In this paper we extend Varian's (1984) nonparametric production analysis to situations when the set of observed output, input, and price data is not consistent with profit maximization for at least one firm. In such cases, Varian's results imply that no production possibility set containing all observations can rationalize the observed data. We identify each firm whose performance, given the prices faced by it, may be found consistent with profit maximization relative to some production possibility set containing all observed output-input vectors. We show that the set 4' of all such firms can itself be weaklv rationalized in the sense that there exists a (closed, convex, and monotone) production possibility set that contains all the observations, and relative to which the performance of all the firms in the set 8O is consistent with profit maximization given their respective prices. By definition, firms not included in this largest set d of efficient observations unambiguously deviate from profit maximizing behavior for any production possibility set containing all observations. We follow Farrell (1957) and analyze these deviations into technical and allocative efficiency measures, considering as admissible all closed, convex, and monotone production possibility sets relative to which the performance of each firm in the set g remains consistent with profit maximization. We then describe nonparametric methods for determining the tightest upper and lower bounds on the technical, allocative, and aggregate efficiency measures evaluated relative to all such admissible production possibility sets. It is seen that the tightest upper bound on the technical efficiency measure is the same as the value computed by the nonparametric efficiency evaluation technique known as data envelopment analysis, thus establishing a link between this literature in management science/operations research and the nonparametric production analysis in economics.

Abstract. This paper employs a generalized principal‐agent model to analyze accounting situations in which the outcome is not jointly observable and the principal's and agent's preferences are multiattribute in nature. This requires the consideration of accounting signals for risk‐sharing (or insurance) information in addition to performance evaluation (or incentive) information. It is shown that precisely two factors determine whether a signal will be valuable in the agency relationship: Observability of the agent's effort and the principal's multivariate risk neutrality. Sufficient conditions for various accounting signals to have value are also developed. Furthermore, when multiple accounting signals are available, it is shown that under certain conditions, the insurance components of the multiple signals can be aggregated into a single aggregate insurance measure and the incentive components of the signals can be aggregated (via a different aggregation procedure) into another aggregate incentive measure. Résumé. Les auteurs utilisent un modèle généralisé mandant‐mandataire pour analyser les situations comptables dans lesquelles le résultat n'est pas observable conjointement et les préférences du mandant et du mandataire comportent, par nature, de multiples attributs. Cela exige la prise en considération d'indicateurs comptables relatifs à l'information sur le partage des risques (ou de l'assurance) en plus de l'information relative à l'évaluation du rendement (ou aux stimulants). Les auteurs démontrent que deux facteurs permettent de déterminer avec précision si un indicateur sera valable dans la relation de mandataire: le caractère observable de l'effort du mandataire et la neutralité multivariée du mandant à l'égard du risque. Des conditions suffisantes pour que les divers indicateurs comptables soient valables sont également établies. En outre, lorsque des indicateurs comptables multiples sont disponibles, les auteurs démontrent que dans certaines conditions, les éléments des indicateurs multiples liés à l'assurance peuvent faire l'objet d'une regroupement en une seule mesure globale d'assurance, et que les éléments des indicateurs liés aux stimulants peuvent faire l'objet d'une regroupement (au moyen d'une méthode différente) en une autre mesure globale des stimulants.