Exit from poverty and policy analysis: a method and an application to Malawi by Richard Mussa

Exit from Poverty and Policy Analysis: A Method and anApplication to Malawi

Richard MussaInaugural ECAMA Research Symposium

Sogecoa Golden Peacock HotelLilongwe

10 October 2014

Richard Mussa (University of Malawi) Exit from Poverty and Policy Analysis 01/07 1 / 24

Outline

Motivation

A Regression Based Average Exit Time Model

Empirical Application to Malawi

Results

Conclusion


Motivation 1

Reducing poverty is key development goal

A clear understanding of what factors determine poverty status ofindividuals 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 andHarttgen, 2009; Echevin, 2012).

One dimension of poverty which is also important is an understandingof how long poor individuals or households would take on average toexit from poverty

The average exit time is meaningful in the sense that it describes aninteresting "if-then" relationship (Morduch, 1998)

There is no paper which has provided a framework for analysingdeterminants of exit time from poverty


Motivation 2

This paper develops an integrated model which can be used toexamine changes in the average exit time from poverty arising fromchanges in:

consumption growthhousehold and community characteristicsthe cost of living of the poorwelfare inequality.

This is done while controlling for spatial random e¤ects

FactMorduch (1998) states that his average exit time measure "It doesnot measure .....average expected duration based on individualspeci�c factors.


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 akalinear random e¤ects model

2 STEP 2: Speci�cation of the individualised and average exit time3 STEP 3: Derivation of marginal/partial e¤ects and elasticities of theexit time


A Regression Based Model of Exit from Poverty 2STEP 1: Linear Random E¤ects Model 1

Household data is hierarchical/multilevel in the sense that householdsare nested in communities.

Households in the same cluster/community are likely to be dependent.

This dependency ) downward biased standard errors) manyspurious signi�cant results (Hox, 1995; Rabe-Hesketh and Skrondal,2008); McCulloch et al., 2008).

Consider the following two level linear additive poverty regression forhousehold i (i = 1....Mj ) in community j (j = 1....J).

ln yij = β0xij + uj + εij (1)

= β0xij + ζ ij


A Regression Based Model of Exit from Poverty 3STEP 1: Linear Random E¤ects Model 2

ln yij is the log of per capita annualized household consumptionexpenditure,

β are coe¢ cients, xij is a set of observed household (or community)characteristics,

uj � N�0, σ2u

�are community-level spatial random e¤ects (random

intercepts),

εij � N�0, σ2ε

�is a household-speci�c idiosycratic error term

The assumptions about uj , and εij imply that ζ ij � N�0, σ2ζ

�, where

σ2ζ = σ2u + σ2ε .

Most importantly, ln yij � N�

β0xij , σ2ζ�


A Regression Based Model of Exit from Poverty 3STEP 2: Average exit time 1

De�nitionI de�ne the exit time for a household (tij ) as the time it will take thehousehold 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 currentconsumption is expressed as (Morduch, 1998):

z = yijetijg (2)

Taking logarithms, and solving for tij gives

tij =ln z � ln yij

g(3)



De�ne a consumption shortfall or excess variable as follows

mij =�gtij if ln z � ln yij > 00 if ln z � ln yij � 0

(4)

The average exit time from poverty for the entire population is foundby taking a weighted average of equation (4) to get

Tg =1g

∑Nij wijmij

∑Nij wij

(5)

=Wg

where W =∑Nij wijmij∑Nij wij

is the Watts Index (Watts, 1968)



Recall ln yij � N�

β0xij , σ2ζ�, and that yij is log normally distributed.

Muller (2001) shows that the parametric formula of the Watts Indexof a log normal variable in discrete form can be expressed as

W =∑Nij wij

�ln z � β0xij

�Φ�ln z�β0xij

σζ

�∑Nij wij

+∑Nij wijσζφ

�ln z�β0xij

σζ

�∑Nij wij

(6)

Where Φ and φ are respectively cumulative and probability densityfunctions of the standard normal distribution, and

H =∑Nij wijΦ

�ln z�β0xij

σζ

�∑Nij wij

(7)



I next introduce the random e¤ects linear regression into the averageexit time from poverty.

Substituting equation (6) into equation (5), gives the average exittime from poverty in terms of regression parameters and independentvariables as follows

Tg =1g

26664∑Nij wij(ln z�β0xij)Φ

�ln z�β0xij

σζ

�∑Nij wij

+∑Nij wijσζ φ

�ln z�β0xij

σζ

�∑Nij wij

37775 (8)


A Regression Based Model of Exit from Poverty 7STEP 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 householdand community characteristics) ∂Tg

∂xijk= �βk

�Hg

�Or elasticity instead) ∂Tg

∂xijk

xijkTg

= �βk∑Nij wijxijk

∑Nij wij

�HW

�3 Changes in within community consumption inequality

) ∂Tg∂σε

= 1g

∑Nij wijφ(uij )

∑Nij wij

> 0

4 Changes in between community consumption inequality

) ∂Tg∂σu

= 1g

∑Nij wijφ(uij )

∑Nij wij

> 0

5 Changes in the poverty line) ∂Tg∂z =

1zgH > 0





Wg 2 < 0


∂xijk= �βk

�Hg


∂xijk

xijkTg


∑Nij wij

�HW

�

3 Changes in within community consumption inequality

) ∂Tg∂σε

= 1g

∑Nij wijφ(uij )

∑Nij wij

> 0


) ∂Tg∂σu

= 1g

∑Nij wijφ(uij )

∑Nij wij

> 0


1zgH > 0





Wg 2 < 0


∂xijk= �βk

�Hg


∂xijk

xijkTg


∑Nij wij

�HW

�3 Changes in within community consumption inequality

) ∂Tg∂σε

= 1g

∑Nij wijφ(uij )

∑Nij wij

> 0


) ∂Tg∂σu

= 1g

∑Nij wijφ(uij )

∑Nij wij

> 0


1zgH > 0


Empirical Application to Malawi 1Context

The economy grew at an average annual rate of 6.2% between 2004and 2007, and surged further to an average growth of 7.5% between2008 and 2011

However, poverty reduction in Malawi has been marginal 7! was52.4% in 2004, and marginally declined to 50.7% in 2011.

A recent re-examination by Beck, Mussa, and Pauw (2014) showsthat the decrease in poverty was much larger than o¢ cially estimated.


Empirical Application to Malawi 2Data description, poverty lines, and variables used

I use the Third Integrated Household Survey (IHS3)

I use an annualized consumption aggregate for each householdgenerated by Beck et al. (2014) as a welfare indicator i.e. thedependent variable

Two area-speci�c utility-consistent poverty lines generated by Beck etal. (2014))MK 37705 for rural areas, and MK 50735 for urban areasThree groups of independent variables are included in the regressionsnamely;

household)demographic,education, agricultural, employment variablescommunity)health infrastructure and economic infrastructureindices) constructed by using multiple correspondence analysis�xed e¤ects variables)agro-ecological zone dummies, seasonalitydummies


Results 1Exit times with 6% growth

Figure 1 . Distribution of exit times when growth is at 6%0

.1.2

.3.4

de

nsi

ty

0 1 0 2 0 3 0e x it t im e

R u ra l U rb a nRichard Mussa (University of Malawi) Exit from Poverty and Policy Analysis 01/07 15 / 24

Results 1Exit 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 longexit times

Rural areas have longer right tail

Minimum exit time: rural 0 years, urban 0 yearsMaximum exit time: rural 30.33 years, urban 17.33 yearsGini coe¢ cient of exit times: rural 0.39, urban 0.54


Results 2Average exit times for di¤erent growth rates

Figure 2. Average exit times for different growth rates

05

10

15

20

Av

era

ge

ex

it t

ime

(y

ea

rs)

0 2 4 6 8 1 0R a te o f g ro w th o f c o n s u m p tio n

R u r a l U rb a n


Results 2Average exit times for di¤erent growth rates

At all growth rates, exit times for urban areas are lower than those forrural areas

The gap however narrows at high growth rates


Results 3Required growth rates to exit within one year and �ve years

Figure 3. Boxplots of required growth rates to exit within one year and five years0

50

10

01

50

20

0 R

eq

uir

ed

gro

wth

(%

)

u rb a n ru ra l

e x it i n 1 y e a r e x it i n 5 y e a rsRichard Mussa (University of Malawi) Exit from Poverty and Policy Analysis 01/07 19 / 24

Results 3Required 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


Results 4Re-distribution and average exit times

Variable Rural UrbanElasticity 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%.


Results 4Re-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 femaleshave 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 timeby a larger amount than employment in the primary and secondaryindustries

In urban areas, improvements in economic infrastructure have a largere¤ect on the exit time than health infrastructure

The reverse holds in rural areas


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 theimpact of the four factors on exit time

CAVEAT: The methods developed here are built around thedimension of time, however, they are still a measure of staticconditions


THANKS!


Exit from poverty and policy analysis: a method and an application to Malawi by Richard Mussa

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