1. Discussion of “Has consumption inequality mirrored income inequality
Discussion of “Has consumption inequality mirrored income inequality?” by Mark Aguiar and Mark Bils
Main idea of paper: Compare increase in spending on total number of new cars relative to the average monthly spending in the previous year in cities with high clunkers per 2004 auto sales to low clunkers to 2004 auto sales.
Like it.
What the experiment answers: run the program, change the world, now fix the bc and consider removing the CARS program for one city and see what would be different. All we measure is individual relative responses in the in the world with the policy. If we found no effect on car purchase for that city, we would conclude the program had no effect, we find sales, so we measure a direct effect. But only the direct effect!
The results say nothing about the multiplier!! It could be that the program was critical in ending the recession – it’s last month was JUNE 2009 – CARS started in July 2009.
Now kick the tires and discuss importance.
NBER Economic Fluctuations and Growth Program Meeting
July 2011, Cambridge MA
Jonathan A. Parker
Kellogg School of Management, Northwestern University

2. Very nice paper
In this discussion:
Background and possible explanations for lack of increase in c ineq
Explain the main intuition for the AB result
Two key assumptions
Corroborating/related evidence

3. I. Background
Krueger Perri (2003, 2006)

4. Possible explanations
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
1. Poor smoothing of cohort specific shocks

5. Three possible problems with CEX
Decreasing coverage or participation of high-consumption households
Cannot explain
Decreasing coverage/measurement of luxury goods
Decreasing measurement or coverage of all expenditures of high-consumption households
2: Implies the expenditures of the high-consumption households are increasingly understated

6. increased as much as income inequality
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
But first some background or complementary evidence
Bottom line: I think this is probably correct

7. The essence of the exercise
Log budget share of good:
ln wi = ln (xi /X )
Inferred
2007
Observed
2006
Estimated Engel curve for luxury
Observed 1980
Inferred adjustment to ln X90
Estimated Engel curve for normal good
Log total real expenditure:
X = xLux+xNormal+xNec
ln X10
ln X90
ln X90
ln X90
ln X10

8. III. Two key assumption in method
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

9. wi,t = xi,t / Xi, = αi + γi’ ln pt + βi ln ( Xi,t / a(pt)) + εi,t
Elasticities are well-measured
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 AB framework is nonstandard
Usually instrument for X due to noise in x getting into X
Observation: slope of late-sample Engels curves should be steeper

10. 2006 estimate of βLux should be larger than 1980 estimate
Log budget share of good:
ln wi = ln (xi /X )
Observed
2006
Estimated Engel curve for luxury 2006
Estimated Engel curve for luxury 1980
Observed 1980
Observed 1980 and 2006
Estimated Engel curve for normal good
Log total real expenditure:
X = xLux+xNormal+xNec
ln X10
ln X90
ln X90

11. But Figure 5: Elasticities are stable

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

13. IV. Corroborating/related evidence

14. Fact 1: consumption inequality (mostly) tracks income inequality across groups of households
But why does not under-measurement error confound this inference?
Cutler and Katz (1991)

15. Fact 2: improved consumption measurement shows slightly more consumption inequality
Attansio, Battistin, Ichimura (2004)

16. Fact 3: CEX shows increased saving rates and bigger increases for high-income households
Parker, Vissing-Jorgensen, Ziebarth (Summer Institute 2009)

17. Inconsistent with NIPA & FOF & SCF
Maki 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)
Agree with AB that the CEX measures of Consumption inequality are fishy

18. Recall: Three possible problems with CEX
Decreasing coverage or participation of high-consumption households
Cannot explain
Decreasing coverage/measurement of luxury goods
Decreasing measurement or coverage of all expenditures of high-consumption households
2: Implies the expenditures of the high-consumption households are increasingly understated

19. On 2: measurement of luxuries Parker, Vissing-Jorgensen, Ziebarth (Summer Institute 2009)

20. On 2: measurement of luxuries Parker, Vissing-Jorgensen, Ziebarth (Summer Institute 2009)
Calculate the ratio of aggregate CEX consumption to NIPA consumption for each goods in each year
Scale up CEX expenditures by good and time specific factors
Recalculate CEX consumption inequality
Finding: adjustment makes little difference
=> 0.04 higher increase in log expenditure
PVZ also estimated group mismeasurement necessary to generate ratios, but AB method better
=> no PVZ paper
CONCLUDE four pieces of corroborating evidence: cross-group, diary/recall, saving rates, inference from NIPA shares

21. 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

22. The essence of the exercise
Log budget share of good:
ln wk= ln (xk /X )
Inferred
2007
Observed
2006
Estimated Engel curve for luxury
Observed 1980
Inferred adjustment to ln X90
Estimated Engel curve for normal good
Log total real expenditure:
X = xLux+xNormal+xNec
ln X10
ln X90
ln X90
ln X90
ln X10

23. Appendix

24. 90-10 Inequality in men’s log wages
Juhn Murphy Pierce (1993)

25. 90-10 Inequality in men’s log income
Gordon (2008)