Article Summary: Economics and Identity

You can access the published paper here and the unpublished technical appendices here.  The authors are George Akerlof [Ideas, Berkeley] and Rachel Kranton [Duke University].  The full reference is:

Akerlof, George A. and Kranton, Rachel E. “Economics and Identity.” Quarterly Journal of Economics, 2000, 115(3), pp. 715-53.

The abstract:

This paper considers how identity, a person’s sense of self, affects economic outcomes.We incorporate the psychology and sociology of identity into an economic model of behavior. In the utility function we propose, identity is associated with different social categories and how people in these categories should behave. We then construct a simple game-theoretic model showing how identity can affect individual interactions.The paper adapts these models to gender discrimination in the workplace, the economics of poverty and social exclusion, and the household division of labor. In each case, the inclusion of identity substantively changes conclusions of previous economic analysis.

I’m surprised that this paper was published in such a highly ranked economics journal.  Not because of a lack of quality in the paper, but because of it’s topic.  It reads like a sociology or psychology paper.  99% of the mathematics were banished to the unpublished appendices, while what made it in were the justifications by “real world” examples.  The summary is below the fold …

The authors propose a model whereby a) there are abstract social identities or categories (e.g. “man” and “woman”); b) there are also prescriptions on what actions each identity ought (or ought not) to take; c) individuals’ payoffs are identity-based; d) individuals’ payoffs derive from both their own actions and from others’ actions; and e) some people may be able to choose their identity.  In particular, $$j$$’s utility function is:

$$!U_{j}=U_{j}\left(a_{j},a_{-j},I_{j}\right)$$

Where $$a_{j}$$ are $$j$$’s actions (including consumption decisions), $$a_{-j}$$ are the actions of everyone other than $$j$$ and $$I_{j}$$ is $$j$$’s identity or self-image.  $$I_{j}$$, in turn, is represented as:

$$!I_{j}=I_{j}\left(a_{j},a_{-j};c_{j},\epsilon_{j},P\right)$$

Where $$c_{j}$$ describes how $$j$$ believes everyone is assigned to identities/categories, $$\epsilon_{j}$$ is a measure of the extent to which $$j$$’s own given characteristics match the social ideal of $$j$$’s assigned category and $$P$$ is the set of prescribed ideal actions for each identity.

A series of examples are then given for the four main assertions made about this utility framework:

The impact of a person’s actions ($$a_{j}$$) on their utility depends in part on their sense of identity ($$I_{j}$$)

  • Self-Mutilation (tattooing, body-piercing, steroid abuse, plastic surgery, circumcision, etc.)
  • Gender and Occupations (a woman in a “man’s job”)
  • Alumni Giving
  • Mountaineering

People have identity-related payoffs that are affected by others’ actions ($$a_{-j}$$ affects utility both directly and through $$I_{j}$$)

  • Gender and Occupations (when confronted by a woman in their profession, men might tease her)
  • Manhood and Insult
  • Those who seek upward mobility are often teased by their peers

To some extent, people may choose their identity ($$c_{j}$$)

  • Parents choosing schools for their children
  • Entering particular fraternities or sororities at college
  • Moving from permanent residency to citizenship

(Self-choice of an identity can still be constrained by appearance, voice or accent)

How social categories ($$C$$) and prescriptions ($$P$$) are created

  • Advertising
  • Professional and Graduate Schools, Military Training
  • Political Identity (populist leaders fostering racial or cultural divisions)

They next present a simple model capturing some of these aspects, summarised in this extensive-form dynamic game:

akerlof_and_kranton

There are two social identities or categories:  Green and Red.    Social prescriptions dictate that a “true” Green will choose Activity One.  Both players start out being thought of as Green, but Person Two has a private desire to perform Activity Two (this need not require that they think of themselves as Red).

Person One goes first and chooses Activity One (the possibility of their choosing Activity Two is suppressed because it would never be chosen in a Subgame-Perfect equilibrium).

If Person Two chooses to conform to the societal prescription and perform Activity One, Person One gets $$V$$ while Person Two gets nothing.

If Person Two instead chooses Activity Two (as indeed they would if their utility were solely determined by their own action), then this creates an identity conflict.  Person Two gets $$V$$ from the activity, but also suffers anxiety at the loss of self-identity ($$-I_{s}$$).  In addition, an externality is imposed on Person One, who has the value of their identity threatened ($$-I_{o}$$).

In this case, Person One has an opportunity to respond to Person Two’s deviation from the prescription.  If they do so, a further loss ($$-L$$) is imposed on Person Two and Person One no longer suffers a loss from questioning their identity but instead incurs a cost of the response.

Subject to the parameters, there are four possible subgame-perfect equilibria:

  • $$c<I_{o}$$ and $$I_{s}<V<I_{s}+L$$:  The threat of response is credible so that Person One successfully deters Person Two from engaging in Activity Two.
  • $$c<I_{o}$$ and $$I_{s}+L<V$$: Person One responds (as it minimises their own loss) so the threat is credible, but it has insufficient effect to deter Person Two from choosing Activity Two.
  • $$c>I_{o}$$ and $$I_{s}<V$$: Person One will not respond so the threat is not credible, and Person Two chooses Activity Two.
  • $$c>I_{o}$$ and $$I_{s}>V$$: Person One will not respond so the threat is not credible, but Person Two still doesn’t choose Activity Two because the loss of self-identity exceeds the benefit.

Clearly, government intervention to impose a “tax” or certain actions can serve to change the equilibrium.

The authors acknowledge that while the set of identities, prescriptions and the pairing of Persons One and Two were imposed here, they might be endogenous in a more complete model.

The model is then applied to three different scenarios:  Gender and the Workplace, Poverty and Social Exclusion, and The Economics of the Household.

(I’ll finish this summary once I can install the fonts needed to read the technical appendices)

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