Knowledge that Transforms

We investigate a class of semiparametric ARCH(∞) models that includes as a special case the partially nonparametric (PNP) model introduced by Engle and Ng (1993) and which allows for both flexible dynamics and flexible function form with regard to the “news impact” function. We show that the functional part of the model satisfies a type II linear integral equation and give simple conditions under which there is a unique solution. We propose an estimation method that is based on kernel smoothing and profiled likelihood. We establish the distribution theory of the parametric components and the pointwise distribution of the nonparametric component of the model. We also discuss efficiency of both the parametric part and the nonparametric part. We investigate the performance of our procedures on simulated data and on a sample of S&P500 index returns. We find evidence of asymmetric news impact functions, consistent with the parametric analysis.

We develop general model-free adjustment procedures for the calculation of unbiased volatility loss functions based on practically feasible realized volatility benchmarks. The procedures, which exploit recent nonparametric asymptotic distributional results, are both easy-to-implement and highly accurate in empirically realistic situations. We also illustrate that properly accounting for the measurement errors in the volatility forecast evaluations reported in the existing literature can result in markedly higher estimates for the true degree of return volatility predictability.

In this paper, I consider a dynamic economy in which a government needs to finance a stochastic process of purchases. The agents in the economy are privately informed about their skills, which evolve stochastically over time; I impose no restriction on the stochastic evolution of skills. I construct a tax system that implements a symmetric constrained Pareto optimal allocation. The tax system is constrained to be linear in an agent's wealth, but can be arbitrarily nonlinear in his current and past labor incomes. I find that wealth taxes in a given period depend on the individual's labor income in that period and previous ones. However, in any period, the expectation of an agent's wealth tax rate in the following period is zero. As well, the government never collects any net revenue from wealth taxes. Copyright The Econometric Society 2005.

It is well known that standard asymptotic theory is not applicable or is very unreliable in models with identification problems or weak instruments. One possible way out consists of using a variant of the Anderson–Rubin ((1949), AR) procedure. The latter allows one to build exact tests and confidence sets only for the full vector of the coefficients of the endogenous explanatory variables in a structural equation, but not for individual coefficients. This problem may in principle be overcome by using projection methods (Dufour (1997), Dufour and Jasiak (2001)). At first sight, however, this technique requires the application of costly numerical algorithms. In this paper, we give a general necessary and sufficient condition that allows one to check whether an AR-type confidence set is bounded. Furthermore, we provide an analytic solution to the problem of building projection-based confidence sets from AR-type confidence sets. The latter involves the geometric properties of “quadrics” and can be viewed as an extension of usual confidence intervals and ellipsoids. Only least squares techniques are needed to build the confidence intervals.

Each agent in a finite set requests an integer quantity of an idiosyncratic good; the resulting total cost must be shared among the participating agents. The Aumann–Shapley prices are given by the Shapley value of the game where each unit of each good is regarded as a distinct player. The Aumann–Shapley cost-sharing method charges to an agent the sum of the prices attached to the units she consumes. We show that this method is characterized by the two standard axioms of Additivity and Dummy, and the property of No Merging or Splitting: agents never find it profitable to split or to merge their consumptions. We offer a variant of this result using the No Reshuffling condition: the total cost share paid by a group of agents who consume perfectly substitutable goods depends only on their aggregate consumption. We extend this characterization to the case where agents are allowed to consume bundles of goods.

International audience

This paper develops theoretical foundations for an error analysis of approximate equilibria in dynamic stochastic general equilibrium models with heterogeneous agents and incomplete financial markets. While there are several algorithms that compute prices and allocations for which agents' first-order conditions are approximately satisfied (“approximate equilibria”), there are few results on how to interpret the errors in these candidate solutions and how to relate the computed allocations and prices to exact equilibrium allocations and prices. We give a simple example to illustrate that approximate equilibria might be very far from exact equilibria. We then interpret approximate equilibria as equilibria for close-by economies; that is, for economies with close-by individual endowments and preferences. We present an error analysis for two models that are commonly used in applications, an overlapping generations (OLG) model with stochastic production and an asset pricing model with infinitely lived agents. We provide sufficient conditions that ensure that approximate equilibria are close to exact equilibria of close-by economies. Numerical examples illustrate the analysis.

This paper uses the marginal treatment effect (MTE) to unify the nonparametric literature on treatment effects with the econometric literature on structural estimation using a nonparametric analog of a policy invariant parameter; to generate a variety of treatment effects from a common semiparametric functional form; to organize the literature on alternative estimators; and to explore what policy questions commonly used estimators in the treatment effect literature answer. A fundamental asymmetry intrinsic to the method of instrumental variables (IV) is noted. Recent advances in IV estimation allow for heterogeneity in responses but not in choices, and the method breaks down when both choice and response equations are heterogeneous in a general way.

Repeated games with unknown payoff distributions are analogous to a single decision maker's “multi-armed bandit” problem. Each state of the world corresponds to a different payoff matrix of a stage game. When monitoring is perfect, information about the state is public, and players are sufficiently patient, the following result holds: For any function that maps each state to a payoff vector that is feasible and individually rational in that state, there is a sequential equilibrium in which players experiment to learn the realized state and achieve a payoff close to the one specified for that state.