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

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 Economic Analysis of Risk

Summary > Evaluate expected welfare gain of index insurance o Take into account individual’s risk preferences > Compound nature of basis risk in index insurance o Reduces take-up as well as welfare of individual’s insurance choices > Welfare drivers o No significant effect from correlation and premia o Significant effect of consistency with ROCL 2

Overview > Motivation o How are insurance products evaluated > How do we evaluate welfare (Theory) o Index insurance o Risk preferences > Experimental Design o Insurance choices o Risk lotteries > Results > Conclusions 3

Motivation – Evaluation of Insurance > Index insurance o Basis risk is a compound risk > Welfare gain o Future risky benefits versus certain upfront costs o Requires risk preferences o Use economic theory to measure welfare > We run lab experiments to test this o Ideal controlled environment o Complementary to the field 4

Methodology

Index Insurance Same: $5 (q × c) c Index Bad Diff: $20 (q × [1-c]) q 1-c Do not purchase Same: $20 ([1-q] × c) c Index insurance 1-q Diff: $5 ([1-q] ×[1-c]) Good 1-c $20 Same: $20 - P (q × c) c Index q Bad Diff: $20 - P + $15 (q × [1-c]) Purchase 1-c insurance c Same: $20 - P ([1-q] × c) Index 1-q Good Diff: $20 - P - $15 ([1-q] ×[1-c]) 1-c 6

Index Insurance Same: $5 (q × c) c Index Bad Diff: $20 (q × [1-c]) q 1-c Do not purchase Same: $20 ([1-q] × c) c Index insurance 1-q Diff: $5 ([1-q] ×[1-c]) Good 1-c $20 Same: $20 - P (q × c) c Index q Bad Diff: $20 - P + $15 (q × [1-c]) Purchase 1-c insurance c Same: $20 - P ([1-q] × c) Index 1-q Good Diff: $20 - P - $15 ([1-q] ×[1-c]) 1-c 7

Index Insurance Same: $5 (q × c) c Index Bad Diff: $20 (q × [1-c]) q 1-c Do not purchase Same: $20 ([1-q] × c) c Index insurance 1-q Diff: $5 ([1-q] ×[1-c]) Good 1-c $20 Same: $20 - P (q × c) c Index q Bad Diff: $20 - P + $15 (q × [1-c]) Purchase 1-c insurance c Same: $20 - P ([1-q] × c) Index 1-q Good Diff: $20 - P - $15 ([1-q] ×[1-c]) 1-c 8

Index Insurance Same: $5 (q × c) c Index Bad Diff: $20 (q × [1-c]) q 1-c Do not purchase Same: $20 ([1-q] × c) c Index insurance 1-q Diff: $5 ([1-q] ×[1-c]) Good 1-c $20 Same: $20 - P (q × c) c Index q Bad Diff: $20 - P + $15 (q × [1-c]) Purchase 1-c insurance c Same: $20 - P ([1-q] × c) Index 1-q Good Diff: $20 - P - $15 ([1-q] ×[1-c]) 1-c 9

Index Insurance > Insurance task o Correlation defined as probability an individual’s personal outcome matches that of a separate index o 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 o Compare insurance take-up and expected welfare gains evaluated for both treatments 12

How do we evaluate welfare? > CRRA: U(x) = x (1-r) /(1-r) o Here r = 0 is RN, r > 0 is RA, r < 0 is RL > EUT: EU i = ∑ j=1,J [ p(x j ) × U(x j ) ] > RDU: RDU i = ∑ j=1,J [ w(p(M j )) × U(M j ) ] o w j = ω (p j + ... + p J ) - ω (p j+1 + ... + p J ) o ω j is the probability weighting function, w j is the decision weight o Alternative probability weighting functions ω (p) = p γ  power: ω (p) = p γ / ( p γ + (1-p) γ ) 1/ γ  inverse-S: ω (p) = exp{- η (-ln p) ϕ }  Prelec: 13

How do we evaluate welfare? > CRRA: U(x) = x (1-r) /(1-r) o Here r = 0 is RN, r > 0 is RA, r < 0 is RL > EUT: EU i = ∑ j=1,J [ p(x j ) × U(x j ) ] > RDU: RDU i = ∑ j=1,J [ w(p(M j )) × U(M j ) ] o w j = ω (p j + ... + p J ) - ω (p j+1 + ... + p J ) o ω j is the probability weighting function, w j is the decision weight o Alternative probability weighting functions ω (p) = p γ  power: ω (p) = p γ / ( p γ + (1-p) γ ) 1/ γ  inverse-S: ω (p) = exp{- η (-ln p) ϕ }  Prelec: 15

Index Insurance Same: $5 (q × c) c Index Bad Diff: $20 (q × [1-c]) q 1-c Do not purchase Same: $20 ([1-q] × c) c Index insurance 1-q Diff: $5 ([1-q] ×[1-c]) Good 1-c $20 Same: $20 - P (q × c) c Index q Bad Diff: $20 - P + $15 (q × [1-c]) Purchase 1-c insurance c Same: $20 - P ([1-q] × c) Index 1-q Good Diff: $20 - P - $15 ([1-q] ×[1-c]) 1-c > Consumer Surplus (CS) from insurance o CE(with insurance) – CE(without insurance) 16

Experiment > Insurance task (32 choices) o Loss probability = 10% or 20% o Premium = $0.50, $1.20, $1.80, $3.50 o Correlation = 100%, 80%, 60%, 40% 18

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Experiment > Insurance task (32 choices) o Loss probability = 10% or 20% o Premium = $0.50, $1.20, $1.80, $3.50 o Correlation = 100%, 80%, 60%, 40% > Insurance contracts o Index Insurance contract o Actuarially Equivalent simple contract o Index Insurance contract with a Contextual Clue 20

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Contextual Clue treatment (33 subjects)

Experiment > Insurance task (32 choices) o Loss probability = 10% or 20% o Premium = $0.50, $1.20, $1.80, $3.50 o Correlation = 100%, 80%, 60%, 40% > Insurance contracts o Index Insurance contract o Actuarially Equivalent simple contract o Index Insurance contract with a Contextual Clue > Risk preferences (76 choices) o Test for IA of EUT (30 choices) o Test for ROCL (30 choices) o “Naked AE” (16 choices) 23

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Risk preferences assuming ROCL

Results > Comparing welfare gain against actual take-up o Significant difference between predicted and observed take-up 28

Welfare-reducing

Should take-up

Should not take-up

Results > Comparing welfare gain against actual take-up o Significant difference between predicted and observed take-up > Impact of compound risk in basis risk o II has lower take-up and welfare than AE o Efficiency – actual CS as a % of total possible CS 34

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Results > Comparing welfare gain against actual take-up o Significant difference between predicted and observed take-up > Impact of compound risk in basis risk o II has lower take-up and welfare than AE o Efficiency – actual CS as a % of total possible CS > Proponents of II advocate… o Lowering premia and/or increasing correlation o No statistically significant effect on welfare for compound risk > But improving ROCL consistency does help o Each subject has a ROCL consistency count between 0 and 15 o ∆ ROCL consistency count by 1 → ∆ 5% impact on efficiency 38

Summary > Evaluate expected welfare gain of index insurance o Take into account individual’s risk preferences o Economic theory > Compound nature of basis risk in index insurance o Reduces take-up as well as welfare of individual’s insurance choices > Welfare drivers o No significant effect from correlation and premia o Significant effect of consistency with ROCL 40