Knowledge that Transforms

‘If empirically meaningful interpersonal comparisons have to be based on indifference maps, as we have argued, then the Independence of Irrelevant Alternatives must be violated. The information which enables us to assert that individual A prefers x to y more strongly than B prefers y to x must be based on comparisons by A and B of x and y not only to each other but also to other alternatives. Kenneth J. Arrow, ‘Social Choice and Individual Values, p. 112. In a framework of preferences over lotteries, we show that an axiom system consisting of weakened versions of Arrow's axioms has a unique solution. ‘Relative Utilitarianism’ consists of first normalizing individual von Neumann-Morgenstern utilities between 0 and 1 and then summing them.

This paper defines a general equilibrium model with exchange and club formation. Agents trade multiple private goods widely in the market, can belong to several clubs, and care about the characteristics of the other members of their clubs. The space of agents is a continuum, but clubs are finite. It is shown that (i) competitive equilibria exist, and (ii) the core coincides with the set of equilibrium states. The central subtlety is in modeling club memberships and expressing the notion that membership choices are consistent across the population.

This paper develops a regression limit theory for nonstationary panel data with large numbers of cross section (n) and time series (T) observations. The limit theory allows for both sequential limits, wherein T→∞ followed by n→∞, and joint limits where T, n→∞ simultaneously; and the relationship between these multidimensional limits is explored. The panel structures considered allow for no time series cointegration, heterogeneous cointegration, homogeneous cointegration, and near-homogeneous cointegration. The paper explores the existence of long-run average relations between integrated panel vectors when there is no individual time series cointegration and when there is heterogeneous cointegration. These relations are parameterized in terms of the matrix regression coefficient of the long-run average covariance matrix. In the case of homogeneous and near homogeneous cointegrating panels, a panel fully modified regression estimator is developed and studied. The limit theory enables us to test hypotheses about the long run average parameters both within and between subgroups of the full population.

A game is better-reply secure if for every nonequilibrium strategy x* and every payoff vector limit u* resulting from strategies approaching x*, some player i has a strategy yielding a payoff strictly above ui* even if the others deviate slightly from x*. If strategy spaces are compact and convex, payoffs are quasiconcave in the owner's strategy, and the game is better-reply secure, then a pure strategy Nash equilibrium exists. Better-reply security holds in many economic games. It also permits new results on the existence of symmetric and mixed strategy Nash equilibria.

In this paper, we consider the following classical public goods problem. A group of individuals must decide on a level of public good that is produced according to constant returns to scale up to some capacity constraint. In addition to deciding the level of public good, the group must decide how to tax the individuals in the group in order to cover the cost. The distribution of the burden of taxation is important because different individuals have different marginal rates of substitution between the private good (taxes) and the public good, and may have different incomes as well. These individual marginal rates of substitution are private information; that is, each individual knows his or her own marginal rate of substitution, but not those of the other members of the group. Adopting a Bayesian mechanism design framework, we assume that the distribution of marginal rates of substitution is common knowledge.

Why do both left and right political parties typically propose progressive income taxation schemes in political competition? Analysis of this problem has been hindered by the two-dimensionality of the issue space. To give parties a choice over a domain that contains both progressive and regressive income tax policies requires an issue space that is at least two-dimensional. Nash equilibrium in pure strategies of the standard two-party game, whose players have complete preferences over a two-dimensional policy space, generically fails to exist. I introduce a new equilibrium concept for political games, based on the fact of factional conflict within parties. Each party is supposed to consist of reformists, militants, and opportunists: each faction has a complete preference order on policy space, but together they can only agree on a partial order. Nash equilibria of the two-party game, where the policy space consists of all quadratic income tax functions, and each party is represented by its partial order, exist, and it is shown that, in such equilibria, both parties propose progressive income taxation.

This paper presents a simple two-step nonparametric estimator for a triangular simultaneous equation model. Our approach employs series approximations that exploit the additive structure of the model. The first step comprises the nonparametric estimation of the reduced form and the corresponding residuals. The second step is the estimation of the primary equation via nonparametric regression with the reduced form residuals included as a regressor. We derive consistency and asymptotic normality results for our estimator, including optimal convergence rates. Finally we present an empirical example, based on the relationship between the hourly wage rate and annual hours worked, which illustrates the utility of our approach.

The proportional hazard model with unobserved heterogeneity gives the hazard function of a random variable conditional on covariates and a second random variable representing unobserved heterogeneity. This paper shows how to estimate the baseline hazard function and the distribution of the unobserved heterogeneity nonparametrically. The baseline hazard function and heterogeneity distribution are assumed to satisfy smoothness conditions but are not assumed to belong to known, finite-dimensional, parametric families. Existing estimators assume that the baseline hazard function or heterogeneity distribution belongs to a known parametric family. Thus, the estimators presented here are more general than existing ones.