Knowledge that Transforms

MUCH OF THE UNCERTAINTY concerning the likely outcome of a typical management-labor conflict pertains to the cost of possible conflict to the two sides. In this paper, we consider situations of this kind, where the cost of conflict is not known with certainty. However, we will assume the benefits from cooperation to be known. We place our analysis in the abstract framework formulated by Nash (1950): Nash described a bargaining problem as a pair consisting of a feasible set (the amount to be divided among management and labor) and a disagreement point (giving the payoffs to both sides when they fail to reach agreement on a division, that is, the strike). Nash investigated the existence of solutions to such problems that would satisfy a certain list of appealing properties. In his analysis both feasible set and disagreement point were assumed to be known. Here, we assume only the feasible set to be known. Several studies have appeared of bargaining situations where the feasible set is unknown but the disagreement point is known. While we are of course not denying the relevance of such studies, we believe that an analysis of situations where it is the consequences of conflict that are unknown might be equally, and perhaps even more, relevant to industrial experience. Indeed, consider a management-labor conflict over wages and benefits. In many industries, the future profitability of the enterprise can be predicted with reasonable accuracy on the basis of its performance in the previous years, whereas the impact of a strike might depend on a number of factors that are significantly harder to evaluate. This is because strikes are infrequent and conjectures about these factors are often not put to the test (a strike is a threat that is often not carried out), and because they involve a number of parameters that are difficult to quantify, such as the psychological readiness of the strikers, the support they might receive from the population and the media, and the likely response of competing and related industries. We impose on solutions a new condition of disagreement point concavity guaranteeing that agents will agree on a compromise before the uncertainty concerning the disagreement point is resolved. To illustrate this requirement somewhat more concretely, suppose that bargaining takes place today, without the precise location of the disagreement point being known, this uncertainty being resolved tomorrow. The bargainers have two options: the first option is simply to wait until tomorrow and solve then whatever problem has come up. Unfortunately, the resulting pair of contingent compromises, evaluated today, is in general strictly Pareto-dominated. The other possibility is to solve today the problem obtained by replacing the uncertain disagreement point by its expected value (this represents the cost of conflict evaluated today) and to solve the resulting problem today. This second option has the advantage of yielding Paretoundominated compromises (provided, of course, that agents would, in the case of no uncertainty, select such compromises), but unfortunately, it may make one of the agents worse off than under the first option. In order to ensure that all agents agree to reaching a compromise today, we require that the second option always Pareto-dominate the first one. We show that disagreement point concavity, when used in conjunction with three standard properties that are satisfied by virtually all of the solutions commonly discussed

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.

A scheme of plain conversation is constructed, which is a universal mechanism for all noncooperative games with incomplete information with at least four players, in the following sense: every solution that can be achieved by means of an arbitrary communication mechanism is a correlated equilibrium payoff of the game extended by the scheme of plain conversation. By a property of the correlated equilibrium, a similar result holds also with the Nash equilibrium solution concept. The universal mechanism can be used without any loss of efficiency.

It is often argued that a rational bubble, because it is positive, must increase the price of a stock. This argument is not valid in general: as soon as bubbles affect interest rates, the fundamental value of a stock depends on whether or not a bubble is present. The existence of a rational bubble then might, by raising equilibrium interest rates, depress the fundamental to such an extent that the sum of the positive bubble and decreased fundamental falls short of the fundamental, no-bubble price. Under conditions made precise below, there can therefore be price decreasing bubbles, and an asset can be undervalued.

This article proposes a general method to build exact tests and confidence sets in linear regressions with first-order autoregressive Gaussian disturbances. Because of a nuisance parameter problem, we argue that generalized bounds tests and conservative confidence sets provide natural inference procedures in such a context. Given an exact confidence set for the autocorrelation coefficient, we describe how to obtain a similar simultaneous confidence set for the autocorrelation coefficient and any subvector of regression coefficient. Conservative confidence sets for the regression coefficients are then deduced by a projection method. For any hypothesis that specifies jointly the value of the autocorrelation coefficient and any set of linear restrictions on the regression coefficients, we get exact similar tests. For tesing linear hypotheses about the regression coefficients only, we suggest bounds-type procedures. Exact confidence sets for the autocorrelation coefficient are built by "inverting" autocorrelation tests. The method is illustrated with two examples.

In this paper, it will be shown that any conditional moment test of functional form of nonlinear regression models can be converted into a chi-square test that is consistent against all deviations from the null hypothesis that the model represents the conditional expectation of the dependent variable relative to the vector of regressors.

Alternating price competition between firms selling differentiated products to nonhomogeneous consumers can yield two different types of equilibria. One, which we call "disciplined, " arises when products are close substitutes. Another, which we call "spontaneous, " emerges when products are more differentiated. In disciplined equilibria, an implicit threat to cut price further, in response to an initial price cut, supports quite collusive outcomes, which become less collusive as product differentiation increases. In spontaneous equilibria, no such threat is needed. Consumers in the smaller market tend to pay a higher price, as do consumers served by the more efficient firm.

THIS PAPER PROVIDES the large sample properties of two inequality indices, Atkinson's (1970) index and the generalized entropy index (Cowell and Kuga (1981), Shorrocks (1984)). The large sample properties of the equally-distributed-equivalent (e.d.e.) income measures associated with these indices are also derived. The asymptotic distributions of these inequality and welfare measures allow the construction of confidence intervals and tests for differences in the measures; these confidence intervals and tests are asymptotically distribution-free. Given the increasing availability of large micro-data sets on incomes, these results are directly applicable to empirical work on income distributions. The sampling distributions of some inequality indices, such as the Gini coefficient and Pietra index, are known.' But the ethical bases of these indices have been subject to criticism, and some researchers may prefer the Atkinson or generalized entropy indices on ethical grounds. These researchers are confronted with a choice between using an ethically unattractive index with a known sampling distribution, or using an ethically preferable index whose sampling properties are unknown. The increasing use of the Atkinson and generalized entropy indices in empirical analyses of income distributions suggests many are choosing the second option. It then becomes important to understand the sampling properties of these indices, so that statistical inference procedures may be applied. The analysis in this paper complements the recent research on sampling properties and inference for Lorenz curves. For example, Beach and Davidson (1983), and Gastwirth and Gail (1985) propose tests for equality of Lorenz curves, and Beach and Richmond (1985) provide joint confidence intervals for the Lorenz ordinate vector. Bishop, Chakraborti, and Thistle (1987, 1988a, 1988b) and Bishop, Formby, and Thistle (1989) provide a number of extensions. These papers utilize results from the theory of linear functions of order statistics.2 However, this approach is not directly applicable to the Atkinson and generalized entropy indices; these indices are not linear functions of order statistics. The Atkinson and generalized entropy indices are functions of fractional and negative moments of the distribution, and their large sample properties follow from the properties of the sample moments.

The authors analyze the principal-agent relationship when the principal has private information as a three-stage game: contract proposal, acceptance/refusal, and contract execution. They assume that the information does not directly affect the agent's payoff (private values). Equilibrium exists and is generically locally unique. Moreover, it is Pareto optimal for the different types of principal. The principal generically does strictly better than when the agent knows her information. Equilibrium allocations are the Walrasian equilibria of an "economy" where the traders are different types of principal and "exchange" the slack on the agent's individual rationality and incentive compatibility constraints.

This paper presents a simple estimator of the shape parameter in a Weibull duration model with unobserved heterogeneity. The estimator is consistent and asymptotically normal under mild conditions, and a consistent estimator of the asymptotic variance is available. A Monte Carlo study indicates that the asymptotic distribution of the estimator provides a good approximation to the finite sample distribution. The estimation strategy can be extended to a model with regressors and to a log-logistic model with unobserved heterogeneity. The advantages of the estimator are that it is easy to calculate and that its asymptotic distribution can be derived.