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Six weeks of take-home pay.

That's how much cash families should aim to set aside to ride out gyrations in their income and expenses, said a new analysis from JPMorgan Chase's research arm.

The recommendation, based on an analysis of millions of Chase checking accounts, is considerably less than the traditional rule of thumb of three to six months of take-home pay.

But even so, most households fall short, the report found: About two-thirds lack the recommended buffer.

To cushion against a simultaneous spike in expenses and dip in income, a middle-income family needs about $5,000 in a rainy-day fund but has just $2,000. Lower-income families need about $2,500 but have just $700.

A smaller buffer, however — just less than three weeks of pay — can help families get through a lesser jolt, from either a dip in income or a jump in expenses, the report found.

The findings were part of a report on income volatility that the JPMorgan Chase Institute published this week. The report examined inflows and outflows from 6 million active checking accounts over a period of about six years that ended in December. The checking account data was anonymous.

Americans' lack of emergency savings has been a concern for years. The Pew Charitable Trusts found in 2015 that many families lacked funds to cover a $2,000 expense.

In the current long period of economic growth and low unemployment, it is especially frustrating that many families continue to lack a cash buffer, according to a report this month from the AARP Public Policy Institute. AARP found that more than half of U.S. households — 53% — lacked an emergency savings account, including a majority of people older than 50.

While it's easier for more affluent people to save, some low-income families do manage to set aside money while higher-income families do not, AARP found. For instance, a quarter of Americans earning more than $150,000 a year have no emergency savings account, the report found.

Regardless of their income, families with no emergency savings are more likely to suffer financial hardship, said Catherine S. Harvey, the author of the AARP report.

Emergency savings are "necessary to meet the obvious issues that arise on a consistent basis for all of us, whether it's costs for our home, car or health," said George Barany, director of America Saves, a campaign that is managed by the Consumer Federation of America.

One idea gaining traction is to help people contribute to emergency funds through their place of work, much as employees contribute to workplace retirement plans like 401(k) accounts.

Prudential Financial, for example, last year began offering "sidecar" saving accounts, which allow employees to contribute after-tax money for emergency purposes alongside their pretax savings in 401(k) plans. The program helps workers avoid taking out loans or hardship withdrawals from their retirement plan, which can hurt long-term savings, said Harry Dalessio, head of institutional retirement plan services at Prudential.

A dozen of its corporate clients offer employees the savings accounts, Prudential said, and 10 more are expected to add them by spring.

Ann Carrns writes for the New York Times.