Risk and Insurance in Village India

Transcription

1 Risk and Insurance in Village India Robert M. Townsend (1994) Presented by Chi-hung Kang November 14, 2016 Robert M. Townsend (1994) Risk and Insurance in Village India November 14, / 31 1/ 31

2 Motivation Poor agricultural villages in Southern India face high risk from weather and crop diseases Are landless labors more vulnerable than the landlords? Does consumption fluctuate with the income shocks? Are people fully insured at the village level? Which economic activity is better insured? Is there any scope for policy reform? Robert M. Townsend (1994) Risk and Insurance in Village India November 14, / 31 2/ 31

3 Data Data of southern India villages from International Crops Research Institute of the Semi-Arid Tropics (ICRISAT) Annual data Three villages: Aurepalle, Shirapur, Kanzara 40 households for each village Panel data for 35, 32, 36 households respectively Robert M. Townsend (1994) Risk and Insurance in Village India November 14, / 31 3/ 31

4 Table I: Composition of Income Robert M. Townsend (1994) Risk and Insurance in Village India November 14, / 31 4/ 31

5 Figure 1 and Figure 3: Deviation From the Village Average Deviation of individual income from the village average income is quite volatile Deviation of individual consumption from the village average consumption is relatively small Robert M. Townsend (1994) Risk and Insurance in Village India November 14, / 31 5/ 31

6 Prediction From the Model Proposition By Wilson (1968) and Diamond (1967), if the following assumptions hold, 1 Preferences are time separable 2 Weak risk aversion 3 All individuals have the same discount rate 4 All information is held in common then a Pareto optimal allocation of risk bearing of a single good in a stochastic environment implies that all individual consumption is determined by aggregate consumption Idiosyncratic shocks should not influence individual consumption The implication holds in a multiple commodity world under separable preferences Robert M. Townsend (1994) Risk and Insurance in Village India November 14, / 31 6/ 31

7 The Model: Individual Preferences (1) W k (c k t, l k t ) = U k (c k t ) + V k (l k t ) (2) U k (c k t ) = 1 σ i e σ i c k t ct k lt k consumption of individual k of household i at time t leisure of individual k of household i at time t Utility function is separable between consumption and leisure All individuals in household i are equally risk averse Robert M. Townsend (1994) Risk and Insurance in Village India November 14, / 31 7/ 31

8 The Model: Household Decision For a househould i with M individuals, the maximization problem is: ( M T ] max λ k β t E 0 [U ) k (ct k ) + V k (lt k ) k=1 t=1 s.t. M M ct k c t ; lt k l t, k=1 k=1 ct k 0; 0 lt k Tt k, M 0 < λ k < 1, λ k = 1 k=1 λ k is the utility weight of individual k in the household Robert M. Townsend (1994) Risk and Insurance in Village India November 14, / 31 8/ 31

9 The Model: Household Decision For any two individuals k and j in household i at time t, the weighted marginal utility should be the same to achieve Pareto optimal within the household: λ k Uk c k t = λ j Uj c j t = µ c µ c Lagrange multiplier for consumption constraint Robert M. Townsend (1994) Risk and Insurance in Village India November 14, / 31 9/ 31

10 The Model: Household Decision Assume that σ i = σ, summing over the FOC of total individuals in household i and total households N in the village gives Pareto optimal consumption of household i: (3) c i t = 1 N i t N i t k=1 c k t = 1 σ ( c t = 1 N ln(λ i ) 1 N N i=1 ) N ln(λ i ) + c t i=1 Assume that λ i are the same for each household, then c i t (4) c i t = c t 10/ 31 Robert M. Townsend (1994) Risk and Insurance in Village India November 14, / 31

11 Equivalence Scales c i t is adjusted by household size Is c i t = N i t k=1 ck t N i t a good adjustment? Deaton (2003) Simply deflating by total household size has two major problems Ignoring the household composition Ignoring any economies of scale in consumption within the household; public goods of the household Browning, Chiappori and Lewbel (2010) Equivalence scales measure the ratio of costs of attaining the same utility level 11/ 31 Robert M. Townsend (1994) Risk and Insurance in Village India November 14, / 31

12 Equivalence Scales Construct the equivalence scale A k t for individual k at time t according to the caloric intake from the survey of Ryan, Bidinger, Pushpamma and Rao (1985) Age-sex categories Equivalence Scales Adult Males 1.00 Adult Females 0.90 Males aged Females aged Children aged Children aged Toddlers 0.32 Infants / 31 Robert M. Townsend (1994) Risk and Insurance in Village India November 14, / 31

13 The Model: Household Decision Incorporate the equivalence scale A k t in the individual utility function: W k (c k t, l k t, A k t ) = U k (c k t, A k t ) + V k (l k t, A k t ) U k (ct k, A k t ) = 1 e σ i c k t A k t, σ i U k A k t = ck σ i ct k t (A k t ) 2 e A k t < 0 Given the same consumption, with a higher equivalence scale A k t, individual k has a lower utility level. 13/ 31 Robert M. Townsend (1994) Risk and Insurance in Village India November 14, / 31

14 The Model: Household Decision The Pareto optimal consumption of household i can be rewritten as: (5) c i t = c t 1 σ Ai t c i t = N i t k=1 N i t k=1 c k t A k t, c t = 1 N N i=1 c i t 14/ 31 Robert M. Townsend (1994) Risk and Insurance in Village India November 14, / 31

15 The Model: Household Decision Where A i t is defined as: (6) A i t = A k t ln(a k t ) N i k=1 N i k=1 A k t 1 N A N k t ln(a k t ) i=1 N i k=1 N i k=1 A k t 15/ 31 Robert M. Townsend (1994) Risk and Insurance in Village India November 14, / 31

16 Time Series Estimation Estimate the following equation for each household: (7) c i t = α + β c t + δh i t + ζx i t + u i t H i t are control variables for household composition, e.g. number of household members, number of kids, and number of adults X i t is one control variable, such as income source One β for each household. For example, Aurepalle has 44 households, so it generates 44 β estimates for Aurepalle By the model derivation, β = 1 and δ = 1 σ 16/ 31 Robert M. Townsend (1994) Risk and Insurance in Village India November 14, / 31

17 Figure 5: Time Series Estimates For each village, rank households according to the magnitude of β. The dots in the figure are β for each household i, and the lines are 95% confidence interval 17/ 31 Robert M. Townsend (1994) Risk and Insurance in Village India November 14, / 31

18 Table IV: Null Hypothesis Test for β Table IV: Number of Times Failing to Reject the Null Fail to reject β = 1 for 107 households, and fail to reject β = 0 for 55 households Impose β = 1 for the panel estimation 18/ 31 Robert M. Townsend (1994) Risk and Insurance in Village India November 14, / 31

19 Panel Estimation Fixed effect estimation: (8) c i t First-difference estimation (9) c i t c t = α i + δh i t + ζ w X i t + e i t c t = δ H i t + ζ i X i t + e i t α i is household fixed effect H i t are the control variables for household composition, e.g. Number of household members, number of kids, number of adults X i t is one control variable ζ i w Within-village estimate ζ i First-difference estimate Regress with one control variable each time 19/ 31 Robert M. Townsend (1994) Risk and Insurance in Village India November 14, / 31

20 Table VIII: Panel Estimates From Equation (8) and (9) One coefficient represents one regression 20/ 31 Robert M. Townsend (1994) Risk and Insurance in Village India November 14, / 31

21 Panel Estimation: Control for All Income Sources Fixed effect estimation with income sources: (10) c i t c t = α i + δh i t + ζ w X i t + Y i t Γ + e i t H i t are the controls of household composition X i t average village labors Y i t is a vector of income variables, including crop profit, labor income, trade and handicrafts, and animal husbandry If the consumption is fully insured against income shocks, the coefficients of income variables should be jointly zero 21/ 31 Robert M. Townsend (1994) Risk and Insurance in Village India November 14, / 31

22 Table IX: Control for All Income Sources 22/ 31 Robert M. Townsend (1994) Risk and Insurance in Village India November 14, / 31

23 Effect of Landholding on Insurance Estimate the effect of village consumption on the landless household l (11) c l t = α l + β c t + δh l t + γy l t + u l t α l is household fixed effect Ht l are the controls for household composition yt l all income of landless household l β = 1 if the idiosyncratic shocks are fully insured at the village level γ = 0 if the income shocks are fully insured 23/ 31 Robert M. Townsend (1994) Risk and Insurance in Village India November 14, / 31

24 Table X: Effect of Landholding on Insurance 24/ 31 Robert M. Townsend (1994) Risk and Insurance in Village India November 14, / 31

25 Kinship and Financial Networks, Formal Financial Access, and Risk Reduction Cynthia Kinnan and Robert Townsend (2012) Presented by Chi-hung Kang November 14, / 31 Kinnan and Townsend (2012) Financial Networks and Risk Reduction November 14, / 31

26 Motivation Access to borrowing and lending can be helpful to insure against short-term idiosyncratic risks Informal credit: borrowing from relatives Formal financial institution: banks What are the effect of these two channels on consumption smoothing? 26/ 31 Kinnan and Townsend (2012) Financial Networks and Risk Reduction November 14, / 31

27 Consumption-smoothing specification c ivt =α 1 y ivt + α 2 y ivt d i,b + α 3 y ivt r i,b + α 4 y ivt k i + α 5 y ivt w i + δ B,t + ɛ it c ivt Difference of consumption for household i in village v at time t y ivt Difference of income for household i in village v at time t d i,b = 1 if i borrows directly from the bank r i,b = 1 if i borrows from someone who borrows from the bank k i = 1 if having any kin in the village w i household i s average net worth over the sample period δ B,t common time effect of households directly connected to the bank 27/ 31 Kinnan and Townsend (2012) Financial Networks and Risk Reduction November 14, / 31

28 Result for Consumption-smoothing specification c ivt = y ivt y ivt d i,b y ivt r i,b y ivt k i y ivt w i + δ B,t + ɛ it c ivt Difference of consumption for household i in village v at time t y ivt Difference of income for household i in village v at time t d i,b = 1 if i borrows directly from the bank r i,b = 1 if i borrows from someone who borrows from the bank k i = 1 if having any kin in the village w i household i s average net worth over the sample period δ B,t common time effect of households directly connected to the bank 28/ 31 Kinnan and Townsend (2012) Financial Networks and Risk Reduction November 14, / 31

29 Investment-smoothing specification ( I ) ) ) ) A) y y ( y ( y 1( 2( =α ivt A + α ivt A r i,b + α 4 ivt A k i + α 5 ivt A + β 1 r i,b + β 2 k i,b + β 3 w i + δ v + δ B,t + ɛ it ivt w i I is total household investment y is total household income A is total household assets r i,b = 1 if i borrows from someone who borrows from the bank k i = 1 if having any kin in the village w i household i s average net worth over the sample period δ v village fixed effect δ B,t common time effect of households directly connected to the bank 29/ 31 Kinnan and Townsend (2012) Financial Networks and Risk Reduction November 14, / 31

30 Table 1: Kinship, Financial Access, and Investment 30/ 31 Kinnan and Townsend (2012) Financial Networks and Risk Reduction November 14, / 31

31 Extension An indicator for having a kin in the village does not capture the whole effects of personal networks Network characteristics rather than just an indicator The indicator for direct connection to the bank can be endogenous For US data, use the total banks around the neighborhood as a proxy for formal financial access 31/ 31 Kinnan and Townsend (2012) Financial Networks and Risk Reduction November 14, / 31