In this subsection, we derive an estimation strategy from the assumptions above for the test of the propositions specifically under Hypothesis 3. Each household may grow a different crop portfolio, selected based on the accumulated weather experiences (and resulting expectations), capital constraints, technologies, and other economic and environmental factors. Although crops may respond only to temperature and precipitation events above or below certain thresholds (Schlenker & Roberts, 2009; Roberts et al. 2012), quantifying such thresholds is not feasible for our sample, as it includes more than 250 crop species (not including livestock). Other studies have shown that temperature and precipitation matter most in the growing and harvesting season, and thus used seasonal temperature and precipitation variables (Mendelsohn et al. 1994; Kurukulasuriya et al. 2006).However, most of our sites are located in areas with more than one cropping season (Zabel et al. 2014). As the start and end of each cropping season depends on geographic location, with our villages located both north and south of the Equator, this approach becomes cumbersome to implement. We therefore use average annual temperatures and annual precipitation as the relevant climate variables. Several studies have shown that the response of crops to changing temperature and precipitation may be approximated by a quadratic function (Lobell et al. 2011; Burke & Emerick 2015). If the yield of each crop to weather can be approximated by a quadratic function, we can conclude that the yield of an aggregated crop portfolio can also be approximated by a quadratic function, for the common support of crops
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