“The utility function defines a relationship between utility (value to the individual) and the individual’s consumption over a given time period”.

“One common form [of the utility function] is the isoelastic utility function”.

According to this, the increase in utility per increase in consumption is directly proportional to c^-e (where c=“consumption”, and e=“elasticity”).

Consequently, giving a dollar to someone with k times as much consumption is worth only k^-e as much.

The elasticity “is typically found to be between about 1 and 2”.

Consumption multipliers

The “median US income” is about 120 times as large as that of “GiveDirectly’s average recipients”.

Consequently, for e between 1 and 2, the utility of 1$ to “GiveDirectly’s average recipients” is 120 to 14,000 as large as for someone whose consumption is the “median US income”.

“Any particular intervention might be better or worse than a cash transfer by some leverage factor, but if we have no reason to believe these factors are generally higher for one type of poverty than the other, then this ratio is unchanged”.

“This approach is very general, and can be used in many different types of impact evaluation”:

“Compare the additional value of targeting the poorest people in a country rather than the median”.

“Adjust unweighted cost-benefit analysis: weighting each person’s willingness to pay by the relevant multiplier”.

Leverage

“The ‘leverage’ of a particular intervention is its benefit-cost ratio”.

GiveWell “tried to judge the relative value of donating a dollar to GiveDirectly to that of donating a dollar to the Against Malaria Foundation (AMF)”.

“The median estimate was that the AMF programme does about 2.2 times as much good per dollar, whilst the highest estimate was that AMF is 13 times more effective”.

“Effectiveness is consumption multiplier multiplied by leverage ratio”.

“A dollar to AMF” “would create ~1,200 times as much value if donated to AMF (a hundredfold multiplier with a tenfold leverage)”.

Case study: remittances

“The total of remittances [440 G$] is worth the same as about $4 billion [e=2] to $40 billion [e=2] allocated through GiveDirectly” (assuming the relevant average consumption of the recipients is about 10 times as large as that of the GiveDirectly beneficiaries).

“Since total aid spending is around $160 billion, the mean value of aid dollars only needs to be something like 2.5% or 25% that of GiveDirectly for the value of aid to outweigh that of remittances”.

“It seems likely that total aid spending is worth at least as much as remittances are”.

“The average cost of sending back remittances is about 8%”:

“The amount currently wasted in transaction fees is worth something like $340 million to $3.4 billion to GiveDirectly per annum”.

## Summary: The Value of Giving Money to Different Groups | Toby Ord

This post is a summary of the article The Value of Giving Money to Different Groups from Toby Ord. Any errors/misinterpretations are my own.

## Assessing the marginal value of an extra dollar

“The utility function defines a relationship between utility (value to the individual) and the individual’s consumption over a given time period”.

“One common form [of the utility function] is the isoelastic utility function”.

According to this, the increase in utility per increase in consumption is directly proportional to c^-e (where c=“consumption”, and e=“elasticity”).

Consequently, giving a dollar to someone with k times as much consumption is worth only k^-e as much.

The elasticity “is typically found to be between about 1 and 2”.

## Consumption multipliers

The “median US income” is about 120 times as large as that of “GiveDirectly’s average recipients”.

Consequently, for e between 1 and 2, the utility of 1$ to “GiveDirectly’s average recipients” is 120 to 14,000 as large as for someone whose consumption is the “median US income”.

“Any particular intervention might be better or worse than a cash transfer by some leverage factor, but if we have no reason to believe these factors are generally higher for one type of poverty than the other, then this ratio is unchanged”.

“This approach is very general, and can be used in many different types of impact evaluation”:

“Compare the additional value of targeting the poorest people in a country rather than the median”.

“Adjust unweighted cost-benefit analysis: weighting each person’s willingness to pay by the relevant multiplier”.

## Leverage

“The ‘leverage’ of a particular intervention is its benefit-cost ratio”.

GiveWell “tried to judge the relative value of donating a dollar to GiveDirectly to that of donating a dollar to the Against Malaria Foundation (AMF)”.

“The median estimate was that the AMF programme does about 2.2 times as much good per dollar, whilst the highest estimate was that AMF is 13 times more effective”.

“Effectiveness is consumption multiplier multiplied by leverage ratio”.

“A dollar to AMF” “would create ~1,200 times as much value if donated to AMF (a hundredfold multiplier with a tenfold leverage)”.

## Case study: remittances

“The total of remittances [440 G$] is worth the same as about $4 billion [e=2] to $40 billion [e=2] allocated through GiveDirectly” (assuming the relevant average consumption of the recipients is about 10 times as large as that of the GiveDirectly beneficiaries).

“Since total aid spending is around $160 billion, the mean value of aid dollars only needs to be something like 2.5% or 25% that of GiveDirectly for the value of aid to outweigh that of remittances”.

“It seems likely that total aid spending is worth at least as much as remittances are”.

“The average cost of sending back remittances is about 8%”:

“The amount currently wasted in transaction fees is worth something like $340 million to $3.4 billion to GiveDirectly per annum”.