Jean Mercenier, Philippe Michel, Discrete-Time Finite Horizon Approximation of Infinite Horizon Optimization Problems with Steady-State Invariance, Econometrica, Vol. 62, No. 3 (May, 1994), pp. 635-656
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.
Knowledge of the asymptotic variance of an estimator is important for large sample inference, efficiency, and as a guide to the specification of regularity conditions.The purpose of this paper is the presentation of a general formula for the asymptotic variance of a semiparametric estimator.A particularly important feature of this formula is a way of accounting for the presence of nonparametric estimates of nuisance functions.The general form of an adjustment factor for nonparametric estimates is derived and analyzed.The usefulness of the formula is illustrated by deriving propositions on asymptotic equivalence for different nonparametric estimators of the same function, conditions for estimation of the nuisance functions to have no effect on the asymptotic variance, and the form of a correction term for the presence of linear function of a conditional expectation estimator, or other projection estimator (e.g.partially linear and/or additive nonparametric projections), and for a function of a density.Specific results cover a semiparametric random effects model for binary panel data, nonparametric consumer surplus, nonparametric prediction, and average derivatives.Regularity conditions are given for many of the propositions.These include primitive conditions for v'n-consistency, asymptotic normality, and consistency of an asymptotic variance estimator with series estimators of conditional expectations (or projections), in each of the examples.
The authors provide a convergence theory for adaptive learning algorithms useful for the study of learning by economic agents. Their results extend the framework of L. Ljung previously utilized by A. Marcet-T. J. Sargent and M. Woodford by permitting nonlinear laws of motion driven by stochastic processes that may exhibit moderate dependence, such as mixing and mixingale processes. The authors draw on previous work by H. J. Kushner and D. S. Clark to provide readily verifiable and/or interpretable conditions ensuring algorithm convergence, chosen for their suitability in the context of adaptive learning. Copyright 1994 by The Econometric Society.
This paper provides a general framework for proving the "square root of" T-consistency and asymptotic normality of a wide variety of semiparametric estimators. The class of estimators considered consists of estimators that can be defined as the solution to a minimization problem based on a criterion function that may depend on a preliminary infinite dimensional nuisance parameter estimator. The method of proof exploits results concerning the stochastic equicontinuity of stochastic processes. The results are applied to the problem of semiparametric weighted least squares estimation of partially parametric regression models. Primitive conditions are given for "square root of" T-consistency and asymptotic normality of this estimator. Copyright 1994 by The Econometric Society.
A model of trade with m buyers and m sellers is considered in which price is set to equate revealed demand and supply. In a Bayesian Nash equilibrium, each trader acts not as a price-taker, but instead misrepresents his true demand/supply to influence price in his favor. This causes inefficiency. We show that in any equilibrium the amount by which a trader misreports is O(1/m) and the corresponding inefficiency is O(1/m2). The indeterminacy and the inefficiency that is caused by the traders' bargaining behavior in small markets thus rapidly vanishes as the market increases in size.
We study the indeterminacy of equilibria in infinite horizon capital accumulation models with technological externalities. Our investigation encompasses models with bounded and unbounded accumulation paths, and models with one and two sectors of production. Under reasonable assumptions we find that equilibria are locally unique in one-sector economies. In economies with two sectors of production it is instead easy to construct examples where a positive external effect induces a two-dimensional manifold of equilibria converging to the same steady state (in the bounded case) or to the same constant growth rate (in the unbounded case). For the latter we point out that the dynamic behavior of these equilibria is quite complicated and that persistent fluctuations in their growth rates are possible.
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.
The Bertrand-Edgeworth model describes competition among price setting sellers with production capacity constraints. The authors report on laboratory experiments that permit evaluation of different theories of Bertrand-Edgeworth competition: competitive pricing, Edgeworth cycles in prices, mixed strategy Nash equilibrium pricing, and tacit collusion. Each of the theories helps to explain some aspects of the data. However, none of these theories are completely consistent with the data. In relative terms, the Edgeworth cycle theory provides better predictions of key aspects of the data than the other theories. Coauthors are Stephen Rassenti, Stanley S. Reynolds, and Vernon L. Smith. Copyright 1994 by The Econometric Society.