Profiles and Transitions of Groups at Risk of Social Exclusion: Lone Parents

8. Low Income Spells

8.1 Introduction

One of the main interests of the study is to understand why some lone mothers have longer low income spells than others. The expectation is that such an understanding may help develop better policies for shortening low income spells.

Analysis of spells is complex, both conceptually and in terms of the required estimation techniques. Conceptually, there are two types of spell measures: in progress spells and completed spells. The difference can be best illustrated with a simple arithmetic example (Box C).

Box C: In-progress vs. Completed Spells

An Illustrative Example:

Let us consider the following purely hypothetical situation. Suppose over the six year period 1993-98, a lone mother was in low income from 1994 to 1997, while four other lone mothers were in low income only in a single year, each in a different year over the period 1994-97. From this example, we can calculate two different low income spells:

If we examine a single year, say 1994, then we find two low income lone mothers: one with a spell of four years and another one with a spell of one year. We can conclude from this that the average low income spell was: (4+1)/2=2.5 years.
But if we take into account all the low income spells that started during the period, then we can conclude that the average low income spell was: (4+1+1+1+1)/5=1.6 years.

Applying the Two Concepts to the SLID Data:

The first type of measure presented above corresponds to the following question: "How many years did the average low income lone mother in 1993 remain in low income without interruption?" As we will see later in this section, the answer is 3.4 years. In fact, the average low income spell was likely longer, since some spells may have started before 1993, or ended after 1998.
The second type of measure corresponds to the following question: "When a new low income spells starts, how long is it expected to last on average?" As we will see later in this section, the answer is 2.2 years. The estimates for the two measures correspond only notionally to the figures presented in the hypothetical example above.

The most intuitive way to explain the difference between the two measures is the following one: most low income spells are short, while a smaller number of low income spells last for many years. Since the long-term low income appear in the statistics for many years, in any given year one finds a disproportionate number of this group.

8.2 Methodology

The main analytical challenge of this section is the small size of the sample. In what follows, we provide a simplified explanation of the two methodologies, and their strengths and weaknesses.

(a) OLS analysis of in-progress spells

In-progress spells were measured by selecting first everybody who was in low income in 1993 and measuring the length of their uninterrupted low income spell over the period 1993-98. In-progress spells were analyzed in two ways: (i) using a simple cross-tabulation; and (ii) using an OLS regression, where the dependent variable was the duration of the in-progress spell of low income. The three main limitations of this technique are:

the independent variables do not change during the duration of the spell and, as a result, the OLS model captures mostly the impact of the characteristics at the start of the in-progress spell;
in-progress spells are a proxy of the length of completed spells, since some spells may have started before 1993, or ended after 1998; and
the results are valid only to the extent that the length of spells outside the observed period are, on average, proportional to the duration of spells during the observed period.

(b) "Hazard" analysis of low income spells

A more commonly used technique in the literature is to estimate the duration of low income spells indirectly, by first estimating exit rates (also referred to as "hazard" rates, because of the medical origin of this technique). By knowing the probability of exiting low income after one, two, or more years, we can estimate the expected average (or more commonly the median) duration of a low income spell.

The unit of analysis of this technique is not the individual, but low income transitions. For example, someone who became low income in 1994 and exited low income in 1998 has four transitions (three from low income to low income; and one from low income to non-low income).

"Hazard" analysis is the only way of estimating the expected duration of new spells. A strength of the technique is that all independent variables can be specified to be time-dependent meaning that they can change every year, as long as the individual stays in low income.

The main limitation of this technique is that we assume that those individuals who had a completed spell during the period are representative of: (a) those with censored spells (i.e. those who were still in low income in 1998); and (b) those who were excluded from the analysis because their low income spell started before 1993. This is an important concern, particularly with the second assumption, since one-quarter of the observations were excluded because they were in low income throughout the period, while an additional significant part was excluded because they did not start a new low income spell during the period.

In what follows, we present the results of both types of analysis. Despite the various limitations, they provide an insight into the factors likely to be associated with longer low income spells.

8.3 Analysis of In-progress Low Income Spells

According to the OLS methodology, the three characteristics most closely associated with longer low income spells were: no change in lone motherhood status; presence of pre-school age children; and being a student or a high school dropout. Also, low income spells tended to be longer in Quebec and the Prairie region.

The average in-progress low income spell of lone mothers in the period 1993-98 was 3.4 years. This is the average length of uninterrupted low income spells of those who were in low income in 1993, regardless of how long they had already been in low income before 1993. Table 8.1 shows that the longest durations are observed among:

those whose family situation did not change (i.e. remained lone mothers and the major income recipient through the entire period); and
residents of Quebec (and regions with below average employment rates).

The effect of various personal characteristics on low income spells is explored more systematically using an OLS regression (Table 8.2). The dependent variable of the regression equation is the in-progress low income spell of those who were in low income in 1993. The independent variables consist of several dummy variables representing various personal characteristics.

The OLS regression results generally confirm the results of the cross-tabulation:

Change in family status: The event that had the strongest impact on low income spells was a change in family status (i.e. forming a union; someone else becoming the main income recipient; or the youngest child reaching age 18). The low income spells of lone mothers who experienced a change in family status were on average 2.1 years shorter. Over the period 1993-98, 55% of low income lone mothers experienced a change in family status.
Region: We also found that there is statistically significant variation in low income spells by region. For example, living in Ontario compared to Quebec adds 1.7 years to the low income spell.
The OLS regression results also show that pre-school age kids also contribute to longer low income spells, although the coefficient was just over the significance threshold.

The rest of the factors tested through the OLS regression do not appear to have a statistically significant effect on the length of in-progress low income spells.

Table 8.1 Incidence and duration of low income by personal characteristics. Among lone mothers with children under 18 yrs of age in 1993
	All lone mothers	Low income in at least one year in 1993-98		Low income in 1993
	All lone mothers	Number of low income	Incidence of low income	Number of low income	In-progress low income spell
*Age in 1993*
16-29	138,344	110,546	80%	89,951	3.1
30-55	396,645	210,492	53%	145,663	3.5
*Age of youngest child in 1993*
0-5	225,181	171,410	76%	132,839	3.4
6-11	149,247	74,278	50%	54,090	3.4
12-17	160,560	75,349	47%	48,685	3.3
*Student in 1993*
Yes	76,156	64,581	85%	52,738	3.7
No	455,918	255,907	56%	182,327	3.3
*Education of non-students in 1993*
Less than high school	109,026	92,971	85%	70,201	3.7
High school diploma	84,839	57,979	68%	48,662	3.3
Some post-secondary	65,361	36,903	56%	***	***
Post-secondary degree	196,692	68,054	35%	42,996	2.9
*Immigrant, aboriginal, or disabled*
Yes	108,633	86,801	80%	55,609	3.4
No	426,355	234,237	55%	180,005	3.4
*Family status*
There was a change in 1993-98	315,699	183,874	58%	128,980	2.6
There was no change in 1993-98	219,289	137,163	63%	106,634	4.4
*Moved to another region after 1993*
Yes	66,114	39,797	60%	32,700	2.9
No	468,874	281,240	60%	202,914	3.4
*EI regional employment rate in 1993*
At/below average	207,125	123,079	59%	90,919	3.9
Above average	327,863	197,958	60%	144,694	3.1
*Broad region in 1993*
Atlantic	44,042	30,682	70%	24,529	3.4
Quebec	123,228	75,370	61%	59,192	4.4
Ontario	214,024	131,655	62%	90,022	2.9
Prairie	90,359	55,406	61%	46,275	3.3
B.C.	63,334	***	***	***	***
*All*	*534,988*	*321,038*	*60%*	*235,614*	*3.4*
(1) Immigrated in last 10 years; or aboriginal origin; or work limiting disability. *** Less than 30 observations.

Table 8.2 OLS analysis of in-progress low income spells, 1993-98, among low income lone mothers with children under 18 yrs of age in 1993
Variable	Explanation	B-coef	Std err	t-stat.
*Dependent*
SPELL93	Uninterrupted low income spell of low income in 1993
*Age in 1993*
GAGE93(1)	- 16-29	-0.190	0.292	-0.651
GAGE93(2)	- 30-55 (omitted)
*Age of youngest child in 1993*
YKID93(1)	- 0-5	0.640	0.317	2.018
YKID93(2)	- 6-11 (omitted)
YKID93(3)	- 12-17	0.693	0.375	1.849
*Level of education in 1993*
STEDUC(1)	- student	0.024	0.347	0.069
STEDUC(2)	- non-student: less than high school	0.396	0.339	1.170
STEDUC(3)	- non-student: high school diploma (omitted)
STEDUC(4)	- non-student: some post-second.	-0.937	0.464	-2.022
STEDUC(5)	- non-student: post-sec. degree	-0.748	0.392	-1.910
*Recent immigrant, aboriginal, or disability in 1993*
HIGHRISK(1)	- yes	-0.097	0.279	-0.347
HIGHRISK(2)	- no (omitted)
*Lone mother/major earner/child under 18 in all years*
FAMILYF(1)	- there was a change	-2.070	0.253	-8.189
FAMILYF(2)	- there was no change (omitted)
*Moved to another region after 1993*
FEIR(1)	- yes	0.142	0.332	0.426
FEIR(2)	- no (omitted)
*Broad Region*
REGION(1)	- Atlantic	0.659	0.381	1.732
REGION(2)	- Quebec	1.703	0.304	5.594
REGION(3)	- Ontario (omitted)
REGION(4)	- Prairie	1.092	0.331	3.299
REGION(5)	- B.C.	-0.684	0.466	-1.466
*Constant*		3.508	0.378	9.281
Adjusted R-squared Number of cases			34.6% 234

8.4 "Hazard" Analysis of Low Income Spells

According to the "hazard" methodology, the three characteristics most closely associated with longer low income spells were: no change in lone motherhood status; being in one of the three high risk categories (recent immigrant; aboriginal; disabled); and being a high school dropout or having some post-secondary education.

The results of the "hazard" analysis, summarized in Table 8.3, show that:

Each new low income spell is expected to last, on average, about 2.2 years; this estimate is considerably lower than the average in-progress low income spell (for the reasons given in Box C).
One interesting finding is that low income exit rates ("hazard" rates) decline over time. Thus while about one-third of the low income exit low income after one year, the rate declines to 7% after six years in low income.

The above results indicate that most low income spells are short, but those who do not exit low income soon stay on for many years, which also explains the discrepancy between the two measures of low income spells.

Exit rates may decline over time for at least two reasons: (a) those with better employment options tend to exit soon; and (b) those who stay in low income for longer periods see their employment skills deteriorate, which makes it even more difficult to escape low income.

From the policy point of view, the key is to be able to identify which characteristics are at high risk of prolonged low income and develop programs that reach these groups as early as possible, thus avoiding the "scarring" effect of prolonged low income on the ability of individuals to escape from low income.

The "hazard" results help identify some of the factors associated with a higher risk of prolonged low income. The most significant negative factors are:

No change in family status: For example, the average low income spell of those who remained lone mothers was 6.1 years, compared to one year for those who changed their status (either through the formation of a union, or someone else becoming the main income recipient). This result is also confirmed by the OLS results.
High school dropout or incomplete post-secondary education: High school dropouts have the longest expected low income spells (8.8 years) a result also supported by the OLS results.⁹ Interestingly enough, those with incomplete post-secondary education also tend to stay longer in low income (5.4 years). However, this result is not supported by the OLS results.
High risk characteristics: Recent immigrant, disabled and aboriginal lone mothers are also at risk of staying in low income for an extended period (4 years vs. 1.8 years for those without other high risk characteristics). This result was not confirmed by the OLS analysis. The most likely reason is that one important high risk characteristics (disability) is fairly volatile over time. It would appear that, because the OLS model does not include time-dependent variables, it failed to capture the importance of this variable.

The results with respect to region were not statistically significant. This does not necessarily contradict the OLS results. The most likely explanation is that the coefficients were not significant because of large sample variability, due to the small size of the sample.

Finally, the presence of young kids did not have a significant effect on low income spells. As was pointed out earlier, the OLS results in this case were just above the significance threshold. Therefore there is no major discrepancy between the two methods.

Box D: Estimation of Spell Durations
The length of low income spells is calculated indirectly from estimates of low income exit rates. Exit rates are in turn estimated using the logit regression in Table 8.3. The logit transformation of the exit rate is specified to be a linear function of time and several other variables. Based on this relationship, we can estimate the exit rate after one year, two years, and so forth. In fact, we can estimate exit rates past the six year period covered by SLID (by simply inserting the year in the logit regression). Having estimated exit rates for the next several years, we can then calculated how long it would take for half of the people to exit low income (i.e. calculate what is the median spell duration). Thus in Table 8.3, 31.9% exit after the first year. Of the remaining 68.1% of low income lone mothers, 24.2% exit after the second year. This means that after two years, 31.9% + 68.1% x 24.2% = 48.3% of low income lone mothers have exited low income. The median, which is 2.2 years, was calculated using linear interpolation (since, only by coincidence, exactly 50% of lone mothers would have exited low income after a certain number of years).

Table 8.3 "Hazard" analysis of low income spells, 1993-98
In all cases, the regression variables reflect the status at the end of each spell (time dependent)	Logit coeff.	Stand. error	t- stat	Exit rates by duration of poverty (yrs)						Median spell
	Logit coeff.	Stand. error	t- stat	1	2	3	4	5	6	Median spell
*Dependent variable: probability of exiting poverty*
*Change in lone motherhood status*
there was no change in status	-2.050	0.261	-7.854	21.0%	15.3%	10.9%	7.7%	5.4%	3.7%	6.1
status changed (omitted)				67.3%	58.4%	48.8%	39.4%	30.6%	23.1%	1.0
*Was recent immigrant; disabled; aboriginal*
yes	-0.576	0.266	-2.165	23.8%	17.5%	12.6%	9.0%	6.3%	4.4%	4.0
no (omitted)				35.7%	27.4%	20.5%	14.9%	10.6%	7.5%	1.8
*Age of lone mother*
16-29	0.874	0.284	3.077	46.3%	37.0%	28.5%	21.4%	15.6%	11.2%	1.2
30-55 (omitted)				26.5%	19.7%	14.3%	10.2%	7.2%	5.0%	3.1
*Age of youngest child*
0-5	-0.228	0.273	-0.835	28.9%	21.7%	15.8%	11.3%	8.0%	5.6%	2.6
6-17 (omitted)				33.8%	25.8%	19.1%	13.8%	9.9%	6.9%	2.0
*Level of education*
student	-1.013	0.460	-2.202	35.0%	26.8%	19.9%	14.5%	10.3%	7.3%	1.9
non-student: less than high school	-1.796	0.427	-4.206	19.7%	14.3%	10.2%	7.2%	5.0%	3.5%	8.8
non-student: high school diploma (omitted)				59.7%	50.2%	40.7%	31.8%	24.1%	17.8%	1.0
non-student: some post-second.	-1.681	0.451	-3.727	21.6%	15.8%	11.3%	8.0%	5.6%	3.9%	5.4
non-student: post-sec. degree	-0.385	0.410	-0.939	50.2%	40.7%	31.8%	24.1%	17.8%	12.8%	1.0
*Region*
Atlantic	-0.199	0.383	-0.520	28.4%	21.3%	15.5%	11.1%	7.8%	5.5%	2.7
Quebec	-0.142	0.293	-0.485	29.6%	22.3%	16.3%	11.7%	8.3%	5.8%	2.5
Ontario (omitted)				32.7%	24.8%	18.3%	13.3%	9.4%	6.6%	2.1
Prairie	0.038	0.366	0.104	33.5%	25.5%	18.9%	13.7%	9.7%	6.8%	2.0
B.C.	0.311	0.418	0.744	39.8%	31.0%	23.5%	17.3%	12.4%	8.8%	1.5
*Spell duration in years (continuous independent)*	-0.385	0.140	-2.750
*Constant*	2.275	0.512	4.443
*Estimates for average lone mother*				31.9%	24.2%	17.9%	12.9%	9.1%	6.4%	2.2
Nagelkerke R² (similar concept to the OLS adjusted R²):		31.0%		Number of cases:			510

⁹See Box D below for an explanation of how it is possible for the estimated duration of spells to be longer than the period of analysis.