shocks. Thus the empirical approach is very much in line with the strong identification properties of the weathershock approach summarized by Dell, Jones, and Olken (2014). It should be noted that with district fixed effects, , included in the specification, the coefficients 1 can be estimated only if the values of vary within districts. kk Otherwise, the use of the district dummies will absorb the effects of these environmental factors. μμ hkk γγ EE The impact of drought on consumption expenditures is the cumulative effect of a household’s crop loss and a series of entitlement failures in a local economy that are triggered by this initial loss (Sen, 1981; Deveraux, 2007). Devereux (2007) characterizes a sequence of four entitlement failures: first, production fails as a result of the rains failing; then labor markets fail as households are less and less able to find work opportunities on other farms or in off-farm activities; then commodity markets fail as grain prices increase and prices of liquid assets decrease. Finally, transfers fail as households cannot rely on the support of others in their network who face the same constraints in meeting everyday basic needs. The formulation outlined here is agnostic as to how rainfall is impacting consumption. However, the spatial measure of drought used and the necessity of incorporating district fixed effects focuses the analysis more on picking up production failures and failures in the immediate labor and commodity local market in which the drought is measured. The impact of drought through commodity markets that span a larger geographic area or transfer networks over a larger geographic space will not be picked up. If higher levels of k indicate rainfall sufficiency, it is anticipated that 2 > 0 such that lack of rainfall and droughts have a negative effect on welfare (especially when a monetary welfare measure is used, such as consumption expenditures per adult equivalent). RR ββ̂ The extent to which hazards experienced by households in the sample are associated with sufficiently significant declines in their welfare depends in part on the degree to which there is variability in the exposure to and intensity of the shocks experienced. For example, if the value of k is the same for all in the sample and not just for those within a given cluster, then there is no way to identify the parameter 2 . Hence, it is critical to derive estimates of 2 based on data that include significant variability in RRk . This task is a particular challenge when analyzing the impact of drought because these events are spatially correlated and not localized. Increasing the number of years ββ and the number of countries included increases the variation in ββ̂ RR k . For this reason, the analysis prioritizes inclusion of countries where multiple rounds of survey data were available. In addition, by estimating this relationship at the level of the livelihood zone and not the country, the analysis increases the number of years and RR variation in hazards available.

Based on the general but unknown function _f_ , the effect of exposure to the hazard on welfare depends on the specific values of the determinants of welfare summarized by the variables k , and , i.e., <u>hk</u> = k d <u>( k hk hk )</u> ddWW k ~~.~~ The linear specification in regression equation (2) assumes a constant effect of the hazard on RR , XXhkk EEhkk ddRR RR =rr,XX =xx,EE =ee welfare (i.e., ddRR <u>hk</u> = 2 ) that is independent of the level of the hazard and of specific household characteristics k ddWW and environmental factors . It is important to relax this assumption in two ways: first, by allowing the ddRR ββ impact of the hazard to vary by the size of the hazard deviation; and second, by allowing the impact of the hazard hkk hkk XX to vary by characteristics of the household. EE To explore the functional form of the hazard, several different approaches were adopted. Two approaches were visual: a simple plot of welfare against hazard and a binned scatterplot of the residualized welfare against the residualized hazard. Another approach estimated linear, quadratic, and cubic hazard specifications, as well as the best fractional polynomial specification, and compared the fit and plotted residuals.<sup>6</sup> A final approach explored further nonlinearities with step and piecewise linear functional forms. This involved segmenting the continuous hazard distributions into 5 (or 10) bins for use as a set of indicator variables to capture the hazard intensity. Results for linear, quadratic and cubic specifications are shown. Parsimonious specifications that best described the underlying relationship, especially in hazard range where 90 percent of the observed events occurred, were used for the simulations.

> 6 In Stata, the _binscatter2_ command was used to visualize the overall relationship between hazard and welfare. The _fp_ and _fp plot_ commands were used to explore the fit and residuals of different polynomial specifications.

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