Testing estimates of housing cost differences among U.S. metropolitan areas

Objectives

Labor economists want to investigate real earnings differences, but data on living-cost differences among US metropolitan areas are flawed.  The CPI is constructed to estimate changes in costs, not levels, and only in 26 major metropolitan areas.  The ACCRA Cost of Living Index, produced by C2ER, estimates living costs in cross-section and is available for more cities, but is of unknown quality.

This project investigates alternatives to the ACCRA Index, focusing on housing cost measures as a proxy for living cost differences.  This is defensible because the cost of housing is by far the biggest source of variation in living costs among metropolitan areas.

In an article to be published in 2013, Easton developed five measures of metropolitan housing costs.  The first three were hedonic estimates, including just tenant rents or tenant rents and estimated owner-occupied rents.  The fourth was average rent per room.  The fifth was the Fair Market Rent for a two-bedroom apartment.

Easton tested these five measures, along with the housing-cost portion of the ACCRA index, as predictors of the housing portion of Aten's area price index (2006).  This research extends the 2013 paper by performing two additional tests.  First, it tests the ability of the six housing cost measures to predict a housing-cost proxy: residential crowding.  Second, it tests the ability of changes in the six housing cost measures to predict changes in the metropolitan CPI.  The first test is conducted in the 177 largest metropolitan areas; the second is conducted in 26 large, CPI-covered metropolitan areas. 

Data and methods

The data to calculate most of the housing cost measures and the residential crowding measure come from the 5% Public Use Microdata Set of the 1990 and 2000 Censuses.  Additional data to compute housing-cost measures come from HUD Fair Market Rents.  The housing-cost portion of the ACCRA index comes from C2ER.   The residential portion of the CPI comes from the BLS.

To perform the first test I estimate:

1) PplPerRm_i = a + bX_i + cHCMeasure_i + ε_i,

where

PplPerRm	is the average number of people per room across all households in metropolitan area i,
X	is a vector of controls for metropolitan area i, including average household income and measures of ethnic mix,
HCMeasure	is the value of a particular housing cost measure for metropolitan area i, and
ε	is a random disturbance term.

To perform the second test, I estimate (for changes from 1990 to 2000):

2) ChHCCPI_i = a + bChHCMeasure_i,

where:

ChHCCPI	is the change in the housing cost portion of the CPI in metropolitan area i and
ChHCMeasure	is the change in a particular housing cost measure in metropolitan area i.

Expected results

In his 2013 article, Easton discovered that the fourth and fifth measures were the best predictors.  It seems probable the tests proposed here will produce the same result.  However, those results may have stemmed from idiosyncrasies of the area price index.  Given the importance of studying the determinants of real earnings, it seems vital to gather additional evidence.