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Approximate Cores of Large Games

Econometrica 1984 52(6), 1327
[The core of a game, which is an abstraction of the core or set of cooperative equilibrium states of an economy, is a fundamental notion of social equilibrium. However, except for games derived from special kinds of economic situations or satisfying restrictive (balancedness) conditions, the core is usually empty. In contrast, this paper shows that, with mild and economically natural assumptions, large games always have non-empty approximate cores. The game-theoretic framework is sufficiently general to cover a wide variety of economic situations.]

Testing a Subset of Coefficients in a Structural Equation

Econometrica 1984 52(2), 427
[We often see that the F test is applied to testing significance of a subset of coefficients even in a structural equation. This is obviously a doubtful method because the sum of squared errors is not distributed as χ ^2 in a simultaneous equation system. It is known, however, that the likelihood ratio test is asymptotically distributed as χ ^2 with proper degrees of freedom. We analyze the asymptotic properties of these two kinds of test statistics. We find the likelihood ratio method associated with limited information maximum likelihood estimation is reliable in practice.]

Nonlinear Regression with Dependent Observations

Econometrica 1984 52(1), 143
This paper provides general conditions which ensure consistency and asymptotic normality for the nonlinear least squares estimator. These conditions apply to time-series, cross-section, panel, or experimental data for single equations as well as systems of equations. The regression errors may be serially correlated and/or heteroscedastic. For an important special case, we propose a new covariance matrix estimator which is consistent regardless of the presence of heteroscedasticity or serial correlation of unknown form. We also give some new tests for model misspecification, based on the information matrix testing principle

The Returns to Schooling: A Selectivity Bias Approach with a Continuous Choice Variable

Econometrica 1984 52(5), 1199
The essence of selection bias is that we do not observe nonoptimal choices. This applies whether the choice variable is discrete or continuous. This paper extends the selection bias methodology to the case where the choice variable is continuous and the choice set is ordered. The leading practical application of this analysis is the schooling choice problem. Schooling is treated as a continuous choice variable and selectivity corrected rates of return are estimated. The findings suggest selectivity is of considerable importance and support the comparative advantage hypothesis of Willis and Rosen [18].

A Reformulation of the Marginal Productivity Theory of Distribution

Econometrica 1984 52(3), 599
Reformulating marginal productivity theory by replacing productivity with respect to commodities with productivity with respect to persons and then defining perfectly competitive equilibrium as an allocation at which each person receives the marginal product of his/her contribution called a no-surplus allocation there emerges a competitive theory of price determination. Characterizations of no-surplus allocations are given in models with a nonatomic continuum of agents and an infinite-dimensional commodity space. Comparisons between the no-surplus and Walrasian equilibrium definitions of competitive equilibrium are made and some sufficient conditions are obtained for the existence of a no-surplus allocation.