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We use a theoretical approach common to the labor economics discipline to explore homeownership as a “match” between renter households and single-family for-sale inventory. Renter households do not own their primary residence but are assumed to be looking for one, while the single-family for-sale inventory represents the homes available to purchase. Using this approach, we demonstrate that between 1994 and the first quarter of 2024, periods of more for-sale supply coincide with a lower share of renter households, and conversely a higher homeownership rate. In contrast, periods of less supply correlate with a higher share of renter households and a lower homeownership rate. We use this evidence to construct a ratio of renter households to available supply, akin to a Beveridge Curve in the labor literature, and find that this ratio, the number of renter households for every single-family home for sale, is near its highest level over the past nearly 30 years. Finally, we decompose renter households by race and ethnicity and find that periods of more supply coincide with higher homeownership rates for whites as well as Black and Hispanic households. However, for a given level of supply, the share of renter households is greater among Black and Hispanic households compared to white households and the homeownership rate is lower. Our results therefore suggest that more supply can boost homeownership rates, including for many homeowners of color. However, more supply by itself has not historically coincided with a closed racial homeownership rate gap. We conclude by offering recommendations that can, with more supply broadly, help to close the racial homeownership gap and improve data collection within our theoretical framework.