In this context, the missing joint distribution, i.e., the value for c, does not contain much of the information that is relevant to perform cross-regions well-being comparisons. Most of the relevant information is available in the two separate surveys. By ignoring one of the separate survey, the classical approach wastes relevant information and yields suboptimal well-being comparisons. Shockingly, “making up” (overlap) data improves well-being comparisons. The reason is that the “made up” data allows using more “true” data, i.e., from both partial distributions.

More generally, these results illustrate a sometimes overlooked point: when dealing with data constraint, the objective is not to approximate the ideal indicator we could construct in the absence of constraint. Rather, the objective is to construct an indicator that makes better well-being comparisons than the comparisons made by the alternative indicators that are currently used. In other words, what matters the most is not whether the value of H<sup>ˆˆ</sup> is “close enough” to the value of H<sup>ˆ</sup> . The relevant question to ask is whether the well-being comparisons by H<sup>ˆˆ</sup> are better than the well-being comparisons by H<sup>ˆ</sup> M (and those by H<sup>ˆ</sup> OD).

The results presented in Table 2 are valid only for one context using one particular definition for H<sup>ˆ</sup> and one way of quantifying the deviations from H<sup>ˆ</sup> .<sup>48</sup> They call for more research to check that the proposed method can reliably improve on the classical “wasteful” approach. In particular, it would be interesting to investigate the performance of the proposed method for a multidimensional poverty measure constructed from the data available in a typical LSMS survey and a typical DHS or MICS survey. This performance can be assessed in contexts where the full multidimensional poverty measure can be constructed, e.g., those considered in Table 6 in Evans et al. (2023). Similarly, it could be interesting to study simple ways of extending the proposed method to multidimensional poverty measures for which the monetary dimension is not captured by a dichotomous status (i.e., monetary poor or not monetary poor) but by a trichotomous status (i.e., extremely, moderately or not monetary deprived) or by a continuous variable.

# **3.4.2 Imputing incomes into the non-monetary survey**

The method mentioned here is a more elaborate variant of the method proposed in the Section 3.4.1. It also makes assumptions on the missing joint distribution between monetary and non-monetary outcomes. The idea is to impute consumption or income into the non-monetary survey, say DHS or MICS.<sup>49</sup> One way of doing it is to use survey-to-survey imputation techniques, as pioneered by Elbers et al. (2003).<sup>50</sup> These techniques build an imputation model based on the common variables in the two surveys, e.g., demographic variables and maybe some common outcomes. This model is trained in a similar context

> 48See Section 3.2 for one alternative quantification of deviations.

> 49Another possibility is to impute non-monetary outcomes in an LSMS survey.

> 50See Dang and Lanjouw (2023) for a recent review.

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