Using Subjective Well-Being to Estimate the Moral Weights of Averting Deaths and Reducing Poverty

[Edit: 03/​09/​2020: a few minor ty­pos cor­rected]

Sum­mary[1]

To de­ter­mine how to do good as cost-effec­tively as pos­si­ble, it is nec­es­sary to es­ti­mate the value of bring­ing about differ­ent out­comes. We briefly out­line the re­cent meth­ods GiveWell has used to do this. We then in­tro­duce an al­ter­na­tive method – Well-Be­ing Ad­justed Life-Years, or ‘WELLBYs’ – and use it to es­ti­mate the val­ues of two key in­puts in GiveWell’s anal­y­sis: dou­bling con­sump­tion for one per­son for one year and avert­ing the death of a child un­der 5 years old. On the WELLBY ap­proach, out­comes are as­sessed in terms of their im­pact on sub­jec­tive well-be­ing – here, we use self-re­ported life satis­fac­tion.

Our pri­mary aim is to show that the WELLBY ap­proach could be used, rather than that it should be used. Our es­ti­mate of the rel­a­tive value of the two out­comes should be taken as pre­limi­nary rather than defini­tive.

We es­ti­mate the effects of dou­bling con­sump­tion us­ing ev­i­dence from ran­domised con­trol­led tri­als of cash trans­fers in Kenya con­ducted in col­lab­o­ra­tion with GiveDirectly. The to­tal effect of the trans­fers is calcu­lated by in­fer­ring an an­nual de­cay in life satis­fac­tion. We in­clude in­tra-house­hold spillovers but ex­clude, due to mixed ev­i­dence, in­ter-house­hold effects[2]. To ac­count for un­cer­tainty in our model, we in­put 90% sub­jec­tive con­fi­dence in­ter­vals and run Monte Carlo simu­la­tions.

The value of sav­ing a life to the per­son whose life is saved is es­ti­mated on two philo­soph­i­cal views of death: de­pri­va­tion­ism (the dis­value is the to­tal lost life satis­fac­tion) and the time rel­a­tive in­ter­est ac­count (TRIA) (the dis­value is to­tal lost life satis­fac­tion, dis­counted by the psy­cholog­i­cal con­nect­ed­ness to one’s fu­ture self). In effect, de­pri­va­tion­ism holds it’s bet­ter to save 2-year-olds than 20-year-olds; TRIA the re­verse. We also as­sess the effect of grief on fam­ily mem­bers us­ing life satis­fac­tion data.

Th­ese es­ti­mates rely on cer­tain (im­plicit) philo­soph­i­cal as­sump­tions. We note how differ­ent as­sump­tions would sub­stan­tially change the re­sults and re­duce the rel­a­tive value of sav­ing lives. Th­ese is­sues are sep­a­rate from how or whether to use WELLBYs; given differ­ent as­sump­tions, one would sim­ply calcu­late the WELLBYs differ­ently. Our task is only to high­light the im­pli­ca­tions of (some) the­o­ries, rather than eval­u­ate them.

Our model es­ti­mates that the value ra­tio of avert­ing the death of an un­der-5 to dou­bling con­sump­tion of one per­son for one year is 240:1 on de­pri­va­tion­ism (90% con­fi­dence in­ter­val (CI) of 37:1–650:1), and 50:1 on TRIA (90% CI 6:1–160:1). For refer­ence, GiveWell cur­rently uses a ra­tio of 100:1[3], based on a staff ag­gre­gate of 47:1 and an es­ti­mate of 230:1 from IDin­sight’s benefi­ciary prefer­ence sur­vey (de­scribed in the main text).[4]

We close by set­ting out var­i­ous un­cer­tain­ties with the WELLBY es­ti­mate that are tractable with fur­ther re­search: the effects of cash trans­fers over time; spillover effects (of cash trans­fers and of deaths); the lo­ca­tion of the ‘neu­tral point’ equiv­a­lent to non-ex­is­tence; and the im­pacts as­sessed in terms of hap­piness rather than life satis­fac­tion.

Introduction

There are many ways to help oth­ers. Any­one al­lo­cat­ing re­sources to­wards this end – rang­ing from policy-mak­ers dis­burs­ing gov­ern­ment bud­gets to in­di­vi­d­u­als giv­ing to char­ity – must choose be­tween pro­grammes with differ­ent out­comes, such as avert­ing deaths, alle­vi­at­ing poverty, en­hanc­ing ed­u­ca­tion and im­prov­ing men­tal health. Com­par­ing the value of these out­comes is a difficult, but nec­es­sary, task if we want to use these re­sources to benefit oth­ers as much as pos­si­ble.

Much of the re­search to iden­tify the world’s most cost-effec­tive char­i­ties is pro­duced by GiveWell. GiveWell is cur­rently re-con­sid­er­ing their frame­work for as­sess­ing the value of out­comes, what they call ‘moral weights’. There­fore, we (at the Hap­pier Lives In­sti­tute) thought it would be timely to pre­sent one method for com­par­ing the value of differ­ent out­comes: us­ing well-be­ing ad­justed life years, or WELLBYs. On the WELLBY ap­proach, mea­sures of sub­jec­tive well-be­ing (SWB), self-re­ports of hap­piness and life satis­fac­tion, are used as the com­mon cur­rency by which the im­pact of changes is mea­sured. We use this ap­proach to es­ti­mate the (rel­a­tive) val­ues of two of the three key out­comes in GiveWell’s model: dou­bling con­sump­tion for a year and avert­ing the death of a child un­der 5 years old. While this post is fo­cused on GiveWell’s frame­work, this method is gen­er­ally ap­pli­ca­ble.

We first set out GiveWell’s ap­proaches to date. Then we in­tro­duce our al­ter­na­tive, make an ini­tial es­ti­mate us­ing it, and com­pare the re­sults.

Our main pur­pose here is not to ar­gue that the WELLBY method should be used, al­though we will briefly mo­ti­vate it later. Rather, we want to show how it can be used; this post is in­tended as a ‘proof of con­cept’. We aim to in­tro­duce read­ers to the method­ol­ogy and to provide an ini­tial re­view of the SWB data available in the con­texts we are in­ter­ested in – very low-in­come pop­u­la­tions. We con­sider our es­ti­mate pre­limi­nary rather than defini­tive; we cau­tion against strongly up­dat­ing based upon it. We men­tion later the fur­ther em­piri­cal and the­o­ret­i­cal work that is re­quired.

GiveWell’s ap­proaches to date

GiveWell’s cost-effec­tive­ness model uses three main out­comes:

  • Dou­bling a per­son’s con­sump­tion for one year.

  • Avert­ing the death of an un­der-5-year-old.

  • Avert­ing the death of an over-5-year-old.

In the past, GiveWell de­ter­mined its moral weights by first ask­ing its staff to give their own es­ti­mates of the rel­a­tive value of the three out­comes. The me­dian of the staff’s as­sign­ments was then used as the rel­a­tive val­ues of these out­comes in their cost-effec­tive­ness anal­y­sis. This method al­lows dis­agree­ments to be re­solved – it ap­peals to a sort of wis­dom of the crowds – but it does not an­swer the ques­tion of how some­one might, in the first place, form a jus­tifi­able, ev­i­dence-based view of what the ap­pro­pri­ate moral weights are; staff mem­bers were free to choose their own method. What method might some­one use?

An op­tion, and one GiveWell has re­cently ex­plored, is ‘benefi­ciary prefer­ences’. IDin­sight, a re­search or­gani­sa­tion, con­ducted sur­veys in Ghana and Kenya to cap­ture the choices of the benefi­cia­ries of the pro­grammes that GiveWell recom­mends (full re­port). IDin­sight asked in­di­vi­d­u­als both for their ‘will­ing­ness to pay’ to re­duce the risk of death to them­selves and their chil­dren, and to choose – tak­ing the per­spec­tive of a de­ci­sion-maker in their com­mu­nity – be­tween pro­grammes that save a life or provide a num­ber of cash trans­fers. We briefly dis­cuss the spe­cific method­ol­ogy and the re­sult of these sur­veys later.

While re­li­ance on prefer­ences (re­vealed or stated) to de­ter­mine the value of out­comes is stan­dard in eco­nomics, the ap­proach faces an ar­ray of challenges – see Bron­steen, Buc­cas­fuso and Ma­sur (2013) for an ex­ten­sive re­view. One un­avoid­able difficulty of us­ing prefer­ences is that they rely on peo­ple mak­ing pre­dic­tions about how var­i­ous hy­po­thet­i­cal situ­a­tions would af­fect them­selves (and oth­ers) if they hap­pened. Psy­cholog­i­cal re­search into af­fec­tive fore­cast­ing has demon­strated that peo­ple are not very good at pre­dict­ing how they will feel and such fore­casts suffer from a num­ber of bi­ases (Gilbert and Wil­son 2006). One ex­am­ple is fo­cus­ing illu­sions, where we over­rate the effect of eas­ily imag­in­able fac­tors (Kah­ne­man et al. 2006). Even for re­vealed prefer­ences (choices peo­ple ac­tu­ally make, and of­ten seen as the gold stan­dard by economists) peo­ple still need to fore­cast how they will feel as a re­sult of their choice. Kah­ne­man and Thaler (2006) ar­gue de­ci­sion util­ity (what peo­ple choose) and ex­pe­rienced util­ity (how they feel) are there­fore prac­ti­cally differ­ent. As it is much eas­ier for in­di­vi­d­u­als to say how they cur­rently feel, this is a cen­tral ad­van­tage of us­ing re­ports of sub­jec­tive well-be­ing to value out­comes, as­sum­ing ex­pe­rienced util­ity is valuable.

The well-be­ing ad­justed life year (WELLBY) approach

WELLBYs, in struc­ture, are quite similar to the well-es­tab­lished qual­ity and dis­abil­ity ad­justed life year (QALYs and DALYs) health met­rics, which com­bine qual­ity and quan­tity of health into a sin­gle num­ber. A year in perfect health is worth 1 QALY, whereas a liv­ing for a year with a con­di­tion that had a util­ity weight of 0.5 would be worth 0.5 QALYs, and so on[5]. A QALY weight of 0 is equiv­a­lent to be­ing dead, and there can be states worse than death (Tilling et al. 2010). Every Q/​DALY is taken to have the same benefit to one per­son as an­other, which then al­lows health treat­ments to be com­pared for cost-effec­tive­ness (if cost in­for­ma­tion is known). Q/​DALY weights for differ­ent health states are de­ter­mined by ask­ing peo­ple to make hy­po­thet­i­cal trade-offs be­tween health states, and hence use the same un­der­ly­ing method as the benefi­ciary prefer­ence ap­proach.

The key differ­ence is that WELLBYs are con­structed by us­ing mea­sures of sub­jec­tive well-be­ing, namely self-re­ports of hap­piness and life satis­fac­tion (Frijters et al. 2020; Birk­jaer, Kaats and Ru­bio 2020). One WELLBY, in this doc­u­ment, is equiv­a­lent to a 1-point in­crease on an 0-10 life satis­fac­tion scale for one per­son for one year. Life satis­fac­tion is typ­i­cally mea­sured by ask­ing “Over­all, how satis­fied are you with your life nowa­days” (0 - not at all, 10 - com­pletely). A differ­ence is that a QALY weight of 0 is equiv­a­lent to be­ing dead, while life satis­fac­tion scales do not have a clear ‘neu­tral point’ equiv­a­lent to non-ex­is­tence, an is­sue we re­turn to later.

While re­searchers have sur­veyed SWB for sev­eral decades (Diener, Lu­cas and Oishi 2018), pro­pos­als to base de­ci­sion-mak­ing on SWB are rel­a­tively re­cent, and have mostly been fo­cused on pub­lic policy-mak­ing in high-in­come coun­tries (e.g. GHC 2018; O’Don­nell et al. 2020). Efforts to use SWB to as­sess cost-effec­tive­ness in low-in­come con­texts are even more nascent.[6]

We break our WELLBY es­ti­mate into sev­eral parts. We first dis­cuss the effect from dou­bling con­sump­tion, then avert­ing the death of a child un­der 5. In both cases, we start by con­sid­er­ing the ‘di­rect’ effects: those on the per­son whose con­sump­tion has dou­bled, or who has died, re­spec­tively. We go on to con­sider the effects on the house­hold of that per­son, in each case. We briefly dis­cuss effects on the wider com­mu­nity but do not in­clude these in our model, as they would be very spec­u­la­tive.

A model of this anal­y­sis in Guessti­mate can be viewed here.[7]

Guessti­mate al­lows users to in­put their un­cer­tainty (and its dis­tri­bu­tion) for each pa­ram­e­ter. Guessti­mate runs Monte Carlo simu­la­tions, which are re­runs of the same calcu­la­tion us­ing ran­dom val­ues from the prob­a­bil­ity dis­tri­bu­tion for each pa­ram­e­ter. This means that you can pro­duce an es­ti­mate of the un­cer­tainty for the value of the out­come . We de­scribe the in­puts to our model through­out the post.

A fi­nal com­ment be­fore we be­gin: the choice to base WELLBYs on life satis­fac­tion, rather than hap­piness, may seem con­tro­ver­sial to some. There is a long-stand­ing view that well-be­ing – what ul­ti­mately makes our lives go well – con­sists in hap­piness (a pos­i­tive bal­ance of pleas­ant over un­pleas­ant con­scious states) as op­posed to any­thing else, such as life satis­fac­tion (a judge­ment of how life is go­ing over­all). While we have sym­pa­thy with this view, we are pushed to use life satis­fac­tion data be­cause they are so much more abun­dant than hap­piness data. When more data are available, it would be straight­for­ward to re­place the in­puts in our model. It re­mains open ex­actly how much differ­ence this would make to pri­ori­ti­sa­tion de­ci­sions in prac­tice: re­search in­di­cates that what makes peo­ple hap­pier tends to also make them more satis­fied with their lives, al­though some things have a greater im­pact on hap­piness than life satis­fac­tion, or vice versa (Kah­ne­man and Deaton 2010; Boar­ini et al. 2012).[8] In any case, the use of ei­ther sub­jec­tive mea­sure en­hances our un­der­stand­ing of what im­pacts peo­ple’s lives.

Es­ti­mat­ing the effect on SWB from dou­bling con­sump­tion for one per­son for one year. [9]

Es­ti­mates from ex­ist­ing literature

We start by pre­sent­ing effect sizes of SWB in stan­dard de­vi­a­tions, (as is stan­dard in the liter­a­ture.[10] Pre­vi­ous cross-sec­tional[11] work look­ing at the re­la­tion­ship be­tween in­come and life satis­fac­tion (LS) in low-in­come coun­tries sug­gests that dou­bling in­come leads to an in­crease of 0.24[12] stan­dard de­vi­a­tions (SDs) of life satis­fac­tion.[13]

His­tor­i­cally, much of the causal liter­a­ture on the effect of in­come on SWB came from lot­tery stud­ies. A no­table re­cent study in this vein by Lindqvist et al. (2020) es­ti­mates that among Swedish lot­tery win­ners (sur­veyed 5–22 years af­ter the lot­tery), a win equiv­a­lent to dou­bling an­nual in­come for 20 years causes an in­crease in life satis­fac­tion of 0.26 SDs[14]. The stan­dard de­vi­a­tion of LS is 1.93 in this study (see Table 3), so this roughly equates to a change of 0.5 LS points.

Direct effect of dou­bling con­sump­tion on recipient

Re­cently, study­ing the effects of pro­vid­ing cash trans­fers (CTs) in low-in­come coun­tries via ran­domised con­trol­led tri­als (RCTs) has pro­vided fur­ther and more rele­vant causal ev­i­dence. Re­sults from sev­eral stud­ies done in col­lab­o­ra­tion with GiveDirectly are pre­sented in Table 1. We base our Guessti­mate model on these stud­ies. Eg­ger et al. (2019) has the largest sam­ple size, and is the most similar to GiveDirectly’s cur­rent pro­gramme. In a forth­com­ing meta-anal­y­sis McGuire, Bach-Mortensen and Kaiser (n.d.) will con­sider a much larger num­ber of stud­ies[15], and will pre­sent a more for­mal ap­proach to ag­gre­ga­tion.

Table 1: GiveDirectly stud­ies. PPP = Pur­chas­ing power par­ity; SE = stan­dard er­ror; SD = stan­dard de­vi­a­tion.

Table 1: GiveDirectly stud­ies. PPP = Pur­chas­ing power par­ity; SE = stan­dard er­ror; SD = stan­dard de­vi­a­tion.

As you can see in Table 1, the size of the CTs range be­tween $709 and $1,871, and the av­er­age time the sur­veys are con­ducted af­ter re­ceiv­ing the CT ranges be­tween 7 and 34 months. Given that both of these fac­tors likely af­fect the mea­sured effect size, com­bin­ing the re­sults in Table 1 is not triv­ial. We next de­scribe our model based on this in­for­ma­tion; we hope to im­prove on the ag­gre­ga­tion in our fu­ture work by in­cor­po­rat­ing more stud­ies.

We con­struct a sim­ple ex­po­nen­tial de­cay model for the SWB effect through time, by say­ing that the effect will be some fixed per­centage com­pared to the pre­vi­ous year:

SWB (1)

where SWB is the effect size (in SDs), c is a con­stant (the effect at time = 0), d is the an­nual de­cay rate of the effect size, and t is the time in years. We es­ti­mate the pa­ram­e­ters that best fit this equa­tion based on the four data points from the GiveDirectly stud­ies.[16] Figure 1A shows the cen­tral es­ti­mate, as well as the 66% and 90% con­fi­dence in­ter­vals. The cen­tral es­ti­mate cor­re­sponds to an an­nual de­cay rate of 32% and an ini­tial effect size of 0.26 SDs. We in­put the con­fi­dence in­ter­vals in­ferred for these pa­ram­e­ters into Guessti­mate. Figure 1B shows the dis­tri­bu­tion of 5000 sam­ples of each pa­ram­e­ter, and Figure 1C shows the re­sult­ing tra­jec­to­ries (i.e. a re­flec­tion of the Monte Carlo simu­la­tions run in Guessti­mate).

Figure 1: Ex­po­nen­tial de­cay model of life satis­fac­tion effect size (in stan­dard de­vi­a­tions) through time. (A) Mea­sured LS effect sizes from the GiveDirectly stud­ies are shown as coloured cir­cles. The cen­tral es­ti­mate, 66% and 90% con­fi­dence in­ter­vals of the model, fit with a lin­ear re­gres­sion, are shown. (B) 5,000 sam­ples of the dis­tri­bu­tions of de­cay rate and ini­tial effect size shown as his­tograms. (C) The tra­jec­to­ries of LS through time based on the sam­ples of pa­ram­e­ters shown in (B). This illus­trates the Monte Carlo simu­la­tions run in Guessti­mate.

Model­ling the effect on SWB through time based on only four data points is un­for­tu­nate, but the most jus­tifi­able ap­proach given the limited rele­vant in­for­ma­tion. The con­fi­dence in­ter­vals are cor­re­spond­ingly wide: 2–53% for the de­cay rate, and 0.14 to 0.48 SDs for the ini­tial effect. A 32% an­nual de­cay rate im­plies the effect size falls be­low 0.05 SDs at five years and be­low 0.01 SDs at nine years. In Ap­pendix 1 we de­scribe other pa­pers that study the effects on SWB through time, al­though each is dis­similar to the GiveDirectly stud­ies in at least one way, and re­sults are mixed, so we do not up­date our model in ei­ther di­rec­tion. We do not let the effect con­tinue in­definitely, but in­stead in­put a time of five years when the effect ends (90% CI: 2–10 years). The to­tal effect through time in WELLBYs is the area un­der the curve (de­ter­mined by in­te­grat­ing equa­tion 1).

What’s the effect in WELLBYs?

To con­vert the effect size from SDs to WELLBYs we need to know the stan­dard de­vi­a­tion (SD) of the life satis­fac­tion (LS) data in the GiveDirectly stud­ies. The baseline SD of LS for the shared sam­ple used in Haushofer and Shapiro (2016, 2018) and re­ported in Haushofer, Reis­inger and Shapiro (2019) is 2.66.[17] Other stud­ies have a lower SD[18]; we put 1.9 to 2.7 as our sub­jec­tive 90% con­fi­dence in­ter­val. We es­ti­mate the to­tal effect on the di­rect re­cip­i­ent of a CT to be ~1.8 (0.6–5.0) WELLBYs.

Fur­ther considerations

We have not con­sid­ered that rais­ing in­come ap­pears linked to life ex­pec­tancy[19] and that higher re­ports of SWB[20] ap­pear re­lated to re­duc­tions in all-cause mor­tal­ity.

Spillover effects

If we can, we also want to count the ‘spillover’ effects, the im­pact of an in­ter­ven­tion on those be­sides the di­rect benefi­ciary (in this case, the re­cip­i­ent of the cash trans­fer). Here, we con­sider, in turn, spillovers within the house­hold, i.e. to fam­ily mem­bers, and to those out­side it, e.g. neigh­bours.

Haushofer and Shapiro (2016) ad­ministered sur­veys to the heads of the house­hold re­ceiv­ing a CT; some­times this was two peo­ple (usu­ally a wife and hus­band), and some­times this was one per­son.[21] Life satis­fac­tion re­sults are there­fore already av­er­aged across the heads of a house­hold; we use the effect on the re­cip­i­ent (already es­ti­mated) as the av­er­age effect on the heads of a house­hold. In the treat­ment group, there were 369 dou­ble-headed house­holds and 102 sin­gle-headed house­holds, which cor­re­sponds to an av­er­age of 1.78 heads per house­hold.

We then need to es­ti­mate the spillover effects on other mem­bers of the house­hold. There are no es­ti­mates of the di­rect im­pact of a cash trans­fer on the sub­jec­tive well-be­ing of house­hold mem­bers who are not the house­hold heads; this is a promis­ing area for fu­ture re­search. How­ever, pos­i­tive spillovers seem likely for sev­eral rea­sons stem­ming from shared ex­pan­sion of re­sources. Haushofer and Shapiro (2013) re­port large in­creases in house­hold com­mon goods such as live­stock and fur­ni­ture, and the like­li­hood of hav­ing an iron roof; house­holds also spend about $25 more per month on food (see a sum­mary from GiveWell here). In Eg­ger et. al (2019), chil­dren’s ed­u­ca­tion and food se­cu­rity in­dex im­prove. CTs ap­pear to de­crease chil­dren’s eco­nomic ac­tivity (de Hoop and Rosati, 2014), which is likely benefi­cial for men­tal health of chil­dren and ado­les­cents (Stur­rock and Hodes, 2016). CTs have been linked to a de­cline in the in­ter­gen­er­a­tional trans­mis­sion of de­pres­sion (Eyal and Burns, 2019).

In the ab­sence of much more in­for­ma­tion, we as­sume that the spillover effect on the other mem­bers of the house­hold – aside from the house­hold head(s) – has 90% con­fi­dence in­ter­vals of 20–100% of the effect on LS for the re­cip­i­ent. We note this is a non-triv­ial un­cer­tainty given there are nearly twice as many ‘other’ mem­bers as heads of house­hold.[22] House­hold size is re­ported in Eg­ger et al. (2019) as 4.3, and in Haushofer, Reis­inger and Shapiro (2015)[23] as 5.1; we in­put this range into Guessti­mate. Our model calcu­lates the to­tal effect per GiveDirectly CT is 3.2 (1.0–8.9) WELLBYs to the head(s) of the house­hold and 2.2 WELLBYs (0.5–6.9) to the other mem­bers of the house­hold.

We do not in­clude effects to those out­side the house­hold, be­cause we are suffi­ciently un­cer­tain of what they are – in this case but even more in the next sec­tion (avert­ing a death). The most rele­vant, causal ev­i­dence of spillovers to the com­mu­nity is from the GiveDirectly stud­ies them­selves. Whilst Haushofer and Shapiro (2018) found ev­i­dence of nega­tive psy­cholog­i­cal spillovers to the com­mu­nity, the more re­cent GiveDirectly stud­ies (Eg­ger et al., 2019; Haushofer, Mu­dida and Shapiro, 2020) – with larger sam­ple sizes, and based on a ver­sion of the pro­gramme more similar to cur­rent prac­tice – did not. A syn­the­sis of stud­ies that mea­sured com­mu­nity effects sug­gests the spillovers to SWB are over­all in­signifi­cant (see Ap­pendix 2).

It’s worth not­ing the lack of nega­tive com­mu­nity spillovers is un­usual, in light of the wider SWB liter­a­ture, al­though not nec­es­sar­ily sur­pris­ing. In a re­view that draws on high-in­come coun­try data, Clark (2016) ar­gues there is a “con­sid­er­able va­ri­ety of ev­i­dence that well-be­ing is rel­a­tive in in­come”; in other words, it mat­ters not just how wealthy you are, but how wealthy are those you com­pare your­self to, and hence oth­ers be­com­ing richer would make you feel worse. The rel­a­tive effect of in­come has been pro­posed as an ex­pla­na­tion for the ‘Easter­lin Para­dox’, the find­ing that ris­ing in­comes do not seem to in­crease av­er­age hap­piness over the long run, even though richer peo­ple and coun­tries are hap­pier than poorer peo­ple and coun­tries (Easter­lin 2016; Kaiser and Ven­drik, 2018). Clark notes that while the ev­i­dence in­di­cates there is, in gen­eral, a rel­a­tive in­come effect, it’s un­clear how large it is and whether it func­tions differ­ently for those in poverty, a topic which has not re­ceived much study.[24] We wel­come fur­ther re­search in­ves­ti­gat­ing rel­a­tive in­come effects at these low lev­els.

Ad­just­ment for dou­bling consumption

So far, we have con­sid­ered the effects of re­ceiv­ing a CT on a house­hold. How­ever, GiveWell’s moral weight speci­fi­cally con­cerns dou­bling con­sump­tion for one per­son for one year; we take two steps to reach an es­ti­mate for this value. An­nual house­hold con­sump­tion (rather than in­di­vi­d­ual con­sump­tion) is re­ported in the GiveDirectly stud­ies. The size of the CT is not the same as an­nual house­hold con­sump­tion; our first step is to ad­just the effect from the CT to re­flect what pro­por­tion it is of dou­bling an­nual house­hold con­sump­tion. Eg­ger et al. (2019) state that the CT ($1,871 PPP) cor­re­sponds to 75% of mean an­nual house­hold ex­pen­di­ture in re­cip­i­ent house­holds. There is a roughly lin­ear-log­a­r­ith­mic re­la­tion­ship[25] be­tween in­come and LS (Jebb et al. 2018) (which means that in­come changes have less of an effect on LS at higher in­comes). We use this re­la­tion­ship to ad­just to a 100 % change in con­sump­tion (i.e. dou­bling) for one year, which in­creases the effect size by 24 %.[26] This is a non-triv­ial ad­just­ment, and it is pos­si­ble that a lin­ear-log re­la­tion­ship does not hold in this con­text; this could be de­ter­mined with fur­ther re­search. Se­condly, we ac­count for dou­bling con­sump­tion for one per­son (rather than the house­hold) for one year. We do this by di­vid­ing the (mod­el­led) effect of dou­bling house­hold con­sump­tion by the av­er­age num­ber of house­hold mem­bers.[27]

WELLBYs Lost from Death of an Un­der-5

Direct Loss of WELLBYs from Death

Depri­va­tion­ist account

We first es­ti­mate the num­ber of WELLBYs lost due to the death of an un­der-5 by us­ing the most math­e­mat­i­cally sim­ple ap­proach: the bad­ness of death is the to­tal well-be­ing the per­son is de­prived of by not liv­ing longer, i.e. years of life lost mul­ti­plied by the coun­ter­fac­tual well-be­ing. This is called the ‘de­pri­va­tion­ist’ ac­count of the bad­ness of death.[28]

Life expectancy

We use Kenyan data, in line with the es­ti­mate from dou­bling con­sump­tion. The UN pro­vides life ex­pec­tancy es­ti­mates pro­jected into the fu­ture[29]; for a one-year-old in Kenya, born in 2020-2025, the me­dian life ex­pec­tancy is 69.6 (95% CI: 68.9–71.5). GiveWell’s char­i­ties de­liber­ately fo­cus on helping the poor­est, who are likely to have a lower life ex­pec­tancy. Achoki et al. (2020) show the vari­a­tion in life ex­pec­tancy across Kenyan coun­ties: in 2016, three coun­ties had a life ex­pec­tancy higher than 71 years, and 2 coun­ties were lower than 60 years. In Guessti­mate we in­put a 90% sub­jec­tive con­fi­dence in­ter­val of 62–72 for life ex­pec­tancy. We also in­put a uniform dis­tri­bu­tion of ages be­tween 0 and 5 to rep­re­sent chil­dren un­der the age of 5 years old.

Life satisfaction

Es­ti­mated av­er­age life satis­fac­tion in Kenya is 4.4/​10.[30] Again, this is prob­a­bly not rep­re­sen­ta­tive of benefi­cia­ries of GiveWell-recom­mended pro­grammes. For the GiveDirectly sam­ples that re­port un­stan­dard­ized LS scores, the baseline LS is 3.9 /​ 10 with a SD of 2.66 (Haushofer & Shapiro 2019). IDin­sight asked an SWB ques­tion in their benefi­ciary prefer­ences sur­vey; those sur­veyed in Kenya had an av­er­age life satis­fac­tion score of 2.3/​10 (n = 1,808, SD = 2.32 ).[31] As IDin­sight com­ments, this is lower than ex­pected based on ex­trap­o­la­tion of re­sults from na­tion­ally rep­re­sen­ta­tive sur­veys.[32] IDin­sight sug­gests this could be be­cause the life satis­fac­tion ques­tion was asked at the end of their sur­vey, bi­as­ing the an­swers, or be­cause the rough lin­ear-log­a­r­ith­mic re­la­tion­ship be­tween in­come and LS does not hold at the bot­tom of the wor­ld­wide in­come dis­tri­bu­tion. In our model, we in­put a 90% sub­jec­tive con­fi­dence in­ter­val of 2.3–4.4.

Ac­count­ing for the future

So far, we have fo­cused on the ev­i­dence of the cur­rent SWB level. How­ever, it is likely that av­er­age SWB will change in the fu­ture (as two ex­am­ples, eco­nomic de­vel­op­ment may bring about pos­i­tive effects on LS, but cli­mate change could have nega­tive effects). Fore­cast­ing fu­ture SWB is a promis­ing area for fu­ture work, but so far, we have spent very lit­tle time on this. Nev­er­the­less, it is clear changes to qual­ity of life in the fu­ture could be large, so we want to ac­count for this in the model.

On top of changes to qual­ity of life, there are also risks from global, re­gional or na­tional catas­trophic events, i.e. risks (not in­cor­po­rated in life ex­pec­tancy) that could cur­tail their quan­tity of life and so to­tal life­time SWB.[33]

Th­ese two fac­tors (change in lev­els of LS, and ac­count­ing[34] for fu­ture risks) are tricky to in­cor­po­rate neatly in Guessti­mate. Given this, and the fact that our cur­rent thoughts are some­what spec­u­la­tive, we use one cell to com­bine these effects and make an over­all ad­just­ment. We es­ti­mate the sub­jec­tive con­fi­dence in­ter­val for this ad­just­ment in this spread­sheet, by con­sid­er­ing up­per and lower es­ti­mates of the fi­nal im­pact in WELLBYs. For the up­per bound, we use an an­nual dis­count rate of 0.18%[35] and as­sume LS will rise lin­early by 4 points over the next 70 years. For the lower bound, we use an an­nual dis­count rate of 0.4%[36] and as­sume that LS will stay the same. Com­pared to ig­nor­ing both fac­tors, the up­per bound es­ti­mate in­creases the WELLBY value caused di­rectly by sav­ing the child by 63%, and the lower bound re­duces it by 17%. Hence, ac­count­ing for these, in our model in­creases the di­rect value of avert­ing deaths.

The neu­tral point

An im­por­tant and difficult ques­tion is where on the 0-10 scale is equiv­a­lent in value to non-ex­is­tence; in other words, the level at which con­tinued ex­is­tence would be over­all nei­ther good nor bad for the per­son if they con­tinued to live at that level. We re­fer to this as the ‘neu­tral point’.

It is not clear where the neu­tral point is and there has been lit­tle dis­cus­sion of how, in prin­ci­ple, to de­ter­mine this. SWB re­searchers some­times treat the mid-point of SWB scales (e.g 510) as where some­one is nei­ther satis­fied nor dis­satis­fied, or nei­ther happy nor un­happy (e.g. Diener et al. 2018). If we took this as the neu­tral point, this would have the con­tro­ver­sial im­pli­ca­tion that many peo­ple, in­clud­ing the av­er­age Kenyan, have lives cur­rently not worth liv­ing (con­sid­er­ing just their well-be­ing). Other re­searchers treat the bot­tom of the scale, e.g. 010 for life satis­fac­tion, as the neu­tral point (e.g. La­yard et al. 2020). This has a differ­ent con­tro­ver­sial im­pli­ca­tion: it is not pos­si­ble for any­one, us­ing a life satis­fac­tion scale, to have a life not worth liv­ing.

One, not ob­vi­ously cor­rect, method would be to ask mem­bers of the pub­lic at what level they would be in­differ­ent be­tween ex­is­tence and non-ex­is­tence. A small (n<100) sur­vey in the UK found that at a life satis­fac­tion level of about 210 re­spon­dents would choose death over life[37]. The IDin­sight benefi­ciary sur­vey, us­ing an equally small sam­ple size, es­ti­mated the neu­tral point as be­ing 0.56.[38] We use a range of 0.05–2.5 for the neu­tral point.

Sum­mary: de­pri­va­tion­ist estimate

The di­rect effect es­ti­mated by the de­pri­va­tion­ist ac­count is then:

(Depri­va­tion­ist:) WELLBYs lost = (ex­pected well-be­ing level—neu­tral point) * (life ex­pec­tancy—age at death) = ex­pected net well-be­ing * ex­pected years of life

In words, the net WELLBY per year of life is the differ­ence be­tween the ex­pected life satis­fac­tion and the neu­tral point. The num­ber of WELLBYs lost by a death is the net WELLBYs per year of life mul­ti­plied by the ex­pected re­main­ing num­ber of years of life if the in­di­vi­d­ual had lived. For ex­am­ple, if a child would have died at the age of four, the ex­pected well-be­ing level over their life-time is 410, and their life ex­pec­tancy is 66 years:

(Depri­va­tion­ist:) WELLBYs = (4 − 2) * (66 − 4) = 2 * 62 = 124

In Guessti­mate, this works out to be about ~210 (50–360) WELLBYs lost due to the death of an un­der-5.

Time Rel­a­tive In­ter­est Ac­count (TRIA)

On the pre­vi­ous es­ti­mate, it is more valuable to save the life of a 2-year-old than a 20-year-old. Some peo­ple find this un­in­tu­itive and think the re­verse is true. In con­trast to the 20-year-old, the 2-year-old is not yet fully de­vel­oped, they do not have a strong psy­cholog­i­cal con­nec­tion to their fu­ture selves, nor do they have as many in­ter­ests that will be frus­trated if they do not keep liv­ing.

In the philo­soph­i­cal liter­a­ture, the view that cap­tures the in­tu­ition that it is (usu­ally) worse for some­one to die at 20 than at 2 is called the time-rel­a­tive in­ter­est ac­count (TRIA) of the bad­ness of death (Holtug 2011; McMa­han 2019). On TRIA, the bad­ness of death is a product of the fu­ture well-be­ing the per­son is de­prived of mul­ti­plied by how psy­cholog­i­cally con­nected the per­son presently is to their fu­ture self. We do not ad­vo­cate for one view over the other (de­pri­va­tion­ism or TRIA) but rather sketch the differ­ent im­pli­ca­tions of the views.

It’s un­clear ex­actly how TRIA should be rep­re­sented: two peo­ple could hold the view “sav­ing 20-year-olds is bet­ter than sav­ing 2-year-olds” but dis­agree over how to make this math­e­mat­i­cally pre­cise.[39] But in terms of the rel­a­tive moral weights of sav­ing an un­der-5 to dou­bling con­sump­tion for a year, the ba­sic im­pli­ca­tion of mov­ing from de­pri­va­tion­ism to TRIA is that the rel­a­tive value of sav­ing un­der-5s will go down.

(TRIA): WELLBYs lost = (ex­pected well-be­ing level—neu­tral point) * [(life ex­pec­tancy—age at death) * dis­count]

The TRIA dis­count re­duces the value of avert­ing the death of some­one younger than the age of full psy­cholog­i­cal con­nect­ed­ness. We rep­re­sent this as a sim­ple lin­ear func­tion, dis­count­ing from zero at three months be­fore birth and one at the age of ‘full psy­cholog­i­cal con­nect­ed­ness’ (see Figure 2). We use a range of val­ues be­tween 10 and 21 years for the age of ‘full psy­cholog­i­cal con­nect­ed­ness’ in our model. The WELLBYs lost di­rectly due to the death of an un­der-5 un­der TRIA are then es­ti­mated to be 45 (9–110) in Guessti­mate. It is plau­si­ble that the gra­di­ent of the TRIA dis­count be­com­ing less steep with greater age might bet­ter cap­ture some­one’s in­tu­ition of TRIA.

Figure 2: Dis­value of death at a given age, for the de­pri­va­tion­ist and TRIA ac­counts. On de­pri­va­tion­ism (red line), the num­ber of years lost at death equals the life ex­pec­tancy at zero, and de­creases lin­early as the age at death in­creases. Our sim­ple TRIA dis­count func­tion (shown in B) goes from 0 at 3 months be­fore birth to 1 at the age of ‘full psy­cholog­i­cal con­nect­ed­ness’. This dis­count is mul­ti­plied by the num­ber of years of life left to es­ti­mate the TRIA “years” lost due to death at a given age (blue dashed line).We have said that life ex­pec­tancy is con­stant.

Spillover effects to house­hold: im­pact on SWB of bereavement

The clear­est effect on the other mem­bers of the house­hold due to a death is through grief. The ev­i­dence base for the effects of grief on SWB is both slim and pre­dom­i­nantly from high-in­come coun­tries.

In our judge­ment, Oswald and Powdthavee (2008) is the most rele­vant study.[40] They use a Bri­tish panel dataset (gen­er­ally stronger ev­i­dence than a cross-sec­tional study[41]) and es­ti­mate the effect on some­one’s LS af­ter the death of their child. The au­thors es­ti­mate the effect of a child’s death on their par­ents is −0.49 LS points[42] on a 7-point scale (-0.7 points on an 11-point scale). By com­par­i­son, the effect of the death of a part­ner is stronger (but not statis­ti­cally sig­nifi­cantly so) at −0.63 points (-0.9 on an 11-point scale). The sam­ple size is large (n = 28,418), but only 49 in­di­vi­d­u­als re­ported the death of a child and 89 the death of a part­ner in the last 12 months, and the stan­dard er­rors are cor­re­spond­ingly large (0.25 and 0.24, re­spec­tively, on the 7-point scale).

Clark et al. (2018)[43] give some in­di­ca­tion of the effect through time. Us­ing panel datasets in Bri­tain, Ger­many and Aus­tralia they es­ti­mate that the loss of a part­ner is as­so­ci­ated with a drop within the fol­low­ing year of nearly 1 life satis­fac­tion point on a 11-point scale. Life satis­fac­tion for women and men in the three coun­tries usu­ally re­turns to pre-loss lev­els over a five-year pe­riod. The to­tal av­er­age loss is roughly 2 WELLBYs.

Given this, we in­put a mean value of −0.7 LS points in our model due to grief to one par­ent, fol­low­ing Oswald and Powdthavee (2008), with wide con­fi­dence in­ter­vals (-0.2 to −1.7). We model the effect as re­cov­er­ing lin­early to baseline over 5 (2–10) years. In the stud­ies, the deaths could have oc­curred any­time in the last year, so a rea­son­able ap­prox­i­ma­tion is that the mea­sured change in LS is at 6 months af­ter the death. Fi­nally, we say the effect is the same for the other mem­bers of the house­hold, to give a rough to­tal es­ti­mate of 6 (1–20) WELLBYs for the effect from grief.

The effects of grief would be diminished if we were to in­clude the coun­ter­fac­tual – that grief will also oc­cur when the in­di­vi­d­ual dies at a later point. It seems rea­son­able, how­ever, to as­sume that the (more un­likely) death of a child from malaria will have a much larger effect on some­one’s grief than the (more likely) case of some­one dy­ing from old age.

Fur­ther considerations

Our anal­y­sis uses SWB data to (re)es­ti­mate the val­ues of two out­comes – in­creas­ing con­sump­tion and avert­ing the death of un­der-5s – whilst im­plic­itly hold­ing var­i­ous back­ground as­sump­tions. How­ever, there are other as­sump­tions one could make that would change the anal­y­sis, per­haps sub­stan­tially, that we will briefly men­tion.

Above, we’re im­plic­itly as­sum­ing a per­son-af­fect­ing view of pop­u­la­tion ethics on which the only lives that mat­ter are those that will ex­ist what­ever we do – in slo­gan form, per­son-af­fect­ing views hold “moral­ity is about mak­ing peo­ple happy, not about mak­ing happy peo­ple” (Narve­son 1973). GiveWell does not have an offi­cial stance on pop­u­la­tion ethics, and its staff are sym­pa­thetic to a range of views.[44] One might in­stead hold a view like to­tal­ism (on which the best state of af­fairs is the one with the largest sum of well-be­ing of ev­ery­one who ever lives) where, saliently, cre­at­ing happy lives is good. On such views, the value of sav­ing lives would be quite sen­si­tive to the effect re­duc­ing child mor­tal­ity has on ma­ter­nal fer­til­ity. To ex­plain, par­ents of­ten seek a par­tic­u­lar fam­ily size and so have fewer to­tal chil­dren if the chance of each dy­ing re­duces. A re­port writ­ten for GiveWell es­ti­mated that in some ar­eas where it recom­mends char­i­ties the num­ber of births averted per life saved is as large as 1:1, a ra­tio at which pop­u­la­tion size and growth are left effec­tively un­changed by sav­ing lives.[45] For to­tal­ists, the value of sav­ing lives in a 1:1 con­text would be very small (com­pared to one where there was no fer­til­ity re­duc­tion) as the value of sav­ing one life is ‘negated’ by the dis­value of caus­ing one less life to be cre­ated.[46] One would still need to count other im­pacts in a 1:1 con­text, such as pre­vent­ing grief. Per­son-af­fect­ing views will gen­er­ally not hold these fer­til­ity effects are rele­vant for as­sess­ing im­pact. It’s worth not­ing philoso­phers widely agree that pop­u­la­tion ethics is a no­to­ri­ously in­tractable area of ethics where all of the views have some (very) counter-in­tu­itive re­sults. See Greaves (2017) for a re­view of the differ­ent the­o­ries and their is­sues.

Another con­sid­er­a­tion is that one might take an ‘Epicurean’ view of death. In this case, death is not bad for the per­son that dies, hence there is no value in sav­ing lives re­lated to the per­son whose life is saved; of course, grief and other effects would still be counted.[47] On this view, sav­ing lives is un­sur­pris­ingly lower in value.

Given this moral un­cer­tainty, one might want to some­how com­bine differ­ent views, weighted by one’s strength of be­lief in them, al­though it’s un­clear ex­actly how this should be done and we do not do so here – see Bykvist (2017) for dis­cus­sion.

The use­ful­ness of SWB met­rics is that they are a plau­si­ble means of mea­sur­ing well-be­ing, one that al­lows us to put the differ­ent out­comes that cre­ate, ex­tend, and im­prove lives into a sin­gle cur­rency. Deter­min­ing the value of out­comes is, of course, sen­si­tive to a range of eth­i­cal is­sues – such as how much one val­ues cre­at­ing lives – be­sides how to mea­sure well-be­ing. One still needs to have a mea­sure of well-be­ing how­ever those other eth­i­cal is­sues are re­solved.

Dis­cus­sion of model results

We will briefly de­scribe our ini­tial es­ti­mates of the rel­a­tive value of avert­ing the death of an un­der-5 and dou­bling con­sump­tion for one per­son for one year. We will com­pare the re­sults to pre­vi­ous es­ti­mates and dis­cuss their un­cer­tain­ties and sen­si­tivity fur­ther.

Our results

As­sum­ing the de­pri­va­tion­ist ac­count of the bad­ness of death, the ra­tio of avert­ing the death of an un­der-5 to dou­bling con­sump­tion for one house­hold for one year in our model is about 56:1 (un­cer­tainty: 9–150). In other words, dou­bling the con­sump­tion of 55 house­holds for one year would be of ap­prox­i­mate equal value to avert­ing the death of one child who is un­der-5, al­though with a wide range of un­cer­tainty. Ac­cord­ing to TRIA, as we have mod­el­led the view, the ra­tio of moral weights re­duces to about 12:1 (1–37). To get the re­spec­tive moral weights for dou­bling con­sump­tion for one per­son for one year, we di­vide by the av­er­age num­ber of house­hold mem­bers. The re­sults are sum­marised in Table 2.

Table 2: Our re­sults.

Com­par­i­son to other methods

Hav­ing pro­duced our model and its re­sults, the nat­u­ral step is to com­pare these to the es­ti­mates used by GiveWell. While we can com­pare the end re­sults—and these turn out to be similar—it is un­clear what to in­fer from this, given the differ­ent meth­ods used.

GiveWell’s moral weight ra­tio in 2018, us­ing the me­dian of their staff mem­bers, was 50 (the range was 8 to 100).[48] The me­dian falls ex­actly on our TRIA re­sult, but is within the un­cer­tainty of the de­pri­va­tion­ist re­sult. It is hard to com­ment on this com­par­i­son be­cause we only know how some of the GiveWell staff gen­er­ated their weights.[49]

IDin­sight’s benefi­ciary prefer­ences re­port pro­vides an es­ti­mate of 230 for the moral weight ra­tio.[50] This is an av­er­age from their two prefer­ence-based meth­ods, which we de­scribe in turn.

In the first method, IDin­sight asked re­spon­dents about their own will­ing­ness to pay for a (hy­po­thet­i­cal) medicine or vac­cine to re­duce the risk to them­selves or to their child of dy­ing from a (hy­po­thet­i­cal) dis­ease. Speci­fi­cally, they were asked how much they would pay to re­duce the risk of dy­ing from the dis­ease from 20 in 1,000 to 5 in 1,000 or 10 in 1,000 (ran­domised) over the next 10 years. This re­quires in­di­vi­d­u­als to think in terms of small prob­a­bil­ities, which is quite un­in­tu­itive.[51] The av­er­age will­ing­ness-to-pay was $40,763 (nom­i­nal USD) to avert the death of an un­der-5. This is com­pared to the av­er­age an­nual con­sump­tion per cap­ita as­sumed for the typ­i­cal benefi­ciary pop­u­la­tion through­out the GiveWell model ($286 in nom­i­nal USD) to give a moral weight ra­tio of 140.

In the sec­ond method, re­spon­dents were asked to take the per­spec­tive of a de­ci­sion-maker in their com­mu­nity and to choose be­tween sav­ing one life (via a hy­po­thet­i­cal in­ter­ven­tion) and giv­ing a num­ber of $1,000 cash trans­fers, where the max­i­mum num­ber of cash trans­fers pos­si­ble was 10,000, i.e. a value of $10m. The sur­vey found 38% of re­spon­dents preferred to save one life rather than provide 10,000 cash trans­fers (the ‘never switch­ers’). In Ghana, the me­dian switch­ing point was >9,995 cash trans­fers (i.e. at least $9 mil­lion)[52], which seems im­plau­si­bly high. IDin­sight took the cen­tral es­ti­mate from their model[53] – 91 cash trans­fers – as the in­put for the moral weight, i.e. the benefi­ciary prefer­ence was in­ter­preted as an in­differ­ence be­tween sav­ing one life and $91,000 of cash trans­fers. This gives an es­ti­mated moral weight ra­tio of 319.

IDin­sight also provide ‘liter­a­ture pri­ors’ of the moral weight ra­tio[54], a me­dian of 145 (min­i­mum in the liter­a­ture of 10 and max­i­mum of 240). Th­ese are based on es­ti­mates of the value of a statis­ti­cal life (from re­vealed and stated prefer­ences) in the US and ex­trap­o­lated to the benefi­ciary pop­u­la­tion. You can read about other es­ti­mates on this GiveWell page. As noted in the In­tro­duc­tion, how­ever, there are gen­eral wor­ries about rely­ing on any kinds of prefer­ence-based meth­ods as a guide to how peo­ple feel dur­ing their lives (see Ma­sur et al. 2013).

Uncer­tain­ties and sensitivity

Sum­mary of main re­sults in WELLBYs (with 90% con­fi­dence in­ter­vals):

  • Dou­bling con­sump­tion: 7 (2 to 19)

  • Depri­va­tion­ist – avert­ing death of an un­der-5: 220 (58 to 360)

  • TRIA – avert­ing death of an un­der-5: 45 (9 to 110)

For dou­bling con­sump­tion, the largest un­cer­tain­ties come from (at least in the pa­ram­e­ters of this model, i.e. not in­clud­ing model un­cer­tainty):

The long-run effect of dou­bling con­sump­tion (pri­mar­ily given by the effect de­cay rate). This can be an­swered em­piri­cally al­though RCTs over long time pe­ri­ods are very rare, given the cost and effort in­volved.

Spillovers to the house­hold. Fur­ther work on the effects on other mem­bers of the house­hold (not just the cash trans­fer re­cip­i­ent) seems fairly tractable, and would tighten up the con­fi­dence in­ter­vals. As men­tioned, we have not in­cluded the spillover effects on the wider com­mu­nity, but provide a syn­the­sis in Ap­pendix 2. We plan to com­ment on this fur­ther in our forth­com­ing meta-anal­y­sis (McGuire, Bach-Mortensen and Kaiser, n.d.).

For avert­ing a death, the out­come of the de­pri­va­tion­ist ap­proach is dom­i­nated by the net WELLBY per year of life, which is it­self roughly equally sen­si­tive to the av­er­age life satis­fac­tion and the neu­tral point. Im­prov­ing the es­ti­mate of life satis­fac­tion for this pop­u­la­tion should be rea­son­ably straight­for­ward—we sim­ply need to sur­vey more peo­ple. How­ever, there is a great deal of un­cer­tainty around fu­ture SWB. The challenge for im­prov­ing the es­ti­mate of the neu­tral point is that we lack a the­o­ret­i­cal un­der­stand­ing of how best to de­ter­mine this. If the ideal method in­volves con­duct­ing a few sur­veys, then fur­ther em­piri­cal work would be straight­for­ward. We plan to con­duct more re­search on this is­sue in fu­ture.

The es­ti­mated to­tal grief effect is ~6 WELLBYs, which is rel­a­tively more sig­nifi­cant for TRIA (~39 WELLBYs lost from the death it­self) than the de­pri­va­tion­ist ap­proach (~210 lost from the death it­self). As men­tioned pre­vi­ously, there is lit­tle high-qual­ity ev­i­dence from rele­vant con­texts.

A fur­ther is­sue for es­ti­mat­ing WELLBYs on the TRIA ap­proach is that the view it­self is un­der­de­ter­mined: there are many ways to make pre­cise the idea “sav­ing 20-years-olds is bet­ter than sav­ing 2-year-olds”. Ad­vo­cates of the view would want to make a philo­soph­i­cally and em­piri­cally in­formed de­ter­mi­na­tion of its de­tails. Nev­er­the­less, we think our as­sump­tion gives a rea­son­able in­di­ca­tion of how TRIA ad­vo­cates might rep­re­sent the view.

Con­clud­ing remarks

We have illus­trated one co­her­ent method to es­ti­mate the rel­a­tive val­ues, in a low-in­come con­text, of avert­ing a death of an un­der-5 com­pared to dou­bling some­one’s con­sump­tion for a year. Speci­fi­cally, we used life satis­fac­tion, a mea­sure of sub­jec­tive well-be­ing, to as­sess the value of each out­come in terms of well-be­ing ad­justed life years (WELLBYs). The anal­y­sis was fea­si­ble given the data available, but the rele­vant ev­i­dence was thin in some ar­eas, such as the long-run effects of cash trans­fers and the effect of grief on SWB in rele­vant pop­u­la­tions. This ap­proach could be straight­for­wardly ex­tended to other types of life-im­prov­ing in­ter­ven­tion, such as treat­ing de­pres­sion, re­duc­ing chronic pain, or im­prov­ing ed­u­ca­tion. It can also be re­pro­duced in terms of hap­piness, rather than life satis­fac­tion, if and when the rele­vant data ex­ists. We ex­plained the philo­soph­i­cal and em­piri­cal con­sid­er­a­tions our es­ti­mates are sen­si­tive to and com­pared them to some al­ter­na­tives. We also stated ar­eas where fur­ther work would be par­tic­u­larly use­ful.

Ap­pendix 1 - effects on SWB from cash trans­fers in the long-run

Below we briefly de­scribe the most rele­vant stud­ies we found of the effects on SWB over longer time pe­ri­ods (greater than two years). Each of these stud­ies is differ­ent from the GiveDirectly stud­ies (for ex­am­ple, in the na­ture or size of the CT, or the out­come mea­sured), and there is wide va­ri­ety in the long-run effects. Given this, we do not feel we have good ev­i­dence to up­date our es­ti­mate of the effect through time in ei­ther di­rec­tion.

  • Blattman et al. (2018), work­ing pa­per: $400 grants were pro­vided to help peo­ple start skil­led trades in Uganda. At a fol­low-up nine years later, there was no sig­nifi­cant differ­ence in a men­tal health in­dex be­tween treat­ment and con­trol. Men­tal health and SWB can­not be used in­ter­change­ably, but we think MH mea­sures at least re­veal some­thing about some­one’s cur­rent feel­ings.

  • Gali­ani et al. (2018): stud­ied the pro­vi­sion of ba­sic hous­ing (so not a CT, but CTs are com­monly spent on hous­ing) in El Sal­vador, Mex­ico and Uruguay. After 16 months, SWB im­proved sub­stan­tially for re­cip­i­ents of bet­ter hous­ing but then af­ter eight ad­di­tional months (on av­er­age), 60% of that gain dis­ap­pears. The au­thors’ model sug­gests the effect com­pletely dis­ap­pears af­ter 28 months (2.33 years).

  • Natali et al. (2018): RCT of a pro­gram pro­vid­ing bi-monthly $24 trans­fers (i.e. not a lump-sum trans­fer) to moth­ers in Zam­bia. 0.19 SDs in­crease in hap­piness at three years and 0.25 SDs at four years (i.e. in­creas­ing through time).

  • Lind­vqist et al. (2020): a Swedish lot­tery study (i.e. high-in­come coun­try) finds the effects on life satis­fac­tion per­sist for over a decade and show no ev­i­dence of dis­si­pat­ing over time.

  • Di Tella et al. (2010): us­ing Ger­man panel data (also high-in­come), sug­gest that the in­come effect on life satis­fac­tion de­creases by 65 % over four years, which, naively, im­plies the effect of an in­come shock on SWB will be com­pletely ex­tin­guished in around 5 ½ years.

Ap­pendix 2 - com­mu­nity spillovers

Three of the four GiveDirectly stud­ies shown in Table 1 re­port effects on ‘psy­cholog­i­cal well-be­ing’ (PWB) in­dexes to the com­mu­nity. The PWB in­dex con­tains hap­piness and life satis­fac­tion ques­tions as well as mea­sures of men­tal health (for com­mu­nity spillovers, we do not have the life satis­fac­tion re­sults for ev­ery study). We perform two mul­ti­level ran­dom effects ag­gre­ga­tions of the stan­dard­ized effect sizes, in­verse-weighted by stan­dard er­ror with er­rors clus­tered at the level of the sam­ple of the stan­dard­ized effect sizes. Both show no sig­nifi­cant spillover effects (95% CI) on mea­sures of SWB and men­tal health (MH). This anal­y­sis is pre­limi­nary as there is a large amount of var­i­ance in how CTs are im­ple­mented and re­ported and it is un­clear whether a syn­the­sis is in­sight­ful with­out a cor­re­spond­ing anal­y­sis of likely mod­er­at­ing effects such as size and time.

Figure 3 is a sim­ple ag­gre­ga­tion of the GiveDirectly stud­ies in Table 1. Figure 4 in­cludes all quan­ti­ta­tive mea­sures of spillovers on SWB or MH we have found, which in­cludes one non-GiveDirectly study (Baird et al., 2013) look­ing at the im­pact of monthly CTs on ado­les­cent girls’ GHQ-12 [55] scores. In Figure 4 we con­vert all effect sizes into Co­hen’s d^[The re­la­tion­ship be­tween na­tive effect sizes (Spillover_es) and Co­hen’s d is cap­tured in the fol­low­ing pseudo code:

                  t         = (Spillover_es /​ Spillover_SE),
                  dt        = t * sqrt((1/​(Spillover_n /​ 2)) + (1/​((Spillover_n /​2 ))) ), 
                  d_se      = sqrt(((Spillover_n /​2)/​ ((Spillover_n /​ 2)^2)) + 
                                            ((dt^2) /​ (2*(Spillover_n /​ 2)))))

] since the Baird et al., study used the nat­u­ral units of the GHQ-12 lik­ert scale.

There is some het­ero­gene­ity in how spillovers are ac­counted for. Most spillovers are from within the (treated) village ex­cept in Eg­ger et al. 2019, which looks at spillovers across treated and un­treated villages.[56] All stud­ies iden­tify the spillover treat­ment cat­e­gor­i­cally with ge­o­graphic prox­im­ity of a non-re­cip­i­ent to a re­cip­i­ent (usu­ally in the same village) ex­cept in the case of “Is Your Gain My Pain” (Haushofer, Reis­inger and Shapiro, 2019) where the spillover is for­mu­lated as how many re­cip­i­ents live near a non-re­cip­i­ent (prox­ied by in­creases in av­er­age wealth of the village). Thus it is the only study that looks at the de­gree of spillover in­ten­sity.[57]

Figure 3: A for­est plot of the spillovers of Give Directly stud­ies. Stan­dard er­rors are clus­tered on the study level to ac­count for de­pen­dence. All spillovers are within the (treated) village ex­cept Eg­ger et al., which looks at spillovers across treated and un­treated villages.

Figure 4: For­est plot of all CT stud­ies that cap­ture psy­cholog­i­cal spillovers. The lump value ($PPP to­tal) varies be­tween the Baird et al. (2013) fol­low-ups be­cause the vari­able is gen­er­ated from the sum of all monthly cash trans­fers and it is the only study where the CT was dis­tributed in monthly in­stal­l­ments.


  1. Thanks to Derek Foster for sig­nifi­cant in­put. ↩︎

  2. Although in Ap­pendix 2 we plot known com­mu­nity spillover effects and illus­trate a pre­limi­nary ag­gre­ga­tion. ↩︎

  3. See GiveWell’s 2019 cost-effec­tive­ness anal­y­sis. ↩︎

  4. See table 4 (row 1) of IDin­sight’s re­port. ↩︎

  5. QALYs are a mea­sure of health gained, whereas DALYs are a mea­sure of health lost. A re­view of other differ­ences can be found in Gold, Steven­son and Fry­back (2002). ↩︎

  6. Efforts to use SWB: we are only aware of at­tempts by one of us (Plant, 2019, ch 7), who pro­vides back-of-the-en­velope point-es­ti­mate as­sess­ments of the value sav­ing lives, re­duc­ing poverty, and treat­ing men­tal health. We im­prove on Plant’s prior es­ti­mate of the value of dou­bled con­sump­tion and sav­ing lives in sev­eral ways: we draw on a wider range of stud­ies to in­form the value of dou­bling (house­hold) con­sump­tion and as­sess its to­tal effect over time, mod­el­ling this as an an­nual de­cay; we use a Monte Carlo simu­la­tion with 90% sub­jec­tive con­fi­dence in­ter­vals to ac­count for un­cer­tainty; and we es­ti­mate the bad­ness of death ac­cord­ing to two philo­soph­i­cal views. ↩︎

  7. You can edit the in­puts in Guessti­mate to see how the re­sults vary. The re­sults will change slightly just by re­fresh­ing the page, be­cause the simu­la­tions are re-run. The large value dis­played in a cell is the mean; if you click on ‘Ex­pand’ for any given cell you can view the me­dian (the 50th per­centile). Th­ese val­ues can be quite differ­ent, par­tic­u­larly if the pres­ence of a few ex­treme val­ues changes the mean more than the me­dian. You can read more about Guessti­mate in the doc­u­men­ta­tion. ↩︎

  8. In a back-of-the-en­velope-calcu­la­tion, Plant (2019) p228-9 claims that, as de­pres­sion and anx­iety have a rel­a­tively big­ger im­pact on hap­piness than life satis­fac­tion, and in­creas­ing in­come has a rel­a­tively smaller effect on hap­piness than life satis­fac­tion, the rel­a­tive val­ues of treat­ing anx­iety or de­pres­sion com­pared to dou­bling in­come is about three times higher us­ing hap­piness than life satis­fac­tion (which leaves open which has higher cost-effec­tive­ness in ab­solute terms on ei­ther mea­sure). ↩︎

  9. GiveWell prefers to con­sider con­sump­tion rather than in­come (see Guide to GiveWell CEAs). Con­sump­tion in­cludes the value of all items used within a house­hold. For in­stance, if crops are grown and eaten at home, the value of this would be in­cluded in con­sump­tion, but not in­come. How­ever, con­sump­tion is more of­ten op­er­a­tional­ized as to­tal ex­pen­di­tures rather than the value of all goods con­sumed. ↩︎

  10. If a study finds a 1-point in­crease in LS, and the stan­dard de­vi­a­tion is 2 LS points, then the effect size is 0.5 SDs. Stan­dar­d­is­ing like this means you can eas­ily com­pare the size of effects mea­sured on differ­ent scales. ↩︎

  11. Purely cross-sec­tional work suffers from two draw­backs when we are try­ing to es­ti­mate the to­tal im­pact of an in­come shock on SWB. First, cross-sec­tional es­ti­mates have no time com­po­nent, so we do not know how long the effect lasts. Se­cond, it is non-causal. We do not know how much of this co­effi­cient can be ex­plained by greater satis­fac­tion with life lead­ing to a higher earn­ings or vice versa. ↩︎

  12. The re­sult comes from 0.36*ln(2) = 0.24 where 0.36 was the log(in­come) co­effi­cient. The benefit of us­ing a lin­ear-log­a­r­ith­mic model is it al­lows co­effi­cients to be in­ter­preted as per­cent change so you can es­ti­mate the effect of dou­bling with­out know­ing the origi­nal units (al­though the larger the change, the poorer an ap­prox­i­ma­tion it pro­vides). ↩︎

  13. From Gal­lup World Poll 2005 to 2012 (Steven­son and Wolfers 2013, p. 601). Steven­son & Wolfers also con­sider re­sults from the Cantril Lad­der, a life eval­u­a­tion ques­tion which asks in­di­vi­d­u­als to imag­ine a lad­der with steps from 0 to 10, where 0 is the best pos­si­ble life, 0 the worst pos­si­ble life, and to place them­selves on it. In this case, dou­bling in­come leads to an in­crease of 0.25*ln(2) SDs in LS. ↩︎

  14. “The causal effect of log in­come on over­all LS im­plied by our es­ti­mate is 0.38”, which cor­re­sponds to 0.38*ln(2) for dou­bling in­come. Also see Figure 4 in Lind­vqist et al. ↩︎

  15. A re­cent pa­per by Ridley et al. (2020) ag­gre­gates effects on men­tal health and psy­cholog­i­cal well-be­ing from cash trans­fers. Figure 10 shows the effects per $1000 (PPP) spent. ↩︎

  16. Us­ing a lin­ear re­gres­sion model (there­fore con­strain­ing pa­ram­e­ter es­ti­mates – log(de­cay rate) and ini­tial effect size – as nor­mally dis­tributed). ↩︎

  17. This is the only un­stan­dard­ized value for a SD pro­vided in the GiveDirectly stud­ies. ↩︎

  18. Steven­son & Wolfers (2013) ap­pear to have an SD of 2; Bri­tish House­hold Panel sur­vey = 1.9; Lindqvist et al. = 1.93, IDin­sight benefi­ciary re­port = 2.32. Kilburn et al. re­ports 1.3 SDs of LS on a 1-5 scale. ↩︎

  19. See O’Hare et al. (2013), Bastagl et al. (2019) and the Our World in Data page. ↩︎

  20. See Martín-María et al. (2017). ↩︎

  21. In Eg­ger et al 2019, in house­holds with a mar­ried or co­hab­it­ing cou­ple, one of the part­ners was ran­domly se­lected as the tar­get sur­vey re­spon­dent. ↩︎

  22. There is some ev­i­dence of differ­ent out­comes de­pend­ing on whether a woman or a man is the re­cip­i­ent of the CT, for ex­am­ple, Haushofer and Shapiro (2016) find sig­nifi­cant differ­ences (at the 10 % level) in psy­cholog­i­cal well-be­ing and fe­male em­pow­er­ment be­tween fe­male and male re­cip­i­ent house­holds (but no sig­nifi­cant differ­ence for any other treat­ment effects). They illus­trate these differ­ences fur­ther in Haushofer et al (2019), where they show the effects on psy­cholog­i­cal well-be­ing ap­pear driven by women. This re­sult meshes with an­other eval­u­a­tion of a CTs which found that the im­pact on SWB is driven by fe­male-led (and re­spond­ing) house­holds (Handa and Mark, 2014). It is pos­si­ble that there will be differ­ences for the other mem­bers of the house­hold, too, for fe­male and male re­cip­i­ent house­holds. Given the GiveDirectly stud­ies ran­domly se­lect whether a re­cip­i­ent is male or fe­male, and so re­sults re­flect both cases, we have not tried to ac­count for any differ­ences be­tween male and fe­male re­cip­i­ent house­holds. ↩︎

  23. Another work­ing pa­per based on the ex­per­i­ments stud­ied in Haushofer and Shapiro 2016, 2018. ↩︎

  24. The work that has been done sug­gests that the rel­a­tive in­come effect re­mains large in lower in­come set­tings (Reyes-Gar­cía et al., 2016). In the case of Natali et al.’s RCT of a CT in Zam­bia they find “ev­i­dence that the rel­a­tive poverty path­way dom­i­nates the ab­solute poverty path­way in ex­plain­ing treat­ment effects” (2018). ↩︎

  25. y = a + b . log(x) + er­ror ↩︎

  26. See the top of page 4 in these notes: “for a lin­ear-log model, the ex­pected change in Y as­so­ci­ated with a p% in­crease in X can be calcu­lated as βˆ · log([100 + p]/​100)”. There­fore, the mul­ti­plier on the effect of a 75 % change in con­sump­tion for a 100 % change in con­sump­tion = (log(200/​100) /​ log(175/​100)) = 1.24, or 24 %. In Haushofer & Shapiro (2016), the av­er­age $709 CT is 37% of an­nual house­hold con­sump­tion ($1,896, monthly is $158). Us­ing the same equa­tion to calcu­late how to ad­just the effect size in this case pro­duces a mul­ti­plier of (log(200/​100) /​ log(137/​100)) = 2.2. In­tu­itively, this seems too high and we do not use it in our model. $709 is an av­er­age of a small and large trans­fer; in fu­ture, we could ob­tain the sep­a­rate effect sizes. ↩︎

  27. It is there­fore im­por­tant to note that the effect ‘on one per­son’ is re­ally the av­er­age effect on a house­hold mem­ber (adults and chil­dren). In gen­eral, we pre­fer to work at the house­hold level, rather than the in­di­vi­d­ual level, be­cause we do not have a great deal of in­for­ma­tion about how ei­ther baseline con­sump­tion or the CT is split up amongst the house­hold. ↩︎

  28. This is akin to how DALYs are used to es­ti­mate the bur­den of dis­ease. See Gam­lung and Solberg (2019) for a col­lec­tion of philo­soph­i­cal es­says on the harm of death. ↩︎

  29. Often, “pe­riod” life ex­pec­tancy is re­ported (see Our World in Data for an ex­pla­na­tion). We prob­a­bly ex­pect life ex­pec­tancy to rise in the fu­ture for most peo­ple, which would not be re­flected in pe­riod life ex­pec­tan­cies. This is an ad­van­tage of the pro­jected life ex­pec­tan­cies pro­vided by the UN. ↩︎

  30. See World Hap­piness Re­port 2013. We use 2013 for the sake of con­sis­tency be­cause this is around the time pe­riod of the Haushofer & Shapiro (2016) study. It does not mat­ter much which year one chooses, for 2019 es­ti­mated LS is 4.5. ↩︎

  31. Figure 8, page 42. ↩︎

  32. To demon­strate this, IDin­sight as­sumed that life satis­fac­tion varies with the log of an­nual con­sump­tion per cap­ita. They used three es­ti­mates of the re­gres­sion co­effi­cient, one from their own re­sults, and also from Deaton (2008) and Steven­son (2013). The pre­dicted life satis­fac­tion of the sam­ple in their sur­vey is 3.62, 3.35 and 4.22. See foot­note on page 95. ↩︎

  33. E.g. Toby Ord, The Precipice (80,000 Hours pod­cast tran­script can be seen here). ↩︎

  34. Dis­count­ing money or as­sets ob­tained in the fu­ture is sen­si­ble, but this rea­son­ing does not nec­es­sar­ily ap­ply to health or well-be­ing. See this Giv­ing What We Can re­port by Ord and Wiblin. Note that, here, we are con­sid­er­ing the effects of pro­grammes oc­cur­ring to­day (so dis­cus­sion of dis­count­ing to ac­count for pro­grammes con­ducted in the fu­ture is not rele­vant). ↩︎

  35. This is calcu­lated by tak­ing Toby Ord’s es­ti­mate of a 1 in 6 chance of hu­man­ity not mak­ing it through the next cen­tury and as­sum­ing the risk is con­stant in that pe­riod. ↩︎

  36. This is very spec­u­la­tive, but is calcu­lated based on ad­di­tional risks to the rele­vant pop­u­la­tion (e.g. re­gional catas­tro­phes) be­ing equally as likely as ex­is­ten­tial risks. ↩︎

  37. Peas­good et al. (un­pub­lished draft) ↩︎

  38. Ap­pendix 6, p94 ↩︎

  39. See Greaves (2019) for a dis­cus­sion of how the view is un­der­de­ter­mined and the difficulty of find­ing a plau­si­ble pre­cisifi­ca­tion. ↩︎

  40. We found one study in a more rele­vant con­text: Deaton et al.’s work­ing pa­per (2009), us­ing cross-sec­tional data from sub-sa­haran Africa. The death of an “im­me­di­ate fam­ily mem­ber” in the last year is es­ti­mated to re­duce SWB by 0.1 points (on Cantril’s 0-10 lad­der). The effect on hap­piness ap­pears much larger, al­though it is difficult to com­pare be­cause the hap­piness ques­tion was bi­nary (prob­a­bil­ity of ex­pe­rienc­ing en­joy­ment yes­ter­day). We have not up­dated based on this study, the main rea­sons be­ing: (1) The sur­vey did not ask if any­one died in their fam­ily in the last year due to any cause, only a sub­set of causes (AIDS, malaria, tu­ber­cu­lo­sis and child­birth). The claim that the study is com­par­ing peo­ple who had im­me­di­ate fam­ily mem­bers die in the last year against those who did not does not ap­pear to be true; (2) the re­sults are ex­tremely het­ero­ge­neous and er­rors are not given. (3) It is hard to know how widely peo­ple will have in­ter­preted the death of an ‘im­me­di­ate fam­ily mem­ber’; it may be quite differ­ent to the death of a child. ↩︎

  41. In a panel you can of­ten con­trol for the time-in­var­i­ant char­ac­ter­is­tics of the in­di­vi­d­ual, thereby re­duc­ing like­li­hood of omit­ted vari­able bias. This doesn’t get you to a causal re­la­tion­ship as you still have to con­tend with time-vary­ing fea­tures of the in­di­vi­d­ual, but it’s much bet­ter than cross-sec­tions where you likely only have poor mea­sure­ments of a few of the time-in­var­i­ant fea­tures of an in­di­vi­d­ual. ↩︎

  42. By com­bin­ing the ad­justed OLS and IV es­ti­mates: death of a part­ner has an effect of (-0.590 − 0.661) /​ 2 im­pact on LS points (7-point scale). For the death of a child it’s (-0.556 −0.430) /​ 2. ↩︎

  43. The Ori­gins of Hap­piness, p81 (not available on­line). ↩︎

  44. See this or this doc­u­ment from cur­rent or former GiveWell staff mem­bers. ↩︎

  45. It if turned out not to be 1:1, then there would be re­lated con­cerns about whether the Earth was un­der or over­pop­u­lated. See Greaves (2015) and Plant (2019) ch. 2 for dis­cus­sion of is­sues of op­ti­mum pop­u­la­tion. ↩︎

  46. See this 2017 blog post on GiveWell’s web­site for some dis­cus­sion. ↩︎

  47. While it is com­mon to dis­cuss Epicure­anism as a pos­si­ble view, it is not a com­mon one to hold. See e.g. Cush­ing (2007) and Ru­bio (forth­com­ing) for two of the few (sym­pa­thetic) con­tem­po­rary dis­cus­sions. ↩︎

  48. See the 2018 CEA: “Value of dou­bling con­sump­tion for one per­son for one year rel­a­tive to sav­ing the life of a child un­der-5 (AMF)” is given as per­centages, with the me­dian be­ing 2%, cor­re­spond­ing to a moral weight of 50. In the 2019 CEA, GiveWell uses a moral weight ra­tio of 100:1, in­fluenced by the IDin­sight sur­vey re­sults. ↩︎

  49. Links to the rea­son­ing of some staff mem­bers are given in the CEAs, e.g. the 2018 CEA. ↩︎

  50. See p10 and p102. This re­sult is av­er­aged across Kenya and Ghana. There were sig­nifi­cant re­gional differ­ences in re­sults; see sec­tion 1 of the IDin­sight re­port for fur­ther dis­cus­sion. ↩︎

  51. IDin­sight as­sessed re­spon­dents’ un­der­stand­ing of prob­a­bil­ity by ask­ing them sev­eral ques­tions, such as “Imag­ine two lot­ter­ies. The chance of win­ning in one lot­tery is 5 in 1000, the chance of win­ning in the other lot­tery is 10 in 1000. Which lot­tery has the larger chance of win­ning?” 58% of re­spon­dents cor­rectly an­swered all of the four ba­sic ques­tions the first time. Only 34% of re­spon­dents cor­rectly an­swered a more ad­vanced ques­tion: “Which risk of death is larger: 1 in 100 or 2 in 1,000?”. The sur­veyor then trained re­spon­dents, pro­vid­ing ad­di­tional ex­pla­na­tions un­til they could cor­rectly an­swer the ques­tions. See Ap­pendix 2 of the IDin­sight re­port for fur­ther dis­cus­sion. ↩︎

  52. Table 28, p 78. ↩︎

  53. A lo­gis­tic re­gres­sion model ↩︎

  54. See re­sult on page 28, and fur­ther in­for­ma­tion on p8, foot­note 14. ↩︎

  55. The GHQ-12 is a widely used screen­ing tool for com­mon men­tal ill­nesses. ↩︎

  56. They did this by com­par­ing con­trol villages near treat­ment villages to con­trol villages farther from treat­ment villages. ↩︎

  57. In eco­nomics jar­gon this is known as the in­ten­sive as op­posed to the ex­ten­sive mar­gin. ↩︎