Evaluating the Welfare of Index Insurance Joint with Glenn Harrison, - - PowerPoint PPT Presentation

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Evaluating the Welfare of Index Insurance Joint with Glenn Harrison, - - PowerPoint PPT Presentation

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Jia Min Ng Evaluating the Welfare of Index Insurance Joint with Glenn Harrison, Jimmy Martinez-Correa, and J. Todd Swarthout Academic Session 12 th International Microinsurance Conference Colombo, Sri Lanka, 16 November 2016 Center for the

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Evaluating the Welfare of Index Insurance

Jia Min Ng

Center for the Economic Analysis of Risk

Academic Session 12th International Microinsurance Conference Colombo, Sri Lanka, 16 November 2016 Joint with Glenn Harrison, Jimmy Martinez-Correa, and J. Todd Swarthout

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Summary

> Evaluate expected welfare gain of index insurance

  • Take into account individual’s risk preferences

> Compound nature of basis risk in index insurance

  • Reduces take-up as well as welfare of individual’s insurance choices

> Welfare drivers

  • No significant effect from correlation and premia
  • Significant effect of consistency with ROCL

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Overview

> Motivation

  • How are insurance products evaluated

> How do we evaluate welfare (Theory)

  • Index insurance
  • Risk preferences

> Experimental Design

  • Insurance choices
  • Risk lotteries

> Results > Conclusions

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Motivation – Evaluation of Insurance

> Index insurance

  • Basis risk is a compound risk

> Welfare gain

  • Future risky benefits versus certain upfront costs
  • Requires risk preferences
  • Use economic theory to measure welfare

> We run lab experiments to test this

  • Ideal controlled environment
  • Complementary to the field

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Methodology

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Index Insurance

$20 Do not purchase insurance Purchase insurance Index Bad Index Good Index Good Index Bad Same: $5 (q × c) Diff: $20 (q × [1-c]) Same: $20 ([1-q] × c) Diff: $5 ([1-q] ×[1-c]) Diff: $20 - P - $15 ([1-q] ×[1-c]) Same: $20 - P ([1-q] × c) Diff: $20 - P + $15 (q × [1-c]) Same: $20 - P (q × c)

q 1-q q 1-q c 1-c c 1-c c 1-c c 1-c

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Index Insurance

$20 Do not purchase insurance Purchase insurance Index Bad Index Good Index Good Index Bad Same: $5 (q × c) Diff: $20 (q × [1-c]) Same: $20 ([1-q] × c) Diff: $5 ([1-q] ×[1-c]) Diff: $20 - P - $15 ([1-q] ×[1-c]) Same: $20 - P ([1-q] × c) Diff: $20 - P + $15 (q × [1-c]) Same: $20 - P (q × c)

q 1-q q 1-q c 1-c c 1-c c 1-c c 1-c

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Index Insurance

$20 Do not purchase insurance Purchase insurance Index Bad Index Good Index Good Index Bad Same: $5 (q × c) Diff: $20 (q × [1-c]) Same: $20 ([1-q] × c) Diff: $5 ([1-q] ×[1-c]) Diff: $20 - P - $15 ([1-q] ×[1-c]) Same: $20 - P ([1-q] × c) Diff: $20 - P + $15 (q × [1-c]) Same: $20 - P (q × c)

q 1-q q 1-q c 1-c c 1-c c 1-c c 1-c

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Index Insurance

$20 Do not purchase insurance Purchase insurance Index Bad Index Good Index Good Index Bad Same: $5 (q × c) Diff: $20 (q × [1-c]) Same: $20 ([1-q] × c) Diff: $5 ([1-q] ×[1-c]) Diff: $20 - P - $15 ([1-q] ×[1-c]) Same: $20 - P ([1-q] × c) Diff: $20 - P + $15 (q × [1-c]) Same: $20 - P (q × c)

q 1-q q 1-q c 1-c c 1-c c 1-c c 1-c

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Index Insurance

> Insurance task

  • Correlation defined as probability an individual’s personal
  • utcome matches that of a separate index
  • Two different treatments
  • II treatment – Index loss probability presented separately from

correlation probability in insurance choice

  • Actuarially-equivalent (AE) treatment – Index loss probability and

correlation combined to reflect probability of personal outcomes

  • Compare insurance take-up and expected welfare gains

evaluated for both treatments

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How do we evaluate welfare?

> CRRA:

U(x) = x(1-r)/(1-r)

  • Here r = 0 is RN, r > 0 is RA, r < 0 is RL

> EUT:

EUi = ∑j=1,J [ p(xj) × U(xj) ]

> RDU:

RDUi = ∑j=1,J [ w(p(Mj)) × U(Mj) ]

  • wj = ω(pj + ... + pJ) - ω (pj+1 + ... + pJ)
  • ωj is the probability weighting function, wj is the decision weight
  • Alternative probability weighting functions
  • power:

ω(p) = pγ

  • inverse-S:

ω(p) = pγ / ( pγ + (1-p) γ )1/γ

  • Prelec:

ω(p) = exp{-η(-ln p)ϕ}

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How do we evaluate welfare?

> CRRA:

U(x) = x(1-r)/(1-r)

  • Here r = 0 is RN, r > 0 is RA, r < 0 is RL

> EUT:

EUi = ∑j=1,J [ p(xj) × U(xj) ]

> RDU:

RDUi = ∑j=1,J [ w(p(Mj)) × U(Mj) ]

  • wj = ω(pj + ... + pJ) - ω (pj+1 + ... + pJ)
  • ωj is the probability weighting function, wj is the decision weight
  • Alternative probability weighting functions
  • power:

ω(p) = pγ

  • inverse-S:

ω(p) = pγ / ( pγ + (1-p) γ )1/γ

  • Prelec:

ω(p) = exp{-η(-ln p)ϕ}

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Index Insurance

$20 Do not purchase insurance Purchase insurance Index Bad Index Good Index Good Index Bad Same: $5 (q × c) Diff: $20 (q × [1-c]) Same: $20 ([1-q] × c) Diff: $5 ([1-q] ×[1-c]) Diff: $20 - P - $15 ([1-q] ×[1-c]) Same: $20 - P ([1-q] × c) Diff: $20 - P + $15 (q × [1-c]) Same: $20 - P (q × c)

q 1-q q 1-q c 1-c c 1-c c 1-c c 1-c

> Consumer Surplus (CS) from insurance

  • CE(with insurance) – CE(without insurance)

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Experiment

> Insurance task (32 choices)

  • Loss probability = 10% or 20%
  • Premium = $0.50, $1.20, $1.80, $3.50
  • Correlation = 100%, 80%, 60%, 40%

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Experiment

> Insurance task (32 choices)

  • Loss probability = 10% or 20%
  • Premium = $0.50, $1.20, $1.80, $3.50
  • Correlation = 100%, 80%, 60%, 40%

> Insurance contracts

  • Index Insurance contract
  • Actuarially Equivalent simple contract
  • Index Insurance contract with a Contextual Clue

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Contextual Clue treatment (33 subjects)

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Experiment

> Insurance task (32 choices)

  • Loss probability = 10% or 20%
  • Premium = $0.50, $1.20, $1.80, $3.50
  • Correlation = 100%, 80%, 60%, 40%

> Insurance contracts

  • Index Insurance contract
  • Actuarially Equivalent simple contract
  • Index Insurance contract with a Contextual Clue

> Risk preferences (76 choices)

  • Test for IA of EUT (30 choices)
  • Test for ROCL (30 choices)
  • “Naked AE” (16 choices)

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Risk preferences assuming ROCL

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Results

> Comparing welfare gain against actual take-up

  • Significant difference between predicted and observed take-up

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Welfare-reducing

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Should take-up

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Should not take-up

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Results

> Comparing welfare gain against actual take-up

  • Significant difference between predicted and observed take-up

> Impact of compound risk in basis risk

  • II has lower take-up and welfare than AE
  • Efficiency – actual CS as a % of total possible CS

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Results

> Comparing welfare gain against actual take-up

  • Significant difference between predicted and observed take-up

> Impact of compound risk in basis risk

  • II has lower take-up and welfare than AE
  • Efficiency – actual CS as a % of total possible CS

> Proponents of II advocate…

  • Lowering premia and/or increasing correlation
  • No statistically significant effect on welfare for compound risk

> But improving ROCL consistency does help

  • Each subject has a ROCL consistency count between 0 and 15
  • ∆ ROCL consistency count by 1

→ ∆ 5% impact on efficiency

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Summary

> Evaluate expected welfare gain of index insurance

  • Take into account individual’s risk preferences
  • Economic theory

> Compound nature of basis risk in index insurance

  • Reduces take-up as well as welfare of individual’s insurance choices

> Welfare drivers

  • No significant effect from correlation and premia
  • Significant effect of consistency with ROCL

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