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Sample selection bias as a specification error This paper discusses the bias that results from using non-randomly selected samples to estimate behavioral relationships as an ordinary specification error or «omitted variables» bias. A simple consistent two stage estimator is considered that enables analysts to utilize simple regression methods to estimate behavioral functions by least squares methods. The asymptotic distribution of the estimator is derived.

The purpose of this note is to show that the so-called Principle of Minimum Differentiation, as based on Hotelling’s 1929 paper “Stability in Competition” is invalid. The purpose of this note is to show that the so-called Principle of Minimum Differentiation, as based on Hotelling’s 1929 celebrated paper (Hotelling [3]), is invalid. Firstly, we assert that, contrary to the statement formulated by Hotelling in his model, nothing can be said about the tendency of both sellers to agglomerate at the center of the market. The reason is that no equilibrium price solution will exist when both sellers are not far enough from each other. Secondly, we consider a slightly modified version of Hotelling’s example, for which there exists a price equilibrium solution everywhere. We show however that, for this version, there is a tendency for both sellers to maximize their differentiation. This example thus constitutes a counterexample to Hotelling’s conclusions. We shall first recall Hotelling’s model and notations. On a line of length `, two sellers A and B of a homogeneous product, with zero production cost, are located at respective distances a and b from the ends of this line (a+ b ≤ `; a ≥ 0, b ≥ 0). Customers are evenly distributed along the line, and each customer consumes exactly a single unit of this commodity per unit of time, irrespective of its price. Since the product is homogeneous, a customer will buy from the seller Econometrica, 47(5), 1145–1150, September 1979. Center for Operations Research and Econometrics

[We study a team with many processes; the output process depends on the resources allocated to it by the resource manager, on a local decision by the process manager, and on a (random) parameter of the process. We compare two communication patterns: (1) resource allocations are based on full information, but local decisions are based only on corresponding local information; (2) all decisions are based on full information. We show that, if the criterion is expected average output per process, and if the process parameters are independent and identically distributed, then (under certain regularity assumptions) for "large" teams the additional communication among process managers in (2) over (1) has approximately no value.]

[Suppose that social choice is based on interpersonal comparisons of welfare levels. Suppose too that, whenever all but two persons are indifferent between two options, a choice is made between these options which is equitable, in some sense. Then provided that individual welfare functions are unrestricted, and social choice is independent of irrelevant alternatives, it follows that social choice is always equitable, in the same sense. This applies when equity means satisfying Suppes' indifference rule, or Suppes' original justice criterion, or the lexicographic extension of Rawls' difference principle.]