There are conflicting theories on whether house prices and income should share a long-run relationship. Empirical work on the topic has yielded mixed results. Most previous studies have investigated whether the house price/income ratio is stationary (short memory) or non-stationary (has a unit root) but have not allowed for the intermediate possibility of long memory or fractional integration. We estimate fractional integration for the house price/income ratio for US states. We find most states exhibit long memory in their ratios. The states with the most long memory tend to be in the high-priced east coast and California. Southern and great plains states, in contrast, tend to exhibit the least persistence in the house price/income metric. In some housing markets ? some east coast states, California, Arizona, Florida, and Nevada, home costs can become less and less affordable for local residents, with no tendency to reverse this unaffordability within a reasonable time horizon for potential buyers. In addition to the univariate estimates, multivariate fractional cointegration tests are implemented, and the results support the findings of non-affordability hypothesis.