Discussion of “Has consumption inequality mirrored income

inequality?”by

Mark Aguiar and Mark Bils

NBER Economic Fluctuations and Growth Program MeetingJuly 2011, Cambridge MA

Jonathan A. ParkerKellogg School of Management, Northwestern University

I. Background

Krueger Perri (2003, 2006)

Possible explanations

1. Near-complete consumption insurance

2. Self-insurance • Increase in Var(ln y) due to transitory shocks to income

(Krueger Perri)• Income changes expected (Primiceri van Rens)

3. CEX under-measures increase in consumption inequality• And so do related expenditure datasets

Three possible problems with CEX

1. Decreasing coverage or participation of high-consumption householdsCannot explain

2. Decreasing coverage/measurement of luxury goods

3. Decreasing measurement or coverage of all expenditures of high-consumption households

II. Bils and Aguiar In the CEX, • There is not increasing under-measurement of

luxuries vs. necessities• But there is increasing under-measuring of the

all expenditures of high-consumption households over time . .

• So consumption inequality has actually increased as much as income inequality

Bottom line: I think this is probably correct

Log budget share of good: ln wi = ln (xi /X )

Log total real expenditure:

X = xLux+xNormal+xNecln X10 ln X90 ln X90

Estimated Engel curve for luxury

Estimated Engel curve for normal good

ln X90

Observed 1980

Observed2006

Inferred2007

The essence of the exercise

Inferred adjustment

to ln X90

ln X10

III. Two key assumption in method1. Prices don’t matter

Typical demand system x, X nominal expenditures:wi,t = xi,t / Xi, = αi + γi’ ln pt + βi ln ( Xi,t / a(pt )) + εi,t

+ Restrictions of demand theory– The danger: In AB framework, real shares could vary due to

substitution due to changes in relative prices– Partly an issue of question, partly of restricting data– Dora Costa and James Hamilton infer bias in CPI assuming

well-measured total and shares• Infer pt from parameters and xi,t and Xi,t

• If AB had blamed under-measurement of luxuries, this would be more of a worry

2. Elasticities are well-measuredTypical demand system x,X nominal expenditures:

wi,t = xi,t / Xi, = αi + γi’ ln pt + βi ln ( Xi,t / a(pt)) + εi,t

+ Restrictions of demand theory– The AB framework is nonstandard

a) Usually instrument for X due to noise in x getting into Xb) Observation: slope of late-sample Engels curves should be

steeper

ln X10 ln X90

Estimated Engel curve for luxury 1980

Estimated Engel curve for normal good

ln X90

Observed 1980

Observed2006

2006 estimate of βLux should be larger than 1980 estimate

Observed 1980 and

2006

Estimated Engel curve for luxury 2006

Log budget share of good: ln wi = ln (xi /X )

Log total real expenditure:

X = xLux+xNormal+xNec

But Figure 5: Elasticities are stable

alcbevauto

cashcont

chldrnclothes

clothes

educent

equpmt

foodaway

foodhome

furniture

healthhousingperscare

shoes

svcs

tobacco

trans

tv

utilities

-.50

.51

1.5

219

92-1

995

elas

ticiti

es

-.5 0 .5 1 1.5 21972-1973 elasticities

Slope of fitted line = 0.996 (0.108)

But OK: because elasticities have measurement error, reverse regression shows change we expect

alcbevauto

cashcont

chldrnclothes

clothes

educent

equpmt

foodaway

foodhome

furniture

healthhousingperscare

shoes

svcs

tobacco

trans

tv

utilities

-.50

.51

1.5

219

72-1

973

elas

ticiti

es

-.5 0 .5 1 1.5 21992-1995 elasticities

Slope of fitted line = 0.828 (0.090)

IV. Corroborating/related evidence

Fact 1: consumption inequality (mostly) tracks income inequality across groups of households

Cutler and Katz (1991)

Fact 2: improved consumption measurement shows slightly more consumption inequality

Attansio, Battistin, Ichimura (2004)

Fact 3: CEX shows increased saving rates and bigger increases for high-income households

Parker, Vissing-Jorgensen, Ziebarth (Summer Institute 2009)

Inconsistent with NIPA & FOF & SCFMaki and Palumbo (2001) use SCF/FOF data• Saving rates by quintiles of income from

changes in wealth, returns, and income– Increase in saving rates for low income– But decrease in saving for high income: 9% to -2%

Parker, Vissing-Jorgensen, Ziebarth: this implies– CEX measures low consumption about right– CEX measures 74% of top consumption in 1980

and this falls to 51% in 1990(problem: assumed homogeneity in returns by class)

Recall: Three possible problems with CEX

1. Decreasing coverage or participation of high-consumption householdsCannot explain

2. Decreasing coverage/measurement of luxury goods

3. Decreasing measurement or coverage of all expenditures of high-consumption households

On 2: measurement of luxuriesParker, Vissing-Jorgensen, Ziebarth (Summer Institute 2009)

On 2: measurement of luxuriesParker, Vissing-Jorgensen, Ziebarth (Summer Institute 2009)

1. Calculate the ratio of aggregate CEX consumption to NIPA consumption for each goods in each year

2. Scale up CEX expenditures by good and time specific factors

3. Recalculate CEX consumption inequality Finding: adjustment makes little difference

=> 0.04 higher increase in 90-10 log expenditure PVZ also estimated group mismeasurement necessary

to generate ratios, but AB method better=> no PVZ paper

Summary

• For high consumption households, the budget share of luxuries has risen more than implied by their rise in total spending and Engel curves

• Implication: their total spending is undermeasured• Consistent with corroborating evidence• Relies on stability of demand system and well-

measured prices

ln X10 ln X90 ln X90

Estimated Engel curve for luxury

Estimated Engel curve for normal good

ln X90

Observed 1980

Observed2006

Inferred2007

The essence of the exercise

Inferred adjustment

to ln X90

ln X10

Log budget share of good: ln wk= ln (xk /X )

Log total real expenditure:

X = xLux+xNormal+xNec

Appendix

90-10 Inequality in men’s log wages

Juhn Murphy Pierce (1993)

90-10 Inequality in men’s log income

Gordon (2008)