China’s skewed sex ratios by birth order

Although my independent study on the strategic fertility and child investment decisions in China under the “one-child” policy has come to an end, my interest in the topic has not. This afternoon I was playing with the China Geo-Explorer this afternoon, and generated the following graphs about sex ratios of births in 2000.

First, let’s look at the aggregate statistics. This picture shows the sex ratios by province in 2000. The sex ratios of newly born are the highest in Henan, Anhui, Jiangxi, Guangdong, and Hainan, while autonomous regions represented by minorities enjoy much more balanced gender composition of births.

2000-birth-sex-ratioThese aggregate numbers can be misleading as it does not address the different concerns (and gender preference) parents have for births at different parity. For example, in places where second births are not strictly prohibited, parents might have little incentive to select the gender of their first child. To address this, I plot the sex ratios of first, second, and third births separately below.


2000-third-birth-sex-ratioSeveral provinces in central China has many more boys born than girls at each parity. It is obvious that sex ratios rise with birth order, probably reflecting the fact that some parents keep having children unless they have a boy. But we need to be aware that sex ratios of higher parity capture only the parents who have the resources to have more children than stipulated by the OCP. Also, it’s interesting to see Beijing’s sex ratio become much higher for first births.

Professor Averham Ebenstein has kindly shared his data and programs on Chinese fertility trends (from three censuses) and OCP fines with me. Currently I also have Chinese Household Income Project (CHIP) and Chinese Health and Nutrition Survey (CHNS) at hand. It will take me some time to figure out how to best utilize these data for my purpose.

Economics of the Family (2): Defining “Family”

Family clip art
Blogging has been light for the past few days, partly because I was preparing for an academic presentation and partly because I was a bit lazy as the Lunar New Year approached. Now that celebrations are over, I am back to my normal blog schedule.

This is the second post in my “family economics” series. Following our last discussion, we talked about how to define “family” or “household” in economics.

The US Census defines the family as “a group of two people or more (one of whom is the householder) related by birth, marriage, or adoption and residing together”. This definition differs from that of a “household” because the latter only requires joint residence. Relative to households, families not only share public goods (e.g. heating) but also pool their resources and make consumption choices together.

The economic theory of the family was established most notably by Gary Becker in his book A Treatise on the Family. For a long time, economists treated the family as a single consumption unit which maximizes its utility given a budget constraint. However, a family contains individuals of different objectives and incomes sharing certain public goods yet retaining some degree of autonomy. In addition, there are production-type activities within a family, ranging from household chores to raising a kid. These distinct features of the family require us to model it like a firm where production and consumption choices are jointly made.

Gary Becker incorporated the production component of the family in the so-called “Z” goods, which are produced using a combination of market goods (X) and time devoted by family members (t). In a single-person household, the individual (household head) maximizes his own utility subject to an income constraint (with respect to market goods), a time constraint (he only has 24 hours a day), and a home production function describing how X and t are transformed into Z. These constraints can be condensed into one equation which says the total amount of income spent on market goods plus the forgone wages cannot exceed the individual’s full income (if he spends all his time working) and unearned income. Optimal allocations equalize the marginal utility from purchasing each market good and the that from devoting time to home goods production. The key insight is that market goods must be purchased such that they are equally “productive” given individual’s preferences over Z goods. Marginal utilities are now determined by production as well as inputs. Being in a family, where individuals can complement each others’ skills and enjoy economies of scale, might change the production function of the Z goods.

Parallel to the advances in theoretical work, applied economists have explored how different definitions of the family affect individuals’ response in household surveys. Beaman and Dillon (2011) carried out a randomized control trial in Mali where they surveyed villagers about household composition, assets and consumption using four different definitions of the household. They found additional keywords in definition, such as joint food preparation and cooperation in agricultural production, tend to increase rather than decrease household size. Definitions emphasizing joint consumption or production increases the levels of household assets and consumption statistics, but not on per adult equivalence terms. Their findings suggest that household survey questions should be carefully framed to address the purpose of the specific study. Moreover, a consistent household definition is essential for comparisons over time and across populations.

Next week we will dive deeper into the decision-making process within the family, and explore the merits and flaws of different household bargaining models with empirical examples. Highlights include Gary Becker’s Rotten Kid Theorem, Christopher Udry’s agricultural production model, and empirical evidence from West Africa.

Beaman, L and Dillon, A. (2011) “Do Household Definitions Matter in Survey Design? Results from a randomized survey experiment in Mali” Journal of Development Economics 98(1):124-135.
Becker, GS.(1991). “A Treatise on the Family: Enlarged edition,” Chapter 1.
Becker, GS.(1965). “A Theory on the Allocation of Time” Economic Journal 75(299):493-517.
World Bank. (2000). “Designing Household Survey Questionnaires for Developing Countries: Lessons from 15 years of the Living Standards Measurement Study,” vol 1, chapter 6, section 1 (Pp.135-137).

Economics of the Family (1): Measuring Living Costs at the Household Level

This is the first of a series of posts on the economics of the family, based on lectures and in-class discussions of Professor Amar Hamoudi‘s seminar course on this topic.

The central discussion of our first class was a fundamental question in economic research and policy design: how should we define poverty? An economics student might think naively construct a minimum income threshold as the poverty line, but this effectively classifies all infants as poor. While children do not earn an income, they enjoy food and housing which are shared among family members. This extremely example highlights the public good nature of domestic goods and services and calls for measures of well-being that takes demographic composition into consideration.

To make households with different demographic characteristics comparable, we need to make select a reference household structure and use equivalence scales, which are “measures of the relative costs of living of families of different sizes and compositions that are otherwise similar” (Citro and Michael, 1995). For example, if the equivalence scale of a single adult family is 0.5 and the reference family has two adults and two children, then a single adult can live as well as a family of two adults and two children while spending only half as much. For economists, equivalence scales directly measures the impact of changes in demographic composition on the cost of living.

An example of the policy application of equivalence scales is Mollie Orshansky’s calculation of poverty thresholds in the US (Orshansky, 1965). Orshansky used USDA “economy food plan” to compute the food costs for families of different size and composition, and then adjust for the fraction of expenditure spent on food.

It is useful to narrow our scope to calculating the costs of an additional household member, in particular, an additional child. This calculation can be done using the Engel Curve or Rothbarth measure (Nelson, 1993). Engel equivalence scales draw from empirical evidence that the share of food expenditure decreases as families become better off, and compute the costs of a child to be the compensated income needed for a family to restore its share of food expenditure before the childbirth. By contrast, Rothbarth estimates child costs by selecting a group of adult goods (such as alcohol and adult clothing) and calculating the income needed to restore the consumption of these goods. Deaton and Muellbauer (1986) innovatively modeled changes in the demographic composition of the family as variations in the prices of goods (food and nonfood, for the simplest case). Consumption demand for different goods is regressed on the adjusted “prices” and duality is used to interpret the results.

At the end of the lecture, Amar raised two interesting points for further discussion. First, why do we measure everything at the household level? Assume there are two households, each including one elderly couple with the same level of household income. Couple A cooks dinner for their son who lives just next door (but not in their house), while couple B only takes care of themselves. Which couple is better off? Maybe they are equally well off because couple A might gain utility from cooking for their son. But the question does not stop here. We need to ask if the son brings additional income to the household or share resources with his elderly parents. In this case, public goods provision and resource sharing might expand well beyond the boundary of the household. In essence, we are assuming that the household is a shared consuming unit where everyone inside shares resources and reaps utilities that are inter correlated. Second, households do not only consume, they also produce. It is more realistic to model the household as a firm where production and consumption are jointly decided.

Our topic for the next class is gender and resource allocation. Looking forward to discussing about the interesting literature on intra household bargaining and gender bias in child investment.

Citro, C. and Michael, R., eds. (1995). “Measuring Poverty: A New Approach“.
Deaton, A. and Muellbauer, J. (1986). “On Measuring Child Costs, with Applications to Poor Economies”. Journal of Political Economy 94(4): 720-744.
Nelson, JA. (1993). “Household Equivalence Scales: Theory versus Policy?” Journal of Labor Economics 11(3): 471-493.
Orshansky, M. (1965). “County the Poor: Another Look at the Poverty Profile.” Social Security Bulletin (January 1965): 3-29.

China’s One Child Policy and Parental Investment in Children (1)

This is the first post of a series of reflective essays on fertility choice/human investment models in economics. My goal for this semester is to present a model of parental investment in children under birth planning policies, hopefully with empirically testable hypotheses.

I look at how parents invest in children given multiple constraints. In addition to the usual budget constraint, parents are limited to two children and have to pay a fine if they decide to have a second child. The amount of the fine represents the difficulty of having a second child (i.e. the level of enforcement of One Child Policy). A zero fine suggests that it is legitimate to have a second child, while a fine going to infinity implies that having a second child is strictly prohibited. China’s OCP yields a perfect context to study how parents make fertility decisions and allocate their resources among their children given birth restrictions.

The classic Becker model (Becker 1994, Becker and Tomes 1986) makes two assumptions of parents’ fertility choices that I think are unrealistic. First, it assumes that parents put equal weight on children’s consumption (the only “utility” by the children in the unitary utility function). This is hardly realistic in developing countries where there is a strong preference for sons over daughters. Second, it assumes that “quality of children” can be purchased at a fixed price. This is key to the famous “quality-quantity tradeoff” result. What we observe more often is that parents need to devote time to their children and invest in their education and health in order to enhance the children’s abilities. Some question the unitary model assumption, but bargaining models are hard to estimate empirically. For the bargaining approach, see papers by Chiappori and Browning and the “separate spheres” paper by Shelly Lundberg and her coauthors.

A paragraph from Alderman and King (1998) elucidate the importance of preference:

There are issues not only of the efficiency of the investment, but also of the intra household allocation of the expected benefits. Preferences, then, matter for two distinct reasons. First, learning may contribute directly towards the welfare of the child and of parents, over and above its productive return as an investment. That is, learning may be a consumption good. Second, the decision-makers’ preference for equity among-est children influences how investments in education are allocated to children with different expected rates of return.

There are several ways to incorporate gender bias in the model. One can assume different marginal utility from sons’ and daughters’ consumption (or outcome variable, in general), or even put substitution/complementarity assumptions by restraining the second-order derivatives. A model with remittances can allow for different contribution rates from children to parents. Some papers also assume different labor market returns of parents’ investment by the gender of the child.

One piece of advice for graduate students who are trying to get identifiable information which requires IRB approval: don’t expect the data to arrive any time soon. Work on the theory first so that you will have something to present if your data request gets stuck in the administrative files.

A heart devoid of love — thoughts on documentary Last Train Home

There are 130 million migrant workers in China. It is the biggest human migration in the world.

This is the opening sentence of the documentary Last Train Home . This movie follows a typical rural household in Sichuan, China for three years and tracks the changing migration and life decisions of household members.

Last Train Home

This is a typical family in rural Sichuan. Both parents were working in Guangdong province, a popular migrant destination in China. Once every year, they took the train back home to celebrate Chinese New Year with their daughter, Qin, and their son, Yang. Qin and Yang lived with their grandmother. Qin appeared to be very mature for her age.  Apart from school work, Qin also had to feed farm animals and tend to crops. She was also skilled in joking with grandmother and creating a warm atmosphere in the family. Since her parents have started working in Guangdong when she was a baby, she barely remembers the time they spent together — there is not much to begin with.

In the first year, the New Year dinner was peaceful. The parents brought Qin a brand new cellphone and Yang some new toys. They urged Qin and Yang to study hard:”You can get out of here and be successful only if you study hard and get good grades. Don’t be like us. We would have earned a lot more if we were more educated.” The children nodded absent-mindedly. Unfortunately, or maybe expectedly, Qin dropped out in the second year. She pursued the same path as her parents — migrating for work. In a manufacture factory in Guangdong, she sewed and packed clothes everyday, while making friends and dressing herself up at the same time. When asked about why she dropped out, she answered “I don’t find school interesting. It’s not useful at all.”

Conflicts burst out in the third year. When Qin was working in another city in Guangdong, she didn’t contact her parents often. Nor did she feel the need to. She dyed her hair, bought new clothes, and tried to make herself look as hot as other city girls. This year at the New Year dinner, she challenged her father, saying he had no power over her because he never cared about her. The family went through a serious fight in which both parties lose. Qin only became more detached from her family.

At the end of the movie, Qin became a bartender in Shenzhen, a metropolitan city in Guangdong. She was dancing disco in a crowd, with the usual absent-mindedness on her face. You can hardly tell her apart from the urban girls with heavy make-up and hot skirts. Qin’s mother was considering going back to home to take care of her son. But this would mean her husband will have to work harder and send more money back home.

I have relatives like Qin and Yang, who suffered and are still suffering from their parents’ migration. I remember a woman working in a charity agency for rural children’s welfare once talked about left behind children: “These children have never been loved. When they grow up, how can we expect them to love others? How can we expect them to love the society?”

I could hardly stop crying as I was watching this movie. If you are Chinese and you are away from home, you will find sentiments throughout the movie. I was especially impressed by the movie’s great depiction of the snow storms in 2008.  This movie is also a great source for people who want to know more about internal migration within China. Many thanks to Daniel Xu for recommending.

By the way, the title of this post is adapted from A Heart Full of Love in Les Miserables, one of my favorite musicals.

Reevaluating the cost of exit — how unilateral divorce law has changed US divorce patterns

Gary Becker, in his famous book A Treatise on the Family, proposed a pragmatic way to analyze marriage and divorce. Before entering marriage, the male and the female know their own benefits of staying single. They will marry if their joint payoff from the marriage exceeds the total of their benefits when single. The payoff (benefit) here is assumed to be income for simplicity. Of course, marriage produces non monetary output, such as children and the feeling of security, which are evaluated separately.

After getting married, a couple might find their benefit of staying in the marriage lower than expected — their partner may be earning less or the two of them simply don’t get along well. At the same, their outside options — denoted as earning potential when they’re single — is also likely to change as well. Many women give up their job after getting married, which decreases their wage if they want to reenter the labor force. On the contrary, married men often earn a higher wage (sometimes called a marital wage premium) than single men.

Unilateral divorce law was widely adopted by the US states during the 1980s. Before that most states supported only bilateral divorce which requires the consent from both parties of the marriage. By the Coase Theorem, if a couple knows each others’ payoffs from the marriage and their outside options and they can bargain costlessly, divorce is always efficient. If the husband wants to divorce but the wife does not, he can always transfer some of his gains from exiting the marriage to his wife and make both of them better off than staying married. Therefore if the Coase Theorem holds, the switch from bilateral to unilateral divorce law should not affect individual’s propensity to divorce.

Several empirical studies attempted to test this. One of the earliest and most influential is Peters (1981). She used Current Population Survey (CPS) data and found support for symmetric information model in marriage. Friedberg (1998) used state panel data and found that unilateral law had considerably raised divorce rates. Justin Wolfers (2006) added dynamics into the model by introducing lagged effects along with state time trends. His findings are consistent with Friedberg’s but he also found the impact of unilateral divorce laws fade away after a decade. Recently, Iyavarakul, McElroy, and Staub (2011) developed Cohort Panel Data Model (CPDM) and summarized the strengths and weaknesses of previous findings. Their results corroborate the Coase Theorem.

Policies aimed at encouraging marriages can also increase divorce.

Zax and Fleuk’s working paper “Marriage, Divorce, Income and Marriage Incentives” describes how military benefits raised the value of marrying male officers and encouraged more unhealthy marriages. They used data on two groups of 18-year-olds, one drafted and the other not, and tracked their military activities, marriage status, and earnings. Surprisingly, there appeared a tide of marriages at the time that those young men were drafted, but many ended up in divorce. They also found that the marriages formed at the end of their military service tend to last much longer and those men earn a higher income.


Friedberg, L. 1998. “Did Unilateral Divorce Raise Divorce Rates? Evidence from Panel Data,” American Economic Review 88(3): 608-627.

Iyavarakul T., McElroy M. , and Staub, K. 2011. “Dynamic Optimization in Models for State Panel Data: A Cohort Panel Data Model of the E§ects of Divorce Laws on Divorce Rates.”

Peters, E. 1981. “Marriage and Divorce: Informational Constraints and Private Contracting,” American Economic Review 76(3): 437-454.

Partrick Sharkey on the impact of community violence on children

This afternoon I attended a seminar by Patrick Sharkey, associate professor at NYU. The name of his talk was “the effects of community violence on child cognitive skills and academic performance”.

His research measures the impact of neighborhood violence on children academic performance. he uses”coincidence” estimation. Within each neighborhood, he argues that the relative timing of homicides and interviews produces exogenous variation of timing. He interviews a child four days after a homicide happened in the neighborhood, and sees if her test score changes relative to children who are unaffected by homicides. He measures “neighborhood” using block group, census tract, and neighborhood cluster. Note that this method only picks up short run effects. Sharkey emphasized on the importance of evaluating how kids are functioning on a DAY-TO-DAY basis (e.g. mindset) because it is those incremental changes that lead to differential personal development in the future. His methodology is novel in two aspects: First, he employs the different timing of violence as exogenous variation and measures its impact on the test scores of school children. Second, he targets on specific incidents, e.g. homicide in the Chicago data, instead of the aggregate crime rates. This breaks down the impact of violence by category so that we can get a better idea of whether a particular type of violence affects children’s cognitive ability and extrapolate the mechanism of the impact.

However, this method is not free from flaws. African-American children are overrepresented (nine times the number of white children), and this weakens his later argument on the comparative statistics between white and black children. Furthermore, there may be a systematic difference between treatment and control group children since an interviewer might not want to go to the same neighborhood until some days after the interview is done.
The results are consistent with his hypothesis that neighborhood violence does affect a child’s academic performance. His paper on New York City public schools also found that black students are affected more by the violence in the community. Students who have experienced violence in the neighborhood are 1.13% less likely to pass the exam, and the reduction is 3% for black students. These results imply that violence has a long reach. It also suggests tha violence may be a central mechanism by which neighborhood disadvantage affects child development (cognitive skills and academic outcomes) and other health outcomes in adulthood (e.g. the feeling of safety).
There were a lot of insightful comments from the audience in the Q&A session. One professor suggested that parenting strategy might play a role in determining the level to which children are affected by local violence. Someone suggested finding news coverage on local violence and assess whether the widely covered events affect people only in the neighborhood or the whole city/state. It might also be useful to look at whether the victim is in the network of the child and control for this variable when running the regression.