Interplay among credit, insurance and savings for farmers in. developing countries

Transcription

1 Inerplay among credi, insurance and savings for farmers in developing counries Francesca de Nicola Ruh Vargas Hill Miguel Robles Inernaional Food Policy Research Insiue March 30, 2012 Preliminary and incomplee Absrac Agriculural income in low income counries is subjec o many risks, such as weaher uncerainy, pess and disease. Much of his risk remains uninsured by exising risk managemen ools and his uninsured risk consrains invesmen. In his paper we examine he poenial benefis of hree financial producs-weaher index insurance, savings accouns, and insured agriculural loans-ha could improve a household s abiliy o manage agriculural risks o answer he quesion of wha financial insrumens do farmers really need? We develop and esimae a dynamic sochasic model ha quanifies he impac of hese hree producs on consumpion, invesmen and welfare. The parameers of he model are calibraed wih daa from farmers in Ehiopia All hree insrumens offer welfare gains o farmers. The gains from index insurance and insured credi are paricularly high, bu basis risk mues hese gains. When basis risk is high he invesmen response o index insurance is weaker which resuls in lower consumpion gains. Combined wih higher consumpion volailiy, his resuls in lower welfare. However, we find ha improved access o savings limis he negaive effecs of basis risk, suggesing ha an approach ha develops muliple financial insrumens for farmers may be beer han an approach focused on one insrumen alone. 1

2 1 Inroducion In all counries, agriculural income is subjec o many risks, such as weaher uncerainy, pess and disease. The inensiy of hese risks is ofen higher in developing counries where many households derive a large share of heir income from agriculural enerprises. Alhough farmers use asses, neworks and informal credi o manage as much of his risk as hey can, much of his risk remains uninsured. Wihou formal insurance, farmers have a number of sraegies ha help hem manage risk. They run down asses or borrow in bad years and save or pay loans back in good years. They ask for help from a nework of friends and family members in bad years, and help ou hose in heir nework in good years. However, hese sraegies are limied in heir effeciveness in managing cerain ypes of agriculural risk. A large shock, a shock ha affecs many farmers in one area (a covariae shock), or a series of repeaed shocks in quick succession prove paricularly difficul for households o insure. In hese cases farmers reduce food consumpion, ake children ou of school, sell-off producive asses and engage in risky income-earning aciviies. These have immediae and long-run welfare coss. These have deleerious long-run effecs on welfare (Dercon (2004); Alderman, Hoddino and Kinsey (2006); Burke, Gong and Jones (2011)). The cos of his uninsured risk on he welfare of farmers suggess ha, were he righ financial insrumens available, farmers would be beer off. Addiionally, uninsured risk discourages innovaion and risk aking. Absen he special case of oupu risk ha is posiively correlaed wih consumpion prices, heoreical work has shown ha increases in risk reduce he scale of risky crop producion (Sandmo (1971), Fafchamps (1992), Fafchamps and Kurosaki (2002)) as households limi heir exposure o risk ha hey canno insure agains. Empirical sudies have confirmed he predicions of hese models: households wih less insurance devoe less land o high-yielding bu volaile rice varieies and casor in India (Morduch (1990)); more land o low-risk and low-reurn poaoes in Tanzania (Dercon (1996)); and less labor o price-volaile coffee in Uganda (Hill (2009)). Walker and Ryan (1990) found ha in semiarid areas of India, households may sacrifice up o 25% of heir average incomes o reduce exposures o shocks. The hrea of shocks can also make households relucan o access credi markes because hey fear he consequences of an inabiliy o repay (Carer, Cheng and Sarris (2011)). This in urn limis 2

3 a household s abiliy o use cosly inpus. In Ehiopia, households ha are less able o manage income risk are less likely o apply ferilizer available on credi (Dercon and Chrisiaensen (2011)). This work suggess ha reducions in risk, such as hose ha would resul from an insurance conrac or oher financial producs ha allow households o manage agriculural risk, will increase invesmens ha are suscepible o weaher risk and resul in welfare benefis. Evaluaions of he impac of index insurance sugges his may be he case (Karlan e al. (2011), and Cole, Giné and Vickery (2011)) alhough he analysis of impacs has been hindered by limied ake-up. In his paper we examine he quesion of wha ypes of financial producs will enable farmers o beer insure yield risk, and yield higher reurns as a resul. We consider hree commonly proposed financial producs, and examine how hey perform under sandard assumpions. We also consider wha happens when a combinaion of hese producs are available. The hree producs we consider are weaher index-insurance conracs, savings accouns, and lending by a bank ha reinsures is agriculural loan porfolio o cover weaher risk. There is a convincing raionale as o why each produc could help farmers manage risk; and equally each produc is also limied in he degree o which i is able o insure farmers. Innovaions in weaher index insurance conracs have provided new insurance possibiliies no provided by radiional indemniy insurance conracs. Under index insurance conracs payous are based on an independenly observable and verifiable index (such as weaher a a local weaher saion) raher han an on-field assessmen of farmer losses. As such, problems of adverse selecion, moral hazard and cosly loss assessmen ha have made indemniy insurance conracs prohibiively expensive for smallholder farmers (o he exen ha hese markes do no exis) are overcome, allowing insurance conracs insuring small plos of land o be sold (Skees, Hazell and Miranda (1999)). However, because he payou is based on he index and no on loss-assessmen esimaes, he farmer akes on basis risk in hese conracs and may experience losses ha are no indemnified. For his, and oher reasons (such as high insurance premiums, liquidiy consrains, lack of rus and poor undersanding) ake-up has been low. We also expec ha he basis associaed wih hese conracs will limi he gains resuling from hem, alhough his has only been modeled in de Nicola (2010). Index insurance can also be used by rural banks o help hem manage he risk hey hold by making agriculural loans. Higher raes of defaul are likely when producion losses are realized 3

4 which makes lending o agriculure inherenly risky. However, banks can purchase index insurance o insure his risk and guaranee o farmers ha hey will no ask for repaymen when index insurance pays ou. This ype of scheme has been examined by Miranda and Gonzalez-Vega (2011) and an example is a weaher index insurance policy ha will be sold o rural microfinance insiuions in Peru o help offse loan defauls and liquidiy problems caused by El Niño-induced excess rainfall (Skees and Collier (2010)). Evidence has suggesed ha in many conexs lending o agriculure currenly includes excusable sae-coningen defaul (see for example, Udry (1994), Giné and Yang (2009)) which is effecively priced ino he cos of he loan conrac. However in Ehiopia saeconingen defaul has no been widely praciced wih defaul punished quie severely (Dercon and Chrisiaensen (2011)). This has resuled in a relucance o ake credi for he use of agriculural inpus. Offering a loan wih excusable sae-coningen defaul may hus be a means by which access o agriculural finance is increased for smallholder farmers. However, hese schemes also have heir challenges. Banks are also subjec o basis risk and will have o engage in discussions wih farmers o explain o hem when deb is forgiven and when i is no. Banks may be concerned ha condiional deb forgiveness will undermine a repaymen culure. Alhough farmers will increase heir access o credi and insure lending as a resul of his scheme hey will no be able o insure heir livelihoods. Savings may also allow an individual o beer insure agains risk, by allowing an individual o accumulae savings in good years and use hese savings o cover uninsured losses. In fac, we may expec insurance and savings o be subsiues (Dionne and Eeckhoud, 1984). Savings and index-insurance, however, have somewha differen srenghs and disadvanages in his conex. Unlike index-insurance, savings can be used o insure farmers agains covariae and idiosyncraic shocks. However, alhough savings may have a beneficial role, i is no clear how much given hey are very expensive form of insurance agains large shocks and are an ineffecive means of insuring agains shocks ha occur in quick succession (Deaon and Paxson (1994)). We se-up a dynamic sochasic opimizaion problem wihin he conex of an agriculural household model in which hese hree risk managemen insrumens are each made available in urn. A key feaure of his model is ha invesmens in agriculure are subjec o muliple sources of risk, boh idiosyncraic and covariae in naure, and ha a large par of his uncerainy is covariae. This allows us o correcly model he basis risk inheren in some of he financial innova- 4

5 ions available. We numerically solve he opimizaion problem using calibraed parameers from Ehiopian household survey daa o show he impac of each of hese insrumens on consumpion, invesmen and welfare. We also consider wha happens when more han one of hese insrumens is made available, and examine wheher here are synergies among hem (e.g. insurance and insured credi) or subsiuion (e.g. saving and insurance) and heir combined effec on farmers choice. We find ha weaher insurance increases invesmen in agriculural producion and increases household consumpion. As a resul of boh increased consumpion and reduced consumpion volailiy, welfare gains o he household are posiive. However, higher levels of basis risk mue he welfare gains from index insurance. Increased basis risk reduces he amoun ha households are willing o inves in agriculural producion, and increases he resources ha a household chooses o keep in risk-free asses insead. As a resul consumpion improvemens are lower and welfare gains in shor and long run are more mued for households a all wealh levels, bu paricularly for he poores. Improved access o savings is also welfare increasing, however under his scenario welfare gains come largely from increased consumpion, raher han subsanial reducions in consumpion volailiy. When availed wih a high reurn savings insrumen, farmers reduce heir invesmen in agriculural producion swiching resources ino he higher reurn savings accoun insead. We also find ha, when offered wih index insurance, savings enables households o increase heir welfare gains in he presence of subsanial basis risk. This is because savings can be used o help farmers manage he basis risk associaed wih he index insurance produc. Finally, we show ha insured credi for agriculural producion can also be used as a form of insurance by avoiding repaymen in case of negaive shocks. The paper proceeds as follows, in he following secion we se-ou he model used, in Secion 3 we presen he Ehiopian daa se used in calibraing he model. In Secion 4 we presen and discuss he resuls and in Secion 5 we conclude. 2 Model We consruc a dynamic model of farmers in developing counries facing aggregae weaher risks and idiosyncraic shocks, in order o characerize heir consumpion and invesmen decisions and 5

6 he relaive welfare levels. 2.1 Baseline scenario We firs presen a baseline model ha capures he living condiions of Ehiopian farmers, in he absence of financial markes. In each period a farming household decides how much of heir resources o consume, c i,, how much o keep in asses, a i,, and how much o inves in agriculural inpus, k i, from which farm income in he following period, w i,+1, is derived. The household is assumed o have limied asse opions available o hem; as such he resources invesed in asses have zero reurn. However, we assume ha hese asses are riskless. We could hink of hese asses as being grain kep in sore, or cash kep under he bed (in boh cases assuming minimal crop losses and inflaion raes respecively). The household earns farm income according o a producion funcion wih decreasing marginal reurns. There are wo inpus o his producion funcion, agriculural inpus, k i, and labor l i,. Furhermore here are wo muliplicaive shocks o he producion funcion: a covariae shock η +1 whose realizaion is unknown o farmers a he ime he invesmen decision is made, and an idiosyncraic shock o farmers produciviy, ɛ i,+1, also unknown o farmers a he ime he invesmen decision is made. We can hink of he covariae shock as a weaher shock whose realizaion is unknown a he ime of invesmen in seeds and ferilizer; and he idiosyncraic shock as a healh shock. The presence of muliple uninsured risks is an imporan feaure of many rural seings, where informal insurance markes, alhough beer a insuring idiosyncraic raher han covariae shocks, do no perfecly insure idiosyncraic risk. These muliple sources of uninsured risks influence invesmen decisions and lower welfare. This feaure of he environmen will have an effec on he uiliy of he insrumens considered. I is also imporan ha we hink of hese shocks as muliplicaive. Shocks ha affec agriculural profis are highly unlikely o ener as addiive independen erms. This is because if a household loses is crop from drough, i canno lose i again due o labor consrains resuling from ill-healh. I is also no reasonable o assume ha you can lose your enire crop only if every shock occurs o is maximum possible exen. As such i is more appropriae o model agriculural losses as muliplicaive (Clarke e al. (2012)). 6

7 The household s income in period + 1, w i,+1 is going o be given as follows: w i,+1 = A i ɛ i,+1 ki,l α i, 1 α η +1 + a i, where A i is an individual-specific ime-invarian produciviy coefficien. The idiosyncraic erms, A i and ɛ i,+1, are boh log-normally disribued wih mean 1 and variance, respecively, of σ 2 A, and σ2 ɛ. The disribuion of he weaher shock, η +1, is empirically calibraed from he daa as discussed in Secion 3. The household maximizes he expeced presen discouned value of consumpion E j=0 βj u(c i,+j ) where u(c i, ) = c1 ρ i, 1 ρ of relaive risk aversion ρ. is a consan relaive risk-aversion (CRRA) uiliy funcion wih a coefficien The household s opimizaion problem can hus be wrien as: (1) V (w i, ) = max k i, 0 [u(c i,) + βe V (w i,+1 )] w i, = c i, + a i, + k i, w i,+1 = A i ɛ i,+1 ki,l α i, 1 α η +1 + a i, The firs-order condiions are compued by equaing he marginal uiliy of consumpion oday o he expeced discouned marginal uiliy of consumpion omorrow: u (c i, ) = βe [u (c i,+1 )αa i ɛ i,+1 k α 1 i, η +1 ] (2) u (c i, ) = βse [u (c i,+1 )] Solving for Equaion 2 allows us o derive he finie arge level of wealh owards which he household will converge, i corresponds o he level of wealh in he h period ha corresponds o he expeced amoun in he following period h + 1. I plays an imporan role in he analysis, since he calculaion of he welfare gains from he differen inervenions are based on i. The scope of he paper is o invesigae he qualiaive impac of he provision of index insurance, improved savings and insured credi on consumpion, invesmen and welfare for farmers. We hus 7

8 incorporae hese financial insrumens in our heoreical framework. For clariy, we inroduce one elemen a he ime 2.2 A marke for weaher insurance Now, we assume ha a well-funcioning marke for weaher insurance has been esablished. This marke for weaher insurance allows he household o insure agains he covariae shock η +1 ha affecs heir producion income. However, as discussed in he inroducion, i is unlikely ha he weaher insurance produc will insure households perfecly agains η +1. These design limiaions will lead o a source of basis risk, which means ha no all of he covariae shock will be covered. Two recen heoreical papers -Clarke (2011) and de Nicola (2010)- have furhered our undersanding of he naure of demand for index insurance. Each paper models basis risk differenly, bu imporanly hey boh rea i as quie differen from he addiive background risk ha is presen in models of demand for indemniy insurance in which he uninsured losses are enirely independen of he insured even. We use he framework se-up by de Nicola (2010) because de Nicola s model highlighs an imporan insigh for he conex we are considering. For an agriculural household, all non-insured shocks o agriculural producion-even healh shocks o he labor a household can allocae o crop producion-are muliplicaive and as such if farmers can purchase only weaher insurance, even if i insured perfecly agains he covariae source of risk, hey would no fully insure. This framework allows us o consider boh he design issues associaed wih he conrac and he fac ha, however well designed, a conrac designed o insure covariae sources of yield risk will no insure farmers agains idiosyncraic shocks such as healh shocks ha consrain he supply of labor o agriculural producion in a given season. The ake-up and welfare impac of insurance is limied by design imperfecions, bu also by hese oher uninsured sources of non-covariae risk. We denoe basis risk as ξ +1 and assume ha i is lognormally disribued wih mean one and sandard deviaion, σ ξ. The idiosyncraic source of risk, ɛ i,+1, is lef enirely uninsured by his insurance produc, and his will be anoher source of basis risk o he household, as ulimaely hey would like o insure he risk o heir crop producion income. A household can buy muliple unis of weaher insurance. The acuarially fair price of each uni is given as P = 1 0 (1 η)f(η)dη. However, we assume ha he insurance is priced a some 8

9 muliple, θ 1, above is acuarially fair price, in order o cover he coss of markeing he produc, and of ransferring some risk o inernaional markes. The decision problem for he household hus becomes: (3) V (w i, ) = max k i,ι i, 0 [u(c i,) + βe V (w i,+1 )] w i, = c i, + a i, + k i, w i,+1 = A i ɛ i,+1 k α i,η +1 + a i, + ι i, ((1 η +1 )ξ +1 P (1 + θ)) where ι i, are he number of unis of weaher insurance he household decides o purchase. If θ and σ ξ are zero, and farmers can observe he realizaion of heir idiosyncraic produciviy before deciding how much insurance o purchase, i.e. if he insurance conrac is acuarially fair priced and absracs from basis risks, farmers are fully insured and opimally se ι i, = A i ɛ i,+1 ki, α.1 However, i is no longer opimal o be fully insured as soon as one of hese hree condiions fails o hold, and numerical soluions need o be found o deermine he opimal amoun of weaher insurance ha a farmer will purchase, ι i,. 2.3 Beer savings insrumens Currenly, households have access o risk-less asses ha allow hem o save income in one period and ransfer i o fuure periods. However, hese asses have zero reurn. Our second financial inervenion is improved access for farmers o savings accouns ha allow hem o save money in one period for posiive reurn in fuure periods should improve heir welfare. Incenivizing saving may also allow he household o beer smooh income shocks from one period o anoher. However, as discussed in he inroducion, savings will always be limied in his regard. We formally model he inroducion of improved savings insrumens, by inroducing a posiive reurn, S, on resources held as asses, a i, : (4) V (w i, ) = max k i,,a i, 0 [u(c i,) + βe V (w i,+1 )] w i, = c i, + k i, + a i, 1 See de Nicola (2010) for a deailed analysis of he impac on consumpion, invesmen and welfare of acuarially-fair basis-risk-free weaher insurance. The qualiaive resuls apply also o he curren conex, even hough he analysis in de Nicola (2010) is based on daa from Malawi. 9

10 w i,+1 = A i ɛ i,+1 ki,l α i, 1 α η +1 + Sa i, When deciding he opimal allocaion of capial, farmers will balance wo conrasing effecs. On he one hand, he marginal produciviy of capial of agriculural producion is inversely proporional o he amoun of resources invesed, hus a low level of capial farmers may inves more in agriculural producion and less in he safe asse ha yields a lower reurn. On he oher hand, farmers wans o inves in he safer asse ha guaranees a consan reurn in order o proec heir fuure consumpion from he higher income volailiy ha would derive from invesing all heir resources in more producive bu riskier echnology. 2.4 Lending for agriculural invesmen Finally, we consider he effecs of providing access o formal credi for financing capial invesmens in producion. Typically banks are relucan o lend o agriculural invesmens, given he high level of risk hey are perceived o hold as a resul of producion shocks. We herefore assume ha access o lending for agriculural invesmen is underaken by he bank only when he bank is able o insure heir loan porfolio agains producion shocks experienced by he farmer. The loan ha he farmer receives is one in which defaul is allowed when a shock is experienced. This defaul risk is priced ino he loan offered by he bank hrough he ineres rae, and is insured by he bank purchasing insurance for he porfolio of agriculural lending producs i offers. We assume, for now, ha he bank is able o observe boh he covariae and idiosyncraic shock. However, in fuure work we will wan o revise his assumpion so ha he bank only has access o he same covariae index and insurance as he farmer (bu a a lower uni price given he larger scale of conrac i purchases). Farmers borrow d i, o finance capial expendiure. We allow farmers o defaul on heir credi when hi by a severe shock, ha is: A i ɛ i,+1 ki, α w i,+1 = η +1 Rd i,, if ɛ i,+1 > ɛ i, and η +1 > η +1 ; A i ɛ i,+1 ki, α η +1, oherwise. where η +1 is he exreme weaher even and ɛ i,+1 is he exreme idiosyncraic even ha riggers defaul. However he ineres rae hey pay, R reflecs he higher cos of lending for he bank due 10

11 o defaul, ha is R = R(1 d), where d corresponds o he probabiliy of defaul. 3 Daa and Calibraion We need o pin down he parameers of he model in order o numerically solve he model and show he impac of insurance, credi and savings on farmers allocaion of resources beween consumpion and invesmen and ulimaely quanify he impac on welfare of hese financial asses. In paricular, he value of β, ρ, α, and S, and he parameers of he disribuion of ɛ and η are required o solve he baseline framework, and he value of R and he parameers of he disribuion of ξ, in order o solve he oher frameworks. Table 1: Calibraed Parameers Parameers Value Parameers Value CRRA coefficien, ρ 3.9 Ineres rae on savings, S 0 (3)% Discoun facor, β 0.96 Capial share, α 0.39 Ineres rae on deb, R 30% SD of idiosyncraic shock, σ ɛ 80%σ η Loading facor, θ 0.5 Design effec 70%σ η Disribuion of weaher shock Empirical disribuion from LEAP The seleced values are summarized in Table 1 and are based on household survey daa o pin he main parameers of he model and meeorological and agroecological daa o esimae he weaher shock. In paricular, we use he Ehiopian Rural Household Survey (ERHS), a mulipurpose panel survey of approximaely 1,400 households locaed in 15 Ehiopian villages ha have been inerviewed seven imes since While hese daa are no naionally represenaive, he survey included he main agroclimaic zones of he counry. Each round colleced daa on demographic characerisics, asses, occupaion, cropping paerns, nonagriculural income, consumpion, and experiences wih shocks. The 2009 survey round included specialized modules on risk and ime preferences ha allow us o compue he coefficien of relaive risk aversion and he discoun facor. The former, ρ, is compued from he choices of farmers among a series of loeries wih real (moneary) payous à la Binswanger (1981). Specifically, he payoffs are ranked on he basis of heir riskiness, and by 11

12 equaing he expeced uiliy from he differen gambles, we calculae he upper and lower bounds for he rue value of ρ, and hen ake he average of he median value for each inerval. The poin esimae is 3.9 indicaing ha farmers are risk averse. Time preferences were elicied by asking individuals o consider a siuaion in which hey were abou o receive a gif. They could choose o receive he gif of ETB 100 oday or could insead choose o receive a gif of ETB X one monh from now, where X was increased by ETB 25 up o he poin a which he household chose o wai. The discoun rae, β, is calculaed using he informaion on how much an individual = X 1 requires o be paid o choose o wai. Specifically β is compued as and is on X average 0.6, consisen wih esimaes from oher developing counry (Duflo, Kremer and Robinson (2011)). Such low level of discoun rae suggess ha farmers end o be presen biased which may lead o underesimae he benefis of fuure policy inervenions. The producion funcion parameer, α, is se a 0.39 which is he coefficien from regressing he agriculural oupu (in logs) on he value of agriculural inpus (also in logs). The ineres rae on savings, S, is is given as 3%. This assumpion is poenially generous in ha real ineres raes could acually be negaive because of he double-digis inflaion rae ha Ehiopia experienced in he pas. The Commercial Bank of Ehiopia offers savings accoun accruing 5.5% ineres raes on deposis. However, according he World Bank esimaes, he inflaion rae is more han 20% in 2011 increasing from he 8% level in 2009 and Thus assuming a 3% ineres rae, if anyhing, could overesimaes he value of savings. The ineres rae on deb, R, is calculaed as he average value farmers pay on loans from a formal source such as he Commercial Bank of Ehiopia, a privae bank, or microfinance insiuion. The disribuion of he weaher shock, η, is approximaed using he LEAP (Livelihoods, Early Assessmen and Proecion) sofware esimaing he sensiiviy of crop producion across Ehiopia o changes in rainfall. 2 These calculaions are based on (i) he rainfall daa, i.e. he 10-day Africa esimaes from 1995 onwards obained from he US Climae Predicion Cener, and (ii) he agroecological informaion of Ehiopia s main saple crops simulaing he growh and crop waer requiremens during he growing season. The calculaion are based on he mehodology developed by he FAO and provide esimaes of yield changes due o moisure sress. We mach he meeorological daa wih he locaion of he ERHS farmers and he agroecological daa wih 2 The sofware developed by Peer Hoelsloo can be downloaded from 12

13 he crops ypically grown. From he ERHS, we see ha he principal crops varied by locaion. The idiosyncraic shock is assumed o be lognormally disribued wih mean one and sandard deviaion σ ɛ. If σ ɛ is zero, hen farm income is exposed only o weaher shocks. However, households repor suffering also from oher shocks. Beyond droughs households cie pes infesaions, deah, and illness as serious shocks experienced in he pas years. 3 We herefore accoun also for idiosyncraic shocks and assume a non-zero σ ɛ. We fix i a a lower level han σ η (σ ɛ = 0.8σ η ) o reflec he fac ha hese shocks are less frequenly repored. Figure 1 plos he disribuion of he wo shocks. The weaher shock is normalized o be disribued beween zero and one, where zero corresponds o he mos disrupive even, eiher a drough or a flood. The idiosyncraic shock has posiive suppor, aking values beween 0.5 and 1.5. Finally, in he heory secion we allowed for he fac ha he index conrac may no be designed o perfecly insure he covariae shock. In he simulaions ha follow we look a he impac of index insurance under wo scenarios regarding his design problem. Under one scenario we assume ha here is no design problem and ha he covariae shock is perfecly insured by he index. In his scenario he only source of basis risk resuls from he presence of he idiosyncraic shock o producion. In he second scenario we assume ha he design problem resuls in σ ξ = 0.7σ η which resuls in a correlaion beween losses and payou of 0.8. This correlaion beween losses and payous reflecs analysis conduced in an ongoing IFPRI pilo sudy on he degree o which insurance conracs designed in he pilo sudy were able o insure droughs repored by farmers over he las 25 years. 4 Resuls Under he benchmark calibraion (Table 1), we solve he opimizaion problem (1) and compue he opimal consumpion and invesmen decisions in he absence of funcioning financial markes. Exremely poor farmers inves all heir resources in he risky farm invesmen, k, because he higher reurns o capial compensae he larger volailiy ha farmers expose hemselves o. As households become richer, hey subsanially increase he amoun of resources o he risk-free asse, 3 In he quesionnaire, he shock is referred o as an even ha led o a serious reducion in your asse holdings, caused your household income o fall subsanially, or resuled in a significan reducion in consumpion. 13

14 a. In his conex, we inroduce one financial insrumen a a ime and evaluae is impac on average wealh, consumpion, farm-invesmen and invesmen in he risk-free asse over ime. Finally, we examine he welfare gains ha farmers may achieve depending on heir level of wealh and on he ime he policy change was inroduced. Firs, we sudy he effec of providing weaher index insurance. In developed markes index insurance is priced a a low muliple above he acuarially fair price. For example he muliple of unsubsidized index insurance in he US is abou 1.11 (Deng e al 2007). However in markes where index insurance is newer, such as India, he muliple can range from 1.8 o 4.5 (Cole e al 2009). A more suble concern regards he presence of basis risk whereby he insurance payou is no perfecly correlaed wih he farmers losses, boh as a resul of he idiosyncraic shock and as a resul of a design effec which causes he index o imperfecly predic covariae weaher shocks. We incorporae boh hese aspecs in our analysis and in Figure 2 we plo he impulse response funcions from he inroducion a ime of weaher insurance. We show he impac of insurance on he amoun of capial invesed in farm producion (k ), he level of risk-free asses held (a ), he consumpion of he household (c ) and he income earned by he household (w ). The simulaions are iniialized a he arge level of wealh derived under he baseline scenario, and seing idiosyncraic and weaher shocks o heir mean values in order o beer capure he effec of he policy inervenion. 4 The squares indicae he impac of providing households wih he opporuniy o buy a weaher insurance ha is perfecly correlaed wih he covariae shock, and he circles indicae he impac of providing households wih he opporuniy o buy weaher index insurance ha has a correlaion of 0.8 wih losses from he covariae shock. Boh conracs are priced a 1.5 imes he acuarially fair price. The impac on consumpion and invesmen, boh in risky and risk-free asses, are qualiaively similar, irrespecive of he level of basis risk. The availabiliy of insurance allows farmers o more effecively shield hemselves agains he covarian shock and herefore weakens he precauionary moives ha led o over invesmen in he safe asse. This is well capured by he iniial fall in a, and he increased invesmen in k. The fall in a is larger among richer farmers ha were overinvesing a larger amoun of resources in order o proec hemselves agains weaher variaions. 4 The acual realizaion of he shocks is insead used when calculaing he policy funcions. 14

15 Invesing in he more producive echnology, farmers earn higher income and are able o susain a higher level of consumpion over ime and across all level of wealh. When basis risk is increased due o a fall in he correlaion beween losses and payous from 1 o 0.8, he change in a and k is mued: he fall in a is reduced and he increase in k is smaller. Because his weaher insurance conrac is less effecive i produces a smaller conracion of he precauionary moives ha lead farmers o accumulae unproducive asses. This is refleced in he welfare gains ha are defined as he permanen increase in consumpion ha would make farmers wihou weaher insurance equally well off as farmers wih weaher insur- ance. Formally, hey correspond o he χ such ha E j=0 βj u(c baseline +j (1 + χ )) = E j=0 βj u(c insurance +j ). 5 As expeced, welfare gains are higher when basis risk is lower. They are also larger a low levels of wealh since poorer households benefi he mos from improving he risk-coping mechanism used agains covarian shocks. The dynamic srucure of he model allows us o look a how he welfare gains change across ime. We find ha he welfare gains from he inroducion of weaher insurance are increasing over ime. This is because he more efficien allocaion of resources brough abou by weaher insurance allows farmers o enjoy higher and less volaile consumpion over ime. Farmers can alernaively shield heir consumpion from negaive shocks by puing money in a savings accoun earning a posiive consan rae of reurn, S. Such a fund can be used o insure agains boh covarian and idiosyncraic shocks. In Figure 3, we plo he impulse response funcions from he sudden and unexpeced provision of saving accouns. Farmers increase he invesmen in he risk-free asse a ha now earns a 3% reurn. The iniial increase in a is financed by reducing he invesmen in farm inpus, k. Afer he iniial conracion, he invesmen in risky asses gradually increases and levels off a a level lower han he iniial seady sae. The fall in farm income is more han compensaed by he increase in off-farm income ha allows farmers o enjoy higher consumpion. In conras o he case of weaher insurance, he welfare gains are an increasing funcion of wealh. Richer farmers are able o inves more in a and are herefore also exracing larger benefis. Similarly o he case of weaher insurance, we find ha welfare gains are increasing over 5 Given he properies of he CRRA uiliy funcion, his expression can be solved by aking he raio of he respecive value funcions. 15

16 ime. When weaher insurance is combined wih he provision of savings accouns, we observe ha he impulse response funcions mimic hose from he provision of weaher insurance alone (Figure??), hus farmers reac by iniially cuing a despie is higher reurn. However, we also find ha he provision of savings accouns improves farmers abiliy o cope wih he basis risk associaed wih hese conracs. As such he impac of increased basis risk on lowering invesmens in farm inpus is less pronounced when savings are presen. In urn his resuls in consumpion levels being less affeced by basis risk which increases welfare gains. Poorer farmers benefi he mos from he join provision of weaher insurance and savings. Finally, in Figure 5 we plo he impulse response funcions from he supply of weaher insurance, savings and insured credi. As menioned in Secion 2, insured credi allows farmers o ake a loan and receive deb forgiveness for heir loan if hey are hi by he wors idiosyncraic or covarian shock. Such a generous credi conrac allows farmers o subsanially cu savings, a and redirec heir invesmen o farm inpus. A he same ime, farmers are able o increase heir level of consumpion which remains a a sable higher level over ime. The combinaion of weaher insurance, insured credi and savings accouns ranslaes ino high welfare gains, especially a low levels of wealh where farmers no only benefi from he insurance bu also from he addiional resources available o finance agriculural invesmen and grow faser. 5 Conclusions Farmers in low income counries are culivaing under high levels of uninsured risk. As a resul much work over he las decade has looked a he quesion of how o develop financial producs ha farmers can use o insure some of his risk. Innovaions in weaher index insurance, insured credi and savings accouns for smallholder farmers, offer considerable promise. However, much of he analysis has looked a hese producs in isolaion, making i difficul o answer he quesion of which financial produc may prove more useful o farmers under which seings, and also wha he complemenariy and subsiuion beween producs migh look like. In his paper we have examined he poenial benefis of hree financial producs-weaher index insurance, savings accouns, and insured agriculural loans-o explore hese quesions. We developed and esimaed a dynamic 16

17 sochasic model ha quanifies he impac of hese hree producs on consumpion, invesmen and welfare. We calibraed he model wih daa from farmers in Ehiopia. Under he assumpions of our model all hree insrumens offer welfare gains o farmers. The gains from index insurance and insured credi are paricularly high. We also find ha basis risk mues he gains from index insurance. As such he degree o which index insurance is a useful ool for smallholder farmers depends on he level of basis risk ha is presen. Basis risk resuls boh from he inadequacy of he index o insure he covariae shock and he fac ha farmers face muliple sources of uninsured risk, some of which is idiosyncraic in naure and canno be insured by an indexed insurance insrumen. However, we find ha improved access o savings limis he negaive effecs of basis risk, suggesing ha an approach ha develops muliple financial insrumens for farmers may be beer han an approach focused on one insrumen alone. 17

18 A Figures Densiy Weaher shock Idiosyncraic shock Figure 1: Disribuion of he weaher shock, η, and idiosyncraic shock, ɛ 18

19 insurance w k insurance c insurance insurance a Figure 2: Impulse response funcions of wealh, consumpion and invesmen o he inroducion of weaher insurance. Squares indicaes ha weaher insurance absracs from basis risk, circles indicaes i does no w savings k savings savings c a savings Figure 3: Impulse response funcions of wealh, consumpion and invesmen o he inroducion of savings 19

20 w insurance savings k insurance savings c insurance savings insurance a Figure 4: Impulse response funcions of wealh, consumpion and invesmen o he inroducion of savings and weaher insurance. Squares indicaes ha weaher insurance absracs from basis risk, circles indicaes i does no ins cred w ins cred k ins cred c a ins cred Figure 5: Impulse response funcions of wealh, consumpion and invesmen o he inroducion of insured credi, weaher insurance and savings 20

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