# Low income measures

## What is the LIM?

For the purpose of making international comparisons, the LIM is the most commonly used low income measure. The use of the low income measure (LIM) was suggested in 1989 in a discussion paper written by Wolfson, Evans, and the OECD1 which discussed their concerns about the LICOs. In simple terms, the LIM is a fixed percentage (50%) of median adjusted economic family2 income, where "adjusted" indicates that family needs are taken into account. Adjustment for family sizes reflects the fact that a family's needs increase as the number of members increases. Most would agree that a family of five has greater needs than a family of two. Similarly, the LIM allows for the fact that it costs more to feed a family of five adults than a family of two adults and three children.

The LIMs are calculated three times; with market income, before-tax income, and after-tax income using the Survey of Labour and Income Dynamics (SLID). They do not require updating using an inflation index because they are calculated using an annual survey of family income. Unlike the low income cut-offs, which are derived from an expenditure survey and then compared to an income survey, the LIMs are both derived and applied using a single income survey.

## How is the LIM calculated?

In order to calculate the LIMs, first determine the "adjusted size" of each family. The first person is counted as 1.0 and the second person is counted as 0.4, regardless of age. Additional adults count as 0.4 and additional children count as 0.3 (where a child is defined as being under age 16). See the following section on adjustment for family size for more information. Next, calculate "adjusted family income" for each family by dividing family income by "adjusted family size". Then determine the median of this "adjusted family income", such that half of all families will be above it and half below. The LIM for a family of one person with no children is 50% of this median "adjusted family income", and the LIMs for other kinds of family are equal to this value multiplied by their "adjusted family size".

When comparing family incomes to study such things as income adequacy or socio-economic status, one often wants to take family size and composition into account—the income amount itself is not sufficient to understand a family's financial well-being without knowing how many people are sharing it. In general, two approaches have been used to help with the analysis of family income. One is to produce data by detailed family types, so that within a given family type, differences in family size are not significant. In fact, many income measures have been crossed by detailed family types in the published tables. The other way to take into account family size and composition is to adjust the income amount by an adjustment factor.

The simplest method is to use per capita income, that is, to divide the family income by the family size. A limitation of per capita income, however, is that it tends to underestimate economic well-being for larger families as compared to smaller families. This is due to the fact that it assumes equal living costs for each member of the family, but some costs, primarily those related to shelter, decrease proportionately with family size (they may also be lower for children than for adults). For example, the shelter costs for an adult married couple with no children are arguably not much more than those for an adult living alone.

To take such economies of scale into account, it is common to use an "equivalence scale" to adjust family incomes. Instead of implicitly assuming equal costs for additional family members as the per capita approach does, the equivalence scale is a set of decreasing factors assigned to the first member, the second member, and so on. The adjusted income amount for the family is obtained by dividing the family's income by the sum of the factors assigned to each member.

There is no single equivalence scale in use in Canada. The one used in the published income tables and in concepts such as the low income measure (LIM) has, however, achieved a high degree of acceptance. In this equivalence scale, the factors are as follows:

• the oldest person in the family receives a factor of 1.0;
• the second oldest person in the family receives a factor of 0.4;
• all other family members aged 16 and over each receive a factor of 0.4;
• all other family members under age 16 receive a factor of 0.3.

Other equivalence scales in use include:

Organization for Economic Co-operation and Development (OECD) scale

• the oldest person in the family receives a factor of 1.0;
• all other family members aged 15 and over each receive a factor of 0.5;
• all other family members under age 15 receive a factor of 0.3.

Square root of family size (this is a close approximation to the LIM equivalence scale, particularly for families with 6 members or less).

Table 1 gives the adjusted family size using the three methods. Note that the LIM equivalence scale produces different adjusted family sizes than the OECD scale. As well, the LIM scale produces similar results to the scale that uses the square root approach but differs because it takes age into account.

1. 'Statistics Canada's Low Income Cut-offs: Methodological Concerns and Possibilities' (Wolfson, Evans, and OECD).

2. All persons living in the same dwelling and related by blood, marriage, common-law relationship or adoption.

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