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 .
- The social utility function is the sum of their utilities, .
- 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 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 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: where 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: 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 . Researchers have tried to estimate empirically from people's decisions and found that people's behavior is better described by (Evans 2005, Maddison and Groom 2019).
The isoelastic utility function with 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 .
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 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.
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.
Hey Karthik, starting separate thread for a different issue. I opened your main spreadsheet for the first time, and I'm not positive but I think the 90% reduction claim is due to a spreadsheet error? The utility gain in B5 that flows through to your bottom line takeaway is hardcoded as being in log terms, but if eta changes than the utility gain to $s at the global average should change (and by the way I think it would really matter if you were denominating in units of global average, global median, or global poverty level). In this copy I made a change to reimplement isoelastic utility in B7 and B8. In this version, when eta=1.00001, OP ROI is 169, and when eta=1.5, OP ROI is 130, for a difference of ~25% rather than 90%. I didn't really follow what was happening in the rest of the sheet so it's possible this is wrong or misguided or implemented incorrectly.
You... are absolutely right. That's a very good catch. I think your calculation is correct, as the utility translation only happens twice - utility from productivity growth, which I adjusted, and utility from cash transfers, which I did not. Everything else is unchanged from the original framework.
You're definitely right that it matters whether this is global average/median/poverty level. I think that the issue stems from using productivity A as the input to the utility function, rather than income. This is not an issue for log utility if income is directly proportional to A, since it cancels out, but it is probably better to redo this with income statistics/income growth and see how that changes things.
I'll make a note about this at the top of the post and update it with a more substantive change to the conclusion when I've dug into it further.
Thanks for the thoughtful post, I really appreciate it!
Open Phil has thought some about arguments for higher eta but as far as I can find never written them up, so I'll go through some of the relevant arguments in my mind:
On your 36% adjustment within the log framework: I don't think our estimates for this are accurate to anything like 36%; I'd be happy if they turn out to be within a factor of 2-3x. So I find it easy to believe you could be right here. But I think your changes come from a period when inequality increased substantially, to a historically unusual level, and I would be surprised if it made sense to predict a continuation of that increasing trend indefinitely over the relevant horizon for Tom's model (many decades to centuries).
More broadly, I agree that the gains from redistribution can be substantial and I think our work reflects that (e.g., our Global Aid Policy program).
Thanks for the points, I should have done more due diligence into the arguments for each framework. That said, I don't see these as fatal flaws:
Tl, dr; I think most of the features of high η that you identify can be solved by having a high baseline welfare component of the utility function, and the others are not problems.
Thanks Karthik. I think we might be talking past each other a bit, but replying in order on your first four replies:
Thanks, appreciate it! I sympathize with this for some definition of low FWIW: "I have an intuition that low VSLs are a problem and we shouldn't respect them" but I think it's just a question of what the relevant "low" is.
“ 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.”
I thought this was a great point!
The Open Philanthropy report is not narrowly about the cost-effectiveness of increasing economic growth, it is about the cost-effectiveness of spending on R&D, which is one way to increase economic growth but not the only way.
Indeed, that's why I removed the discounting factors that were specific to R&D from their model (only crediting R&D with 40% of growth, and assuming only 70% diffusion of R&D to the rest of the world). Once you remove these factors, their model is a classic semi-endogenous growth model and is thus focused on the cost-effectiveness of TFP growth in the aggregate - no matter what the cause. Insofar as any path to sustained economic growth goes through productivity growth, I think their modelling framework is still very useful for evaluating the social returns to economic growth.
The only thing that is really specific to R&D is that in a semi-endogenous growth model, the number of researchers is an important input to the growth trajectory. But I am not focusing on the growth trajectory itself (which is affected by how you choose to model growth and what path is taken) - rather, I am focusing on the population welfare that arises from any given level of growth. Different paths to economic growth may yield different levels of economic growth, but they do not change the fundamental growth --> welfare mapping. So I don't think that the focus on R&D takes away from this argument in any way.
You say things like "Once we include inequality, economic growth looks a lot less beneficial than interventions that target the extreme poor." Insofar as I understand this sentence, you cannot conclude this unless you know about the cost of the intervention to increase economic growth. Your argument implies that the benefits of growth are lower than some models suggest, but since we don't know anything about costs, you cannot conclude anything about cost-effectiveness. So, it's not possible for you to conclude anything about the relative cost-effectiveness of different approaches
It's fair to say that I'm not rigorously comparing these two approaches. What I am doing is showing that one has a 90% lower value than estimated, and the other is not affected. In general, this would lead you to update in favor of targeted interventions - hence saying that it looks better. The strength of that update may not be enough to overcome your prior. But I'm not litigating the entire growth vs RD debate here. The argument is just "inequality is a big problem for growth".
Agreed. I would like to see this done for LMICs and not rich countries as it seems that could make a big difference.
For what it's worth the Open Phil framework (with R&D discount factors removed) is looking at the effect of global growth, not growth in rich countries. That should attenuate the gap between their results and the results of modelling this just in LMICs. And I don't know how big a big difference is, but to take it from my final estimate of 12X to 1000X would require growth promotion in LMICs to be over 80 times more cost effective than global growth promotion, which seems like a lot.
Yes and to be clear, I think the analysis is well done and think this adds to the debate, so I appreciate you doing this
Another point: it seems intuitively plausible that redistribution promotes growth because it would likely tend to increase human capital. If someone is consuming $2.30/day with subsistence farming, there is low human capital, but redistribution allows them to increase human capital, this will tend to promote economic growth.
Does anyone know where literature is on the growth effects of Global health and development charities vs traditional economic investment?
This is not usually the comparison that is made in the literature, so it's not definitively answered. This comment thread on Hauke and John's original post has some back and forth. Basically human capital interventions definitely have an aggregate effect, but the strength of that effect compared to growth-promoting policies is unclear.
It seems odd that this has not been explored more thoroughly by the EA community, especially given its proclivity for consideration of the long-term.
Great work – I've been waiting for someone to use the isoelastic utility model! Are you going to submit this to the Criticism and Red Teaming Contest?
Thanks! I hadn't thought about it and frankly don't know if this is substantive criticism/red teaming, but I'll think about it.
I'm confused how this squares with Lant Pritchett's observation that variation in headcount poverty rates across nations, regardless of where you set the poverty line, is completely accounted for by variation in the median of the distribution of consumption expenditures.
Pritchett's argument is about the correlation between average income and poverty rates. My argument is about the welfare that people experience from any given level of growth. I'm claiming that conventional evaluations of growth overestimate the value of growth because they weight income growth of middle-income and rich people too heavily. Once you adjust for that, the population welfare from economic growth is now driven mostly by increase in incomes for poor people, and it is much lower than before (90% lower)
If you wanted to value growth solely based on its ability to reduce poverty, an isoelastic utility function does that as well. In the spreadsheet calculations I did, the isoelastic utility penalizes inequality less (24% vs 36%) because the bottom 50%'s income growth of 50% is almost as good on its own as the whole population income growing 90%.
Separately, I don't interpret Pritchett's observation as meaning "and therefore the best way to minimize poverty is to maximize median consumption". That doesn't follow at all from a cross-country correlation. For one thing, correlation is not causation and this correlation does not prove that increasing median consumption will decrease poverty. For another thing, we have to consider the costs as well: increasing median consumption through growth could be much more expensive than giving all that money to poor people directly.
While it is true that correlation is not causation, the fact that high median income is empirically necessary and sufficient for eliminating poverty on any poverty line is extremely strong evidence that increasing median income is a cause of eliminating poverty at any poverty line. There's also a fairly obvious causal explanation i.e. growth increases everyone's income. What else could be going on that explains the connection?
You say that "increasing median consumption through growth could be much more expensive than giving all that money to poor people directly." This is very implausible. Globally, around $180bn is spent on aid per year—roughly $500 million per day. There are 500 million people who are extremely poor. Assuming that all the extreme poor have $1 per day already, we could double their income with the entire global aid budget. But, on any reasonable definition of poverty people with $2 per day are still extremely poor. The only thing that has ever pulled extremely poor people above more humane high bar poverty lines is economic growth.
I agree that your (excellent) analysis shows that the welfare increase is dominated by lifting the bottom half of the income distribution. I agree that this welfare effect is what we want. Pritchett's argument is linked to yours because he claims the only (and therefore best) way to cause this effect is national development. He writes: "all plausible, general, measures of the basics of human material wellbeing [including headcount poverty] will have a strong, non-linear, empirically sufficient and empirically necessary relationship to GDPPC." (Here non-linear refers to a stronger elasticity of these wellbeing metrics at lower than higher levels of GDPPC).
Of course as you point out national development can't really be the only thing that decreases poverty - redistribution would too. But every single data point we have of countries shows that the rich got rich through development, not redistribution. And every single data point we have of rich countries shows that the bottom half of their income distributions is doing very well, relative to LMICs. So yes, redistribution would cause great welfare gains for a bit, but it's not going to turn a $5000 GDPPC nation to a $50000 one. And the welfare gains from that nation's decreased poverty headcount are going to dwarf the redistribution-caused welfare gains, even given your adjustments. (This isn't an argument against redistribution as EA cause area, which could still be great; it's an argument that redistribution's efficacy isn't really a point against the greater importance of the search for growth).
Regarding the correlation/causation, I'd be more sympathetic to your point if it was a nice and average correlation. Pritchett: "The simple correlation between the actual $3.20/day or $5.50/day headcount poverty rate and headcount poverty as predicted using only the median of the country distribution is .994 and for $1.90 it is .991. These are about as high a correlation as real world data can produce." It's very implausible that this incredibly strong relationship would break with some new intervention that increases median consumption. Not a single policy in the history of the world that changed a country's median consumption has broken it.
To your final point that the cost of increasing median consumption might be way too high (relative to redistribution) - first of all, as Hillebrandt/Halstead pointed out, evaluating that claim should be a much larger priority in EA than it is right now. But development economics seems to have worked in the past, with just the expenses associated with a normal academic field! I'm sorry but I'm going to quote Pritchett again:
TL;DR: Increasing productivity still beats redistribution in the long-term given reasonable assumptions about costs.
I'm not really interested in dismissing growth as a cause area. (I am annoyed at how little EAs mechanize it beyond "advocate for policies --> ??? --> growth", but I'm going to write that up soon!) I wrote this because I think people who advocate for growth largely ignore inequality and should discount growth heavily because of inequality. If growth still beats targeted interventions after that heavy discounting, then so be it.
That makes sense! I was interpreting your post and comment as a bit more categorical than was probably intended. Looking forward to your post.
FYI, I think one of your hyperlinks is linking to the wrong place.
I think that should instead link to: https://www.openphilanthropy.org/research/social-returns-to-productivity-growth/
Eek, good catch!