country separately, we derive probabilities for an _increase_ , _decrease_ , or _no change_ in income based on certain household and demographic characteristics – namely, where they reside (urban or rural area), the number of members in the household, the education of the head of household, and the age of the head of household (Table B.1. reports the coefficients from these regressions).

Then, in the 2019 welfare distribution, we randomly assign each household an increase, decrease, or no change in income based on the probabilities derived from the multinomial logit regression on the phone survey. Suppose that the phone survey revealed that a particular household type in a country had a 75% probability of experiencing an income loss, 20% probability of experiencing no change, and 5% probability of experiencing an income increase. Then, all households in the 2019 welfare vector that are of this type are randomly assigned such that 75% have an income loss in 2020, 20% have no change, etc.

In the robustness checks section, we validate this matching procedure in Nigeria, where the phone survey sample was drawn from the 2019 survey. Therefore, we know which households experienced an income gain, loss, or no change. We show that the results are very similar whether we use the observed matching or the random matching.

# _(b) Estimating the size of the income gains and losses_

Whereas we now have an approximation of _which_ households experienced a gain, loss, or had no change in income in the 2019 distributions, we still do not know the size of the income losses and increases. We need the latter to estimate the 2020 welfare vector.

We first split the sample into rural and urban households. We then allocate sectoral growth rates from national accounts – growth in income from agriculture, industry, and services –to rural and urban areas, which requires several strong assumptions. Growth in the agricultural sector is allocated to rural households. Growth from industry is applied to urban households, which is a reasonable assumption at least in most developing countries (which are the countries for which we use the HFPSs). The service sector is the most difficult to allocate. On the one hand, both urban and rural household benefit from government services such as education and health care services. On the other hand, financial services, retail, ITS and more, are all likely to be predominantly present in urban areas. Even government services are likely to be overrepresented and of greater value in urban areas. In our analysis we use growth in service sector income, but the argument likely carries over from levels of service sector income to its growth. One extreme assumption would be to assign all service sector growth to urban areas. Another option would be to assign the growth according to population weights. We opt for a middle way by assuming that the growth (or more likely, declines) in service income in low- and middle-income countries experienced in 2020 is distributed according to the urban and rural _income_ shares. Since urban areas are richer than rural areas, using the income share gives a higher share of service growth to urban areas compared with using population shares. The results are very similar whether income or population shares are used (Table B.4).

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