Until the end of 1977, the U.S. consumer price index (CPI) for rents tended to omit rent increases when units had a change of tenants or were vacant, biasing inflation estimates downward. Beginning in 1978, the Bureau of Labor Statistics (BLS) implemented a series of methodological changes that reduced this nonresponse bias, but substantial bias remained until 1985. We set up a model of nonresponse bias, parameterize it, and test it using BLS microdata. From 1940 to 1985, the official BLS CPI for urban wage earners and clerical workers (CPI-W) price index for tenant rents rose 3.6% annually; we argue that it should have risen 5.0% annually.