October 3, 2011

Fighting Poverty in a Bad Economy, Americans Move in with Relatives

Appendix B: Adjusting Household Income for Household Size

Household income data reported in this study are adjusted for the number of people in a household. That is done because a four-person household with an income of, say, $50,000 faces a tighter budget constraint than a two-person household with the same income.

At its simplest, adjusting for household size could mean converting household income into per capita income. Thus, a two-person household with an income of $50,000 would have a per capita income of $25,000, double the per capita income of a four-person household with the same total income.

A more sophisticated framework for household size adjustment recognizes that there are economies of scale in consumer expenditures. For example, a two-bedroom apartment may not cost twice as much to rent as a one-bedroom apartment. Two household members could carpool to work for the same cost as a single household member, and so on. For that reason, most researchers make adjustments for household size using the method of “equivalence scales” (Garner, Ruiz-Castillo and Sastre, 2003, and Short, Garner, Johnson and Doyle, 1999).

A common equivalence-scale adjustment is defined as follows:

Adjusted household income = Household income / (Household size)N

By this method, household income is divided by household size exponentiated by “N,” where N is a number between 0 and 1.

Note that if N = 0, the denominator equals 1. In that case, no adjustment is made for household size. If N = 1, the denominator equals household size, and that is the same as converting household income into per capita income. The usual approach is to let N be some number between 0 and 1. Following other researchers, this study uses N = 0.5 (for example, see Johnson, Smeeding and Torrey, 2005). In practical terms, this means that household income is divided by the square root of household size—1.41 for a two-person household, 1.73 for a three-person household, 2.00 for a four-person household, and so on.

Once household incomes have been converted to a “uniform” household size, they can be scaled to reflect any household size. The income data reported in this study are computed for three-person households. That is done as follows:

Three-person household income = Adjusted household income * [(3)0.5]

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