Remote sensing in an index-based insurance design for hedging economic impacts on rice cultivation

Rice production in Ecuador is steadily affected by extreme climatic events that make it difficult for farmers to cope with production risk, threatening rural livelihoods and food security in the country. Developing agricultural insurance is a policy option that has gained traction in the last decade. Index-based agricultural insurance has become a promising alternative that allows insurance companies to ascertain and quantify losses without verifying a catastrophic event in situ, lowering operative costs and easing implementation. But its development can be hindered by basis risk, which occurs when real losses in farms do not fit accurately with the selected index. Avoiding basis risk requires assessing the variability within the insurance application area and considering it for representative index selection. In this context, we have designed an index-based insurance (IBI) that uses a vegetation index (normalized difference vegetation index – NDVI) as an indicator of drought and flood impact on rice in the canton of Babahoyo (Ecuador). Babahoyo was divided in two agro-ecological homogeneous zones (AHZs) to account for variability, and two NDVI threshold values were defined to consider, first, the event impact on crops (physiological threshold) and, second, its impact on the gross margin (economic threshold). This design allows us to set up accurate insurance premiums and compensation that fit the particular conditions of each AHZ, reducing basis risk.

27 (Montaño, 2005), which represent currently an annual demand of 714,000 tonnes. Additionally, rice production in Ecuador 28 offers employment to 22% of the economically active population, involving around 140,000 families. For these reasons, 3 index over the IIA. Nevertheless, these conditions of homogeneity are rarely found because agriculture is practiced in 75 heterogeneous areas. To keep basis risk in non-significant levels, index selection and analysis may be crucial, very especially 76 with respect to the way variability within the IIA could influence index values.

77
Among the indexes used in IBI design, several authors (e.g. Jensen    135 years of historical data are needed for an insurance design (Rao, 2010). Despite this, Sentinel will become in the coming 136 years an important alternative in the insurance field. Also, Sentinel 1, which is a radar sensor, could be an interesting option

204
For the economic threshold, we set an NDVI_ave value that let farmers cover at least their production cost. Thus, we 205 considered the sale price at farm gate for a tonne of rice and the production cost in two scenarios: scenario 1 (when we 206 consider differentiated production cost for AHZs f7 and f15) and scenario 2 (non-differentiated production cost for AHZs).

7
According to CGSIN, there are officially three different rice-crop production systems in Ecuador for rainfed agriculture and 208 two for irrigated agriculture in 2017. Each of them has different production costs as shown in Table 1, and they depend on 209 the level of farm modernization and whether they are rainfed or irrigated.

212
Since, we assessed rice production during rainy season (January-May); irrigation is not required in normal conditions. For 213 this reason, we use production costs of rainfed agro-systems. Among rainfed production systems, we chose the non-technical 214 and semi-technical systems, which are more exposed to suffer the impacts of extreme climatic events, and therefore are the 215 ones that should adopt insurance. We assigned to f7 the production cost of a non-technical production system (1022 USD/ha) 216 and for f15 the cost of semi-technical production system (1629 USD/ha) for the scenario one (see Table 1), as according to

253
The indemnity is the amount of money that an insured individual receives when a covered hazard occurs. In this case, we 254 have two insurance policies options. The first one is the working capital, where the insured amount corresponds to the 255 money necessary for recovering the investment (production cost) that a farmer has spent. The second one is the profit (gross 256 margin), where the insured amount is the money that a farmer would obtain selling his production after covering his 257 production cost in a normal year.

258
In other words, for the first option the compensation will cover the yield reduction between the economic and physiologic 259 threshold. In the second case, the compensation will cover the difference between the expected yield in a normal year and the 260 yield obtained at the economic threshold.

266
is the expected yield (tones/ha), in normal years for zone.

267
is the price of a ton of rice at farm (USD/t).

268
is the production cost per hectare of rice cultivation (USD/ha), differentiated by s scenario (it could be 1 or 2), and 269 zone (f7, f15 or cantonal).

270
is obtained applying Eq. (1), was calculated from rice price monthly variation along the last two years. This value is 271 assumed to be constant (371 USD/t) for both AHZs and cantonal, and for scenario 1 or 2.

272
To estimate , we evaluated two scenarios. Scenario 1, with production costs differentiated for each zone (f7, f15 or 273 cantonal); and scenario 2, with the same production costs for all zones (f7, f15 or cantonal). 9 2.7.2 Premium determination

275
The commercial or loaded premium cost CP sz is equal to the net premium multiplied by a factor that covers the insurance 276 company profit and loading cost. The net premium or risk premium NP sz has to cover the expected compensations that an Where: 285 is net premium rate (USD/ha) for scenario s (scenario 1 or 2) and zone (f7, f15 and cantonal).

287
is the probability of sinister occurrence for s scenario (scenario 1 or 2) and z zone (f7, f15 and cantonal).

289
2 is the operative cost of the insurance plus taxes (5% of ).

290
The commercial premium value in index-based insurance is generally subsidized by the government in around 60% to  From descriptive statistical analysis, the kurtosis (0.56) and a skewness (-0.78) indicated that the data set of NDVI_ave fits a 295 normal distribution; however, the Lilliefors (Kolmogorov-Smirnov) normality test showed: D = 0.080207 and a p-value < 296 2.2e -16 lower than 0.05; then we rejected the null hypothesis because the data set does not come from a normal distribution.

297
We have found that our data fits a Generalized-minimum extreme value (GEVmin) distribution (Kotz and Nadarajah, 2000) 298 for the cantonal data set and for the two AHZs (f7 and f15) based on 2 statistics (Table 2).

299
16) shows us that the null hypothesis of f7 and f15 being equal can be rejected because the p-value is lower than 0.05. The

304
10 same test mentioned before shows us that years are also significant different ( 2 = 7507.4, F.D. = 16, p-value < 2.2e-16 is 305 also lower than 0.05). Five categories in years are established when LSD (Mean) and Bonferroni (Median) test are applied 306 on NDVI_ave values (see Table 3).

322
Since that the years have been classified in five categories, we could define the different levels of impact or no impact over 323 rice crop (NDVI_ave), as shown in Table 3. When rice yield is less than 0.5 t/ha (NDVI_ave ≤ 0.26), due to damage in rice 324 crop by extreme events, the total loss threshold is neither detectable at cantonal level nor at AHZs (f7 and f15) level.

325
Individual NDVI_ave observations equal or under the total losses' threshold can be found but not as a regional measure of

326
NDVI_ave. However, in our IBI design the index measure is an average of all observations within a homogeneous zone, 327 being these cantonal or AHZs (f7 and f15).

328
The physiologic threshold represents the maximum rice-crop damage that can be detected through NDVI_ave at regional 329 scale, which has been caused by an extreme climatic event. It is fixed (0.4) for both AHZ (f7 and f15) and cantonal (see

342
On the other hand, the economic threshold depends on economic factors such as sale rice price and production cost. These

343
are not constant and must be set regarding the necessary yield for covering the farmer's expenses during the rice cultivation 344 campaign, as it is shown in Table 4.

13
The economic threshold represents the minimum yield that farmers must reach for covering at least the production cost. It is 346 higher than physiologic threshold, and it varies according to the scenario. In scenario 1, the economic threshold is different 347 for each AHZ (f7 and f15); f7's being lower production cost (1022 USD/ha) than that for f15 (1629 USD/ha). Thus, the 348 economic threshold of f7 is 0.41, while for f15 is 0.47 (see Table 4). The years from our dataset that reached the economic

351
For scenario 2, the production cost is a weighted average (1259 USD/ha) both for AHZs (f7 and f15) and cantonal.

352
Therefore, the economic threshold (0.43) is the same for AHZs and cantonal, see Table 4.

354
The risk status of f7 and f15 were found to differ based on the following results. We found that 25% of events under the 355 physiologic threshold for f7 and 17% for f15 (see Fig. 4 B, C); and when we do not consider AHZs (cantonal) 21% (Fig. 4 356 A). AHZ f7's probability is higher because of its soil conditions (see Table 5). These conditions make the zone more 357 vulnerable to floods due to its very fine texture (>60% clay), flat lands (0-5% slope), very low altitude (1-12m) and 358 proximity with rivers' banks that contribute to very poor drainage of this zone. In the same way, these characteristics could

359
give to f7 better capacity for long-term water retaining, during a drought. However, when drought is extreme, the f7's soil   For economic thresholds, we also found differences between the risk status of AHZs f7 and f15. Furthermore, for scenario 1, 370 the probability of having events equal or under the economic threshold is higher in f15 (37%) than that in f7 (26%) and that 371 in cantonal (29%), as we can see in Fig. 5 A, C and E. The reason for this is that in this scenario, f15's farmers have to cover 372 a higher production cost (which corresponds to semi-technical production system), and, therefore, they have to reach an 373 economic threshold also higher (0.47) than that one in the f7.

378
In scenario 2, the economic threshold is equal (0.43) for f7, f15 and cantonal, but the probability to find events under the 379 threshold is higher in f7 (32%) than that in f15 (25%) and that in cantonal (29%). Although the economic threshold is the 380 same for both AHZs (f7 and f15) and at cantonal level, in this scenario, the frequency distributions of NDVI_ave were 381 different for each zone. Consequently, they accumulated different probabilities under the same threshold, as shown in Fig. 5 382 B, D and F.

383
At this point, we evaluated the Z-test results for determining if the found differences have statistical significance. Based on 384 the Z-test (see Table 6), the null hypothesis (H 0 : 1 = 2 ) can be rejected in both scenarios 1 and 2, so we can assert that the

398
We have found that the basis risk for this estimation is negligible according to Adjusted R-squared shown in Fig. 6 A, B and

399
C. Therefore, we can confidently use these estimations for determining the events proportion that reached the physiologic

406
The indemnity for farms that reach the physiological threshold in scenario 1 is reported in Table 7. These values show us the 407 deficit (negative numbers) that farmers face for recovering their production costs when their crop yield falls below the break 408 even, in each AHZ (f7 and f15) and cantonal. The indemnity would make up the difference between crop's costs and revenue 409 in case of extreme event. In f7 the indemnity would be 38 USD/ha, it means that when a farmer reaches physiologic 410 threshold, he only lacks 38 USD/ha for covering his production cost. A farmer from this scenario could dispense with the 411 insurance contract, because the deficit to hit the break-even is not representative. On the contrary, when f15 reaches the 412 physiologic threshold, its deficit is very high (645 USD/ha), which is the money that an f15's policyholder would receive as 413 compensation in case of an extreme event occurrence. Table 7. Indemnity calculation for physiologic and economic thresholds, for each AHZ (f7 and f15)

418
For scenario 2 of physiological threshold, the indemnity would be 275 USD/ha for all AHZ (f7 and f15) and for cantonal, 419 due to their same production cost (1259 USD/ha). As was mentioned before, in Ecuador, currently, it exist an agricultural 420 conventional insurance that covers the rice growers' working capital; but we included this calculation as an alternative to 421 conventional insurance or for these areas where conventional insurance is not feasible.

422
When looking at the economic threshold, as we can observe in Table 7, the indemnity (Gross Margin) in scenario 1 is very 423 similar between AHZs (f7 and f15) and cantonal though their expected yields are different. This is because their assigned 424 production cost has been related with their expected yield. For example, since farmers have invested more money in their 425 crop in f15, their expected yield is higher. Moreover, the difference in the premium price of these zones will be determined 426 by the different probability of extreme events occurrence in each AHZ (f7 and f15) and cantonal.

427
In scenario 2, on the other hand, we have assumed the same production cost for f7 and f15; thus, f15 has higher expected 428 yield in normal years than f7. Obviously, in this scenario f15 obtains the highest gross margin (1223 USD/ha), having also 429 the highest compensation, which would be reflected in a higher premium cost. However, f7 has the lowest insured amount 430 (640 USD/ha), so that its premium cost should be low. But we have to consider that premium cost calculation also depends 431 on the occurrence probability of the insured event.

432
For economic threshold, the indemnity calculation (840 USD/ha) for cantonal is equal in both scenarios 1 and 2, as shown in 433 Table 7; because, we used the same weighted average as production cost (1259 USD/ha). For f7 it is expected a higher gross 434 margin in scenario 1 than that in scenario 2, due to scenario 2's production cost being higher. On the contrary, for f15 the 435 gross margin is higher in scenario 2 than that in scenario 1; because in scenario 2, f15 has lower production cost than in 436 scenario 1.

438
The premium value is related to the insured amount (the indemnity or compensation that insurance company must pay to 439 farmers when an insured extreme event occurs), and the probability of the ensured extreme event occurs in a determined 440 period. Table 8 shows the net and commercial premium calculation for the two different thresholds under both scenario1 and 441 scenario 2, and for each AHZ and at cantonal level.

442
In general terms, it can be appreciated that premium cost for economic thresholds are more expensive than that for 443 physiologic threshold, in both scenarios (1 and 2). This is because the insured amounts for economic threshold are higher 444 than that for physiologic threshold. In the first case, the compensation covers the entire lost profit; while in the second one,

445
the compensation covers only the deficit necessary for recovering the investment (production cost).

446
If the insured amounts are similar among AHZs (f7 and f15) and cantonal, the difference among premium costs is 447 determined by the occurrence probability. However, when there are sharp differences among insured amounts of AHZs (f7 448 and f15) and cantonal, these influence more the premium cost variation than the occurrence probability.

449
Moreover, for physiologic threshold in scenario 1, the premium cost is determined mainly by the insured amount, for 450 instance, for f15 the premium cost is the highest (136.98 USD/ha) despite of its occurrence probability being the lowest. On 451 the contrary, for f7 its premium cost is very low, despite its highest occurrence probability, because of having a greater 452 insured amount.

453
While under economic threshold in scenario 1, the insured amount of AHZs (f7 and f15) and cantonal are similar, the 454 premium cost for f15 is the highest (394.66 USD/ha), due to its highest occurrence probability.

455
When costs are not differentiated across AHZ (scenario 2), for the physiologic threshold the insured amount is equal in all

456
AHZs (f7 and f15) and cantonal, and thus their premium cost has been differentiated through the occurrence probability,

457
being the highest for f7 (85.82 USD/ha). In the same scenario, for the economic threshold f15 has the highest gross margin,

458
and therefore a high-insured amount despite its low occurrence probability (0.25). It has a high premium price (382.29 459 USD/ha), but it is lower than in scenario 1 (394.66 USD/ha) where the occurrence probability is the highest (0.37).

460
As it can be appreciated in in f7 are non-technical production systems that achieve lower yields and get lower economic returns, providing access to 471 affordable insurance with fair premium prices may importantly contribute to expand insurance uptake and reduce 472 substantially socio-economic vulnerability in this area.

476
Yet, the price of the premium could be expensive for some farmers, but we must consider that this insurance will cover both 477 of the most frequent and intense extreme events that affect Babahoyo canton (drought and flood). For example, for the 478 economic threshold in scenario 1, the premium cost without subsidy would reach the 22% of the total production cost of a 479 policy holder of f7 and the 20% for f15. This means that subsidizing premium cost may still be necessary in order to

488
Floods and droughts are a major threat for rice production in Ecuador that undermine food security and endanger 489 sustainability of rural livelihoods in many areas of the country. Risk management mechanisms, such as agricultural 490 insurance, may play an important role in stabilizing production and contributing to reduce the vulnerability of rice farmers.

491
In this context, IBI is a promising tool that facilitates the implementation of agricultural insurance and reduces operational

20
In this research, we developed an IBI based on NDVI_ave that accounts for variability across the insured area. For this, we 496 considered AHZs as the starting point for risk assessment and indemnity calculation and compared it with the insurance 497 design at cantonal level. Two levels of climatic impact over rice cultivation have been identified. The first one is the 498 physiological impact that is determined by a physiological threshold when a climatic event is extreme, its policy contract 499 will cover losses related to the rice grower's working capital. The second level is the economic impact when the climatic 500 event is moderate, and its policy will cover the crops' gross margin.

501
The results of the analysis performed evidence that the two AHZs show significantly different risk profiles for physiologic 502 and economic thresholds. Therefore, the design of differentiated premium calculation based on the risk status and insured 503 amount of each AHZ (f7 and f15) will facilitate that farmers pay a fair insurance premium. This insurance premium would be 504 as consistent as possible with their risk status and would help them to receive compensations that effectively cover the 505 totality of their losses.

506
The basis risk arising from modelling the risk frequency of drought and flood events in Babahoyo (cantonal) and in AHZs 507 (f7 and f15) through GEVmin distribution is negligible. The basis risk associated with the spatial heterogeneity of Babahoyo 508 canton has been reduced in our IBI design. We have accomplished this by dividing this canton into f7 and f15 homogeneous 509 zones which have a significant different risk status, different expected yields and may have also different production costs.

510
Considering all these factors and the two different impact levels in the IBI design have allowed to set up a fair premium, 511 reducing in this way the possible bias caused for not discriminating Babahoyo variability.

512
The cost for contracting an insurance policy could be expensive in some cases. However, the fact that this kind of insurance 513 is generally partially subsidized by the government in developing countries (as Ecuador) could make this insurance 514 affordable to farmers. Moreover, even if the premium price may be high, the index design guarantees to policyholders that 515 the premium price is fair and proportional with the risk they are facing.

516
The implementation of IBI for rice crop in Babahoyo could let Ecuadorian Government to respond efficiently and rapidly in 517 the case of an extreme climatic event, paying compensations faster than with the conventional insurance. It could stabilize 518 rice-producer incomes and reduce small farmers' vulnerability by providing access to insurance through premium and 519 indemnities adjusted to the specific risk and technology conditions. Consequently, it can incentivise rice cultivation to the 520 desirable levels for covering national demand ensuring food security of Ecuador.

521
Finally, it is worth mentioning that even if the IBI has been defined for rice crop in a particular area, the methodology 522 applied for developing such an insurance scheme can be applied for other crops and regions if the data to define AHZs,

523
NDVI distributions, crop yield and cost productions are available. This is, therefore, a promising approach for defining IBI 524 schemes minimizing basis risk, which can importantly profit from current advances in remote sensing, satellite imagery and 525 improved information systems.