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.A. Bishop et al. Economics Letters 67 2000 75 –85
4. Empirical results
The food energy and nutrient distributions cdfs for the experimental cash and control coupon groups in the cashout experiments contain all of the information necessary to apply the first-order
dominance criterion in Proposition 1. As noted above, it is both equivalent and more convenient to
2 1
conduct the inference tests and present the results in terms of the inverse cdf, F , which is widely
1
Fig. 1. Distributions of food energy availability and key micronutrients in Alabama.
J .A. Bishop et al. Economics Letters 67 2000 75 –85
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referred to as the quantile function. Fig. 1 shows quantile functions estimated at quintiles for food energy and selected micronutrients in the Alabama sample. Fig. 2 provides similar information for
San Diego. Some of the quantile functions appear to cross and others appear not to differ. By applying inference tests we can answer the following questions. Do the quantile functions differ? If yes, where
and how do they differ?
Fig. 2. Distributions of food energy availability and key micronutrients in San Diego.
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.A. Bishop et al. Economics Letters 67 2000 75 –85
Table 3 reports inference tests for first-order stochastic dominance comparisons of distributions of food energy, vitamin B , and vitamin E availability for the cash and coupon recipients in Alabama.
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By inspection of the food energy quintile means for coupon and cash recipients panel a, it appears that the quantile functions intersect. That is, coupon recipients have higher mean food energy
availability in the bottom two quintiles than cash recipients, while the opposite is true in the remaining quintiles. But the test statistic reveals that no difference in quintile means is statistically significant.
Therefore, we reject the null hypothesis and conclude that the distributions of food energy for coupon and cash recipients are statistically equivalent.
In Table 3 we also find apparent crossings in quantile functions for vitamins B and E panels b and
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c. But the inference tests reveal that, in both cases, only the difference in the bottom quintile is statistically significant. Thus, for vitamins B and E, coupon recipients FOD cash recipients, which
6
means undernutrition is greater for cash recipients than coupon recipients. For all other micronutrients not shown in Table 3, we find no significant differences between cash and coupon recipients, as in the
food energy comparison. The corresponding results for San Diego are shown in Table 4. Once again, as in Alabama, there is
an apparent crossing in quantile functions for food energy availability in the treatment cash and control coupon groups, but the differences are not significant at any of the quintiles panel a. Hence,
coupon and cash recipients are statistically equivalent with respect to the availability of food energy.
Table 3 Dominance comparisons of nutrient distributions in Alabama: cash vs. coupon recipients
a
Sample quintile Quintile mean:
Test statistic Cash recipients
Coupon recipients a Food energy availability kcal per adult male equivalent per day, RDA52700
1 2137.40
2238.87 2
1.30 2
3306.04 3334.10
2 0.35
3 4253.59
4206.49 0.50
4 5470.21
5348.04 0.91
5 8433.48
8224.15 0.72
b Vitamin B availability mg per adult male equivalent per day, RDA52
6
1 1.30
1.41 2
2.11 2
2.15 2.18
2 0.52
3 2.87
2.80 0.93
4 3.74
3.66 0.86
5 5.73
5.67 0.31
c Vitamin E availability IU per adult male equivalent per day, RDA515 1
5.50 6.19
2 2.11
2 11.54
12.13 2
1.15 3
17.48 17.33
0.27 4
24.93 23.81
1.38 5
43.21 41.88
0.73
a
The test statistic for the differences in quintile means is the Student Maximum Modulus SMM — a joint test statistic. Significantly different from zero at the 10-percent level using a one-tailed test.
J .A. Bishop et al. Economics Letters 67 2000 75 –85
83 Table 4
Dominance comparisons of nutrient distributions in San Diego: cash vs. coupon recipients
a
Sample quintile Quintile mean
Test statistic Cash recipients
Coupon recipients a Food energy availability kcal per adult male equivalent per day, RDA52,700
1 2036.90
2016.95 0.23
2 2850.66
2919.38 2
0.76 3
3462.75 3601.93
2 1.31
4 4336.07
4533.07 2
1.25 5
6301.61 6937.74
2 1.88
b Phosphorous availability mg per adult male equivalent per day, RDA5800 1
734.65 732.55
0.07 2
1024.48 1040.86
2 0.47
3 1289.05
1330.55 2
0.86 4
1619.98 1707.32
2 1.58
5 2326.72
2581.16 2
2.19 c Vitamin B availability mg per adult male equivalent per day, RDA52
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1 1.50
1.53 2
0.42 2
2.21 2.20
0.13 3
2.81 2.86
reformat20.49 4
3.44 3.68
2 2.00
5 5.37
5.91 2
1.45
a
The test statistic for the differences in quintile means is the Student Maximum Modulus SMM — a joint test statistic. Significantly different from zero at the 10-percent level using a one-tailed test.
Table 4 also shows the importance of taking into account the RDA in nutrition comparisons. Consider phosphorous availability panel b for coupon and cash recipients. Coupon recipients have
greater phosphorous availability than cash recipients in every quintile except the first. However, only one of these differences is statistically significant and it is in the fifth quintile — far above the
recommended amount for phosphorus RDA5800. In this case, it is reasonable to use truncated dominance, which leads to the conclusion that coupon and cash recipients are equivalently
undernourished with respect to phosphorus.
Comparisons for all other micronutrients in the San Diego experiment reveal no significant differences between coupon and cash recipients. For vitamin B Table 4, panel c, the difference in
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means in the fourth quintile is nearly significant, but the means are far above the recommended allowance RDA52 at this quintile. Therefore, we find no evidence that cash recipients are more
undernourished than coupon recipients in the San Diego experiment. Overall, our findings reveal that food stamp cashout leads to few changes in undernutrition. Among
these changes, reductions in the availability of vitamins E and B in Alabama may be cause for
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concern, because the proportions of the sample below the RDA are relatively high for these nutrients more than 40 percent for vitamin E and the significant change in availability occurs in the lowest
quintile for both samples. The finding that cashout alters few dimensions of undernutrition in Alabama and has no significant effects in San Diego is consistent with a standard analysis of in-kind versus
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.A. Bishop et al. Economics Letters 67 2000 75 –85
cash transfers in economic theory. The theory predicts that conversion from coupon to cash benefits will effect behavior only if food assistance exceeds the desired level of food consumption in the
absence of assistance — a condition met in only a small proportion of food stamp households.
5. Conclusions
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