How to understand and interpret Statistics Canada’s measurement of the poverty gap

While I haven’t seen much chatter about this, on Tuesday Sept. 8, 2020 Statistics Canada released new statistics related to Canada’s official measure of poverty, the Market-Basket Measure (MBM). This new release updates the base for MBM from 2008 to 2018 and has been long awaited by the academic community. Of course, though, these statistics sometimes become political fodder.

I noticed that Pierre Poilievre decided to make hay with the poverty gap measure.

I can’t let this go because this tweet shows he does not have a clue as to what the poverty gap measure means and how to interpret it. Just because the gap widens actually does not mean poverty worsened. Come along for a basic arithmetic ride!

The MBM threshold is the disposable income below which someone would be considered living in poverty. The gap, or the depths of poverty, is defined as the gap between the MBM income thresholds and the average income of those whose income is below the MBM.

Technically referred to as the “average gap ratio”, it is expressed as a percentage of the MBM income threshold. For example, a family of four living in Vancouver with an income of $30,000 and an MBM income threshold of $40,644 (that is what it was under the 2008 base) would have a gap ratio of 26.2%. The average gap ratio for a given population (e.g. all families of four) is the average of these values as calculated for each family.

Examining depths of poverty over time is potentially problematic as interpretation of the movement over time is difficult. Consider this example: suppose there are only two families. Family A has an income of $19,000/year and family B has an income of $15,000/year. Otherwise, both families are exactly the same. Suppose as well that the poverty line is $20,000. Given these incomes, the average gap ratio is 15%. Suppose that due to some policy change, both families receive an extra $1,000 of income. Family A is moved out of poverty to an income of $20,000 and family B remains in poverty with an income of $16,000. After this policy change, the average gap ratio is 20%—the average gap ratio has gotten worse however both families have a higher income. Thus, as the average poverty gap increases, it is possible that all families are better off. This occurs because as there is an improvement in poverty reduction, i.e. there are fewer families with income below the income threshold, the number of persons/families over which the average gap ratio is measured decreases.

Regardless of this shortcoming, the average gap ratio is useful in assessing how much resources are needed at a point in time to eradicate poverty through a perfectly targeted cash transfer. For example, an average gap ratio of 15% means that a perfectly targeted cash transfer that is 15% of the poverty line is needed to eradicate poverty. This provides intuition on the magnitude of the average gap ratio and intensity of poverty.

Additionally, this shortcoming has implication for governments as they work towards their defined poverty reduction targets: there is a trade off between an improved poverty rate and an improved average gap ratio. On the one hand, the government could focus on moving those persons/families just below the poverty line to the poverty line (or above). This would decrease the poverty rate but could potentially increase the average gap ratio. On the other hand, focusing on those persons/families in the greatest depths of poverty and helping them move closer or above the poverty line would decrease the average gap ratio but may have less of an impact on the poverty rate and would potentially be more costly.

Either way, comparing gap numbers over time as Pierre has done is just not an appropriate use of the gap measure. And by inappropriately using the measure, he also came to an incorrect conclusion. That is politics for you, I suppose. All bluster, no fact.

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