Where and How Index Insurance Can Boost the Adoption of Improved Agricultural Technologies

Transcription

1 Where and How Index Insurance Can Boost the Adoption of Improved Agricultural Technologies Michael R. Carter University of California, Davis Lan Cheng Unviversity of California, Davis Alexandros Sarris National and Kapodistrian University of Athens July 214 Abstract Remote sensing and other advances have led to an outpouring of programs that offer index insurance to small scale farmers with the expectation that this insurance will enable adoption of improved technologies and boost living standards. Despite these expectations, the evidence to date on the impacts of insurance is mixed. This paper steps back and considers theoretically where index insurance might be most effective, and whether it should be offered as a stand alone contract, or explicitly interlinked with credit contracts. Emerging from this analysis is a set of nuanced recommendations based on the structure of risk and the property rights (collateral) environment. Keywords: Agricultural index insurance, Credit rationing, Interlinkage, Technology adoption JEL classification: O17, O32, Q14, D83, G22 Acknowledgments. We thank for thoughtful comments seminar participants at the University of California, San Diego; the University of California, Davis; Montana State University; the 212 American Agricultural and Applied Economics Association annual meeting; the 212 I4 Index Insurance Innovation Initiative workshop; and, the 211 FAO workshop on Small Farm Participation in Value Chains. This work has been supported in part by the American people through the United States Agency for International Development Cooperative Agreement No. AID-OAA-L-12-1 with the BASIS Feed the Future Innovation Lab. Neither supporting nor employing institutions are responsible for the ideas and opinions expressed in this paper. addresses: mrcarter@ucdavis.edu (Michael R. Carter), lancheng@ucdavis.edu (Lan Cheng), alekosar@otenet.gr (Alexandros Sarris)

2 1. Introduction Decades of research have identified risk as a primary impediment to the adoption of improved agricultural technologies that can, on average, substantially boost the incomes of poor, small-farm households (for a survey of early work, see Feder et al. [9]). 1 Risk directly discourages technology adoption by making farmers unwilling to productively invest their own savings, which they otherwise need to buffer consumption against potential income shortfalls. Risk may also discourage low wealth households from investing funds borrowed from others, when available, for fear of the default consequences, a phenomenon that Boucher et al. [2] dub risk rationing. Indirectly, risk that is correlated across farmers, such as weather risk, poses a portfolio problem for microfinance and other potential lenders, raising further the cost of credit to the small farm sector, further discouraging technology adoption. While insurance mechanisms would seem to be a natural response to this problem of risk-inhibited technology adoption, an earlier generation of efforts to employ individual indemnity-based agricultural insurance collapsed under the weight of asymmetric information and transaction costs (Hazell [12]; Barnett et al. [1]). 2 Recent technological innovations in remote sensing, as well as the rediscovery of old ideas like area yield insurance (see Halcrow [11]), have reignited efforts to use insurance to crowd-in technology adoption, but this time relying on index insurance that makes payments based on an easy-to-measure index, which cannot be influenced by the individual, but which is correlated with (but not identical to) individual outcomes. 3 With the outpouring of new index insurance schemes (see International Fund for Agricultural Development and World Food Program [13], Miranda et al. [16] and Carter et al. [6] for listings of new programs), reliable impact evaluations are beginning to appear. While several show strongly positive impacts of index insurance on small farm investment and technology adoption (e.g., Mobarak and Rosenzweig [17], Karlan et al. [14] and Elabed and Carter [8] find that index insurance significantly boosts investment at the intensive and, or extensive margins), the study by Giné and Yang [1] finds contrary results, with an index insurance contract significantly reducing investment in a new agricultural opportunity. The goal of this paper is to step back from both the policy excitement and the mixed impact evaluation results and theoretically consider where and how index insurance can be expected to be effective as an instrument to boost small farm technology adoption. To do this, we put forward a model of a risk averse household that is exposed to both idiosyncratic 1 This is no more evident than in the sub-saharan Africa where irrigation is scarce, risk is high and the use of improved seeds and fertilizers stands at a tiny fraction of the levels in other areas of the developing world (World Bank [2]). 2 Conventional insurance relies on loss verification to control moral hazard. Unfortunately, for a small, remote farmer, a single loss verification will consume multiple years of premium payments, rendering this kind of insurance economically infeasible. Similarly, individual-specific loss rating is non-economic for small-scale, exposing conventional insurance schemes to adverse selection. 3 Index insurance indemnifies insured farmers based on an external index such as directly measured average yields in a region or average yields as predicted by rainfall, remotely sensed measures of plant growth such as evapotranspiraiton. Because these area measures are beyond the influence of any individual producer, index insurance is largely immune to the moral hazard and adverse selection problems that sank earlier efforts to use conventional insurance for small-scale agriculture. Carter [5] discusses technical design issues and options, while Miranda et al. [16] and Carter et al. [6] review experience with index insurance to date. 1

3 and covariant risk. The household chooses between a low-input, low risk and low yield technology versus a high input, high risk and high yielding technology. We next examine the technology choice of the household in three, perfectly competitive financial environments: one in which credit alone is available; one in which credit and separate standalone index insurance contracts are available; and, one in which an interlinked credit and index insurance contract is available. 4 Within each contractual environment, we consider the impact of property rights regimes, ranging from those in which land is not mortgageable and loans are under collateralized, to those in which land is mortgageable and loans fully collateralized. Finally, because individual household choices generate externalities (via their impact on lender portfolio risk), we assemble a financial market equilibrium model of technology choice. For a typical distribution of initial wealth and risk aversion, we consider the equilibrium effectiveness of index insurance as a device to boost technology adoption across a variety of agro-ecological environments distinguished by the aggregate level of risk as well as by the degree to which risk is covariate or idiosyncratic. Emerging from this exploration is the identification of stylized areas where index insurance will be ineffective, or even counterproductive if required as a condition for borrowing; areas where standalone contracts will be effective; and, areas where standalone index insurance will be ineffective, but where interlinked credit and insurance will crowd-in technology adoption. The remainder of this paper is organized as follows. Section 2 puts forward the basic farm household technology choice model and introduces index insurance contracts. Section 3 considers loan offers by a perfectly competitive banking sector under alternative property rights and collateral regimes. Section 4 then considers the impact of different financial contracts on the adoption of improved technologies under different property rights regimes. Finally Section 5 examines aggregate technology uptake in different agro-ecological environments. Section 6 concludes with recommendations on where and how to introduce index insurance as a potentially important development tool. 2. Risk and Insurance Options for the Small Farm Household This section models the technology choices and the financial contracts potentially available to households in a stylized small farm sector. Central to our model is the assumption that farm households face two sources of risk: idiosyncratic risk, and correlated or covariate risk that simultaneously affects all farms in the sector. Later section use these elements to explore the impact of index insurance and interlinked credit and insurance on technology uptake Risk and Self-insurance through Technology Choice Small farm households are assumed to have access to two technologies, a traditional technology with low, but stable returns, and a higher yielding, but riskier technology. The latter requires substantial use of purchased inputs. Both technologies are subject to idiosyncratic (θ s ) and covariant shocks (θ c ). We assume a multiplicative risk structure and write the 4 As detailed below, an interlinked contract is one in which the lender has first claim on any insurance payments up to the level of outstanding loan liability. 2

4 output of low-yielding technology as: y T = θg T (1) where θ = (θ c + θ s ) with support [, θ], probability distribution function denoted f N (θ), cumulative distribution function denoted F N (θ) and E(θ) = 1. We assume that this traditional technology does not require any purchased inputs so that the returns to household-owned factors from the low yielding technology is ρ T = y T. The output of the improved, high-yielding technology is: y H = θg H (K), (2) where K is the amount of purchased inputs required. We assume that these inputs are financed by borrowing from a rural credit market that offers loans of size K at contractual interest rate r and a collateral requirement χ (section 3 gives details on the determination of contract terms). 5 Net returns to the household under this loan contract are as follows: { yh (1 + r)k = θg ρ H = H (K) (1 + r)k, if θ > θ χ, otherwise (3) where θ = (1+r)K χ g H is the level of the shock such that the value of the collateral plus the (K) output produced just equals the value required for full loan repayment. This specification follows Stiglitz and Weiss [18] and assumes that the household retains no income (or pledged collateral assets) until the loan is fully repaid. To make the technology choice problem meaningful, we assume that the higher-yielding technology offers higher expected returns to the farm household: E[ρ H ] > E[ρ T ]. At the end of the production period, consumable household wealth c j is equal to ρ j + W + B, where j equals T or H. It is the sum of returns to production plus the household s inherited wealth (W ) and its risk-free income from non-farm activities (B). The lowest consumable wealth under the high-yielding technology is c(χ) = W + B χ, while it is c T = W +B under the traditional technology. Figure 1 shows household consumption as a function of the stochastic factor under the two technologies. The dashed line represents potential consumption as a function of the stochastic factor under the low technology, whereas the solid curve represents consumption under the high technology when collateral is high. As the collateral requirements decreases, the consumption floor under the high technology rises as more of the down-side risk is borne by the lender. The dotted line in Figure 1 illustrates the zero collateral case in which the consumption floor, c(χ = ) = W + B, is the same as the consumption floor under the low technology. Figure 2 uses the stylized numerical specification detailed in Appendix A to illustrate the risk-return tradeoffs captured by the farm household model. Consumption values in the graph are normalized by expected consumption under the traditional technology. The black, solid line shows the cumulative distribution of household consumption when the improved 5 Self-finance exposes the farmer to unlimited liability and is equivalent to a fully collateralized loan contract if the savings rate is equal to the loan. 3

5 Figure 1: Risk, Technologies and Loan Contracts technology is adopted and financed with a fully collateralized loan contract (χ = K). Compared to the traditional activity (shown here as the blue, dotted line), the high returning activity is assumed to have mean returns that are 3% higher than the traditional agricultural activity. Some 4% of the time household consumption will be at least 25% higher than average consumption under the low technology. However, as can be seen, under the improved technology the household faces a 1% chance that its total consumption will be less than 6% of the average consumption it can obtain under the traditional technology. There is a near zero probability of outcomes that low under the traditional technology. Adoption of the low technology can thus function as self-insurance for the farm household, protecting it from the risks that attain when the high technology is adopted. To put this kind of self-insurance in context, it is useful to compare it with an idealized, individual indemnity insurance contract that would pay off any time returns under the high technology fell below expected income (E[ρ T ]) under the traditional technology. The green dash-dot line in Figure 2 illustrates the cumulative distribution of consumption that would occur if adoption of the high technology could be insured with this idealized contract. Compared to this idealized contract, self-insurance through reliance on the safe technology is neither actuarially fair (its implicit premium reduces expected household income by a whopping 3%) and it offers only partial protection as there is a 5% probability that consumption will fall below the level insured by the idealized contract. As can be seen in Figure 2, the idealized fail-safe contract first order stochastically dominates self-insurance, reflecting both the costliness and incompleteness of the self-insurance option. Unfortunately, for the reasons already discussed above, this kind of idealized individual indemnity insurance is not implementable for small scale farmers, traditionally leaving 4

6 Figure 2: Cumulative Distribution of Returns under Different Technology Choices households the choice of bearing the full risk of adopting the new technology or engaging in costly self-insurance. However, the innovation of index insurance contracts offers a third alternative, and we turn now to consider how such contracts might function and ultimate influence the adoption of improved technologies Feasible Index Insurance for the Small Farm Sector: Interlinked and Stand-alone Unlike individual indemnity insurance that pays based on verified individual losses, index insurance pays based on an index or measure correlated with losses. An insurance index is typically designed to predict average losses within a specified geography. It will be an imperfect predictor of an individual loss to the extent that the individual suffers an idiosyncratic shocks unrelated to average losses in the geographic zone. It will also correlate poorly if the index is an imperfect predictor of average losses. While the latter source of poor correlation is important in practice, 6 we will here simplify things and assume that the covariant shock, θ c, is observed without error so that an insurance contract can be constructed around actualized high technology yields in the insured area (θ c g h ). For the analysis here, we assume a linear indemnity function that compensates the farmer for any shortfall between average realized yields a threshold or trigger level defined as g H ˆθc. That is, payments to the farmer are g H (ˆθ c θ c ) any time the realized covariant shock θ c 6 See Clarke et al. [7] for detailed discussion of the poor correlation between commonly used rainfall indices and average farm outcomes. 5

7 falls below the insurance strike point, ˆθc. Denote the actuarially fair premium for this contract (normalized by the long-term expected output level under high technology g H ) as z = E[1( ˆθ c > θ c )( ˆθ c θ c )]. Finally let β be the total mark-up beyond the actuarially fair premium associated with this contract. In the numerical analysis to follow, we assume a 3% mark-up on the the actuarially fair premium (i.e., β =.3(zg H ).) Under this insurance contract, gross returns to the farm household are given by: y I = { (θc + θ s )g H + (ˆθ c θ c )g H zg H β = (ˆθ c + θ s z)g H β, if θ c < ˆθ c (θ c + θ s )g H zg H β, = (θ c + θ s z)g H β, otherwise. (4) As can be seen from this expression, we can rewrite the random shock that determines gross returns under the insurance contract as θ I = θ + s(θ), where s(θ) = 1( ˆθ c > θ c )( ˆθ c θ c ) z. Because z is the normalized actuarially fair premium, E[θ I ] = E[θ] = 1 and the probability function describing the distribution of the net output shock is a mean preserving squeeze of the original distribution function. Denote the pdf and cdf of θ I as f I (θ) and F I (θ). For later analysis, it will be useful to note that we can express the original distribution of θ as a mean preserving spread of the insured distribution and show that the following integral properties hold (see Appendix B): y θ [F N (θ) F I (θ)]dθ = (5) [F N (θ) F I (θ)]dθ > y < θ (6) In the analysis to follow, we will assume that insurance premium and indemnity payments are treated as part of the cash flow used by the farmer to repay loans. That is, when the farmer has insurance, net returns to the farmer are as given by expression 3, with y I replacing y H : { yi (1 + r)k, if θ > ρ I = θ I, (7) χ, otherwise where θ I = (1+r)K χ+β g H = θ + β /g H. While θ I > θ, recall that the pdf of the transformed random variable, f I (θ) is a mean-preserving squeeze of the original random variable, f N (θ). In the analysis to follow, we will consider two variants of this basic contract structure. We define we define an insurance contract as interlinked if it is purchased as part of a package with a credit contract, such that the lender is fully aware that the borrower has insured the production stream on which loan repayment depends. 7 Under the repayment rule given in expression 7, the bank is the first claimant on insurance proceeds. As we shall see later, interlinkage internalizes the externality effect that insurance has on the lender s portfolio. In contrast, we define an insurance contract as stand-alone if it is purchased by the farm household independently of the loan contract. While the lender may benefit from insurance payments that augment the borrower s repayment capacity, when a contract is stand-alone, 7 For examples of interlinked credit contracts, see the discussion of the Mongolian livestock project in Miranda et al. [16] and the discussion of an Ethiopian scheme in McIntosch et al. [15]. 6

8 we assume that the lender acts as if the borrower had no insurance (i.e., the insurance externality is not internalized by the lender). 8 Note that our use of the term interlinkage is similar to that by Braverman and Stiglitz [3]. The red, dot-dash line in Figure 2, shows the cumulative distribution of consumption for the producer if she adopts the high technology and purchases the standalone index insurance contract just described. The contract illustrated in the figure assumes that 8% of all risk faced by the household is covariant and covered by the index contract (that the diagram is σ drawn assuming that c σ c+σ s =.8). It also assumes that the loan is fully collateralized and that the insurance contract is priced 3% above the actuarially fair premium. Relative to the idealized individual indemnity contract represented by the green dash-dot line in Figure 2, the uncovered idiosyncratic or basis risk is visible under the index contract. Because of this basis risk under index insurance, there is still a 35% probability that consumption will fall below the level that would be guaranteed by the idealized indemnity contract. While index insurance is visibly inferior to the idealized contract, the key question from the perspective of technology uptake and financial market deepening is whether this index contract is superior to the income-smoothing, self-insurance option represented by the blue, dotted line in Figure 2. Under the particular numerical specification used to generate Figure 2, the index insurance contract does not first order stochastically dominate the traditional technology. 9 However, mean consumption is unambiguously higher under the index contract, and it outperforms the self-insurance option 8% of the time. While it is true that index insurance is expensive (the numerical example assumes a 3% mark-up over the actuarially fair premium), it is a bargain compared to self-insurance which costs a 3% reduction in expected household agricultural income. It is this potential gain that makes index insurance a possibly important option in small farm sectors where uptake of improved technologies have been historically low. 1 Against this backdrop, later sections will consider optimal farmer choice of technology with and without insurance. First, however, the next section develops a model of the credit market and the impact of insurance on competitive loan contracts in different property rights and collateral environments. 8 Note that under repayment assumption expression 7, insurance payments are treated like crop income for purposes of loan repayment, even under the stand-alone contract. We could alternatively assume that under the stand-alone contract as hidden income that the borrower keeps even in the case of default. Employing this alternative assumption would modestly affect the demand for standalone insurance in low collateral environments, as will be discussed below. 9 The figure is drawn based on the numerical specification in Appendix A and assumes that the loan contract for the high technology is fully collateralized, and that the nominal rate of interest charged the borrower is identical to that charged in the absence of insurance. The assumption that 8% of all risk is covered by the index insurance contract would be generous in some environments. When that fraction is dropped to 5%, the index contract yields worse results than self insurance about 25% of the time, although consumption never falls to less than about 5% of the average of the low technology option. 1 In discussing the weaknesses of index insurance Clarke (212) makes the point that the worse that can happen is made worse by index insurance (because losses can occur and no payment is received despite the payment of the insurance premium). The force of this comment is reduced, however, when index insurance is combined with the adoption of an improved technology as modeled here. 7

9 3. The Impact of Index Insurance on the Agricultural Loan Market This section models the operation of a competitive credit market for loans to agricultural producers who, as modeled above, face both covariant and idiosyncratic risks. There are three interest rates that matter in the model: 1. π is the exogenous (risk-free) opportunity cost of capital to the lender. 2. π a (n a π, f j ) is the portfolio-risk-adjusted rate of return that a lender must earn on an agricultural loan portfolio comprised of n a agricultural loans. This risk-adjusted rate will in general depend on the probability distribution that drives borrower income, f j (j = N, I), where f N indicates the probability distribution without insurance and f I indicates the probability with insurance. 3. r( π a χ, f j ) is the contractual interest charged to an individual borrower, which depends directly on f j, the portfolio risk adjusted interest rate, π a, and the level of collateral, χ, that the borrower can offer given the extant property rights regime. As is intuitive, we will see that r( π a χ, f j ) π a (n a π, f j ) π. The key issue to be explored in this section is how index insurance influences the pricing of agricultural production loans. We will first look at the determination of the contractual interest rate, r, taking as given π a. We will then turn to the determination of π a, taking as given π and n a The Iso-expected profit contract locus Matching the specification for borrower returns (equation 3), lender gross returns on a loan to farmer i under a loan contract with contractual interest rate r and collateral requirement χ are: { r, if θi > π i = θ χ+θ i g H (K) 1, otherwise. (8) K As in Stiglitz and Weiss [18], under this specification, lender s profits are concave in the random variable θ i and expected profits are given by: E(π i ) = [1 F ( θ)]r + θ ( χ + θ ig H (K) K 1)f(θ i )dθ i, (9) where as before θ = (1+r)K χ g H is the value of the random variable that just allows full loan (K) repayment. Using this expression, we can define the iso-expected profit locus as those r, χ combinations that just yield expected returns equal to π a, the portfolio risk-adjusted return that the lender must earn on its agricultural loan portfolio. By assuming that loan terms lie on this locus, we are imposing the assumption of a perfectly competitive credit market with zero expected profits. Using the implicit function theorem, we can characterize the iso-expected profits contract locus as those combinations of interest rates and collateral requirements that just yield expected returns equal to π a. As shown in Figure 3, which is drawn under the numerical 8

10 Contractual interest rate(%) r( π a χ,f N ) without insurance r( π a χ,f I ) with insurance Collateral (% of loan value) Figure 3: Iso-expected profit locus with π a = 2% specifications of Appendix A with 8% covariant risks, the locus is downward sloping as r = χ F ( θ) <, and lies above (1 F ( θ))k πa for all loans that are undercollateralized (χ < (1 + r)k). 11 In general, we would not expect a lender to be indifferent between the different points on the iso-expected profit loci. As explored by a number of papers, higher collateral/lower interest rate contracts diminish incentives for morally hazardous behavior and adverse selection by lenders (for a recent treatment, see Boucher et al. [2]). In the analysis here, we ignore borrower heterogeneity that might generate adverse selection (e.g., differences in borrower honesty or individual level heterogeneity in the structure of risk). We also ignore potential sources of morally hazardous behavior (e.g., credit diversion as in Carter [4] or non-contractible effort as in Boucher et al. [2]). Instead, we follow Stiglitz and Weiss [18] and simply assume that lenders demand that borrowers present a fixed amount of collateral in order to leverage a loan of size K. While this assumption is somewhat artificial, it allows us to focus on the impact of index insurance in two distinctive, but empirically important environments. The first of these might be considered to be representative of areas of Latin America where agricultural land is often individually titled and potentially can be seized by a lender in the event of loan default. In these environments, we will assume that lenders require a collateral of 11 The contractual interest rate r will exactly equal π a when the loan is fully collateralized (χ = (1 + r)k) as there is no probability of default in this circumstance. 9

11 value χ h, as shown in Figure 1. In other areas where agricultural land ownership is less individualized and less securely titled (as in many parts of Africa), we will assume that the the loan package requires a lower amount of collateral, denoted χ l in Figure 1. While we could impose additional structure on the model to endogenize collateral levels, our goal here is to show that index insurance and its interaction with small farm productivity and financial markets will exhibit differences across these two types of stylized agricultural economies. Whether index insurance affects the iso-expected profit locus depends on whether the insurance is a stand-alone or an interlinked contract. In the former case, the existence of the insurance contract is private information and the lender will use the uninsured probability distribution (f N ) and calculate the contractual interest rate, r( π a χ, f N ). In this case, the iso-expected profit locus is unaffected and is identical to the solid curve in Figure 3. When the loan and insurance contracts are explicitly interlinked as described above, lender returns are driven by the insured probability functions f I and F I defined in section 3.2 above. The dashed (red) curve in Figure 3 illustrates how interlinkage flattens the iso-expected profit locus. As can be seen, the impact of interlinkage on contractual interest rates is substantial in low collateral environments, but not so in high collateral environments (where the lender faces little default risk even without insurance). As the next section will now show, interlinkage will also impact π a, the average earnings required by a competitive lender on the agricultural portion of its loan portfolio Aggregate credit supply under stand-alone and interlinked contracts The analysis in the previous section analyzed competitive loan supply taking the lender s overall loan portfolio as given. When loan repayment is subject to purely idiosyncratic shocks, the lender s overall portfolio will be self-insuring within any given time period. However, a portfolio of agricultural loans will not be purely self-insuring as a negative covariant shock (e.g., a drought) could trigger a large scale episode of default. Lenders in general, and regulated financial intermediaries in particular, are of course allergic to this kind of portfolio risk. To explore this issue further, this section examines lenders pricing of agricultural loans and aggregate supply of credit to the agricultural sector. We assume that in the short-run, the lender has sufficient loanable funds to extend N loans of size K. We further assume that the lender can extend type a agricultural loans, which is the one described in the above to finance the high-yielding technology, or type b loans, which we assume to be risk free. 12 The lender s realized gross rate of return, Π g, on a portfolio of N = n a + n b loans will be given by: Π g (n a, π a χ, f) = na i=1 π i(r( π a χ, f), θ i ) + n b π, (1) N where the index i = 1,..., n a represents the individual agricultural loans in the lender s portfolio. We assume that the collateral level, χ, is fixed by the local property rights regime. 12 Type b loans can also be subject only to idiosyncratic shocks and therefore be self-insuring. 1

12 The lender faces a penalty function, P, P (Π g ) = {, if Π g > Π Ω( Π Π g ), otherwise, where Ω >, Ω (11) The penalty function reduces net lender portfolio returns by Ω( Π Π g ), when gross returns, Π g, fall below the threshold Π. Portfolio returns net of the penalty function, Π n, are given by: { Π Π n (n a, π a χ, f j g,if Π g > ) = Π Π g Ω( Π Π g (12) ), otherwise, where Ω >, Ω where the superscript j on the probability function again indicates whether or not loan returns are driven by uninsured or insured pdf. The penalty for low portfolio return occurs for several reasons. First, when the lender realizes too low a return on the loan portfolio, it runs afoul of reserve and other regulatory requirements. Second, when the portfolio return is too low, the lenders have to sell a large amount of collateral at the same time to repay depositors, which drives down the price of collateral and lenders net return. Third, low return from the portfolio forces lenders to borrow from the money market and pay for high interest rates. Lastly, from a political economy perspective, the lender understands that a massive default, driven by a drought or other unfavorable event, will likely trigger a political economy reaction with the government tempted to mandate at least partial default forgiveness. 13 Note that agricultural loans have an externality effect. Each additional agricultural borrower may raise the cost of capital to all agricultural borrowers through this penalty mechanism. We are now in a position to explore the lender s supply of agricultural loans to the market. Maintaining the assumption of risk neutrality, the lender will supply n a agricultural loans to the market if E(Π n (n a )) π, where π is the exogenous opportunity cost of capital to the lender. Letting φ g denote the pdf of Π g, 14 this condition can be rewritten as: π + [ na ] π n ( πa π) Ω(Π g )φ g (Π g )dπ g π, (13) The integral term is the expected penalty (denoted as E(Ω)), whereas the term in square brackets is the additional gains the lender can earn on agricultural loans by setting the expected return on such loans ( π a ) above the opportunity cost of capital. Using the implicit function theorem, we can identify the lender s market supply or offer curve of agricultural loans for adoption of the agricultural technology in an environment without insurance, n H a ( π a χ, f). Figure 4 illustrates the main results and their intuition. Drawn for the case in which risk 13 For example, following the 1998 El Nino event, the Peruvian government instituted a financial rescue that instructed agricultural lenders to forgive outstanding debt (see Tarazona and Trivelli [19]). 14 Note that Π g is essentially the sum of n a random loan returns that are driven by either f I or f N. 11

13 Ag. loan portfolio rate of return(% of π) π a without insurance π a with interlinked insurance Agricultural loans (% of portfolio) Figure 4: Aggregate supply of agricultural loans portfolio rate of return is predominately covariate, this figure illustrates the loan offer curve for the case of a low collateral economy (collateral is set at zero). In Figure 4, the horizontal axis is the fraction of the lender s loan portfolio allocated to agricultural loans, while the vertical axis expresses π a as a percentage of the opportunity cost of capital, π. As can be seen from the solid line, π a begins to increase dramatically once agricultural loans increase beyond 3% of the loan portfolio. It is important to stress that this increase in π a is not an increase in expected lenders earning, but simply the cost of doing business in a sector with covariate risk and low levels of collateral. As would be expected, the loan offer curve flattens as the level of collateral increases, and becomes completely flat when loans are fully collateralized (as the lender bears no risk whatsoever). How then would the introduction of index insurance affect the loan offer curve? Standalone insurance has no impact as it is assumed to be private information between the farmer and the insurance company. However, when insurance is explicitly tied to the loan contract through interlinkage, it alters the probability function, φ g, that determines whether the lender realizes returns below the penalty level, Π. The dashed line in Figure 4 illustrates the impact of index insurance on π a in the low collateral, high covariate risk, economy. As can be seen, interlinked index insurance flattens the offer agricultural loan offer curve. By removing covariate risk from the portfolio of the lender, index insurance almost completely decouples the probability that the penalty will be imposed from the fraction of the lender s portfolio that is in agricultural loans. As mentioned earlier, interlinkage internalizes the externality 12

14 effect that insurance purchase has on lender earnings. 4. The Impact of Index Insurance on the Adoption of Improved Technology The previous section has shown that when interlinked with credit, index insurance can reduce the contractual interest rate faced by the farm household, directly by shifting down the iso-expected profit locus, r( π a χ, f), and indirectly by reducing π a, the earnings required on the competitive lenders agricultural loan portfolio. Both of these impacts are more pronounced in low collateral environments. This section now explores the choice of technology by a representative risk averse farm household in different collateral environments. We assume that the household has adequate wealth to fully collateralize the loan if required. Absent insurance, we show that in some environments (and for some levels of risk aversion), the household will forego the higher returns offered by the the high technology, risk-rationing themselves in the language of Boucher et al. [2]. 15 We then go on to analyze the impact of insurance on technology adoption and the demand for credit. In low collateral environments, the impact of stand-alone index insurance is minimal due to the implicit insurance provided by loan contracts, while in high collateral environments, the insurance substantially improves household welfare, crowding in demand for credit and adoption of the improved technology. In contrast, interlinked insurance and credit in the low collateral environment reduce contractual interest rates, potentially crowding-in credit demand and the adoption of the improved technology Technology Choice without Formal Insurance Absent formal insurance, the farm household must choose between the traditional technology and the loan-financed improved technology. Assuming that household decisions are guided by expected utilty maximization, we can write the expected utility value of using the traditional technology (V T ) and the improved technology (V H ) as: V T = θ u(θg T + W + B)f(θ)dθ (14) V H = F ( θ)u(c) + θ θ u(θg H (1 + r)k + W + B)f(θ)dθ. (15) Note that c = W + B χ is the consumption floor under the loan contract and is decreasing in the amount of collateral required for the production loan. To reduce notation clutter, we suppress the conditioning of c and θ on the collateral level χ. 15 A risk rationed agent is one who has access to a risky technology that is profitable in expectation; has access to the finance needed to adopt the technology; but who chooses the low risk fallback option in preference to the higher retruning alternative. Boucher et al. present evidence that upwards of 2% of small scale producers in (relatively high collateral) Latin American environments are risk rationed and produce at the same input and income levels as farmes who completely lack access to capital. 13

15 We assume that the household will choose high technology and to take the loan contract if H = V H V T >. Using the expressions above, we can rewrite H as: H = F ( θ)u(c) θ + u(θg T + W + B)f(θ)dθ θ θ [u(θg H (1 + r)k + W + B) u(θg T + W + B)]f(θ)dθ, (16) where the first term in square brackets is strictly negative (even when χ = ) indicating that the traditional technology outperforms (in utility terms) the improved technology in bad states of the world (as shown in Figure 1). The second term in square brackets is nonnegative and represents the expected utility gains for better states of the world (θ > θ). Note that in a high collateral environment, the consumption floor falls and more risk averse agents may choose the traditional technology. Such agents would be risk rationed, in the language of Boucher et al. [2] as they have access to a loan contract to finance a profitable technology, but choose not to adopt it because of fear of default. On the other hand, in a low collateral environment, lending costs to agriculture ( π a ) are higher, reducing the size of the second term and again making it possible that some risk averse agents will choose the traditional technology. Figure 5 illustrates the interactions between these various forces. The figure is drawn for a modestly risk averse household (with constant relative risk aversion of 2) and assumes that a majority of risk is covariant and that the lender s loan portfolio is comprised exclusively of agricultural loans (n a = N). The horizontal axis displays collateral as a function of the loan amount, while the vertical axis measures the certainty equivalent of consumption for the different choices as a percentage of the certainty equivalent value of the traditional technology. The horizontal line across the middle of the figure is certainty equivalent of the traditional technology, which is of course independent of the collateral level associated with loan contracts. Under the numerical specification used to generate the figure, we see that demand for a loan and uptake of the new technology would be lowest in low collateral environments, and only becomes positive when collateral levels passes 1%. This perhaps surprising pattern reflects the fact that the costs of default risk including those associated with the lender s risk of correlated default are pushed onto the contractual interest rate in the low collateral environment, lowering the profitability of the high technology. Higher collateral partially ameliorates this problem, though it of course shifts risk on to the borrower. These results are not, however, general. Higher levels of risk aversion will completely eliminate demand for the improved technology. A market with fewer agricultural loans (and a lower cost of agricultural lending) will boost the certainty equivalent of the improved technology in low collateral environments. The general point is that H can be negative for the farm household in different credit market scenarios. We turn now to see how index insurance influences the choice of technology and demand for working capital loans. 14

16 Figure 5: Insurance and Choice of Technology Certainty equivalent of consumption (% of low technology value) Low technology High technology High technology with stand alone insurance High technology with interlinked insurance Collateral (% of loan value) 4.2. Standalone Index Insurance Contracts We now consider introduction of the stand-alone index insurance contract. Recall that under the standalone insurance contract, insurance proceeds are available to repay the loan contract, but because the insurance is not explicitly interlinked with the loan, the contractual interest rate is not affected by the household s (voluntary) purchase of insurance. 16 The expected utility value of adopting the improved technology and purchasing the standalone insurance contract is given by: V I = U(c)F I ( θ I ) + θ θ I U[θg H (1 + r)k + W + B]f I (θ)dθ. 16 In results available from the authors, we show that if insurance proceeds are held privately and not used to repay loans, then the desirability of standalone insurance increases modestly. The increase is only modest because in this case, household consumption is partially destabilized by the simultaneous presence of both limited liability and insurance. Specifically, household consumption is higher when θ = then it is when θ = θ. 15

17 Denote the expected utility gain of standalone insurance relative to the traditional technology as I = V I V T. After adding and subtracting expected utility associated with the uninsured adoption of the high technology (V H ), this gain can be rewritten as: I = [V I V H ] + [V H V T ] = [V I V H ] + H. To understand whether and when index insurance crowds in the adoption of the high technology by households that would not otherwise use it, we are especially interested in the risk rationing case in which H <. Note that in order for the standalone insurance to have these impacts, it must be the case that [V I V H ] > H >. We can gain further insight on the conditions under which insurance induces the riskrationed to adopt the high technology by examining the relatively favorable case in which the standalone insurance is actuarially fair, meaning that β = and that θ I = θ. Under this assumption we can rewrite [V I V H ] as: U(c)[F I ( θ) F ( θ)] + After integrating twice by parts, we have: [V I V H ] = U (c)g h θ θ θ U[θg h (1 + r)k + W + B](f I (θ) f(θ))dθ (17) [F I (θ) F (θ)]dθ + θ [ θ (F I (y) F (y))dy]u g 2 hdθ. (18) θ Because θ is a mean-preserving spread of θ I, the first term on the right hand side of equation 18 is negative for all undercollateralized loan contracts (with θ > ), while the second part is strictly positive for all risk averse farm households. Each of these terms has a precise economic meaning. The negative first term reflects the fact that the expected consumption when standalone insurance is purchased and the loan is undercollateralized is lower than that under no insurance. 17 This drop in expected consumption occurs because some of the 17 Denoting the expected consumption under standalone insurance and without insurance as E I and E H, the change of expected consumption (conditional on adoption of the high technology) is equal to θ E I E H = χ[f ( θ) F I ( θ)] [θg H (K) (1 + r)k][f(θ) f I (θ)]dθ (19) θ Integrating by parts and using the properties of mean-preserving spread (equation 5 and 6 ), the above expression reduces to: E I E H = g H θ [F I (θ) F (θ)]dθ (2) which is always negative when loans are not fully collateralized and equal to zero when loans are fully collateralized. It indicates that at least in terms of expected income, the lower the collateral level, the more households lose from the non-interlinked contract. 16

18 risk is being carried by the lender and yet the borrower pays for the insurance that reduces risk for the lender. Note that this reduction in expected consumption occurs even when the index insurance contract is actuarially fair. The second term on the right hand side of equation 18 measures the increase in expected utility that results because index insurance reduces fluctuations in consumption. This conventional value of insurance will be larger when the absolute value of U is greater and the individual is more risk averse. If a loan is fully collateralized, then θ = and the first term of Equation 18 is equal to zero. Hence, [V I V H ] is unambiguously positive, making it at least possible that standalone index insurance will crowd-in adoption of the high technology for risk rationed farm households with H <. If the standalone insurance is not actuarially fair, then this likelihood decreases. To more fully explore these complex interactions, we return to the numerical analysis presented in Figure 5. The (green) dash-dot line in that figure shows the certainty equivalent of V I as a percentage of that of low technology under the assumptions detailed above, assuming that the index insurance is priced 3% above the actuarially fair rate. We see that the certainty equivalent under non-interlinked insurance is even lower than that under implicit insurance ([V I V H ] < ) when collateral χ is less than 15% of the loan value. In this case, standalone insurance were it required would actually reduce borrowing and uptake of the improved technology, a result consistent with the randomized controlled trial reported in Giné and Yang [1]. As collateral rises, the certainty equivalent of the standalone insurance becomes higher than the traditional technology (V T ) and then higher than the certainty equivalent of adopting the high technology without insurance (V H ). For these particular parameter values, standalone insurance would not crowd-in adoption of the high technology for any farm households, although it would meet with strong demand in higher collateral environments Interlinked insurance contracts As defined in Section 2, an interlinked insurance-loan contract is one in which the lender is explicitly assigned rights to insurance payoffs and takes the insurance into account when pricing the loan contract. As analyzed above, for undercollateralized loan contracts, interlinkage will lower the competitive interest rate charged to borrowers, with this interest rate effect becoming larger as the fraction of the lender s portfolio dedicated to agricultural loans increases. From the farm household s perspective, interlinkage lowers the contractual interest rate and reduces the kink point ( θ) in the payoff function relative to what attains under standalone insurance. Expected utility under the interlinked contract is given by: θ V L = U(c)F I ( θ L ) + θ L U[θg H (1 + r L )K + W + B]f I (θ)dθ, (21) where r L = r( π a χ, f I ) and θ L = (1+rL )K χ+β g H are the loan contract terms under interlinkage. We can write the expected utility gain of interlinked insurance relative to the adoption of the traditional technology as: L = V L V T = [V L V I ] + [V I V H ] + H, (22) 17

19 where the new term [V L V I ] represents the expected utility gain from insurance interlinkage relative to standalone insurance. Assuming that the index insurance contract is actuarially fair (β = ), this additional gain from interlinkage can be expressed as: [V L V I ] = θ θ (U[θg H (1 + r L )K + W ] U[θg H (1 + r)k + W + B])f I (θ)dθ + θ θ L (U[θg H (1 + r L )K + W + B] U(c)) f I (θ)dθ. (23) The discussion in Section 3 indicates that r L < r if loans are not fully collateralized with χ < (1 + π)k; r L = r and thus θ L = θ when loans are fully collateralized with χ = (1 + π)k. As can be seen from inspection of equation 23, this gain will be positive for all undercollateralized loans (such that θ > θ I > ). 18 When loans are fully collateralized [V L V I ] =, and there are no further gains to interlinkage. From the farm household s perspective, interlinked insurance is always at least as good as non-interlinked insurance ( L I ), with this differential decreasing in collateral χ. In this sense, interlinked insurance serves as a collateral substitute. The (red) dashed line in Figure 5 denotes the relative certainty equivalent of interlinked insurance, V L. Because interlinked insurance serves as a collateral substitute, the certainty equivalent value of the high technology becomes independent of the level of physical collateral, and hence the line measuring the relative value of V L is horizontal with respect to collateral χ. As can be seen, the gap between interlinked and standalone insurance, L I, is largest at low collateral levels. Under the parameters used to construct the figure, we can see that interlinked insurance would actually crowd-in adoption of the high technology in low collateral environments ( χ < 1%) by households that would not adopt the high technology K at all absent the interlinked insurance. That is, in this environment, interlinked insurance reduces risk rationing, whereas standalone insurance does not (and may even have perverse consequences as in the Giné and Yang [1] experiment). While this result is not general, we turn in the next section to explore the likely impacts of index insurance across a range of different environments. 5. Equilibrium Impacts of Index Insurance in Different Agro-ecological Environments The prior section analyzed the impact of index insurance on the technology and contractual choices of a representative agent, taking as given the risk-adjusted cost of capital to the agricultural sector, and assuming an agro-ecological environment that is relatively favorable to index insurance (moderate levels of risk, with the majority of that risk being 18 When θ θ L, θg H (1 + r L )K χ and hence θg H (1 + r L )K + W + B c. 18