Statistical analysis of rainfall insurance payouts in southern India.

Results in table 3 provide some evidence that measured payouts, beyond being spatially correlated within Andhra Pradesh, are also correlated with aggregate Indian economic activity. This suggests that remittances to drought-stricken areas from family members in other parts of India may provide only incomplete sharing of risk associated with extreme rainfall events, since transfers within risk-sharing groups cannot smooth shocks that are aggregate to the group (Townsend 1994). The finding also potentially strengthens the case for ICICI Lombard to hedge its exposure to weather risk arising from rainfall insurance. The balance sheet of a foreign reinsurer is likely to be less exposed than ICICI Lombard to Indian macroeconomic risk.

The last part of table 3 displays the correlation of insurance payouts with Indian SENSEX stock market returns. For each year and station we calculate stock returns between the start and end dates of each insurance phase, then convert them to an annualized rate. Thus, returns match up exactly to the period covered by the contract, rather than just the year of the contract, as for the macroeconomic data. Payouts are not significantly correlated with Indian stock returns, however, perhaps reflecting that most Indian agricultural output is produced by small farms, rather than large traded firms.

Conclusions

We use historical rainfall data to estimate a putative history of payouts on Indian rainfall insurance policies. We find that indemnities are concentrated in the extreme tail of adverse rainfall events. This insures households against severe shocks, but also creates a highly skewed distribution of losses for an insurer writing rainfall insurance policies. This balance sheet exposure can be partially ameliorated by holding a portfolio of geographically segmented insurance contracts, or by using reinsurance markets.

We emphasize that much more research is needed to evaluate the promise of weather index insurance. For example, to shed further light on welfare benefits and to inform optimal contract design, theoretical and empirical work is needed to improve our understanding of the types of weather shocks against which rural household consumption is not well insured.

We acknowledge the financial support of the Swiss State Secretariat for Economic Affairs, SECO, CRMG and the Global Association of Risk Professionals, GARP We thank representatives from ICICI Lombard for their assistance, and Zhenyu Wang for comments. Paola de Baldomero Zazo and Sarita Subramanian provided outstanding research assistance. Views expressed in this paper are the authors' and should not be attributed to the World Bank, Federal Reserve Bank of New York, or the Federal Reserve System. Email: xgine@worldbank.org, rtownsen@uchicago.edu, and james.vickery@ny.frb.org.

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(1) Some adjustments are made to accumulated rainfall when constructing the rainfall index used to calculate payouts. If daily rainfall exceeds 60 ram, only 60 mm is counted toward the cumulative rainfall index. Also, rainfall <2 mm is ignored. These adjustments reflect that heavy rain may generate water runoff, resulting in a less than proportionate increase in soil moisture, while very light rain is likely to evaporate before it soaks into the soil. We take these adjustments into account when constructing putative insurance payouts.

Dr. Xavier Gine (World Bank, DECRG), Prof. Robert Townsend (University of Chicago), Dr. James Vickery (Federal Reserve Bank of New York).

This article was presented in a principal paper session at the AAEA annual meeting (Portland, OR, July 2007). The articles in these sessions are not subjected to the journal's standard refereeing process. Table 1. Summary Statistics of Rainfall Insurance Payouts

Percent Mean

Average Positive Average Rainfall

Payout Payouts Premium Index Phase one 20.9 13.7% 98.3 176.0 Phase two 46.4 13.0% 102.8 192.9 Phase three 22.0 5.4% 98.5 211.6 All phases 29.7 10.7% 99.9 193.4

Average Number

Triggers of Obs.

Strike Exit (Phases) Phase one 78 26 322 Phase two 72 12 316 Phase three 499 580 316 All phases n/a n/a 954 Note: Table relates to rainfall insurance contracts written against 14 IMD rainfall stations in Andhra Pradesh, India, in 2006. Estimates of average payouts are based on historical IMD rainfall data from 1963-2000 and 2004-06. Note that in all cases, insurance contracts pay out Rs 10 per millimeter of rainfall deficiency relative to the "strike." until the "exit" is reached. Beyond the exit (i.e., below the exit in the case of Phases 1 and 2, and above the exit for Phase 3), the insurance pays out a fixed indemnity of Rs 1,000. Table 2. Time Series Dependence in Insur-ance Phase Payouts Lagged Variables Bivariate Multivariate Intercept 34.4 *** 46.5 **

(9.4) (19.0) Insurance Payout (Rs.) 0.017 0.004

(0.04) (0.05) Dummy for positive -3.214

payout [0,1] (17.25) Phase rainfall (mm) -0.061

(0.07) [R.sup.2] 0.000 0.002 N 603 603 Note: Dependent variable is insurance phase payout. The regression sample consists of estimated putative insurance payouts relating to phases 2 and 3. These are regressed on explanatory variables, which are lagged by one phase. Numbers in parentheses are standard errors, which are clustered by time period (i.e., phase interacted with year). Asterisk (***). (**), and (*) indicate two-sided statistical significance at the 1%, 5%. and 10% level, respectively. Table 3. Correlation of Insurance Payouts with Aggregate Variables Variable Macroeconomic Name Variables GDP growth (% change, -4.19 *

real GDP per capita) (2.21) Inflation (% change, 0.26

GDP deflator) (1.02) Change in Treasury bond yield 0.24

(1-5 year maturity) (2.49) Change in Treasury bond yield

(> 15 year maturity) India SENSEX index [R.sup.2] 0.011 0.000 0.000 Number of observations 922 922 871 Years of data, RHS variable 38 38 30 Variable Macroeconomic Stock Name Variables Returns GDP growth (% change, -5.41 **

real GDP per capita) (2.54) Inflation (% change, -1.65

GDP deflator) (1.16) Change in Treasury bond yield -0.02

(1-5 year maturity) (2.08) Change in Treasury bond yield 3.77 3.48

(> 15 year maturity) (8.66) (9.04) India SENSEX index -0.02