Responsibility and Cross-Subsidization in Cost Sharing

We propose two axiomatic theories of cost sharing with the common premise that agents demand comparable -though perhaps different- commodities and are responsible for their own demand. Under partial responsibility the agents are not responsible for the asymmetries of the cost function: two agents consuming the same amount of output always pay the same price; this holds true under full responsibility only if the cost function is symmetric in all individual demands. If the cost function is additively separable, each agent pays her stand alone cost under full responsibility; this holds true under partial responsibility only if, in addition, the cost function is symmetric. By generalizing Moulin and Shenker’s (1999) Distributivity axiom to cost-sharing methods for heterogeneous goods, we identify in each of our two theories a different serial method. The subsidy-free serial method (Moulin, 1995) is essentially the only distributive method meeting Ranking and Dummy. The cross-subsidizing serial method (Sprumont, 1998) is the only distributive method satisfying Separability and Strong Ranking. Finally, we propose an alternative characterization of the latter method based on a strengthening of Distributivity.

Correcting the Errors : A Note on Volatility Forecast Evaluation Based on High-Frequency Data and Realized Volatilities

This note develops general model-free adjustment procedures for the calculation of unbiased volatility loss functions based on practically feasible realized volatility benchmarks. The procedures, which exploit the recent asymptotic distributional results in Barndorff-Nielsen and Shephard (2002a), are both easy to implement and highly accurate in empirically realistic situations. On properly accounting for the measurement errors in the volatility forecast evaluations reported in Andersen, Bollerslev, Diebold and Labys (2003), the adjustments result in markedly higher estimates for the true degree of return-volatility predictability.

Finite-Sample Diagnostics for Multivariate Regressions with Applications to Linear Asset Pricing Models

In this paper, we propose several finite-sample specification tests for multivariate linear regressions (MLR) with applications to asset pricing models. We focus on departures from the assumption of i.i.d. errors assumption, at univariate and multivariate levels, with Gaussian and non-Gaussian (including Student t) errors. The univariate tests studied extend existing exact procedures by allowing for unspecified parameters in the error distributions (e.g., the degrees of freedom in the case of the Student t distribution). The multivariate tests are based on properly standardized multivariate residuals to ensure invariance to MLR coefficients and error covariances. We consider tests for serial correlation, tests for multivariate GARCH and sign-type tests against general dependencies and asymmetries. The procedures proposed provide exact versions of those applied in Shanken (1990) which consist in combining univariate specification tests. Specifically, we combine tests across equations using the MC test procedure to avoid Bonferroni-type bounds. Since non-Gaussian based tests are not pivotal, we apply the “maximized MC” (MMC) test method [Dufour (2002)], where the MC p-value for the tested hypothesis (which depends on nuisance parameters) is maximized (with respect to these nuisance parameters) to control the test’s significance level. The tests proposed are applied to an asset pricing model with observable risk-free rates, using monthly returns on New York Stock Exchange (NYSE) portfolios over five-year subperiods from 1926-1995. Our empirical results reveal the following. Whereas univariate exact tests indicate significant serial correlation, asymmetries and GARCH in some equations, such effects are much less prevalent once error cross-equation covariances are accounted for. In addition, significant departures from the i.i.d. hypothesis are less evident once we allow for non-Gaussian errors.

Exact Skewness-Kurtosis Tests for Multivariate Normality and Goodness-of-fit in Multivariate Regressions with Application to Asset Pricing Models

We study the problem of testing the error distribution in a multivariate linear regression (MLR) model. The tests are functions of appropriately standardized multivariate least squares residuals whose distribution is invariant to the unknown cross-equation error covariance matrix. Empirical multivariate skewness and kurtosis criteria are then compared to simulation-based estimate of their expected value under the hypothesized distribution. Special cases considered include testing multivariate normal, Student t; normal mixtures and stable error models. In the Gaussian case, finite-sample versions of the standard multivariate skewness and kurtosis tests are derived. To do this, we exploit simple, double and multi-stage Monte Carlo test methods. For non-Gaussian distribution families involving nuisance parameters, confidence sets are derived for the the nuisance parameters and the error distribution. The procedures considered are evaluated in a small simulation experi-ment. Finally, the tests are applied to an asset pricing model with observable risk-free rates, using monthly returns on New York Stock Exchange (NYSE) portfolios over five-year subperiods from 1926-1995.

Projection-Based Statistical Inference in Linear Structural Models with Possibly Weak Instruments

It is well known that standard asymptotic theory is not valid or is extremely unreliable in models with identification problems or weak instruments [Dufour (1997, Econometrica), Staiger and Stock (1997, Econometrica), Wang and Zivot (1998, Econometrica), Stock and Wright (2000, Econometrica), Dufour and Jasiak (2001, International Economic Review)]. One possible way out consists here in using a variant of the Anderson-Rubin (1949, Ann. Math. Stat.) procedure. The latter, however, 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, which in general does not allow for individual coefficients. This problem may in principle be overcome by using projection techniques [Dufour (1997, Econometrica), Dufour and Jasiak (2001, International Economic Review)]. AR-types are emphasized because they are robust to both weak instruments and instrument exclusion. However, these techniques can be implemented only by using costly numerical techniques. In this paper, we provide a complete analytic solution to the problem of building projection-based confidence sets from Anderson-Rubin-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 required for building the confidence intervals. We also study by simulation how “conservative” projection-based confidence sets are. Finally, we illustrate the methods proposed by applying them to three different examples: the relationship between trade and growth in a cross-section of countries, returns to education, and a study of production functions in the U.S. economy.

Identification, Weak Instruments and Statistical Inference in Econometrics

We discuss statistical inference problems associated with identification and testability in econometrics, and we emphasize the common nature of the two issues. After reviewing the relevant statistical notions, we consider in turn inference in nonparametric models and recent developments on weakly identified models (or weak instruments). We point out that many hypotheses, for which test procedures are commonly proposed, are not testable at all, while some frequently used econometric methods are fundamentally inappropriate for the models considered. Such situations lead to ill-defined statistical problems and are often associated with a misguided use of asymptotic distributional results. Concerning nonparametric hypotheses, we discuss three basic problems for which such difficulties occur: (1) testing a mean (or a moment) under (too) weak distributional assumptions; (2) inference under heteroskedasticity of unknown form; (3) inference in dynamic models with an unlimited number of parameters. Concerning weakly identified models, we stress that valid inference should be based on proper pivotal functions —a condition not satisfied by standard Wald-type methods based on standard errors — and we discuss recent developments in this field, mainly from the viewpoint of building valid tests and confidence sets. The techniques discussed include alternative proposed statistics, bounds, projection, split-sampling, conditioning, Monte Carlo tests. The possibility of deriving a finite-sample distributional theory, robustness to the presence of weak instruments, and robustness to the specification of a model for endogenous explanatory variables are stressed as important criteria assessing alternative procedures.

In Search of Advice for Physicians in Entry-Level Medical Markets

We consider entry-level medical markets for physicians in the United Kingdom. These markets experienced failures which led to the adoption of centralized market mechanisms in the 1960's. However, different regions introduced different centralized mechanisms. We advise physicians who do not have detailed information about the rank-order lists submitted by the other participants. We demonstrate that in each of these markets in a low information environment it is not beneficial to reverse the true ranking of any two acceptable hospital positions. We further show that (i) in the Edinburgh 1967 market, ranking unacceptable matches as acceptable is not profitable for any participant and (ii) in any other British entry-level medical market, it is possible that only strategies which rank unacceptable positions as acceptable are optimal for a physician.

Short run and long run causality in time series: Inference

We propose methods for testing hypotheses of non-causality at various horizons, as defined in Dufour and Renault (1998, Econometrica). We study in detail the case of VAR models and we propose linear methods based on running vector autoregressions at different horizons. While the hypotheses considered are nonlinear, the proposed methods only require linear regression techniques as well as standard Gaussian asymptotic distributional theory. Bootstrap procedures are also considered. For the case of integrated processes, we propose extended regression methods that avoid nonstandard asymptotics. The methods are applied to a VAR model of the U.S. economy.

Methods to Estimate Dynamic Stochastic General Equilibrium Models

This paper employs the one-sector Real Business Cycle model as a testing ground for four different procedures to estimate Dynamic Stochastic General Equilibrium (DSGE) models. The procedures are: 1 ) Maximum Likelihood, with and without measurement errors and incorporating Bayesian priors, 2) Generalized Method of Moments, 3) Simulated Method of Moments, and 4) Indirect Inference. Monte Carlo analysis indicates that all procedures deliver reasonably good estimates under the null hypothesis. However, there are substantial differences in statistical and computational efficiency in the small samples currently available to estimate DSGE models. GMM and SMM appear to be more robust to misspecification than the alternative procedures. The implications of the stochastic singularity of DSGE models for each estimation method are fully discussed.

Time Reversibility of Stationary Regular Finite State Markov Chains

We propose an alternate parameterization of stationary regular finite-state Markov chains, and a decomposition of the parameter into time reversible and time irreversible parts. We demonstrate some useful properties of the decomposition, and propose an index for a certain type of time irreversibility. Two empirical examples illustrate the use of the proposed parameter, decomposition and index. One involves observed states; the other, latent states.

Bayesian Analysis for a Theory of Random Consumer Demand: The Case of Indivisible Goods

McCausland (2004a) describes a new theory of random consumer demand. Theoretically consistent random demand can be represented by a \"regular\" \"L-utility\" function on the consumption set X. The present paper is about Bayesian inference for regular L-utility functions. We express prior and posterior uncertainty in terms of distributions over the indefinite-dimensional parameter set of a flexible functional form. We propose a class of proper priors on the parameter set. The priors are flexible, in the sense that they put positive probability in the neighborhood of any L-utility function that is regular on a large subset bar(X) of X; and regular, in the sense that they assign zero probability to the set of L-utility functions that are irregular on bar(X). We propose methods of Bayesian inference for an environment with indivisible goods, leaving the more difficult case of indefinitely divisible goods for another paper. We analyse individual choice data from a consumer experiment described in Harbaugh et al. (2001).

Aumann-Shapley Pricing : A Reconsideration of the Discrete Case

We reconsider the following cost-sharing problem: agent i = 1,...,n demands a quantity xi of good i; the corresponding total cost C(x1,...,xn) must be shared among the n agents. The Aumann-Shapley prices (p1,...,pn) 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 assigns the cost share pixi to agent i. When goods come in indivisible units, 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 merge their demands.

The Ghost in the Machine: Inferring Machine-Based Strategies from Observed Behavior

We introduce a procedure to infer the repeated-game strategies that generate actions in experimental choice data. We apply the technique to set of experiments where human subjects play a repeated Prisoner's Dilemma. The technique suggests that two types of strategies underly the data.

Nearly Serial Sharing Methods

A group of agents participate in a cooperative enterprise producing a single good. Each participant contributes a particular type of input; output is nondecreasing in these contributions. How should it be shared? We analyze the implications of the axiom of Group Monotonicity: if a group of agents simultaneously decrease their input contributions, not all of them should receive a higher share of output. We show that in combination with other more familiar axioms, this condition pins down a very small class of methods, which we dub nearly serial.

Monte Carlo Tests with Nuisance Parameters: A General Approach to Finite-Sample Inference and Nonstandard Asymptotics

The technique of Monte Carlo (MC) tests [Dwass (1957), Barnard (1963)] provides an attractive method of building exact tests from statistics whose finite sample distribution is intractable but can be simulated (provided it does not involve nuisance parameters). We extend this method in two ways: first, by allowing for MC tests based on exchangeable possibly discrete test statistics; second, by generalizing the method to statistics whose null distributions involve nuisance parameters (maximized MC tests, MMC). Simplified asymptotically justified versions of the MMC method are also proposed and it is shown that they provide a simple way of improving standard asymptotics and dealing with nonstandard asymptotics (e.g., unit root asymptotics). Parametric bootstrap tests may be interpreted as a simplified version of the MMC method (without the general validity properties of the latter).