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The Impact of Interlinked Insurance and Credit Contracts on Financial Market Deepening and Small Farm Productivity Michael Carter, Lan Cheng & Alexander Sarris June 2011 Michael Carter, Lan Cheng & Alexander Sarris Insurance-Credit

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The Impact of Interlinked Insurance and Credit Contracts on Financial Market Deepening and Small Farm Productivity

Michael Carter, Lan Cheng & Alexander Sarris June 2011

Michael Carter, Lan Cheng & Alexander Sarris Insurance-Credit Interlinkage

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Summary

Twin puzzles

Ample evidence that uninsured risk depresses small holder productivity and the development of rural financial markets Yet, to date it has proven hard to sustain formal agricultural insurance despite apparent need (Gine/Yang; Sarris et al.)

Explore prospects for resolving these twin puzzles with formal theory of the behavior of smallholder household and a competitive sector of rural lenders Demonstrate that

Neither credit nor insurance markets likely to fully develop in isolation However, “interlinking” these markets and contracts is more likely to succeed How interlinkage works depends on collateral environment Insurance subsidies may be smart Account theoretically for some surprising empirical results

Michael Carter, Lan Cheng & Alexander Sarris Insurance-Credit Interlinkage

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Outline

Small farm household model

Technology choices & self-insurance Credit contracts & collateral environments Index insurance as ’mean preserving squeeze’

Competitive lender model

Iso-expected profit contract locus (partial equilibrium) Interlinkage pivots contract locus Portfolio composition & supply price of risky ag credit

Partial Equilibrium Analysis of Technology Choice (exogenous cost of capital to agriculture)

No insurance baseline Independent & interlinked index insurance

Numerical Simulation of Equilibrium Credit Market

Agents differentiated by wealth & risk aversion Credit market equilibrium concept Technology choice with & without index insurance Are insurance subsidies ’smart’?

Michael Carter, Lan Cheng & Alexander Sarris Insurance-Credit Interlinkage

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Household Model

Technology & self-insurance

’Safe,’ low yielding technology: yℓ = θgℓ; ρℓ = yℓ where θ = (θc + θs) with support [0, ¯ ¯ θ] , pdf f (θ), cdf F(θ) and E(θ) = 1. Capital-using, high returning technology: yh = θgh(K), where K is the amount of purchased inputs and we assume that gh > gℓ .

Michael Carter, Lan Cheng & Alexander Sarris Insurance-Credit Interlinkage

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Household Model

Technology & self-insurance

To buy K need loan contract, denoted ℓ < K, r, χ > and returns to household are: ρh =

θgh(K) − (1 + r)K, if θ > ˜

θ −χ, otherwise , where ˜ θ = (1+r)K−χ

gh(K)

just permits full loan repayment Consider case where high technology profitable for all: E[ρh] > E[ρℓ] > 0 Implies that no one will be price-rationed out of credit market as always have a profitable project Consumption: ct = B + ρt + W , t = h, ℓ, and lowest possible consumption under high technology is c = B + W − χ.

Michael Carter, Lan Cheng & Alexander Sarris Insurance-Credit Interlinkage

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Household Model

Collateral & Returns

Michael Carter, Lan Cheng & Alexander Sarris Insurance-Credit Interlinkage

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Low Technology as Self Insurance

Basis risk & actuarially unfair

Michael Carter, Lan Cheng & Alexander Sarris Insurance-Credit Interlinkage

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Index Insurance

Express as mean preserving ’squeeze’

Index insurance contract, It < ˆ θc, zt, β >, pays off when covariant shock (θc) is less than ˆ θc the strike point; has actuarially fair premium zt (normalized by gt); and a markup β. Payoff to insured producers given by: yI

t =

(θc + θs)gt + (ˆ

θc − θc)gt − ztgt − β = (ˆ θc + θs − zt)gt − β, if θ (θc + θs)gt − ztgt − β, = (θc + θs − zt)gt − β otherwise By defintion of actuarial fairness: ztgt = gtE[1( ˆ θc > θc)(ˆ θc − θc)]. Under insurance, gross farm income is determined by transformed random variable: θI = θ + s(θ) where s(θ) = 1( ˆ θc > θc)( ˆ θc − θc) − zt where E[θI] = E[θ] = 1 and pdf [cdf], f I [F I] is a mean preserving squeeze of f :

Michael Carter, Lan Cheng & Alexander Sarris Insurance-Credit Interlinkage

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Mean Preserving Squeeze

Key integral properties

ˆ ¯

¯ θ

[F(θ) − F I(θ)]dθ = 0; ˆ y [F(θ) − F I(θ)]dθ > 0 ∀y < ¯ ¯ θ

Michael Carter, Lan Cheng & Alexander Sarris Insurance-Credit Interlinkage

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Intuition on Index Insurance

Can it stochastically dominate self-insurance?

Michael Carter, Lan Cheng & Alexander Sarris Insurance-Credit Interlinkage

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Competitive Credit Market Model

Three interest rates matter in the model:

¯ π is the exogeous (risk-free) opportunity cost of capital ¯ πa is the portfolio risk adjusted interested rate that a lender must earn on its agricultural loan portfolio r is the nominal interest charged to an individual borrower

r(χ|¯ πa) ≥ ¯ πa(na) ≥ ¯ π Let’s look at each of these in turn

Michael Carter, Lan Cheng & Alexander Sarris Insurance-Credit Interlinkage

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Competitive Credit Market Model

Iso-expected profit contract locus

Under standard loan contract ℓ(K, r, χ), lender profits are: π =

rK, if θ > ˜

θ χ + θgh(K) − K, otherwise . Under this specification, lender profits are concave in the random variable θ and expected lender earnings are: E(π) = [1 − F( ˜ ˜ θ)]rK +

˜

θ ˆ (χ + θgh(K) − K)f (θ)dθ . Iso-expected profit locus defined by the interest rate-collateral combinations that just yield expected returns equal to ¯ πa.

∂r ∂χ = −F(˜ θ) 1−F(˜ θ))K < 0

Michael Carter, Lan Cheng & Alexander Sarris Insurance-Credit Interlinkage

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Competive Credit Market Model

Iso-expected profit locus & interlinkage

Michael Carter, Lan Cheng & Alexander Sarris Insurance-Credit Interlinkage

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Competitive Credit Market Model

Insurance-Credit Interlinkage

A credit contract is interlinked with insurance when the bank has first claim on insurance proceeds and thus treats its returns as driven by the insured probability functions f I and F I The insured iso-expected profit will lie below uninsured locus for all undercollateralized contracts (see figure again)

Michael Carter, Lan Cheng & Alexander Sarris Insurance-Credit Interlinkage

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Competitive Credit Market Model

Portfolio composition and supply price of risky credit

Assume lender has funds for n loans of size K that can divided between agricultural loans (na) and non-agricultural loans (nb) that pay ¯ π for certain Lender’s gross rate of return on the portfolio of n loans will be given by: G = nA

i=1 π(θi)/K + nb¯

π n . Because of reserve requirements and political economy risk, lender faces a penalty function, P(G), that reduces net lender portfolio returns when G falls below a critical threshold level ˜ π. Net portfolio returns (N) are given by: N = G if G > ˜ π G − P(G) otherwise, with P

′, P ′′ ≤ 0 Michael Carter, Lan Cheng & Alexander Sarris Insurance-Credit Interlinkage

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Competitive Credit Market Model

Market Supply of Agricultural Credit

To supply na agricultural loans, the lender must fulfill a standard, zero profit participation constraint: E(N) ≥ ¯ π Letting ¯ πa denote E(πi), and FG (fG) denote the cdf (pdf) of G, this condition can be rewriten as: ¯ π + na n ( ¯ πa − ¯ π) −

˜ π

ˆ P(G)fG(G)dG ≥ ¯ π This condition implicitly defines the market supply function, ¯ πa(na) By elminating covariant risk, index insurance (which is a mean preserving squeeze of fG) flattens this supply relationship

Michael Carter, Lan Cheng & Alexander Sarris Insurance-Credit Interlinkage

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Competitive Lender Model

Portfolio composition and supply price of risky credit

Michael Carter, Lan Cheng & Alexander Sarris Insurance-Credit Interlinkage

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Techology Uptake Absent Formal Insurance

Expected utility under low technology (self-insurance via income smoothing): Vℓ =

¯ ¯ θ

ˆ u(θgℓ + W + B)f (θ)dθ Expected utility under high technology (some implicit insurance if limited liability): Vh = F(˜ θ)u(c) +

¯ ¯ θ

ˆ

˜ θ

u(θgh − (1 + r)K + W + B)f (θ)dθ

Michael Carter, Lan Cheng & Alexander Sarris Insurance-Credit Interlinkage

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Technology Uptake Absent Formal Insurance

Farmers’ decision on technology: ∆hℓ = Vh − Vℓ =   F(˜ θ)u(c) −

˜ θ

ˆ u(θgℓ + W + B)f (θ)dθ    +   

¯ ¯ θ

ˆ

˜ θ

[u(θgh − (1 + r)K + W + B) − u(θgℓ + W + B)]f (θ)dθ    First term is negative, second term is non-negative Under high collateral, c is low and risk averse may choose low technology(risk rationing) Under low collateral, lending is risky, r is high and risk averse may also choose low technology

Michael Carter, Lan Cheng & Alexander Sarris Insurance-Credit Interlinkage

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Technology Uptake under Alternative Insurance Schemes

Highly risk averse farmers (CRRA=3) & na = N

Michael Carter, Lan Cheng & Alexander Sarris Insurance-Credit Interlinkage

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Technology Uptake under Index Insurance

High tech with non-interlinked index insurance V I

h = U(c)F I(˜

θ) +

¯ ¯ θ

ˆ

˜ θ

U[θgh − (1 + r)K + W + B]f I(θ)dθ Decision on technology: ∆I

hℓ = V I h − Vℓ = (V I h − Vh) + (Vh − Vℓ) = ∆I hh + ∆hℓ

The change in expected consumption under limited liability loan contract (actuarially fair contract is not ’fair’): E(cI

h) − E(ch) = gh ˜ θ

ˆ [F I(θ) − F(θ)]dθ ≤ 0

Michael Carter, Lan Cheng & Alexander Sarris Insurance-Credit Interlinkage

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Technology Uptake under Index Insurance

∆I

hh = U′(c)gh ˜ θ

ˆ [F I(θ)−F(θ)]dθ+

¯ ¯ θ

ˆ

˜ θ

[

θ

ˆ (F I(y)−F(y))dy]U′′g2

hdθ

The first term ≤ 0 ( expected consumption); the second term ≥ 0 ( consumption flunctuation) for the risk averse,

high collateral χ = (1 + r)K, ˜ θ = 0: ∆hI

h > 0

low collateral χ = 0, ˜ θ > 0: ∆I

hh is more likely to be negative

∆I

hh increases in χ

Michael Carter, Lan Cheng & Alexander Sarris Insurance-Credit Interlinkage

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Technology Uptake under Alternative Insurance Schemes

Highly risk averse farmers (CRRA=3) & na = N

Michael Carter, Lan Cheng & Alexander Sarris Insurance-Credit Interlinkage

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Technology Uptake under Interlinked Index Insurance

High tech with interlinked index insurance V II

h = U(c)F I( ˜

θI) +

¯ ¯ θ

ˆ

˜ θI

U[θgh − (1 + rI)K + W + B]f I(θ)dθ with endogenous rI = rI(χ, na, f I(θ)). Decision on technology: ∆II

hℓ = V II h − Vℓ = ∆II hh + ∆I hh + ∆hℓ

Michael Carter, Lan Cheng & Alexander Sarris Insurance-Credit Interlinkage

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Technology Uptake under Interlinked Index Insurance

∆II

hh = V II h − V I h =

´ ¯

¯ θ ˜ θ (U[θgh − (1 + rI)K + W ]−

U[θgh − (1 + r)K + W + B])f I(θ)dθ+ ´ ˜

θ ˜ θI (U[θgh − (1 + rI)K + W + B] − U(c)) f I(θ)dθ

∆II

hh ≥ 0, decreasing in χ

High collateral χ = (1 + r)K, rI = r, and ˜ θI = ˜ θ: ⇒ ∆II

hh = 0

Low collateralχ < (1 + r)K, rI < r, and ˜ θI < ˜ θ: ⇒ ∆II

hh > 0

Michael Carter, Lan Cheng & Alexander Sarris Insurance-Credit Interlinkage

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Technology Uptake under Alternative Insurance Schemes

Highly risk averse farmers (CRRA=3) & na = N

Michael Carter, Lan Cheng & Alexander Sarris Insurance-Credit Interlinkage

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Credit Market Equilibrium for Stylized Economy

Economy defined as a distribution of agents over risk aversion-wealth space, h(ψ, W ) and a collateral rule Write the aggregate supply of agricultural loans, ns

a, as a

function of the price r: ns

a = ns a(r | χ, f (θ), f I(θ), P)

Aggregate demand of agricultural loans, nd

a , is a function of

r: nd

a = nd a (r | χ, f (θ), f I(θ), h(ψ, W ))

Taking ¯ π and χ as given, market equilibrium defined by the value of r such that: ns

a = nd a = na

Michael Carter, Lan Cheng & Alexander Sarris Insurance-Credit Interlinkage

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Equilibrium Uptake of High Technology

Low Collateral Case

Michael Carter, Lan Cheng & Alexander Sarris Insurance-Credit Interlinkage

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Equilibrium Uptake of High Technology

Intermediate Collateral Case

Michael Carter, Lan Cheng & Alexander Sarris Insurance-Credit Interlinkage

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Equilibrium Uptake of High Technology

High Collateral Case

Michael Carter, Lan Cheng & Alexander Sarris Insurance-Credit Interlinkage

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Technolgy Adoption Heterogeneity

Low Collateral Case

Michael Carter, Lan Cheng & Alexander Sarris Insurance-Credit Interlinkage

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Technolgy Adoption Heterogeneity

High Collateral Case

Michael Carter, Lan Cheng & Alexander Sarris Insurance-Credit Interlinkage

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Uptake, Loadings & Smart Subsidies

High basis risk and loading costs undermine the performance

f interlinked contracts.

Is there a role for ’smart subsidies?

Calculate the tax rate that would have to be charged so that incremental tax collections on new production cover load ing costs Under ’reasonable assumptions,’ a 16% tax rate will cover a 30% loading cost

Michael Carter, Lan Cheng & Alexander Sarris Insurance-Credit Interlinkage

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Summary of Impact on Technology Uptake

Low collateral environment High collateral environment Self-insurance

Low uptake (credit expensive; induces risk rationing) Very low uptake (risk rationing) Insurance as separate contract No demand for Insurance & Technology Adoption Does Not Improve Increases uptake by reducing farmers’ risks (Demand Effect; Supply Limits) Interlinked insurance & credit Increases uptake by lowering interest rates (Supply Effect) Relaxes supply constraints

Michael Carter, Lan Cheng & Alexander Sarris Insurance-Credit Interlinkage

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Conclusions & Challenges for Program Design

Linkage with opportunity for improved technology opens the door to stochastically dominate actuarially unfair self-insurance Neither the credit market nor the insurance market can fully develop in isolation Subtle interplay with collateral requirements and implicit insurance of credit contracts Implications for determining insured party

retail insurance to farmer versus sell as insurance to lenders key question: how to simulate competitive market and shift of benefits to small farm households? State contigent loan contracts as in Ahmed=McIntosh-Sarris project is one way

Michael Carter, Lan Cheng & Alexander Sarris Insurance-Credit Interlinkage