daniel clarke, world bank and university of oxford 12...

Can unsubsidised weather-index products be good microinsurance products?

Daniel Clarke, World Bank and University of Oxford

12 April 2012

1.The economic theory is interesting

2.Ultimately it’s an empirical question

3.Existing empirical evidence is (very) negative

4.Making agricultural insurance safe: the quest for better indices

A simple model: what does unsubsidised insurance do?

No insurance

Wealth

Probability mass functions Probability of outcome

Daniel Clarke - http://www.stats.ox.ac.uk/~clarke/ 3

No insurance

Indemnity insurance

1. Reduces risk

2. Reduces mean outcome

Wealth





No insurance

Indemnity insurance

Index insurance

1. Reduces risk when the hedge works

2. Increases risk when it doesn’t


1. Reduces risk


Downside basis risk

Upside basis risk

Wealth




Who ‘should’ buy unsubsidised indexed insurance?

There is an upper bound for ‘rational’ purchase

• ‘If you care enough about risk to want to hedge, you care enough about the downside basis risk to limit the size of your hedge’

0%

10%

20%

30%

40%

0 2 4 6 8 10

Op

tim

al d

em

and

un

de

r C

RR

A

Coefficient of relative risk aversion

Infinitely risk averse will optimally purchase zero • Purchasing worsens the

worst that could happen

Risk neutral will optimally purchase zero • Purchasing worsens

the mean outcome

0 0.5 1 1.5 2 2.5 3

Incr

eas

e in

Ce

rtai

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Eq

uiv

ale

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as

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sura

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e

Coefficient of Relative Risk Aversion

Benefit from increasing trustworthiness or reducing basis risk by one third

Benefit from subsidising premium by one third

Investing in indices with low basis risk is most valuable for the most risk averse (typically also the poorest)


Technical comment: How not to model index insurance


Weather is important for agriculture…

• …but what is the joint distribution of loss and index…

• … and how high is the premium loading

If we can estimate these we can use a structural model to assess value (e.g. de Nicola, 2011)

• Certainty equivalent of the optimal level of demand

It’s an empirical question; plausible stories are not enough


Across all 318 products sold in one state in India

• If lost entire crop there is a 1-in-3 chance you would get no claim payment

How high is basis risk in weather index insurance?

Source: Clarke et al. (2012)

0%

20%

40%

60%

80%

100%

0% 50% 100% 150% 200%

Pro

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WB

CIS

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pay

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Subdistrict average yield, as percentage of average historical yield 1999-2007


Across all 318 products sold in one state in India

• Correlation between yield and claim payment only -13%


0%

10%

20%

30%

40%

50%

0% 50% 100% 150% 200%

WB

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Subdistrict average yield, as percentage of average historical yield 1999-2007

Source: Clarke et al. (2012) Daniel Clarke - http://www.stats.ox.ac.uk/~clarke/ 13

Station Crop DSSAT/hist. yields WRSI/hist. yields

Lilongwe Groundnut 13% 31%

Maize 17% 38%

Kasungu Groundnut -1% 39%

Maize 37% 77%

Nkhotakota Groundnut 10% 35%

Maize -22% -6%

Chitedze Groundnut 30% 52%

Maize 1% 24%

Average 11% 36%



Source: Osgood et al. (2007), excerpt from Table 4.3

• Giné et al. (2007): Average premium multiple of 3.4

• Cole et al. (2009): Premium multiples of seven products, ranging from 1.7 to 5.3

The combination of high basis risk and commercial loading can lead to poor products.

– E.g. I find that given the average level of basis risk in 31 weather index insurance products designed for maize any risk averse expected utility maximiser would optimally purchase zero if the premium multiple was above 1.7.

How expensive is unsubsidised weather index insurance?


• A good index should capture local aggregate shocks – Particularly if there is some risk pooling within a community

• Weather indices seem to miss too many of these shocks – Due to imperfect calibration, imperfect functional form, or missing perils

• Total production indices can accurately capture aggregate shocks – Based on sample (e.g. sample-based area yield) or population mean

– Area yield can be nearly as good as MPCI (Deng et al. 2007)

The quest for better indices


Cost

Basis risk

Weather index

insurance

Group indemnity

insurance

Area yield index

insurance

This presentation tells the story of: 1. Clarke, D.J., (2011). “A Theory of Rational Demand for Index Insurance,” Department of

Economics Discussion Paper Series 572, University of Oxford. Other references: 1. Clarke, D.J., O. Mahul, K.N. Rao, and N. Verma, (2012). “Weather Based Crop Insurance

in India,” World Bank Policy Research Working Paper No. 5985. 2. Cole, Shawn A., Xavier Giné, Jeremy B. Tobacman, Petia B. Topalova, Robert M.

Townsend, and James I. Vickery, (2009). “Barriers to Household Risk Management: Evidence from India,” Working Paper 09-116, Harvard Business School.

3. Deng, Xiaohui, Barry J. Barnett, and Dmitry V. Vedenov, (2007). “Is there a viable market for area-based crop insurance?” American Journal of Agricultural Economics, 89(2), 508–519.

4. de Nicola, F., (2010). “The impact of weather insurance on consumption, investment, and welfare,” mimeo.

5. Giné, X., R. Townsend, and J. Vickery, (2007). “Statistical Analysis of Rainfall Insurance Payouts in Southern India,” American Journal of Agricultural Economics, 89 (5), 1248–1254.

6. Osgood, D., M. McLaurin, M. Carriquiry, A. Mishra, F. Fiondella, J. Hansen, N. Peterson and N. Ward, (2007). “Designing Weather Insurance Contracts for Farmers in Malawi, Tanzania, and Kenya,” Final Report to the Commodity Risk Management Group, ARD, World Bank

Insurance products for the poor should not be poor products


daniel clarke, world bank and university of oxford 12...

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