A discussion on status motives and optimal social decision

It is useful to consider the properties of an equilibrium in which many effort decision-makers act as in the model presented. Observe that both status motives affect individual effort decisions. As agents ignore the externalities that their decisions generate, the equilibrium based on individual decisions will be sub-optimal. This is because effort decisions affect the relative deprivation of others and the social status rewards. This prediction is in accordance with the findings of economic models in which individual utility depends on relative situation (Clark and Oswald, 1998; Piketty, 1998; Frank, 2005), and status motives lead to sub-optimal decisions.

As a result, the equilibrium defined by equations (2.9b) and (2.7b) are never first-best efficient because of the status-induced externality of social rewards and the rat-race effect induced by the reference group. As Piketty (1998) and chapter 1 noted, the socially optimal effort level is lower than the effort level chosen by agents individually. The additional effort of agents with originI_L generated by expected social status rewards and reference group effect is inefficiently, while the effort level chosen by agents with high social origin is higher than the socially optimal effort level. This is because the social reward that agents with origin I_U receive due to economic success is supported by beliefs, and it does not depend on their real effort. Furthermore, their effort is socially sub-optimal because it affects the reference group income of agents with origin I_L, which induces an additional inefficient effort from them. Finally, when there are multiple equilibrium (cases cand c⁰), as Piketty (1998) demonstrated low-effort equilibrium are always less inefficient

than high effort equilibrium.

2.4 An extension: Heterogeneity in reference groups and intergenerational learning

In the previous section we assume identical agents who only differ in their social origins.

Furthermore agents with origin ILhave the same reference group, which leads to the same and unique effort decision. They anticipate the actions of others identical agents when they take effort-decisions, which implies perfect forward-looking agents and that public beliefs about e^b_Lande^b_U are known. As a result, we do not care about how they form their expectation about their peer effort.

Now we introduce an analytical form to consider heterogeneity in the reference group of agents with origin I_L. We assume that each agent i knows his P_i, which is a random variable with the distribution function F(Pi) for all Pi : 0 ≤ Pi ≤ 1. Observe that Pi

incorporates the idea that individuals with similar characteristics may present differences in their reference group. As a result, the expected income of the reference group, y^RG, is defined as y^RG =P_i(E(y|I_U)) + (1−P_i)E(y|I_L).

As there are differences in the reference group composition of agents with social origin I_L, there could be differences in the effort decisions among them. An implication of this is that the expected effort of agents with origin I_L represents an average of their effort decisions.

ˆ

P e_Li(P)dp=e^mean_L (2.10)

Assumption A.II stated that individual effort levels are not publicly observable (e^mean_L is unknown) and agents choose their effort based on the public beliefs e^b_L about e^mean_L .

Agents with origin I_L do not know the effort of the peers of their generation, but each generation updates their beliefs with respect to previous generation belief by a backward-looking learning process, that is, in light of the recent experience of peers with the same social origin from a previous generation.²²

The updating effort belief function is defined as an adaptive process (Assumption VIII):

4e^b_L =e^b_{L current}−e^b_{L parents}= Φ(real mobility_parents−Expected mobility_parents) (2.11)

where “current” and “parents” indicate the beliefs of current and previous generations respectively. The mobility experienced by the previous generation is observable by the

“next generation” (real mobility_parents), and it represents a signal of peers’ effort levels (observable from previous generation).²³ On the other hand, theExpected mobility_parents are transmitted from previous generations (intergenerational inherited beliefs) and repre-sentsa priori public beliefs for the current generation. As a result, the current generation knows the arguments of the updating belief function. To simplify, the real mobility and expected mobility of the parents’ generation, are expressed as a function of their real mean effort and their expected mean effort respectively.

4e^b_L =φ(e^mean_{L parents}−e^b_{L parents}) (2.12)

22Bowles (2004) argues that backward-looking learning approach has advantages when compared to the forward-looking learning process.

23Observe that the signal of previous generations, not only provides information about peer effort, but also provides valuable information about the effectiveness of the effort of agents with low social origins to achieve economic success and social ascent.

The parameter φ represents the speed of error correction and we assume that 0< φ <1.

Finally, we assume that agents know that there is an exogenous maximum effort level E. Under these assumptions the updating effort belief function is defined as:

e^b_Lcurrent =min(φ(e^mean_{L parents}−e^b_{L parents}) +e^b_{L parents}; E) (2.13)

The rationality of the updating belief rule is the following: when the current generation has an a priori belief that their peers in the past had made a high effort but were not rewarded with upward mobility, there will be some downward adjustment of the expected effort for their current peers 4e^b_L < 0. A high achievement performance in the previous generation should induce rational agents to expect higher effort in their next generation peers, namely 4e^b_L>0, or 4e^b_L= 0 ife^b_Lparents=E.

2.4.1 Long term effort equilibrium with learning processes and