Development Economics Part II Lecture 7 Risk and Insurance Theory: How do households cope with large income shocks? What are testable implications of different models? Empirics: Can households insure themselves (fully) and what are the mechanisms they use to insure themselves? 1
Risk and Insurance Introduction: fluctuations in consumption reduce the utility of risk averse individuals See graphical example: concave utility function, either low C or high C with probability ½ or middle C =(low C+high C)/2 with probability 1 There are two ways to keep C constant when Y fluctuates: 1. self-insurance (saving and borrowing) and 2. mutual insurance A third possibility to reduce fluctuations in consumption C is by reducing the fluctuations in income Y. How? For example chosing a less risky occupation or less risky crop to plant. 2
Risk and Insurance Three methods of consumption smoothing: 1. Mutual insurance: smoothing through interaction between people smoothing over different states of the world at one point in time 2. Self-insurance: consumption smoothing using one s own assets intertemporal smoothing over time, borrow or use up assets in bad times and save in good times ex-post consumption smoothing given the income process 3. Chosing economic activities that have a smoother income process ex-ante (e.g. plot and crop diversification) Potential efficiency loss, as less risky projects are often the ones with lower expected returns. Thus not being able to insure oneself might imply, that these HH have to pick low risk-low return projects. 3
Credit versus Insurance The distinguishing feature of mutual insurance (compared to self-insurance via credit): a certain lack of regard for history. transfers do not carry an obligation to repay example: medical insurance 4
Insurance: Example Two farmers 1 and 2: Both farmers produce the same crop and use the same amount of inputs Harvest can take two values (prob ½ each, independent for 1, 2): $2000 if things go well $1000 if there is damage to the crop Assume: Farmers are risk-averse theywouldliketosmooth consumption 5
Insurance: Example Case 1: Farmers 1 and 2 do not know each other Self-insurance Farmers have to rely on self-insurance using own wealth, that is assets can be run down in bad times and added to in good times. Possible assets are: Credit: saving and borrowing Stocks of cash or accumulated savings in banks Stocks of grain (though not perfectly durable) Livestock or jewlry can be sold (dangers of selling productive assets lower production in the future, costly means of insurance) 6
Insurance: Example Case 2: Farmers 1 and 2 know each other Mutual insurance between economic agents Without insurance: Farmer 1: C(H)=2000, C(L)=1000 with prob ½ each (independent of harvest outcome of other farmer) Farmer 2: same With insurance: C(1=H, 2=H)=2000 C(1=L, 2=L)=1000 C(1=L, 2=H)=1500 C(1=H, 2=L)=1500 withprob¼foreachstate In the first two cases farmers 1 and 2 cannot help each other, as both are either in the good or both are in the bad state. In the last two they can agree to share the output equally (farmer 1 pays farmer 2 $500 if 1 produces high and 2 produces low) 7
Distinct features of insurance (in contrast to credit): At any date, the farmer with the high outcome makes a unilateral payment After this transfer the slate is wiped clear, i.e. next year the SAME person may be asked to pay up again Past transfer from one person to the other does not carry a historical burden for the recipient 8
Possibility of insurance crucially depends on correlation between outcomes of the two farmers: 1. Independent outcomes: each of the four states (HH, LL, HL, LH) happens with prob ¼ as shown before scope for insurance in the last two states 2. Outcomes are perfectly positively correlated: HH or LL with probability ½ NO scope for insurance (e.g. for aggregate shocks such as weather) 3. Outcomes are perfectly negatively correlated: HL or LH Farmers can insure themselves completely and receive a certain income $1500. 9
General points: For mutual insurance to work, outcomes cannot be perfectly positively correlated Problem for crop insurance: agriculture does present large correlations because of the weather. Results suggests that insurance groups are most likely to be formed among people whose fortunes are as negatively correlated as possible We will see in a few slides that there are also reasons to avoid such extremes connected to the fact that one knows less about people who live far or do very different things ( Limited information ) 10
Another determinant of the possible degree of insurance is group size For a very large group of farmers, people can completely insure their income even without perfect negative correlation (only need independence) What will be the average income of a large string of people in any given year? Problem is identical to coin-tossing problem: toss a coin several times, each time write down $2000 for head and $1000 for tail. The average income will be $1500 (identify each independent coin toss with a person), provided that the number of farmers is large ( Law of large numbers ). 11
Show formally (HERE OR BEFORE LIMITED ENFORCEMENT??): Two outputs: H with probability p, L with probability (1-p) Without insurance (or savings), C=Y: EU=pU(H)+(1-p)U(L) Perfect insurance: Everyone with Y=H pays (1-p)(H-L) Everyone with Y=L pays p(h-l) EY=p[H-(1-p)(H-L)] + (1-p)[L-p(H-L)]=pH+(1-p)L as certain income regardless of state of the world U(EY)>EU 12
The Perfect Insurance Model Theory: Large number of identical farmers with income: Farmer s average income Idiosyncratic shock may have the same distribution across farmers, but affects each independently Aggregate shock captures common variation in village, affects all farmers in the same way in any year (example: weather shocks such as flood or drought) as is average income 13
If there are a large number of farmers, all the idiosyncratic variation can be insured away. Illustration: Farmers pay their realized value of epsilon into a common fund and get back the average income. As epsilon is sometimes positive and sometimes negative, this implies that some farmers make positive contributions, whereas others receive payouts from the common fund. idiosyncratic variation can be ironed out. Farmer s insured income is now given by: 14
Farmer s insured income is now given by: Income is less risky than as the idiosyncratic component is removed. risk averse individuals will prefer this system of mutual insurance What about the aggregate shock? The realization of theta is the same for all the farmers in the village, so there is no insurance possible here. Thus under perfect insurance income may still fluctuate, but the ONLY source of fluctuation in that case is the aggregate uncertainty in the system (that cannot be insured away with a common pool of funds) Important determinant of degree of insurance: relative significance of idiosyncratic to aggregate risk. 15
Farmer s insured income is now given by: This is the Pareto-efficient solution. Income is less risky than as the idiosyncratic component is removed. risk averse individuals will prefer this system of mutual insurance What about the aggregate shock? The realization of theta is the same for all the farmers in the village, so there is no insurance possible here. Thus under perfect insurance income may still fluctuate, but the ONLY source of fluctuation in that case is the aggregate uncertainty in the system (that cannot be insured away with a common pool of funds) Important determinant of degree of insurance: relative significance of idiosyncratic to aggregate risk. 16
Pareto efficient allocation of risk Setup Assume households cannot store income from one period to the next. There are i=1,..., N households, t=1,...,t periods and s=1,...,s states of nature (each occuring with probability ) Income received by household i in state s at time t: Consumption of household i in state s at time t: Each household has an additively separable utility function where and 17
Pareto efficient allocation of risk The problem to be solved to find the consumption levels that achieve the Pareto efficient allocation of risk is: where is the weight of household i in the social welfare function, with 18
Pareto efficient allocation of risk We set up the Lagrangian and derive the first order conditions as follows 19
Pareto efficient allocation of risk We set up the Lagrangian and derive the first order conditions as follows The first order conditions imply for HH i and j 20
Pareto efficient allocation of risk Assume the utility function exhibits constant absolute risk aversion (CARA) We use this to derive the first order condition Taking logs leads to Rearranging give us consumption of HH i in state s at time t 21
Pareto efficient allocation of risk We can write consumption of HH i in state s at time t as: Implication: Average village consumption Household consumption is given by the village average plus an individual specific term that depends only on the household's weight in the Pareto programme. 22
Pareto efficient allocation of risk Key predictions for the Pareto efficient allocation of risk in mutual insurance: Household consumption is given by the village average plus an individual specific term that depends only on the household's weight in the Pareto programme. In particular, household i s consumption does not depend on household i s income, which is an implication that can be tested in the data. The reason is that when households can efficiently insure within the community, idiosyncratic income shocks are fully insured and only aggregate risk remains. 23
Benchmark Model: Perfect Insurance Large number of people who face an aggregate shock that is common to all of them (say weather) and the additional possibility of idiosyncratic variations in income Optimal to pool all the idiosyncratic variation, which reduces the idiosyncratic risk to zero (for uncorrelated shocks of a large number of people) while the aggregate shock can not be insured against Testable hypothesis: If the model is good, then we should see that individual (HH) consumption is unaffected by individual incomes, but it should move in perfect correlation with the aggregate consumption of the entire group (eg entire village) 24
Test of Model of Perfect Insurance Method: Regression analysis Dependent variable: Household consumption Independent variables: Group consumption, household income, and other household observables (such as spell of unemployment, sickness, etc) Test: If the theory of perfect insurance is right, then the estimated coefficients on all the household-specific variables should be zero and the coefficient on group average consumption should be unity Testable equation: Test: If there is perfect insurance 25
TestsofRiskSharing Specific mechanisms: Udry (94), Platteau and Abraham (97): informal credit Rosenzweig and Wolpin (93): bullock sales Rosenzweig (88): transfers between family members By studying one mechanism at a time, one may miss others. General equilibrium framework take into account all channels by looking at outcomes, i.e. consumption and labor supply 26
Townsend (1994) Risk and Insurance in Village India General equilibrium framework: Data: ICRISAT, 1975-84, 3 villages in semi-arid rural India, 40 HH in each village Methodological questions: What is the relevant group that is engaged in insurance? This determines how we construct average consumption. Is a village the natural unit to study? Why? What other unit would be reasonable? Pareto optimum was formulated for individual How go to HH? 27
Test of Model of Perfect Insurance First question: What is the potential for mutual insurance? Even within villages not all HH are planting the same crops in the same soil. They are not engaged in the same income-generating activities. Figure 1: difference between HH income and average income to remove aggregate risk lots of idiosyncrativ risk that fluctuates independently across HH, i.e. no comovement potential for mutual insurance Problems of Implementation: missing data, as we do not observe consumption of everyone in village but only sample HH 28
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Test of Model of Perfect Insurance Method: Regression analysis Dependent variable: Household consumption Independent variables: Group consumption, household income, and other household observables (such as spell of unemployment, sickness, etc) Test: If the theory of perfect insurance is right, then the estimated coefficients on all the household-specific variables should be zero and the coefficient on group average consumption should be unity Testable equation: Test: If there is perfect insurance 31
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Results (see table): The coefficient on HH income is usually small, but significantly different from zero some smoothing is taking place, but not clear if insurance or some other form of smoothing such as self-insurance or credit Individual and aggregate consumption do move together some insurance 33
Potential caveats/extensions: Even amonmg the ICRISAT villages, the ability to smooth may vary significantly across HH The better-off farmers are able to smooth but no the small farmers and landless laborers. Insurance might look good simply because HH try to smooth their INCOME streams so that the remaining fluctuations can be absorbed by the available consumption smoothing mechanisms 34
Constraints on degree of insurance Why is there no perfect insurance? Two factors that put constraints on insurance: 1. Limited information about outcomes or what led to the outcomes (for example luck or insufficient effort) 2. Limited enforcement Townsend s framework implicitly assumes perfect enforcement (to prevent people from not paying into the pool if their own harvest is good). If you need self-enforcing contracts, best implementable scheme may differ from the First Best. study models with imperfect insurance Remember: Perfect insurance means full insurance of idiosyncratic shocks, income can still fluctuate due to aggregate shocks!! 35
1. Limited Information Limited information creates moral hazard problems, which means group members: 1. may not be able to verify the outcome on which the insurance transfers are based Person might provide wrong or misleading information about economic state, e.g. size of the harvest). 2. Or it may be possible to verify outcome, but not what led to it (i.e. occurence of some insurable event can be influenced by the unobservable action of the individual) Example: Did a farmer suffer a bad harvest because he was really unlucky (eg sick) or did he apply inadequate levels of effort to cultivation. 36
1. Limited Information Implementing perfect insurance would then lead to efficiency losses, because people have an incentive to apply inadequate effort to income-generating activities Intuition: if each farmer receives amount ph+(1-p)l regardless of wether his output is high or low, then why incur the extra effort to raise the probability that output will be high? Thus each farmer has an incentive to slack off under the perfect insurance scheme, and if all farmers think this way, the scheme cannot survive. Implement the Second-Best Insurance Arrangement, constrained by limited information i.e. only provide some insurance, so that individual consumption does move with individual income to some degree. In that case the individual has an incentive to excert effort to raise the probability of high output. 37
1. Limited Information Practical Implication: trade-off between diversification and moral hazard 1. Diversified uncorrelated incomes across group members are easiest to achieve when members are in different occupations or geographically separated 2. But an extension of insurance schemes across villages increases probability of moral hazard because it is harder to verify output Informational problems are increased, unless for example through marriage to people from different region so that there are family ties making up for geographic distance see next paper we discuss (Rosenzweig (1988)) 38
1. Limited Information Possible solutions to problem of limited information: Traditional societies are highly endowed with social capital: social capital provides a fund of socially available information Problems: increasing migration or segmentation of village into subgroups, e.g. caste lines insurance schemes might not cut across these lines of segmentation because flow of information is restricted (IMPORTANT: for empirical work one has to define the relevant community ) 39
Limited Information: Formal Treatment Formal treatment to see what is the best implementable risk sharing agreement under limited information Eliana addressed the problem of moral hazard in the discussion of credit markets Key point: trade-off between provision of insurance and provision of incentives if the community wants to maintain a high level of effort, it will have to offer incomplete insurance so that individual incentives are not destroyed Formally: can compute second-best insurance scheme that secures high effort but only incomplete insurance 40