that fell into poverty by the third wave.<sup>10</sup> A household is resilient if it was never poor in all three survey waves or escaped from poverty by the third wave.<sup>11</sup> Because we can only observe whether a household is vulnerable or resilient at the third survey wave, we generally use covariates in the third wave in a cross-sectional sense.

# 4.2.2 Independent variables

In addition to the usual socioeconomic and demographic factors that may influence whether a household is vulnerable and its level of resilience, we computed variables to measure rainfall variability and exposure to climate shocks. We computed a _Standard Precipitation Index_ (SPI) that measures rainfall variability following Patel et al. (2007). Using 30-year spatial rainfall data, we computed the SPI as in Equation 1: where _SPIit_ is the SPI for household _i_ in year _t_ , _cagrainit_ is total rainfall for the agricultural season in year _t_ , _bar_cagrain30_ is the average seasonal rainfall over the last 30 years, and _sdagrain30_ is the standard deviation for seasonal rainfall over the last 30 years.

We adapt the approach of Azzarri et al. (2020) to compute a _drought risk variable_ that measures exposure to climate risk as seasonal rainfall that is less than the average seasonal rainfall at the enumeration area level minus two standard deviations of the enumeration area seasonal rainfall. We define _flood risk_ as seasonal rainfall that is more than the average seasonal rainfall at the enumeration area level plus two standard deviations of the enumeration area seasonal rainfall. We measured _rainfall variability_ using the coefficient of variation of the 30-year rainfall and a measure of _rainfall stress_ . Following agronomic recommendations as implemented in Ngoma et al. (2015), we define _rainfall stress_ as the number of consecutive 20-day periods with less than 40mm of rainfall.<sup>12</sup> We also include _30-year average rainfall_ to measure the long-term effects, and the current growing season corresponding to the survey reference period to measure short-term effects. In addition to these climate shocks, we also control for CSA adoption, crop diversity,<sup>13</sup> and access to credit, since these might influence how climate shocks affect vulnerability and

> 10 In terms of poverty transitions, vulnerable households are those who are chronically poor, or those who fell into poverty by the third survey wave regardless of whether they were poor or not in the first and second survey waves. This includes households that were poor in the first and thirds wave but not in the second wave, those poor in the second and third waves but not in the first wave or indeed those that were not poor in the first and second waves but fell into poverty in the third wave.

> 11 This includes households that were never poor across the three survey waves, those poor in the first and second waves but not in the third wave, or poor in the first wave but not in the second and third waves, or ones that were not poor in the first and third waves but were poor in the second wave.

> 12 We constructed this measure based on personal communications with agronomists based at the Zambia Agricultural Research Institute (ZARI).

> 13 Computed as the Simpson index based on area cultivated per crop relative to total area cultivated.

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