Transcript unitary model - OFCE

Gary Becker’s household economics:
how unitary and how unified?
By Shoshana Grossbard
Prepared for Sciences Po
March 2010
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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 decisionmaking 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.
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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, Tak Wai Chau, Hongbin Li, Pak Wai Liu and
Junsen Zhang (2007) contrast their ‘collective’ or
‘individual’ labor supply model with “the unitary 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.
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Cont.
• Models of care work such as Suzanne Bergeron (2009), child labor and
school attendance such as Patrick Emerson and 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 decisionmaking. It is one of the models found in his theory of marriage, originally
published in the JPE in 1973
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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.
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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)
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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
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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.”
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• 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.
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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.
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•
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 thoughtprovoking 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.
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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.
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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.
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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.
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model of allocation of time in labor and
marriage (Grossbard 1984)
1. 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
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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
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Budget constraint
•
•
•
•
•
•
•
•
•
•
I+ 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:
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Different kinds of marriage
1. 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 of yjhj cancel each other out.
3. Reversed-role marriage: yjhj < yi*hi , husband works
more in hh than wife
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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
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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)
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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.
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