âThe utility function defines a relationship between utility (value to the individual) and the individualâs consumption over a given time periodâ.
âOne common form [of the utility function] is the isoelastic utility functionâ.
According to this, the increase in utility per increase in consumption is directly proportional to c^-e (where c=âconsumptionâ, and e=âelasticityâ).
Consequently, giving a dollar to someone with k times as much consumption is worth only k^-e as much.
The elasticity âis typically found to be between about 1 and 2â.
Consumption multipliers
The âmedian US incomeâ is about 120 times as large as that of âGiveDirectlyâs average recipientsâ.
Consequently, for e between 1 and 2, the utility of 1$ to âGiveDirectlyâs average recipientsâ is 120 to 14,000 as large as for someone whose consumption is the âmedian US incomeâ.
âAny 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 unchangedâ.
âThis approach is very general, and can be used in many different types of impact evaluationâ:
âCompare the additional value of targeting the poorest people in a country rather than the medianâ.
âAdjust unweighted cost-benefit analysis: weighting each personâs willingness to pay by the relevant multiplierâ.
Leverage
âThe âleverageâ of a particular intervention is its benefit-cost ratioâ.
GiveWell âtried to judge the relative value of donating a dollar to GiveDirectly to that of donating a dollar to the Against Malaria Foundation (AMF)â.
âThe 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 effectiveâ.
âEffectiveness is consumption multiplier multiplied by leverage ratioâ.
âA dollar to AMFâ âwould create ~1,200 times as much value if donated to AMF (a hundredfold multiplier with a tenfold leverage)â.
Case study: remittances
âThe total of remittances [440 G$] is worth the same as about $4 billion [e=2] to $40 billion [e=2] allocated through GiveDirectlyâ (assuming the relevant average consumption of the recipients is about 10 times as large as that of the GiveDirectly beneficiaries).
âSince 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 remittancesâ.
âIt seems likely that total aid spending is worth at least as much as remittances areâ.
âThe average cost of sending back remittances is about 8%â:
âThe amount currently wasted in transaction fees is worth something like $340 million to $3.4 billion to GiveDirectly per annumâ.
Summary: The Value of Giving Money to Different Groups | Toby Ord
This post is a summary of the article The Value of Giving Money to Different Groups from Toby Ord. Any errors/âmisinterpretations are my own.
Assessing the marginal value of an extra dollar
âThe utility function defines a relationship between utility (value to the individual) and the individualâs consumption over a given time periodâ.
âOne common form [of the utility function] is the isoelastic utility functionâ.
According to this, the increase in utility per increase in consumption is directly proportional to c^-e (where c=âconsumptionâ, and e=âelasticityâ).
Consequently, giving a dollar to someone with k times as much consumption is worth only k^-e as much.
The elasticity âis typically found to be between about 1 and 2â.
Consumption multipliers
The âmedian US incomeâ is about 120 times as large as that of âGiveDirectlyâs average recipientsâ.
Consequently, for e between 1 and 2, the utility of 1$ to âGiveDirectlyâs average recipientsâ is 120 to 14,000 as large as for someone whose consumption is the âmedian US incomeâ.
âAny 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 unchangedâ.
âThis approach is very general, and can be used in many different types of impact evaluationâ:
âCompare the additional value of targeting the poorest people in a country rather than the medianâ.
âAdjust unweighted cost-benefit analysis: weighting each personâs willingness to pay by the relevant multiplierâ.
Leverage
âThe âleverageâ of a particular intervention is its benefit-cost ratioâ.
GiveWell âtried to judge the relative value of donating a dollar to GiveDirectly to that of donating a dollar to the Against Malaria Foundation (AMF)â.
âThe 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 effectiveâ.
âEffectiveness is consumption multiplier multiplied by leverage ratioâ.
âA dollar to AMFâ âwould create ~1,200 times as much value if donated to AMF (a hundredfold multiplier with a tenfold leverage)â.
Case study: remittances
âThe total of remittances [440 G$] is worth the same as about $4 billion [e=2] to $40 billion [e=2] allocated through GiveDirectlyâ (assuming the relevant average consumption of the recipients is about 10 times as large as that of the GiveDirectly beneficiaries).
âSince 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 remittancesâ.
âIt seems likely that total aid spending is worth at least as much as remittances areâ.
âThe average cost of sending back remittances is about 8%â:
âThe amount currently wasted in transaction fees is worth something like $340 million to $3.4 billion to GiveDirectly per annumâ.