James Heckman on Gary Becker’s approach to economic research

Nice IZA discussion paper by James Heckman on Gary Becker’s distinctive abductive scientific method.

Becker created a powerful body of economic science. He did so by relentlessly applying three principles: (a) economic agents act in their self interest (broadly defined and ever more broadly defined over his career); (b) preferences are stable (but they can evolve through practice, habituation, learning and hence they can differ among people); and (c) markets—broadly defined—are in equilibrium (both formal markets and informal nonmarket settings using explicit and implicit “shadow” prices respectively) (Becker, 1978).

Worth a read, especially for those who want a quick overview of Becker’s major contributions. IIf you are interested in labor economics, you should consider subscribing to the newsletters from the Institution for the Study of Labor (IZA).


Economics of the Family (5): Investment in Children


Here comes the long-awaited discussion on the economic modeling of parental investment in children. It took us two classes to cover the classic quality-quantity tradeoff theory and its recent empirical tests.

Becker and Tomes (1976) model the parents’ utility as a function of the number of children, the quality of each child (assumed to be equal), and other goods produced in the family (“Z goods”). Costs of raising children is multiplicative in the quantity and quality of children because of “equal concern”. The resulting conditions indicate that shadow price of children is endogenous because the number of children is a choice variable. While this model provided a basic framework to think about fertility decisions, it has two important flaws. First, counter-factual questions are hard to make sense because “n” and “q” are jointly determined. Second, they assume costless transfers between children in terms of income and other outcomes to achieve equality. This assumption might be plausible for outcomes like welfare or happiness, which are difficult to take from one person to another. By contrast, Behrman, Pollak and Taubman (1982) addressed equal concern in aspects other than income. They incorporated endowment as complementary to education (i.e. parental investment) and argued that equal concern would not necessarily lead to equal investments.

For empirical results on the topic, Schultz (2001) provides a comprehensive account of the opportunity costs of having children. A clever strategy mentioned in the paper is to use labor market conditions that affect the career prospects of the male but not the female to identify the costs of having children. It is also important that opportunity cost may not be the whole story: the increasing bargaining power in the family might allow women to have their desired number of children, which could be fewer than what their husbands want.

Researchers have used data from developed and developing countries to test the quantity-quality tradeoff and differential investment by gender. In class we touched upon a few papers on “If parents’ income expands, how do they allocate the additional money towards investments in their children?” Paxson and Shady (2010) assessed the “intent to treat” effects of cash transfers on the health of children; De Brauw and Hodinott (2011) investigated whether taking away the school enrollment conditions hurt the effectiveness of the cash transfer program in Mexico. But it is important to bear in mind that the benefits and costs of enrollment are not examined in their paper. The goal of the policy is to increase enrollment.

I think there should be more research on fertility and child investment decisions in a dynamic framework. Parents might time their births to reap the most benefits from scale economies, and the gender of firstborn might affect subsequent childbearing decisions. There is a lot to be learned.


Becker, G., & Tomes, N. (1976). Child endowments, and the quantity and quality of children.
Behrman, J. R., Pollack, R. A., & Taubman, P. (1982). Parental preferences and provision for progeny. Journal of Political Economy, 90(11), 52-73.
De Brauw, A., & Hoddinott, J. (2011). Must conditional cash transfer programs be conditioned to be effective? The impact of conditioning transfers on school enrollment in Mexico. Journal of Development Economics, 96(2), 359-370.
Paxson, C., & Schady, N. (2010). Does money matter? The effects of cash transfers on child development in rural Ecuador. Economic Development and Cultural Change, 59(1), 187-229.
Schultz, T. P. (2001). The fertility transition: Economic explanations. Economic Growth Center Discussion Paper, (833).

Economics of the Family (4): marriage and matching

A friend of mine, a future environmental economist, once questioned the practicality of marriage sorting theories: “Can marriage decisions really be modeled in economics? It seems impossible to me, because these are complicated decisions that affect life outcomes over a long time. And even if we can model it, what’s the use?”

Such concerns are probably widely held. One might doubt the validity of marriage theories for they assume people rationally weigh their benefits against costs in their lifetime before they say “I do”. Obviously, economists cannot model everything that is involved in marriage decisions, but can outline several aspects that are likely to govern marriage decisions. Gary Becker (1973) models marriage decision as a two-way matching process, where people get married only when both individuals are better off married than single and prefer this spouse than all other potential spouses. Individuals get married in order to produce household goods (“Z goods” in Becker terms) that contribute to their well-being (utility). If we assume there is only one attribute (say, intelligence) that matters in Z good production, then individuals will find partners with similar (opposite) levels of this attribute if men and women’s attributes are complementary (substitutes) in the production. These are called positive (negative) sorting.

Note that the “Z goods” are loosely defined and can range from meals cooked together to children raised. Becker’s framework is no longer applicable if we want to incorporate gay marriage, as we have to rearrange the groups according to people’s sexuality preferences.

Does getting married affect people’s earnings? There is evidence that married white men enjoy a “marriage premium”. On its surface one might conclude that getting married makes men more productive. But higher earnings might reflect the selection of capable individuals into marriage (Chun and Lee, 2001) or a correlation between higher valuation of family goods and greater earning potential (Reed, Robert, and Harford, 1989). Moreover, economists do not perfectly observe how people define “before” and “after” marriage. Surveys do not accurately reflect the true timeline of individual decisions because “after” might appear way before than economists realize it. Respondents might actively seeking promotion and pay increases before marriage to prepare for a married life. Such patterns are shown in Dougherty (2006).

My next post will be on fertility decisions and investment in children. Quality-quantity tradeoff will surely be covered.


Becker, G. 1973. “A Theory of Marriage: Part I.” Journal of Political Economy 81(4): 813-846.

Chun, Hyunbae, and Injae Lee. 2001. “Why do married men earn more: Productivity or marriage selection?.” Economic Inquiry 39(2): 307-319.

Dougherty, C. 2006. “The Marriage Earnings Premium as a Distributed Fixed Effect.” Journal of Human Resources 41(2): 433-443.

Reed, W. Robert, and Kathleen Harford. 1989. “The marriage premium and compensating wage differentials.” Journal of Population Economics 2(4): 237-265.

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 (3): Gender and Resource Allocation within the Household

Here is the much awaited discussion about the theoretical underpinnings and empirical implications of intra-household resource allocation models. As noted in the previous two posts, the household is most appropriately treated as a “firm” which makes production and consumption decisions simultaneously. The next question is, then, how should we represent the preference of the whole household?

Take an analogy from the voting behavior models. By Arrow’s Impossibility Theorem, no rank order system can convert the ranked preferences of individuals into a community-wide (complete and transitive) ranking while meeting the following criteria:

1. Non-dictatorship, i.e. everyone’s preference needs to figure in.

2. Unrestricted domain, i.e. there exists a deterministic function linking constituencies to outcomes.

3. Pareto principle.

4. Independence of Irrelevant Alternatives (IIA for short).

5. Rationality, which is needed for utility function specification.

There are three approaches to analyze household resource allocations. Samuelson (1956) first points out a common preference model where household “consensus” can be seen as a single representative. Gary Becker, on the other hand, added altruism into the model and elaborates the “consensus” process. The other class of models are collective models by Chiappori, McElroy and Hearney, Lundberg and Pollak, etc. In particular, Chiappori’s general collective model address the violation of unrestricted domain by assuming outcome of household decisions to depend on income distributions and other factors affecting bargaining power (modeled as “lamda”).

Becker’s Rotten Kid Theorem generated quite a bit of discussion in class. The critical assumption here is that an altruist fully incorporates the utility function of the beneficiary into his own. Therefore, when he is faced with lower incomes, he “punishes” his beneficiary in a way that lowers his utility as well. Knowing this unfavorable consequence, the selfish beneficiary (the “rotten kid”) is induced to behave in a way that maximizes household’s welfare. This approach has been criticized as unrealistic and largely rejected by empirical evidence.

The empirical papers discussed were quite interesting. Udry’s paper on inefficient farming households in Burkina Faso is flawed because plots controlled by men and women are likely to differ in unobservable characteristics which also drives the productivity gap. Amar pointed out that by the same reasoning, since plot decile effects are quite significant, dividing a big plots into smaller ones should increase yields by a substantial margin, which does not make sense at all.

Lundberg, Pollak and Wales (1997) and Hotchkiss (2005) investigate the impacts of child subsidy on household expenditure on women’s and children’s clothing relative to men’s. Hotchkiss flunked LPW’s findings, but neither accounts for a potential “labeling effect” which results from the change in the way families receive the child subsidy.

My next post will be about marriage markets and investments in children.


Becker, G. 1991. “A Treatise on the Family: Enlarged edition.” Chapter 8.

Browning, M., Chiappori, P., and Weiss, Y. 2011. “Cooperative Models: The collective approach.” Section 3.5 in Family Economics.

Lundberg, S and Pollak, R. 1996. “Bargaining and Distribution in Marriage.” Journal of Economic Perspectives 10(4): 139-158.

Hotchkiss, J. 2005. “Do Husbands and Wives Pool Their Resources? Further Evidence.” Journal of Human Resources 50(2): 519-531.

Udry, C. 1996. “Gender, Agricultural Production, and the Theory of the Household.” Journal of Political Economy 104(5): 1010-1046.

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.