When to carry eccentric products? Optimal retail assortment under consumer returns

To understand whether retailers should consider consumer returns when merchandising, we study howthe optimal assortment of a price-taking retailer is influenced by its return policy. The retailer selects itsassortment from an exogenous set of horizontally differentiated products. Consumers make purchase andkeep/return decisions in nested multinomial logit fashion. Our main finding is that the optimal assortmenthas a counterintuitive structure for relatively strict return policies: It is optimal to offer a mix of the mostpopular and most eccentric products when the refund amount is sufficiently low, which can be viewed asa form of risk sharing between the retailer and consumers. In contrast, if the refund is sufficiently high, orwhen returns are disallowed, optimal assortment is composed of only the most popular products (a commonfinding in the literature). We provide preliminary empirical evidence for one of the key drivers of our results:more eccentric products have higher probability of return conditional on purchase. In light of our analyticalfindings and managerial insights, we conclude that retailers should take their return policies into accountwhen merchandising.

Relative and absolute reliability of the clinical version of the Narrow Path Walking Test (NPWT) under single and dual task conditions.

Decline in gait stability has been associated with increased fall risk in older adults. Reliable and clinically feasible methods of gait instability assessment are needed. This study evaluated the relative and absolute reliability and concurrent validity of the testing procedure of the clinical version of the Narrow Path Walking Test (NPWT) under single task (ST) and dual task (DT) conditions. Thirty independent community-dwelling older adults (65-87 years) were tested twice. Participants were instructed to walk within the 6-m narrow path without stepping out. Trial time, number of steps, trial velocity, number of step errors, and number of cognitive task errors were determined. Intraclass correlation coefficients (ICCs) were calculated as indices of agreement, and a graphic approach called "mountain plot" was applied to help interpret the direction and magnitude of disagreements between testing procedures. Smallest detectable change and smallest real difference (SRD) were computed to determine clinically relevant improvement at group and individual levels, respectively. Concurrent validity was assessed using Performance Oriented Mobility Assessment Tool (POMA) and the Short Physical Performance Battery (SPPB). Test-retest agreement (ICC1,2) varied from 0.77 to 0.92 in ST and from 0.78 to 0.92 in DT conditions, with no apparent systematic differences between testing procedures demonstrated by the mountain plot graphs. Smallest detectable change and smallest real change were small for motor task performance and larger for cognitive errors. Significant correlations were observed for trial velocity and trial time with POMA and SPPB. The present results indicate that the NPWT testing procedure is highly reliable and reproducible.

Shared knowledge

Agents use their knowledge on the history of the economy in orderto choose what is the optimal action to take at any given moment of time,but each individual observes history with some noise. This paper showsthat the amount of information available on the past evolution of theeconomy is an endogenous variable, and that this leads to overconcentrationof the investment, which can be interpreted as underinvestment in research.It presents a model in which agents have to invest at each period in one of$K$ sectors, each of them paying an exogenous return that follows a welldefined stochastic path. At any moment of time each agent receives an unbiasednoisy signal on the payoff of each sector. The signals differ across agents,but all of them have the same variance, which depends on the aggregate investmentin that particular sector (so that if almost everybody invests in it theperceptions of everybody will be very accurate, but if almost nobody doesthe perceptions of everybody will be very noisy). The degree of hetereogeneityacross agents is then an endogenous variable, evolving across time determining,and being determined by, the amount of information disclosed.As long as both the level of social interaction and the underlying precisionof the observations are relatively large agents behave in a very preciseway. This behavior is unmodified for a huge range of informational parameters,and it is characterized by an excessive concentration of the investment ina few sectors. Additionally the model shows that generalized improvements in thequality of the information that each agent gets may lead to a worse outcomefor all the agents due to the overconcentration of the investment that thisproduces.

Crises and growth: A re-evaluation

We address the question of whether growth and welfare can be higher in crisis prone economies. First, we show that there is a robust empirical link between per-capita GDP growth and negative skewness of credit growth across countries with active financial markets. That is, countries that have experienced occasional crises have grown on average faster than countries with smooth credit conditions. We then present a two-sector endogenous growth model in which financial crises can occur, and analyze the relationship between financial fragility and growth. The underlying credit market imperfections generateborrowing constraints, bottlenecks and low growth. We show that under certain conditions endogenous real exchange rate risk arises and firms find it optimal to take on credit risk in the form of currency mismatch. Along such a risky path average growth is higher, but self-fulfilling crises occur occasionally. Furthermore, we establish conditions under which the adoption of credit risk is welfare improving and brings the allocation nearer to the Pareto optimal level. The design of the model is motivated by several features of recent crises: credit risk in the form of foreign currency denominated debt; costly crises that generate firesales and widespread bankruptcies; and asymmetric sectorial responses, wherethe nontradables sector falls more than the tradables sector in the wake of crises.

On optimal location with treshold requirements

The optimal location of services is one of the most important factors that affects service quality in terms of consumer access. On theother hand, services in general need to have a minimum catchment area so as to be efficient. In this paper a model is presented that locates the maximum number of services that can coexist in a given region without having losses, taking into account that they need a minimum catchment area to exist. The objective is to minimize average distance to the population. The formulation presented belongs to the class of discrete P--median--like models. A tabu heuristic method is presented to solve the problem. Finally, the model is applied to the location of pharmacies in a rural region of Spain.

Optimal regulation of a fully insured deposit banking system

We analyze risk sensitive incentive compatible deposit insurancein the presence of private information when the market value of depositinsurance can be determined using Merton's (1997) formula. We show that,under the assumption that transferring funds from taxpayers to financialinstitutions has a social cost, the optimal regulation combines differentlevels of capital requirements combined with decreasing premia on depositinsurance. On the other hand, it is never efficient to require the banksto hold riskless assets, so that narrow banking is not efficient. Finally,chartering banks is necessary in order to decrease the cost of asymmetricinformation.

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.

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.