welfare cost of business cycles when markets are incomplete

This paper analyzes the welfare effects of business cycles when workers face uninsurable idiosyncratic labor income risk that has a cyclical component. In accordance with the recent literature, this paper assumes that eliminating business cycles amounts to integrating out aggregate shocks (the integration principle) and that idiosyncratic shocks and aggregate shocks are stochastically independent (the independence assumption). This paper provides two arguments why the previous literature has underestimated the welfare costs of business cycles. First, the welfare cost of business cycles are in general indeterminate, and the previous literature has only reported the lower bound that is consistent with the data. In a simple example calibrated to match the observed cyclical variations in displacement probabilities, the lower bound is .35 percent of average consumption and the upper bound is 1.39 percent (using log-utility). Second, the previous literature has only focused on cyclical variations in job displacement (unemployment) probabilities, but neglected cyclical variations in the average income loss of displaced workers. In a simple calibrated example, the introduction of cyclical variations in the average income loss of displaced workers increases the lower bound from .35 percent of average consumption to .94 percent and the upper bound from 1.39 percent to 1.89 percent (again for log-utility)welfare cost of business cycles, incomplete markets

Bounds on the Size of the Likelihood Ratio Test of Independence in a Contingency Table

AbstractBounds are obtained on the limiting size of the nominal level-α likelihood ratio test of independence in a r × c contingency table. The situations considered include sampling with both marginal totals random and with one margin fixed. Upper and lower bounds are obtained. The limiting size is greater than α when some marginal probabilities are small. As the degrees of freedom increase, the limiting size tends to 1 for all α-values

An Axiomatic Framework for Propagating Uncertainty in Directed Acyclic Networks

This paper presents an axiomatic system for propagating uncertainty in Pearl's causal networks, (Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference, 1988 [7]). The main objective is to study all aspects of knowledge representation and reasoning in causal networks from an abstract point of view, independent of the particular theory being used to represent information (probabilities, belief functions or upper and lower probabilities). This is achieved by expressing concepts and algorithms in terms of valuations, an abstract mathematical concept representing a piece of information, introduced by Shenoy and Sharer [1, 2]. Three new axioms are added to Shenoy and Shafer's axiomatic framework [1, 2], for the propagation of general valuations in hypertrees. These axioms allow us to address from an abstract point of view concepts such as conditional information (a generalization of conditional probabilities) and give rules relating the decomposition of global information with the concept of independence (a generalization of probability rules allowing the decomposition of a bidimensional distribution with independent marginals in the product of its two marginals). Finally, Pearl's propagation algorithms are also developed and expressed in terms of operations with valuations.Commission of the European Communities under ESPRIT BRA 3085: DRUM

Credal Networks under Epistemic Irrelevance

A credal network under epistemic irrelevance is a generalised type of Bayesian network that relaxes its two main building blocks. On the one hand, the local probabilities are allowed to be partially specified. On the other hand, the assessments of independence do not have to hold exactly. Conceptually, these two features turn credal networks under epistemic irrelevance into a powerful alternative to Bayesian networks, offering a more flexible approach to graph-based multivariate uncertainty modelling. However, in practice, they have long been perceived as very hard to work with, both theoretically and computationally. The aim of this paper is to demonstrate that this perception is no longer justified. We provide a general introduction to credal networks under epistemic irrelevance, give an overview of the state of the art, and present several new theoretical results. Most importantly, we explain how these results can be combined to allow for the design of recursive inference methods. We provide numerous concrete examples of how this can be achieved, and use these to demonstrate that computing with credal networks under epistemic irrelevance is most definitely feasible, and in some cases even highly efficient. We also discuss several philosophical aspects, including the lack of symmetry, how to deal with probability zero, the interpretation of lower expectations, the axiomatic status of graphoid properties, and the difference between updating and conditioning