A few months ago, Matt Bedsole got a call from two real estate developers asking for his help. Their plan to build a four-story apartment complex in Chattanooga, Tenn., had a financial hole that no backer seemed eager to fill. The developers needed $8 million. Would Mr. Bedsole be interested in stepping in?

Mr. Bedsole is not a normal investor. He is the chief executive of Invest Chattanooga, a fund set up by the city of 200,000 to invest in local apartment projects. Unlike private equity firms — the main backers of new construction — he judges deals not solely on their financial return, but on how much housing they can deliver the city.

The apartment complex cleared that hurdle. It called for 170 new units that would replace a self-storage center ringed by barbed wire, in a gentrifying part of the city. But Mr. Bedsole had terms. In exchange for the $8 million investment, he got a 51 percent stake in the building and an agreement that 30 percent of its units be priced below market rate. The developers said yes. They closed the deal over pastrami sandwiches.

“Money is tight and developers don’t have a ton of options for capital right now,” Mr. Bedsole said in an interview. “We have it, but we want affordable units in the deal.”

Invest Chattanooga is part of a new class of government-backed funds that invest directly in new housing. The aim is to speed up construction and create housing that is permanently affordable and controlled locally. In the process they are rewriting how local housing programs have traditionally operated.

Each effort is a little different, but the guiding principle is to get developers to build more housing, with lower rents, in exchange for public investment. Instead of asking a high rate of return, as a private investor would, these funds require less money back from developers but stipulate that a portion of the units carry below market-rate rents.

They come at a time when a mix of higher interest rates and rising costs for insurance and materials like lumber have caused investors to run from new construction. Economists estimate the nation needs about 2 million new housing units, yet the pace of home building slowed last year.

Some states, like Hawaii, have created funds that lend money to developers on more favorable terms than Wall Street or a bank would, while others, including New York, have created funds to accelerate stalled projects. Atlanta aims to use public land to stimulate new home building: The city’s Urban Development Corporation contributes city-owned land to private development projects and keeps a stake after the building is completed.

Then there are public investment funds like the one in Chattanooga.

There are about two dozen of these funds in the United States, said Shaun Donovan, the chief executive of Enterprise Community Partners, which recently created a team to help them and is trying to set up its own fund to augment their efforts. The funds provide “capital, but capital at this moment of maximum impact, which is getting the building out of the ground,” said Mr. Donovan, who served as the housing secretary in the Obama administration.

Most of these efforts were inspired by Montgomery County, Md., whose Housing Opportunity Commission has for decades been a kind of national laboratory for affordable housing innovation. Mr. Bedsole has been something of a human catalyst in this process: He helped create Atlanta’s system based on the Montgomery County model, then took these ideas to Chattanooga last year.

“The cavalry isn’t coming, so we have to figure this out on our own,” said Tim Kelly, Chattanooga’s mayor.

From Public Housing to Patchwork

Figuring out how to produce low-cost housing for people who cannot afford market rents is a riddle that has vexed cities throughout the modern era. Governments have spent much of the past century veering between public and private sector solutions. Today most new affordable housing is delivered by a hybrid system, in which public subsidies finance private development.

That system is a product of shifting politics more than considered policy design. Starting in the 1970s, the federal government essentially stopped building public housing as part of a broader shift away from welfare benefits. What replaced it was a patchwork of rental vouchers and tax benefits — the biggest of which, the Low-Income Housing Tax Credit (LIHTC), was created in 1986 — for companies that provide affordable housing. Local governments now depend on that credit to build everything from low-cost apartments for teachers to supportive housing for people leaving homeless shelters.

One of the problems with low-income tax credits is that they are complicated to use and expire over time, often between 15 and 30 years, at which point the building’s owner can start charging market rents. It’s a galling turn for cities, since they often give millions in grants to finance affordable projects. To prevent building owners from evicting low-income tenants after the affordability restrictions lapse, many governments end up buying buildings back.

“So now the state has paid for the building twice — initially with subsidies, and then by giving a wad of cash to the developer,” said Stanley Chang, a state senator in Hawaii. “That is obscene.”

A Small Chip at a Growing Problem

Mr. Kelly, the mayor of Chattanooga, said he created Invest Chattanooga to prevent that obscenity. A businessman who ran car dealerships and co-founded the local soccer club, he was elected in 2021 (and re-elected last year) on an affordable housing platform.

At first, Chattanooga responded to its housing crisis by overhauling its zoning laws to allow more density, and legalizing backyard units on residential lots. This was the formula followed by many state and local governments over the past decade as rent and house prices have ballooned. But, as in many cities, the construction that followed leaned heavily toward higher-end buildings, where rents are too expensive for large swaths of the work force.

According to a city report, over the past five years Chattanooga has lost about half of its apartments that rent for less than $1,000 a month. The new apartments rent for too much, while federal programs do not produce enough units to meet the need.

But there are two ingredients in construction: land and money. So Chattanooga decided to focus on the second of these and became an investor, putting up $20 million to create Invest Chattanooga and hiring Mr. Bedsole from Atlanta to run it.

Invest Chattanooga is run like a business that makes money, then turns profits into cheaper housing. It puts up the initial cash, usually a mix of equity and debt financing, that developers need to get a bank loan. In exchange for the money, projects built with the fund must have at least 30 percent of their units reserved for families making below the median income in the area.

The city gets a return but it’s low — about 8 percent on the recent deal to replace the storage center, versus private equity firms that in many cases ask for double that amount. That difference can mean a developer saves several million dollars on a multiunit building, making it possible to lower the rent. And unlike units built with federal tax credits, Invest Chattanooga owns the building so can capture the upside of higher land values down the line.

Mr. Bedsole said Invest Chattanooga has a relatively modest goal of producing 100 affordable units a year by 2030, and to raise an additional $20 million for more projects. It is one little chip in a problem that gets bigger every day. Unlike the public housing agencies of old, his agency is not replacing developers in the process of building housing. Rather, it is trying to replace the financiers who decide what does and does not get built.

“I’m not competing with developers,” Mr. Bedsole said. “I’m competing with private equity.”