Historically, poverty measurement relied primarily on the average income of the poor, assuming a regular distribution of income within society. Traditional measures were limited in their ability to represent the poorest segments or to reveal disparities within the population of the poor. Over the past decades, the field of poverty measurement has witnessed a qualitative evolution, moving from unidimensional income-based metrics to more comprehensive models that integrate statistical rigor with ethical and philosophical depth. In response to these limitations, this study developed new, fairer, and more realistic indicators to assess suffering of the poor by combining quantitative and social dimensions, utilizing advanced analytical tools that incorporate income, education, and working hours.
In Chapter Three, a novel indicator, Weighted Reversed Poverty Gap (WRPG), was derived. This index extends conventional poverty gap concept by introducing flexible social weights that differentiate poor individuals according to severity of their deprivation. WRPG embodies the ethical principle of “priority to the poorest”, assigning higher weights to individuals at the economic, analysis confirmed that new index satisfies the fundamental axiomatic properties of poverty measures: Focus, Monotonicity, Transfer Sensitivity, Scale Invariance, and Decomposability.
In Chapter Four, Multidimensional Weighted Reversed Poverty Gap was introduced as a natural extension of WRPG. It integrates multiple dimensions, namely income, working hours, and education level, through flexible social weights that capture disparities within the poor themselves. This index provides an advanced analytical framework for decomposing poverty by regions, social groups, or dimensions, making it a precise tool for policy targeting and decision-making toward most vulnerable populations. It also practically reflects Amartya Sen’s capability approach, redefining poverty as a deprivation of essential capabilities and human choices, rather than merely a lack of income. MWRPG strikes a balance between rigorous quantitative analysis and ethical social vision. the study presents a pioneering model for next generation of poverty indices, combining theoretical consistency, ethical depth, and practical applicability, thereby representing a significant scientific contribution to 21st-century poverty measurement tools. I did not just extend a poverty index, I redesigned the measurement framework to make it ethically aware, sensitive distribution, and policy relevant at the same time.
In applications and simulation results reflecting an increasing ethical sensitivity to poverty and confirming index’s alignment with distributive justice principles of Amartya Sen. Principal scientific contribution of this study is the reconceptualization of poverty measurement from a neutral descriptive framework to a rigorously normative and interactive one. The proposed index transcends mere quantification of poverty levels, incorporating an explicit reflection of social prioritization among the poor.
Consequently, the index functions not only as a quantitative assessment tool but also as an analytical instrument capable of informing policy decisions grounded in distributive justice, by precisely identifying those individuals who are most disadvantaged. In this regard, the study constitutes a substantive advancement in the field, shifting perspective on poverty from a purely statistical construct to an ethically informed phenomenon with deep distributive implications. This dissertation moves poverty measurement from counting the poor to understanding the structure of deprivation among them.
Chapter One: Introduction Pages
1.1 Introduction 1
1.2 Problem Statement 2
1.2.1 Absence of Explicit Social Weighting Mechanisms 3
1.2.2 Limited Sensitivity to Inequality Among the Poor 3
1.2.3 Arbitrariness of Dimensional Weights in Multidimensional Indices 4
1.3 Critical Review of Contemporary Poverty Measurement (2000–2025) 4
1.3.1 Unidimensional versus Multidimensional Frameworks 4
1.3.2 Normative versus Empirical Approaches 5
1.3.3 Distributional Sensitivity and Decomposability 5
1.4 Persistent Methodological Challenges 5
1.5 Research Objectives 6
1.6 Structure of the Dissertation 7
Chapter Two: Theoretical Foundations And Literature Review 9
2.1 Introduction 10
2.2 Conceptual Framework 11
2.2.1 Definitions of Poverty 11
2.2.2 Absolute vs. Relative Poverty 14
2.2.3 Unidimensional vs. Multidimensional Approaches 16
2.3 Axiomatic Properties of Poverty Measures 17
2.3.1 Focus Axiom 17
2.3.2 Monotonicity Axiom 18
2.3.3 Transfer Principle 18
2.3.4 Decomposability 18
2.3.5 Scale Invariance `18
2.3.6 Population Principle 18
2.4 Traditional Poverty Measures 19
2.4.1 Headcount Ratio (HCR) 19
2.4.2 Poverty Gap Index (PG) 20
2.4.3 Sen Index (1976) 21
2.4.4 Foster, Greer and Thorbecke (FGT) Class 22
2.4.5 Watts Index (1968) 23
2.5 Multidimensional Poverty Measurement Frameworks 24
2.5.1 Theoretical Foundations (Sen's Capability Approach) 24
2.5.2 Alkire-Foster Methodology (2011) 25
2.5.3 Multidimensional Poverty Index (MPI) 26
2.5.4 Critiques of Multidimensional Approaches 27
2.6 Evolution of Poverty Measurement Literature (2000-2025) 27
2.6.1 Unidimensional Studies 27
2.6.2 Multidimensional Studies 30
2.6.3 Comparative Studies 36
2.7 Studies on Social Weighting in Poverty Measurement 49
2.7.1 Theoretical Contributions 49
2.7.2 Empirical Applications 49
2.7.3 Methodological Challenges 50
2.8 Inequality-Sensitive Poverty Measures 50
2.8.1 Theoretical Developments 50
2.8.2 Empirical Evidence 51
2.8.3 Ethics and Empirical Precision 51
2.9 Country-Specific Studies: Focus on Egypt and MENA 52
2.9.1 Egyptian Poverty Studies 53
2.9.2 Regional Comparisons 54
2.9.3 Methodological Adaptations 56
2.10 Critical Analysis and Research Gaps 57
2.10.1 Theoretical Gaps 57
2.10.2 Methodological Gaps 59
2.10.3 Empirical Gaps 59
2.10.4 Policy-Oriented Gaps 60
2.11 Positioning the Current Study 60
2.11.1 How WRPG Addresses Identified Gaps 60
2.11.2 How MWRPG Extends Existing Frameworks 61
2.11.3 Expected Contributions 62
Chapter Three: A New Weighted Class of Poverty Measures: WRPG Framework 63
3.1 Introduction to Weighted Reversed Poverty Gap (WRPG) 64
3.1.1 Background for Developing Weighted Reversed Poverty Gap (WRPG) 64
3.1.2 Conceptual Framework of Weighted Reversed Poverty Gap (WRPG) 65
3.1.3 Basic Definitions of Weighted Reversed Poverty Gap (WRPG) 66
3.2 Formulation of Weighted Reversed Poverty Gap (WRPG) 66
3.2.1 General Formula of (WRPG) 66
3.2.2 Role of Weighting Function 70
3.2.3 Reversed Gap Structure and its Intuition 72
3.2.4 Relationship with Income and Poverty Line 74
3.2.5 Meaning and Importance Ratio approach (R-approach) 74
3.3 Selecting Social Weight Function v_i for Sensitivity to Extreme Poverty, Formulation and Methods 75
3.3.1 Social Weight Function and its Properties 76
3.4 Axiomatic Properties of Weighted Reversed Poverty Gap (WRPG) 82
3.4.1 Focus Axiom (Exclusivity to the Poor Population) 82
3.4.2 Monotonicity (Sensitivity to Income Changes Below Poverty Line) 85
3.4.3 Transfer Sensitivity (Pigou–Dalton Principle) under R-approach of WRPG Index 92
3.4.4 Scale Invariance (Independence of Measurement Units) of WRPG Index 104
3.4.5 Population Invariance (Robustness to Population Size) of WRPG 108
3.4.6 Sensitivity to Depth and Severity of Poverty 110
3.4.7 Subgroup Decomposability (Regional and Group Analysis) of WRPG 112
3.5 Development of New Weighted Reverse Poverty Gap and Advancement of Poverty Measurement 117
Chapter Four: New Multidimensional Socially Weighted Reversed Poverty Gap Index 119
4.1 Introduction to Multidimensional Weighted Reversed Poverty Gap Index (MWRPG) 120
4.2 From WRPG to MWRPG, Measurement of Poverty 121
4.3 Advantages of Multidimensional Weighted Reversed Poverty Gap 122
4.4 Multidimensional Structure of Multidimensional Weighted Reversed Poverty Gap 122
4.5 The Social Weighting Function v_i of Multidimensional Weighted Reversed Poverty Gap 123
4.6 Axioms Properties of Multidimensional Weighted Reversed Poverty Gap (MWRPG) 125
4.6.1 Focus Property of Multidimensional Weighted Reversed Poverty Gap 125
4.6.2 Monotonicity Property of Multidimensional Weighted Reversed Poverty Gap 128
4.6.3 Transfer Sensitivity of Multidimensional Weighted Reversed Poverty Gap Index 133
4.6.4 Scale Invariance Property of Multidimensional Weighted Reversed Poverty Gap 138
4.6.5 Population Invariance Property of Multidimensional Weighted Reversed Poverty Gap Index 143
4.6.6 Sensitivity to Depth and Severity of Poverty in Multidimensional Weighted Reversed Poverty Gap Index 145
4.6.6.1 Sensitivity to Depth of Poverty in Multidimensional Weighted Reversed Poverty Gap Index 146
4.6.6.2 Sensitivity to Severity of Poverty in Multidimensional Weighted Reversed Poverty Gap Index 146
4.6.7 Decomposability Property of Multidimensional Weighted Reversed Poverty Gap Index 150
Chapter Five: Application and Simulation Study of Weighted Reversed Poverty Gap 154
5.1 Application of Weighted Reversed Poverty Gap (WRPG) using CAPMAS Data 155
5.1.1 Introduction to Application of Weighted Reversed Poverty Gap 155
5.1.2 Estimation of Weighted Reversed Poverty Gap Index 156
5.2 Simulation of Weighted Reversed Poverty Gap (WRPG) using Simulated Data and β-Sensitivity Analysis 161
5.2.1 Introduction to Simulation of Weighted Reversed Poverty Gap 162
5.2.2 Estimation of Weighted Reversed Poverty Gap 162
Bibliography 168
List of Tables
Table
Definition Pages
Table (2.1) Special cases of Foster, Greer and Thorbecke 22
Table (2.2) Varying by income group and cost of living World Bank (2018) 26
Table (2.3) Transition from Sen → Thon → FGT encapsulates a broader evolution in poverty measurement theory one grounded in both ethics and empirical precision 52
Table (3.1) Focus property’s WRPG Considers Only the Poor 83
Table (3.2) Monotonicity property can be used to analyse the impact of policies 90
Table (3.3) Case 1 Monotonicity of Increasing the income of person 1 by 10 (still poor) 91
Table (3.4) Case 2 Monotonicity of Decreasing the income of person 2 by 5 (still poor) 91
Table (3.5) Special case of Transfer Principle 100
Table (3.6) Transfer Principle of WRPG 100
Table (3.7) Transfer Principle of WRPG with Different Social Weights 102
Table (3.8) Scale Invariance (Independence of Measurement Units) of WRPG Index 106
Table (3.9) Scale Invariance of WRPG Index 107
Table (3.10) Subgroup Decomposability of WRPG 115
Table (4.1) Focus Property of Multidimensional Weighted Reversed Poverty Gap (MWRPG) 127
Table (4.2) Monotonicity Property of Multidimensional Weighted Reversed Poverty Gap (MWRPG) 132
Table (4.3) Scale Invariance Property of Multidimensional Weighted Reversed Poverty Gap (MWRPG) 141
Table (4.4) Population Invariance Property of MWRPG 145
Table
(5.1) Descriptive Statistics of Variables 155
Table (5.2) Weighted Poverty Measures 155
Table (5.3) Sensitivity of WRPG to β 157
Table (5.4) Comparison of WRPG with Traditional Poverty Index 157
Table (5.5) Results of Descriptive Statistics of Simulated Variables 162
Table (5.6) WRPG Sensitivity to the Social Parameter β 162
Table (5.7) Comparison between Traditional Indices and WRPG 164
List of Figures
Figure Definition Page
Figure (2.1) Poverty Gap (Depth) Vs. Poverty Severity 24
Figure (3.1) Poverty Sensitivity Curve (Social Weight Vs Income Ratio) 79
Figure (3.2) Comparison of Poverty Gaps with Weights 81
Figure
(3.3) Focus property’s WRPG Considers Only the Poor 84
Figure (3.4) Monotonicity Property in WRPG 92
Figure (3.5) Transfer Principle of WRPG 103
Figure (3.6) Scale Invariance of WRPG Contributions 108
Figure (3.7) Subgroup Decomposability of WRPG 116
Figure (4.1) Monotonicity Property of MWRPG 133
Figure (4.2) Transfer Sensitivity of MWRPG Index 138
Figure (4.3) Scale Invariance Property of MWRPG Index 142
Figure (4.4) Sensitivity to Depth and Severity of MWRPG 149
Figure (5.1) Distribution of log (Income per Capita) 157
Figure (5.2) Sensitivity of WRPG to β 157
Figure (5.3) Comparison of WRPG with Traditional Poverty Indices 159
Figure (5.4) Distribution of log(Per Capita Income) 160
Figure (5.5) Distribution of Individual Poverty Gap 162
Figure (5.6) Sensitivity of WRPG to β 164
Figure (5.7) Comparison of WRPG with Traditional Poverty Indices 165
List of Symbols
Symbol Definition
I(y_i |
