This paper proposes simple tests of error cross section dependence which are applicable to a variety of panel data models, including stationary and unit root dynamic heterogeneous panels with short T and large N. The proposed tests are based on average of pair-wise correlation coefficients of the OLS residuals from the individual regressions in the panel, and can be used to test for cross section dependence of any fixed order p, as well as the case where no a priori ordering of the cross section units is assumed, referred to as CD(p) and CD tests, respectively. Asymptotic distribution of these tests are derived and their power function analyzed under different alternatives. It is shown that these tests are correctly centred for fixed N and T, and are robust to single or multiple breaks in the slope coefficients and/or error variances. The small sample properties of the tests are investigated and compared to the Lagrange multiplier test of Breusch and Pagan using Monte Carlo experiments. It is shown that the tests have the correct size in very small samples and satisfactory power, and as predicted by the theory, quite robust to the presence of unit roots and structural breaks. The use of the CD test is illustrated by applying it to study the degree of dependence in per capita output innovations across countries within a given region and across countries in different regions. The results show significant evidence of cross dependence in output innovations across many countries and regions in the World.

General Diagnostic Tests for Cross Section Dependence in Panels

The author systematically examines one of the important issues of information — establishing the market price. He introduces the concept of «search» — where a buyer wanting to get a better price, is forced to question sellers. The article deals with various aspects of finding the necessary information.

Economics of Information

Publisher Summary This chapter reviews the supply chain coordination with contracts. Numerous supply chain models are discussed. In each model, the supply chain optimal actions are identified. The chapter extends the newsvendor model by allowing the retailer to choose the retail price in addition to the stocking quantity. Coordination is more complex in this setting because the incentives provided to align one action might cause distortions with the other action. The newsvendor model is also extended by allowing the retailer to exert costly effort to increase demand. Coordination is challenging because the retailer's effort is noncontractible—that is, the firms cannot write contracts based on the effort chosen. The chapter also discusses an infinite horizon stochastic demand model in which the retailer receives replenishments from a supplier after a constant lead time. Coordination requires that the retailer chooses a large basestock level.

Supply Chain Coordination with Contracts

The theory of precautionary saving is shown in this paper to be isomorphic to the Arrow-Pratt theory of risk aversion, making possible the application of a large body of knowledge about risk aversion to precautionary saving, and more generally, to the theory of optimal choice under risk In particular, a measure of the strength of precautionary saving motive analogous to the Arrow-Pratt measure of risk aversion is used to establish a number of new propositions about precautionary saving, and to give a new interpretation of the Oreze-Modigliani substitution effect

Precautionary Saving in the Small and in the Large

Foundations Of Statistics

This paper examines preferences toward particular classes of lottery pairs. We show how such concepts as prudence and temperance can be fully characterized by a preference relation over these lotteries. If preferences are defined in an expected-utility framework with differentiable utility, the direction of preference for a particular class of lottery pairs is equivalent to signing the nth derivative of the utility function. What makes our characterization appealing is its simplicity, which seems particularly amenable to experimentation.

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Putting Risk in Its Proper Place

The effects of risk and risk aversion in the single-period inventory "newsboy" problem are examined. Comparative-static effects of changes in the various price and cost parameters are determined and related to the newsboy's risk aversion. The addition of a random background wealth and of an increase in the riskiness of newspaper demand are also examined. Although many of the comparative effects generally are ambiguous, some fairly simple restrictions on preferences and/or risk increases are shown to lead to qualitatively deterministic results.

The Risk-Averse and Prudent Newsboy

ECONOMIC DECISION MAKING UNDER UNCERTAINTY often takes place in the presence of multiple risks and in markets that are less than complete. As a consequence, choices about endogenous risks sometimes must be made while simultaneously facing one or more immutable exogenous "background risks" that are not under the control of the agent, and that are independent of endogenous risks. It is somehow natural to assume that an exogenous deterioration in background wealth will cause an individual to take more care elsewhere. If we define a deterioration, for example, as making the individual poorer by removing a fixed amount of initial wealth, we know from Pratt (1964) that decreasing absolute risk aversion (DARA) of an individual's von Neumann-Morgenstern utility function yields this natural result. If, on the other hand, background wealth becomes riskier due to the addition of a zero-mean risk, that is also statistically independent of all other risks, behavior will be more risk averse if and only if preferences are risk vulnerable as defined by Gollier and Pratt (1996). Risk vulnerability (described below in Section 4) is a stronger notion than DARA and includes proper risk aversion (Pratt and Zeckhauser (1987)) and standard risk aversion (Eeckhoudt and Kimball (1992), Kimball (1993)) as particular cases. But a deterioration in background wealth may encompass more complicated distribution changes than the introduction of another statistically independent risk. In this paper, we examine background wealth deteriorations that take the form of both general firstand second-degree stochastic dominance changes in risk (FSD and SSD respectively). In particular, we determine conditions that are both necessary and sufficient for each of these two types of background risk changes to imply more risk-averse behavior on the part of the individual. For the case of FSD changes, this condition turns out to be Ross' stronger characterization of decreasing absolute risk aversion. In the case of general SSD changes in the distribution of background wealth, the condition derived is a stronger version (in Ross' sense) of the conditions characterizing preferences that are locally risk vulnerable in the sense of Gollier and Pratt. The necessary and sufficient conditions derived are fairly restrictive upon preferences. However, if we take as positive behavior that individuals act in a more risk-averse manner whenever the distribution of background wealth deteriorates, these conditions place canonical limits upon appropriate utility representations. At the very least, they

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Changes in Background Risk, and Risk Taking Behaviour

An understanding of risk and how to deal with it is an essential part of modern economics. Whether liability litigation for pharmaceutical firms or an individual's having insufficient wealth to retire, risk is something that can be recognized, quantified, analyzed, treated--and incorporated into our decision-making processes. This book represents a concise summary of basic multiperiod decision-making under risk. Its detailed coverage of a broad range of topics is ideally suited for use in advanced undergraduate and introductory graduate courses either as a self-contained text, or the introductory chapters combined with a selection of later chapters can represent core reading in courses on macroeconomics, insurance, portfolio choice, or asset pricing. The authors start with the fundamentals of risk measurement and risk aversion. They then apply these concepts to insurance decisions and portfolio choice in a one-period model. After examining these decisions in their one-period setting, they devote most of the book to a multiperiod context, which adds the long-term perspective most risk management analyses require. Each chapter concludes with a discussion of the relevant literature and a set of problems. The book presents a thoroughly accessible introduction to risk, bridging the gap between the traditionally separate economics and finance literatures.

Economic and Financial Decisions under Risk

This paper examines the theory of optimal insurance purchasing in the presence of uninsurable background risk. Existing theorems concerning the optimal level of insurance and the optimal form of an insurance contract are shown to hold only under restricted market and risk assumptions. In particular, conditions sufficient for the optimality of full coverage or sufficient for the optimality of deductible policies depend on the correlation between insurable and uninsurable risks. These results may provide a partial explanation why existing theory is often contradicted by observable behavior.

Harris Schlesinger

Papers

Putting Risk in Its Proper Place

The Risk-Averse and Prudent Newsboy

Changes in Background Risk, and Risk Taking Behaviour

Economic and Financial Decisions under Risk

Optimal Insurance in Incomplete Markets