To low-income residents and the groups that fight for them in expensive cities, new market-rate housing often feels like part of the problem. If San Francisco and Washington are becoming rapidly unaffordable to the poor, why build more apartments for the rich?

New housing, these voices fear, will only turn affordable neighborhoods into unaffordable ones, attracting yet more wealth and accelerating the displacement of the poor. And so protesters rally against new market-rate apartments in Oakland. Politicians propose halting construction in San Francisco’s Mission District.

Economists typically counter with a lesson about supply and demand: Increase the sheer amount of housing, and competition for it will fall, bringing down rents along the way to the benefit of everyone.

It is understandable that skeptics raise their eyebrows at this argument. It’s theoretical, based on math models and not peoples’ lives. It seems counterintuitive — that building for people who are not poor will help the poor. But the California Legislative Analyst’s Office recently released some positive data backing up this point: Particularly in the Bay Area since 2000, the researchers found, low-income neighborhoods with a lot of new construction have witnessed about half the displacement of similar neighborhoods that haven’t added much new housing.

Here’s another way to look at that: Places without much new market-rate construction have more displacement. That is, no doubt, the opposite of what protesters want.

Importantly, the benefits of all this building are not about inclusionary policies, which require developers to set aside some affordable units in market-rate buildings. There is less displacement in high-construction neighborhoods whether they have inclusionary policies or not.

In this research (hat tip to Daniel Hertz for noticing it), displacement is defined as when census tracts have population growth over time but a simultaneous decline in low-income households. The researchers also counted census tracts where the overall population was falling — but falling particularly rapidly among the poor.

In tight markets, poor and middle­-class households are forced to compete with one another for scarce homes. So new market-rate housing eases that competition, even if the poor are not the ones living in it. Over time, new housing also filters down to the more affordable supply, because housing becomes less desirable as it ages. That means the luxury housing being built today will contribute to the middle-class supply 30 years from now; it means today’s middle-class housing was luxury housing 30 years ago.

Here is the average rent for housing built in San Francisco and Los Angeles between 1980-1985. Relatively speaking, these homes were substantially more expensive in 1985 when they were brand new than they were in 2011:

If you don't build much new housing, though, this filtering process breaks down over time. And, in fact, the LAO report shows that rents have risen a lot faster for the poor in coastal California communities that have been stingy with new housing than in counties across the nation that built a lot:

The report concludes that boosting private construction would do more to broadly help poor households than expanding small and costly affordable housing programs that can serve only a fraction of them. Those programs also do not resolve the underlying cause of high rents — the housing shortage itself.

And that shortage actually undermines affordable programs such as housing vouchers, because it’s a lot harder for the poor to use vouchers in a market where they’re fiercely competing with everyone else.

Adding one more point: None of this dismisses the fact that displacement from specific homes happens when low-income housing is literally knocked down to build high-end towers. A good amount of new supply in cities, though, can rise on under-utilized land (former industrial plots, surface parking lots, abandoned properties, etc.). And the cumulative effect of all that new supply can hold down rents across neighborhoods and cities, including for the poor.

For an extended debate between economists and sociologists about this report and the larger role of market-rate supply in affordability, read more here.