in Table 6 in Evans et al. (2023). All six coefficients of overlap lie in the range (1.5, 3.6).<sup>44</sup> We illustrate the proposed method’s potential to improve on cross-regions comparisons (Objective 2). We consider the multidimensional poverty indicator constructed by Decerf and Fonton (2023) to compare the 36 Nigerian states in 2019. This indicator considers four dimensions, namely consumption (monetary), health, housing and security.<sup>45</sup> At national level, Decerf and Fonton (2023) estimate H<sup>ˆ</sup> at 52 percent, H<sup>ˆ</sup> M at 40 percent and ˆ HOD at 28 percent. There are large differences in multidimensional poverty rates across states, with H<sup>ˆ</sup> being around 20 percent for some states and around 90 percent for other states. The coefficients of overlap of all 36 states lie in the range (0.8, 2.7), with median value 1.7.

Table 2 compares the cross-states comparisons of various indicators with those obtained with the “true” indicator H<sup>ˆ</sup> . Most indicators considered correspond to H<sup>ˆˆ</sup> (ˆc) when assuming the same (counterfactual) value cˆ for all Nigerian states. The deviations from ˆ H are quantified through a “bias” index, which sums over all 36 states the absolute difference in the state’s rank for the indicator considered and for H<sup>ˆ</sup> .<sup>46</sup> The larger the bias index, the less reliably the indicator considered yields cross-states comparisons in line with those of H<sup>ˆ</sup> .

**Table 2:** Assuming the joint distribution yields better comparisons than wasting the data on one partial distribution.

<!-- Start of picture text --> ˆ ˆ ˆ ˆ ˆˆ ˆˆ ˆˆ<br>HM HOD HM + HOD H(0.8) H(1.7) H(2.7) max( H ˆ M , H ˆ OD)<br><!-- End of picture text -->

||ˆHM|ˆHOD|ˆHM + ˆHOD|ˆˆH(0.8)|ˆˆH(1.7)|ˆˆH(2.7)|max(<sup>ˆ</sup>HM, <sup>ˆ</sup>HOD)|
|---|---|---|---|---|---|---|---|
||||�<br>∼<sup>ˆˆ</sup>H(0)<br>�||||�<br>∼<sup>ˆˆ</sup>H(∞)<br>�|
|Bias|72|194|32|18|16|22|60|

<!-- Start of picture text --> ∼ H ˆˆ (0) ∼ H ˆˆ (∞)<br>� � � �<br><!-- End of picture text --> The key insight from Table 2 is that, in this context, the proposed method yields a ˆ smaller bias than the classical “wasteful” approaches for all possible values of c. Recall the classic approach consists in using an indicator coming from a single survey, which at global level essentially means using either H<sup>ˆ</sup> M or H<sup>ˆ</sup> OD when the joint distribution is missing. Even when assuming the most extreme values for cˆ, either 0 or ∞, indicator ˆˆ ˆ ˆ 47 H yields a smaller bias than both HM and HOD. The method performs much better when assuming a value for cˆ equal to the median value for c among Nigerian states.

> 44Also see Tran et al. (2015) on the overlap between monetary poverty and the global MPI.

> 45The baseline version of this indicator satisfies the necessary assumptions for this exercise. Individuals are considered monetary poor when their consumption is below the extreme IPL, in which case they receive a weight of wM = 1/4. The identification threshold used is also k = 1/4. Note that the nonmonetary dimensions of this indicator do not correspond to those of the global MPI.

> 46For instance, this difference is equal to 2 if a state is ranked 1 by the indicator considered and ranked 3 by H<sup>ˆ</sup> .

> 47 ˆ ˆ ˆ Formally, indicator max( ˆHM , HOD) yields the same ranking as H<sup>ˆ</sup> (∞) when c tends to ∞. Also, indicator H<sup>ˆ</sup> M + H<sup>ˆ</sup> OD yields the same ranking as H<sup>ˆˆ</sup> (0) when H<sup>ˆ</sup> M + H<sup>ˆ</sup> OD ≤ 100.

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