The Nonlinear Library EA - We should value income doublings equally across time and place (Founders Pledge) by NicoT
Jun 23, 2024
22:30
Welcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio. This is: We should value income doublings equally across time and place (Founders Pledge), published by NicoT on June 23, 2024 on The Effective Altruism Forum.
Hi! I'm Nico and I'm on the research team at Founders Pledge. We noticed that the way we compare current to future income benefits is in tension with how we compare income benefits across interventions. However, aligning these two comparisons - choosing the same function for utility from consumption for both - might lead to large changes in our CEAs. So, we are now thinking about how to choose the right approach.
Since our framework is based on GiveWell's, which is used by other organisations, too, I expect that we're facing the same issues. I'm posting here as a way of thinking out loud and with the hope of getting input from others.
Summary
Founders Pledge and GiveWell both use different values of η (elasticity of marginal utility from consumption) when modelling isoelastic utility from consumption depending on the context. Across interventions, we assume η=1. Over time within an intervention, we assume η1.59. We should choose the same η for both models as having different η values leads us to prefer doubling the incomes of richer people relative to poorer people.
Practically, this inconsistency leads to strange conclusions in existing CEAs. Taking GiveWell's Unlimit Health (deworming) CEA as a stylised example:
For two people in Madagascar, we value doubling the income of someone who makes $2,500 30% as much as for someone who makes $500.
When the person making $2,500 lives in Côte d'Ivoire, however, we value doubling their income the same (100% as much) as for the person in Madagascar who makes $500.
Resolving this isn't straightforward and has large implications for our prioritisation. For example:
Using η=1 everywhere - which implies that income doublings have the same value regardless of absolute income levels - doubles the cost-effectiveness of education and deworming programs and makes economic growth and poverty graduation interventions look substantially better.
Using η=1.87, which is implied by our discount rate, everywhere requires our evaluations to take into account the income levels of recipients and prioritise lower-income regions more. An income doubling in Malawi would be worth roughly 1.9x as much as in Ethiopia, 3.4x as much as in Kenya, 6.4x as much as in Egypt, and 75x as much as in the US. The same is true within countries: in India, an income doubling in Bihar would be worth 3.4x as much as an income doubling in Andhra Pradesh.
I'm hoping this post will start a conversation around what the right value of η is.
Our inconsistent η values
Summary: GiveWell's framework, which we use, explicitly uses log-utility from consumption, which implies isoelastic utility with η=1. However, our (and GiveWell's) discount rate uses η1.59. We use η=1 when comparing between interventions/places. But we use η1.59 for comparisons across time, where income doublings are worth 2.6% less in a year from now solely because incomes will be higher then. We should use the same η for comparisons across time and place.
Not doing so leads us to prefer doubling the incomes of richer vs poorer people (see next section).
We use η=1 (log-utility) to compare the value of income benefits across people or interventions[1]. That assumption is convenient because it allows us to disregard absolute income levels: an income doubling is as valuable from $250 to $500 as it is from $2.5k to $5k.
Because of that, we can make statements like "the value of a 10% income increase from a deworming program in India equals the value of a 10% income increase from a cash transfer program in Kenya" without knowing the incomes of the recipients.
At the same time, we use η1.59 when comparing the value of income benefits in different years within an inte...
Hi! I'm Nico and I'm on the research team at Founders Pledge. We noticed that the way we compare current to future income benefits is in tension with how we compare income benefits across interventions. However, aligning these two comparisons - choosing the same function for utility from consumption for both - might lead to large changes in our CEAs. So, we are now thinking about how to choose the right approach.
Since our framework is based on GiveWell's, which is used by other organisations, too, I expect that we're facing the same issues. I'm posting here as a way of thinking out loud and with the hope of getting input from others.
Summary
Founders Pledge and GiveWell both use different values of η (elasticity of marginal utility from consumption) when modelling isoelastic utility from consumption depending on the context. Across interventions, we assume η=1. Over time within an intervention, we assume η1.59. We should choose the same η for both models as having different η values leads us to prefer doubling the incomes of richer people relative to poorer people.
Practically, this inconsistency leads to strange conclusions in existing CEAs. Taking GiveWell's Unlimit Health (deworming) CEA as a stylised example:
For two people in Madagascar, we value doubling the income of someone who makes $2,500 30% as much as for someone who makes $500.
When the person making $2,500 lives in Côte d'Ivoire, however, we value doubling their income the same (100% as much) as for the person in Madagascar who makes $500.
Resolving this isn't straightforward and has large implications for our prioritisation. For example:
Using η=1 everywhere - which implies that income doublings have the same value regardless of absolute income levels - doubles the cost-effectiveness of education and deworming programs and makes economic growth and poverty graduation interventions look substantially better.
Using η=1.87, which is implied by our discount rate, everywhere requires our evaluations to take into account the income levels of recipients and prioritise lower-income regions more. An income doubling in Malawi would be worth roughly 1.9x as much as in Ethiopia, 3.4x as much as in Kenya, 6.4x as much as in Egypt, and 75x as much as in the US. The same is true within countries: in India, an income doubling in Bihar would be worth 3.4x as much as an income doubling in Andhra Pradesh.
I'm hoping this post will start a conversation around what the right value of η is.
Our inconsistent η values
Summary: GiveWell's framework, which we use, explicitly uses log-utility from consumption, which implies isoelastic utility with η=1. However, our (and GiveWell's) discount rate uses η1.59. We use η=1 when comparing between interventions/places. But we use η1.59 for comparisons across time, where income doublings are worth 2.6% less in a year from now solely because incomes will be higher then. We should use the same η for comparisons across time and place.
Not doing so leads us to prefer doubling the incomes of richer vs poorer people (see next section).
We use η=1 (log-utility) to compare the value of income benefits across people or interventions[1]. That assumption is convenient because it allows us to disregard absolute income levels: an income doubling is as valuable from $250 to $500 as it is from $2.5k to $5k.
Because of that, we can make statements like "the value of a 10% income increase from a deworming program in India equals the value of a 10% income increase from a cash transfer program in Kenya" without knowing the incomes of the recipients.
At the same time, we use η1.59 when comparing the value of income benefits in different years within an inte...