24 equation (13). Therefore, we simply set _φ_ to 1.05%, the lowest reported food expenditure share in our 2019 household data. Parameter _ν_ is set to 0.12, following Eckert and Peters (2023).

To estimate the Engel elasticity _η_ , we take logs of equation (13), add household subscripts, collect relevant terms into a region fixed effect, and add a household size control variable and an error term, thus obtaining the following equation, which is estimated on 2019 data from Sri Lanka’s Household Income and Expenditure Survey (HIES): where _h_ indexes households, _n_ indexes regions, _ξnh_<sup>_A_is the share of income the household spends on</sup> food, _ynh_ is household income, _hhsizenh_ is household size, _ωn_ is a region fixed effect, and _εnh_ is an error term.<sup>55</sup> To allay concerns about the potential endogeneity of household income (e.g. due to seasonality in prices and employment opportunities), we follow an IV approach. We instrument household income _ynh_ with two arguably exogenous sources of income: income obtained from lottery (and other _ad hoc_ gains) and income obtained from disasters and other relief payments.<sup>56</sup> To our knowledge our paper is the first to estimate the Engel elasticity off exogenous income variation generated by a lottery.<sup>57</sup> The resulting IV estimate for _η_ , shown in Table II, is 0.656.<sup>58</sup> To estimate the elasticity of substitution across crops ( _σA_ ), we take logs of equation (17), add household subscripts, collect relevant terms into crop- and household-specific fixed effects, and add an error term, obtaining the following equation, which is estimated on 2019 HIES data: where _k_ indexes crops, _βnhk_<sup>_A_is the share of crop</sup><sup>_k_in the household’s total food expenditures,</sup><sup>_Pnhk_</sup> is crop price, _ωk_ and _ωh_ are crop and household fixed effects (respectively), and _ε_<sup>_A_</sup> _nhk_<sup>isanerror</sup> term. To address the potential endogeneity of crop prices (e.g. due to unobserved region-specific tastes affecting both prices and expenditure shares), we follow the IV approach in Sotelo (2020), instrumenting price variable ln( _Pnhk_ ) with a dummy variable _Dnk_<sup>_GAEZ_</sup> , which takes value one if the potential yield of crop _k_ in region _n_ is nonzero, according to FAO-GAEZ data (see Appendix A.F). Thus, our identification of the cross-crop elasticity of substitution _σA_ comes from variation in crop prices due to regional shifters of agricultural supply driven by climatic and geological endowments, arguably orthogonal to unobserved factors that affecting consumer behavior. Our

> 55Here a region is one of Sri Lanka’s 25 districts since DS are not recorded in the household data.

> 56Both exogenous sources of income refer to the previous 12 months.

> 57 Boppart (2014) finds Engel elasticities around 0 _._ 20 _−_ 0 _._ 25 for the U.S., Fan et al. (2023) report an IV estimate of 0.395 for India, and Eckert and Peters (2023) calibrate an Engel elasticity of 0 _._ 93 within a spatial model. These estimates are not directly comparable due to differences in context, aggregation, and identification, but our estimates lie within the range estimated in the literature.

> 58See Appendix D.A for details on the 2SLS estimation results of ( _η_ , _σA_ ), including first stage results.