Where and how index insurance can boost the adoption of improved agricultural technologies

Journal of Development Economics 118 (2016) 59–71

Contents lists available at ScienceDirect

Journal of Development Economics journal homepage: www.elsevier.com/locate/devec

Regular article

Where and how index insurance can boost the adoption of improved agricultural technologies Michael R. Carter a,b,c,d,⁎, Lan Cheng a, Alexandros Sarris e a

University of California, Davis, United States NBER, United States BREAD, United States d The Giannini Foundation, United States e National and Kapodistrian University of Athens, Greece b c

a r t i c l e

i n f o

Article history: Received 11 July 2014 Received in revised form 12 August 2015 Accepted 25 August 2015 Available online 2 September 2015 Keywords: Agricultural index insurance Credit rationing Interlinkage Technology adoption

a b s t r a c t 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 uptake and 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 standalone 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. © 2015 Elsevier B.V. All rights reserved.

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., 1985).1 Risk directly discourages technology adoption by making farmers unwilling to 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. (2008) 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 ⁎ Corresponding author at: Department of Agricultural and Resource Economics, University of California, Davis, Davis, CA 95618, USA. E-mail addresses: [email protected] (M.R. Carter), [email protected] (L. Cheng), [email protected] (A. Sarris). 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 (Bank, 2007).

http://dx.doi.org/10.1016/j.jdeveco.2015.08.008 0304-3878/© 2015 Elsevier B.V. All rights reserved.

insurance collapsed under the weight of asymmetric information and transaction costs (Barnett et al., 2008; Hazell, 1992).2 Recent technological innovations in remote sensing, as well as the rediscovery of old ideas like area yield insurance (see Halcrow, 1949), 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 At best, index insurance can only protect individuals against covariant risk, meaning shocks, like droughts, that are correlated across individuals. With the outpouring of new index insurance schemes (see Carter et al., 2014; International Fund for Agricultural Development World Food Program, 2010; Miranda et al., 2012 for listings of new programs), 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 (2012) discusses technical design issues and options, while Miranda et al. (2012) and Carter et al. (2014) review experience with index insurance to date.

60

M.R. Carter et al. / Journal of Development Economics 118 (2016) 59–71

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., Elabed and Carter, 2014; Karlan et al., 2014; Mobarak and Rosenzweig, 2013) find that index insurance significantly boosts investment in high returning technologies in the 25 to 35% range), the study by Giné and Yang (2009) 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 and covariant risk. The household chooses between a lowinput, low risk and low yielding technology versus a high input, high risk and high yielding technology. We 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 and hence of loan pricing), we assemble a financial market equilibrium model of technology choice. For a typical distribution of initial wealth and risk aversion, we consider the equilibrium impact of index insurance on technology adoption across a variety of agro-ecological environments distinguished by the aggregate level of risk as well as by the degree to which that risk is covariant or idiosyncratic. Table 1 reports the main dimensions of the analysis, as well as summarizing the key implications of our model under our “base case” assumption of an agro-ecology that that is relatively favorable for index insurance. This base case scenario assumes that agricultural production risk is high, and that a large fraction of that risk is covariant risk that can be effectively covered by an index insurance contract. As can be seen in Table 1, absent insurance, uptake of the new profitable technology is modest, especially when loans are fully collateralized such that the farmer bears the risk of default. Standalone insurance roughly doubles technology uptake in the case of fully collateralized loans, but has no impact when lenders bear default risk when loans are undercollateralized. Indeed, requiring standalone insurance for the undercollateralized case would likely reduce uptake of loans and the improved technology. However, when index insurance is explicitly interlinked in the low collateral case, it pushes technology uptake to almost 100% as competitive lenders lower the cost of capital to farmers. While these are striking results, we show that they are not general and where and how index insurance works very much depends on the underlying severity and structure of risk. 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 credit supply by a perfectly competitive banking sector under alternative property rights and collateral regimes. Section 4 then considers the impact of insurance on technology adoption under these different regimes. While Sections 2–4 operate under base case assumptions that are favorable to the effective functioning of index insurance, Section 5 then examines the impact of index insurance on technology uptake in different agroecological environments characterized by different intensities of risk and variation in the extent to which risk is covariant. Drawing all our results together, Section 6 concludes with recommendations on where 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.

Table 1 Percentage of farmers adopting improved technology under different scenarios. Property rights regime

No insurance

Standalone insurance

Interlinked insurance

Under-collateralized Fully collateralized

20–40% 0–20%

No impact 20–40%

70–100% 20–40%

Assumes a high risk environment where the coefficient of variation of production exceeds 35% and at least 40% of total risk is insurable, covariant risk.

and how to introduce index insurance as a tool to accelerate the adoption of improved agricultural technologies. 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: an idiosyncratic risk, and a correlated or covariant 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. 2.1. 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 (θs) and covariant shocks (θc). We assume a multiplicative risk structure and write the output of low-yielding technology as: yT ¼ θg T

ð1Þ

where θ = (θc + θs) with support ½0; θ, probability distribution function denoted f N(θ), cumulative distribution function denoted F N(θ) and E(θ) = 1. The superscript N denotes the absence of insurance. 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 ρT = yT. The output of the improved, high-yielding technology is: yH ¼ θg H ðK Þ;

ð2Þ

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.5 Net returns to the household under this loan contract are as follows: ( ρH ¼

yH −ð1 þ r ÞK ¼ θg H ðK Þ−ð1 þ r ÞK; if θ N ~θ −χ; otherwise

ð3Þ

where ~θ ¼ ð1þrÞK−χ g ðKÞ is the level of the shock such that the value of the colH

lateral plus the output produced just equals the value required for full loan repayment. This specification follows (Stiglitz and Weiss, 1981) 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[ρH] N E[ρT]. At the end of the production period, consumable household wealth cj is equal to ρj + W + B, j = T,H. Consumable household wealth is the sum of rurns to production (ρj) plus the household's inherited wealth (W) and its risk-free income from non-farm activities (B). The lowest consumable 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 rate.

M.R. Carter et al. / Journal of Development Economics 118 (2016) 59–71

wealth under the high-yielding technology is cðχÞ ¼ W þ B−χ, while it is c T ¼ W þ B under the traditional technology. Fig. 1 shows household consumption as a function of the stochastic factor under the two technologies. The dashed line represents 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 Fig. 1 illustrates the zero collateral case in which the consumption floor, cðχ ¼ 0Þ ¼ W þ B, is the same as the consumption floor under the low technology. Fig. 2 uses our base case agro-ecological scenario to illustrate the risk-return tradeoffs captured by the farm household model. As mentioned in the Introduction above, our base case parameters assume that yield risk is relatively high (with a coefficient of variation of 38%) and that risk is predominantly (80%) covariant. In Fig. 2, consumption values are normalized by expected consumption under the traditional technology. The curve marked with “+” signs displays the cumulative distribution of household consumption when the improved technology is adopted and financed with a fully collateralized loan contract (χ = K). Compared to the traditional activity (shown here as the dotted line), the high returning activity is assumed to have mean returns that are 30% higher than the traditional agricultural activity. Moreover, 35% of the time, household consumption under the improved technology will exceed the best possible outcome that can occur with the traditional technology. However, despite this upside potential, adoption of the improved technology creates a 15% chance that total household consumption falls below the worst state possible under the traditional technology. By avoiding this risk of extremely low consumption outcomes, the traditional technology functions as a kind of self-insurance against the downside risk of the improved technology. To put this kind of self-insurance in context, it is useful to compare the traditional technolgoy with an idealized, individual indemnity insurance contract that would pay off any time returns under the high technology yields fall below mean consumption under the low technology. The solid line in Fig. 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 via the traditional technology is neither actuarially fair (its implicit premium reduces expected household income by 30%) and it offers only partial protection as there is a 50% probability that consumption will fall below the level insured by the idealized

Fig. 1. Risk, technologies and loan contracts.

61

Fig. 2. Cumulative distribution of returns under different technology choices.

contract. As can be seen in Fig. 2, the idealized fail-safe contract almost first order stochastically dominates self-insurance, reflecting both the costliness and incompleteness of the self-insurance option. Unfortunately, for the reasons discussed above, this kind of idealized individual indemnity insurance is not implementable for small scale farmers, traditionally leaving 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 influence the adoption of improved technologies.

2.2. 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 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 shock unrelated to average losses in the geographic zone. It will also correlate poorly if the index itself 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 an “area yield” insurance index in which yields in the insured area (θcgh) are measured without error and used as the basis for insurance payments. The analysis here thus applies to this best case of area yield insurance. We will later discuss how our results change if we were to consider other types of index insurance (e.g., rainfall-based indexes), which not only fail to cover idiosyncratic shocks, but can also be imperfect predictors of average losses. Because index insurance only covers losses related to the covariant shock, θc, the utility of the insurance for the farmer will depend on the magnitudes and joint distribution of the covered covariant shocks (θc) and the uncovered idiosyncratic shocks (θs). While biology imposes the overall limits on the aggregate shock (yields cannot fall below zero, nor can they exceed the biological maximum given by θg T and θg H ðKÞ for the traditional and improved technologies, respectively) there are multiple ways to model covariant and idiosyncratic elements consistent with these limits. In the numerical analysis to follow, we will

6 See Clarke et al. (2012) for detailed discussion of the poor correlation between commonly used rainfall indices and average farm outcomes.

62

M.R. Carter et al. / Journal of Development Economics 118 (2016) 59–71

Under this insurance contract, gross returns to the farm household are given by: ( yI ¼

    ðθc þ θs Þg H þ ^θc −θc g H −zg H −β ¼ ^θc þ θs −z g H −β; if θc b ^θc ðθc þ θs Þg H −zgH −β; ¼ ðθc þ θs −zÞg H −β; otherwise

:

ð6Þ As can be seen from this expression, we can rewrite the random shock that determines gross returns under the insurance contract as θI = θ + s(θ), where sðθÞ ¼ 1ðθ^c Nθc Þð^θc −θc Þ−z . Because z is the

Fig. 3. Efficacy of index insurance.

assume that θc. is a truncated normal (TN) variable, with the points of lower and upper truncation set equal to 0 and θ7:   θc ∼ TN 1; σ 2c ; 0; θ :

ð4Þ

We will further assume that the idiosyncratic shock has the following conditional truncated normal distribution:   θs ðθc Þ ∼ TN 0; σ 2s ; 0−θc ; θ−θc :

ð5Þ

normalized actuarially fair premium, E[θI] = E[θ] = 1 and E[s(θ)] = 0. Under the stochastic specification given by expressions (4) and (5), there is always some probability of low or even zero yields irrespective of the value of the covariant shock. The worst outcome that can befall the farmer thus becomes worse when insurance is purchased. Without insurance, the worse outcome is zero yield. With insurance it is zero yield minus the cost of an insurance that did not pay because the shock driving the zero yield was entirely idiosyncratic. As stressed by (Clarke, forthcoming), it is this increase in downside risk that diminishes the value of index insurance to the individual producer, especially as the magnitude of σ2s increases.8 Indeed, if farmers are not standard expected utility maximizers, but are ambiguity averse, then this prospect that the worst possible outcome becomes even worse will strongly undercut farmers' perceived value of index insurance as Bryan (2013) and Elabed and Carter (2015) show. We 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 yI replacing yH: ( ρI ¼

yI −ð1 þ r ÞK; if θN~θ −χ; otherwise

I

I

where ~θ ¼ ð1þrÞK−χþβ ¼ ~θ þ β g H

Note that under this specification, θs becomes heteroscedastic, with largest variance when the covariant shock, θc, is at its mean. As θc approaches its lower limit of 0, downside risk from idiosyncratic shocks disappears (i.e., in a complete drought year, idiosyncratic shocks cannot further worsen the situation). Given this stochastic structure, we turn now to the specification of an area yield index insurance contract. We assume a linear index indemnity function that compensates the farmer for any shortfall between average realized yields and a threshold or trigger level defined as g ^θc . That is, payments to the farmer are g ð^θc −θc Þ any time the reH

H

alized area yields, θcgH falls below the insurance strike point, ^θc g H . Note that if there were only covariant risk, then this contract would be identical to the idealized individual indemnity contract illustrated in Fig. 2. The actuarially fair premium for the index contract is given by:

ð7Þ  gH

.

In the analysis to follow, we will consider two variants of this basic contract structure. 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.9 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 standalone 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, we assume that the lender acts as if the borrower has no insurance (i.e., the

8 8 If idiosyncratic risk is less severe than implied by expression 5, then it is possible that the original shock, θ = θc + θs can be expressed as a mean preserving spread of the insurance-transformed variable, θI = θ + s(θ), with the two integral conditions holding:

h   i θc N θc ^θc −θc ; A FP ¼ g H E 1 ^

Z θh

and we define the normalized actuarially fair premium as: z ¼

A FP gH ;

where the normalizing factor, gH is simply expected output under the high technology. 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 30% mark-up on the actuarially fair premium (i.e., β = 0.3(AFP).) 7 θ−1 More formally, let z ¼ θcσ−1 ; α ¼ 0−1 σ c ; β ¼ σ c and D = Φ(β) − Φ(α), where Φ is the c CDF for the standard normal distribution. The PDF for θc can be written as σ1c D ϕðzÞ., where ϕ. is the PDF for the standard normal distribution.

Z y0h 0

i F N ðθÞ− F I ðθÞ d i F N ðθÞ− F I ðθÞ dθN0∀ybθ

where FN and FI denote the cdf's for θ and θI, respectively. A necessary condition for insurance to act as a “mean preserving squeeze” of the original random variable is that the lower limit of truncation is greater than −θc + z. Note that under expression 5, the lower limit is simply −θc. We will see in section expression 5 that there are important limitations to index insurance even under these more favorable assumptions of limited idiosyncratic risk. 9 For examples of interlinked credit contracts, see the discussion of the Mongolian livestock project in Miranda et al. (2012) and the discussion of an Ethiopian scheme in McIntosh et al. (2013).

M.R. Carter et al. / Journal of Development Economics 118 (2016) 59–71

insurance externality is not internalized by the lender).10 Note that our use of the term interlinkage is similar to that by Braverman and Stiglitz (1982). Fig. 3 illustrates how standalone index insurance works using the base case parameters that assume that 80% of all risk faced by the σc ¼ household is covariant and covered by the index contract (i.e., σ c þE½σ s 80%).11 To abstract away from the partial insurance provided by a limited liability contract, we assume for this picture that the loan is fully collateralized so that the borrower is always fully liable for repayment. The horizontal axis shows realized individual yields for the high technology, as a percentage of expected yields. The vertical axis shows net insurance payments (payouts minus premium) under both the standalone index insurance contract and an idealized individual indemnity contract with the same strike point as the index contract. The latter is priced under the unrealistic assumption that individual insurance can be sold at the same markup as index insurance, (see Castillo et al., 2014 for an empirical comparison of the cost of individual versus index insurance for small scale farmers). Alternatively, the idealized contract can be seen as an index contract in a world without basis risk. The dotted line illustrates insurance payouts (net of premium payments) under the idealized insurance for an individual who adopted the high technology. An individual adopting the high technology without insurance would be represented by the solid horizontal line at zero. As can be seen, in good states of the world, the individual is worse off with insurance by the amount of the marked up premium. In bad states of the world (yields less than 80% of average) the individual is always better off with the idealized insurance. To illustrate the working of index insurance, we took a large number of random draws from the stochastic structure represented by Eqs. (4) and (5) using the base case numerical parameters. The dashed curve is a non-parametric fit to the individual yield draws (a random sample of which are shown as dots on the figure). The impact of basis risk is shown by bad states of the world in which the individual is worse off with insurance than without. What some authors call “positive basis risk events,” in which the individual is compensated for losses she did not individually experience, are evidenced by green dots that lie above the idealized insurance line. The impact of this index insurance contract on the cumulative distribution of consumption is shown by the dashed line in Fig. 2 above. Relative to the idealized individual indemnity contract represented by the solid line in Fig. 2, the uncovered idiosyncratic or “basis risk” is visible under the index contract. Because of this basis risk, there is 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 is whether this index contract is superior to the income-smoothing, self-insurance option represented by the dashed line in Fig. 2. Under the base case agro-ecological specification used to generate Fig. 2, the index insurance contract does not first order stochastically dominate the traditional technology.12 However, mean consumption is unambiguously higher under the index contract, and it outperforms the self-insurance option 70% of the time. While it is true that index insurance is expensive (the

63

numerical example assumes a 30% mark-up over the actuarially fair premium), it is a bargain compared to self-insurance which costs a 30% 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. 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. 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. There are three interest rates in the model: 1. π is the exogenous (risk-free) opportunity cost of capital to the lender. j 2. πa ðna jπ; f Þ is the portfolio-risk-adjusted rate of return that a lender must earn on an agricultural loan portfolio comprised of na agricultural loans. This risk-adjusted rate will in general depend on the probability distribution that drives borrower income, fj (j = N,I), where fN indicates the probability distribution without insurance and fI indicates the probability with insurance. j 3. rðπa jχ; f Þ is the contractual interest charged to an individual borrower, which depends directly on fj, the portfolio risk adjusted interest rate, πa , and the level of collateral, χ, that the borrower can offer given the extant property rights regime. j

j

As is intuitive, we will see that rðπa jχ; f Þ≥πa ðna jπ; f Þ≥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 a determination of the contractual interest rate, r, taking as given π . We will then turn to the determination of πa , taking as given π. 3.1. The Iso-expected profit contract locus Matching the specification for borrower returns (Eq. (3)), lender gross returns on a loan to farmer i under a loan contract with contractual interest rate r and collateral requirement χ are: 8 < r; if θi N ~θ : πi ¼ χ þ θi g H ðK Þ : −1; otherwise K

ð8Þ

As in (Stiglitz and Weiss, 1981), under this specification, lender's profits are concave in the random variable θi and expected profits are given by:  Z~θ   i χ þ θi g H ðK Þ ~ Eðπ i Þ ¼ 1− F θ r þ −1 f ðθi Þdθi ; K h

ð9Þ

0 10 Note that under repayment assumption expression (7), insurance payments are treated like crop income for purposes of loan repayment, even under the standalone contract. We could alternatively assume that under the standalone 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. 11 Note that σs is conditionally heteroscedastic and the term E[σs] represents the expected idiosyncratic variation taken over the distribution of the covariant shock σc. 12 If we were to assume lower levels of basis risk, the cdf for the index contract would begin to approach the idealized insurance line. If we were to assume higher levels of basis risk, then the cdf would begin to approach the cdf for the uninsured high technology. Later sections of this paper explicitly explore the impacts of index insurance depending on the level and structure of risk.

whereas before ~θ ¼ ð1þrÞK−χ g ðKÞ is the value of the random variable that just H

allows full loan repayment. Using this expression, we can define the isoexpected profit locus. as those r,χ combinations that just yield expected a returns equal to π , 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 shown in Fig. 4, which is drawn for the base case scenario, the locus is downward sloping

64

M.R. Carter et al. / Journal of Development Economics 118 (2016) 59–71

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 to finance the high-yielding technology, or type b loans, which we assume to be risk free.15 The lender's realized gross rate of return Πg, on a portfolio of N = na + nb loans will be given by:

28

Contractual interest rate(%)

27

26

  j Π na ; πa jχ; f ¼

24

23

22

21

20 0

10

20

30

40

50

60

70

80

90

100

Collateral (% of loan value)

Fig. 4. Iso-expected profit locus with πa ¼ 20%.

as

Xna

π i¼1 i

g

25

∂r ∂χ

~

− FðθÞ ¼ ð1− b0 , and lies above πa for all loans that are Fð~ θÞÞK

undercollateralized (χ b (1 + r)K).13 Whether index insurance affects the iso-expected profit locus depends on whether the insurance is a standalone 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 N

distribution (fN) and calculate the contractual interest rate, rðπa jχ; f Þ. In this case, the iso-expected profit locus is unaffected and is identical to the solid curve in Fig. 4. When the loan and insurance contracts are explicitly interlinked as described above, lender returns are driven by the insured probability functions fI and FI fined in Section 2.2 above. The dashed curve in Fig. 4 illustrates how interlinkage flattens the isoexpected profit locus. As can be seen, the impact of interlinkage on contractual interest rates is substantial in low collateral environments, but has little impact in high collateral environments, where the lender faces little default risk even without insurance.14 As the next section a will now show, interlinkage will also impact π , the average earnings required by a competitive lender on the agricultural portion of its loan portfolio. 3.2. Aggregate credit supply under stand-alone a 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. a

13 The contractual interest rate r will exactly equal π when the loan is fully collateralized (χ = (1 + r)K) as there is no probability of default in this circumstance. 14 While there is a substantial theoretical literature that treats collateral requirements as an endogenous loan contract term (Bester (1987) is the classic reference, while Boucher et al. (2008) look specifically at the impacts of endogenous collateral on agricultural lending), in many places, small-scale farmers lack individual, marketable and collateralizable property rights to land, a reality that sharply limits the collateral that can be presented to secure a loan. We thus treat the collateral environment as an exogenous constraint that limits the types of loan contracts that lenders can devise.

    a r π jχ; f ; θi þ nb π N

;

ð10Þ

where the index i = 1,…,na 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. If we were to consider the lender to be risk averse (as would make sense if thought of an informal lender offering loans out of equity), then this portfolio problem could be naturally approached as a CAPM problem. Each additional agricultural loan would raise the correlation between the incremental loan and the overall loan asset portfolio of the lender. From a CAPM perspective, this would imply that the supply price of agricultural loans (πa ) would increase with the number of agricultural loans in the portfolio (na). The result would be an upward sloping supply of agricultural loans as illustrated in Fig. 5. While appealing, this CAPM approach is less obviously applicable to formal institutional lenders who maximize expected profits, as in expression (9) above. However formal banks are subject to numerous regulations designed to protect depositors against risky lending practices. In addition to reserve requirements, banks, under the Basel Accords and national regulations, are also subject to minimum Capital Adequacy Ratio (CAR) thresholds.16 CAR thresholds create two types of sensitivity to correlated default. Directly, a correlated default event consumes available bank capital, threatening the ability of the bank to exceed its minimum CAR threshold. Indirectly, a default event would be expected to trigger a reevaluation of the riskiness of the bank's lending portfolio, a move which would push required capital even higher in order to meet the CAR threshold.17 To capture the incentives created by CAR regulation, we assume that bank's face a financial penalty anytime realized gross earnings on their loan portfolio fall below the critical level needed to preserve capital and meet CAR threshold regulations. We denote this realized return ~ and write the penalty function P as: level as Π,   P Πg ¼

(

~ 0;if Πg N Π g ~ Ω Π−Π ; otherwise

ð11Þ

where we assume Ω′ N 0,Ω″ = 0.18 The penalty function reduces net g ~ lender portfolio returns by ΩðΠ−Π Þ, when gross returns, Πg, fall

~ Portfolio returns net of the penalty function, below the threshold Π. Πn, are given by:

  j a Π na ; π jχ; f ¼ n

(

~ Πg ; if Πg NΠ  g ~ Πg −Ω Π−Π

ð12Þ

15 Type b loans can also be subject only to idiosyncratic shocks and therefore be selfinsuring. 16 The Capital Adequacy Ratio is the ratio of paid up capital plus liquid reserves to a riskweighted measure of total loan assets. 17 In addition to these conventional regulatory considerations, lenders likely perceive that a massive default, driven by a drought or other unfavorable event, will trigger a political economy reaction with the government tempted to mandate at least partial default forgiveness. For example, following the 1998 El Nino event, the Peruvian government instituted a “financial rescue” that instructed agricultural lenders to forgive outstanding agricultural debt (see Tarazona and Trivelli, 2005). 18 Most likely, the penalty function, Ω is convex, but we conservatively assume that it is linear. Allowing the function to be convex would strengthen our results on the interest rate impacts of interlinked index insurance.

M.R. Carter et al. / Journal of Development Economics 118 (2016) 59–71

portfolio. It is important to stress that this increase in πa 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. While not illustrated here, the loan offer curve flattens as the level of collateral increases, and becomes completely flat when loans are fully collateralized and the lender bears no risk of penalty.21 How then would the introduction of index insurance affect the loan offer curve? Stand-alone 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, ϕg, that determines ~ The whether the lender realizes returns below the penalty level, Π.

220

200

180

160

140

120

100

80

65

0

10

20

30

40

50

60

70

80

90

100

Agricultural loans (% of portfolio)

Fig. 5. Aggregate supply of agricultural loans–portfolio rate of return.

where the superscript j on the probability function again indicates whether or not loan returns are driven by the uninsured or the interlinked insurance pdf. We are now in a position to explore the lender's supply of agricultural loans to the market. Intuitively, the existence of the penalty function will make the risk neutral lender sensitive to correlated risk. As with a CAPM approach, each additional agricultural loan will have an externality effect, raising the cost of capital to all agricultural borrowers. To see this formally, the profit-maximizing lender will supply na agricultural loans to the market if

dashed line in Fig. 5 illustrates the impact of index insurance on πa 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.22 It is important to stress that these impacts of interlinkage on the loan offer curve depend on our assumption that the insurance index is an area yield (or other high quality) index, which will not cover idiosyncratic shocks, but will correctly predict average losses. As stressed in Section 2.2 above, a rainfall insurance index will not only miss idiosyncratic events, but it may also fail to provide insurance payouts even when losses have been triggered by a covariant event that lowers average yields (e.g., an insect invasion). Rainfall and similar kinds of index insurance will thus imperfectly protect the lender's portfolio against correlated default, and will therefore have a more modest effect on the loan offer curve than what is shown in Fig. 5.

  E Π n ðna Þ ⩾ π;

4. The impact of index insurance on the adoption of improved technology

where π is the exogenous opportunity cost of capital to the lender. Letting ϕg denote the pdf of Πg,19 this condition can be rewritten as:

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, rðπa jχ; f Þ, and indirectly by reducing πa , 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 high technology, risk-rationing itself in the language of Boucher et al. (2008).23 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

πþ

Zπ~ hn  i     a πa −π − Ω Πg ϕg Πg dΠg ≥π: n

ð13Þ

0

The integral term is the expected penalty, whereas the term in square brackets is the additional gains the lender can earn on agricultura al loans by setting the expected return on such loans (π ) 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. Denote this supply function as:   N na πjχ; f ; π :

ð14Þ

Fig. 5 illustrates the main results and their intuition.20 Drawn for the base case parameters in which risk is predominately covariate, this figure illustrates the loan offer curve for the case of a low collateral economy (collateral is set at zero). In Fig. 5, the horizontal axis is the fraction of the lender's loan portfolio allocated to agricultural loans, while the a vertical axis expresses π as a percentage of the opportunity cost of capital, π. As can be seen from the solid line, πa begins to increase dramatically once agricultural loans increase beyond 30% of the loan 19 Note that Πg is the sum of a constant plus na random loan returns that are driven by either f I or f N. 20 While the specific slope shown in Fig. 5 is an artifact of the underlying numerical assumptions, the implicit function theorem can be used to analytically demonstrate that the slope of this supply curve will be increasing for all undercollateralized loans.

21 Such risk would, however, continue to exist if the perception of the penalty is driven by the political economy considerations discussed in footnote 17. 22 As mentioned earlier, interlinkage internalizes the externality effect that insurance purchase has on lender earnings. In this sense, the interlinkage logic is quite similar to Braverman and Stiglitz (1982) in which externality effects from one contract (loans in their case) create gains when bundled with another contract (sharecropping contracts in the Braverman and Stiglitz analysis). 23 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 returning alternative. Boucher et al. (2008) present evidence that upwards of 20% of small scale producers in (relatively high collateral) Latin American environments are risk rationed and produce at the same input and income levels as farmers who completely lack access to capital.

66

M.R. Carter et al. / Journal of Development Economics 118 (2016) 59–71

credit in the low collateral environment reduce contractual interest rates, crowding-in credit demand and the adoption of the improved technology. 4.1. 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 utility maximization, we can write the expected utility value of using the traditional technology (VT) and the improved technology (VH) as: Zθ VT ¼

uðθgT þ W þ BÞf ðθÞdθ

ð15Þ

0

Zθ   V H ¼ F ~θ uðcÞ þ uðθg H −ð1 þ rÞK þ W þ BÞf ðθÞdθ:

ð16Þ

~θ

Recall that c ¼ W þ 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. We assume that the household will choose high technology and to take the loan contract if ΔH = VH − VT N 0. Using the expressions above, we can rewrite ΔH as: 2

3 Z~θ   6 ~ 7 Δ ¼ 4 F θ uðc Þ− uðθg T þ W þ BÞf ðθÞdθ5 H

0 2 3 Zθ 6 7 þ 4 ½uðθgH −ð1 þ r ÞK þ W þ BÞ−uðθg T þ W þ BÞf ðθÞdθ5; ð17Þ ~ θ

where the first term in square brackets is strictly negative (even when χ = 0) indicating that the traditional technology outperforms (in utility terms) the improved technology in bad states of the world (as shown in Fig. 1). The second term in square brackets is non-negative and represents the expected utility gains for better states of the world (θN~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. (2008) 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 (πa ) are higher, reducing the size of the second term and again making it possible that some risk averse agents will choose the traditional technology. Fig. 6 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 our base case agro-ecological scenario and that the lender's loan portfolio is comprised exclusively of agricultural loans (na = 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 absent insurance, risk blocks the adoption of the high technology in the lowest and the highest collateral environments. The solid line shows that the certainty equivalent of adopting the new technology without insurance falls below the certainty equivalent of the traditional technologies for collateral levels below 15% of the loan amount and

Fig. 6. Insurance and choice of technology.

more than 75% of the loan amount. Perhaps somewhat surprisingly, the certainty equivalent of adopting the technology increases over some range with the collateral requirement. This increase 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 ΔH 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. 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.24 The expected utility value of adopting the improved technology and purchasing the standalone insurance contract is given by:  I  Zθ I V I ¼ U ðc ÞF I ~θ þ U ½θg H −ð1 þ r ÞK þ W þ B f ðθÞdθ: ~θI

Denote the expected utility gain of standalone insurance relative to the traditional technology as ΔI = VI − VT. After adding and subtracting expected utility associated with the uninsured adoption of the high technology (VH), this gain can be rewritten as: ΔI ¼ ½V I −V H þV H −V T ¼V I −V H  þ ΔH : To understand whether and when index insurance crowds in the adoption of the high technology by households that would not 24 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 = 0 then it is when θ ¼ ~θ.

M.R. Carter et al. / Journal of Development Economics 118 (2016) 59–71

otherwise use it, we are especially interested in the risk rationing case in which ΔH b 0. Note that in order for the standalone insurance to have these impacts, it must be the case that [VI − VH] N −ΔH N 0. We can gain further insight on the conditions under which insurance induces the risk-rationed to adopt the high technology by examining the relatively favorable case in which the standalone insurance is actuI arially fair, meaning that β = 0 and that ~θ ¼ ~θ. Under this assumption we can rewrite [VI − VH] as:   h    i Zθ I U ðc Þ F I ~θ −F ~θ þ U ½θgh −ð1 þ r ÞK þ W þ B f ðθÞ−f ðθÞ dθ:

ð18Þ

~θ

After integrating twice by parts, we have:

0

½V I −V H  ¼ U ðc Þg h

Z~θ h

2 3 Zθ Zθ  i  I F ðθÞ− F ðθÞ dθ þ 4 F ðyÞ− F ðyÞ dy5U ″ g 2h dθ: I

0

~θ

ð19Þ

0

If we assume that idiosyncratic risk is limited such that θ is a meanpreserving spread of θI (see note 8 above), the first term on the right hand side of Eq. (19) is negative for all under-collateralized loan contracts (with ~θN0), 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 under-collateralized is lower than that under no insurance.25 This drop in expected consumption occurs because some of the 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. It is important to stress that this result holds even under the highly favorable assumption of limited idiosyncratic risk. The second term on the right hand side of Eq. (19) measures the increase in expected utility that results because index insurance reduces fluctuations in consumption. The 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 ¼ 0 and the first term of Eq. (19) is equal to zero. Hence, [VI − VH] 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 ΔH b 0. If the standalone insurance is not actuarially fair, then this likelihood decreases. Returning to our base case agro-ecological scenario (in which basis risk is more less severe), we use the numerical analysis presented in Fig. 6 to explore the complex interactions between insurance and technology up-take. The widely-spread dotted line shows the certainty equivalent of VI as a percentage of that of low technology under the assumptions detailed above, assuming that the index insurance is priced 25 Denoting the expected consumption under standalone insurance and without insurance as EI and EH, the change of expected consumption (conditional on adoption of the high technology) is equal to

h  i Zθ h i I EI −EH ¼ χ F I ~θ − ½θg H ðK Þ−ð1 þ r ÞK  f ðθÞ− f ðθÞ dθ ~θ

Integrating by parts and using the properties of mean-preserving spread (equation ?? and ??), the above expression reduces to:

EI −EH ¼ g H

Z~θ h

i F I ðθÞ−F ðθÞ dθb0

0

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.

67

30% above the actuarially fair rate. We see that the certainty equivalent under standalone insurance is below the certainty equivalent of adopting the technology without insurance (i.e., [VI − VH] b 0) for collateral levels less than 40% of the loan value. For these low collateral levels, 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 (2009) (VH). For very high collateral levels (great than 75% of loan value), standalone insurance crowds in adoption of the high technology in high collateral situations. 4.3. 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 under-collateralized 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:  L  Zθ  

I V L ¼ U ðc ÞF I ~θ þ U θg H − 1 þ rL K þ W þ B f ðθÞdθ;

ð22Þ

~θL L

where r L ¼ rðπa jχ; f Þ and ~θ ¼ ð1þr I

L

ÞK−χþβ gH

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: ΔL ¼ V L −V T ¼ ½V L −V I þV I −V H  þ ΔH ;

ð23Þ

where the new term [VL − VI] represents the expected utility gain from insurance interlinkage relative to standalone insurance. Assuming that the index insurance contract is actuarially fair (β = 0), this additional gain from interlinkage can be expressed as: Z ½V L −V I  ¼

θ

Z~θ þ



 I   U θgH − 1 þ rL K þ W−UθgH −ð1 þ r ÞK þ W þ B f ðθÞdθ

ð24Þ

~ θ

  I  

U θgH − 1 þ r L K þ W þ B −U ðc Þ f ðθÞdθ: L

~ θ

The discussion in Section 3 indicates that rL b r if loans are not fully L collateralized with χbð1 þ πÞK; rL = r and thus ~θ ¼ θ~ when loans are fully collateralized with χ ¼ ð1 þ πÞK. As can be seen from inspection of Eq. (24), this gain will be positive for all under-collateralized loans I (such that ~θN~θ N0).26 When loans are fully collateralized [VL − VI] = 0, and there are no further gains to interlinkage. From the farm household's perspective, interlinked insurance is always at least as good as noninterlinked insurance (ΔL − ΔI ≥ 0), with this differential decreasing in collateral χ. In this sense, interlinked insurance serves as a collateral substitute. The dashed line in Fig. 6 denotes the certainty equivalent of interlinked insurance, VL under the assumptions enumerated above. As can be seen, the gap between interlinked and standalone insurance, ΔL − ΔI, is largest at low collateral levels, as expected. Whereas requiring standalone insurance would be ineffective and even counterproductive at low collateral levels, the certainty equivalent of interlinked insurance always dominates both self-insurance and adoption of the high technology without insurance. While this result is not general, 26

L

When θ≥ ~θ , θgH − (1 + rL)K ≥ −χ and hence θgH − (1 + rL)K + W + B ≥ c.

68

M.R. Carter et al. / Journal of Development Economics 118 (2016) 59–71

we turn in the next section to explore the likely impacts of index insurance across a range of different environments and given a distribution of agent types. 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 a risk structure that is relatively favorable to index insurance. While attentive to the impact of different property rights regimes on the functioning of index insurance, the prior analysis did not address three key issues: 1. Economies are characterized by heterogeneous agents who differ in both their levels of wealth and their degree of risk aversion. 2. Individual decisions to borrow generate pecuniary externalities for others by influencing the cost of capital to the agricultural sector, π a and thereby the ultimate equilibrium extent of adoption. 3. The structure of risk varies across agro-ecological regions, both in terms of its overall magnitude, as well as the degree to which risk is correlated across individuals and hence insurable with an index contract. This section generalizes the prior analysis, exploring the impacts of index insurance on equilibrium technology adoption across a variety of agro-ecological environments.

technology equals average earnings under the traditional technology, this assumption means that the modal agent can qualify for any loan that requires no more than a 50% collateral requirement. Across the overall economy, household wealth varies from zero to 100% of average low technology income, while constant relative risk aversion ranges between 0 and 4. Extending the notation developed in the prior section, let ΔH pq be the difference in expected utility from adopting the high technology without insurance versus adopting the low technology for a type p,q agent. The technology adoption indicator function h  i N ¼ 1Hpq r πa jχ; f

(

h  i N a 1 if ΔHpq r π jχ; f N0 0; otherwise

takes on the value of one when its logical argument is true and is otherwise zero. The indicator functions 1Ipq and 1Lpq are similarly defined for the cases of technology adoption under standalone and interlinked index insurance. Using this indicator function, we can define the market demand for credit as the number of adopters of the high technology. Absent informal insurance, the number of agents demanding agricultural loans of size K can be written as: Q P X h  i   X N : mpq 1Hpq r πa jχ; f nHd π a jχ; f ¼ p¼1 q¼1

We denote the analog expressions for loan demand under standalone a

5.1. Household heterogeneity and financial market equilibrium Consider an economy comprised of M agents. Each agent is characterized by a level of constant relative risk aversion, ψ, and an initial wealth, W. Let p = 1,P index the discrete levels of risk aversion, and q = 1,Q index the discrete levels of initial wealth, and mpq measure the number of agents with risk aversion p and wealth q such that P

Q

∑ ∑ mpq ¼ M . For purposes of the numerical simulation, we will

p¼1 q¼1

assume that risk aversion and initial wealth are uncorrelated in the population and that the joint distribution of agents over the W,ψ space is represented by the level curves imposed on Fig. 7. We assume a smooth, symmetric, single-peaked probability structure with the modal agent having constant relative risk aversion equal to 2 and a wealth level equivalent to 50% of the arage income under the traditional technology. Under our numerical specification, in which the capital costs of the new

Fig. 7. Equilibrium technology adoption.

I

a

I

and interlinked cases as nId ðπ jχ; f Þ and nLd ðπ jχ; f Þ, respectively. As defined by Eq. (14) above, the market supply or offer curve for agricultural loans of size K in the absence of insurance is given by:   N na π a jχ; f ; π :

ð25Þ

This same supply function will characterize the number of loans offered under standalone insurance, whereas we denote supply under a

I

interlinked insurance as na ðπ jχ; f Þ. Credit market equilibrium is defined as the cost of agricultural a capital, π , that equates the supply and demand for credit. For the una insured case, π fulfills the following condition:     N N nHa πa jχ; f ; π ¼ nd πa jχ; f :

ð26Þ

Note that these demand and supply relationships have the usual slopes. Low levels of adoption and borrowing will lead to a drop in the cost of agricultural loans (via the portfolio risk mechanism discussed in Section 3 above), whereas high levels of adoption will induce an increase in the cost of capital, choking back adoption. Analog conditions will define credit market equilibrium in the presence of standalone and interlinked insurance. Using our base case agro-ecological scenario, which is favorable for index insurance, Fig. 7 shows the equilibrium uptake of the high technology for an economy with agents distributed across wealth-risk aversion space as shown by the contour lines. For purposes of this diagram, we assume that loans require collateral equal to one third of the loan amount. All agents with initial wealth less than 33% are rationed out of the loan market. The solid line in the figure partitions the wealthrisk aversion space into those who would adopt the new technology (southeast of the line) absent insurance and those who would not (the higher levels of risk aversion or lower wealth to the northwest of the solid line). In the language of Boucher et al. (2008), non-adopting agents with wealth in excess of 33% of the low technology average are risk-rationed in the sense that that they qualify for a loan contract, but prefer not to borrow given the riskiness of the high technology activity and the available loan contract. Under the numerical specification used

M.R. Carter et al. / Journal of Development Economics 118 (2016) 59–71

to draw the base case scenario in Fig. 7, about 35% of all agents in the economy would adopt the high technology in the absence of formal insurance. The dotted line in the figure illustrates the shift in technology uptake that occurs when standalone insurance is offered, while the dashed line illustrates the shift that follows the introduction of interlinked insurance. Because we assume that loans are only partially collateralized, the largest impacts occur with the introduction of interlinked insurance. Under the numerical specification used to generate the figure, standalone insurance boosts technology uptake by about 10 percentage points, while insurance interlinkage boosts it another 20 percentage points so that total technology uptake rises to about 65% of the total population. Neither insurance contract has any impact on low wealth agents who cannot meet the collateral requirements. Insurance, does, however, substantially diminish the fraction of the population that is risk-rationed and would otherwise retreat into self-insurance rather than take on the risk of the high technology. Consistent with Clarke (forthcoming), it is the most risk averse agents who do not purchase insurance and adopt the improved technology. Under the base case agro-ecological scenario illustrated in Fig. 7 index insurance–particularly interlinked index insurance–effectively crowds in entrepreneurial risk-taking by the stylized small farmer population, almost doubling the uptake of the improved technology. But how general is this result, both as collateral rules change and as the structure of risk varies across distinct kinds of agro-ecological environments?

69

When limited liability disappears under the weight of a 100% collateral requirement, technology uptake drops to around 35%, with that drop largely driven by a quantity rationing (agents who lack the collateral wealth to qualify for a loan contract). A second type of environment is found in the southern region of the risk space. In this region, risk is relatively high (with a coefficient of yield variation in excess of 35%), but a majority of the risk is idiosyncratic and not covered by index insurance. The increase in risk pushes down adoption rates substantially in both low and high collateral environments compared to the low risk environment. While risk thus becomes a constraint, index insurance is ineffective at ameliorating it and has minimal impact on technology uptake. A final type of environment is found in the eastern portion of the risk space where risk is high and at least half of all risk is covariant. In high collateral environments, insurance of either sort almost doubles technology uptake, boosting it by 20 percentage points. Quantity rationing, however, remains a problem as many farms are unable to quality for the credit needed to adopt the new technology. In low collateral environments, standalone insurance is almost completely ineffective, whereas interlinked insurance boosts technology uptake by 50 to 60 percentage points, meaning technology adoption becomes nearly complete in this environment when index insurance becomes available. As stressed at the end of Section 4, the effectiveness of index insurance–interlinked or otherwise–is predicated on an area yield or other index which accurately predicts average losses and insulates the lender's portfolio from large-scale, correlated default events.

5.2. Where does index insurance make sense? 6. Conclusions: where and how index insurance can have impacts The base case agro-ecological scenario assumed that production risk was relatively large and predominately covariant (and hence insurable with index insurance). However, there are a multiplicity of agroecologies, including some where yield risk is less (e.g., irrigated rice systems), and others where the proportion of yield risk that is correlated across individuals, and insurable with an index contract is modest (e.g., mountainous areas with extreme spatial variability in yields). To explore the effectiveness of index insurance across a variety of environments, the 3-dimensional graphs in Fig. 8 replicate the Section 5.1 analysis of equilibrium technology uptake across an array of agro-ecological environments. Each point in the x–y plane that forms the base of each graph represents a different type of agro-ecological environment, ranging from low risk to high risk along one dimension (as measured by the coefficient of variation of yields), and ranging from largely idiosyncratic risk to completely covariant risk along the other. The eastern corner of the plane should be most favorable to index insurance impacts (risk is high and largely covariant), whereas the opposite is true on the western corner of the plane (low, largely idiosyncratic risk). Two property rights regimes or collateral regimes are illustrated. The figures in the left column illustrate the case of zero collateral, whereas those in the right column illustrate a high collateral environment. Finally, the first row of figures illustrates the total percentage of the populations that adopts the new technology absent insurance. The second and third rows respectively show the incremental impact of standalone and interlinked insurance contracts on the technology uptake rate. Recall that the base case agro-ecological scenario analyzed above assumes a coefficient of variation of 38%, with 80% of that variation coming from covariant sources.27 Fig. 8 identifies three distinct regions. The first is the low risk environments in the west/northwest portion of the space where the coefficient of variation of yields is below about 35%. In these environments, our model predicts that index insurance has no impact on technology uptake. When there is no collateral required in this low risk environment, then the implicit insurance offered by the limited liability loan contract suffices to almost completely crowd in technology adoption. 27 The base case analysis assumed a 30% collateral requirement and is thus in between the two scenarios illustrated in Fig. 8.

Agricultural index insurance has gained prominence as a potential solution to long-standing problem of low rates of adoption of improved agricultural technologies, especially in risk-prone regions of SubSaharan Africa. While several new studies give evidence that index insurance can boost adoption of new technologies (Elabed and Carter, 2014; Karlan et al., 2014; Mobarak and Rosenzweig, 2013), other pilot projects have struggled with low rates of purchase of insurance. Indeed, one carefully implemented study found that insurance actually reduced adoption of a new cropping opportunity (Giné and Yang, 2009). Given the importance of this topic, and these puzzling empirical findings, this paper has stepped back and formally modeled the impact of insurance on the adoption of a stylized improved technology. Several insights emerge from this theoretical impact exercise. First, there are a number of agro-ecological and economic environments in which index insurance is unlikely to have an impact on technology adoption. This zero impact scenario can occur either because risk is intrinsically low, or because risk is adequately covered by low collateral, limited liability loan contracts. If required collateral levels are high, adoption rates may still be low in these environments, but the solution to the adoption problem will be found in finding collateral substitutes and not from risk transfer arrangements. A second kind of environment in which index insurance is predicted to be ineffective is one in which risk is high and indeed constrains technology adoption, but yield risk is not well-covered by an insurance index. The analysis here has assumed an area yield-based index insurance that fails only because of idiosyncratic events. However, contract failure occurs even if risk is covariant, if the underlying insurance index does not reliably predict average yield outcomes (see Clarke et al., 2012). In this latter case, technology uptake could be boosted through the innovation of insurance indexes that better track yields, such as area yield indexes or perhaps improved satellite measures that better predict crop yields than do the simple rainfall indexes that have been piloted in many places (see Carter et al., 2014). While these are important limitations, the analysis here has also shown that when risk is large, and largely covariant, index insurance can have a substantial impact on the uptake of improved technological and economic opportunities. In the stylized equilibrium simulations,

70

M.R. Carter et al. / Journal of Development Economics 118 (2016) 59–71

Fig. 8. Impact of index insurance in different agro-ecological and collateral environments.

insurance boosts equilibrium uptake of the new technology from as little as 20% of the population to as much as 80% of the population. While large, these impacts are not out of line with the empirical studies that have found statistically and economically significant investment impacts of insurance in the risky rain-fed environments of West Africa (Elabed and Carter, 2014; Karlan et al., 2014). A final insight emerging from the analysis here is that how index insurance is implemented depends critically on the collateral or property

rights structure surrounding agricultural lending. In low collateral environments, such as those found in areas of sub-Saharan Africa, index insurance is shown to only be effective if it is explicitly interlinked with credit contracts.28 In this low collateral environment, substantial risk 28 However, as Elabed and Carter (2014) note based on their experience in Mali, formally uncollateralized loans may be highly collateralized informally at the level of a local borrowing group.

M.R. Carter et al. / Journal of Development Economics 118 (2016) 59–71

is carried by the lender, and interlinkage of credit with insurance internalizes the positive externality that insurance has on the stability of the lender's loan portfolio. Without this interlinkage, index insurance is likely to be ineffective as insurance purchased by the farm household primarily benefits the lender. In addition, as stressed throughout this paper, the efficacy of interlinked insurance requires a high quality index (such as an area yield index) that accurately captures average losses and insulates lender portfolios from correlated defaults driven by covariant shocks. The story is rather different in high collateral environments (or if the technology is simply self-financed by the farm household). In that environment, standalone index insurance is adequate to boost the adoption of higher returning, but risky technologies when risks are well covered by index insurance. In conclusion, from a theoretical perspective, index insurance can, in the right environment and done in the right way, serve to incentivize the uptake of improved technologies by the small-scale farming sector. It is not, however, a panacea for all environments, and will certainly be ineffective if too much of the risk is idiosyncratic or if the index itself is poorly designed and fails to cover a substantial amount of the risk that farm households face. Acknowledgment This work has benefited from exceptionally thoughtful comments provided by referees of this journal as well as those by seminar participants at the University of California, San Diego; the University of California, Davis; Montana State University; the 2012 American Agricultural and Applied Economics Association annual meeting; the 2012 I4 Index Insurance Innovation Initiative workshop; and, the 2011 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-L12-00001 with the BASIS Feed the Future Innovation Lab. Neither supporting nor employing institutions are responsible for the ideas and opinions expressed in this paper. Appendix A. Numerical specification This appendix details the functional form and specific parameter assumptions used in the numerical analysis. • Technology parameters - Traditional technology: gT = 10 - High technology: yH = θ * 25 * K, where K = 10 - Random shocks: ⁎ Total shock, θ: E(θ) = 1 and θ∈[0,2] ⁎ Covariant shock, θc: E(θc) = 1 ⁎ Idiosyncratic shock: E(θs) = 0 ⁎ Both shocks are considered to be independent and distributed with a truncated normal distribution • Preference parameters 1−ψ - CRRA utility function: uðxÞ ¼ ðxÞ 1−ψ • Insurance contract parameters

71

- Normalized actuarially fair premium: z ¼ E½1ð^θc Nθc Þð^θc −θc Þ - Mark-up: zgβ ¼ 30% H - Threshold payment parameter (strike point): ^θc ¼ 1 • Financial system parameters - Risk free opportunity cost of capital: π ¼ 20% g g ~ ~ ¼ 8%, α = 10 ~ Þ ¼ α  ðΠ−Π Þ, where Π - Penalty function: ΩðΠ−Π • Population distribution - Total population: M = 1001 - Risk aversion: ψ∈[0,4] - Normalized initial wealth: W gT ∈ [0.1, 1.5] - Joint distribution of ϕ and W g T : Normalized variables independently distributed as Beta(2, 2) References Bank, World, 2007. Agriculture for Development: World Development Report 2008. World Bank. Barnett, B.J., Barrett, C.B., Skees, J.R., 2008. Poverty traps and index-based risk transfer products. World Dev. 36 (10), 1766–1785. Bester, H., 1987. The Role of Collateral in Credit Markets with Imperfect Information. Boucher, S., Carter, M.R., Guirkinger, C., 2008. Risk rationing and wealth effects in credit markets: theory and implications for agricultural development. Am. J. Agric. Econ. 90 (2), 409–423. Braverman, A., Stiglitz, J.E., 1982. Sharecropping and the interlinking of agrarian markets. Am. Econ. Rev. 72 (4). http://dx.doi.org/10.2307/1810011. Bryan, G., 2013. Ambiguity Aversion Decreases the Impact of Partial Insurance: Evidence from African Farmers. Carter, M.R., 2012. Designed for development impact: next generation approaches to index insurance for small farmers Vol. Microinsurance Compendium vol. II. International Labor Organization. Carter, M.R., de Janvry, A., Sadoulet, E., Sarris, A., 2014. Index-based weather insurance for developing countries: a review of evidence and a set of propositions for up-scaling. FERDI Working Paper 112. Castillo, M.J., Carter, M.R., Boucher, S.R., 2014. Index Insurance: Innovative Financial Technology to Break the Cycle of Risk and Rural Poverty in Ecuador. Clarke, D., 2015. A theory of rational demand for insurance. Am. Eco. J. Microeconomics (forthcoming). Clarke, D., Mahul, O., Rao, K.N., Verma, N., 2012. Weather based crop insurance in india. Policy Research Paper 5985. World Bank (March). Elabed, G., Carter, M.R., 2014. Ex-ante impacts of agricultural insurance: evidence from a field experiment in mali. Working Paper. Elabed, G., Carter, M.R., 2015. Compound-risk aversion, ambiguity and the willingness to pay for microinsurance. J. Econ. Behav. Organ. Feder, G., Just, R., Zilberman, D., 1985. Adoption of agricultural innovations in developing countries: a survey. Econ. Dev. Cult. Chang. 255–298. Giné, X., Yang, D., 2009. Insurance, credit, and technology adoption: field experimental evidence from Malawi. J. Dev. Econ. 89 (1), 1–11. http://dx.doi.org/10.1016/j. jdeveco.2008.09.007 (May). Halcrow, H., 1949. Actuarial structures for crop insurance. J. Farm Econ. 21, 15–28. Hazell, P.B.R., 1992. The appropriate role of agricultural insurance in developing countries. J. Int. Dev. 4 (6), 567–581. http://dx.doi.org/10.1002/jid.3380040602. International Fund for Agricultural Development World Food Program, 2010. The potential for scale and sustainability in weather index insurance for agriculture and rural livelihoods. Tech. rep. Karlan, D., Osei, R., Osei-Akoto, I., Udry, C., 2014. Agricultural decisions after relaxing risk and credit constraints. Q. J. Econ. 129 (2), 597–652. McIntosch, C., Sarris, A., Papadopoulos, F., 2013. Productivity, credit, risk, and the demand for weather index insurance in smallholder agriculture in ethiopia. Agric. Econ. 44 (4–5), 399–417. Miranda, M.J., Farrin, K., Romero-Aguilar, R., 2012. Weather index insurance for developing countries. Applied Economics Perspectives and Policy. Mobarak, M., Rosenzweig, M., 2013. Risk, Insurance and Wages in General Equilibrium. Stiglitz, J.E., Weiss, A., 1981. Credit rationing in markets with imperfect information. Am. Econ. Rev. 71 (3), 393–410. http://dx.doi.org/10.2307/1802787. Tarazona, A., Trivelli, C., 2005. Situación del financiamiento rural en piura. BASIS Brief.