# Subsistence and Self-perpetuating Inequality

Posted by {"login"=>"dvollrath", "email"=>"[email protected]", "display_name"=>"dvollrath", "first_name"=>"", "last_name"=>""} on July 09, 2014 · 6 mins read

It's common in development or growth to think about subsistence constraints. From a macro perspective, we think of them as an explanation for the low income-elasticity of food expenditures, and therefore a cause of structural change away from agriculture. The idea has there in development for years. I don't know the full intellectual history here, but my understanding of it goes back to The Moral Economy of the Peasant by James C. Scott. He says you can understand a lot about the peasant mind-set by realizing they face subsistence constraints, and that this makes them incredibly risk averse. Kevin Donovan has a recent paper that looks at the macro consequences of this risk-aversion for agricultural development.

I think the concept of subsistence constraints and risk aversion is useful for thinking about inequality in general, even outside of developing countries. In particular, it offers an explanation for why inequality will be self-perpetuating and how mitigating inequality will be growth-enhancing.

If there is some subsistence constraint in your utility function, then your risk aversion is declining with income. You can take my word for it, or if you'd like to see it more clearly, let utility be

$$U = \ln{y-\overline{y}}$$

and the coefficient of relative risk aversion is then

$$\frac{-yU''}{U'} = \frac{y}{y-\overline{y}}.$$

Risk aversion approaches infinity as income approaches the subsistence constraint, meaning people will refuse to take any gamble that might put them below ${\overline{y}}$. Risk aversion approaches 1 as income rises. The value 1 itself isn't important, what's important is that as people get richer, they are willing to accept bigger and bigger gambles with their income, because they are less and less danger of falling below ${\overline{y}}$. Richer people are more risk-tolerant.

Combine this conception of subsistence and risk aversion with the commonly understood relationship of risk and reward. In finance and entrepreneurship, we generally believe that those willing to absorb higher risks are able to reap higher rewards. Entrepreneurs earned that money by taking a risk in starting a company. Aside from entrepreneurship, big fixed investments in education -- quitting your job to go back to school -- are very risky moves that in turn have high expected rewards.

Together, subsistence and the risk/reward correlation imply that inequality will be self-perpetuating. Poor people will not take on big risks (starting a business) because they cannot handle even a small probability of failure that takes them below subsistence. So they stay in low-wage jobs and don't undertake investments that might make them better off.

Well-off people are able to tolerate bigger risks, and so also earn higher rewards. They start businesses, get more education, or move across country for a new job. If it doesn't work out, they won't starve, so it's worth the risk. And because they undertake big risks, they tend to earn high rewards. The rich can expand their incomes and/or wealth at a faster rate than the poor, because of their higher risk tolerance. This naturally acts to expand inequality over time.

The crucial point is that there is no pathology to the poor refusing to take big risks. With subsistence constraints, the poor don't remain poor because they are lazy or stupid, but because they are rationally avoiding big risks that might push them below subsistence.

The conceit of people who espouse a "just deserts" theory of inequality (Greg Mankiw, Sean Hannity, et al) is that they would have been well-off regardless of where they start in life. They believe that they possess qualities -- smarts, skills, work ethic -- that make them valuable to the market, and that they are rewarded for that. But start them off in a truly poor household, one where the next meal is uncertain, and with 99.99% certainty they would not end up a professor at Harvard or, well, whatever Hannity is. There were big risks taken in their lives that had big payoffs. Risks they or their family would not have been able to conceive of taking if they were truly poor.

Subsistence constraints also imply that acting to mitigate inequality -- whether by raising incomes of the poor or making their incomes less uncertain -- would have a distinct positive effect on economic growth. Ensuring that people won't fall to subsistence (or below) means that more people are willing to start a business, and we get more economic activity, more competition, and more innovation. If more people are willing to go for advanced training (college or vocational school) then we get a more skilled workforce. Acting to insure or support poor incomes has positive spillovers.

Won't providing income support just incent all the poor people to stop working? Remember that most of the people screaming loudest about this - Casey Mulligan - are tenured professors who cannot be fired. Despite having no incentives whatsoever to continue working on research or provide more than perfunctory teaching, Mulligan continues to work. Why? Why does he not rationally show up to collect his check and then go home to eat Cheetos and watch Dr. Phil? If Casey Mulligan continues to work despite a guaranteed income, I'm fairly confident that the vast, vast majority of people will continue to work even if they are no longer at risk of falling into destitution.