Insurance and rural welfare: what can panel data tell us?

Abstract

Assessing the scope for insurance in rural communities usually requires a structural model of household behaviour under risk. One of the few empirical applications of such models is the study by Rosenzweig and Wolpin (1993) who conclude that Indian farmers in the ICRISAT villages would not benefit from the introduction of formal weather insurance. In this article we investigate how models such as theirs can be estimated from panel data on production and assets. We show that if assets can take only a limited number of values the coefficients of the model cannot be estimated with reasonable precision. We also show that this can affect the conclusion that insurance would not be welfare improving.

Notes

¹ See Tanner (1997) for US evidence and Elbers et al. (forthcoming) for Zimbabwe evidence.

²Elbers and Gunning (2002).

³ From a positive economics perspective this is the very reason for writing accumulation as an optimization problem instead of being satisfied with a purely descriptive function ϕ.

⁴ This is similar to the situation studied by RW where asset ‘k’ is in fact a vector of stocks: bullocks, pump and calves of various ages, all integer valued. The number of bullocks can take only three values as 0, 1 and 2.

⁵ It is possible that a ₁ = 2, in which case only w ₁ can be estimated.

⁶Rust (1994) provides detailed discussion of the identification of dynamic discrete choice models, presenting sufficient conditions under which the model can be identified and a simple and general estimation theory is available. One of the restrictions required in his discussion is that shocks enter into the utility function additively, which is violated in the RW model. As Rust (1994) mentions, no general estimation theory exists for this case.

⁷ In this model consumption smoothing is the only coping mechanism. Maitra (2001) finds evidence of another coping mechanism, changes in labour supply.

⁸ In this RW specification c _min has unfortunately a dual role: it is the level of consumption below which a household cannot survive and also the level guaranteed by the informal insurance arrangement. It would be more natural to specify different parameters for these roles so that the welfare effect of a change in the protection offered by the insurance scheme can be analyzed.

⁹ There are two possible cases for the order of the thresholds. Besides the case used in this article, the only possible case is the one mentioned in footnote 5. Since we do observe households with one bullock in the data, we exclude this case in this article.

¹⁰ Note that the threshold values are insensitive to pump ownership.

¹¹ Eight is also the number of periods in RW. RW do not mention the number of households, but the ICRISAT data set contains 30 medium-size households with two or more observations. RW use the data from this medium-size group of households.

¹² This is, of course, a simplification; in practice there will be covariance, for example, in the case of weather shocks.

¹³ Note that .

¹⁴ The interpolation method used is a trivariate version of the ‘Four Point Formula’in Abramowitz and Stegun (1972, p. 882).

¹⁵ Recall that this measure is biased since (as RW recognize) the cost of the informal arrangement would be reflected in a premium which would not have to be paid under AFI. Since RW do not know this cost (which is reflected in α(k)) they ignore it in the comparison. Hence, under AFI the household continues to pay the same premium. This is a major issue, given the choice between AFI (i.e. constant consumption) and an arrangement where the household would receive positive shocks but (as a result of the c _min floor) no negative shocks it might well prefer the latter if the two schemes did not differ in cost. This would, obviously, say nothing about the desirability of AFI. Rather, it would reflect the failure to model explicitly the cost of the c _min scheme.

¹⁶ The welfare changes can only be compared within rows since different rows correspond to different preferences.