Social Interaction

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Social Interaction

• An individuals preferences, and therefore
  behaviour, may depend on what others in society
  are perceived to be doing.
• Learning (e.g. new technology and uncertainty).
• Social influence a persons preferences may be
  altered by those with whom the person interacts.

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Social influence

• Utility from taking particular action (e.g. have
  a birth outside marriage)
• V1?1 ?1Pe(x) -? z??1 ?1
• Pe(x) expected proportion of women in a womans
  reference group x (e.g. nationality, religious
  or ethnic group) who take the action
• Utility from not taking the action
• V0?0 ?0Pe(x) -? z??0 ?0

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Social influence/social stigma

• Social, or normative, influences on utility are
  indicated by the terms ?1(Pe(x) -?) and ?0(Pe(x)
  -?), with ?0?0lt?1.
• ? is a threshold parameter, such that when
  Pe(x)lt?, the expected proportion taking the
  action in a womans reference group exerts
• a negative influence on taking the action.
• a positive influence on not taking the action.
• the opposite is the case when Pe(x)gt?.
• A value of Pe(x) below ? could reflect social
  stigma .

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Other definitions

• zobservable individual attributes (e.g.
  educational attainment, wages, non-labour income)
  affecting utility in the two states.
• ?1 and ?0 are unobserved woman-specific variables
  affecting utility in the two states.
• ?j may reflect policy variables (e.g. state
  benefits to single mothers (in which case ?1gt
  ?0), cost and availability of abortion if action
  is non-marital birth).

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Decision

• Take action if and only if V1gtV0 that is, when
  ??1-?0gt-??Pe(x) -? z??,
• where ??1-?0, ??1-?0 and ??1-?0.
• Social influence exists when ?gt0
• taste variable ? is assumed to have some
  random, symmetric (about the origin) distribution
  in the reference group population (e.g.
  logistic).

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Probability of taking action

• the probability that a woman with reference group
  x takes the action is given by
• H? ?(Pe(x) -?) z??
• where H? is a continuous, strictly increasing
  distribution function.

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Proportion in reference group taking the action

• The actual proportion in the reference group who
  take the action is
• P(x) ?H? ?(Pe(x) -?) z??dP(zx),
• where P(zx) is the distribution of z in the
  reference group defined by x.

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Social equilibrium

• A social equilibrium occurs when peoples
  expectations are consistent with the average
  proportion in the reference group who take the
  action.
• In equilibrium, peoples expectations are
  consistent with the mathematical expectation
  P(x).
• That is, Pe(x)P(x).

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Unique equilibrium or multiple equilibria?

• E.g. H? is the logistic distribution function
  and ?z?? is distributed symmetrically about the
  origin.
• If ?lt4, there is a unique social equilibrium.
• If ?gt4, then there are at least three social
  equilibria.

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Why ? 4?

• In the neighbourhood of middle equilibrium in
  Figure 1, at which P(x)0.5, ?P(x)/?Pe(x)gt1.
• With the logistic distribution,
• ?P(x)/?Pe(x) ?P(x)1-P(x).
• Around middle equil, ?P(x)/?Pe(x)0.25?.
• Implies ?P(x)/?Pe(x)gt1 in the neighbourhood of
  equil. requires ?gt4.

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?gt4 is not a sufficient condition for multiple
equilibria

• E.g. the distribution of observable attributes
  (z) is sufficiently skewed toward people who
  favour (are against) the action.
• Or the symmetry is not around the origin.
• Then there can be one high-level (low-level)
  equilibrium.

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Stability of equilibria and dynamics

• Denote the middle equilibrium in first Figure
  as P.
• For Pe (x)gtP, Pe(x)gtP(x), which increases P(x)
  in next cohort
• ? converge to high level equilibrium.
• Conversely, starting at values of the expected
  proportion below P.
• ? converge to low level equilibrium.
• Middle equilibrium is unstable.

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Implications

• History matters (e.g. initial expectations) for
  the selection of the low-level or high-level
  equilibrium.
• Temporary changes in the socio-economic
  environment that alter behaviour and/or
  expectations can produce dramatic changes
• ? move from low level to high level equilibirum

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Multiplier effects (low ?, larger ?)
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Shift in the distribution of attributes
favourable to action from skewed against
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Shift from multiple equilibria to unique high
level equilibrium, e.g. larger ?)
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Example rapid increase in non-marital
childbearing in Europe
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Explosion of births outside marriage in Britain
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Who has a birth before marriage?

• Costs of non-marital birth in terms of labour and
  marriage market opportunities lost are smaller
  for women with poorer prospects in these
  markets
• E.g. women with less education.
• Expect women with poorer prospects to be more
  likely to have a birth before marriage.

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Social interaction and differentials

• If reference group for social influence is
  people of a similar background, then
  differences in birth rates by education levels
  would be larger when non-marital childbearing is
  more common.
• If reference group for social influence is
  wider population, then educational differentials
  would be smaller when non-marital births are more
  common.

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Different equilibria by education group
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Comparison of birth rates

• Estimate proportional hazard models of first
  birth rates
• within cohabiting unions (at risk from start of
  union to break-up/marriage/childbirth).
• Outside live-in union (at risk from age 14
  until union is formed or child is born).
• Compare birth rates of less educated relative to
  more educated women, as defined earlier.

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Geographic clustering and social interaction

• If reference groups are within a country,
  country-clustering is consistent with a social
  interaction model with multiple equilibria (e.g.
  social stigma).
• Example cohabiting unions in Europe.
• Three broad groups in terms of the percentage of
  women aged 25-29 who live in a cohabiting union.

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Dramatic increase in cohabitation in Britain
Percent who cohabited in their first live-in
partnership, by birth cohort
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Cohabitation in first union

• Cohabitation was more likely for more educated
  women for women born in 1950s and 1960s.
• Less educated women had caught up by 1970s
  cohort.
• More educated were pioneers in cohabitation.

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Markets and Multipliers

• Social multipliers and multiple equilibria can
  also arise through market interactions.
• E.g. positive social interaction mediated by the
  marriage market.
• Example 1 Divorce
• Example 2 The impact of the contraceptive pill
  on womens career decisions

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Divorce and prospects of remarriage

• Divorce brings costs, because finding another
  partner involves time and effort, and there is a
  risk of remaining single.
• The expected gain from divorce depends,
  therefore, on the prospects of remarriage.
• These prospects depend on the decisions of others
  to divorce and remarry.
• ? a high-divorce or a low-divorce equilibrium may
  be supported with the same set of fundamental
  factors affecting divorce decisions.

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Divorce and prospects of remarriage

• If many couples are expected to divorce, then the
  prospects of remarriage are high because there
  are more people in the remarriage market
• ?divorce less costly ?more divorce.
• Low divorce rates ?divorce more costly ?fewer
  divorce.
• the possibility of multiple equilibria
  (self-fulfilling nature of divorce expectations).

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Multiplier effects search externalities

• Even if there is a unique equilibrium, an
  increase in the divorce rate generated by a small
  change in its fundamental determinants can give
  rise to a large change in the divorce rate.
• Because people do not take into account that
  ones own divorce increases the remarriage
  chances of all other divorcees, the marriage
  market produces too few divorces ? inefficiency.

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The Pill and Womens Careers

• In the absence of reliable contraception, women
  undertaking lengthy professional education would
  have to incur
• the cost of sexual abstinence
• or the risk of pregnancy.
• The Pill decreased the cost of investment.
• Encouraged more women to enter professional
  careers.

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The costs of delaying marriage

• Lengthy education generally requires the delay of
  marriage.
• In the interim other women marry.
• Career women are more likely to have to settle
  for a poorer match (smaller pool of eligible
  bachelors).
• Argument and evidence in C. Goldin and L. Katz
  (2000).

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Indirect social multiplier effect

• By reducing the penalty of delaying marriage
  (sexual abstinence or pregnancy risk), the Pill
  encouraged all women and men to delay marriage to
  a time when their tastes and character were
  better formed.
• Created a better (thicker) marriage market for
  career women.
• Reduced the cost of delaying marriage.
• Encouraged them to pursue a career.