THE IMPACT OF INTERLINKED INDEX INSURANCE AND CREDIT CONTRACTS ON FINANCIAL MARKET DEEPENING AND SMALL FARM PRODUCTIVITY

Transcription

1 THE IMPACT OF INTERLINKED INDEX INSURANCE AND CREDIT CONTRACTS ON FINANCIAL MARKET DEEPENING AND SMALL FARM PRODUCTIVITY Micael R. Carter Lan Ceng Alexander Sarris University of California, Davis University of California, Davis University of Atens Marc 16t, 2011 Abstract. Tis paper explores te relationsip between credit and index insurance market development using a teoretical model in wic small farm ouseolds ave te option to eiter (i) adopt a capital-intensive tecnology tat is risky but ig-yielding, or (ii) self-insure by adopting a traditional low-input tecnology. We sow tat neiter market is likely to develop in isolation from te oter, and tat uptake of improved tecnology will be low absent efforts to link credit and insurance. Te failure of index insurance markets to independently develop is not per se due to te existence of basis risk or to its expense as self-insurance strategies are similarly caracterized by basis risk and are costly to te ouseold as tey reduce mean incomes. However, we sow tat te interlinkage of credit and index insurance contracts can allow bot markets to develop because te interlinked contract is more likely to stocastically dominate self-insurance. Te analysis also sows tat te way interlinkage will work depends fundamentally on te nature of te agricultural credit market and te degree to wic lenders are able to demand and seize collateral in te event of loan default. Tis interplay between collateral and te nature of credit-insurance interlinkage as direct and important implications for te design of programs to simultaneously boost small farm productivity and deepen rural financial markets. Keywords: Index insurance, Credit rationing, Interlinkage, Tecnology adoption Department of Agricultural and Resource Economics, mrcarter@ucdavis.edu. Department of Agricultural and Resource Economics, lanceng@ucdavis.edu. Department of Economics, alekosar@otenet.gr. Acknowledgments. We tank participants at te 2010 I4 Index Insurance Innovation Initiative worksop and te FAO worksop on small farm participation in value cains for elpful comments. Neiter tey nor our employing institutions are responsible for te ideas and opinions expressed in tis paper.

2 1. Introduction Te correlated risks and information asymmetries tat typify many low income smallolder agricultural economies can keep rural financial markets (for credit and insurance) tin or even absent. 1 Te costs of tese tin markets are obvious (and well documented), but te solution is far less clear. An earlier generation of efforts to employ conventional agricultural insurance to address te risk needs of te small farm sector failed under te weigt of transactions costs, adverse selection and moral azard (Hazell, 1992).Wile it is tempting to declare te problem unsolvable, te pernicious role tat risk plays in te construction and perpetuation of rural poverty demands furter efforts in tis area. Enabled by tecnological advances in remote sensing and meteorological data, novel forms of agricultural index insurance (wic indemnifies insured farmers based on an index tat is correlated wit individual outcomes, but is not influenced by individual beavior) would appear to offer a solution to tis problem of tin financial markets twinned wit low small farm productivity. And yet, despite teir compelling logic, agricultural index insurance contracts ave met wit sometimes indifferent demand and low uptake by te intended beneficiary populations. Wile tere can be multiple explanations for low uptake rates, tis paper argues on teoretical grounds tat uptake and impacts will be iger wen index insurance is interlinked wit credit contracts. Put simply, our argument is tat eiter market, credit or insurance, in isolation is likely to be tin or slow to develop in smallolder agriculture. But wen contracts are interlinked, te gains in market deepening and productivity growt are likely to be iger. Among oter tings, we will sow tat impacts of interlinkage are somewat subtle, and differ across different types of economic environments. Tendency to try to explain by inappropriate analogy to developed country experience, or by general statements/unadorned observations tat basis risk too ig or costs/loadings too ig. 2 However, te reality is tat te self-insurance strategies employed by small farmers expose farmers to significant basis risk and are actuarially unfair, wit ig implicit loadings and premia. Te question is tus not weter or not tere is basis risk under index insurance, but weter index insurance can stocastically dominate self-insurance. Asking te question tis way motivates te searc for ways to combine index insurance wit adoption of iger-yielding, but riskier tecnologies. Tat is, index insurance will more likely 1 See Binswanger and Rosenzweig (1986)for a persuasive, if somewat informal discussion of tese points. 2 See Smit and Watts (2009) for an analysis of te relevance of developed country experience for developing country index insurance scemes. 1

3 stocastically dominate self-insurance if it is a non-zero sum proposition tat simultaneously allows an increase in expected income even as it reduces risk exposure. We ere explore ways in wic tis migt appen troug te interlinkage of index insurance wit credit contracts. To do tis, Section 2 reviews related teoretical studies and empirical evidence from developing countries. Section 3 presents a stylized model/representation of te tecnology and contracts potentially available to producer-consumer ouseolds in a low income agricultural economy. We sow tat index insurance contracts can be represented as a mean preserving squeeze of te stocastic distribution determining output, and te agricultural credit supply is determined by lenders exposure to covariant default risks. Section 4 ten explores ouseolds demand for tecnology and financial products (credit and insurance) under tree insurance scemes: 1) no insurance available, 2) stand-alone/non-interlinked index insurance, 3) interlinked index insurance wit credit. We analyze eac scemes in two stylized environments: one caracterized by ig levels of collateral ( Latin America ) and anoter caracterized by low levels of collateral ( Africa ). Te analysis sows tat wile it substantially improves te demand for ig-yielding tecnology and financial products wen collateral level is ig, te introduction of non-interlinked insurance as small positive or even negative impacts on ouseolds demand wen collateral level decreases. In contrast, te interlinked index insurance sustantially boosts ouseolds demand for ig-yielding tecnology in a low collateral environment. Section 5 analyzes te impacts of different insurance scemes wen te credit market reaces an market equilibrium by endogenizing te quantity of agricultural loans. We sow tat te demand for new tecnology and financial products under no insurance and non-interlinked insurance scemes discussed in Section 4, will be coked off by te increased price of credit. However, wen insurance is interlinked wit credit, te lender is willing to provide any amount of agriculturl loans at a fixed low price so tat any expansion of te demand will not be coked off. Te performance of te interlinked contract also depends on basis risk and loading costs of index insurance and ouseold eterogeneity of risk preference and wealt. Te last part of tis section explores te sustainablity of government subsidy program tat subsidizes insurance premium. Section 6 concludes. 2. literature review A very recent teoretical paper by Miranda and Gonzalez-Vega (2010) is te most related to our study. Miranda and Gonzalez-Vega focus on te impact of index insurance on lenders profitability 2

4 wen bot basis risk and loading costs are extremely ig. Tey argue tat te lender s mandatory requirement tat borrowers ave to purcase index insurance to renew loans, would induce borrowers to default te existing loan contracts and tus lowers te lender profits since te ig basis risk and ig insurance loading costs make te bundled loan contract less valuable and costly for borrowers. Altoug te eavily subsidized insurance could reduce default rates and increase lenders profits, profit-maximizing lenders would increase interest rates so tat te benefit of insurance could not accure to borrowers. Tey propose tat instead of borrowers purcasing insurance, lenders direct purcase of unsubsidized index insurance can stablize lenders equity growt rate, because lenders can diversity te idiosycratic risks and ave small basis risk. However, Miranda and Gonzalez-Vega neglect te positive impact of index insurrance wen basis risk and loading costs are in a reasonably moderate range. Second, tey overestimate te negative impact of mandatory index insurance on lenders profitability wen basis risks and loading costs are extremely ig by assuming tat 1) lenders use dynamic incentive to reduce intentional default; 2) te lender reinforces te purcase of index insurance wit future loans before te borrower repays te existing loan. Tese assumptions indicate tat if index insurance lowers te expected utility of future borrowing, te borrower would not only refuse to borrow in te future but also default te existing loan. Tis exaggerates te negative influence of mandatory indxe insurance policy on default rates wen basis risk and loading costs are ig. If lenders eiter employ current losses suc as collateral requirement instead of future loss suc as dynamic incentive, or use dynamic incentive but introduce index insurance after borrowers fulfill teir existing liability 3, mandatory index insurance would mainly affect ouseolds demand for loans but ave small impact on default rates and lenders profits. In oter words, ouseolds would not borrow at all in te first place if te bundled insurance and loan contract does not peform well. Tird, tey do not sow wy systematic risk matters for lenders. Altoug tey argue tat systematic risk increases te variance of rate of return on equity, tere is no structure to sow tat lenders profitability depends on te variance of equity growt. Terefore, it is not convincing to conclude tat lenders lose from borrowers purcase of index insurance or benefit from teir direct purcase. Finally, wile arguing tat expected-profit maximizing lenders will not allow teir benefit from borrowers purcasing insurance to accrue to borrowers. tey do not sow weter lenders allow te benefit from teir own purcase of insurance 3 If insurance does increase default rate, lenders are very likely to coose to introduce insurance after borrower repay te loan rater tan before te repayment. 3

5 to accure to borrowers. Terefore, we cannot draw te conclusion tat borrowers benefit more from lenders being directly insured tan lenders being indirectly insured troug borrowers. Our study contributes to te deeper understanding of te effect of borrowers purcase of index insurance on lenders ( and oter firms) profitability. First, we analyze bot good index insurane program (wit moderate basis risk and loading costs) and bad index insurance program (wit extremely ig basis risk and loading cost as specified in Miranda and Gonzalez-Vega (2010)). Second, in our model farmers endogenously coose to borrow or not (wic is exogenous in Miranda s model), knowing tat if tey coose to borrow tey ave to follow an exogenous repayment rule. We explicitly sow ow index insurance contract alters te risk structure and ow covariant socks influence lenders expected profits given difference collateral environment. Te results sow tat wit good index insurance, mandatory insurance would reduce default rates and increase lenders expected profits substantially in a low collateral environment. Wit bad index insurance as sown in Section 5.3, mandatory insurance would lower lender s profits by raising default rates as predicted by Miranda s model, but by a very small sift. Tird, we analyze ow te interlinked insurance and credit contract can transfer lenders benefits from index insurance to borrowers by endogenizing interest rates. Given a competitive credit market wit a fixed level of expected profits, lenders are willing to lower interest rates wen borrowers purcase of insurance raises teir profits. Tis interlinked contract is te key to make te lenders profit level exogenously fixed. Since te interlinked contract enforces te insurance and credit contracts to be agreed upon simultaneously, borrowers can use teir bargaining power to control lenders profit level. In contrast, if lenders directly purcase insurance, tey are likely to be profit-maximing and witold te benefit as sown in Miranda and Gonzalez-Vega (2010). To te best of our knowledge, our paper is te first teoretical study to systematically analyze te impact of index insurance troug te synergy wit credit and production-enancing tecnology on te financial market deepening, tecnology adoption and farmers welfare. Specifically it is te first one to 1) endogenize credit supply wen lenders profitability depends on covariant socks; 2) construct te market equilibrium of te credit market by endogenizing te quantity of agricultural loans; 3) analyze te impact of collateral environment, representing te implicit insurance provided by te loan contract, on te performance of formal index insurance, 4) analyze te impact of te interlinkage on a eterogeneous population instead of a typical representative. Our results sows 4

6 tat index insurance is valuable to individual farmers wen insurance is associated wit productionenancing activities. Index insurance is also valuable to lenders wen borrowers purcases index insurance. Index insurance beomces even more valuable to ouseolds wen insurance is interlinked wit credit tat transfers te benefit of insurance from lenders to borrowers. Tere is one related empirical study by Giné and Yang (2009) wo try to test te effect of bundled index insurance and loan contract on te demand of credit for te purpose of adopting new tecnology in Malawi. Tey use randomized field experiment were farmers in te treatment group ave to purcase index insurance contracts in order to obtain loans and farmers in control group are offered loan contracts only. Note tat te loan contract terms for te treament group are te same as tat for te control group, wic means te bundled contract in teir experiment is essentially a non-interlinked index insurance and credit contract. Teir result sows tat te take-up rate of te bundled loan contract was 13% lower tan tat of uninsured loan, because te limited liability clause provides implicit insurance crownding out te demand for formal insurance. Tis result coinsides wit te prediction of our model tat te non-interlinked contract as a lower demand tan stand-alone loan contract wen te collateral level is low. More importantly, our model proposes an innovation of te interlinked index insurance and credit contract to solve tis puzzle. Our model sugguests tat te interlinked contract outperforms te non-interlinked and te stand-alone loan contract, especailly in a low collateral ( limited liability) environment, by inducing a iger take-up rate of credit and new tecnology. 3. Environment, Tecnology and Financial Contracts Tis section lays out a stylized model of te risk-averse and small farm ouseold. Wile igly simplified, te model captures te key elements of te small farm problem tat are relevant to te problem at and, including te self-insurance options available to te ouseold. Agricultural production is influenced by bot covariant and idiosyncratic socks. Against tis backdrop we define te set of potential financial contracts tat could be offered by competitive lenders and insurance firms Risk and Houseold Production and Consumption. Small farm ouseolds are assumed to ave access to two tecnologies, a traditional tecnology wit low, but stable returns, and a iger yielding, but riskier tecnology tat requires substantial use of purcased inputs. Bot tecnologies are subject to idiosyncratic (or specific) socks, θ s and covariant socks, θ c. We assume 5

7 a multiplicative structure and write te output of low-yielding tecnology as: (3.1) y l = θg l were θ =(θ c + θ s ) wit support [0, θ], probability distribution function denoted f(θ), cumulative distribution function denoted F (θ) and E(θ) = 1. From now on utill Section 5.3 we assume covariant risk dominates idiosyncratic risk. 4 Te net income from low yielding tecnology is denoted as ρ l = y l. Similarly, we write te output of te ig-yielding tecnology as (3.2) y = θg (K) were K is te amount of purcased inputs required. Te superiority of ig-yielding tecnology is te iger expected net return, g (K) K > g l. We furter assume capital K can only be financed by borrowing from te rural credit market. Denote te loan contract as l < K, r, χ >, were r is te contractual interest rate and χ is te collateral required (Section 3.3 gives details on te determination of contract terms). Net returns to te ouseold under tis loan contract are as follows: θg (K) (1 + r)k, if θ> θ (3.3) ρ = χ, oterwise were θ = (1+r)K χ g (K) is te level of te sock suc tat te value of te collateral plus te output produced just equals te value required for full loan repayment. Note tat tis specification sarply assumes tat te ouseold retains no income (or collateral assets) until after te loan is repaid. Assuming te separability between ouseold s consumption and production, ouseold consumption is given by c t = ρ t +W +B, t =, l, were W is te ouseold s consumable and collateralizable wealt and B is te risk-free income from off-farming activities. Te lowest consumption can be under te ig-yielding tecnology is c = W + B χ. Figure 3.1 sows ouseold consumption as a function of te stocastic factor under te two tecnologies in ig and low tecnology environments. Te dased line represents consumption as a function of te stocastic factor under te low tecnology, wereas te solid curve represents consumption under te ig tecnology wen collateral is ig and θ is low. As collateral requirements decreases, te consumption floor rises 4 Te simulation uses 75% of covariant risk over te total risk. 6

8 under te ig tecnology illustrated by te dotted line, as more of te down-side risk is borne by te lender. Assume te ouseold is risk-averse and as a conventional concave utility function, u(c). For purposes of later numerical analysis tat we will use to illustrate various propositions, we assume tat te utility function exibit Constant Relative Risk Aversion (CRRA). Houseolds coose tecnologies and contracts to maximize expected utility. Te population of te economy is distributed following te joint probability distribution function (ψ, W ), were ψ is te Arrow-Pratt measure of relative risk aversion. Figure 3.1 allows furter exploration of risk under te ig tecnology and te effectiveness of self-insurance. Using te numerical specification detailed in Appendix A, te solid line in Figure 3.1sows te CDF of ouseold consumption under te self-financed ig tecnology, wile te das dotted line sows te CDF of consumption under te low tecnology. Under tis specification, te low tecnology substantially reduces te probability of low outcomes. However, tis self-insurance strategy is far from perfect. First, it is actuarially unfair, reducing expected ouseold income (and consumption) by te difference in expected incomes between te ig and low tecnologies (23% of expected income reduction in te numerical parameters used to generate te figure). Second, compared to an idealized contract tat sielded te ouseold against any consumption losses any time te ig yielding tecnology resulted in production less tan its expected value (illustrated in Figure 3.1by te dased line), 5 self-insurance exposes te ouseold to residual or basis risk as tere is still a substantial probability of consumption well below te expected level. As can be seen, tis idealized contract stocastically dominates self-insurance. Wile te index insurance contracts discussed in te next section are clearly not going to dominate tis type of idealized contract eiter, te relevant question is weter tey can dominate self-insurance given te basis risk and implicit loadings associated wit it Index Insurance Contracts. Unlike conventional agricultural insurance tat pays off based on individual outcomes (y t in our notation), an index insurance contract contract pays off based on direct observation of te covariant sock (θ c ) or on average yields (θ c g t ). 6 To keep matters simple, 5 Te contract illustrated in Figure 3.1is emulates a multi-peril contract tat restores farm income to its average level any time an idiosyncratic or covariant sock occurs. Subtracted from consumption is te actuarially fair premium for suc coverage. Suc contracts typically do not exist for te small farm sector because of moral azard, adverse selection and ig transaction costs. 6 As discussed by many autors, index insurance avoids te moral azard, transactions costs and adverse selection problems tat render conventional agricultural insurance unsustainable. 7

9 Figure 3.1. Tecnologies Figure 3.2. CDF of ig tec, low tec and ig tec wit conventional insurance 8

10 we will assume tat te index insurance contract is based directly on θ c. We denote te insurance contract for tecnology t as I t < ˆθ c, t,z t,β t >, were ˆθ c is te strike point for te contract, t is indemnity normalized by g t, z t is te normalized actuarially fair premium and β t is te normalized loading or markup of te insurance as a percentage of z t. To simplify te matmatical analysis te following teoretical strcuture assumes te insurance contract is actuarially fair, but te simulation uses a 30% of loading costs. Te indemnity is defined by t (θ c ) = 1( ˆθ c >θ c )(ˆθ c θ c ) 7. Under te actuarially fair insurance contract, gross returns to te farm ouseold are given by: (3.4) y I = (θ c + θ s )g t +(ˆθ c θ c )g t z t g t =(ˆθ c + θ s z t )g t, if ˆθ c >θ c. t (θ c + θ s )g t z t g t, =(θ c + θ s z t )g t oterwise were z t = E[1( ˆθ c >θ c )(ˆθ c θ c )]. Note tat tis specifications assumes tat te ouseold first receives indemnity and pays insurance preimum, ten applies te net income to repaying outstanding debt before bolstering its consumption. As a prelude to later analysis, define θ I = θ + s(θ), were s(θ) = 1( ˆθ c >θ c )( ˆθ c θ c ) z t. Note tat index insurance contract transforms te multiplicative sock tat determines output suc tat te net output sock under insurance is equal to θ I. Because z t is te actuarially fair premium, E[θ I ]=E[θ] =1and te probability function describing te distribution of te net output sock are a mean preserving squeeze of te original distribution function. Denote te PDF and CDF of θ as f(θ) and F (θ) and tat of θ I as f I (θ) and F I (θ). We can express te original distribution of θ as a mean preserving spread of te insured distribution and sow tat te following properties old (see matematical proof in Appendix B): (3.5) θ 0 [F (θ) F I (θ)]dθ =0 (3.6) y 0 [F (θ) F I (θ)]dθ > 0 y < θ Figure 3.2illustrates te squeezing of te PDF created by index insurance Credit Supply. We assume tat credit markets are competitive and tat banks are willing (at te margin) to offer an agricultural loan tat offer an expected return equal to an endogenously given opportunity cost of funds, π a. After first exploring te nature of marginal loan offer (and 7 Tis implicitly assumes tat te farmers can coose te optimal insurance coverage level to reduce te basis risk, so tat insurance contract always reduces farmers risks 9

11 Figure 3.3. Index Insurance as Mean Preserving Squeeze te impact of insurance on contract terms), Section 3.3will explore aggregate supply of agricultural credit by te lender wit and witout insurance. Te Iso-expected profit contract locus. Under a standard loan contract l(k, r, χ), lender profits are given by: (1 + r)k, if θ > θ (3.7) π = χ + θg (K), oterwise. Under tis specification, lender s profits are concave in te random variable θ so tat tey would act like as if tey are risk averse. Lenders expected profits is given by: θ (3.8) E(π) = [1 F ( θ)]rk + (χ + θg (K) K)f(θ)dθ 0 First we assume tat π a is fixed and E(π) = π a. Using te implicit function teorem, we can caracterize te iso-expected profits contract locus as tose combinations of interest rates and 10

12 collateral requirements tat just yield expected returns equal to π a. As sown in Figure 3.3, te locus is downward sloping as r χ = F ( θ) (1 F ( θ))k less steep as risk diminises troug mean preserving squeezes ( < 0. Wen borrowers are insured te locus becomes F ( θ) < (1 F ( θ))k F I ( θ) (1 F I ( θ))k < 0) 8. Te insured iso-expected profit locus lies below te uninsured locus if loans are not fully collateralized (χ < (1 + r)k). 9 In general, we would not expect a lender to be genuinely indifferent between te different points on te iso-expected profit loci. As explored by a number of papers, iger collateral/lower interest rate contracts diminis incentives for morally azardous beavior and adverse selection by lenders (for a recent treatment, see Boucer et al. (2008)). In te analysis ere, we ignore borrower eterogeneity tat migt generate adverse selection (e.g., differences in borrower onesty or individual level eterogeneity in te structure of risk). We also ignore potential sources of morally azardous beavior (e.g., credit diversion as in Carter (1988) or non-contractible effort as in Boucer et al. (2008)). Instead, we follow Stiglitz and Weiss (1981)and simply assume tat lenders demand tat borrowers present a minimum amount of collateral in order to leverage of a loan of size K. Wile tese assumption are somewat artificial, tey allows us to focus on te impact of index insurance in two distinctive, but empirically important environments. Te first of tese migt be considered to be representative of areas of Latin America were agricultural land is individually titled and potentially can be seized in te event of loan default. In tese environments, we will assume tat lenders require a collateral of value χ, as sown in Figure 3.1. In oter areas were agricultural land ownersip is less individualized and less securely titled (e.g., in many parts of Africa), we will assume tat te te loan package requires a lower amount of collateral, denoted χ l in Figure 3.1. Wile we could impose additional structure on te model to endogenize collateral levels, our goal ere is to sow tat index insurance and its interaction wit small farm productivity and financial markets will exibit subtle differences across tese two types of stylized agricultural economies. Aggregate credit supply to te agricultural sector. Te analysis in te prior section considered te conditions of competitive loan supply taking te lender s overall loan portfolio as given. Wen 8 Te slope of te iso-profit locus under insurance is flatter tan under no insurance but it is still downward sloping, since uninsured idiosyncratic risks can cause default 9 As discussed in Section 3, we assume tat ouseolds use all income, including insurance indemnity payments, to retire debt before consumption. 11

13 Figure 3.4. Iso-expected profit locus wit π a = 20% loan repayment is subject to purely idiosyncratic socks, te lender s overall portfolio will be selfinsuring. However, a portfolio of agricultural loans will not be purely self-insuring as a negative covariant sock (e.g., a drougt) could trigger a large scale episode of default. To explore tis issue furter, tis section examines te lender s portfolio decision and aggregate credit supply. We assume tat in te sort-run, te lender as sufficient loanable funds to extend n loans of size K. We furter assume tat te lender can extend type a agricultural loans, or type b loans, wic we assume to be risk free (or subject only to idiosyncratic socks and terefore self-insuring). Te lender s gross rate of return, G, on te portfolio of n loans will be given by: (3.9) G = na i=1 π i( π a )+n b π. n were π a = E(π i ). In addition, te lender faces a penalty function, P (G), tat reduces net lender portfolio returns wen te G falls below a critical tresold level π. Specifically, net portfolio returns (N) are given by: G,if G> π (3.10) N = G P (G) = G P (G), oterwise, were P, P 0 12

14 Te penalty for low portfolio return occurs for several reasons. First, wen te lenders realize too low a return on te loan portfolio, it runs afoul of reserve and oter regulatory requirements. Second, wen te portfolio return is too low, te lenders ave to sell a large amount of collateral at te same time to repay depositors, wic drives down te price of collateral and lenders net return. Next, low return from te portfolio forces lenders to borrow from te money market and pay for ig interest rates. Lastly, from a political economy perspective, te lender understands tat a massive default, driven by a drougt or oter unfavorable event, will likely trigger a political economy reaction wit te government tempted to mandate at least partial default forgiveness. 10 Now assuming te expected net portfolio return is exogenous in a competitive market, lenders ave to satisfy te participation constraint in wic E(N) π. Given tis constraint, lenders ave to adjust π a as te composition of te wole portfolio canges. Let F G and f G denote te CDF and PDF of G. Taking te expected value of N, te Lender s Participation Constraint (LPC) can be written as: (3.11) π + n π a n ( π a π) 0 P (G)f G (G)dG π (LPC) were te integral term is te expected penalty. Using implicit function teorem, te expected return of agricultural loan can be written as a function of te quantity of agricultural loans, π a = π a (n a ). π a (n a ) depicts a aggregate supply curve of agricultural loans. Figure 3.5 sows tat in absence of formal insurance and wit low collateral requirement, π a as to increase dramatically above π to maintain te participation constraint as te sare of agricultural loans rises in te lending portfolio (te black solid line). Tis is because low collateral requirement exposes lenders to large covariant risk and increases te probability of paying penalty. Te penalty policy P implies an increasing marginal cost of unit agricultural lending wen lenders are exposed to covariant risks. Te introduction of formal insurance reduces te cost of credit and tus flattens te supply curve (te black dased line). Tus, wen loans are insured, π a keeps constant at a low level of π as te number of agricultural loans increases. Furtermore, as te collateral level increases, uninsured π a (te red and blue solid lines) decreases and insured π a (te red and blue dased lines) keeps equal to π. In Figure 3.5, all te dased lines and te blue solid line overlap as a straigt line at te level of π. Insurance isolates te rate of returm of agricultural loans π a from te impact of te collateral 10 Following te 1998 El Nino event, te Peruvian government instituted a financial rescue tat instructed agricultural lenders to forgive outstanding debt (see Trivelli ). 13

15 Figure 3.5. Aggregate Supply of Agricultural Credit Rate of return level. Appendix C provides a matematical proof of te sape of te function π a = π a (n a ) and te determinant factors. Given a fixed level of χ, te aggregate supply function can also be written as r = r(n a χ, f I (θ),f(θ),p). Figure 3.6 sows te supply curve of credit as collateral level canges and index insurance is introduced. Similar wit Figure 3.5, te lower te collateral level, te steeper te uprising supply curve wen index insurance is unavailable. Under index insurance te supply curves all become straigt lines and lenders would supply as many loans as tey could at a fixed price. Note te price level is sligtly different: te insured supply curve under low collateral (te black dased line) is iger tan tat under median and ig collateral (te red and blue dased line wic overlaps) as low collateral exposes lenders to more idiosyncratic risks. 4. Demand for credit, insurance and tecnology Under Alternative Insurance Scemes Tis section analyzes farmers optimal coices of tecnology and financial contracts. We first analyze te income CDF under four insurance scemes to escew te risk of ig tecnology: self-insurance by adopting low-yielding tecnology, implicit insurance provided by loan contracts, formal non-interlinked index insurance and interlinked index insurance. Ten we go deeper to look 14

16 Figure 3.6. Aggregate supply of agricultural loans Interest rates at farmers expected utility wen formal insurance is unavailable in Section 4.2. We sow tat in low collateral environment, loan contract provides implicit insurance for borrowers but lenders carge ig interest rates. In ig collateral environment, interest rates are low but farmers are risk rationed. In bot cases, farmers are likely to coose self-insurance and ave low demand for credit and ig tecnology. Section 4.3 analyzes te introduction of formal index insurance as an independent market. We sow tat in low collateral environments, te impact of formal insurance is adverse or minimal due to te existing implicit insurance provided by loan contracts. In contrast, in ig collateral environments, te independent insurance substantially improves ouseold welfare, crowding in demand for credit and ig tecnology. We ten turn to examine contractual interlinkage in wic loans and insurance are linked as a single contract (i.e., because loans are linked, lenders know wen a loan is or is not secured by an insurance contract) and loan contract terms are endogenously determined by borrowers purcase of insurance. We sow tat even in low collateral environments, interlinked insurance increases uptakes of credit and ig tecnology by inducing lender to lower interest rates and crowding in credit supply. It sould be stressed tat te analysis is predicated on te simultaneous existence of an improved, capital-dependent tecnology. 15

17 Figure 4.1. Cumulative Distribution of Consumption 4.1. Stocastic dominance of interlinked index insurance. Tis section compares te income CDF under four insurance scemes. In Figure 4.1, te implicit insurance associated wit loan contract (te solid line) is ard to compete wit te self-insurance (te das-dotted line) wen no formal insurance is available. As mentioned above, owever, tis self insurance strategy is caracterized by uninsured basis risk as well as by substantial loading (i.e., te self-insurance is actuarially unfair as it reduced mean income). Te question we ask ere is weter index insurance can dominate self-insurance despite te basis risk and loadings associated wit it. Te introduction of te stand-alone index insurance (te dased line) makes a small improvement over te implicit insurance but still ardly stocastically dominates self-insurance. Te interlinked index insurance sifts te income CDF forward from te dased line to te red solid line, so tat it is very likely to stocastically dominate self-insurance. Tus wen interlinked insurance is available, ouseolds are more likely to coose ig-yielding tecnology, borrow money and purcase insurance Absent formal insurance. Wen formal insurance is unavailable, poor small ouseolds face two coices, self-insurance of low-yielding tecnology versus implicit insurance of ig-yielding tecnology financed by credit. Under te specification in Section 3, ouseold expected utility under 16

18 te low tecnology (V l ) and ig tecnology (V ) are given by: (4.1) V l = u(θg l + W + B)f(θ)dθ θ 0 θ (4.2) V = F ( θ)u(c)+ θ u(θg (1 + r)k + W + B)f(θ)dθ. Note tat c is a function of χ and θ depends on bot χ and r. Te ouseold will coose ig tecnology and to take te loan contract if l = V V l > 0. Using te expressions above, we can rewrite l as: (4.3) l = F ( θ)u(c) θ 0 u(θg l + W + B)f(θ)dθ + θ θ [u(θg (1 + r)k + W + B) u(θg l + W + B)]f(θ)dθ were te first term in square brackets is strictly negative (even wen χ = 0) indicating low tecnology outperforms ig tecnology wen adverse socks appen. To make farmers coose ig tecnology, te second term as to be positive. In ig collateral environment, since c is very low, te first term is negatively big. Risk-averse farmers are likely to ave negative l, coosing low tecnology and not to borrow. Tis is called risk rationing by Boucer et al. (2008). In low collateral environment, te first term becomes negatively smaller. As te lower bound c rises, low collateral offers implicit insurance to borrowers. But meanwile, since covariance risk is passed to lenders, lenders ask for ig expected rate of return and interest rates as discussed in Section 3.3, wic makes te second term positively small. Farmers wo cannot afford te ig interest rates will coose low tecnology and not to borrow, wic we called price rationing. Terefore, in absence of formal insurance te demands for ig tecnology and credit are likely to be low in bot low and ig collateral environments as sown by te black solid line in Figure 4.2. Te rest of te paper focuses on suc scenario were l < 0 eiter because of risk rationing (in ig collateral environments), or price rationing (in low collateral 17

19 environments). Te next two subsections will analyze ow index insurance reduces te two types of credit rationing and crowd in credit supply and credit demand Non-interlinked index insurance contracts. Tis section introduces te first type of formal index insurance contract, te non-interlinked index insurance, and focuses on wat section 4.2 called te risk-rationed. Te risk-rationed are tose ouseolds wo escewed te risk of te ig tecnology and instead self-insured teir liveliood by coosing te low income activity wen collateral level is ig. Te non-interlinked index insurance contract is independent of te credit market, terefore only influencing te ouseolds. We first exam te impact of te actuarially fair non-interlinked contract (defined as above as te contract in wic expected indemnities equal te premium) on ouseold expected consumption. Formally, te cange of expected consumption (conditional on adoption of te ig tecnology) is equal to θ (4.4) E(c I ) E(c )=χ[f ( θ) F I ( θ)] [θg (K) (1 + r)k][f(θ) f I (θ)]dθ θ Integrating by parts and using te properties of mean-preserving spread (equation 3.5 and 3.6 ), te above expression reduces to: (4.5) E(c I ) E(c )=g [F I (θ) F (θ)]dθ 0 θ 0 wic is always negative wen loans are not fully collateralized and equal to zero wen loans are fully collateralized. It indicates tat at least in terms of expected income, te lower te collateral level, te more ouseolds lose from te non-interlinked contract. Strictly speaking, farmers make optimal coices based on V I and V l, wic represent te value function of ig tecnology under non-interlinked insurance and low tecnology respectively. Weter farmers will adopt ig tecnology depends on te sign of V I V l, wic can be written as (4.6) I l = V I V l =(V I V )+(V V l ) = I + l 18

20 were l < 0, but te sign of I is ambiguous. Since te non-interlinked insurance contract is isolated from loan contract, interest rate is determined by r = r(χ, n a,f(θ),p), not affected by insurance contract. Ten we ave θ (4.7) V I = U(c)F I ( θ)+ and θ (4.8) I = V I V = U(c)[F I ( θ) F ( θ)] + θ U[θg (1 + r)k + W + B]f I (θ)dθ θ U[θg (1 + r)k + W + B](f I (θ) f(θ))dθ After integrating by part of I twice, we ave (4.9) I = U (c)g θ 0 θ [F I (θ) F (θ)]dθ + [ θ θ 0 (F I (y) F (y))dy]u g 2 dθ Since θ is a mean-preserving spread of θ I, te first part of I part is positive. As can be seen from equation (4.5), te first part of I is non-positive and te second represents te marginal utility of te cange in expected consumption, and te second part means te cange of utility due to reduction of consumption fluctuation. Tis indicates tat risk neutral farmers for wo te first term is negative and te second term is zero, would always prefer witout te implicit insurance rater tan te non-interlinked insurance. Tis is consistent wit te conclusion drawn from te expected income. As for te risk-averse farmers, te sign and magnitude of I can be determined by collateral requirement. If fully collateralized wit χ = (1 + r)k and θ =0, te first part srinks to zero and I is positive, indicating tat farmers will be willing to buy te non-interlinked insurance since te expected income is uncanged and te risk exposure is reduced. Te insurance would crowd in risk-rationed by reducing ouseold s risk of losing collateral. If χ =0and θ > 0, I decreases and is more likely to be negative, indicating farmers will not be willing to buy te non-interlinked insurance since tey are already insured by loan contract and insurance premium lowers te expected income. Intuitively, under a low collateral environment, te lender bears most of te risk. Insurance is valuable to lenders by transferring te risk from te lender to te insurance provider, but yields 19

21 no benefit to te ouseold wo noneteless pays for insurance premium. In contrast, under a ig collateral environment, te ouseold wo bears nearly all te risk, enjoys te gains from te insurance. Te dased line in Figure 4.2 illustrates te certainty equivalent of V I as a percentage of tat of low tecnology. We see tat te CE under non-interlinked insurance is even lower tan tat under implicit insurance ( I is negative) wen χ is low. As collateral rises, te CE of te non-interlinked becomes iger tan implicit insurance, and finally iger tan self-insurance of low tecnology. Tis indicates tat te non-interlinked insurance only works for te risk rationed in a ig collateral environment Interlinked insurance contracts. Tis section introduces te oter type of formal insurance, te interlinked index insurance, and focuses on te price-rationed. We define te price-rationed as tose wo refuse to borrow due to te ig interest rates. Farmers coose between te interlinked insurance and self-insurance, V II and V l, wic represent te value function of ig tecnology under interlinked insurance and low tecnology respectively. Farmers make decisions based on te sign of V II V l, wic can be disaggregated as (4.10) II l = V II V l =(V II V I )+(V I V )+(V V l ) = II I + I + l were l < 0 and I te factor influencing te sign of II I. increases in χ as sown in te above section. Te rest of tis section explores As sown in Section 3.3, ouseolds purcase of index insurance influences lenders expected return. Under te interlinked insurance, te interest rate te lender offers is endogenously determined by index insurance contract as r I = r m (χ, n a,f I (θ)). Because θ is a function of interest rates, te critical point wit interlinked insurance is denoted as θ I = θ(r I ). Ten te value function of ig tecnology wit interlinked insurance V II becomes θ (4.11) V II = U(c)F I ( θ I )+ θ I U[θg (1 + r I )K + W + B]f I (θ)dθ Te difference of expected utility between interlinked and non-interlinked insurance, II I written as 20 can be

22 (4.12) II = V II I θ V I = (U[θg (1 + r I )K + W ] U[θg (1 + r)k + W + B])f I (θ)dθ θ θ + (U[θg (1 + r I )K + W + B] U(c)) f I (θ)dθ θ I As Figure 3.6 sows, wen χ< (1 + r)k, r I <r, and θ I < θ. Ten II is positive wen loans I are not fully collateralized. Wen χ = (1 + r)k, II is equal to zero. Tus I II I is always nonnegative and decreasing in χ. Tis means te interlinked insurance is always at least as good as non-interlinked insurance for ouseolds. Interlinkage will tus being to crowd-in more credit demand because te interest rates will be lower wen farmers purcase interlinked insurance. Since I is increasing in χ, te interlinked insurance as advantages over te non-interlinked in te low collateral environment. Te dotted line in Figure 4.2 denotes te CE of V II as a percentage of tat under low tecnology, wic always lies above te CE of V I. Te gap between te dased and te dotted line representing II decreases as collateral increases. I Combining II, I I, l togeter, te dotted solid line in Figure 4.2 demonstrates II l. Te Certainty Equivalent (CE) of te interlinked ig tecnology for a typical ouseold is almost constant around 1.5% more tan tat of low tecnology as te collateral level canges. Tis can be explained by te mean and variance of te income from interlinked ig tecnology. Since interlinked insurance always brings te cost of unit loan back to a constant level π as sown in Figure 3.5, farmers expected income from ig tecnology is equal to (4.13) E(c II )=E(y ) (1 + π)k + W + B wic is independent of collateral level. Te income variance satisfies (4.14) V ar(c II )= V ar(y )V ar(θ I ) V ar(θ) 21

23 Figure 4.2. Certainty Equivalent of ig tec as a percentage of low tec for a igly risk-averse ouseold ψ =3 wic is also independent of collateral level. Since te expected utility is mainly determined by te first and second order of income, te above two equations indicate tat te CE under interlinked insurance mainly depends on te productivity of te tecnology and risk structure (basis risk), but is not influenced by te caracteristics of te credit market suc as collateral level and numbers of agricultural loans. 5. Farm Productivity and te financial Market development in te Equilibrium of te credit market Tis section analyzes te farm productivity and te credit market development wen te credit market reaces an equilibrium. In absence of interlinked insurance or witout fully collateralization, te aggregate supply curve of credit is uprising and tus any increase in demand discussed in Section 4 will raise interest rates tat coke off te increased expansion. Wen insurance and credit are interlinked, te credit supply curve is flattened at a constant level and tus te increased demand induced by insurance will not be coked off. As a result, te interlinked index insurance can induce te igly risk-averse and poor smallolders to adopt ig tecnology and purcase financial products. In addition to collateral environment, te performance of interlinked index insurance 22

24 contract also depends on basis risk and loading costs of insurance premium. We also analyze te sustainability of te subsidized interlinked index insurance program Credit Market Equilibrium. According to Section 3.3, we can write te aggregate supply of agricultural loans, n s a, as a function of te price r given exogenous factors including collateral level, te distribution function of θ, purcase of insurance and penalty function: (5.1) n s a = n s a(r χ, f(θ), f I (θ), P) According to Section 4, aggregate demand of agricultural loans, n d a, is a function of r given exogenous factors of collateral, te distribution of θ, purcase of insurance and te distribution of population on risk preference and wealt: (5.2) n d a = n d a(r χ, f(θ), f I (θ), (ψ, W )). Because te population is eterogeneous in ψ and W, te demand function is strictly decreasing in r. Te credit market reaces an equilibrium wen demand equals supply, (5.3) n s a = n d a = n a Te quantity of agricultural loans and interest rates at te equilibrium, n a and r vary on te different insurance scemes associated wit ig tecnology: implicit insurance, non-interlinked and interlinked index insurance. Figure 5.1 sows te supply and demand curve of credit under te tree insurance scemes in different collateral environments. Te equilibrium point of n a% represents te equilibrium precentage of farmers wo obtain an agricultural loan and adopt ig tecnology. Te rest of population, 1 n a%, use traditional low tecnology. In a low collateral environment (te first grap), demand and supply curve under implicit insurance interact at a point wit ig price and relatively low quantity. Wen loans are insured wit non-interlinked contract, supply curve keeps uncanged but a big part of demand curve moves to te left due to te implicit insurance provided by low collateral. Te declined demand drives down bot r and n a as sown by te black arrow to te left, wic coincides wit te empirical observation of low uptakes of bundled loan contract by Giné and Yang (2009). Wen te two financial contracts are interlinked, 23

25 te demand curve is te same as te one under te non-interlinked but te supply curve sifts down and becomes flat. Te increased credit supply moves te equilibrium rigtward as sown by te red arrow to a point wit lower r and iger n a. In a median collateral environment, te non-interlinked contract increases demand and improves te equilibrium towards a iger n a but also drives up te price. Te interlinked contract increases n a furter by lowering te supply curve. Finally in te ig collateral environment, te non-interlnked contract induces a big expansion of te demand so tat almost te wole population obtain credit. Since te lender is fully insured by te ig collateral, te interlinked contract performs as well as te non-interlinked but could not do better Te eterogenous impact of index insurance. Te impact of insurance on individuals varies as teir risk preference and wealt cange. Te empirical evidence from Giné and Yang (2009) sows tat wealter indicators ave positive (altoug not significant) impact and risk aversion as negative impact on uptakes of stand-alone/non-interlinked insurance and loan contracts. Figure 5.2 sows critical levels of risk aversion coefficient and wealt (ψ,w ) wen te credit market reaces an equilibrium, below wic ouseolds adopt te ig tecnology and below wic tey do not. Except risk and price rationing as discussed above, tis figure also considers te quantity-rationed wo cannot borrow wen teir wealter level is below te collateral requirement. Te solid lines represent l (ψ,w )=0, te dased lines I l =0, and te das-dotted lines II l =0. Te black lines denote low collateral environment and te red lines denote ig collateral environment. In a low collateral environment, igly risk-averse and poor farmers are price-rationed out of te credit market and cannot afford te ig tecnology. Te non-interlinked index insurance worsens te price-rationing and expand te rationing area to te souteast. Tis is because te implicity insurance provided by low collateral renders insurance effectively an increases in te interest rate on te loan (Giné and Yang, 2009). However, te introduction of te interlinked index insurance reduces te price rationing and moves te boundary towards te nortwest so muc tat igly risk-averse and poor farmers are able to borrow from te credit market. In a ig collateral environment, two types of credit rationing occur wen stand-alone loan contract is offered. First, poor farmers wo are lack of wealt to put as collateral are quantityrationed out. Second, among tose farmers wo are eligible to apply for a loan, igly risk-averse farmers are risk-rationed because tey fear te loss of collateral. Te introduction of non-interlinked insurance contract can reduce risk rationing and crown in te risk-averse farmers into te credit 24