# **Appendix 2: Parametric values for the normative weight of mortality**

In this appendix, we provide one way to derive a parametric value for the normative weight given to mortality. As shown by Baland et al (2022), from a theoretical perspective, the normative parameter θ captures the fraction of utility lost when poor, i.e.,<sup>uu(NNPP) −uu(PP)</sup> (3) θθ= where u denotes the Bernouilli utility associated with being (multidimensionally) poor (P) and not uu(NNPP) where u denotes the Bernouilli utility associated with being (multidimensionally) poor (P) and not (multidimensionally) poor (NP). By assumption, the Bernouilli utility of being dead is . As discussed in Section 3.2, under the two deprivation mappings presented in section 3.1 and in particular uu(DD) = 0 the fact that being below the national poverty line is considered an extreme monetary deprivation, the Bernouilli utility associated with being (multidimensionally) poor (P) can plausibly be equated to the Bernouilli utility associated with being below the national poverty line. As the national poverty line corresponds to the extreme poverty line, we can thus interpret as the Bernouilli utility associated with being below the extreme poverty line, which is $2.15 a day (2017 PPPs). uu(PP) Clearly , the value of θ will depend on the assumptions made on the Bernouilli utility function selected. Indeed, computing a parametric value for θ requires selecting a particular Bernouilli utility function of “income” (=the monetary welfare aggregate), say a constant elasticity of substitution function:

> <sup>mm1−εε−mm01−εε</sup> (4) where denotes income, 0 denotes the subsistence income, for which uu(mm) = 0) = 0 , and is the coefficient 1 −εε of relative risk aversion that captures the curvature of utility function . A parametric value for θ also mm mm uu(mm εε requires defining representative incomes for the (monetary) poor and not (monetary) poor status because ) and c ) . Typically, could be mean or median income among the uu (monetary) poor and ooc oo c could be mean or median income among the not (monetary) poor. cc−ooc oo ooc oo uu(PP) = uu(mm uu(NNPP) = uu(mm mm cc−ooc oo Parametric values obtained for θ are sensitive to the values selected for these parameters, and in mm particular for the curvature parameter and the subsistence income 0 . As an illustration we provide the results for the parametric values of 1/θ obtained for India in 2019 as a function of different parameter values for the CES utility function presented in Eq (4). We assume that εε mm and c respectively capture mean consumption among the (monetary) poor and the not (monetary) poor. We estimate these ooc oo cc−ooc oo mm mm two mean consumption values from the estimates provided by the Poverty and Inequality Platform of the World Bank. We check for robustness for different values of curvature parameter and the subsistence consumption parameter 0 . As suggested by the results shown in Table A3, the theoretical predictions for εε 1/θ based on these assumptions depend on the values selected for these two parameters.<sup>23</sup> mm

> 23 We consider a plausible lower bound for the value for the subsistence consumption y0 to be $0.5 a day. It is biologically impossible to survive with zero consumption. In the micro-data reported in PovCalnet, values for reported consumption below $0.5 a day are very infrequent. The value $0.5 a day is also consistent with the methodology outlined Ravallion (2016) to estimate minimum consumption levels.

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