Income Research Paper Series
Market Basket Measure Research: Additional income inequality indicators using the Market Basket Measure

The Market Basket Measure (MBM) establishes poverty thresholds based on the cost of a basket of food, clothing, shelter, transportation and other items for a family of four that reflects a modest, basic standard of living. A family^Note  with a disposable income below the appropriate MBM threshold for the size of the family and its region is considered to be living in poverty.^Note 

This discussion paper describes considerations for the addition of three inequality indicators using the 2018-base MBM thresholds, and it provides an opportunity for feedback and comments to the proposed inequality indicators.

Introduction

During the consultations leading to the creation of the 2018-base MBM, topics were identified as requiring more study before determining if they should be adopted.^Note  These topics formed the basis for a forward looking research agenda, and will be explored in detail in preparation for the next MBM rebasing exercise, scheduled to begin in 2023.

In general, income inequality in4s the extent to which there are income disparities within a country. There are different ways to measure income inequality. For example, the United Nations^Note  (UN) compares the change in household income of the poorest 40 per cent with that of the population as a whole to measure income inequality. Another popular measure of inequality is the Gini coefficient. The Gini coefficient is an index that takes a value ranging from 0, which indicates a state of perfect equality of incomes within a given population, to 1 which indicates a state of perfect inequality where one individual possesses all the income.

This publication builds on these more commonly used methods and introduces three income inequality indicators proposed in 2021 in the following paper by Mathieu Dufour, Vivian Labrie et Simon Tremblay-Pepin: Using the Market Basket Measure to Discuss Income Inequality from the perspective of basic needs. In doing so, it also serves to advance the MBM research agenda by exploring ways in which the MBM could be used to facilitate analyses of inequality as it relates to the ability to afford a basic, modest standard of living among Canadian families. By enhancing our understanding of income inequalities with regards to the affordability of a set standard of living, these indicators have the potential to shed light on long-term socioeconomic trends which could require policy intervention.

This discussion paper presents the estimates obtained by applying these indicators to the Canadian Income Survey^Note  (CIS) data using the 2018-base MBM methodology, it provides the opportunity to gage the interest of including these three indicators into the current suite of income inequality indicators to facilitate the analysis of existing disparities and obstacles to income equality.

Rationale

Opportunity for All – Canada’s First Poverty Reduction Strategy is based on three pillars guiding ongoing federal government actions to reduce poverty: Dignity; Opportunity and Inclusion; and Resilience and Security. These pillars recognize that poverty is a multifaceted experience that is more than just lack of money.

The Poverty Reduction Strategy and the Poverty Reduction Act established the MBM as Canada’s Official Poverty Line, which is used to track progress towards the national poverty reduction targets set by the Poverty Reduction Strategy and its supporting legislation. Currently, MBM-based indicators being produced by Statistics Canada inform primarily on the number of persons and the proportion of the population living under the poverty line, as well as on the dollar gap between a family’s disposable income and its MBM threshold. However, notions of inequality as it relates to affording a basic, standard of living as measured by the MBM are yet to be explored. The additional inequality indicators presented in this paper capture more clearly income disparities among Canadians, by providing a more complete understanding of the dynamic nature of inequality with regards to the ability to afford a basic standard of living. Over time these indicators could complement Canada's Official Poverty Line and the existing 12 indicators currently available on Canada's Official Poverty Dashboard (See the text box, Canada's Official Poverty Dashboard). Start of text box

Canada's Official Poverty Dashboard

With the adoption of Opportunity for All, Statistics Canada publishes 12 indicators to track progress on deep income poverty as well as the aspects of poverty other than income, including indicators of material deprivation, lack of opportunity and resilience. These indicators are:

Dignity

• Deep income poverty
• Unmet housing needs and chronic homelessness
• Unmet health need
• Food insecurity

Opportunity and inclusion

• Relative low income
• Bottom 40% of income share
• Youth engagement
• Literacy and numeracy

Resilience and security

• Median hourly wage
• Average poverty gap
• Asset resilience
• Low income entry and exit rates

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Definitions

The definitions for the three inequality indicators used in this analysis were first published in the previously mentioned paper, Using the Market Basket Measure to Discuss Income Inequality from the Perspective of Basic Needs.

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Overview of the inequality indicators

1. Distance to the MBM indicator: The difference between the disposable income for the MBM of a family and the associated MBM threshold adjusted for family size.
2. Basket coefficient indicator: The number of adjusted MBM baskets (applicable threshold) that could be purchased with the disposable income of the family.
3. Components of after-tax income according to the MBM threshold indicator: The absolute after-tax income decomposed according to each component of the disposable income for the MBM [i.e., realised part of the adjusted MBM threshold, surplus or deficit and all adjustments (non-discretionary expenses and potential income adjustments)].

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Distance to the MBM indicator

The first indicator, called the distance to the MBM indicator, corresponds to the difference between the disposable income for the MBM^Note  of a family and its MBM threshold, after adjusting for family size and region of residence. A family, and all its members, is said to be living in poverty when its distance indicator is negative. The absolute value of the negative distance, called the deficit to the MBM, represents the amount of disposable income the family would have needed to exit poverty in a given year.^Note  In this sense, the distance indicator adds to the explanatory quality of the MBM which is commonly concentrated around the prevalence of poverty, by expanding its analytical usefulness to include the minimum average amount of disposable income families would have actually needed to exit poverty. Conversely, the MBM surplus corresponds to the distance indicator for families not considered to be in poverty according to the MBM, and the magnitude of the surplus is representative of the financial well-being of the family.

The distance indicator can also be used to understand the differences in financial well-being as the MBM deficit and surplus can both be aggregated according to several types of demographic characteristics to help identify the groups within which the income needs are larger, thus allowing policy programs to target those most at-risk. The typical statistics produced using this indicator would be an average or a total by after-tax income deciles of families for different groups of interest.

Finally, the distance indicator is conceptually easy to understand and communicate and allows Canadians a simple way to understand how income inequality is changing over time.

This first example shows how the distance indicator can be used to better describe the income distribution among Canadian families. Charts 1.1 and 1.2 show the Canadian total and average deficit respectively, between 2015 and 2020. As the total deficit decreased between 2015 and 2020, the average deficit of families presenting a deficit generally increased between 2015 and 2019 and decreased much less than the total deficit in 2020 implying that Canadian families who moved out of poverty were most likely families whose disposable income was close to their respective MBM threshold. The steep decrease between 2019 and 2020 is mainly due to the new COVID-19 relief programs that have been introduced in 2020. Since these programs did not continue in 2021, it will be important to study the evolution of the surplus and the deficit after 2020.

Data table for Chart 1



Data table for chart 1
Table summary
This table displays the results of Data table for chart 1 2015, 2016, 2017, 2018, 2019 and 2020, calculated using 2020 constant dollars units of measure (appearing as column headers).

	2015	2016	2017	2018	2019	2020
	2020 constant dollars
Total deficit in billions, Canada, 2015 to 2020
Total deficit	27.9	26.3	26.1	27.6	26.3	17.7
Error	1.3	1.4	1.2	1.4	1.7	1.0
Average deficit in thousands, Canada, 2015 to 2020
Average deficit	8.8	8.8	9.2	9.8	9.8	9.1
Error	0.3	0.3	0.3	0.4	0.4	0.4
Notes: Thresholds are based on the 2018-base MBM methodology. The vertical bars correspond to the 95% confidence interval. Source: Statistics Canada, Canadian Income Survey. Custom Tabulation.

Similarly, Charts 2.1 and 2.2 shows the Canadian total and average surplus, respectively, between 2015 and 2020. The increase in both the total and the average surplus may indicate that families with a higher surplus have generally experienced a larger growth of income than families with a smaller surplus. A second example showing the deficit and surplus by after-tax income decile is presented in appendix.

Data table for Chart 2



Data table for chart 2
Table summary
This table displays the results of Data table for chart 2 2015, 2016, 2017, 2018, 2019 and 2020, calculated using 2020 constant dollars units of measure (appearing as column headers).

	2015	2016	2017	2018	2019	2020
	2020 constant dollars
Total surplus in billions, Canada, 2015 to 2020
Total Surplus	488.5	502.5	554.8	594.8	630.8	703.0
Error	8.3	7.8	8.3	9.6	10.4	8.9
Average surplus in thousands, Canada, 2015 to 2020
Average Surplus	40.7	40.6	43.3	45.6	47.1	49.2
Error	0.7	0.7	0.7	0.8	0.8	0.7
Source: Statistics Canada, Canadian Income Survey. Custom Tabulation.

Basket coefficient indicator

The second indicator presented, called the basket coefficient, corresponds to the ratio between the disposable income and the adjusted MBM threshold, which can be interpreted as the number of MBM baskets a family could afford with its disposable income. Chart 3 shows the average number of baskets that Canadian families could afford from 2015 to 2020. Thereby, the basket coefficient indicator represents a relative economic well-being indicator compared to the MBM threshold, not just a dollar amount which is typically the case with the other metrics produced using the MBM thresholds. Again, the typical statistics produced using this indicator would be an average or a total for after-tax income and could be presented by deciles of after-tax income and for different groups of interest.

While the basket coefficient indicator follows a similar trend as the distance indicator, the basket coefficient indicator is a relative measure of distance, thus it is not affected by the size of the different MBM thresholds, by the growth in population or by the inflation. This is because the coefficient is calculated by dividing the MBM disposable income for each family by the applicable MBM threshold for that family (i.e., taking into account place of residence and family size). This coefficient is then averaged across all considered families.

Data table for Chart 3



Data table for chart 3
Table summary
This table displays the results of Data table for chart 3 2015, 2016, 2017, 2018, 2019 and 2020, calculated using Number of baskets units of measure (appearing as column headers).

	2015	2016	2017	2018	2019	2020
	number of baskets
Income decile
Lowest decile	0.44	0.46	0.46	0.45	0.48	0.62
2nd decile	0.92	0.95	0.97	0.97	1.00	1.14
3rd decile	1.21	1.23	1.26	1.27	1.28	1.44
4th decile	1.47	1.49	1.51	1.56	1.57	1.69
5th decile	1.70	1.72	1.78	1.81	1.81	1.93
6th decile	1.96	1.95	2.02	2.03	2.02	2.14
7th decile	2.22	2.21	2.25	2.27	2.28	2.40
8th decile	2.50	2.50	2.56	2.55	2.58	2.66
9th decile	2.97	2.92	3.02	3.04	3.05	3.11
Highest decile	4.49	4.43	4.70	4.64	4.61	4.72
Canada	1.99	1.99	2.05	2.06	2.07	2.19
Notes: Thresholds are based on the 2018-base MBM methodology. Source: Statistics Canada, Canadian Income Survey. Custom Tabulation.

Chart 3 shows the evolution in the number of baskets that families can buy by after-tax income deciles. For readability only deciles one to six, nine and ten are shown on the graph. The graph shows an upward trend in the average number of baskets available to Canadian families between 2015 and 2020. It also shows the impact the pandemic emergency relief benefits had on the disposable income of people in 2020, compared to previous years. In addition, one can easily see the large inequality in financial well-being between persons with an income in the highest income decile and all other families.

Another way of using the basket coefficient indicator to study income inequality over time is to look at the inter-decile ratios as they account for the coverage of basic needs, the absolute changes in MBM thresholds and/or disposable income, and the fluctuations in socio-economic conditions over time. The inter-decile ratios of the average basket coefficients between 2015 and 2020 are shown in Graph A.2 in the Appendix section.

Components of after-tax income according to the MBM threshold

The third indicator presented in this paper is called components of after-tax income according to the MBM threshold. This indicator decomposes the after-tax income into five distinct components: the cost of the basket (adjusted MBM threshold for family size and place of residence), the deficit, the surplus, the realised part of the basket, and the adjustments^Note  as shown by Equation 1. This indicator provides a simple and comprehensible definition of the disposable income for the MBM in comparison with after-tax income for people to understand the difference between those two concepts, and it can also be used in conjunction with the National Economic Accounts as there is a common definition of after-tax income that can be compared.

Equation 1: Components of after-tax income according to the MBM threshold

As Equation 1 shows, the after-tax income could be mathematically expressed as the sum of the following individual components: the basket cost, less the deficit to the MBM^Note  if so, plus the surplus to the MBM if so and the adjustments^Note . Looking at each of these components of the after-tax income gives further insights on the socioeconomic characteristics of the families. For example, Table 1 presents the aggregated total of each individual components of the after-tax income by family income decile.^Note  The increase in the aggregated costs of the basket as the income decile increases, recalls that as the size of the family increases, the family income and the cost of the basket also increases accordingly. Moreover, families with higher incomes could also tend to live in regions where the cost of living is high.

Analysing the deficit and surplus columns, the table shows the disparities in income capacity regarding basic needs coverage at the level of the MBM basket across the income deciles. For example, the gap to cover the cost of the basket is almost entirely focused on families in the lowest income decile. Simultaneously, families in the highest income decile have almost twice as much surplus as families in the ninth income decile.



Conclusion

This paper is part of the research discussion paper series that will help inform the next MBM comprehensive review, scheduled to begin in 2023. The new inequality indicators have the ability to clearly show the impact of income inequalities in the ability to access a modest standard of living. These indicators are easy to understand and to interpret by non-experts, which encourage a broad social conversation on those inequality issues.

This paper series aims to foster engagement with users, the public and stakeholders to propose research topics that could help inform discussions for the next comprehensive review or improve the understanding of the MBM methodology, and potentially expand analytical tools that involve or rely on the MBM. The proposed research discussion topics are intended to provide users with preliminary discussion on a wide variety of topics. We encourage users to ask questions, provide feedback and make suggestions for future work.

Following the release of this paper, there will be a period during which Statistics Canada and Employment and Social Development Canada (ESDC) will engage experts, stakeholders, and federal, provincial and territorial officials to evaluate the responses and recommendations we receive. Users are welcome to ask questions or share their feedback. Persons interested in contacting us are encouraged to do so by sending an email to: statcan.market.basket.measure-mesure.du.panier.de.consommation.statcan@canada.ca.

Appendix A

Formula

Summary of the three indicators

• The distance to the MBM indicator

$$d_i={\text{DI}}_i-{\text{MBM}}_i$$

• The “basket coefficient”

$$b_i={\text{DI}}_i/{\text{MBM}}_i$$

• Components of after-tax income according to the MBM threshold

$${\text{AT}}_i={\text{MBM}}_i-{\text{deficit}}_i+{\text{surplus}}_i+{\text{total\_adjustments}}_i$$

where;

• DI_i refers the disposable income of the i^th family,
• AT_i refers to the after-tax income of the i^th family,
• MBM_i is the MBM threshold corresponding to the i^th family

Data preparation

The following rules were applied to the CIS data prior to the analysis.

• We have capped the after-tax income of the family to $0 when it is below $0.
• We have capped the MBM disposable income of the family to $0 when it is below $0.
• We have set the MBM disposable income (DI) to the after-tax income when the DI is larger than the after-tax income.

Complementary analysis

Distance to the MBM indicator

The distance indicator also allows comparison between the average deficit and the average surplus by after-tax income decile as shown in Charts A.1.1 to Chart A.1.4. In general, families with an after-tax income in the lower deciles have the largest average deficits, while families in the highest decile have the largest average surplus. This chart shows 1) the inequalities in revenue across the Canadian population through the exponential curve followed by the average surplus and 2) the impact of the income measures implemented during the first year of the COVID-19 pandemic.

Data table for Chart A.1



Data table for chart 4
Table summary
This table displays the results of Data table for chart 4 Average deficit and Average surplus (appearing as column headers).

	Average deficit	Average surplus
Average deficit and surplus, 2015
Lowest decile	7,060	4,876
2nd decile	8,739	9,648
3rd decile	10,606	14,695
4th decile	9,371	20,151
5th decile	9,831	25,063
6th decile	9,913	31,899
7th decile	5,595	39,421
8th decile	Note x suppressed to meet the confidentiality requirements of the Statistics Act	49,569
9th decile	8,328	66,987
Highest decile	Note ...: not applicable	123,440
Average deficit and surplus, 2018
Lowest decile	8,869	5,455
2nd decile	9,769	11,450
3rd decile	10,801	17,211
4th decile	7,610	23,704
5th decile	8,011	29,760
6th decile	8,185	36,930
7th decile	5,549	45,418
8th decile	17,954	57,089
9th decile	Note x suppressed to meet the confidentiality requirements of the Statistics Act	76,155
Highest decile	Note ...: not applicablen	141,103
Average deficit and surplus, 2019
Lowest decile	8,823	6,543
2nd decile	11,294	12,553
3rd decile	14,789	18,165
4th decile	8,434	24,745
5th decile	7,838	31,331
6th decile	7,281	38,436
7th decile	11,872	46,991
8th decile	Note x suppressed to meet the confidentiality requirements of the Statistics Act	60,117
9th decile	Note x suppressed to meet the confidentiality requirements of the Statistics Act	80,326
Highest decile	Note ...: not applicable	145,833
Average deficit and surplus, 2020
Lowest decile	7,957	8,289
2nd decile	8,357	15,558
3rd decile	7,335	22,130
4th decile	8,528	28,203
5th decile	11,059	35,360
6th decile	6,950	42,636
7th decile	Note x suppressed to meet the confidentiality requirements of the Statistics Act	52,313
8th decile	2,408	64,849
9th decile	Note x suppressed to meet the confidentiality requirements of the Statistics Act	85,172
Highest decile	Note ...: not applicable	154,562
... not applicable x suppressed to meet the confidentiality requirements of the Statistics Act Note : The thresholds are based on the 2018-base MBM methodology. Source: Statistics Canada, Canadian Income Survey.

Basket coefficient indicator

Table A.1 gives the average basket coefficients by after-tax income deciles.



Inter-decile ratios

Data table for Chart A.2



Data table for chart A.2
Inter-decile^{Data table for chart A.2 Note 1} ratios of the average basket coefficient,^{Data table for chart A.2 Note 2} Canada, 2015 to 2020
Table summary
This table displays the results of Inter-decile ratios of the average basket coefficient 2015, 2016, 2017, 2018, 2019 and 2020, calculated using inter-decile ratio units of measure (appearing as column headers).

	2015	2016	2017	2018	2019	2020
	inter-decile ratio
Ratio
(Highest decile / lowest decile)	10.28	9.68	10.11	10.21	9.56	7.60
(Highest decile / 2nd decile)	4.89	4.68	4.86	4.76	4.59	4.13
Note 1 The deciles are the after-tax income deciles. Return to note 1 referrer Note 2 Thresholds are based on the 2018-base MBM methodology. Return to note 2 referrer Source: Statistics Canada, Canadian Income Survey.

The change over time of the inter-decile ratios of the basket coefficient are good indicators of income inequality over time as can be seen on Chart A.2. The change over time of the ratios suggests that in 2020 the income inequality decreased faster between the poorest and the richest people than between people in the second income decile and the richest people. This result is also present in the current inequality indicators published by Statistics Canada. For example, the share of Canadians' adjusted after-tax income that went to the bottom four income deciles increased from 21.0% in 2019 to 22.2% in 2020, representing the largest annual change and highest proportion since the beginning of the series in 1976.

Components of after-tax income according to the MBM threshold

Table A.2 is similar to Table 1, but it gives the average of each component per decile, that is the average family income composition for each decile, instead of showing the total which can be more informative at the family level.



Appendix B



References

Djidel, Samir, Burton Gustajtis, Andrew Heisz, Keith Lam, Isabelle Marchand and Sarah McDermott (2020), “Report on the second comprehensive review of the Market Basket Measure”. Catalogue no. 75F0002M2020002.

Dufour, Mathieu, Vivian Labrie and Simon Tremblay-Pépin (2021), “Using the Market Basket Measure to Discuss Income Inequality from the perspective of Basic Needs, Social Indicator Research”, Social Indicators Research, 155, 455–478.

Employment and Social Development Canada (2018), “Opportunity for All – Canada’s First Poverty Reduction Strategy”. Catalogue no. SSD-212-08-18E.

Langevin, Raphaël (2022), “New inequality indicators based on MBM disposable income”. Internal document (unpublished). Statistics Canada.