Towards a Sustainable Agricultural Credit Guarantee Scheme
aa r X i v : . [ q -f i n . GN ] A ug Towards a Sustainable Agricultural Credit GuaranteeScheme
Reason L. Machete
August 5, 2020
Abstract
Since 1986, Government of Botswana has been running an Agricultural CreditGuarantee Scheme for dry-land arable farming. The scheme purports to assistdry-land crop farmers who have taken loans with participating banks or lendinginstitutions to help them meet their debt obligations in case of crop failure due todrought, floods, frost or hailstorm. Nonetheless, to date, the scheme has focusedsolely on drought. The scheme has placed an unsustainable financial burden onGovernment because it is not based on sound actuarial principles. This paperargues that the level of Government subsidies should take into account the gainsmade by farmers during non-drought years. It is an attempt to circumvent thechallenges of correlated climate risks and recommends a quasi self-financing mech-anism, assuming that the major driver of crop yield failure is drought. Moreover,it provides a novel subsidy and premium rate setting method. c (cid:13) In many countries around the world, the importance of agricultural produce is under-scored by the efforts to establish insurance for this specific sector of the economy. TheUSA, Germany, Italy, France and Spain are examples of countries that have establishedagricultural insurance (Dick and Wang, 2010). Agricultural insurance in these countriesdepends heavily on Government subsidies. The subsidies tend to be channelled towardspremiums. Among these countries, Spain is said to have the most developed system ofagricultural insurance that covers several risks (Colovic and Petrovic, 2014). In essence Email: [email protected], [email protected], [email protected]; Tel: +267-77610677.
1t provides a full-risk coverage. It is noteworthy that increasing the number of perilscovered will, inevitably, increase the premiums.Let it be noted, however, that the term agricultural is broad and includes manyperils that affect crops and livestock such as hail, floods, frost, etc. Drought is butjust one of these many perils that are grouped together under agricultural insurance.When drought is frequent as is the case in the US, Spain and China, it is difficult, ifnot impossible, to insure without Government subsidy. Actually, agricultural insurancein developing countries is mostly subsidised (Alam et al. , 2020). There is a sizablebody of literature on Government subsidised multi-peril crop insurance in the USA (e.g.Du and Hennessey, 2017; Duncan and Myers, 2000; Glauber, 2004; Ker and Goodwin,2000) and most of it is not solely focused on drought insurance for crops. Some literaturetalks of yield insurance, which naturally includes drought insurance (e.g. Eze et al. , 2020;Wang and Zhang, 2003). In this paper we consider yield to be a good proxy for droughtand use it to make an empirical assessment of drought in Botswana. It is preferredto rainfall because our analysis has shown rainfall to be a poor index of crop yield.While there are other possible indices to consider, these also fail to capture crop yieldfor dry land crops (Reeves, 2017). In particular, it is difficult to detect any correlationsbetween yield for dry land crops and any of the indices. Such problems can lead to whatis referred to as basis risk . Basis risk refers to a case where the payout is not sufficientto defray the losses incurred by the insured (Eze et al. , 2020).Meanwhile, Botswana has had an Agricultural Credit Guarantee Scheme to managethe agricultural drought that is specific to dry-land crops since 1986. Administered byGovernment, this is supposed to be a multi peril insurance even though, since its in-ception, it has solely covered drought following presidential declarations. Every year,at the end of the harvest, a team of experts from various Government departmentstravels around the country to perform drought assessment and subsequently make rec-ommendations to Government. The team is referred to as an Inter-Ministerial DroughtAssessment Committee. Following the team’s recommendations, a national or regionaldrought may be declared with relevant interventions to be implemented. The inter-ventions entail two aspects: (i) Drought Relief Interventions and (ii) Contributions toinstalments for loans taken by arable farmers under the Agricultural Credit GuaranteeScheme. These interventions are performed only if a presidential declaration of droughthas been made. Drought interventions can include supplementary feeding for childrenunder 5 years old, employment of casual workers, construction projects, seed subsidyfor farmers, subsidy on selected cattle feeds and maintenance of fire breaks. In additionto being given loan subsidies when they have taken loans within participating banks,subsidy for commercial farmers is limited to Government contributing 65% towards thecost of fertilisers, herbicides and pesticides. Several years, the Ministry of Agriculturein Botswana commissioned a consultancy to investigate the possibility of supportingfarming through an agricultural insurance sscheme Kerapeletswe-Kruger et al. (2007),but this did not bear significant fruit because it lacked concrete recommendations ofhow to setup such a scheme.A sample of Government expenses following drought declarations is shown in Table 1.A number of observations can be made based on past drought declarations and subse-quent payouts. Most importantly, an analysis of the data indicates that, on average,2EASON 2004/5 2005/6 2006/7 2014/15 2015/16DRI P 205 M P 324 M P 77 M P 632 MACGS P 17 M P 22 M P 8 M P 244 M P 115 MTOTAL P 222 M P 22 M P 332 M P 321 M P 747 MTable 1:
A sample of Government expenses following the drought seasons indicated. DRI de-notes Drought Relief Interventions and ACGS denotes Agricultural Credit Guarantee Scheme.The ACGS amounts indicated were taken only through the National Development Bank. Theamounts taken through CEDA were not supplied. drought is declared about twice in every three years and is thus a high-frequency event.It has been argued that insurance is not the right mechanism for such high frequencyevents (e.g. Clarke and Hill, 2013). Some of the droughts can be quite extreme, suchas that of the 2015/2016 season. It is worth noting that such an extreme drought isa one in 35 year event. Irrespective of the impact of the drought, we argue here thatthe Agricultural Credit Guarantee Scheme is not sustainable because it is not based onactuarial sound principles. In essense, Government may have irrationally committeditself to highly subsidise dry land arable farming. The level of cover it provides is incon-sistent with contributions to the scheme. This paper further argues that contributionsshould be specific to the crops planted in a given season rather than just remain generic.It provides novel tools that can be used to determine the level of Government subsidynecessary to keep farmers solvent.
It has been highlighted in the previous section that drought declarations are made 2/3of the time and, after each declaration, Government spends millions of Pula on droughtrelief interventions. A simple average of data on Table 1 suggests that an average ofaround P322 million per annum is spent by Government on drought interventions. Thisis surely a lot of money that Government spends every year. It should be understood,however, that any insurance company should charge not less than the Government’saverage loss per annum. Otherwise the insurer cannot remain solvent. In fact, theinsurer should charge more than the Government’s average loss to take into accountadministrative costs of running the insurance.What then is the value of insurance and how does it work? Insurance derives itsvalue from keeping expenses (in the form of premiums) fixed from year to year whilstthe insurance company takes the risk of fluctuating payouts. As defined by Mehr et al. (1985), insurance is an instrument for reducing risk by combining a sufficient numberof exposure units to make their individual losses collectively predictable. Combiningseveral exposure units is called r isk pooling. What is the benefit of risk pooling then?An insurer benefits from risk pooling in the sense that the law of large numbers insuresthat fluctuations are reduced when the insured entities increase. Furthermore, the in-sured can benefit from the law of large numbers through reduced administrative andbuffer load costs due to cost sharing (Wang and Zhang, 2003). The benefit of risk pool-3ng is not loss reduction but risk reduction! Whereas, traditionally, the insured unitshave been required to be uncorrelated (e.g. see Brown and Gottlieb, 2007), it has beenshown that risk pooling can still reduce risk even when the insured units are imperfectlycorrelated (Annan et al. , 2013; Wang and Zhang, 2003).Consider an insurer who receives gross premium P . The gross premium is the sum P = P n + L + A, (1)where P n is the net premium, L is the buffer load and A is the term for administrativecosts (Wang and Zhang, 2003). The buffer load term takes care of variations in claimsfrequency and severity and it diminishes to zero as the pool gets larger. Each insuredcontributes an amount equivalent to their average loss to the net premium and some ad-ditional amount to the buffer load and administrative costs (Brown and Gottlieb, 2007).It is important to note that the insured benefit from risk pooling through a reduction intheir contributions towards the buffer load and administrative costs. Risk pooling willnot and cannot reduce their individual contributions towards the net premium!It might seem to some that the case of Botswana’s drought is markedly differentfrom the car insurance industry. In the case of car insurance, it would appear thatone contributes low premiums relative to the size of possible damages for which theyare covered. In fact, in Botswana, insurers typically charge premiums not more than5% of the value of the car. Such a low percentage could be the one that inspired the5% premiums charged under the Agricultural Credit Guarantee Scheme. A fractionconsistent with the drought situation of Botswana should, however, not be less thanthe horrifying 2/3 (or 66.67%). In contrast, why do insurers charge low percentagepremiums for car insurance? The reason is that the low percentages are consistent withthe risk that is underwritten. In particular, one should imagine that the risk of a carbeing damaged beyond economic value is below 5% on average. In order to appreciatethis percentage, think of how rare it is that one gets involved in a serious accident.Perhaps in your lifetime you have had no more than one or two serious accidents. Mostof the minor ones can typically be settled by excess , perhaps avoiding the fines incurredwhen incidents are reported to the police. Bearing the foregoing issues in mind, can wecome up with a contribution plan that is based on sound actuarial principles? From the past records, it could not be established which declarations were regional andwhich were national. Therefore, we will assume that all declarations that resulted inpayouts were national because an overwhelming majority of declarations appear to havebeen national. This assumption also aids tractability of the problem. We argue thatcontributions should be specific to the crops planted in a given planting season andconsistent with the respective area planted. If there are J types of crops, we can let j be the index for a given crop, with j ∈ { , . . . , J } . In the subsequent discussions, ω willbe taken to be the frequency of drought declarations. Taking Υ j ( t ) to be the yield for Simply put, excess is the amount below which an insurance company does not issue a payout. Inactuarial language, this is called a deductible (Brown and Gottlieb, 2007). j th crop at time t , we can define the corresponding crop-specific drought thresholdto be µ ( j ) c such that F j (cid:0) µ ( j ) c (cid:1) = ω, (2)where F j ( · ) is the cumulative distribution function of the yield for the j th crop. Thethreshold may also be thought of as a prescribed coverage level. For a given crop, someof the declarations might coincide with yields that are above the drought threshold, µ ( j ) c . For that particular crop, the declaration of drought can be thought of as a falsedeclaration. This leads us to define the proportion of coincident (or ‘true’) declarationsto be ψ τj = 1 | Γ | X t ∈ Γ H (cid:0) µ ( j ) c − Υ j ( t ) (cid:1) , (3)where H ( · ) is the Heaviside step function and Γ is the set of times when drought dec-larations were made. The proportion of declarations that are false is then given by ψ f = 1 − ψ τ . The proportion ψ f gives an indication of how often farmers get financialassistance when they should not. The crop-specific drought threshold need not cor-respond to the frequency of drought declarations. It can be selected purely by otherconsiderations such as the yield potential of the specific crop. If selected by other con-siderations, it leads us to define the crop-specific drought frequency as ω j = F j (cid:0) µ ( j ) c (cid:1) . (4)The threshold µ ( j ) c can also be thought of as the pre-specified crop-specific coverage level.Given that λ j ( t ) is the price per hectorage, the crop will experience a production lossamounting to L j ( t ) = λ j ( t ) max (cid:8) , µ ( j ) c − Υ j ( t ) (cid:9) , (5)which can be thought of as an indemnity payment for the specific crop. The distributionof L j ( t ) can be obtained from the truncated distribution of the yield, following whichwe can obtain the mean loss E [ L j ( t )]. The weighted loss for the cluster of crops is L θ ( t ) = J X j =1 θ j ( t ) L j ( t ) , (6)where θ j ( t ) is the random variable for the proportion of area in which the j th crop wasplanted. Moreover, P Jj =1 θ j ( t ) = 1. The above model sees each individual loss as arandom variable. Consequently, the weighted loss experienced by the pool of crops isalso a random variable. The expectation of the weighted loss is thus given by E [ L θ ( t )] = J X j =1 E [ θ j ( t ) L j ( t )] (7)= J X j =1 E [ θ j ( t )] E [ L j ( t )] + J X j =1 Cov[ θ j ( t ) , L j ( t )] (8)5he variance of the weighted loss at year t is then given byVar( L θ ( t )) = Var J X j =1 θ j ( t ) L j ( t ) ! (9)= J X i =1 J X j = i Cov[ θ i ( t ) L i ( t ) , θ j ( t ) L j ( t )] (10)= J X j =1 Var [ θ j ( t ) L j ( t )] + J X i =1 J X j =1 ,j = i Cov[ θ i ( t ) L i ( t ) , θ j ( t ) L j ( t )] (11)= J X j =1 Cov (cid:2) θ j ( t ) , L j ( t ) (cid:3) + J X j =1 E (cid:2) θ j ( t ) (cid:3) E (cid:2) L j ( t ) (cid:3) − J X j =1 n Cov [ θ j ( t ) , L j ( t )] + E [ θ j ( t )] E [ L j ( t )] o + J X i =1 J X j =1 ,j = i Cov[ θ i ( t ) L i ( t ) , θ j ( t ) L j ( t )] . (12)If θ i , θ j , L i and L j , where i = j , are pairwise independent, then the above formulareduces to Var( L θ ( t )) = J X j =1 Cov (cid:2) θ j ( t ) , L j ( t ) (cid:3) . (13)Setting Z ( t ) = L ( t ) − E [ L θ ( t )] p Var[ L θ ( t )] , (14)we can approximate Z ( t ) by the standard normal distribution, meaning that Z ( t ) ∼ N (0 , P (cid:16)(cid:12)(cid:12) L θ ( t ) − E [ L θ ( t )] (cid:12)(cid:12) < . p Var[ L θ ( t ] (cid:17) ≈ .
95 (15)can be thought of as the probability that the fund set up to finance the scheme will notbe exhausted. Therefore, the buffer fund needs to be set at E [ L θ ( t )] + 2 p Var[ L θ ( t )] perhectorage to maintain the probability of ruin at 2.5%. More generally, the fund shouldbe set to be F θ = A (cid:16) E [ L θ ( t )] + η p Var[ L θ ( t )] (cid:17) (16)where A = P Jj =1 A j and η is a parameter to be chosen to be consistent with the riskappetite of the insurer or fund manager. In essence the η should be chosen to minimisethe probability of ruin.It is important to measure the effect of using mixed farming to mitigate risk. Whetheror not mixing crops is effective as a risk mitigation strategy can be determined byassessing how the variance of L θ ( t ) compares with the weighted average variance of each L j ( t ). The coefficient of effectiveness can be used for this. If V denotes the weightedaverage variance of the losses, then the coefficient of effectiveness is given by φ θ = Var[ L θ ] E [ V ] , (17)6here V = J X j =1 θ j Var[ L j ] . (18)Setting E [ θ j ] = α j , it turns out that E [ V ] = J X j =1 α j Var[ L j ] , (19)from whence the coefficient of effectiveness becomes φ θ = Var[ L θ ] P Jj =1 α j Var[ L j ] . (20)The lower the value of φ θ , the more effective the risk pooling approach. If θ j is constantfor all j with θ j = α j , then the above formula reduces to φ θ = (cid:16)P Jj =1 α j ( t ) Var [ L j ( t )] + P Ji =1 P Jj = i α i ( t ) α j ( t )Cov ( L i ( t ) , L j ( t )) (cid:17)(cid:16)P Jj =1 α j Var [ L j ( t )] (cid:17) . (21)If the losses are independent, in which case Cov ( L i ( t ) , L j ( t )) = 0 whenever i = j , thenthe coefficient of effectiveness becomes φ θ = J X j =1 α j ( t ) Var [ L j ( t )] ! , J X j =1 α j ( t )Var [ L j ( t )] ! . (22)In addition, if the variances are equal, then the formula for the coefficient of effectivenessbecomes φ θ = J X j =1 α j ( t ) . (23)Consequently, using the method of Lagrangian multipliers under uncorrelated risk, itfollows that φ θ attains a minimum when α i = α j for all i = j , in which case the minimumis φ θ = 1 /J .The gain made from the j th crop in the year t , denoted by G j ( t ), can be defined via G j ( t ) = λ j ( t ) max (cid:8) , Υ j ( t ) − µ ( j ) c (cid:9) . (24)The total gain during a given season is G θ ( t ) = J X j =1 θ j G j ( t ) (25)A payout to farmers should be made as long as L θ ( t ) >
0, in which case the losses arenon-zero. Otherwise there should be no payout. The surplus for the j th crop in a givenplanting season is then given by S j ( t ) = G j ( t ) − L j ( t ) . (26)7f E [ S j ( t )] ≤
0, then the j th crop is not insurable and should be removed from thecluster of crops that are covered. In essence the crop makes no business sense. Withoutloss of generality, we assume that each crop in the cluster satisfies the condition that E [ S j ( t )] >
0, implying that it makes business sense. The weighted surplus per hectorageis S θ ( t ) = J X j =1 θ j ( t ) S j ( t ) . (27)The expected surplus per hectorage is E [ S θ ( t )] = J X j =1 E [ θ j ( t ) S j ( t )] . (28)If E [ S θ ( t )] >
0, then the cluster of crops makes business sense and may be insurable.Note, however, that the condition that E [ S j ( t )] > E [ S θ ( t )] > E [ S θ ( t )] >
0. In thecase that the proportion of hectorage planted is constant, i.e. θ j ( t ) = α j , then E [ S θ ( t )] = J X j =1 α j E [ S j ( t )] , (29)where the linear property of the expectation operator has been used. Similarly, if θ j ( t )and S j ( t ) are independent for all j , then E [ S θ ( t )] = J X j =1 E [ θ j ( t )] E [ S j ( t )] . (30)Since the proportion of hectorage planted for each crop cannot be negative, it followsthat E [ θ j ( t )] ≥
0. Consequently, under the foregoing independence condition, it isguaranteed that expected surplus per hectorage will be non-negative, i.e. E [ S θ ( t )] ≥ E [ S θ ( t )] ≥
0. In this case, the farming is profitable. Given thatthe loan instalment per area planted per season is l , it is important to have E [ S θ ( t )] > l to be able to use the proceeds of farming to service the instalments. Without insurance,the amount left after paying instalments is R = E [ S θ ( t )] − l. (31)If the frequency of drought declarations is ω , then the average amount paid towardsinstalments per season is l = (1 − ω ) l + pωl, (32)8here (1 − p ) is the insured benefit level, with 0 ≤ p ≤
1. Denoting the premium rateby γ θ , the amount of premium paid to take out insurance is γ θ l , the portion of surplusleft after making payments towards instalment and premiums is R = E [ S θ ( t )] − (1 − ω ) l − pωl − γ θ l. (33)Note that ω can be chosen to be consistent with a specific collection of crops. The pre-mium contributions and subsidies may be set to reflect both the frequency and severityof the drought events. In order for the farmer to remain solvent, it is important to have R >
0. This condition translates to the inequality( γ θ + pω ) < E [ S θ ( t )] l − (1 − ω ) . (34)An actuarially sound premium level should satisfy the equation γ θ = ω (1 − p ) . (35)When premiums are actuarially fair, inequality (34) reduces to the requirement that E [ S θ ( t )] > l . What happens if actuarially sound premiums lead to insolvency, i.e. R ≤ E [ S θ ( t )] ≤ l ? In this case, under the condition that E [ S θ ] ≥ ν ≥ − E [ S θ ( t )] l . (36)The farmer’s premium rate should then be set to γ θ = ω (1 − p )(1 − ν ) . (37)If E [ S θ ] <
0, then this is a case for full Government subsidy and Government shouldpay the full premium rate. The formulae for premium rate and Government subsidy arerespectively given by γ θ = E [ S θ ] < ,ω (1 − p )(1 − ν ) if E [ S θ ] ∈ [0 , l ) ω (1 − p ) if E [ S θ ] ≥ l (38)and κ θ = ω (1 − p ) if E [ S θ ] < ,ω (1 − p ) ν if E [ S θ ] ∈ [0 , l )0 if E [ S θ ] ≥ l. (39)where ν ∈ h − E [ S θ ] l , i . It is possible to deduce that γ θ + κ θ = ω (1 − p ) for all E [ S θ ].In the next section, we select ν = 1 − E [ S θ ] /l whenever E [ S θ ] ∈ [0 , l ). In applications,Government is free to select greater subsidy rates within the range according to whatit can afford. In the special case when θ j = 1 /J , then the corresponding variables andthe parameters become φ , L ( t ), G ( t ), γ , κ , S ( t ), etc.9
980 1985 1990 1995 2000
Years r e v enue ( P u l a / H a ) SorghumMaizeCow Peas , years I n s t a l m en t ( M illi on P u l a ) not adjustedinflation adjusted Figure 1:
Graphs showing the (left) revenue per hectare for the three field crops, sorghum, maizeand cow-peas and (right) the total instalments paid towards arable farming loans. Thestraight lines on the left graph correspond to the input costs for the three field crops.
In this section, we consider the potential benefit of drought management through plant-ing multiple field crops, applying the theory from the previous section. This approach isa form of risk pooling strategy. In order to apply the theory from the previous section,we consider three field crops, Sorghum, Maize and Pulses that are planted in Botswana.The data for these crops dates from 1979 to 2003 and was obtained from the Ministry ofAgriculture. This study considers commercial farming and focuses on the variables, areaplanted in hectares and crop yield in terms of Kilograms per hectare. In order to plantthese crops, farmers can take loans from participating lending institutions. The loansare subject to annual instalments. When they take the loans, they are also required totake out insurance offered through the agricultural credit guarantee scheme.In order to benefit from the scheme, each farmer pays 5% of the instalment towardsan insurance premium whilst the lending institution contributes 5%. In total, 10% ispaid as an insurance premium. An analysis of claims data from the Ministry of Financeand Economic Development indicates that payouts from the scheme were made 2/3 of thetimes, which implies that the probability of drought is ω = 2 /
3. The contribution of 10%entitles the insured (who is the farmer) to a cover of up to 85% of his annual instalmentif a drought is declared. According to Equation (35), a corresponding actuarially soundpremium rate is 56.7% of the instalment. The premium rate is actuarially sound as longas the insured benefit level is exactly 85% and not less. Equation (35) applies when theinsured benefit level is exactly (1 − p ) and overall operations are not conducted at a loss.Since insurance requires an understanding of the revenue that proceeds from thesecrops, yield time series for these crops can be multiplied by costs per kilogram to obtainrevenue per hectare. Using the variables from the previous sections, we want to obtaina time series plot of λ j ( t ) Υ j ( t ), where Υ j and λ j are the yield and price per hectarerespectively, for the j th crop in the cluster. In order to obtain the variations in rev-enue over time, having taken inflation adjustments into account, 2016/2017 prices fromBotswana Agricultural Marketing Board (BAMB) were used. Those prices were, P1.75,10
20 40 60 80 100 (probability of drought, %) -2500-2000-1500-1000-500050010001500 E x pe c t ed p r o f i t ( P u l a / H a ) E[S ] , (probability of drought, %) c oe ff i c i en t o f e ff e c t i v ene ss Figure 2:
Graphs showing the (left) expected profit per hectare for the three field crops, sorghum,maize and cow-peas and (right) the coefficient of effectiveness.
P1.70 and P11.90 for maize, sorghum and cow peas respectively. Using those valuesallowed comparison with estimates of farm input costs provided by the Department ofCrop Production. The graphs for Maize, Sorghum and Cow peas are shown in Figure 1.The three straight lines indicate the corresponding estimates of farm inputs provided bythe Department of Crop Production. These costs have been heavily subsidised underISPAAD, Integrated Support Programme for Arable Agricultural Development. Thecolour of each straight line matches that of the corresponding crop. According to thesegraphs, the revenue for each crop is always (except once for maize and cow peas) lowerthan the cost of inputs. This implies that the farming of the respective crops is generallyoperated at a loss. If these estimates of farm inputs are accurate, then the farming ofthese field crops requires full subsidy every year in order to be sustained. In that case,giving partial financial assistance only during the years of national drought declarationscannot suffice. Since farmers have remained in business under the current arrangementof the Agricultural Credit Guarantee Scheme, it is highly likely that the yield figuresreported by the commercial farmers are grossly inaccurate. The under reporting canhappen especially when the commercial farmers hope to attract more subsidy fromGovernment.An alternative way of setting up a loss threshold is to use the percentage of droughtdeclarations as discussed in the previous section. Using data for commercial farmingat a national level, graphs of the profit obtained under varying values of probabilityof drought are shown in Figure 2. Figure 2 shows the expected profit E [ S θ ] and thecoefficient of effectiveness φ θ , each as a function of the probability of drought, ω . E [ S θ ]is the expectation of the surplus revenue due to mixing the field crops. On the righthand of the figure are graphs of the coefficient of effectiveness for the surplus revenue persquare area. On the graphs, φ θ is the coefficient of effectiveness resulting from mixingup the crops. Recall that the lower the coefficient of effectiveness, the more effective therisk pooling approach. According to these graphs, mixing field crops is an effective riskpooling strategy as the probability of drought increases. In what sense is mixing of fieldcrops effective? It leads to lower variations in the fund due to claims, thus reducing the11
20 40 60 80 100 (probability of drought, %) p r e m i u m r a t e ( % ) Figure 3:
Graphs of premium rate versus probability of drought. In the graphs, γ θ is the pre-mium rate that the farmer should pay subject to a government subsidy κ θ . probability of ruin.To assess what premium rate should be paid by farmers subject to Governmentsubsidy, one should consider Figure 3. The nonlinear formulae upon which the graphsin the figure are based are given in Equations (38) and (39). The loan instalment perarea planted was computed based on an average of instalments paid and area plantedfor the past 10 years. The idea was to use a moving average of instalments to accountfor climate change. The choice of the length of time over which to compute the averageannual instalment per hectare is based on no hard rule, except that we suggest usinga time period that is less than climate time scales. In producing the graphs, the valueof instalments used was l = P / Ha. Here, the farmer’s premium rate is γ θ whilstthe Government subsidy is κ θ , where the subscript θ denotes that the expectationswere weighted by the area planted for each field crop. According to the graphs inFigure 3, Government subsidy is required when a threshold of 17% probability of droughtis crossed. From then on, the subsidy rate required increases nonlinear until the droughtfrequency exceeds 43%, at which drought frequency full subsidy is required. Thesefindings suggest that the current rate of drought declarations merits full subsidy onseasonal loans, which is doubtful because the farmers have not gone burst without it. This paper sought to investigate the possibility for Government of Botswana to setup afund to finance annual instalments for dry-land arable farming in times of drought. Itnotes that, at the moment, there is no fund setup to assist farmers who have taken loanswith participating banks. If available, loss data can be used to determine what the sizeof the fund should be. The fund should be setup to minimise the probability of ruin byan aggregate loss that is large enough to do so. In this paper, it is suggested that yield12ata for insurable crops provides a good proxy for loss data. Whilst there is no one wayfor setting up the threshold that determines losses and gains, for a start, past recordsof drought declarations could be used to set the thresholds. Each crop would then havea threshold consistent with the probability of drought. The thresholds can then beused to determine the financial losses (or gains) corresponding to the yield shortfalls (orexcesses). The fund should then be setup to be equivalent to the area weighted lossesfor the several crops within an insured cluster. The concept of using the area weightedlosses is supported by results of the empirical example considered in this paper. Thesaid fund is meant to assist farmers who have taken out loans with participating banksto pay instalments in years of poor yield or crop failure. If a drought has been declared,their instalments should be paid off through funds from the scheme. This paper arguesthat these funds need not and should not be sought in an adhoc manner.It should be understood that in order for farmers to benefit from the scheme, theyshould each pay a premium that is actuarially sound. The current status quo is thatall farmers pay a flat rate regardless of what crops they are growing. This paper arguesthat a more prudent approach is to set rates that are crop specific and it provided analgorithm that also determines an appropriate Government subsidy for each cluster ofcrops under consideration. As an empirical example, a cluster of field crops comprisingMaize, Sorghum and Cow Peas was considered. It was found that when the probability ofdrought exceeds 43%, yield data at a commercial scale indicates a lack of profitability.This finding is in conflict with the fact that farmers still remain in business when,according to national declarations, the climatological probability of drought is about2/3 ( ∼ et al. (2020) suggested that basis risk can be reducedby calibrating the indices according to local areas where specific farms are located.13 Conclusions
This paper argued for mixing field crops as a drought mitigation strategy and presenteda methodology that is applicable to any chosen cluster of dry-land crops. It presenteda way for Government to setup a drought fund for dry-land arable farming. Nonlinearformulae for setting up premium rates and subsidies were presented and tested witha numerical example. The formulae provide thresholds for Government subsidy ratesand indicate when a full subsidy is warranted. In here was also presented empiricalevidence that national drought declarations are not consistent with yield data for themain field crops. If current drought declaration mechanisms are appropriate for dryland arable farming of field crops, then full Government subsidy is warranted. The useof area-specific, satellite based, drought indices should be explored as a way of makingdrought declarations. Should these be used, care should be taken to minimise basis riskand provide early compensation or assistance to affected farmers.The drought risk management approach presented relies solely on climatologicalinformation to make farming decisions and set up a subsidy fund. Moving forward, itwill be interesting to consider using seasonal climate forecasts to decide whether or not tofarm and determine appropriate quantities to plant. If the forecasts are more skillful thanthe climatological distribution, then the losses can be reduced. Consequently, requiredGovernment subsidies can be lowered. There are already some developments on the useof seasonal forecasts. For instance, Yi et al. (2020) discuss the use of ENSO forecasts forrate making. Further work should consider the use of country or region-specific SeasonalClimate Forecasts by different stakeholders, including farmers and Governments.
Acknowledgements
Thanks to Segomotso Sabone, Benjamin Goemekgabo, Bright Ramaina, Nnyaladzi Bati-sani and Kebitsang Powe for providing useful data and engaging in discussions thathelped put this document together. This work was financially supported by BotswanaGovernment.
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