Where Table 1 presented distributions of new spells of uninsurance that began in FY93, Table 2 presents distributions of all spells that were active at the end of FY93. For all children who were uninsured in September 1993, Table 2 tells us how long they had been uninsured. The distribution of these “current” durations can be compared to the distribution of completed durations of new spells, which is reproduced from Table 1 in the right hand columns of Table 2.
It is important to understand how the durations of active spells reported in the left side of Table 2 differ from the durations of new spells reported in the right side (and in Table 1). First, the durations of active spells are incomplete. More specifically, they are “right censored.” If we think of a duration as spanning from left to right on a time line, in other words, what we do not observe for these active spells is how far their durations extend to the right. All of the spells terminate at the same point in time--September 1993. We do not know how long these durations will be when they are completed. The second respect in which the active spells portrayed in Table 2 differ from the completed spells presented earlier is that they share a common month. All of the active spells include September 1993. While there is a lot of overlap in the spells reported in Table 1, these spells do not share a common month.
|Spells Active in September 1993||Spells Starting 10/92 to 9/93|
|Duration of Spell||Number||Percent||Cumulative Percent||Number||Percent||Cumulative Percent|
SOURCE: Survey of Income and Program Participation, 1992 Panel.
NOTE: Reported durations for active spells represent current durations as of September 1993. Reported durations for spells starting during FY93 represent completed durations.
These two differences have important implications for how the distributions of durations differ. First, let us consider what the durations reported on the left side of Table 2 represent. Durations of one month represent spells that started in September. Ultimately, very few of these spells will end at one month. Instead, if we could follow them through to completion, we would find that they have essentially the same distribution as the spells reported in Table 1. Durations of two months refer to all spells that started in August 1993, minus those that ended in that same month--that is, spells with completed durations of one month. If we were to follow these spells to completion, they too would have the same distribution as the spells reported in Table 1 except for the complete absence of spells of one month duration. Similarly, the 12-month durations include all spells that started in October 1992 minus those that ended in any of the months from October 1992 through August 1993.3
What we notice first in the distribution of active spells is the absence of a seam effect. There are no peaks whatsoever at multiples of four months. This absence of a seam effect is due entirely to the right censoring. Most of these spells are not complete, so the seam effect is hidden. One quarter of the spells that will eventually end in four months shows up as one month in length, one quarter shows up as two months in length, one quarter appears as three, and one quarter as four months in length. Far from producing peaks at four months, the seam effect actually contributes to the relative evenness of the distribution of spells across durations of one to four months.
The second thing we notice is that apart from the higher proportion of spells with durations of three months or less, the spells that are active at the end of the year (and this would be true of spells that were active during any given month of the year) are longer, on average, than the spells that started during the year--even though most of the active spells are not yet complete. The median length of the active spells lies between 9 and 10 months whereas the median completed length of the new spells lies close to 4 months. Nearly 46 percent of the active spells have durations in excess of 12 months compared to just 20 percent of the spells that started during the year.
If we followed the active spells to their completion, we would obtain a distribution that is heavily skewed toward long durations. Why is this? It turns out that the representation of spells among active spells is directly proportional to their completed duration. Spells of one month duration are represented solely by spells that began in a single month: September 1993. Spells of two months duration are represented solely by spells that began in either of two months: August or September. Spells of three months duration are represented by spells that began in any of three months, and so on. Thus spells of 12 months duration are represented by spells that began in any of 12 months--October 1992 through September 1993--while spells of 36 months duration are represented by spells that began in any of 36 months--from October 1990 through September 1993. Compared to a distribution of spells starting in the same month or the same year, therefore, spells of exactly 36 months in length are represented at 36 times their relative frequency.
We could estimate the distribution of completed durations among spells that were active in September 1993 by taking the completed distribution of new spells reported in Table 1 and multiplying the number of one-month spells by 1, the number of two-month spells by 2, number of three-month spells by 3, and so on. Obviously, we cannot complete this exercise with the data presented in Table 1 because we do not know the completed duration of spells that exceeded 18 months in length. But if we make an assumption about the average completed duration of spells that were completed in more than 18 months, then we can estimate the relative frequency of such spells among active spells.
Table 3 displays this projected distribution of the completed duration of spells that were active in September 1993. These calculations assume, of course, that the distribution of completed durations did not change over time, so that the relative frequency of, say, an 18-month spell is the same for spells starting at any time between October 1991 and September 1993. Whether or not this assumption is satisfied, the projected distribution illustrates our point. In Table 3 we see that only 22 percent of these spells are completed in six months or less compared to about 60 percent of the new spells in Table 1. At the other end of the distribution, 49 percent of the spells reported in Table 3 extend beyond 18 months compared to only 15.5 percent of the spells in Table 1.
If these different ways of measuring the duration of uninsurance yield such different distributions, can they all be useful? The answer is yes, but the different distributions address different questions. Table 1 reflects a representative sampling of spells. It tells us that most spells of uninsurance among children are relatively short in length, 60 percent being six months or less. The distribution has a long tail, however, with at least 20 percent of spells (we suggested somewhat higher) exceeding 12 months in length and about three-fourths of these surpassing 18 months. It is this long tail that makes possible the skewed distribution that we see when we look at the spells of a representative sample of people with spells active in a give month. People who experience long spells are more likely to be uninsured in a given month than people who experience short spells, so children who are uninsured at a point in time exhibit disproportionately many long spells. Table 3 suggests that about half of the 9 million children who were uninsured in any given month of FY93 will have had spells of more than 18 months in length by the time they become insured (again), and most of these spells will extend well beyond 18 months. Finally, Table 2 addresses a question that is becoming very pertinent with the introduction of CHIP--namely, if eligibility is limited to children who have been uninsured for a specified number of months, how many children will satisfy these criteria? Table 2 indicates that with a 12 month minimum, about 47 percent of all uninsured children would meet this requirement. The percentage among children who meet the income and other requirements is likely to be higher. Lowering the duration requirement to 6 months would add another 16 percent of children--a relatively modest increase given that the minimum duration would be cut in half.
|Projected Completed Duration of Spell||Percent||Cumulative Percent|
SOURCE: Mathematica Policy Research, Inc.
NOTE: In calculating these projections from the distribution of new spells, as reported in Table 1, we assumed that spells of more than 18 months' duration had a mean duration of 30 months. Lowering this assumed mean duration to 24 months would reduce the share of spells with durations of 19+ months to 43.9 percent and increase the cumulative share of spells with durations less than 12 months to 38.2 percent.
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