A theory of esteem based peer pressure

Transcription

1 A theory of esteem based peer pressure Fabrizio Adriani University of Leicester Silvia Sonderegger University of Nottingham

2 Status and Esteem [A]part from economic payoffs, social status seems to be the most important incentive and motivating force of social behavior. John Harsanyi (Essays on Ethics, Social Behavior, and Scientific Explanation)

3 Modelling Status Class of models using signaling theory to formalize status Bernheim, 1994, Ireland, 1994, Glazer and Konrad, 1996, Benabou and Tirole, 2006 and 2011, Ellingsen and Johanneson, 2008, Andreoni and Bernheim, 2009 Main insight: Agents care about others perception of their type (ability, wealth, altruism). Agents choose their behavior (study toward a degree, buy an expensive car, donate to charity) taking its signaling content into account.

4 Peer pressure Signaling models have implications for peer pressure. Different peer groups carry different prior distributions e.g. job market candidates from better academic institutions perceived as more talented Incentive to engage in status seeking behavior depends on characteristics of one s peer group Effect of changes in peer distribution not well understood.

5 The honor-stigma model Benabou and Tirole (2006, 2011) honor-stigma model: Continuum of types + binary action Very simple model but ideally suited to analyze peer pressure Use the model to ask the following questions

6 Effect of average peer quality Q: What happens to the incentive to exert effort when peer quality increases? A: Both a positive ( keeping up with the Joneses effect ) and a negative ( Big fish in a little pond ) effects may arise. Answer depends on the characteristics of the task (difficult, easy) and on the shape of the peer distribution (unimodal, bimodal, etc.).

7 Effect of average peer quality Q: What happens to the incentive to exert effort when peer quality increases? A: Both a positive ( keeping up with the Joneses ) and a negative ( Big fish in a little pond ) effects may arise. The answer depends on the characteristics of the task (difficult, easy) and on the shape of the peer distribution (unimodal, bimodal, etc.).

8 Effect of peer dispersion Q: What happens to the incentive to exert effort when peer heterogeneity increases? A: A more heterogenous peer group always provides stronger incentives.

9 Effect of peer dispersion Q: What happens to the incentive to exert effort when peer heterogeneity increases? A: A more heterogenous peer group always provides stronger incentives.

10 Effect of group truncations Q: What is the effect of segregation by ability (e.g. admissions policies to academic programmes)? What happens when the upper tail self selects out of the group? A: Truncations always weaken the incentive to exert effort, independently of whether they occur on the upper or lower tail.

11 Effect of group truncations Q: What is the effect of segregation by ability (e.g. admissions policies to academic programmes)? What happens when the upper tail self selects out of the group? A: Truncations always weaken the incentive to exert effort, independently of whether they occur on the upper or lower tail.

12 Plan of the talk Review the honor-stigma model Comparative statics on first moment of peer distribution Comparative statics on truncations Comparative statics on dispersion

13 Other stuff Relevant strands of the literature ignored here 1. Other theories of peer pressure/ peer effects (Arnott and Rowse, 1987, Benabou, 1993, Lazear, 2001, Banerjee and Beasley, 1991, Kandel and Lazear, 1992). 2. Relative consumption effects (e.g. Abel, 1990, Gali, 1994) 3. Status and conspicuous consumption (see e.g. various works by Robert Frank) 4. Empirical (Economics) literature on peer effects in education (see e.g. Epple and Romano, 2011)

14 Model Each agent belongs to a group g (school, firm, fraternity, sport club). A group has a continuum of members over the interval [0, 1]. Each group member simultaneously chooses whether or not to exert effort e {0, 1} toward performing a task.

15 Information A group member s type is unobservable. Others can only observe his behavior (e) and the group to which the individual belongs. Each group g is characterized by a distribution of types with density f g : [X g, X g ] R +, f g is continuous with full support in [X g, X g ], has (strictly increasing) cumulative function F g, quantile function F 1 g, and finite mean θ g.

16 Preferences A type x individual has preferences U(e, x) + µe(x e, g) (1) Intrinsic pr. Esteem Net intrinsic reward from effort: v(x) U(1, x) U(0, x) [Assumed strictly increasing and differentiable]. Net esteem reward φ E(x e = 1) E(x e = 0)

17 The net esteem function Let φ(x) E(X X x) E(X X < x). Lemma 1 (Jewitt, 2004) If f has exactly one change in monotonicity and this is from increasing to decreasing (from decreasing to increasing), then φ has exactly one change in monotonicity from decreasing to increasing (from increasing to decreasing).

18 Lemma 2 Unimodal case: If f is symmetric and strictly increasing (decreasing) on the left (right) of the mode, then φ is strictly decreasing (increasing) on the left (right) of the mode. U-shaped case: If f is symmetric and strictly decreasing (increasing) on the left (right) of the anti-mode, then φ is strictly increasing (decreasing) on the left (right) of the anti-mode.

19 φ(x) φ(x) x x

20 Equilibrium Throughout, assume v(x g ) + µ(x g θ g ) > 0 > v(x g ) + µ(θ g X g ). (2) Then, there exists an interior equilibrium cutoff x determined by the condition φ(x ) = v(x ) µ, (3) Sufficient condition for uniqueness: v (x)/µ < φ (x) for all x.

21 φ(x) φ(x) x v(x)/µ x x v(x)/µ x

22 Honor and Stigma If effort is widespread agents main concern is avoiding stigma Those who fail to exert effort are pooled with the lower tail If effort is rare main concern is reaping honor Exerting effort means pooling with the upper tail

23 Comparative Statics on the peer group distribution Analyze how peer pressure changes as we change the peer group distribution Changes in the peer group distribution affect the incentive to exert effort for signaling purposes Use equilibrium cutoff x as a measure of the strength of incentives

24 Better peers How does peer pressure change when one moves to a group of better peers? Equivalent to asking: What happens to the cutoff if we shift the group distribution to the right?

25 Unimodal case φ l (x) φ h (x) φ l (x) φ h (x) x x x h x l x l x h v(x)/µ v(x)/µ

26 Intuition Keeping up with the Joneses since effort is more widespread in group h, stigma-avoidance incentives are stronger in h Big fish in a little pond since effort is more widespread group h, honor-reaping incentives are stronger in l

27 U-shaped case φ l (x) φ h(x) φ l (x) φ h(x) x x x l x h x l x h v(x)/µ v(x)/µ

28 Unimodal v U-shaped Unimodal: peer pressure strongest when most group members adopt same behavior (effort/not) U-shaped: peer pressure strongest when group is evenly split (50/50) When effort is widespread (rare) group h (l) is less polarized.

29 Proposition 1 Consider two groups h and l with f h and f l belonging to the same location family of densities and θ h > θ l. Provided that X l > X h, there always exists ˆx (θ l, θ h ) such that (Unimodal) the cutoff of group h is lower than that of l whenever x h < ˆx and is higher than that of l whenever x h > ˆx. (U-shaped) the cutoff of group h is higher than that of l whenever x h < ˆx and is lower than that of l whenever x h > ˆx.

30 Truncations What happens when the peer group distribution is truncated? Ex. of left truncation: admission to academic programs Ex. of right truncation: semi-pro sport circuits

31 Proposition 2 Consider groups g and g, where g is a truncation of g. Then, irrespectively of whether the truncation is on the left or right tail (or on both tails), group g has a lower cutoff (i.e. provides stronger incentives) than g.

32 The Black middle class puzzle Austen-Smith and Fryer (2005): Why do middle class Black pupils perform worse than White middle class? Fryer and Torelli (2004): Weaker relationship between status and academic achievement for Blacks than for Whites. Effect is stronger in racially diverse suburban schools

33 Partial desegregation Wilson: desegregation process induces Black middle class to migrate from Black neighborhoods to suburbs In the process, left tail is left behind (in the ghetto) If ability is determined by socio-economic background, Black pupils attending suburban schools may have a left-truncated distribution Less incentive to signal ability through academic achievement

34 Dispersion What happens when an agent moves to a more unequal group?

35 f g f G φ G φ g x x G x g v(x)/µ x

36 Proposition 3 Consider two groups with densities f G and f g with identical mean. Then, if f G is second order stochastically dominated by f g, then group G has a lower cutoff (i.e. provides stronger incentives) than group g.

37 Application: inequality and conspicuous consumption Consider consumers endowed with wealth x solving max C,Z U(Z, C) + E(x Z) s.t. x = C + πz (4) C = (unobservable) composite good, Z = discrete (conspicuous) good, π = price of Z.

38 Application: inequality and conspicuous consumption Assume Z is a normal good π is neither too large nor too small Then, aggregate demand for conspicuous good 1 F (x ) is increasing in inequality.

39 Conclusions More heterogenous peers provide stronger incentives Effect of increase in peer quality is ambiguous Agents may feel discouraged when peer quality increases Link to Psychology evidence (work by Herbert Marsh and co-authors)