We will be interested in three summary statistics that describe an individual's welfare participation experiences over a fixed calendar interval:
(1) The total number of periods the individual is on welfare in the interval (T);
(2) The total number of welfare "spells" experienced by the individual within the interval (N); and
(3) The average length of these "spells" (L).
The first of these is the total-time-on measure mentioned previously. The second counts the number of separate welfare "spells" in the interval, where a welfare "spell" is defined as a sequence of consecutive periods on welfare. This is a measure of turnover, for it is closely related to the number of transitions on or off welfare that are experienced in the calendar interval. It should be noted that, here, a spell can be in progress at the beginning of the calendar interval or in progress at the end and still be counted as a spell. The third measure is the average length of these spells. Given these definitions, T=N*L. Consequently, any two of these measures for any individual determines the third.(11)
In addition to measuring T, N, and L themselves, we also define three combinations of these variables that together define long-termers, short-termers, and cyclers, the classification scheme proposed by Bane and Ellwood. The definitions we use are:
Long-termers: N < a and L > b
Short-termers: N < a and L < b
Cyclers: N > a
where "a" and "b" are some constants to be selected after an initial examination of the data, and which will be varied as part of a sensitivity analysis. Thus long-termers are defined as having relatively few spells but spells with long average lengths; short-termers are also defined as having relatively few spells but as having short average lengths; and cyclers are defined simply as those with a relatively high number of spells, regardless of their lengths (but, for a fixed interval length [t0 ,t 1], a high number of spells must necessarily ultimately lead to shorter average lengths).
Note that these groups are defined solely on the basis of N and L, not T. The total-time-on surely will be high for long-termers and surely will be low for short-termers, given the definitions provided, but whether T will be high or low (by some definition of those terms) for cyclers is ambiguous. There is no clear definition of these groups in the literature, so it is unclear whether this approach to the definition is the same or different as that used by others. Certainly some appear to use the term "long-termer" to refer to women who have high T per se, regardless of whether they have such a high T because of a small number of long spells or a large number of short spells (thereby using the word "long" to refer to the magnitude of total-time-on, not the length of spells).(12) In part this is just a terminological matter, but defining "long-termer" in this way does have unsatisfactory aspects. It leaves as undefined women who have large numbers of spells but a modest level of T, for example, who do not fall into any category. Moreover, the literal interpretation of the verb "to cycle" implies a definition based purely on turnover rates and numbers of spells, not a total-time-on definition; hence it makes more sense in terms of language to let T be an outcome of a turnover definition of cycling, not as a definitional characteristic. One could stick with a T-defined classification scheme by parceling out cyclers to the long-termer and short-termer groups by saying that there are two types of cyclers--those with high T, whom we will call long-termers, and those with modest T, who will be called short-termers. But in this case, the latter group is lumped in with the more conventional short-termers with low turnover rates. The consequence would be that one would move from a definitional scheme that allows cyclers to be a heterogeneous group to one that allows long-termers and short-termers to each be heterogeneous, which would not appear to be a gain in terms of clarity. Alternatively, one could move to a classification scheme that has more than three groups, but then simplicity begins to be lost.
For all these reasons, we will use the three-fold classification based solely on N and L. However, we will examine the heterogeneity of the cycler group by examining their distributions of T and compare the different subgroups of cyclers so defined to short-termers and long-termers.
There is surprisingly little evidence in the literature on the characteristics of individuals with different turnover rates and overall spell patterns, or on how groups of individuals defined by long-termer, short-termer, and cycler status differ by characteristics. The vast majority of studies of welfare dynamics present estimates of the determinants of exit from welfare spells or entry onto welfare or, sometimes, of rates of reentry onto welfare after an exit. These econometric models are not set up to distinguish the determinants of turnover per se from the determinants of total-time-on because they impose a restrictive relationship between the effects of the independent variables on turnover rates, total-time-on, and spell lengths. For example, it would not be possible in these models to find that some variable for labor market potential (e.g., mean potential earnings off welfare) could differ between short-termers and cyclers but not between cyclers and long-termers, to take one case. To distinguish these, a more sophisticated statistical specification would be required. Alternatively, and as a first step, it is more natural to simply examine the characteristics of individual recipients as ranked by their turnover rates, total-time-on, and spell lengths, or by their classification into short-termers, long-termers, or cyclers, as is done in this chapter.
A few recent studies have already attempted this, however. Stevens (2000:Table 4), in a study using administrative data from Maryland, found earnings of AFDC long-termers and cyclers to be not very different for white women. But cyclers had higher earnings than long-termers among the population of black women. In a study using administrative data from Wisconsin, Ver Ploeg (this volume: Table 13-5) examined employment rates of individuals on Temporary Assistance for Needy Families (TANF) and found them to be higher for cyclers than for long-termers. Cancian et al. (1999) also provided evidence on how leaver outcomes in Wisconsin vary with the amount of previous time on welfare.(13)
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