6 Income stability during retirement

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Another aspect of income security relates to the relative stability, or instability, of income sources during retirement. Instability in family income may affect the well-being of individuals in many ways, most notably by affecting consumption levels and by creating uncertainty. As a result, high income instability may create a good deal of stress and anxiety among seniors. In this section, we attempt to provide some insights about income instability, or the degree of year-over- year variation in income levels, at various stages of the retirement years.

To study income instability, we adopt the methodology developed by Gottschalk and Moffit (1994) and more recently applied by Morissette and Ostrovsky (2005) to examine earnings instability at various points of the life-cycle, and by Heisz and LaRochelle-Côté (2006) to examine the degree of instability in work hours.

This method separates the income variance in a cohort over some interval of time (say five years) into two components: (a) permanent differences in income between people; and (b) transitory differences in yearly income for individuals. While the first part is useful, in the sense that it provides a general idea of 'permanent' income differences across individuals (i.e., inequality in permanent income), it is the second part that is of interest here, as it directly relates to the degree of income instability experienced by individuals, the year-over-year variation in individual incomes.

We examine income instability over six age intervals: 55-to-59, 60-to-64, 65-to-69, 70-to-74, 75- to-79 and 80-to-84 years. Our focus is on two cohorts of individuals from the Longitudinal Administrative Data base. The first cohort was aged 55 years in 1985, and it can be used to examine the degree of income instability during the first four periods mentioned above. The second cohort of individuals was aged 65 years in 1985, and it can be used to examine income instability from the age of 75 to 84 years.¹⁸ We still use adult-equivalent-adjusted family income after taxes, but since the objective is to quantify the degree of year-over-year variation in income levels, we make use of annual income values instead of permanent income. Finally, we also compute income instability into top, middle and bottom thirds (income tertiles) of the population. Individuals were classified across tertiles by using their average income in 1982, 1983 and 1984 in order to minimize the influence of unusually good or bad years, a problem that would plague the classification of individuals if a single year of observation was used.¹⁹

Our method can be described as follows. First, suppose that log earnings of individual i in period t, y_it, are generated by the following random-effects model:

where X_it is a vector of observable characteristics, e_i is an error term specific to the individual, μ_it is a general error term and where cov[e_i, μ_it] = cov[e_i, X_it] = cov[μ_it, X_it] = 0. While Equation (1) assumes a common slope for the age-income profile of individuals, it allows for a distinct intercept for each family (e_i). This is useful because it allows low-income individuals to have a lower 'permanent' income level than high-income individuals. We capture the age-income profile of a group of individuals by including in X_it a quadratic term for age. We abstract from mobility associated with the life cycle by replacing the actual log of individual incomes y_it by the life-cycle adjusted (log) individual incomes derived from Equation (1):

If we observe N individuals across T years, the total variability of individual incomes (h) across individuals and years is given by:

This total variation in income levels can be decomposed into a permanent and a transitory component. The permanent component reflects the degree of income variation among individuals, while the 'within' component reflects the degree of instability over time in an individual's income. The 'within' component can be thought of as the 'income instability' measure, and the 'between' component can be thought of as being related to 'income inequality.'

The 'within' component is given by:

Intuitively, s²_within is the average (across individuals) of individual specific variances (over time) of annual income levels.

The 'between' component is given by:

where ?_i represents the average income for person i during a given period of time (say, from 55 to 59 years old), and ?  is the average of ?_i across individuals. Hence, s²_between represents the variance of annual income levels among individuals, after averaging out the part of income variation due to individual income instability.

It should be noted that for each group (or tertile) of individuals and for each age period, we estimate specific age-income profiles; in other words, we re-estimate Equation (1) separately for each group and for each period. This is necessary, because the age-income profile of individuals changes over time. As a result, the 'within' variance can simply be interpreted as an average deviation from the specific age-income profile of a given period.

Table 9 shows the total variance in income levels across persons and years (for each age period), as well as the variation associated with instability in individual income (the 'within' component) and the variation associated with the 'between' component, which is related to income inequality between individuals. It shows that (1) total variance in income levels fell by more than half over the course of retirement; (2) total variance declined both as a result of reductions in instability and in the permanent differences across individuals. That is, both income inequality (the variation in income between individuals at a point in time) and income instability (the variation over time of an individual's income) decline as cohorts age.

While the method used by Morissette and Ostrovsky (2005) provides a useful way to decompose the total variance of income, it might not be the most intuitive one to evaluate individual-income instability. Another, more intuitive measure that can be used to evaluate instability at the individual level is the mean absolute deviation (MAD) and can be expressed as follows:

The MAD measures the average deviation, in percentage terms, of actual income from expected income levels during the observation period. For instance, if an individual has a MAD of 0.2, it means that his/her annual income level (over a given period of time) typically deviated from its mean income level by 20% during that period.

Table 10 shows the levels of income instability experienced by individuals that were in the bottom, middle and top tertiles of the income distribution, using results from the MAD. (We also provide the results obtained by the method of variance decomposition, as results from the MAD can be compared with the square root of σ²_within .)

There are two major observations: (1) income instability declines as the cohorts age, and (2) instability was higher among low-income individuals at the beginning of the period, but became very similar to the instability levels of the other two groups after age 65. From age 55 to 59, individuals in the bottom tertile diverted from their mean income by an average 25.0%, while individuals in the middle and the top tertiles typically diverted by 16.2% and 18.2%, respectively. Annual income deviation became much lower after age 70 (below 10%) and did not vary significantly across income groups. These results indicate that the higher levels of instability experienced by low-income individuals (due to unstable employment earnings) are eventually dampened by the stable influx of cash provided by public pensions. The main implication of this is that the pensions system not only provides income security to low-income individuals, but also significantly reduces their degree of income instability.

To assess the extent to which the public pensions and taxes dampen income instability among older individuals, we re-estimated Equation (1) by using the following income concepts: (a) market income, which includes income from earnings, private pensions, investments and capital gains; (b) market income plus public pensions, which includes benefits from the Old Age Security, the Guaranteed Income Supplement and the Canda and Quebec Pension Plans; (c) total income before taxes; and (d) total income after taxes.²⁰ The results are shown in Table 11.

From ages 55 to 59, instability in market income was relatively high among low-income individuals (mean absolute deviation was 30.0%, compared with 23.6% for all individuals). After adding pension incomes, transfers and taxes to obtain after-tax family income, instability is reduced significantly, particularly in the bottom quintile. Hence, those income sources (and taxes) do tend to reduce income instability. But even after considering the effect of these sources, instability remained marginally higher in the bottom tertile. This is not a surprise, as income comes mainly from earnings at this age.

From age 60 to 64, instability in market income rose, especially for market income. Higher instability in market income was likely the result of declining earnings, as many individuals choose to retire during this period. Furthermore, not everyone has access to a well-defined set of benefits from private pensions, which may also cause instability to rise. At this point, public pensions reduced instability substantially among individuals in the bottom tertile, but even after considering the effect of public pensions, low-income individuals still faced higher instability in their income than individuals in the other tertiles. With the effect of transfers and taxes, however, instability among individuals in the bottom tertile became similar to that of individuals in the other tertiles, at approximately 21.6%.

Instability in market income among the 65-to-69-year olds was similar to that at age from 60 to 64, but public pensions contributed more to reduce instability, especially among individuals in the bottom tertile. Indeed, as a result of public pension income, income instability in the bottom tertile became similar to that of the other two tertiles at approximately 15%. At this point, taxes contributed little to reduce instability. Similar trends were found for the other two periods above age 70.

It is also informative to examine the distribution of income instability. To do so, we rank individuals by their mean absolute deviation, from those who have the smallest deviation to those who have the highest deviation from expected income. In so doing, we obtain a distribution of instability among seniors at various stages of their retirement years. If the distribution is skewed to the left, it means that there is a higher concentration of individuals with less instability. Conversely, a distribution that is skewed to the right means that there is a larger portion of seniors with more instability.

In Figure 25, we follow a cohort of individuals aged 55 in 1985 and we study the changes in the distribution of instability over four age periods: from 55 to 59, from 60 to 64, from 65 to 69 and from 70 to 74. The results clearly show that the distributions move to the left after age 64, indicating that income levels became increasingly stable for most seniors as they advanced into their retirement years. By age from 70 to 74, individuals were largely concentrated around very low instability levels. By and large, these findings suggest that the pension system contributes to reduce income instability among seniors, in addition to providing minimum levels of income security, especially among low-income seniors.

¹⁸ The use of two separate cohorts to compare the evolution of income instability might cause a problem, as it ignores the possibility of cohort effects. The use of two cohorts is necessary to examine income instability over the long run. This is because the Longitudinal Administrative Data base starts in 1982, which implies that income instability can be analysed just over two decades (we use the three first years of data to classify individuals across tertiles). However, cohort effects are likely to be small for two reasons: (1) individuals from the first cohort are only 10 years older than individuals in the second cohort, and (2) when comparisons could be made across the two cohorts, the trends from the first cohort did not differ significantly from the second.

¹⁹ We keep individuals who reported positive income levels in all years until their death (or until 2004). In the previous section, we kept individuals who reported at least $10,000 in the first year of their respective panels to obtain equivalent samples. This precaution was not necessary for the analysis of income instability, because our sample was entirely selected in 1985. Individuals who died during the period are also kept in the sample for all completed age intervals. For instance, if an individual dies at age 67, he will be included in instability measures produced for the analysis of the age period from 55 to 59, the age period from 60 to 64, but not the age period from 65 to 69.

^20. For convenience, Table 5 only includes individuals who had positive market income in all years, but individuals were similarly classified across tertiles (similar boundaries).