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OCR for page 179
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
OCR for page 180
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
OCR for page 181
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 = ~/
OCR for page 182
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-
OCR for page 183
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
OCR for page 184
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).
OCR for page 185
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
OCR for page 186
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
OCR for page 187
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.
Representative terms from entire chapter:
nutritional screen
