Robust response transformations based on optimal prediction

Nonlinear regression problems can often be reduced to linearity by transforming the response variable (e.g., using the Box-Cox family of transformations). The classic estimates of the parameter defining the transformation as well as of the regression coefficients are based on the maximum likelihood criterion, assuming homoscedastic normal errors for the transformed response. These estimates are nonrobust in the presence of outliers and can be inconsistent when the errors are nonnormal or heteroscedastic. This article proposes new robust estimates that are consistent and asymptotically normal for any unimodal and homoscedastic error distribution. For this purpose, a robust version of conditional expectation is introduced for which the prediction mean squared error is replaced with an M scale. This concept is then used to develop a nonparametric criterion to estimate the transformation parameter as well as the regression coefficients. A finite sample estimate of this criterion based on a robust version of smearing is also proposed. Monte Carlo experiments show that the new estimates compare favorably with respect to the available competitors.

Aspects thérapeutiques de la vitamine D: quels taux cibler avec quels traitements [Therapeutic goal of vitamin D: optimal serum level and dose requirements].

Therapeutic goal of vitamin D: optimal serum level and dose requirements Results of randomized controlled trials and meta-analyses investigating the effect of vitamin D supplementation on falls and fractures are inconsistent. The optimal serum level 25(OH) vitamin D for musculoskeletal and global health is > or = 30 ng/ml (75 nmol/l) for some experts and 20 ng/ml (50 nmol/l) for some others. A daily dose of vitamin D is better than high intermittent doses to reach this goal. High dose once-yearly vitamin D therapy may increase the incidence of fractures and falls. High serum level of vitamin D is probably harmful for the musculoskeletal system and health at large. The optimal benefits for musculoskeletal health are obtained with an 800 UI daily dose and a serum level of near 30 ng/ml (75 nmol/l).

The optimal length of contracts with application to outsourcing

This paper resolves three empirical puzzles in outsourcing by formalizing the adaptationcost of long-term performance contracts. Side-trading with a new partner alongside a long-term contract (to exploit an adaptation-requiring investment) is usually less effective than switching to the new partner when the contract expires. So long-term contracts that prevent holdup of specific investments may induce holdup of adaptation investments. Contract length therefore trades of specific and adaptation investments. Length should increase with the importance and specificity of self-investments, and decrease with the importance of adaptation investments for which side-trading is ineffective. My general model also shows how optimal length falls with cross-investments and wasteful investments.

Optimal monetary and fiscal policy in a currency union

We lay out a tractable model for fiscal and monetary policy analysis in a currency union, and study its implications for the optimal design of such policies. Monetary policy is conducted by a common central bank, which sets the interest rate for the union as a whole. Fiscal policy is implemented at the countrylevel, through the choice of government spending. The model incorporates country-specific shocks and nominal rigidities. Under our assumptions, the optimal cooperative policy arrangement requires that inflation be stabilized at the union level by the common central bank, while fiscal policy is used by each country for stabilization purposes. By contrast, when the fiscal authorities act in a non-coordinated way, their joint actions lead to a suboptimal outcome, and make the common central bank face a trade-off between inflation and output gap stabilization at the union level.

Population based resource allocation: The use of hybrid risk adjustment

The emphasis on integrated care implies new incentives that promote coordinationbetween levels of care. Considering a population as a whole, the resource allocation systemhas to adapt to this environment. This research is aimed to design a model that allows formorbidity related prospective and concurrent capitation payment. The model can be applied inpublicly funded health systems and managed competition settings.Methods: We analyze the application of hybrid risk adjustment versus either prospective orconcurrent risk adjustment formulae in the context of funding total health expenditures for thepopulation of an integrated healthcare delivery organization in Catalonia during years 2004 and2005.Results: The hybrid model reimburses integrated care organizations avoiding excessive risktransfer and maximizing incentives for efficiency in the provision. At the same time, it eliminatesincentives for risk selection for a specific set of high risk individuals through the use ofconcurrent reimbursement in order to assure a proper classification of patients.Conclusion: Prospective Risk Adjustment is used to transfer the financial risk to the healthprovider and therefore provide incentives for efficiency. Within the context of a National HealthSystem, such transfer of financial risk is illusory, and the government has to cover the deficits.Hybrid risk adjustment is useful to provide the right combination of incentive for efficiency andappropriate level of risk transfer for integrated care organizations.

Revenue management under general discrete choice model of consumer behavior

Customer choice behavior, such as 'buy-up' and 'buy-down', is an importantphe-nomenon in a wide range of industries. Yet there are few models ormethodologies available to exploit this phenomenon within yield managementsystems. We make some progress on filling this void. Specifically, wedevelop a model of yield management in which the buyers' behavior ismodeled explicitly using a multi-nomial logit model of demand. Thecontrol problem is to decide which subset of fare classes to offer ateach point in time. The set of open fare classes then affects the purchaseprobabilities for each class. We formulate a dynamic program todetermine the optimal control policy and show that it reduces to a dynamicnested allocation policy. Thus, the optimal choice-based policy caneasily be implemented in reservation systems that use nested allocationcontrols. We also develop an estimation procedure for our model based onthe expectation-maximization (EM) method that jointly estimates arrivalrates and choice model parameters when no-purchase outcomes areunobservable. Numerical results show that this combined optimization-estimation approach may significantly improve revenue performancerelative to traditional leg-based models that do not account for choicebehavior.

Optimal negligence rule under limited liability

We study the standard economic model of unilateral accidents, in its simplest form, assumingthat the injurers have limited assets.We identify a second-best optimal rule that selects as duecare the minimum of first-best care, and a level of care that takes into account the wealth ofthe injurer. We show that such a rule in fact maximizes the precautionary effort by a potentialinjurer. The idea is counterintuitive: Being softer on an injurer, in terms of the required level ofcare, actually improves the incentives to take care when he is potentially insolvent. We extendthe basic result to an entire population of potentially insolvent injurers, and find that the optimalgeneral standards of care do depend on wealth, and distribution of income. We also show theconditions for the result that higher income levels in a given society call for higher levels of carefor accidents.

Optimal second-degree price discrimination and arbitrage: On the role of asymetric information among buyers

The traditional theory of monopolistic screening tackles individualself-selection but does not address the possibility that buyers couldform a coalition to coordinate their purchases and to reallocate thegoods. In this paper, we design the optimal sale mechanism which takesinto account both individual and coalition incentive compatibilityfocusing on the role of asymmetric information among buyers. We showthat when a coalition of buyers is formed under asymmetric information,the monopolist can do as well as when there is no coalition. Although inthe optimal sale mechanism marginal rates of substitution are notequalized across buyers (hence there exists room for arbitrage), theyfail to realize the gains from arbitrage because of the transaction costsin coalition formation generated by asymmetric information.

Probabilistic maximal covering location-allocation models with constrained waiting time or queue length for congested systems

When dealing with the design of service networks, such as healthand EMS services, banking or distributed ticket selling services, thelocation of service centers has a strong influence on the congestion ateach of them, and consequently, on the quality of service. In this paper,several models are presented to consider service congestion. The firstmodel addresses the issue of the location of the least number of single--servercenters such that all the population is served within a standard distance,and nobody stands in line for a time longer than a given time--limit, or withmore than a predetermined number of other clients. We then formulateseveral maximal coverage models, with one or more servers per service center.A new heuristic is developed to solve the models and tested in a 30--nodesnetwork.

Optimal magnitude and probability of fines

The economic literature on crime and punishment focuses on the trade-off between probability and severity of punishment, and suggests that detection probability and fines are substitutes. In this paper it is shown that, in presence of substantial underdeterrence caused by costly detection and punishment, these instruments may become complements. When offenders are poor, the deterrent value of monetary sanctions is low. Thus, the government does not invest a lot in detection. If offenders are rich, however, the deterrent value of monetary sanctions is high, so it is more profitable to prosecute them.

Competition and cost overruns. Optimal misspecification of procurement contracts

Most cases of cost overruns in public procurement are related to important changes in the initial project design. This paper deals with the problem of design specification in public procurement and provides a rationale for design misspecification. We propose a model in which the sponsor decides how much to invest in design specification and awards competitively the project to a contractor. After the project has been awarded the sponsor engages in bilateral renegotiation with the contractor, in order to accommodate changes in the initial project s design that new information makes desirable. When procurement takes place in the presence of horizontally differentiated contractors, the design s specification level is seen to affect the resulting degree of competition. The paper highlights this interaction between market competition and design specification and shows that the sponsor s optimal strategy, when facing an imperfectly competitive market supply, is to underinvest in design specification so as to make significant cost overruns likely. Since no such misspecification occurs in a perfectly competitive market, cost overruns are seen to arise as a consequence of lack of competition in the procurement market.

Research joint ventures and optimal R&D policy with asymmetric information

When to allow Research Joint Ventures (RJVs) or not is an importantinstrument in the development of an optimal R&D policy. Theregulator, however, is unlikely to know all the relevant informationto regulate R&D optimally. The extent to which there existappropriability problems between the firms is one such variable thatis private information to the firms in the industry. In a duopolysetting we analyze the characteristics of a second-best R&D policywhere the government can either allow RJVs or not and give lump-sumsubsidies to the parties involved. The second-best R&D policy withoutsubsidies will either block some welfare improving RJVs or allow somewelfare reducing ones. With lump-sum subsidies, the second-best policytrades off the expected subsidy cost with allowing welfare decreasingRJVs or blocking welfare increasing ones.

Contractual allocation of decision rights and incentives: The case of automobile distribution

We analyze empirically the allocation of rights and monetary incentives in automobile franchise contracts. These contracts substantially restrict the decision rights of dealers and grant manufacturers extensive contractual completion and enforcement powers, converting the manufacturers, de facto, in a sort of quasi-judiciary instance. Variation in the allocation of decision rights andincentive intensity is explained by the incidence of moral hazard in the relation. In particular, when the cost of dealer moral hazard is higher and the risk of manufactureropportunism is lower, manufacturers enjoy more discretion in determining the performance required from their dealers and in using mechanisms such as monitoring, termination and monetary incentives to ensure such performance is provided. We also explore the existence of interdependencies between the different elements of the system. and find some complementarities between completion and termination rights, and between monitoring rights and the intensity of incentives.

Optimal contracts, adverse selection and social preferences: An experiment

It has long been standard in agency theory to search for incentive-compatible mechanisms on the assumption that people care only about their own material wealth. However, this assumption is clearly refuted by numerous experiments, and we feel that it may be useful to consider nonpecuniary utility in mechanism design and contract theory. Accordingly, we devise an experiment to explore optimal contracts in an adverse-selection context. A principal proposes one of three contract menus, each of which offers a choice of two incentive-compatible contracts, to two agents whose types are unknown to the principal. The agents know the set of possible menus, and choose to either accept one of the two contracts offered in the proposed menu or to reject the menu altogether; a rejection by either agent leads to lower (and equal) reservation payoffs for all parties. While all three possible menus favor the principal, they do so to varying degrees. We observe numerous rejections of the more lopsided menus, and approach an equilibrium where one of the more equitable contract menus (which one depends on the reservation payoffs) is proposed and agents accept a contract, selecting actions according to their types. Behavior is largely consistent with all recent models of social preferences, strongly suggesting there is value in considering nonpecuniary utility in agency theory.