level in the country. However, concerns on the overgrowth of population slow down the pace of One Child Policy relaxation. In this paper, we look into a 30-year two-child policy experiment in Yicheng, Shanxi to examine its impact on crude birth rate. We adopt a synthetic control approach which allows us to conduct a rigorous counterfactual analysis. We fail to find any short-term impact of two-child policy in Yicheng before the 1990s. In the long run, our estimation suggests that the two-child policy may bring around 3 million newborns to China every year, which is significantly lower than the official prediction.

JEL Code: J13, J18

1. Introduction China’s One Child Policy (OCP) is accompanied by low fertility rates after its implementation for more than 30 years. According to the most recent 2010 population census, the total fertility rate (TFR) in China has dropped to 1.18, far below the replacement level. The low fertility level has been accelerating China’s movement towards a challenging aging society. In response to the declining fertility rate, Chinese government took steps to gradually loosen the OCP. For example, the Government announced in November of 2013 that couples can have two children if one parent is an only child. However, China has not yet completely replaced OCP with two-child policy possibly due to concern that population may over-grow upon full relaxation of OCP.

Therefore, it is of great policy interest to understand the impact of replacing OCP with two-child policy on population growth. Predictions made by Zhai, Zhang and Jin (2014) suggest that if there was an immediate transition to a universal two-child policy, the number of annual births would sharply increase with the peak value up to nearly 50 million and a total fertility rate of about 4.5 due to the sudden release of their unrealized demand of the second child. These predictions are based on the population size of the only child below age 30 calculated from the census, and their mothers’ fertility desires collected from different surveys. They also predict that the fertility peak will last for four to five years. In addition, total population will reach around 1.5 billion at the peak, and then gradually decline. However, fertility desires often fail to predict actual fertility behaviors (e.g. Adsera 2006).

Among all these discussions on the potential impact of OCP relaxation, Wu (2014) and Wei and Zhang (2014) look into a unique policy experiment implemented in Yicheng, Shanxi Province 30 years ago. Since 1985, Yicheng, a rural county in the south of Shanxi, was granted with an exception of OCP. It was designated as an experiment locality for two-child policy, where almost all couples had the option to have two children. This unique experiment provides a great opportunity for scholars to investigate the potential consequences of two-child policy from historical data. By comparing the demographics in Yicheng before and after the experiment, the two papers mentioned above conclude that replacing OCP with two-child policy had little impact on crude birth rate.

However, it is statistically challenging to estimate the impact of two-child policy in Yicheng in an unbiased way. On the one hand, the before and after comparison of Yicheng’s birth rate may not be able to generate the pure effects of the changing population policy due to possible impact of changes in other determinants of fertility. On the other hand, it is also not easy to carry out a traditional difference-in-difference (diff-in-diff) analysis, which accounts for the before-after differences in the jurisdictions serving as a control group to Yicheng, mainly for two reasons. First, inference on diff-in-diff is likely to be biased if the number of treatment units is small.

Second, the control and treatment units must hold parallel growth trend in terms of the outcome variables before the policy experiment, which is referred to as the “parallel trend assumption” in the diff-in-diff framework. However, as suggested in our data, the birth rates in Yicheng and other control counties had significantly different growth patterns, which violates the assumption.

In this paper, we adopt the synthetic control approach to re-examine Yicheng’s two-child policy experiment. The synthetic control method is most suitable for comparative case studies, where there is only one or a few treated units. Positive weights are assigned to a number of control units from a donor pool of counties in the same province, such that the weighted average birth rates of the selected control counties can best mirror Yicheng’s birth rate trend prior to the two-child policy, and the weighted averages of fertility’s determinants from the control counties are also be able to match the counterparts in Yicheng before the treatment. The construction of synthetic control units to the treatment group provides rigorous counterfactual analysis to evaluate policy effectiveness.

Comparing the crude birth rate in Yicheng to a “synthetic Yicheng”, we find that during 1985-1990, the first six years’ implementation of the two-child policy, the birth rate in Yicheng was not significantly different from other counties and districts within the same province, which is likely to be attributed to the weak enforcement of two-child policy in Yicheng and OCP in other counties during that time. However, the impact unveils in the long run with strictly enforced policies, as revealed from the inference using the 2000 and 2010 population census. It is estimated that the two-child policy may bring around 3 million newborns to China every year in the long term, as an upper bound.

This paper is among the first to conduct rigorous counterfactual analysis on the potential impact of OCP relaxation on birth rate using a two-child policy experiment, and is likely to provide important policy reference for the further relaxation of OCP nationwide. Our analysis suggests that replacing OCP with two-child policy may have little impact on crude birth rate in the short run. The long run impact, if there is any, is also rather limited comparing to the prevailing estimated magnitude. Considering that our estimation is likely to be an upper bound of the true impact, the relaxation of OCP may have very limited impact on China’s birth rate and fertility level.

The rest of the paper is organized as follows. Section 2 introduces the background of Yicheng’s two-child policy experiment; Section 3 provides a conceptual framework to think through the potential impact of OCP relaxation; Section 4 describes the data used in this paper; Section 5 introduces the empirical strategy; Section 6 presents the main findings; Section 7 conducts a few robustness checks; Section 8 concludes.

2. Policy Background

China began to implement OCP in 1980. A married couple could generally have at most one child.1 However, OCP was difficult to enforce nationwide, especially in rural areas, as the policy significantly reduced household labor force for agricultural production. In addition, son preference was more prevalent in rural areas. Birth controls consequently reduced their chances of having a son. Observing the realities of OCP implementation in rural areas, Chinese authorities relaxed OCP in the mid-1980s, allowing a rural married couple to have a second child if the first child is a daughter, on the premise of a sufficiently long spacing between the two births (Yang 2004, pp. 136-137).2

Some scholars proposed alternative solutions. In the spring of 1984, Liang Zhongtang, who was at that time a demographer at the Shanxi Province People’s Government Economic Research Center, proposed a two-child policy with certain restrictions, including late marriage and increased birth spacing. With his effort on advocating for the policy, the provincial government allowed Yicheng, a county in Linfen prefecture city to replace OCP in 1985 with the two-child policy proposed by Liang. Figure 1 shows the location of Shanxi province in China and the location of Yicheng in Shanxi. Shanxi is in the middle of North China, and Yicheng locates in South Shanxi.

In fact, Yicheng was not chosen at random. In an interview,3 Liang summarized three reasons for selecting Yicheng as a pilot for the experiment. First, it was more difficult to enforce OCP in the rural areas as compared to cities. Therefore, it made more sense to implement the two-child policy in a county with a large share of rural population. Back to 1985, over 90% of Yicheng’s population lived in rural areas. Second, Yicheng had railroad access, therefore it would provide more convenience for the implementation of the program. Lastly, Yicheng’s cadres and rural residents welcomed and supported the pilot experiment.

The two-child policy in Yicheng includes the following measures: 1) all couples are encouraged to delay marriage, to postpone parenthood and to have fewer children; 2) the “one-child-per couple” norm should be enthusiastically promoted; 3) rural one child families will be offered financial incentives (financial rewards and preferential access to education and health services); 4) state employees and urban couples are limited to one child only, except under special circumstances; and 5) rural couples fulfilling these requirements can have two children: a) they should marry three years later than the minimum age at marriage as specified in The Law of Marriage (men at 22 and women at 20); (b) the wife should have a first birth at 24 and have a second birth at 304 (the requirement of birth spacing was adjusted from 6 years to 4 years in 2007); (c) the wife should apply for a birth permit for her second birth and wait for a

1 Wang (2014) introduces more about OCP and its earlier policy versions, as well as their effects on fertility. 2 Urban residents and rural residents with the first birth being a son were generally subject to the one-child birth quota as before. Therefore, we still refer to the policy as OCP. 3 Jiao, H. (2012, August 21). Interview Liang Zhongtang, a Family Planing Expert and Demographer. Legal Weekly. Retrieved September 19, 2015, from http://www.legalweekly.cn/index.php/Index/article/id/718. 4 Women who only want one child do not have to marry late and give the birth late.

4 quota; and (d) couples should take effective contraception after a first birth and must accept sterilization after a second birth. Births beyond the second child are strictly prohibited without any exception, otherwise subject to financial and disciplinary sanctions. (Wei and Zhang, 2014)

There is limited references to learn about the enforcement of Yicheng’s two-child policy experiment. In the first decade of Yicheng’s experiment, more than half of the second child was without birth permit due to the violation of late marriage or insufficient birth spacing. However, the ratio of unpermitted second child significantly dropped since 1995, and almost to zero in 2010 as late marriage and long birth spacing became much more prevalent (Wu 2014).

Yicheng was the first county implementing the two-child policy experiment, followed by a dozen of more pilot counties, including one jurisdiction in Shanxi, i.e., Xinrong district in Datong prefecture, and a number of others in Liaoning, Heilongjiang, Shandong, Guangdong, Guangxi, Gansu, Qinghai, and Ningxia. However, due to various reasons, most of the pilot programs were cancelled in the early and mid 1990s, except for Yicheng. Therefore, Yicheng is the only county which stick to the two-child policy for 30 years.5

3. Conceptual Framework This paper estimates the impact of the two-child policy on fertility as compared to OCP at the aggregate (county) level, due to the unavailability of disaggregate (individual) data in Yicheng and other counties. The only measure of county fertility levels that is available to us is crude birth rate (CBR, i.e., number of births per 1,000 people in a year). In contrast to the total fertility rate that has been adjusted by the age of females, the CBR of a county is likely to be affected by the gender and age structure of the county (Easterlin 1978). For example, more girls at fertile ages in a county could lead to higher CBR. Therefore, we need to collect information on the shares of population by gender and age in a county in the analysis.

In addition to gender and age structure, Easterlin and Crimmins (1985) summarize three sets of factors which could determine fertility levels: the demand for children, the supply of children and the costs of fertility regulation.

The demand for children is largely driven by socioeconomic factors. At the county level, we consider the share of rural population, economic conditions and education in our analysis. The supply of children is mainly determined by people’s fecundity and the infant mortality rate. Fecundity cannot be directly measured at the county level, but can be broken down to measurable determinants, such as age structure, economic conditions and health variables. These variables are related to nutritional and

5 Chen, X. (2012, August 22). 27 Years of Two-child Experiment in Yicheng.Legal Weekly. Retrieved September 19, 2015, from http://www.legalweekly.cn/index.php/Index/article/id/719

5 biological determinants of fecundity (Frisch 1982; Wood 1989). The data of infant mortality rate is unavailable, but can be approximated by health factors.

The costs of fertility regulation include people’s attitudes towards family planning, the accessibility of fertility control methods and supplies, and penalties from violating family planning policies. We assume that the differences in the costs of fertility regulation between Yicheng and other counties are primarily accounted for by their different family planning policies. The policies also differ between urban and rural areas, and between ethnic majority Han people and minorities (Wang 2014). Therefore, the residential and ethnic structure of population needs to be considered as well, so that the differences in policy intensities between Yicheng and other counties are only generated from the distinct policies rather than the residential and ethnic population structure. Thus, we need to consider the share of rural population and the ethnic population structure in a county in the analysis. However, the county level ethnic population structure is not available. It is unlikely to be a problem in our study as Shanxi province, where Yicheng locates, has been keeping extremely low fractions of ethnic minorities in the past decades.6

In addition, people’s tastes and culture may also affect birth rates, no matter in China (Arnold and Liu 1986), or in other countries (Fernández and Fogli 2006). We consider these factors in our analysis either by proxying them with the best available observed variables, or assuming the unobservables are similar between Yicheng and other counties if appropriate.

4. Data Sources As stated above, our main variables of interests are county level CBR and its determinants in Shanxi province. We restrict our data to the counties in Shanxi for two reasons. First, the number of counties in Shanxi is large enough for a comparative case study; second, the unobservables at the county level are likely to be more similar within the same province. It is worth noting that the average CBR over years in Shanxi is very similar to the national average, suggesting the representativeness of Shanxi in studying the relaxation of OCP (Figure 2).

We collect CBR and crude death rate (CDR, number of deaths per 1,000 people in a year), treated as a health variable, for all the 116 counties and districts in Shanxi from 1949 to 1990 from the published book “40 years of population in Shanxi: 1949-1990”. The data availability varies across jurisdictions. The shortest panel contains the population measures from 1972 to 1990, while the longest panel records both variables since 1949. Among the 116 counties, we dropped Xinrong district in Datong prefecture from our sample as Xinrong was once assigned as one of the localities implementing two-child policy during late 1980s and early 1990s, which may

6 The 1953 census of China showed that the percentage of ethnic minorities in Shanxi was only 0.14%. In the 2010 census, the figure slightly rose to 0.26%.

6 contaminate our estimation. In addition, we made adjustments accordingly to correct for the administrative unit changes during our sample period.7 In order to look into the long term impact of Yicheng’s two child policy, we also collect the CBR and CDR for all the counties in Shanxi from the 2000 and 2010 population census.8

In addition to CDR, we also need other predictors of CBR. Based on the literature as discussed in the above section, we include the following sets of variables: 1) population by age cohort (age 0-14, 15-59 and 60 and above) and gender for each prefecture from the 1982 population census. As the age by gender population is not available at the county level, we assume that the age-gender structure in each county is the same as the prefecture that it is affiliated to.9 In addition, we use the population by gender in each county from 1949-1990 to complement the prefecture level age-gender structure, which is collected from “40 years of population in Shanxi: 1949-1990”. All these variables aim to control the variations of CBR that are generated from the differences in age-gender structure; 2) other indicators include the share of agricultural population, GDP per capita, rural personal income, number of elementary schools per 1,000 people, number of middle schools per 1,000 people and number of hospitals per 1,000 people. For districts and counties in Linfen prefecture, which Yicheng is affiliated to, we collect these variables at the county level from “50 years of Linfen”, a statistical publication presenting yearly statistics for all the jurisdictions in Linfen prefecture. For other counties and districts, we can only collect the share of agricultural population at the county level, from the “40 years of population in Shanxi: 1949-1990”.10,11 The rest of these variables are only available at the prefecture level, collected from “60 years of Brilliant Shanxi province”.12 Again, we assume that these variables in each county have the same value as the prefecture that it is affiliated to.

5. Empirical Strategy Figure 3 presents the trend of CBR in Yicheng and other 114 districts and counties in Shanxi province. It is clearly suggested that the growth pattern of CBR in Yicheng is

7 We removed Yanbei District from our sample, which was withdrawn in 1993, and reassigned the ten affected counties to their corresponding prefectures based on current administrative hierarchy. Specifically, we assigned Tianzhen, Yanggao, Guangling, Lingqiu, Hunyuan, Zuoyun and Datong county to Datong prefecture, and Huairen, Ying county and Youyu to Shuozhou prefecture. 8 There are quite a number of administrative changes in the 2000 and 2010 population census as compared to earlier data, especially in the urban districts. If the administrative boundary did not change, we simply matched the new jurisdiction name with the old name. In addition, we made the three further changes: 1) we match the weighted average of Jinyuan district and Xiaodian district in Taiyuan prefecture to the old Nanjiao district in Taiyuan; 2) we match the weighted average of urban district and suburb district in Changzhi prefecture to the old urban district in Changzhi; 3) we match the urban district and Zezhou county in Jincheng prefecture to the old urban district in Jincheng. 9 The ten counties administered by Yanbei district, which was cancelled thereafter, were assigned with the values of Yanbei district. 10 The data for urban districts in Taiyuan, Yangquan and Datong is missing. We impute these values using the share of agricultural population in the whole prefecture as a proxy. 11 The data in Gujiao city in Taiyuan is missing. We infer the value based on the share of agricultural population in Taiyuan prefecture the other the jurisdictions in Taiyuan. 12 The data in the three books, “40 years of population in Shanxi: 1949-1990”, “60 years of Brilliant Shanxi province”, and “50 years of Linfen” are all sourced from local statistical authorities.

7 very different from the rest of the province. First, the CBR in Yicheng was significantly below the average CBR in other jurisdictions. In addition, the growth of CBR is also different in Yicheng comparing to other jurisdictions. A formal test of the differences between Yicheng and other jurisdictions is carried out using a diff-in-diff analysis. Using the data of 115 counties in 1972-1990, 2000, and 2010, we regress CBR on county dummies, year dummies, and the interactions of Yicheng and year dummies. 13 Figure 4 reports the 95% confidence band of the coefficients of interactions, with the interaction in 1984 as the baaseline group. Almost all the coefficients are significantly negative before year 1985, indicating a significantly larger CBR gap between Yicheng and other counties in these years compared to 1984. In addition, any pair of coefficients in adjacent years before 1985 are significantly different from each other, which clearly suggests different growth patterns for Yicheng and the rest of the province. Therefore, the estimated impact of two-child policy is likely to be biased if we directly implement a diff-in-diff analysis. Moreover, Cameron and Miller (2015) indicate that a diff-in-diff model is likely to be inconsistent if the treated groups are too few compared to the control groups, which is the case in our study.

As diff-in-diff cannot appropriately identify the policy impact of Yicheng’s experiment, we adopt a synthetic control approach which remedies the drawbacks of traditional diff-in-diff. The synthetic control method (see Abadie and Gardeazabal, 2003; Abadie et al., 2010 and Abadie et al., forthcoming) allows us to construct an artificial control group which almost exactly mimics the growth patterns of the treated unit before the policy experiment.

Assume that there are J units. The first unit is the treated unit, and the rest J-1 units are used to construct a synthetic control unit that is comparable to the treated unit. Assume is the dependent variable for unit i in period t. is determined by the following factor model for in the pre-treatment periods. � � � � � = , … � .

� � � � � The factor model allows� time-varying= + � � + effects + of both observables , and unobservables, , which is less restrictive than traditional diff-in-diff models with fixed effects. Suppose there is a set of nonnegative weights � and , such that �, �, … , �� = ∑ � = , for each pre-treatment period � = � � ∑ � � = � . � Then, Abadie et al (2010) show that∑ the= treatment�� = � effect in any post-treatment period t

13 The standard errors are clustered at the county level.

8 would be , as long as the characteristics of the donor pool of counties � are not substantially�� − ∑= different�� from those of Yicheng, and the pre-treatment period used to match Yicheng and its synthetic counterpart is sufficiently long.14

In our study, Yicheng is the treated unit, and the other 114 counties of Shanxi form a donor pool that is used to construct the synthetic Yicheng. Weights are assigned to the donor pool units, such that 1) the CBR of Yicheng is as close as possible to the weighted average of CBR of the donor pool units in each period before year 1985; 2) for each determinant of CBR, its average value over the pre-intervention periods in Yicheng is as close as its counterpart in the weighted donor pool. With such a set of weights, synthetic Yicheng can be constructed from the donor pool, and mirrors Yicheng before the policy intervention in terms of CBR and its determinants.

Our core dependent variable is CBR at the county level. As introduced in previous sections, we include the following variables as predictors. First, we include variables related to gender by age cohort (age 0-14, 15-59, and age 60 and above) population structure. Specifically, we include the share of male and female for the three age cohorts, respectively. It is also worth noting that sex ratio below age 15 may reflect gender preferences in the area to some extent. Second, we include health measures, such as CDR and the number of hospitals per 1,000 people. Third, we include a series of socioeconomic indicators, including a) the share of agricultural population, as CBR in urban and rural areas are different; b) GDP per capita and rural income in natural log form, which measures the income level of a region; c) measures of education level in a region, which is likely to affect CBR, including number of elementary schools and middle schools per 1,000 people. Lastly, Abadie et al. (2010) suggest that controlling for lagged values of dependent variable helps to better fit the trend of dependent variable. Thus we also include historical birth rate from 1972 to 1984 as predictors.

We use 1972-1984 as the sample period to fit the CBR growth trend between Yicheng and the “synthetic Yicheng”, as it is the longest period that is covered by all the 115 counties and districts in Shanxi province.15 We did not include any jurisdictions outside Shanxi province as family planning policies vary in different provinces, making the comparison less convincing. We then use the data from 1985 to 1990 to estimate the short-run impact, the data in 2000 and 2010 to infer the long-run impact.

6. Main Results As shown in Table 1, the synthetic control method delivers positive weights for Kuangqu in Datong prefecture (0.302), Hexi district in Taiyuan prefecture (0.283),

14 Abadie et al (2010) also show that, with such conditions, both observables and unobservables are matched between Yicheng and synthetic Yicheng. 15 Except for Xinrong in Datong which was affected by two-child policy before early 1990s.

Fushan county in Linfen prefecture (0.195), Qinyuan county in Changzhi prefecture (0.184) and Pianguan county in Xinzhou prefecture (0.036). The “synthetic Yicheng” is similar to Yicheng in many aspects, as suggested in Table 2, particularly the birth rates before 1985. The simple average birth rates of the whole donor pool are substantially larger than those in Yicheng, but the synthetic Yicheng matches well with Yicheng in terms of birth rates. However, three predictors are not balanced between the treated and the synthetic control group, including mortality rate per 1,000 people, number of hospitals per 1,000 people, and the share of agricultural population. The “synthetic Yicheng” has lower mortality rate, more hospitals and fewer agricultural population. All these unbalances suggest that the synthetic control group is more urbanized, healthier, and thus likely to have lower birth rate. Therefore, our method may over-estimate the impact of two-child policy on birth rate.

Figure 5 presents the time series of CBR in Yicheng and its synthetic counterpart. Generally speaking, the synthetic control group closely follows the time trend of birth rates in Yicheng before the implementation of two-child policy in 1985. Both the birth rate series show downward trends before 1985, which reflects the effects of both family planning policies and socioeconomic development. The birth rate increased both in Yicheng and the “synthetic Yicheng” during 1985-1990, and then both fell in 2000 and 2010. However, it seems that the synthetic control group fell at a larger magnitude as compared to Yicheng.

One possible reason for the inverse-U patterns of both series is the change in policy enforcement. In Yicheng, as mentioned in previous sections, a large portion of the second births was unpermitted before the mid-1990s, which may result in a fertility boom in the first decade of the two-child policy. After the mid-1990s, unpermitted second births became much less common due to stricter enforcement, which may explain the downward trend in 2000s. For other counties, the Chinese central government relaxed OCP to a one-and-half-child policy in rural areas around the mid-1980s. However, the policy relaxation was not clearly comprehended, so that a number of local authorities and people thought that two children were generally allowed (Yang 2004, pp. 137). This may explain the fertility rise in synthetic Yicheng, and the similarity of birth rates between Yicheng and synthetic Yicheng in the late-1980s. Shanxi legislated on family planning in 1989, and the policy enforcement got stricter thereafter (Yang 2004, pp. 138, 161), which may lead to part of the fertility decline in the 2000s. In other words, the birth rate gaps in 2000 and 2010 may better reflect the differences between the real OCP and the two-child policy.16 The 2000 and 2010 CBR gaps between Yicheng and synthetic Yicheng are 2.35 and 1.97, respectively, indicating that the two-child policy would at most lead to about 2 more births per 1,000 people every year compared to the OCP. Given the 1.4 billion population of China, the two-child policy would at most result in around 3 million more births every year.

16 Another reason for the fertility rise in the late-1980s is that, the generation of baby booms around the mid-1960s reached childbearing ages in the late-1980s.

Our estimate is much smaller than the predictions made by some influential demographers. Zhai, Zhang and Jin (2014) predict that China would have 97 million more births in the first four years of the two-child policy, while our estimate implies at most 12 million more births during the same length of time. However, our estimated magnitude may be somewhat conservative for the short-run impact of two-child policy for two reasons. On the one hand, we cannot precisely capture the sudden release of fertility control in Yicheng immediately after the two-child policy, due to loose enforcement of OCP in synthetic Yicheng in the late-1980s. On the other hand, the suppressed fertility desire in Yicheng in 1985 is likely to be of a less extent than today since two children were allowed prior to 1980.

Due to these two concerns, we re-estimate the potential impact of two-child policy in the first few years with the following two assumptions: first, we assume that the other counties in Shanxi remained CBR levels as low as in year 1984; and second, we assume that the CBR in Yicheng reached its peak, not as recorded in year 1990, but immediately followed the implementation of two-child policy. With these two assumptions, we can mitigate the first concern raised above by re-estimating the upper bound of CBR gaps between Yicheng and its synthetic counterpart in the short run, which is 4.6 births per thousand population, translating into an increase of around 6.4 million population per year. Again, this is still much smaller than the effect estimated by Zhai, Zhang and Jin (2014). Unfortunately, we do not yet have good remedies to address the second concern. However, as fertility declines with age, the impact of supressed fertility desire on CBR is also likely to decline with the years being supressed. Having said that, the fertility peak in the short-run in Yicheng after 1985 may not be so different than nowadays if nationwide two-child policy was to be implemented.

As mentioned in Abadie et al (2010), the results could be driven entirely by chance, therefore we use placebo tests to generate the significance of our estimates. In Figure 6(a), the dark line represents gaps in CBR between Yicheng and synthetic Yicheng over years. We further assume each of the control units to be the treated county, figure out the gaps in CBR between the county and its synthetic counterpart, and plot the gaps with a light line in Figure 6(a). As a number of control units are badly matched with their synthetic counterparts before the treatment, Figure 6(b) only keeps the counties whose pre-treatment MSPE (mean squared prediction error, the average of the squared discrepancies between CBR in a county and in its synthetic counterpart during the period 1972–1984) is not greater than that of Yicheng, reducing the number of counties from 115 to 62. If the CBR gaps between Yicheng and synthetic Yicheng are mainly driven by the two-child policy but not by chance, the dark line should stand above most, if not all, light lines.

In both graphs of Figure 6, Yicheng’s dark line does not stand out among all the light lines. However, in 2000 and 2010, Yicheng’s effects are clearly larger than most of other counties. Table 3 further shows the percentiles of Yicheng’s dark line in each

11 year after the treatment. According to Table 3, Yicheng’s policy effects are not prominent enough during 1985-1990. However, in 2000 and 2010, the effects can be interpreted to be significant at 5% or 10% levels.

7. Robustness Checks The synthetic control approach requires similarities between Yicheng and its donor pool of control counties. If we construct the synthetic Yicheng only on the counties that closely surround Yicheng, the assumption is more likely to hold. Unfortunately, neither the counties in Linfen prefecture, nor the counties in the neighbouring four prefectures of South Shanxi could form a well-matched synthetic Yicheng. Nevertheless, if we further include the counties in the four prefectures of Central Shanxi, a synthetic Yicheng can be well established, and the policy effects are similar to those from all the counties in Shanxi province (Figure 7(a)). Moreover, the robustness check also confirms that, if we exclude the county with the largest weight, Kuangqu in Datong prefecture, a county in North Shanxi, the results remain stable.

The effectiveness of synthetic control method also needs a sufficiently long pre-treatment period.17 The main results presented in previous sections are based on the matching between Yicheng and a donor pool of 114 counties in 1972-1984. During 1970-1984, data remain available to Yicheng and 108 other counties. Figure 7(b) shows the results from the matching between Yicheng and the donor pool of 108 counties in 1970-1984. The quality of matching gets worse, but is still acceptable.18 It turns out that the results remain robust if the pre-treatment period is extended by two years. Unfortunately, further extension of the pre-treatment period cannot yield well-matched results. Compared to literature, it is not improper to argue that the pre-treatment period in our study is long enough.19

8. Conclusion In this paper, we study the two-child policy experiment implemented in Yicheng since 1985. We adopt a synthetic control approach which allows us to conduct a rigorous counterfactual analysis by constructing an “artificial Yicheng” which mirrored the growth of birth rate in Yicheng before the policy experiment. We fail to find any impact of two-child policy in Yicheng before the 1990s which is possibly due to the loose enforcement of two-child policy in Yicheng and OCP in other control counties. However, in the long run, our estimation suggests that the two-child policy may bring around 3 million newborns to China every year, which is likely to be an upper bound due to the differences in socioeconomic factors between Yicheng and its synthetic counterpart.

17 Abadie et al (2010) indicate that the number of pre-treatment periods should be large enough compared to the scale of error term of the factor model. As the scale of error term is immeasurable, there is no clear criterion for determining a proper length of the pre-treatment period. 18 The MSPE of the matching in 1970-1084 is about 4 times the MSPE from the matching in 1972-1984. 19 In the classic example of Abadie et al (2010), the pre-treatment period has 19 years, similar to our best try, 15 years.

The estimated magnitude of two-child policy’s impact on birth rate in our paper is lower than the estimates by some influential demographers, such as Zhai, Zhang and Jin (2014). Based on their estimate, they conclude that the relaxation of OCP is likely to bring 97 million newborns in the short run. But such overgrowth of population would slow down the pace of aging in China. In contrast, our analysis suggests that replacing OCP with two-child policy will have very limited impact on population growth both in the short run and long run, which will also have very limited effect on the age structure of an aging society like China. Therefore, it is not likely to be too early, but probably too late, for a nationwide two-child policy in China.

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Wu, Yanwen. (2014). Preliminary Analysis of A Second-child Experiment on “Later Marry, Later Birth and Longer Interval” in Yicheng County. Population Journal, (4), 103-112. Yang, F. (2004). Historical Research on Family Planning of Contemporary China, Doctoral dissertation, Zhejiang University. Zhai, Z., Zhang, X., Jin, Y. (2014). Demographic Consequences of an Immediate Transition to a Universal Two-child Policy. Population Research, 38(2).

Figure 1. Locations of Shanxi and Yicheng

(a) Shanxi province (shaded area) in China

(b) Yicheng county (shaded area) in Shanxi

Data source: Michigan China Data Center.

Figure 2. Crude Birth Rate in Shanxi and China

Data source: Shanxi Statistical Bureau and National Bureau of Statistics.

Figure 3. Crude Birth Rate in Yicheng and other Counties in Shanxi

Data source: Please refer to Section 4.

Figure 4. Difference-in-Difference Analysis

Note: Year 1984 is taken as the baseline year.

Figure 5. Crude Birth Rate in Yicheng and “synthetic Yicheng”

Figure 6. Placebo tests (a) All 115 counties

(b) Yicheng and 61 counties with smaller pre-treatment MSPE than Yicheng

Figure 7. Robustness Check

(a) Using a small donor pool surrounding Yicheng

(b) Extending the pre-treatment period to 1970

Table 1. Weights of Synthetic Control Groups County Weight Kuangqu, Datong 0.302 Hexi, Taiyuan 0.283 Fushan, Linfen 0.195 Qinyuan, Changzhi 0.184 Pianguan, Xinzhou 0.036

Table 2. Balancing Properties Average of control Yicheng Synthetic Yicheng counties % Female, 0-14 (city level) 17.05 15.02 16.12 % Male, 0-14 (city level) 17.98 16.34 17.43 % Female, 15-59 (city level) 28.32 29.15 27.90 % Male, 15-59 (city level) 29.60 33.16 30.73 % Female, 60+ (city level) 3.58 3.08 3.84 % Female (county level) 48.60 42.79 47.16 Deaths per 1,000 people 7.28 5.28 7.12 Hospitals per 1,000 people 0.07 0.22 0.18 % Agricultural population 92.98 56.26 84.48 Log of GDP per capita 5.24 6.17 5.86 Log of rural personal income 4.38 4.54 4.56 Elementary schools per 1,000 people 2.24 1.78 1.75 Middle schools per 1,000 people 0.40 0.41 0.44 Births per 1,000 people (1972) 18.98 20.22 29.70 Births per 1,000 people (1973) 18.23 18.28 27.40 Births per 1,000 people (1974) 17.73 17.85 26.39 Births per 1,000 people (1975) 17.42 16.41 23.67 Births per 1,000 people (1976) 15.35 15.51 19.76 Births per 1,000 people (1977) 14.21 14.36 17.58 Births per 1,000 people (1978) 14.05 13.34 15.91 Births per 1,000 people (1979) 13.65 12.82 15.99 Births per 1,000 people (1980) 12.16 12.78 16.16 Births per 1,000 people (1981) 11.64 12.26 17.01 Births per 1,000 people (1982) 12.10 13.84 18.78 Births per 1,000 people (1983) 10.93 11.23 15.23 Births per 1,000 people (1984) 10.96 11.26 14.42 Data source: please refer to Section 4.

Table 3. Percentage of counties having smaller treatment effects than Yicheng Year Full sample Restricted sample 1985 69.6 74.2 1986 43.5 38.7 1987 68.7 74.2 1988 89.6 85.5 1989 61.7 61.3 1990 58.3 62.9 2000 96.5 96.8 2010 92.2 95.2 # counties 115 62