process, with as a vector of constants, as a matrix of autoregressive parameters, as a matrix of coefficients for the exogenous variables, and as a vector of innovations. cc<sup>YY</sup> KK× 1 AA<sup>YY</sup> KK× KK YY tt BB<sup>YY</sup> KK× MM εε • is a vector of observations of binary outcomes, generated by applying the inverse logit transformation to a linear combination of the lagged endogenous variables , the tt exogenous variables FF DD× 1 , and innovations . Here, is a vector of constants, is a tt−1 matrix of coefficients for the lagged endogenous variables, and FF FF is a matrix of YY FF tt tt coefficients for the exogenous variables. XX εε cc DD× 1 AA DD× KK BB<sup>FF</sup> DD× MM The regression system can be estimated equation by equation and interpreted as interconnected panel time-series models, but the parameters should always be considered within the context of a larger dynamic system. Climatic conditions , driven by external influences , affect the endogenous variables (representing the agricultural economy) and reverberate through the XX tt tt XX εε system via autoregressive dynamics. Food security outcomes are determined by both the lagged tt YY state of the agricultural economy and climatic shocks, meaning food security is impacted by both tt FF direct and indirect climatic effects. As a result, climatic shocks can have lingering impacts on food security outcomes over multiple periods, capturing complex real-world phenomena. For example, consider a drought event (entering the system as a shock in ). In the first period, the drought reduces crop yields (entering through ) , leading to a decline in agricultural wages, XX tt εε represented by , due to decreased demand for labor. In the following period, this wage reduction tt XX lowers household purchasing power, diminishing food demand and affecting prices. Over time, this tt YY initial drought shock propagates through the economy, influencing wages and prices (represented by for h> 1), which can have long-term effects on food security outcomes. tt+h Finding insignificant coefficients for climatic impacts in the food security outcome equations, while YY observing significant coefficients in the wage or price equations, does therefore not imply that food security is unaffected by climatic shocks. Rather, it suggests that these shocks indirectly affect food security through their impact on the agricultural economy. Similarly, variables not explicitly included in the food security outcome equation can still influence the system. For instance, may capture the price impacts of conflict shocks, which can subsequently propagate through . YY tt εε tt FF

# 4.2 Regression Specification

For the food security outcomes, we employed two logit specifications to capture different levels of food insecurity. The first specification uses a binary indicator as the dependent variable, set to 1 when the IPC phase is 2 or higher (food stress). The second specification denotes 1 when the IPC phase is 3 or higher (food crisis). For food prices and agricultural wages, the dependent variables are the percentage changes in local domestic food prices and local agricultural wages, respectively.

The primary independent variables are drought and flood anomalies derived from rainfall data and vegetation health, measured using NDVI anomalies. We also include a range of control variables such as fuel prices, global food prices, demographic factors, seasonal dummies, and time trends. Compared to the conceptual model, this expands (climatic shocks) by introducing (additional economic variables like exchange rates and global food prices that enter contemporaneously and with lags) , tt tt (additional economic variables that enter with lags) and XX (time-invariant controls), to allow for WW tt additional covariates to enter the model differently. ZZ tt GG 13