A new structure for difference matrices over abelian pp-groups

A difference matrix over a group is a discrete structure that is intimately related to many other combinatorial designs, including mutually orthogonal Latin squares, orthogonal arrays, and transversal designs. Interest in constructing difference matrices over $2$-groups has been renewed by the recent discovery that these matrices can be used to construct large linking systems of difference sets, which in turn provide examples of systems of linked symmetric designs and association schemes. We survey the main constructive and nonexistence results for difference matrices, beginning with a classical construction based on the properties of a finite field. We then introduce the concept of a contracted difference matrix, which generates a much larger difference matrix. We show that several of the main constructive results for difference matrices over abelian $p$-groups can be substantially simplified and extended using contracted difference matrices. In particular, we obtain new linking systems of difference sets of size $7$ in infinite families of abelian $2$-groups, whereas previously the largest known size was $3$.Comment: 27 pages. Discussion of new reference [LT04

Family Income and Child Outcomes:The 1990 Cocoa Price Shock in Cote d'Ivoire

We study the drastic cut of the administered cocoa producer price in 1990 Cote d'Ivoire and investigate the extent to which cocoa producers' children suffered from this severe income shock in terms of school enrollment, increased labor, height stature and sickness. Comparing pre-crisis (1986-1988) data and post-crisis (1993) data, we propose a difference-in-difference within-village strategy in order to identify the causal effect of family income on children outcomes. We find a strong impact of family income variation for the four variables we examine.