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Hidden Information, Bargaining Power and Efficiency: An Experiment by Antonio Cabrales X ** Gary Charness *** Marie Claire Villeval DOCUMENTO DE TRABAJO 2009-08

Serie Talento, Esfuerzo y Movilidad Social CÁTEDRA Fedea – Banc Sabadell

Serie Capital Humano y Empleo CÁTEDRA Fedea – Santander

February 2009

Universidad Carlos III de Madrid, CEPR

** University of California at Santa Barbara.

*** University of Lyon, CNRS, and IZA, Bonn.

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Hidden Information, Bargaining Power, And Efficiency: An Experiment

Antonio Cabrales, Gary Charness and Marie Claire Villeval

January 18, 2009

Abstract: We devise an experiment to explore the effect of different degrees of bargaining power on the design and the selection of contracts in a hidden-information context. In our benchmark case, each principal is matched with one agent of unknown type. In our second treatment, a principal can select one of three agents, while in a third treatment an agent may choose between the contract menus offered by two principals. We first show theoretically how different ratios of principals and agents affect outcomes and efficiency. Informational asymmetries generate inefficiency. In an environment where principals compete against each other to hire agents, these inefficiencies remain. In contrast, when agents compete to be hired, efficiency improves dramatically, and it increases in the relative number of agents because competition reduces the agents’ informational monopoly power. However, this environment also generates a high inequality level and is characterized by multiple equilibria. In general, there is a fairly high degree of correspondence between the theoretical predictions and the contract menus actually chosen in each treatment. There is, however, a tendency to choose more ‘generous’ (and more efficient) contract menus over time. We find that competition leads to a substantially higher probability of trade, and that, overall, competition between agents generates the most efficient outcomes.

Keywords: Experiment, Hidden Information, Bargaining Power, Competition, Efficiency

JEL Classification: A13, B49, C91, C92, D21, J41

Contact: Antonio Cabrales, Universidad Carlos III de Madrid, antonio.cabrales@uc3m.es Gary Charness, University of California at Santa Barbara, charness@econ.ucsb.edu Marie Claire Villeval, University of Lyon, CNRS, and IZA, Bonn, villeval@gate.cnrs.fr

1. INTRODUCTION

The theory of markets with asymmetric information has been a “vital and lively field of economic research” (2001 Nobel Prize committee) for decades. The classic ‘lemons’ paper (Akerlof 1970) illustrated the point that asymmetric information led to economic inefficiency, and could even destroy an efficient market. Since the seminal works of Vickrey (1961) and Mirrlees (1971), research on mechanism design has sought ways to minimize or eliminate this problem.¹ In an environment with hidden information (sometimes characterized as adverse selection), each agent knows more about her² ‘type’ than the principal does at the time of contracting. In the standard labor scenario, a firm hires a worker but knows less than the worker does about her innate work disutility. Other typical applications include a monopolist who is trying to price discriminate between buyers with different (privately known) willingness to pay, or a regulator who wants to obtain the highest efficient output from a utility company with private information about its cost.³

The fact that agents know their own ability levels while principals may not causes difficulties in contracting, as an agent may not choose the action that is in the best interest of the principal. If outcomes are related to actions, firms with complete information could design ‘first-best’ contracts that theoretically induce truthful revelation of types and generate economic efficiency by making the contract contingent on the outcome. However, in contracting under hidden information, the problem is how to induce the efficient action without being able to observe the agent’s true type; in this case, it is typically necessary to devise ‘second-best’ contracts that lead to separation of types, but which are somewhat distorted and less than fully efficient.

In this paper we report the results of experiments designed to test the influence of competition when there is hidden information. This can be seen as a question of organizational or institutional design – what effects do different rules and markets have on performance and efficiency?⁴ We examine how differing degrees of relative bargaining power between principals and agents affect outcomes and efficiency when there is a problem of hidden information.

¹ Applications include public and regulatory economics (Laffont and Tirole 1993), labor economics (Lazear 1999), financial economics (Freixas and Rochet 1997), business management (Milgrom and Roberts 1992), and development economics (Ray 1998).

² Throughout this paper we assume that the principals are male and the agents are female.

³ One-shot contracts are common in consumer transactions. In the public sector, government procurement is often conducted on a one-shot basis.

Our approach is to consider three environments that differ according to the type of competition present in the environment. In our benchmark case, each principal is matched with one agent of unknown type. In our second treatment, a principal can select one of three agents, while in a third treatment an agent may choose between the contract menus offered by two principals. Principals can choose to offer one of six feasible contract menus, which are held constant across our treatments; in turn, agents can select high or low effort, or reject the contract menu entirely and receive reservation payoffs. We derive the equilibrium predictions for each environment and include the induced contract menus for each treatment among the six feasible choices for the principal. We examine the outcomes in each treatment, ranking the institutions as a function of their relative efficiency, both in terms of effort and the probability of trade.

In this respect theory provides a first answer. To understand the theoretical efficiency ranking, it is important to realize that incomplete information in markets creates inefficiencies because the agents have a certain monopoly power. More precisely, they are the sole ‘owners of a valuable resource – information about their type. We first show from a theoretical point of view how different degrees of bargaining power between principals and agents, related to various degrees of competition in the market, affect outcomes and efficiency. In an environment where principals compete against each other to hire agents, inefficiencies remain. In contrast, in an environment where agents compete to be hired, efficiency improves dramatically and increases in the relative number of agents because competition reduces the agents’ informational monopoly power. However, this environment also generates a high inequality level and is characterized by multiple equilibria, which may have important behavioral implications in the field if people have social preferences such as inequality aversion.

Although we use the standard static screening model, it is worth noting that Kanemoto and MacCleod (1992) examine the effect of competition in a dynamic environment and find that one obtains the first-best outcome if there is sufficient competition for workers, even with asymmetric information. Perhaps there is some empirical analog to this result in the static case.

Our experiment constitutes the first test of the impact of varying the relative bargaining power between principals and agents on the selection of contracts in the presence of both heterogeneous agents and hidden information, and their subsequent efficiency. Our results are mostly supportive of the theory and the major implication is that the bargaining power directly affects the choice of contract menus. In comparison with environments in which there is either no competition or a competition among principals, our experiment finds that the institutional environment in which agents compete against each other is the most efficient as far as we consider the contracting pairs.

Even though, in general, there is a fairly high degree of correspondence between the theoretical predictions and the contract menus actually chosen in each treatment, there is a tendency to choose more ‘generous’ (and more efficient) contract menus over time. We find that competition leads to a substantially higher probability of trade, and that, overall, competition between agents generates the most efficient outcomes. We observe a fairly high degree of separation of agents’ types in the choices made in response to the various contract menus; interestingly, with agent competition we observe the more able agents strategically foregoing the option that would pay them more (if they are chosen), in order to signal their type by choosing the option that less able agents should never choose. Our data also show considerable evidence of changes in behavior over time, as participants learn what is effective and what is not.

The remainder of the paper is structured as follows: We review the relevant literature in section 2, and we describe our theoretical model and derive its predictions in section 3. We present our experimental design and implementation in section 4, with the results given in section 5. We discuss welfare and efficiency considerations in section 6, and conclude in section 7.

2. RELATED LITERATURE

Perhaps due to the complexity of business relationships, it is difficult to find support from field data for principal-agent theory. While there has been considerable theoretical work on contracts in recent decades, empirical tests of the theory have long remained scarce, particularly as far as hidden information is concerned. The Prendergast (1999) and Chiappori and Salanié (2003) surveys show that the econometrics of contracts has recently become a burgeoning field of research. However, the latter study points out that a number of empirical tests suffer from selection and endogeneity biases. In addition, many papers use similar data because of a lack of data on contracts. These difficulties explain that only few empirical tests of the hidden-information problem are available in the literature (see notably Cawley and Philipson, 1999; Chiappori and Salanié, 2000; Dahlby, 1983; Dione and Doherty, 1994; Finkelstein and Poterba, 2000; Genesove, 1993; Puelz and Snow, 1994; Young and Burke, 2001). Given the difficulties inherent with field data in this area, laboratory experiments offer a complementary approach that offers some promise, since it is possible to isolate and vary the factors of interest while keeping all others constant.

Previous experimental studies on asymmetric information have typically examined contracting with hidden action (moral hazard), where effort is not contractible; these include Berg, Daley, Dickhaut, and O’Brien (1992), Keser and Willinger (2000), Anderhub, Gächter, and Königstein (2002), and Königstein (2001).⁵ They observe that contracts are usually more generous than theoretically predicted. Charness and Dufwenberg (2006) find that cheap-talk statements of intent help to achieve desirable outcomes (the Nash bargaining solution).

There is little experimental work on hidden information and certainly no study considers the effect of varying the relative bargaining power on contracts and efficiency. In Miller and Plott (1985), the proportion of buyers varies but it never exceeds one; signaling is observed in most markets and market processes allow the buyers to extract private information from the sellers. Lynch, Miller, Plott and Porter (1986) confirm the existence of a market for “lemons” in experimental oral double auctions, and Holt and Sherman (1990) do so in posted–offer auctions. Experiments by Brandts and Holt (1992) and Banks, Camerer and Porter (1994), however, provide mixed evidence about the ability of subtle equilibrium refinements to predict players’ behavior in simple signaling games. In the context of team production, Cabrales and Charness (2004) observe that when more equitable menus are proposed, rejection rates are

⁵ Other studies involving moral hazard include Bull, Schotter, and Weigelt (1987), who examine the incentive effects of piece rate and tournament payment schemes, and Nalbantian and Schotter (1997), who investigate group incentive contracts. Plott and Wilde (1982), and DeJong, Forsythe, Lundholm, and Uecker (1985) consider moral hazard problems with multiple buyers and sellers. Güth, Klose, Königstein, and Schwalbach (1998)

lower and agents select actions according to their types. Charness and Dufwenberg (2008) find that communication is useful for achieving efficient outcomes in a hidden-information environment when it is possible for low-ability agents to achieve a Pareto-improvement over the principal’s outside option, but not otherwise.

There are three studies of the dynamic contracting problem: Chaudhuri (1998), Cooper, Kagel, Lo, and Gu (1999), and Charness, Kuhn, and Villeval (2008) study the problem of the ratchet effect, where the agent has an incentive to conceal her true type, as the principal may use this information to ratchet up the demands for performance in later periods. Nevertheless, principal-agent interactions in the field are frequently one-shot affairs; furthermore, if the principal could commit to an ex ante contract, it would be optimal to implement the one-shot problem in the dynamic setting.

One might predict that different relative bargaining power for principals and agents should lead to different contract menus being selected. However, results from the handful of experimental papers on the effects of unbalanced competition on the outcomes between firms and workers (or principals and agents) is somewhat mixed. Brandts and Charness (2004) find little difference in the gift-exchange outcomes according to whether there are more workers than firms or vice versa. Fehr, Kirchler, Weichbold, and Gächter (1998) find that an unbalanced market does not eliminate fairness when contracts are incomplete.

However, Roth et al. (1991) find that principals capture nearly the entire surplus when 10 agents compete in a “demand game” similar to the ultimatum game. Davis and Holt (1994) show that the ability of a buyer to switch between two sellers provides a strong incentive to develop reputation in a repeated game. In an ultimatum game with responders’ competition, Grosskopf (2003) finds that (the initially-similar) demands in the game with competition grow more over time than in the game with no competition. Finally, Fischbacher, Fong and Fehr (2003) demonstrate that the introduction of even a little competition provokes large behavioral changes. A model combining heterogeneous social preferences with decision errors enables to predict most of the experimental evidence with various degrees of competition. Thus, it is not clear ex ante what effects unbalanced competition will have on the hidden-information problem, particularly in terms of economic efficiency.

consider a dynamic moral hazard problem where trust and reciprocity issues impede obtaining the first-best outcome.

3. THE MODEL

In this section we describe the theoretical model that serves as the basis for the experimental design. In this game, the principal offers one contract that is intended for lowability-type agents and one contract intended for high-ability-type agents; these contracts are designed such that the agents have an incentive to self-select the appropriate contract. We vary the bargaining power by altering the relative proportion of principals and agents. As a preview, we note that the case with competition between principals (more principals than agents) yields a Rothschild-Stiglitz type of solution, which is invariant to the number of agents and generally inefficient. On the other hand, the case of competition between agents is not invariant to the (relative) number of agents. The presence of more agents relaxes the binding incentive-compatibility constraint (for the high-ability type), yielding a level of effort that decreases towards the efficient level with the number of agents. In the limit, the only relevant constraint for the high-ability type agent is the participation constraint. As a result, there are no inefficiencies.

Imagine that a firm needs one worker in order to be able to operate. The profits for the firm when it is operating are:

\[\Pi = e - w\]

where w are the effort levels and wages of the worker. Each worker has a utility function which depends on her ability type , which is her private information:

\[u _ {j} (e, w) = w - \frac {k _ {j}}{2} e ^ {2}\]

where and . That is, the high-ability type of agent has a lower cost of effort than the low-ability type. Thus, only the individual agent knows j, but e is observable and contractible.

From the utility functions of the principal and the agents we have that the first-best effort levels are:

\[\hat {e} _ {j} = \frac {1}{k _ {j}}, j \in \{H, L \}\tag{1}\]

We call the efficient level of effort.⁶ If we denote by the outside option of the worker (which we assume for simplicity to be type-independent) we can induce optimal effort, with:

\[\hat {w} _ {j} = \underline {{{U}}} + \frac {1}{2 k _ {j}}, j \in \{H, L \}\]

If the (independent) probability that an agent is a high- or low-ability type is denoted respectively by or , then the expected (optimal) profits for the principal are given by:

\[\Pi^ {E} = \frac {p _ {L}}{2 k _ {L}} + \frac {p _ {H}}{2 k _ {H}} - \underline {{U}}\]

In order to make some comparisons across treatments we hold this first-best contract fixed in all the treatments. However, the second-best optimal equilibrium contracts, when the types are private information of the agents, depend on the structure of the market, which is our treatment variable. Then the equilibrium contract menu in the Benchmark (B) treatment, with one principal and one agent, results from the solution of the maximization program:

\[\max _ {w _ {H}, w _ {L}, e _ {H}, e _ {L,}} p _ {H} (e _ {H} - w _ {H}) + p _ {L} (e _ {L} - w _ {L})\]

subject to

\[\begin{array}{c} w _ {H} - \frac {k _ {H}}{2} (e _ {H}) ^ {2} \geq \underline {{U}} (\mathrm{IR} _ {H}) \\ w _ {L} - \frac {k _ {L}}{2} (e _ {L}) ^ {2} \geq \underline {{U}} (\mathrm{IR} _ {L}) \\ w _ {H} - \frac {k _ {H}}{2} (e _ {H}) ^ {2} \geq w _ {L} - \frac {k _ {H}}{2} (e _ {L}) ^ {2} (\mathrm{IC} _ {H}) \end{array}\]

e ˆ _j

⁶ This is an appropriate terminology because in all the Pareto-efficient allocations of this problem (with complete information) the level of effort is always . This is so because of the quasi-linearity of the utility function of the agents, a common assumption in this field. Thus, the Pareto-efficient allocations only differ in the wages and profits of the principal and agent.

\[w _ {L} - \frac {k _ {L}}{2} (e _ {L}) ^ {2} \geq w _ {H} - \frac {k _ {L}}{2} (e _ {H}) ^ {2} \quad (\mathrm{IC} _ {\mathrm{L}})\]

where and are respectively the individual rationality and incentive compatibility constraints of an agent of ability type . As usual in these problems (see for example Mas-Colell, Green, and Whinston 1995, ch.14C), it turns out that the active constraints in the optimal solution are and , so that the solution is:

\[\begin{array}{l} e _ {H} ^ {B} = \frac {1}{k _ {H}} = 1; \quad e _ {L} ^ {B} = \frac {p _ {L}}{k _ {L} - k _ {H} (1 - p _ {L})} = \frac {1}{k _ {L} + \frac {1 - p _ {L}}{p _ {L}} (k _ {L} - k _ {H})}; \\ w _ {L} ^ {B} = \underline {{U}} + \frac {k _ {L}}{2} (e _ {L} ^ {B}) ^ {2}; \quad w _ {H} ^ {B} = \frac {1}{2} + w _ {L} ^ {B} - \frac {1}{2} (e _ {L} ^ {B}) ^ {2} \end{array}\tag{2}\]

The high-ability type of agent provides the ‘efficient’ level of effort and obtains utility above . These informational rents (rents are defined here as the utility an agent gets above her reservation utility) are equal to:

\[w _ {H} ^ {B} - \frac {1}{2} - \underline {{U}} = \frac {k _ {L} - 1}{2} (e _ {L} ^ {B}) ^ {2}\tag{2e}\]

The effort of the low-ability type of agent is ‘inefficiently’ low and she obtains no rents, because she is held to the reservation value (the constraint is binding). This is the subgame-perfect equilibrium of this game.

Assume now that the each principal is matched with three agents (this is the Excess Agent, or treatment). Then an equilibrium contract menu results from the solution of a slightly different maximization program. Given that high-ability types are ‘harder-working (they have a lower disutility of effort), they cost less per unit of output. Thus when any of the matched agents chooses the contract designed for the high-ability type, the principal always chooses her. If more than one agent chooses the high contract, the principal chooses randomly among those selecting the high contract.⁷

\[\max _ {w _ {H}, w _ {L}, e _ {H}, e _ {L,}} (1 - p _ {L} ^ {3}) (e _ {H} - w _ {H}) + p _ {L} ^ {3} (e _ {L} - w _ {L})\]

subject to

\[\begin{array}{c} w _ {L} - \frac {k _ {L}}{2} (e _ {L}) ^ {2} \geq \underline {{U}} \quad (\mathrm{IR} _ {L}) \\ \left(\frac {(1 - p _ {L}) ^ {2}}{3} + 2 \frac {(1 - p _ {L}) p _ {L}}{2} + p _ {L} ^ {2}\right) \left(w _ {H} - \frac {k _ {H}}{2} (e _ {H}) ^ {2}\right) + \left(1 - \frac {(1 - p _ {L}) ^ {2}}{3} - 2 \frac {(1 - p _ {L}) p _ {L}}{2} - p _ {L} ^ {2}\right) \underline {{U}} \geq \\ \frac {p _ {L} {} ^ {3}}{3} \left(w _ {L} - \frac {k _ {H}}{2} (e _ {L}) ^ {2}\right) + \left(1 - \frac {p _ {L} {} ^ {3}}{3}\right) \underline {{U}} \end{array}\tag{\((\mathrm{IC}_{H})\}\]

The can also be written

\[w _ {H} - \frac {k _ {H}}{2} (e _ {H}) ^ {2} \geq q \left(w _ {L} - \frac {k _ {H}}{2} (e _ {L}) ^ {2}\right) + (1 - q) \underline {{{U}}}\tag{\((\mathrm{IC}_{H})\}\]

where . The solution is now:

\[e _ {H} ^ {E A} = \frac {1}{k _ {H}} = 1; e _ {L} ^ {E A} = \frac {1}{k _ {L} + \frac {(1 - p _ {L}) ^ {3}}{p _ {L} ^ {3}} q (k _ {L} - k _ {H})};\tag{3}\]

\[w _ {L} ^ {E A} = \underline {{U}} + \frac {k _ {L}}{2} (e _ {L} ^ {E A}) ^ {2}; w _ {H} ^ {E A} = \frac {1}{2} + w _ {L} ^ {E A} - \frac {1}{2} (e _ {L} ^ {E A}) ^ {2}\]

The effort of the low-ability type of agent in the EA treatment, , is closer to the efficient effort than that in the B treatment . To see this note that both and are smaller than ; we now show , so that the distortion is lower in EA than in

\[e _ {L} ^ {E A} = \frac {1}{k _ {L} + \frac {(1 - p _ {L}) ^ {3}}{p _ {L} ^ {3}} q (k _ {L} - k _ {H})} > e _ {L} ^ {B} = \frac {1}{k _ {L} + \frac {1 - p _ {L}}{p _ {L}} (k _ {L} - k _ {H})} \Leftrightarrow \frac {(1 - p _ {L}) ^ {2}}{p _ {L} ^ {2}} q < 1\tag{3'}\]

\[\frac {(1 - p _ {L}) ^ {2}}{p _ {L} ^ {2}} q = \frac {(1 - p _ {L}) ^ {2}}{p _ {L} ^ {2}} \frac {\frac {p _ {L} ^ {3}}{3}}{\frac {(1 - p _ {L}) ^ {2}}{3} + 2 \frac {(1 - p _ {L}) p _ {L}}{2} + p _ {L} ^ {2}} = \frac {(1 - p _ {L}) ^ {2} \frac {p _ {L}}{3}}{\frac {(1 - p _ {L}) ^ {2}}{3} + 2 \frac {(1 - p _ {L}) p _ {L}}{2} + p _ {L} ^ {2}} < \frac {(1 - p _ {L}) ^ {2} \frac {p _ {L}}{3}}{\frac {(1 - p _ {L}) ^ {2}}{3}} \leq 1\]

⁷ We only write the binding constraints, in what follows.

The reason for this enhanced efficiency is that the principal distorts the low-ability agent in order to lower the rents to the high-ability agent. To see this, note that the informational rents in the Benchmark treatment (equation 2e) are increasing in , so the principal prefers to lower (thus reducing efficiency) in order to get higher profits. But in the EA treatment there is a competitive pressure on the high-ability types. In fact, it is easy to check that in the general model where the principal confronts n agents, the difference between the equilibrium and the efficient level of effort for the low-ability type goes to zero as n goes to infinity.

Nevertheless, there is an additional problem with this treatment. We have found the equilibrium by assuming that the high-ability types assume that other high-ability types choose the high contract. But that is not the unique equilibrium here. In the second stage, where a menu is offered, it is also possible that both types of agents select the low option for the menu. If all agents are choosing the low option, it is indeed a best response to choose low for all of them. But in this case, it need not be optimal to propose the menu of contracts specified in (3). In the design of the experiment we provide another menu, which is the equilibrium under the assumption that whenever there is multiplicity of equilibria in the second stage, the worst equilibrium for the principal is selected. The equilibrium menu in that case would solve:

\[\max _ {w _ {H}, w _ {L}, e _ {H}, e _ {L}} (1 - p _ {L} ^ {3}) (e _ {H} - w _ {H}) + p _ {L} ^ {3} (e _ {L} - w _ {L}),\]

subject to

\[\begin{array}{c} w _ {L} - \frac {k _ {L}}{2} (e _ {L}) ^ {2} \geq \underline {{U}} (\mathrm{IR} _ {L}) \\ w _ {H} - \frac {k _ {H}}{2} (e _ {H}) ^ {2} \geq \frac {1}{3} \left(w _ {L} - \frac {k _ {H}}{2} (e _ {L}) ^ {2}\right) + \frac {2}{3} \underline {{U}} (\mathrm{IC} _ {H}) \end{array}\tag{4}\]

where the incentive constraint now ensures that it is dominant to choose the high option for a high-ability type (thus she will do it independently of what other individuals of her type are doing).⁸ Choosing the high contract when the low contract gives a higher payoff makes sense to reduce competition from other workers. In fact the ‘attractiveness’ of the high contract increases with the probability that a competing worker also chooses the high option. So the worst-case scenario for the principal is when no competitor chooses the high contract. If even in that case a high type should choose the high over the low contract, then it is dominant for a high-ability type to choose the high option, and that is exactly what the constraint in equation (4) does.

(IC_H)

If the contract offered by the principal did not satisfy the constraint in program (4), there would be a pooling equilibrium in the contract acceptance subgame, where both the H and L types would accept the L contract. To see this, notice that the utility for the H type of accepting the H contract would be: _Hw WH ²( )^H e^k , kH H 2 2

Finally, we also have a treatment (Excess Principals, or EP) where several principals compete for one agent. In that case, the equilibrium of the game is such that the principals make zero profits for each type of contract, the low-ability agent gets an undistorted contract and the high-ability agent is held to her Incentive Compatibility constraint (see e.g. Mas-Colell, Green and Whinston 1995, ch.14D).

\[\begin{array}{l} {e _ {H} ^ {E P} = w _ {H} ^ {E P}; e _ {L} ^ {E P} = w _ {L} ^ {E P};} \\ {e _ {L} ^ {E P} = \frac {1}{k _ {L}}; e _ {H} ^ {E P} = \frac {2}{k _ {H}} - \frac {1}{k _ {L}}} \end{array}\tag{5}\]

where comes from the Incentive constraint for the high type, which solves

, which from (5) can be rewritten as:

\[e _ {H} ^ {E P} - \frac {1}{2} k _ {H} (e _ {H} ^ {E P}) ^ {2} = \frac {1}{k _ {L}} - \frac {1}{2} k _ {H} (\frac {1}{k _ {L}}) ^ {2} \Leftrightarrow (e _ {H} ^ {E P}) ^ {2} - \frac {2}{k _ {H} ^ {2}} e _ {H} ^ {E P} + \frac {2}{k _ {L} k _ {H}} - (\frac {1}{k _ {L}}) ^ {2} = 0,\]

\[\text {which leads to} e _ {H} ^ {E P} = \frac {\frac {2}{k _ {H}} + \sqrt {\frac {4}{k _ {H} ^ {2}} - \frac {8}{k _ {H} k _ {L}} + \frac {4}{k _ {L} ^ {2}}}}{2} = \frac {1}{k _ {H}} + \sqrt {\left(\frac {1}{k _ {H}} - \frac {1}{k _ {L}}\right) ^ {2}} = \frac {2}{k _ {H}} - \frac {1}{k _ {L}}.\]

1 1 3 w _L WL k_H kH e ( ) ² L  + 2 2 U  2 2 3 3

(IC_H)

since by being the only agent departing from the pooling strategy, he would guarantee being chosen. On the other hand, if he chose to accept the L contract he would get a utility of: , since he would only

be chosen one-third of the time. Thus, if the constraint in program (4) is violated it is indeed optimal for the H type to pool with the L type. If the pooling equilibrium is always selected when available, the optimal way to screen types is given by the solution to (4). As usual, one still has to check that screening types is optimal for the principal.

We implemented the theoretical model in our experiment by choosing a single set of six menus allowable in all contracts. For the parameter values , equation (3) leads to menu 1, equation (4) induces menu 2, equation (2) leads to menu 3, and equation (5) induces menu 6. We provide the details of these mappings into experimental payoffs in section 3. In addition we chose two non-equilibrium menus, in order to provide a richer contractual environment. Menu 4 is similar to menu 3, but has a little more effort for the lowability type, and respects the IC constraint for the high-ability type. Menu 5 is fully efficient, for both types.

Each menu consisted of a choice of two (enforceable) effort levels and payments that depend on the type of agent involved; if neither choice seemed attractive to the agent, she could veto the contract menu. We chose for all menus, in order to give relatively large rents to the high-ability type (under her preferred contracts). The parameters, efforts, and wages for the six different menus in the experiment are summarized in Table 1:

Table 1 – Parameter Values

One of the criticisms of models of contract design with hidden information is that the contract menus are more ‘complex’ than one observes in reality. In an environment like ours, these often employ a nonlinear structure and a very large number of possible choices of pairs of wages and efforts. Using a continuous strategy space would be quite complicated to design for the principal, and even the choice of the agent would not be simple without adding much insight; this would also make the data analysis problematic. We have selected a relatively small number of menus of contracts; since they include all forms of equilibrium in some versions of the game, this number is sufficiently large for exploring how the choice of contracts is affected by relative bargaining power. While we have selected a very simple

structure (only two types), we feel that a ‘simple’ menu can serve as an approximation for a full schedule. As Wilson (1993) points out (p. 146) in a representative example: “The firm’s profits from the five-part and two-part tariffs are 98.8% and 88.9% of the profits from the nonlinear tariff.”

4. EXPERIMENTAL DESIGN

We conducted three different treatments, which differed according to the numbers of principals and agents in the treatment to study how offered contracts depend on the structure of bargaining power. In our B treatment, there were 10 principals and 10 agents in each session. In the EA treatment, there were four principals and 12 agents, while in the EP treatment, there were 12 principals and six agents.⁹ In all cases, there were equal numbers of high-ability (H) agents and low-ability (L) agents and this was made common knowledge among the participants. In order to observe roughly similar numbers of observations (matches) in each treatment, we conducted four sessions of the EA treatment, three sessions of the EP treatment, and two sessions of the B treatment. Each session consisted of 40 periods of play to allow for possible learning dynamics, with random and anonymous re-matching after every period. The re-matching procedure was common information to the participants.

The organization of our sessions is summarized in Table 2.

Table 2 – Treatments and sessions

The sessions were conducted at the Groupe d’Analyse et de Théorie Economique (GATE), Lyon, France. Participants were recruited from undergraduate courses in local Engineering and Business schools using ORSEE (Greiner, 2004). Some had participated in previous experiments, but they were all inexperienced in this type of experiment. No one participated in more than one session of the study. On average, a session lasted 60 minutes, including initial instructions and payment. The experiment was computerized using the REGATE program developed at GATE (Zeiliger, 2000).

⁹ We chose three agents per principal in the EA treatment because the theoretical model shows that the distortion between the efficient level of effort and the equilibrium effort reduces in the number of competing agents; in

The participants were privately informed of their roles; agents were also informed of their type. One’s role and/or type were kept constant throughout the session. The participants also knew that there were the same number of L and H agents in the room. In our B treatment, the “proposer” (principal) first makes a selection from among the six “offers” (feasible contract menus). The “responder” (agent) is informed of this choice, and then selects “option X” (high contract), “option Y” (low contract), or rejects the contract menu. Each person then learns his or her payoff and play then continues on to the next period. The sequence in the EA treatment is similar, except that the principal is informed of the options chosen by each of the three agents and then selects one of these agents. No agent is informed about the choices of the two other agents. The EP treatment has the same sequence as the B treatment, with the proviso that an agent can accept at most one offer from the two principals with whom she is paired. When both principals make the same offer, the agent chooses at random between them if she is willing to accept the offer. The principal is not informed of the offer of the other principal.

We used the parameter values in Table 1 to generate experimental payoffs for the feasible contract menus. We first derived the payoffs from these parameters to three decimals and then multiplied these by one thousand. We next rounded these payoffs to the nearest multiple of 5. In the case of the principals, we added 250 to each of the non-rejection payoffs; this reflects the notion that setting up the firm requires some capital, and the minimum level of revenues that are needed to recoup the cost of capital is 250. In the case of the agents, we added 10 to each non-rejection payoff, in order to provide some minimal separation (avoiding the possibility of equilibrium failure due to indifference) between the payoff for a low agent

addition, it increases the probability to be matched with at least one high agent. In the EP treatment, we chose to match two principals with one agent, as the theoretical predictions are unaffected by adding more principals

who accepts the least favorable offer and her payoff from rejecting the contract menu in its entirety.¹⁰ Unmatched principals or agents received 125 points in the period.¹¹ This process leads to Table 3 that was distributed to the subjects to help them to make their decisions (except that the term “menu” was replaced by that of “offer”).¹²

We used a conversion rate of 100 points for each Euro. At the end of each session, we selected (at random) four of the 40 periods for actual payment. In this way, we avoided possible income effects from having already accumulated a known amount of money in the session. The average payoff was 14.9 Euros in the B treatment, and 13.5 Euros in both the EA and the EP treatments; on average the principals received 17 Euros, the high-ability agents 13 Euros and the low-ability agents 10 Euros, including a four Euro show-up fee.

0 As it happens, we inadvertently added 20 points to the L payoffs from option Y with menu 4. Perhaps this turns out to be useful for testing what is needed to obtain efficiency. The reason is that even with this extra kick, the B treatment is least efficient once rejections are considered. Thus, there is an argument that competition between agents is good for efficiency because it reduces informational rents, both in theory and in practice. And that principal competition enhances efficiency as it reduces the envy-driven rejections that hurt efficiency in the benchmark.

¹¹ We note that adding the same constant to the payoffs for all agents or to the payoffs for all principals cannot change the equilibrium, since these are Von Neumann-Morgenstern utilities.

¹² See the instructions in Appendix A.

Table 3 – Payoff Table

5. EXPERIMENTAL RESULTS

An overview of our experimental results is that we find substantial treatment effects in our sessions, with large differences in the contract menus offered and accepted, substantially in line with the equilibrium predictions. The menus that are offered (and accepted) evolve over time. In general, rejections and competition drive behavior. We first give descriptive statistics for principal behavior and agent behavior, supplemented with charts. We then consider the determinants of such behavior, providing statistical tests and regression analysis.

Note: In the left panel, equilibrium menus are in bold and percentages are in parentheses. In the right panel, the payoffs for the last eight periods are in parentheses.

5.1 Descriptive statistics

Principal behavior

While there is certainly some heterogeneity present among the principals, we do observe some clear patterns and differences for the menus chosen in each treatment. We list the menus offered in each treatment in the left panel of Table 4 while the right panel displays the average ex post principals’ payoffs by treatment.

Table 4 – Menus offered and principal’s payoffs, by treatment

The EA treatment has the ‘lowest’ contract menus (the ones most favorable to the principal), the EP treatment has the ‘highest’ menus (the ones most favorable to the agents), and the B treatment features intermediate menus. There is some support for the equilibrium predictions, as 30% of the menus offered in the B treatment, 34% of the menus offered in the EA treatment, and 47% of the menus offered in treatment EP are equilibrium menus (menus 1 and 2 with EA, menu 3 with B, and menu 6 with EP). However, menu 4 is the most common choice in the B treatment and menu 3 is the most common choice in the EA treatment.

As menu 3 has a more egalitarian distribution than menu 1 (EA treatment) and also provides greater efficiency (higher total payoffs), one might suspect that social preferences such as those expressed in the Charness and Rabin (2002) model play a role here; a similar comment applies vis-à-vis menu 4 and menu 3 (B treatment). However, to the extent that these represent social preferences on the part of the principals, we should expect to see these choices from the beginning. Instead, the menu offered evolves over time (see Figures 1-3).

Figure 1: Menu Offered over Time, Benchmark

Figure 2: Menu Offered over Time, EA

Figure 3: Menu Offered over Time, EP

In each of these treatments, there is some distribution across menus in the initial periods, but we typically see that two menus comprise the great majority of the menus offered thereafter in each treatment. In every case, it is the ‘higher’ menu that grows in frequency over time. Thus, it seems that some other force is inducing principals to choose more generous menus over time, even though principals’ social preferences may perhaps account for some of the generous menu choices. In every treatment, one menu predominates in the last group of periods, averaging about 60% of all menus offered (although there is a dip in favor of the equilibrium menu in EA)

While we postpone an in-depth analysis of the determinants of the contract menu choices, it is clear from the right panel of Table 4 that the profitability of a particular contract menu depends greatly on the environment. Menus 1 and 2 yield highest profits for the principal in the EA treatment, but generate low profits in the B and EP treatments. Similarly, menu 6 is quite unattractive for the principal in the EA and B treatments, but provides nearly the best profits in the EP treatment (and the best in the final periods). Overall, we observe a good correspondence between the most frequent offers made and their profitability; thus, to a large extent, it seems that principals are influenced by considerations of their own profits.

Agent behavior

The menus accepted by the agents naturally mirror the menus that were offered; however, there are some substantial differences, due primarily to rejections in the B treatment and selection pressures in the EP treatment. More favorable menus are more likely to be accepted in the B treatment, with 142 rejections of the 800 contract menus offered. The acceptance rate is 90% for menu 4, 75% for menu 3, but only 61% for menu 1. In addition, less favorable menus are not likely to be selected by agents in the EP treatment although rejections of offers from both principals occurred only twice. The punishment for offering an unfavorable contract menu is simply that no agent will select it. Menus 1 to 3 are only accepted about 5% of the time; in fact, these menus were never accepted in the final eight periods, and menu 4 was only accepted two of the 144 times it was offered in these periods. Finally, rejections in the EA treatment are not actually costly for the principal, since an offer has always been accepted by at least one agent.

We summarize agent behavior by listing the number of accepted menus (column 1), the rate of acceptance (column 2), and the proportion of X option chosen (column 3) in each treatment in Table 5 for the high-ability agents and Table 6 for the low-ability agents.

Table 5 – High-ability agents' choices, by treatment

Table 6 – Low-ability agents' choices, by treatment Note: Equilibrium menus are in bold.

The rejection rate for low-ability agents is always much higher than the rate for highability agents, more than four times as high in both treatments B and EA. When they accept an offer, low-ability agents rarely (14 of 1477 times, or 0.95%) chose option X, which would generate negative earnings. The behavior of high-ability agents is more complex. Note that option X pays more than option Y for high-ability types with menus 3-5, but option Y pays

more with menus 1 and 2. In addition, both options give the same payoff to the high-ability type with menu 6. In the EP treatment, high-ability agents nearly always maximize own payoffs (356 of 360 non-rejections). While they also do so with menus 1, 2, 5, and 6 in treatment B, we observe a substantial proportion of option-Y choices with menus 3 and 4 (42% and 21% of the non-rejection choices, respectively).

In the EA treatment, the principals know the agents’ choices prior to selecting one, so that agents must compete in their choices to be selected. High-ability agents do maximize own profits with menus 3-5, since this maximization also coincides with maximizing the profits for the principal. However, with menus 1 and 2, an agent who myopically chooses option Y runs the risk that she will not be selected if another agent has chosen option X. Since some agents appear to realize this, we see that 64% of the high-ability agents choose option X when accepting menus 1 or 2. Figure 4 shows that high-ability agents appear to be learning to do so over time, as this likelihood increases during the first half of the sessions.¹³ We also chart menu 3 for comparison, to show a ‘best-case scenario’ for the X option, since a highability agent trying to compete should always choose it; note the lack of a time trend.

As a consequence of these decisions, the proportion of high-ability agents actually recruited is larger in EA (81%) than in B (57%). While in B this distortion of the initial distribution of the population reflects the higher frequency of rejections of offers by lowability agents, in EA this reflects the process of selection related to the competitive

environment. In EP, the proportion of high-ability agents (50%) corresponds roughly to the initial distribution of the population since almost all the agents accept an offer. Regarding the evolution over time of the proportion of high-ability agents, the selection process does not take a long time before being fully operative in EA, whereas there is almost no evolution in B. The percentage of high type among the agents recruited in EA rises from 71% in periods 1 to 8 up to 87% in periods 9 to 16 and stays above 81% in the following periods, whereas the proportion stays between 55% and 57% in B throughout the game.

5.2 Regression analysis

It appears that there are substantial and significant differences in both principal and agent behavior across treatments. We now turn to multiple-regression analysis of the determinants of the observed behavior, first considering the menus offered by principals. ^14,15 In order to disentangle the motivations underlying offers of the different categories of menus, we estimate multinomial Logit models in which the reference category is the offer of the equilibrium menu. To better understand the choice of the most frequent menu that is not the equilibrium one, we also estimate ordered Probit models with robust standard errors in which the switch to the most frequent menu offer is the dependent variable, equal to +1 if the menu increased, 0 if unchanged, and -1 if it decreased. In all the regressions, we include a time trend to identify a possible evolution over time. The first three columns of Table 7 presents the results of the multinomial Logit model and the fourth column the results of the ordered Probit model for the contract menus chosen in the B treatment.

¹⁴ All of these estimations were done using Stata9, with robust standard errors and clustering at the individual level to account for the fact that a same individual makes several decisions over time.

⁵ We also performed nonparametric Mann-Whitney rank-sum tests, with both session-level and individual-level data (see Appendix B). These tests find that the average menu offered is lowest in the EA sessions and highest in the EP sessions. They also indicate that rejection rates of menus below 4 are significantly higher in the B than in the EA treatments and that high-ability agents in B are more likely to choose option X in response to menus 1 and 2 than in EA, the reverse being true for menu 3. Overall, they show that the proportion of high-ability agents is higher in EA than in B.

Table 7: Determinants of the choice of menus in the Benchmark Treatment

Note: These estimations have been conducted with robust standard errors (in parentheses) and clustering at the individual level; *** and ** denote two-tailed statistical significance at the 1%, 5%, and 10% level, respectively.

Menus 1 and 2 are chosen less frequently over the course of the sessions, while menu 4 is increasingly preferred to menu 3 in the latter periods of the sessions. The offer of very generous menus 5 or 6 (11% of offers) does not follow a clear trend. A principal who experiences a high proportion of rejections of his previous offers is more likely to offer menus 1-2 and less likely to offer menu 4. This may suggest some inertia in the motivations driving behavior. Indeed, a principal who is driven by social preferences makes more generous offers, experiences fewer rejections, and is encouraged to continue to offer generous menus. An agent choosing the X option in the previous period (which never occurs in response to menu 1 or 2) decreases the likelihood of menu 1 or 2 being chosen by the principal. This makes sense because offering these menus would induce both types to switch to the low option.

The ordered Probit regression regarding switching from any menu to the most frequent menu 4 shows that such a switch is more frequent at the beginning of the game. It is less likely if the agent has chosen the X option in the previous period, with no significance for whether the principal has experienced a high proportion of rejections in the past. In contrast, a similar regression in which the lagged option is replaced by the rejection of the menu offer in the previous period (not reported here) indicates that a rejection strongly favors such a switch. Overall, these regressions suggest that offering a more generous menu than the equilibrium is driven by the experience of recent rejections and the selection of low-type agents, whereas offering very generous menus (5 or 6) does not depend on any of these variables, suggesting a preference for more egalitarian outcomes.

Table 8 presents the results for the menus chosen in the EA treatment. In the first two columns, we pool together the offers of menus 4 to 6 since they represent only 12% of the observations. The third column displays the results of the ordered Probit model in which the switch to the most frequent menu 3 is explained. In contrast with the previous regression, we do not consider the lagged rejection rate since all the contracts are accepted.

Table 8: Determinants of the choice of menus in the Excess Agent Treatment

Note: These estimations have been conducted with robust standard errors (in parentheses) and clustering at the individual level; *** and ** denote two-tailed statistical significance at the 1% and 5% level, respectively.

Menu 3 is chosen more frequently over time (we know from an alternative regression that this is particularly the case in periods 17-32, significant at 1%), whereas the frequency of menus 4-6 decreases but not significantly (it decreases significantly in the final eight periods, at the 5% level). If the X option was chosen in the previous period in response to the offer of the equilibrium menu, this decreases the likelihood of non-equilibrium menus being offered; this makes sense, since the X option leads to a higher payoff for the principal, and so there is less motivation to offer a more generous menu. On the other hand, if the X option was chosen in the previous period (in reaction to whichever offers), this increases the likelihood of menu 3 being chosen but this has no significant effect on the offer of menu 4-6. If we separate out the case when menu 3 is chosen (column 3), we see that switching to menu 3 is much less likely when the X option has been chosen in the previous period.

Table 9 presents the results for the contract menus chosen in the Excess Principal treatment. In the first two columns, we estimate multinomial Logit models with menu 6 as the reference. We pool menus 1 to 4 since they only represent 19% of the observations. We include among the independent variables both the lagged acceptance of the principal’s offer and the lagged rejection rate instead of the lagged option chosen by the agent, in order not to eliminate half of the observations and because both the principal and the high-type agent are indifferent between the two options with menu 6. Column 3 displays the results of a Probit model in which the switch to both the equilibrium and most frequent menu offer is the explained variable.¹⁶

¹⁶ Indeed, an ordered Probit model would not be appropriate because data are censored at menu 6.

Table 9: Determinants of the choice of menus in the Excess Principal Treatment

Note: These estimations have been conducted with robust standard errors (in parentheses) and clustering at the individual level; *** and * denote two-tailed statistical significance at the 1% and 10% level, respectively.

The offer of less egalitarian menus than menu 6 decreases strongly over time. Although the acceptance of the offer in the previous period has little effect on the choice of any kind of menu, there is a strong and positive correlation between a high rejection rate in the past and the offer of less generous menus. In contrast, the Probit regression regarding switching to menu 6 shows that an offer rejected in the previous period makes such a switch more likely, while the overall lagged rejection rate exerts is no longer significant. The switch is also more likely in the early periods of the game. The competitive pressure to choose a favorable menu is naturally a major factor in the principal’s choice of contract to offer.

Another approach is to focus directly on whether a principal changes the contract menu from one period to the next.¹⁷ We might expect that a principal who is primarily interested in maximizing his own payoff would change the contract menu offered on the basis of expected profit, so that the payoff received from the previous menu offered would be critical. We consider this factor, along with a time trend in the following ordered Probit

¹⁷ A possible limitation is that the menu change is censored if the prior menu was 1 or 6 in these regressions.

regressions in which data from all treatments are pooled. Menu change is the dependent variable, equal to +1 if the menu increased, 0 if unchanged, and -1 if it decreased. The results of these regressions are reported in Table 10:

Table 10: Contract menu changes and lagged payoffs (ordered Probit models)

Note: These estimations have been conducted with robust standard errors (in parentheses) and clustering at the individual level; *** denote two-tailed statistical significance at the 1% level.

In all cases, the lagged payoff is a significant determinant of whether or not the principal left the contract menu unchanged. Menus increased (decreased) when the previous payoff was lower, as with rejection or the Y option being chosen. When we consider lagged payoffs separately for each treatment, we find that the coefficient is significantly negative in the EA treatment, and is even more negative (and significant) in the B and EP treatments. The effect of lagged payoffs is strongest in the EP treatment, as not being chosen generates a low payoff and so is avoided. We also observe a negative time trend in all cases. An additional regression (not reported here) indicates little difference in this trend across treatments.

We next analyze the agents' decisions of whether to accept a contract menu and (for high-ability agents) which option to choose if accepting a contract. Table 11 shows Probit regressions for the three treatments. Note that regarding the EP treatment, we explain the likelihood of an acceptance from the principal’s and not from the agent’s point of view since, with the exception of two rejections of both offers, the agent always accepts one offer and selects the best one among the two, or chooses at random in case of a tie.

Table 11: Determinants of accepting a contract offer (Probit models)

Note: These estimations have been conducted with robust standard errors (in parentheses) and clustering at the individual level; ***, and ** denote two-tailed significance at the 1% and 5% level, respectively.

In all three treatments, the table confirms that higher offers (indexed from 1 to 6) are more likely to be accepted. High-ability agents in both the B and EA treatments are significantly more likely to accept an offered contract than are low-ability agents in these treatments. This cannot influence offers’ acceptance in the EP treatment, since each type of agent is able to accept the best offer. A couple of more ‘psychological’ factors come into play as well. In the B treatment, agents are influenced by the previous contract offered to them;

holding the current offer constant, the better the previous offer, the less likely the agent will accept a contract offer. This effect vanishes in the EA treatment, where we instead observe that an agent who was hired less often in the prior periods is significantly more likely to accept the current offer. When we pool the EA and B data, we find that a contract is much more likely to be accepted in the EA treatment, illustrating the effect of competitive pressure.

We then explore the determinants of the option chosen by an agent who accepts a contract. Since low-ability agents incur serious losses if they choose the X option, we focus only on high-ability agents. Since the payoff for the high agent is the same for menu 6, regardless of the option chosen, we also omit this menu (5 observations in B and in EA) and the EP treatment, where it prevails, from the analysis. These estimations are displayed in Table 12.

Table 12: Determinants of the choice of option X by the high-type agents who accepted an offer (Probit models)

Note: These estimations have been conducted with robust standard errors (in parentheses) and clustering at the individual level; *** and ** denote two-tailed significance at the 1% and 5% level, respectively.

Not surprisingly, the higher the contract, the more likely the high agent is to choose option X. Option X is chosen less frequently over time in the B treatment, as it seems that high-ability agents develop a taste for more favorable contracts and make modest sacrifices by choosing Y instead of X (rather than costly rejections) to punish the principal for a lack of generosity in choosing low menus. In contrast, option X is chosen more frequently (but not significantly so) over time in the EA treatment since the high-ability agents also learn to make modest sacrifices, by choosing X instead of Y when they accept contracts 1 or 2, to increase the likelihood of their hiring. Finally, we see a significant effect in the EA treatment of having been hired in the previous period.

6. WELFARE AND EFFICIENCY COMPARISONS

Welfare comparisons across treatments are complicated for at least two reasons. One is that in EA and EP there is an unbalanced structure of principals and agents, so that some parties remain unmatched. The right assumption in this case, we think, is to consider only the individuals who are actually matched; equivalently, one might think of this is how much benefit society derives from a match. More importantly, the numbers of matches with the high-ability agents is likely to be higher in the EA treatment, which necessarily gives a boost to the total payoffs in this treatment. In order to deal with this, we supply separate comparisons matches involving high- and low-ability agents. Finally, the kinds of theoretical distortions at the equilibrium are different in the EP treatment (where the high-ability agents contract forces them to work more than the efficient level) than in either the EA or the B treatments (where the low-ability types work less than the efficient level).

Having said this, the equilibrium prediction (given by equation (3)) of the EA treatment seems unambiguously better when compared with the B treatment (given by equation (1)). There is a higher proportion of the matches with the more productive high-ability agents in EA than in B. In addition, in the equilibrium of the EA treatment there is less distortion for the high agent than in the equilibrium of B; this can be seen in both equation (3’) and Table 1.

¹⁸ There are three potential sources of inefficiency. One is that an agent might choose the wrong contract given her type. As shown in Tables 5 and 6, this is relatively rare and occurs mostly in the case of indifference or nearindifference. A second source is that agents may reject contracts, which we see happens with some frequency, particularly in the EP treatment. The third source is that principals offer the wrong contracts; since this seems driven by rejections, our sense is that rejections are (either directly or indirectly) the main source of inefficiency.

The comparison between the B and the EP treatment is theoretically more complicated, since the distortion occurs for different individuals, the high-ability agents in the EP treatment and the low-ability agents in the B treatment. But since we expect an equal number of highand low-ability agents to be matched in both cases, we can compare the relative value of the distortions of high and low types in both treatments. The loss in welfare with respect to first best (in equilibrium) for the low-ability agents’ contract in B is

and the loss for the high-ability agents’ contract under EP is . With our parameterization, the loss in B is 0.03 whereas the loss in EP is 0.12. Thus, in our experimental framework, the equilibrium in EP would lead to lower overall welfare than the equilibrium in B, which in turn would lead to lower overall welfare than the equilibrium in EA.

With the contract menus and payoff parameters we chose, we find that the greatest benefits accrue to society from a match when there are many agents competing to be hired. If we consider the theoretical predictions regarding efficiency, we should observe menu 1 or 2 in EA, menu 3 in B, and menu 6 in EP. While only half of the matches in B and EP would involve high-ability agents, 87.50% (on average) of the matches in EA should be with highability agents. So in EA (with menu 2, the worst case for efficiency), the average total payoff should be 720, in B the average total payoff should be 620, and in EP the average total payoff should be 572.50. EA gives the most efficiency; the ordering also matches the pattern for accepted contracts.

The data show a qualitatively similar pattern. The overall average payoffs per treatment, which are a direct measure of efficiency since they take into account both the type and the effort of the recruited agents, are ordered in the same manner as that predicted theoretically. These welfare considerations/average payoffs are shown in Table 13:

¹⁹ As we noted previously, the EA treatment has other equilibria, and we selected the contracts of one of those equilibria for one of the available menus in the experiment. The equilibrium given by (3) is the one, however, tha seems more relevant for the data.

Table 13: Welfare comparisons (average total payoffs) across treatments

We see that the EA treatment easily yields the highest average total payoff (line 1). One reason for this is that (ex post) every contract is accepted by at least one of the paired agents in the EA treatment. The EP treatment slightly dominates B in terms of average total payoff since only 2 agents reject the offer of both principals, while the B treatment has a substantial rejection rate. Nevertheless, if we ‘level the playing field’ by considering only accepted contracts, the EA treatment still generates the highest degree of efficiency. Mann-Whitney tests find that the total payoffs are higher in EA than in both B (Z = 1.85 and p = 0.06) and EP (Z = 2.14 and . One reason why EA empirically yields higher payoffs than B or EP is for one of the two theoretical reasons: the possibility of selection means that there are more matches with high-ability agents in EA (81%, against 57% in B and 50% in EP) and these yield higher total payoffs per match.

Nevertheless, even if there were an equal number of matches with high- and lowability agents in EA, it would still be the treatment with the highest total payoffs, either with or without rejections (615.04). Note, however, that our theory over-predicts payoffs in the presence of competition among agents and under-predicts them in the presence of competition between principals. The total payoff in EA is slightly under the predicted 720 2 according to a t-test), whereas the total payoff in B is not different from the predicted 620 (p = 0.420) and it is even higher in the EP treatment than the predicted 572.50

If we only consider welfare with low-ability agents, the best treatment is the EP treatment. Perhaps this is because high- and low-ability agents each net the principal the same profits, regardless of the option chosen, and so are equivalent in some sense. However, option

X is so relatively inefficient in menu 6 (total payoffs of 635, compared to 760 with all other menus) that the EP treatment cannot be the best overall.

One immediately wonders just how robust the EA-efficiency result is to alternative specifications. The EA treatment is necessarily better than the benchmark, since when the number of excess agents goes to infinity, there is no distortion for even low-ability agents, so we obtain first-best efficiency (proof upon request). The comparison with EP is a matter of parameterization, for fixed numbers (3) of excess agents. With EP the outcome is the same no matter how many principals you have, so there would always be some inefficiency. Thus, there is a sense in which EA is ‘best’, if the relative number of agents can grow large.

However, this conclusion about the higher efficiency of the EA institutional environment should be qualified if we account for those agents who get unmatched. If the EA environment provides the biggest benefit to society from a match, it may generate a higher social cost than the benchmark if the unmatched agents remain unemployed. Including all participants, the average individual payoff amounts to 269 in B, 237 in EA and 238 in EP. Therefore, there may be a dilemma: a higher competitive pressure among agents helps in getting closer to the first-best efficiency with the matched agents but could generate a higher social cost related to the unmatched agents if these ones, especially the low type, do not get an alternative occupation. We acknowledge that our measure of welfare, based on the total surplus, is purely utilitarian, and a Rawlsian approach would somewhat qualify our conclusions.

7. CONCLUSION

We conducted an experiment based on a model of contracting under asymmetric information. We show theoretically that, in this context, various degrees of relative bargaining power affect outcomes and efficiency. In this environment, efficiency improves in the relative number of agents because competition reduces the agents’ informational monopoly power. However, this environment also generates high inequality levels and is characterized by multiple equilibria, which may have important behavioral implications in the field and suggests that empirical testing could produce valuable insights

Our results provide qualitative support for the theory. We find that the institutional environment in which agents compete against each other is indeed the most efficient one. We also show that behavior evolves over time. People make errors, learn and adjust their decisions accordingly in order to increase their payoffs. In particular, the payoff obtained in the previous period, especially related to the ability to separate between types, is a driving force of the evolution of principals’ menu offers. Our results also indicate that principals offer more generous menus than predicted, although less frequently in the context of competition.

These results question the interaction between the various degrees of bargaining power and social preferences. In many experimental papers, social preferences are shown to interfere with the predictions of standard contract theory. In our treatment without competition, we also observe that principals offer menus of contracts that are more generous than the equilibrium. When agents compete, principals tend also to offer more generous contract menus than the equilibrium, but this is less the case when they are able to separate the agents by type with the equilibrium menus; this calls into question the true generosity of these offers. In addition, the existence of social preferences can hardly change the outcome for the low-ability type agents: due to the heterogeneity among agents, offering a more generous menu increases the selected agent’s expected payoff but also increases the likelihood of the repeated exclusion of the lowability agents.

Finally, the superiority of the institutional environment with competition among agents is shown in terms of total surplus of the matched pairs. The higher total surplus is achieved by making the payoff of the principal higher and lowering those of the agents. Thus, there is a genuine tradeoff between equity and efficiency in this environment, both theoretically and empirically.

REFERENCES

1. Akerlof, G. (1970). The Market for ‘Lemons’: Quality Uncertainty and the Market Mechanism. Quarterly Journal of Economics, 84, 488-500.
2. Anderhub, V., Gächter, S., and Königstein, M. (2002), Efficient Contracting and Fair Play in a Simple Principal-Agent Experiment. Experimental Economics 5(1), 5-27.
3. Ausubel, L.M. (1999). Adverse Selection in the Credit Card Market. Mimeo, University of Maryland.
4. Banks, J., Camerer, C.F., and Porter, D. (1994). An experimental analysis of Nash refinements in signaling games. Games and Economic Behavior, 6, 1-31.
5. Berg, J.E., Daley, L.A., Dickhaut, J.W. and O’Brien, J. (1992) Moral Hazard and Risk Sharing: Experimental Evidence. Research in Experimental Economics, 5, 1-34.
6. Brandts, J., and Holt, C. (1992). An experimental test of equilibrium dominance in signaling games. American Economic Review, 82, 1350-1365.
7. Brandts, J., and Charness, G. (2004). Do Labour Market Conditions Affect Gift Exchange? Some Experimental Evidence. Economic Journal, 114, 684-708.
8. Bull, C., Schotter, A., and Weigelt, K. (1987). Tournaments and Piece-Rates: An Experimental Study. Journal of Political Economy, 95(1), 1-33.
9. Cabrales, A., and Charness, G. (2000). Optimal contracts with team production and hidden information: An experiment. Mimeo, University of California at Santa Barbara.
10. Cawley, J., and Philipson, T. (1999). An Empirical Examination of Information Barriers to Trade in Insurance. American Economic Review, 89, 827-846.
11. Charness, G., and Dufwenberg, M. (2006). Promises and Partnership. Econometrica, 74, 1579-1601.
12. Charness, G., and Dufwenberg, M. (2008). Contracts and Communication. Mimeo.
13. Charness, G., Kuhn, P. and Villeval, M.C. (2008), Competition and the Ratchet Effect. IZA Discussion Paper 3784, Bonn.
14. Charness, G., and Rabin, M. (2002). Understanding Social Preferences With Simple Tests, The Quarterly Journal of Economics, 117(3), 817-869,
15. Chaudhuri, A. (1998). The ratchet principle in a principal agent game with unknown costs: An experimental analysis. Journal of Economic Behavior and Organization, 37, 291-304.
16. Chiappori, P.A., and Salanié, B. (2000). Testing for Asymmetric Information in Insurance Markets. Journal of Political Economy, 108, 56-78.
17. Chiappori, P.A., and Salanié, B. (2003). Testing Contract Theory: A Survey of Some Recent Work in Dewatripont, M., Hansen, L., and Turnovsky, S. (Eds), Advances in Economics and Econometrics, Vol 1, Cambridge: Cambridge University Press.
18. Cooper, D., Kagel, J., Lo, W., and Gu, Q.L. (1999). Gaming against managers in incentive systems: Experimental results with Chinese students and Chinese managers. American Economic Review, 89, 781-804.
19. Dahlby, B. (1983). Adverse Selection and Statistical Discrimination: An Analysis of Canadian Automobile Insurance. Journal of Public Economics, 20, 121-130.
20. Davis, D., and Holt, C.A, (1994). Equilibrium Cooperation in Three-Person, Choice of Partner Games, Games and Economic Behavior, 7, 39-53.
21. DeJong, D., Forsythe, R., Lundholm, R., and Uecker, W.C. (1985). A Laboratory Investigation of the Moral Hazard Problem in an Agency Relationship, Journal of Accounting Research, 23, 81-120.
22. Dione, G., Doherty, N. (1994). Adverse Selection, Commitment and Renegotiation: Extension to and Evidence from Insurance Markets. Journal of Political Economy, 102 (2), 210- 235.
23. Fehr, E., Kirchler, E., Weichbold, A., and Gachter, S. (1998). When social norms overpower competition: Gift exchange in experimental labor markets. Journal of Labor Economics, 16, 324-351.
24. Finkelstein, A., and Poterba, J. (2004). Adverse Selection in Insurance Markets: Policyholder Evidence from the U.K. Annuity Market. Journal of Political Economy, 112 (1), 183- 208.
25. Fischbacher, U., Fong, C.M., and Fehr, E. (2003). Fairness, Errors, and the Power of Competition. Institute for Empirical Research in Economics, University of Zürich Working Paper n°133.
26. Freixas, X., and Rochet, J.C. (1997). Microeconomics of Banking. Cambridge: MIT Press,
27. Genesove, D. (1993). Adverse Selection in the Wholesale Used Car Market. Journal of Political Economy, 104, 644-665.
28. Greiner, B. (2004). An Online Recruitment System for Economic Experiments. In: K. Kremer, V. Macho (Eds.): Forschung und wissenschaftliches Rechnen 2003. GWDG Bericht 63, Göttingen: Ges. für Wiss. Datenverarbeitung, 79-93.
29. Grosskopf, B. (2003). Reinforcement and Directional Learning in the Ultimatum Game with Responder Competition. Experimental Economics, 6, 141-158.
30. Güth, W., Klose, W., Koenigstein, M., and Schwalbach, J. (1998). An Experimental Study of a Dynamic Principal-Agent Relationship, Managerial and Decision Economics, 19:327- 341.
31. Holt, C.A., and Sherman, R. (1990). Advertising and product quality in posted-offer experiments. Ecnomic Inquiry, 28, 39-56.
32. Kanemoto, Y., and MacLeod, B.W. (1992). The Ratchet Effect and the Market for Secondhand Workers. Journal of Labor Economics, 10(1), 85-98.
33. Keser, C., and Willinger, M. (2000), Principals’ principles when agents’ actions are hidden. International Journal of Industrial Organization, 18, 163-185.
34. Königstein, M. (2001). Optimal Contracting with Boundedly Rational Agents, Homo oeconomicus, XVIII (2): 211-228.
35. Laffont, J.J., and Tirole, J. (1993). A Theory of Incentives in Procurement and Regulation. Cambridge: MIT Press.
36. Lazear, E.P. (1999). Personnel Economics: Past Lessons and Future Directions. Journal of Labor Economics, 17(2), 199- 236.
37. Lynch, M., Miller, R.M., Plott, C.R., and Porter, R. (1986). Product Quality, Consumer Information, and ‘Lemons’ in Experimental Markets, in Ippolito, M., and Scheffman,
38. D.T. (Eds.), Empirical Approaches to Consumer Protection Economics. Washington, D.C. : Federal Trade Commission, Bureau of Economics, 251-306.
39. Mas-Colell, A., Whinston, M.D., and Green, J. R. (1995). Microeconomic theory. Oxford: Oxford University Press.
40. Milgrom, P., and Roberts, J. (1992). Economics, Organization and Management. Englewood Cliffs: Prentice Hall.
41. Miller, R.M., Plott, C.R. (1985). Product Quality Signaling in Experimental Markets. Econometrica, 53(4), 837-872.
42. Mirrlees, J.A. (1971). An Exploration in the Theory of Optimum Income Taxation. Review of Economic Studies, 38(114), 175-208.
43. Nalbantian, H.R., and Schotter, A. (1997). Productivity under Group Incentives: An Experimental Study. American Economic Review, 87, 314-41.
44. Plott, C., and Wilde, L.L. (1982), Professional Diagnosis vs. Self-Diagnosis: An Experimental Investigation of Some Special Features of Markets with Uncertainty; Research in Experimental Economics, Vol.2; JAI Press, 63-112.
45. Prendergast, C. (1999). The Provision of Incentives in Firms. Journal of Economic Literature, 37, 7-63.
46. Puelz, R., and Snow, A. (1994). Evidence on Adverse Selection: Equilibrium Signalling and Cross-Subsidization in the Insurance Market. Journal of Political Economy, 102, 236- 257.
47. Ray, D. (1998). Development Economics. Princeton: Princeton University Press.
48. Roth, A., Prasnikar, V., Okuno-Fujiwara, M., and Zamir, S. (1991). Bargaining and Market Behavior in Jerusalem, Ljubljana, Pittsburgh, and Tokyo: An Experimental Study. American Economic Review, 81(5), 1068-1095.
49. Vickrey, W. (1961). Counterspeculation, Auctions, and Competitive Sealed Tenders. Journal of Finance, 16, 8-37.
50. Wilson, R. (1993). Nonlinear Pricing. Oxford: Oxford University Press.
51. Young, P.H., and Burke, M.A. (2001). Competition and Custom in Economic Contracts: A Case Study of Illinois Agriculture. American Economic Review, 91, 559-573.
52. Zeiliger, Romain, (2000). A Presentation of Regate, Internet Based Software for Experimental Economics. http://www.gate.cnrs.fr/~zeiliger/regate/RegateIntro.ppt., GATE.

APPENDIX A - Instructions for the Excess Agent treatment (the instructions for the other treatments are available upon request)

You are about to participate in an experiment on decision-making carried out by researchers from the Universitat Pompeu Fabra, the University of California at Santa Barbara and GATE. During this session, you can earn money. The amount of your earnings depends on your decisions and on the decisions of the other participants in this session. During the session, your earnings will be calculated in points,

\[\text { with 100 points } = 1 \text { Euro }\]

During the session, losses are possible. However, they can be avoided with certainty by your decisions.

The session consists of 40 independent periods. Only 4 periods will be chosen at random for actual payment, at the end of the session. The earnings you have made during these 4 periods will be added up and converted into Euros. In addition, you will receive € 4 for participating in the experiment. Your earnings will be paid to you in cash in private to preserve confidentiality. Your decisions are anonymous and confidential.

During this session, there are two categories of participants: 4 participants are proposers and 12 participants are responders. The responders can be of two types: A or B.

The category to which the participant is assigned (proposer or responder) and the type of participant in the case the participant is a responder are chosen randomly at the beginning of the session. Each responder has an equal initial probability to be of either type A or type B. Half of all responders will be of each type.

You will be informed of your category and of your type if you are a responder at the beginning of the session and you will keep the same category and the same type throughout the session. If you are a responder, no one knows your type.

Description of each period

At the beginning of each period, each proposer is randomly matched with 3 responders. The responders may be either type, but the proposer does not know their types when making a proposal. The identity of your co-participants is unknown to you. The composition of the group changes randomly every period.

Each period consists of four stages.

In the first stage, the proposer makes a selection from one of 6 possible “offers” {1,2,3,4,5 or 6} by checking a box on his screen.

In the second stage, the three responders are informed of this offer. Each can then choose one either option X or option Y or “rejection” by checking the corresponding box on his screen.

In the third stage, the proposer is informed of the choices of the three responders. If more than one responder has accepted the proposer’s offer, the proposer will select one of the responders among those who accepted his offer. He can accept at most one responder. The responders are not informed about the choices made by the other responders. The responders who have not been selected receive a payoff of 125 points.

In the fourth stage, each person is informed of his own payoff in that period.

How are payoffs calculated?

The payoffs depend on the offer made by the proposer, on the responders’ decisions and on the choice made by the proposer among the responders. When a proposer chooses a responder, his payoff depends only on his offer and on the option chosen by this responder; the responders who have not been selected do not provide him with any additional payoff.

Please refer to the Table provided. This Table displays the 6 possible offers and their associated payoffs.

Corresponding to each offer, you can see 3 rows:

- The first row, in blue, indicates the payoffs of the proposer.

- The second row, in yellow, indicates the responder’s payoffs if his type is A.

- The third row, in pink, indicates the responder’s payoffs if his type is B.

The 3 columns represent the decisions made by the responder:

- The column (1) corresponds to the choice of option X if the responder accepts the offer

- The column (2) corresponds to the choice of option Y if the responder accepts the offer

- The column (3) corresponds to the case of the responder rejects the offer.

At the intersection of a row and a column, you can read the payoffs associated with an offer and a choice as a function of the role of proposer or responder.

Here are some examples.

Example 1. The proposer has chosen the offer 1. One responder of type B has accepted this offer and chosen option Y. The two other responders have rejected this offer. In this case, the proposer will receive 355 points; the responder who has accepted the offer will receive 135 points; the responders who have rejected the offer will receive 125 points.

Example 2. The proposer has chosen the offer 3. One responder of type A and one responder of type B have accepted this offer and chosen option Y; the other responder of type A has also accepted the offer and chosen option X. The proposer chooses the responder who chose option X. The proposer will receive 550 points; the responder who has been chosen will receive 210 points; the responders who have not been chosen will receive 125 points.

Example 3. If the proposer has chosen the offer 6 and if no responder has accepted his offer, both the proposer and the responders receive 125 points.

To sum up, in each period, if you are a proposer, you choose an offer from among the six feasible options and you choose between the responders who have accepted your offer; you cannot accept more than one responder. If you are a responder, you choose either option X or option Y or you reject the offer. Your payoffs for the current period are then computed.

At the end of a period, a new period starts automatically. Each period is independent.

If you have any question regarding these instructions, please raise your hand. Your questions will be immediately answered in private. Throughout the entire session, direct communication between participants is strictly forbidden.

APPENDIX B - Nonparametric tests

Our nonparametric tests are Wilcoxon-Mann-Whitney rank-sum tests, conducted with both session-level and individual-level data. In a strict sense each session is only one independent observation, since there is interaction between parties over the course of each session. Table A presents a summary of principal and agent choices in each of our sessions.

Table A: Session-level data

The average contract menu offered is lowest in the four EA sessions and highest in the three EP sessions. Rank-sum tests find and , comparing between EA and and for the comparison between EA and B, and and for the comparison between B and . The likelihood that (for average menu offered) is only . Principals offer significantly different contract menus in each treatment.

We also see that rejection rates of the less generous menus (1-3) are substantially higher in both B sessions than in any of the four EA sessions, yielding and In addition, high-ability agents in the B treatment are less likely to choose option X in response to menus 1 and 2 than are high-ability agents in the EA treatment (insufficient observations in the treatment); recall that the myopic profit-maximizing choice in the EA treatment is Y. As the rate is lower in both B sessions than in any of the four EA sessions; this gives and The rate of option X being chosen by the high agent is lower in both B sessions than in any of the four EA sessions, with Z and This is consistent with the fact that the offer of menu 3 is already more ‘generous’ than the equilibrium in the EA treatment. Finally, the proportion of high-ability agents in the actual contracts is higher in the EA sessions than in the B sessions and and it is smaller than a random draw of 0.875 . This proportion is also higher in the B than in the EP sessions and it is larger than a random draw of 0.50

Since we have only a few sessions in each treatment, we supplement these tests by collapsing the 40 choices of each participant to one number; while this approach ignores the interaction between parties, we feel it is nevertheless informative. These results confirm the patterns above, but with a higher degree of statistical significance. The Wilcoxon-Mann-Whitney tests find that there are significant differences in the average menu offered between each pair of treatments and 5.69 for EA vs. B, EA vs. EP, and B vs. EP, respectively; all of these test statistics give . The test also indicates that the rejection rates of menus 1-3 are significantly higher in the B treatment than in the EA treatment . Finally, the test confirms that the proportion of highability agents in the actual contracts is larger in the EA than in the B treatment but this test fails when comparing the B and treatments

²⁰ We choose menus 1-3 as there are few rejections of menus 4-6 and these all occurred in the B treatment.

References

1. 2009-08: “Hidden Information, Bargaining Power and Efficiency: An Experiment”, Antonio Cabrales, Gary Charness y Marie Claire Villeval.

References

1. 2009-07: “Democracy and the curse of natural resources”, Antonio Cabrales y Esther Hauk.

References

1. 2009-06: “Social Interactions and Spillovers: Incentives,Segregation and Topology”, Antonio Cabrales, Antoni Calvó-Armengol e Yves Zenou.

References

1. 2009-05: “Chance Constrained Programming with one Discrete Random Variable in Each Constraint”,Emilio Cerdá Tena y Julio Moreno Lorente.

References

1. 2009-04: “Economic Value of Weather Forecasting Systems Information: A Risk Aversion Approach”, Emilio Cerdá Tena y Sonia Quiroga Gómez.

References

1. 2009-03: “Population Ageing, Inequality and the Political Economy of Public Education”, Francisco Martínez-Mora.

References

1. 2009-02: “Real Wages over the Business Cycle: OECD Evidence from the Time and Frequency Domains”, Julian Messina, Chiara Strozzi y Jarkko Turunen.

References

1. 2009-01: “The Determinants Of Misreporting Weight And Height: The Role Of Social Norms”, Joan Gil y Toni Mora.

References

1. 2008-42: “Social Security incentives, exit from the workforce and entry of the young”, Michele Boldrin, Pilar García-Gómez y Sergi Jiménez-Martín.

References

1. 2008-41: “The evolution and main determinants of productivity in Brazilian electricity distribution 1998- 2005: an empirical analysis”, Francisco Javier Ramos-Real, Beatriz Tovar, Mariana Iootty, Edmar Fagundes de Almeida y Helder Queiroz Pinto Jr..

References

1. 2008-40: “Immigration and Housing Prices in Spain”, Simón Sosvilla.

References

1. 2008-39: “Modeling the Immigration Shock”, Ana Montes y Michele Boldrin.

References

1. 2008-38: “Immigration and the Demand for Health in Spain”, Sergi Jiménez, Natalia Jorgensen y José María Labeaga.

References

1. 2008-37: “Immigration and Students' Achievement in Spain”, Natalia Zinovyeva, Florentino Felgueroso y Pablo Vázquez.

References

1. 2008-36: “Immigration and Social Security in Spain”, Clara Isabel González, J. Ignacio Conde-Ruiz y Michele Boldrin.

References

1. 2008-35: “Complements or Substitutes? Immigrant and Native Task Specialization in Spain”, Catalina Amuedo-Dorantes y Sara de la Rica.

References

1. 2008-34: “Immigration and Crime in Spain, 1999-2006”, Cesar Alonso, Nuno Garoupa, Marcelo Perera y Pablo Vázquez.

References

1. 2008-33: “A Social Network Approach to Spanish Immigration: An Analysis of Immigration into Spain 1998- 2006”, Rickard Sandell.

References

1. 2008-32: “The Consequences on Job Satisfaction of Job-Worker Educational and Skill Mismatches in the Spanish Labour Market: a Panel Analysis”, Lourdes Badillo Amador, Ángel López Nicolás y Luis E. Vila.

References

1. 2008-31: “Students’assessment of higher education in Spain”, César Alonso-Borrego, Antonio Romero-Medina.

References

1. 2008-30: “Body image and food disorders: Evidence from a sample of European women”, Joan Costa-Font y Mireia Jofre-Bonet.

References

1. 2008-29: “Aggregation and Dissemination of Information in Experimental Asset Markets in the Presence of a Manipulator”, HelenaVeiga y Marc Vorsatz.

References

1. 2008-28: “The Measurement of Consensus: An Axiomatic Analysis”, Jorge Alcalde-Unzu y Marc Vorsatz.

References

1. 2008-27: “Macroeconomic Consequences of International Commodity Price Shocks”, Claudia S. Gómez-López y Luis A. Puch.

References

1. 2008-26: “The Effect of Short–Selling on the Aggregation of Information in an Experimental Asset Market”, Helena Veiga y Marc Vorsatz.

References

1. 2008-25: “Adult height and childhood disease”, Carlos Bozzoli, Angus Deaton y Climent Quintana-Domeque.

References

1. 2008-24: “On Gender Gaps and Self-Fulfilling Expectations: Theory, Policies and Some Empirical Evidence” Sara de la Rica, Juan J. Dolado y Cecilia García-Peñalosa.

References

1. 2008-23: “Fuel Consumption, Economic Determinants and Policy Implications for Road Transport in Spain”, Rosa M. González-Marrero, Rosa M. Lorenzo-Alegría y Gustavo A. Marrero.

References

1. 2008-22: “Trade-off between formal and informal care in Spain”, Sergi Jiménez-Martín y Cristina Vilaplana Prieto.

References

1. 2008-21: “The Rise in Obesity Across the Atlantic: An Economic Perspective”, Giorgio Brunello, Pierre-Carl Michaud y Anna Sanz-de-Galdeano.