FORECASTING WOMEN, INFANTS, AND CHILDREN CASELOADS: A COMPARISON OF VECTOR AUTOREGRESSION AND AUTOREGRESSIVE INTEGRATED MOVING AVERAGE APPROACHES

1. INTRODUCTION Forecasting the number of participants is an integral part of the oversight of every public assistance program in the United States. This is particularly true for programs where there is only a fixed amount of money available for the program. These programs differ from "entitlement programs" where the amount of money available is not capped. One nonentitlement program in the United States, and the topic of this paper, is the Special Supplemental Nutrition Program for Women, Infants, and Children (WIC). Under WIC, each state receives a federal grant from the U.S. Department of Agriculture (USDA) for the operation of WIC for the upcoming federal fiscal year. Because of the limitation of funds, states may not be able to serve all people eligible to receive WIC services. Therefore, states have to estimate the caseload levels that can be supported with available funding. If a state exceeds this fixed amount of money, the state may bear the fiscal burden of any additional expenditure. If a state does not spend 97% of the grant received, the state has to return funds to USDA which may impact the next year's appropriation level. As a consequence, accurate forecasting is vital in WIC. There are, of course, many different ways one can forecast caseloads in WIC or in other programs. The most straightforward method is to assume that future caseloads are only dependent on past and present caseloads. In considerations of other assistance programs, however, other factors, including participation in similar programs and macroeconomic conditions also matter for these forecasts. (In the case of the Supplemental Nutrition Assistance Program [SNAP, formerly known as the Food Stamp Program] see, e.g., Ziliak, Gundersen, and Figlio 2003.) In this paper, we consider the extent to which these other factors matter by comparing structural vector autoregression (VAR) models with univariate AR models. This comparison is especially relevant for two reasons. First, if the differences are meaningful, states may wish to consider using structural VAR models akin to those described in this paper. Second, even if the differences are meaningful, states must still decide whether or not the extra cost to estimating structural VAR models (especially with respect to collecting the additional data) is worthwhile. In our discussion of structural VAR and univariate AR models, we address both these issues. II. BACKGROUND The Special Supplemental Nutrition Program for WIC was established as a pilot program in 1972 and was made permanent in 1974. This program, administered by the Food and Nutrition Service of the U.S. Department of Agriculture, was founded in recognition of the relationship between inadequate nutritional patterns and health behaviors of low-income women, infants, and children. These inadequacies during critical periods of growth and development lead to subsequent adverse health outcomes. In response, WIC was designed to ameliorate these adverse outcomes through the provision of nutritious supplemental foods, nutrition education, and free health care referrals. The foods are generally distributed either through checks or vouchers. Because the optimal intakes of these nutrients will differ for women, infants, and children, so too do the food packages for each of these categories. There are three criteria that establish eligibility to receive WIC services. The population identified as categorically eligible consists of pregnant and postpartum women, infants under 1 yr of age, and children under the age of 5. In 2004, nationwide, over 7.9 million people received WIC services--1.9 million women, 2 million infants, and 3.9 million children. Along with meeting the categorical eligibility criterion, the family income of WIC applicants must meet specified guidelines. This is the second criterion for eligibility. WIC regulations state that the maximum allowable family gross income must not exceed 185% of the poverty threshold. …