An adjustment to the likelihood ratio statistic when testing hypotheses in the multivariate linear model using large samples: A note

Leamer's (1978) criterion for testing restrictions in the single equation linear model in which the level of significance decreases with sample size is generalized to the case of common, within equation linear restrictions in the multivariate linear model.     

The quartiles of the maximum entropy distribution

The quartile points and interquartile range of the maximum entropy (ME) distribution and sample distribution are compared, using expected values for sampling from a standard normal population. For sample sizes n?20 such that the sample quartile points are uniquely defined, the ME quartile points and interquartile range are found to have lower mean-squared error (MSE).     

An algorithm for the generalized transportation problem

This paper describes a new computational technique for solving spatial economic equilibrium problems which are generalizations of the classic transportation problem. This technique makes use of a type of algorithm which has been developed in recent years to compute Kakutani fixed points and solve related problems. Existing algorithms for the generalized transportation problem employ quadratic programming, and therefore require that demand and supply functions be linear. By contrast, the algorithm of this paper can handle demand and supply relationships which are nonlinear or even semi-continuous. It can also handle non-constant transport costs and various other complications. The technique is capable of yielding highly accurate solutions, and appears to be computationally efficient on problems of reasonable size.     

The Under-Exploitation of Natural Resources: A Model with Overlapping Generations*

It is well known that competitive markets may fail to generate an optimal rate of extraction of a natural resource-stock. The barrier to optimality may be uncertainty about tenure, commonality of property rights in the resource, or uncertainty about the extent of the resource. In all these cases, suboptimality takes the form of over-extraction. We draw attention to an additional source of suboptimality. In an economy with overlapping generations, the resource-stock plays the double role of repository of savings and source of productive inputs. The decline in the supply of the resource-stock may eventually force its price so high that it ceases to perform its second function. Extraction comes to an end even though the resource has a positive marginal productivity in producing consumption goods. This is inefficient, hence suboptimal. This time, however, suboptimality takes the form of under-extraction.     

Utility theory based on rational probabilities

Classical utility theory assumes that a preference order is defined for all mixtures αa+(1?α)b of pure prospects a,b for all real numbers α between 0 and 1. If α is irrational such mixtures are hard to interpret intuitively. We show here how to modify the usual axiomatisations to deal with the case where α is restricted to rational values, or even further to values of the form m/2ⁿ corresponding to mixtures built up from even bets.