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How does household production affect measured income inequality?


Theory predicts that lower-income households will produce more goods at home. Thus extended income, which includes household production, should be more equally distributed than money income. Previous studies have confirmed the greater equality of extended income and speculated that the result is due to the weak correlation between money income and household production. We also confirm this result and identify the true reason. We show that the weak correlation cannot be the explanation and that virtually all of the difference in measured inequality between the two measures is due to the addition of a large constant—the average value of household production—to money income.

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  1. For more details, please see the Appendix of the Working Paper version of this paper (available from the authors upon request), which presents the Gronau (1986) model, extends the model to two-person households, and discusses the assumptions that drive these results.

  2. The exceptions are Bonke et al. (2004) and some specifications in Bonke (1992). Note that both use Danish data with markedly smaller money income inequality than the US or UK.

  3. The earnings data are carried over from the final CPS interview. The earnings questions are asked in ATUS if the respondent had a new job in ATUS—either changed jobs or made a non-employment-to-employment transition—or earnings were allocated in the last CPS interview.

  4. Households are in the CPS for 4 consecutive months, out for 8, then back in for 4. Because of the sample rotation scheme used in CPS, only about one-third of ATUS respondents—those whose final CPS interviews were in March–June—were interviewed in March. There is a lag between the final CPS interview and introduction into the ATUS, so that most of the ATUS respondents who were matched to March were interviewed for ATUS in June through September.

  5. Respondents frequently do not respond to the income questions in the CPS. In these cases, the Census Bureau imputes the income variables using a hot-deck procedure, where recipient observations receive data from donor observations with the same demographic characteristics.

  6. Bonke et al. (2004) and some specifications of Bonke (1992) use the opportunity cost method, which is one reason for their finding of greater inequality of extended income relative to money income.

  7. An hours-weighted mean weights individuals with earnings in part-time jobs less heavily. Letting E denote weekly earnings, H denote weekly hours, and W denote the person weight; the hours-weighted mean is calculated as: \({\sum {W_i E_i } } \mathord{\left/ {\vphantom {{\sum {W_i E_i } } {\sum {W_i H_i } }}} \right. \kern-\nulldelimiterspace} {\sum {W_i H_i } }\), whereas the person-weighted mean is calculated as: \({\sum {W_i \left( {{E_i } \mathord{\left/ {\vphantom {{E_i } {H_i }}} \right. \kern-\nulldelimiterspace} {H_i }} \right)} } \mathord{\left/ {\vphantom {{\sum {W_i \left( {{E_i } \mathord{\left/ {\vphantom {{E_i } {H_i }}} \right. \kern-\nulldelimiterspace} {H_i }} \right)} } {\sum {W_i } }}} \right. \kern-\nulldelimiterspace} {\sum {W_i } }.\)

  8. For example, Wolff et al. (2004) multiplied this wage by a performance index that depends on household-level characteristics as well as characteristics of household members.

  9. Details on ATUS sampling and weighting procedures are contained in Bureau of Labor Statistics (2009).

  10. We predict the equivalence-scale-normalized value of household production directly, rather than applying the equivalence scale to predicted time spent in household production. Let P i  = w i H i denote the normalized amount of time spent in household production for household i, where w i is the normalizing factor for the equivalence scale and H i is hours of production. Then \(E(P_{i}\vert X_i)=E(w_iH_i\vert X_i)\ne w_iE(H_i \vert X_i)\). Thus regressing hours of production on the covariates and then applying the equivalence scale will not yield a consistent estimate of normalized production.


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The authors thank Peter Gottschalk, Jim Spletzer, Frank Stafford, and participants in sessions at the 2004 meetings of the International Association of Research on Income and Wealth, the 2005 Allied Social Science Associations meetings, and the Levy Economics Institute conference “Time Use and Economic Well-Being.” We also thank two anonymous referees for their helpful comments. The views expressed here are those of the authors and do not necessarily reflect the views of the U.S. Department of Labor or the Bureau of Labor Statistics.

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Correspondence to Jay Stewart.

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Frazis, H., Stewart, J. How does household production affect measured income inequality?. J Popul Econ 24, 3–22 (2011).

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  • Income distribution
  • Household production
  • Time use

JEL Classification

  • D31
  • D13
  • J22