The paper proposes a new theoretical explanation for the spatial sorting that the skill distribution has fatter tails in big cities. The ownership of the house make people face the constraint of house’s minimum area when purchasing it, therefore, and finally induces the spatial sorting. The new theory could distinguish buying and renting houses, and identify public services attached to housing ownership and enjoyed by all people no matter who buy or rent houses. The policy implications are also different from those in previous theories: when land supply is reduced in big cities, it predicted a decrease in the number of low-skilled workers in previous theories, whereas it predicts an increase in the theory of housing ownership constraints. In big cities, public services attached to housing ownership would attract more high-skilled workers and decrease low-skilled workers, while public services enjoyed by all people would attract both of them.