'POVTIME':
module to compute
aggregate intertemporal
poverty measures
Carlos Gradín
Universidade de Vigo
1
Description
• ‘povtime’ computes aggregate intertemporal poverty measures
(poverty accounting for time) in a balanced panel of individuals.
• The program computes the family of FGT-type intertemporal
poverty measures proposed in:
– Gradin, Del Rio, and Canto ("Measuring Poverty Accounting
for Time", Review of Income and Wealth, 58(2): 330-354, 2012).
• Other measures that can be interpreted as particular cases of this
general family:
– Foster (“A Class of Chronic Poverty Measures” in Poverty
Dynamics: Interdisciplinary Perspectives, OUP, 2009) and
– Bossert, D'Ambrosio and Chakravarty ("Poverty and Time",
Journal of Economic Inequality, 2012.
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Measuring poverty
• Poverty in a cross-section of individuals
• y=(y1, y2, ... , yq , yq+1, ... , yN)
Poor
z
Non poor
• Poverty index: P(y; z)
1
FGT ( ) 
N
  z  yi  

 z  ,

i 1 
q

 0
FGT(0) = Headcount rate (H=q/N)
FGT(1) = Poverty gap ratio (HI)
FGT(2) = Poverty severity
• Stata modules: povdeco, apoverty, sepov
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Measuring longitudinal poverty
• Poverty in a (balanced) panel
• N Individuals observed T times




Y 






y11
y12
...
y21
y22
...
.
.
...
.
.
...
.
.
...
yN 1
yN 2
...
y1T 

y2 T 
. 

. 

. 

y NT 

y1
y2
Y   y1 , y2 ,..., yN 
'
yN
• Poverty index?: P(y; z)
• Stata modules: povtime
 z  y 
t
it




git   zt 

0

if
yit  zt
otherwise
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i) summarize the complete individual information in time
individual intertemporal poverty index
1 T 
pi  yi ; z    g it wit
T t 1
 sit 
wit   
T 

 0  0
ii) then construct an aggregate poverty index that takes into account a social
preference for equality among individuals
p1  p2  ...  pN
  pi  if pi  0

pi  
 0
if pi  0
1
P Y ; z  
N

p
 i
N
i 1
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Gradín, Cantó and del Río (RIW, 2012)
 
 1 N 1 T

  sit 

  git   

 N i 1  T t 1  T  
P Y ; z   

1 N 0 q

pi 

N i 1
N

𝛽 ≥ 0; 𝛼 ≥ 0; 𝛾 ≥ 0
if   0
if
 0
P satisfies all desirable properties for
 0
,   1
Foster (OUP 2009)
𝛽 = 0; 𝛼 = 1; 𝛾 ≥ 0
Bossert, D’Ambrosio and Chakravarty (JOEI 2012)
𝛽 = 1; 𝛼 = 1; 𝛾 ≥ 0
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Advantages
• A code that allows for measuring agggregate poverty in a panel
– complementing existing codes for measuring poverty in a cross-section
– following various measures recently proposed in the literature,
– in a way consistent with how poverty is measured in a cross-section.
• Easy to undertake in-depth analysis
– robustness (dominance analysis),
– decomposition into components (incidence, intensity, inequality),
– analysis of the distribution of individual poverty indices, etc.
• Easy to obtain inference using bootstrapping
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