An alternate development of conditioning

Abstract  The "classical" development of conditioning, due to K olmogorov , does not agree with the "practical" (more intuitive, but unrigorous) way in which probabilists and statisticians actually think about conditioning. This paper describes an alternative to the classical development. It is shown that standard concepts and results can be developed, rigorously, along lines, which correspond to the "practical" approach, and so as to include the classical material as a special case. More specifically, let Xand Y be random variables (r.v.'s) from (Ω, f, P) to ( x, f_x ) and (y. f^y.), respectively. In this paper, the fundamental concept is the conditional probability P(AX = x ), a function of xε x which satisfies a "natural" defining condition. This is used to define a conditional distribution P_y/x, as a mapping x × f^y-R such that, as a function of B, P_ylx=x,(B ) is a probability measure on f^y. Then, for a numerical r.v. Y , conditional expectation E(Y/X) is defined as a mapping x → whose value at x isE(Y/X = x) = ydP_Y/x=i(y ). Basic properties of conditional probabilities, distributions, and expectations, are derived and their existence and uniqueness are discussed. Finally, for a sub-o-algebra and a numerical r.v. Y , the classical conditional expectation E(Y) is obtained as E(Y/X) with X = i , the identity mapping from (Ω, f) to (Ω).     

Is Technology-ridden U.S. Agriculture in a Long-run Decline?

Abstract . The American family farm is threatened by the combination of low, unstable commodity prices and high costs of machine and chemical technology. Overplanting, erosion, excessive taxation, and non-farm development diminish the best cropland. Government and corporate business policy have encouraged overproduction and soil abuse. To survive, the small farmer takes a second job or joins the urban industrial proletariat. No single national organization protects agriculture or equals the effective lobbying of business and unions for their own interests. “Modern” technology often produces less per land unit than traditional labor-intensive cultivation and costs more in terms of energy, capital, and depleted soil and natural resources. Usurious interest, archaic tax laws, and rapid rise of current technological production costs force insolvency of the small farm while facilitating expansion of giant agribusiness corporations, but technological innovation may have reached the point of diminishing returns. Meanwhile disruption of rural society continues, aggravating metropolitan overpopulation, unemployment, and social disorganization.     

The supply of consumption goods in centrally planned economies

Estimates are given, based on annual time series from the mid-1950s to 1975, of planner's supply functions for consumption goods in Czechoslovakia, the GDR, Hungary, and Poland. The supply function is specified in the form of a behavioral rule describing the planners' short-run adjustment of consumption away from its long-run trend. The fits are good, and the estimates support the a priori specification and the maintained hypothesis of stable resource-allocation behavior. These supply functions, together with household demand functions estimated in a separate paper, will provide a starting point for disequilibrium estimation of the consumption-goods market for these economies.     

Invisible costs in offshoring services work

Offshoring service work is an accelerating trend. While the cost-savings from offshoring service work are usually clear, operating at a distance also brings with it certain “invisible costs.” We combine existing service operations theory with insights from the literature on communications and culture to present a new conceptual framework, organized around interaction intensity and interaction distance. We identify the drivers of these costs. We conclude with recommendations for controlling or attenuating invisible costs in offshoring service work.     

Property appraisal in high-rises: A cooperative game theory approach

The construction of the higher stories in a building is utterly contingent upon the construction of the lower ones, while the construction of lower stories does not require the construction of the higher ones. This rationale underlies our adoption of a cooperative game theory methodology for examining the value of units based on the cost approach of land appraisal. Particularly, we propose the Shapley value solution to examine the allocation of the land and construction cost among the stories of the building. We explore the allocation mechanism and derive several closed-form properties by which the value pattern of stories in a building is rationalized. The proposed cost allocation may, among other things, generate values when comparable market prices are unobservable (consistent with the cost approach); may be used by courts in order to compute compensations in cases of disputes regarding expansions and redevelopments of existing structures among co-owners; and may determine the rent cost allocation in an organization with several profit centers located on different floors of a building.     

Structural measurement errors in nonseparable models

This paper considers measurement error from a new perspective. In surveys, response errors are often caused by the fact that respondents recall past events and quantities imperfectly. We explore the consequences of limited recall for the identification of marginal effects. Our identification approach is entirely nonparametric, using Matzkin-type nonseparable models that nest a large class of potential structural models. We show that measurement error due to limited recall will generally exhibit nonstandard behavior, in particular be nonclassical and differential, even for left-hand side variables in linear models. We establish that information reduction by individuals is the critical issue for the severity of recall measurement error. In order to detect information reduction, we propose a nonparametric test statistic. Finally, we propose bounds to address identification problems resulting from recall errors. We illustrate our theoretical findings using real-world data on food consumption.