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Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia

Chronic and Transient Poverty in Rural Ethiopia: A New Decomposition

Natalie Na¨ ıri Quinn

University of Oxford

21 September 2013

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia

Outline

Preliminaries Motivation and Literature Objective and Overview Characterisation of General Form Analytical Framework Ethical Framework General Form Social Aggregation Chronic Poverty Ordering of Trajectories Decomposition Properties For Chronic-Poverty Trajectory Ordering Proposed Trajectory-Ordering Function Application: Poverty in Rural Ethiopia Data and Results Concluding Remarks

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Motivation and Literature Objective and Overview

Outline

Preliminaries Motivation and Literature Objective and Overview Characterisation of General Form Analytical Framework Ethical Framework General Form Social Aggregation Chronic Poverty Ordering of Trajectories Decomposition Properties For Chronic-Poverty Trajectory Ordering Proposed Trajectory-Ordering Function Application: Poverty in Rural Ethiopia Data and Results Concluding Remarks

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Motivation and Literature Objective and Overview

Motivation

Why measure poverty?

▶ Identify targets for poverty alleviation policies ▶ Evaluate poverty alleviation policies

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Motivation and Literature Objective and Overview

Motivation

Why measure poverty?

▶ Identify targets for poverty alleviation policies ▶ Evaluate poverty alleviation policies

Why distinguish between chronic and transient?

▶ Transient: intervene with insurance against shocks ▶ Chronic: insurance not sufficient; constraints to accumulation

• f human or physical capital.

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Motivation and Literature Objective and Overview

Motivation

Why measure poverty?

▶ Identify targets for poverty alleviation policies ▶ Evaluate poverty alleviation policies

Why distinguish between chronic and transient?

▶ Transient: intervene with insurance against shocks ▶ Chronic: insurance not sufficient; constraints to accumulation

• f human or physical capital.

Always helps to understand the nature of the problem.

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Motivation and Literature Objective and Overview

Literature

‘Spells’ Approach:

▶ ‘Still poor after x years’; compare headcount. ▶ Chronic Poverty Reports (CPRC, 2005 and 2009)

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Motivation and Literature Objective and Overview

Literature

‘Spells’ Approach:

▶ ‘Still poor after x years’; compare headcount. ▶ Chronic Poverty Reports (CPRC, 2005 and 2009)

‘Components’ Approach:

▶ Poverty of permanent component of (or average) income;

transient fluctuations.

▶ Rodgers and Rodgers (1993; US); Jalan and Ravallion (2000).

Both based on poverty-gap-squared (Foster, Greer and Thorbecke, 1984).

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Motivation and Literature Objective and Overview

Literature

More recent proposals (all indices aggregating over individuals and time):

▶ Calvo and Dercon (2009), Foster (2009), Gradin, Del Rio and

Canto (2011), Hoy and Zheng (2011), Bossert, Chakravarty and D’Ambrosio (2012), Foster and Santos (2013).

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Motivation and Literature Objective and Overview

Literature

More recent proposals (all indices aggregating over individuals and time):

▶ Calvo and Dercon (2009), Foster (2009), Gradin, Del Rio and

Canto (2011), Hoy and Zheng (2011), Bossert, Chakravarty and D’Ambrosio (2012), Foster and Santos (2013). None combine all of the properties that we might want a chronic poverty measure to embody:

▶ Either: Not sensitive to chronicity/persistence (so more

appropriate to measure ‘total’ intertemporal poverty)

▶ Or: Discontinuities lead to counter-intuitive ordering of

trajectories

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Motivation and Literature Objective and Overview

Objective and Overview

Objective:

▶ Construct a chronic poverty measure that combines attractive

properties (in particular sensitivity to chronicity, and continuity)

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Motivation and Literature Objective and Overview

Objective and Overview

Objective:

▶ Construct a chronic poverty measure that combines attractive

properties (in particular sensitivity to chronicity, and continuity) Overview:

▶ Characterise a general class

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Motivation and Literature Objective and Overview

Objective and Overview

Objective:

▶ Construct a chronic poverty measure that combines attractive

properties (in particular sensitivity to chronicity, and continuity) Overview:

▶ Characterise a general class ▶ Choose function that captures required properties

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Motivation and Literature Objective and Overview

Objective and Overview

Objective:

▶ Construct a chronic poverty measure that combines attractive

properties (in particular sensitivity to chronicity, and continuity) Overview:

▶ Characterise a general class ▶ Choose function that captures required properties ▶ Apply to analyse chronic poverty in rural Ethiopia

(No proofs; informal presentation.)

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Analytical Framework Ethical Framework General Form Social Aggregation

Outline

Preliminaries Motivation and Literature Objective and Overview Characterisation of General Form Analytical Framework Ethical Framework General Form Social Aggregation Chronic Poverty Ordering of Trajectories Decomposition Properties For Chronic-Poverty Trajectory Ordering Proposed Trajectory-Ordering Function Application: Poverty in Rural Ethiopia Data and Results Concluding Remarks

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Analytical Framework Ethical Framework General Form Social Aggregation

Analytical Framework

Instantaneous individual indicator of wellbeing xit ∈ 핏:

▶ For each individual i = 1, 2, . . . , n in each time period

t = 1, 2, . . . , T.

▶ xit = ritu where rit ∈ ℝ and u is the unit of measurement (of

the indicator).

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Analytical Framework Ethical Framework General Form Social Aggregation

Analytical Framework

Instantaneous individual indicator of wellbeing xit ∈ 핏:

▶ For each individual i = 1, 2, . . . , n in each time period

t = 1, 2, . . . , T.

▶ xit = ritu where rit ∈ ℝ and u is the unit of measurement (of

the indicator).

▶ Population size n ∈ ℕ, n ≥ 3. ▶ Fixed number T of discrete time periods.

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Analytical Framework Ethical Framework General Form Social Aggregation

Analytical Framework

Instantaneous individual indicator of wellbeing xit ∈ 핏:

▶ For each individual i = 1, 2, . . . , n in each time period

t = 1, 2, . . . , T.

▶ xit = ritu where rit ∈ ℝ and u is the unit of measurement (of

the indicator).

▶ Population size n ∈ ℕ, n ≥ 3. ▶ Fixed number T of discrete time periods. ▶ xit comparable across individuals (per-adult-equivalent) ▶ xit comparable across time (deflated)

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Analytical Framework Ethical Framework General Form Social Aggregation

Analytical Framework

Instantaneous individual indicator of wellbeing xit ∈ 핏:

▶ For each individual i = 1, 2, . . . , n in each time period

t = 1, 2, . . . , T.

▶ xit = ritu where rit ∈ ℝ and u is the unit of measurement (of

the indicator).

▶ Population size n ∈ ℕ, n ≥ 3. ▶ Fixed number T of discrete time periods. ▶ xit comparable across individuals (per-adult-equivalent) ▶ xit comparable across time (deflated)

Thus domain of analysis is 풳T =

∞

∪

n=3

핏nT.

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Analytical Framework Ethical Framework General Form Social Aggregation

Analytical Framework

Each X ∈ 풳T is a profile of wellbeings, X = ⎛ ⎜ ⎜ ⎜ ⎝ x11 x12 ⋅ ⋅ ⋅ x1T x21 x22 ⋅ ⋅ ⋅ x2T . . . . . . ... . . . xn1 xn2 ⋅ ⋅ ⋅ xnT ⎞ ⎟ ⎟ ⎟ ⎠ in which each row represents an individual’s trajectory of wellbeings; n(X) is the number of individuals and T(X) is the number of time periods.

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Analytical Framework Ethical Framework General Form Social Aggregation

Analytical Framework

Each X ∈ 풳T is a profile of wellbeings, X = ⎛ ⎜ ⎜ ⎜ ⎝ x11 x12 ⋅ ⋅ ⋅ x1T x21 x22 ⋅ ⋅ ⋅ x2T . . . . . . ... . . . xn1 xn2 ⋅ ⋅ ⋅ xnT ⎞ ⎟ ⎟ ⎟ ⎠ in which each row represents an individual’s trajectory of wellbeings; n(X) is the number of individuals and T(X) is the number of time periods. We are interested in real-valued intertemporal poverty measures 풫 : 풳T → ℝ.

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Analytical Framework Ethical Framework General Form Social Aggregation

Ethical Framework

Start with two fundamental ethical principles:

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Analytical Framework Ethical Framework General Form Social Aggregation

Ethical Framework

Start with two fundamental ethical principles:

▶ (A) Anonymity or Symmetry

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Analytical Framework Ethical Framework General Form Social Aggregation

Ethical Framework

Start with two fundamental ethical principles:

▶ (A) Anonymity or Symmetry ▶ (SC) Subgroup Consistency

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Analytical Framework Ethical Framework General Form Social Aggregation

Ethical Framework

Start with two fundamental ethical principles:

▶ (A) Anonymity or Symmetry ▶ (SC) Subgroup Consistency

And a third:

▶ (PN) Population-Size Neutrality

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Analytical Framework Ethical Framework General Form Social Aggregation

Ethical Framework

Start with two fundamental ethical principles:

▶ (A) Anonymity or Symmetry ▶ (SC) Subgroup Consistency

And a third:

▶ (PN) Population-Size Neutrality (cf replication invariance)

(Perhaps not so fundamental. . . )

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Analytical Framework Ethical Framework General Form Social Aggregation

(A) Anonymity

Y Z

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Analytical Framework Ethical Framework General Form Social Aggregation

(A) Anonymity

Y Z 풫(Y ) = 풫(Z)

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Analytical Framework Ethical Framework General Form Social Aggregation

(A) Anonymity

Y Z 풫(Y ) = 풫(Z) The poverty analyst evaluates as equivalent profiles which differ

• nly by a permutation of trajectories among individuals.

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Analytical Framework Ethical Framework General Form Social Aggregation

(A) Anonymity

The poverty analyst evaluates as equivalent profiles which differ

• nly by a permutation of trajectories among individuals.

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Analytical Framework Ethical Framework General Form Social Aggregation

(A) Anonymity

The poverty analyst evaluates as equivalent profiles which differ

• nly by a permutation of trajectories among individuals.

This is less innocuous than it seems:

▶ Normative judgement that each individual’s trajectory of

wellbeing indicators contains all information relevant for measurement of chronic poverty.

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Analytical Framework Ethical Framework General Form Social Aggregation

(A) Anonymity

The poverty analyst evaluates as equivalent profiles which differ

• nly by a permutation of trajectories among individuals.

This is less innocuous than it seems:

▶ Normative judgement that each individual’s trajectory of

wellbeing indicators contains all information relevant for measurement of chronic poverty.

▶ Multiple dimensions, environmental factors etc. must be

embodied in the wellbeing indicator.

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Analytical Framework Ethical Framework General Form Social Aggregation

(SC) Subgroup Consistency

Y Z If 풫(Y ) ≤ 풫(Z)

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Analytical Framework Ethical Framework General Form Social Aggregation

(SC) Subgroup Consistency

Z’ Y’ then 풫(Y ′) ≤ 풫(Z ′)

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Analytical Framework Ethical Framework General Form Social Aggregation

(SC) Subgroup Consistency

Y’’ Z’’ and 풫(Y ′′) ≤ 풫(Z ′′)

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Analytical Framework Ethical Framework General Form Social Aggregation

(SC) Subgroup Consistency

▶ If the measure of poverty increases in a subset of the

population (e.g. region) while the profile of individual characteristics remains unchanged in the rest of the population then overall poverty must increase.

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Analytical Framework Ethical Framework General Form Social Aggregation

(SC) Subgroup Consistency

▶ If the measure of poverty increases in a subset of the

population (e.g. region) while the profile of individual characteristics remains unchanged in the rest of the population then overall poverty must increase.

▶ (Regardless of the number of individuals and the profile of

their characteristics in the unchanging part of the population.)

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Analytical Framework Ethical Framework General Form Social Aggregation

(PN) Population Size Neutrality

Y Z

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Analytical Framework Ethical Framework General Form Social Aggregation

(PN) Population Size Neutrality

Y Z 풫(Y ) = 풫(Z)

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Analytical Framework Ethical Framework General Form Social Aggregation

(PN) Population Size Neutrality

Y Z 풫(Y ) = 풫(Z) The measure of poverty is the same for any two profiles in which all individuals experience the same trajectory of wellbeings (within and between profiles), regardless of population size.

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Analytical Framework Ethical Framework General Form Social Aggregation

General Form

Characterise general class of intertemporal poverty measures consistent with the ethical framework:

Proposition 1

An intertemporal poverty measure 풫 : 풳T → ℙ satisfies properties (A), (SC) and (PN) if and only if it has the form 풫(X) = g ⎛ ⎝ 1 n(X)

n(X)

∑

i=1

f (p(xi1, xi2, . . . , xiT)) ⎞ ⎠ where g : ℝ → ℝ and f : ℝ → ℝ are strictly increasing and p : 핏T → ℝ is any function.

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Analytical Framework Ethical Framework General Form Social Aggregation

General Form

풫(X) = g ⎛ ⎝ 1 n(X)

n(X)

∑

i=1

f (p(xi1, xi2, . . . , xiT)) ⎞ ⎠

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Analytical Framework Ethical Framework General Form Social Aggregation

General Form

풫(X) = g ⎛ ⎝ 1 n(X)

n(X)

∑

i=1

f (p(xi1, xi2, . . . , xiT)) ⎞ ⎠ Notes:

▶ p : 핏T → ℝ embodies an unambiguous ordering of the set of

all possible trajectories of individual wellbeing.

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Analytical Framework Ethical Framework General Form Social Aggregation

General Form

풫(X) = g ⎛ ⎝ 1 n(X)

n(X)

∑

i=1

f (p(xi1, xi2, . . . , xiT)) ⎞ ⎠ Notes:

▶ p : 핏T → ℝ embodies an unambiguous ordering of the set of

all possible trajectories of individual wellbeing.

▶ Thus far, no restriction on this ordering (other than

representable by a real-valued function hence not pathologically discontinuous).

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Analytical Framework Ethical Framework General Form Social Aggregation

General Form

풫(X) = g ⎛ ⎝ 1 n(X)

n(X)

∑

i=1

f (p(xi1, xi2, . . . , xiT)) ⎞ ⎠ Notes:

▶ p : 핏T → ℝ embodies an unambiguous ordering of the set of

all possible trajectories of individual wellbeing.

▶ Thus far, no restriction on this ordering (other than

representable by a real-valued function hence not pathologically discontinuous).

▶ Recursive form: aggregate over time (p) before (possibly)

transforming (f ), aggregating over society via arithmetic mean and (possibly) transforming again (g). Compare Calvo and Dercon (2009).

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Analytical Framework Ethical Framework General Form Social Aggregation

Social Aggregation

▶ Before proceeding with analysis of p, choose a specific

functional form for f .

▶ A useful trick: restrict attention to subset of domain 풳T,

space of constant-wellbeing trajectories: X = ⎛ ⎜ ⎜ ⎜ ⎝ x1 x1 ⋅ ⋅ ⋅ x1 x2 x2 ⋅ ⋅ ⋅ x2 . . . . . . ... . . . xn xn ⋅ ⋅ ⋅ xn ⎞ ⎟ ⎟ ⎟ ⎠ .

▶ Restricted domain is isomorphic to space of one-period

trajectories 풳1; context for static/ unidimensional poverty analysis.

▶ Exploit this analogy.

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Analytical Framework Ethical Framework General Form Social Aggregation

Social Aggregation

Introduce (normative) properties standard for static/ unidimensional poverty measures:

▶ (CWF) CW-Focus: 풫 is not sensitive to (constant) levels of

wellbeing above some ‘poverty line’ z ∈ 핏.

▶ (CWM) CW-Strict Monotonicity: 풫 strictly increases under a

fall in (constant) wellbeing for any individual whose level of wellbeing is below the poverty line.

▶ (CWT) CW-Strict Transfer: 풫 strictly increases if some

quantity of (constant) wellbeing is transferred from an individual below the poverty line to any individual with a higher level of (constant) wellbeing. (Depends on the indicator! Ok for consumption.)

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Analytical Framework Ethical Framework General Form Social Aggregation

Social Aggregation

And one more (technical, mild?) property:

▶ (CWC) CW-Compact: 풫 attains its upper limit at X where

xit = 0 for all i, t and its lower limit 0 at Z where zit = z for all i, t and furthermore the range of 풫 is the closed interval of the real line [0, 풫(X)].

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Analytical Framework Ethical Framework General Form Social Aggregation

Social Aggregation

Characterise more restricted class of measures:

Proposition 2

An intertemporal poverty measure 풫 : 풳T → ℙ satisfies properties (A), (SC), (PN), (CWF), (CWM), (CWT) and (CWC) if and only if it has the form 풫(X) = g ⎛ ⎝ 1 n(X)

n(X)

∑

i=1

h(cp(p(xi1, xi2, . . . , xiT))) ⎞ ⎠ where g : ℝ → ℝ is strictly increasing, h : [0, z] → ℝ is strictly decreasing, continuous and convex with h(z) = 0, cp(p(x, x, . . . , x)) = x for all x ∈ [0, z], cp(p(x, x, . . . , x)) = z for all x ≥ z and p : 핏T → ℝ with p(x, x, . . . , x) continuous and strictly decreasing for x ∈ [0, z].

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Analytical Framework Ethical Framework General Form Social Aggregation

Social Aggregation

Writing c(xi) = cp(p(xi1, xi2, . . . , xiT)) for the constant-wellbeing equivalent of trajectory xi = (xi1, xi2, . . . , xiT) gives a clearer expression for the class of measures: 풫(X) = g ⎛ ⎝ 1 n(X)

n(X)

∑

i=1

h(c(xi)) ⎞ ⎠ where g : ℝ → ℝ is strictly increasing and h : [0, z] → ℝ is strictly decreasing, continuous and convex with h(z) = 0.

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Analytical Framework Ethical Framework General Form Social Aggregation

Social Aggregation

Writing c(xi) = cp(p(xi1, xi2, . . . , xiT)) for the constant-wellbeing equivalent of trajectory xi = (xi1, xi2, . . . , xiT) gives a clearer expression for the class of measures: 풫(X) = g ⎛ ⎝ 1 n(X)

n(X)

∑

i=1

h(c(xi)) ⎞ ⎠ where g : ℝ → ℝ is strictly increasing and h : [0, z] → ℝ is strictly decreasing, continuous and convex with h(z) = 0.

▶ Looks like a static poverty measure! See Chakravarty (1983),

Foster, Greer and Thorbecke (1984), Foster and Shorrocks (1991).

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Analytical Framework Ethical Framework General Form Social Aggregation

Social Aggregation

Writing c(xi) = cp(p(xi1, xi2, . . . , xiT)) for the constant-wellbeing equivalent of trajectory xi = (xi1, xi2, . . . , xiT) gives a clearer expression for the class of measures: 풫(X) = g ⎛ ⎝ 1 n(X)

n(X)

∑

i=1

h(c(xi)) ⎞ ⎠ where g : ℝ → ℝ is strictly increasing and h : [0, z] → ℝ is strictly decreasing, continuous and convex with h(z) = 0.

▶ Looks like a static poverty measure! See Chakravarty (1983),

Foster, Greer and Thorbecke (1984), Foster and Shorrocks (1991).

▶ Choose g(x) = x and h(x) =

( z−x

z

)2 to give poverty-gap-squared measure (FGT-2).

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Decomposition Properties For Chronic-Poverty Trajectory Ordering Proposed Trajectory-Ordering Function

Outline

Preliminaries Motivation and Literature Objective and Overview Characterisation of General Form Analytical Framework Ethical Framework General Form Social Aggregation Chronic Poverty Ordering of Trajectories Decomposition Properties For Chronic-Poverty Trajectory Ordering Proposed Trajectory-Ordering Function Application: Poverty in Rural Ethiopia Data and Results Concluding Remarks

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Decomposition Properties For Chronic-Poverty Trajectory Ordering Proposed Trajectory-Ordering Function

Decomposition

Choice of FGT-2 for social aggregation gives general form: 풫(X) = 1 n(X)

n(X)

∑

i=1

(z − cp(p(xi1, xi2, . . . , xiT)) z )2

▶ All such measures coincide for profiles of constant-wellbeing

trajectories.

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Decomposition Properties For Chronic-Poverty Trajectory Ordering Proposed Trajectory-Ordering Function

Decomposition

Choice of FGT-2 for social aggregation gives general form: 풫(X) = 1 n(X)

n(X)

∑

i=1

(z − cp(p(xi1, xi2, . . . , xiT)) z )2

▶ All such measures coincide for profiles of constant-wellbeing

trajectories.

▶ Given total intertemporal poverty 풫T(X) and chronic poverty

풫C(X) of this form, it is natural to decompose to find transient poverty 풫R(X) = 풫T(X) − 풫C(X).

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Decomposition Properties For Chronic-Poverty Trajectory Ordering Proposed Trajectory-Ordering Function

Decomposition

Choice of FGT-2 for social aggregation gives general form: 풫(X) = 1 n(X)

n(X)

∑

i=1

(z − cp(p(xi1, xi2, . . . , xiT)) z )2

▶ All such measures coincide for profiles of constant-wellbeing

trajectories.

▶ Given total intertemporal poverty 풫T(X) and chronic poverty

풫C(X) of this form, it is natural to decompose to find transient poverty 풫R(X) = 풫T(X) − 풫C(X).

▶ It remains to determine pC appropriate for measurement of

chronic poverty (and pT for total poverty).

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Decomposition Properties For Chronic-Poverty Trajectory Ordering Proposed Trajectory-Ordering Function

Decomposition

Note that the chronic and transient measures of poverty proposed by Jalan and Ravallion (2000; study in Rural China) are exactly of this form, with: pT(x) = max [ 0,

T

∑

t=1

(z − xt z )2 핀(xt ≤ z) ] ,

▶ FGT-2 aggregated over time periods as well as individuals;

reasonable choice for total intertemporal poverty, and pJR(x) = max [ 0, z − 1 T

T

∑

t=1

xt ] ,

▶ FGT-2 applied to individuals’ average consumption over time;

perhaps not so reasonable choice for chronic poverty.

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Decomposition Properties For Chronic-Poverty Trajectory Ordering Proposed Trajectory-Ordering Function

Properties For Chronic-Poverty Trajectory Ordering

Two properties for all intertemporal poverty measures:

▶ (M) Monotonicity: Reduction in wellbeing in any period for

any poor trajectory increases p.

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Decomposition Properties For Chronic-Poverty Trajectory Ordering Proposed Trajectory-Ordering Function

Properties For Chronic-Poverty Trajectory Ordering

Two properties for all intertemporal poverty measures:

▶ (M) Monotonicity: Reduction in wellbeing in any period for

any poor trajectory increases p.

▶ Shared by all measures proposed in the literature (at least in

weak form; headcount version of Foster (2009)).

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Decomposition Properties For Chronic-Poverty Trajectory Ordering Proposed Trajectory-Ordering Function

Properties For Chronic-Poverty Trajectory Ordering

Two properties for all intertemporal poverty measures:

▶ (M) Monotonicity: Reduction in wellbeing in any period for

any poor trajectory increases p.

▶ Shared by all measures proposed in the literature (at least in

weak form; headcount version of Foster (2009)).

▶ (C) Continuity: p is a continuous function of all periods’

wellbeings, so a marginal change in wellbeing in any period cannot cause a finite change in p.

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Decomposition Properties For Chronic-Poverty Trajectory Ordering Proposed Trajectory-Ordering Function

Properties For Chronic-Poverty Trajectory Ordering

Two properties for all intertemporal poverty measures:

▶ (M) Monotonicity: Reduction in wellbeing in any period for

any poor trajectory increases p.

▶ Shared by all measures proposed in the literature (at least in

weak form; headcount version of Foster (2009)).

▶ (C) Continuity: p is a continuous function of all periods’

wellbeings, so a marginal change in wellbeing in any period cannot cause a finite change in p.

▶ Does not hold for many proposed ‘chronic poverty’ measures:

Foster (2009), Gradin, Del Rio and Canto (2011), Bossert, Chakravarty and D’Ambrosio (2012). Failure leads to counter-intuitive ordering of trajectories.

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Decomposition Properties For Chronic-Poverty Trajectory Ordering Proposed Trajectory-Ordering Function

Properties For Chronic-Poverty Trajectory Ordering

Two properties for chronic poverty measures:

▶ (D) Duration-Sensitivity: p increases when wellbeing is

transfered between periods with the effect of increasing the number of periods below the poverty line.

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Decomposition Properties For Chronic-Poverty Trajectory Ordering Proposed Trajectory-Ordering Function

Properties For Chronic-Poverty Trajectory Ordering

Two properties for chronic poverty measures:

▶ (D) Duration-Sensitivity: p increases when wellbeing is

transfered between periods with the effect of increasing the number of periods below the poverty line.

▶ Holds for some but not all of the measures proposed. (Not

Jalan and Ravallion (2000), Calvo and Dercon (2009), Hoy and Zheng (2011) or Foster and Santos (2013)).

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Decomposition Properties For Chronic-Poverty Trajectory Ordering Proposed Trajectory-Ordering Function

Properties For Chronic-Poverty Trajectory Ordering

Two properties for chronic poverty measures:

▶ (D) Duration-Sensitivity: p increases when wellbeing is

transfered between periods with the effect of increasing the number of periods below the poverty line.

▶ Holds for some but not all of the measures proposed. (Not

Jalan and Ravallion (2000), Calvo and Dercon (2009), Hoy and Zheng (2011) or Foster and Santos (2013)).

▶ (C) Contiguous Poverty: Contiguous periods of low wellbeing

have a greater detrimental effect than p separated periods.

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Decomposition Properties For Chronic-Poverty Trajectory Ordering Proposed Trajectory-Ordering Function

Properties For Chronic-Poverty Trajectory Ordering

Two properties for chronic poverty measures:

▶ (D) Duration-Sensitivity: p increases when wellbeing is

transfered between periods with the effect of increasing the number of periods below the poverty line.

▶ Holds for some but not all of the measures proposed. (Not

Jalan and Ravallion (2000), Calvo and Dercon (2009), Hoy and Zheng (2011) or Foster and Santos (2013)).

▶ (C) Contiguous Poverty: Contiguous periods of low wellbeing

have a greater detrimental effect than p separated periods.

▶ Holds for Gradin, Del Rio and Canto (2011) and Bossert,

Chakravarty and D’Ambrosio (2012) but not Jalan and Ravallion (2000), Calvo and Dercon (2009), Foster (2009) or Foster and Santos (2013).

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Decomposition Properties For Chronic-Poverty Trajectory Ordering Proposed Trajectory-Ordering Function

Properties For Chronic-Poverty Trajectory Ordering

▶ None of the measures proposed combine all of the properties

appropriate for measurement of chronic poverty.

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Decomposition Properties For Chronic-Poverty Trajectory Ordering Proposed Trajectory-Ordering Function

Properties For Chronic-Poverty Trajectory Ordering

▶ None of the measures proposed combine all of the properties

appropriate for measurement of chronic poverty.

▶ Some might be more appropriate for ‘total’ intertemporal

poverty.

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Decomposition Properties For Chronic-Poverty Trajectory Ordering Proposed Trajectory-Ordering Function

Properties For Chronic-Poverty Trajectory Ordering

▶ None of the measures proposed combine all of the properties

appropriate for measurement of chronic poverty.

▶ Some might be more appropriate for ‘total’ intertemporal

poverty.

▶ Challenge: construct a measure that combines all appropriate

properties.

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Decomposition Properties For Chronic-Poverty Trajectory Ordering Proposed Trajectory-Ordering Function

Proposed Trajectory-Ordering Function pN

Proposition 3

The function pN(x) = max [ 0, z − 1 T ((1 3(2x2

i1 + x2 i2)

)1/2 +

T−1

∑

t=2

( 1 3

t+1

∑

s=t−1

x2

is

)1/2 + (1 3(x2

iT−1 + 2x2 iT)

)1/2 ⎞ ⎠ ⎤ ⎦ satisfies properties (C), (M), (D) and (CP).

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Decomposition Properties For Chronic-Poverty Trajectory Ordering Proposed Trajectory-Ordering Function

Proposed Trajectory-Ordering Function pN

0.8-1 0.6-0.8 0.4-0.6 0.2-0.4 0-0.2

Isoquants of pN in x1 – x2 plane; x3 = 0.

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Decomposition Properties For Chronic-Poverty Trajectory Ordering Proposed Trajectory-Ordering Function

Proposed Trajectory-Ordering Function pN

0.6-0.8 0.4-0.6 0.2-0.4 0-0.2

Isoquants of pN in x1 – x2 plane; x3 = 0.5.

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Decomposition Properties For Chronic-Poverty Trajectory Ordering Proposed Trajectory-Ordering Function

Proposed Trajectory-Ordering Function pN

0.4-0.6 0.2-0.4 0-0.2

Isoquants of pN in x1 – x2 plane; x3 = 1.

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Data and Results Concluding Remarks

Outline

Preliminaries Motivation and Literature Objective and Overview Characterisation of General Form Analytical Framework Ethical Framework General Form Social Aggregation Chronic Poverty Ordering of Trajectories Decomposition Properties For Chronic-Poverty Trajectory Ordering Proposed Trajectory-Ordering Function Application: Poverty in Rural Ethiopia Data and Results Concluding Remarks

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Data and Results Concluding Remarks

Data

Ethiopian Rural Household Survey (ERHS):

▶ Joint project: Addis Ababa University, CSAE(Oxford), IFPRI

(Washington DC).

▶ Funding: UK ESRC, SIDA, USAID, World Bank. ▶ 7 rounds to date: 1994, 1994, 1995, 1997, 1999, 2004, 2009. ▶ Comprehensive household survey; 1477 households from

eighteen PAs.

▶ Self-weighting sample to represent climatic zones.

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Data and Results Concluding Remarks

Data

ERHS poverty analysis:

▶ Studies include Dercon and Krishnan (1998), Porter (2008),

Dercon, Hoddinott and Woldehanna (2012).

▶ Overall reduction in poverty until 2009. . .

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Data and Results Concluding Remarks

Data

ERHS poverty analysis:

▶ Studies include Dercon and Krishnan (1998), Porter (2008),

Dercon, Hoddinott and Woldehanna (2012).

▶ Overall reduction in poverty until 2009. . . ▶ Indicator of wellbeing: real per-adult-equivalent consumption

expenditure.

▶ Deflator(s): 1994 village-specific poverty lines (Dercon and

Krishnan 1998), updated with village-specific prices in subsequent rounds. Restrict sample to the 1136 households for which we have consumption data in all four utilised rounds.

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Data and Results Concluding Remarks

Results: Jalan-Ravallion Decomposition

Peasant Association 풫T 풫JR 풫T − 풫JR % chronic % transient Haresaw .0668342 .0028732 .063961 1.8 98.2 Geblen .1504773 .0534743 .097003 26.0 74.0 Dinki .0447244 .0084647 .0362596 7.0 93.0 Yetmen .0058968 .0058968 0.0 100.0 Shumsha .0040872 .0000118 .0040755 0.1 99.9 Sirbana Godeti .0020922 .0020922 0.0 100.0 Adele Keke .0379529 .0001914 .0377616 0.1 99.9 Korodegaga .0553191 .0020981 .0532209 1.2 98.8 Trirufe Ketchema .024877 .0041737 .0207033 4.2 95.8 Imdibir .0407047 .0084567 .032248 9.3 90.7 Aze Deboa .0411501 .0057057 .0354444 6.2 93.8 Adado .043913 .0057793 .0381337 7.5 92.5 Gara Godo .1907494 .0706493 .1201 26.0 74.0 Doma .1148332 .0336721 .0811611 16.7 83.3 Debre Berhan Mil .0112358 .0112358 0.0 100.0 Debre Berhan Kor .0104418 .0104418 0.0 100.0 Debre Berhan Kar .0095046 .0095046 0.0 100.0 Debre Berhan Bok .013391 .013391 0.0 100.0 Total .0515465 .011725 .0398215 8.9 91.1 Source: Ethiopian Rural Household Survey, rounds 1, 5, 6, 7; own calculations.

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Data and Results Concluding Remarks

Results: Jalan-Ravallion Decomposition

▶ Wide variation in total poverty across PAs (0.0021 in Sirbana

Godeti to 0.197 in Gara Godo).

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Data and Results Concluding Remarks

Results: Jalan-Ravallion Decomposition

▶ Wide variation in total poverty across PAs (0.0021 in Sirbana

Godeti to 0.197 in Gara Godo).

▶ Percentage ‘chronic’ varies between zero (several PAs) and

26% (Geblen and Gara Godo).

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Data and Results Concluding Remarks

Results: Jalan-Ravallion Decomposition

▶ Wide variation in total poverty across PAs (0.0021 in Sirbana

Godeti to 0.197 in Gara Godo).

▶ Percentage ‘chronic’ varies between zero (several PAs) and

26% (Geblen and Gara Godo).

▶ Burden of ‘chronic’ poverty strongly correlated with the total

burden of poverty (correlation coefficient 0.6755).

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Data and Results Concluding Remarks

Results: Jalan-Ravallion Decomposition

▶ Wide variation in total poverty across PAs (0.0021 in Sirbana

Godeti to 0.197 in Gara Godo).

▶ Percentage ‘chronic’ varies between zero (several PAs) and

26% (Geblen and Gara Godo).

▶ Burden of ‘chronic’ poverty strongly correlated with the total

burden of poverty (correlation coefficient 0.6755).

▶ Percentage ‘chronic’ fairly strongly correlated with total

poverty across the whole sample (correlation coefficient 0.5716).

▶ High correlation between proportion of ‘chronic’ and burden

• f total poverty reflects the properties of this ‘chronic’

measure which actually reflects poverty of time-averaged consumption rather than chronicity as such.

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Data and Results Concluding Remarks

Results: New Decomposition

Peasant Association 풫T 풫N 풫T − 풫N % chronic % transient Haresaw .0668342 .0197871 .0470471 29.0 71.0 Geblen .1504773 .071698 .0787793 43.6 56.4 Dinki .0447244 .0189449 .0257795 32.9 67.1 Yetmen .0058968 .0016786 .0042182 26.0 74.0 Shumsha .0040872 .001093 .0029942 24.7 75.3 Sirbana Godeti .0020922 .0005658 .0015264 24.4 75.6 Adele Keke .0379529 .0101588 .0277941 25.0 75.0 Korodegaga .0553191 .0155156 .0398035 26.7 73.3 Trirufe Ketchema .024877 .0079264 .0169507 28.3 71.7 Imdibir .0407047 .0179463 .0227584 35.5 64.5 Aze Deboa .0411501 .0157111 .025439 31.8 68.2 Adado .043913 .0158629 .0280501 33.4 66.6 Gara Godo .1907494 .0956478 .0951016 43.0 57.0 Doma .1148332 .0494942 .0653391 37.8 62.2 Debre Berhan Mil .0112358 .002757 .0084788 25.1 74.9 Debre Berhan Kor .0104418 .0022903 .0081515 24.7 75.3 Debre Berhan Kar .0095046 .0026911 .0068135 24.5 75.5 Debre Berhan Bok .013391 .0023608 .0110301 22.9 77.1 Total .0515465 .0210471 .0304994 32.5 67.5 Source: Ethiopian Rural Household Survey, rounds 1, 5, 6, 7; own calculations.

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Data and Results Concluding Remarks

Results: New Decomposition

▶ Total poverty is as J-R decomposition.

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Data and Results Concluding Remarks

Results: New Decomposition

▶ Total poverty is as J-R decomposition. ▶ Percentage of total poverty evaluated as ‘chronic’ is much

higher, varying between 22% in Debre Berhan–Faji Bokafia, and 43% in Geblen.

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Data and Results Concluding Remarks

Results: New Decomposition

▶ Total poverty is as J-R decomposition. ▶ Percentage of total poverty evaluated as ‘chronic’ is much

higher, varying between 22% in Debre Berhan–Faji Bokafia, and 43% in Geblen.

▶ Burden of chronic poverty very strongly correlated with the

total burden of poverty, correlation coefficient 0.8907.

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Data and Results Concluding Remarks

Results: New Decomposition

▶ Total poverty is as J-R decomposition. ▶ Percentage of total poverty evaluated as ‘chronic’ is much

higher, varying between 22% in Debre Berhan–Faji Bokafia, and 43% in Geblen.

▶ Burden of chronic poverty very strongly correlated with the

total burden of poverty, correlation coefficient 0.8907.

▶ Percentage chronic much less strongly correlated with the

total poverty level (correlation coefficient 0.4578). Some PAs with low overall poverty, (e.g. Dinki) have relatively high incidence of chronic poverty.

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Data and Results Concluding Remarks

Results: New Decomposition

▶ Total poverty is as J-R decomposition. ▶ Percentage of total poverty evaluated as ‘chronic’ is much

higher, varying between 22% in Debre Berhan–Faji Bokafia, and 43% in Geblen.

▶ Burden of chronic poverty very strongly correlated with the

total burden of poverty, correlation coefficient 0.8907.

▶ Percentage chronic much less strongly correlated with the

total poverty level (correlation coefficient 0.4578). Some PAs with low overall poverty, (e.g. Dinki) have relatively high incidence of chronic poverty.

▶ Perhaps reflects the different economic environments and

vulnerabilities in the different agrico-climatic zones represented by the different villages.

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Data and Results Concluding Remarks

Concluding Remarks

▶ Framework for constructing intertemporal measures of poverty.

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Data and Results Concluding Remarks

Concluding Remarks

▶ Framework for constructing intertemporal measures of poverty. ▶ Decomposition into chronic and transient components.

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Data and Results Concluding Remarks

Concluding Remarks

▶ Framework for constructing intertemporal measures of poverty. ▶ Decomposition into chronic and transient components. ▶ Proposed a new measure with properties appropriate for

measuring chronic poverty.

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Data and Results Concluding Remarks

Concluding Remarks

▶ Framework for constructing intertemporal measures of poverty. ▶ Decomposition into chronic and transient components. ▶ Proposed a new measure with properties appropriate for

measuring chronic poverty.

▶ Applied to poverty in rural Ethiopia between 1994 and 2009;

contrasted results with earlier method proposed by Jalan and Ravallion.

Preliminaries Characterisation of General Form Chronic Poverty Ordering of Trajectories Application: Poverty in Rural Ethiopia Data and Results Concluding Remarks

Concluding Remarks

▶ Framework for constructing intertemporal measures of poverty. ▶ Decomposition into chronic and transient components. ▶ Proposed a new measure with properties appropriate for

measuring chronic poverty.

▶ Applied to poverty in rural Ethiopia between 1994 and 2009;

contrasted results with earlier method proposed by Jalan and Ravallion.

▶ Further work: characterise entire class of measures with

properties appropriate for chronic poverty.