Exact Distribution Theory in Structural Estimation with an Identity

Some exact distribution theory is developed for structural equation models with and without identities. The theory includes LIML, IV and OLS. We relate the new results to earlier studies in the literature, including the pioneering work of Bergstrom (1962). General IV exact distribution formulae for a structural equation model without an identity are shown to apply also to models with an identity by specializing along a certain asymptotic parameter sequence. Some of the new exact results are obtained by means of a uniform asymptotic expansion. An interesting consequence of the new theory is that the uniform asymptotic approximation provides the exact distribution of the OLS estimator in the model considered by Bergstrom (1962). This example appears to be the first instance in the statistical literature of a uniform approximation delivering an exact expression for a probability density.Exact distribution, Identity, IV estimation, LIML, Structural equation, Uniform asymptotic expansion

Voluntary Contributions to a Public Good: Non-neutrality Results / Contributions volontaires, biens publics

We show that the famous neutrality result in the theory of public good contributions (Warr, Kemp, Bergstrom, Blume and Varian) depends crucially on the assumption that agents do not take into account the effect of their public good contribution decisions on the relative price of the private goods. Thus, the scope of applicability of their result is not as large as one might at first think. Our non-neutrality results hold even if all countries are identical in technology, preferences, and endowments. Nous démontrons que le théorème sur l’invariance du stock total d’un bien public par rapport à la distribution de revenus n’est valable que si les contributeurs ignorent l’impact de leurs contributions sur le prix relatif des biens privés. Par conséquent, le résultat de Warr, Kemp, Bergstrom, Blume et Varian n’a qu’une sphère d’application limitée. Nos résultats sur le manque de neutralité sont valables même si les préférences, les technologies, et les dotations de ressources de tous les pays sont identiques.public goods, voluntary contributions,

On the irreducibility of a competitive economy.

In the case of a private ownership economy, we unify McKenzie-Debreu's and Arrow-Hahn's concepts of irreducibility by a generalization of Bergstrom irreducibility to economies with production. This, together with existence of a quasi-equilibrium, will be shown to imply existence of a Walras equilibrium.

Alan Bergstrom interview

Alan Bergstrom taught in the education department at Central Washington University, 1960-1983.https://digitalcommons.cwu.edu/cwura_interviews/1103/thumbnail.jp

Comment on Bergstrom

This comment on a 2002 article by Theodore Bergstrom in the Journal of Economic Perspectives argues that group or multilevel selection in haystack models does not require assortative mating. If the various subgroups into which the population periodically divides are sufficiently small, random variation will assure that some groups have more altruists than others, and these groups will have more surviving offspring than others. Under conditions in which the subgroups are periodically repooled into a larger population, it is possible for altruists to increase over time in the general population even though they are declining (or not increasing) at all times in every subgroup

Does Mother Nature Punish Rotten Kids?

This paper studies the evolutionary game theory of parent-offspring conflict. It revisits a question posed by Gary Becker in economics and Richard Alexander in biology, namely "when do children act in accord with the reproductive interests of their parents?"biology evolutionary game theory parent-offspring conflict family economics

Discussion of Recent Decisions

Notes by G. Kloek, R. W. Bergstrom, H. Weinstein, L. N. Conklin, J. P. McGuire, H. B. Hard