This equation accurately predicted the happiness of over 18,000 people (during research). That's huge and potentially very important for economic development. As I've argued before, the purpose of economic development, indeed of any public program is to try to increase happiness. You can see the University College London's explanation for the formula here.
In short this formula means that momentary happiness is based not just on how things are going, but whether they are going better than expected. Further, happiness is largely momentary, because things which made someone happy tend to fade fairly quickly once the moment has passed.
Of course this formula is still only based on the ebb and flow of momentary happiness, it doesn't predict overall life satisfaction. There are many other traits involved in this, many of which are very subjective and cultural. THis, however, is an economic blog so I'm going to discuss the impact of the economy a.k.a the economy on happiness.
As the "Brookings Institute" reports Cross-National surveys indicate that wealthier countries tend to be happier than poorer countries to a limited extent. However, the primary indicator of happiness was an individuals income compared to other people within one's own country, that is, people tended to be happier based on how much money they were earning compared to the other people in their country. Remember that the above formula indicates that happiness is largely based on expectations.
This effect, however, isn't entirely comparative, as within developed economies such as the United States and Europe, the over all level income inequality tended to have very little impact on happiness, Income inequalities negative impact on happiness is primarily related to developing countries. I would postulate that this is in part because needs aren't being met among the poor in developing countries. Though a large part of this comes from the fact that in developed countries there is a perceived ability for people to move up the economic ladder.
The most important thing to note from an economic development perspective, however, is that annual income, however, did have a direct impact over all on reported levels of happiness. You can read more about that research here.
Perhaps more interesting, however, is that economic improvement is correlated to greater life satisfaction, you can read the Pew Research study on this here.
This lends credence to LinChiat Chang and Robert M. Arkin's research which found that people turn to materialism to deal with uncertainty. While many would deride this behavior I would point out that cultural traits like this are important survival methods and we should be focused on how to harness them to make people happier, not on how to change people's culture.
In fact, culture must be considered in all attempts at improving people's lives, as the differences between countries and happiness levels are likely largely cultural. So while higher incomes increase happiness within a culture, other aspects of a persons culture have a much larger impact on their happiness. One of these, which is important to economic development is Uncertainty Avoidance.
It's likely that in many cases uncertainty is one of the key causers of unhappiness, I.E. even if you have a great job, if you're uncertain whether you're going to be laid off or not, you'll potentially be more unhappy than someone with a worse job but knows they are secure.
Uncertainty Avoidance is one of the big traits Cross-Cultural Psychologists use to determine the difference between two cultures, By way of comparison, Japan and have a high level of Uncertainty Avoidance. You can see a complete list of countries by level of UA here.
So what does all this mean?
It means that economies need to be structured in such a way as to allow people to be actually achieve something, to fulfill their dreams when ever possible, while helping reduce uncertainty (the likelihood that they'll loose their job, home, etc). Finally economic growth is incredibly important to a persons happiness within every country which has been studied.
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