Don't update too much on money-happiness correlations
Survey evidence on money vs. happiness isn't that informative. A simulation model to make some sense of it all.
I. The debate
Does money bring happiness?
This question has intrigued philosophers, economists, and poets for centuries. Wasn’t it Shakespeare who wrote:
I yearn to be a billionaire, so verily, To purchase all the treasures I lack sorely. To grace the cover of Forbes, my visage seen, With smiles beside fair Oprah and the Queen.
I mean, obviously it wasn’t, but it’s still a really important question.1
I found myself diving into it after listening to an episode of the “80,000 Hours” podcast. In this episode, host Rob Wiblin spoke with Spencer Greenberg about the relationship between money and well-being.2
A famous study by Nobel laureates Angus Deaton and Daniel Kahneman found that beyond $75,000 per year, money doesn’t increase well-being. However, a decade later, Matthew Killingsworth found a stable positive correlation between income and well-being, even after $75,000. After some debate, an adversarial collaboration by Kahneman and Killingsworth concluded that well-being does rise with income.
Cool story of scientific progress, right? Unfortunately, as Rob noted, all of this evidence is just correlations. As a result, we could be misled in many ways.
For example, you probably need to work harder to get more money:
[…] there's a really obvious way in which you could have no correlation […] people face this lifestyle choice between going and getting jobs where often they work long hours in unpleasant work in order to make more money, or do they take an easy job that doesn't pay very much and work fewer hours and enjoy more leisure?
There are other problems, too. Some people may have a cheerful disposition, which makes them perform better at work and report higher levels of well-being. Or there could be a third factor—such as good health—that increases both income and well-being.
In other words, wasn’t all this debate much ado about nothing?
II. A simulated world
To find out, I created a simple simulation model.
In this model, more money is unambiguously good (i.e., it increases utility). We can use the model to generate artificial data on income and well-being to check how they interact. If we find that, even in this idealized setting, income is not always positively correlated with well-being, that’s bad news for the survey evidence.
Spoiler alert: Bad news is exactly what we’ll get.
I’ll spare you the technical details (you can find them in the technical report; here’s the Colab notebook). However, here are the main elements:3
Trading off consumption vs. leisure. People have stable preferences over consumption and leisure and choose how many hours to work based on these preferences. (Technically, they have log utility over consumption and leisure.)
Mapping utility to well-being. To keep things simple, reported well-being is just utility plus noise. To simulate reported well-being, I first transform utility to range from 1 to 10. Then, I calculate reported well-being as transformed utility plus some random noise. The noise captures measurement error or elements of well-being that are orthogonal to consumption/leisure.
Generating variation in income. In this model, income is endogenous, meaning that it’s partially determined by people’s decisions (specifically, how many hours they choose to work). To generate variation in income, we need to vary something exogenous. I’ll consider several different scenarios below.
III. Results
OK, let’s start simulating.
Scenario #1: Different wages
Imagine a world where people have different incomes because they get paid different wages. Think of it as simulating an ideal experiment: Start with a set of identical people and assign some to high-paying and some to low-paying jobs. Then, check who’s happier.
Rob mentioned this in the podcast:
[…] something that would truly be more convincing […] would be to find a case where people, for random reasons, end up getting a salary increase versus other people in the same job, who for basically random reasons don’t.
Even in this idealized setting, hours worked—an endogenous choice—affect the income-happiness correlation.
The scatterplot below shows the relationship between income (x-axis, in thousands of dollars) and well-being (on a scale from 1 to 10). The parameters are chosen to be somewhat realistic, reflecting typical income ranges and well-being scores. More details on the methodology can be found in the technical report.
We get a moderate positive correlation:
Takeaway: If wage differences are mostly random, we should see a positive correlation between income and well-being in survey data. Unfortunately, that’s unlikely to be the case in reality, since wages vary systematically with skills, education, and experience, and these may directly influence happiness.
Scenario #2: Different preferences
Next, let's consider differences in preferences. Here, everyone is the same except in how much they value consumption vs. leisure. Those who prioritize leisure end up working fewer hours and earning less.
There’s essentially zero correlation between income and well-being in this scenario:
What’s happening? The relationship between income and well-being is now U-shaped.4 Agents with a strong preference for consumption work long hours to consume a lot. They sacrifice leisure, but they don’t care much about that. As a result, agents with high incomes are close to their “ideal” consumption/leisure point. Similarly, agents with very low incomes are content with their situation because it provides them with ample leisure time. In contrast, agents in the middle of the income distribution struggle to achieve their “ideal” balance, as they neither earn enough to satisfy their consumption aspirations nor have enough leisure.5
The story makes intuitive sense. However, it’s all driven by how utilities are mapped to well-being. You could argue that the agents are all equally well-off in this scenario. Yes, they have different preferences, but they face identical constraints and endowments. They should all report the same level of well-being. However, that doesn’t happen.
Takeaway: The correlation between income and well-being can be misleading when people have different preferences. Even if everyone faces the same constraints, their reported well-being can vary a lot.
Scenario #3: Mistakes
Income-happiness studies hold the promise to improve our life choices. Should you pursue a high-powered career that requires spending the weekends away from your family? If income doesn’t increase well-being, maybe you shouldn’t.
This observation suggests that we actually don’t know how much money we need. We can capture this uncertainty in the model by assuming that we don’t optimize perfectly.
Here’s what the income vs. well-being relationship looks like with such choice errors:
Again, almost zero correlation.
The intuition is similar to the case with preference differences. People who make the optimal choice obtain the highest well-being. In the simulation, that occurs at $100,000. Folks above $100,000 are working too much, and they would be happier by reducing the hours worked. Vice versa, below $100,000, the agents are working too little, and they could increase happiness by putting in more time. When you average across everyone, you get close to zero correlation.
This scenario illustrates that income-happiness correlations are likely context-dependent. If you’re looking at a sample of quiet quitters, you may see a positive correlation. But if you’re studying over-achieving workaholics, you could see the opposite.
Takeaway: The true relationship between income and well-being might be positive, but survey evidence can show zero correlation due to choice mistakes. The context of the sample (e.g., over-achievers vs. quiet quitters) can also change the observed correlation.
Scenario #4: Unhappy materialists
Finally, let’s consider a more complex case in which people who care more about consumption are inherently less happy. This models the idea of “unhappy materialists,” something mentioned by Rob in the podcast:
These may be broad stereotypes, but it wouldn’t surprise me if the kind of people who feel like they need money in order to be happy might be less happy to start with. They might be different personality types, someone who is more material focused, and they might indeed need money to be happier, but they’re starting from a lower baseline […].
We now obtain a negative correlation between income and well-being:
Takeaway: Observational data is complicated. Different factors can interact, impacting the correlations between income and well-being in hard-to-predict ways.
IV. Lessons learned
The main lesson from the simulation is this: Even if more money does make people happier, that may not be obvious in the survey evidence. You may get a negative correlation, and that could still be consistent with “more money = more happiness.”
This shouldn’t be too surprising. Income and well-being are both endogenous variables. You shouldn’t expect to uncover any causal relationship by just regressing one endogenous variable on another. Yet somehow that’s what this literature has been doing.
What should we be doing instead? I’ll second Rob’s call for more research using natural experiments and other tools of the credibility revolution. Randomized experiments are hugely important, too. For example, a recent randomized trial of universal basic income studied how income affects mental health; similar trials could be done for experienced well-being. Given how expensive it is to run well-powered experiments, there’s also a role for structural econometric models.
In the end, was this happiness debate much ado about nothing? Should we just ignore the survey evidence on income vs. happiness?
I wouldn’t go that far. All evidence is evidence, even if it doesn’t come from a randomized experiment. However, I don’t think there’s that much we can learn from these surveys. This evidence is fundamentally limited.
So, don’t update too much on happiness-income correlations. For as Shakespeare never did utter:6
Heed not the surveys, where mere shadows dance, For joy's true essence lies beyond their trance. The fool who trusts each chart and fleeting trend, Shall find that happiness doth not depend.
Thanks, ChatGPT, for the Shakespearean translation.
Spencer has an awesome show of his own, ”Clearer Thinking”.
To avoid complexity, the simulation doesn’t include two features that likely matter a lot in practice: Hedonic adaptation and compensating differentials. With hedonic adaption, it’s not income levels but income changes that impact well-being. However, capturing this would require a dynamic model. With compensating differentials, firms must pay more to attract talent if a job requires long hours or is otherwise unpleasant. In equilibrium, we may observe different combinations of hours and income, yet they will yield similar utility because of competition between firms.
If you play with the code, set sigma = 0 to see this.
In this model, agents don’t technically have an “ideal” consumption/leisure point since utility is unbounded. However, I’m effectively using an “ideal” consumption/leisure point to map utilities to [1, 10]. See the technical report for details.
Thanks again, ChatGPT.