"With the focus of international development resources increasingly turned toward poverty reduction, the demand for reliable empirical estimates of poverty levels has grown dramatically... This paper contributes to the poverty measurement literature by introducing an information theoretic approach to assuring the utility consistency of poverty lines. Even though the philosophical roots of information theory and the links between information theory and other estimation criteria fill volumes, the actual practical application of the approach is quite straightforward." From TextPoverty lines ,Poverty alleviation ,Development projects Evaluation ,measurement ,Entropy estimation ,

Arndt, Channing

Simler, Kenneth R.

English

Research Papers in Economics

 
Discussion Paper 154 
 
 
 
 
 
ith the focus of international development 
resources increasingly turned toward poverty 
reduction, the demand for reliable empirical 
estimates of poverty levels has grown dramatically. Gov-
ernments and donors are particularly interested in making 
valid poverty comparisons across space and through time. 
In many poor countries, failure to reduce poverty would 
likely catalyze calls for policy reform and reconsideration 
of donor assistance levels. 
In fluid developing country environments, generating 
these comparisons is challenging. But reasonably precise 
measures of poverty levels and changes in poverty levels 
through time are needed. 
This paper contributes to the poverty measurement 
literature by introducing an information theoretic 
approach to assuring the utility consistency of poverty 
lines. Even though the philosophical roots of information 
theory and the links between information theory and other 
estimation criteria fill volumes, the actual practical appli-
cation of the approach is quite straightforward. 
For the case of Mozambique, the approach permits 
estimation of poverty measures based on utility-consistent 
poverty lines, despite substantial changes in relative 
prices and consumption patterns over the period 1996–97 
and 2002–03. Relative to other approaches, the entropy-
adjusted “Cost of Basic Needs” (CBN) bundles provide 
more credible results, with the larger adjustments con-
forming to available information on correlates of poverty 
such as asset ownership. Utility consistency substantially 
enhances the credibility of the results obtained and should 
facilitate welfare comparisons in the future. 
Overall, we conclude that this approach for estimating 
utility-consistent bundles represents a 
powerful addition to the poverty 
analyst’s tool kit and enhances the 
attractiveness of the CBN approach for 
practical poverty measurement problems. 
Consistency of Poverty Comparisons 
The poverty line is an essential element 
in most poverty analysis. It is the cost of attaining a 
minimum acceptable level of well-being, or utility. Since 
poverty lines are intended to reflect a fixed standard of 
living, they will vary over space and time with changes in 
the cost of basic necessities. Adjusting for spatial and 
temporal differences in the cost of reaching a basic 
standard of living is fundamental in poverty analysis. 
Although poverty lines are sometimes criticized as 
artificial dividing lines separating the poor and nonpoor, 
this overlooks their more important function: they serve 
as low-income cost-of-living indices that permit consis-
tent poverty comparisons across space and over time. 
Recent evidence from countries as diverse as Russia, 
Papua New Guinea, and Mozambique has shown that the 
widely accepted CBN method for setting poverty lines 
often yields poverty lines that are utility inconsistent. That 
is, the standard of living associated with the poverty line 
is not held fixed in real terms, rendering poverty com-
parisons unreliable. 
This paper draws upon information theory and 
revealed preference conditions of consumer theory to 
propose a method of adjusting CBN poverty lines to 
ensure utility consistency. 
Methodology and Data 
Previous studies in Mozambique employed the CBN 
approach to set poverty lines, using data from the 1996–
97 national household survey to specify separate poverty 
lines for 13 different regions in Mozambique. Because the 
relative prices for basic commodities vary considerably 
by locale, the basic needs bundle was allowed to vary by 
region as well, reflecting both the consumption choices 
and prices faced by poor households. 
A second national household survey was conducted in 
2002–03. An important objective of the second survey 
was to update the poverty lines to capture the change in 
prices over the intervening six years, and to update esti-
mates of poverty levels in Mozambique. The two surveys 
showed that relative prices of basic food items vary not 
only regionally, but also over time. Predictably, house-
holds adjust their consumption 
patterns in response to changing 
prices. Therefore, simply apply-
ing the 2002–03 prices to the 
quantities specified in the 1996–
97 CBN bundles is likely to 
produce poverty lines that 
correspond to a higher level of 
utility than the 1996–97 poverty lines, because they 
ignore the substitution effects associated with changes in 
prices. 
Four alternative methods for updating the poverty 
lines were examined. The first was the “naïve” approach 
outlined above, based on the cost of the original 13 
bundles from 1996–97 when evaluated at 2002–03 prices. 
The second  method  explored the  potential  magnitude of  
W 
 
Discussion Paper BRIEFS 
Food Consumption and Nutrition Division of the International Food Policy Research Institute 
Discussion Paper 189 
Estimating Utility-Consistent Poverty Lines 
Channing Arndt and Kenneth R. Simler 
Ensuring the utility consistency 
of poverty lines enhances the 
reliability of poverty estimates 
and facilitates future welfare 
comparisons.  
consumer substitution effects on poverty lines by allow-
ing the composition of the CBN bundles to vary between 
the two surveys, assuming a Cobb-Douglas functional 
form for consumer preferences. The third method derived 
new bundles based on consumption patterns observed in 
the 2002–03 data, without reference to the CBN bundles 
derived from the 1996–97 survey. 
The fourth method introduces the innovation that 
provides the most consistent and reliable poverty lines. 
The results of the third method are subjected to a set of 
revealed preference tests, which indicate whether the 
CBN consumption bundle in one period or region is 
inferior to that specified for a different period or region. 
Numerous violations of revealed preference conditions 
were detected, implying that the CBN poverty lines did 
not represent a fixed standard of living, and that poverty 
comparisons based on such lines are inconsistent. To 
make them consistent, we employ entropy estimation 
methods, which are motivated by information theory. In 
particular, we approach the composition of the poverty 
line bundles as a minimum cross entropy (CE) 
optimization problem. In this problem, the budget shares 
observed in the data serve as prior information about the 
likely parameter values, and the revealed preference 
conditions enter as constraints on the possible values that 
the parameters can take. The solution to the problem is 
the set of budget shares that conforms to the system’s 
constraints and minimizes the CE function. These are the 
budget shares that are as close as possible (in terms of 
entropy distance) to the original budget shares while 
obeying the revealed preference constraints. 
Results 
It was estimated that in 1996–97, 69 percent of 
Mozambicans lived below the poverty line. Poverty levels 
were lower in 2002–03 regardless of the method used to 
set poverty lines, although the choice of method affects 
the magnitude of estimated poverty reduction. As 
expected, the first method, which does not allow for con-
sumer substitution in response to price changes, yielded 
the highest poverty lines and poverty levels, with a 
headcount ratio estimate of 63 percent. The second 
method, which assumes Cobb-Douglas preferences, pro-
duced a headcount estimate of 52 percent. The third 
method, i.e., updating the CBN bundles to reflect changed 
prices and consumption patterns but not imposing re-
vealed preference constraints, generated the lowest 
poverty headcount estimate, at 48 percent. 
The fourth method, which ensures utility consistency 
of the poverty lines using the entropy estimation 
approach, estimates the national headcount at 54 percent. 
The increase in estimated poverty when utility con-
sistency is imposed is driven in large part by adjustments 
to the CBN bundle in rural Nampula Province, which 
comprises more than 10 percent of the country’s popula-
tion. From several perspectives, the consumption bundles 
and poverty estimates using the utility-consistent poverty 
lines are more credible, and correspond more closely with 
information available about correlates of poverty, such as 
asset ownership. 
Although the various poverty line methods differ in 
the magnitude of estimated poverty reduction, the qualita-
tive story in terms of directions of movement compared 
with the levels estimated for 1996–97 is robust, especially 
for the three approaches that allow for consumer substitu-
tion effects between the two survey periods. Regardless of 
the poverty line methodology employed, poverty levels 
declined substantially nationwide, with poverty reduction 
occurring more rapidly in rural areas than in urban areas. 
The utility-consistent estimates derived from the adjusted 
bundles present, in our view, the preferred estimates. 
 
Keywords: poverty lines, entropy estimation, revealed 
preferences, Mozambique 
 
 
Copyright © 2005 International Food Policy Research Institute. The full text of this document and other FCND Discussion 
Papers are available on our Website (www.ifpri.org/divs/fcnd/dp.htm) or via M.Aspillera@cgiar.org 
 
 
 
FCND BRIEFS 
 
 
 
 
 
 
 
 
 
 
2033 K Street, N.W. 
Washington, D.C. 20006 U.S.A. 
 
Ensuring the utility consistency of poverty lines enhances 
the reliability of poverty estimates and facilitates future 
welfare comparisons.—DP189 

Estimating utility-consistent poverty lines

http://www.ifpri.org/sites/default/files/publications/fcnbr189.pdf

Estimating utility-consistent poverty lines

Abstract

Similar works

Full text

Available Versions

Research Papers in Economics