78 J
.A. Bishop et al. Economics Letters 67 2000 75 –85
Maximum Modulus SMM distribution Miller, 1981. An approximately a -level test of the equality of two vectors of conditional quantile means rejects each of the k sub-hypotheses if
uT u . m k,`,
i a
4
where m k,` is the upper-a critical value of the SMM distribution with ` degrees of freedom. The
a
SMM critical values are obtained from Stoline and Ury 1979. In general, joint tests of the conditional means generate only partial orderings of distributions. If no
pair of conditional means is significantly different, then the two quantile functions are statistically equivalent. If a positive negative and significant difference exists at one or more quantile means and
no negative positive significant differences exist, then we have FOD. Finally, if tests yield both positive and negative significant differences, the two quantile functions intersect and no FOD ranking
is possible. However, truncated dominance may still hold below reasonable requirement thresholds. The next section describes the nutrient data provided by the cashout experiments.
3. Data
The data for this study were obtained from parallel surveys, conducted in 1990, of households that participated in food stamp cashout demonstrations in Alabama and San Diego, California. The
Alabama sample included residents of rural 52 percent and urban 48 percent counties; the California sample was drawn entirely from San Diego county. Therefore, the two experiments
represent not only different regions, but contrasting social settings as well. Fraker et al. 1995b, p. 388, point out that the implementation of the two experiments also differed. The San Diego
experiment was scheduled to run 5 years or longer and was given much publicity. In contrast, the Alabama experiment ran only 8 months and received little publicity.
We represent nutrient status by nutrient availability, which exceeds nutrient intake because some food is wasted or fed to pets. For comparability across households that differ in size and composition,
we express nutrients in adult male equivalent AME units. In Tables 1 and 2 we compare nutrient availability to the RDA in the Alabama and San Diego experiments. In both experiments, nutrient
availability at the sample means surpasses the RDA for food energy and each nutrient in the treatment and control groups. But 16 percent of the Alabama sample and about 25 percent of the San Diego
sample fall short of the RDA for food energy. Moreover, the incidence of undernutrition is more than 10 percent in each sample for phosphorus, iron, vitamin B , magnesium, vitamin E, calcium, and
6
folacin. In contrast, relatively few households in either sample experience a shortfall in protein, vitamin C, thiamin, niacin, and vitamin B .
12
In a 1983 study of low-income families in Cleveland, Emmons 1986 finds that diets contain inadequate amounts of vitamin B , vitamin E, iron, calcium, and magnesium her study provides no
6
information on folacin. Using the 1977–1978 Nationwide Food Consumption Survey, Silberberg 1985 concludes that consumption of folacin and magnesium may be inadequate. Thus, our findings
reinforce the results of previous studies using other data sources. Before moving to our main results, we point out that the number of observations generated by the
4
Bishop and Formby 1999, provide evidence that the test is conservative and has good power against dominance in sample sizes of 50 or more per quantile. Given the conservative nature of the test, we use a one-tailed test at the 10-percent
level of significance.
J .A. Bishop et al. Economics Letters 67 2000 75 –85
79 Table 1
a
Nutrient availability relative to the RDA: Alabama Nutrient
RDA Sample mean:
Proportion of Sample mean:
Proportion of coupon recipients
coupon recipients cash
cash recipients below RDA
recipients below RDA
Energy kcal 2700
4670 0.16
4722 0.16
Protein g 56
161 0.01
162 0.01
Vitamin E IU 15
20.3 0.41
20.5 0.41
Vitamin C mg 45
153 0.09
151 0.08
Thiamin mg 1.4
3.2 0.08
3.2 0.09
Niacin mg 18
42 0.06
42 0.08
Vitamin B mg 2
3.1 0.24
3.2 0.26
6
Vitamin B mg
3 10.7
0.08 10.3
0.09
12
Folacin mg 400
444 0.54
446 0.51
Calcium mg 800
940 0.49
971 0.47
Phosphorus mg 800
1675 0.11
1703 0.11
Magnesium mg 350
466 0.34
473 0.35
Iron mg 10
18.4 0.20
18.5 0.18
a
The Alabama sample contains 2184 observations, including 1025 coupon recipients and 1159 cash recipients.
FSP cashout experiments is sufficient to perform statistical comparisons of distributions of nutrients by quintile. Even the smaller San Diego sample contains more than 90 observations per quintile in the
treatment and control groups. Information about the randomness of the treatment and control groups is
5
given by Fraker et al. 1995a, p. 639.
Table 2
a
Nutrient availability relative to the RDA: San Diego Nutrient
RDA Sample mean:
Proportion of Sample mean:
Proportion of coupon recipients
recipients cash
cash recipients below RDA
recipients below RDA
Energy kcal 2700
4001 0.24
3797 0.25
Protein g 56
163 0.04
153 0.03
Vitamin E IU 15
16.9 0.53
16.8 0.55
Vitamin C mg 45
164 0.06
161 0.06
Thiamin mg 1.4
2.9 0.08
2.8 0.11
Niacin mg 18
37.6 0.09
36.1 0.07
Vitamin B mg 2
3.2 0.22
3.1 0.23
6
Vitamin B mg
3 9.7
0.05 9.0
0.05
12
Folacin mg 400
468 0.47
451 0.53
Calcium mg 800
972 0.45
931 0.45
Phosphorus mg 800
1478 0.12
1399 0.12
Magnesium mg 350
519 0.28
495 0.28
Iron mg 10
16.1 0.24
15.8 0.24
a
The San Diego sample contains 935 observations, including 463 coupon recipients and 472 cash recipients.
5
For additional information on the cashout data and the contexts in which they were collected see, Fraker et al., 1992, 1995a,b; Ohls et al., 1992.
80 J
.A. Bishop et al. Economics Letters 67 2000 75 –85
4. Empirical results
