# Characteristics of Low-Wage Workers and Their Labor Market Experiences: Evidence from the Mid- to Late 1990s. Life Table Methods

To examine the duration of job, employment, and nonemployment spells, we used "life table analyses." Spells can be broken down into months; for each month, the life table displays the estimated hazard rate and cumulative exit rate. The hazard rate is the probability that a spell ended in a particular month, given that the spell lasted at least until the beginning of that month. The cumulative exit rate, obtained from the estimated hazard rates, is the unconditional probability that a spell ended within a given number of months. The cumulative exit rate enables policymakers to answer such questions as: Of the next 100 people who begin a low-wage job spell, how many will exit their low-wage jobs within one year?

A major advantage of using life table methods is that they can effectively treat right-censored spells (that is, spells still in progress at the end of the observation period). Right-censored spells contribute information to the life table up to the month in which they are right-censored (that is, up to the time we no longer have information on them). For example, if a spell is right-censored 12 months after the spell started, then that spell is included in the hazard rate calculations (that is, enters the denominator of the calculations) for months 1 to 12, but not afterward.

The treatment of left-censored spells (that is, spells in progress at the start of the panel) is more problematic, because the duration distributions of left-censored and non-left-censored spells are likely to differ. For example, suppose a low-wage job spell started one year prior to the start of the panel period. Then, that spell would be observed in the data only if it lasted longer than one year (it would not be observed if it ended prior to the panel period). Furthermore, counting from month 1 of the panel period, the spell is likely to last longer than a typical non-left-censored low-wage spell because of duration dependence (that is, spell exit rates often decrease the longer the spell has been in progress). Thus, left-censored spells are likely to be longer on average and to have a different duration distribution than are typical spells.

Left-censored spells, however, can be included in the life table analysis, because the wave 1 core files contain information on the start dates of left-censored spells. The left-censored spells contribute information to the life table starting in the month in which they are left-censored. For example, a spell that had been in progress for 12 months would enter the life table starting in month 12. This procedure, however, produces unbiased estimates only if we assume a stationary environment (that is, if spell duration distributions did not change over time). This assumption, however, may be unrealistic for spells that had been in progress for a long time due to changes in labor market structure and conditions. Furthermore, because SIPP does not contain prepanel information on hourly wages, left-censored spells can be included in the analysis only if we assume that left-censored low-wage jobs were low-wage jobs for the entire period between job start and month 1 of the panel period.

For these reasons, we excluded left-censored spells in our main spell duration analyses (the approach that most researchers conducting event history studies use). However, left-censored spells were included in some analyses to examine issues pertaining to the duration of longer spells than could be observed in the panel period and to check the robustness of study findings.

The life table methods described above can be extended to examine the rate at which workers leave the low-wage labor market, by type of exit. In this "competing risks" framework, the dependent variable for the analysis was set to zero in months the spell was in progress and to a positive code--signifying the specific exit type--in the month the spell ended. Thus, spells contributed information to the life table up to the month that they ended (that is, until a positive code appeared) or until the end of the panel period for right-censored spells. In this framework, the estimated monthly hazard and cumulative exit rates across the exit types sum to the corresponding values for the overall spell analysis where we did not distinguish between exit types.

The life tables themselves contain a great deal of information and can be complicated. Because the cumulative exit rates efficiently and intuitively summarize the life table results, our presentation focuses on them. Furthermore, when presenting results for the subgroup analyses, we present summary information such as the median spell duration, as well as the percentage of spells that ended within a given number of months. We also conducted statistical tests to gauge whether the spell duration distributions differed across levels of a subgroup using the log-rank statistic.(46) All statistics were constructed using the longitudinal panel weight.

Finally, for several reasons, we present life table results by wave only (that is, in four-month intervals from 4 to 44 months after job start). First, as discussed in the Methodological Appendix, the constructed hourly wage for a particular job or business was constant within a wave. Second, sample members tended to report being employed (or unemployed) for the entire wave rather than for only specific months covered by the wave. Consequently, we find more changes in low-wage job status across waves than within waves, so that the estimated hazard rates spike at the "seam" points. Thus, we present the life table results in four-month intervals only.

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