Poverty and some basic calculations index

Poverty

1. Chapter 3
Poverty

2. Measuring Poverty: The
Headcount Index
•q = Number of people with income below
the poverty line (which we’ll call z)
•N = Total population (the max that can be in
poverty—if everyone were poor)
N
q
P
H


3. Advantages/Disadvantages
•Easy to calculate
•Just need z, q (add up how many people are
in households below the poverty line), and
N
•Insensitive to how far below the poverty line
the poor people are

4. The Poverty Gap (Depth) and
Gap-squared (Severity)
•For person i:
iYz
•Total Poverty Gap: 


q
i
iYz
1
)(
•Poverty Gap-Squared
2
( )
i
z Y

5. Measuring Poverty: FGT
•Headcount
•Poverty Gap (Depth)
•Severity of Poverty
•3 in One: The Foster-Greer-Thorbecke measure (ranges
from 0 (no poor) to 1 (everyone’s poor with zero
income))
1
1
( )
q
i
i
i
P z y
Nz
N Population
z Povertyline
y Incomeof poor personi



 





6. The Three FGT Measures
Derived from:
•Headcount (=0):
•Poverty Gap (=1)
•Poverty Severity
(=2)
q
P
N

1
( )1
( )
q
poor
i
i
z yq
P z y
Nz N z


  
2
2
1
1
( )
q
i
i
P z y
Nz

 
1
1
( )
q
i
i
P z y
Nz



 

7. Recipe for Calculating the FGT
1. For each POOR household (y
i<z), calculate the
poverty gap: ( )
i
z y
1
1
( )
q
i
i
z y
Nz




2. Raise it to the  power:( )
i
z y


3. Take the sum (Σ) of gaps across all q poor
households (add ‘em up):
1
( )
q
i
i
z y



4. Divide by (multiply by 1 over) Nz

:

8. FGT: An Example
Person Income
1 if in
Poverty, 0
Otherwise
Poverty
Gap
Poverty
Gap-
squared
1 5 1 23 529
2 12 1 16 256
3 22 1 6 36
4 24 1 4 16
5 30 0 0 0
6 40 0 0 0
7 50 0 0 0
8 70 0 0 0
9 80 0 0 0
10 100 0 0 0
Sum

4 49 837
z 28

9. Where’s the Poverty Line?
-Average developing-country z: $2/day (PPP adjusted)
-U.S. poverty income for a family of 4 in 2012 was $23,050
(15.79/person/day)

10. Poverty Dynamics: It’s Harder than
You Think
A Transition Matrix of Poverty Dynamics in Rural Mexico
Poor 2007 Non Poor 2007
Poor 2002 (45.56%) 50.92% 49.08%
Non Poor 2002 (54.44%) 30.00% 70.00%

11. Convex Asset Growth Curve
A
t+1
:
Assets
next year
A
t
: Assets
this year

12. A*
B
Convex Asset Growth Curve with Steady-
state at B
A
t+1> A
t
A
t+1< A
t
A
t+1= A
t
along
45
line
A
t+1
:
Assets
next year
A
t
: Assets
this year

13. A
B
0
Non-convex Asset Growth and the Poverty
Trap (Steady-states at B & 0)
The poverty
trap zone
A*
A
t+1
:
Assets
next year
A
t
: Assets
this year
A
t+1> A
t
A
t+1< A
t