How many families would be helped by raising the minimum wage?

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Question: 

How many families would be helped by raising the minimum wage?

This week the Congressional Budget Office analyzed the effects of raising the minimum wage to $10.10. They say (Table 4) that it will raise the average income for families in poverty by $300, but also (Table 1) that it will raise the total income for families in poverty by $5 bn.

These two numbers would make sense if there were 17 million families in poverty, but the census says there are only 9.5 million families in poverty. The numbers about families at other income levels have the same issue. Somewhere a number or an interpretation is wrong -- but where?

CBO link: www.cbo.gov/publication/44995

Census link: www.census.gov/hhes/www/cpstables/032013/pov/pov04_000.htm

Answer: 

That’s an astute observation. As you say, $5 billion divided by $300 per family in poverty suggests there are about 17 million families in poverty. But the Census data cited in the CBO report indicate far fewer families in poverty. Updating your link to the most recent data, the Census reports about 9.1 million families in poverty in 2013 (similar to your 9.5 million figure), not 17 million families:

www.census.gov/hhes/www/poverty/data/incpovhlth/2013/table4.pdf

Delving deeper into this question, we learned that the discrepancy is related to the way the CBO weighted the household data. Specifically, income gains in larger households were given more weight than gains in smaller households. Our understanding is that the $5 billion gain going to households at or below the poverty level is the correct aggregate benefit. Dividing by the number of households in poverty, we find that the average gain per poor household is ($5 billion)/(9.1 million households), or $549 per poor household. The lower $300 number presented in the report reflects the weighting by household size. Larger households tended to have smaller gains than smaller households, so the weighted average gain is less than the unweighted average gain.

Highlighting an important tradeoff, the nonpartisan CBO report also estimates that raising the federal minimum wage from $7.25 an hour to $10.10 would reduce total employment in the U.S. by about 500,000 workers over the next two years as some less-skilled workers would become priced out of the market.