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.     

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.     

The rise of economics in competition policy: A Canadian perspective

Competition policy in Canada and elsewhere has changed remarkably over the last 50 years—in large measure due to advances in economics. In this article, we trace the impact of developments in industrial organization on the three central areas of competition policy: cartels, single firm conduct and mergers. We focus on Canadian competition policy but draw comparisons with developments in the United States and Europe.     

The impact of government debt on the long-run natural real interest rate – a quantitative evaluation

Persistently low natural real interest rates are a problem for monetary policy and financial stability. I analyse to what extent a permanent increase in government debt that is financed by higher taxes could raise the long-run natural real interest rate. As a measurement tool, I use an incomplete markets model with capital and government bonds. Increasing the public debt/GDP ratio by one percentage point raises the real interest rate by between 0.4 and 1.5 basis points, depending on the degree of inequality generated by the model and the tax instrument used to balance the government’s budget constraint. I also show that the interest rate effect of a change in public debt/GDP predicted by the model is significantly smaller than its empirical counterpart for the US, due to the fact that the model understates the empirical fraction of households that are constrained in their consumption decision.