A discrete-time multivariate hazard model is used to analyze events that trigger individuals’ entries into and exits from poverty. A hazard model simply provides information about the likelihood (i.e., probability) of experiencing an event at time t (e.g., exiting poverty) given that the event has not occurred prior to time t (e.g., the person is in poverty in the period prior to t, t-1).(15) Our multivariate hazard model allows the probability of experiencing an event at time t (e.g., exiting poverty) to depend on a set of explanatory variables, which includes among other characteristics, age, race, gender, and educational attainment, as well as the trigger events. This multivariate framework allows us to determine the relative importance of multiple events in poverty transitions, something that cannot be learned from a descriptive analysis. Separate poverty entry and exit equations are estimated.
Our discrete-time hazard model assumes that the probability of entering (or exiting) poverty in a given period (e.g., year) is represented by a logit specification.(16) The logit specification is popular as it is very tractable and restricts the transition probabilities to lie between zero and one (Allison 1984). Several studies of poverty dynamics have used the logit specification (Stevens 1994 and 1999, Iceland 1997b). With this assumption, the probability of entering (or exiting) poverty for person i at time t can be written as:
In this model, the vector T represents transition events, the primary focus of this analysis, and the vector X represents control variables.(17) The transition and control variables are based on our conceptual model. Our model of poverty entries includes the following transition events: (1) child under age six enters household, (2) two-adult household becomes female-headed household,(18) (3) young adult (under age 25) sets up own household, (4) loss of employment (of head, spouse, and other household members)—measured as a change from positive to zero hours work (PSID) and from with job to no job (SIPP), (5) nondisabled household head becomes disabled, and (6) weakening economy (change in state unemployment rate and change in GDP).
Our model of poverty exits include similar, although slightly different transition events: (1) female-headed household becomes two-adult household, (2) gain in employment (of head, spouse, and other household members)—measured as a change from zero to positive hours work (PSID) and from no job to with job (SIPP), (3) disabled household head becomes nondisabled, (4) household head receives high school degree, (5) household head receives advanced degree (associates degree or higher), and (6) strengthening economy (change in state unemployment rate and change in GDP). Because some of these events are choice variables (and thus potentially endogenous), this model does not necessarily identify causal relationships. Instead, it measures conditional relationships—the relationship after controlling for other events and characteristics.
An important issue is the extent to which events that occur in earlier periods are allowed to affect transitions in the current period. That is, to what extent lags enter the model. An immediate fall in income, say due to the loss of a job, may not cause a household to instantly fall below the poverty threshold if it is eligible for unemployment insurance. A household may fall below the poverty threshold only when unemployment insurance benefits run out. Similarly, a young adult who sets up her/his own household may only fall into poverty after private transfers from parents stop; and a change in educational attainment may only help an individual out of poverty after she/he obtains a higher paying job. Based on this theory of the timing between events and a poverty transition, we allow lags to enter the model for up to one year. In the yearly PSID data, we include a measure of the event at time t and a one year lag (t-1). In the monthly SIPP data, we include the event at time t and four quarterly lags.
Control variables include characteristics of the household head (age, race, and educational attainment), household (female-headed household, single male-headed household, number of adults 18-61, number of children), geographic characteristics (region and MSA), economic indicators (state unemployment rate and GDP), poverty spell information (observed duration of current spell at time t, observed number of prior spells, left censored spell identifier), and year identifiers.
Control variables that are tied to the event variables, such as female-headed household, are defined so that the event variable captures the full effect of the event. Using female-headed household as an example, three categories are created such that the first category captures the event at time t, the second category captures the event at time t-1 (lagged one period), and the third category captures the control (or level) variable: (1) female-headed household at time t and became female-headed at t (i.e., between t-1 and t); (2) female-headed household at time t and became female-headed at t-1 (i.e., between t-2 and t-1); and (3) female-headed household at time t and became female-headed prior to time t-1. To capture all possible household combinations at time t, single male-headed household at time t is included as a control variable, leaving two-adult household at time t as the omitted variable. In this example, the third variable (female-headed household at time t and became female-headed prior to time t-1) provides information about how living in a female-headed household for two or more years affects the probability of entering and exiting poverty relative to living in a two-adult household. The following six control variables are defined with their interaction with the event variable in mind: (1) female-headed household for two or more years; (2) number of adults 18-61 in the household, less the head and wife; (3) number of children in the household less those who enter at time t and t-1; (4) graduated from high school two or more years ago; and (5) received an associates degree or higher two or more years ago.(19)
Our analysis with PSID data further examines whether the events that trigger entries and exits differ for persons in long versus short poverty spells. It may be the case that changes in household composition, such as a shift from a two-adult to a female-headed household, result in long spells of poverty, whereas changes in employment cause only short poverty spells. We define a "long" poverty spell as one that has lasted four or more years and a "short" poverty spell as one that has lasted less than four years. We estimate separate models for short and long poverty spells.