Underreporting of Top Incomes and Inequality: A Comparison of Correction Methods using Simulations and Linked Survey and Tax Data

• Published date: 01 December 2023
• Author: Emmanuel Flachaire,Nora Lustig,Andrea Vigorito
• Date: 01 December 2023
• DOI: http://doi.org/10.1111/roiw.12618

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Review of Income and Wealth

Series 69, Number 4, December 2023

DOI: 10.1111/roiw.12618

UNDERREPORTING OF TOP INCOMES AND INEQUALITY: A

COMPARISON OF CORRECTION METHODS USING SIMULATIONS

AND LINKED SURVEY AND TAX DATA

BY EMMANUEL FLACHAIRE

Aix-Marseille Université,AMSE

NORA LUSTIG

Tulane University

AND

ANDREA VIGORITO

Instituto de Economía, FCEA, Universidad de la República (Uruguay)

Household surveys do not captureincomes at the top of the distribution well. This yields biased inequal-

ity measures. We compare the performance of the reweighting and replacing methods to address top

incomes underreporting in surveys using information from tax records. The biggest challenge is that

the true threshold abovewhich underreporting occurs is unknown. Relying on simulation, we construct

a hypothetical true distribution and a “distorted” distribution that mimics an underreporting pattern

found in a novel linked datafor Uruguay. Our simulations showthat if one chooses a threshold that is

not close to the true one,corrected inequality measures may be signicantly biased. Interestingly,the bias

using the replacing method is less sensitive to the choice of threshold. Weapproach the threshold selec-

tion challenge in practice using the Uruguayanlinked data. Our ndings are analogous to the simulation

exercise.These results, however, should not be considered a generalassessment of the two methods.

JEL Codes: C81, D31

Keywords: correction methods, household surveys, income underreporting, inequality, linked data,

replacing, reweighting, tax records

Note: Wethank Uruguay’s Instituto Nacional de Estadística and Dirección General Impositiva for

providingthe data used in this research. We are verygrateful to Sean Higgins for his contributions at ear-

lier stages of this project.Two anonymous peer reviewersprovided very useful comments, we thank them

for that. We are also grateful for very useful comments from François Bourguignon and other partici-

pants of the workshop “MethodologicalAdvances in Fiscal Incidence Analysis: Commitment to Equity

Institute” (Universidad de San Andres, Buenos Aires,2017); participants in LACEA 2017 annual con-

ference; participants of the “Workshopon harmonization of household surveys, scal data and national

accounts: comparing approaches and establishing standards” (Paris School of Economics, 2018); par-

ticipants of Instituto de Economía Seminar (2018); participants of ECINEQ 2019; Thomas Blanchet,

Mauricio De Rosa,Ignacio Flores, Johannes Koenig, Marc Morgan, Christian Schluter, and Joan Vilá;

and Siyu Quan for research assistance. Emmanuel Flachaire thanks the nancial support from the

projectsANR-17-EURE-0020, ANR-17-CE41-0007, and ANR-19-FRAL-0006 managed by the French

National ResearchAgency and from the Excellence Initiative of Aix-Marseille University– A*MIDEX.

Nora Lustig acknowledgesthe generous support of the Bill & Melinda Gates Foundation (grantnumber:

OPP1135502). Andrea Vigoritoreceived nancial support from Universidad de la República (Uruguay).

*Correspondenceto: AndreaVigorito, Instituto de Economía, FCEA, Universidad de la República

(Uruguay), Av. Gonzalo Ramírez1926, 11200 Montevideo, Uruguay (andrea.vigorito@fcea.edu.uy).

© 2022 The Authors.Review of Income and Wealth published by John Wiley & Sons Ltd on behalf of

International Association forResearch in Income and Wealth.

This is an open access article under the terms of the Creative Commons Attribution License,which

permits use, distribution and reproductionin any medium, provided the original work is properly cited.

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Review of Income and Wealth, Series 69, Number 4, December 2023

1. INTRODUCTION

Household surveys suffer from representation errors, errors due to item and

unit nonresponse, and measurementerrors.1Such errors can affect the entire survey,

but here we are particularly concerned when they occur in the upper tail. House-

hold surveys do not capture incomes at the top of the distribution well because the

rich may be harder to reach, leading to unit nonresponse; more likely to refuse to

answer when reached, resulting in item nonresponse; or may report a lower frac-

tion of their income when responding to the survey, resulting in underreporting

(Atkinson, 2007). In addition, in nite samples the upper tail is not captured well

due to sparseness or because data producers truncate or top code the distribu-

tions in the upper tail (Cowell and Flachaire,2007,2015; Biemer and Christ, 2008).

These issues can lead to signicant bias in inequality measures, and this bias can be

either positive or negative (Deaton, 2005). Recognizing this, throughout the years

researchers have resorted to using other sources of information to correct survey

data or survey-based inequality estimates. These other sources include National

Accounts (Altimir, 1987;Pikettyet al.,2018), administrative data from tax and

social security records (Burkhauser et al.,2016; Jenkins,2017;Pikettyetal.,2019),

complementary surveys (Fisher et al.,2022), and the so-called rich lists (Brzezin-

ski, 2014). For a survey, see Lustig (2019).

Here we focus on comparing correction methods to address one type of mea-

surement error: underreporting of income in the upper tail.2Two main approaches

have been used in the literature to correct survey upper-tail errors,including under-

reporting. FollowingHlasny and Verme (Hlasny and Verme, 2018,pp.1–2),wecall

these approaches “replacing” and “reweighting” (see details on these two meth-

ods in Section 3). Both correction approaches rely on implicit assumptions that are

often untestable.3In particular, they rely on the appropriate selection of the thresh-

old beyond which survey data tend to underreport income. The biggest challenge

in applying correction methods is that the true income distribution is unknown;

therefore, one does not know the threshold above which underreporting occurs.

To analyze the sensitivity of correction methods to the choice of threshold,

we rely on simulation. The approach allows us to focus on underreporting and not

consider sampling errors in the upper tail, a common problem in nite samples. We

simulate a hypothetical true distribution and a “distorted” distribution that suffers

from underreporting. (Relying on hypothetical distributions has the additional

advantage that we can focus on underreporting and not consider sampling errors

in the upper tail, a common problem in nite samples). The distorted distribution

is not just arbitrarily constructed. It mimics an actual pattern of underreporting

1The total survey erroris composed of the sum of three distinct elements: representation error,error

due to non-response, and measurement error(Groves and Lyberg, 2010; Meyer and Mittag, 2019).

2Wedo not address the case in which the entire income is not reported (item nonresponse). Because

most likely the behaviorunderlying item nonresponse is different from misreporting, this wouldwarrant

a separate type of analysis.

3In fact, the survey earnings validation literature concludes that the denition of a true distribu-

tion largely depends on priors chosen by researchers, which lead to different measurement error esti-

mates (Kapteyn and Ypma, 2007; Abowd and Stinson, 2013; Jenkins and Rios-Avila, 2020). See also

Gottschalk and Huynh (2010), Hyslop and Townsend(2020), and Adriaans et al. (2020).

© 2022 The Authors.Review of Income and Wealth published by John Wiley & Sons Ltd on behalf of

International Association forResearch in Income and Wealth.

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