Economists say this is the minimum amount of money you need in an emergency fund

Money experts generally encourage you to set aside three to six months' worth of living expenses in an emergency fund. Some even want you to stash away a year's worth.

After all, life doesn't usually go as planned: There could be another recession, you could lose your job, have a medical emergency or have to deal with a car breaking down. That's why, when it comes to emergency savings, "more is always better," personal finance author David Bach says.

But economists Emily Gallagher and Jorge Sabat challenge the oft-cited savings rules in their 2019 report, "Rules of Thumb in Household Savings Decisions." "People are usually given really high savings thresholds, like you should be saving six months' worth of income or you should have $15,000 squirreled away," Gallagher tells CNBC Make It. But those numbers aren't "based on much," she adds.

After crunching the numbers, Gallagher and Sabat found a more realistic amount for low-income households, specifically, to aim for: $2,467. If you have that much saved, your probability of falling into financial hardship (not being able to pay rent, bills or medical care) is low.

To get to that number, Gallagher and Sabat, who are also assistant professors of finance, used data from the Survey of Income and Program Participation (SIPP) to graph the relationship between falling into hardship in the next six months and how much you have saved as a buffer. They looked at financial information on more than 70,000 lower-income households, which the report defines as those earning under 200% of the poverty line. To put that into context, that's up to about $30,000 a year for a family of four, says Gallagher. This group represents "about 30% of the U.S. working-age population," she adds.

They found that if you have very little saved — say $200 to $500 — each additional dollar you set aside dramatically reduces your likelihood of falling into financial hardship. But once you have at least $2,467, "all of a sudden, saving an additional dollar didn't seem to be that helpful anymore," says Gallagher. "It still reduced your probability of falling into hardship a little bit, but it wasn't nearly as effective as when you were at low levels of savings."

Most money experts agree that the more you can save, the better off you'll be.

"We're not saying that $2,467 is the optimal savings level," Gallagher emphasizes. "Our results don't speak at all to achieving longer term financial goals, like paying for college or affording a house." Especially if you're planning ahead for bigger expenses in the future, you'll want to aim to save much more.

For people who struggle to set aside a portion of their income, though, $2,467 represents a good "minimum savings rule that you should be working toward," says Gallagher.

"Our data doesn't speak to middle- or higher-income people, but if this rule works for lower-income people, it should also work for middle- and higher-income people," she adds.

It's more important, though, for low-income households to build a buffer. "If middle- and higher-income people get hit with a major expense shock, like a car repair that costs $2,000, they might have enough discretionary income coming in that they could use to absorb the shock," Gallagher says.

"The problem for lower income people is that the majority of their income needs to cover everyday expenses. They don't have much discretionary income to work with and that's why having a savings buffer becomes particularly important."

"The basic genesis of this research came from looking around at the types of financial advice that people are given about how much to save," says Gallagher. "Households are given really lofty savings goals. If you're only making $25,000, someone telling you that you have to save six months' worth of income is really hard."

Even if you're making more than $25,000, building a substantial rainy day fund is difficult. In fact, nearly half of U.S. households can't cover a $400 unexpected expense.

"Our concern was that giving people really lofty savings goals might actually be discouraging them from saving," Gallagher adds.

She cites the "goal-gradient hypothesis," which is the idea that people work harder as they get closer to achieving a goal. "For example, when people have coffee punch cards, people actually start going to the coffee store more often as they get closer to the 10th punch," she explains.

Offering a minimum savings rule of $2,467 that may be more achievable for people could lead to more savings, says Gallgher. However, "we leave the task of testing this hypothesis to future research," she adds.

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