Assessing the feasibility of a weather index insurance for the semi-arid region of Brazil

Mateus Pereira Lavorato*

Marcelo José Braga*

Área 11 – Economia Agrícola e Meio Ambiente

Abstract: The semi-arid region of Brazil is historically plagued by catastrophic events, among which stand out the droughts that severely threaten the livelihood of its residents. Seen this, we assessed the feasibility of implementing a weather index insurance in this region. To this end, we applied a multi-step approach. First, crop yield responses to weather—which is captured by an index of aridity—were thoroughly investigated, enabling the selection of locations for which the WII product was later evaluated. Second, selected locations were grouped into specific contracts according to geographical proximity and each of these contracts are evaluated in order to attest the effectiveness of the proposed WII product in mitigating downside risk. More than half of locations analyzed presented statistically significant coefficients. Such locations were divided in three groups and a weather index insurance contract was developed for each of them. The contracts proved to be effective in reducing downside risk, although expected revenues were slightly diminished.

Keywords: weather index insurance; semi-arid; Brazil

JEL: Q14, Q18

* Universidade Federal de Viçosa, Viçosa, Minas Gerais, Brazil.

1. Introduction

Agriculture directly depends on the nature. As climatic and biological processes are usually out of the control of human beings, agriculture is exposed to an extremely high level of risks. Among the mechanisms developed to manage and mitigate the uncertainty that surrounds the agricultural activity, crop insurance stands out. It reduces risks without significantly impacting the expected return of activity, effectively transferring risks from the agriculture to other economic sectors. Crop insurance allows greater financial stability for farmers and the agricultural sector as a whole, enabling the full development of sector’s productive forces (Maia et al., 2010).

Seen this, crop insurance schemes have long been implemented worldwide. Indemnities are paid according to effective losses, which are locally evaluated by insurance experts. High transaction costs and asymmetric information problems inherent to this type of insurance increases premium values, inhibiting insurance adoption. Thus, the most successful crop insurance initiatives rely on governmental support. The crop insurance scheme currently in force in Brazil follows this pattern. Through the Rural Insurance Premium Subsidy Program (PSR), the Brazilian Government subsidizes part of the premium charged by insurance companies.

In regions with comparatively lower levels of socioeconomic development, however, the establishment and development of a well-structured crop yield insurance scheme is considerably complex. The spatial dispersion of small-scale rural properties and the characteristically poor transport infrastructure make on-site investigation of claims even more time-consuming and expensive. In this way, transaction costs often reach very high levels, which translates into the collection of prohibitive premiums. In fact, only 1.67% of the policies subsidized under the PSR were contracted by farmers from the North and Northeast regions of Brazil.

Considering these features, some alternative schemes started to be proposed. Among them, weather index insurance (WII) stands out. Payouts are conditioned to the realization of an independent and transparent weather parameter in order to circumvent the aforementioned issues and offer to poor, vulnerable farmers the possibility to stabilize their incomes and prevent asset losses. According to Hellmuth et al. (2009), WII products are designed to help farmers in overcoming poverty traps or to assist governments and relief agencies in disaster management initiatives aimed at supporting the livelihood of vulnerable populations.

In Brazil, the semi-arid region, which comprises most of the Northeast region and the northern portion of Minas Gerais state, stands out as the one that concentrates the ideal conditions for the implementation of a WII product. First, while temperature does not show much oscillation, precipitation has a wide spatiotemporal variation, which facilitates the occurrence of severe drought episodes (Correia et al., 2011). Second, its rural population is mainly composed by family farmers whose livelihoods often exclusively depend on rainfed agriculture (Melo and Voltolini, 2019). Ultimately, these farmers are highly exposed to climate risks.

Seen this, we propose to investigate the feasibility and effectiveness of a WII product for the semi-arid region of Brazil. To do so, we apply a multistep approach. First, crop yield responses to weather—which is captured by an index of aridity—are thoroughly investigated, enabling the selection of locations for which the WII product is posteriorly evaluated. Second, selected locations are grouped into specific contracts according to geographical proximity and each of these contracts are evaluated in order to attest the effectiveness of the proposed WII product in mitigating downside risk.

Throughout the world, several WII initiatives have been implemented for the last decade. Nevertheless, the effectiveness of potential index-based climate risk management tools continues to be analyzed for a variety of crops and countries† (e.g., Berg, Quirion and Sultan, 2009; Kellner and Musshoff, 2011; Zhu, 2011; Spicka and Hnilica, 2013; Conradt, Finger and Sporri, 2015; Choudhury et al., 2016; Adeyinka et al., 2016; Black et al., 2016; Poudel, Chen and Huang, 2016; Shi and Jiang, 2016; Kusuma, Jackson and Noy, 2018; Nogales and Cordova, 2019; Shirsath et al., 2019; Williams and Travis, 2019; Boyd et al., 2020; Eze et al., 2020).

† A comprehensive review of the literature on weather index insurance is provided by Singh and Agrawal (2020).

The aforementioned papers vary considerably in terms of the scope of analysis as well as the econometric and actuarial methods employed. For Brazil, to the best of our knowledge, Raucci et al. (2019) is the sole study investigating the development of a WII product. They design a WII contract for soybean cultivation in selected locations from southern Brazil and evaluate hedging efficiency against lack of rainfall during the growing season. It should be noted, however, that our analysis significantly differs to theirs as we work with different geographical focus, scope and methodology.

We contribute to the literature by providing evidence on the viability and effectiveness of developing and implementing a WII product for vulnerable farmers residing in one of the poorest areas of Brazil. Since the semi-arid has historically been neglected by the crop insurance model currently in force in the country, the suggested WII product may be viewed as a complement to that scheme, being explored in areas whose characteristics favor the implementation of this kind of climate risk management tool. Ultimately, we also hope to inspire the investigation of the viability of WII products for other vulnerable areas of Brazil.

2. Principles of weather index insurance

The innovative feature of the weather index insurance comes from its main characteristic: the methodology for payout calculation. Indemnities do not depend on the actual losses, but on exogenous realizations of a certain weather parameter. When this index exceeds a certain threshold pre-established in the contract, the farmer can claim the payment of indemnity. Therefore, the effectiveness of this type of insurance directly depends on the level of correlation between the realizations of the underlying weather index and the variations in crop yields observed for the region of the insured producer.

In this context, the concept of basis risk arises, which refers exactly to the imperfect correlation between the values of the weather parameter and the actual crop yield. Basis risk is an inherent characteristic of weather index insurance, emerging because of the way in which the payouts are determined under this type of contract, being the most notable obstacle to the development of this market (Skees, 2008; Clarke, 2011; Miranda and Farrin, 2012). Thus, it is clear that basis risk is directly related to the design of the contract and the parameters specified therein.

Among contract parameters, those governing the payout structure deserve great attention: the trigger and the exit point. The former indicates the point at which the contract starts to payout, whilst the latter gives the maximum payment. Moreover, several payout structures exist (Figure 1). In a simple zero/one contract, indemnity corresponds to liability and is paid in full once the trigger is surpassed. A layered scheme, in turn, has a set of triggers and exit points. In proportional payment schedule, which is the one considered here, payouts increase proportionally as index realizations moves toward the exit point.

(a) (b) (c)

Figure 1. Types of payout structures: (a) zero/one, (b) layered, (c) proportional.Source: Elaborated by the authors.

3. Study area

The Brazilian semi-arid, depicted in Figure 2, is composed by a total of 1,262 municipalities located in the states of Maranhão, Piauí, Ceará, Rio Grande do Norte, Paraíba, Pernambuco, Alagoas,

Sergipe, Bahia and Minas Gerais. In terms of territorial extension, it covers more than 1.1 million square kilometers, corresponding to slightly more than 13% of the national territory. With respect to population, the semi-arid region houses approximately 27.9 million inhabitants, leading to a population density of 24.5 inhabitants per square kilometer.

The current geographical delimitation of the semi-arid region was defined by the Deliberative Council of the Superintendência do Desenvolvimento do Nordeste (Sudene) through the Resolution N. 115, of November 23, 2017. Sudene, an autarchy linked to the Ministry of Regional Development, aims to promote the inclusive and sustainable development of its area of activity—which includes the semi-arid—and the competitive integration of the regional productive base in both the national and international economy (Sudene, 2019).

The semi-arid of Brazil is located in the extreme northeast of South America, to the east of the Amazon rainforest, running from the 3rd to the 18th parallel south. Kayano and Andreoli (2009) highlight that, despite its location, rainfall distribution within the region does not follow an equatorial pattern. In fact, precipitation in the Brazilian semi-arid is marked by a great spatial-temporal variability, enabling the occurrence of drought episodes that are directly associated with losses in the agricultural production of the region (Correia et al., 2011).

Figure 2. The semi-arid region of Brazil.Source: Elaborated by the authors.

Family farmers, which are extensively present in the semi-arid, have a prominent role in the sustainable development of the region as they provide food on local scale while promoting the conservation of natural resources (Angelotti and Giongo, 2019). Residents of the semi-arid, which often exclusively depend on agriculture for their livelihood, face the challenge of achieving a sustainable rainfed production with limited water supply (Melo and Voltolini, 2019). Additionally, it is worth noting that family farmers usually form the target audience of WII products.

Among the annual crops produced in the semi-arid of Brazil, Silva and Regitano-Neto (2019) highlight those that historically are the most produced: beans, cassava, maize, sugarcane, peanut, sorghum and cotton. These species normally occupy most of rainfed cropland in the region. Finally, it is worth highlighting that, in spite of the number of households for which agriculture is the main source of income and the occasional devastating effects of droughts, the take-up of crop yield insurance in the Brazilian semi-arid is still highly incipient.

4. Methods

4.1. Geographically Weighted Panel Regression

Crop yield responses to weather conditions are empirically modeled by means of a Geographically Weighted Panel Regression (GWPR). Conceptually, this model can be taken as a natural extension of the Geographically Weighted Regression (GWR) model as the only practical difference between them regards the explicit consideration of the time dimension by the former. In order to derive the GWR model and, ultimately, the GWPR model, one must first consider a global regression model (Fotheringham, Brunsdon and Charlton, 2002):

Y=Xβ+ε (1)

where Y denotes the vector of crop yields; X denotes the matrix of weather conditions; β denotes the vector of parameters to be estimated; and ε denotes the vector of errors. Estimates of β, which is constant across observations, are given by

β=( X ' X )−1 X ' Y . (2)

The GWR model is obtained when local parameters are allowed:

Y i=X i β i+εi (3)

where i denotes a given location within the analyzed sample.The vector of estimated regression coefficients, which now vary across observations, is

β i=( X ' W i X )−1 X ' W i Y (4)

where W i denotes a n-by-n spatial weighting matrix whose diagonal elements indicate the weight assigned to each of the n observations for the regression point i.

The regression model presented in the Eq. 3 is calibrated via Weighted Least Squares (WLS), assuming that the closer an observation is to the regression point i, the greater its influence on the estimation of β i. Spatial weighting matrices, in turn, are calculated by a kernel function and its respective bandwidth, which provides weights that are inversely related to distance. Therefore, the weighting process takes the assumption that spatial autocorrelation exists, possibly resulting in non-stationary patterns in estimated coefficients (Wheeler and Páez, 2010).

Finally, when the temporal component is considered, the GWPR model is obtained:

Y ¿=X¿ β i+ε ¿ (5)

where estimates of β vary across space but not across time. This occurs because the spatial relationship between locations does not change over time and thus both the bandwidth and the kernel function are time-invariant (Yu, 2010).

The key point in estimating the GWPR model regards the calculation of the matrix of local weights. As previously mentioned, W i is calculated by a spatial kernel, a function that uses the distance between locations (d ij) and a parameter of the bandwidth (b) to determine weights (Almeida, 2012). We use an adaptive spatial kernel since data density varies considerably across space. In such kernel function, b is adjusted to data density so a fixed number of observations is considered in each subsample (Fotheringham, Brunsdon and Charlton, 2002).

The bi-square nearest neighbor kernel, specified below, is used in the weighting process:

w ij ¿ [ 1−(d ij /d ik )2 ]2if j∈Z i (k )¿ ¿ ¿

(6)

where w ij denotes the weight assigned to j when calibrating the model for i; and Zi (k ) denotes the set of kth nearest neighbors of i.

The reliability of GWPR estimates is directly influenced by the selection of b and the cross-validation (CV) criterion is considered in the optimization of the bandwidth. Specifically, the following ‘drop-1’ score is minimized:

CV =∑i=1

n

[ y i− y≠i (b ) ]2(7)

where y≠i (b ) is the estimated value of y i when the location i is dropped.As some time-invariant aspects specific to each unity of analysis can interfere in the relationship

between crop yields and weather conditions, the use of a fixed effects specification is readily justified. Among such aspects, one could highlight both altitude and soil quality. The spatial rigidity of altitude is straightforward. For soil quality, in turn, this consideration is not so simple. However, for not-so-long time spans one could expect soil quality to remain relatively constant as both the degradation or correction of soil take some time to occur.

Evidence shows that crop yields respond nonlinearly to weather (Schlenker and Roberts, 2009). In fact, it is expected that after a certain point, water availability, could negatively affect crop yields. The opposite is true for temperature, as it is expected to negatively affect crop yields. Therefore, we include quadratic terms of the aridity index in the estimation. Ultimately, the following model is estimated for each of the crops investigated:

yld ¿=ci+β1 i arid¿+β2 i arid¿2+trend+ε ¿ (8)

where yld ¿, and arid ¿ respectively denote crop yield and the aridity index of location i in year t ; c i denotes location-specific, time-invariant fixed effects; trend denotes a linear time trend; and ε ¿ denotes the error term.

The analysis was conducted with R (R Core Team, 2019). Additional models were estimated for robustness check. A fixed effects panel model was estimated using the package ‘plm’ (Croissant and Millo, 2008), whilst both spatial lag and spatial error models were estimated using the package ‘splm’ (Millo and Piras, 2018). As the GWPR model was estimated‡ using the package ‘spgwr’ (Bivand and Yu, 2017), which is intended for cross-sections, demeaned data for crop yield and weather conditions were used.

4.2. Model-Based Clustering

Among the possible types of indemnity functions, we opt for a proportional payout structure. In this case, the indemnity is paid in percentage terms when the index falls below a pre-specified threshold, which is known as strike level or trigger. In particular, the payout is governed according to the following scheme

Payout=[ 1if I t ≤ I E

I T−I t

I T−I Eif I E< I t ≤ I T

0if I T< I t]× Liability (9)

‡ The authors are grateful to Michael Oppenheimer, Danlin Yu and, mainly, Ruohong Cai for providing the necessary R script for the estimation of the GWPR model.

where I T denotes the trigger threshold, I E denotes the exit threshold. When the value of I t falls below the exit threshold no additional incremental payout is applied. In this case, maximum indemnity equals total liability.

The values of I T and I E are empirically determined in the same fashion as Choudhury et al. (2016). Specifically, a model-based clustering is employed in order to identify two heterogeneous groups regarding the weather index and crop yields, one possibly with high values of such variables, and another with low values. The trigger threshold, I T, is defined as the average weather index of the low cluster, whilst the exit threshold, I E, is defined as the lowest weather index observed for this same cluster.

The model-based clustering is conducted with R (R Core Team, 2019). Using the package ‘mclust’ (Scrucca et al., 2016), a model-based clustering built on parameterized finite Gaussian mixture models is estimated. Such models are estimated by the expectation-maximization (EM) algorithm, which is initialized by a hierarchical model-based agglomerative clustering. Subsequently, the optimal model is selected according to the Bayesian Information Criterion (BIC). Detailed information about this method can be found in Bouveyron et al. (2019).

4.3. Burning Cost Analysis

We rely on burning cost analysis for pricing the proposed weather index insurance product. This pricing method uses the empirical distribution of insurance losses to calculate the premium (Heimfarth and Musshoff, 2011). Burning cost analysis is often used for weather index insurance when a sufficient long time series of weather data can be used. In fact, Hohl (2019) states that such method is suitable if at least 15 years of weather data are available. This is exactly the number of years considered in our analysis.

As observed by Parodi (2015), burning cost analysis is essentially a multi-step procedure. Accordingly, we follow four steps in the calculation of the risk premium rate. First, payouts are retrospectively calculated from 2003 to 2017. Second, both liability§ and payout values are forwardly discounted at a 5% rate. Third, annual loss cost ratios are obtained by averaging the ratio of payouts to liabilities over locations. Fourth, the risk premium rate is computed by averaging the loss cost ratio over the analyzed years.

4.4. Downside Risk and Semideviation

The effectiveness of the weather index insurance as a climate risk management tool is evaluated by comparing crop revenues with and without insurance adoption. When no insurance is contracted, per hectare revenue corresponds to the multiplication of crop yield (kg ha-1) by postharvest crop price (R$ kg-

1). Data on both yield and price are gathered from IBGE. For the case where index insurance is contracted, in turn, the premium is reduced and the (possible) payout is added to the previous per hectare revenue.

Semideviation is used to compare crop revenues with and without index insurance. Estrada (2007) points out that, in this framework, the risk is measured by the asset’s downside standard deviation of returns. Then, the semideviation** Σi is given by

Σi=√ E {min [ (CRevi−CRev i ) ,0 ]2 } (10)

where CRevi denotes crop revenue.

§ Liability is calculated as the expected yield times the coverage level. In order to account for operational costs, a deductible of 15% is considered and thus coverage level is set at 85%.** If the semideviation calculated for the insured scenario, i=1, is smaller than that calculated for the uninsured case, i=0, the proposed weather index insurance product is efficient at the pre-determined strike level.

4.5. Data

The relationship between crop yield and weather conditions is investigated for two of the crops most cultivated in the semi-arid region of Brazil. Our dataset comprises a large panel of municipality-level crop yield merged with high-resolution, grid-based weather information. Yield data were obtained from IBGE’s Municipal Agricultural Production, whilst weather data were collected from the database of Matsuura and Willmott (2018) accessed on the National Oceanic and Atmospheric Administration’s (NOAA) Physical Sciences Laboratory (PSL) website.

Measured in kilograms per hectare, crop yield data are gathered for beans and maize††, covering a period of 15 years (2003 to 2017). According to data from the 2017 Census of Agriculture, these are some of the most cultivated crops throughout the semi-arid of Brazil. This is true especially for family farmers, which are the main target audience for weather index insurance. We follow the schedule of the National Food Supply Company (Conab, 2019) to determine the planting season of each crop/state combination‡‡, which are presented in Table 1.

As previously informed, the Brazilian semi-arid comprises 1,262 municipalities within ten different states. However, only municipalities with consistent and complete information on crop yield are investigated as a balanced panel is required for the estimation of the GWPR model. While both crops are examined for the same time period of 15 years, each panel has a different spatial dimension. Specifically, 594 (47% of total) municipalities were considered for beans and 581 (46%) for maize.

Table 1. Crop calendar for beans (1st and 2nd harvests), maize (1st harvest) and rice, northeastern Brazil.

State Spring Summer Fall WinterOct. Nov. Dec. Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sep.

Beans, 1st harvest

BAMAMGPI

Maize, 1st harvest

BACEMAMGPBPEPIRN

Note: Growing season months are those highlighted in gray.Source: Adapted from Conab (2019).

Weather data, in turn, come from a high-resolution latitude/longitude grid of 0.5-degree by 0.5-degree. The original grid presents monthly data on total precipitation (millimeters) and mean temperature (degree Celsius) for the whole globe, comprising the period between 1900 and 2017. Data was extracted for the centroid of each municipality using the R packages ‘ncdf4’ (PIERCE, 2019) and ‘raster’

†† Specifically, crop yield data refer to the first harvest of beans and maize as this is the most cultivated harvest for both crops in the analyzed region.‡‡ Since Conab’s crop calendar does not consider beans cultivation in the states of Ceará, Rio Grande do Norte and Pernambuco, we used Piauí’s growing season for these states due to geographical proximity.

(HIJMANS et al., 2019). Weather variables are aggregated considering the semi-arid’s planting season of each crop analyzed.

Specifically, we investigate crop yield responses to an aridity index, which is constructed with temperature and precipitation data and, consequently, is expected to adequately capture the weather conditions in which the analyzed crops are grown. The inclusion of composite weather indexes into econometric models of the crop-weather relationship has been advocated, at least since the 1960s (e.g., Stallings, 1960; 1961; Shaw, 1964; Oury, 1965), in order to avoid functional misspecification of the relationship between crop yields and weather conditions.

Due to the minimal data requirement, we opted to use (an adaptation of) the index developed by de Martonne (1926):

M ¿=P¿× 12T¿+10 (11)

where M ¿ is the aridity index for location i in growing season t ; P¿ is the average of accumulated monthly rainfall; and T ¿ is the average of mean monthly temperature. The ‘+ 10’ term in the denominator was introduced by de Martonne in order to avoid negative values for the aridity index.

As can be observed, the lower the precipitation and the higher the temperature, the lower the aridity index and, consequently, the lower the degree of moisture or humidity. When de Martonne’s index lies below 20, a drought event in characterized, whereas a value below 10 indicates desert-like weather (Oury, 1965). Since a higher index value translates into better conditions for agricultural production, crop yields are expected to be positively correlated with the realizations of de Martonne’s aridity index.

5. Results

Table 2 presents the results for the modelling of beans and maize yield responses to weather. Considering that coefficients are estimated for each location, results are presented by quantiles. As initially expected, estimates vary considerably across the region. In fact, the interquartile range of estimates is considerably larger than the standard errors of the comparative models (Table A1 – Appendix). This indicates that responses are characteristically heterogenous in space, endorsing the validity of estimating local coefficients.

Before delving into the results of the GWPR model, we first analyze those of the fixed effects, spatial error and spatial lag models. Estimating a global parameter for the relationship of interest, these models provide robust evidence that crop yields indeed respond to variations in the weather of the semi-arid as most of estimates is statistically significant. As expected, the coefficients estimated for the linear term of the aridity index are positive, while those for the quadratic term have the opposite sign, indicating a parabolic relationship.

In this sense, crop yields initially respond positively to increases in humidity and, after some point, they start to decrease as the level of humidity continues to rise. When analyzing the coefficients estimated for the linear time trend, one can easily observe that beans yields tended to decrease over the analyzed period while maize yields evolved positively. Nevertheless, the magnitude of trend coefficients—both positive and negative—is relatively low.

Table 2. Estimation results for the Geographically Weighted Panel Regression model, semi-arid region of Brazil, 2003-2017.Dependent variable: GWPRcrop yield (kg ha-1) Min Q1 Median Q3 Max

Beans (N = 8,910)

arid -1.7494 2.6101 4.2846 6.7142 17.9235arid 2 -0.8704 -0.1918 0.0097 0.1833 1.4378

trend -10.4179 -3.2596 -0.9085 1.7670 7.7670Adjusted R2 0.0859AIC 119,599.30

Maize (N = 8,715)

arid -188.7425 12.3085 18.0087 26.1308 85.5448arid 2 -15.7915 -1.4865 -0.6338 -0.1732 12.6683trend -31.1673 -0.2034 5.8901 13.3074 93.9915Adjusted R2 0.1734AIC 135,975.90

Source: Research results.

Crop yield responses to changes in weather can be obtained by analyzing the average marginal effect observed for each of the variables of interest. When analyzing the fixed effects panel model, it is observed that, on average, a one-point increase in the aridity index leads to an increase of roughly 4.34 kilograms per hectare of beans. A greater influence of weather conditions is seen for maize as yields increase by 18.68 kilograms per hectare for each increase in the level of aridity.

Estimates for the spatial error model were relatively close to the fixed effects ones, while the smallest ones were found for the spatial lag model§§. The spatial parameters (rho and lambda) were statistically significant for both crops, confirming spatial dependency among observations. By allowing for non-stationarity in the regression parameters, the GWR model—and, by extension, the GWPR—accounts for a large part of the autocorrelation observed in the error terms of a global model calibrated with spatial data (Fotheringham, Brunsdon and Charlton, 2002).

Although R-Squared (and its variants) has long been considered an outdated measure of model’s goodness-of-fit (Lewis-Back and Skalaban, 1990), the values obtained for the Adjusted R-Squared show that the GWPR model fits the relationship of interest way better than the fixed effects panel model, for example. The Akaike Information Criterion (AIC) also indicates that the GWPR model is preferable over the fixed effects one. However, the smallest values for the AIC were found for the spatial error and spatial lag models.

As earlier discussed, adaptive bandwidths were optimized by cross-validation. For this kind of bandwidth, window size varies according to data density so the number of observations in each local regression is kept constant. Therefore, one could expect the proportion of municipalities considered in each local estimation to be inversely related to data density. For beans (maize), the number of data points used for the calibration of the aridity specification*** was 600 (200) over the 15 years of analysis—roughly 40 (13) municipalities per year.

Considering the coefficients in level, 76.09% (61.45%) of municipalities presented pseudo-significant††† estimates for the linear responses of beans (maize) yields to the aridity index. In order to mitigate basis risk, only these municipalities are considered for investigating the viability of the WII product. These locations are depicted in Figure 2. Therefore, the semi-arid region of Brazil is divided in three parts according to geographical proximity and the product is priced for each of them.

§§ Cai, Yu and Oppenheimer (2014) and Kusuma, Jackson and Noy (2018), who also used the GWPR model to examine crop yield responses to the weather, found a similar discrepancy between models’ estimates for weather variables.*** For the model specification in which crop yields are regressed against precipitation and temperature, the number of data points used was 290 (242) for beans (maize) over the 15 years of analysis—approximately 19 (16) locations per year.††† Pseudo-significance, in this case, refers to the t-statistic for the coefficient of each regression point (Kusuma, Jackson and Noy, 2018).

(a) (b)

Figure 2. Analyzed municipalities according to contract groups.Source: Elaborated by the authors.

As previously described, the first step in designing a weather index insurance product concerns the definition of the parameters governing indemnity payments according to the payout scale chosen. Results for the model-based cluster analysis are presented in Figure 3. The leftmost clusters are those considered for determining the trigger and exit parameters. Within-cluster expected value for index realizations (midpoint of ellipsis) is taken as the insurance trigger, while the minimum value corresponds to the payout exit.

(a) (b) (c)

(d) (e) (f)

Figure 3. Model-based clustering for (a) 1st, (b) 2nd and (c) 3rd contracts for beans, and (d) 1st, (e) 2nd and (f) 3rd contracts for rice.Notes: Ellipses and its center point indicate, respectively, within-cluster covariance and mean value.

Source: Research results.

After finding the value of the parameters of interest for the contracts of each crop analyzed, we proceed with the burning cost analysis in order to determine the premium rate related to each of the contracts. The information presented in Table 3 shows how parameters vary between as well as within crops. On average, premiums estimated for maize are higher than those for beans, indicating that it is riskier to grow the former that the latter in the semi-arid as the premium rate is expected to be directly proportional to risk exposure.

When analyzing the contracts specified for each of the three sub-regions, it is observed that, for beans, the third contract presents the highest premium rate. This contract covers the municipalities located in Maranhão, Piauí and Ceará. For maize, in turn, the highest premium was defined for the second contract, which comprises the municipalities within the states of Rio Grande do Sul, Paraíba, Pernambuco, Alagoas and Sergipe. It evidences that riskiness indeed geographically varies among the analyzed crops.

Table 3. Parameters of weather index insurance for the Brazilian semi-arid

ContractAverage liability Trigger Exit Average payout Premium

(R$ ha-1) (index points) (index points) (R$ ha-1) (%)

Beans

1 536.18 26.20 1.40 32.61 7.482 715.53 16.86 4.01 78.25 11.913 1,185.59 25.90 10.10 160.68 16.54

Maize

1 453.46 33.43 3.88 47.40 16.112 336.52 36.43 8.99 77.58 30.423 1,044.56 25.47 8.53 150.93 16.35

Source: Research results.

Lastly, having defined the premium rates associated to each of the suggested contracts, we are able to evaluate the effectiveness of the WII product in reducing unexpected variation the income of family farmers of the Brazilian semi-arid. To this end, we explore the notion of semideviation, which, differently than standard-deviation, accounts only for deviations of observations below the average, capturing downside risk. Results for revenue and semideviation as well as the changes related to the adoption of the suggested WII products are presented in Table 4.

Table 4. Revenue and semideviation for the contracts designed for beans and maize

Contract Revenue (R$ ha-1) Semideviation (R$ ha-1)No insurance Insurance Change No insurance Insurance Change

Beans

1 630.80 623.30 -1.19% 318.49 312.26 -1.96%(425.05) (413.87) (-2.63%)

2 841.80 834.83 -0.83% 411.27 406.27 -1.22%(508.40) (514.64) (1.23%)

3 1,394.81 1,359.34 -2.54% 774.88 743.30 -4.08%(1,250.30) (1,281.92) (2.53%)

Maize

1 533.48 507.85 -4.80% 319.89 294.78 -7.85%(553.68) (510.65) (-7.77%)

2 395.91 371.13 -6.26% 243.51 214.32 -11.99%(443.30) (510.61) (15.18%)

3 1,228.89 1,209.00 -1.62% 705.05 685.61 -2.76%(1,724.34) (1,673.59) (-2.94%)

Source: Research results.Notes: Revenue is averaged across space and time and standard deviation is shown in parenthesis.

On average, the introduction of the suggested WII product, independently of the contract analyzed, leads to a decline on farmer’s per hectare revenue. The magnitude of such decreases, however, is not so high. Among the crops analyzed, it is observed that maize farmers have their revenues comparatively more penalized with insurance adoption than those of beans growers. The size of revenue reductions varies considerably across the different contracts of each crop as well. Variation in average maize revenues, for instance, ranges from -1.62% to -6.26%.

For the standard deviation of revenues, on the contrary, does not present such a clear pattern. In fact, mixed evidence if found regarding the change in revenue dispersion after the establishment of the insurance. This is true for both beans and corn. When one focuses on the values found for revenue semideviations, however, it is noticed that downside risk is indeed lessened as insurance becomes available. In general, the biggest changes in the risk of negative variations in revenue are observed for maize.

6. Discussion

As previously described, we found robust evidence that crop yields positively respond to changes in the degree of aridity, i.e., the less (more) arid (humid) a location is, as classified according to index values, more prone to the cultivation of both beans and maize it is. In fact, as stated by Hoogenboom (2000), in addition to solar radiation, precipitation and air temperature—which compose the index of aridity—are the key agrometeorological variables associated with agricultural production. The difference observed across crops in terms of the magnitude of the estimated marginal effects reflects the existing difference in water (humidity or moisture) requirement. In fact, Guerra et al. (2003) showed that, in certain parts of Brazil, beans require comparatively less water than maize during the growing season, with emphasis on the flowering stage of the plants.

In an index insurance context, it is worth highlighting the proportion of observations for which the GWPR model provided statistically pseudo-significant estimates. It indicates the municipalities where the underlying index effectively works as a proxy for crop yield results. Given the relatively high proportion of analyzed locations for which the aridity level proved to significantly influence crop yields, the use of the aridity index as a proxy for local weather conditions is in fact relevant. It must be stressed that, in general, the percentage for which our GWPR model provided pseudo-significant coefficients are reasonably in line with the (scarce) literature on the same subject that also relied on GWPR estimations. Investigating rice with a GWPR model, Kusuma, Jackson and Noy (2018) found that half of their observations had pseudo-significant estimates.

Crop yield responses to weather conditions considerably fluctuate across the semi-arid region of Brazil. Accordingly, so do the parameters governing the payouts of the WII we designed. Trigger and exit thresholds, as calculated through a model-based clustering algorithm, vary expressively among the different contracts designed for a same crop. This is, therefore, another piece of evidence on the spatially non-stationary nature of risk exposure to the weather, which corroborates the idea of offering different contracts to different parts of the Brazilian semi-arid.

With the payout parameters in hand, we were able to calculate the premium rate of each contract by means of a burning cost analysis. Except for the region for which contract 3 was designed, which comprises municipalities from the states of Bahia and Minas Gerais, an expressive divergence regarding the premium rate was observed between the crops analyzed. In fact, the maize premiums calculated for contracts 1 and 2 are more than twice as high as those computed for beans.

As premiums are estimated in order to capture the risk faced by farmers, which ultimately are transferred to insurers, they provide an approximation of how much the farmers of a given crop in a given region are exposed to risk. According to our findings, beans and maize farmers located in the southernmost part of the semi-arid do not have, between them, major differences in risk exposure. For the remainder of the region, however, maize production is much more susceptible to the weather. In fact, as showed elsewhere, maize requires greater water availability.

In regard of the effectiveness of the proposed WII product in reducing income variability, interesting features of our results worth highlighting. Not all contracts provide a reduction in the standard deviation of revenues, which one could see as an evidence against the effectiveness of the insurance product. Notwithstanding, semideviation attest exactly the contrary. Therefore, if standard deviation increases with insurance but semideviation goes in the opposite way, variation in revenues are guided by positive deviances from average values.

In general, the introduction of the WII in the semi-arid of Brazil would lead to a slight reduction in the average income of agriculture. To a certain extent, this can affect the likelihood of the success of the initiative as family farmers in the region often rely on a relatively short income. The lowering in downside risk, in turn, is proportionally greater than reductions in average income. Therefore, farmers that adopt the WII product ultimately substitute the possibility of suffering episodic catastrophic losses by a modest reduction in recurrent income.

7. Conclusion

The semi-arid region of Brazil is historically plagued by catastrophic events, among which stand out the droughts that severely threaten the livelihood of its residents. In fact, most of the population of this region is comprised by family farmers whose income directly depend on the small-scale agricultural production. Despite this scenario, crop insurance adoption in the region is historically very low, even though the Federal Government has been providing premium subsidies for over a decade.

With this in mind, it is of great relevance to analyze the feasibility of implementing a weather index insurance (WII) scheme in the region. Such type of climate risk management tool is developed toward supporting the livelihood of vulnerable smallholders when catastrophes occur. As the payouts of WII products are driven by a pre-specified index, whose realizations depend on a given underlying weather variable, most of the issues that characteristically harm crop yield insurance schemes are addressed.

While mitigating asymmetric information and transaction costs, WII adds a different variable to this complicated equation. Basis risk arises in WII products because crop yield responses to the weather are inherently non-stationary across the area for which the contract is designed. Taking this into consideration, we investigate the association between crop yields and weather conditions through a Geographically Weighted Panel Regression (GWPR), a method that provides local estimates for the relationship of interest.

Based on the findings of the GWPR model, we were able to define a sample of municipalities in the Brazilian semi-arid region for which a WII product was designed, priced and evaluated for effectiveness in mitigating downside risk. Develop a single contract for the whole region, which comprises an area of more than one million square kilometers, would naively exacerbate the basis risk that we parsimoniously tried to take care with the estimation of the local responses of crop yields to the weather.

In this sense, the sample of municipalities analyzed was divided into three groups according to geographical proximity and a WII contract was designed for each group. Thus, exactly the same contract was offered for farmers residing in the municipalities within a same group. Ultimately, we dealt with six

different contracts—three for beans and three for maize. The payouts of all contracts follow the same structure as indemnities are proportionally paid according to the realizations of the underlying index, which, in our case, is an index of aridity.

The utilization of a model-based clustering algorithm led to the definition of the parameters that guide payout payments, namely the trigger and exit points. Based on the historical distribution of index realizations and crop yields, the parameters estimated varied considerably across crops and contracts. Having set the trigger and the exit point, we performed a burning cost analysis to estimate premiums. The difference in the rates calculated reflects the diverse risk exposure, which is higher for maize than for beans.

Lastly, with all the necessary information, we evaluated the effectiveness of our WII product and its respective contracts in mitigating downside risk. To this end, we calculated the semideviation associated to each of the sub-regions of semi-arid for two scenarios. In the first, farmers have no insurance. In the second, in turn, the WII product is adopted. Although insurance adoption leads to a slight decrease in the average income, the percentage decrease in downside risk is twice as high as it.

Seen this, we are able to conclude that a WII product, as the one proposed here, would indeed help the farmers of the semi-arid region of Brazil in decreasing the interannual variability in their income. Ultimately, by adopting insurance, farmers opt for a small decrease in recurring income in exchange for protecting their assets when extreme events such as droughts occur. Therefore, WII can be seen as a powerful climate risk management tool as it enables the maintenance of smallholder livelihoods.

Our analysis contributes to the literature and perhaps more importantly to practitioners. Based on investigations conducted worldwide, we provide a simple yet powerful methodological framework in which both insurers and the government may rely on to design and implement WII initiatives in Brazil. As a drawback, we highlight the quality and length of the time series of local crop yields, which may obstruct the development of more reliable products. Data on the weather are also an issue, but it is easily addressed by using remotely sensed data, as we did.

References

ADEYINKA, A. A.; KRISHNAMURTI, C.; MARASENI, T. N.; CHANTARAT, S. The Viability of Weather index Insurance in Managing Drought Risk in Rural Australia. International Journal of Rural Management, v. 12, n. 2, p. 125-142, 2016.

ALMEIDA, E. S. Econometria Espacial Aplicada. Campinas: Alínea Editora, 2012. 498p.

ANGELOTTI, F.; GIONGO, V. Ações de mitigação e adaptação frente às mudanças climáticas. In: MELO, R. F.; VOLTOLINI, T. V. (Ed.). Agricultura familiar dependente de chuva no Semiárido. Brasília: Embrapa, 2019.

BERG, A.; QUIRION, P.; SULTAN, B. Weather-Index Drought Insurance in Burkina-Faso: Assessment of Its Potential Interest to Farmers. Weather, Climate and Society, v. 1, n. 1, p. 71-84, 2009.

BIVAND, R.; YU, D. spgwr: Geographically Weighted Regression. R package version 0.6-32. 2017.

BLACK, E.; TARNAVSKY, E.; MAIDMENT, R.; GREATREX, H.; MOOKERJEE, A.; QUAIFE, T.; BROWN, M. The Use of Remotely Sensed Rainfall for Managing Drought Risk: A Case Study of Weather Index Insurance in Zambia. Remote Sensing, v. 8, n. 4, p. 1-16, 2016.

BOYD, M.; PORTH, B.; PORTH, L.; TAN, K. S.; WANG, S.; ZHU, W. The Design of Weather Index Insurance Using Principal Component Regression and Partial Least Squares Regression: The Case of Forage Crops. North American Actuarial Journal. Advance online publication. doi:10.1080/10920277.2019.1669055

CHOUDHURY, A.; JONES, J.; OKINE, A.; CHOUDHURY, R. Drought-Triggered Index Insurance Using Cluster Analysis of Rainfall Affected by Climate Change. Journal of Insurance Issues, v. 39, n. 2, p. 169-186, 2016.

CLARKE, D. J. A Theory of Rational Demand for Index Insurance. American Economic Journal: Microeconomics, v. 8, n. 1, p. 283–306, 2016.

CONRADT, S.; FINGER, R.; SPORRI, M. Flexible weather index-based insurance design. Climate Risk Management, v. 10, p. 106-117, 2015.

CORREIA, R. C.; KIILL, L. H. P.; MOURA, M. S. B.; CUNHA, T. J. F.; JESUS JÚNIOR, L. A.; ARAÚJO, J. L. P. A região semiárida brasileira. In: VOLTOLINI, T. V. (Ed.). Produção de Caprinos e Ovinos no Semiárido. Petrolina: Embrapa Semiárido, 2011.

CROISSANT, Y; MILLO, G. Panel Data Econometrics in R: The plm Package. Journal of Statistical Software, v. 27, n. 2, p. 1-43, 2008.

ESTRADA, J. Mean-semivariance behavior: Downside risk and capital asset pricing. International Review of Economics & Finance, v. 16, n. 2, p. 169-185, 2007.

EZE, E.; GIRMA, A.; ZENEBE, A. A.; ZENEBE, G. Feasible crop insurance indexes for drought risk management in Northern Ethiopia. International Journal of Disaster Risk Reduction, v. 47, p. 1-11, 2020.

FOTHERINGHAM, A. S.; BRUNSDON, C.; CHARLTON, M. Geographically Weighted Regression: the analysis of spatially varying relationships. Chichester: John Wiley & Sons Ltd, 2002.

HELLMUTH, M. E.; OSGOOD, D. E.; HESS, U.; MOORHEAD, A.; BHOJWANI, H. Index insurance and climate risk: Prospects for development and disaster management. New York: IRI, 2009.

HIJMANS, R. J. raster: Geographic Data Analysis and Modeling. R package version 3.0-7. 2019.

HOHL, R. M. Agricultural Risk Transfer: From Insurance to Reinsurance to Capital Markets. Chichester: John Wiley & Sons, 2019.

KAYANO, M. T.; ANDREOLI, R. V. Clima da Região Nordeste do Brasil. In: CAVALCANTI, I. F. A.; FERREIRA, N. J.; SILVA, M. G. A. J.; DIAS, M. A. F. S. (Org.). Tempo e clima no Brasil. São Paulo: Oficina de Textos, 2009.

KELLNER, U.; MUSSHOFF, O. Precipitation or water capacity indices? An analysis of the benefits of alternative underlyings for index insurance. Agricultural Systems, v. 104, n. 8, p. 645-653, 2011.

KUSUMA, A.; JACKSON, B.; NOY, I. A viable and cost-effective weather index insurance for rice in Indonesia. The Geneva Risk and Insurance Review, v. 43, n. 2, p. 186-218, 2018.

LEWIS-BECK, M. S.; SKALABAN, A. The R-Squared: Some Straight Talk. Political Analysis, v. 2, p. 153-171, 1990.

MAIA, G. B. S.; ROITMAN, F. B.; GONÇALVES, F. C. S.; DE CONTI, B. M. Seguros agrícolas: experiências internacionais e reflexões para o caso brasileiro. Revista do BNDES, n. 34, p. 53-100, 2010.

MATSUURA, K.; WILLMOTT, C. J. Terrestrial Precipitation: 1900-2017 Gridded Monthly Time Series. http://climate.geog.udel.edu/~climate/html_pages/download.html#P2017.

MELO, R. F.; VOLTOLINI, T. V. Agricultura familiar dependente de chuva no Semiárido. Brasília: Embrapa, 2019.

MILLO, G.; PIRAS, G. splm: Spatial Panel Data Models in R. Journal of Statistical Software, v. 47, n. 1, p. 1-38, 2012.

MIRANDA, M. J.; FARRIN, K. Index Insurance for Developing Countries. Applied Economic Perspectives and Policy, v. 34, n. 3, p. 391–427, 2010.

NOGALES, R.; CORDOVA, P. On the Advantages and Feasibility of Weather Index-Based Crop Insurance Schemes in Bolivia. Emerging Markets Finance and Trade. Advance online publication. doi:10.1080/1540496X.2019.1677226

OURY, B. Allowing for Weather in Crop Production Model Building. American Journal of Agricultural Economics, v. 47, n. 2, p. 270-283, 1965. DE MARTONNE, M. E. Une nouvelle fonction climatologique: l’Indice d’Aridité. La Météorologie, n. 19, p. 449-458, 1926.

PARODI, P. Pricing in General Insurance. Boca Raton: CRC Press, 2015.

PIERCE, D. ncdf4: Interface to Unidata netCDF (Version 4 or Earlier) Format Data Files. R package version 1.17. 2019.

POUDEL, M. P.; CHEN, S. E.; HUANG, W. C. Pricing of Rainfall Index Insurance for Rice and Wheat in Nepal. Journal of Agricultural Science and Technology, v. 18, n. 2, p. 291-302, 2016.

RAUCCI, G. L.; LANNA, R.; SILVEIRA, F.; CAPITANI, D. H. D. Development of weather derivatives: evidence from the Brazilian soybean market. Italian Review of Agricultural Economics, v. 74, n. 2, p. 17-28, 2019.

SCRUCCA, L.; FOP, M.; MURPHY, T. B.; RAFTERY, A. E. mclust 5: Clustering, Classification and Density Estimation Using Gaussian Finite Mixture Models. The R Journal, v. 8, n. 1, p. 289-317, 2016.

SHAW, L. H. The Effect of Weather on Agricultural Output: A Look at Methodology. American Journal of Agricultural Economics, v. 46, n. 1, p. 218-230, 1964.

SHI, H.; JIANG, Z. The efficiency of composite weather index insurance in hedging rice yield risk: evidence from China. Agricultural Economics, v. 47, n. 3, p. 319-328, 2016.

SHIRSATH, P.; VYAS, S.; AGGARWAL, P.; RAO, K. N. Designing weather index insurance of crops for the increased satisfaction of farmers, industry and the government. Climate Risk Management, v. 25, p. 1-12, 2019.

SILVA, A. F.; REGITANO NETO, A. As principais culturas anuais e bianuais na agricultura familiar. In: MELO, R. F.; VOLTOLINI, T. V. (Ed.). Agricultura familiar dependente de chuva no Semiárido. Brasília: Embrapa, 2019.

SKEES, J. R. Challenges for use of index‐based weather insurance in lower income countries. Agricultural Finance Review, v. 68, n. 1, p. 197-217, 2008.

SPICKA, J.; HNILICA, J. A Methodical Approach to Design and Valuation of Weather Derivatives in Agriculture. Advances in Meteorology, v. 5, p. 1-8, 2013.

STALLINGS, J. L. A Measure of the Influence of Weather on Crop Production. American Journal of Agricultural Economics, v. 43, n. 5, p. 1153-1160, 1961.

STALLINGS, J. L. Weather Indexes. American Journal of Agricultural Economics, v. 42, n. 1, p. 180-186, 1960.

WHEELER, D. C.; PÁEZ, A. Geographically Weighted Regression. In: FISCHER, M. M.; GETIS, A. (Ed.). Handbook of Applied Spatial Analysis: Software Tools, Methods and Applications. Berlin: Springer-Verlag, 2010.

WILLIAMS, T. M.; TRAVIS, W. R. Evaluating Alternative Drought Indicators in a Weather Index Insurance Instrument. Weather, Climate and Society, v. 11, n. 3, p. 629-649, 2019.

YU, D. Exploring Spatiotemporally Varying Regressed Relationships: The Geographically Weighted Panel Regression Analysis. In: Joint International Conference on Theory, Data Handling and Modelling in Geospatial Information Science, 2010, Hong Kong. Proceedings… Hong Kong: ISPRS, 2010.

ZHU, J. Evaluation of an Insurance Scheme Based on the Weather Index. The Chinese Economy, v. 44, n. 6, p. 56-72, 2011.

Appendix

Table A1. Estimation results for the Fixed Effects, Spatial Error and Spatial Lag panel data models, semi-arid region of Brazil, 2003-2017.Dependent variable:

Panel Data Model

crop yield (kg ha-1) Fixed Effects Spatial Error Spatial Lag

Beans (N = 8,910)

arid 4.3428*** (0.2765) 4.3466*** (0.5171) 1.9147*** (0.2356)arid 2 -0.0116 (0.0212) 0.0109 (0.0385) 0.0030 (0.0180)trend -0.7402** (0.3100) -0.9244 (0.5874) -0.3990 (0.2642)rho 0.5577*** (0.0102)lambda 0.5572*** (0.0102)Adjusted R2 0.0334AIC 119,992.26 117,820.56 117,825.42

Maize (N = 8,715)

arid 18.6815*** (0.9470) 18.6918*** (1.4825) 10.9389*** (0.8773)arid 2 -0.6278*** (0.0640) -0.6508*** (0.0992) -0.3858*** (0.0593)trend 7.3851*** (1.0680) 8.1398*** (1.6785) 4.8306*** (0.9894)rho 0.4186*** (0.0122)lambda 0.4178*** (0.0122)Adjusted R2 0.0444AIC 136,891.62 135,903.49 135,907.13

Notes: *, ** and *** represent, respectively, significance at the 10%, 5%, and 1% level. Standard errors are shown in parentheses. All models are estimated with municipality fixed effects.Source: Research results.