Table 7 reports summary estimates from estimating equation (1) with (peak) NDVI on winter wheat fields as dependent variable with panel A is identical to table 5 and panel B adds farm size interactions.<sup>22</sup> In the preferred specification (column 6) all coefficients of interest are significant at 1% (panel A) and interactions at 5% (panel B). With a R<sup>2</sup> of 0.36, independent variables explain large part of within VC variation and the significance of coefficients on weather and year effects highlights the importance of a regression approach to obtain unbiases estimates.

To translate regression coefficients into expected outcomes, note that a conservative reading of the literature suggests a 0.01 change in NDVI to translate into a yield change of some 112 kg. The point estimate (-0.002) on area directly damaged by war-related activity together with a mean of about 500 ha of direct damage would imply a yield reduction of 112 kg/ha. With a coefficient of -0.019 on the conflict indicator, exposure to direct manifestations of conflict throughout the period would imply an additional yield reduction of 213 kg/ha per ha of winter cereal in the VC. Noting that conflict-affected VCs cover about 1 mn. ha and have on average been exposed to conflict action for 4 of the 8 two-week periods, this implies a direct conflictinduced loss of up to 120,000 t of winter cereal.

Regarding indirect effects, we find a statistically highly significant year dummy, with a point estimate for the 2022 year dummy of -0.052.<sup>23</sup> Using the above parameters, this would translate into an upper bound for the indirect conflict-induced yield reduction of 582 kg/ha or close to 15%. With the 2022 winter wheat area at 7.274 mn ha, this would imply conflict-induced output losses of 4.2 mn t. Adding the 2.9 mn. t of lost output due to area reduction implies a total war-induced loss of winter cereal of 7.1 mn t or about 20% of the total.

To test if farmers with larger operational holdings that are more likely to be geographically diversified and have links to foreign sources of capital or inputs are better positioned to cope with indirect conflict effects than smaller ones, we interact the 2022 dummy with the share of land in the rayon cultivated by producers with operational size above 2,500 ha or between 500 and 2,500 ha. Results, in panel B, support this notion; although none of the farm size groups can entirely eliminate conflict effects, the smallest farm size group is estimated to incur an output loss of about 0.81 t/ha (coefficient of 0.072) compared to 0.62 t/ha for medium sized and 0.45 t/ha for the largest group.

As an independent robustness check, we computed NDVI for the area covered by each year’s winter crop mask from Landsat and MODIS imagery instead of Sentinel-2. Except for reinforcing the need to account for time variation in exposure to conflict action, results are consistent though regressions have lower

> 22 See appendix tables 2 and 3 for a full set of coefficients where the consistent high significance of climate variables suggests that ignoring these would yield biased estimates. Substantively, results imply that GDD and precipitation increase yield at a decreasing rate while zero rain days in fall are estimated to have a convex and zero rain days in spring a concave relationship with winter wheat NDVI and winter rain is insignificant.

> 23 Coefficients also suggest that, after adjusting for weather effects NDVI in 2020 and 2021 was less (coefficient of -0.023) and more favorable (0.015) than in 2019 as the excluded category.

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