Table 1 Comparison of different energy poverty indices.

From: A chronic multidimensional measure of energy poverty and its impacts on physical and mental health

Index

Formula

Rationale

Source

EPI

\(EPI=\mathop{\sum }\limits_{i=1}^{n}{w}_{i}{D}_{i}\)

Aggregating weighted deprivations across multiple dimensions.

Pachauri et al. (2004)

LIHC

\(LIHC=I[(Y < {Y}_{m})\wedge (C\, >\, {C}_{m})]\)

Comparing income levels and energy expenditures.

Hills (2012)

MEPI

\(MEPI=\frac{1}{N}\mathop{\sum }\limits_{j=1}^{N}\left(\mathop{\sum }\limits_{i=1}^{n}{w}_{ij}I\,\left({D}_{ij}\, >\, {\theta }_{i}\right)\right)\)

Using household weights and thresholds.

Nussbaumer et al. (2012)

FGT

\({P}_{\alpha }=\frac{1}{N}{\mathop{\sum }\limits_{i=1}^{N}\left[\frac{({z}_{i}-{y}_{i})\times I(\,{z}_{i}\, >\, {y}_{i})}{{z}_{i}}\right]}^{\alpha }\)

Comparing a household’s energy expenditure with the household-specific energy poverty line.

Ye and Koch (2021)

  1. wi represents the weight of the i-th dimension, Di represents the level of energy poverty in the i-th dimension, and n is the total number of dimensions in energy poverty; Y represents household income, Ym is the median income, C denotes household energy expenditure, and Cm is the median energy expenditure; N denotes the total number of households, wij represents the deprivation weight of household j, Dij is the deprivation of household j in a specific dimension, θi is the threshold of deprivation; zi is the household-specific energy poverty line, yi is household i’s actual energy expenditure, I(·) is an indicator function