My comments on Moffitt's useful chapter include a narrow technical issue, elaborations on the explanation for increases in female-headed households, and discussion of the interrelatedness of demographic problems.

A Narrow Technical Issue

Many outcomes, such as the aggregate incidence of AFDC recipiency, can be viewed as the product of two components. Typically, one component is the number or population share of the subpopulation at risk (called “composition”), and the other is the rate at which those at risk experience some event, such as receipt of AFDC. Decomposition analysis attempts to allocate responsibility for overall change between changes in composition and changes in rates. While there is much that is intuitive about decomposition, there are also inherent complexities. Given two components (here, composition and rates) and two time points (before and after the change), there will be an effect of changes in the first (with the second held constant) and a comparable effect for changes in the second. The influence of both changes simultaneously adds a residual, interaction effect. More components and more years make these interaction effects numerous, and their magnitude will vary by the year chosen as the baseline and the order in which components are introduced. Moffitt (in Table 9.4) chooses the earliest and latest time period (only two time periods) and to include six “weighting types” that allow for all possible orderings of the three components.