One argument against new housing is that it creates demand for housing, thus increasing housing prices.

One argument against new housing in popular cities is the “induced demand” argument—the idea that new housing merely creates demand for more new housing, thus ultimately raising housing prices.
As journalist Tim Redmond argues: "When you build a new luxury housing complex, new residents move into it. For the most part, they result in net additions to the number of people in the city: If the person who buys a new condo moves out of a rental unit, someone else will move into that rental.…The people with high disposable incomes who fill those condos or luxury rentals will spend money in town, creating a demand for jobs – restaurant workers, grocery clerks, cops and firefighters, bank tellers…and those people will also need a place to live."
In other words, if the city permits 1,000 new housing units (other than government-subsidized housing, which is somehow exempt from this rule), dozens, or even hundreds, of people will magically appear from elsewhere in the United States to occupy those units. And the consumer spending of these new residents will create service-industry jobs, which in turn creates additional housing demand, thus raising housing prices. (Or in plain English: the only thing worse than new housing is new jobs.)
Why do I find this theory implausible? First, I find it hard to believe that a resident of a new apartment building has moved from Sacramento or Des Moines just because a new apartment was built in San Francisco; after all, when San Francisco adds a new building, Des Moines residents aren't likely to know of the building's existence, let alone move to San Francisco because of the new building.
It seems to me more probable that the new building's residents already lived in the city (or perhaps one of its suburbs). They might have been living with roommates, or in less desirable buildings in the city, or in suburbs that are also part of the region’s housing market. So it seems to me unlikely that new apartments create a significant number of new city residents—unless, of course, the apartments actually lower other buildings' rent enough to make city living more popular (in which case the entire "induced demand" argument is wrong, because new supply in fact lowers rents rather than raising them).
Second, the "induced demand" argument assumes that new affluent residents lead to new working-class residents. But even if the new residents spend enough money to create new working-class service jobs, it seems hard to believe that large numbers of people will move to high-cost San Francisco to be grocery clerks (unless labor demand is so high as to induce significant wage increases and thus make housing more affordable rather than less affordable). It seems more likely that these jobs will be filled by existing residents lured off the unemployment rolls, and that if urban housing prices are high, these residents will live in low-cost suburbs.
Third, "induced demand" doesn't fit the data. If new housing really increased prices, places that would allowed lots of new housing would consistently have higher prices, and thus the most affordable places would be places where new construction was virtually impossible. But in reality, it appears that places that build a lot of housing, and that impose fewer restrictions on building, seem to have lower housing prices—which is why some high-growth Sun Belt cities are less expensive than San Francisco. (See for example the graph of the bottom of this trulia.com post.)
Redmond cites a decade-old study prepared for the city's planning department. The study states (p. 7): "An underlying assumption of the study is that households that rent or purchase new units represent net new households in the city of San Francisco." In other words, induced demand is not a conclusion of the study, but an assumption of the study. If you assume that new buildings mean new residents, of course you will find that new housing means new demand for housing. In short, garbage in, garbage out.
Moreover, this study was hardly an impartial examination of evidence. Rather, it was a "nexus study"—that is, it was designed to show that there was a nexus between new housing and the need for inclusionary zoning. Why was the study necessary? Because, under state law,* if there is no reasonable relationship (or "nexus") between a development fee imposed by the city (such as inclusionary zoning) and the impact of development, the fee is illegal. So if the city's consultants had failed to find such a nexus, they would have found that the city’s program would be illegal—a result not conducive to the consultants getting hired in the future.
In sum, the old-fashioned conventional wisdom of economics stands—more supply still means lower prices, and less supply means higher prices.
*In particular, the study references California's Mitigation Fee Act.

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HUD's Office of Policy Development and Research
HUD's Office of Policy Development and Research
Chaddick Institute at DePaul University
Park City Municipal Corporation
National Capital Planning Commission
City of Santa Fe, New Mexico

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