AFTER-SCHOOL PROGRAM EFFECTS ON BEHAVIOR: RESULTS FROM THE 21ST CENTURY COMMUNITY LEARNING CENTERS PROGRAM NATIONAL EVALUATION

This paper presents evidence on after-school programs' effects on behavior from the national evaluation of the U.S. Department of Education's 21st Century Community Learning Centers after-school program. Findings come from both of the study's components: (1) an elementary school component based on random assignment of 2,308 students in 12 school districts and (2) a middle school component based on a matched comparison design including 4,264 students in 32 districts. Key findings include higher levels of negative behavior for elementary students and some evidence of higher levels of negative behaviors for middle school students . ( JEL I21)     

Increasing Risk: Some Direct Constructions

This article extends the classic RothschildNStiglitz characterization of comparative risk ("increasing risk") in two directions. By adopting a more general definition of "mean preserving spread" (MPS), it provides a direct construction of a sequence of MPS's linking any pair of distributions that are ranked in terms of comparative risk. It also provides a direct, explicit construction of a zero-conditional-mean "noise" variable for any such pair of distributions. Both results are extended to the case of second order stochastic dominance.     

Performance of Robust GCV and Modified GCV for Spline Smoothing

Abstract. While it is a popular selection criterion for spline smoothing, generalized cross‐validation (GCV) occasionally yields severely undersmoothed estimates. Two extensions of GCV called robust GCV (RGCV) and modified GCV have been proposed as more stable criteria. Each involves a parameter that must be chosen, but the only guidance has come from simulation results. We investigate the performance of the criteria analytically. In most studies, the mean square prediction error is the only loss function considered. Here, we use both the prediction error and a stronger Sobolev norm error, which provides a better measure of the quality of the estimate. A geometric approach is used to analyse the superior small‐sample stability of RGCV compared to GCV. In addition, by deriving the asymptotic inefficiency for both the prediction error and the Sobolev error, we find intervals for the parameters of RGCV and modified GCV for which the criteria have optimal performance.     

PRICE‐DEPENDENT INVENTORY MODELS WITH DISCOUNT OFFERS AT RANDOM TIMES*

We consider an inventory model with a supplier offering discounts to a reseller at random epochs. The offer is accepted when the inventory position is lower than a threshold level. We compare three different pricing policies in which demand is induced by the resellers price variation. Policy 1 is the EOQ policy without discount offers. Policy 2 is a uniform price, stock‐independent policy. Policy 3 is a stock level‐dependent, discriminated price policy. Assuming constant demand rates, expressions are obtained for the optimal order quantities, prices, and profits. The numerical experiments show that if it is better to accept a suppliers discount, then it benefits the reseller to transfer the discount to downstream customers.