metadata: authors: 0: author: Dang,Hai-Anh H.
1: author: Jolliffe,Dean Mitchell
2: author: Carletto,Calogero
count: World
docna: 0: docna: Data gaps, data incomparability, and data
            imputation : a review of poverty measurement methods for
            data-scarce environments
docty: Policy Research Working Paper
theme: Poverty strategy, analysis and monitoring,Economic statistics, modeling and forecasting
majtheme: Social protection and risk management,Economic management
subtopic: Inequality,Poverty Diagnostics,Poverty Monitoring & Analysis,Poverty Lines,Poverty Impact Evaluation,Small Area Estimation Poverty Mapping,Poverty Assessment,Educational Sciences,Labor & Employment Law,Demographics
teratopic: Poverty Reduction,Education,Law and Development,Health, Nutrition and Population
abstracts: cdata!: This paper reviews methods that have
            been employed to estimate poverty in contexts where
            household consumption data are unavailable or missing. These
            contexts range from completely missing and partially missing
            consumption data in cross-sectional household surveys, to
            missing panel household data. The paper focuses on methods
            that aim to compare trends and dynamic patterns of poverty
            outcomes over time. It presents the various methods under a
            common framework, with pedagogical discussion on the
            intuition. Empirical illustrations are provided using
            several rounds of household survey data from Vietnam.
            Furthermore, the paper provides a practical guide with
            detailed instructions on computer programs that can be used
            to implement the reviewed techniques.
repnme: repnme: Data gaps, data incomparability, and data
            imputation : a review of poverty measurement methods for
            data-scarce environments
display_title: Data gaps, data incomparability, and
            data imputation : a review of poverty measurement methods
            for data-scarce environments
listing_relative_url: /research/2017/12/29285218/data-gaps-data-incomparability-data-imputation-review-poverty-measurement-methods-data-scarce-environments
topicv3: Poverty m1326687 695,Poverty Measurement and Analysis m1326941 707,Demographic Change m1327040 1448,Education m1327048 470,Household Surveys m1504071 2761
publishtoextweb_dt: 2017-12-19T00:00:00Z
historic_topic: Poverty Reduction,Education,Law and Development,Health, Nutrition and Population
no_of_pages: 65
author_keys: 0: author_key: 747967
1: author_key: 773551
2: author_key: 550790
model_extractions: WPS8282 Policy Research Working Paper 8282 Data Gaps, Data Incomparability, and Data Imputation A Review of Poverty Measurement Methods for Data-Scarce Environments _Hai-Anh Dang Dean Jolliffe Calogero Carletto_ Development Economics Development Data Group December 2017
Policy Research Working Paper 8282

# **Abstract**

This paper reviews methods that have been employed to estimate poverty in contexts where household consumption data are unavailable or missing. These contexts range from completely missing and partially missing consumption data in cross-sectional household surveys, to missing panel household data. The paper focuses on methods that aim to compare trends and dynamic patterns of poverty outcomes over time. It presents the various methods under a common framework, with pedagogical discussion on the intuition. Empirical illustrations are provided using several rounds of household survey data from Vietnam. Furthermore, the paper provides a practical guide with detailed instructions on computer programs that can be used to implement the reviewed techniques.

This paper is a product of the Development Data Group, Development Economics. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The authors may be contacted at hdang@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
**Data Gaps, Data Incomparability, and Data Imputation: A Review of Poverty Measurement Methods for Data-Scarce Environments**

Hai-Anh Dang, Dean Jolliffe, and Calogero Carletto<sup>*</sup> Key words: poverty, mobility, imputation, consumption, wealth index, synthetic panels, household survey JEL: C15, I32, O15

* Dang (hdang@worldbank.org; corresponding author) is an economist in the Survey Unit, Development Data Group, World Bank, and a non-resident senior research fellow with Vietnam’s Academy of Social Sciences; Jolliffe (djolliffe@worldbank.org) is a lead economist in the Survey Unit, Development Data Group; Carletto (gcarletto@worldbank.org) is the manager of Center for Development Data, Rome, Italy. All authors are with the World Bank. We would like to thank Alemayehu Ambel, Andrea Brandolini, Grant Cameron, Shatakshee Dhongde, Sam Freije-Rodriguez, John Gibson, Peter Lanjouw, Haizheng Li, Michael Lokshin, David Newhouse, Franco Peracchi, Kinnon Scott, Jacques Silber, Alessandro Tarozzi, Renos Vakis, and participants at the China meeting of the Econometric Society (Wuhan) and seminars at Georgia Tech and World Bank for helpful discussions on earlier versions. We are grateful to the UK Department of International Development for funding assistance through its Knowledge for Change (KCP) Research Program.
# **I. Introduction**

Poverty reduction consistently ranks among the most prioritized tasks of developing countries as well as the international community. For example, the Sustainable Development Goals (SDGs) recently adopted by the United Nations General Assembly call for eliminating poverty by 2030 in its very first goal. But effective and efficient poverty eradication entails the prerequisite of accurate poverty measurement, since it would be hardly possible to claim progress with decreasing poverty—or perhaps good performance with diminishing just about almost all other undesirable phenomena—if we cannot measure it well.

Three questions usually come up in the context of poverty measurement. The first question concerns, unsurprisingly, what represents the best yardstick that reliably measures poverty. For example, should it be household consumption (or income), or household wealth? Second, once we have a good poverty measure, how best to track the trends of poverty over time? Put differently, it is useful to understand the issues that can potentially affect the comparability of poverty estimates over time. Finally, what are the composition of poverty transitions over time? In particular, what is the proportion of the poor in one period that remain poor or escape poverty in the next period? Or what is the proportion of the non-poor that fall into poverty in the next period?

A sizable literature exists on the first question, and some consensus has perhaps been reached that household consumption data can be employed as a good proxy for household living standards—thus such data can provide the types of poverty estimates that are often sought.<sup>1</sup> Yet, the implementation of this idea in practice still remains a challenging task; we thus focus in this

> 1 Throughout this paper we are focused primarily on consumption as this is the measure of well-being that is most frequently used in the world for assessing poverty status, but we also note that income is used as a measure of wellbeing in many cases. For example, the 2012 global poverty estimates reported in Ferreira _et al._ (2016) are based on data from 131 countries, of which 99 use consumption as the measure of well-being and 32 use income. In an abuse of terminology, we refer to “consumption” and “income” interchangeably as the measure of household living standards in this paper. See also Ravallion (2016) for a comprehensive discussion on the history of thought on poverty and other measurement approaches.

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paper on the remaining other questions. The main reason is simply that household consumption data are often either unavailable, or infrequently collected, particularly for low-income countries.

Using the World Bank’s PovCalNet database, which covers the period 1981-2014, we plot in Figure 1 the number of data points of poverty estimates against a country’s income level (as measured by its consumption level in the household survey). For better presentation, we also graph the fitted line for the regression of the former outcome on the latter outcome. The estimated slope of this regression line is positive and strongly statistically significant, suggesting that countries with higher incomes more frequently implement household surveys. Indeed, a 10 percent increase in a country’s household consumption is associated with almost one-third (i.e., 0.3) more surveys. Figure 1 thus helps highlight the—perhaps paradoxical—fact that poorer countries with a stronger need for poverty reduction also face a more demanding challenge of poverty measurement given their smaller numbers of surveys. This is unsurprisingly consistent with a prevailing perception among some development practitioners that collecting survey data may not be the top priority for many developing countries (see, for example, Devarajan (2013)).

The observed pattern between missing data and national income is also particularly relevant for assessing methods to fill data gaps. As one example, the World Bank monitors the global headcount of people living in extreme poverty and these counts are used by many institutions, including the United Nations, previously for the purposes of monitoring the Millennium Development Goals, and now the Sustainable Development Goals.<sup>2</sup> Jolliffe _et al._ (2015) indicate that the approach used by the World Bank to imputing poverty rates for those countries with missing poverty data is simply to assume that the data are missing at random within each region. So, if poverty data are missing for the Democratic People’s Republic of Korea, the global poverty

> 2 For recent examples of the literature documenting the World Bank’s global poverty counts, see Ravallion, Chen and Sangraula (2009) and Ferreira _et al._ (2016).

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headcount assumes that the rate of poverty in the Democratic People’s Republic of Korea is the average poverty rate in East Asia. The systematic correlation between missing survey data and national income observed in Figure 1 suggests that the assumption of missing at random is untenable, and can result in a downward bias in the global poverty count.

While the availability of household consumption surveys is essential for tracking poverty, the quality of these surveys is no less important. In particular, where household consumption data are available, it should not be taken for granted that these data are comparable over time. For example, Serajuddin _et al._ (2015) find that over the period 2002- 2011, almost one-fifth (i.e., 28) of the 155 countries for which the World Bank monitors poverty data using the WDI database have only one poverty data point.<sup>3</sup> As another example, a recent survey by Beegle _et al._ (2016) points out that just more than half (i.e., 27) of the 48 countries in Sub-Saharan Africa had two or more comparable household surveys for the period between 1990 and 2012. Even countries with a respectable and long-running household survey such as India from time to time run into issues with survey comparability (Deaton and Kozel, 2005; Dang and Lanjouw, forthcoming).<sup>4</sup> Perhaps this lack of survey comparability may be ameliorated if (better) data can be produced more frequently.

A less rosy picture emerges with panel survey data, where far fewer developing countries can afford to collect such data. Tracking the same household (or individual) over time is a costly undertaking for various reasons. For example, households can grow larger with new members (through birth or marriage) or smaller (with previous members dying or migrating) over time, or the whole household can migrate, making it more difficult for interviewers to follow them.

> 3 In addition, Serajuddin et al. (2015) also find that as many as 29 countries do not have any poverty data point in the same period.

> 4 Household consumption data may not exactly be comparable across different countries without a common conversion system for prices of goods and services. The International Comparison Program (ICP) is an international effort to address this issue (World Bank, 2015). See also Crossley and Winter (2015) and the 2015 special issue of the _Journal of Development Studies_ for further discussion on survey comparability issues.

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Consequently, even where panel data exist, the estimates of poverty mobility based on these panel data are often found to be affected by various data quality issues such as national representativeness or cross-country comparability.<sup>5</sup> Still, financial constraints aside, it is common knowledge that a certain level of technical and logistical capacity is required to implement a high-quality consumption survey. For example, fielding an LSMS-type (Living Standards Measurement Survey) household survey is a demanding task that often involves a number months—if not years—of preparation, which consists of a variety of steps ranging from pre-survey stages (e.g., questionnaire design, sample selection, enumerator training, survey firm selection) to post-survey stages (e.g., data entry, data cleaning and checking, post-survey weighting or stratification).<sup>6</sup> Put differently, available resources may provide the necessary condition, but it is technical/ logistical capacity that forms the sufficient condition for producing high-quality survey data. The latter issue is perhaps a common challenge for which most national statistical agencies are keen on finding a solution.

Furthermore, development practitioners working on smaller-scale projects have been more and more interested in collecting consumption data, say, for project evaluation purposes. Such projects more often than not lack the financial and technical resources, nor the intention, to implement an LSMS-type regular household consumption survey. But properly evaluating such projects would clearly rely on good-quality consumption data. As such, data gaps and the need to come up with innovative measurement methods—particularly those that can be implemented at scale—to fill in these gaps are increasingly receiving more attention.

> 5 Beegle _et al._ (2016) offer a review of studies that use the existing panel data for African countries and find much variation in the estimates for chronic poverty and transient poverty. Furthermore, it is argued that a considerable proportion of these estimates of poverty mobility are subject to measurement errors in income or consumption (Dercon and Krishnan, 2000; Glewwe, 2012; Lee _et al._ , 2017). See also Dercon and Shapiro (2007) for a brief discussion of various panel data sources for developing countries.

> 6 See Grosh and Glewwe (2000) for a systematic treatment of the different steps involved in fielding an LSMS-type survey.

5
We make several contributions in this paper. On the conceptual front, we offer a review of methods that have been employed to provide estimates of welfare in the absence of consumption data, with a particular focus on comparing trends of poverty outcomes over time. Since the existing studies are presented in a variety of formats and technical approaches, we attempt to consistently present these various methods, some new and some more established, under a common framework. For this purpose, we provide some rather simple, but new theoretical results to help fix ideas for better discussion and also to highlight the nuanced differences between the methods that appears to have received scant, if any, attention in previous studies. For example, most development practitioners would likely implement a full-fledged household consumption survey—if given this choice—to produce poverty estimates, rather than attempt to do so using household assets alone. But to our knowledge, there has been no formal discussion to provide insights into this choice, and possibly other similar choices as well. Our paper attempts to fill in this gap in the literature by offering a review on poverty imputation methods.

Furthermore, we focus on providing the intuition behind each estimation method in an effort to make these techniques accessible to a larger audience. For this objective, we refer to the most important theoretical results in the text, and offer a more detailed technical discussion of these results in Appendix 1. In addition, we mostly review the economics literature in this paper, but will also refer to the statistics literature where it is relevant.

On the empirical front, we provide illustrations using real household survey data from Vietnam. We also offer a practical guide in an appendix offering detailed instructions on computer programs (mostly in Stata) that can be used to implement the reviewed techniques. In an effort to make these methods more accessible, and where there is not yet an established literature, we also aim to provide more specific—and somewhat prescriptive—discussion of best-practices methods.

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Given our focus on data-scarce environments, we emphasize methods with operationally feasible implementation, which can be practiced at scale.

We discuss a typology of data scarcity situations, including the overall analytical framework and data source in the next section. This is subsequently followed by more detailed discussion for key data shortage situations, which range from the cross-sectional consumption data being completely missing (Section III) to being partially missing (Section VI). We then discuss the situation of missing panel data in Section V and other related topics in Section VI before concluding in Section VII.

# **II. Typology of Data Scarcity Situations and Imputation Methods**

Given the conceptually broad meaning of household welfare, it is useful to lay out in the beginning the practical strategy that we will employ in this paper. More precisely speaking, we sidestep the theoretical debates about the various approaches to measuring household welfare, and are mostly concerned with the most common practice with measuring household welfare. We will focus accordingly on the money-metric aspect of household welfare that can be measured with household consumption (or income) data that are widely collected from household surveys. In particular, our central premise is that household consumption (or income) data provide the benchmark measure of household welfare.<sup>7</sup> This key assumption helps operationalize and better focus the measurement of household welfare, whereby a household’s position in the welfare space can be quantitatively identified by their consumption level. For example, households can be identified as poor if their consumption levels are below a specified threshold (i.e., the poverty line).

As another example, since we can rank different households’ welfare against each other on a

> 7 There is perhaps some strong consensus among policy makers regarding this as well. For example, the United Nations most recently decided to monitor the global poverty rate as the proportion of the population living below the international poverty line of US$1.90 per day. But see also Alkire _et al._ (2015) for a comprehensive discussion of the alternative approach of multi-dimensional poverty.

7
common scale according to their consumption, we can obtain the relative distribution of household welfare, or measures of inequality.

We next provide an overview of data situations and imputation methods before discussing the analytical framework and data.

# **II.1. Overview Data Situations**

For presentation purposes, we group all situations of missing data into three broad categories as follows (Table 1): A. the cross-sectional household consumption data are _completely_ missing B. the cross-sectional household consumption data are _partially_ missing, and C. although the cross-sectional consumption data are available, the panel household consumption data are (completely or partially) missing These categories can also be thought of as being ranked, in a roughly decreasing order, according to their severity of data scarcity. Put differently, we assume that the ideal data scenario is one where we have (high-quality) panel consumption data, the second-best scenario is one where we have cross sectional consumption data (but no panel data), and the least desirable scenario is one where we have no consumption data.

Group A thus represents the most data-scarce situation, where no (cross-sectional) data are collected on household consumption, although some data may be collected on other household characteristics.<sup>8</sup> Clearly, a typical example of the surveys that belong to Group A is nonconsumption surveys where no consumption data are collected by design. Group A remarkably covers quite a few surveys that are commonly implemented. For example, these surveys include the popular Demographic and Health Surveys (DHS), (most) Labor Force Surveys (LFS), and other surveys such as school-based surveys. In fact, implementing a household consumption

> 8 Unless otherwise noted, for brevity we hereafter follow the common practice and do not use the term “cross sectional” when referring to such data, but we explicitly mention the term “panel data” when discussing these data.

8
module requires considerable resources and logistic arrangement, thus almost all small-scale surveys that are conducted on an _ad hoc_ basis would normally fall into this category.

Group B represents data situations that are less data-scarce but, on the other hand, cover a large number of cases. Consequently, it is useful to break this group into the following three smaller sub-cases i) the (cross-sectional) consumption data not comparable across survey rounds, ii) the (cross-sectional) consumption data unavailable in the current survey but available in another related survey, and iii) the (cross-sectional) consumption data unavailable at more disaggregated administrative levels than those in the current survey. Sub-case (i) thus concerns the data situations with most Sub-Saharan African countries and India as discussed earlier. Sub-case (ii) is relevant to all situations where we do not have consumption data in the survey under consideration, but have consumption data in other similar surveys that somehow can be linked to the former. An example of this sub-case is where we have a more recent LFS that has no consumption data but has a similar design to an older household consumption survey.<sup>9</sup> Given the significantly higher costs of implementing panel surveys, Group C represents situations with least data availability. This is especially true for developing countries. For example, two major household consumption surveys that are commonly employed to provide poverty estimates in China and India—the China Household Income Project (CHIP) survey and the National Sample Survey (NSS)—are both cross-sectional surveys.<sup>10</sup> For countries where panel surveys exist, few such surveys are likely to be representative of the population over a long period of time without a great deal of efforts. One major reason is that the surveyed household unit can

> 9 There is thus some overlap between this sub-case and the non-consumption surveys in Group A. But note that we focus on the _absence_ of consumption data in Group A, and the _similarity_ between consumption surveys and other surveys in Group B. Put differently, we consider non-consumption surveys on their own in Group A but highlight their relationship with other consumption surveys in Group B.

> 10 See also Gustafsson, Shi, and Sato (2014) for a detailed discussion of the various consumption surveys in China.

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change (e.g., household members can die, split off to form a new household, or simply migrate to another place) and it is very costly to track all household members over time. For example, due to attrition, the percentage of households that remain in the panel Russia Longitudinal Monitoring Survey (RLMS) in the first 10 years after it was fielded is around 60 percent; this figure further decreases by half to 29 percent after another 10 years (Kozyreva, Kosolapov, and Popkin, 2016). But as global living standards are rising, this data situation can be improved as more resources may be invested in fielding panel surveys.

# **Imputation Methods**

We briefly show in Table 1 (last column) the imputation methods that can be used to provide poverty estimates in the absence of consumption data. These imputation techniques vary depending on whether the consumption data in need are cross-sectional or panel. For data situations in Group A, the most commonly used method is to generate a wealth index from household assets and the physical characteristics of the house (e.g., the material of the floor or the wall, or which type of toilet is available). For data situations in Group B, techniques have been developed to offer survey-to-survey imputation (i.e., imputation from one survey to another) for sub-cases (i) and (ii), and survey-to-census imputation (i.e., imputation from a survey into a census) for sub-case (iii). Finally, data situations in Group C can be addressed with recently developed methods that construct synthetic panel data from cross-sectional data, which can substitute for actual panel data to some extent. We return to more detailed discussion of each of these imputation methods in the following section.

# **II.2. Analytical Framework**

Following Deaton and Muellbauer (1980), we assume that a household maximizes utility subject to an income budget constraint that includes choice variables such as quantities of goods, durables, and leisure (or labor supply). These in turn are determined by different factors, such as 10
household tastes. This results in the common practice in most, if not all, household consumption surveys of constructing total household consumption as an aggregate of consumption of different items such as food, non-food (including clothing, education, and/ or health expenses), durable goods, and housing (Deaton and Zaidi, 2002).

For brevity, let _xj_ be a vector of characteristics that represent all these factors, where _j_ indicates the survey type. More generally, _j_ can indicate either another round of the same household expenditure survey, or a different survey (census), for _j_ = 1, 2.<sup>11</sup> Subject to data availability, _xj_ can include household variables such as the household head’s age, sex, education, ethnicity, religion, language (i.e., which can represent household tastes), occupation, and household assets or incomes. Occupation-related characteristics can generally include whether household heads work, the share of household members that work, the type of work that household members participate in, as well as context-specific variables such as the share of female household members that participate in the labor force.<sup>12</sup> Other community or regional variables can also be added since these can help control for different labor market conditions.

It follows that the following linear model is typically employed in empirical studies to project household consumption on household and other characteristics ( _x_ ) for household _i_ in survey _j_ , for _i_ = 1,..., N. Equation (1) thus provides a standard linear model that can be estimated using most available statistical packages.

# **II.3. Data Sources**

> 11 More generally, _j_ can indicate any type of relevant surveys that collect household data sufficiently relevant for imputation purposes such as labor force surveys or demographic and health surveys. To make notation less cluttered, we suppress the subscript for each household in the following equations.

> 12 Regional characteristics related to macroeconomic trends such as (un)employment rates or commodity prices can also be included if such data are available.

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We use the latest three rounds of the household survey data from Vietnam—the Vietnam Household Living Standards Surveys (VHLSSs)—in 2010, 2012, and 2014. Being similar to the Living Standards Measurement Study (LSMS) surveys supported by the World Bank, these surveys are implemented biennially by Vietnam’s General Statistical Office (GSO) and collect rich data on household demographics, education, occupation, assets, and consumption. These surveys are regularly employed by the Government of Vietnam and international organizations to provide estimates on household welfare and poverty measures.<sup>13</sup> Since the VHLSSs collect panel data, these surveys offer an ideal setting for us to evaluate the different imputation methods. The key idea is to construct each welfare measure as if we did not have consumption data, and then evaluate the former against the latter.

In particular, we can construct a wealth index and compare how it performs against the actual consumption data in measuring poverty (Category A), impute consumption from one previous round to the next round and compare the imputed consumption against the actual consumption (Category B), and compare the synthetic panels against the actual panel data (Category C). For this category, a particularly useful feature of the VHLSSs is that it has a rotating panel design, whereby approximately half of the households are followed and half are refreshed in each new survey round. We will make use of this feature to provide poverty estimates using the synthetic panels constructed from the cross-sectional component of the VHLSSs, and then validate these estimates against the “true” rates that are based on the panel component of the VHLSSs.

# **III. Completely Missing Consumption Data**

> 13 An additional advantage of these data is the availability of community targeting, i.e., a household poverty status as classified by the local government. We will make use of this feature and present it together with the analysis based on consumption data.

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In the absence of consumption data, wealth indexes can be constructed that can offer a measure of household welfare. We discuss in this section the construction and some main properties of the wealth index (Section III.1) and the application of the wealth index to tracking household welfare over time (Section III.2).

# **III.1. Measuring Welfare with Wealth Indexes Definition**

Wealth indexes were used in earlier studies to measure household consumption and poverty (see, e.g., Montgomery _et al._ (2000)), but perhaps the study by Filmer and Pritchett (2001) helps significantly popularize its usage. Non-consumption surveys such as the DHS now automatically offer some version of wealth indexes in all their new data releases. Perhaps the main reason behind its popularity is—compared to the typical survey module that consists of hundreds of consumption items required to construct the consumption aggregate—data on a list of assets are both cheaper and easier to collect.

The idea behind a wealth index is, in fact, rather straightforward: it is a single-variable measure for household wealth that can be used to rank household welfare. In practice, it is essentially some combination of the various components of household wealth such as household assets (e.g., whether the household has a television, a car, and a telephone), the living area of the house, and the physical materials out of which the walls (or roof) of the house are constructed (e.g., whether more durable materials such as cement or bricks or less durable materials such as mud or grass are used). The types of a house’s facilities such as the toilet are also commonly used since a better type of toilet such as a flush toilet is often observed to proxy for more wealth than other flimsier ones such as a pot toilet or no toilet at all (i.e., open defecation).

To be more precise, consider a variant of Equation (1) where the left-hand side variable, household consumption<sup>_y_</sup> _ij_<sup>, is now missing, but we have data on household assets�</sup> ��<sup>—a subset</sup> 13
of ���. Still, we want to generate a wealth index _wij_ which offers the best combination of (the elements of the different) household assets ���. Our problem can then be expressed as follows where we now place the term �<sup>�</sup> ��� on the left-hand side to emphasize that � are the (vector of) weights we place on the ��� in an effort to generate the best possible measure of wealth. Note that household assets are just a component of the household and community characteristics ��� in Equation (1).

There are two common approaches to obtaining these weights: the first is to simply let all of them equal 1 (i.e., using simple aggregation that provides a count of the number of assets a household possesses), and the second is to search for a combination of weights that captures the most variation of the ��� by statistical techniques such as the principal component (PCA) method. Some remarks are, however, in order. The PCA method is data-driven by definition, and offers weights that vary depending on the specific data set that is analyzed. For example, a motorbike would be given a small and perhaps statistically insignificant weight in a setting where it is a commonplace asset (i.e., all households have a motorbike), but would be given a larger weight in another setting where the opposite is true. On the other hand, the simple aggregation method would apply the same equal weights in all the settings. As such, the PCA method appears to be best suited for analysis that is restricted to one setting, while the simple aggregation method may be better for comparison of results across different settings.<sup>14</sup> Wealth indexes are a useful substitute for household consumption in the absence of the latter, since almost all surveys these days collect the relevant information on household assets and housing characteristics. However, note that wealth indexes are less accurate than household

> 14 See, for example, Jolliffe (2002) for a comprehensive treatment of PCA methods.

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consumption in proxying for household welfare.<sup>15</sup> Since poverty is a function of household consumption, wealth indexes offer biased estimates as well. These results intuitively follow from our assumption that household consumption provides the benchmark measure of household welfare, but can be formalized in the following proposition and corollary.

**Proposition 1:** _Wealth indexes tend to provide biased estimates of poverty rates (as measured by household consumption)._ **Proof** : Appendix 1.

# _Illustrative Example 1_

We provide an illustrative example where the wealth index is generated using both the simple aggregation (Table 2, Model 1) and the PCA method (Table 2, Models 2 and 3) on the VHLSSs in 2012 and 2014. (Further details on the implementation are provided in Appendix 2.) Each cell in the first five rows shows the proportion of each quintile of the consumption distribution that is correctly captured by each quintile of the wealth index. These quintile divisions may also be considered as different poverty lines. The list of assets for Model 1 includes (whether the household has) a car, a motorbike, a bicycle, a desk phone, a mobility phone, a DVD player, a television set, a computer, a refrigerator, an air conditioner, a washing machine, and an electric fan. Model 2 adds to Model 1 the construction materials for the house’s roof and walls, Model 3 adds to Model 2 the type of water and toilet the household has access to.

Estimation results concur with Proposition 1, where each of the quintiles based on the wealth index can only capture around half of the corresponding quintile based on the consumption distribution. For example, the poorest wealth index quintile in Model 3 can correctly capture only 57 and 47 percent of the poorest consumption quintile respectively in 2012 and 2014. Alternatively, we also show the proportion of the cumulative consumption distribution that is

> 15 In addition, assets take time to depreciate and to be sold/ bought so they are not as smooth as consumption in capturing household welfare.

15
correctly captured by the wealth quintiles in Appendix 3, Table 3.1.<sup>16</sup> Estimation results are, however, qualitatively similar where taken altogether, the wealth quintiles can correctly capture between 60 percent and 80 percent of the corresponding consumption quintiles. Notably, the correlation between asset indexes and household consumption is higher for the PCA wealth index than for the simple aggregation method (e.g., this correlation is 0.61 for Model 1 in 2012, but increases to 0.67 and 0.70 respectively for Models 2 and 3 in the same year).

These results are broadly consistent with the empirical evidence offered in recent studies. Reviewing 17 studies that analyze 36 different data sets, Howe _et al._ (2009) observe a poor correlation between wealth indexes and household consumption. Filmer and Scott (2012) analyze survey data from 11 countries from four continents and find a similar result. Furthermore, Filmer and Scott (2012) also find that the correlation between wealth indexes and consumption is only stronger under certain, and more demanding, conditions such as urban settings, limited measurement errors, and a small share of individually consumed goods (e.g., food) in total expenditures.<sup>17</sup> The latter caveats can perhaps also be partly explained by the fact that, wealth indexes are a stock measure, rather than a flow measure as with household consumption.

# **III.2. Tracking Welfare over Time with Wealth Indexes**

_Illustrative Example 2_ As earlier discussed, since wealth indexes are biased estimates of household consumption levels, they appear likely to provide biased estimates of consumption trends as well. We provide

> 16 In this case, the poverty line can equal the 20th, 40th, or 60th (and so on) percentile of the wealth index distribution. 17 Some other practical issues with using wealth indexes to measure poverty are that it is unclear how to set the poverty line for wealth indexes (compared with the more established calorie-intake or cost-of-basic-needs with the consumption-based poverty line) or that asset ownership may also be affected by factors related to supply but not household consumption (e.g., inadequate water supply may result in less ownership of flush toilets or washing machines). An alternative approach is to collect data on a reduced set of consumption items that may offer strong correlation with the total consumption aggregate (Morris _et al._ , 2000). Another approach is to produce households’ ranks in the population with the number of consumption items they own, if we make the additional assumption that households place an order of importance on their consumption items when having to reduce their consumption expenditure (Deutsch, Silber, and Wang, 2017).

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an illustrative example in Table 3, where we compare the growth of consumption (second column) against those of wealth indexes. We use two versions of the wealth indexes, the first is the simple aggregation method (or wealth index 1), and the second the PCA method (or wealth index 2, same as Model 3 in Table 2) after pooling all data for the three survey years. The list of the assets that are used is the same as that used for Model 1 in Table 2.<sup>18</sup> Table 3 shows that the growth rate of mean per capita consumption widely differs from that of the wealth indexes between 2010 and 2012: while the former is around 2 percent, the growth rate of wealth index 1 is higher at 10 percent, and even negative and much higher at more than 100 percent for wealth index 2 (Panel A). The growth rate of mean per capita consumption and the growth rate of the wealth indexes differs as well between 2012 and 2014 (Panel B), but a different result emerges where the former is now larger than that of wealth index 1 but still smaller than that of wealth index 2.

This empirical result qualitatively concurs with that offered by Harttgen, Klasen, and Vollmer (2013), who analyze 160 DHS surveys from 33 African and 34 non-African countries and construct wealth indexes in different ways as well. In particular, Harttgen _et al._ (2013) argue that employing wealth indexes as a proxy for trends in household consumption is subject to several different types of biases. For example, one is due to changing preferences for certain assets (e.g., the increasing ownership of smart phones), another changing relative prices among different assets leading to more demand for one asset at the expense of others (e.g., the dramatically decreasing price of smart phones).<sup>19</sup>

> 18 The reason we pool the data is to make the wealth indexes comparable over time, since applying the PCA method to each year separately as with Table 2 would standardize these indexes to a mean 0 for each year. We use the same assets as in Model 1, Table 2 for easier interpretation with the count index; estimation results (not shown) using additional assets in the other models (Models 2 and 3) provide qualitatively similar results.

> 19 Although providing biased poverty estimates in a static period, wealth indexes may not necessarily provide biased estimates of trends in household consumption (or poverty) over time. If the degree of bias for both wealth indexes and household consumption is similar over time, wealth indexes can provide unbiased estimates. As an (extreme) example, if the bias of the mean of a wealth index as a measure of mean household consumption remains constant at 10 percent

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Still, we end this section on an optimistic note that more methods have recently been developed in an effort to provide more comparable wealth indexes over time. For example, a promising direction of research is offered by Rutstein and Staveteig (2014), who adjust, relative to a reference country, a country-specific wealth index using the country-level relationship between some “unsatisfied basic needs” and ownership of certain basic assets such as a car, a refrigerator, a landline telephone, and a television. This study builds on earlier studies that employ asset indexes to analyze poverty trends over time (e.g., Sahn and Stifel (2000)), but it does not use consumption data to validate its estimates based on the asset indexes.

# **IV. Partially Missing Consumption Data**

To further operationalize our estimation framework, we extend Equation (1) to a more general model where the error term ��� is now broken down into two components, one (���� a cluster random effects and the other (��� the idiosyncratic error term. Note that we also suppress the subscript that indexes households to make the notation less cluttered. Conditional on household characteristics, the cluster random effects and the error terms are usually assumed uncorrelated with each other � � and to follow a normal distribution such that ���|��~��0, ���� and ��|��~��0, ����. While the normal distribution assumption results in the standard linear random effects model that is more convenient for mathematical manipulations and computation, it is not necessary for this type of model. As can be seen later, we can remove this assumption and use the empirical distribution of the error terms instead, albeit at the cost of somewhat more computing time.

for all time periods, this bias would cancel out for estimates of the trends in consumption—or the relative growth of the mean. We provide more formal discussion of this result in the proof for Proposition 1.

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Without loss of generality, assume for now that consumption data are available for survey 1 but missing for survey 2, for which we are most interested in the poverty estimates. Let z2 be the poverty line in period 2, and ��� be the imputed consumption for survey 2, the poverty rate P2 in this period could be estimated with the following quantity ����� ���� (4) where P(.) is the probability (or poverty) function that gives the percentage of the population that are under the poverty line z2 in survey 2.

Imputation methods differ in how they estimate ���. We discuss in this section methods that have been developed to impute consumption, either within the same type of surveys or across different survey types. We start first with discussing a commonly used method, proxy means testing, before discussing how consumption can be imputed to measure poverty trends and “poverty-mapping” (or small area estimation) methods.

# **IV.1. Proxy Means Testing**

Most of the estimates based on proxy means testing are usually estimated as where the vector of coefficients ��� is often obtained from the regression using another data set (see, e.g., Grosh _et al._ (2008), Coady _et al._ (2014), Brown, Ravallion, and van de Walle (2016)). For example, ���can be obtained from a regression using the household consumption data, and then be imposed on the data from a special—and often smaller—survey that aims at targeting poor households for a social protection program. Alternatively, ���can also be obtained from a regression using data from a neighboring country. But regardless of the specific application, the error terms ��� ��� (in Equation (3)) are often omitted in Equation (5). As a result, the mean and the variance of the predicted consumption based on proxy means testing would likely provide 19
biased estimates of those of household consumption. Put differently, the better ���,� can capture the variables in ���, the less biased the predicted consumption-based proxy means tests is. When ���,� is identical to ���, (that is, the estimation model for Equation (5) is fully specified except for the error terms ��� ���), there is no bias in the estimated mean consumption, but there is still bias in the estimated variance.

These results have direct implications for poverty estimation, and are formally stated in Proposition 2 below.

**Proposition 2:** _Proxy means testing tends to offer biased poverty estimates._ **Proof** : (Appendix 1).

As discussed above, if the estimation model is fully specified (i.e., x��,� is a smaller subset of x��), there is no bias in the estimated mean consumption. This result, however, generally does not translate directly into poverty estimates, unless the poverty line is exactly set at the mean consumption level. Nevertheless, proxy means testing offers better estimates of household consumption than those offered by wealth indexes. The intuition is rather straightforward: since we employ an estimation model that is more closely related to household consumption (e.g., ��� is obtained from a regression using household consumption as the dependent variable) with the former, we should expect to have better estimates for household consumption.<sup>20</sup> Since the empirical example for proxy means testing is closely related to our discussion of imputed consumption, we return to more discussion in the next section.

# **IV.2. Monitoring Poverty Trends over Time with Imputed Consumption**

The United Nations—through the Sustainable Development Goals (SDGs)—recently set the ambitious targets of eliminating extreme poverty and reducing national poverty levels at least by

> 20 We offer more formal discussion of these results in the proof for Proposition 2 in Appendix 1.

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half by 2030.<sup>21</sup> Such efforts are predicated on an ability to reliably assess and monitor progress since tracking poverty trends can help us understand which policies work and which do not work, and how efficient they are. Producing reliable poverty estimates by conducting household expenditure (consumption) or income surveys, however, requires significant financial and technical resources. As a result, consumption surveys are typically conducted every few years by statistical agencies, and poverty estimates are not available in the intervening years during which surveys have not been implemented. Another challenge to tracking poverty trends is that questionnaire design may change over time, thus making consumption data and poverty estimates not comparable between different rounds.

A notable example of incomparable consumption data over time is perhaps India’s NSSs. In the late 1990s, the National Sample Survey Office (NSSO) revised the questionnaire of the NSS in 1999/2000 (55<sup>th</sup> round) to make household survey consumption data more consistent with those from national accounts. Major changes to the questionnaire were implemented such as changing the recall period for household durables and education expenses from a 30-day interval to a 365day interval, and using both the traditional 30-day recall period as well as a new 7-day recall period for food items. The Government of India subsequently estimated that the poverty rate fell by 10 percentage points between 1993/1994 and 1999/2000. However, researchers provided different estimates ranging from only somewhat lower than the official estimates to a mere three percentage point decline in poverty during the decade of the 1990s (see, e.g., Deaton and Kozel (2005)).<sup>22</sup> Where consumption data are either incomparable across two survey rounds or missing in one survey round but not the other, but other characteristics (��) that can help predict consumption data

> 21 For details see https://sustainabledevelopment.un.org/sdg1.

> 22 See also Dang and Lanjouw (forthcoming) for a discussion of more recent, albeit less severe, comparability issues with the NSSs in the late 2000s.

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are available in both survey rounds, we can apply survey-to-survey imputation methods. In particular, Dang, Lanjouw, and Serajuddin (2017) propose a simple imputation framework that builds on earlier studies (Elbers, Lanjouw, and Lanjouw, 2003; Tarozzi, 2007).<sup>23</sup> Compared to previous studies, the Dang _et al._ (2017) method provides a more explicit theoretical modeling framework, with new features such as model selection and standardization of surveys of different designs (e.g., for imputing from a household survey into a labor force survey).

Assume that the explanatory variables �� are comparable for both surveys (Assumption IV.1), and that the changes in �� between the two periods can capture the change in poverty rate in the next period (Assumption IV.2). Suppressing the subscript for households in the following equations, Dang _et al._ (2017) define the imputed consumption y�� as and estimate it as where the parameters ��� are estimated using Equation (3), and ����,� and �̂��,� represent the sth random draw from their estimated distributions, for s= 1,..., S. The poverty rate<sup>_P_</sup> 2<sup>in period 2 and its</sup> variance can then be estimated as

> 23 Elbers _et al._ (2003) provide a method that imputes household consumption from a survey into a population census. Adapting this approach for survey-to-survey imputation, Christiaensen _et al._ (2012) impute poverty estimates using data from several countries, including China, Kenya, the Russian Federation, and Vietnam; other studies analyze data from Uganda (Mathiassen, 2013).

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Indeed, these estimates of poverty improve on those offered by proxy means testing method. This result is formalized in the following proposition.

**Proposition 3:** _Given assumptions IV.1 and IV.2, the imputed household consumption in equation (7) offers unbiased poverty estimates._ **Proof** : Appendix 1.

We can test for Assumption IV.2 if consumption data exist in both survey rounds. We can use a decomposition that is similar in spirit to the Oaxaca-Blinder framework (Oaxaca, 1973; Blinder, 1973), where the change in poverty between the survey rounds can be broken down into two components, one due to the changes in the estimated coefficients (the first term in square brackets in Equation (10) below) and the other the changes in the _x_ characteristics (the second term in square brackets in Equation (10) below). Assumption IV.2 would be satisfied if the poverty change is mostly explained by the latter component. This can be expressed as where  _j_ is defined as  _j_  _j_ , j= 1, 2, for less cluttered notation.

However, we want to predict poverty rate for the current period where consumption data are missing. Thus a practical use of Assumption IV.2 is model selection; in particular, we can test for this assumption in contexts where consumption data exist for earlier survey rounds (i.e., there are two earlier survey rounds with consumption data), and select the imputation model that offers estimation results that are most satisfactory for this assumption.

This imputation method is also related to a larger literature on missing data (or multiple) imputation (MI) in statistics (see, e.g., Little and Rubin, 2002; Carpenter and Kenward, 2013). Official agencies such as the U.S. Census Bureau routinely use imputation to fill in important missing data on various statistics for income (Census Bureau, 2014a) and labor (Census Bureau, 2014b). However, several differences exist between the two literatures. First, MI studies often 23
employ Bayesian techniques for their estimation, which requires multiple drawing from posterior distributions and consequently, more computing time. Second, MI studies often impute missing data within the same survey where usually less than half of the data are missing, rather than imputing consumption for a whole new survey (census) round. Finally, MI studies, unsurprisingly, do not use economic theory for model selection (as in Dang _et al._ , 2017).<sup>24</sup> A recent champion of the application of MI methods to poverty is the SWIFT method (Survey of Well-being via Instant and Frequent Tracking), which is developed by Yoshida _et al._ (2015). Besides sharing the features of MI methods discussed above, perhaps SWIFT’s most important contribution is its proposal to rapidly collect data on a key and reduced set of variables that can be used for faster and less expensive poverty imputation.<sup>25</sup> However, it can be useful to note some potential limitations of SWIFT. First, the (distributions of the) parameters �� , ��, and �� are likely to change more over longer time periods. Consequently, these parameters would need to be updated more frequently for better predictions, which would effectively require the implementation of the full household consumption survey rather than just a reduced set of variables. Second, a full household survey (with or without consumption data) may likely offer more precision with reproducing the whole income distribution

> 24 Douidich _et al._ (2016) offer an early application of MI methods to poverty imputation. See also Davey, Shanahan, and Schafer (2001) and Jenkins _et al._ (2011) for studies that apply MI techniques to economic issues. More discussion on the differences between the two literatures and references to earlier imputation studies are provided in Dang _et al_ . (2017).

> 25 Due to various post-survey data quality control procedures such as data entry, cleaning and checking, household survey data are usually unavailable for use from until half a year to longer with most household surveys. But this situation may improve with the increased use of tablet-based (or hand-held devices-based) data collection. Another notable feature of SWIFT is its statistical approach to model selection (see, e.g., James _et al._ (2013)), and building estimating models (say, by using stepwise regression to screen out variables with low p-values, rather than selecting these variables based on economic theory on household consumption).

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and related welfare measures (such as inequality measures). Furthermore, more validation of this method is needed.<sup>26</sup> We return to more discussion with the illustrative example below.

# _Illustrative Example 3_

We start with checking Assumptions IV.1 and IV.2 before discussing estimation results. Since all the 2010, 2012, and 2014 rounds of the VHLSS share the same sampling frame based on the 2009 Population and Housing Census, and their questionnaire design remains almost identical,<sup>27</sup> Assumption IV.1 for a similar survey design is satisfied. We can test for Assumption IV.2 for the period 2010-2012 using the decomposition provided in Equation (10).

We start first with building the estimation models on a cumulative basis for illustration purposes, with later models sequentially adding more variables to earlier models. Model 1 is the most parsimonious model and consists of household size, household heads’ age, gender, highest completed levels of schooling, a dummy variable indicating whether the head belongs to the ethnic majority group, and a dummy variable indicating urban residence. Model 2 adds to Model 1 the household demographics such as the shares of household members in the age ranges 0-14, 15-24, and 25-59 (with the reference group being those 60 years old and older), a dummy variable indicating whether the head worked in the past 12 months. Model 3 adds to Model 2 asset variables, the construction materials for the house’s roof and walls, and the type of water and toilet the household has access to, which are the same as those employed in our earlier analysis of wealth indexes. Full model specifications are provided in Appendix 3, Table 3.2.

> 26 This practically implies that SWIFT has to rely more heavily on the assumption of constant parameters than most other previous studies. As yet, there appear to be no published validation studies besides those offered in Yoshida _et al._ (2015).

> 27 The VHLSSs have a rotating module that collect more detailed data on certain topic in each survey round. For example, the 2014 VHLSS collects more data on land access and ownership. But more importantly for our purposes, the core modules that collect data on household demographics, education, assets, and house materials remain the same over these survey rounds.

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We then predict consumption, using the estimated coefficients from the preceding years (i.e., the estimated coefficients are respectively from 2010 and 2012 for our predicted consumption in 2012 and 2014). Decomposition results, shown in Table 3.3, suggest that as the list of control variables becomes richer, the change in poverty that can be explained by the _x_ characteristics grows proportionately larger. For example, this component increases from around 60 percent in Model 1 to 62 percent in Model 2, and then close to 100 percent in Model 3 for the period 2010-2012. For the period 2012-2014, Models 1 and 2 do not perform as well with less than 20 percent of the change in poverty being explained by the _x_ characteristics under these models. However, Model 3 offers a good estimation model and can explain almost all the change in poverty.<sup>28</sup> This indicates that Assumption 2 is largely satisfied with Model 3 for both periods, and less likely to be satisfied with the remaining models.

Table 4 provides the estimation results for the predicted poverty rates based on the imputed data. Estimation results show that our estimates using Model 3 indeed fall within one standard error of the true poverty rates for both 2012 and 2014. For example, our predicted poverty rate for 2014 is 13.1 percent using the normal linear regression model, which is inside the one-standarderror interval of the true poverty rate of [13.0, 14.0] for the same year. As a further robustness check, we also show the estimation results where we predict consumption for 2014, but use the estimated coefficients from 2010 (instead of those from 2012). The longer time interval may reduce the precision of the estimates if the changes in the estimated coefficients dominate the

> 28 The switch from positive to negative of these models can suggest that Assumption IV.2 is more flexible compared to the commonly made assumption of constant parameters in previous studies. This is further supported by the Wald test that rejects the latter assumption for all models (Table 3.3). But also note that model specifications where the changes in the explanatory variables _x_ can explain much more than 100 percent of the changes in poverty may also indicate model overfitting. Furthermore, Dang _et al._ (2017) observe that it is generally ill-advisable to include certain assets whose correlations with consumption change dramatically over the two periods due to other factors such as technology. A notable example is that in certain developing countries cell phones could get mass produced quickly and their prices were lowered to the extent that they could no longer be considered a luxury good in the second period.

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change in the _x_ characteristics. However, the estimates shown under Model 3 in Table 3.4 show that we have similar, or even somewhat better, results.

For further comparison, we also provide estimates using MI methods in Table 3.5. Two imputation models are used, one is the normal linear regression and the other the predictive mean matching, which offer the closest corresponding modeling options to the normal linear regression model and the empirical distribution of the error terms model provided in Table 4. Estimation results suggest that both methods, in particular the predictive mean matching method, work reasonably well (using our preferred Model 3). In fact, the predictive mean matching method may offer even slightly better estimates than those in Table 4. However, there are two limitations with MI methods: the variance for MI estimates are larger than those offered in Table 4, and it takes more computer time to obtain these estimates.<sup>29</sup> It can be useful to briefly discuss estimation results based on proxy means testing. As discussed earlier, proxy means testing would likely provide biased poverty estimates (Proposition 2). The intuition behind this result is that predicted poverty does not appropriately adjust for the error term, and is based on the deterministic part of Equation 1 only (see Equation 5). Indeed, estimation results (Table 3.6) show that the estimated poverty rates are much lower than the true poverty rates, with the difference ranging around 5 percentage points for Model 3 in both years.

# **IV.3. Spatial Targeting with Poverty Map**

While tracking poverty trends over time requires the temporal imputation of poverty, monitoring poverty on a larger and more disaggregated scale would require the spatial imputation of poverty. Government agencies in richer countries such as the U.S. Census Bureau regularly rely

> 29 Furthermore, as earlier discussed, these estimates are based on Model 3, which is selected using the method proposed in Dang _et al._ (2017). These results are also consistent with MI estimation results using household survey data from Jordan offered in this study.

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on statistical techniques known as “small-area” estimation methods (see, e.g., Bell _et al._ (2007)) to impute poverty numbers at different administrative levels. These methods essentially impute from a household (income or) consumption survey into a population census to provide more spatially disaggregated measures of consumption and poverty for better targeting purposes. Put differently, consumption data are imputed using a data source that is representative at a higher administrative level to another data source that is representative at a lower administrative level. The higher administrative level can be the state or province level, for example, while the lower administrative level can be the district or community level.

This approach has also been widely employed by international organizations such as the World Bank to impute poverty in a developing country context. Since poverty rates are often visually represented on the country map, it is also commonly known as the “poverty mapping” approach. The most commonly used framework developed by Elbers, Lanjouw, and Lanjouw (2003) proposes that we estimate Equation (3) using the household consumption survey. Then these estimated (distributions of the) parameters can be imposed on the same variables in the population census in a similar spirit as with the temporal imputation of poverty. But importantly, techniques differ on how this is implemented. In particular, Elbers _et al._ (2003) suggest a Bayesian estimation method where the distribution of �<sup>�</sup> ��, rather than ���, is employed for the imputation. In fact, various methods have also been employed for the imputation model.<sup>30</sup> However, Tarozzi and Deaton (2007) note that two assumptions are relevant for the implementation of the poverty map method. The first assumption is similar to Assumption IV.1 discussed earlier, and states that the explanatory variables �� are comparable for both the survey

> 30 The Elbers _et al._ method has also been employed to provide other development outcomes such as child malnutrition (Fujii, 2010). See also Rao and Molina (2015) for a text-book treatment of the statistical literature on small area estimation.

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and the census. The second assumption is more specific, and states that the conditional distribution of household consumption given �� is the same for both the survey and the census. This latter assumption is in fact indispensable for the inference from the estimates for the larger areas (as representative in the survey) to the smaller areas (as representative in the survey).

_Illustrative Example 4_ Figure 2—produced by the World Bank Poverty Team in Vietnam—provides a map of poverty estimates by imputing from the VHLSS in 2008 into the population census in 2009.<sup>31</sup> The differing poverty rates at the province level are depicted by the color intensity, where a darker color indicating a higher poverty rate. Figure 2 shows that provinces with the highest concentration of poverty are in the Northern region, the North West region, and the Central Highland. On the other hand, provinces in the coastal regions including the Red River Delta and the Mekong Delta have the lowest poverty rates.

# **V. Missing Panel Consumption Data**

We now turn the last category of missing panel data (Table 1, Category C). New methods have recently been proposed to deal with situations with missing panel household consumption by constructing synthetic panels from cross sections that can help provide insights into the dynamics of poverty (Dang _et al._ , 2014; Dang and Lanjouw, 2013) and other related welfare outcomes such as vulnerability and shared prosperity (Dang and Lanjouw, 2016 and 2017). These synthetic panels have also been increasingly employed in a variety of contexts.<sup>32</sup>

> 31 See Demombynes (2015) for an introduction on this map.

> 32 Recent applications and further validations include Ferreira _et al._ (2013), Cruces _et al._ (2015) and Vakis _et al._ (2015) for Latin American countries, Martinez _et al._ (2013) for the Philippines, Garbero (2014) for Vietnam, Bourguignon and Moreno (2015) and Foster and Rothbaum (2015) for Mexico, Cancho _et al._ (2015) for countries in Europe and Central Asia, Dang and Ianchovichina (2016) for countries in the Middle East and North Africa region, Dang and

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Let xij be a vector of household characteristics observed in survey round _j_ (j= 1 or 2) that are also observed in the other survey round for household i, i= 1,..., N. These household characteristics can include such time-invariant variables as ethnicity, religion, language, place of birth, parental education, and other time-varying household characteristics if retrospective questions about the round-1 values of such characteristics are asked in the second-round survey. To reduce spurious changes due to changes in household composition over time, we usually restrict the estimation samples to household heads age, say 25 to 55 in the first cross section and adjust this age range accordingly in the second cross section. Note that this age range is usually used in traditional pseudo-panel analysis but can vary depending on the cultural and economic factors in each specific setting.

Let yij represent household consumption or income in survey round j, j= 1 or 2. The linear projection of household consumption (or income) on household characteristics for each survey round is given by Let zj be the poverty line in period j. We are interested in knowing the unconditional measures of poverty mobility such as which represents the percentage of households that are poor in the first survey round (year) but nonpoor in the second survey round, or the conditional measures such as Dabalen (forthcoming) and Dang, Lanjouw and Swinkels (2017) for countries in Suh-Saharan Africa, and Dang and Lanjouw (2017 and forthcoming) for India, Vietnam, and the United States.

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which represents the percentage of poor households in the first round that escape poverty in the second round.

If panel data are available, we can estimate the quantities in (12) and (13); but in the absence of such data, we can use synthetic panels to study mobility. To operationalize the framework, we make two standard assumptions. First, we assume that the underlying populations being sampled in survey rounds 1 and 2 are identical such that their time-invariant characteristics remain the same over time (Assumption V.1). More specifically, coupled with Equation (11), this implies the conditional distribution of expenditure in a given period is identical whether it is conditional on the given household characteristics in period 1 or period 2 (i.e., x�� �x�� implies y��|x�� and y��|x�� have identical distributions). Second, we assume that ��� and ��� have a bivariate normal distribution with positive correlation coefficient  and standard deviations σ�� and σ�� respectively (Assumption V.2). Quantity (12) can be estimated by

where  2 (.) stands for the bivariate normal cumulative distribution function (cdf)) (and  2 (.) stands for the bivariate normal probability density function (pdf)). Note that in Equation (14), the estimated parameters obtained from data in both survey rounds are applied to data from the second survey round (x2) (or the base year) for prediction, but we can use data from the first survey round as the base year as well. It is then straightforward to estimate quantity (13) by dividing quantity function (cdf).

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In Equation (14), the parameters<sup></sup> _j_<sup>and</sup>  _j_ are estimated from Equation (1), and  can be estimated using an approximation of the correlation of the cohort-aggregated household consumption between the two surveys (<sup></sup> _yc_ 1<sup>_y_</sup> _c_ 2 ). In particular, given an approximation of<sup></sup> _yc_ 1<sup>_y_</sup> _c_ 2 , where c indexes the cohorts constructed from the household survey data, the partial correlation coefficient  can be estimated by Note that the standard errors of estimates based on the synthetic panels can in fact be even smaller than that of the true (or design-based) rate if there is a good model fit (or the sample size in the target survey is significantly larger than that in the base survey; see Dang and Lanjouw (2013) for more discussion).

Equation (14) can be extended to the more general case of vulnerability. For example, we can estimate the percentage of poor households in the first period that escape poverty but still remain vulnerable in the second period (joint probability) as Other formulae and more detailed derivations for other measures of vulnerability dynamics are provided in Dang and Lanjouw (2017).

# _Illustrative Example 5_

Table 5 provides the estimates for both unconditional and conditional poverty mobility using the synthetic panels, and then compares these estimates with those based on the true panels. Several remarks are in order for this table. First, the synthetic panel estimates approximate those of the 32
true panel estimates reasonably well. In particular, all the point estimates based on the synthetic panels fall within the 95 percent confidence intervals (CIs) of those based on the true panels, and even fall within one standard error of the latter in one case. That is, the unconditional probability estimate for those who remain poor in both years is 10.8 percent, which is almost identical to the corresponding estimate based on the true panel of 10.7 percent. Second, all the 95 percent CIs of the synthetic panel estimates overlap with those of the true panels for at least half or more. This is due to the fact that the synthetic panel estimates are model-based estimates, thus these estimates generally should have smaller standard errors than those using the actual panels (which are usually referred to in the survey statistics literature as the design-based estimates). Finally, estimates for the conditional probabilities are somewhat less accurate than those for the unconditional probabilities since obtaining the latter entails prediction for both the numerator and the denominator of (12)-type quantities.<sup>33</sup>

# **VI. Other Topics**

We briefly review some other issues that are related to poverty measurements that are increasingly receiving attention.

# _Measurement Errors_

Measurement errors are known to be a common issue with micro survey data, and can bias poverty estimates (see, e.g., Deaton, 1997: Chesher and Schluter, 2003). Particularly with lowquality panel data sets, these errors may result in spurious movements that can be incorrectly attributed to poverty mobility. While some researchers argue that up to 50 percent of the transitory poverty may be accounted for by measurement error in income or consumption (Dercon and Krishnan, 2000; Glewwe, 2012; Lee _et al._ , 2017), others suggest the magnitudes of bias rely on

> 33 This is also consistent with the theoretical and empirical evidence provided in Dang and Lanjouw (2013).

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the particular form of errors (Gottschalk and Huynh, 2010).<sup>34</sup> Thus much research still appears to be needed on this topic. One promising direction can be the application of synthetic panels to correct for “bad” panel data.

# _Big Data_

Various Big Data sources have been proposed as viable substitutes for missing household consumption data. For example, Jean _et al._ (2016) combine nighttime maps with high-resolution daytime satellite images to provide poverty maps for five African countries, while Blumenstock _et al._ (2015) use mobile phone records to estimate poverty. Most recently, Steele _et al._ (2017) employ cellphone data and satellite data to evaluate poverty mapping for Bangladesh. These recent advances thus offer a promising avenue where intensive machine learning techniques can be introduced to substitute for traditional econometric methods.

# _Subjective Poverty_

Subjective well-being data can be employed to provide richer analysis of poverty. In fact, if can be argued that if poverty is multi-dimensional, subjective assessment of poverty is an integral part of its measurement. It is even proposed that a “social subjective poverty line”, below which people tend to think they are poor, but above which they do not, can be a conceptual alternative to defining poverty (Ravallion, 2014). But on the other hand, some empirical evidence suggests that poverty may not necessarily overlap with unhappiness in a number of developing countries including India, Mexico, Peru, and the Russian Federation (Banerjee and Duflo (2007), Rojas

> 34 See also Jantti and Jenkins (2015) for a recent overview of other studies that investigate the impacts of measurement errors on intra-generational mobility, and Nybom and Stuhler (2016) for an analysis in the context of inter-generational mobility.

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(2008), Graham, 2010)).<sup>35</sup> Still, one potentially promising direction for further research is to employ subjective well-being data to provide better imputed household consumption.

# **VII. Conclusion**

We offer in this paper a review of poverty measurement methods in contexts where consumption data are missing or have inadequate quality. Some of the methods we reviewed are more established, but some are rather recent. While micro survey data are becoming available and more frequently collected in developing countries, we expect these methods to be useful at least in the immediate term, and particularly when a need arises for backcasting consumption from a more recent survey for better comparison with older surveys.

In addition, these imputation methods may also be appropriate in contexts where survey costs and/or survey implementation pose a challenge. For example, perhaps most national statistical agencies are keen on producing annual poverty statistics. But few, if any, developing countries can afford the associated expenses and demanding logistics of fielding a household consumption survey every year; rather, they are likely to implement the household consumption survey every few years. In such contexts, poverty rates can be imputed for the intervening years between the surveys at just a fraction of the cost of fielding a full-fledged consumption survey by, say using other non-consumption data or implementing a lighter (non-consumption) version of the survey in the spirit of the SWIFT approach.<sup>36</sup> Seen in this light, imputation techniques can offer a low-cost and arguably wieldy approach to poverty estimation. While we should be mindful of the various assumptions underlying imputation

> 35 There appears no consensus yet even on the use of subjective well-being data. While some researchers (see, for example, Bond and Lang (2014) and Gibson (2016)) remain skeptical, others are more optimistic (see, for example, Allin and Hand (2017) and Helliwell, Layard, and Sachs (2017)).

> 36 Kilic _et al._ (2017) estimate the average cost of implementing a recent household consumption survey (in 2014 or later) to range from approximately US$800,000 to US$5 million, depending on the context and sample sizes. On the other hand, applying poverty imputation methods would most likely require only researchers’ time costs.

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methods as discussed in this paper, we would cautiously call for more attention to further developing these methods, and particularly validation studies to provide richer evidence on contexts where these methods may or may not work, or how well these methods work. Besides providing the typical (regional or national) capacity building exercises for staff at different national statistical agencies, a possibly useful way to proceed is perhaps some subsequent selective pairing of international experts with these staff, who can form small teams that provide further analysis with low costs. Another approach is to incorporate these imputation methods in existing popular software platforms with an accompanying guidebook (see, for example, Foster _et al._ (2013)) that can provide user-friendly and self-contained access to development practitioners.

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