The number of transitions attributable to a particular trigger event is a function of both the net effect of that event and its frequency in the population. 31 If two trigger events have similar effects on the likelihood of a particular transition, but one event occurs much more often than the other, then the more commonly occurring event will induce a larger number of transitions. Because of their nonlinearity, the net effects that we reported in the preceding section do not translate directly into probabilities that children will experience transitions, but the gross or unadjusted effects do, and estimates of the frequencies of individual types of events are readily obtainable. In this section we examine the frequencies of the 12 types of transitions while conditioning on each of the events that was included in our final regression models. While these conditional frequencies are based on unadjusted effects, meaning that they do not control for the effects of other events, we calculated them only for events that the regression analysis identified as the strongest predictors of transitions from each initial coverage status. As a result, we can be certain that we are restricting our attention to those events with the strongest net effects.
Children with ESI. On average, 41.8 million children were covered by ESI at any one time from June 1993 through May 1994. 32 For this group of children, Table 18 reports the average number who experienced individual events in the next month and, for each event, the percentage who retained their ESI for at least the next four months or lost their coverage and became uninsured, enrolled in Medicaid, or obtained other insurance. In the final three columns Table 18 gives the actual number of transitions implied by the average monthly number of events listed in the first column and the four-month transition probabilities reported in the previous three columns. For the group of children as a whole--most of whom experienced no events--94 percent remained covered by ESI, 3 percent became uninsured, and between 1 and 2 percent enrolled in Medicaid or obtained other insurance. 33 For children who experienced an event, however, we find as many as 31 percent losing their ESI, with most of these becoming uninsured. For example, among the nearly 200,000 children covered by ESI whose fathers lost employment in an average month, 23 percent became uninsured in the next four months, 4 percent enrolled in Medicaid, and an additional 4 percent obtained other insurance. In combination with the average monthly frequency of children's fathers losing employment, these transition probabilities imply that about 46,000 children moved from ESI to uninsured, 8,000 moved from ESI to Medicaid, and 7,000 moved from ESI to other insurance.
The greatest number of transitions from ESI to uninsured is associated with children whose family income fell markedly in the past month. While declines in family income were associated with a very modest transition probability--only 7 percent--declines in income were the most common event, occurring nine times as often as fathers losing employment, for example. Children whose fathers lost employment were the most likely to lose ESI in the next four months--23 percent did so--but they accounted for only one-third as many transitions as children who experienced a marked reduction in family income.
Children with marked reductions in family income also accounted for the most transitions from ESI to Medicaid and ESI to other insurance. In the regression analysis, however, declines in family income had significant coefficients for transitions from ESI to either uninsured or other insurance but not to Medicaid, suggesting that we should discount the 47,000 transitions to Medicaid. Similarly, marked increases in family income were nearly as common as marked decreases and were also associated with large numbers of transitions of all three types, but the regression analysis indicated that a decline in income had a significant effect only on transitions to other income.
Further underscoring the importance of looking at both the effect of a given event on the probability of a transition and the frequency of that event, we see that the father's and mother's loss of employment had roughly similar gross effects on the probability of a child moving from ESI to Medicaid, but the mother's loss of employment was associated with three times as many transitions as the father's, owing primarily to the greater frequency of employment loss among the mothers than among the fathers of ESI children. Likewise, a parent's leaving the family was associated with the largest conditional probability of a child leaving ESI for Medicaid (and also the largest net effect in the regression analysis), yet because of the relatively low frequency of ESI children losing parents, the associated transitions are less than 7,000 or the second lowest among all of the events reported in Table 18.
Children Without Insurance. Transitions out of uninsurance occur at a much higher rate than transitions out of ESI. In the first row of Table 19 we see that 29 percent (100 minus 71) of the 9.0 million children who were without insurance in an average month from June 1993 through May 1994 became insured over the next four months. Roughly equal fractions moved into ESI and Medicaid while a much smaller fraction obtained other insurance. Because transitions out of uninsurance were so common, we see rather substantial transition rates associated with individual trigger events. More
than two-thirds of the children who experienced a parent joining the family became insured in the next four months, with 31 percent obtaining ESI and 37 percent enrolling in Medicaid. Likewise, nearly half of the children whose parents increased their hours of work to 30 or more became insured, with 30 to 33 percent obtaining ESI, 12 to 16 percent obtaining Medicaid, and 2 to 3 percent obtaining other insurance.
Because transitions out of uninsurance occurred at such a high rate in general, we must compare the transition rates associated with individual triggers to the rates for all uninsured children to properly interpret the numbers of transitions reported in the final three columns. For example, there were 75,000 transitions from uninsured to ESI among children whose family incomes fell markedly, but the 13.0 percent rate that these transitions represent is lower than the unconditional 13.6 percent rate among all uninsured children, and the regression coefficient in Table 15 indicated no relationship between such changes in income and transitions from uninsured to ESI. The implication is that none of these transitions should be attributed to the family income change. At the same time, however, the transition rate from uninsured to other insurance among children with a sharp drop in family income is nearly twice the average rate, and the regression coefficient in Table 15 showed a doubling of the odds of this particular transition when family income dropped markedly. Thus the 28,000 transitions from uninsured to other insurance reflect both a strong effect of a family's loss of income and the high frequency with which uninsured children experienced a sharp drop in family income. The mother's changing jobs is associated with a comparable transition rate from uninsured to other insurance, yet the lower frequency of such job changes translates into only 9,000 transitions.
The high rate of transitions from uninsured to ESI among children who gained a parent yields a relatively small number of transitions--10,000--compared to parents increasing their hours of work, which is associated with a comparable transition rate but six times as many transitions.
Children With Medicaid. Transitions out of Medicaid also occurred at a much higher rate than transitions out of ESI but not as high as transitions out of uninsurance. Table 20 reports the distribution of outcomes among all children with Medicaid and the subsets who experienced individual trigger events. About 15 percent of the 13 million children who were reported to be enrolled in Medicaid in an average month between June 1993 and May 1994 left Medicaid within four months. Of these, nearly 10 percent became uninsured while 5 percent obtained ESI and only one-tenth that number (.5 percent) acquired other insurance.
Four events were associated with particularly large movements from Medicaid to uninsured: the family's loss of AFDC benefits, the father's gaining employment, the father's increasing his hours to 30 or more, and a parent joining the family. In each case between 28 and 31 percent of the children recorded such a transition in the next four months. The numbers of transitions associated with these events ranged from about 8,000 for the family demographic change to 75,000 for the loss of AFDC. Transitions associated with income changes once again dominated the movements, and while the corresponding transition rates were not nearly as high as those associated with the other four variables, they were sufficiently above the average rate that the residual transitions are still high.
For transitions to ESI there were no events that clearly dominated the others with respect to rates of change. These rates ranged from 4.7 percent for all children with Medicaid to nearly 11 percent for those whose fathers gained employment. The actual numbers of transitions varied over a much broader range, of course. For the strongest net predictors from the regression analysis the numbers of transitions ranged from 11,000 to nearly 24,000. Children with family income changes had more numerous transitions, but these events had no net effects in the regression analysis, so we must discount their importance here.
Transitions from Medicaid to other insurance were infrequent generally. Consistent with the findings from the regression analysis the father's loss of employment was associated with the highest transition rate--at 2 percent--but children with large changes in family income appear to account for more transitions, even after we allow for the weaker association of income changes with this particular type of transition.
Children with Other Insurance. The overall rate at which children left other insurance was even higher than the exit rate from uninsurance. In Table 21 we see that an average of 30 percent of the children who were covered by other insurance at any one time between June 1993 and May 1994 left that coverage over the next four months. Most of the movement--22 percent--was to ESI, with 6 percent becoming uninsured and little more than 1 percent enrolling in Medicaid. Consistent with the interpretation of other insurance as generally privately purchased coverage, the high rate of movement from other insurance to ESI is consistent with the view that other insurance serves as an imperfect substitute for ESI.
The highest conditional exit rates from other insurance ranged from 63 to 74 percent (that is, the proportion retaining other insurance was between 37 percent and 26 percent). Interestingly, the father's gaining employment was associated with the highest exit rate from other insurance, but a substantial proportion of the children with this event became uninsured--26 percent compared to the 40 percent who obtained ESI. When fathers increased their weekly hours to 30 or more--which happened nearly three times as often as employment gains--54 percent of their children gained ESI, and less than 7 percent became uninsured. Children whose family income fell markedly had the most transitions from other insurance to ESI, but the transition rate of 21 percent was no higher than the unconditional average rate, implying that these transitions reflect no more than a small impact of the event per se. This contrasts with the smaller numbers of transitions associated with some of the employment changes, where many of the transitions truly reflect the impact of the events with which they correspond.
Both the father's gaining employment and losing employment are associated with high rates of children's movement from other insurance to uninsured, as is true as well of a parent leaving the family. All three of these events are relatively infrequent compared to the family's income falling markedly, which has a much weaker association with the transition but may still account for more transitions.
Transitions from other insurance to Medicaid were infrequent generally, and we found the regression results difficult to interpret. Compared to all children with other insurance there are very high transition rates associated with several trigger events, but we can infer from the magnitudes of the odds ratios in Table 17 that the standard errors were very large as well. As a result, we hesitate to attach much importance to the exit rates and transitions reported in Table 21.