Low Income (Poverty) Dynamics in Canada: Entry, Exit, Spell Durations, and Total Time - June 2000

6. The Hazard Models: Duration Effects

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6.1 Introduction

In this section, a hazard model framework is employed to estimate the rates at which individuals i) exit current low income spells on a year-by-year basis from the point of entry, and ii) re-enter another spell of low income after a previous exit. These models thus permit the estimation of the underlying duration effects ? the relationship between the amount of time already spent in (or out of) low income and the probability of exiting (or re-entering) in a given year ? which comprise interesting, important, and policy relevant aspects of the low income dynamic. (See the box for more details regarding the structure of these models.)

The findings are again presented in the more accessible probability framework and only the baseline probability, duration term, and year effects are shown here, as the results for the other variables generally resemble those for the annual entry and exit models seen above. (See the appendix for the more complete set of findings and the full regression model parameter estimates.)

6.2 The Hazard Exit Models

The samples used in the hazard models differ from those employed in the annual exit models seen above in that only observations for which the start of the low income spell is observed are included (see the box). In particular, individuals who were continually in low income over the sample period are excluded from the estimation samples.²⁴ As a result, the baseline exit probabilities reported in Table 9a are considerably higher than those shown for the annual exit models seen above since the most chronically poor are excluded. Both sets of results are meaningful and simply represent different perspectives of the low income exit dynamic: the hazard model results represent the probability of leaving low income at each point in time over a given spell for a representative sample of low income spells (as generated by the selection procedure of selecting all observations related to spells observed to begin over the 1992-96 period in question), while the annual models seen above represent the exit rates for the representative "stock" of individuals in low income in a given year. Such reasoning applies to the other parameter estimates of the models as well.

The key duration terms generated by the hazard exit models indicate how the probability of exiting low income shifts with the number of years already spent in that state. The results indicate that the probability of exiting low income in a given year declines substantially with the length of time the person has already spent in that state, the probabilities declining 16-27 percentage points after four years across the various groups. The rate at which individuals exit low income falls between 40 and 57 percent relative to the baseline rates (representing spells which have lasted just one year) ? large effects by any standard.²⁵

Table 9a: Probability Effects for the Hazard Exit Models, Selected Results (%)

	Men				Women
	Single	Attached with Children	Attached no Children	Lone Parent	Single	Attached with Children	Attached no Children	Lone Parent
Base Line Probability	34.22**	48.78	43.79**	38.22**	34.33**	53.20**	54.85**	41.96**
Duration (One Year)
Two Years	-11.20**	-13.89**	-12.43**	-11.50**	-11.73**	-13.84**	-14.94**	-12.10**
Three Years	-15.79**	-19.93**	-14.99**	-18.11**	-17.05**	-21.07**	-21.12**	-17.74**
Four Years	-16.70**	-21.10**	-19.50**	-18.40**	-19.42**	-21.05**	-26.57**	-17.76**
Year (1992)
1993	2.71**	2.00**	0.49	4.68	2.21**	-0.28	1.32	-2.80**
1994	1.50	-2.54**	11.43**	-3.88	3.20**	-2.74**	1.61	-6.75**
1995	-1.81*	-2.35**	3.53**	-6.59*	-1.41	-4.49**	-2.81*	-10.46**
* Significance at the .05 level ** Significance at the .01 level ~~ The coefficient had to be suppressed to alleviate convergence problems.

The fact that the magnitudes of the duration effects are roughly the same across the various models implies that the rate of exiting low income drops off to a similar degree over the course of a given spell for the different age-family type groups ? an interesting and important (policy relevant) finding. It also means that exit rates do not generally "cross": the groups which have higher (or lower) rates of exiting poverty after one year generally have higher (or lower) exit rates after a greater number of years as well.

The specific shapes of the duration effects are also interesting, with the hazard rates generally declining quite steeply at first, but then largely flattening out by the final year, suggesting that the probability of exiting poverty declines most rapidly over the first few years of a spell after, which it remains at a more or less constant annual rate. The five years of LAD data used here thus appear to provide a good indication of the full shape of the relevant hazard profiles over time ? a fortunate outcome in analytical terms.

For example, after four years spent in low income, single mothers (who remained such) would be predicted to have an approximately one-in-four chance of exiting low income in any given year (given the other baseline characteristics in the models) ? as opposed, for example, to the greater than one-in-two chance of exiting low income for married women with children (and an even slightly higher rate for those without children). In the former case, 44 percent of those who remained single mothers would be expected to be still in low income after an additional three years, versus just 10 percent of those who remained married with children.²⁶

From a policy perspective, these findings suggest that a given low income spell is likely to either end quite quickly or, once it has lasted a few years, to continue for a relatively longer period of time. (This is especially true for individuals from certain provinces and with certain other "low exit rate characteristics" as broadly indicated by the annual exit model results seen above or more precisely in the complete hazard model results reported in Finnie [2000]). Predictions of the amount of (future) time an individual is likely to spend in low income could thus be usefully based on the elapsed time of the current spell (along with other personal and situational attributes.) ^{27, 28}

The year effects largely correspond to those already seen for the annual exit models except that the exit rates drop off more sharply for single mothers ? 10.5 points on a baseline of 42, a decline of a full 25 percent over the short period from 1993 through 1996. Put another way, the expected length of a given poverty spell increased especially sharply for single mothers entering that state over the 1992-96 period.

6.3 The Re-Entry Models

Table 9b shows the baseline probability, duration, and year effects for the hazard re-entry models. As with the exit models, the baseline rates differ substantially from those of the annual entry rate models seen previously, and again primarily due to the differences in the samples used in the two approaches. More specifically, the re-entry rates seen here are much higher than the more general entry rates seen above, reflecting the fact that those who have already experienced a low income spell over the period covered by the data are more likely to begin another spell than is the general population of non-poor individuals in a given year.

The extent of these baseline differences is in fact itself interesting, as it begins to give us an idea of the importance of "occurrence dependence" (as opposed to the duration dependence focused on in these hazard specifications) ? a topic which is pursued further below. Thus, the annual entry models previously seen had baseline rates ranging from under 2 percent to around 8 percent, whereas the hazard specifications seen here generate rates which vary between 18 and 36 percent. In short, entering low income in a given year is at least several times more likely for individuals who have just completed a spell than for the general population ? which might provide a useful guide as to where "anti-entry" policies should be targeted.

Table 9b: Probability Effects for the Hazard Re-Entry Models, Selected Results (%)

	Men				Women
	Single	Attached with Children	Attached no Children	Lone Parent	Single	Attached with Children	Attached no Children	Lone Parent
Base Line Probability	26.61**	20.28**	21.89**	36.17**	24.79**	18.56**	16.33**	27.83**
Duration (One Year)
Two Years	-10.11**	-7.88**	-8.36**	-7.47**	-10.33**	-7.45**	-6.57**	-8.92**
Three Years	-13.24**	-11.46**	-11.86**	-12.30**	-14.58**	-10.16**	-9.28**	-11.45**
Year (1992)
1994	3.26**	2.43**	-3.93**	0.20	1.78*	2.91**	1.62*	12.17**
1995	3.33**	1.55**	-3.02**	1.39	3.78**	2.04**	2.58**	8.99**
* Significance at the .05 level ** Significance at the .01 level ~~ The coefficient was suppressed to alleviate convergence problems.

As with the exit models, the duration terms are strong, here indicating that the rate of re-entering low income declines significantly with the number of years spent out of that state after a previous spell. More specifically, comparisons of the baseline rates (which implicitly represent individuals who have been out of poverty just one year) to those which obtain after three full years spent out of low income indicate that re-entry rates drop between 41 and 59 percent (in relative terms) across the different groups. Also of interest is that the greatest declines again come initially, although the hazard rates still fall to a significant degree from two to three years, suggesting that further declines might be observed were the data more extended.²⁹

One important policy implication of these results is that efforts directed at helping individuals who have recently escaped low income from falling back into that state might have quite early and long-term benefits, since if such individuals could be helped through the first few years, the likelihood of re-entering would appear to then decline substantially. If, on the other hand, the estimated duration effects largely reflect unobserved heterogeneity (see previous discussions of this issue), any interventions would likely have to be of a more fundamental and sustained nature, such as improving individuals' labour market skills, providing child care, changing attitudes (providing hope and motivation), and so on.

Also of some policy relevance is that regardless of what the underlying factors might be, there are ? unlike the exit models ? some notable differences in the extent of the declines of the hazard rates by family type, with single parents (especially males) declining the least, and these smaller declines coming on top of baseline re-entry rates which are already the highest. Any assistance aimed at preventing re-entry into poverty offered would, therefore, appear to be required over different periods of time (and perhaps be of a different nature) for different groups of individuals.

Finally, the calendar year variables are almost all statistically significant and, in some cases, quite strong (attached females with no children are the only clear exception), and point to significant increases in the probability of re-entering low income over the period covered by the analysis for most groups. These shifts presumably reflect the cut-backs in social assistance, unemployment insurance, and other social programmes implemented by provincial and federal governments over these years, while also indicating that the underlying economic recovery did not extend to those individuals most at risk of (re-)entering poverty.

The shifts vary in magnitude, but are as great as around 10 percentage points for single mothers, thus representing relative increases of as much as 44 percent (for the 1994-95 period) in relative terms as compared to the baseline hazard rates for this group (representing the 1993-94 period). Not only, therefore, did given spells of low income increase in expected length over this period (as seen in the exit models just above), but so too did the probability of re-entering a subsequent spell. In short, escaping poverty and then remaining out of that state on any sort of longer-term basis became less common over this short period ? obviously a very worrying trend.

• ²³This general approach is used by Huff-Stevens [1994, 1995] to analyse poverty dynamics, by Gunderson and Melino [1990] to model strike durations, and by Ham and Rae [1987] to analyse jobless durations, while Keifer [1990] shows that the likelihood function for this model corresponds to that of the standard logit model specification.
• ²⁴In technical terms, such spells are "left-censored" and cannot be included because the critical duration terms cannot be identified. Observations associated with "right-censored" spells are, in contrast, included in the estimation up to the relevant point. All this is standard with the hazard model approach.
• ²⁵More specifically, the probability of exiting low income in a given year falls from a baseline rate of 34.2 percent to 17.5 percent after four years in the case of single men (holding other factors constant), from 48.8 to 27.7 percent for attached men with children, from 43.8 to 24.3 percent for attached men with no children, and from 38.2 to 19.2 percent for single fathers. For women, the results are qualitatively similar, with exit rates falling from 34.3 percent to 14.9 percent for singles, from 53.2 to 32.1 percent for those attached with children, from 54.9 to 28.3 percent for those attached without children, and from 42.0 to 24.2 percent for single mothers. The declines in the exit rates after four years are, therefore, in percentage terms: 49.3, 43.2, 44.5, and 48.2 percent for the four male groups (in order), and 56.5, 39.7, 48.5, and 42.4 percent for the female groups.
• ²⁶These calculations represent the relevant survivor rates assuming that the exit rates remain at their four year levels after that point in time ? a not unreasonable assumption given the observed flattening of the hazard profiles seen above.
• ²⁷The points regarding the contribution of unobserved heterogeneity versus "pure" duration effects to the observed patterns made in the relevant box earlier apply here as well.
• ²⁸This is not to simply state the trivially obvious notion that longer spells can be identified after the fact, but to say rather that the elapsed length of a spell can help predict how much longer it is likely to last from a given point in time. In particular, for a given set of personal characteristics, individuals who have already spent a number of years in low income would be expected to spend more additional years in low income than someone who just started a spell. One could, at the same time, of course condition such predictions on other individual characteristics ?including those represented in the model, which could be used precisely for such predictive purposes.
• ²⁹One less duration year is available for the re-entry models relative to the exit models due to the fact that the first year of exiting low income covered in these samples is the 1992-93 period, whereas entries into low income from 1991 to 1992 were included due to the fact that such individuals would almost certainly have done so even were social assistance income better reported in the earlier year (for obvious reasons), whereas the same could not be said about exits from 1991 to 1992 (a year in which social assistance income reporting improved in the LAD).