A provision in President Biden’s American Jobs Plan to make housing more affordable by giving cities incentives to abolish single-family zoning has a number of flaws. Most important, single-family zoning didn’t make housing expensive and abolishing single-family zoning won’t make it more affordable.

To understand this, we have to go back before the invention of single-family zoning when less than 20 percent of urban households owned their own homes. Homeownership rates weren’t low because housing was expensive; in fact, people could buy new homes, complete with indoor plumbing, for $1,000, which is less than $30,000 in today’s money.

The problem with homeownership in 1890 was that people didn’t know what was going to happen to nearby properties. Without zoning, your dream house might end up next door to a brickyard, gravel pit, or some other use that would reduce its property value. Except for those wealthy enough to buy large estates, most people rented so they could move if incompatible uses opened next door.

Single-family zoning was created specifically to solve this problem. In effect, buyers of single-family homes were willing to say, “We’ll give up the right to develop our property to more than a single house provided our neighbors give up their rights to do the same.” Single-family zoning was, in effect, a property right.

Competition among developers and builders ensured that zoning didn’t increase the price of housing, but it did increase sales. By 1960, nearly 60 percent of urban households owned their own homes, nearly all of them in areas that had been single-family zoned for decades. Despite such zoning, housing markets remained affordable throughout the country.

High homeownership rates produced enormous benefits. Since both working-class and middle-class families owned their homes, income inequality dropped to its lowest level in American history in about 1970. People could use the equity in their homes to start small businesses, and small-business formation reached record levels.

Many single-family homes were built in the suburbs, that is, outside the jurisdiction of major cities. The cities resented the suburbs, whose residents often worked in the cities but didn’t pay property taxes to the cities. Out of spite, the cities demonized what they called “urban sprawl” and several states passed legislation to confine urban growth within established urban boundaries.

Hawaii passed such a law in 1961, followed by Oregon in 1973, Florida in 1985, and Washington in 1992. A 1963 California law passed for another purpose morphed into one of the most restrictive land-use laws in the nation. Several New England states also passed laws that had the same effect. Although only a minority of states passed such growth-management laws, these states have nearly half the population of the country.

Restrictions on urban growth made land within the growth boundaries expensive. Some 70 percent of the land in the San Francisco-Oakland metropolitan area is off-limits to development, and the land that can be developed costs well over $3 million an acre. Land in fast-growing urban areas that have no growth boundaries, such as Atlanta, Dallas, and Houston, sells for less than a tenth of that cost.

High land prices make housing expensive. Developers can build higher-density housing, but — as California developer Nicholas Arenson testified before a regional planning commission — buildings more than three stories tall require more steel, concrete, and elevators, making the construction cost per square foot much higher than single-family homes. A comparison of the density of American urban areas with their housing affordability shows a clear correlation: density makes housing less affordable, not more.

One of the effects of growth management has been an increase in wealth inequality. A Northwestern University economist named Matthew Rognlie has shown that the main source of growing inequality is housing: growth management has made already-wealthy homeowners even more wealthy while people who have to rent must devote increasing shares of their incomes to housing.

Almost every city in America except Houston has single-family zoning and housing remains affordable in all of them that have not used growth management. Abolishing single-family zoning won’t make housing more affordable, but it will make homeownership less desirable, and the nation will lose the benefits of such homeownership. It will also have other unintended consequences, including a further increase in inequality and more obstacles to small-business formation.

People who sincerely want to make housing more affordable will work to repeal the growth-management laws that make housing expensive. Unfortunately, Biden’s proposal will have no effect on such laws and should be rejected by anyone who cares about equality and housing affordability.