expenditure on water is greater than zero, and (iii) there is a specific provider for which we have tariff structure information. For households that pay a fixed rate per cubic meter, the monthly quantity of water consumed equals the total expenditure on water divided by the rate. For households facing unit prices that vary by quantity consumed (such as increasing block or volume-differentiated tariffs), each block within the tariff structure is assigned a maximum expenditure level and associated quantity of water consumed. Then quantities are assigned to the household sample by matching self-reported household water expenditure with the corresponding level of the tariff structure. For the remainder of households, for which (i) the bill is a flat rate unrelated to water quantities consumed or (ii) self-reported expenditure on water equals zero,<sup>11</sup> we assume consumption quantities at the median of those households in the same country for which we could assign quantities. For those households that report a positive expenditure on piped water but are located in areas where they cannot be mapped to a specific provider, we use a median unit price derived from households with data, and recover the quantity of water consumed.

We then define _QP|T_ as the average quantity consumed by the poor, conditional on receiving a subsidy and being connected, and _QH|T_ as the analogous measure for the population as a whole. This variable is related to the subsidy design because the quantity of water consumed by subsidy recipients determines the total value of the subsidy each recipient will receive.

# **Average unit price of water paid among those connected (UP)**

We define this variable as the ratio of (i) water expenditure (as self-reported in household surveys) to (ii) assigned quantities, as described above. For a household with a water expenditure of zero, the unit price would also be zero.

# **Subsidy beneficiaries among those connected (B), and targeting measures (T)**

We define variable _B_ as equal to 1 if a household is connected and pays a unit price ( _UP_ ) for water that is lower than the cost-reflective tariff ( _CRT_ , as defined in above).

We then define _BH_ as the total number of households that receive water consumption subsidies, _BP_ as the total number of poor households that receive water consumption subsidies, and _BNP_ as the total number of non-poor households that receive water consumption subsidies. We then define as the share of households that receive a subsidy (or are targeted) conditional on _C_ (that is, being connected to the network within a service area). Analogously, HH|CC TT represents the share of poor households that receive a subsidy conditional on _C_ . Therefore, the beneficiary incidence of the consumption subsidy is determined by _SA, C,_ and _T._ The share PP|CC TT of all households receiving the subsidy is equal to S HH<sup>xCC</sup> HH|S<sup>xTT</sup> HH|CC<sup>.</sup>

> 11 In many countries, and particularly Ethiopia and Nigeria, many households appear to be connected to the network and use piped water as their main source of drinking water but report paying zero for their water. Anecdotal evidence indicates that many households are connected illegally to the network or that utilities do not invoice and collect payments as they should.

9