Gary Becker’s household economics: how unitary and how unified?

1. Gary Becker’s household economics: how unitary and how unified? By ShoshanaGrossbardPrepared for Sciences Po March 2010

2. Introduction • There are hundreds of references to Gary Becker’s ‘unitary’ models--the reference often being to his paper on the allocation of time (Becker 1965) or his Treatise on the Family (1981, 1991), models of the household that don’t distinguish between decision-making agents. • The alternative to unitary models are models assuming that multi-person households include individual decision-makers. Such models have been coined ‘individual models’ (Apps and Rees 2010) or ‘collective models’ (Bourguignon, Browning, and Chiappori 1995). Most of those who refer to Becker’s unitary model prefer to use such individual models.

3. Examples of lack of recognition of Becker’s individual models • As editor of Review of Economics of the Household I have read many papers who attribute unitary models to Becker. I googled to see how common this is and found many other articles giving Becker this same credit • For example, TakWaiChau, Hongbin Li, Pak Wai Liuand Junsen Zhang (2007) contrast their ‘collective’ or ‘individual’ labor supply model with “theunitary model pioneered by Becker (1991) Other individual models of labor supply in multi-person households that have contrasted their own model with Becker’s “unitary” model include Chiappori (1988) and Chiappori, Fortin and Lacroix (xx). Jill Tiefenthaler (1999) and Emily Klawon and Tiefenthaler (2001) have contrasted their bargaining models with Becker’s unitary model of fertility.

4. Cont. • Models of care work such as Suzanne Bergeron (2009), child labor and school attendance such as Patrick Emersonand André Souza (2007) and of the demand for pets (see Peter Schwarz, Jennifer Troyer, and Jennifer Walker 2007) all contrast their individual model, which is typically a bargaining model or a collective model, with Becker’s unitary model. • Most of these papers give credit to their favorite model, not recognizing that earlier models also took an individual non-unitary perspective. In fact, to the best of my knowledge, one of the many models that Gary Becker published is the FIRST individual economic model of household decision-making. It is one of the models found in his theory of marriage, originally published in the JPE in 1973

5. Basic competitive model of marriage in Becker • This model appears in both 1973 and 1981 • Assume that • identical men and identical women are in the market for one another. • as a couple, a man and a woman can produce a composite good Zmf • This marital good exceeds the sum of the Zf a woman could produce alone and the Zm that a man could produce alone. • The market then may determine how the total gain from marriage Zmf – Zm – Zf is subdivided between husband and wife. • [graph] • if the number of men exceeds the number of women, i.e. the sex ratio exceeds one, the entire gain from marriage goes to women. • If the number of women exceeds the number of men, the entire gain from marriage goes to men. • If the number of men and women are the same, ?? No market solution. This opens the door for (collective or private?) bargaining models.

6. Examples of insights from Becker’s simple D&S model of marriage • The higher women’s productivity in marriage, the more men are willing to pay • One can infer that when men have more income they will demand more wives • More advantageous marriage market conditions for women when number of men exceeds number of women, and vice versa (sex ratio effect)

7. Second D&S model only found in Becker 1973; hedonic model • choice between mates of different types: market for men of type i and women of type j • “Hedonic” to the extent that there are no prices for the valuable characteristics serving as the basis for distinguishing various types of men and women. • supply and demand takes account of possible substitution between mates belonging to a continuum of different types. • in these circumstances the equilibrium division of output in marriage can fall anywhere between the best division from a male point of view and the best division from a female point of view

8. Why second model only in 1973? • In a 2004 email I asked Becker that question In his emailed response, he explained: “My Treatise was considered by me to be a complement to my previous work, not a substitute. So I did not go over everything in the earlier papers that I considered to be valid and sometimes even important.” “I never abandoned my view that imputations to men and women are determined by a competitive marriage market - what you call the supply demand framework.”

9. Becker thus played a pivotal role in the development of individual decision-making models by couples, and deserves some of the credit that is generally given to the bargaining theorists. • Now I want to share with you why it bothers me so much that contemporary economists often overlook Becker’s individual models. I am not an objective observer here.

10. A variety of Becker models My own exposure to such variety of models • As a first-year student at Chicago, in January 1973, I first got to know Gary Becker as my professor in price theory, a course packed with a variety of maximization models and aimed at getting us to practice his specialty: Applying calculus to everything. Just identify a utility function and some constraints and you are in business. • Two years later I took his course on the economics of the family. It was the first time he was teaching it. I was lucky he had an interest in preparing such course while he was working on his Treatise on the Family, which eventually got published in 1981. Again, Becker showered us with what seemed like an endless stream of optimization models, but this time they all addressed issues related to household economics.

11. Furthermore, given that I wrote my dissertation with him, I got to participate in Becker’s workshop on Applications of Economics in the years 1974-1976. Regular participants included the Who is Who in economics at Chicago including Jim Heckman, T W Schultz, Ed Lazear, George Stigler and Richard Posner. Neither Becker nor Heckman had yet received their Nobel prizes, and Lazear was a beginner level assistant professor. Milton Friedman also attended occasionally. • We as students got the impression that Becker is a virtuoso, a brilliant performer on the academic stage, able to produce a variety of thought-provoking intellectually stimulating models. Like an artist, he had a whole palette of models, and he and his students could chose the one that adapted best to a given problem. Some were unitary, some not. We did not experience that there was a unified Becker theory on anything. It was my impression that “good economists” can pick and choose their models, depending on what works best.

12. More specifically: not even a unified theory of marriage • At one of the weekly meetings of the workshop, he, Lisa Landes and Bob Michael presented a draft of what became their 1977 JPE article on divorce. Whether it was on that day or during another workshop dealing with marriage, I am not sure, but I have clear memories of a big discussion about Becker’s theory of marriage. More precisely, I recall that another one of my thesis advisors, Ed Lazear, was critical of Becker’s matching model of marriage and pointing out some of the contradictions between that model and what we perceived as Becker’s principal model of marriage: his Demand and Supply model. • Another of my thesis advisors was critical of Becker’s theory of marriage: Jim Heckman, who had recently arrived from Columbia where he had advised Fredericka Pickford Santos, a student trained by Becker and Mincer there who wrote her dissertation on “the economics of marital status” using a trade model of marriage (see Santos 1975 cited in Becker 1981). Heckman tried to convince me to apply such model to my dissertation on polygamy.

13. Intro, cont • After considering all the models of marriage available—including a few Becker models-- and hours of heated one-to-one discussions with Lazear, Heckman, T.W. Schultz and a number of fellow students just as enthusiastic about Chicago imperialism as I was, I opted for a marriage model that I adapted from labor economics that is closely related to Becker’s D and S model of marriage. In part, I was attracted to this model because in his workshop Becker had demonstrated that when he engaged in an empirical application of his own theories—in joint work with Landes and Michael—he relied mostly on his demand and supply models of marriage. These are the models that were most inspiring to students writing their dissertations on marriage at the time. This applies not only to my own experience, but also to the case of Michael Keeley. • Likewise, when it comes to models of the family in general, including marriage, fertility and intergenerational relations, we as students got the impression that Becker’s models were far from unified. Most of them were unitary, but the economics of marriage was a central piece of Becker’s perspective on the family, and a central model of his economics of marriage was an individual—not a unitary—model.

14. More general lessons from studying with Becker • We also got a clear impression of Becker’s ideological bent. He presented his work on gender specialization in the household and on sociobiology. Here he emphasized biological differences between male and female. The few women amongst us dissociated themselves from Becker’s ideology on these matters. • In historical perspective, after so many years went by, I wonder to what degree Becker’s insistence on biological differences between men and women clouded his judgment regarding my own theory of marriage.

15. model of allocation of time in labor and marriage (Grossbard 1984) • Utility Function • (1) Ui ( li,hi,si, hj, xi,) where U: Utility x: Commercial goods and services s: Time for self, often called leisure. l: Labor ( If you go to work) h: Household labor i: maximizes utility function 2. Three uses of time • (2) Ti= Si + Li + hi (explained on next slide) Utility maximization: individual i maximizes utility function (1) subject to time constraint (2) and Budget constraint

16. More on utility function Utility Function Ui ( li,hi,si, hj, xi,) • hi and hj contribute to individual I’s utility. • h is household labor. It is labor in the sense that (1) it is an activity that people have to put up even though it is not their favorite activity (i.e. there is an opty cost) and (2) the activity benefits another person/organization who is willing and able to compensate the worker. if I is husband and j is wife: U i (..hj..) means that husband benefits from wife’s hh labor. Ex: wife Doing her husband’s laundry. Gender symmetric: husbands may work for wives si: Time for self (Leisure time) hj: potential or actual spouse

17. Budget constraintI+ wili + yihi = Pixi + yjhj • LHS: income • I: non-work income ( EX: rental income) • w:wage • l:labor • yihi :Earnings from household labor • yi: “quasi-wage” for household labor ( It may not be monetary or material , could consist of psychic, spiritual, emotional benefits) • h: hours of household labor • RHS: expenditures • Pi: :Is the price of commercial goods • yjhj: payment for spouse j’s household labor; it is assumed that j gets an hourly rate of yj:

18. Different kinds of marriage • Traditional marriage : yjhj > yi*hi , wife works more in hh than husband (could be that both spouses are in the labor force), where i: male and j: female 2. Egalitarian marriage: this is where the value of work of yihi and the value ofyjhj cancel each other out. 3. Reversed-role marriage: yjhj < yi*hi , husband works more in hh than wife

19. Equilibrium condition MUs = y + MUhi = w+ MUli MUx MUx MUx • MU: marginal utility • y + MUhi/MUx : Total compensation and benefits per hour of own hh labor MUx MU from x • w + MUli/MUx: total compensation per hour of labor in labor market

20. Marriage markets and quasi-wages y • These quasi-wages are established in markets. Effect of Demand and Supply • One basic inference: higher opportunity cost of LFP if higher y due to more relative demand in marriage (see lecture 2) • Other basic inference: compensating differentials (see Grossbard-S and Neuman 1988)

21. In conclusion • 1/ Becker’s individual models have been overlooked, especially in recent years. This is related to the false impression that Becker himself fostered in his Treatise on the Family: that his theory of the family is a unified framework (see p x Becker 1981). This encouraged readers to view the dominant unitary models in his book as a unified theory and to overlook the individual models that are also covered in the Treatise. • 2/ Individual models by Becker students are often overlooked, including my own. This may be related to Becker’s attitude towards women.