Researchers often need to work with categorical income data. The typical nonparametric (including midpoint) and parametric estimation methods used to estimate summary statistics both have advantages, but they carry assumptions that cause them to deviate in important ways from real-world income distributions. The method introduced here, random empirical distribution imputation (REDI), imputes discrete observations using binned income data, while also calculating summary statistics. REDI achieves this through random cold-deck imputation from a real-world reference data set (demonstrated here using the Current Population Survey Annual Social and Economic Supplement). This method can be used to reconcile bins between data sets or across years and handle top incomes. REDI has other advantages for computing values of an income distribution that is nonparametric, bin consistent, area and variance preserving, continuous, and computationally fast. The author provides proof of concept using two years of the American Community Survey. The method is available as the redi command for Stata.
AllisonPaul D.2000. “Multiple Imputation for Missing Data.”Sociological Methods & Research28(3):301–309.
2.
AllisonPaul D.2002. “Multiple Imputation: Basics.” Pp. 27–49 in Missing Data. Thousand Oaks, CA: Sage.
3.
BaileyStanley R.SapersteinAliyaPennerAndrew M.2014. “Race, Color, and Income Inequality across the Americas.”Demographic Research31(24):735–56.
4.
BauldryShawn. 2015. “Structural Equation Modeling.” Pp. 615–20 in International Encyclopedia of the Social and Behavioral Sciences, 2nd ed., Vol. 23, edited by WrightJames D.Oxford, UK: Elsevier.
5.
BhatChandra R.1994. “Imputing a Continuous Income Variable from Grouped and Missing Income Observations.”Economics Letters46(4):311–19.
6.
BlanchetThomasGarbintiBertrandGoupille-LebretJonathanMartínez-ToledanoClara. 2018. “Applying Generalized Pareto Curves to Inequality Analysis.”AEA Papers and Proceedings108:114–18.
7.
BollingerChristopher R.HirschBarry T.HokayemCharles M.ZiliakJames P.2019. “Trouble in the Tails? What We Know about Earnings Nonresponse 30 Years after Lillard, Smith, and Welch.”Journal of Political Economy127(5):2143–85.
8.
ChettyRajHendrenNathanielKlinePatrickSaezEmmanuelTurnerNicholas. 2014. “Is the United States Still a Land of Opportunity? Recent Trends in Intergenerational Mobility.”American Economic Review104(5):141–47.
9.
CoderJohnScoon-RogersLydia. 1996. “Evaluating the Quality of Income Data Collected in the Annual Supplement to the March Current Population Survey and the Survey of Income and Program Participation.” Working Paper No. SEHSD-WP1996-20. Retrieved June 10, 2022. https://www.census.gov/library/working-papers/1996/demo/SEHSD-WP1996-20.html.
10.
CollinsLinda M.SchaferJoseph L.KamChi-Ming. 2001. “A Comparison of Inclusive and Restrictive Strategies in Modern Missing Data Procedures.”Psychological Methods6(4):330–51.
DonnellyMichael J.Pop-ElechesGrigore. 2018. “Income Measures in Cross-National Surveys: Problems and Solutions.”Political Science Research and Methods6(2):355–63.
13.
EvansJames A.FosterJacob G.2019. “Computation and the Sociological Imagination.”Contexts18:10–15.
FontenotKaylaSemegaJessicaKollarMelissa. 2018. “Income and Poverty in the United States: 2017.” Current Population Reports. Washington, DC: U.S. Government Printing Office.
16.
FranciscoCarol A.FullerWayne A.2008. “Quantile Estimation with a Complex Survey Design.”Annals of Statistics19(1):454–69.
GelmanAndrewHillJennifer. 2006. “Missing-Data Imputation.” Pp. 529–44 in Data Analysis Using Regression and Multilevel/Hierarchical Models, edited by GelmanA.HillJ.New York: Cambridge University Press.
19.
GoergSebastian J.KaiserJohannes. 2009. “Nonparametric Testing of Distributions: The Epps–Singleton Two-Sample Test Using the Empirical Characteristic Function.”Stata Journal9(3):454–65.
20.
GrahamJohn W.2009. “Missing Data Analysis: Making It Work in the Real World.”Annual Review of Psychology60:549–76.
HensonMary F.1967. “Trends in the Income of Families and Persons in the United States, 1947–1964.”Washington, DC: U.S. Department of Commerce, Bureau of the Census.
23.
HoutMichael.2004. “Getting the Most out of the GSS Income Measures.” GSS Methodological Report No. 101. Berkeley, University of California, Berkeley Survey Research Center.
24.
HuMing-xiuSalvucciSameena. 2001. “A Study of Imputation Algorithms.” Working Paper No. 2001-17. Washington, DC: U.S. Department of Education, National Center for Education Statistics,
JargowskyPaul A.WheelerChristopher A.2018. “Estimating Income Statistics from Grouped Data: Mean-Constrained Integration over Brackets.”Sociological Methodology48:337–74.
MarquisKent H. M.MarquisSusanPolichJ. Michael. 1986. “Response Bias and Reliability in Sensitive Topic Surveys.”Journal of the American Statistical Association81(394):381–89.
29.
McDonaldJames B.1984. “Some Generalized Functions for the Size Distribution of Income.”Econometrica52(3):647–63.
30.
McDonaldJames B.RansomMichael R.1979. “Alternative Parameter Estimators Based upon Grouped Data.”Communications in Statistics—Theory and MethodsA8(9):899–917.
31.
MellonJonathanProsserChristopher. 2018. “Constructing Continuous Household Income Measurement on the British Election Study Internet Panel.”SSRN Electronic Journal. Retrieved June 10, 2022. https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3153831.
32.
Minnesota Population Center. 2018. “CPS Income and Tax Variables User’s Note: Missing Cases, N.I.U. Cases, Top Codes and Bottom Codes.”Minneapolis: University of Minnesota. Retrieved June 10, 2022. https://cps.ipums.org/cps/inctaxcodes.shtml#topcodes.
PikettyThomas. 2014. Capital in the Twenty-First Century. Cambridge, MA: Belknap.
37.
PikettyThomasSaezEmmanuel. 2006. “The Evolution of Top Incomes: A Historical and International Perspective.”American Economic Review96:200–205.
38.
PikettyThomasSaezEmmanuel. 2014. “Inequality in the Long Run.”Science344(6186):838–43.
39.
ReardonSean F.2011. “Online Appendix 5: The Widening Academic-Achievement Gap between the Rich and the Poor: New Evidence and Possible Explanations.” In Whither Opportunity? edited by DuncanG. J.MurnaneR. J.New York: Russell Sage.
40.
RothPhilip L.1994. “Missing Data: A Conceptual Review for Applied Psychologists.”Personnel Psychology47(3):537–60.
41.
RothbaumJonathan L.2015. “Comparing Income Aggregates: How Do the CPS and ACS Match the National Income and Product Accounts, 2007–2012.”Social, Economic, and Housing Statistics Division Working Papers Working Paper No. 2015-01. Washington, DC: U.S. Census Bureau.
42.
RugglesStevenFloodSarahFosterSophiaGoekenRonaldPacasJoseSchouweilerMeganSobekMatthew. 2021. “IPUMS USA: Version 11.0.”Minneapolis, MN: IPUMS. Retrieved June 10, 2022. https://www.ipums.org/projects/ipums-usa/d010.v11.0.
43.
SchenkerNathanielRaghunathanTrivellore E.ChiuPei LuMakucDiane M.ZhangGuangyuCohenAlan J.2006. “Multiple Imputation of Missing Income Data in the National Health Interview Survey.”Journal of the American Statistical Association101(475):924–33.
U.S. Census Bureau and U.S. Bureau of Labor Statistics. 2018. “Current Population Survey March Annual Social and Economic Supplement (CPS ASEC).” Retrieved June 10, 2022. https://cps.ipums.org/cps/asec_sample_notes.shtml.
von HippelPaul T.HunterDavid J.DrownMcKalie. 2017. “Better Estimates from Binned Income Data: Interpolated CDFs and Mean-Matching.”Sociological Science4:641–55.
50.
von HippelPaul T.PowersDaniel A.2015. “RPME: Stata Module to Compute Robust Pareto Midpoint Estimator.”Boston College Department of Economics. Retrieved June 10, 2022. https://ideas.repec.org/c/boc/bocode/s457962.html.
51.
von HippelPaul T.ScarpinoSamuel V.HolasIgor. 2016. “Robust Estimation of Inequality from Binned Incomes.”Sociological Methodology46:212–52.
52.
WangWeidongXieGuihuaHaoLingxin. 2014. “Rural Panel Surveys in Developing Countries: A Selective Review.”Economic and Political Studies2(2):151–77.
53.
YanTing. 2011. “Hot-Deck Imputation.” Pp. 316–17 in Encyclopedia of Survey Research Methods, edited by LavrakasP. J.Thousand Oaks, CA: Sage.
