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APPENDIX B Nutritional Screening and Budget Estimates Gaining eligibility for the WIC program requires applicants to be cat- egorically eligible along three separate dimensions categorical eligibility (pregnant or postpartum women, infants and children under the age of five), income eligible (income less than or equal to 185 percent of federal poverty guidelines or adjunctive eligibility through enrollment in selected means tested programs), and nutritionally eligible. An applicant must also be a resident of the state in which she is applying. Screening applicants for nutritional risk is the most problematic eligibility criterion for WIC staff to administer for the reasons described in Chapter 7 of the report. Perhaps the greatest difficulty in assessing nutritional risk in the field is assessing who among the income eligible population is not at dietary risk. A recent report of the Institute of Medicine (IOM) highlights these prob- lems, arguing that a WIC staff worker has such limited information on an applicant's usual food intake and this information is measured with so much error that it is nearly impossible to identify applicants who are not at risk. Estimates of the prevalence of nutritional risk that are available indicate that nearly all income-eligible children ages 2-5 years and women would qualify as nutritionally at risk. On the basis of these findings, the IOM report recommends the presumption that all income-eligible women and children ages 2-5 years are at dietary risk. This appendix formalizes the conditions under which it is appropriate for budgetary purposes to pre- sume that all categorically- and income-eligible people are at nutritional risk. 179
180 APPENDIX B NUTRITIONAL RISK SCREENING We assume that individuals are correctly identified as categorically and income eligible for WIC. To complete the eligibility process and gather information needed for WIC's nutrition services if the individual were found eligible, WIC staff obtain anthropometric measurements, laboratory test results, and medical, dietary, and social information about the appli- cant. In collecting these data, the WIC office is constrained by resources and time and thus cannot collect ideal information to determine whether an applicant is truly at nutritional risk and hence WIC eligible. This lack of information could lead to errors in the screening process. Some applicants that are truly at risk will be identified as not at risk, while some who are truly not at risk will be labeled as being at nutritional risk. We use R to denote that an individual is truly at risk while r denotes that the screening process found them to be at risk. A bar over either R or r denotes that the individual was not at risk. The screening process can be described by four conditional probabilities where p[rlR] p[r l R] probability of correctly identifying someone at risk; probability of incorrectly labeling someone who truly was at risk as not at risk; p[r | R] = probability of correctly identifying someone not at risk; and p[r | R ] = probability of incorrectly labeling someone who was not at where risk as being at risk I[r l R]+ p[r I R] = 1 and p[r l R]+p[r- l R] = 1. If the screening process is perfect in the sense that it does not make errors, then p[r~R]=l= p[r OR] and p[r ~R]=O=l[r~R] Screening Procedures and the Social Net Benefit of WIC We assume that a dollar of WIC vouchers produces B dollars of ben- efits (both to the recipient and to society) if the recipient is at nutritional
NUTRITIONAL SCREENING AND BUDGETESTIMATES 181 risk. Otherwise, if the recipient is not at nutritional risk, then a dollar of WIC vouchers will create only a dollar of benefits for the individual. How- ever, the cost to society of the dollar of WIC vouchers is the opportunities that society had to forgo in order to provide the necessary funds for the WIC program. For society to provide a dollar of taxes for the WIC pro- gram, it will have to give up a dollar of spending and the associated net benefits that dollar of spending would have provided had it gone to a dif- ferent use. We denote the net benefit of the private spending that society had to forgo as the excess burden of the tax (q). Hence the total cost of raising a dollar of taxes for WIC would be 1 + q. We will assume that WIC does provide a net benefit to society of pro- viding WIC to an individual who is at nutritional risk. Thus NBtR] = B - (1 + q) > 0 . The net benefits to society of providing WIC to an individual who is not at nutritional risk equals NBtR ~ = 1 - (1 + q\) = -q < 0 . (In all cases, net benefits are stated relative to no WIC program at all.) Clearly it would not be rational to provide WIC to those who are not at nutritional risk if we could perfectly determine whether or not an applicant was at nutritional risk. The question we entertain is, if the procedure for screening for nutritional risk is less than perfect, is society better off using the results of the screening procedure for determining WIC eligibility, or is society better off presuming that all are at nutritional risk and granting eligibility to all categorical and income-eligible applicants? The expected net benefit per applicant, presuming that all are at nutri- tional risk and thus ignoring the results of the nutritional risk screen equals ENBtIgnore j = ~/<B - (1 + q\J) - (1 - Eta = RIB - 1) - a Jl \ ~ l where ~ is the true proportion of the population that is at nutritional risk. Note that the first term is the amount that the WIC benefits realized by individuals who are at nutritional risk exceed their budget cost ($1) times the probability an individual is at risk. To compute the expected net benefit per applicant of using an imper- fect screening procedure, we consider the following four outcomes of the screen. If the applicant is found to be at risk when they truly are at risk, then the net benefit to society of giving these individuals WIC will be
182 APPENDIX B NB[r | R] = NB[R] = B (1 + q) If the individual is found to be at risk but is not truly at risk, then the net benefit to society of giving benefits to these individuals is NB[r I R ] = NB[R ] q . If, on the basis of the screening procedure, the individual is found not to be at risk, then WIC vouchers are not provided to the individual and hence the net social benefits are zero in both cases. No program costs are incurred and no program benefits are received. Therefore NB[r-lR]=O=NB[r JR]. The expected benefit per applicant of using the results of the screening procedure equals [ ] ( p[r I R] X NB[r I R]) + (1 - err\) ( p[r | R] x NB[r I R ]) p[r | R] X (B - (l + q))- (l - are X P[r I R] x q. After some algebra, the above expression can be written as ENB[Use] = ENB[Ignore] + (1 - A\) p[r I R ] q it p[r I R] ( ( q)) There will be net gain to society of using the results of the nutritional screen when ENB[Use] > ENB[Ignore] or when (land) p[r IR] q > ~p[r IR] (B-(l+q)) (1) The term B - (1 + q) represents the opportunity cost to society of the error from labeling someone who is truly at risk as not at risk. Hence the right- hand side of equation 1 is the expected costs of making this type of mis- take, which will not occur if one ignores the results ofthe nutritional screen. The left-hand side represents the expected benefits of using the results of the screen to identify those not at risk and denying them benefits. Hence the above condition states that if the expected net benefits to society of using the results of the nutritional screen exceed the expected costs, then the results of the screen should be used for eligibility and budget determi- nation. However, if the opposite is true, then it is rational to ignore the results of the nutritional screen for budgetary purposes. Of course, the gath- ered information on the applicant's nutrition is still available for other pur-
NUTRITIONAL SCREENING AND BUDGETESTIMATES 183 poses, such as tailoring the food package to the individual, planning nutri- tion education, and making referrals. Should Nutritional Risk Screening Be Used to Determine Elig~bilit~r' The answer to this question depends on the relative magnitude of the benefits of the WIC program, the excess burden to the tax system, the true proportion of the WIC population at risk, and the accuracy of the screen- ing procedure. In the absence of precise information about any of these dimensions, we first restate the condition for when not to use the nutri- tional screen for budgetary purposes. Let C denote the total economic cost of $1 of WIC expenditures, 1 + q. Then the condition for when to ignore the results of the nutritional test can be written as Ignore nutritional screen if B 1 1-lr~,Ptr IR is, q C BE pro R] ~ I + q . (2) In the previous discussion, we already assumed that when WIC is provided to an individual truly at risk, the program generates a net benefit for society (B/C > 11. While this assumption is necessary, it is not sufficient for us to ignore the results of the nutritional screen for the determination of WIC eligibility or to construct the budget request for the program. The assump- tion would be sufficient in the unlikely situations in which either (1) all applicants are truly at risk (n = 1), or (2) the screening procedure would never determine anyone not at risk when they truly are not at risk ~ per I R] = 0), or (3) the excess burden of tax is zero (q = 0~. Since these conditions are unlikely to be met, the question of whether or not one should use the results of the nutritional screen for eligibility determination must include consideration of what is known about each of these parameters. What is the true proportion of the WICpopulation who are at nutritional or medical risk 6~? Based on previous estimates, the Food and Nutrition Service (ENS) has assumed that 95 percent of income-eligible infants, 89 percent of in- come-eligible pregnant women, 93 percent of income-eligible postpartum women, and 75 percent of children are at nutritional or medical risk. The panel has discussed in this report that these estimates are most likely an
184 APPENDIX B underestimate of the true proportions. In particular, the panel concludes that the true proportions for all groups would be in the 95 to 99 percent range. If we adopt a broader range fork from .90 to .99 then the term (1 - n)/n would range from 0.010 to 0.1 11. What is the relative predictive power of the screeningproced[ure per R] p[r-I R] ? Little is known about the ability of the screening procedure to predict those individuals who are not at nutritional risk. In general, one would expect screening procedures to be more likely to find an applicant at risk when they are at risk, than finding someone at risk when they are not. Thus ptrIRj> ptrIRj. Equivalently, we expect that per IRj> per IR] We expect the ratio per | R j/ptr | R] to range from 1 to infinity; the limit- ing case is when the screening procedures always correctly identify those at risk. Since we do not have any definitive information on how accurate the screening procedure is, we will allow this ratio to range from 1.0 (the screen- ing process is random) to 10.0 (a highly discriminating procedure). What is the size of the excess IDurd~en of taxation (q9? The taxation literature has attempted to quantify this concept in the United States and there is a wide range of estimates of the excess burden of taxation.] Estimates of the excess burden range from $0.15 to $0.40 per dollar of taxes collected. Since most of the estimates are based on the tax system prior to the 1986 tax reform act, which lowered the marginal tax rates that many taxpayers faced, the panel judges that an estimate of$0.25 for the excess burden of taxation is a reasonable assumption. We can use these estimates to determine a range for the critical values for the benefits of WIC per dollar of WIC spending (B) that would have to 1See Browning (1976, 1978, 1987), Hausman (1981), Ballard, Shoven, and Fullerton (1987) and Stuart (1984).
NUTRITIONAL SCREENING AND BUDGETESTIMATES 185 be achieved in order to justify ignoring the screening test for eligibility determination. Taking the lowest values ofthe respective ranges for (1 - Id/ it, the relative predictive power of the screen procedures, and q, then B must exceed $1.15 in order to justify ignoring the results of the screen procedure. If we use these upper bound values for these variables, then B must exceed $1.84. To consider some intermediate values for the critical value for B. Table B-1 employs the midrange value for the excess burden of taxation. These critical values are generated by assuming an excess burden of $0.25 per dollar of taxes collected. For WIC to generate a net benefit, it must gener- ate at least $1.25 of benefits for the government to rationally fund this program; thus, the WIC benefits to at-risk individuals must be only mod- estly higher to ignore the nutritional screen in determining eligibility for WIC. For example, if the true probability of being at risk is 90 percent, then the benefits have to be only $1.53 or $0.28 higher than the program costs to ignore the nutritional screen even if the screen is highly reliable at detecting those not at risk (assuming a value of 10.01. What Are the Economic Benefits of WIC' An early study of the WIC program by the U.S. General Accounting Office (GAO) found that a dollar of WIC spending could generate $3.50 of savings to medical and disability programs (U.S. General Accounting Office, 19921. If this finding is true, then based on the above calculations we could safely ignore the nutritional risk criteria for eligibility determina- tion. Yet Besharov and Germanis (2001) note that this $3.50 to $1 benefit TABLE B-1 Critical Values for B to Ignore the Screen Procedure When q Equals 0.25 Value of p[r I R]/p[r I R] 0.90 Value for ~ equals 0.95 0.99 1.0 2.0 5.0 10.0 1.28 1.31 1.39 1.53 1.26 1.28 1.32 1.38 1.25 1.26 1.26 1.28
186 APPENDIX B to cost ratio pertains to pregnant women and that caution should be used before one generalizes to other target groups in the WIC program: postpar- tum women, infants, and children. Furthermore, they contend that evalua- tion studies that have produced these results are susceptible to a self-selec- tion bias in their design and hence overstate the true effect of the WIC program. Researchers who have attempted to control for self-selection and po- tential simultaneity in the evaluation have found lower levels of benefits to the program. For example, Devaney et al. (1992) found that WIC created lower savings for pregnant women than previously estimated by GAO. With lower future savings in other government programs, the upper bound esti- mate of the net benefit per dollar of WIC spending fell to $2.29. For other categorically eligible groups, the body of estimates of the benefits from WIC is less robust. While WIC is believed to reduce anemia among infants and children and to provide modest improvements in children's diets, little is known about the dollar value of these improve- ments. Little is known about the impact of WIC for postpartum women. Hence some caution should be exercised when generalizing the benefits of the WIC program for pregnant women to other groups participating in the program. CONCLUSION If a low-cost screening procedure existed that could perfectly deter- mine which applicants are at nutritional and medical risk, then it should be used for eligibility determination. Such a screening procedure does not ex- ist and errors in eligibility determination will be made. Some applicants who are at risk and are truly eligible will be denied participation in the WIC program. Others who are not at risk and not truly eligible will be allowed to participate based on the faulty procedure. Both types of errors impose a CoSt on society. This appendix explored the conditions in which it is in society's interest of maximizing the net benefits from the administered WIC program to presume that all categorically eligible and income-eligible persons are at nutritional risk and thus to ignore nutritional risk in the budgetary process. The potential gain to society of the presumption of nutritional risk is created because there is no chance that an applicant that is truly eligible would be denied eligibility on the basis of a faulty screening procedure. The magnitude of the social gain reflects two factors: the probability of making
NUTRITIONAL SCREENING AND BUDGETESTIMATES 187 this type of error and the magnitude ofthe net benefits to society of provid- ing WIC to those who are at risk. However, presuming that all are at nutri- tional risk imposes a cost on society by providing WIC benefits to those applicants who were truly not eligible and would have been identified as ineligible by the screening procedure. The magnitude of these costs reflects the probability of providing benefits to those who would have been screened as ineligible, multiplied by the net cost of raising the necessary funds for the program. Whether or not society is better off by presuming that all categorically and income-eligible persons are at nutritional risk is theoretically indeter- minate. However, it is very likely that presuming nutritional risk can be justified given the high probability in the population that income-eligible individuals are at nutritional risk. For example, let us assume that 99 per- cent of the population is at risk and we have a relatively accurate procedure of detecting those individuals who are not at risk the probability of de- tecting an individual not at risk who is truly not at risk is 10 times more likely than mistakenly identifying an individual not at risk who was truly at risk. Even when we assume a very high net cost of raising revenues ($0.40 per dollar raised), as long as benefits from spending a dollar on WIC are $0.84 more then the total cost of raising the dollar ($1.40), it would be rational to ignore the results of the screening procedure for eligibility deter- mination and consequently for budget proposals. We stress, however, that a decision to presume that all are at nutritional risk does not mean that a nutritional screen should not be performed. Nutritional screening is used to implement the priority system when funds are limited, and the informa- tion obtained is used in tailoring the food package to the individual, plan- ning nutrition education, and making appropriate referrals.
