response to the nature of the shock; but, also, it shows that providing all/most extreme poor households with a lower transfer (i.e. columns 5 and 6) tends to deliver higher impacts than providing a more generous transfer to only a subset of them (columns 1a and 1b), even when poor households cannot be perfectly identified (i.e. need to rely on a PMT score).<sup>23</sup> _Table 9 : North Macedonia – Proportional loss shock_ <!-- Start of picture text --> Proportional Shock<br>Targeting → Household<br>Eligibility ↓<br>PMT Ex- PMT Post<br>Means<br>Means Perfect Imperfect ante or Shock or<br>Orginal Testing PMT Ex- PMT Post<br>Expansion Testing (Ex- Universal Loss Loss Perfect Perfect<br>Beneficiaries (Post Shock ante Shock<br>Ante Poor) Indicator Indicator Loss Loss<br>Poor)<br>Budget ↓ Indicator Indicator<br>(1a) (1b) (2) (3) (4) (5) (6) (7) (8) (9) (10)<br>Poverty Rate Pre-shock: 0.169; Post-shock: 0.219<br>(1) 0.09% GDP -0.021 -0.023 -0.024 -0.035 -0.027 -0.027 -0.027 -0.025 -0.025 -0.022 -0.024<br>(2) 1.0% GDP -0.048 -0.088 -0.097 -0.110 -0.037 -0.061 -0.059 -0.042 -0.045 -0.040 -0.045<br>Poverty Gap Sqr. Pre-shock: 3.523; Post-shock: 4.205<br>(1) 0.09% GDP -0.851 -0.816 -0.997 -0.906 -0.604 -0.851 -0.832 -0.594 -0.601 -0.670 -0.629<br>(2) 1.0% GDP -1.410 -1.760 -3.439 -3.164 -1.219 -2.665 -2.492 -1.193 -1.166 -1.306 -1.318<br>Gini Pre-shock: 0.330; Post-shock: 0.331<br>(1) 0.09% GDP -0.009 -0.010 -0.010 -0.011 -0.009 -0.010 -0.010 -0.009 -0.008 -0.008 -0.010<br>(2) 1.0% GDP -0.019 -0.031 -0.042 -0.042 -0.015 -0.031 -0.029 -0.016 -0.016 -0.017 -0.017<br>Coverage<br>(1) Avera ge Transfer $ 1,413.1 $ 1,634.5 $ 345.1 $ 267.2 $ 44.3 $ 346.3 $ 267.3 $ 52.6 $ 71.1 $ 50.0 $ 49.4<br>(2) Avera ge Transfer $ 15,041.3 $ 8,057.8 $ 3,673.7 $ 2,844.0 $ 471.3 $ 3,685.7 $ 2,845.3 $ 560.2 $ 759.9 $ 532.5 $ 525.6<br> (1) 15,380<br>Beneficiaries 17,790 72,839 94,088 567,743 72,601 94,045 477,689 353,594 502,500 509,066<br>(2) 33,208<br>Ex-ante poor 0.15 0.35 1.00 1.00 1.00 0.59 0.66 0.79 0.61 0.98 0.98<br>Ex-ante non-poor 0.01 0.02 0.00 0.06 1.00 0.08 0.11 0.93 0.67 0.94 0.94<br>Ex-ante Vulnerable 0.02 0.04 0.00 0.16 1.00 0.15 0.20 0.94 0.66 0.96 0.96<br>Post-shock poor 0.12 0.31 0.77 1.00 1.00 0.50 0.57 0.84 0.62 0.98 0.99<br>Note: impacts are color-coded from dark red (highest impacts) to dark blue (lowest impact). Not all households declare<br>labor income.<br><!-- End of picture text -->

# Random loss shock

To conclude, we analyze best responses when the shock affects some workers randomly, albeit in a profound and radical manner: whenever a worker is hit by a shock, her labor income drops to zero. Note that such a shock has the potential to profoundly change rankings of the income distribution, with some households – especially the ones with one main breadwinner – facing a significantly higher risk of falling into extreme poverty. Note also that not all households who are hit by a shock will face zero labor income: the shock is given to individuals, hence if there is more than one worker in a household the likelihood of labor income falling to zero is lower.

> 23 In practical terms there may be however limits on how much one can “spread thinly”. The poverty gap squared measure is concave, hence the marginal gains in welfare are inversely proportional to the transfer amount. In reality, however, there may be a transfer threshold below which the marginal welfare impacts are minimal. If this is the case, limiting the number of beneficiaries may deliver greater welfare gains.

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