Weather-index drought insurance: an ex ante evaluation for millet growers in Niger
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Weather-index drought insurance: an ex ante
evaluation for millet growers in Niger
Antoine Leblois∗& Philippe Quirion†
Abstract
In the Sudano-Sahelian region, which includes South Niger, the inter-annual vari-
ability of the rainy season is high and irrigation is scarce. As a consequence, bad
rainy seasons have a massive impact on crop yield and regularly entail food crises.
Traditional insurances based on crop damage assessment are not available because of
asymmetric information and high transaction costs compared to the value of produc-
tion. We assess the risk mitigation capacity of an alternative form of insurance which
has been implemented in India since 2003: insurance based on a weather index. We
compare the capacity of various weather indices to increase utility of a representative
risk-averse farmer. We show the importance of using plot-level yield data rather than
village averages, which bias results upward. We also illustrate the need for out-of-
sample estimations in order to avoid overfitting. Even with the appropriate index and
assuming a substantial risk aversion, we find a limited gain of implementing insurance,
roughly corresponding to the cost of implementing such insurances observed in India.
However, when we treat separately the plots with and without fertilizers, we show that
the benefit of insurance is higher in the former case. This suggests that insurances may
increase the use of risk-increasing inputs like fertilizers and improved cultivars, hence
average yields, which are very low in the region.
Keywords: Agriculture, index insurance.
JEL Codes: G21, O12, Q12, Q18, Q54.
∗
CIRED (Centre International de Recherche sur l’Environnement et le Développement), leblois@centre-
cired.fr
† CIRED, LMD (Laboratoire de Météorologie Dynamique), Paris.
1
1 Introduction
During the 1973, 1984 and 1991 droughts in Niger, the productive assets of growers and
pastoral households have be largely destroyed (Fewsnet, 2010). More recently, the sahelian
zone suffered from many droughts and the 2005 and 2010 food crisis were mainly triggered
by a lack of rainfall or a short rainy season. “During 2004 and 2005 the implications of these
underlying vulnerabilities were powerfully demonstrated by a climate shock, with an early
end to rains and widespread locust damage” (chapter two of Human Development Report,
2008).
Traditional agricultural insurance, based on damage assessment cannot efficiently shelter
farmers because they suffer from an information asymmetry between the farmer and the
insurer, especially moral hazard, and from the cost of damage assessment. An emerging
alternative is insurance based on a weather index, which is used as a proxy for crop yield. In
such a scheme, the farmer, in a given geographic area, pays an insurance premium every year,
and receives an indemnity if the weather index of this area falls below a determined level (the
strike). Index based insurance does not suffer from the two shortcomings mentioned above:
the weather index provides an objective, and relatively inexpensive, proxy of crop damages.
However, its weakness is the basis risk, i.e., the imperfect correlation between the weather
index and the yields of farmers contracting the insurance. The basis risk can be considered
as the sum of two risks: first, the risk resulting from the index not being a perfect predictor
of yield in general (the model basis risk). Second, the spatial basis risk: the index may not
capture the weather effectively experienced by the farmer, all the more that the farmer is
far from the weather station(s) provides data on which index is calculated.
Niger is the third world producer of millet, succeeding to India and Nigeria. Millet
covers almost 70% of its cultivation surface dedicated to cereal (FAO, 2008) and is almost
only produced for internal consumption. The prevalence of millet, especially the traditional
Haini Kiere cultivar, the one studied in this article, is due to its resistance to drought.
Nevertheless, dryness of the region in a context of largely non-irrigated agriculture suggests
that water provision could become the major limiting factor.
Very few article in peer reviewed journals have investigated the impact of crop insurance
based on weather index in developing or transition countries (Zant, 2008 in India, Breustedt
et al., 2008 in Ukraine, Molini et al., 2008 in Ghana, Chantarat et al., 2008 in Kenya and Berg
et al., 2009 in Burkina Faso) and ex-post studies (Hill and Viceisza, 2010; Gine, Townsend,
and Vickery 2008; Cole et al. 2009; Gine and Yang, 2009) are quite limited due to the recent
development of such products. However, many reports, recent work or unpublished papers
also inquired such topic (Hellmut et al., 2009 and Hazell et al., 2010 that exhaustively lists
recent index insurance programmes) even in West Africa (DeBock, 2010).
This article aims at quantifying the risk pooling capacity of a rainfall index-based insur-
ance by using plot level yields observations matched with a high density rain gauge network.
It evaluates the impact of insurance on plot level yields distribution, improving statisti-
cal inference as compared to aggregated data. It also illustrates, in this particular case,
the necessity to run out-of-sample estimations of insurance ex ante impact to control for
2overfitting.
We first describe the region and data, then set the insurance policy design and under-
lying methods to estimate farmers gain. Then we compare overall insurance return to its
experienced costs and finally we try to estimate the relative gain for farmers depending on
their technical itineraries.
2 Data and method
2.1 Study area
We study the Niamey squared degree area, where are situated thirty meteorological stations
(Figure 1). High density of meteorological station network is needed for a region known
for its high spatial variability of rainfall. We also dispose of four years of yields and other
precise agronomic data in ten of the thirty villages. Yield data were collected by Agrhymet
between 2004 and 2007 in two plots for each grower, about 30 per village. The first plot
is cultivated following traditional technical itineraries and with no additional inputs. From
2005 to 2007 additional mineral fertilizers were freely allocated to growers for applications
in a second plot together with agronomical and technical advices from surveyors. There
are approximately 30 plots in each of the ten villages. Every plot is situated at less than 3
kilometres away from the nearest meteorological station. We only study in this article the
Haini-Kiere (also called HK) millet cultivar, which represents 87% of the plots. The rest of
the plots, in which the Somno cultivar was sown, could not be used because Somno has a
different cycle duration than HK. Therefore, the growth phases, which are used in some of
our indices, differ between HK and Somno.
Figure 1: Rain gauges (all dots) and inquired villages (circled in black) network across
Niamey Squared Degree.
Table 1 displays the summary statistics of the first plots i.e. traditional itineraries that
3includes 30% of organic fertilization, 8% of mineral fertilization and two percent of farmers
are using both in our sample.
There is a high variability of yield distribution across villages (CV=1.7). Intra-village
yield variation is even larger (CV=2.1), inducing a likely basis risk stemming from the
fact that rainfall is observed at the village level. It is due to a significant occurrence of
idiosyncratic shocks, for a large part explained by insects ravages that account for more
than 80% of all surveyed non-water-related damages1 that hit 50% of the whole surveyed
growers sample.
Table 1: Summary statistics: regular plots (2004-2007)
Variable Mean Std. Dev. Min. Max. N
Farm Yields (kg/ha) 654.19 375.72 43 2284 921
Organic fert. only (1 if yes) 0.30 . 0 1 921
Mineral fert. only (1 if yes) 0.08 . 0 1 921
Both fert. (1 if yes) 0.02 . 0 1 921
Non water-related (NWR) damage (1 if yes) 0.50 . 0 1 921
Among which (non exclusive categories):
Locusts & other insects (1 if yes) 0.39 . 0 1 921
Birds (1 if yes) 0.11 . 0 1 921
Pests (1 if yes) 0.05 . 0 1 921
Other NWR damage 0.05 . 0 1 921
2.2 Indemnity schedule
The concept of such scheme is that insurance indemnities are triggered by low values of an
underlying index that is supposed to explain yield variation. The indemnity is a step-wise
linear function with 3 parameters: the strike (S), i.e. the index level threshold triggering
indemnity; the maximum indemnity (M) and λ, the slope-related parameter. When λ equals
one, insurance is correspondign to a lump sum transfer to every village where rainfall index
fall below the strike level. The strike represents the level at which the meteorological factor
becomes limiting. We thus have the following indemnification function depending on x, the
meteorological index realization:
M,
if x ≤ λ.S
S−x
I(S, M, λ, x) = S−λ.S (1)
, if λ.S < x < S
0,
if x ≥ S
2.3 Index choice
We first review different indices that could be used in a weather-index insurance, from the
simplest to more complex ones. The trade-off, brought up by an emerging literature (Patt
et al., 2009), between accuracy and simplicity of the index would suggest to use the most
transparent index among indices reaching similar outcomes. We tested seasonal cumulative
rainfall, the number of big rains (defined as superior to 15 and 20 mm.) often quoted by
1
Their occurrence is not significantly correlated with rainfall during the cropping season.
4farmers (Roncoli et al., 2002) as a good proxy of yields, Effective Drought Index (EDI, Byun
and Wilhite, 1999) computed on a decadal basis and Antecedent Precipitation Index (API,
Shinoda et al., 2000) calibrated on a close area with similar characteristics than our study
site (Yamagushi and Shinoda, 2002). Those indices are not studied in the paper because
they were quite poor in terms of pooling capacity.
We finally retained three different types of indices computed on the Sivakumar (1988)
crop growth phase schedule2 that were performing better in explaining the yields variations.
This growing season schedule is defined by its onset triggered by a minimum level of rainfall
(20mm.) occurring in a minimum of three days after Mai the first and its offset triggered
by 20 dry days occurred after September the first. Millet first (vegetative) growth phase
is triggered by the germination and ends with flowering, the second (reproductive) roughly
corresponds to panicle development and the third and fourth (maturation phases), called
’grain filling’ phases are corresponding to the development of grains.
Indices are displayed here by increasing complexity:
The first is the cumulative rainfall on critical phenological phases. We improved the
index by bounding it to a daily maximum (30 mm.) corresponding to an excess of water and
cutting off low daily precipitations (< .85 mm. following Odekunle, 2004) that are probably
entirely evaporated. Bounded Cumulative Rainfall (BCR) for the 4th crop phenological
phase3 was most clearly fitting observed yields.
We secondly retained the average daily Available Water Resource Index for the same
growth phase (AWRI, Byun et al., 2002) that takes run-off and soil water stocks into account.
It cumulates rainfalls of preceding days (here ten) weighted with an exponentially decreasing
factor.
Finally a water balance model (Water Resource Satisfaction Index, FAO/FEWSNET
millet, referred as WRSI in the paper) was computed on a daily basis, then averaged on each
growth phase. We used Eagleman equation (following Affholder, 1997) to evaluate actual
evapotranspiration, as compared to calculated reference crop evapotranspiration (calculated
thanks to FAO Penman-Monteith method, Allen et al., 1998) enhanced by multiplying each
crop phase by its corresponding FAO coefficients. The moisture ratio is the daily rainfall
bounded by a fixed maximum Available Water holding Capacity of soil (AWC=50). We
used a sum of critical crop growth phases (namely 1, 3, 4) WRSI. This methodology is
predominantly used in existing indexed insurance projects (such as in India and Malawi).
Such association of different critical growth phase was also tested for BCR and AWRI, but
they did not increase insurance return.
2
The HK cultivar is photoperiodic which obliged us to set sowing and growth phases windows that
depends on rainfall distribution during the season. Different growing season schedules were tested but they
also were inferior to Sivakumar onset and offset definitions.
3
On a total of 5, corresponding to the grain-filling period at end of the crop cycle.
52.4 Parameter optimization
We used a grid optimization process to maximize the objective function. The literature
brought multiple different objective functions such as the semi variance (following Vedenov
and Barnett, 2004) or the mean-variance criterion. We finally retained the Constant Relative
Risk Aversion (CRRA) utility function in order to compute the certain equivalent income
(CEI) and value overall insurance gain. CRRA appears appropriate to describe farmers’
behaviours according to Chavas and Holt, 1996 or Pope and Just, 1991.
1
h (W + Y )(1−ρ) i 1−ρ
0
CEI(Y ) = (1 − ρ) × E − W0 (2)
(1 − ρ)
Y is the yield distribution, W0 the initial wealth (representing off- and non-farm revenues,
about 40 to 60% of total revenues according to Abdoulaye and Sanders, 2006) and ρ the
relative risk aversion parameter.
Adding a certain income (W0 ), the initial wealth, allows the premium to be superior to
the lowest yield observation. It lowers the gain from insurance in term of certain equivalent
income by increasing the certain part of total income. We set W0 at a third of the average
yield (216kg of millet), lower than the rate proposed by Abdoulaye and Sanders, since those
revenues probably also show some uncertainty. We tested a range of values for the relative
risk aversion parameter from .5 to 4. This range encompasses the values usually used in the
literature in econometric studies (Cardenas and Carpenter, 2008) as well as in theoretical or
ex ante frameworks in developing countries (Coble et al., 2004; Wang et al., 2004; Carter et
al., 2007 and Fafchamps, 2003). A relative risk aversion of 4 may seem high but empirical
estimates of relative risk aversion indicate a wide variation across individuals; therefore, if
insurance is not compulsory, only the most risk adverse farmers are likely to be insured, so
such a high value is not unrealistic.
We used yields (in kg per ha) as income variable for each observed plot regrouping the
10 villages during 4 consecutive years. Since the use (but also the impact on yields) of costly
inputs such as mineral fertilizers is very limited4 and because a major part of the harvest
is used for self consumption, with limited associated price risk, yield in kg/ha is considered
a satisfying proxy for on-farm revenue. The insurance contract parameters S, M and λ
are optimized in order to maximize the certain equivalent income of equation (2) with the
following income after insurance:
Yi = Y − P S ∗ , M ∗ , λ∗ , x + I S ∗ , M ∗ , λ∗ , x (3)
Yi is the income after indemnification and Y the income before insurance, P the premium,
I the indemnity and x the rainfall index realizations associated with each plot. We bounded
the premium range of values to the minimum endowments, in accordance to the choice of
the power utility function, only defined on R+ . The actuarially fair premium is simply the
expected indemnity of the policy given the historical distribution of the weather events. A
loading factor is defined as a percentage of total indemnifications on the whole period (fixed
4
8% (cf. table 1), plots with encouragement to fertilizer use will be considered in the section 3.3.
6at 10% following a private experiment that took place in India, cf. Horréard et al., 2010)
and a transaction cost for each indemnification is fixed exogenously to one percent of the
average yield. We finally bounded the indemnification rate to a 25% ad-hoc level.
3 Results
For the two first part of this section we will only consider regular plots (921 observations),
representing the traditional technical itineraries for the farmers in this area’s growers. The
last part will compare different technical itineraries using only 2005-2007, period for which
both plots (encouraged and regular) were available.
3.1 Plot-level vs. aggregated data
Calibration on the whole sample allows taking intra-village yield variation into consideration,
which is rarely the case in such studies due to a lack of quality data at the plot level. In
tables 2, 3, and 4 we present for each index the grower average gain from insurance, in
certain equivalent income, and insurance parameters depending on risk aversion parameter
values. We estimate here the optimal (insample) calibration of contract parameters, taking
in the first place the whole sample into account, then only the village average and we finally
calibrate insurance parameters on the village average yields and and test it on the whole
sample.
First we can underline the fact that the strike level (which drives the indemnification
rate displayed in Table 2, 3 and 4) is robust to the risk aversion parameter calibration. No
insurance is supplied for BCR and AWRI calibrations when assuming that risk aversion is
low (.5). Second calibration with village average leads to overestimation of indemnification
level (drived by M), but in the case of BCR for ρ = 1.
Finally high intra-village yield standard deviation increases actual basis risk when work-
ing on village average, and thus limits insurance outcome. Taking average value for each
village leads to an overestimation of insurance gain when computed with a concave utility
function that depends on income distribution and sample size. I our case a misapprehension
of village yield distribution therefore lead to a ‘bad’ calibration of insurance parameters.
The presence of village yield heterogeneity within villages could lower the effective gain of
an insurance calibrated on village averages.
3.2 Need for cross-validation
In the previous section, we optimized the parameters and evaluated the insurance contracts
on the same data. This creates a risk of overfitting due to the fact that parameters will not
be calibrated and tested on the same sample of data in a real insurance implementation.
We can identify such effect by running a cross-validation analysis to avoid the overfitting of
input data (as do Vedenov and Barnett, 2004; Berg et al., 2009). We thus ran a ‘leave one
(village) out’ method, optimizing the 3 parameters of the insurance contract for each village
7Table 2: Average income gain and contract characteristics of BCR based index insurance
ρ = .5 ρ=1 ρ=2 ρ=3 ρ=4
Whole sample
CEI gain 0% 0.15% 0.73% 1.29% 1.70%
Indemnification rate . 10.21% 10.21% 10.21% 10.21%
M (kg of millet) . 454 355 410 565
Strike . 12.07 12.13 12.62 12.44
λ . 0.95 0.95 0.80 0.75
Village averages
CEI gain 0% 0.30% 0.87% 1.38% 1.81%
Strike . 12.28 12.18 12.265 12.15
Indemnification rate . 10.21% 10.21% 10.21% 10.21%
M (kg of millet) . 447 638 447 571
λ . 0.85 0.90 0.95 0.85
Vil. av. calibration, whole sample test
CEI gain 0% 0.15% 0.72% 1.27% 1.64%
Table 3: Average income gain and contract characteristics of AWRI based index insurance
ρ = .5 ρ=1 ρ=2 ρ=3 ρ=4
Whole sample
CEI gain 0% 0.78% 2.45% 4.25% 6.06%
Indemnification rate . 24.86% 24.86% 24.86% 24.86%
Strike . 5.59 4.09 5.72 3.08
M (kg of millet) . 155 166 155 144
λ . 0.95 0.90 0.85 0.75
Village averages
CEI gain 0% 0.81% 2.93% 5.18% 7.51%
Strike . 3.22 2.30 3.56 3.33
Indemnification rate . 22.26% 22.26% 22.26% 22.26%
M (kg of millet) . 201 224 213 202
λ . 0.40 0.55 0.10 0.10
Vil. av. calibration, whole sample test
CEI gain 0% 0.42% 1.79% 3.34% 4.73%
Table 4: Average income gain and contract characteristics of WRSI based index insurance
ρ = .5 ρ=1 ρ=2 ρ=3 ρ=4
Whole sample
CEI gain 0.09% 0.49% 1.65% 2.98% 4.37%
Indemnification rate 5.54% 19.11% 19.11% 19.11% 19.11%
Strike 0.36 0.49 0.49 0.49 0.49
M (kg of millet) 144.144 144.144 155.232 144.144 133.056
λ 0.95 0.95 0.95 0.95 0.95
Village averages
CEI gain 0.038% 0.56% 2.23% 4.08% 6.10%
Strike 0.36 0.48 0.48 0.48 0.48
Indemnification rate 5.54% 19.11% 19.11% 19.11% 19.11%
M (kg of millet) 156 179 190 190 179
λ 0.95 1 1 1 1
Vil. av. calibration, whole sample test
CEI gain 0.028% 0.37% 1.56% 2.95% 4.23%
using data from the 9 other villages, for each of the three different indices and on the whole
sample of growers first plots.
Figures 2, 3 and 4 show the relative robustness of out-of-sample estimation as compared
to the in sample case. In the in-sample estimations, by construction, the premium equals
total indemnities plus 10% (cf. section 2.2 above). Therefore we cannot compare outcomes
8500
450
Indemnity in kg/ha and index distribution
400
350
300
250
200
150
100
50
0
11 11.5 12 12.5 13 13.5 14
Index
Figure 2: Insample (solid black line) and out-of-sample (dotted gray lines) indemnity sched-
ules (kg/ha) for BCR insurance, for ρ = 2 and kernel smoothing estimated of index density
function.
200
180
Indemnity in kg/ha and index distribution
160
140
120
100
80
60
40
20
0
−5 0 5 10 15 20 25
Index
Figure 3: Insample (solid black line) and out-of-sample (dotted gray lines) indemnity sched-
ules (kg/ha) for AWRI insurance, for ρ = 2 and kernel smoothing estimated of index density
function.
of insurance contracts simply by comparing the difference in CEI. This is not the case in
the out-of-sample estimations, which prevents us from comparing the outcome by simply
looking at the CEI gain: the insurer can be better off or worse off than in the corresponding
contract optimized with the in sample method5 .
In- and out-of-sample estimates are displayed in tables 5, 6 and 7. Growers gain in percent
CEI is multiplied by the CEI level expressed in kg per hectares. Insurer gain includes the
loading factor but not the fix indemnification cost that could be interpreted as a lump-sum
transaction cost of indemnification. More specifically, the insurer is better off in out-of-
sample calibrations with the AWRI and with WRSI in case of high risk aversion, and worse-
off with BCR, and with WRSI in case of low risk aversion. Moreover we cannot simply add
the outcomes for the insurer and for the farmers since we did not specify a profit or utility
function for the insurer. Since contract parameters are different for each village, the ex post
5
This is also the case in Berg et al. (2009, Fig. 4)
9200
180
Indemnity in kg/ha and index distribution
160
140
120
100
80
60
40
20
0
0 0.2 0.4 0.6 0.8 1
Index
Figure 4: Insample (solid black line), out-of-sample (dotted gray lines) indemnity schedules
(kg/ha) for WRSI insurance, for ρ = 2 and kernel smoothing estimated of index density
function.
sum of premiums can differ from the total indemnifications, which can lead to a a lower gain
for the insurer (AWRI and WRSI for low risk aversion values) but also for farmers (BCR
and WRSI for high risk aversion values). We finally found that out-of-sample estimation
however limits insurance gain either for the insurer, for growers or even for both of them.
Table 5: Average gain to BCR insurance depending on risk aversion parameter.
ρ = .5 ρ=1 ρ=2 ρ=3 ρ=4
In sample
Growers average CEI gain 0% 0.154% 0.733% 1.292% 1.698%
Growers gain (kg/ha) 0 0.890 3.732 5.779 6.688
Insurer (kg/ha) . 1.286 1.346 1.190 1.007
Insurer loss ratio . .9 .9 .9 .9
Indemnification rate . 10.21% 10.21% 10.21% 10.21%
M (kg of millet) . 454 355 410 565
Strike . 12.07 12.13 12.62 12.44
λ . 0.95 0.95 0.80 0.75
Out-of-sample
Grower average CEI gain 0% 0.423% 1.055% 1.781% 2.410%
Growers gain (kg/ha) 0 2.452 5.376 7.965 9.490
Insurer loss ratio . 0.967 0.950 0.954 0.965
Insurer gain (kg/ha) . 0.491 0.773 0.635 0.411
Indemnification rate . 10.21% 10.21% 10.21% 10.21%
M (kg of millet) . 540.339 526.039 558.246 515.486
λ . 0.805 0.855 0.735 0.761
10Table 6: Average gain to AWRI insurance depending on risk aversion parameter.
ρ = .5 ρ=1 ρ=2 ρ=3 ρ=4
In sample
Grower average CEI gain 0% 0.474% 2.031% 3.778% 5.593%
Growers gain (kg/ha) 0 2.744 10.346 16.898 22.027
Insurer (kg/ha) . 3.455 3.682 3.359 3.041
Insurer loss ratio . .9 .9 .9 .9
Indemnification rate . 24.86% 24.86% 24.86% 24.86%
Strike . 5.59 4.09 5.72 3.08
M (kg of millet) . 155 166 155 144
λ . 0.95 0.90 0.85 0.75
Out-of-sample
Growers average CEI gain 0% -0.520% 0.292% 1.052% 1.827%
Growers gain (kg/ha) 0 -3.012 1.485 4.705 7.194
Insurer loss ratio . 0.782 0.774 0.753 0.740
Insurer gain (kg/ha) . 8.507 9.323 9.425 8.786
Indemnification rate . 22.26% 22.26% 22.26% 22.26%
M (kg of millet) . 152.840 163.805 152.644 136.636
λ . 0.208 0.165 0.101 0.123
Table 7: Average gain to WRSI insurance depending on risk aversion parameter.
ρ = .5 ρ=1 ρ=2 ρ=3 ρ=4
In sample
Grower average CEI gain 0.029% 0.389% 1.718% 3.226% 4.778%
Growers gain (kg/ha) 0.70 4.55 12.55 19.10 23.94
Insurer in kg/ha 0.798 2.755 2.966 2.755 2.543
Insurer loss ratio . .9 .9 .9 .9
Indemnification rate 5.54% 19.11% 19.11% 19.11% 19.11%
Strike 0.36 0.49 0.49 0.49 0.49
M (kg of millet) 144.144 144.144 155.232 144.144 133.056
λ 0.95 0.95 0.95 0.95 0.95
Out-of-sample
Growers average CEI gain 1.500% 2.098% 0.843% 0.991% 0.766%
Growers gain (kg/ha) 9.242 12.151 4.296 4.435 3.016
Insurer loss ratio 2.420 1.854 0.949 0.854 0.822
Insurer gain (kg/ha) -10.794 -12.213 1.504 4.246 4.636
Indemnification rate 2.82% 13.79% 21.72% 21.72% 21.72%
M (kg of millet) 170.277 219.680 162.499 145.478 129.098
λ 0.728 0.927 0.950 0.950 0.950
3.3 Potential intensification due to insurance
As pointed out by Zant (2008) our ex ante approach does not take into account the potential
intensification due to insurance. Indeed, many agricultural inputs, especially fertilizers,
increase the average yield but also the risk, because if the rainy season is bad, the farmer
still has to pay for the fertilizers even though the increase in yield will be very limited or
even nil. The literature on micro-insurance indeed suggests that the supply of mitigating risk
products is often used as an incentive to use more intensive production, directly by lowering
the level of risk faced by growers (Hill, 2010), or even induced by a higher credit supply at
lower rate (Dercon and Christiaensen, 2007).
To address the first point we use additional data concerning ‘encouragement’ plots: where
more inputs are used because they were freely allocated by surveyors. Each grower has a
‘regular’ plot and an ‘encouragement’ plot, the latter being only available for the 2005-2007
11period. Our hypothesis is the following: since the cost of a bad rainy season is higher for
intensified production insurance gain must be also higher. In such a case insurance should
foster intensification therefore bring a higher gain than with a lower level of fertilizers.
Table 8 displays the summary statistics, the BCR and the AWRI are in millimeters and
the WRSI is the available part (%) of the necessary water resource for the three phases.
The average yield is inferior to those of the 2004-2007 period displayed in Table 1 since
2004 was a good rainy season. We valorized production at the annual average market price
of millet in Niamey from SIM network6 in order to compute on-farm income for each plot.
Fertilizers prices are taken from the ‘Centrale d’Approvisionnement de la République du
Niger’. Quantities are fixed to 40kg per hectares, the average between the minimal level
required (20kg/ha) according to Abdoulaye and Sanders (2005) and the maximum (60kg/ha).
The incentive to invest in fertilizers is quite low when taking the input costs into account.
On-farm income of plots where organic, mineral or both fertilizers were used is about 8%
superior in average but with higher variations (corresponding to a CV increase of 13%)
compared to regular plots that were grown under traditional technical itineraries.
Table 8: Summary statistics: all plots (2005-2007)
Variable Mean Std. Dev. Min. Max. N
Farm Yields (kg/ha) 600.84 363.24 31 2284 1356
On-farm income (FCFA) 109,783.16 70,969.97 2,536 405,570 1356
Organic fert. only (1 if yes) 0.126 . 0 1 1356
Mineral fert. only (1 if yes) 0.423 . 0 1 1356
Both fert. only (1 if yes) 0.1 . 0 1 1356
Bounded cumulative rainfall 30.57 27 11.9 119.4 1356
4th growth ph. AWRI 36.102 43.027 0 165.175 1356
WRSI (1st , 3rd and 4th growth ph.) 0.607 0.165 0.34 1 1356
Among which
Regular plots:
Farm Yields (kg/ha) 562.31 327.14 43 2284 675
On-farm income (FCFA) 105,549.24 664,56.17 3,620 405,570 675
Organic fert. only (1 if yes) 0.253 . 0 1 675
Mineral fert. only (1 if yes) 0.102 . 0 1 675
Both fert. (1 if yes) 0.019 . 0 1 675
Bounded cumulative rainfall 30.59 27.05 11.9 119.4 675
4th growth ph. AWRI 36.16 43.087 0 165.175 675
WRSI (1st , 3rd and 4th growth ph.) 0.607 0.165 0.34 1 675
Encouragement plots:
Farm Yields (kg/ha) 639.037 392.303 31 2218 681
On-farm income (FCFA) 113,979.77 74,990.34 2,536 395,515 681
Organic fert. only (1 if yes) 0 . 0 0 681
Mineral fert. only (1 if yes) 0.74 . 0 1 681
Both fert. only (1 if yes) 0.181 . 0 1 681
Bounded cumulative rainfall 30.55 26.98 11.9 119.4 681
4th growth ph. AWRI 36.05 43 0 165.175 681
WRSI (1st , 3rd and 4th growth ph.) 0.608 0.166 0.34 1 681
Tables 9 displays the gain from insurance in FCFA for risk averse growers and risk neutral
insurer in insample. Gain from insurance is higher in the encouragement plot sample, due
to a greater risk in income caused by costly input use.
6
Millet price are the average prices of Niamey market taken from the SIM network: an integrated
information network across 6 countries in West Africa (resimao.org).
12Table 9: In sample average gain of insurance depending on the index.
ρ = .5 ρ=1 ρ=2 ρ=3 ρ=4
All sample (N=1356)
Gain from BCR based insurance (% of CEI) .00% .16% 1.00% 1.91% 2.69%
Insurer profit (FCFA/ha) . 426.03 450.17 420.09 381.82
Gain from AWRI based insurance (% of CEI) .00% .58% 2.70% 5.44% 8.53%
Insurer profit (FCFA/ha) . 843.79 928.35 879.81 832.01
Gain from WRSI based insurance (% of CEI) .16% .61% 1.79% 3.21% 4.68%
Insurer profit (FCFA/ha) 195.18 218.18 205.98 184.67 164.40
Regular plots (N=675)
Gain from BCR based insurance (% of CEI) .00% -.01% .52% 1.05% 1.35%
Insurer profit (FCFA/ha) . 428.41 452.75 422.41 383.81
Gain from AWRI based insurance (% of CEI) .00% .26% 1.84% 3.98% 6.42%
Insurer profit (FCFA/ha) . 875.30 964.44 915.59 867.24
Gain from WRSI based insurance (% of CEI) .07% .46% 1.55% 2.97% 4.64%
Insurer profit (FCFA/ha) 247.51 278.38 262.01 233.42 206.22
Encouragement plots (N=681)
Gain from BCR based insurance (% of CEI) .00% .33% 1.48% 2.77% 3.95%
Insurer profit (FCFA/ha) . 423.68 447.60 417.78 379.84
Gain from AWRI based insurance (% of CEI) .00% .90% 3.56% 6.90% 10.56%
Insurer profit (FCFA/ha) . 812.56 892.58 844.36 797.10
Gain from WRSI based insurance (% of CEI) .25% .76% 2.02% 3.44% 4.72%
Insurer profit (FCFA/ha) 143.31 158.51 150.45 136.36 122.96
Figures 5, 6 and 7 display the CEI level of an average grower depending on the risk
aversion parameter and for both technical itineraries. Arrows shows the threshold level of
risk aversion for which it is no more interesting for growers to use costly inputs. Those figures
underline the importance to take into account the higher incentive to use costly inputs when
insurance is supplied.
4
x 10
12
Unfertilized plots without insurance
Fertilized plots without insurance
11 Unfertilized plots with insurance
Fertilized plots with insurance
10
Certain equivalent income
9
8
7
6
5
0 0.5 1 1.5 2 2.5 3 3.5 4
Risk aversion parameter
Figure 5: CEI without and with BCR based insurance, depending on risk aversion parameter,
ρ, and technical itineraries.
134
x 10
12
Unfertilized plots without insurance
Fertilized plots without insurance
11 Unfertilized plots with insurance
Fertilized plots with insurance
10
Certain equivalent income
9
8
7
6
5
0 0.5 1 1.5 2 2.5 3 3.5 4
Risk aversion parameter
Figure 6: CEI without and with AWRI based insurance, depending on risk aversion param-
eter, ρ, and technical itineraries.
4
x 10
12
Unfertilized plots without insurance
Fertilized plots without insurance
11 Unfertilized plots with insurance
Fertilized plots with insurance
10
Certain equivalent income
9
8
7
6
5
0 0.5 1 1.5 2 2.5 3 3.5 4
Risk aversion parameter
Figure 7: CEI without and with WRSI based insurance, depending on risk aversion param-
eter, ρ, and technical itineraries.
3.4 Insurance impact
A totally private experience took place between 2003 and 2009 in 8 districts in India, selling
about 34,000 insurance policies without any subsidies (Horréard, et al., 2010). They are
stabilized in 2010 to 10,000 annual insurance policies sold to voluntary farmers (contrarily
to mandatory insurance linked with credit products supply) based on a network of 40 weather
stations. The average loss ratio for the 6 years is 65%. The total cost of such operation
was about US$47,800 among which 30% is dedicated to design and implementation (ICICI
Lombard), another 30% to reinsurance (SwissRe) and 40% to distribution (Basix); each of
them showing about 10% benefit. The pure operation costs are thus US$7,000 per year also
corresponding to US$1.3 per policy sold.
In our case a 1% increase in CEI can be valued at about US$2 per hectare when millet is
valorized at the period average price (SIM network cf. section 3.3) for the period considered.
We found in section 3.2 that the gain from insurance is quite limited in out-of-sample as
compared to in-sample estimations. However we also showed in section 3.3 that insurance
14impact on CEI could be higher when production is intensified, when only considering inten-
sive plots and reasonable risk aversion (say 2) and that a larger part of growers are up to use
costly inputs. If insurance actually creates an incentive to intensification, its performance
finally could then become significant compared to its cost.
4 Discussion
The article brings three major conclusions. First it underlines the need to use plot level data
to study and get robust estimation of the impact of insurance. Then it uses out-of-sample
estimation to show that mis-calibration is a risk either for the insurer or for growers. Finally,
by using encouragement to fertilization design, we show that the plot level impact of insur-
ance for pearl millet in Niger is not largely superior as compared to its implementation cost.
However, even if our ex-ante estimation cannot rigorously take such impact into account,
we suggest that the use of such financial risk transfer product should be accompagnied with
credit and/or input supply. It is also the case for imperfect weather forecasts or other com-
plementary tools that are often implemented in order to increase intensification. Insurance
outcome is indeed more probably superior to its estimated cost when taking potential inten-
sification into account since it increase the risk taken by growers.
Acknowledgements: We thank A. Alhassane and S. Traoré from Agrhymet for the
data, P. Roudier for sowing dates calculations, J. Sanders for kindly providing input price
series and R. Marteau for drawing the Niamey Squarred Degree map.
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