[edited] Inequality is a (small) problem for EA and economic growth

By Karthik Tadepalli @ 2022-08-08T09:42 (+99)

This post was formerly titled "Inequality is a problem for EA and economic growth". Alexander Berger pointed out a spreadsheet error, and after updated calculations the extent to which inequality is bad for growth is much, much smaller (25% vs 90%). I've thus changed the conceptual takeaways from this exercise. You can find the original version of the post here.

Recently, EAs have considered economic growth as a potential way to improve overall wellbeing and also help the worst-off people. The recently-influential Progress Studies movement focuses on economic growth as the most important way to improve people's lives. In an essay that won the EA Forum Decade Review, Hauke Hillebrandt and John Halstead argued that we should focus on promoting economic growth in developing countries as a better alternative to targeting the extreme poor with health programs or cash transfers.

This essay quantifies a common objection to economic growth as the best way to improve wellbeing: the objection that growth is unequally distributed. Inequality has been shockingly neglected by EAs, to the point that I literally had to create the inequality tag for posting this essay. This is probably because EAs care about maximizing welfare, not about reducing inequality: but I demonstrate that inequality can reduce the welfare gains from economic growth, so we have to consider it as a factor that could reduce the social value of economic growth.

To quantify this argument, I build on Open Philanthropy's framework for modelling the cost-effectiveness of growth. I extend this framework to account for inequality in two ways:

• I use an empirically grounded (isoelastic) utility function, rather than the more commonly used (logarithmic) utility function that overvalues consumption growth for well-off people. This change reduces the social value of economic growth by 25%.
• I use data on inequality of income growth, and show that adjusting for this inequality reduces the social value of economic growth by 36%, independently of the above change.

These magnitudes are not dramatic, but they are not trivial. They are worth considering for close comparisons between economic growth and other interventions, but they do not change the returns to growth by an order of magnitude.

Why inequality matters, even to utilitarians

Inequality is usually framed as a concern for egalitarian-minded people. But if you want to maximize utility, you also have to care about inequality, because of the simple fact of diminishing marginal utility. Inequality means that more income is accruing to people who don't derive as much utility from that income. Consider a toy example:

• There is an economy with two agents, Alice and Bob.
• Alice and Bob each have the logarithmic utility function $u\left(c\right)=\ln \left(c\right)$.
• The social utility function is the sum of their utilities, $U\left(c\right)=\ln \left(c_A\right)+\ln \left(c_B\right)$.
  • Note that this social utility function is completely neutral to inequality: it does not place any inherent weight on Alice and Bob having similar incomes, or penalize deviations from that.
• Initial GDP is $100, split unevenly: Alice has an income of $80 and Bob has an income of $20.

Now consider two scenarios of economic growth:

Scenario 1: GDP grows by 10% ($10). Alice and Bob split this surplus evenly, so Alice gets $5 and Bob gets $5. The change in social welfare is $$\Delta U=\left[\ln \right(85)+\ln (25\left)\right]-\left[\ln \right(80)+\ln (20\left)\right]$$ $$⟹\Delta U=\ln \left(85/80\right)+\ln \left(25/20\right)\approx 0.28$$ so utility increases by 0.28 log units.

Scenario 2: GDP grows by 10% ($10). Alice and Bob split this surplus unevenly, but proportional to their income, so that Alice gets $7 and Bob gets $3. The change in social welfare would be $$\Delta U=\ln \left(88/80\right)+\ln \left(22/20\right)\approx 0.19$$ so utility increases by 0.19 log units, which is a smaller increase than in scenario 1.

What's going on here? Even though aggregate income growth is the same in both scenarios, in the second, Alice gets a larger share of the surplus. Since she has more money than Bob, she has a lower marginal utility of consumption, so this uneven growth raises social welfare less than if both of them experienced the same $5 income growth. Inequality hurts social welfare even when you don't care intrinsically about inequality at all.

Utility functions and inequality

The above example uses a logarithmic utility function to translate income to welfare (the quantity we care about). This is very common in cost-effectiveness analysis. Open Philanthropy uses a logarithmic utility framework for all of their cost-effectiveness analyses.

Logarithmic utility functions display diminishing marginal utility of consumption, as the above example shows. However, the rate at which utility diminishes is unrealistically slow. For individuals with log utility, percentage changes in income are enough to summarize changes in utility: $\ln \left(c_{new}\right)-\ln \left(c_{old}\right)=\ln \left(c_{new}/c_{old}\right)=\ln (1+g)$ where $g$ is the percentage growth of income. This means that a 10% increase in income is equally valued by millionaires and by people in poverty. This is an implausible description of how changes in income actually benefit people.

An alternative approach to modelling utility is the isoelastic utility function: $$U\left(c\right)=\frac{c^{1-\eta }-1}{1-\eta }$$ $\eta$ is the elasticity of marginal utility of income: how much the marginal utility of income changes as income changes. This is actually a logarithmic utility function when $\eta ⟶1$. Researchers have tried to estimate $\eta$ empirically from people's decisions and found that people's behavior is better described by $\eta \approx 1.5$ (Evans 2005, Maddison and Groom 2019).

The isoelastic utility function with $\eta =1.5$ places much higher weight on income growth for the poor, and much lower weight on income growth for the rich, compared to logarithmic utility. Acknowledging this, GiveWell uses an isoelastic utility function to calculate their discount rate with $\eta =1.59$.

This difference in modelling is especially important for economic growth, which improves aggregate wellbeing and not just the wellbeing of the extreme poor. Logarithmic utility will substantially overstate the benefits of economic growth, by overvaluing increases in consumption for already well-off people, compared to how much they actually value it.

To concretely calculate how much this overstatement is, I used Open Philanthropy's cost-effectiveness estimates for productivity growth and adjusted the calculations for them in this spreadsheet.

• OP's modelling framework is used for computing the cost-effectiveness of R&D specifically, so I removed discounting factors that were specific to R&D. These changes mean that OP's framework is estimating the cost-effectiveness of globally increasing productivity growth, which has a new cost-effectiveness estimate of 169X (1.69 times as good as cash transfers to the poor).
• Using an isoelastic utility function with $\eta =1.5$ reduces cost-effectiveness from 169X to 130X, a 25% reduction in the estimated social returns to growth.

Thus, even conservative groundings of the utility function reduce the returns to growth by a tremendous amount.

An important caveat is that this idea relies on Open Philanthropy's framework for modelling growth, and their productivity growth parameters are calibrated with data from the US. This means that the discount factors could be different for other countries, especially for LMICs.

Inequality in income growth

Even if you believe that logarithmic utility is the best approach to modelling utility, you can't ignore inequality in income growth. That is, the reality of growth is not that every person is seeing their income grow by [average growth rate]%: income growth is highly unequally distributed. If the vast majority of people are seeing very little growth while a few see large growth, then economic growth is not increasing utility very much.

To incorporate these concerns, we need data on how much each income group has actually seen its income grow. Blanchet, Saez and Zucman (2022) provide such estimates for the US from 1976 onwards. I calculate the change in log utility using their data, and I find that inequality in income growth reduces cost-effectiveness from 169X to 108X, a 36% reduction in the social value of growth, even when assuming utility is logarithmic in income.

It's worth noting that unlike with the section above, this discount factor of 36% doesn't rely on any modelling assumptions for how growth arises. It is directly calculated from the income growth data.

This 36% discount is robust to different specifications on what "income" is, but it is unfortunately limited to the US in the past 50 years. How unequal income growth is globally is an open question. On the one hand, the US over the past 50 years has seen exceptionally unequal growth, and the stylized fact that LMICs are growing much faster than rich countries suggests that growth is accruing more to the poor than to the rich. On the other hand, the US's inequality over the past 50 years is not exceptional in a global context: most LMICs are comparably unequal to or more unequal than the US by Gini coefficient. So their aggregate growth does not necessarily translate into large income growth for their poor or middle class.

In the end, I would stand by this adjustment factor applying to global income growth, because the US is comparably unequal to the world's largest countries (China, India, Indonesia are slightly more equal while Brazil is much more unequal), and the US is also in between more equal OECD countries and less equal LMICs. For people who want to emphasize growth in LMICs which are even more unequal than the US, inequality would discount the social value of economic growth even more than what I've calculated.

Conjecture - redistribution as a cause area?

A natural objection to these calculations is that inequality might be causing growth to be higher, so the right comparison is not as if everyone got the average growth rate, but if everyone got a lower growth rate of income. This would be the right comparison if I were making an argument about promoting growth vs promoting large-scale redistribution to reduce inequality as an EA cause area. That would require knowing how changing inequality would change growth. But the comparison scenario in all of these calculations is not equitable growth or large-scale redistribution - the comparison is always cash transfers to individuals in Open Philanthropy's framework (recall that 1X is giving cash transfers to someone on $50,000 a year, and 100X is cash transfers to the extreme poor).

My goal with these calculations is just to show that our estimates of the social return to growth - that is, the actual utility that people derive from growth - is biased by ignoring inequality of income growth. Once we include inequality, economic growth looks less beneficial, and possibly less beneficial than interventions that target the extreme poor.

That said, a reasonable takeaway from this analysis is that reducing inequality itself would be a desirable goal for EAs to promote. Since unequal distributions of income lead to unequal marginal utility of consumption, they are inefficient: we could increase overall welfare by redistributing income. Of course, to quantify how desirable this would be as a policy agenda, we would need to know the relationship between inequality and growth. If an economic system that creates high levels of inequality also creates the most growth, then we need to quantitatively compare the benefits of reducing inequality with the costs of reducing growth.

Unfortunately, the academic literature on this question is not very confident. All studies I could find caution about error in measurement of inequality, omitted variable bias and reverse causality. Banerjee and Duflo (2003) showed an inverse U-shaped relationship: changes in inequality in either direction were associated with reduced growth. This nonlinear relationship between inequality and growth is generally plausible, and it makes it impossible to draw universal conclusions about the value of reducing inequality: its effect on growth will depend on the current level of growth and inequality.

So I am sympathetic to the extreme conclusion that large-scale redistribution is a desirable agenda based purely on the marginal utility of consumption. But that is an area where my intuition is not supported by any data.

Conclusion

When focusing narrowly on policies to target the extreme poor, inequality is small and thus may not change our conclusions very much: but as EA has expanded its focus to aggregate interventions like technological innovation and economic growth, inequality becomes more and more important to factor into our estimates. In the quantification exercise I have considered, it reduces the social value of economic growth by a modest amount, which could matter in close comparisons but would not change our estimates by an order of magnitude.

In general, considering inequality will reduce the value of aggregate policies like technological innovation and economic growth compared to analyses that assume they change everyone's income by the same amount. Redistribution may even be an important end on its own because of how much welfare is lost through the rich consuming income that they don't derive much utility from - but without knowing how redistribution affects growth, that's just a conjecture.