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RECURSIVE METHODS AND DYNAMIC CONTRACTS UNDER COMPLETE INFORMATION: THEORY AND APPLICATIONS
PAVONI, NICOLA
1999-01-28
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Contributor(s)
ZECCHIN, MARCO
Abstract
The title itself describes the methodology and the thesis' field of research. Broadly speaking, for contract we mean an allocation mechanism. The methodology of contracts is characterized by the fact that a constrained maximization (a Pareto optimal ) problem substitute an equilibrium one. This substitution is made also when we do not ha ve only technological constraints ( and the constraint of giving to the other party a minimum expected utility level). When t h ere are other constraints (for example informational constraints) we talk about second-best problems. The analysis is focused on the intertemporal aspects of allocation mechanisms, in particular we study ways of adapting recursive dynamic programming techniques to characterize multiperiod second-best contracts. Complete information in the title emphasizes that we do not analyze adverse selection problems, we assume instead that agents know perfectly other agents payoffs. Finally, "theory and applications" means the thesis is divided in two parts: a methodological part and an applied one. In this part we present the methodological foundations of the techniques object of this thesis. Game Theoretical Foundations: Repeated Games. The chapter analyzes some aspects of repeated games with complete information. The chapter is focused on the Abreu (Econometrica 1988) and Abreu Pierce and Stacchetti (Econometrica 1990) approach that links the analysis of equilibrium payoffs sets to recursive set-valued maps. In the first part of the chapter we present the approach applied to games with perfect monitoring. In the second part we show how those techniques can be extended to the case with imperfect monitoring. Games, these last ones, strictly linked with the classica! Principal-Agent model. The originai contributions in this chapter are: (i) some proof simplification due to the fact that we impose more stringent assumptions in order to keep an unified analysis. (ii)· In the second part of the chapter two new propositions are proved about the stationarity of the equilibrium payoff set with imperfect monitoring. Contractual Approach: Recursive Contracts. This chapter presents more specifically the methodological approach and the recursive techniques object of the thesis. The chapter is, to our knowledge, the first unitary formai analysis of those techniques; techniques used by many economists without giving rigorous foundations. Most of the results in Section 3.1 and 3.2.3 can be seen as formai proofs of existing conjectures. One of the classica! paradigms in economics is the insurance problem with risk adverse agents. Symmetrically t o the previous chapter, the first part of the Chapter assumes perfect monitoring and focuses the analysis on the insurance problem with limited commitment. These models of default are the theoretical basis of the new applications to consumption theory and credit models with default (sovereign debt, small firm financing, etc ... ). The second part of the chapter analyses the classica! Principal-Agent model (or moral hazard). In this model, insurance is limited because the principal has to give the right incentives to the agent who has to supply an unobservable effort (imperfect monitoring). The essential characteristic that allows to write the problem in recursive form is said sequential efficiency. The optimal contract is characterized by the fact that in each period it solves a second-best problem where the state variable in the expected utility level guaranteed to the agent. This second part contains two originai applied contributions. Inefficiencies in Dynamic Family Decisions: An Incomplete Contracts Approach to Labor Supply. In this chapter we criticize the principal assumption used in modern (theoretical and applied) analysis of labor supply: the Pareto optimality of intrahousehold resources allocation. The work proposes a contractual approach to the economie of the family and see the marriage as an essentially incomplete contract (i.e. it does not specifies how the partners should behave in all future contingencies). We show how inefficiencies can arise only because of this contractual incompleteness; thus we assume throughout perfect information and the possibility of writing long-term contracts. The inefficiencies are due to the fact that divorce can be asked without requiring the other party consensus, because of that, in each period, each partner can threaten divorce to recontract the division of unexpected surpluses. As a consequence the activities that generate such surpluses are discouraged and, in contrast, are encouraged those activities that raise the bargaining power (such as the accumulation of human capitai). The model has an important empirica! implication. We can explain an anomaly on the US labor supply time series motivating it with the change in divorce law occurred during 70s. Moral Hazard, Career Concerns and the Trade-off Between Incentives, Intertemporal Consumption Smooting and Human Capital Insurance: Some Preliminary Results. Chapter 5 applies and extends the recursive techniques presented in Chapter 3 to analyze an important variation of the Principal-Agent model: the case with career concerns. The literature presents the model as a repeated moral hazard problem where is introduced a process of learning on the productivity parameter of the worker. Moreover, there is limited commitment: the agent can, in any period walk away from the contract and accept a profitable offer from the market. The complexity of the problem induced economists to restrict the analysis to the case where the production technology is linear and additively separable in: productivity parameter, effort and technological shock. Finaliy, the few contributions about the analysis of the optimal contract assume that the agent do not like intertemporal consumption smoothing. Using recursive techniques we can analyze a more generai case and obtain new interesting results. First, as expected, one of the main components that characterize the optimallong term contract is the trade-off between incentives, intertemporal consumption smoothing and insurance against shocks on human capitai endowment. Secondly, there is a new effect that we cali information effect. In the proposed model is possible that a costly and non remunerative action be implemented. This result is due to the fact that- in contrast to the linear technology model where ali actions are equaliy informative about the productivity parameter - this action has high informational content. This new information aliows to reduce the uncertainty about the productivity parameter, reducing incentive costs in future periods. In this chapter we present only preliminary results. In particular - although some results have more generai applications - the model has been fuliy analyzed only for the case in which agent has log-utility. For this particular case we further find a closed form solution of the infinite horizon optimal wage contract for the repeated case ( without learning).
Publisher
Università degli studi di Trieste
Languages
en
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