Tadelis (2001) - The Market For Reputations As An Incentive Mechanism

• This page is referenced in BPP Field Exam Papers

Reference(s)

Tadelis, S. (2001) "The Market for Reputations as an Incentive Mechanism," Journal of Political Economy 110(4):854-882 pdf

Abstract

Reputational career concerns provide incentives for short-lived agents to work hard, but it is well known that these incentives disappear as an agent reaches retirement. This paper investigates the effects of a market for firm reputations on the life cycle incentives of firm owners to exert effort. A dynamic general equilibrium model with moral hazard and adverse selection generates two main results. First, incentives of young and old agents are quantitatively equal, implying that incentives are "ageless" with a market for reputations. Second, good reputations cannot act as effective sorting devices: in equilibrium, more able agents cannot outbid lesser ones in the market for good reputations. In addition, welfare analysis shows that social surplus can fall if clients observe trade in firm reputations.

Summary

The model seperates identities from entities (which have names), with the later having reputations. There is a market for names and two types of agent: good and opportunistic. The agents are short-lived but the transferability of the names creates a long-lived entity seperate from the identity of the agents. There is no seperating equilibria where only good or bad types buy names, but there are reputation dynamics - reputations increase after good performance and decrease after bad performance.

The Model

The model has the full base assumptions:

• Buyers and sellers are risk neutral
• Types of sellers are indistinguishable and are active for two periods with overlapping generations
• Sellers can choose a new name, keep their name or buy a name
• Only names have track records
• There is a competitive market of buyers so that prices are bid up to their expected surplus
• There is no discounting

In addition there are the following driving assumptions:

• There are no contingent contracts
• Shifts of name ownership are not observable
• Name changes are costless
• With probability [math]\epsilon \ge 0\,[/math] a seller can not change his name (note that this is a technical assumption to rule out some 'bad' equilibria from costless name changes)

The model uses a rational expectations equilibrium.

There are two types of seller: [math]G\,[/math] (good) exist in proportion [math]\gamma\,[/math] and succeed with probability [math]P_G \in (0,1)\,[/math], and [math]O\,[/math] (opportunistic) exist in proportion [math]1-\gamma\,[/math] and success with probability [math]eP_G\,[/math] where [math]e \in [0,1]\,[/math] and have a cost of effort [math]c(e)\,[/math] that satisfies Inada conditions.

The sequence of events is:

1. New agents chooses or buys his name
2. Buyer pays upfront
3. Opportunistic type chooses effort
4. Success or failure realized
5. Retiring agent can sell his name/continuing agent can change their name

Benchmark: No Reputations Markets

Here we assume that names can not be traded and restrict attention to two periods with three generations as depicted below.

[math] \vskip 5pt \hskip 200pt$t=1$\hskip 57pt$t=2$ \hskip 80ptGeneration 0:\hskip 10pt\TEXTsymbol{\vert}\_\_\_\_\_\_\_\_\_\_% \TEXTsymbol{\vert} \vskip 2pt \hskip 80ptGeneration 1:\hskip 10pt\TEXTsymbol{\vert}\_\_\_\_\_\_\_\_\_\_% \TEXTsymbol{\vert}\_\_\_\_\_\_\_\_\_\_\TEXTsymbol{\vert} \vskip 2pt \hskip 80ptGeneration 2:\hskip 105pt\TEXTsymbol{\vert}\_\_\_\_\_\_\_\_\_\_% \TEXTsymbol{\vert} \,[/math]

In period 1 there is one wage as everyone has a new name. In period 2 there are three wages depending on the [math]h\,[/math] (histories) observed which are either [math]S\,[/math] (success), [math]F\,[/math] (failure), or [math]N\,[/math] (new name). [math]F\,[/math] histories are irrelevant as sellers who failed are better off costly changing their name.

[math]O\,[/math] types will exert zero effort in the second period (as it is costly and contracts are made in advance) so [math]w_{2}(h)\,[/math] only depends on clients' beliefs about the likelihood of [math]h\,[/math] belonging to a [math]G\,[/math] type.

Expected period 2 utility of an [math]O\,[/math] type is:

[math]\mathbb{E}u_{O} =w_{1}+eP_{G}w_{2}(S)+(1-eP_{G})w_{2}(N)-c(e) =w_{1}+eP_{G}\Delta w+w_{2}(N)-c(e)\,[/math]

where [math]\Delta w\equiv w_{2}(S)-w_{2}(N)\,[/math]

The equilibrium is characterized by the tuple [math]\left\langle w_{1},w_{2}(S),w_{2}(N),e\right\rangle\,[/math] such that [math]e\,[/math] is a best response given [math]w_{2}(S)\,[/math] and [math]w_{2}(N)\,[/math], and all wages are correct given rational expectations about [math]e\,[/math]

Equilibrium beliefs imply:

[math]\Pr \{G|S\}=\frac{\gamma P_{G}}{\gamma P_{G}+(1-\gamma )eP_{G}}\,[/math]

[math]\Pr \{G|N\} =\frac{\gamma (1-P_{G})+\gamma }{\gamma (1-P_{G})+(1-\gamma)(1-eP_{G})+1} =\frac{2\gamma -\gamma P_{G}}{2-P_{G}[\gamma +(1-\gamma )e]}\,[/math]

Equilibrium wages are:

[math]w_{2}(h)=\Pr \{G|h\}\cdot P_{G}\,[/math]

Fixing [math]\Delta w\,[/math] the equilibrium [math]e\,[/math] solves the FOC:

[math]P_{G}\Delta w=c^{\prime}(e)\,[/math]

However, optimal effort must solve:

[math]P_{G} \ge c^{\prime }(e)\,[/math]

[math] \,[/math]