M ANY cross-section studies exist in the literature attempting to explain variations in per capita state and local expenditures on such services as highways, municipal services, health, and education. Differences in per capita expenditures across states are explained in terms of such factors as differences in population densities, urban-rural distributions, average income levels, age distributions, and numbers of school-age children.' In most of these studies, however, the underlying theory has not been carefully spelled out and, in particular, it is never made clear whether the demographic variables are thought to enter on the demand side or on the supply side of the market for state and local services. In the first part of this paper we look at the theory underlying such regression studies of the determinants of state and local expenditures. We attempt to distinguish between the demand side of the market for such services and the supply (cost) side. In the second part of the paper we obtain empirical estimates of price and income elasticities of demand for state and local services for three broad classifications of services. Finally we discuss a number of interesting applications of our results.

IN 1966, the Coleman Report provided compelling evidence of the importance of the home environment in determining children's cognitive skill levels. This evidence, coupled with doubts about the effectiveness of school-based compensatory education programs, has led policymakers to consider programs that aim at improving school achievement by providing additional resources to the families of low achieving children. Efforts to design such programs have been hindered, however, by a lack of knowledge concerning the key resources in the home that influence children's achievement. This paper reports the results of research that attempts to reduce this knowledge gap by examining the roles played by particular resources in the home in influencing children's achievement. This study extends previous work on home investments in children in two significant ways. First, the analysis focuses on black children living in low income, urban families. Most previous research has studied children in middle class families. Second, the stability of the results is examined by estimating the same model for two samples of children. Previous studies have reported results for a single sample. Differences in results across studies have raised questions concerning the stability of relationships between particular home resources and children's achievement. In this study, the stability issue is addressed directly. The central finding of our research is that the skills of the mother, measured by the extent of her formal schooling, are a critical resource in determining children's achievement. Our results demonstrate that these skills affect children through the mechanism of child care, and not simply through genetically transmitted endowments. Another key result is that goods inputs in the home do not appear to have consistent effects on children's learning. Thus, our findings support the results of other recent research that has emphasized the importance of human resources (such as mothers and teachers) rather than material inputs in determining children's achievement. These and other findings are discussed in detail later in the paper. The next section of the paper lists the hypotheses examined in this study. Section III describes the analytical framework within which these hypotheses were tested. Section IV describes the data. Section V describes the problem of interpreting correlations between attributes of the home environment and children's achievement. Section VI presents the results, and section VII discusses their implications.