This paper presents an analysis of the structure of competitive equilibrium in a smooth, exchange economy where there are incomplete markets in financial instruments whose overall payoffs (both prices and yields) are fixed in units of account. The main result establishes that such market incompleteness generates a comparable degree of allocation indeterminateness. It is also shown how this real indeterminacy may increase when prices and yields are treated as variables rather than parameters.
A concept of an egalitarian solution is developed within the framework of cooperative game theory. The solution is designed to capture the interplay between social values (in this case, egalitarianism) and individual behavior. Both the final outcomes possible coalitional deviations are constrained by these social norms. The authors' main result: despite using a partial order (the Lorenz criterion) to compare allocations, their solution concept yields at most one allocation for each game. The concept is illustrated by a detailed study of convex games, and by a number of examples and applications.
The past decade has seen the econometric implementation of macroeconomic multi-market fix-price models for a number of European countries. The procedure in use, the full information maximum likelihood (FIML) method, unfortunately becomes very cumbersome and seems out of reach when additional features are incorporated in the model (disaggregation into micro markets, opinion surveys,...). One purpose of the present work is to prove the fruitfulness of the following estimation strategy: use Monte-Carlo simulations to compute the first and second order moments of the endogenous variables, and maximize a resulting pseudo likelihood function to estimate the parameters. We first describe the PML method in the context of the so-called canonical disequilibrium model. We then apply it to a small aggregated macroeconomic model previously studied under FIML by Artus, Avouyi-Dovi, Laroque (1985), where we allow for a disaggregation into micro markets. The results we obtain are strikingly similar to theirs. This both demonstrates in this example the robustness of the FIML procedure to the introduction of micro markets and stresses the usefulness of the PML method in obtaining reliable estimates at a smaller cost.
The problem considered is inference in a simple errors-in-variables model where consistent estimation is impossible without introducing additional exact prior information. The probabilistic prior information required for Bayesian analysis is found to be surprisingly light: despite the model's lack of identification a proper posterior is guaranteed for any bounded prior density, including those representing improper priors. This result is illustrated with the improper uniform prior, which implies marginal posterior densities obtainable by integrating the likelihood function; surprisingly, the posterior mode for the regression slope is the usual least squares estimate. KEYwoRDs: Errors-in-variables, Bayesian inference, identification, improper priors, proper posteriors, finitely additive probabilities, coherence. 1.
In this paper, the author considers how boundedly rational agents learn rational expectations when all equilibrium price functions or forecasts of future equilibrium prices are required to be computable. The paper examines two learning environments. In the first, agents have perfect information about the state of nature. In this case, the theory of machine inference can be applied to show that there is a broad class of computable economies whose rational expectations equilibria can be learned by inductive inference. In the second environment, agents do not have perfect information about the state of nature. In this case, a version of Godel's incompleteness theorem implies that rational expectations equilibria cannot be learned.
This paper is concerned with the use of power properties of tests in econometric applications. Inverse power functions are defined. These functions are designed to yield summary measures of power that facilitate the interpretation of test results in practice. Simple approximations are introduced for the inverse power functions of Wald, likelihood ratio, Lagrange multiplier, and Hausman tests. These approximations readily convey the general qualitative features of the power of a test. Examples are provided to illustrate their usefulness in interpreting test results. A COMMON PROBLEM faced in applied econometrics is that of interpreting the results of a hypothesis test when the test fails to reject the null hypothesis. Most practitioners realize that just because a test fails to reject a hypothesis one cannot claim to accept it. Nevertheless, it is common for this to be ignored, since the practitioner is often in a position where he would like the outcome of the test to provide useful inferences whether or not the test rejects. The purpose of this paper is to introduce inverse power (IP) summary measures that enable the practitioner to avoid such errors and make valid inferences when a test fails to reject the null hypothesis. These summary measures are widely applicable, easy to use (especially in the common case of a test concerning a single restriction), and simple to compute. When a test rejects the null hypothesis, the implication is that the data are inconsistent with each parameter point in the null in the sense that the probabil- ity of type I error for each point is small, viz., a or less. Correspondingly, when a test fails to reject the null hypothesis an analogous statement is needed regarding the error probabilities for points in the alternative hypothesis. It is not the case that all points in the alternative are inconsistent with the data in the sense that their probability of type II error is small (a or less). It is possible, however, to determine the region S in the alternative parameter space that is inconsistent with the data in this sense. The IP function introduced below evaluated at
In this note we derive the general form of a utility based system of demand equations that are quadratic in income with coefficients that are functions of prices.Our result turns out to be slightly more general than known till now.
This paper proposes a simple modification of a conventional method of moments estimator for a discrete response model, replacing response probabilities that require numerical integration with estimators obtained by Monte Carlo simulation.This method of simulated moments (MSM) does not require precise estimates of these probabilities for consistency and asymptotic normality, relying instead on the law of large numbers operating across observations to control simulation error, and hence can use simulations of practical size.The method is useful for models such as high-dimensional multinomial probit (MNP), where computation has restricted applications.