that there is a single region. Consider two periods of time t ∈ {0,1}, where 0 is the initial period and 1 is the end period. Let yt denote the distribution of _real_ total expenditures in time t. Taking period 0 as reference, the distribution of real total expenditures y1 is obtained by deflating the total expenditures observed in period 1 for the inflation between period 0 and period 1. Let zt denote the distribution of _real_ poverty lines in time t, where again the effect of inflation has been removed. We denote the poverty rate in period t (computed using the official methodology based on total expenditures) by P(zt, yt).

As the poverty lines have a hybrid definition, we typically have z1 ≠z0. The poverty trend can be decomposed either as P(z1, y1) - P(z0, y0) = P(z1, y1) - P(z0, y1) + P(z0, y1) - P(z0, y0) or alternatively as P(z1, y1) - P(z0, y0) = P(z1, y1) - P(z1, y0) + P(z1, y0) - P(z0, y0) where the difference between the two decompositions lies in the order in which the arguments of P are modified. Indeed, the former decomposition considers the change from period 0 to period 1 by changing yt first and zt second, while the opposite order is considered in the latter decomposition. The SOS decomposition of the change in poverty rates, which we denote by ∆P(z∆, y∆), considers the average effect of each change over all possible orders, which is where the first term captures the effect of the change in real total expenditures, which is and the second term captures the effect of change in real poverty lines, which is To dissipate any potential confusion, we now provide some additional details on how to compute P(z1, y0). To check whether household h is poor under P(z1, y0) we compare its 2015 total expenditure to the (deflated) poverty line that household h would face in 2017/18, where this poverty line is obtained by considering the 2017/18 price of a calorie and the food share that would have been imputed to household h by the regression (run on 2017/18 data).

# **Decomposition results**

The results of the decomposition exercise for all regions are presented in Table 6. At the national level, the poverty rate increases from 24.8 to 31 percent, which is an increase by 6.2 percentage points. This increase can be decomposed into a 9.9 percentage point increase due to the reduction in real total expenditures and a 3.7 percentage point reduction due to the decrease in real poverty lines. This decomposition reveals that the increase in poverty over the period would have been even higher if measured using an absolute measure of poverty, which keeps the real value of the poverty lines fixed over time. The hybrid nature of the official poverty lines yields a smaller increase in poverty rates, because the real values of poverty lines are smaller in 2017/18 than in 2015. As shown in Table 7, the real price of a calorie is, in all regions, smaller in 2017/18 than in 2015. One likely reason for these lower calorie prices has to do with the reduction in real total expenditures. As shown in Table 6, total expenditures per capita (expressed in 2015 prices) are about 8,600 Egyptian pounds in 2015 but decrease to below 7,400 Egyptian pounds in 2017/18. Hence, the reduction in households’ consumption possibilities provided an incentive to switch their food consumption towards cheaper calories.

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