Selling Formal Insurance to the Informally Insured

A. Mushfiq Mobarak Mark Rosenzweig

Yale University

Background • Formal insurance markets largely absent where they

are needed – 75% of the world’s poor engaged in agriculture – 90% of variation in Indian agricultural production

caused by variation in rainfall – 90% of Indians not covered by formal insurance

• Informal risk sharing networks are important – Protects against idiosyncratic risk and perhaps aggregate

risk – But risk-sharing is incomplete (Townsend 1994). Lower

risk-taking by farmers than we would want – Informal risk-sharing can drive out formal insurance,

given moral hazard (Arnott and Stiglitz, 1991) 2

Index Insurance • Low Incidence of Formal Crop Insurance

– Demand: Income/liquidity constraints, Trust/fraud – Supply: High overhead costs (moral hazard, adverse

selection) • Index-based insurance

– Payment schemes based on an exogenous publicly observable index, such as local rainfall

– Mitigates moral hazard and adverse selection • Arnott and Stiglitz (1991) analysis not directly relevant

– Eliminates the need for in-field assessments – But basis risk (Clarke 2011) – Observe low demand (Cole et al 2009, Gine and Yang

2009) 3

Setting and Approach • We design a simple index insurance contract for the

Agricultural Insurance Company of India • We randomize insurance offers to 5100 cultivators and

wage laborers across three states in India – Wage laborers face less basis risk than cultivators

• The sub-caste (jati) is the identifiable risk-sharing network that people are born into.

– Jatis can span districts or even states (permits aggregate risk sharing of village rainfall shocks)

• We make offers to jatis for whom we have rich, detailed histories of both aggregate and idiosyncratic shocks and responsiveness to shocks.

• We randomly allocate rainfall stations to some villages.

4

Research Questions 1. Demand for Insurance: – How does the presence of risk-sharing networks

affect the demand for index insurance? 2. Interaction between Index Insurance with Basis

Risk and Informal Risk Sharing: – How important is basis risk in affecting index

insurance take-up? 3. Risk Taking: – How does formal index insurance affect risk-taking

(in the presence of informal risk sharing)?

5

Research Questions (cont.)

• We use three types of variation: – Estimated variation in informal risk-sharing across

sub-castes (data from 17 states) • Using village censuses (i.e. large sample for each caste)

– Designed variation in index insurance offers (3 states)

– Designed variation in extent of basis risk (1 state)

6

Outline • Theory

– Index insurance with basis risk embedded in a model of cooperative risk sharing (Arnott-Stiglitz 1991 and Clarke 2011)

– Demand for index insurance (with basis risk) by network • (Historical) Survey Data

– Characterize jatis in terms of indemnification of idiosyncratic and aggregate losses

– Effect of informal insurance on risk-taking • Field Experiment

– Demand for formal insurance by different jatis – Effect of formal index insurance on risk-taking

7

A-S Model of Informal Risk-sharing • Game with two identical, cooperative partners and full

information • Each member faces an independent adverse event with

probability P, which causes a loss d • P can be lowered by investing in a risk-mitigating

technology e, but that also lowers w: P(e)’<0, w(e)<0. • If a farmer incurs a loss he receives a payment δ from his

partner if the partner does not incur a loss. Thus, he also pays out δ if his partner incurs a loss and he does not.

• Each partner chooses e and δ to maximize: E(U) = U0(1- P)2 + U1P2 + (1 - P)P(U2 + U3), where U0 = U(w) , U1 = U(w - d), U2 = U(w - δ), U3 = U(w - d + δ). • Arnott-Stiglitz result: informal insurance could decrease risk taking.

8

9

FOC:

e: P'[-2(1 - P)U0 + 2PU1 + (1 - 2P)(U2 + U3)] =

-w'[U0'(1- P)2 + U1'P2 + (1 - P)P(U2' + U3')

δ: (-U2' + U3')P(1 - P) = 0

So, optimal δ, δ*, is

δ* = d /2 where -U2' + U3 = 0 (A-S result)

Aggregate Risk and Index Insurance Now introduce a new aggregate risk and index insurance (No basis risk)

Probability that an adverse event causes losses for all participants = q

Loss from aggregate shock = L Index insurance payout = i

Actuarially-fair index insurance premium = qi

Assume q and P are independent. P is now idiosyncratic risk

E(U) = q [U0(1 - P)2 + U1P2 + (1 - P)P(U2 + U3)] + (1-q) [u0(1 - P)2 + u1P2 + (1 - P)P(u2 + u3)]

where U0 = U(w - L + (1 – q)i), U1 = U(w - d - L+ (1 - q)i),

U2 = U(w - δ - L + (1 -q)i), U3 = U(w - d - L + δ + (1 - q)i),

u0 = u(w - qi) , u1 = U(w - d - qi),

u2 = u(w - δ - qi), u3 = u(w - d + δ - qi)

Proposition 2: If there is no basis risk and index insurance is actuarially fair,

the partners will choose full index insurance. The demand for index insurance is independent of δ.

The FOC’s for δ and i: δ: q(-U2

’+ U3’)P(1-P)+(1-q)(-u2

’+u3’)P(1-P) = 0

i: q(1-q){[U0’(1-P)2+U1

’P2+(U2’+U3

’)P(1-P)] + [u0

’(1-P)2+u1’P2+ (u2

’+u3’)P(1-P]}=0

Thus δ * = d/2 Optimal private individual insurance remains the same i* = L Full index insurance (if actuarially fair) is optimal So aggregate risk or index insurance does not affect optimal informal payout

Informal individual insurance does not crowd out index insurance – in the absence of basis risk Intuition: index insurance and informal risk-sharing address two separate, independent risks.

Introducing Basis Risk (Clarke, 2011) • Insurance company pays out when index passes a

threshold • r = probability a payout is made by insurance

company • q and r correlated imperfectly • Basis Risk parameter ρ :

– ρ = the joint probability that there is no payout from index insurance but each community member experiences the loss L

• α = fraction of loss the agent chooses to indemnify 12

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E(U) = (r - ρ)[U0(1 - P)2 + U1P2 + (1 - P)P(U2 + U3)] + ρ[u0(1 - P)2 + u1P2 + (1 - P)P(u2 + u3)] + (q + ρ - r)[U4(1 - P)2 + U5P2 + (1 - P)P(U6 + U7)] + (1 - q - ρ)[u4(1 - P)2 + u5P2 + (1 - P)P(u6 + u7)], where U0 = U(w - L + (1 - q)αL), U1 = U(w - d - L+ (1 - q)αL), U2 = U(w - δ - L + (1 -q)αL), U3 = U(w - d - L + δ + (1 - q)αL), U4 = U(w + (1 - q)αL), U5 = U(w - d + (1 - q)αL), U6 = U(w - δ + (1 - q)αL), U7 = U(w - d + δ + (1 - q)αL), and u0 = u(w - L(1 - qα)) , u1 = U(w - d - L(1 - qα)), u2 = u(w - δ - L(1 - qα)), u3 = u(w - d + δ - L(1 - qα)), u4 = u(w - qαL), u5 = U(w - d - qαL), u6 = u(w - δ - qαL), u7 = u(w - d + δ - qαL)

Basis Risk, Index and Informal Insurance Proposition 3: Basis risk reduces the demand for index insurance. α* < 1 and dα*/dρ < 0 Proposition 4: When actuarially fair index insurance with basis risk is

purchased, the demand for index insurance is no longer independent of informal idiosyncratic risk sharing

Now, assume δ cannot achieve the optimum

(constraints?) and examine the effect of being able to increase δ on α*

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dα*/dδ =

{(1 - P)P{(r - ρ)(1 - q)(U3 - U2) - ρq(u3 - u2)

+ (q + ρ - r)(1 - q)(U7 - U6) -

(1 - q - ρ)q(u7 - u6)}/Θ,

where Θ =

(1 - q)2{(r - ρ)[U0(1 - P)2 + U1P2 + (1 - P)P(U2+ U3)] + (q + ρ - r)[U4(1 - P)2 + U5P2 + (1 - P)P(U6 + U7)]}+ q2{ρ[u0(1 - P)2 + u1P2 + (1 - P)P(u2 + u3)] + (1 - q - ρ)[u4(1 - P)2 +u5P2 + (1 - P)P(u6 + u7)]}<0

Thus, dα*/dδ 0

but dα*/dδ can be either positive or negative

Intuition • Consider two communities:

– ‘A’ has an informal risk sharing network, ‘B’ does not – The absolute worst state (incur loss d , loss L, pay the

insurance premium but receive no compensation from the contract) is worse for community B

– But, greater indemnification of the idiosyncratic loss when the aggregate loss is partially indemnified by the contract lowers the utility gain from the contract

Proposition 5: At larger values of basis risk ρ informal and formal index insurance may be more complementary. – The first term is larger and the second term is smaller – For example, with larger basis risk, the probability of the

absolute worst state gets larger.

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Implications to be Tested • When there is no basis risk, informal idiosyncratic

coverage should not affect the demand for formal index insurance.

• With larger basis risk, indemnification against idiosyncratic risk and index insurance are complements.

• Index insurance can allow more risk-taking even in the presence of informal insurance

• As wage workers face less basis risk than cultivators, a reduction in basis risk will affect wage workers less than cultivators

• If the informal network already provides index coverage, that can crowd out formal index insurance.

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Setting • Advantages of data on sub-castes:

– The risk sharing network is well defined (jati) – Exogenous (by birth, with strong penalties on inter-

marriage (<5% marry outside jati in rural India) – Jati, not village (or geography) is the relevant risk-sharing

group. Majority (61%) of informal loans and transfers originate outside the village.

– Depending on jati characteristics, both idiosyncratic and aggregate risk may get indemnified to different extents.

– We have historical (REDS) data on jati identity and transfers for a large sample (17 states, N=119,709 for census, and N=7,342 for detailed sample survey) in response to idiosyncratic and aggregate risks

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0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0

25.9

40.1 54

67.4

77.2

86.7 95 132

186

267

305

355

384

432

453

471

498

520

580

Figure 1:Lowess-Smoothed Relationship between Inter-Village Distance (Km) and June-August Rainfall Correlation, Andhra Pradesh and Uttar Pradesh 1999-2006

Key information from 2007/8 REDS 1. Amounts of “assistance received at time of difficulty”+ loans from

relatives/friends within and outside the village in 2005/6 2. Monthly rainfall in each village from 1999/2000 through 2005/6 3. History of Village-level distress events (crop loss, pest attack, drought,

cyclone/floods/hailstrorm, livestock epidemic) 1999/2000 - 2007/8 4. History of Household-specific distress events (fire, deaths of immediate

family, health problems/accidents, crop failure, theft/robbery, dry wells) 1999/2000 - 2007/8

5. Amounts of losses from each event 6. Measures taken by household to reduce impact of events after they

occurred (crop choice, improved technology, livestock immunization) 7. Caste, land holdings, education, occupation, detail for computing farm

profits (Foster and Rosenzweig, 2011). => Can estimate jati responsiveness to idiosyncratic and aggregate

shocks

19

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Distribution of Distress Event Types, 1999-2006

Distress Type Percent Village level

Crop loss 15.9 Drought 18.2 Floods/hailstorm 12.9 Pest attack 8.9 Livestock epidemic 3.1 Dry wells 3.1 Water-borne diseases 2.1 Epidemic 2.2

Household level Price increase 12.4 Crop failure 7.8 Sudden health problem 5.5 Death of immediate family member 5.1 Fire, theft, loss/damage of assets, job loss, theft/robbery, dry well 2.7

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Randomized Field Experiment • Sample drawn from 2006 REDS census data in Andhra

Pradesh, Tamil Nadu and Uttar Pradesh (63 villages, of which 21 were controls)

• Households belonging to large castes (>50 households in census) so that jati indemnification against idiosyncratic risk and aggregate risk can be precisely characterized

• Experiment: – Insurance offer randomized at caste/village level (spillovers) – Price randomized at the individual level (N=4667): 0, 10, 50

or 75% subsidy – Basis risk: 12 of 19 randomly chosen UP villages received

rainfall gauge in the village itself.

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Trigger Number

Range of Days Post Onset (varied across states and

villages)

Payout (made if less than 30-40mm (depending on state) is received at

each trigger point)

1 15-20 Rs. 300

2 20-30 Rs. 750

3 25-40 Rs. 1,200

Delayed Monsoon Onset Insurance Product

Agricultural Insurance Company of India (AICI) AICI offers area based and weather based crop insurance programs in almost 500 districts of India, covering almost 20 million farmers, making it one of the biggest crop insurers in the world.

Timing and Payout Function

Rainfall measured at the block level from AWS (Automatic weather stations)

24

1

1.08

1.38

2.6

1.0

1.1

1.3

1.6

1.0

1.1

2.1

4.9

0

10

20

30

40

50

60

70

80

Discount = 0 Discount = 10% Discount = 50% Discount= 75 %

Rainfall Insurance Take-up Rates and Average Number of Policy Units Purchased

TN

AP

UP

0

2

4

6

8

10

12

14

16

18

Cen

timet

ers

Rain per Day in 2011 Kharif Crop Season in Uttar Pradesh, by Rainfall Station

0

2

4

6

8

10

12

14

16

18

Cen

timet

ers

750

300

1200

300

Rain per Day in 2011 Kharif Crop Season in Andhra Pradesh, by Rainfall Station Insurance Payout Stations in Red (with Rupee Payout)

Identifying the strength of informal, group-based

idiosyncratic and index insurance • Need to estimate the determinants of informal indemnification δ

• Payment δijk made to household i in caste group j in village k in the event of a household-specific loss dijk or an aggregate village production shock ζk

δijk = ηij dijk +ιij ζk + μj where ηij= η(Xj, Xij), ιij= ι(Xj, Xij )

• Indemnification of shocks depends on caste and household characteristics.

• What are the relevant caste-level variables that affect the ability to pool risk? – Group’s ability to indemnify risk and avoid moral hazard depends on the

group’s level of resources, its ability to agree on common actions, its ability to diversify risk, and its ability to monitor.

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Estimate the effect of informal insurance on formal index insurance demand

• Compute from the estimates caste-specific (and household-specific) abilities to indemnify against

actual individual losses: ηj = ΣηjnXjn

aggregate shocks (index) ιij = Σ ι jnXjn

• Use estimates as determinants of formal insurance take-up

• Bootstrap standard errors (1,000 draws) clustered at caste level.

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Estimation of ηj and ιij • Problem:

– Household losses have a caste-level component:(dijk + dj) – Arnott-Stiglitz model indicates that risk-taking is endogenous

at the sub-caste level – Other unobserved caste-level characteristics might also matter.

• Solution: – Can estimate the interaction parameters ηj

n and iim even after adding caste-fixed effects to eliminate, dj , μj (and any unmeasured differences across Indian states)

– Cannot identify the effect of caste variables on the level of transfers, but they are not of direct interest here

– Caste fixed-effects accounts for other caste unobservables such as average risk aversion or how close knit the community is on average transfers

29

Bias from Moral Hazard • Schulhofer-Wohl (JPE 2012) and Mazzocco and Saini (AER

2011) argue that individual losses are correlated with individual preferences for risk, and this biases consumption/income-type tests of risk sharing.

• Unlike this literature, we use direct data on transfers in response to shocks (not income-consumption co-movements).

• However, larger transfers may lead to moral hazard, and individuals face greater shocks as a result – This cannot be true of village-level rainfall shocks (since village

location choices are unlikely to be endogenous in this context) – Arnott-Stiglitz model assumes that the network monitors moral

hazard, so this is not true in the model within castes – Caste (jati) fixed effect absorbs differences across castes in risk-

taking Hausman test: uses rainfall shocks interacted with household characteristics to

predict hh losses; cannot reject exogeneity (net of caste fixed effect) 30

Response to Aggregate Risk

31

Variable/Coefficient type Log-Odds P Log-Odds P -0.00183 -0.00046 -0.00179 0.00045

[2.41] [2.41] [2.35] [2.35]0.000256 0.00006 0.000274 0.00007

[1.64] [1.64] [1.71] [1.71]0.00139 0.00035 0.00165 0.00041[1.35] [1.35] [1.68] [1.68]0.0206 0.00513 0.0207 0.0052[3.29] [3.29] [3.32] [3.32]

-0.00232 0.000579 -0.00426 0.0011[0.18] [0.18] [0.32] [0.32]

0.00109 -0.000273 0.00114 0.00028[0.90] [0.90] [0.93] [0.93]

ML Conditional Logit Estimates of the Determinants of Receiving Financial Assistance(Informal Loans + Non-regular Transfers in Crop Year 2005/6)

Adverse village rain deviation in 05/06

×Caste’s mean land holdings

×Caste’s proportion landless

×Caste’s proportion hh’s with in non-ag. occupations

×Caste’s standard deviation of land holdings (x10-3) ×Number of same-caste households in village (x10-3)

Response to Idiosyncratic Risk

32

-0.833 -0.204251 -0.794 -0.195[2.49] [2.61] [2.38] [2.48]0.144 0.036024 0.165 0.0412[1.68] [1.68] [1.98] [1.98]1.37 0.341520 1.22 0.305

[2.40] [2.40] [2.01] [2.01]3.05 0.761193 3.25 0.81

[1.47] [1.47] [1.53] [1.53]-16.5 -4.1194 -18.8 -4.69[1.84] [1.84] [2.12] [2.12]1.77 0.4415 1.73 0.00043

[2.38] [2.38] [2.37] [2.37]

×Caste’s proportion landless

×Caste’s proportion hh’s with in non-ag. occupations

×Caste’s standard deviation of land holdings (x10-3)

×Number of same-caste households in village (x10-3)

Any individual household loss from distress event in 05/06

×Caste’s mean land holdings

Is there basis risk in this sample?

33

VariableRain per day 0.16516 0.30169 0.13937 0.23606

[1.32] [2.20] [1.40] [2.09]Distance to aws (km) 0.12483 0.08460

[2.40] [1.92]Rain per day x Distance to aws -0.02231 -0.01673

[3.53] [2.81]Number of cultivators 945 936 1,459 1,418

Uttar Pradesh (randomized) UP+AP

6

7

8

9

10

11

12

13

1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6

AWS Outside Village

AWS in Village

Figure 1: Lowess-Smoothed Relationship Between Log Output Value per Acre and Log Rain in the Kharif Season, by Randomized Placement of Rain Station (UP Villages)

Variable/Est. MethodThree States UP only AP only0.125 0.151 0.0228 -0.523 -0.029 - -[0.56] [0.61] [0.07] [0.73] [0.06]

- - 0.151 0.174 0.153 0.139 0.157[3.42] [1.34] [1.16] [2.55] [2.31]

-198 -209.6 -209.7 -78.2 -121.7 - -[1.71] [1.28] [0.94] [0.48] [0.33]

- - - - - - -18.6[-0.528]

- - -0.0254 -0.029 -0.025 -0.0246 -0.019[3.50] [1.67] [0.90] [2.63] [1.50]

-0.0343 -0.0341 -0.028 -0.047 -0.018 -0.0238 -0.0379[2.19] [2.13] [1.58] [1.41] [0.92] [1.49] [1.43]

- - - - - - 0.0033[0.797]

-0.00143 -0.0016 -0.0017 -0.003 -0.001 -0.0015 -0.0016[2.07] [2.07] [2.40] [1.46] [1.81] [2.14] [2.14]0.389 0.355 0.35 0.187 0.447 0.376 0.372[3.38] [2.86] [3.10] [0.68] [3.95] [3.26] [3.20]0.523 0.751 0.747 1.050 0.267 0.874 0.908[2.16] [2.89] [2.77] [2.93] [0.46] [2.92] [3.04]

N 4,260 3,338 3,338 1,693 1,645 3,338 3,338

Village coefficient of variation, rainfall

Two States (AP and UP)

Two States (AP and UP)

Actuarial price

Subsidy

Fixed-Effects Estimates: Determinants of Formal Insurance Take-up (bootstrapped t -ratios)FE-Caste

Agricultural laborer

Agricultural laborer × Distance to aws

η j [Informal idiosyncratic coverage]

η j × Distance to AWS

ι j [Informal aggregate coverage]

ι j × Distance to AWS

Distance to AWS (km)

FE-State

Is it Trust?

• Perhaps distance to the rain station (village presence) allows respondents to trust that they will get a payment

• Lack of trust, when asked why did not purchase, was not a salient issue

• Probability that farmers mentioned trust as an issue in non-purchase not correlated with distance (multinomial logit estimates for purchase versus not purchase by reason)

36

Reasons Table 8

Reasons Given for Not Purchasing Marketed Insurance, by Cultivator Status

Variable Cultivator (%) Non-cultivator (%) Too expensive 2.26 1.32 Currently not holding cash 45.4 49.7 No need 35.5 38.8 Do not trust insurance/payout unlikely 13.8 9.62 Do not understand 3.02 0.62

37

AWS Distance and Trust Table 9

Marginal Effects from Multinomial Logit Regression of Reasons for not Purchasing Insurance [bootstrapped t-ratios]

Purchased Insurance Lack of Trust

ηj -0.034 0.080 [0.23] [1.64]

ηj × Distance to aws 0.200 0.007 [3.40] [0.55]

ιj 213.879 14.481 [1.30] [0.33]

ιj × Distance to aws

Distance to aws (km) -0.036 0.000 [3.67] [0.08]

38

Risk-taking effects of formal index insurance (ITT estimates for Tamil Nadu)

• Compare treated sample to control sample • Control sample: in villages and jatis not receiving offer (N=648)

– No possibility of spillovers • Measures of risk-taking: crop choice

– Average return and resistance to drought of planted rice varieties

– Based on perceived qualities of 94 different rice varieties planted in prior seasons rated on three-category ordinal scale

39

40

The index for yield and drought resistance is

Ili = Σaisσls/Σais

where

l is drought resistance or yield

σls = fraction of all farmers rating rice variety s “good” with respect to the characteristic l

ais=acreage of rice variety s planted by farmer I

Median rice portfolio: 57% “good” for yield, 63% “good” for tolerance Only 5% of farmers planted varieties considered “good” for yield by every farmer Only 9% of farmers planted varieties considered “good” for drought resilience by all farmers

41

Property Yield Drought Resistant

Disease Resistant

Insect Resistant

Good 61.0 58.9 40.3 34.7

Neither good nor poor 30.7 30.9 46.2 50.6

Poor 8.3 10.2 13.5 14.7

Total 100.0 100.0 100.0 100.0

Number of varieties

Number of farmers

Properties of Rice Varieties Planted by Tamil Nadu Rice Farmers

94

364

42

Estimating equation:

Ili = gωlωi + gωlηωiηj + gωlιωiιj + xijg + gj + εij where

ωi = 1 if the index insurance product was offered to the farmer gj = caste fixed effect εij is an iid error

Model suggests that

gωl>0 for l=drought resistance gωl<0 for l=yield

Crop Characteristic:Variable (1) (1)Offered insurance -0.0593 0.0519

[2.67] [1.93]Owned land holdings 0.0000934 0.00056

[0.02] [0.12]Village coefficient of variation, r 0.351 -0.516

[0.88] [0.81]N 325 325

Absolute values of t-ratios in brackets, clustered by caste/village (because the randomized insurance treatment was stratified at the caste/village level).

Intent-to-Treat Caste Fixed-Effects Estimates of Index Insurance on Risk and Yield:Proportion of Planted Crop Varieties Rated "Good" for Drought Tolerance and Yield, Tamil Nadu

Kharif Rice Farmers

Good Drought Tolerance Good Yield

Conclusions • Informal networks lower the demand for formal

insurance only if the network covers aggregate risk. • When formal insurance carries basis risk, informal

risk sharing can be a complement to formal insurance

• Formal insurance enables households to take more risk, and thus assists in income growth.

• Landless laborers’ livelihoods are weather dependent, and they also demonstrate a strong demand for insurance, especially relative to cultivators living farther away from rainfall stations.

45

What is the relationship between risk-taking and

A. Weather Insurance

B. Informal Loss Indemnification

Theory

Empirical findings using rainfall variation:

A. NCAER REDS 2007-8 cultivators

1. Informal jati-level indemnification estimates and rainfalldeviations from 8-year mean

B. RCT in Andhra Pradesh and Uttar Pradesh - cultivators

1. Informal jati-level indemnification estimates

2. Randomized weather insurance

Partners behave cooperatively, choosing e and ä to maximize:

0 1 2 3E(U) = U (1- P) + U P + (1 - P)P(U + U ),2 2

0 1 2 3where U = U(w) , U = U(w - d), U = U(w - ä), U = U(w - d + ä)FOC:

0 1 2 3e: P'[-2(1 - P)U + 2PU + (1 - 2P)(U + U )] =

0 1 2 3-w'[U '(1- P) + U 'P + (1 - P)P(U ' + U ')2 2

2 3ä: (-U ' + U ')P(1 - P) = 0

So, optimal ä, ä*, is

2 3ä* = d /2 where -U ' + U = 0 (A-S result)

Suppose that the group cannot attain “full” insurance ä*(limited commitment,liquidity constraints), so that ä < ä*.

What is the effect of exogenous fall in ä at the optimum ä*, on risk mitigatione?

Proposition 1: A decrease in the ability to informally indemnify individuallosses below the first-best constrained optimum, may increase risk-taking.

2 3 2 3de/dä = -[(1 - 2P)(U ' + U ')P'+ (1 - P)P(-U " + U ")w"]/Ö,

0 1 2 3where Ö = (w') [U "(1 - P) + U "P + (1 - P)P(U " + U ")]2 2 2

0 1 2 3+ [U '(1 - P) + U 'P + (1 - P)P(U ' + U ')][w" - P"W'/P']2 2

0 1 2 3+ 2(P') [U + U - U - U ] < 02

2 3 2 3and -U ' + U > 0, -U " + U "<0 for ä < ä*

For P $ ½, decreased coverage unambiguously decreases risk-mitigation,but below ½, the effect may be negative as well.

More effective informal risk-sharing may be associated with lower risk-taking

B. Sensitivity of output farm profits and output to rainfall (REDS and RCT)

1. Riskier crops, assets, technologies: manifested in greater responsivenessof farm profits to rainfall shock (Rosenzweig and Binswanger, 1993)

j j2. Assess how rain sensitivity varies with ç and é and with index insurance

Informal loss indemnification may lower sensitivity

Index insurance, informal or formal should increase sensitivity

3. Use REDS survey data on profits per acre, shock measured by crop-yeardeviation in village-level rainfall from the eight-year mean

4. RCT:

Compare control and treated per-acre output sensitivity to villagerainfall

Within the control group, look at the effects of the informal risk-sharing indemnification parameters on output-rainfall sensitivity

Table 4Caste Fixed-Effects Estimates: Effect of an Adverse Village-Level Rainfall Shock

on Farm Profits per Acre

Variable (1) (2)

Village adverse rainfall shock -.0457(3.18)

-.0448(2.81)

j×ç .389(3.25)

.404(3.38)

j×é -6.30(0.19)

-6.47(0.19)

×Head’s years of schooling - -.000482(2.10)

×Owned land holdings - -.000346(2.59)

Head’s years of schooling - 57.7(1.45)

Owned land holdings 202.6(5.13)

200.5(4.87)

N 2,669 2,669

Absolute values of bootstrapped t-ratios in parentheses clustered at the village level.

7

7.5

8

8.5

9

9.5

10

10.5

11

0.75 1.25 1.75 2.25 2.75

High Informal Indemnification, No Rainfall Insurance

Low Informal Indemnification, No Rainfall Insurance

Offered Rainfall Insurance

Figure 6: Lowess-Smoothed Relationship Between Log Per-Acre Output Value and Log Rain per Day in the Kharif Season, by Insurance Type and Level