Necessary and sufficient conditions for Pareto optimality are derived for problems involving convex criteria and convex constraints. For a wide class of convex functions, the characterization of Pareto optimality is given in terms of systems of linear programs, which, under suitable regularization conditions, reduce to a single linear program. The consideration of a system of linear programs and their duals leads naturally to a system of partial prices associated with a Pareto optimum. (Author)

This paper studies moral hazard contracts that may be renegotiated after an agent chooses an unobservable effort. Unlike in previous models, a contract here contains only one compensation scheme, and the agent has all the bargaining power in the renegotiation stage. Using a relatively weak forward-induction refinement, all equilibria are shown tb be (second-best) efficient. Renegotiation occurs in every equilibrium. If the effort set is rich, the only equilibrium initial contract is a sales contract, i.e., a scheme which sells the project to the agent. This captures the idea that a party (the principal) who has an inherently weak renegotiation position will sometimes insist on a simple initial contract.

The paper considers the OLS, the IV, and two method-of-moments estimators, MM and MMK, of the coefficients of a single equation, where the explanatory variables are correlated with the disturbance term. The MM and MMK estimators are generalizations of the LIML and LIMLK estimators, respectively. Multivariate first-order approximations to the distributions are derived under normality, using a parameter sequence where the number of instruments increases as the number of observations increases. Numerical results show these approximations are more accurate, compared to large-sample approximations, even if the number of instruments is small. The moments of the multivariate limit distributions of the MM and MMK estimators can be consistently estimated under a variety of parameter sequences, including the large-sample sequence. The new approximate confidence regions perform well in terms of exact levels, compared to traditional ones. The IV estimator of the coefficient of a single explanatory endogenous variable is interpreted as a shrinkage estimator, which is dominated, in practical cases, by the MM and MMK estimators in terms of nearness to the true value in the sense of Pitman.

This paper is concerned with the refined asymptotic properties of several tests for the admissibility of a subset of (overidentifying) instrumental variables. It derives maximum likelihood and linearized maximum likelihood tests and calculates size corrections to the order 1/T. The local power function of the size-corrected tests is the same to the order 1/T, irrespectively of the form of the test statistic or the limited information estimator used in its computation. Futher, it compares these tests with two previously proposed tests. The size and the power of the original and the size-corrected tests are compared by Monte Carlo experiments. Copyright 1994 by The Econometric Society.

A dynamic stochastic model for a competitive industry is developed in which entry, exit, and the growth of firms' output and employment is determined. The paper extends long-run industry equilibrium theory to account for entry, exit, and heterogeneity in the size and growth rate of firms. Conditions under which there is entry and exit in the long run are developed. Cross sectional implications and distributions of profits and value of firms are derived. Comparative statics on the equilibrium size distribution and turnover rates are analyzed. Copyright 1992 by The Econometric Society.

A generalization of the multinomial logit (MNL) model is developed for cases in which discrete alternatives are ordered so as to induce stochastic correlation among alternatives in close proximity. The model belongs to the Generalized Extreme Value class introduced by McFadden, and is therefore consistent with random utility maximization. If the true model is nearly MNL, iterative estimation on an ordinary MNL computer package provides approximate parameter estimates and a test for the hypothesized failure of the MNL'S "independence from irrelevant alternatives" assumption. A straightforward extension can handle cases where observations have been selected on the basis of a truncated choice set. The model's properties are investigated through a numerical example, and through two empirical applications whose rather unsatisfactory results are very briefly described.

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