Following Giles and Murtazashvili (2013), who investigate poverty outcomes in linear and nonlinear settings, our dynamic panel data model with lagged variables takes the following form: where _yit_ is food insecurity for household _i_ at time _t_ . _yit−_ 1 is the lagged value of food insecurity and _divit−_ 1 is the lagged value of the diversity index. We lag these values to account for the time it takes for livelihood diversification to actually affect welfare. Diversification does not have an instant impact. Rather, households may use diversification, _ex ante_ , to cope with shocks and thus improve food security in the future. Including lagged food insecurity _yit−_ 1 in our specifications ensures that the variation we observe in our dependent variable is due to livelihood diversification rather than household level characteristics or differences. In this specification, _β_ 2 is our variable of interest, measuring how lagged income diversification impacts a household’s food insecurity, dependent on that household’s food insecurity status in the prior round of data.<sup>8</sup> In estimation, we account for regional and time differences in COVID-19 policies and mitigation strategies. We include time (i.e., round) indicators ( _δt_ ) to capture variation in COVID-19 cases and COVID-19-related policies occurring nation-wide. This also captures other large-scale temporal events such as elections in Malawi and civil unrest in Ethiopia. Regional indicators ( _rj_ ) are interacted with a time trend _tt_ to control for regional differences in COVID-19 mitigation strategies over the evolution of the pandemic as well as other regional shocks such as drought or conflict. Lastly, _ui_ is a household fixed effect to control for time-invariant, unobservable household heterogeneity, and _εit_ is an idiosyncratic error term. Robust standard errors are clustered by household to correct for within-household correlation over time.

The dynamic panel data specification captures causal impacts if the livelihood diversification index is not correlated with the error term. We address issues of endogeneity which might arise from (1) simultaneity or reverse causality between the independent and dependent variables, (2) omitted variable bias, or (3) non-classical measurement error. With regard to the first issue, it is possible that households with better welfare outcomes have more resources, enabling them to diversify their livelihoods. In this case, a simultaneity problem arises as the dependent and independent variables are co-determined. To account for simultaneity, we use lagged independent variables to ensure temporal precedence of livelihood diversification relative to observed household food insecurity, thus isolating the relationship between past diversification and subsequent outcomes.<sup>9</sup> Our panel data, with a pre-COVID baseline helps us avoid omitted variable bias. By including household

> 8We pre-specified using past income level and focused on diversification as the coping strategy, but our results are robust to alternative proxies, such changes in income level, and use of other coping strategies and alternative estimators. See Online Appendix B for additional details and results.

> 9The use of lagged variables has the potential to bias coefficients downward, which Arellano and Bond (1991) and others address through instrumental variables. In Online Appendix B we implement the Arellano-Blover/BlundellBond (Arellano and Bover, 1995; Blundell and Bond, 1998) GMM estimator and show that the size of the downward bias is small and does not affect the interpretation of our results.

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