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Housing prices vary widely across American cities and clearly affect the standards of living for urban dwellers. But what about the other costs of big-city living: money spent on gas, health care, groceries, entertainment and the daily Starbucks fix?

In a new study, Stanford economist Rebecca Diamond tackles the challenge of looking into the significance of these and other smaller-ticket expenses across the country and how they factor into the standards of living for those who are rich or poor, highly-educated or not, or residing in the country’s most and least affordable urban areas.

The analysis, based on a unique dataset of 3 million households, uncovers fresh evidence that entire urban areas — and not just neighborhoods within cities — are becoming gentrified.

“Income segregation across U.S. cities is big and it’s not getting better,” Diamond says. “And for cities worried about losing their lower and middle classes, there’s reason to worry even more.”

Diamond and her co-author, Enrico Moretti, find, for example, that low-income residents in the country’s most expensive urban areas bought less than half the amount of goods and services than those who lived in the cheapest cities. At the same time, they were far more likely to be spending more than their earnings just to make ends meet. Moretti is an economics professor at the University of California, Berkeley, and was a visiting professor at �������during the 2015 academic year.

(As of 2014 — the year of the spending data studied — the least affordable, or most expensive, urban area in the U.S. was San Jose, Calif.; the cheapest was Natchez, Miss.).

Education levels make a difference

For a high school dropout, moving from the country’s least expensive metro area to its most expensive would result in a nearly 27 percent drop in purchasing power.

This wasn’t the case for college graduates. Whether they lived in a high-priced coastal locale or a cheaper Rust Belt city, they bought similar volumes of appliances, restaurant meals, yoga classes, and other goods and services. That’s because their wages adjusted to the local cost of living. Incomes for high school graduates or dropouts did not: Big-city incomes for lower-skilled workers were not enough to cover higher living expenses, forcing them to cut back substantially on purchases.

Diamond, a senior fellow at the Stanford Institute for Economic Policy Research (SIEPR) and the Class of 1988 Professor of Economics in the Graduate School of Business, says the research adds new weight to a decades-long phenomenon in which the country’s most expensive — and among the most desirable — places to live have become increasingly inaccessible to lower and middle classes. This includes not just city centers, but also inner and outer suburbs.

“Different labor market opportunities have pushed high-skill, high-income workers increasingly into superstar cities like San Francisco or New York and surrounding areas,” Diamond says. “And they have pushed everyone else into smaller, more affordable regions that offer them more bang for their buck.”

The study was published as a working paper on Monday by the .

For low-income households, location matters

In earlier research into a phenomenon she calls “economic well-being inequality,” Diamond has documented how U.S. cities over time are segregating based on education and wages. High-income, high-skill workers, she wrote in a  in the American Economic Review, were clustering in metropolitan areas that had invested in making themselves more attractive to them. As housing and other costs rose in response, these sought-after cities were becoming increasingly out of reach for the lower and middle classes.

For the current study, Diamond and Moretti set out to examine an aspect of standard of living that has proven hard to measure: “market-based consumption,” or the full monetary cost of living from one U.S. city to the next — beyond big-ticket items like housing and taxes and excluding intangible costs like crime rates, school quality or weather. To evaluate living standards, economists weigh market-based consumption against wages.

“In other words,” Diamond says, “how much money would you spend to consume the same goods and services in City A versus City B to achieve the same standard of living, or economic well-being?”

Meaningful comparisons among U.S. cities, however, have been hard to draw because they require a massive dataset on how much people are spending to buy these goods and services and across geographies.

Diamond and Moretti overcame these challenges using a financial software provider’s data on all financial transactions, including credit and debit card purchases, made by 3 million households — the equivalent of 5 percent of U.S. households — in 2014. The scholars then applied these real-life expenses to price indices they created to calculate localized costs of living across 443 metro areas that account for just over 96 percent of the U.S. population.

They find huge variation in living costs across the United States. While high-income households don’t see much impact on their living standards when relocating to a more expensive area, the difference in purchasing power for low-income households is stark. Low-income families in the country’s most affordable urban areas enjoy a level of market-based consumption that is 74 percent higher than that of families with the same income in the least affordable cities.

What’s more, there are signs that low-income households in pricier locales experienced higher levels of financial distress than their counterparts in cheaper cities, according to the study. They were significantly more likely to have a negative savings rate — meaning their spending is greater than their income — and to pay more bank overdraft fees.

Behind the inequality: uneven wages

Diamond and Moretti unearth wide disparities, too, when analyzing spending across urban areas based on education level.

Like their income analysis, the researchers find no difference in living standards — as measured by costs of living — among residents with an undergraduate degree or higher. Whether they live in an expensive coastal spot like Seattle, San Francisco, Boston or New York, their lifestyles are similar to their counterparts in the country’s cheapest urban areas.

For high school graduates in the costliest cities, however, living standards are far worse than they are for their peers in the country’s most affordable places. High school dropouts see significant decreases in consumption no matter where they live, but the declines are especially steep in the priciest locations.

“Metropolitan areas that we think of as expensive don’t make college-educated people sacrifice their standard of living relative to, say, Cleveland because their higher wages compensate for higher prices,” Diamond says. “Lower-skill people don’t earn this income premium, so they have to cut their consumption, or standard of living, by a lot.”

The study’s measures of standards of living and the effects of prices on them have a few limitations. The authors don’t, for example, factor in how climate, crime rates, and other amenities impact quality of life. And because they look at non-cash financial transactions, they can’t assess how consumers without bank accounts — presumably among the lowest wage earners — manage across U.S. cities.

Overall, however, Diamond says the study points to the lack of labor market opportunities for low-skill workers in the country’s biggest and most attractive cities. And they sound yet another alarm that large, upscale cities like San Francisco and New York are failing large portions of their population.

“The wage effects that we identify are exacerbating inequality,” she says.