For those of us frustrated by a lack of cash flow, it’s sometimes hard to believe that money doesn’t actually buy happiness . Could this possibly be true? Mathematical economist Dr. Christian Bayer from the Hausdorff Center for Mathematics has found that the adage has some validity, but only to an extent. Working with Professor Falko Jüssen from Bergische Universitaet Wuppertal, Bayer and his team published the study in the latest issue of the American Economic Journal.

To judge how happy people were based on their income, Jüssen and Bayer used a new method of analysis that hadn’t previously been used to examine the topic. Most studies that previously examined income levels and personal happiness have been based on based on statistical models, meaning they didn’t look at how happiness changes with income. The team of mathematical economists took changing income levels into consideration, and found the answer to their question was more complex than formerly believed.

Overall, they found that long-term, consistent increases in income affected an individual differently than a temporary raise. A person who grows substantially in their income over a long period of time tended to be more satisfied with life, while people who momentarily earned more money by getting a bonus, for example, reported no distinguishable differences in happiness.. More money, therefore, can make you happier , but only when it’s for the long-term.

On top of this, the researchers found that the number of hours an employee worked each week also affected how happy they felt. “Those who consistently have to work more become less happy,” Bayer said in a recent press release . “This finding contradicts many other studies that conclude people are more satisfied when they have any job than none at all.” Bayer noted that these findings suggest people who are unemployed suffer because of lack of income, not necessarily lack of employment.

In addition to this, the state of the financial market also impacts a person’s overall satisfaction, because it directly effects how income may fluctuate, and ultimately, the number of hours a person must work. Researchers therefore concluded that income as well as hours worked were factors that determined a person’s happiness.

Looking at past research, a 2014 study published in the Journal of Positive Psychology also found a more nuanced answer to money buying happiness. After interviewing the patrons of a San Francisco marketplace, researchers found that money can only produce happiness when it buys pleasurable experiences, rather than tangible items. Like Bayer and Jüssen’s conclusions, money-associated happiness was relative based on circumstances.

Ultimately, Bayer concluded that when it came to income specifically, the formula always remained the same; “persistently more money while working the same number of hours” is the key to happiness.

Source: Bayer C, Jueseen F, et al. Happiness and the Persistence of Income Shocks. American Economic Journal. 2015.

Howell, Ryan T., Pchelin, Paulina. The Hidden Cost of Value-seeking: People do not Accurately Forecast the Economic Benefits of Experiential Purchases. Journal of Positive Psychology . 2014.