U . In Figure 2, an individual that would consume endowment ω would not be identified as poor even if endowment ω yields a welfare level smaller than U . However, this does not necessarily mean that the set of poor individuals is unrelated to the set of individuals identified as poor. When measuring monetary poverty, the objective for the practitioner is to select an identification method that perfectly identifies the poor, i.e., such that N<sup>ˆ</sup> p(x) = Np(x). When it is the case, the identification method is considered welfare-consistent.

The monetary poverty measurement literature provides guidance for the practitioner. This literature proposes conditions under which the identification method is welfare-consistent. For instance, the method defined in Eq. (1), which uses prices as weights, is welfare-consistent when bundle z maximizes welfare given prevailing prices and U(z) = U (Ravallion, 1998).<sup>14</sup> Prices are directly connected to welfare as they capture marginal rates of substitution (Sugden, 1993). However, the key reason why perfect identification is possible although the identification contour differs from indifference curve U is the presence of markets. Indeed, an individual whose endowment is ω will trade part of her achievement in dimension 2 in order to increase her achievement in dimension 1. Optimal behavior implies that all bundles are on an increasing path (see Figure 2). Under the conditions stated above, the identification contour ranks all bundles on the increasing path in the same way as the indifference curve U.<sup>15</sup> In the absence of markets, identification methods cannot be welfareconsistent under information constraints. This follows from the fact that (i) the shape of the identification contour differs from the shape of indifference curve U and (ii) individuals consume their endowment in the absence of well-functioning markets.<sup>16</sup> In Figure 2, an individual whose endowment is ω would have no choice but to consume ω. This individual would not be identified as poor since her bundle is above the identification contour. This individual would then be mis-identified because her welfare is smaller than U .<sup>17</sup> More generally, an imperfect identification methods can make two different kinds of mis-identification. An exclusion error arises when a poor individual is not identified as poor. An inclusion error arises when a

> 14 Ravallion (1998) describes the following two-step procedure to identify the poor: (1) specify a reference level of utility and (2) derive a money-metric identification cutoff corresponding to this reference level of utility. In practice, the ideal of welfare-consistency remains challenging when prices vary and requires the use of methods for the estimation of the expenditure function (Deaton and Muellbauer, 1980) and the construction of “equivalent-incomes”, i.e., money-metric utilities (Samuelson and Swamy, 1974; Dimri and Maniquet, 2019). The most complete review of this literature can be found in Ravallion (2016).

> 15 In fact, it is not necessary that weights correspond to prices in order for the method to be welfare-consistent. Indeed, any identification method whose identification contour crosses this increasing path in bundle z (and only in that bundle) is welfare-consistent.

> 16 Constraints like ignorance or administrative barriers may hinder the proper functioning of markets and thus force individuals to consume non-optimal endowments.

> 17 In other words, in the absence of a market, even if the marginal rate of substitution at bundle z in Figure 2 could be correctly estimated, a linear identification method based on this marginal rate of substitution would not be welfare-consistent.

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