AMSTERDAMSCHOOL OFECONOMICS
Hedging Against Mother Nature:
Farmers’ Trust and Demand for
Weather Index-based Microinsurances
Author:
Karlijn H
OYER∗_____
∗Student number: 6180752
Supervisor:
Prof. Matthijs
VANV
EELENThesis submitted in partial fulfilment (15 ECTS) of the requirements for the degree of
MSc. in Economics:
Behavioural Economics and Game Theory
D
ECLARATION OF
A
UTHORSHIP
I, Karlijn Hoyer, declare that this thesis titled, "Hedging Against Mother Nature: Farmers’ Trust and Demand for Weather Index-based Microinsurances" and the work presented in it are my own1. I confirm that:
• This work was done wholly while in candidature for a master degree at this University. • Where any part of this thesis has previously been submitted for a degree or any other qualification at this University or any other institution, this has been clearly stated. • Where I have consulted the published work of others, this is always clearly attributed. • Where I have quoted from the work of others, the source is always given. With the
exception of such quotations, this thesis is entirely my own work. • I have acknowledged all main sources of help.
• Where the thesis is based on work done by myself jointly with others, I have made clear exactly what was done by others and what I have contributed myself.
Date: 22nd August 2016
Signed:
1Note that the body of this declaration of authorship has been taken from the template from Vel et al. (2016), a standard format commonly used e.g. by the University of Edinburgh and the University of Southampton. The LaTex code used throughout this thesis is also mainly based on this template.
"I can show you that when it starts to rain, everything’s the same. I can show you, I can show you. Rain, I don’t mind. Shine, the weather’s fine. Can you hear me, that when it rains and shines, it’s just a state of mind?"
A
BSTRACT
In most developing countries farming is the main source of income. Extreme weather con-ditions significantly affect crop yields and are increasingly likely due to climate change. As a result, poor farmers have little chance to recover. One way to recover is via agricultural insurances. Traditional insurances have several drawbacks. Weather index-based ances are a suitable alternative. Poor individuals are generally risk averse, making insur-ances valuable to them. Adoption and renewal rates, however, remain unexpectedly low, likely due to a distrust of formal financial institutions and a lack of product understanding. This thesis investigates how farmers’ demand for WII’s can be modelled, taking both eco-nomic factors and (the lack of ) institutional trust into account. A game theoretical model is designed and applied to an actuarial fair drought index-based insurance scheme in three districts in Gujarat, India. The final conclusion of this thesis is that farmer’s demand for WII’s can be modelled as a sequential game and that this basic model does reasonably well in accurately resembling predicted demand under full trust and observed demand in the field. When applied to a specific context, policy and design lessons can be drawn from it.
A
CKNOWLEDGEMENTS
I would first like to thank my thesis supervisor Prof. C.M. (Matthijs) VAN VEELEN affili-ated with the Amsterdam School of Economics Faculty of Economics and Business at the University of Amsterdam for guidance and feedback throughout the research and writing processes of this master’s thesis. Secondly, I would like to acknowledge Prof. J.H. (Joep) SONNEMANSfor his input during the "Research Seminar".
Special thanks to Prof. B.W. (Robert) LENSINK affiliated with the Faculty of Economics and Business at the University of Groningen for his insights and for supplying me with ad-ditional spirit, and to all other lecturers and participants of the Groningen summer school 2016 "Experiments in developing countries: methods and applications".
I would like to express my sincere gratitude to my sparring partner Mehmet KUTLUAY for his intellectual input and the use of his office space at the Free University Amsterdam. Furthermore, I would like to thank my colleagues Nard KOEMANand Ralph URLUSfor their support and LaTeX know-how.
Finally, I must express my very profound gratitude to my friends and family for proof-reading this thesis and for providing me with continuous encouragement throughout my years of study and through the thesis process.
This accomplishment would not have been possible without any of them. Thank you.
C
ONTENTS
Declaration of Authorship i
Abstract iii
Ackowledgements iv
List of Figures viii
List of Tables ix
List of Abbreviations x
1 Introduction 1
2 Weather index-based (micro)insurances 3
2.1 Why do farmers need agricultural insurances? . . . 3
2.2 Indemnity-based versus index-based insurances . . . 5
2.3 Contract design and basis risk . . . 7
2.4 Valuation of weather index-based insurances . . . 11
2.5 Adoption of weather index-based insurances . . . 12
2.6 Trust and insurance demand . . . 15
2.7 Summary . . . 17
3 Game theoretical model and methodology 18 3.1 Sequential game and its parameters . . . 18
3.2 To buy or not to buy? . . . 23
3.3 Risk averse utility functions . . . 24
3.4 Summary . . . 25
4 Case study India: drought insurance in Gujarat 26 4.1 Trust in India . . . 26
4.2 Risk aversion in India . . . 28
4.3 Drought in India . . . 29
4.4 Drought in Gujarat . . . 33
4.5 Banaskantha, Gujarat . . . 36
4.5.1 Pearl millet insurance in Banaskantha . . . 38
4.6 Gandhinagar, Gujarat . . . 40
4.7 Patan, Gujarat . . . 44
4.8 Double index-based insurance in Banaskantha . . . 48
4.9 Summary . . . 49
5 Case study India: results 50 5.1 Premiums under full trust . . . 50
5.2 Trust requirements for buying . . . 51
5.3 Premiums under 50% trust . . . 52
5.4 Optimizing insurance design . . . 53
5.5 Summary . . . 54
6 Conclusion and policy recommendations 55
7 Discussion and limitations 58
Appendix A 61
L
IST OF
F
IGURES
2.1 Overview of the largest agricultural insurance schemes (Rural and Agricul-tural Finance Learning Lab, 2016). . . 5 2.2 The growth stages of rice (Fred, 2014). . . 8 2.3 Sample rainfall distribution showing layering of drought risk by rainfall levels
(World Bank, 2011). . . 9 2.4 Payout Structure for a Hypothetical Rainfall Contract (World Bank, 2011). . . . 9 2.5 Basis risk: Farm 2 experiences a drought and has crop failure, but the weather
station readings recorded sufficient rain; the rainfall farm 1 experiences is similar to the weather station’s measurement (Jaques-Leslie, 2016). . . 10 2.6 Penetration of agriculture insurance (including non index-based insurances)
among farmers in 2015 (Karlan et al., 2012). . . . 13 3.1 The weather index-based insurance decision tree. . . 19 3.2 Classification of different levels of constant relative risk aversion coefficientλ
(Cook et al., 2013). . . . 25 4.1 Reactions to the statement "most people can be trusted" (left) and "how much
you trust: people you meet for the first time" (right) in 2012 in India (World Values Survey, 2012). . . 26 4.2 Trust inequality between low- and high-income respondents in the 2016
Edel-man Trust Barometer with India (red arrow) scoring 22% (EdelEdel-man, 2016a). . 28 4.3 Percentage of consumer trust that banks will do the right thing in 2012, with
India scoring 59% (The Financial Brand, 2012). . . 29 4.4 Agricultural regions in India (Mondal, 2015). . . 30 4.5 The probability of occurrence of drought in India (Mohita, 2015). . . 31 4.6 ICICI Lombard’s characterization of drought regions with the (most) affected
regions (green) red (ICICI Lombard, 2016). . . 32 4.7 Location of Gujarat in India (http://www.vishvagujarat.com/, 2015). . . 33 4.8 Agricultural production in Gujarat per district (Mission Mangalam, 2011). . . 34 4.9 Average monthly rainfall in Banaskantha, Gandhinagar and Patan in mm in
the period 1901-2002 (India Water Portal, 2009). . . 35 4.10 Annual rainfall in Banaskantha (Gujarat) in mm in the period 1901-2002
(In-dia Water Portal, 2009). . . 36 4.11 Frequency distribution of the annual rainfall in Banaskantha (Gujarat) in mm
4.12 Distribution of the annual rainfall in Banaskantha (Gujarat) in mm in the period 1901-2002 (blue) (India Water Portal, 2009) and a normal approxim-ation (red). . . 37 4.13 The chance of total loss versus annual rainfall in Banaskantha (Gujarat) in
mm (blue) and a drought index-based payout structure (red) for pearl millet. 38 4.14 The chance of total loss versus annual rainfall in Banaskantha (Gujarat) in
mm (blue) and a drought index-based payout structure (red) for cotton. . . . 40 4.15 Annual rainfall in Gandhinager (Gujarat) in mm in the period 1901-2002
(In-dia Water Portal, 2009). . . 41 4.16 Frequency distribution of the annual rainfall in Gandhinager (Gujarat) in mm
in the period 1901-2002 (India Water Portal, 2009). . . 42 4.17 Distribution of the annual rainfall in Gandhinager (Gujarat) in mm in the
period 1901-2002 (blue) (India Water Portal, 2009) and a normal approxim-ation (red). . . 42 4.18 The chance of total loss versus annual rainfall in Gandhinagar (Gujarat) in
mm (blue) and a drought index-based payout structure (red) for pearl millet. 43 4.19 Annual rainfall in Patan (Gujarat) in mm in the period 1901-2002 (India Water
Portal, 2009). . . 45 4.20 Frequency distribution of the annual rainfall in Patan (Gujarat) in mm in the
period 1901-2002 (India Water Portal, 2009). . . 45 4.21 Distribution of the annual rainfall in Patan (Gujarat) in mm in the period
1901-2002 (blue) (India Water Portal, 2009) and a normal approximation (red). 46 4.22 The chance of total loss versus annual rainfall in Patan (Gujarat) in mm (blue)
and a drought index-based payout structure (red) for pearl millet. . . 47 4.23 The chance of total loss versus annual rainfall in Banaskantha (Gujarat) in
mm (blue) and a drought double index-based payout structure (red) for pearl millet. . . 48 5.1 Level of trust versus expected utility difference for a single index and a double
index with CARA and CRRA utilities andλ = 0.92 in Banaskantha for pearl millet. . . 53 7.1 Fitted normal distributions for the periods 1901-2002 (red) and 1983-2002
L
IST OF
T
ABLES
2.1 Summary of the advantages of weather index-based insurances compared to traditional insurances (Poverty Action Lab, 2016). . . 6 2.2 Examples of drought index-based insurances in India and Africa (Cenacchi,
2014). . . 6 2.3 Resulting take up rates in various randomized control trials offering
index-based insurances (without subsidies) in various countries (De Bock & Gelade, 2012). . . 13 3.1 Legend for the weather index-based insurance decision tree (figure 3.1). . . . 19 3.2 Joint probability structure. . . 20 3.3 Eight state framework, reduced to six, with probability and outcome per state. 20 4.1 Water requirements (mm/total growing period) for selected crops (FAO, 2015;
Gangaiah, 2008; IndiaAgroNet, 2014; DAC, 2011). . . 35 5.1 Highest accepted premium at total trust (t=1) andλ = 0.92 as a multiple of the
AFI premium (PAF I). . . 50
5.2 Lowest level of trust (t) at which the AFI contract is accepted by the farmer. . 51 5.3 Highest accepted premium at 50% trust (t=0.5) andλ = 0.92 as a multiple of
the actuarial fair premium (PAF I). . . 52
5.4 Lowest level of trust (t) at which the double index-based insurance contract is accepted by the farmer in Banaskantha for pearl millet. . . 53 5.5 Highest accepted premium at 50% trust (t=0.5) and full trust (t=1) in Banaskantha
for pearl millet as a multiple of the AFI premium (PAF I≈ 0.26) with λ = 0.92. . 54
7.1 Means and standard deviations for the periods 1901-2002 and 1983-2002 for Banaskantha, Gandhinagar and Patan. . . 58
L
IST OF
A
BBREVIATIONS
AFI: Actuarially Fair Insurance
CARA: Constant Absolute Risk Aversion CE: Certainty Equivalence
CII: Collective Index-based Insurance CRRA: Constant Relative Risk Aversion DARA: Decreasing Absolute Risk Aversion DRRA: Decreasing Relative Risk Aversion HARA: Harmonic Absolute Risk Aversion IARA: Increasing Absolute Risk Aversion IRRA: Increasing Relative Risk Aversion MWP: Maximum Willingness to Pay RCT: Randomized Control Trial SD: Standard Deviation
1 I
NTRODUCTION
In most developing countries farming is the main source of income for a large percentage of the population. Extreme weather conditions significantly affect crop yields and weather patterns are becoming increasingly volatile and severe due to climate change. As a result, already poor farmers are driven into complete poverty with little chance to recover (Okine, 2014). Several informal coping mechanisms have been developed with varying successes (Frankfurt School of Finance & Management, 2013; World Bank, 2011). Another way for farmers to recover from these shocks is via a coverage through an agricultural insurance. Traditional insurances, however, go hand in hand with several drawbacks, such as moral hazard, adverse selection and high operational and transaction costs, driving up premiums and thus making insurances unaffordable (Choudhury et al., 2015). Weather index-based insurances (WIIs) are a suitable alternative (World Bank, 2011).
The WII scheme pays for losses based on an index "an [pre-determined] independent and objective measure that is highly correlated with losses such as extreme weather" (Okine, 2014, p. 4), rather than upon the assessed losses of each individual policyholder, as is the case with traditional insurances (Kilimo Salama, 2010).
At least 20 years of historical data is needed for a accurate construction of the index (International Fund for Agricultural Development, 2011), which often lacks in developing countries (World Bank, 2011; Varangis et al., 2003). Also, most indexes are designed for risks related to rainfall, which is not necessarily the most important weather risk. Furthermore, farm losses often result from a complex interaction of perils, requiring a multiple-index insurance for better coverage or multiple insurances for farmers (World Bank, 2011).
While WIIs help reduce vulnerabilities of rural small-farm-holders, they are unfortunately not a panacea that can cover 100% of risks while also maintaining attractive premium levels. WIIs may be part of the solution, but are not a solution by itself and risk-layering is required to determine who carries which part and how much of a risk (World Bank, 2011).
Poor individuals, generally, display a relatively high level of risk aversion. Under expected utility theory and the assumption of actuarial fairness (AFI), insurances would be valuable to farmers. In an AFI, premiums equal the expected value of the compensation received (Experimental Economics Center, 2006). The adoption and renewal of these insurance contracts, however, remains unexpectedly low, even when farmers face investments with a positive net present value (World Bank, 2015). The most likely reason is that farmers have a deep distrust of formal financial institutions and lack knowledge on how to appropriately use their products to increase their income (Patt et al., 2009).
Understanding the dynamics between trust and demand is crucial for the development of better insurance products and suitable policies, hence this thesis aims to answer the following research question making use of expected utility theory and Constant Absolute Risk Averse (CARA) and Constant Relative Risk Averse (CRRA) utility functions. A game theoretical model is designed based on insights from the literature and applied to an Indian case study in order to evaluate the model, in the hope that policy and design lessons can be drawn from it. Several hypotheses are explored, with regard to rational behaviour under full trust, rational demand under various coefficient of risk aversion, rational behaviour under the observed levels of trust and the effect of better contract design on farmers’ behaviour.
Research question: How can farmers’ demand for WII’s be modelled, whilst taking both
economic factors and (the lack of ) institutional trust into account?
Hypothesis 1: Under full trust a rational risk averse farmers will purchase an AFI contract. Hypothesis 2: Under full trust an insurer can significantly increase the premium above the
AFI premium.
Hypothesis 3: The minimum level of trust required to purchase an AFI contract exceeds the
observed trust.
Hypothesis 4: Large premium cuts are required to increase demand under observed trust. Hypothesis 5: Improving contract design significantly reduces the minimum level of trust
required to purchase an AFI contract.
Chapter 2 presents the literature behind WIIs and answers questions regarding the need for WIIs and their design. Also, the importance of this research will be emphasized. Chapter 3 explains the model used throughout this thesis and the assumptions of the model. In chapter 4 and 5 the model is used to investigate a drought WII in Gujarat, specifically in the districts Banaskantha, Gandhinagar and Patan. The conclusions are presented in chapter 6. I find support for hypotheses 1 to 4, but not for hypothesis 5. A policy implication of these conclusions is that (temporary) subsidies should be implemented to induce trust and increase demand. Some policy ideas other than simply reducing premiums are suggested. The final conclusion is that indeed farmers’ demand for WII’s can be modelled as sequential game and that this basic model does reasonably well in accurately resembling predicted demand under full trust and observed demand in the field. Finally, the limitations of this research are discussed in chapter 7 and will give suggestions for further research.
2 W
EATHER INDEX
-
BASED
(
MICRO
)
INSURANCES
This chapter provides a thorough understanding of WIIs, their importance and the issues involved by discussing relevant literature concerning the need for agricultural insurances for farmers (section 2.1) and the advantages of index-based insurances compared to the traditional indemnity-based insurances (section 2.2). The design and valuation of WIIs by the insurer are discussed in sections 2.3 and 2.4. Sections 2.5 and 2.6 address the low adoption rate of WIIs and the influence of trust on their demand. Finally the main insights are summarized (section 2.7). The information presented serves as input for the game theoretical model developed in chapter 3.
2.1 W
HY DO FARMERS NEED AGRICULTURAL INSURANCES?
In most developing countries agriculture has long been the backbone of the economy and farming is often the main source of income for a large percentage of the population while also providing households with their (basic) dietary needs. Weather conditions such as drought, excessive rains, storms and hurricanes, however, have a significant affect on crop yields 2 and also (in)directly impact other agrarian practices, e.g. livestock. Unsurpris-ingly, when asking farmers about their good and bad agriculture years: good years are re-membered for their adequate rains, while the bad years are generally defined by droughts or other adverse weather conditions. For most small-farm-holders, weather risks thus define their lives (Kilimo Salama, 2010). The risks they face are specific to the country, climate, and local agricultural production systems (World Bank, 2011). In semiarid3areas of India, for example, 89% of farmers mention droughts as the largest threat to their agricultural pro-duction (Poverty Action Lab, 2016).
Unfortunately, weather patterns are becoming increasingly volatile and severe due to cli-mate change (The Guardian, 2015). As a result, crop yields may be negatively affected and already poor farmers are driven into complete poverty, leaving them with little chance to re-cover after such a shock, since they are often also financially excluded. This self-reinforcing mechanism is referred to as the poverty trap (Economic Times of India, 2016). Further-more, the risks associated with agriculture also limits the willingness of farmers to invest in measures that might increase their production and improve their economic status (like fertilizers and irrigation) as the unpredictable weather might wipe out their crops (Okine, 2014) and this also influences farmers’ agricultural decisions as they might choose to only
2Usually measured in kilograms per hectare (Global Yield Gap Atlas, n.d.) 3A climate area with little annual rainfall, usually from 25 to 50 cm (Dictionary)
cultivate low-risk, low-return crops instead of a higher-risk cash crop (e.g. like sorghum instead of groundnut in India) (Poverty Action Lab, 2016).
The amount of rainfall during the growing season is one of the weather factors that has a major influence on crop growth, especially in regions without access to irrigation and for farmers that do not apply product diversification (i.e. rely on monoculture). Even though several (in)formal coping mechanisms have been developed at farmer, community, mar-ket and government levels as response to these shocks (e.g. community savings and buffer stocks) (Frankfurt School of Finance & Management, 2013; World Bank, 2011), these tradi-tional risk management strategies often break down when a disaster affects an entire com-munity or area (Bill & Melinda Gates Foundation, 2010). Another way for farmers to recover from crop loss after weather shocks is via a coverage through agricultural insurance. In this thesis I will focus on one particular weather shock: drought. Droughts are defined as:
"An extended interval of abnormally dry weather sufficiently prolonged for the lack of water to cause serious hydrologic imbalance, such as crop damage, and water supply shortages, in the affected area." (ICICI Lombard, n.d.).
Agricultural microinsurances are designed to on the one hand effectively reduce the im-pact of these severe weather conditions and on the other hand support increased invest-ment in farm productivity. Throughout this thesis, both microinsurance and insurance are used interchangeably. The term ’microinsurance’ was first used around 1999 and refers to:
"A risk transfer device characterised by low premiums and low coverage lim-its, and designed for low-income people not served by typical social insurance schemes" (Micro Insurance Academy, 2007).
Insured farmers can, for example, invest in fertilizers instead of replanting damaged crops, whilst their uninsured colleagues might continue to feel the impact of the drought even several seasons after. On top of that these insurances can help create greater food security (and variety) for the entire community. Therefore, the development of affordable and relevant agricultural microinsurances is critical in order for vulnerable farmers to be able to hedge themselves against weather risks (Kilimo Salama, 2010). An overview of the largest agricultural insurance schemes is given in figure 2.1.
Figure 2.1: Overview of the largest agricultural insurance schemes (Rural and Agricultural Finance Learning Lab, 2016).
2.2 I
NDEMNITY-
BASED VERSUS INDEX-
BASED INSURANCESTraditional (agricultural) insurances, however, go hand in hand with several drawbacks like moral hazard, adverse selection and high operational and transaction costs. This forces insurers to charge higher premiums, making the insurances unaffordable for most farmers. Farmers often do not even have access to indemnity-based insurances. These insurances rely on on-farm monitoring and evaluation of losses through farm inspections, which is costly and time-consuming. Generally "the transaction costs to insure one acre are similar to insuring a 200 acre farm, [and] the premiums from the one acre farm would never cover the related transaction costs" (Kilimo Salama, 2010)(p. 1). Not visiting the farmer on the other hand, incentives moral hazard, i.e. farmers can claim losses that did not actually occur as the insurer will not check their accuracy anyway or they could engage in riskier behaviour once insured. Adverse selection occurs when people who decide to insure more also take more risks. Clearly, this increases the likelihood of higher payouts and increases costs for insurers. For that reason, WIIs are often used as an alternative. The advantages of WIIs are summarized in table 2.1.
Lower transaction costs No need for individual verification of claimed losses
Reduced moral hazard Farmers only have a limited ability to increase damages from adverse weather shocks
No adverse selection Farmers’ characteristics do not affect the likelihood of payout Table 2.1: Summary of the advantages of weather index-based insurances compared to
tra-ditional insurances (Poverty Action Lab, 2016).
WIIs were first offered in the early 2000s, and they are now available to farmers in over fifteen countries (Poverty Action Lab, 2016). WIIs lower the threshold of insurability, since they replace costly farm visits with measurements from weather stations (Kilimo Salama, 2010). The WII scheme pays for losses based on an index "an [pre-determined] indepen-dent and objective measure that is highly correlated with losses such as extreme weather" (Okine, 2014, p. 4), rather than upon the assessed losses of each individual policyholder, as is the case with traditional insurances. The rainfall measures from the weather stations are then compared to an agronomic model specifying crops rainfall needs. The index set may vary per crop, depending on their needs. Farmers receive their insurance payouts once these needs are not met (Kilimo Salama, 2010). WIIs are best suited for infrequent but severe shocks. Localized, independently occurring risks, e.g. hail or fire, are not suited for index insurance (World Bank, 2011). Crops that are likely to be suitable for WIIs include rain-fed maize and rice (Choudhury et al., 2015). Furthermore, the nature of WIIs also offers additional opportunities, e.g. to reach a wider range of market segments (Counts, 2015). Some examples of drought index-based insurances are given in table 2.2.
Country Launch year Name
India Late 1980s NAIS
India 2003 ICICI Lombard
India 2003 ITGI
India 2004 Varsha Bima
India 2007 Weather-based crop insurance
Ethiopia 2007 Horn of Africa Risk Transfer for Adaption (HARITA) Ethiopia 2009 Kilimo Salma
Kenya 2009 Haricot bean insurance
Table 2.2: Examples of drought index-based insurances in India and Africa (Cenacchi, 2014).
Collective index-insurances (CIIs) additionally reduce the transaction costs made by in-surance companies by arranging contracts with collectives, instead of individuals. These collectives bear the responsibility of managing the division of the insurance coverage by its members, also allowing for an asymmetric distribution of the insurance coverage by its members if a collective is not equally affected by the shock (Pacheco et al., 2015). Grouping farmers in homogeneous risk areas, however, might increase the spatial correlation of the risk (World Bank, 2011). Additionally, such a scheme might give rise to trust issues within the collective. CIIs fall outside the scope of this thesis.
2.3 C
ONTRACT DESIGN AND BASIS RISKGenerally, a weather derivative is defined through: a reference weather station (where the data comes from), an underlying index (payout trigger), term period, payout structure and a premium (Lopez-Cabrera & Hardle, 2007). The construction of the index that serves as a proxy for the payout scheme is an important component of the valuation of WII products, but is often technically complex (World Bank, 2011).
WIIs rely on historical and current weather data. Historical data, mainly from weather stations, is used for product design and pricing. Current data is used for operation itself. The completeness of these datasets, however, differs highly per region, particularly with respect to daily data (Okine, 2014). The International Fund for Agricultural Development (2011, p. 31) recommends "that there be at least 20 years of historical daily data and that missing data should not exceed 3% of the total daily dataset". Other sources recommend at least 30-40 years of data (World Bank, 2011; Varangis et al., 2003). A weather variable that can be used as an index must satisfy the following properties (World Bank, 2011): observ-able and easily measurobserv-able, objective and transparent, independently verifiobserv-able, reported in a timely manner, consistent over time and experienced over a wide area. Note that the underlying index has no intrinsic financial value (Lopez-Cabrera & Hardle, 2007). Besides weather data, crop vulnerability throughout the crop cycle should be assessed, as crops’ needs may vary throughout the seasons requiring different indexes, as given in figure 2.2. Multi-crop production systems are even more complex.
Figure 2.2: The growth stages of rice (Fred, 2014).
Unfortunately, WIIs are not a panacea that can cover 100% of risks while also maintaining attractive premium levels. WIIs may be part of the solution, but are not a solution in itself and risk-layering is required to determine who carries which part and how much of a risk. The layers include a self-retention layer (risk carried by the farmer), a market risk trans-fer layer (insurance layer) and a market ‘failure’ layer, as shown in figure 2.3 for a drought shock. A hypothetical, but simplistic, payout structure is given in figure 2.4, again for a drought situation. Here the index is set at 100 mm of rainfall and the payout maximum is reached once rain falls below 50 mm (World Bank, 2011).
Figure 2.3: Sample rainfall distribution showing layering of drought risk by rainfall levels (World Bank, 2011).
The difference between the actual loss and the insured loss is called basis risk. To be precise:
"Basis risk is the risk that the index will not accurately predict a farmer’s loss." (Poverty Action Lab, 2016, p. 2)
As long as the correlation between payout and losses is not perfect, basis risk will be present. The best case scenario for a farmer with a WII is that he experienced no losses but the in-dex was triggered so that he received a payout. The worst case scenario (downside risk) is that he experienced losses but received no payout because the index was not triggered (Patt et al., 2009). Farmers’ payouts are based on the rainfall measure at the weather station and not on actual rainfall on their land. It could be that these measurements differ, see figure 2.5 for example. When the distance from the farm to the weather station increases, basis risk increases (Poverty Action Lab, 2016). Index insurance improves the best possible scenario but also worsens the worst possible scenario (Clarke et al., 2011).
Figure 2.5: Basis risk: Farm 2 experiences a drought and has crop failure, but the weather station readings recorded sufficient rain; the rainfall farm 1 experiences is sim-ilar to the weather station’s measurement (Jaques-Leslie, 2016).
Mathematically the payout belonging to figure 2.4 corresponds to: Payout = IA if RA≤ RS IA(RT−RA RT−RS) if RS< RA≤ RT 0 if RA> RT (2.1)
with IA=insured amount (maximum payout), RT = trigger rainfall/index (here 100 mm),
RS=stop-loss rainfall (here 50mm) and RA=actual rainfall.
Besides the limited availability of data, WIIs also come with even more construction chal-lenges. On the supply side there are currently limited product options for different weather risks and the majority of WII products have been designed for risks related to rainfall. Rain, however is not necessarily the most important weather risk in many areas. Furthermore, farm losses often result from a complex interaction of perils, e.g. increased temperature that leads to pest problems. A ‘simple’ WII product is not suitable for hedging against these risks and thus would need to consist of more than one index rolled into a single product (a multiple-index insurance) or a farmer would need to take up different types of insurance products for the other risks (World Bank, 2011). Risks vary widely: some farmers benefit from a particular insurance product while others do not. A more accurate construction of the index reduces basis risk, but might, however, drive up the premium due to increased transaction costs.
2.4 V
ALUATION OF WEATHER INDEX-
BASED INSURANCESAt the moment, there is no standard model that can be used for the valuation of weather derivatives, as its underlying asset is not tradeable and thus violates a number of key as-sumptions of the Black−Scholes model which is used for the pricing of European-style op-tions and similar derivatives (Investopedia, 2016a). Typically weather derivatives are priced using the following approaches: burn analysis, index value simulation, daily simulation and/or stochastic pricing models (Lopez-Cabrera & Hardle, 2007).
A simplistic example based on a drought scenario as given in figure 2.4, is to set the premium equal to present value of the expected payout, i.e.:
E (Payout) = IA Z RS 0 f (RA)dRA+ IA Z RT RS RT − RA RT − RS f (RA)dRA = IA Z RS 0 f (RA)dRA+ IA RT− RS Z RT RS RTf (RA)dRA− IA RT − RS Z RT RS RAf (RA)dRA = IA(F (RS) + IA RT− RS ³ RT¡F (RT) − F (RS) ¢´ − IA RT − RS Z RT RS RAf (RA)dRA (2.2)
Using the continuous compound interest rate r , the present value (PV) at time 0 of a future value (FV) at time t can be determined in the following way (Math Warehouse, n.d.):
PV = FV ∗ e−r t (2.3)
The premium (P) can be given by the following equation with PV=P and FV=E (Payout):
P = (e−r t) · IA(F (RS) + IA RT − RS ³ RT¡F (RT) − F (RS) ¢´ − IA RT− RS Z RT RS RAf (RA)dRA ¸ (2.4) The World Bank and their NGO partners, generally, aim for an AFI, i.e. premiums equal the expected value of the compensation received (Experimental Economics Center, 2006).
2.5 A
DOPTION OF WEATHER INDEX-
BASED INSURANCESSome consider microinsurances ‘the next revolution’ when addressing risks and vulnera-bility in low-income countries. In correspondence with that idea, huge investments have recently been made by development agencies such as USAID and the Gates foundation (Morduch, 2006).
Poor individuals, generally, display a relatively high level of risk aversion (for an utility function u(x), u0(x) > 0 and u"(x) < 0 hold; the utility function is concave). Some, e.g. Patt
et al. (2009), argue that poorer people are likely to accept a lower certainty equivalent (CE)
since the risk of receiving no harvest at all is detrimental to them. CE "is a guaranteed return that someone would accept, rather than taking a chance on an higher, but uncertain, re-turn" (Investopedia, 2016b). This indicates that the demand for microinsurance products should be high. However, most evidence from randomized control trials (RCT) suggests otherwise, as given in table 2.3. Even when subsidized, the adoption of microinsurance schemes rarely exceeds 30% and renewal rates are also very low (De Bock & Gelade, 2012). About 27 million small farmers, mostly Indian, are covered by large-scale agricultural in-surance schemes (also including non index-based schemes), as can be seen in figure 2.1. Coverage is just 10% across Latin America, Asia and sub- Saharan Africa. More than 90% of these policies are in India, meaning that penetration rates in many other parts of the world are even lower, e.g. 5% in Nigeria and 3% in Vietnam (Rural and Agricultural Finance Learning Lab, 2016), see also figure 2.6. Furthermore, farmers who decided to insure, often did not insure all of their land, e.g. a study in Ghana found that less than 10% of farm-ers’ acreage was insured (Karlan et al., 2012; Poverty Action Lab, 2016) and similar results were found in India where the 16% that decided to insure also purchased only one policy
(Mobarak & Rosenzweig, 2012; Poverty Action Lab, 2016). So, why is demand for microin-surances so poor?
Up take: Country: Source:
20% Ethiopia Hill and Robles (2011) 6-36% Ethiopia Norton et al. (2011)
17% Malawi Giné and Yang (2009)
16% India Cole et al. (2013);
Mobarak & Rosenzweig (2012)
6% India Gaurav et al. (2011)
Table 2.3: Resulting take up rates in various randomized control trials offering index-based insurances (without subsidies) in various countries (De Bock & Gelade, 2012).
6% Sub-Saharan Africa
20% South and South-east Asia
0 100
Figure 2.6: Penetration of agriculture insurance (including non index-based insurances) among farmers in 2015 (Karlan et al., 2012).
Let us assume that farmers maximize their expected utility when deciding whether or not to purchase an insurance product. Under expected utility theory, insurances are valuable to farmers, as farmers are risk-averse. This can be shown by a simple example:
Assume that the price of the insurance equals P for $1 of insurance and x is the amount you are insured for, meaning that your premium is P x. The probability that the insurance pays x is p. With probability p, the insurance company must pay you $x, while they re-ceived $Px in premiums. The expected pay-off of the insurer equals to p(P x −x)+(1−p)P x. For an AFI p(P x − x) + (1 − p)P x = 0, i.e. p = P. A risk-averse individual solves the fol-lowing optimization problem, with his utility function u(.), w being his total wealth and
L being the loss suffered: max pu(w − px − L + x) + (1 − p)u(w − px). Rearranging gives u0(w − px − L + x) = u0(w − px). Since u"(.) < 0, u0(.) is strictly decreasing, so it can only be that u0(w − px − L + x) = u0(w − px) if and only if w − px − L + x = w − px and thus x = L, meaning that one would choose to fully insure against losses. When p 6= r , then x < L and one would underinsure (Experimental Economics Center, 2006).
A risk-averse farmer would, under the assumption of AFI, always prefer receiving a def-inite amount of payout over a risky outcome of losing everything. If price was the only determinant of insurance demand, a premium between a farmer’s maximum willingness to pay (MWP) and the AFI (still assuming MWP>AFI), would suffice to sell the WII (De Bock & Gelade, 2012).
However, in WIIs, as mentioned before, there is always a basis risk, under which the in-surance may become risky in itself and hence reduces the demand for WIIs. In Uttar Pra-desh (India) researchers found that for every increase in perceived kilometre distance from the weather station, demand declined by 6.4% which is similar to removing an earlier given 10% discount from the market price (Poverty Action Lab, 2016). Moreover, there can be substantial transaction costs for the farmer, such as the difficulty of purchasing/renewing the insurance, opportunity cost of time, the ease of paying premiums and receiving payouts (De Bock & Gelade, 2012). Kilimo Salma minimizes transaction costs by using technology like mobile phones. They even send text messages to farmers with advice on how to min-imize losses in case of bad weather (Cenacchi, 2014).
In general, microinsurances require farmers to pay a regular premium for an uncertain payout (De Bock & Gelade, 2012). Several approaches to drought insurance for the poor so far have not been effective, mostly due to inability of the poor farm-holders to afford the premiums. Some innovative ways have been developed, the HARITA programme (also mentioned in table 2.2), for example, allows farmers to partially pay their premium through labour. The activities performed under this programme include work that promotes cli-mate resilience (Cenacchi, 2014). Other microfinance institutions bundle microcredit with insurances, but this mostly involves the bundling of a health insurance product with micro-loans. The opposition argues, however, that this forces a straitjacket onto a farmer. Bund-ling has more negative effects: in Malawi, for example, farmers offered the bundle, bought it at half the rate of those who were offered the credit alone (Jaques-Leslie, 2016), thus re-ducing demand even more. The timing and payment frequency of the premium are also important. An insurance policy may not be immediately affordable due to liquidity con-straints, but paying in more instalments might be possible nevertheless. "Similarly, col-lecting premiums during the lean period before the next harvest may restrict the ability for some farmers to subscribe" (De Bock & Gelade, 2012, p. 6). Another alternative is insurance via subsidy. Generally, studies show that reducing the price of insurance increases take-up, but this requires large discounts, making one wonder whether commercial markets can actually develop (Poverty Action Lab, 2016).
Clearly, the design of the insurance contract affects the demand for WIIs on more levels than just the hight of the premium. Overall, there exists a trade-off between simplicity and sophistication. On the one hand, a complex product might not be understood and there-fore not regarded as trustworthy. On the other hand, simple products may not meet the needs of the farmers and thus not help reduce their substantially vulnerability to weather risk as well as e.g. insurances based on multiple indexes would do.
One example on one side of the spectrum: Hill et al. (2011) created tailor-made fully flexible WIIs based on monthly rainfall. They provided farmers with multiple weather de-rivatives rather than one unique package of dede-rivatives (also called weather securities) and farmers could choose the type and number of securities that they wanted to buy based on their crop portfolio and production history. Take-up rates were relatively high, with about 20% among informed farmers, suggesting that in this particular case complexity does not necessarily result in a substantial barrier to adoption. Their approach allowed for rain in-dexes differing per crop in the portfolio, making it more accurate in covering losses, but did not allow for interacting indexes.
On the other extreme, Gelade (2011) argues in favour of a simple lumpsum contract, which pays the same amount to all when the index is surpassed, as it is more easily un-derstood by farmers and hence increase demand. Its effect on trust and the hight of the premium depend on how often payouts occur.
2.6 T
RUST AND INSURANCE DEMANDDistrust of the insurer also plays a tremendous role in the adoption of WIIs, especially be-cause farmers are generally still unfamiliar with formal financial products, poorly educated and hence it might be difficult for them to assess the benefits of this investment (De Bock & Gelade, 2012). The more standard financial product offered to the poor is microcredit and is very different in nature than insurance products. For microcredits money is offered to clients and it is the responsibility of the financial institution to get this money back. With insurances, however, the financial institution first gets money from the client, making it the clients problem to get a payout in case of a loss or once the index is triggered. Obvi-ously this requires a much higher degree of trust before entering in an insurance contract (Dercon et al., 2011). Farmers may not trust that they will receive payouts once the in-dex is surpassed. This concern is actually quite reasonable, as some insurance providers have delayed payouts for months or sometimes even years (Poverty Action Lab, 2016). It is thus in the interest of the provider to build a strong reputation. This process might take a
significant amount of time due to the low adoption and renewal rates, as they do not get the chance to prove themselves. Trusted intermediaries, like local agrodealers and unions, might help speed up this process (De Bock & Gelade, 2012), but might increase transaction costs. A study in Andhra Pradesh (India) showed that farmers were more likely to purchase an insurance if a well-known agent endorsed the product in a marketing video; in Gujarat a similar endorsement, however, had no effect (Cole et al., 2013; Poverty Action Lab, 2016). Patt et al. (2009) distinguish between three levels of trust. The first level concerns the trust in the product, correlated with the understanding of the product and its payout scheme. The second level, the trust in the institution(s) involved, means that farmers should be convinced that they will receive the promised payout when the index is surpassed. Finally, the interpersonal dimension of trust of an individual plays a role. On the one hand, this means that if one does not trust his (inner)circle to start with than he is likely to also be suspicious of formal risk-pooling mechanisms. These interpersonal dimensions can be influenced by various social factors and may be dependent on cultural background. On the other hand, if a farmer lacks trust in himself, his confidence in his own ability, e.g. to make investment decision, might be low as well.
When determining the index, the insurer must also take into account that it might de-ter (potential) clients from (re)purchasing the insurance, since the frequency of payouts depends on it and a lack of payouts may reduce farmers’ trust in the product. Too fre-quent payouts, however, drive up costs and thus premiums (De Bock & Gelade, 2012). This provides evidence for the use of multiple critical levels, as already shown in the example in figure 2.2. Repurchase increased amongst farmers who received a payout in the previous year, and these farmers also insured more land. Similarly, farmers who saw that friends and family received payouts were also more likely to purchase insurances (Karlan et al., 2012; Poverty Action Lab, 2016). Cole et al. (2013) estimate in Gujarat that the probability that neighbouring farmers purchase an insurance increases by 25-50% when a farmer in that village received a payout of INR 1,000 (US$27.17) in the previous year. The more individu-als in a village who receive payouts, the stronger the effect. In the most recent crop season, village payouts are even more important for the purchasing decision than individual pay-outs. Longer-lagged payout experiences, i.e. two and three years before the current pur-chase decision, have a stronger positive effect when these were for the individual. These results contrast the standard rational models, "in which the realization of recent insurance outcomes should not affect forward-looking insurance decisions" (Cole et al., 2014, p. 3). There seem to be large village spillovers in insurance experience and over-inference from recent individual payouts might distort individual purchasing decisions (Cole et al., 2014).
In the field, trust has been observed to be a serious problem in insurance uptake (Patt
et al., 2009; Dercon et al., 2011). So clearly, price is not the only potential barrier to the
take-up of insurances. Increasing take-uptake is key to maximizing impact and with the increased threats from climate change, getting this right is extremely important: insurers need to provide farmers with what they need, want and can afford. The above suggests that uptake can be improved for example by reducing basis risk or by increasing farmers’ trust in these products (Dercon et al., 2011). In their field experiment, Giné et al. (2015) found an increase in demand after interventions aimed at reducing liquidity constraints and at increasing trust. Efforts to improve farmers’ understanding of the product on the other hand had no significant effect on demand, which emphasizes the difficulty of explaining such complex products (World Bank, 2015). Some studies showed an effect of a financial literacy training but conclude that this was not a cost-effective way to raise demand (Poverty Action Lab, 2016). Reducing basis risk will likely make the product more complex. Basis risk, however, also influences trust, e.g. when a farmer beliefs he deserves a payout but does not receive it, as in for example figure 2.5. Therefore, more insight in the dynamics between trust and demand is likely to be a more useful way to help design better insurance products and is crucial for the design of suitable policies.
2.7 S
UMMARYIn most developing countries farming is the main source of income. Extreme weather con-ditions significantly affect crop yields and are increasingly likely due to climate change. As a result, already poor farmers have little chance to recover. One way to recover is via agri-cultural insurances, but traditional insurances have several drawbacks. WIIs are a suitable alternative, but at least 20 years of data is needed to construct an accurate index and as long as the correlation between payout and losses is not perfect, basis risk will be present. There exists a trade-off between simplicity and sophistication. Poor individuals are generally risk averse, but adoption and renewal rates remain unexpectedly low, likely due to a distrust of formal financial institutions and a lack of product understanding. Insight in the dynamics between trust and demand is likely a useful way to help design better insurance products and suitable policies.
3 G
AME THEORETICAL MODEL AND METHODOLOGY
Using the insights from chapter 2, this chapter develops a game theoretical model that takes farmers’ trust into account. The specifics of the model and its parameters are explained in section 3.1. Section 3.2 discusses when a rational farmer would buy and insurance product and section 3.3 explains the risk averse utility functions that can be used in the model. Fi-nally, the main insights are summarized in section 3.4. The theory developed in this chapter is used in the Indian case study in the following chapters.
3.1 S
EQUENTIAL GAME AND ITS PARAMETERSThe starting point of the model used in this thesis is Clarke et al. (2011)’s rational demand model for index insurances. Trust can be modelled as "a form of the downside of basis risk" (Dercon et al., 2011, p. 2). Trust then measures the farmer’s belief that an insurer commits to its obligation and pays the farmer the contracted coverage when the index is reached. The decision process that the farmer takes part in can be viewed as a sequential game, in which the farmer, the insurer, nature and the weather station play an important role. The game described below is visualized in figure 3.1. Table 3.1 explains all variables used in the model.
1. The insurer designs the insurance contract (AFI): he sets a premium, sets the index and determines a rain-dependent payout function.
2. The farmer decides whether or not to buy the insurance product.
3. Nature determines the annual rainfall experienced by the farmer and whether this results in a (total) loss.
4. Based on data from the weather station, the insurer determines whether or not the index is surpassed and the insurance coverage is triggered.
5. The insurer decides whether or not to default on its obligations or to commit to the contract (farmer’s belief ).
I nsur er F ar mer N at ur e w − L L=1: [p] w L=0: [1-p] NB N at ur e W eat her St at i on I nsur er w + α − P − L C: [t] w − P − L D: [1-t] I: [q] w − P − L NI: [1-q] L=1: [p] W eat her St at i on w − P NI: [1-q] I nsur er w − P D: [1-t] w + α − P C: [t] I: [q] L=0: [1-p] B Contract
Figure 3.1: The weather index-based insurance decision tree.
RA Actual rain with corresponding distribution f (RA), RA≥ 0
P Premium asked by the insurer, P ≥ 0 B Insurance bought by farmer at price P NB Insurance not bought by farmer
L Farmer experienced total loss, L = 1, or no loss, L = 0 p(RA) Chance that loss occurs given annual rainfall, 0 ≤ p ≤ 1
I Index reached; insurance indemnity required I ≥ RA
NI Index not reached; no insurance indemnity required, I < RA
q(RA) Chance that index is reached given annual rainfall, 0 ≤ q ≤ 1
D Insurer defaulted; insurance indemnity not paid,α = 0 C Insurer complies: insurance indemnity paid,α > 0
t Chance that insurer is trustworthy (farmer’s belief ), 0 ≤ t ≤ 1
α(RA) Coverage paid by the insurer given annual rainfall,α ≥ 0
w Initial wealth of the farmer, w ≥ 0
In total there are 8 possible states s ∈ S = {000,00C ,L0C ,0IC ,L00,LI 0,0I 0,LIC } with their corresponding probabilities and outcomes, as can be seen in table 3.2 and 3.3. Here 000 refers to a situation where there is no loss, the index is not reached and the insurer does not comply to the contract; LIC refers to a situation where total loss occurred, the index is reached and the insurer complies to the contract. The eight states can be reduced to six states since it is only relevant whether an insurer defaults or complies once the index is reached, i.e. we can combine 000 with 00C and L0C with L00.
I(ndex)=0 I(ndex)=I L(oss)=0 (1-p)(1-q) (1-p)q 1-p L(oss)=L p(1-q) pq p 1-q q D(efault)=1 (i.e. C=0) (1-t) I(ndex)=0 I(ndex)=I L(oss)=0 (1-p)(1-q) (1-p)q 1-p L(oss)=L p(1-q) pq p 1-q q C(omplies)=1 t Table 3.2: Joint probability structure.
State s 000/00C L0C/L00 0IC LI0 0I0 LIC Probabilityπs (1-p)(1-q) p(1-q) (1-p)qt pq(1-t) (1-p)q(1-t) pqt
No insurance NB w w-L w w-L w w-L
Insurance B w-P w-P-L w + α − P w-P-L w-P w + α − P − L Table 3.3: Eight state framework, reduced to six, with probability and outcome per state.
A farmer suffers a total loss L with probability p and no loss with probability 1-p (see as-sumption 1 below). Probability p differs per rain level and for simplicity it increases in a linear fashion (see assumption 2 below). Water deprivation is assumed more detrimental than water abundance. Plants that get too little water are not getting the nutrients that they need. They might dwarf, not produce or even worse, die. Expert opinions vary, but some argue that "under watering plants is the worst thing you could do" (Mierzejewski, 2015), indeed suggesting that under watering is more damaging to the plant than over watering. But clearly, crops can differ in their tolerance to waterlogging. "Waterlogging occurs when roots cannot respire due to excess water in the soil" (Soil Quality Pty Ltd, 2016). Excessive rainfall can (in)directly lead to yield losses (Ransom, 2014), especially because these crops were chosen particularly with the existing weather conditions in mind, and thus the dam-aging effects of over watering also need to be considered.
Specific crops have ranges in which they grow optimally: annual rainfall exceeds the lower bound of the optimal growth range g , but is less than the upper bound of the op-timal growth range g . As soon as rainfall falls below the extreme lower bound g or exceeds the extreme upper bound g , crops have no chance of survival. In our situation p increase with 4% per decrease of 10 mm rain and increase with 2.5% per increase of 10 mm rain out-side of the optimal growth range, but this can be varied dependent on the optimal growth ranges of crops.
Assumption 1: The farmer owns a single crop (or alternatively the contract concerns a single
crop). Hence loss equals total loss: L =
(
0 no loss
1 total loss (3.1)
Assumption 2: Water abundance is less detrimental than water deprivation, meaning that
g − g < |g − g |. The chance of total loss increases in a linear fashion:
p(RA) = 1 RA< g g −RA g −g g ≤ RA< g 0 g ≤ RA≤ g g −RA g −g g < RA≤ g 1 g < RA (3.2)
The index (I) is reached with probability q or not reached with probability 1-q. Often the index is set close to the crop-specific lower bound of optimal growth g . Reaching the index and loss are not necessarily perfectly correlated, so there exists a basis risk rb. In Clarke
et al. (2011), rbis the joint probability that a farmer experiences loss (Loss=L) but the index
is not reached, i.e. rb= (1 − q)p. In this model basis risk is extended with the chance that
loss occurs, the index is reached but the insurer is not trustworthy and thus defaults, i.e
rb∗= qp(1 − t ). In this model it can also be the case that the farmer experiences a drought situation whilst the index is not triggered at the weather station (see assumption 3 below): the chance that the index is reached close to the index increases linearly from 0.5 to 1 when annual rainfall drops. For simplicity, cases in which the weather station reports a differ-ent value than the actual rain experienced by the farmer, but both fall within the payout
range, are not considered. This means that it is not possible that, for example, the farmer experienced 400 mm of rainfall (requiring saye0.32), but the weather station records 430 (requiring saye0.22), see assumption 4.
Assumption 3: There exists a range (close to the index) where it is possible that the farmer
experiences a drought situation whilst the index is not triggered at the weather station:
q(RA) = 1 RA≤ I − 100 0.5 + 0.5 I −RA I −(I −100) I − 100 < RA≤ I 0 I < RA (3.3)
Assumption 4: If the index is triggered than weather station data and actual rainfall are
equivalent; the only discrepancy concerns the reaching of the index close to the index value as given in assumption 3.
Often drought insurances cover only part of the expected losses per rain level. In this model a coverage of 80% is assumed, as can be seen in assumption 5. Since the chance of total loss increase in a linear fashion, coverage also increases linearly. More complex struc-tures do exist, but the World Bank advices insurers to keep it simple in order for farmers to understand the contract (World Bank, 2011).
Assumption 5: Conditional on that the index is triggered, insurance pays out 80% of the
expected loss at a specific rain level
α(RA) = 0.8p(RA)L = 0.8p(RA) RA≥ I (3.4)
The insurer in this model is not profit-oriented and has no transaction costs: the de-signed contract is thus AFI (see assumption 6). Here we assume that the premium equals the expected value of the coverage with no compound interest. Note however that premi-ums could be reduced if an insurer also operates in microloans and can ‘invest’ the premium paid by the farmer in these microloans. The global interest rate average for microloans is about 35% (Kneiding & Rosenberg, 2008) and between 2011-2014 India capped the mi-crofinance interest at 26% (The Economic Times, 2014; Business Today, 2011).
Assumption 6: The contract is AFI, i.e. the insurer charges a premium equal to the expected
value of the coverage, with a compound interest rate r = 0 (see equation 2.4): P = E(α) =
Z ∞
0 α(RA
As discussed in the literature section, farmers in developing countries are extremely poor and experiencing crop loss can be detrimental to them. Often poor farmers have no excess to formal saving instruments, and since community savings are likely to be affected in a drought situation (Bill & Melinda Gates Foundation, 2010), it is safe to assume that farmers have little or no savings (see assumption 7). Here farmers who experienced total loss (L = 1) still have a small buffer, but these savings are not enough to invest in a new crop. Farmers’ initial wealth is set to 1.75, mostly for the technical reason of ensuring that x > 0 when
u(x) = l n(x).
Assumption 7: Farmer’s initial wealth is less than twice the value of total loss, w<2L=2
3.2 T
O BUY OR NOT TO BUY?
Per rain level a farmer receives a certain utility depending on which state of the world he is in. For an uninsured farmer this can be written as:
uN B= p(RA)u(w − L) + (1 − p(RA))u(w ) (3.6)
For an insured farmer this can be written as:
uB(RA) = u(w − P − L)p(RA)(1 − q(RA)) + u(w − P − L)p(RA)q(RA)(1 − t)
+u(w + α(RA) − P − L)p(RA)q(RA)t + u(w − P)(1 − p(RA))(1 − q(RA))
+u(w − P )(1 − p(RA))q(RA)(1 − t) + u(w + α(RA) − P)(1 − p(RA))q(RA)t
(3.7)
A rational risk averse farmer will buy the insurance contract when the expected utility of buying the contract is at least as big as the expected utility of not buying the contract, i.e:
E(uB
) ≥ E(uN B) (3.8)
For the right side of equation 3.8 the expected utility from not buying equals: E(uN B
) = Z ∞
0
uN B(RA) f (RA)d RA (3.9)
For the left side of the same equation the expected utility of buying equals: E(uB
) = Z ∞
0
3.3 R
ISK AVERSE UTILITY FUNCTIONSAs mentioned before, literature suggests that poor individuals display a relatively high level of risk aversion, meaning that for their utility function u(x), u0(x) > 0 and u"(x) < 0 hold, i.e. the utility function is concave.
The relationship between the coefficient of relative risk aversion rRand the coefficient of
absolute risk aversion rA is as follows. These measures are often called Arrow-Pratt
meas-ures of risk aversion (Stowasser, 2015).
rR(x) = x−u"(x)
u0(x) = xrA(x) (3.11)
rAallows for a comparison of risk attitudes towards situations with outcomes that
con-cern absolute gains or losses from current wealth x (Gonberg, n.d.), e.g. how averse are you towards gambling withe10 of your wealth (Stowasser, 2015). Relative risk aversion meas-ures risk preferences that concern a percentage of wealth, e.g. how averse are you towards gambling with 1% of your wealth (Stowasser, 2015).
An utility function displays harmonic absolute risk aversion (HARA) if the inverse of its absolute risk aversion coefficient, also called the absolute risk tolerance T , is linear in wealth (see equation 3.12). HARA thus implies a rA(x) of the form ax+b1 (Cramton, n.d.).
T (x) = rA(x)−1=−u
0(x)
u"(x) = ax + b (3.12)
When r0A (rR0) is =0, <0 or >0, we speak of constant, decreasing or increasing absolute (relative) risk aversion, i.e. CARA, DARA or IARA (CRRA, DRRA or IRRA). Intuitively people are assumed to exhibit DARA rA0 < 0: the richer you become, the less risk-averse you are, e.g. a beggar will take less risk to losee10 than a millionaire. Furthermore experimental evidence suggest CRRA or IRRA, rR0 ≥ 0 (Stowasser, 2015).
Four kinds of HARA utility functions are commonly used (Gonberg, n.d.; Cramton, n.d.; Stowasser, 2015) and this thesis will focus on the first two utility functions: CARA and CRRA utility (see assumption 8):
1. Constant absolute risk aversion (CARA), a = 0: rA(x) is independent of x, ie rA(x) =
1
b = rA. For example the function u(x) = −e−λx with λ > 0, and the corresponding
rA= λ and rR= λx (IRRA).
2. Constant relative risk aversion (CRRA), b=0: for example the functions u(x) =x1−λ1−λ for
λ 6= 1 and λ > 0, and u(x) = ln(x) for λ = 1. The first is often used due to its flexibility;
decreases when wealth increases (DARA). The relative measure is constant, rR = 1.
Forx1−λ1−λ, rA=λx and rR= λ (DARA). Thus indeed rA(x) =ax1 and rR(x) =1a= rR
3. Quadratic utility: for example u(x) = x −αx2, which shows both IARA and IRRA, since
rA(x) = 2α−x1and rR(x) = 2αx −1 (assuming u(x)0> 0, i.e. 1−2αx > 0). Thus function
is assumed essay to handle
4. Hyperbolic utility: for example function of the form u(x) =1−γγ (1−γαx − β)γ withα > 0,
αx
1−γ−β > 0 and rA(x) = 1−γαxα−β. Depending on the value ofγ this function can be DARA,
CARA or IARA; depending on the values ofβ and γ this function van be DRRA, CRRA or IRRA. This function is also popular due to its flexibility.
Assumption 8: Farmers’ utility is given by a CARA or CRRA utility function withλ ≥ 0.5.
The most widely accepted measures of relative risk aversion coefficientλ lie between 1 and 3, but measures vary widely from as low as 0.2 to 10 or sometimes even higher (Gándel-man & Hernández-Murillo, 2015). Figure 3.2 classifies the different levels ofλ. Since, poor individuals generally display a relatively high level of risk aversion (Patt et al., 2009), we can assume aλ close to 1 or higher (i.e very or highly risk averse), but at least λ ≥ 0.5, i.e. classified as risk averse (see assumption 8).
Figure 3.2: Classification of different levels of constant relative risk aversion coefficientλ (Cook et al., 2013).
3.4 S
UMMARYIn this chapter a game theoretical model was designed that depicts the decision process on whether to buy a drought WII or not based on a certain rain distribution and a by the insurer constructed AFI contract. Farmers are assumed relatively risk averse. Rational risk averse farmers buy the contract once the expected utility of buying is at least as big as the expected utility of not buying. In the next chapters CARA and CRRA utilities are considered.
4 C
ASE STUDY
I
NDIA
:
DROUGHT INSURANCE IN
G
UJARAT
This chapter builds upon the model developed in chapter 3 and applies it to three district in Gujarat, India (Banaskantha, Gandhinager and Patan). In sections 4.1 and 4.2 different measures of trust and risk aversion in India are reviewed as benchmark and input for the model. Section 4.3 discusses the drought situation in India. In sections 4.5, 4.6, 4.7 and 4.8 the model’s parameters are constructed for the above mentioned districts and various crops. Finally, the main insights are summarized in section 4.9. The results of this case study are discussed in chapter 5.4.1 T
RUST INI
NDIAThere are different forms of trust. When people refer to trust, they generally mean interper-sonal trust, e.g. whether or not you agree with the statement "most people can be trusted". In India, about 16% of the population agrees with this statement and only 6.5% completely trust people they meet for the first time, see figure 4.1 (World Values Survey, 2012).
Figure 4.1: Reactions to the statement "most people can be trusted" (left) and "how much you trust: people you meet for the first time" (right) in 2012 in India (World Val-ues Survey, 2012).
Consumer trust in (financial) institutions has been low ever since the 2008 financial crisis. Generally, trust in the financial service industry is lower than in any other industries (The
in nature than microcredit and require a certain level of trust that the insurer will com-mit to the pre-agreed contract. The 2016 Edelman Trust Barometer measures average trust in institutions of government, business, media and NGOs among the general population. Globally the average (over 27 countries) is 49%; India scores higher with 65%. Interestingly, there exists a trust gap in India of 22% between high-income (top quartile of income) and low-income (bottom quartile of income) respondents, with trust measuring 78% and 56% respectively. Globally, this gap is 14%, i.e. 60% and 46% respectively (Edelman, 2016a), suggesting that there is a high degree of trust inequality in India, see figure 4.2. Looking solely at the financial service sector, India shows a relatively high level of trust, 74%, among the general population. 76% of Indians trust that financial services CEOs do what is right (Edelman, 2016b), a number that increased significantly since 2012 where it was only 59%, see figure 4.3. The lower number in 2012 is likely partly a result of the so called ‘2010 Indian microfinance crisis’, as can be seen in the following news quote:
"In Andhra Pradesh in 2010, consistent over-lending led to a pronounced in-crease in over-indebtedness and default. Microfinance organizations resorted to extreme measures to generate loan repayment, driving over 200 individuals to suicide, and causing significant socioeconomic tension. For many house-holds, interactions with microfinance institutions constituted their only rela-tionship with the financial sector, and so the crisis led to a general loss of trust in banking. "The crisis in Indian microfinance has done incalculable damage to an industry that has sustained itself on the basis of reputation and trust" says Joseph Stiglitz, a Nobel Prize recipient [..]" (Aizenman, 2016).
Overall, Indians are categorized as one of the 11 ‘trusters’, ranking second out of a total of 27 countries in 2016 (Edelman, 2016a). The Indian Prime Minister Narendra Modi, might have influenced this result, as he was also featured on the front page of the study’s report.
Unfortunately, the above mentioned measures of trust are not precise enough, since they either contain the entire population (of which farmers are a particular subset) or concern trust in more general terms. Ideally, we would like to ask farmers in India whether they would trust a specific financial institution with their money. Combining the fact that the general public is quite cautious about whom to trust, especially when meeting for the first time (figure 4.1), with the knowledge about the existing trust gap (figure 4.2) and with the general public’s answers to whether CEOs from financial institutions can be trusted (figure 4.3), trust in financial institution of relatively uninformed farmers will roughly be 50%. In our one farmer model, this translates into t = 0.5 (see corollary 1).
Figure 4.2: Trust inequality between low- and high-income respondents in the 2016 Edel-man Trust Barometer with India (red arrow) scoring 22% (EdelEdel-man, 2016a).
Corollary 1: Trust in formal financial institutions by relatively uninformed farmers in India
equals t=0.5.
4.2 R
ISK AVERSION INI
NDIAThe shape of the utility function and the risk aversion parameter are fundamental in de-termining the (dis)satisfaction one obtains from a certain experience like total loss of crops. This case study considers two HARA functions: CARA (u(x) = −e−λx withλ > 0) and CRRA (u(x) = l n(x) and u(x) = x1−λ1−λ withλ > 0 and λ 6= 1). Recall that the most widely accep-ted measures of relative risk aversion coefficient λ lie between 1 and 3 (Gándelman & Hernández-Murillo, 2015).
Gándelman & Hernández-Murillo (2015) estimate this coefficient for 75 countries. For India they reportλ = 0.92, however not statistically significant at the 10% level. The values between -0.2 and 2.2 fall within the 90% confidence interval. This measure, however, is based on all Indian individuals, including non-farmers, and is not region-specific. Cook
et al. (2013) find an average CRRA coefficient of 0.53. Their research however concerns risk
