This story is the fourth in a four-part series. Read Part 1 here, Part 2 here and Part 3 here.

The U.S. has been short of the homes it needs to meet its growing population for more than a decade, driving up prices and shooting down the dreams of millions of would-be buyers.

While buying a starter home was once a safe and attainable way to build wealth, rising home prices, falling construction rates and economic volatility have left the U.S. without nearly enough affordable housing.

Daryl Fairweather, chief economist at Redfin, said there are two basic ways of looking at the depth of the affordable housing shortage: how much of a household’s income it costs to buy a home of average price, and the share of homes for sale in a region that are affordable for someone making the local median income.

For prospective homebuyers, Fairweather said, one way focuses on “how much are they going to have to spend out of their earnings to afford a home,” while the other focuses on “what share of homes in the market are actually priced that way.”

The U.S. has been able to make a small dent in the housing shortage, as a construction boom........

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