_ANDR EE_<sup>_ ́_</sup> _SEPTEMBER 28, 2022_ _16_ Note that the R<sup>2</sup> for South Asia is calculated based on only 22 samples, and hence it should with high probability be lower than in the other regions purely due to the small sample size rather than actual worse prediction performance.<sup>18</sup> The model seems to perform reasonably well still, for instance when the focus is on the MAE of 0 _._ 99 rate points, which is below that of some other regions.

# _B. Prediction Results_

In this section, the final optimized model is used to assess the likely compound effects of the pandemic and Ukraine war and compare the forecast to estimates for the 2008 Global Food Crisis period.<sup>19</sup> The main text presents plots for all countries combined, additional plots for specific regions and incomes are in the appendix (figures A1 and A2).

The results are generated by projecting the covariates forward using the WEO. Outlooks are available for GDP, population sizes, and inflation figures. The WEO tends to have positive bias, documented for instance by Gatti et al. (2022), and may be understood as economic targets that can be met if identified risks are managed. The April WEO is put together during January – March. As such, the data does not yet fully reflect the impacts of recent major events. Risks and associate downside trajectories are however discussed, so counterfactual scenario values of inflation, growth and poverty here are used based on the downside multipliers of the April report to investigate the additional impacts of downside economic risks. Specifically, the downside projections consider a further increase in global food prices of +6% in 2022 and +3% in 2023, and reduced growth of -2% below default projection growth rates in 2022 and 2023, converging to -0.9% by 2027, as a result of increased tightening by central banks to curb inflation.<sup>20</sup>

> 18A proof is beyond the scope of the paper, but note that (squared) correlations cannot be averaged linearly as this results in a biased (underestimate) off total correlation. That is detailed in the literature around the Fischer Z transformation and its adjusted versions. Therefore, by running the logic behind the Fischer Z transformation in reverse, one could show that for a vector pair ( _X_ 1 _, X_ 2) each of length _L_ with a correlation _R_ there exists a partition so that sub-vector pairs with lengths _l_ 1 _, l_ 2 _, ..., lN_ with _l_ 1 _≡ l_ 2 _≡, ..., lN_ and _L_ :=<sup>�</sup> _l_ 1 _, l_ 2 _, ..., lN_ it holds true that the correlations of those sub-vectors satisfy _r_ 1 + _δ_ 1 _→ r_ 2 _− δ_ 2 _→ r_ 3 + _δ_ 1 _→ ... → rN_ + _δ_ 1 _→ R as lN →∞∀ δ_ 1 _< δ_ 2 _and_ 0 _< r_ 1 + _δ_ 1 _<_ 1 _and_ 0 _< r_ 2 _− δ_ 2 _<_ 1 _, ...,_ 0 _< rN_ + _δ_ 1 _<_ 1. A trivial deterministic numerical example is the limit _{r_ 1 = 0 _._ 85 _, δ_ 1 = 0 _._ 05 _}, {r_ 2 = 0 _._ 935 _, δ_ 2 = 0 _._ 035 _}_ and _R_ = 0 _._ 90. In other words, as soon as there are even-length sub-vectors with uneven correlations, which should be expected to occur purely from random draws, then for every sub-vector pair with correlation _δ_ 2 above the total vector correlation, there must be a sub-vector with _δ_ 1 _> δ_ 2 below the total vector correlation. This dis-proportionality increases with a power 2 for squared correlations. Since this argument can be repeated iteratively on the sub-vector pairs, it holds that always a larger divergence _∥rN_ 2 _− R∥ > ∥rN_ 1 _− R∥∀ N_ 2 _< N_ 1 can be found. Note that in all cases, the sub-vector correlations _rN_ 1 _, rN_ 2 _, ..., rNX_ are generated by the same process that has a correlation _R_ . Strictly, this also makes the sample estimates of the R<sup>2</sup> not directly comparable across unequal samples sizes, unless _N →∞_ so that we deal with the deterministic limit _RN → R∞_ .

> 19The 2020 prevalence data were not yet available when this work was done. At the time of reading, the official 2020 figures are likely published and the reader is encouraged to compare, bearing in mind that the model projects unmitigated impacts not reflective of supportive policies. Future updates of the projections will include the new data. Generally, there are three interesting moments in the year to update the results. In April when the WEO is published, after July when the historical annual food insecurity data are published, and in October when the WEO is revised. In January and June, some country projections may also be updated based on the World Bank’s Global Prospects report.

> 20As the WEO identifies only a global average risk, the downside scenario is generated under the sim-