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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
Probability mass functions Probability of outcome
A simple model: what does unsubsidised insurance do?
Daniel Clarke - http://www.stats.ox.ac.uk/~clarke/ 4
Daniel Clarke - http://www.stats.ox.ac.uk/~clarke/ 5
No insurance
Indemnity insurance
Index insurance
1. Reduces risk when the hedge works
2. Increases risk when it doesn’t
3. Reduces mean outcome
1. Reduces risk
2. Reduces mean outcome
Downside basis risk
Upside basis risk
Wealth
Probability mass functions Probability of outcome
A simple model: what does unsubsidised insurance do?
Daniel Clarke - http://www.stats.ox.ac.uk/~clarke/ 6
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
nty
Eq
uiv
ale
nt,
as
sum
ing
op
tim
al in
sura
nce
p
urc
has
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)
Daniel Clarke - http://www.stats.ox.ac.uk/~clarke/ 7
Technical comment: How not to model index insurance
Daniel Clarke - http://www.stats.ox.ac.uk/~clarke/ 8
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
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
Daniel Clarke - http://www.stats.ox.ac.uk/~clarke/ 10
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
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
bili
ty t
hat
WB
CIS
cla
im
pay
me
nt
is p
osi
tive
Subdistrict average yield, as percentage of average historical yield 1999-2007
Daniel Clarke - http://www.stats.ox.ac.uk/~clarke/ 12
Across all 318 products sold in one state in India
• Correlation between yield and claim payment only -13%
How high is basis risk in weather index insurance?
0%
10%
20%
30%
40%
50%
0% 50% 100% 150% 200%
WB
CIS
cla
im p
aym
en
t, a
s p
erc
en
tage
of
sum
insu
red
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%
How high is basis risk in weather index insurance?
Daniel Clarke - http://www.stats.ox.ac.uk/~clarke/ 14
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?
Daniel Clarke - http://www.stats.ox.ac.uk/~clarke/ 15
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 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
Daniel Clarke - http://www.stats.ox.ac.uk/~clarke/ 17
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 - http://www.stats.ox.ac.uk/~clarke/ 18
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