Trends, Events, and Duration of Initial Welfare Spells

Social Service Review

Volumn 72, Issue 4, 1998, Pages 466-492

  Boisjoly, Johanne ^a   Harris, Kathleen Mullan ^b   Duncan, Greg J ^c  

^a UNIVERSITÉ DU QUÉBEC À RIMOUSKI   (Canada)

^b UNIVERSITY OF NORTH CAROLINA   (United States)

^c NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001539669     PISSN: 00377961     EISSN: None     Source Type: Journal    
DOI: 10.1086/515775     Document Type: Article

References (71)

1. R. Mark Gritz and Thomas MaCurdy, "Welfare Entrances, Durations, and Exits: A Comparison of NLSYand PSID" (paper presented at the PSID Event History Conference, Stanford, Calif., June 30-July 2, 1991); Kathleen Mullan Harris, "Work and Welfare among Single Mothers in Poverty," American Journal of Sociology 99 (1993): 317-52; LaDonna A. Pavetti, "The Dynamics of Welfare and Work: Exploring the Process by Which Young Women Work Their Way Off Welfare" (Ph.D. diss., John F. Kennedy School of Government, Harvard University, Cambridge, Mass., 1993); Roberta M. Spalter-Roth, Heidi I. Hartmann, and Linda M. Andrews, "Mothers, Children, and Low-Wage Work: The Ability to Earn a Family Wage," in Sociology and the Public Agenda, ed. W. J. Wilson (Newbury Park, Calif.: Sage, 1993), pp. 316-38.
2. R. Mark Gritz and Thomas MaCurdy, "Welfare Entrances, Durations, and Exits: A Comparison of NLSYand PSID" (paper presented at the PSID Event History Conference, Stanford, Calif., June 30-July 2, 1991); Kathleen Mullan Harris, "Work and Welfare among Single Mothers in Poverty," American Journal of Sociology 99 (1993): 317-52; LaDonna A. Pavetti, "The Dynamics of Welfare and Work: Exploring the Process by Which Young Women Work Their Way Off Welfare" (Ph.D. diss., John F. Kennedy School of Government, Harvard University, Cambridge, Mass., 1993); Roberta M. Spalter-Roth, Heidi I. Hartmann, and Linda M. Andrews, "Mothers, Children, and Low-Wage Work: The Ability to Earn a Family Wage," in Sociology and the Public Agenda, ed. W. J. Wilson (Newbury Park, Calif.: Sage, 1993), pp. 316-38.
3. R. Mark Gritz and Thomas MaCurdy, "Welfare Entrances, Durations, and Exits: A Comparison of NLSYand PSID" (paper presented at the PSID Event History Conference, Stanford, Calif., June 30-July 2, 1991); Kathleen Mullan Harris, "Work and Welfare among Single Mothers in Poverty," American Journal of Sociology 99 (1993): 317-52; LaDonna A. Pavetti, "The Dynamics of Welfare and Work: Exploring the Process by Which Young Women Work Their Way Off Welfare" (Ph.D. diss., John F. Kennedy School of Government, Harvard University, Cambridge, Mass., 1993); Roberta M. Spalter-Roth, Heidi I. Hartmann, and Linda M. Andrews, "Mothers, Children, and Low-Wage Work: The Ability to Earn a Family Wage," in Sociology and the Public Agenda, ed. W. J. Wilson (Newbury Park, Calif.: Sage, 1993), pp. 316-38.
4. R. Mark Gritz and Thomas MaCurdy, "Welfare Entrances, Durations, and Exits: A Comparison of NLSYand PSID" (paper presented at the PSID Event History Conference, Stanford, Calif., June 30-July 2, 1991); Kathleen Mullan Harris, "Work and Welfare among Single Mothers in Poverty," American Journal of Sociology 99 (1993): 317-52; LaDonna A. Pavetti, "The Dynamics of Welfare and Work: Exploring the Process by Which Young Women Work Their Way Off Welfare" (Ph.D. diss., John F. Kennedy School of Government, Harvard University, Cambridge, Mass., 1993); Roberta M. Spalter-Roth, Heidi I. Hartmann, and Linda M. Andrews, "Mothers, Children, and Low-Wage Work: The Ability to Earn a Family Wage," in Sociology and the Public Agenda, ed. W. J. Wilson (Newbury Park, Calif.: Sage, 1993), pp. 316-38.
5. Kathleen Mullan Harris, "Life after Welfare: Women, Work, and Repeat Dependency," American Sociological Review 61 (1996): 407-26; Pavetti, "The Dynamics of Welfare and Work" (n. 1 above); Roberta Spalter-Roth, Beverly Burr, Heidi Hartmann, and Lois Shaw, "Welfare That Works: The Working Lives of AFDC Recipients" (report to the Ford Foundation, Washington, D.C., Institute for Women's Policy Research, 1995).
6. Kathleen Mullan Harris, "Life after Welfare: Women, Work, and Repeat Dependency," American Sociological Review 61 (1996): 407-26; Pavetti, "The Dynamics of Welfare and Work" (n. 1 above); Roberta Spalter-Roth, Beverly Burr, Heidi Hartmann, and Lois Shaw, "Welfare That Works: The Working Lives of AFDC Recipients" (report to the Ford Foundation, Washington, D.C., Institute for Women's Policy Research, 1995).
7. Kathleen Mullan Harris, "Life after Welfare: Women, Work, and Repeat Dependency," American Sociological Review 61 (1996): 407-26; Pavetti, "The Dynamics of Welfare and Work" (n. 1 above); Roberta Spalter-Roth, Beverly Burr, Heidi Hartmann, and Lois Shaw, "Welfare That Works: The Working Lives of AFDC Recipients" (report to the Ford Foundation, Washington, D.C., Institute for Women's Policy Research, 1995).
8. For reviews, see Hillary Hoynes, "Work, Welfare, and Family Structure: A Review of the Evidence," Discussion Paper no. 1103-96, Institute for Research on Poverty, University of Wisconsin - Madison, 1996; Robert Moffitt. "Incentive Effects of the U.S. Welfare System: A Review," Journal of Economic Literature 30 (1992): 1-61; Sara S. McLanahan and Gary D. Sandefur, Growing Up with a Single Parent: What Hurts, What Helps (Cambridge, Mass.: Harvard University Press, 1994).
9. For reviews, see Hillary Hoynes, "Work, Welfare, and Family Structure: A Review of the Evidence," Discussion Paper no. 1103-96, Institute for Research on Poverty, University of Wisconsin - Madison, 1996; Robert Moffitt. "Incentive Effects of the U.S. Welfare System: A Review," Journal of Economic Literature 30 (1992): 1-61; Sara S. McLanahan and Gary D. Sandefur, Growing Up with a Single Parent: What Hurts, What Helps (Cambridge, Mass.: Harvard University Press, 1994).
10. For reviews, see Hillary Hoynes, "Work, Welfare, and Family Structure: A Review of the Evidence," Discussion Paper no. 1103-96, Institute for Research on Poverty, University of Wisconsin - Madison, 1996; Robert Moffitt. "Incentive Effects of the U.S. Welfare System: A Review," Journal of Economic Literature 30 (1992): 1-61; Sara S. McLanahan and Gary D. Sandefur, Growing Up with a Single Parent: What Hurts, What Helps (Cambridge, Mass.: Harvard University Press, 1994).
11. Mary Jo Bane and David Ellwood, Welfare Realities: From Rhetoric to Reform (Cambridge, Mass: Harvard University Press, 1994).
12. Rebecca M. Blank, "Analyzing the Length of Welfare Spells," Journal of Public Economics 39 (1989): 245-73; John Fitzgerald, "Welfare Durations and the Marriage Market: Evidence from the Survey of Income and Program Participation," Journal of Human Resources 26 (1991): 545-61; Harris, "Work and Welfare among Single Mothers in Poverty" (n. 1 above); June A. O'Neill, Laurie J. Bassi, and Douglas A. Wolf, "The Duration of Welfare Spells," Review of Economics and Statistics 69 (1987): 241-49; Pavetti, "The Dynamics of Welfare and Work" (n. 1 above).
13. Rebecca M. Blank, "Analyzing the Length of Welfare Spells," Journal of Public Economics 39 (1989): 245-73; John Fitzgerald, "Welfare Durations and the Marriage Market: Evidence from the Survey of Income and Program Participation," Journal of Human Resources 26 (1991): 545-61; Harris, "Work and Welfare among Single Mothers in Poverty" (n. 1 above); June A. O'Neill, Laurie J. Bassi, and Douglas A. Wolf, "The Duration of Welfare Spells," Review of Economics and Statistics 69 (1987): 241-49; Pavetti, "The Dynamics of Welfare and Work" (n. 1 above).
14. Rebecca M. Blank, "Analyzing the Length of Welfare Spells," Journal of Public Economics 39 (1989): 245-73; John Fitzgerald, "Welfare Durations and the Marriage Market: Evidence from the Survey of Income and Program Participation," Journal of Human Resources 26 (1991): 545-61; Harris, "Work and Welfare among Single Mothers in Poverty" (n. 1 above); June A. O'Neill, Laurie J. Bassi, and Douglas A. Wolf, "The Duration of Welfare Spells," Review of Economics and Statistics 69 (1987): 241-49; Pavetti, "The Dynamics of Welfare and Work" (n. 1 above).
15. Rebecca M. Blank, "Analyzing the Length of Welfare Spells," Journal of Public Economics 39 (1989): 245-73; John Fitzgerald, "Welfare Durations and the Marriage Market: Evidence from the Survey of Income and Program Participation," Journal of Human Resources 26 (1991): 545-61; Harris, "Work and Welfare among Single Mothers in Poverty" (n. 1 above); June A. O'Neill, Laurie J. Bassi, and Douglas A. Wolf, "The Duration of Welfare Spells," Review of Economics and Statistics 69 (1987): 241-49; Pavetti, "The Dynamics of Welfare and Work" (n. 1 above).
16. Rebecca M. Blank, "Analyzing the Length of Welfare Spells," Journal of Public Economics 39 (1989): 245-73; John Fitzgerald, "Welfare Durations and the Marriage Market: Evidence from the Survey of Income and Program Participation," Journal of Human Resources 26 (1991): 545-61; Harris, "Work and Welfare among Single Mothers in Poverty" (n. 1 above); June A. O'Neill, Laurie J. Bassi, and Douglas A. Wolf, "The Duration of Welfare Spells," Review of Economics and Statistics 69 (1987): 241-49; Pavetti, "The Dynamics of Welfare and Work" (n. 1 above).
17. Harris, "Life after Welfare" (n. 2 above).
18. Bane and Ellwood, Welfare Realities (n. 4 above); LaDonna A. Pavetti, "Who Is Affected by Time Limits?" in Welfare Reform: An Analysis of the Issues, ed. Isabel V. Sawhill (Washington, D.C.: The Urban Institute, 1995), chap 7. These estimates come from simulations of total time recipients spend on welfare using exit rates for first and higher-order spells and return rates based on monthly data from the National Longitudinal Survey of Youth (Pavetti, "The Dynamics of Welfare and Work" [n. 1 above]) and from a similar procedure by Bane and Ellwood (1994) using 21 years of annual data from the PSID. Thus, time limits in the new welfare bill may have been linked to the average experiences of welfare recipients based on social science research.
19. Bane and Ellwood, Welfare Realities (n. 4 above); LaDonna A. Pavetti, "Who Is Affected by Time Limits?" in Welfare Reform: An Analysis of the Issues, ed. Isabel V. Sawhill (Washington, D.C.: The Urban Institute, 1995), chap 7. These estimates come from simulations of total time recipients spend on welfare using exit rates for first and higher-order spells and return rates based on monthly data from the National Longitudinal Survey of Youth (Pavetti, "The Dynamics of Welfare and Work" [n. 1 above]) and from a similar procedure by Bane and Ellwood (1994) using 21 years of annual data from the PSID. Thus, time limits in the new welfare bill may have been linked to the average experiences of welfare recipients based on social science research.
20. U.S. House of Representatives, Committee on Ways and Means, 1996 Green Book: Overview of Entitlement Programs (CD-ROM) (Washington, D.C.: U.S. Government Printing Office, 1996).
21. Hillary Williamson Hoynes and Thomas MaCurdy, "Welfare Spells over the Last Two Decades: Do Changes in Benefits Explain the Trends?" (University of California, Berkeley, 1993, mimeographed), and
22. "Has the Decline in Benefits Shortened Welfare Spells?" American Economic Review 84 (1994): 43-48.
23. Bane and Ellwood, Welfare Realities (n. 4 above); Harris, "Work and Welfare among Single Mothers in Poverty" (n. 1 above).
24. Bane and Ellwood, Welfare Realities (n. 4 above); Harris, "Work and Welfare among Single Mothers in Poverty" (n. 1 above).
25. Peter Gottschalk and Robert A. Moffitt, "Welfare Dependence: Concepts, Measures, and Trends," American Economic Review 84 (1994): 38-42. Women who receive AFDC but are not heads of household are typically younger women who may live in a three-generation household or with other adults.
26. Ibid.
27. Mary Jo Bane and David Ellwood, "The Dynamics of Dependence and the Routes to Self-Sufficiency" (final report to the U.S. Department of Health and Human Services, Harvard University, Kennedy School of Government, 1983); David Ellwood, "Targeting 'Would- Be' Long Term Recipients of AFDC" (report prepared for the Department of Health and Human Services, Mathematica Policy Research, Inc., Princeton, N.J., 1986); Bane and Ellwood, Welfare Realities (n. 4 above).
28. Mary Jo Bane and David Ellwood, "The Dynamics of Dependence and the Routes to Self-Sufficiency" (final report to the U.S. Department of Health and Human Services, Harvard University, Kennedy School of Government, 1983); David Ellwood, "Targeting 'Would-Be' Long Term Recipients of AFDC" (report prepared for the Department of Health and Human Services, Mathematica Policy Research, Inc., Princeton, N.J., 1986); Bane and Ellwood, Welfare Realities (n. 4 above).
29. Mary Jo Bane and David Ellwood, "The Dynamics of Dependence and the Routes to Self-Sufficiency" (final report to the U.S. Department of Health and Human Services, Harvard University, Kennedy School of Government, 1983); David Ellwood, "Targeting 'Would- Be' Long Term Recipients of AFDC" (report prepared for the Department of Health and Human Services, Mathematica Policy Research, Inc., Princeton, N.J., 1986); Bane and Ellwood, Welfare Realities (n. 4 above).
30. Blank, "Analyzing the Length of Welfare Spells" (n. 5 above); Fitzgerald (n. 5 above); Gritz and MaCurdy (n. 1 above); Harris, "Work and Welfare among Single Mothers in Poverty" (n. 1 above); June A. O'Neill, Douglas A. Wolf, Laurie J. Bassi, and Michael T. Hannan, "An Analysis of Time on Welfare," Report no. PB84-225713, Urban Institute, Washington, D.C., 1984; O'Neill, Bassi, and Wolf (n. 5 above).
31. Blank, "Analyzing the Length of Welfare Spells" (n. 5 above); Fitzgerald (n. 5 above); Gritz and MaCurdy (n. 1 above); Harris, "Work and Welfare among Single Mothers in Poverty" (n. 1 above); June A. O'Neill, Douglas A. Wolf, Laurie J. Bassi, and Michael T. Hannan, "An Analysis of Time on Welfare," Report no. PB84-225713, Urban Institute, Washington, D.C., 1984; O'Neill, Bassi, and Wolf (n. 5 above).
32. Blank, "Analyzing the Length of Welfare Spells" (n. 5 above); Fitzgerald (n. 5 above); Gritz and MaCurdy (n. 1 above); Harris, "Work and Welfare among Single Mothers in Poverty" (n. 1 above); June A. O'Neill, Douglas A. Wolf, Laurie J. Bassi, and Michael T. Hannan, "An Analysis of Time on Welfare," Report no. PB84-225713, Urban Institute, Washington, D.C., 1984; O'Neill, Bassi, and Wolf (n. 5 above).
33. Kathleen Mullan Harris, Teen Mothers and the Revolving Welfare Door (Philadelphia: Temple Press, 1997).
34. M. Klawitter, R. Plotnick, and M. Edwards, "Determinants of Welfare Entry and Exits by Young Women," Working Paper no. 96-2, Graduate School of Public Affairs, University of Washington, 1996.
35. Harris, "Work and Welfare among Single Mothers in Poverty" (n. 1 above), and Teen Mothers and the Revolving Welfare Door (n. 15 above).
36. Martha S. Hill, The Panel Study of Income Dynamics (Newbmy Park, Calif: Sage, 1992).
37. In these and all subsequent occasions, our calendar-year references to income data are to the calendar years in which the AFDC was received rather than the calendar years in which the information was reported in the PSID interview.
38. We also required that at least one child live with the mother. However, we did not require that the mother herself report AFDC income. In many instances, particularly in three-generation households, the person receiving the AFDC check may not be the mother but rather the grandmother or some other relative of the child on whose behalf the AFDC benefit is paid. We assume in this instance that age-eligible children who lived with the mother are part of the household AFDC "case." In keeping with most other work on AFDC using the PSID, we also consider the PSID's "other welfare" category to be AFDC income. It is a residual category, included in the questionnaire after respondents report explicitly on AFDC, food stamps, SSI, Workers' Compensation, Unemployment Insurance, and Social Security.
39. Bane and Ellwood, Welfare Realities (n. 4 above), table 2.2, p. 38.
40. Analysts include Bane and Ellwood, Welfare Realities (n. 4 above) and " The Dynamics of Dependence" (n. 13 above); Ellwood (n. 13 above); Hoynes and MaCurdy (n. 9 above); and Harris, "Work and Welfare among Single Mothers in Poverty" (n. 1 above).
41. Analysts include Bane and Ellwood, Welfare Realities (n. 4 above) and " The Dynamics of Dependence" (n. 13 above); Ellwood (n. 13 above); Hoynes and MaCurdy (n. 9 above); and Harris, "Work and Welfare among Single Mothers in Poverty" (n. 1 above).
42. Analysts include Bane and Ellwood, Welfare Realities (n. 4 above) and " The Dynamics of Dependence" (n. 13 above); Ellwood (n. 13 above); Hoynes and MaCurdy (n. 9 above); and Harris, "Work and Welfare among Single Mothers in Poverty" (n. 1 above).
43. See, e.g., Pavetti, "The Dynamics of Welfare and Work" (n. 1 above), and "Who Is Affected by Time Limits?" (n. 7 above); and Klawitter et al. (n. 16 above).
44. See, e.g., Pavetti, "The Dynamics of Welfare and Work" (n. 1 above), and "Who Is Affected by Time Limits?" (n. 7 above); and Klawitter et al. (n. 16 above).
45. John Bound, Greg J. Duncan, Deborah Laren, and Lewis Oleinick, "Poverty Dynamics in Widowhood," Journal of Gerontology: Social Sciences 46, no. 3 (1991): 115-24; Greg J. Duncan, Johanne Boisjoly, and Timothy Smeeding, "Earning Mobility of Young Workers in the 1970s and 1980s," Demography 33 (1996): 497-509. In constructing our event histories, we use as much information about AFDC receipt as possible. For example, if a mother was lost to nonresponse at age 23 after 3 years of receipt and 1 year of nonreceipt, then she would be counted as having a censored receipt spell of 3 years.
46. John Bound, Greg J. Duncan, Deborah Laren, and Lewis Oleinick, "Poverty Dynamics in Widowhood," Journal of Gerontology: Social Sciences 46, no. 3 (1991): 115-24; Greg J. Duncan, Johanne Boisjoly, and Timothy Smeeding, "Earning Mobility of Young Workers in the 1970s and 1980s," Demography 33 (1996): 497-509. In constructing our event histories, we use as much information about AFDC receipt as possible. For example, if a mother was lost to nonresponse at age 23 after 3 years of receipt and 1 year of nonreceipt, then she would be counted as having a censored receipt spell of 3 years.
47. Suppose AFDC income was first reported in calendar year t. We considered a welfare spell to be birth related if the birth occurred in calendar rears t - 1, t, or t + 1. The lack of monthly income detail, the possibility of receipt of AFDC benefits during pregnancy, and the assumption that first AFDC receipt as late as 23 months following a birth might indeed be related to the birth led us to use the 3-year window.
48. In a companion paper, we show in more detail the ability of these risk factors to predict recipients most likely to reach the 24- and 60-month time limits under the new law. See Greg J. Duncan, Kathleen Mullan Harris, and Johanne Boisjoly, "Time Limits and Welfare Reform: New Estimates of the Number and Characteristics of Affected Families" (Joint Center for Poverty Research, Northwestern University, 1997).
49. U.S. House of Representatives (n. 8 above). We thank Robert Moffitt for sharing his state-level time series of AFDC benefit levels from 1968 to 1988. We used data from the 1989-96 Green Book to update the series to 1995.
50. We also calculated from CPS data a state-level time series of unemployment rates for women with no more than a high school education. That variable was highly correlated with our employment-rate measure (r = -.64) and, after considerable experimentation, we opted to include only the employment-rate measure.
51. Prior to 1977, both hours worked per week and weeks worked per year were only available as categorical or bracketed variables.
52. States with at least 17 observations were given separate dummy variables. They include California; Arizona; Washington, D.C.; Florida; Georgia; Illinois; Indiana; Louisiana; Maryland; Michigan; Mississippi; Missouri; New York; North Carolina; Ohio; Pennsylvania; South Carolina: Texas; and Virginia.
53. The nature of the PSID sample renders it difficult to develop an ongoing set of cross-sectional weights that could be used to blow up the PSID sample and compare weight sums directly with caseload totals. Initial sampling fractions are known from the sample design, and adjustments for individual-based attrition subsequent to the initial wave are straightforward. What proves difficult are household-based adjustments to the weights because it is not known how many newborns and new families are associated with nonresponse individuals. As a result, we confine our analysis to relative trends.
54. In all of the survivor curves presented in this article, data are included only if the hazard rate is based on at least 30 observations.
55. These spell durations are based on annual data and require 2 consecutive calendar years of nonreceipt to define an exit. As shown in the literature and in a subsequent section of the article, monthly-based spells are even shorter.
56. The log-rank significance test was always significant at the 5 percent level when the 1987-91 spells were tested against the others. The Wilcoxon test showed insignificant differences between the 1987-91 and 1978-81 spells and significant differences between 1987-91 and the two remaining spell cohorts.
57. Small sample sizes precluded a more detailed classification by beginning year.
58. Green Book evidence presented in appendix table A1 shows that between 3 percent and 10 percent of the caseload involves mothers under the age of 20. Those data are not inconsistent with ours given that they measure the current age of the mother and not her age at the time when her first spell began.
59. The drop in the frequency of unmarried-birth welfare spells led us to worry about whether the PSID was failing to track trends in out-of-wedlock teen childbearing. To investigate this issue, we estimated birth rates for unmarried women in the PSID and compared them with rates reported in Vital Statistics. Both the level and trends in these rates were remarkably similar between the two sources of data. For the years 1968-71, 1972-75, 1976-79, 1980-83, 1984-87, and 1988-91, the 4-year average unmarried-birth rates per 1,000 for 15-19-year-olds according to Vital Statistics were 21.2, 23.1, 25.0, 28.4, 31.9, and 41.0. Corresponding figures from the PSID were 19.4, 19.3, 26.6, 21.0, 29.5, and 38.7. The correlation between the two time series was .92. Agreement was not as close for birth rates to 20-24-year-old women, with rates according to Vital Statistics sources climbing from the low 30s to the high 60s and PSID-based rates averaging around 50 for the entire period. A look at the annual detail showed considerable year-to-year variation in the PSID-based rates for all cohorts older than 19. Thus, if anything, the PSID overstates the number of out-of- wedlock births to women in their 20s in its early years, leading to an overstatement of the number of welfare spells associated with nonmarital births in the pre-1983 period.
60. The small number of spell beginnings associated with this combination of characteristics, coupled with the short duration of the spells, led to sample sizes that were too small to support estimates of the survival curves beyond 4 years.
61. Ellwood (n. 13 above).
62. Rebecca M. Blank, "The Employment Strategy: Public Policies to Increase Work and Earnings," in Confronting Poverty, ed. Sheldon H. Danziger, Gary D. Sandefur, and Daniel H. Weinberg (New York: Russell Sage, 1994), chap. 7.
63. Aaron S. Yelowitz, "The Medicaid Notch, Labor Supply, and Welfare Participation: Evidence from Eligibility Expansions," Discussion Paper no. 1084-96, Institute for Research on Poverty, University of Wisconsin - Madison, 1996.
64. Also possible are "age effects," which in our case correspond to the "age" (i.e., duration) of the AFDC spell in progress. Suppose that the chance of ending an AFDC spell drops the longer the mother has already received AFDC. If many mothers had begun to receive AFDC in 1985, and the chance of ending an AFDC spells after 5 years was particularly low, then there would be relative few exits recorded in 1990.
65. Paul D. Allison, "Discrete-Time Methods for the Analysis of Event Histories," Sociological Methodology 12 (1982): 61-98.
66. Suppose that a mother has a first spell of welfare that begins in 1980 and ends in 1985. She would contribute five person-year observations. The first one corresponds to 1980, her first year of receipt, and would show that (1) the spell did not end in 1980, (2) the given year is 1980, (3) the spell began in 1980, (4) this is her first year in that spell, and (5) her demographic and state economic characteristics. The 1985 person-year would show that (1) the spell did indeed end in this (1985) year. (2) the given year is 1985, (3) the spell began in 1980, (4) this is her fifth year in that spell, and (5) her demographic and state economic characteristics.
67. We settled on this particular form for the interaction after considerable experimentation. An examination of interactions between the most recent cohorts and individual-year durations revealed the greatest differences for durations of 3, 4, and 5 years. Because this variable was formed after a considerable degree of data mining, the statistical significance of its coefficient is overstated to some degree.
68. Our estimates of standard errors employ the Huber correction for clustering and come from the STATA program. In the case of the duration by time interaction, the simplerandom-sample standard error was .23 (instead of .39).
69. In the case of the duration and period (i.e., cohort effects) variables themselves, the coefficients come from two regressions that include each set of variables separately. In the case of variables, such as region and age, that are represented by sets of variables, the entire set of variables was included in the "bivariate regression."
70. We experimented with models that included measures of the events associated with the beginning of the given welfare spell. As expected, the "bivariate" version of these models reflected the patterns displayed in the survival curves of fig. 4, with births to unmarried women having the biggest (in this case negative) effect on the chance of exiting from welfare. In models that included both the events and our demographic measures, the latter proved much more important, with the indicator of never-married status proving considerably more powerful than out-of-wedlock births in predicting longer spell durations.
71. Bane and Ellwood, Welfare Realities (n. 4 above), p. 54.