An Alternative Measure of Local Cost of Living
My estimates in Section IIA are based on a definition of cost of living where the
housing component of cost of living varies only by metropolitan area. In online
Appendix Table A2, I show how my estimates change when an alternative definition
of cost of living is adopted. In particular, I allow for the cost of housing experienced
by different individuals to vary depending not just on their city of residence, but
also on their education level, family structure, and race. The idea is that, within a
city, not all households necessarily use the same type of housing. In New York, for
example, the majority of residents in Manhattan have a college degree or more,
while the majority of new residents in Staten Island or the Bronx have a high school
degree or less.
Allowing for the cost of housing faced by different demographic groups in a
given city to be different may matter if tastes and budget constraints differ across
groups, so that the type of housing that is used by some demographic groups in a
city is not identical to the one that is used by other groups. In this case, the groupspecific
rental cost is measured as the predicted value from a regression of rental
cost on identifiers for metropolitan area, education group, number of children, race,
and interactions, where the regression is estimated on the sample of renters of two or
three bedroom apartments, and the predicted values are calculated for all households.
Local CPI 3 only uses local variation in cost of living that arises from variation in
predicted cost of housing. Local CPI 4 uses local variation both in predicted cost of
housing and cost of nonhousing goods and services. Estimates in online Appendix
Table A2 indicate that, relative to Table 5, a larger share of the increase in nominal
wage differences appears to be accounted for by cost-of-living differences.24