This paper develops a model which can be used to examine changes in the average exit time from poverty arising from changes in: consumption growth, household and community characteristics, the cost of living of the poor, and welfare inequality. This is done while controlling for spatial random effects. Poor households face various binding constraints which can be relaxed to reduce the time that they stay poor through deliberate policy interventions. The proposed method is thus useful as it allows one to for instance assess the effect of both consumption growth, and redistribution on the exit time from poverty. The method is then illustrated using Malawian data from the Third Integrated Household Survey.

1. Exit from Poverty and Policy Analysis: A Method and an
Application to Malawi
Richard Mussa
Inaugural ECAMA Research Symposium
Sogecoa Golden Peacock Hotel
Lilongwe
10 October 2014
Richard Mussa (University of Malawi) Exit from Poverty and Policy Analysis 01/07 1 / 24

2. Outline
Motivation
A Regression Based Average Exit Time Model
Empirical Application to Malawi
Results
Conclusion
Richard Mussa (University of Malawi) Exit from Poverty and Policy Analysis 01/07 2 / 24

3. Motivation 1
Reducing poverty is key development goal
A clear understanding of what factors determine poverty status of
individuals and households is crucial to achieving this goal
A number of studies have looked at factors which in‡uence poverty
(e.g. Mukherjee and Benson, 2003; Datt and Jollife, 2004),
vulnerability to poverty (e.g. Zhang and Wan, 2006; Gunther and
Harttgen, 2009; Echevin, 2012).
One dimension of poverty which is also important is an understanding
of how long poor individuals or households would take on average to
exit from poverty
The average exit time is meaningful in the sense that it describes an
interesting "if-then" relationship (Morduch, 1998)
There is no paper which has provided a framework for analysing
determinants of exit time from poverty
Richard Mussa (University of Malawi) Exit from Poverty and Policy Analysis 01/07 3 / 24

4. Motivation 2
This paper develops an integrated model which can be used to
examine changes in the average exit time from poverty arising from
changes in:
consumption growth
household and community characteristics
the cost of living of the poor
welfare inequality.
This is done while controlling for spatial random e¤ects
Fact
Morduch (1998) states that his average exit time measure "It does
not measure .....average expected duration based on individual
speci…c factors.
Richard Mussa (University of Malawi) Exit from Poverty and Policy Analysis 01/07 4 / 24

5. A Regression Based Model of Exit from Poverty 1
I present the average exit time in three steps:
1 STEP 1: Speci…cation of multilevel/hierchical linear regression aka
linear random e¤ects model
2 STEP 2: Speci…cation of the individualised and average exit time
3 STEP 3: Derivation of marginal/partial e¤ects and elasticities of the
exit time
Richard Mussa (University of Malawi) Exit from Poverty and Policy Analysis 01/07 5 / 24

6. A Regression Based Model of Exit from Poverty 2
STEP 1: Linear Random E¤ects Model 1
Household data is hierarchical/multilevel in the sense that households
are nested in communities.
Households in the same cluster/community are likely to be dependent.
This dependency ) downward biased standard errors) many
spurious signi…cant results (Hox, 1995; Rabe-Hesketh and Skrondal,
2008); McCulloch et al., 2008).
Consider the following two level linear additive poverty regression for
household i (i = 1....Mj ) in community j (j = 1....J).
ln yij = b0xij + uj + #ij (1)
= b0xij + zij
Richard Mussa (University of Malawi) Exit from Poverty and Policy Analysis 01/07 6 / 24

7. A Regression Based Model of Exit from Poverty 3
STEP 1: Linear Random E¤ects Model 2
ln yij is the log of per capita annualized household consumption
expenditure,
b are coe¢ cients, xij is a set of observed household (or community)
characteristics,
uj N
0, s2
u
are community-level spatial random e¤ects (random
intercepts),
#ij N
0, s2#
is a household-speci…c idiosycratic error term
The assumptions about uj , and #ij imply that zij N
0, s2z
, where
s2z
= s2
u + s2#
.
Richard Mussa (University of Malawi) Exit from Poverty and Policy Analysis 01/07 7 / 24

8. A Regression Based Model of Exit from Poverty 3
STEP 1: Linear Random E¤ects Model 2
ln yij is the log of per capita annualized household consumption
expenditure,
b are coe¢ cients, xij is a set of observed household (or community)
characteristics,
uj N
0, s2
u
are community-level spatial random e¤ects (random
intercepts),
#ij N
0, s2#
is a household-speci…c idiosycratic error term
The assumptions about uj , and #ij imply that zij N
0, s2z
, where
s2z
= s2
u + s2#
.
Most importantly, ln yij N
b0xij , s2z
Richard Mussa (University of Malawi) Exit from Poverty and Policy Analysis 01/07 7 / 24

9. A Regression Based Model of Exit from Poverty 3
STEP 2: Average exit time 1
De…nition
I de…ne the exit time for a household (tij ) as the time it will take the
household to reach a given poverty line through consumption growth
(Morduch, 1998)
Consumption grows at a constant positive rate of g every year
Then the relationship between the poverty line z, and current
consumption is expressed as (Morduch, 1998):
z = yij etij g (2)
Taking logarithms, and solving for tij gives
tij =
ln z ln yij
g
(3)
Richard Mussa (University of Malawi) Exit from Poverty and Policy Analysis 01/07 8 / 24

10. A Regression Based Model of Exit from Poverty 4
STEP 2: Average exit time 2
De…ne a consumption shortfall or excess variable as follows
mij =
gtij if ln z ln yij 0
0 if ln z ln yij 0
(4)
The average exit time from poverty for the entire population is found
by taking a weighted average of equation (4) to get
Tg =
1
g
åNi
j wijmij
åNi
j wij
(5)
=
W
g
where W =
åNi
j wijmij
åNi
j wij
is the Watts Index (Watts, 1968)
Richard Mussa (University of Malawi) Exit from Poverty and Policy Analysis 01/07 9 / 24

11. A Regression Based Model of Exit from Poverty 5
STEP 2: Average exit time 3
Recall ln yij N
b0xij , s2z
, and that yij is log normally distributed.
Muller (2001) shows that the parametric formula of the Watts Index
of a log normal variable in discrete form can be expressed as
W =
åNi
j wij
ln z b0xij
F
ln zb0xij
sz
åNi
j wij
+
åNi
j wijszf
ln zb0xij
sz
åNi
j wij
(6)
Where F and f are respectively cumulative and probability density
functions of the standard normal distribution, and
H =
åNi
j wijF
ln zb0xij
sz
åNi
j wij
(7)
Richard Mussa (University of Malawi) Exit from Poverty and Policy Analysis 01/07 10 / 24

12. A Regression Based Model of Exit from Poverty 6
STEP 2: Average exit time 4
I next introduce the random e¤ects linear regression into the average
exit time from poverty.
Substituting equation (6) into equation (5), gives the average exit
time from poverty in terms of regression parameters and independent
variables as follows
Tg =
1
g
2
6664
åNi
j wij (ln zb0xij )F
ln zb0xij
sz
åNi
j wij
+
åNi
j wij szf
ln zb0xij
sz
åNi
j wij
3
7775
(8)
Richard Mussa (University of Malawi) Exit from Poverty and Policy Analysis 01/07 11 / 24

13. A Regression Based Model of Exit from Poverty 7
STEP 3: Derivation of marginal/partial e¤ects and elasticities of the exit time 1
One can examine the impact on the average exit time of:
1 Varying the rate of consumption growth g ) ¶Tg
¶g = Wg
2 0
Richard Mussa (University of Malawi) Exit from Poverty and Policy Analysis 01/07 12 / 24

14. A Regression Based Model of Exit from Poverty 7
STEP 3: Derivation of marginal/partial e¤ects and elasticities of the exit time 1
One can examine the impact on the average exit time of:
1 Varying the rate of consumption growth g ) ¶Tg
¶g = Wg
2 0
2 Redistribution through varying policy amenable
observable household
and community characteristics) ¶Tg
¶xijk
= bk
Hg
Or elasticity instead )
¶Tg
¶xijk
xijk
Tg
= bk
åNi
j wij xijk
åNi
j wij
H
W
Richard Mussa (University of Malawi) Exit from Poverty and Policy Analysis 01/07 12 / 24

15. A Regression Based Model of Exit from Poverty 7
STEP 3: Derivation of marginal/partial e¤ects and elasticities of the exit time 1
One can examine the impact on the average exit time of:
1 Varying the rate of consumption growth g ) ¶Tg
¶g = Wg
2 0
2 Redistribution through varying policy amenable
observable household
and community characteristics) ¶Tg
¶xijk
= bk
Hg
Or elasticity instead )
¶Tg
¶xijk
xijk
Tg
= bk
åNi
j wij xijk
åNi
j wij
H
W
Ni
3 Changes in within community consumption inequality
¶Tg
1
åj wij f(uij ) )
= 0
¶s#
g
åj Ni
wij
Richard Mussa (University of Malawi) Exit from Poverty and Policy Analysis 01/07 12 / 24

16. A Regression Based Model of Exit from Poverty 7
STEP 3: Derivation of marginal/partial e¤ects and elasticities of the exit time 1
One can examine the impact on the average exit time of:
1 Varying the rate of consumption growth g ) ¶Tg
¶g = Wg
2 0
2 Redistribution through varying policy amenable
observable household
and community characteristics) ¶Tg
¶xijk
= bk
Hg
Or elasticity instead )
¶Tg
¶xijk
xijk
Tg
= bk
åNi
j wij xijk
åNi
j wij
H
W
Ni
3 Changes in within community consumption inequality
¶Tg
1
åj wij f(uij ) )
= 0
¶s#
g
åj Ni
wij
Ni
4 Changes in between community consumption inequality
¶Tg
1
åj wij f(uij ) )
= 0
¶su
g
åj Ni
wij
Richard Mussa (University of Malawi) Exit from Poverty and Policy Analysis 01/07 12 / 24

17. A Regression Based Model of Exit from Poverty 7
STEP 3: Derivation of marginal/partial e¤ects and elasticities of the exit time 1
One can examine the impact on the average exit time of:
1 Varying the rate of consumption growth g ) ¶Tg
¶g = Wg
2 0
2 Redistribution through varying policy amenable
observable household
and community characteristics) ¶Tg
¶xijk
= bk
Hg
Or elasticity instead )
¶Tg
¶xijk
xijk
Tg
= bk
åNi
j wij xijk
åNi
j wij
H
W
Ni
3 Changes in within community consumption inequality
¶Tg
1
åj wij f(uij ) )
= 0
¶s#
g
åj Ni
wij
Ni
4 Changes in between community consumption inequality
¶Tg
1
åj wij f(uij ) )
= 0
¶su
g
åj Ni
wij
5 Changes in the poverty line) ¶Tg
¶z = 1
zg H 0
Richard Mussa (University of Malawi) Exit from Poverty and Policy Analysis 01/07 12 / 24

18. Empirical Application to Malawi 1
Context
The economy grew at an average annual rate of 6.2% between 2004
and 2007, and surged further to an average growth of 7.5% between
2008 and 2011
However, poverty reduction in Malawi has been marginal7! was
52.4% in 2004, and marginally declined to 50.7% in 2011.
A recent re-examination by Beck, Mussa, and Pauw (2014) shows
that the decrease in poverty was much larger than o¢ cially estimated.
Richard Mussa (University of Malawi) Exit from Poverty and Policy Analysis 01/07 13 / 24

19. Empirical Application to Malawi 2
Data description, poverty lines, and variables used
I use the Third Integrated Household Survey (IHS3)
I use an annualized consumption aggregate for each household
generated by Beck et al. (2014) as a welfare indicator i.e. the
dependent variable
Two area-speci…c utility-consistent poverty lines generated by Beck et
al. (2014))MK 37705 for rural areas, and MK 50735 for urban areas
Three groups of independent variables are included in the regressions
namely;
household )demographic,education, agricultural, employment variables
community)health infrastructure and economic infrastructure
indices) constructed by using multiple correspondence analysis
…xed e¤ects variables)agro-ecological zone dummies, seasonality
dummies
Richard Mussa (University of Malawi) Exit from Poverty and Policy Analysis 01/07 14 / 24

20. Results 1
Exit times with 6% growth
Figure 1 . Distribution of exit times when growth is at 6%
0 .1 .2 .3 .4
d e n s ity 0 10 20 30
exit tim e
Ru ra l Urban Richard Mussa (University of Malawi) Exit from Poverty and Policy Analysis 01/07 15 / 24

21. Results 1
Exit times with 6% growth
Exit times for urban areas are lower than those for rural areas:
average exit time, rural 3.6 years, urban 1.8 years
Exit times are skewed to the right) few individuals have very long
exit times
Rural areas have longer right tail
Minimum exit time: rural 0 years, urban 0 years
Maximum exit time: rural 30.33 years, urban 17.33 years
Gini coe¢ cient of exit times: rural 0.39, urban 0.54
Richard Mussa (University of Malawi) Exit from Poverty and Policy Analysis 01/07 16 / 24

22. Results 2
Average exit times for di¤erent growth rates
Figure 2. Average exit times for different growth rates
0 5 1 0 1 5 2 0
A v e ra g e e x it tim e (y e a rs)
0 2 4 6 8 1 0
R a te o f g ro w th o f c o n s um p tio n
R u ra l U rb a n
Richard Mussa (University of Malawi) Exit from Poverty and Policy Analysis 01/07 17 / 24

23. Results 2
Average exit times for di¤erent growth rates
At all growth rates, exit times for urban areas are lower than those for
rural areas
The gap however narrows at high growth rates
Richard Mussa (University of Malawi) Exit from Poverty and Policy Analysis 01/07 18 / 24

24. Results 3
Required growth rates to exit within one year and …ve years
Figure 3. Boxplots of required growth rates to exit within one year and five years
0 5 0 1 0 0 1 5 0 2 0 0
R e q u ire d g row th (% )
urb a n ru ra l
e xit Richard Mussa (University of Malawi) Exit from P oi vne r1ty yanedaProlicy Analysis e x it i n 5 y e a rs 01/07 19 / 24

25. Results 3
Required growth rates to exit within one year and …ve years
The required growth rates are higher for rural areas
There is a wider variation in the required growth rates in rural areas
Richard Mussa (University of Malawi) Exit from Poverty and Policy Analysis 01/07 20 / 24

26. Results 4
Re-distribution and average exit times
Variable Rural Urban
Elasticity SE Elasticity SE
male headed ­0.3442***
(0.0024) 0.0398*** (0.0005)
age of head ­1.1157***
(0.0063) ­3.3670***
(0.0328)
age of head squared 0.5819*** (0.0057) 1.6265*** (0.0268)
under 9 1.1560*** (0.0094) 1.1764*** (0.0215)
10­17
0.6022*** (0.0073) 0.5549*** (0.0145)
females 18­59
­0.0262***
(0.0002) 0.1446*** (0.0025)
males 18­59
1.3418*** (0.0087) 1.5200*** (0.0205)
over 60 years 0.2095*** (0.0047) 0.0466*** (0.0033)
household size squared ­0.8879***
(0.0088) ­0.8474***
(0.0175)
pslc ­0.0509***
(0.0015) ­0.0325***
(0.0019)
jce ­0.0661***
(0.0022) ­0.1142***
(0.0052)
msce ­0.0615***
(0.0026) ­0.4437***
(0.0164)
tertiary ­0.0393***
(0.0037) ­0.6631***
(0.0371)
females with JCE ­0.0192***
(0.0010) ­0.0316***
(0.0016)
males with JCE 0.0095*** (0.0003) 0.0025*** (0.0001)
females with MSCE ­0.0037***
(0.0003) ­0.0765***
(0.0044)
males with MSCE ­0.0038***
(0.0002) ­0.0132***
(0.0005)
primary industry 0.0006*** (0.0000) 0.0019*** (0.0002)
secondary industry ­0.0031***
(0.0002) 0.0094*** (0.0007)
tertiary industry ­0.0497***
(0.0018) ­0.1071***
(0.0032)
land ­0.0283***
(0.0022)
crops ­0.0176***
(0.0006)
economic index 0.0105*** (0.0023) ­0.0899***
(0.0039)
health index 0.0682*** (0.0011) 0.0497*** (0.0023)
Observations 10038 2233
Notes: Standard errors in parentheses. *** indicates significant at 1%; ** at 5%; and, * at 10%.
Richard Mussa (University of Malawi) Exit from Poverty and Policy Analysis 01/07 21 / 24

27. Results 4
Re-distribution and average exit times
Negative sign means a reduction in the average exit time
In both rural and urban areas, increases in the education of females
have larger impact on exit time
Land has a larger exit-time-reducing than crop diversi…cation
Increases in employment in the tertiary industry reduce the exit time
by a larger amount than employment in the primary and secondary
industries
In urban areas, improvements in economic infrastructure have a larger
e¤ect on the exit time than health infrastructure
The reverse holds in rural areas
Richard Mussa (University of Malawi) Exit from Poverty and Policy Analysis 01/07 22 / 24

28. Conclusion
This adds to literature on the poverty-growth-inequality triangle
It provides analytical tools to consider exit time poverty,
redistribution, and growth jointly
The tools are policy relevant as they allow one to examine the
impact of the four factors on exit time
CAVEAT: The methods developed here are built around the
dimension of time, however, they are still a measure of static
conditions
Richard Mussa (University of Malawi) Exit from Poverty and Policy Analysis 01/07 23 / 24

29. THANKS!
Richard Mussa (University of Malawi) Exit from Poverty and Policy Analysis 01/07 24 / 24