Essays on contract theory and organizational economics

• Main Author: Ke, Rongzhu
• Other Authors: Bengt Holmstrom, Victor Chernozhukov and Panle Jia.
• Format: Others
• Language: English
• Published: Massachusetts Institute of Technology 2010
• Subjects: Economics.
• Online Access: http://hdl.handle.net/1721.1/54639

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Economics, 2009. === "September 2009." Cataloged from PDF version of thesis. === Includes bibliographical references. === Chapter 1 develops a non-parametric methodology for identifying contract optimality in the presence of moral hazard. Following the first order approach, a standard method of computing optimal contracts, the paper first proves two theoretical properties of the solutions to the moral hazard problem. First, we show that the profit loss (relative to the optimal contract) for given effort level has a unique lower bound. The second property is an equivalence between the first order condition (Mirrlees-Holmstrom Condition) and the Cramer-Rao Lower Bound (CRLB). These two properties provide the foundations for (1) identifying optimality, and (2) performing statistical inference on the agent's primitives based on an observed sequence of pairs of outputs and payments. The paper shows that under some weak conditions, contract optimality is identified, as long as the output generating process is additive in effort and noise. Identification does not require the agent's effort to be observed by the principal or the econometrician, and requires no knowledge of (1) the details of the contract, (2) the agent's cost of effort, (3) the agent's monetary utility, or (4) the distribution of output. Based on the approach proposed in this paper, we test contract optimality for a piece-rate contract, and estimate bounds on the profit loss for cotton weavers in Zhejiang Province, China. Chapter 2 develops a new method to justify the validity of the first order approach (FOA). We first prove that checking the validity amounts to checking the existence of a fixed point of the agent's best response against a Mirrlees-Holmstrom (MH) class contract offered by the principal, given some specifications of complemetary conditions. === (cont.) The main advantage of the current approach is the relaxation of the global concavity of agent utility. We show that under a set of mild conditions, the fixed point approach is applicable and the solution to the principal agent problem exists. In particular, if the log likelihood ratio is monotonically increasing in output but decreasing in effort, the best response correspondence against a MK contract has and only has one unique fixed point. Our approach unifies Jewitt's (1988) and Rogerson's (1985) proofs of validity of FOA, and provides a general method to judge validity of FOA. Based on the fixed-point approach, with some additional specifications, we restore Jewitt's (1988) results to situations where the distribution is not convex and the log likelihood ratio is not bounded from below (e.g., normal distribution), or there exists a limited liability constraint. Furthermore, we generalize our results to a situation where the agent's utility is non separable. In this fairly general environment, we prove a necessary and sufficient condition for the FOA to be valid, which provides an important method to identify the validity of FOA and compute the solution of the original problem. Finally, we provide a necessary and sufficient condition for a general non-linear bi-level optimization problem to be solvable based on FOA, without a convex constrained set. Chapter 3 constructs a concrete mechanism/auction to explore the consequence of imposing the ex post participation constraint. === (cont.) The main findings are: (1) In private good cases (symmetric or asymmetric), we can obtain ex post first best, ex post budget balance, at least interim incentive compatibility and ex post individual rationality (we call it ex post social efficiency), whenever the VCG mechanism runs expected surplus. And the mechanism generating an ex post monotonic payoff is generically unique (up to an ex ante side-pay). In addition, compared with standard auctions, our mechanism generates a risk-free revenue to the seller and ex post invidually rational payoff to the bidders. (2) In a general preference case with externality, we show there exists an ex post socially efficient mechanism when the number of participants is sufficiently small (n = 2). And the choice of mechanism depends on whether the quantity is endogenous or not. (3) As an implication, we provide a general discussion on how divisibility, endowment distribution and preference affect the possibility of trade. For the negative result, we show a set of conditions for non-existence of an ex post socially efficient trade, such as either utility is linear or the lowest type agent's utility is independent of his endowment, which can be regarded as stronger version of no-trade theorem (Myerson-Satterthwaite, 1983). This proposition implies non-existence of an ex post socially efficient partner dissolving mechanism. For the positive side, we provide a sufficient condition for existence of ex post socially efficient trade mechanism and show an explicit example. JEL Code: D86 D81 C12 D82 === by Rongzhu Ke. === Ph.D.