Gary Becker

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Gary Beckers household economics how unitary
and how unified? 

• By Shoshana GrossbardPrepared for Sciences Po
• March 2010

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Introduction

• There are hundreds of references to Gary Beckers
  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 dont 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
  Beckers unitary model prefer to use such
  individual models.

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Examples of lack of recognition of Beckers
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 Beckers 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 Beckers
  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
  Beckers 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

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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 Beckers simple DS
model of marriage

• The higher womens 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 DS 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
  Beckers 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 Beckers
  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.

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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 Beckers theory of marriage.
  More precisely, I recall that another one of my
  thesis advisors, Ed Lazear, was critical of
  Beckers matching model of marriage and pointing
  out some of the contradictions between that model
  and what we perceived as Beckers principal model
  of marriage his Demand and Supply model.
• Another of my thesis advisors was critical of
  Beckers 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
  availableincluding 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 Beckers 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 theoriesin joint work
  with Landes and Michaelhe 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 Beckers models were far from
  unified. Most of them were unitary, but the
  economics of marriage was a central piece of
  Beckers perspective on the family, and a central
  model of his economics of marriage was an
  individualnot a unitarymodel.

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More general lessons from studying with Becker

• We also got a clear impression of Beckers
  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
  Beckers ideology on these matters.
• In historical perspective, after so many years
  went by, I wonder to what degree Beckers
  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)

• 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 Is 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 wifes hh labor. Ex
  wife Doing her husbands laundry. Gender
  symmetric husbands may work for wives
• si Time for self (Leisure time)
• hj potential or actual spouse

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Budget constraintI wili yihi Pixi yjhj

• LHS income
• I non-work income ( EX rental income)
• wwage
• llabor
• 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 js household labor it
  is assumed that j gets an hourly rate of yj

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Different kinds of marriage

• Traditional marriage yjhj gt yihi , 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 lt yihi ,
  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/ Beckers 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 Beckers attitude towards women.