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

4. Cross-Sectional Profile of Low Income

4.1 Introduction

This section presents the income and low income profile of lone parents, based on the 1998 cross-sectional SLID data. We have chosen 1998 as the year of analysis because it is the most recent year of the 1993-98 longitudinal panel.

As mentioned above, the sample is restricted to main income recipients age 16 to 55 in 1998 and all results refer to the main income recipient of the economic family. The main focus of the analysis is lone parents with children under 18 years of age. Lone parents are compared to the main income recipients of other family types in the same age group (16 to 55 in 1998).

4.2 Incidence of Low Income

Lone mothers have the highest incidence of low income of any family type. In 1998, 39% of them had incomes below the Statistics Canada post-tax Low Income Cut-Offs (LICO).

The most basic indicator of low income is the incidence of low income, most often defined as the percentage of families whose income fall below the Statistics Canada after tax Low-Income Cut-Off lines (LICO). Table 4.1 provides estimates of the incidence of low income by family type. It also provides the actual sample size by family type so that the reader gets a better sense of the precision of the estimates.

Table 4.1 shows that in 1998, 11.3% of all families were in low income. In particular:

the incidence of low income was highest among lone mothers (39.1%), who accounted for more than one-third of all low income families of two persons or more;
the incidence of low income among lone fathers is similar to the national average (16.7%); however, compared to male main income recipients in couples with children, their incidence of low income is three times as high.

In fact, in relative terms, the incidence of low income among both male and female lone parents is roughly three times the corresponding rate for male and female main income recipients in couples with children (Chart 4.1).

Chart 4.1 Incidence of low income among all major income recipients, by family type and gender, 1998

Table 4.1 Annual incidence of low income among all major income recipients, 1998¹
	Lone parent, kids<18	Unattached individual	Couple without kids<18	Couple with kids<18	Other economic families	All economic families
*Male major income recipients*
All major income recipients	110,545	1,392,465	1,309,674	2,551,716	361,897	5,726,297
Low income major income recipients	18,506	400,738	45,288	149,940	35,069	649,541
Incidence of low income	16.7%	28.8%	3.5%	5.9%	9.7%	11.3%
Low income gap before transfers	77.7%	68.4%	66.5%	64.4%	61.8%	67.2%
Low income gap after transfers	36.9%	41.7%	36.2%	24.6%	35.5%	36.9%
*Female major income recipients*
All major income recipients	630,731	995,847	548,226	682,179	268,630	3,125,613
Low income major income recipients	246,407	349,879	41,682	85,805	45,745	769,518
Incidence of low income	39.1%	35.1%	7.6%	12.6%	17.0%	24.6%
Low income gap before transfers	82.5%	67.5%	61.8%	65.5%	75.6%	72.2%
Low income gap after transfers	29.7%	43.4%	37.6%	28.7%	33.7%	36.5%
*All major income recipients*
All major income recipients	741,276	2,388,312	1,857,900	3,233,895	630,528	8,851,911
Low income major income recipients	264,913	750,617	86,970	235,745	80,813	1,419,059
Incidence of low income	35.7%	31.4%	4.7%	7.3%	12.8%	16.0%
Low income gap before transfers	82.2%	67.9%	64.3%	64.8%	69.6%	69.9%
Low income gap after transfers	30.2%	42.5%	36.9%	26.1%	34.5%	36.7%
*Sample size*
*Male major income recipients*
All major income recipients	296	3,335	3,621	6,337	847	14,436
Low income major income recipients	47	997	103	286	66	1,499
*Female major income recipients*
All major income recipients	1,425	2,379	1,337	1,789	587	7,517
Low income major income recipients	531	946	75	226	80	1,858
(1) Sample of major income recipients, age 16-55, in 1998.

4.3 Low Income Gap

Lone mothers have the largest pre-transfer low income gap of any type of low income family (83%); however, after government transfers their low income gap is one of the lowest (30%).

An indicator of the severity of low income among the low income is the low income gap. It is calculated as the difference between the total income of low income families and the low income line, expressed as a percent of the low income line.

Differences in the low income gap between different types of families are much smaller than differences in the incidence of low income. Chart 4.2 compares the low income gap before and after government transfers among low income families with children:

the low income gap before government transfers is large, particularly for lone mothers (83%);
government transfers reduce the low income gap significantly; in the case of lone mothers the gap is reduced to 30%.

These results suggest that government transfers have a fairly significant impact on reducing the severity of low income.

Chart 4.2 Low income gap among low income major income recipients with children, by family type and gender, 1998

4.4 Characteristics of Low Income Lone Mothers

An estimated 55% of low income lone mothers did not work for pay in 1998. In terms of demographics, the most common characteristics of low income lone mothers were: not being in a union when the first child was born (60%); having a pre-school age child (47%); and being a student (25%) or being a high school drop-out (28%).

This sub-section examines the characteristics of low income lone mothers. The reason we focus on low income lone mothers is because they account for 93% of all the low income lone parent families. However, tables for all lone parents are shown in Appendix A.³

(a) Work Effort

With respect to work effort (measured here in terms of annual hours of paid work) Table 4.2 shows that:

More than half of all low income lone mothers (55%) had no earnings at all during the year. This result suggests that a main policy concern is overcoming barriers to employment through, for example, reinforcing work incentives under social assistance, improving employment placement services, providing better access to daycare, and investing more in skills upgrading. Later on we probe in more detail the factors that may explain the weak attachment of low income lone mothers to the labour force.
At the other end of the work spectrum, about 12% of low income lone mothers worked 1,500 hours or more.⁴ The most obvious difficulty facing this group is low hourly earnings. The reasons behind low earnings are also probed below. The most obvious short term solution is earnings supplementation. However, a long-term solution would require further skills upgrading.
For most of the remaining approximately one-third of lone mothers, low income is the result of a combination of low hours of work and low hourly earnings. These low-income mothers likely experienced both employment barriers and low wages and are, therefore, possible candidates for both types of assistance listed above.

Table 4.2 Distribution and incidence of low income by selected characteristics, 1998. Lone mothers versus female major recipients of couples with children under 18
	Lone mothers			Female major recipients in couples with children under 18
	Distribution of all lone mothers	Distribution of low income lone mothers	Incidence of low income	Distribution of all major recipients	Distribut. of low income major recipients	Incidence of low income
*Age*
16-29	19.2%	30.1%	61.5%	10.4%	22.4%	27.0%
30-55	80.8%	69.9%	33.8%	89.6%	77.6%	10.9%
*Age when first child was born*
Under 20	18.4%	25.2%	52.9%	8.2%	23.8%	34.9%
20 or more	81.6%	74.8%	35.4%	91.8%	76.2%	10.0%
*Marital status when first child was born*
Not in a union	46.4%	60.4%	50.7%	9.0%	16.7%	20.0%
Married	49.6%	34.8%	27.3%	85.0%	83.3%	10.5%
Common law	4.0%	4.8%	46.7%	***	***	***
*Age of youngest child*
0-5	32.6%	46.8%	56.0%	41.0%	49.4%	15.2%
6-11	36.0%	36.4%	39.6%	35.0%	34.3%	12.3%
12-17	31.4%	16.8%	20.9%	24.0%	16.2%	8.5%
*Student during the year*
Yes	17.5%	25.3%	56.3%	***	***	***
No	82.5%	74.7%	35.4%	91.5%	100.0%	12.5%
*Level of education of non-students*
Less than high school	19.0%	28.3%	51.8%	11.6%	36.5%	34.3%
High school diploma	17.8%	15.4%	30.1%	***	***	***
Some post-secondary	15.1%	20.0%	46.0%	12.3%	27.9%	24.6%
Post-secondary degree	48.1%	36.3%	26.2%	59.0%	35.6%	6.6%
*Hours of work during the year*
No work	26.5%	54.8%	80.9%	9.2%	38.3%	51.7%
1-749 hours	12.5%	19.9%	62.2%	5.9%	17.3%	36.3%
750 -1499 hours	14.2%	13.2%	36.5%	12.8%	17.9%	17.3%
1500 + hours	46.9%	12.1%	10.1%	72.1%	26.6%	4.6%
*Immigrant, aboriginal, or disabled¹*
Yes	22.8%	30.1%	51.6%	16.0%	23.9%	18.7%
No	77.2%	69.9%	35.4%	84.0%	76.1%	11.4%
*EI region employment rate*
At, below average	41.0%	44.6%	42.5%	36.5%	44.3%	15.3%
Above average	59.0%	55.4%	36.7%	63.5%	55.7%	11.0%
*Broad region*
Atlantic	8.8%	11.8%	52.7%	8.1%	9.0%	13.9%
Quebec	25.7%	24.1%	36.5%	24.2%	29.7%	15.4%
Ontario	37.7%	38.2%	39.6%	39.5%	31.5%	10.0%
Prairie	15.5%	13.6%	34.4%	16.4%	22.2%	17.0%
B.C.	12.4%	12.3%	38.8%	***	***	***
All lone parents	100.0%	100.0%	39.1%	100.0%	100.0%	12.6%
(1) Immigrated in last 10 years; or aboriginal origin; or work limiting disability. *** Less than 30 observations

(b) Demographic Characteristics

With respect to demographic characteristics of low income lone mothers, Table 4.2 shows that:

Age: 30% of low income lone mothers were under 30 years of age. Younger lone mothers had twice as high an incidence of low income as older lone mothers (62% vs. 34%). However, regression analysis shows that to a large extent this difference reflects the correlation between age and the presence of pre-school age children, low education and student status.
Age when first child was born: About 25% of low income lone mothers were teenagers when they had their first child. This group also had a relatively higher incidence of low income in 1998 than the rest of lone mothers (53% vs. 35%).
Marital status when first child was born: The most common characteristic of low income lone mothers was that they were not in a union when their first child was born (60%). Their incidence of low income in 1998 was considerably higher than for the rest of lone mothers (51% vs. 29%).⁵
Age of youngest child: Almost half of low income lone mothers (47%) had a child under 6 years of age in 1998. The presence of pre-school age children has a strong association with the probability of being in low income. For example, the incidence of low income among lone mothers with children under 6 years of age was 2.5 times higher than that of lone mothers with the youngest child age 12 to 17 (56% vs. 21%).
Student status: One-quarter of all low income lone mothers were students in 1998. Their incidence of low income was higher than the rest of lone mothers. However, this group is perhaps of lesser concern, since one can assume that their long-term employment and income prospects will be better.
Level of Education: 28% of low income lone mothers who were not students were high school drop-outs. Their incidence of low income was 52%. However, although a higher level of education was associated with higher earnings and a lower chance of being in low income, higher education is no guarantee of averting low income. In fact, 36% of non-student low income lone mothers had a post-secondary degree.
Recent immigrant, aboriginal, or disabled: About 30% of low income lone mothers also belonged to at least one more group that has been identified as having a high risk of low income and social exclusion: recent immigrants; persons of aboriginal origin; or persons with a work-limiting disability. This group may present special policy challenges because of the confluence of additional negative factors.
Region: The incidence of low income was highest in the Atlantic region, a reflection of the relatively worse labour market conditions in that region. This conclusion is further reinforced by a comparison of low income rates between EI regions with a high employment rate and EI regions with a low employment rate.⁶

4.5 Multivariate Analysis of the Incidence of Low Income in 1998

Logit multivariate regression analysis shows that, in descending order of importance, the characteristics that are most likely to lead to low income are:

having a pre-school age child;
being a student;
being a high school drop-out;
living in the Atlantic region;
not being in a union when the first child was born;
being a recent immigrant, having a work-limiting disability, or being of aboriginal origin

(a) Logit Regression Methodology

The incidence of low income among lone mothers in 1998 was further probed using multivariate logit regression analysis. Logit regression, rather than the more common Ordinary Least Squares (OLS) regression, was used because the dependent variable takes only the values of 1 or zero. The results of the logit analysis are presented in Table 4.3.

The logit regression results are more difficult to interpret than the results of OLS regression. For the purpose of providing a more intuitive interpretation of the logit regression results, we also present a linear approximation of the logit coefficients. The linearized logit regressions have a similar interpretation to that of OLS regression coefficients and, in fact, in most cases the two are fairly close to each other. Box A provides a simple guide to interpreting the logit results, as well as an explanation of how the linearized logit coefficients were calculated.

The reader must be reminded that cross-tabulation estimates of the effect of various characteristics on the incidence of low income will generally differ from regression estimates. For example, according to Table 4.3 the incidence of low income among younger lone mothers is 27.7% higher than that of older lone mothers (61.5% - 33.8%). On the other hand, according to the logit regression results, the effect of younger age is to increase the incidence of low income by only 3.6%. What these results suggest is that the reason that younger lone mothers have a significantly higher incidence of low income is not age per sé, but other negative characteristics that are associated with younger age, such as a higher probability of being a student or presence of pre-school age children.

Box A: Interpreting Logit Regression Results
In this Box we provide a simplified guide to interpreting the logit results. We use the first line of the results in Table 4.4 as an example.

The b-coefficient is 0.155. The positive coefficient means that younger lone mothers are more likely to be in low income than older lone mothers (which in this case is the omitted or comparison group). It is difficult, however, to interpret the size of the coefficient, since the dependent variable is not the incidence of low income but the logit transformation of the incidence of low income. As a result, the b-coefficients do not have the same direct interpretation as OLS regression coefficients do.

The standard error is 0.187 and the t-statistic is 0.829 (where the latter is simply the ratio of the b-coefficient to the standard error). The t-statistic is used in the same fashion as with OLS meaning that if the t-statistic is greater than 1.96, then there is an at least 95% chance that the coefficient is not zero. In this instance, the coefficient is not significant. This means that the reason young lone mothers have a higher incidence of low income (as shown in Table 4.4) is due to the presence of other characteristics of young lone mothers such as, possibly, the presence of pre-school age children.

The odds ratio is 1.168. This means that the odds of being in low income are somewhat higher when a lone mother is under 30 years of age. If the ratio was 1, that would have meant that age has no effect. The odds are calculated by dividing the probability that something will happen, by the probability that it will not happen. The odds ratio is the ratio of the odds of a variable to that of the omitted variable, and it provides a more intuitive interpretation of the logit b-coefficients.

The linearized logit coefficient is 3.6%. The linearized logit coefficients are a linear approximation of the logit coefficients and have a similar meaning to that of OLS regression. In fact, typically the linearized logit coefficients are close to the OLS linear coefficients. In this particular example, the 3.6% linearized logit coefficient can be explained as follows: if we take lone mothers age 30 to 55 (i.e. the omitted category) and we only change their age group to 16 to 29, the probability of being in low income will increase by 3.6 percentage points.⁷

The Nagelkerke R ² is 21.1%. This indicator measures the goodness of the fit of the logit regression. It is comparable to the more familiar OLS adjusted R².

(b) Logit Regression Results

The regression results show that the most important contributing factors to low income are the following:

age of youngest child: appears to have the most important influence; for example, those with a pre-school age child have a 26% higher incidence than those with children age 12 to 17;⁸
student status: students have a 17% higher incidence of low income than non-students with high school education;
level of education: among non-students, high school dropouts have a 14% higher incidence of low income than those with high school education; interestingly enough, a post-secondary degree does not have a statistically significant effect; it would appear that, as far as avoiding low income is concerned, a high school level of education is sufficient;
region: also has a significant effect; for example, lone mothers in the Atlantic region have a 14% higher chance of being in low income, relative to Ontario (whose incidence of low income is average); the difference is even greater relative to the Prairie regions (which has the lowest incidence of low income);
marital status when first child was born: not being in a union when the first child is born raises the probability of being in low income by 12%; and
belonging to another high risk group: lone mothers who were also recent immigrants, had a work-limiting disability or were of aboriginal origin, had a 12% higher probability of being in low income.

The current age of the lone mother or her age when the first child was born did not have a statistically significant effect on the probability of being in low income.

Table 4.4 Logit regression estimate of determinants of incidence of low income among lone mothers with children under 18, 1998
Variable	Explanation	b-coef	Std err	t-stat.	Odds ratio	Linearized coefficient
Dependent
LICOFA27	1998 income < LICO
*Age*
GAGE(1)	- 16-29	0.155	0.187	0.829	1.168	3.6%
GAGE(2)	- 30-55			(omitted)
*Age when first child was born*
CAGE(1)	- 16-19	0.194	0.177	1.096	1.214	4.5%
CAGE(2)	- 20-55			(omitted)
*Marital status when first child was born*
CSPOUSE(1)	- not in a union	0.568	0.134	4.239	1.765	12.2%
CSPOUSE(2)	- in a union			(omitted)
*Age of youngest child*
YKID(1)	- 0-5	0.396	0.156	2.538	1.486	9.7%
YKID(2)	- 6-11			(omitted)
YKID(3)	- 12-17	-0.770	0.164	-4.695	0.463	-16.3%
*Level of education*
STEDUC(1)	- student	0.726	0.229	3.170	2.067	17.0%
STEDUC(2)	- non-student: less than high school	0.607	0.231	2.628	1.835	14.0%
STEDUC(3)	- non-student: high school diploma			(omitted)
STEDUC(4)	- non-student: some post-second.	0.450	0.241	1.867	1.569	10.2%
STEDUC(5)	- non-student: post-sec. degree	-0.180	0.202	-0.891	0.835	-3.7%
*Immigrant, aboriginal, or disabled*
HIGHRISK(1)	- yes	0.508	0.148	3.432	1.662	12.3%
HIGHRISK(2)	- no			(omitted)
*Broad Region*
REGION(1)	- Atlantic	0.582	0.228	2.553	1.790	14.4%
REGION(2)	- Quebec	0.052	0.163	0.319	1.053	1.2%
REGION(3)	- Ontario			(omitted)
REGION(4)	- Prairie	-0.328	0.200	-1.640	0.721	-7.5%
REGION(5)	- B.C.	0.239	0.215	1.112	1.270	5.8%
*Constant*		-1.107	0.216	-5.125	0.330
Nagelkerke R²(similar concept to OLS adjusted R²)				21.1%
Number of cases				1,262

³The characteristics of lone fathers cannot be studied separately because their sample is too small.
⁴The 1,500 annual hours of work roughly corresponds to the full-time threshold, which is 50 weeks, times 30 hours per week (which is treated in the Labour Force Survey as the minimum weekly hours for full-time employment).
⁵Interestingly enough, the incidence of low income among those who were in a common law relationship when their first child was born, is about the same as for those who were not married. However, the sample is too small for definitive conclusions.
⁶The employment rate was calculated by dividing the weeks of work of each woman (0 to 52) by 52. The ratio was averaged within each of the 54 regions that are designated by the EI program.
⁷A common way of estimating a linear approximation of the logit coefficients is to: (a) estimate the expected probability for each characteristic (assuming the rest of the characteristics equal the average values of the total sample); and (b) subtract from each estimated probability the estimated probability of the reference category.
In our methodology we used a slight variation. Rather than keeping the remaining characteristics equal to the average for the total sample, we kept them equal to the average characteristics of the reference category. So, for example, when assessing the effect of age, we kept all the characteristics (e.g. education, etc.) equal to that of the reference category (age 30 to 55). The actual calculation technique was as follows: we started with the observed probability for the omitted category, and then calculated the probability of the younger age group based on the odds ratio from the logit regression.
From the practical point of view, there is not much difference between the two approaches, since typically the estimates are very similar. However, our approach is intuitively more appealing. Effectively our approach answers the following question: if you take all the lone mothers age 30-55, keep all their characteristics (except their age) unchanged, what would be the impact of lowering their age to 16-29.
⁸Estimated by subtracting from the coefficient of lone mothers with pre-school children the coefficient for lone mothers with the youngest child age 12 to 17 (i.e. 9.7% - (-16.3%)) = 26.0%.

Profiles and Transitions of Groups at Risk of Social Exclusion: Lone Parents - November 2002