Channing Arndt and Finn Tarp

Print publication date: 2016

Print ISBN-13: 9780198744801

Published to Oxford Scholarship Online: January 2017

DOI: 10.1093/acprof:oso/9780198744801.001.0001

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (www.oxfordscholarship.com). (c) Copyright Oxford University Press, 2018. All Rights Reserved. Under the terms of the licence agreement, an individual user may print out a PDF of a single chapter of a monograph in OSO for personal use (for details see http://www.oxfordscholarship.com/page/privacy-policy).date: 23 July 2018

Estimation in Practice

Chapter:
(p.40) 4 Estimation in Practice
Source:
Measuring Poverty and Wellbeing in Developing Countries
Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198744801.003.0004

Abstract and Keywords

This chapter furthers the discussion by outlining how each approach translates from theory to the practical estimation of poverty/wellbeing. It provides an overview of the specific steps involved in estimation and highlights the analyst’s role in customizing procedures to individual country contexts. The procedures in focus here are implemented via sets of Stata and GAMS code. The code whose default stream is associated with the utility-consistent CBN approach is referred to as the Poverty Line Estimation Analytical Software (PLEASe). The procedure for FOD analysis is called executing FOD (EFOD). The PLEASe and EFOD user guides contain more detailed descriptions of the technical aspects of implementation, such as data requirements and particulars of the code.

4.1 Introduction

Chapters 2 and 3 in this book present the theoretical foundations to the cost of basic needs (CBN) and the first-order dominance (FOD) approaches. This chapter furthers the discussion by outlining how each approach translates from theory to the practical estimation of poverty/wellbeing. In this chapter, we provide an overview of the specific steps involved in estimation and highlight the analyst’s role in customizing procedures to individual country contexts.

The procedures in focus here are implemented via sets of Stata and GAMS code. The code whose default stream is associated with the utility-consistent CBN approach is referred to as the Poverty Line Estimation Analytical Software (PLEASe). The procedure for FOD analysis is called Estimating FOD (EFOD). The PLEASe and EFOD user guides contain more detailed descriptions of the technical aspects of implementation such as data requirements and particulars of the code.

The remainder of this chapter provides an overview of the steps taken in the PLEASe and EFOD code streams. Within this overview, references are made to the country-specific applications of PLEASe and EFOD presented in Part II. These references highlight a few of the methodological challenges encountered in implementation, incorporation of country-specific factors, and considerations in interpreting results, including making comparisons with other poverty analyses.

The default PLEASe approach, which follows the basic CBN methodology, has four notable features. First, the typical consumption pattern of the reference (p.41) population, poor households, is estimated using an iterative procedure to identify which households are deemed poor. Second, the approach allows for the definition of multiple spatial domains. Within these domains, poverty lines are estimated allowing for flexible consumption bundles that vary over time and space, thus accounting for differences in regional and temporal consumption patterns. Third, revealed preference tests are employed to ensure that regional and temporal consumption bundles represent a consistent level of utility. Finally, if these revealed preference conditions fail, a minimum cross-entropy methodology is employed to adjust consumption bundles to satisfy constraints. When calculating poverty lines in multiple periods, data is carried forward to enable both spatial and temporal revealed preference comparisons and for the imposition of both spatial and temporal revealed preference constraints on estimated bundles.

It is important to emphasize that the PLEASe approach and the associated Stata and GAMS code are meant to provide a framework for initiating analysis from an advanced base rather than to prescribe an exact set of methodological choices. The analyst must consider the country environment and perhaps the legacy of existing poverty estimation procedures to tailor the methodology as appropriate. The PLEASe methodology can accommodate a wide range of methodological variation, such as whether to use a single national consumption bundle or regional bundles, whether to impose spatial and/or temporal utility consistency, and a multitude of other choices as well.

4.2.1 Consumption

Poverty estimation begins with the choice of a welfare indicator. Consumption is normally the preferred metric in monetary poverty estimation for a number of reasons. Most importantly, consumption is smoother with fewer fluctuations than income. Additionally, consumption is likely to more effectively capture the welfare derived from self-employment, which is particularly relevant in developing countries where large portions of the population engage in self-employed activities, notably in agriculture.

To account for household composition, the default welfare measure in the PLEASe approach is per capita household consumption. An alternative normalization, using some form of adult equivalent scale, can be implemented with relatively little recoding. For instance, to maintain consistency with official methodologies in Pakistan, Whitney et al. (Chapter 9) employ an adult-equivalent scale rather than per capita consumption.

Deaton and Zaidi (2002) and Deaton and Grosh (2000) detail the assembly of consumption data from household surveys. Consumption provides a measure of the total value of food and non-food consumed, which includes purchases, home-produced items, and gifts received, as well as the use values of (p.42) household durable goods and the imputed rent of owner-occupied housing. As stated in Chapter 2, section 2.3, the consumption measure excludes the value of home-produced services and public goods and services. In the default PLEASe code, household consumption provides the basis for estimating food prices, food consumption bundles, and a non-food allowance. Therefore, the value and quantity of food consumed are required at the household and product level whereas non-food consumption values can be aggregated at the household level.1

Seasonal food price fluctuations imply that purchasing power is not constant throughout the year. Without accounting for seasonality, welfare would appear to be higher during relatively expensive periods when the quantity of food consumed remains constant. When appropriate, the PLEASe methodology incorporates an intra-temporal price index to adjust nominal food consumption values within the survey period.

4.2.2 Poverty Lines

4.2.2.1 Food Poverty Lines

Flexible spatial and temporal food poverty lines are determined by the consumption patterns of poor households in a given domain. The methodology allows consumption bundles and the corresponding poverty lines to be estimated regionally in each time period to allow for variations in prices, preferences, and household composition. When relevant, both flexible and fixed (i.e. previous-period bundles with current-period prices) poverty lines are generated.

As discussed in Chapter 2, estimating regional food consumption improves the specificity of the poverty lines, allowing the poverty lines to reflect regional consumption patterns (Thorbecke 2004). These regional bundles capture the substitution between goods that occurs as prices vary by region. Selecting spatial domains merits careful consideration of factors such as rural and urban distinctions and regional homogeneity in pricing and preferences.

When selecting spatial domains, one must be careful not to overlook sample size in each spatial domain. Note that, in the default implementation of PLEASe, consumption bundles are defined based on the consumption patterns of the poor. Thus, in areas with relatively few poor households, the size of the domain may need to be larger in order to generate a sufficiently large sample of poor households.

(p.43) The analyst is encouraged to err initially on the side of defining too few spatial domains rather than too many. Experience in, for example, Ethiopia (Stifel and Woldehanna, Chapter 5) indicates that division into an excessive number of spatial domains can cause computational difficulties and may, as a consequence, generate nonsensical results. The PLEASe framework allows the analyst to easily change the number of spatial domains in order to conduct sensitivity analysis. Analysis of robust price and consumption differentials, along with sample size, should guide the choice of spatial domain.

Regional food poverty lines are based on four factors: average regional caloric needs; the typical composition of the diet consumed in poor households; the caloric content of this diet relative to regional caloric needs; and the cost of obtaining this diet at prevailing domain-specific prices. For the first factor, the default PLEASe approach estimates an average daily regional caloric requirement based on regional demographics. Specifically, target caloric needs within each spatial domain are adjusted not only according to the gender and age composition of each region, but also according to local fertility rates and the probability of breastfeeding.

For the second factor, identifying the typical food choices and prices relevant to poor households requires a method for determining reference households. For instance, the reference households could be all households with consumption below median consumption or below the previous period’s poverty line. The default PLEASe approach aims to define reference households as those who are deemed poor. However, which households are actually poor is not known a priori. To ensure that the subset of poor households selected is actually poor in terms of the poverty lines drawn by the CBN methodology, an iterative procedure is adopted following Ravallion (1994). Initially, households within each spatial domain are ranked by total per capita daily consumption and an arbitrarily specified bottom percentile of households is selected. This initial bottom percentile should be a best prior estimate of the poverty rate.

Preliminary estimates of regional poverty lines are obtained based on the consumption patterns of this initial set of poor households. A series of steps, described in more detail below in this section, are then performed in order to derive a preliminary estimate of poverty rates. The new bottom percentile is then defined by these poverty rates with the reference set of households becoming those who are defined as poor. This process is repeated until estimated poverty rates converge with the rate determining the reference set of households, which generally occurs within only a few iterations.

Though the default PLEASe method identifies reference households via the iterative procedure, the code is flexible, allowing the analyst to choose alternative approaches. For instance, in their analysis of consumption poverty in Ethiopia, Stifel and Woldehanna (Chapter 5) encounter a failure to converge (p.44) in several regions and thus eliminate the iterative procedure. Whitney et al. (Chapter 9) strive to maintain procedural consistency with official poverty estimates for Pakistan by omitting the iterative procedure and instead identifying reference households as those with consumption in the bottom sixtieth percentile. Note that this approach also has the advantage of setting the sample on which calculations are performed to a fixed value. Beck et al. (Chapter 7) also maintain consistency with the official Malawian methodology by selecting reference households as the bottom sixtieth percentile of consumption on a national basis; however, this is accomplished without eliminating the iterative procedure. Rather, consumption is deflated after each iteration using spatial price indices derived from regional poverty lines, thus altering the regional composition of the bottom sixtieth percentile of households on a national basis.

In each iteration, we determine the set of unit prices (i.e. seasonally adjusted consumption value divided by quantity) prevailing among poor households in each spatial domain. After tossing out the top and bottom 5 per cent of household-level prices, food prices in each spatial domain are calculated as the value share weighted mean price per gram. Specifically, in each spatial domain, household weighted aggregate expenditure is divided by household weighted aggregate quantity. As an alternative, mean and median household unit prices are computed and can be substituted for value share weighted prices. These pricing choices frequently have material impacts on calculated poverty rates and should be held constant both across space and through time.

We also trim the bundles in order to focus on the most commonly consumed food items among the poor. Specifically, the top 90 per cent of food items are selected according to their share of the total food expenditure among all poor households. Eliminating this bottom 10 per cent drops a normally long list of foods consumed by a relatively few households. As the bottom echelon of food expenditures tends to contain expensive calories, we assume that 90 per cent of food consumption represents 95 per cent of caloric intake. In line with the third and fourth of the four factors mentioned above, food quantities are scaled such that bundles attain 95 per cent of regional caloric needs while maintaining food share compositions. Finally, the total cost of purchasing food bundles at local prices is divided by 0.9 to reflect 100 per cent of food expenditures, which yields food poverty lines.

4.2.2.2 Non-Food Poverty Lines

Non-food poverty lines estimate the cost of acquiring non-food items essential to achieving minimum welfare. Attaining a minimum welfare level requires certain basic non-food expenditures necessary for both survival and participation in essential aspects of society such as school and employment (p.45) (Ravallion 1998). Therefore, even what is deemed as essential food consumption may be forgone in order to acquire items such as basic shelter, clothing, and healthcare.

Households with total consumption at or below the food poverty line then, by definition, do not meet their basic food needs as long as some consumption expenditure is allocated to non-food. In other words, these households must sacrifice a basic caloric diet in order to acquire non-food items. Therefore, expenditures on non-food items by these households are considered as required for meeting essential non-food needs. In the default PLEASe methodology, regional non-food poverty lines are estimated to be the average non-food consumption of households with total consumption within 20 per cent of the food poverty line. In calculating this average, a triangular weighting scheme is used to give greater weight to households with total consumption closer to the food poverty line.

This is only one of many methods for setting non-food poverty lines. For example, it may be useful to consider households with food consumption rather than total consumption in the neighbourhood of the food poverty line. In this case, the household meets basic food needs and therefore any non-food spending is at or in excess of what is necessary to achieve minimum welfare. Ravallion (1998) refers to this approach as an upper bound on the non-food poverty line. Beck et al. (Chapter 7) maintain consistency with official estimates by following this upper-bound approach in Malawi. Alternatively, rather than calculate the average non-food consumption of households near the poverty line, one could calculate average food shares of total consumption for those with either total consumption or food consumption near the food poverty line. Food shares would then be used to scale the food poverty line to obtain the total poverty line. Each of these approaches may be preferred in a given country context and can relatively easily be implemented with a few lines of recoding.

4.2.3 Poverty Measurement

The total poverty line is the sum of the food poverty line and the non-food poverty line and serves as a threshold for separating poor and non-poor households. From these regional poverty lines, regional poverty rates are derived using the Foster Greer Thorbecke (FGT) class of poverty measures (Foster et al. 1984).

In the iterative procedure for estimating poverty lines, the regional poverty headcount rates calculated as discussed in section 4.2.2 provide an updated estimate of the percentile of per capita consumption that identifies a household as poor. It is now possible to redefine the reference set of poor households and to identify new consumption bundles, prices, and corresponding poverty (p.46) lines. This iterative procedure is repeated a default of five times. After five iterations, it is normally the case that the poverty rates calculated in iteration four are very close to the poverty rates calculated in iteration five. This convergence implies that the estimated food and non-food bundles are based on the consumption patterns of the poor. However, convergence is not guaranteed even with a very large number of iterations. Graphs are produced to provide a visual check of convergence. Analysts are strongly encouraged to verify convergence. If convergence fails, the analyst would then be forced to choose an arbitrary share of the population as the reference population.

4.2.4 Utility Consistency

Having identified a set of regional poverty lines based on the consumption patterns of the poor, the PLEASe methodology addresses the possibility that, while the poverty lines provide a measure of welfare in each region, they may not provide a consistent measure of welfare levels across regions or through time. Utility consistency is assessed by testing revealed preference conditions on the food consumption bundles and prices obtained in the final iteration. Prior to conducting these tests, the bundles are rescaled to provide a constant level of calories across regions (and through time). Should the bundles fail revealed preference tests, the first step is to consider why this may be the case. This is particularly true if failures are widespread and/or of very large magnitude. An error may have entered into the calculations or data. Errors in units are particularly common. If a quantity in a bundle is in grams and its associated price is in currency units per kilogram, then this error has the potential to severely bias estimates.

Aside from checking for errors, the analyst should also consider whether any additional information can be brought to bear in order to arrive at improved estimates. This hunt for additional information is highly consistent with the philosophy of estimation that underlies the minimum cross-entropy procedure presented in Chapter 2, section 2.5. The philosophy of estimation is to impose all available information and nothing more.2 Once all available information has been exploited, the minimum cross-entropy estimation approach can be justifiably applied to adjust consumption bundles to satisfy revealed preference conditions as well as calorie requirements.

Within the minimum cross-entropy procedure, spatial revealed preference conditions are as in equation (2.4a) in Chapter 2 and reproduced in equation (4.1). Temporal conditions are illustrated in equations (4.2) and (4.3). In the (p.47) case where temporal conditions are applied, they are simply added to the constraint set of the optimization problem depicted in Chapter 2, equation 2.4.

$Display mathematics$
(4.1)

$Display mathematics$
(4.2)

$Display mathematics$
(4.3)

In these equations, i indexes food products; r and its alias, s, represent the set of spatial domains; and, p1, p2, q1, q2 represent prices and quantities in the first and second time period. The logic of the temporal constraints is the same as the logic of the spatial bundle. Consider equation (4.3), for example: this condition states that the bundle chosen in period 2 in region r when evaluated at period 1 prices must, by minimization, cost at least as much as the bundle that was actually chosen when period 1 prices prevailed, assuming the bundles provide the same level of utility. The analyst can choose to impose spatial constraints, spatial and temporal constraints, or bypass utility consistency and impose no constraints.3

After entropy-adjusting quantities to obtain utility-consistent food bundles, the bundles are evaluated at the regional food prices obtained in the final iteration. New non-food poverty lines are estimated using the same approach as applied in the iterative procedure. The utility-consistent total poverty line in each domain is the sum of the utility-consistent food poverty line and the updated non-food poverty line. From here, final FGT poverty measures and spatial price indices are computed.

Note that the default PLEASe approach sequentially ensures temporal constraints are met. Consider an analysis of three surveys undertaken in different time periods. First-period poverty lines are estimated imposing only the regional revealed preferences constraint (equation 4.1) because there are no pre-existing bundles. Second-period poverty lines should be utility-consistent between regions (equation 4.1) as well as the first and second periods (equations 4.2 and 4.3), which is achieved by leaving first-period food bundles intact and adjusting second-period bundles to satisfy all three constraints. Finally, third-period utility consistency involves testing revealed preferences spatially as well as between the second and third periods (not the first) and adjusting only third-period food bundles. As emphasized, these are the default settings, not a prescription for how things should be done in every case.

(p.48) 4.3 EFOD

This section considers the estimation of multidimensional poverty and presents the implementation of FOD and its associated package of Stata and GAMS code, EFOD. Compared to poverty line estimation with the complexities of assembling consumption data and the array of choices possible throughout the PLEASe approach, EFOD is relatively easy to implement. In contrast, EFOD requires significant effort in determining which indicators to use and somewhat more effort in interpreting results. Briefly, the procedure involves three key stages: creating indicators, operationalizing FOD, and interpreting results.

4.3.1 Indicators

The heart of FOD analysis involves carefully assembling a set of binary welfare indicators. This process involves several key steps. First, one requires data. This can come in the form of Demographic and Health Surveys, census data, or data from living standards measurement (LSMS-type) surveys, among other possibilities.

Second, one must organize the data into populations and then into groups whose welfare levels one would like to compare. There are enormous possibilities for populations and division into groups. An example of a population to study might be children aged 0–5. This population could be grouped by gender, province, and time period. One would then be setting up to examine whether, for example, girls aged 0–5 in province A at time T are better off than boys aged 0–5 in province A at time T alongside many other possible permutations. A second population example could be households and subsequent groups determined by the ethnicity of the household head. One would then be setting up to examine whether households headed by ethnic group A are better off than households headed by ethnic group B and so forth.

Third, one must define welfare indicators. As noted, proper definition of indicators is critical. The indicators must apply to the population in question. If the population is children aged 0–5, then an indicator like school attendance is not relevant because children that young typically do not attend school. School attendance would more properly apply to the population of children aged 7–17. For children aged 0–5, relevant indicators often include anthropometric data, education level of the mother or primary caretaker, proximity and/or use of health services, and other similar indicators.

Note that FOD analysis requires each observation to have non-missing values in all indicators, which could eliminate particular indicators from consideration. For example, immunization histories are often collected only (p.49) for children under two, thus prohibiting the use of an immunization indicator when analysing children aged 0–5. In a discussion of child and woman indicators in Tanzania, Arndt et al. (Chapter 14) further explore indicator choices for subpopulations.

Mahrt and Nanivaso (Chapter 11) address an additional consideration in selecting indicators—the potential for different patterns of deprivation across indicators to result in indeterminate outcomes. FOD dominance requires superior welfare outcomes to be manifested throughout the population and across indicators. While this property generates robust results, in some cases it may lead to high levels of indeterminacy. For example, if rural and urban deprivation in a given indicator is significantly different from of the deprivation pattern in all other indicators, FOD comparisons are likely to result in a high degree of indeterminate outcomes. This is seen in the inclusion of a bed net indicator in FOD analysis in the Democratic Republic of Congo (Chapter 11) and a shared sanitation facility indicator in Zambia (Mahrt and Masumbu, Chapter 15). In such cases the contribution of the indicator must be weighed against the resulting inability to clarify differences.

Setting thresholds within each indicator to separate the poor from the non-poor requires a careful balance of policy goals, data availability, and consistency between time periods. It is important to highlight that, while the FOD procedure admits in principle ordinal data, in practice, EFOD is coded to consider only binary data. Hence, one might classify children aged 0–5 who are any one of stunted, underweight, or wasted as deprived (0) in the anthropometrics dimension and all others as not deprived (1). Similarly, one might consider children whose primary caretaker has completed at least primary school as not deprived and all others as deprived. As will be discussed in subsequent chapters, these thresholds (e.g. completed primary school) are often important determinants of results and should be considered carefully.4 The end result should be a dataset where each member of the population is an observation. Variables identify the group to which this population member belongs and the welfare status (deprived or not deprived) of the population member for each chosen welfare indicator.

Finally, one must consider the number of binary indicators to employ for the analysis. Note that the number of permutations of welfare states increases by a factor of two with the addition of each indicator. Specifically, there are 2N permutations where N is the number of indicators chosen. There are trade-offs here. More indicators imply a broader analysis. At the same time, more indictors lead to many more permutations, eventually resulting in a very small (p.50) number of observations occupying certain permutations even for very large datasets. For example, if one chooses to make comparisons on the basis of seven indicators, there are then 27=128 possible permutations. Example permutations include those deprived in all indicators {0,0,0,0,0,0,0}, those not deprived in all indicators {1,1,1,1,1,1,1}, those not deprived in indicator one and deprived in all other indicators {1,0,0,0,0,0,0}, and so forth (125 additional permutations). Because of this ‘curse of dimensionality’, the available code handles only up to seven indicators. Further, because we are often making comparisons between specific subgroups (e.g. children aged 0–5 in region A at time T versus children aged 0–5 in region B at time T), the number of observations for these groups may be insufficient to adequately populate 128 permutations. In practice, five dimensions are often chosen, resulting in 25=32 permutations.5

4.3.2 Implementing EFOD

Once a dataset specifying populations, groups, and indicators is assembled, it is straightforward to collapse the data to show means as well as the shares of each group by permutation. For example, with five welfare indicators, mean values of .10, .52, .31, .29, .33 respectively for girls in region A and time T would indicate that 10 per cent of girls in that region and time period are not deprived in indicator one, 52 per cent are not deprived in indicator two, and so forth.

Each permutation also has a corresponding share. If 1 per cent of girls aged 0–5 in region A and at time T are not deprived in any dimensions, then the permutation (1,1,1,1,1) has the corresponding value or share 0.01. Note that each permutation thus corresponds to a particular welfare state. Within each subpopulation, the sum of shares across the thirty-two welfare states (permutations) should be equal to one. This procedure generates the distributions for each subpopulation.

To conduct the FOD analysis, these distributions for all subpopulations to be compared are fed into a GAMS program that implements the linear programming approach to determining FOD presented in Chapter 3. This generates one set of comparisons using the original data. The option exists to draw bootstrap samples from the original data in order to run a much larger number of comparisons, producing an estimated probability of domination.

(p.51) 4.3.3 Output and Interpretation

A series of outputs are automatically generated and presented in three sets of tables consisting of means, shares, and FOD results. Spatial FOD results make comparisons across groups (e.g. girls in region A compared with region B) within a single time period. Temporal results compare each group to itself across time periods. Both spatial and temporal results are presented for the original data (static) and the bootstraps. In static results, 1 indicates dominance and 0 indicates indeterminacy. Bootstrap results indicate the probability of domination over all bootstrap samples. The probability that A dominates B is defined as the number of times A dominates B divided by the number of samples. Recognizing that A can dominate B as well as B dominate A, the probability of net domination measures the probability that A dominates B less the probability that B dominates A. The probability of net domination falls in the interval [−1,1]. Spatial rankings are generated based on a Copeland approach, which is described in Chapter 3. In effect, the Copeland approach calculates the average probability that a given area net dominates all other areas. Care must be taken in interpreting the subset of ranking results where differences in probabilities of domination are very small. In these cases, results are highly sensitive to small perturbations introduced through bootstrap sampling.

Interpreting FOD results may require more investigation than simply glancing over tables. Indeterminate results generally occur when two groups are either very different or very similar. For example, if few areas show signs of advancement or regression over time, it is worth the effort to determine the source of stagnation. Examination of indicator means may shed light on the source of stagnation. A given area may not rigorously progress for dynamic reasons, such as good progress in some indicators and regress in others. Alternatively, very little may have happened over time in any indicator and the FOD analysis is simply reflecting this lack of progress. Finally, recall that FOD results depend on the full distribution of indicator outcomes. Thus, it is possible for a region to progress on average through time but for FOD to result in an indeterminate outcome. Such a result would suggest that the region’s seemingly superior performance did not extend to all segments of the population. In sum, dominant outcomes are strong indicators of broad-based progression throughout the population.

We turn now to a series of practical applications in Part II.

References

Bibliography references:

Deaton, A. and M. Grosh (2000). ‘Consumption’, in M. Grosh and P. Glewwe (eds), Designing Household Survey Questionnaires for Developing Countries: Lessons from Ten Years of LSMS Experience. Washington, DC: World Bank, 91–133.

(p.52) Deaton, A. and S. Zaidi (2002). ‘Guidelines for Constructing Consumption Aggregates for Welfare Analysis’, Living Standards Measurement Study Working Paper No. 135. Washington, DC: World Bank.

Foster, J., J. Greer, and E. Thorbecke (1984). ‘A Class of Decomposable Poverty Measures’, Econometrica, 52(3): 761–5.

Hussain, M. A., M. M. Jørgensen, and L. P. Østerdal (2015). ‘Refining Population Health Comparisons: A Multidimensional First Order Dominance Approach’, Social Indicators Research. Available online: DOI: 10.1007/s11205-015-1115-2

Ravallion, M. (1994). Poverty Comparisons. Geneva: Harwood Academic Publishers.

Ravallion, M. (1998). ‘Poverty Lines in Theory and Practice’, Living Standards Measurement Study Working Paper No. 133. Washington DC: World Bank.

Robinson, S., A. Cattaneo, and M. El-Said (2001). ‘Updating and Estimating a Social Accounting Matrix Using Cross Entropy Methods’, Economic Systems Research, 13(1): 47–64.

Thorbecke, E. (2004). ‘Conceptual and Measurement Issues in Poverty Analysis’, WIDER Discussion Paper 04. Helsinki: UNU-WIDER.

Notes:

(1) When quantities of food consumed are not available, food prices from other sources may be substituted in analysis provided that they are collected for a sufficiently wide variety of foods and at a sufficiently detailed regional level to adequately capture price variation.

(2) See Robinson, Cattaneo, and El-Said (2001) for a discussion and further references.

(3) The existence of viable prices to operationalize revealed preference tests is sometimes an issue. For example, region A may consume a particular type of dried fish, but region B does not consume that particular type at all or only very rarely. The price of dried fish in region B is thus not known. The default PLEASe solution is to apply the maximum price observed in any spatial domain to region B. This default may or may not be appropriate, depending on country and region circumstances.

(4) Survey data may not allow indicator thresholds to align with policy goals or perceptions of deprivation. Chapters 13 and 15 explore the impact of indicator thresholds, in analyses of household welfare in Nigeria and Zambia, respectively.

(5) If the dimensions can be naturally grouped, one may initially collapse related dimensions into a single dimension and then (sequentially) refine dimensions. For more details and an illustration of such an approach, see Hussain et al. (2015).