metadata: authors: 0: author: Kerr,Andrew Nicholas
1: author: Zondi,Mxolisi
count: World
docna: 0: docna: Measuring the Upper Tail of the Income and
            Wealth Distributions
docty: Policy Research Working Paper
theme: Inclusive Growth,Mitigation,Gender,Human Development and Gender,Data Development and Capacity Building,Economic Policy,Rural Development,Social Development and Protection,Economic Growth and Planning,Environment and Natural Resource Management,Disease Control,Pandemic Response,Fragility, Conflict and Violence,Public Sector Management,Climate change,Urban and Rural Development,Adaptation,Geospatial Services,Data production, accessibility and use
abstracts: cdata!: This paper describes the challenges of
            accurately measuring the upper tail of the income and wealth
            distributions in low- and middle-income countries. It
            reviews the seminal contributions in the literature on
            measuring the top of the income distribution and then more
            recent work, focusing on the challenges in doing so and the
            solutions that have been proposed. The paper focuses mostly
            on incomes, but it devotes a specific section to examining
            measurement of the top of the wealth distribution and the
            key differences compared with measuring income. It then
            identifies gaps in the literature and the implications for
            those undertaking research in this area. Finally, the paper
            proposes a research agenda to close the identified key gaps
            for practitioners, distinguishing between steps that can be
            undertaken with current datasets and those that require new data.
display_title: Measuring the Upper Tail of the
            Income and Wealth Distributions
listing_relative_url: /research/2024/07/34358826/measuring-upper-tail-income-wealth-distributions
topicv3: Income Inequality m1503891 2668,Household Surveys m1504071 2761
publishtoextweb_dt: 2024-07-01T00:00:00Z
dois: https://doi.org/10.1596/1813-9450-10836
origu: Off of Sr VP Dev Econ/Chief Econ (DECVP)
no_of_pages: 40
author_keys: 0: author_key: 1053137
1: author_key: NA
model_extractions: Policy Research Working Paper 10836 Measuring the Upper Tail of the Income and Wealth Distributions _Andrew Kerr Mxolisi Zondi_ Poverty and Equity Global Practice July 2024
Policy Research Working Paper 10836

# **Abstract**

This paper describes the challenges of accurately measuring the upper tail of the income and wealth distributions in low- and middle-income countries. It reviews the seminal contributions in the literature on measuring the top of the income distribution and then more recent work, focusing on the challenges in doing so and the solutions that have been proposed. The paper focuses mostly on incomes, but it devotes a specific section to examining measurement of the top of the wealth distribution and the key differences compared with measuring income. It then identifies gaps in the literature and the implications for those undertaking research in this area. Finally, the paper proposes a research agenda to close the identified key gaps for practitioners, distinguishing between steps that can be undertaken with current datasets and those that require new data.

This paper is a product of the Poverty and Equity Global Practice. 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://www.worldbank.org/prwp. The authors may be contacted at andrew.kerr@uct.ac.za.

_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
Measuring the Upper Tail of the Income and Wealth Distributions Andrew Kerr<sup>1</sup> and Mxolisi Zondi<sup>2</sup> JEL Classification: D31, C81 Keywords: Income Distribution, Wealth Distribution, Top tail, Measurement, Household Surveys 1 School of Economics and DataFirst, University of Cape Town. andrew.kerr@uct.ac.za 2 Research Unit on the Economics of Excisable Products, University of Cape Town We thank Utz Pape, Jed Friedman and Matthew Wai-Poi from the World Bank for helpful comments and suggestions. Mxolisi Zondi was employed by DataFirst at the University of Cape Town when he worked on this project.
# Introduction

This paper describes the challenges of accurately measuring the upper tail of the income and wealth distributions in low- and middle-income countries. We first review the seminal contributions in the literature on measuring the top of the income distribution and then more recent work, focusing on the challenges in doing so and the solutions that have been proposed. We focus initially on incomes, but then devote a specific section to examining measurement of the top of the wealth distribution and the key differences compared with measuring income. We then identify gaps in the literature and the implications for those undertaking research in this area. Finally, we propose a research agenda to close the identified key gaps for practitioners, distinguishing between those that can be undertaken with current datasets and those that require new data.

Kuznets and Jenks’s (1953) landmark study brought together tax data, newly created national accounts and population estimates for the United States to estimate shares of income received by the top percentiles. Similar studies were subsequently undertaken in other countries, but the top of the distribution was then neglected, until being revived in the last 20 years thanks to the work of Piketty (2001, 2003). Following Piketty’s work, researchers have used tax tabulations from official reports, but the availability of tax microdata, also used by Piketty, has also generated further impetus to the research agenda of investigating the top of the income and wealth distribution. A 2022 special issue of the Journal of Economic Inequality, entitled “Finding the Upper Tail”, shows that this is an area of active research. We draw from several of the articles from that special issue below, as well as from Lustig (2020), when discussing the challenges that arise when measuring the top tail of the income and wealth distributions and the solutions.

Atkinson (2007) provided two motivations for better measurement of the top tail of the income distribution - to improve knowledge of the capacity of states to raise extra revenue through increased taxation levels and to measure the extent to which those with high incomes have command or power over other people, including the ability to pay for what Atkinson calls “elite separation”, which he emphasized was a bad thing.

Another motivation for better measurement of the top tail of the income distribution is that while much research acknowledges that the top tail is not well measured in surveys, the extent to which it is under-captured is not known. One common but very approximate statistic that is indicative of the problem that is available for many countries is the difference between total income or consumption in surveys compared to national accounts (Lakner and Milanovic, 2016). Prydz et. al. (2022) show that these differences are substantial, and argue that under-estimates of income or consumption in the top tail are thus part of the explanation, although how much of the explanation under-estimates of 2
the top tail account for and how this may vary across countries or time is not yet clear. The research discussed in this paper provides evidence from a number of countries that better measurement of the top tail increases the estimated shares of the top of the distribution and thus can potentially explain much of the difference between survey and national accounts estimates of total income or consumption.

# Seminal papers

In the absence of representative survey data on income, Kuznets and Jenks’s (1953) pathbreaking study used aggregated data from tax statistics in the US to measure incomes at the top of the distribution, as well as population and total national income from national accounts as controls. Kuznets (1963) compiled similar information from a variety of sources for 18 countries, including 11 developing countries.<sup>3</sup> His conclusion was that the share of the top 5 percent was much larger in developing countries than in developed countries, although the share of the bottom 60% was similar in developed and developing countries. Since some of the data came from tax statistics, shares for the middle and bottom of the distribution were sometimes imputed using parametric methods- for example by estimating the Pareto coefficient for the top of the income distribution using tax data and using this to impute the shares for different parts of the rest of the distribution (Kuznets, 1963:15).

# Recent Literature

Piketty et al. (2022) note that after Kuznets’ work in the 1950s and 1960s, household surveys and the microdata produced from them became much more common. This meant that the entire income distribution could be examined, rather than the top (or top and middle) only, encouraging research on poverty as well as inequality in many more countries that undertook representative household surveys. This meant that the focus on the top end of the income distribution was mostly neglected for several decades, in favor of index measures of inequality that did not bring into focus the very top end of the distribution, unlike Kuznets’ work (Milanovic, 2014).

The neglect of the top end of the income distribution ended with Piketty’s publication of long-run estimates of top income and wealth shares for France for the 20<sup>th</sup> century (Piketty, 2001, 2003), which reinvigorated research on the top end of the income and wealth distributions. Piketty (2003) used data and methods when analysing inequality in France for most of the 20<sup>th</sup> century that were similar to those used by Kuznets (1953)- national accounts data, published tax tables with aggregated data

> 3 Alvaredo and Atkinson (2022) note that similar research had already been undertaken for South Africa by Frankel and Herzfeld (1943) - a decade before Kuznets and Jenks' work for the United States, although this was limited to whites only.

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on taxpayers in various tax brackets and interpolation using the Pareto distribution. But Piketty (2003:1007) notes that he could check the reliability of such methods because tax microdata was available for later periods, in addition to the tax tables.

Piketty’s work stimulated the creation of the World Top Incomes Database (WTID) in 2011, which created top income inequality statistics for 30 countries using similar data to that used in Piketty’s original work (Alvaredo et al., 2016). WTID was later subsumed into the World Inequality Database, which extended WTID to create Distributional National Accounts (DINA). The DINA project aims to provide estimates of the distributions of income and wealth that are consistent with national accounts and harmonized over time and countries (Alvaredo et al. 2016). To do so requires household survey data, national accounts data and ideally either tax microdata or aggregated data. And since comparisons of these data sources often show that household surveys do under-capture incomes and wealth, some of the research on measuring the top tail of the income distribution and the challenges of doing so that we discuss in the next section has come from researchers associated with the DINA project directly.

# The Extent of Income Inequality

A reasonable definition of the top tail of the income distribution is the top 10 percent. Using the World Inequality Database (WID) we briefly describe the share of the top 10% of the income distribution, using the most recent estimate for each region or country. Across all countries for which there is data, and excluding extrapolated or interpolated statistics, the share of the top 10% is 47%. It is only 37% in Europe but is 48% in the US, 56% in Sub-Saharan Africa, 58% in Latin America, 43% in China and 57% in India. These estimates are from a variety of sources and are of varying quality, but the bottom line is that the top of the distribution receive a very large share of total income. The next section discusses the challenges of accurately capturing the top tail using survey and administrative data.

# Challenges to Accurately Capturing the Top Tail in Household Surveys

In this section we document the challenges faced by researchers wanting to use household surveys to measure the top tail of the income distribution. Following this, we focus on challenges when using other types of data, mostly administrative data such as tax or social security records or house prices. Administrative data have been used precisely because of the challenges encountered when using household surveys. However, these types of administrative data are very rare in low-income countries and are still unusual in middle income countries. Thus, household surveys are still very important, which is why we spend some time documenting the challenges associated with using them. In doing so we follow recent papers by Lustig (2020) and Ravallion (2022), although we complement these papers in a variety of ways.

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In the discussion below we refer mostly to the challenges of measuring the top tail of the income distribution. But most of the challenges we discuss apply to measuring the wealth distribution as well. We provide a specific section on how these challenges differ for wealth below.

# _Unit non-response_

One key challenge in measuring the top tail of the income distribution is unit non-response. This means that a household was included in the sample, but no information was collected on that household. The main reasons for unit non-response are refusals and non-contact, with refusals likely to be more common (Ravallion, 2022). Unit non-response is usually classified as being missing completely at random (MCAR), missing at random (MAR) or not missing at random (NMAR) (Lohr, 2009). These mean, respectively, that non-response is ignorable, that non-response is ignorable conditional on some covariates or that it is not ignorable, i.e., that it is correlated with the outcome of interest, here income or wealth.

We did not find a comprehensive overview of unit non-response levels and trends for the World Bank’s Living Standards Measurement Surveys (LSMS). Scott et al. (2005) did review response rates from 8 LSMSs in the late 1990s and early 2000s, finding a non-response rate of 11%. Vaessen et al. (2005) reported an average non-response rate of 2.5% to the Demographic and Health Surveys conducted in 44 developing countries between 1990 and 2000. This, plus the fact that questions about incomes are probably less than or similarly sensitive to questions about health, suggests that unit non-response rates to surveys that include questions on incomes are likely to be much lower in low-income countries than in rich countries. Hlasny (2020) uses surveys collated and harmonized by the Luxembourg Income Study for 38 middle- and high-income countries to show that non-response rates are correlated with GDP per capita. Countries with PPP GDP per capita of around $10,000 had an average non-response rate of around 10%, whereas this was around 25% for those with per capita incomes of around $35,000.

When measuring the top of the income distribution, the concern is the unit non-response rate at the top of the distribution. Ravallion (2022) notes that direct evidence that rich people are missing from surveys is scarce. As evidence that they are missing, he cites a paper by Székely and Hilgert (2007), who used household survey data on 18 South American countries which showed that the highest income individual in each survey had incomes that were similar to that of managers in medium-sized companies, meaning that the top of the distribution was missing. Ravallion (2022) notes that one reason that the rich are assumed to be missing is that rich people have a higher opportunity cost of time and may therefore be less like to respond. Choumert-Nkolo et al. (2023) focus on non-response and assert that high income households in low and middle-income countries (LMICs) often live in gated 5
communities that are much harder to access, resulting in higher non-response rates through noncontact, although they do not provide evidence for this (reasonable) assertion.

Kennickel (2019) shows that non-response rates in the US Survey of Consumer Finances are much higher for those at the very top of the income distribution. The survey has two sample frames, one derived using a regular household survey frame and another for rich households, which is derived from tax filer data. For the richest stratum of the tax filer derived sample frame, described as “a group in the upper reaches of the top 1%”, the response rate in 2013 was less than 10%, compared to 66% in the sample obtained from the regular household sample frame (Kennickel, 2019: 446).

Hlasny and Verme (2018) used data from the Egyptian Income and Expenditure Survey to show that unit non-response rates are higher in Egyptian governorates with higher mean income per capita. The National Income Dynamics Study (NIDS) in South Africa obtained much higher unit non-response rates than the previously mentioned LMIC surveys- 31%. Non-response rates by race of the predominant racial group in the primary sampling unit (PSU) also varied. Predominantly white areas had nonresponse rates of 64% while predominantly black areas had a non-response rate of 24% (Leibbrandt et al. 2009). Since race is strongly positively correlated with income in South Africa, the implication is that non-response rates are increasing with income, which is a concern when measuring the top of the income distribution.

# _Item non-response_

We have noted that refusals or non-contacts may limit how well one measures the top of the income distribution if the rich have high non-response rates. But those individuals who do respond to a survey may not answer specific questions about incomes, wealth or consumption, since these are more sensitive. This issue is called item non-response. Like unit non-response, this can be missing completely at random, or it may be related to other individual characteristics or income levels themselves. If the latter, then this is a form of selection bias, like the potential bias of unit nonresponse.

Bollinger et al. (2019) used linked survey and administrative earnings data from the US to show that item non-response is not missing completely at random- it is highest at low and high earnings. Such studies require substantial resources and are thus unfortunately uncommon in LMICs. However, Flachaire et al. (2022) did obtain such linked survey and income tax data from Uruguay. The authors show that item non-response was around 10% in the surveys and that it was highest at the bottom of the income distribution, a surprising result that, taken at face value, suggests that item non-response may not be as much of a concern when measuring the top of the income distribution as one might expect.

6
Many surveys ask for a reason for the item non-response. Both NIDS and Statistics South Africa household surveys allow “refusal” and “don’t know” answers to earnings questions. In the Statistics South Africa surveys, “don’t know” responses are overwhelmingly given by proxy respondents, who are answering on behalf of another household member. In some sense then, don’t know item nonresponse is similar to non-contact unit non-response, but it is a specific household member who cannot be contacted to obtain answers to some questions that another household member does not know the answer to.

Lepkowski (2005) and Si et al. (2023) highlight that item non-response for total individual or household income or wealth may be a combination of item non-response or response for several questions on each subject for the same person or household, making measurement of total income, consumption or wealth even harder. In South Africa wave one of the National Income Dynamics Study (NIDS) in 2008, 41% of households had at least one of a detailed set of consumption items missing (Finn et al. 2009). We discuss solutions to item non-response in the sections that follow.

# _Measurement error_

Even if individuals respond to a survey and to the questions on incomes, there is still a concern that the true income of household members is not accurately captured. The obvious example of measurement error when thinking about the top tail of the income distribution is under-reporting by respondents who do not want to reveal their true incomes, perhaps because of concerns that these will be reported to tax collection agencies (such data sharing is illegal in some countries). Other types of measurement error affecting the top tail could occur when survey questions ask about gross income, but respondents give after tax income or even after other deductions such as medical insurance or pension fund contributions (which could be important in the top tail even in low-income countries and more important in middle income countries).

It is hard to find direct evidence of under-reporting because this requires matched survey and administrative data. We noted above that Flachaire et al. (2022) obtained such data for Uruguay. The authors showed that under-reporting in the household survey they used is, on average, highest at the top of the tax income distribution, as might be expected, but that there is over-reporting at the bottom of the distribution. In the top five percentiles, the tax data values are, on average, around 2 to 2.5 times as large as the values reported in the surveys. This is novel evidence that under-reporting is indeed an important issue when measuring the top tail of the income distribution, although the data requirements are so exacting there are, to our knowledge, no other similar studies for LMICs. Bollinger 7
et al. (2019) also find that similar patterns of measurement error in earnings in the US Current Population Survey (CPS).

# _Sparseness_

Household surveys used to measure the top tail of the wealth or income distribution may have a sample of only a few thousand households. This makes it possible that no very high-income households or individuals are sampled, meaning one has a right truncated distribution. And when such individuals do appear in the sample, they may appear to be incorrect outliers (Jenkins, 2017, Lustig, 2020). This can lead to volatility when measuring the top tail of the distribution over time within countries (Burkhauser et al., 2017) or across countries, meaning it is harder to discern trends or make cross country comparisons. But there may also be incorrect outliers, and discerning which data are real and which are not is thus important.

# _Proxy respondents_

We highlighted above that item non-response can result from proxy respondents answering “don’t know” to questions on incomes of other household members. Many household surveys, including the LSMS, ask most or many questions to the most knowledgeable household member (Kilic et al. 2021, Doss et al. 2008) or, in the US CPS, to any one household member (Bollinger et al. 2019), rather than to each member individually.<sup>4</sup> In discussing the measurement of consumption, Deaton (2005) notes that proxy respondents may also answer incorrectly or under-report and that this is likely to be worse for richer households when the responding household member may not know about all consumption of other household members. This means proxy respondents may introduce additional measurement error, over and above that discussed above.

Hasanbasri et al. (2022) showed that measured wealth inequality is higher when questions about individual asset ownership assets are asked to each household member individually, rather than to a most knowledgeable household member. This research suggests that whether data was collected from each member or from one member in a household survey will matter when measuring the top tail of the wealth distribution.

> 4 The South African National Income Dynamics Study is one example of a survey which attempted to interview each household member separately as well as obtaining household information from the oldest woman in the household. A shorter proxy respondent questionnaire was completed if the individual could not be interviewed.

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_Data processing_ How survey organizations process the data obtained from respondents is also an important issue for measuring the top tail of the income distribution. The main concern is top-coding, where the survey organization does not provide the actual income for individuals close to the top of the distribution but provides the value of some percentile for all respondents above that value- usually as a way of mitigating privacy concerns. The extent of top coding can be large- Burkhauser et al. (2012) document that 4.6% of individuals in the US CPS live in households in which some source of income was top coded.

In LMICs where statistical capacity may not be as good as in rich countries there are other data processing concerns. McLennan et al. (2021) show that in the Tanzanian Household Budget Survey (HBS) public data there are very large labor income values generated from individuals reporting high hourly rates of earnings, which are then multiplied by 8 (hours in a day) and then by 22 days in a month. These errors are so large that the implied tax revenue is substantially higher than actual tax revenue collected. McLennan et al. (2021) highlight that the public release documentation for the Tanzanian HBS contains no information about how such cases are treated. How these were processed and whether enough data is released publicly to allow alternative assumptions will matter when measuring the top tail of the distribution.

Some of the very large hourly earners in Tanzania might be contaminated incorrect outliers but it is possible they could be genuine high earners. The solution used by McLennan et al. (2021) is to cap large values at the 99<sup>th</sup> percentile of the labor income distribution, which is not suitable when trying to measure the top tail of the distribution.

A lack of documentation on this and other edits and decisions taken when processing data from household surveys is likely to be true in other LMICs. Kerr and Wittenberg (2021) note that earnings are imputed in South Africa’s Quarterly Labour Force Surveys, that these imputations are of poor quality but that they are undertaken and how they are undertaken is not mentioned in any public documentation. The obvious recommendation is that survey organizations and statistical offices should release as much documentation and data as possible without compromising respondent anonymity.

# _Lack of income data in household surveys in some LMICs_

A key challenge in measuring the top tail of the income distribution in LMICs is that many household surveys do not collect data on incomes. This is mainly because reported incomes are seen as less 9
reliable than reported consumption in LMICs, where self-employment and/or agriculture predominate, and which makes accurate reporting of incomes difficult (Deaton, 1997). The concerns about the reliability of income data collected in poor countries pertain mainly to measuring poverty. It is possible that income data is more reliable at the top end than at the bottom because agricultural income is likely to be less important at the top. However, self-employment income is still likely to be important, although the extent to which more accurate record keeping in formal or at least larger businesses translates into better income data in surveys is unclear.

# _Lack of common support_

All the challenges discussed thus far can limit the number of observations with incomes close to the top of the true income distribution. At worst, this can result in a lack of common support between the top of the distribution in the household survey and the true distribution, meaning that there are simply no individuals in the surveys with reported incomes near the top of the true income distribution (Lustig, (2020), Ravallion, (2022)). This implies the surveys will not accurately represent the top of the income distribution. But it is also a concern because some of the solutions to the measurement challenges that we discuss below require at least some individuals in the surveys at the top of the distribution.

Table 1 summarizes the challenges described above, in a rough order of their importance when measuring the top tail of the income or wealth distribution. However, we should stress that the order is likely to vary in different countries and/or time periods and depend on the level of development of the country concerned. In the section below outlining the research agenda, we further discuss which challenges are more important and deserve further investigation.

Table 1: Measurement Challenges for the Top tail of the Income and wealth distributions

|**Challenge**|**Description**|
|---|---|
|Unit non-|High Income or Wealth Individuals or Households do not respond to the survey|
|response|at all|
|Item non-<br>response|High Income or Wealth Individuals or Households respond to the survey but do<br>not respond to income or wealth questions|
|Measurement|High Income or Wealth Individuals or Households respond to the survey but|
|Error<br>Sparseness|under-report their incomes or wealth<br>The survey sample size is relatively small, and few or no high income or wealth<br>individuals are sampled|
|Lack of<br>Common<br>Support|The challenges above mean that there are no individuals with income or wealth<br>in the top tail of the distribution|
|Data|The survey organization creates measurement error that makes the measured|
|Processing|top tail unreliable|

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Proxy Respondents High Income or Wealth Individuals do not respond to the survey and other household members answering on their behalf under-state their incomes or wealth Ex ante solutions for the challenges when using household survey data Following a distinction made by Ravallion (2022), in this section we discuss ex-ante solutions to sparseness, unit non-response and item non-response – solutions that can be implemented in survey design. In the next section we discuss ex-post solutions that use survey and administrative data to address the general challenge of missing top incomes.

A summary of all the solutions to the challenges of measuring the top tail of the income and wealth distributions reviewed in this paper, as well as a description of these solutions and key references, can be found in Table 2 below.

Table 2: Solutions to Measurement Challenges for the Top tail of the Income and wealth distributions

|**Ex Ante**|**Solutions**<br>Oversample rich<br>households|**Challenge**<br>Sparsity|**Data Type**<br>Requires tax data<br>with address<br>information or<br>population<br>census or tax<br>data with low<br>geographic level<br>identifiers|**Description**<br>Use tax data or population<br>census data to oversample<br>rich households|**Key**<br>**references**<br>Kennickel<br>(2019)|
|---|---|---|---|---|---|
||Improve<br>fieldworker<br>protocols|Unit non-<br>response|None|Require multiple visits,<br>improve fieldworker training|Ravallion<br>(2022)|
||Questionnaire<br>design<br>improvement|Item non-<br>response|None|Design questionnaire to<br>obtain at least some income<br>information for those who<br>would otherwise not provide<br>any.|Lepkowski<br>(2005)|
|||||Use PSU or regional|Korinek et|
|**Ex Post**|Reweighting|Unit non-<br>response|survey data only|response rates plus an<br>econometric method to|al. (2006),<br>Ravallion|
|||||adjust sample design surveys|(2022)|

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|Reweighting||survey and admin<br>data|Use admin data to adjust<br>sample weights so that<br>shares of high earners in the<br>surveys match the admin<br>data. Requires common<br>support.|Campos-<br>Vazquez and<br>Lustig (2019)|
|---|---|---|---|---|
|Replacing-<br>imputation|Item non-<br>response|survey data only|Use incomes of those who<br>do respond to impute<br>incomes for those who don't|Campos-<br>Vazquez and<br>Lustig (2019)|
|Replacing-<br>parametric<br>distribution<br>Replacing|Various<br>Various|survey data only<br>survey and admin<br>data|Estimate parameters for (for<br>example) a Pareto<br>distribution using the<br>bottom X% of the survey<br>distribution, impute earnings<br>for the top (1-x)%<br>Replace the top X% of the<br>survey distribution using<br>admin data and either<br>parametric or non-<br>parametric methods.<br>Endogenously determine a<br>merging income value,|Jenkins<br>(2017),<br>Hlasny and<br>Verme<br>(2018)<br>Alvaredo<br>and<br>Londono<br>Velez (2013),<br>Bach et al.<br>(2009),<br>Burkhauser<br>et al. (2018),<br>Czajka<br>(2017), Van<br>der Weide et<br>al. (2018)|
|Reweighting and<br>Replacing|Various|survey and admin<br>data|above which use admin data<br>to reweight survey data and<br>then replace survey with tax<br>data to allow representivity<br>at the very top|Blanchet et<br>al. (2022)|

# _Sparseness_

One solution to the lack of sampled households or individuals at the very top of the distribution is to oversample such households. The US Survey of Consumer Finances aims to obtain estimates of the wealth of households in the US. The survey has two independent samples – one that has a positive probability of selection for all US households and a second that includes only the rich in the sample frame, which is derived from tax filings (Kennickel, 2019). Although such a sample design does improve the sample size at the top of the distribution and thus potentially solves the sparseness problem, the response rates for the survey drawn from the rich sample frame survey are still very low, less than 10% for the wealthiest (Kennickel, 2019). The very low response rates implies that sparseness could 12
still be an issue. Oversampling is not common in LMICs but is undertaken in some surveys – for example measuring wealth in Chile and Uruguay (Gandelman and Lluberas, 2023).

## _Unit non-response_

We noted that a solution to sparseness is to oversample high-income individuals. But if there is a lack of high-income individuals because of unit non-response of high-income individuals then oversampling can also play a role in ameliorating possible unit non-response bias.

Unit non-response can also be reduced if survey protocols require enumerators to visit a certain number of times on different days before recording a non-contact (Ravallion, 2022). Another potential solution to unit non-response that has been discussed in the literature is to provide incentives to participate in the surveys. Ravallion (2022) points out that is a concern, especially for measuring the top tail of the income distribution, because the poor may be more likely to be persuaded than the rich, which could make non-response bias worse (Ravallion, 2022). The impact of incentives on response rates was investigated by Stecklov et al. (2018), who randomized a small monetary incentive in an Indian household survey, finding that whilst it did improve response rates it also resulted in those households receiving the incentive reporting lower consumption. The authors hypothesized that this was due to respondents exaggerating their poverty in the hopes of future payments from the surveyors.

## _Item non-response_

Lepkowski (2005) notes that one way of reducing item non-response to income or wealth questions asking for a monetary value a priori is to ask “unfolding bracket” questions if a respondent is unwilling or unable to give a monetary value, in which respondents are asked whether their income lies above or below a certain value. Depending on the answer, further questions about the range in which income lies are asked. This method was used in the South African National Income Dynamics Study. A simpler version of this is one question where individuals are asked which bracket their incomes fall into. This at least provides some indication of the level of income. It is used by Statistics South Africa in the Quarterly Labour Force Surveys and General Household Surveys. In 2020 quarter 1 around 20% of employed individuals give bracket responses, around 50% give amounts and 30% refuse or don’t know.

# Ex post Solutions for the Challenges Encountered When Using Household Survey Data

Despite the best efforts of survey organizations to lessen item and unit non-response and sparsity, the income or wealth data from household surveys may still be missing part of the top of the distribution. In this case ex-post methods are required to solve missing top incomes. Hlasny and Verme (2022) characterized ex-post solutions to under-capturing of the top tail of the income distribution in 13
household surveys as methods that used either replacement or reweighting. Replacement involves replacing some part of the top of the income distribution in the household surveys parametrically- e.g. with values from the Pareto distribution with the parameter estimated using the rest of the survey distribution. Reweighting involves increasing the weights of those at the top of the distribution to account for unit non-response. We now discuss reweighting for unit non-response as well as imputation and parametric replacement, both of which can be classified as methods using replacement. Lustig (2020) highlighted that the replacement and reweighting distinction can also be applied to solutions that use administrative data, and we discuss solutions using administrative data in the following section.

# _Using survey data only_

In this section we first discuss reweighting as a solution to non-random unit non-response and imputation to solve non-random item non-response. These are methods with long histories in the statistics literature and solve very specific problems with specific solutions. We then discuss using consumption data and imputing top incomes using the survey data.

# Reweighting for unit non-response

Unit non-response is unlikely to be MCAR. Ravallion (2022) discusses solutions for non-random unit non-response. One is to find replacement observations, but this is unlikely to solve non-random nonresponse, since presumably the same biases affecting original non-response will affect which households respond as replacements. One benefit of replacement is that it does raise the sample size, which may be important for studying the top of the income distribution since it can reduce sparseness problems.

A commonly used method to solve unit non-response is reweighting, where the respondents in different groups (“weighting classes”) are upweighted to represent themselves and those in the same group that did not respond. The reweighting groups are often regions (Korinek et al. (2006)), which implies that for the method to be successful non-response must be random within regions, or that non-response is “ignorable” within regions (Ravallion, 2022). The size of the regions used is likely to affect the proportion of bias the reweighting can solve, since non-ignorability is likely to be less of a concern when using smaller geographical regions. The US CPS uses 254 cells for the entire country. It is common for the PSU, a much smaller region, to be the area used to undertake the reweighting (Hlasny and Verme (2018) document this for the Arab Republic of Egypt, Kerr and Wittenberg (2015) document this for South Africa).

Korinek et al. (2006) argue that non-response is unlikely to be ignorable and provide an econometric method to adjust survey weights for selective compliance in responding. Korinek et al. (2007) show 14
that responding is positively correlated with incomes in the US CPS and that correcting for this raises the mean income in the top percentile by around 40%. The authors note that only regional level response rates are required to implement the method.

The Korinek et al. (2006) method has subsequently been used in several papers to correct for selective compliance on income. One of these is Hlasny (2020), who used 66 Luxembourg Income Study surveys for 38 upper- and middle-income countries and collected regional unit non-response rates to implement the Korinek et al. (2006) corrections. He finds extremely large effects across the countries for some statistics- the mean top 1% share of income is 6.5% across the 66 surveys but the Korinek et al. (2006) non-response adjustment increases this to 17% (Hlasny (2020), appendix A6). There are also several extreme or even implausible cases- the Italian top 1% share rises from 6% to 44% in the 2008 survey after the unit non-response corrections but only from 5% to 16% in the 2010 survey.

# Imputation for item non-response

Like in the case for unit non-response, it is possible to ignore item non-response by using only the data from responders. To the extent that item non-response is ignorable this is reasonable. It would still mean the sample size is reduced, however, which matters for the variance of any estimates and can worsen sparsity problems.

But the missing data is very unlikely to be ignorable and so other solutions are required. The most common solution is imputation. This involves using responses to other questions in the survey and/or external data to predict earnings for those who did not respond to the question on income. A common method for incomes is hotdeck imputation, in which the income of a person or household with the same set of specified characteristics is “donated” to the individual with missing income (Lohr, 2009).

The problem with single imputation methods, including hotdeck imputation, is that they fail to capture the uncertainty about the true values for those whose values are imputed. Multiple imputation methods (Rubin, 1987) were developed to overcome this problem, in which missing data is imputed multiple times- for example 10 donors are chosen randomly instead of one for hotdeck multiple imputation. The variation across the estimates from the multiple samples captures the uncertainty.

One issue with any imputation method when measuring the top of the income distribution is that there may be a high fraction of individuals with missing incomes at the top of the income distribution. In this case, the few individuals with incomes will each donate their incomes to multiple other sample members. This is a version of the sparsity problem discussed above.

We noted that some surveys allow bracket responses, which is still partial item non-response. Wittenberg (2008) provides a solution when there are bracket responses. The idea is similar to 15
reweighting for unit non-response- to weight up those who respond with amounts so that they represent themselves and the other respondents who responded in the bracket in which the amount reported falls. This improves on single imputation methods (such as mid-point or even hotdeck) because it allows for the uncertainty in the true value, which other single imputation methods do not.

# Imputing the income distribution from consumption data

Household surveys in many LMICs collect only consumption data, since income data is assumed to be less reliable, particularly for measuring poverty. Chancel et al. (2023) attempt to estimate income inequality levels and trends in Africa between 1990 and 2010 for countries covering 60% of the population (and 80%-90% of the population from 1995-2010). But because of the complete lack of income data or harmonized and publicly available consumption microdata for most of these countries, Chancel et al. (2023) used the World Bank’s Povcalnet consumption data on shares of consumption by decile and then data for five countries where both income and consumption microdata were available was used to impute the income distribution in the rest of the countries. This lack of income data implies that estimating the income distribution in many African countries, let alone the top end of this distribution, is impossible with the data that currently exists and is publicly available. As we discuss below, there are other African countries with surveys that asked about income and consumption that were not used by Chancel et al. (2023). We also note that limited income data collection is not prevalent in all LMICs - Latin America has long had income data collected in household surveys (Lustig, 2020).

Using survey data and parametric distributions estimated from survey data Imputation for item non-response and reweighting for unit non-response are specific solutions for specific problems. A more general solution to the more general problem of missing top income recipients (whether due to sparsity, measurement error, non-random unit non-response etc.) is to replace the incomes at the top of the distribution with values drawn from a specific distribution. For example, if top incomes are assumed to have a Pareto distribution it is possible to estimate inequality measures for the top X% of observations assuming the incomes are Pareto distributed, where the Pareto parameter is estimated using the survey data above the Xth percentile. An overall measure of inequality, like the Gini coefficient or the share of the top 1%, is then estimated from the top X percentiles and the bottom (100-X) percentiles.

Jenkins (2017) argues that this method of replacement of top incomes does not work very well in the UK for solving under-capturing of top incomes, by comparing it to methods using tax data. Hlasny and Verme (2018) use this method to estimate income inequality in Egypt. In their preferred results Hlasny and Verme (2018) replace the top 10% of the distribution with a Pareto distribution estimated using 16
the rest of the distribution, finding that the estimated income Gini coefficient is unchanged by this replacement of top incomes.

# _Using survey data and administrative data_

As noted above, Hlasny and Verme (2017, 2022) described solutions to under-capturing of the top tail of the income distribution in household surveys as methods that used either replacement or reweighting. Lustig (2020) used this distinction to also classify many of the methods that use both household survey and administrative data as methods using either replacing and/or reweighting. In the context of combining administrative and household survey data, replacement involves replacing some part of the top of the income distribution in the household surveys with data from another source. Reweighting involves increasing the weights of those at the top of the distribution, to match the distribution of income in the administrative data source. We now discuss each of these methods and provide examples.

# Reweighting

Survey calibration means the adjustment of survey weights, usually after unit non-response adjustment of the weights, so that the weighted population estimates for basic demographics (such as age, sex or regions) from the household surveys matches information from demographic models or other external sources of population information. These “reweighting” methods have also since been used to improve estimates of the top tail of the income distribution when administrative data on earnings has been available. For example, Campos-Vazquez and Lustig (2019), obtained Mexican Social security administrative earnings data between 2000 and 2017. The admin data they had access to is the proportion of employed individuals in 25 earnings categories representing multiples of the minimum wage. The authors’ comparison of the survey and admin data clearly shows the undercapturing of the top tail of the earnings distribution. In 2017 the admin data showed that 9% of formal sector workers earned more than 10 times the minimum wage, whereas the proportion was only 2% in the labor force survey. The authors then adjust the survey weights so that the proportion of formal sector workers in each earnings category in the surveys matches the proportion in the administrative data.

Campos-Vazquez and Lustig (2019) note that the item non-response rate for the earnings questions in the Mexican labor force survey rose from 5% in 2002 to 30% by 2017. To solve this issue one of the sets of corrections implemented by the authors is to first undertake hot deck imputation for the item non-response and then the reweighting explained above. So this set of corrections actually involves replacement and then reweighting. As well as mechanically increasing the share of individuals in the 17
top earnings bracket due to the calibration, the corrections make a substantial difference to trends over time in the top tail. Without imputation and reweighting the earnings for the top 10 percentiles supposedly shrank by between 25% and 30%, whereas with these corrections they rose by between 1 and 8 percent.

# Replacement

Replacement using household and administrative data means that some of the incomes in the household surveys are replaced with incomes in the administrative data. There are various methods that have been used in this broad approach. One distinction is between those that use parametric and non-parametric replacement (Lustig 2020). Parametric replacement involves estimating the Gini coefficient or some other inequality measure for the top x% of the income distribution from tax or other administrative data by assuming the top incomes follow a Pareto distribution, estimating the Pareto parameter and using this to obtain the implied Gini coefficient of the top x%. This is very similar to the methods described above using survey data only. One can then estimate the Gini coefficient for the bottom (1-x) % of the population using survey data and combine them to obtain an overall measure of inequality, using the results of Alvaredo (2011) that the Gini can be decomposed using shares of the top (say) 1% and the bottom (say) 99%. Alvaredo (2011) used tax data and the Current Population Survey for the US to show that the increase over time in the Gini coefficient doubled when adjusting for missing top earners. This method was also used by Alvaredo and Londono Velez (2013) for Colombia, who showed that when using tax data to replace the top 1% of incomes in the surveys, inequality levels were substantially higher, and the trend of declining inequality was much smaller than when using uncorrected household surveys.

Non-parametric replacement with admin data involves either replacing higher income individuals in the household surveys with individuals from admin data or imputation of incomes in surveys using incomes in admin data observably similar individuals. Bach et al. (2009) undertook this this for Germany, using unit record tax data and the German Socio-Economic Panel to match individuals in the survey and tax data and replace the survey respondents with similar individuals in the tax data. They found that the Gini increased by 6 percentage points, and that increases among individuals at the very top of the income distribution drove the increase in inequality in Germany between 1992 and 2003. Non-parametric replacement was also undertaken by Burkhauser et al. (2018), who used UK household surveys but replaced top incomes with cell means from tax data for the UK, which is a method applied by the UK Department of Work and Pensions. This increased Gini coefficients in most years between 1994 and 2014 and reduced volatility over the different surveys compared to the 18
estimates using household survey data only. Czajka (2017) used tax and survey data from Côte d’Ivoire to implement a similar correction- he adjusted the survey data incomes in the formal private sector in each percentile by the ratio of the tax to survey ratio of mean incomes in each percentile. This adjustment increased the share of the top 1 percent by nearly 50 percent.

Van der Weide et al. (2018) examine inequality in urban Egypt and are concerned with the under capturing of top incomes in household surveys. They note that in most developing countries tax data, even in tabulated form, are not available. The authors also highlight that tax evasion is common in LMICs, as is a large informal sector, which limits the usefulness of tax data even when it does exist. To solve the lack of administrative data in Egypt, Van der Weide et al. (2018) use data on urban house prices, obtained from a private company, to improve estimates of top incomes. There are several steps undertaken by Van der Weide et al. (2018) to use house prices to replace top incomes, not all of which seem reliable. One obvious issue is the lack of house prices in the surveys to estimate a relationship between household income and house prices, which would then be applied to the admin data on house prices. The lack of house prices means the authors estimate the relationship between household incomes and housing rents, which are imputed for owner occupied housing. There is also no detail provided on how rents are imputed. Despite these issues, this is an example of a method that can be used when tax data are not available. The impact of the adjustments using house price data to impute incomes is very substantial- the Gini rises by around 30% after the replacement of top incomes.

# Reweighting and replacement

The third solution to missing top incomes that uses household and administrative data is a combination of the previous two methods. Blanchet et al. (2022) focus on reweighting to solve the under capturing of the top tail in household surveys, but they also use replacement. The authors highlight that in previous work using replacement of household survey top incomes with admin data (including Alvaredo (2011) for the US, Burkhauser et al. (2018) and Alvaredo and Londono Velez (2013), all discussed in the previous section), the point in the distribution where survey data information is replaced with administrative data is chosen arbitrarily (e.g. the top 1%). The novel contribution of the authors is to endogenously determine the optimal merging point between household surveys and tax data. Having done so, the authors use survey calibration methods to ensure that the numbers of individuals in each tax bracket in the surveys and the tax data match.

Whilst the calibration solves non-sampling error problems, Blanchet et al. (2022) note that the method still leaves small samples at the top of the distribution, which can, as discussed above, result in large 19
sample to sample variation. If there is a substantial lack of common support simply because of sampling error, then reweighting can also not solve this. To make progress Blanchet et al. (2022) use a replacement step, creating duplicates of observations in the surveys and assigning to each observation above the merging point the average income for its population share (the population share is determined by each individual’s weight and the population size) in the tax data. This replacement step also preserves the distribution of other variables and their relationship with income in the survey data.

Alvaredo’s (2011) analysis for Argentina assumed that the top 1% was completely missing from the household surveys, and therefore tax data should be used for the top 1%. Blanchet et al. (2022) point out that this is an extreme form of reweighting where the weights of the survey respondents are rescaled, so they represent the bottom 99% and then tax data completely represents the top 1%. Alvaredo (2011) showed that the Gini was 6-7 percentage points higher when correcting for missing top incomes using this method for Argentina.

Chancel et al. (2023) estimate inequality and provide distributional national accounts for African countries between 1990 and 2017. In doing so the authors attempt to overcome several challenges, as discussed above, including a lack of income data in many African countries, poor quality of national accounts and the assumed under-representation of the top tail of the distribution. Their starting point is not raw survey data, but tabulations on consumption per capita from the World Bank’s Povcalnet database, from which they impute consumption percentiles. They do use household survey microdata for five African countries, because these surveys asked respondents about income and consumption, and so are used to determine the relationship between the two over the distribution of consumption, meaning consumption can then be used to impute incomes where only consumption data is available from Povcalnet.

Chancel et al. (2023) then use tax data from South Africa and Côte d’Ivoire, the only African two countries where such data was available to the authors, to determine the extent of under capturing of top incomes and then to use this to correct the income distributions for the rest of the countries, themselves almost all imputed from consumption decile share data derived from surveys. Chancel et al. (2023) then parameterize the under-capturing of incomes by percentile using the tax data. They use their results to assume that the bottom 80% of the distribution is unaffected while the top 1% is adjusted upwards by between 50 and 100%.

This summary of differing methods using survey and administrative data shows that attempts to solve the under-capturing of the rich in household surveys have common elements, although the (non-) 20
availability of administrative data sources is a key determinant of what is possible. Increasing access to tax data, even in summarized form, seems like a key goal if under-capturing of the top tail of the income distribution is to be solved.

# Challenges in Using Administrative Data

The discussion above has highlighted that administrative data can be used in several ways to solve challenges encountered in measuring the upper tail in household surveys. But these data also come with their own challenges, particularly in LMICs. In this section we discuss some of these challenges. Awareness of the challenges of using admin data is not new. Kuznets (1963:12), in comparing top income shares across countries produced by several different researchers, noted that “it may not be an exaggeration to say that we deal here not with data on the distribution of income by size but with estimates or judgments by courageous and ingenious scholars relating to size distribution of income in the country of their concern.” Haq (1964) lists several specific concerns in her analysis of income inequality in Pakistan using aggregated tax data. These concerns have subsequently been highlighted in recent research using admin data to better measure the top tail of the income distribution. These include the very small proportion of the population covered by tax data, which was one tenth of one percent in Pakistan at the time, changes in tax legislation that limited comparability over time (for example changes in the tax threshold), changes in efficiency of tax collection over time and the extent of the unregistered (i.e., informal) sector.

Other issues have also been highlighted in more recent research. Ravallion (2022) cautions that comparisons of surveys and national accounts data that show lower total incomes in surveys compared to national accounts could reflect the poor quality of national accounts rather than missing top incomes. Blanchet et. al (2022) note that in LMICs tax data is almost always in the form of aggregated tables rather than microdata, which limits what it can be used for and point out that even when microdata is available it contains few covariates, which can limit how the data can be used to improve estimates of the top tail from household surveys.

Kerr (2021) highlights that researchers using and comparing tax and survey data for South Africa created yearly earnings from household surveys obtained by multiplying monthly earnings by 12 for those employed at the time the survey was undertaken. This is very different conceptually to tax data on earnings in the last year, since the surveys exclude those employed at other points in the year, who are more likely to be low earners. Kerr (2021) show that, in the South African case, this error makes 21
the household survey and tax data earnings distributions look closer than they are, and thus understates the extent of under-capturing of high earners.<sup>5</sup> Piketty et al. (2022) note that tax evasion and avoidance can reduce measured top income shares compared to the true number and that these can both vary across time and countries, making within and between country comparisons difficult. Jouste et al. (2023) show that an increase in the top marginal tax rate in Tanzania, from 30% to 40%, which affected the top 1% of earners, may have resulted in declines in reported incomes. In addition, that income in tax data does not include incomes important at the top of the distribution, like retained earnings in firms (Piketty et al., 2022), is also likely to be important in middle-income countries, although probably not for low-income countries with very large informal sectors.

A final challenge is the survey and tax data may not identify the same units, and tax and other forms of administrative data may not give a welfare measure that economists care about (Ravallion, 2022). Many countries have joint tax filing for married couples, and this can make it more difficult to use the tax data to complement surveys. Tax data also usually tell us little about households and thus cannot easily be used to create a measure of household per capita income. Ravallion (2022) points out that using tax data to improve surveys can often require researchers to define and use taxable income from the surveys to match what is available in the tax data, but that taxable income is not an appropriate measure of welfare, ignores transfers and is thus likely to overestimate income inequality.

# Measuring the Upper Tail of the Wealth Distribution

Thus far we have focused on the challenges when measuring the top of the income distribution. But much of the preceding discussion applies directly to wealth. In this section we focus on aspects of measuring the top of the wealth distribution where there is not a simple correspondence between the literatures on measuring the top of the income and wealth distributions.

All of the challenges that we have discussed above in measuring the top of the income distribution using household surveys also apply to measuring the wealth distribution, although some are even more of a concern. The ex-ante solutions we discussed above can also be used to solve wealth challenges, as can the ex-post solutions using survey data. But other solutions that researchers have used have relied on novel types of data. We discuss these issues in this section.

> 5 This is not an issue if a survey asks about earnings over the last year to all individuals, including those not currently employed, as the US CPS does. In countries where most employed people are employed throughout the year, this may also not be a substantial concern.

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# Sources of Wealth Data

Wealth data is collected less frequently than incomes, which are themselves not as common as consumption, particularly in low-income countries. But wealth surveys do exist- China and India have household surveys that collect detailed data on assets and liabilities of households- the Household Income Project (CHIP) for China and the All-India Debt and Investment Survey (AIDIS). There are also wealth focused surveys in Latin America- the Chilean Household Financial Survey, Colombian Household Financial Burden and Financial Education Survey, Mexican National Survey on Household Finances and the Financial Survey of Uruguayan Households (EFHU) (Gandelman and Lluberas, 2023). But such surveys are not common in LMICs. One recent example to improve data on assets is the World Bank Living Standards Measurement Study-Plus (LSMS+) program to measure the ownership of, and rights to, selected physical and financial assets in various African countries ( <mark>Hasanbasri et al., 2021</mark> ). These surveys collected the value of assets but do not measure liabilities, so net wealth cannot be computed.

Administrative data may provide information on wealth, although this is sometimes harder to utilize than administrative data on incomes. This is because most tax administration systems do not collect data on all or most forms of wealth directly. The most common wealth data collected through tax administration systems is estate records (Piketty and Saez, 2006). Wealth data is also collected when countries have wealth taxes, but these are not common. Some tax authorities ask questions about assets, even though they are not taxed, but, given that they are not taxed, the accuracy of the data can be questioned. To estimate wealth from income tax data, researchers use the capitalization method, in which capital income and an assumed or observed rate of return are used to estimate the value of the capital generating the observed capital income (Roine and Waldenstrom, 2015, Saez and Zucman, 2016).

In recent times other less traditional forms of data have been used to measure the top of the wealth distribution. One source is rich lists compiled by Forbes or other organizations (Piketty et al. 2022, Bach et al. (2019), Xie and Jin (2015)). These sources provide wealth estimates for the extreme top of the wealth distribution and can be used as a check on the household survey or administrative data wealth estimates.

A second set of non-traditional data sources was used by Alstadsæter et al. (2019). These sources were an HSBC Switzerland leak of customer data, voluntary declarations of hidden assets from tax amnesties in Norway, Sweden and Denmark and leaked information of shell company owners in Panama, the Panama Papers.

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# Concentration of Wealth

Wealth is even more unequally distributed than income. Saez and Zucman (2016) measure wealth inequality in the United States and find that in 2012 the top 10% of households owned a staggering 87.7% of the total wealth. In LMICs, wealth is also highly concentrated. In South Africa the top 10% owned 85% of total wealth (Chatterjee et al, 2022), while in Latin America, the World Inequality report estimated that the top 10% owned 77% of total household wealth (Chancel et al, 2022). The top 10% owned 67% of wealth in China (Piketty et al., 2019) and 63% in India (Anand and Thampi, 2016). The extreme inequality of wealth in many parts of the world means that the same challenges researchers face when measuring the top of the wealth distribution using household surveys are even more of a concern. For example, unit and item non-response and sparseness are much more severe problems when wealth is concentrated in the hands of fewer people than incomes.

# Solutions to Challenges of Measuring the Top of the Wealth Distribution

The solutions to challenges to measuring the top of the wealth distribution are similar to those described above for income, so we do not discuss the methods themselves again. Instead, we discuss research that has used these solutions to improve estimates of the wealth distribution in LMICs. We noted above that wealth data is much less common than income data. This means that there is much less research on wealth that attempts to improve measurement of the top of the wealth distribution in LMICs.

Alstadsæter et al. (2018) is an example of using non-traditional data on wealth to supplement administrative data estimates of the share held by the top of the wealth distribution. The authors used the data described in Alstadsæter et al. (2019), discussed above, to improve the estimates of the shares of wealth held by the top 0.01% for 10 countries, although the only LMIC included was the Russian Federation, where the share held by the top 0.01% more than doubled once offshore wealth is included. This implies that government-collected administrative data may have important weaknesses when measuring the top tail of the wealth distribution.

Xie and Jin (2015) provide an example of improving the measurement of the top of the wealth distribution using replacement and reweighting. The authors assume that the bottom 99.9% of the Chinese wealth distribution is well represented by the household survey data they use. They then use a Chinese rich list of the top 1,000 wealthiest Chinese and, assuming that the top can be represented by the Pareto distribution, estimate the Pareto parameter from the rich list and then use this to replace the top 0.1% with the values implied by the estimated Pareto parameter. This adjustment means that the estimated share of wealth held by the top 1% rises from 16% to 35%.

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Chatterjee et al. (2022) combine surveys and income tax data to estimate wealth inequality in South Africa, using a replacement method. They use incomes from household surveys and tax data and replace the top of the distribution in the surveys with tax data at the point where survey data incomes are lower than in the tax data, which they find to be around the 25<sup>th</sup> to 30<sup>th</sup> percentile. The authors then use the income data to capitalize asset classes where capitalization can be applied and use survey and tax data to estimate capital for other asset classes. The key finding is that South Africa has an extremely unequal wealth distribution. The top 1% own 55% of total wealth, whilst the net wealth held by the bottom 50% is negative due to liabilities exceeding assets.

Gaps in the Research on Measuring the Upper Tail of the Income and Wealth Distributions In this section we document gaps in the research that has been conducted on measuring the top tail of the income distribution in LMICs. In the next section we discuss how these gaps can be filled by outlining a possible research agenda.

Chancel et al. (2023) highlighted the limited availability of household surveys with income data in Africa, as well as the lack of harmonized consumption data. This is very clearly an important gap- there is no way to directly investigate the top of the income distribution without income data from surveys.

We have noted that a few papers using tax data from LMICs have shown important differences between administrative and survey data at the top of the income distribution. But there is a need for more studies in a wider variety of LMICs to further investigate the top of the income distribution in surveys and admin data. This requires the availability of administrative tax data, at least in tabulation form for different income groups. This type of data is not easily accessible and may best be pursued on a country-by-country basis.

The use of other forms of data to check surveys in the absence of tax data is still uncommon. Van der Weide et al. (2018) concluded that the Egyptian Income and Expenditure household survey severely under-estimated inequality using external house price data but given the number of strong assumptions required for their methods to be valid, it is possible that some of differences may be due to the inadequacies of the method and/or the administrative house price data used rather than the surveys.

Researchers finding solutions to the challenges of measuring the top of the income or wealth distributions that use admin data generally do not investigate _why_ the surveys and admin data find substantially different incomes at the top of the distribution. To improve the methods for solving the measurement challenges described above, to establish new methods and to improve the quality of 25
survey and administrative data it would be useful to better understand why the distributions differ when they do, especially because the few answers that have been given are for rich countries and are not consistent, as we now describe.

A priori, unit non-response of high income or wealth individuals would seem to be the most important factor explaining why surveys under-capture the top of these distributions. Evidence for this proposition comes from J **ohansson-Tormod and Klevmarken (2022), who use administrative data and two wealth surveys from Sweden in -2002 and 2003. The data is unusual because the authors could match both survey responders and non-responders to the admin data they accessed. The authors find that the survey underestimates mean wealth within the top 1 percent by 40 percent relative to the admin data. For the top percentile,** J **ohanssonTormod and Klevmarken (2022)** show that the mean of the top 1% using the survey response values is very similar to the mean when using the same survey respondents (i.e. excluding nonrespondents) but using the wealth values from the admin data for those survey respondents (which they can do because the surveys and admin data are linked). But the means for the top 1% are very different when comparing the survey respondents using their wealth information from the admin data and the full set of respondents plus non-respondents again using their wealth information from the admin data. This implies that under-reporting is not a concern, but that unit non-response is.

J **ohansson-Tormod and Klevmarken (2022) use two surveys, finding similar results in both. One of these is Share. The documentation for the survey indicates that for the Swedish Share survey the only adjustment of the design weights is calibration to eight age and sex totals from external demographic data. It is then perhaps unsurprising that unit nonresponse is found to be the cause of the differences in the top 1%.** Burkhauser et al. (2017) compare UK household surveys and admin data based on tax records. They show that the surveys diverge from tax data around the 95<sup>th</sup> percentile of the income distribution and argue that under-reporting rather than unit non-response is responsible for this divergence, because the 95<sup>th</sup> percentiles and below are similar in both data sources. Burkhauser et al. (2023) provide further evidence in support of under-reporting being more important than unit non-response in the UK, in the context of investigating the share of women in the top 1%. They show that the top 1% in surveys and tax data have very similar observable characteristics, and that these are distinctly different to the 9 percentiles below the top 1%.

We noted above that Flachaire et al. (2022) found that under-reporting at the top of the distribution was important in Uruguay using linked survey and tax data, but the authors did not investigate unit 26
non-response and thus could not examine the importance of unit non-response relative to underreporting.

The extent of item non-response to income or wealth household survey questions has not, as far as we can tell, been the subject of any cross-country research. Campos-Vazquez and Lustig (2019) showed that in Mexico the labor force survey has shown dramatic increases in item non-response to labor income questions, from around 6% in 2002 to 30% by 2017, whereas the income and expenditure survey item non-response has been roughly constant around 3%. The South African Labour Force survey item non-response rate for labor income was around 5%-8% in the 2000s. The publicly available Quarterly Labour Force Survey data from 2010 onwards does not allow for the creation of reliable item non-response rates due to imputation but non-public data shows it also increased to close to 30% in 2020. Further research on the broader trends in middle income countries especially, where item (and unit) non-response rates are much higher, seems like an important gap, as does the extent to which imputation improves the estimates of inequality and the top tail of the income distribution.

# A Research Agenda

Using Existing Data _Household surveys_ Since we have noted that there is very limited income data in the public domain for some LMICs (e.g. African countries), one crucial part of the research agenda measuring the top of the income distribution would be to harmonize and make easily and publicly available the surveys that already exist. The World Bank’s publicly available Statistics Online platform is one example of making data public and more easily available, although this currently seems to include only data on consumption and not income. It also seems to have been entirely ignored outside the World Bank.<sup>6</sup> The World Bank is well placed to lead research that harmonizes the data that does exist, and ideally makes it publicly accessible.

The Rural Income Generation Activities (RIGA) project is one example of a project that did make available and harmonize household surveys with income data across countries. It was driven by the World Bank and the Food and Agriculture Organization.<sup>7</sup> The project created harmonized and publicly available microdata, including incomes, from 35 surveys for 22 countries, most of which were the

> 6 On June 26, 2023, there were no references to Statistics Online on Twitter by anyone outside the World Bank and only three in total. I added a fourth on the June 26. 7https://www.fao.org/economic/riga/en/

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World Bank’s LSMSs. Carletto et al. (2007) describe how the income data across the surveys were harmonized. It appears that the microdata are available for both rural and urban areas, in which case this is a potentially valuable source of income data to study the top tail of the income distribution. Kerr et al. (2019) undertook harmonization of 26 years of household surveys on earnings income in South Africa and made the harmonized data publicly available. Changes over time in the surveys, the sampling, and the questionnaires meant that obtaining comparable earnings distributions over time even for one country required a substantial amount of work.

We have described the method of Korinek et al. (2006) to adjust survey weights to correct for unit non-ignorable non-response and we discussed several papers that implemented these corrections. Ravallion (2022) notes that implementing this method requires regional non-response rates but that these are seldom available. He argues for the inclusion of PSU-level response rates and notes that this would be simple to include for survey data producers. Hlasny (2020) documents that some of the surveys available through the Luxembourg Income Study (LIS), including Brazil and South Africa, include non-responding households.

## _Administrative data_

The UNU WIDER project “Regional Growth and Development in Southern Africa” resulted in access to South African tax microdata through the South African National Treasury from 2015. This model of partnership between international organizations and national governments, including tax offices, has since been replicated by WIDER in Tanzania, Zambia, Uganda, and Rwanda.<sup>8</sup> Such data can be used to improve the measurement of the top tail of the income distribution in these countries, especially since publicly available household survey data on incomes exists for all these countries. Having a larger number of countries with tax and survey data and undertaking comparisons would allow for more general conclusions about the extent of the differences between survey and tax data for Africa, rather than just two as in Chancel et al. (2023).

# Using New Sources of Data

The most obvious research that could be undertaken using new data sources is obtaining and analyzing administrative tax data for a larger number of LMICs than is currently available. Ideally this would be tax microdata but even tax tabulations would be very useful. The first step would be to compare estimates of top incomes from surveys and administrative data, and then examine the extent to which under-reporting, item non-response and unit non-response and other challenges create any differences between household survey and administrative data.

> 8 <u>https://www.wider.unu.edu/project/building-efficient-and-fair-tax-systems-lessons-based-administrativetax-data</u>

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Ravallion (2022) argues that for some research on the top of the distribution, survey data will be adequate. The evidence we have discussed above suggests that in South Africa and Côte d’Ivoire, a divergence between survey and tax data starts quite far down the distribution and thus that tax data are required to accurately measure the top tail. Further work comparing tax (both new and already existing) and survey data will shed light on the extent to which surveys can be reliably used to measure top incomes.

Making use of other types of administrative data may also be useful. Further work could use house price data and improve the methods of Van der Weide et al. (2018). This is likely to be available only in urban areas in low-income countries, and many middle-income countries as well. House price data could be complemented with land record data for rural areas, where this exists. The extent to which the top tail is comprised of those who live in rural areas in low-income countries could then be investigated more comprehensively, a topic that there has not been much research on.

A second useful part of a research agenda using new data would link survey and tax microdata at the individual level, to provide further insight into the reasons for differences across tax and survey data, specifically the role of unit non-response, measurement error and under-reporting. We are only aware of one study in a LMIC that uses linked survey and tax data – Flachaire et al. (2021) for Uruguay. The links were only available for couples with children aged 0-3 so the extent to which this generalizes to the adult population in Uruguay is unclear. Further research would thus be extremely useful.

A third part of the research agenda would be to undertake future household surveys asking about incomes or wealth that oversample high-income or high-wealth households or areas. Oversampling rich households using tax or other forms of administrative data is not common, even in high income countries, probably because it requires coordination between various public agencies (for example national statistical offices and tax authorities). In addition, administrative tax data in LMICs may miss the rich whose incomes are outside the tax system, which may be a large proportion of those at the top of the income distribution (Haq, 1964, Ravallion, 2022). Nevertheless, it would be useful, perhaps as a pilot, for an LSMS to oversample high income households using tax data, where this can be obtained. A less ambitious method of oversampling would be to use population census data to oversample small areas with high incomes or with characteristics that are correlated with high incomes, if income data is not collected in the census. A version of this was attempted in the NIDS panel fifth wave in South Africa to increase the sample size of white and Indian South Africans, by drawing a top-up sample from enumeration areas with large proportions of these groups, using estimates from the most recent population census (Branson, 2019).

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Most of the work improving measurement of the top tail of the income or wealth distributions uses administrative data. But there is very little work on how one might improve estimates of incomes or wealth (and income from that wealth) that are outside the tax system. This is very important in LMICs where the informal sector is a large share of economic activity (Ravallion, 2022). Ravallion (2022) notes that if economic growth improves state capacity and this shifts more activity into the formal sector then this could generate rising measured top income shares, even when there is no actual change. This does not seem to have been investigated in the research discussed in this paper. Ravallion (2022) also highlights that there is little evidence on how large the informal or hidden sector share of top incomes or wealth is in any LMICs. This also seems an important area for further work. Alstadsæter et al. (2022) used leaked data on Dubai real estate ownership to show that the value of property ownership in Dubai by LMIC residents is a large share of GDP for several of these LMICs. Such data would be useful to improve the measurement of the top of the wealth distribution in these countries and serve as estimates for how much administrative tax data misses important sources of wealth at the top of the distribution.

# Conclusion

There has been a resurgence in research on the measurement of the top tail of the income and wealth distribution in the last 20 years. Kuznets and Jenks (1953) were the key authors that began this research agenda, but it declined in importance as household surveys became more widely available and researchers turned their attention to microdata. Piketty (2001, 2003) put the measurement of the top tail back onto the research agenda with his long run measurement of top incomes in France, and subsequently this area of research has exploded.

In this paper we have surveyed this literature, focusing on the challenges that have been identified when trying to measure the top of the income and wealth distributions, as well as the solutions that have been used to overcome these challenges. Our focus has been low- and middle-income countries, although we have discussed research from high-income countries, particularly when no research on a specific topic has been undertaken in any LMIC.

There are multiple challenges that researchers measuring the top end of the wealth and income distributions face. We focused first on the challenges when using household survey data, given that this is the most common form of data on incomes and wealth available in LMICs and that other forms of data (like administrative tax microdata or even tax tabulations) are uncommon. These include missing high income or wealth individuals due to non-random non-response (item or unit) or due to sampling error and measurement error (either from respondents themselves, proxy respondents or 30
because of data processing errors). We also highlighted that there is a lack of publicly available survey data with income questions for some LMICs, particularly in Africa.

We then discussed solutions to the challenges encountered when using household surveys that use survey data and no external data. The first set of solutions are those that can be undertaken before a survey starts. These include oversampling high income or wealth individuals, better fieldwork protocols to minimize unit and item non-response, and questions to elicit at least some information when a respondent does not want to give their exact income or wealth.

The second set of solutions are those that use only household survey data and are used ex-post. These can be broadly classified as either reweighting or replacement methods and include reweighting for unit non-response, imputation for item non-response and replacing the top of the distribution using a parametric distribution estimated from the survey itself, usually the Pareto distribution.

The third set of solutions combines survey data with administrative data, usually tax data, to improve measurement at the top, where researchers believe incomes are not well captured. These can also be broadly classified as replacement or reweighting methods. They include replacing top incomes in surveys with incomes from tax data above a certain threshold or reweighting so that the survey income or wealth distribution matches that in administrative data. Most solutions using administrative data use a combination of reweighting and replacement.

The research we have surveyed has resulted in a much better understanding of the challenges when measuring the upper tail of the income and wealth distributions and improved estimates of the incomes or wealth in the upper tail. But we have outlined gaps and thus areas in which future research should concentrate.

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