# Faculty bad credit equity home by jolinmilioncherie

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```									      Lecture 2:
Consumption (Continued)
Wrapping Up from Last Time: Non Separabilities

My belief:

U(C,N) can be written as u(C) + v(N)

However – we do not measure C directly:

C = f(x,h) where h is directly related to N (through time budget
constraint).

We measure X and N in the data.

X = f-1(C,h(N))

Implication:

U(X,N) cannot be written as U(X) + V(N).
Take Away

Non Separabilities between X and N (expenditure and labor supply) are
important.

When is it important to implicitly model the home production sector?

When changes to home production technology are important!
When care about cross good predictions.
When have actual consumption (intake) measures.

For most applications, a reduced form assumption that X and N are non-
separable can be important.
Wrapping Up from Last Time: Synthetic Cohorts

From last time, we estimate:

ln ( C it )   0   a g e A g e it   c C o h o r t it   t D t        F a m ily it   it
k                                                                                       k
fs

What is the intuition of this regression? (I went through it fast last time).

Underlying the estimation is repeated cross section of regressions.

Hard to identify lifecycle or time series effects from cross sectional data.

Use the repeated cross sections to create “synthetic cohorts” based on
observables.
Examples (Done in class)
Another Data Set: Survey of Consumer Finances (SCF)

Detailed data on household balance sheets.

Cross sectional in design (small panel 1983 – 1989).

Data:              1983, 1986, 1989, 1992, 1995, 1998, 2001, 2004, and 2007

Sample Size:       ~5,000 households per wave

Quality of Data:

Assets (general balance sheet, housing, some pension) – very good
Demographics and Income – very good

Some data imputed (need to account for the imputations – each
observation has 5 “records” given the imputations).
Other Wealth Surveys: Health and Retirement Survey

•   Surveys “Older Households” (not too old – over the age of 50)

•   Panel data (same households are tracked)

•   Years:       Every two years starting in 1992.

•   Detailed wealth and pension data (along with very good income, health
and demographic data).

•   Can apply to get the social security earnings records of participants!

•   Have full income data and detailed wealth data on the eve of retirement.
Can explore retirement saving adequacy in detail.
Scholz, Seshadri, and Khitatrakun (JPE 2006)

“Are Americans Saving ‘Optimally’ For Retirement?”

•   Great use of HRS data (I love this paper)

•   Writes down an individual optimization problem (with stochastic income,
stochastic length of life, imperfect capital and insurance markets, realistic
government programs, and a bequest motive).

•   Solves the optimal saving rule for each household given their actual
income (from their social security records), health trajectories, and
expected length of life (from life tables based on observables).

•   Assumes everyone has the same preferences and preference parameters.

•   Computes the optimal amount of wealth they should have (on the eve
of retirement) and compares that to the households actual wealth.
Scholz, Seshadri, and Khitatrakun: Key Findings
Other Wealth Surveys: PSID

•   Panel Study of Income Dynamics (PSID) – Discussed in last class

•   Panel data (same households are tracked)

•   Years:       1984, 1989, 1994, 1999, 2001, 2003, 2005, 2007 and 2009

•   Detailed wealth data for broad asset classes “stocks”, “checking
accounts”, “debt”, etc. Until recently, pension data is not that good.

•   Housing wealth (and mortgage debt) asked every year.

•   Very good income and demographic data.

•   See description in Hurst, Luoh, and Stafford (1996 – Brookings Papers on
Economic Activity).
Topics for Today (May Extend Into Next Week)

Part 1. Estimating preference parameters using consumption data

Part 2. Discuss parts 1 and 3 of homework

Part 3. Discuss how consumption data can be used to learn about the income
process households are facing.

Part 4. Discuss CEX data (part 2 of homework) and link to measures of
changing consumption inequality.

Part 5. Discuss risk sharing and consumption

Part 6. Discuss my favorite of my papers (which empirically documents
the importance of “status” in determining household consumption
decisions).
Part 1:
Estimating Household Preferences
Part 1: Estimating Preferences

•   Intertemporal elasticity of substitution (I.E.S.)

•   Risk Aversion

•   Time discount rates

Note:   Risk aversion = (1/I.E.S.) with CES preferences

Note:   Using notation from last week:

(1/ρ) = I.E.S.
δ = time discount rate
Why is the I.E.S. important?

•   The intertemporal elasticity of substitution determines how levels of
consumption respond over time to changes in the price of consumption
over time (which is the real interest rate – or more broadly – the real return
on assets).

•   This parameter is important for many macro applications.

•   Economics:

Raising interest rates lowers consumption today (substitution effect)

Raising interest rates raises consumption today (income effect – if net
saver)

Consumption tomorrow unambiguously rises
Estimating I.E.S.
t j               1 
T t
 1                    (C t  j )       
m ax E t                              



j0    1                     1            


 C                                
t 1
Et                    (1  rt  1 )   1
 C t                              
                                    

1
 ln C t  1         t 1
       ln (1  rt  1 )   t  1

Graphical Illustration – No Substitution Effect
C

High interest rate

ΔC2 = X

ΔC1 = X                           Low interest rate

1                                 2       period

With only an income effect – consumption growth rate will not respond to interest
rate changes. Estimate of (1/ρ) = 0.
Graphical Illustration – With Substitution Effect
C                                                  High interest rate

ΔC2 > X

Low interest rate
ΔC1 < X

1                                  2       period

As the substitution effect gets stronger, the growth rate of consumption
increases more as interest rates increase. Estimate of (1/ρ) > 0.
Issues With Estimating I.E.S.
1
 ln C t  1   t  1        ln (1  rt  1 )   t  1


•   Use of data source (micro or aggregate)

•   Forecast of future interest rates?

•   Correlation of forecast of interest rate with error term (things that make
interest rates go up could be news about permanent income – which effect
consumption).
Hall 1988

“Intertemporal Substitution in Consumption” (JPE)

Uses aggregate data (National Accounts)

Attempts to deal with time aggregation

Uses various measures of interest rates (stock market return, t-bill, etc.)

Instruments interest rate with lag interest rates and lags of consumption.

Estimate:         1/ρ        ≈ 0.00
Attanasio and Weber 1993
“Consumption Growth, the Interest Rate and Aggregation” (ReStud)

Uses micro data (cohort data – British Family Expenditure Survey)

-   Aggregate the micro data appropriately to aggregate data

Use aggregate data (from National Accounts)

Uses building society deposit rate as measure of interest rate

Instruments interest rate with lag interest rates.

Estimate:          1/ρ       ≈ 0.35 (National Accounts)
≈ 0.60 (FES Data - aggregating)
≈ 0.75 (FES Data – micro data)
Vissing-Jorgensen (2002)
“Limited Asset Market Participation and the Elasticity of
Intertemporal Substitution” (JPE)

Data:           CEX

Innovation:     Split sample to those who are “saving” in financial markets

Bond returns should only apply to bond holders
Stock returns should only apply to stock holders

Others are not on the margin because of fixed costs of
participating.

Estimate:       1/ρ      ≈ 0.8 (Bond holders)
≈ 0.3 (Stock holders)
Gourinchas and Parker (2002)

“Consumption Over the Lifecycle” (Econometrica)

Estimates lifecycle consumption profiles in the presence of realistic labor
income uncertainty (via calibration).

Use CEX data on consumption (synthetic cohorts).

Estimates the riskiness of income profiles (from the Panel Study of Income
Dynamics) and feeds those into the model.

Use the model and the observed pattern of lifecycle profiles of expenditure to
estimate preference parameters (risk aversion and the discount rate).
Gourinchas and Parker Structure

                                                         
N

m a x E    u (C t ,  )  
t                        N 1
VN   1
(W   N   1
)
 t 1                                                    

W t  1  (1  r ) (W t  Y t  C t )

1 
C
u (C , Z )  v ( )
1 

Y t  Pt V t

Pt  G t Pt  1 N   t
Methodology

Find in the income process (use different education and occupation groupings)

Using PSID

•   Computed “G” from the data (mean growth rate of income over the
lifecycle).

•   Estimated the variances from the data.

Using CEX

•   Compute lifecycle profiles of consumption

•   Compute lifecycle profile of wealth/income (at beginning of life)
Intuition

No Uncertainty:

No “Buffer Stock Behavior”
Consumption growth determined by Rβ         (where β = 1/(1+δ))

With Income Uncertainty

Buffer stock behavior takes place (household reduce consumption and increase
saving to insure against future income shocks).

Consumption will track income if households are sufficiently “impatient”

Sufficiently Impatient with Uncertainty:     RβE[(GN)-ρ] < 1
Results

Estimates (Base Specification):

δ        = 4.2% - 4.7%               (higher than chosen r = 3.6%)

ρ        = 0.5 – 1.4                 (1/ρ = 0.6 – 2.0)

Interpretation

Early in the lifecycle, households act as “buffer stock households”. As income
growth is “high”, consumption tracks income (do not want to accumulate too
much debt to smooth consumption because of income risk)

In the later part of the lifecycle, consumption falls because households are
sufficiently impatient such that δ > r.
Barsky, Juster, Kimball, and Shapiro (1997)

Preference Parameters and Behavior Heterogeneity: An Experimental
Approach in the Health and Retirement Survey (QJE)

“Suppose that you are the only income earner in your family, and you have a
good job guaranteed to give you (and your current (family)) income every year
for life. You are given the opportunity to take a new and equally good job, with
a 50-50 chance it will double your (family) income and a 40-40 chance that it
will cut your (family) income by a third. Would you take the new job?”

If answer yes to base question, give a new question changing “third” to “half”.

If answer no to base question, give a new question changing “third” to “20
percent”.
Barsky, Juster, Kimball, and Shapiro (1997)

No – No              ‘Low Risk Tolerance’

No – Yes             ‘Medium Low Risk Tolerance’

Yes – No             ‘Medium High Risk Tolerance’

Yes – Yes            ‘High Risk Tolerance’
Use Survey Evidence to Measure Risk Parameters

Risk Grouping                                            Percent

Low Tolerance “reject all gambles”                       64.6%

Medium Low Tolerance                                     11.6%

Medium High Tolerance                                    10.9%

High Tolerance “accept 50-50 gamble”                     12.8%

Using some structure (on distributions and preferences), estimate the coefficient
of relative risk aversion (ρ) to be about 4.0 (standard error of 5 or so).

Implication: (1/ρ) = 0.25 (lower than other estimates)
Summary of Estimated I.E.S and Risk Aversion

For those that ignore non-separabilities (or labor supply broadly), researchers
usually use CES utility such that:

t j             1 
T t
 1             (C t j )      
m ax Et                                        
 1            
j0   1                           

ρ = 1.5 – 2.0         (1/ρ = 0.5 – 0.66)

δ = r = 3.0 – 3.5% (sometimes δ > r )

We will talk about preferences with non-separable leisure in a few weeks.
A Separate Question:
The Importance of Precautionary/Buffer Stock Savings

•    How much of total wealth accumulation can be attributed to a
precautionary motive?

•    Carroll and Samwick “How Important is Precautionary Saving?” (ReStat,
1998)

•    Hurst et al “The Importance of Business Owners in Assessing the Size of
Precautionary Savings” (ReStat, forthcoming).

•    Use panel data from the PSID and estimate:

ln (W it )   0   1                2                  3 ln ( y it )  Z it   u it
p erm y            tr a n s y
it                  it

•    Precautionary savings model predicts wealth will be higher the more risk
that households face.
The Importance of Precautionary Savings

•   Use income data to predict the transitory and permanent shocks to income
by occupation and industry (specifically, we compute the variances for
each individual and then instrument the two variances with income and
occupation)

•   Identifying assumption:

Occupation and Industry are independent of wealth aside from their effect
on the variances of income.

•   Focus on households aged 26 – 50 (years 1984 and 1994)
The Importance of Precautionary Savings
Permanent   Transitory    Percent
Group                                 variance    variance    of sample

Total sample                          0.0162      0.0513        100
(0.0023)    (0.0040)

Professional and technical workers    0.0135      0.0404       23.74
(0.0042)    (0.0069)

Managers (non self-employed)          0.0171      0.0305       14.60
(0.0048)    (0.0083)

Managers (self-employed)              0.0272      0.0866        5.27
(0.0163)    (0.0270)

Clerical and sales workers            0.0192      0.0541       13.25
(0.0075)    (0.0128)

Craftsmen                             0.0129      0.0524       20.10
(0.0043)    (0.0079)

Operatives and laborers               0.0199      0.0592       15.35
(0.0055)    (0.0094)

Farmers and farm laborers             0.0079      0.1414        2.01
(0.0209)     (0.05)

Service workers                       0.0126      0.0547        5.69
(0.0096)    (0.0184)
Results

Variables                                     Pooled        Pooled

Variance of Permanent Income Shocks (α1)      15.91         -1.57
(2.98)        (4.35)

Variance of Transitory Income Shocks (α2)      7.52         -0.27
(1.48)        (1.87)

Percentage of Net Worth Explained by          47.5%         13.3%
Precautionary Savings

Dependent Variable (Log)                      Total         Total
Net Worth     Net Worth

Permanent Income Measure (Averaged)         Non-capital   Non-capital
Income        Income

Sample Size                                   2,144         1,729

•   Carroll/Samwick results (our replication) in column I
•   Our results (controlling for business owners) in column II

•   Our results ranged from 0.0 – 14% of total wealth.
An Aside

•   Here are some good notes from Chris Carroll on the underpinnings of the
“Buffer Stock Saving Model”

http://econ.jhu.edu/people/ccarroll/public/lecturenotes/Consumption/Tract
ableBufferStock/

They can be found on Chris Carroll’s Johns Hopkins web site.
Things I am Interested In: Heterogeneity of Preferences

•   “Grasshoppers, Ants, and Pre-Retirement Wealth” (Erik Hurst ;
permanent working paper) – my dissertation

“It was wintertime, the ants’ store of grain had got wet and they were
laying it out to dry. A hungry grasshopper asked them to give it
something to eat. ‘Why did you not store food in the summer like us?’
the ants asked. ‘I hadn’t time’, it replied. ‘I was too busy making sweet
music.’ The ants laughed at the grasshopper. ‘Very well’, they said.
‘Since you piped in the summer, now dance in the winter’.”

•   Permanent income hypothesis (broadly defined) describes well roughly
80% of the population. Roughly 20% appear “rule of thumb” or “time
inconsistent”.
Discussion of My Dissertation (including origins)

•   Discuss in class
Things I am Interested In: Stability of Preferences

•    “The Correlation of Wealth Across Generations” (Kerwin Charles and
Erik Hurst ; JPE 2002)

•    Do high saving parents have high saving kids? (Not the question I
was originally interested in).

•    Real question of interest:

“Can shocks to “preferences” today have long lasting effects on
economic decisions?”

“If we disenfranchise a group (Blacks) in the past – and then stop –
how long will differences between two groups persist”
Estimating Parent-Child Correlations
Use data from the Panel Study of Income Dynamics and estimate:

2                                2
W k = a + d1 W p + a 1 k A g e k + a                2k   A g ek + a 1 p A g e p + a   2p   Age p + ek

W k     2W p   1 k A g e k   2 k A g e k   1 p A g e p   2 p A g e p   k Z k   p Z        uk
2                             2
p

δ1 ≈ 0.40
δ2 ≈ 0.20              (where Z vectors include permanent income, direct transfers,
education, etc.)

δ2 can be interpreted as the correlation in saving rates (conditional on income,
how similar are parent and child wealths)

Can be do to “active” component or “passive” component.
Wealth Persistence

Parental Age-Adjusted Log Wealth Quintile (1984-1989)
Quintile (1999)            1           2          3           4          5

1                    36         26          16         15          11

2                    29         24          21         13          16

3                    16         24          25         20          14

4                    12         15          24         26          24

5                    7          12          15         26          36

Total                100         100        100         100        100
Persistence in Portfolio Persistence
I                        II                        III
Child Owns Stock?        Child Owns Business?       Child Owns Home?
A      B        C         A       B       C         A       B     C

Parent Owns Stock                             0.133 0.057 0.058
(0.039) (0.041) (0.041)

Parental Owns Business                                                  0.110 0.081 0.065
(0.033) (0.034) (0.034)

Parental Owns Home                                                                                0.245 0.145 0.147
(0.073) (0.072) (0.073)

Parent and Child Age Controls a               Yes     Yes     Yes       Yes     Yes     Yes       Yes     Yes     Yes
Parent and Child Income Controls b            No      Yes     Yes       No      Yes     Yes       No      Yes     Yes
Parent and Child Risk Tolerance Controls c    No      No      Yes       No      No      Yes       No      No      Yes

Adjusted R-Squared                           0.030   0.115    0.138    0.029   0.062    0.072    0.087   0.180    0.181
Persistence in Portfolio Persistence
Child’s Risk Tolerance Measure
Very Low              Low                Medium                High
Regressors          A        B          A         B         A        B          A          B

Parental Risk Tolerance

Low Risk Tolerance         0.059     0.064     0.008    -0.021    -0.054    -0.042     -0.012   -0.001
(0.065)   (0.066)   (0.051)   (0.052)   (0.054)   (0.054)   (0.057)   (0.058)

Medium Risk Tolerance      -0.117    -0.125    0.072     0.039     0.081     0.107     -0.037   -0.021
(0.079)   (0.083)   (0.062)   (0.065)   (0.065)   (0.068)   (0.069)   (0.072)

High Risk Tolerance       -0.138     -0.098   -0.005    -0.013    -0.010    -0.012     0.154     0.123
(0.057)   (0.057)   (0.045)   (0.047)   (0.047)   (0.049)   (0.050)   (0.053)
Part 1: Thoughts/Conclusions

• Use consumption data to estimate preference parameters

• Precautionary savings is an important feature in modern macro models

• The importance of precautionary saving depends on household risk
aversion, their impatience, and the risk they face.

• Empirically, the importance of “precautionary savings” in explaining
aggregate wealth holdings is mixed. Recent evidence suggests that it is
small.

• Preference heterogeneity seems to exist in the data. How important is it?

• Are preferences stable?
Part 2:
Homework Part 1 and Part 3
Discussion of “The Age of Reason:
Financial Decisions Over the Lifecycle”

Erik Hurst
University of Chicago, GSB
Paper Synopsis
•   The main findings

–   Focus on a cross section of households
–   Within the cross section, interest rates paid (fees, inverse of financial
sophistication) is U-shaped
–   Holds in a wide variety of settings

•   Emphasized interpretation

–   Financial learning and declining cognitive ability

•   Other interpretations offered (differing risk, opportunity cost of time,
medical expenses, sample selection, cohort effects, etc.)
•   I will focus on the “old” vs. “middle age” results (the upward sloping
portion of the U-shaped profiles). I am going to ignore the young.

•   Comment 1: The importance of selection?

Use data from existing nationally representative surveys to show that
selection issues are very important (the 60-70 year olds that are borrowing
are not random 60-70 year olds).

•   Comment 2: Are these magnitudes big?

Maybe….Aggregating across all different debt types, difference in rates/fees
paid by 55 year olds relative to 75 year olds is about \$175 per year
(~\$3.50/week).
Two (related) Questions
•   Why do people hold debt? (people do not hold debt randomly)

–   Smooth out consumption over their lifecycle
–   Borrowing will be peak when household income profiles are “low” or
household consumption needs are “high”
–   Who borrowers when they are 20? when they are 50? when they are
70?

•   What interest rate will borrowers pay? (interest rates not charged
randomly)

–   Function of default probabilities
–   Function of collateral amounts
–   Function of borrower search (opportunity cost of time and value of
lower interest rate)
–   Function of financial sophistication
Issue 1: Examining Selection
•   Use data from 2003 PSID

•   Nationally representative
•   Cross sectional comparisons (just like in this paper)

•   Focus on 25 – 75 year olds.

•   Look at:

Lifecycle profile of credit card debt and mortgage debt

Differences in the types of people (based on observables) that hold debt
over the lifecycle
Proportion of households with positive debt levels

80%

70%
Any Mortgage
60%

50%
Credit Card
40%

30%

20%

10%

0%
25-29   30-34   35-39   40-44   45-49     50-54   55-59   60-64   65-69   70-74   75-79
Average debt levels, conditional on having positive debt

160,000                                                                                              32,000

140,000                                                                                              28,000

120,000                                                                                              24,000
Mortgage Levels (Left Axis)
100,000                                                                                              20,000

80,000                                                                                              16,000

60,000                                                                                              12,000

Credit Card (Right axis)
40,000                                                                                              8,000

20,000                                                                                              4,000

0                                                                                               0
25-29   30-34   35-39   40-44    45-49   50-54   55-59     60-64   65-69   70-74   75-79
Are the people that hold debt at older ages representative?

•   Not Really - For example, sizeable differences by race:

Have Mortgage debt
Age          Non-Borrower         Borrower    Difference
50s              0.150                0.082    -0.068
60s              0.134                0.100    -0.034
0.035 *

Have Credit Card debt
Age          Non Borrower         Borrower    Difference
50s              0.122                0.100    -0.021
60s              0.102                0.146     0.044
0.065*

* Indicates significance at the 1% level
Are the people that hold debt at older ages representative?
•   Why is the racial composition important?

Blacks are found to pay higher interest rates than Whites in many markets
adjusting for a full vector of demographics (including age).

Charles, Hurst and Stephens (2008) – presented in a AEA session earlier
today.

Blacks pay higher rates for car loans than otherwise comparable whites
(using SCF data). The effect is entirely due to the type of establishments
frequented by blacks.

Consistent with a plethora of recent lawsuits against vehicle finance service
companies (GMAC, Ford Credit, etc.)

Discrimination or financial sophistication?
Are the people that hold debt at older ages representative?

•   Not Really - Health Differences:

Report Health Deterioration in Prior Two Years
Have Mortgage debt
Age         Non-Borrower          Borrower             Difference
50s             0.246               0.141               -0.105
60s             0.223               0.203               -0.020
0.085 *

Have Credit Card debt
Age         Non Borrower          Borrower             Difference
50s             0.179               0.190                0.011
60s             0.186               0.259                0.073
0.062*
Are the people that hold debt at older ages representative?

•   Additional differences by age (conditional on borrowing):

- Self reported health much worse (mortgage and credit card)

- Hospitalization more likely in the prior two years (credit card)

- Gross wealth much lower (mortgage and credit card)

•   No difference by education (interesting)
Summary: Is selection important? --- Yes

•   Probability of holding debt (and conditional levels of debt) diminish rapidly
with age.

•   Who holds debt among older households?

Much more likely to be Black.

Much more likely to have received an adverse health shock (even if health
spending is not put on the credit card, health shocks have occurred).

Poorer individuals.
Issue 2 – Examining Magnitudes
•   Cost of interest burden between 55 and 75 year olds:         Annual Cost*

Home equity loan interest gap: (~25 basis points)                 \$100

Home equity line interest gap: (~30 basis points)                 \$180

Credit card interest gap: (~5 basis points)                        \$4

Auto interest rate gap: (~5 basis points)                          \$2

Mortgage interest rate gap: (~12 basis points)                     \$53

Total                                                           \$350/year

* All costs valued at the mean level of debt (as reported in the Appendix)
Magnitudes?
•   Numbers on the previous page are likely way overstated!

•   As seen above, the amount of debt holdings seem to fall with age by
roughly 50% (so my estimated costs should fall by 50%).

•   Suggestion: Why not compute exact dollar differences by different age
ranges using data from SCF, PSID, HRS, AHEAD which tells the amount of
debt of each type held at each age.

•   Prediction: For those holding debt, my guess is that the annual difference
in expenditures is going to be less than \$175/year (between 55 and 75 year
olds). (About 50 minutes a month valued at pre-retirement wages)

•   Note: This number again would still be biased upwards if borrower
composition is changing between 55 and 75.
Conclusion
•   The policy prescription (particularly for the aged) depend on the reasons for
the upward sloping interest rate profile.

Are the old unable to process complex interest rate tasks (relative to their
young selves)? I am not sure.

•   Selection seems to be important – much more work can be done on this (the
data sets to address this are readily available). Moreover, interest rate data
exists in some of these other data sets.

•   Race and health composition changes over the lifecycle!

•   The magnitudes are pretty small (not zero – just small). Would a cost
benefit analysis recommend a policy intervention (again – particularly for
the old)? A table of costs would be a great addition to the paper.
Thoughts on “Depression Babies”
Why Has The U.S. Saving Rate Declined?
Part 3:
Consumption and Income
Consumption and Income Shocks
st
   1                    1                      
   C  C      
2
m ax Et                                                  
 st  1                2                      
                                                    

B t  1  ( B t  Y t  C t ) (1  r )

w h e r e C is b lis s p o in t c o n s u m p tio n , B is b e g i n n in g o f p e r io d

w e a lth , a n d Y is la b o r in c o m e .

N o te :   A s s u m p tio n o f " lo g u tility "

F o r s im p lic ity :   A ssum e   r.
Income Shocks and Consumption Growth

• Given above preferences, consumption is a random walk such that:

 C t 1   t 1 ,           E t [ t  n ]  0  n  0

• Suppose, income process is as follows:

Pt  1  Pt       t 1

Y t  1  Pt  1   t  1

E t [ t  n ]  E t [     tn
] 0

• Optimal Consumption Growth:

 r 
 C t 1           t 1            t 1
1 r 
64
Deaton and Paxson (1994)
“Intertemporal Choice and Inequality” (JPE)

Hypotheses:      PIH implies that for any cohort of people born at the same
time, inequality in both consumption and income should
grow with age.

How much consumption inequality grows informs

o    Lifecycle shocks to permanent income
o    Insurance mechanisms available to households.

Data:            U.S., Great Britain, and Taiwan

65
Deaton and Paxson Methodology (U.S. Application)

•     Variance of Residual Variation

ln C it   0   a g e A g e it   c o h o r t C o h o r t it   t D t   fs F a m ily it   it
k               k                 k                         k           k                    k

•     Compute variance of εkit at each age and cohort

•     Regress variance of εkit on age and cohort dummies (equation
(2))

•     Plot age coefficients (deviation from 25 year olds)

Note: This is my application of the Deaton/Paxson Methodology
(very similar in spirit to theirs).
66
Figure 1b: With and With Out Housing Services
0.24

0.20
Log Deviation From Age 25

0.16

0.12

0.08

0.04

0.00
25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75
Figure 1b: With and With Out Housing Services
0.24

Cross Sectional Variance of Total Nondurables for 25 Year Olds = 0.16
0.20

0.16
Log Deviation From Age 25

0.12

0.08

0.04

0.00
25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75

-0.04
Figure 1b: With and With Out Housing Services
0.24

Cross Sectional Variance of Total Nondurables for 25 Year Olds = 0.16
0.20

0.16
Log Deviation From Age 25

0.12

0.08

0.04

0.00
25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75

-0.04
More Aguiar/Hurst (2009)

•   Examine lifecycle profile of cross sectional inequality by
category

•   Goods which have expenditures that increase with market
work (due to home production or complementarity) should
experience increasing dispersion when the dispersion of work
increases.

•   Portion of lifecycle profile of cross sectional inequality due to
these goods does NOT inform researchers about:

o Lifecycle profile of shocks to permanent income
o Insurance mechanisms available to households
70
Dispersion of Propensity to Work Over Life Cycle
0.60

0.50

0.40

0.30

0.20

0.10

0.00
25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75
Age
Cross Sectional Lifecycle Dispersion: Entertainment
0.4

0.2
Difference in Variance From Age 25

0.0

-0.2

-0.4

-0.6

-0.8
25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75
Non Increasing Dispersion Categories
0.5

0.0
Difference in Variance From Age 25

-0.5

-1.0

-1.5

-2.0

-2.5

-3.0

-3.5
25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75

Entertainment      Utilities   Housing Services   Food At Home   Other Non Durable
Where is the Increase in Dispersion Coming From?
4.0

3.5

3.0
Difference in Variance From Age 25

2.5

2.0

1.5

1.0

0.5

0.0

25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75
-0.5

-1.0
Clothing     Transportation   Domestic Services    Food Away From Home
Lifecycle Variation in Standard Deviation
Variance at   Change    Change    Change    Change
Consumption Category     Age 25      25 - 44   45 - 59   59 - 68   25 - 75

Increasing
Transportation         0.70        -0.14     0.11      0.04      0.38
Clothing/P. Care       0.63         0.18     0.53      0.09      0.91
Food Away              1.54         0.00     1.29      0.42      1.91
Alcohol /Tobacco       5.80         1.53     2.62      1.05      4.82
Domestic Services      6.82         0.84     1.15      0.47      2.85

Non Increasing
Housing Services        0.41        -0.07     -0.12     -0.07     -0.27
Utilities               0.89        -0.56     -0.09     -0.05     -0.76
Entertainment           1.29        -0.31     -0.10     -0.17     -0.69
Other Non-Durable       9.57        -0.71     -0.91     -0.27     -2.39
Food at Home            0.41        -0.05      0.02      0.01     -0.02
Cross Sectional Dispersion Over Lifecycle
0.50

0.40
Percentage Point Deviation From Age 25

0.30

0.20

0.10

0.00
25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75

-0.10

-0.20
Core Nondurable
Cross Sectional Dispersion Over Lifecycle
0.50

0.40
Percentage Point Deviation From Age 25

0.30

0.20

0.10

0.00
25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75

-0.10

-0.20
Core Nondurable       Work Related      Food At Home
Cross Sectional Dispersion Over Lifecycle: Figure 6b
0.50

0.40
Percentage Point Deviation From Age 25

0.30

Total
0.20

0.10

0.00
25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75
Core
-0.10

-0.20
Cross Sectional Dispersion Over Lifecycle: Figure 6b
0.50

0.40
Percentage Point Deviation From Age 25

0.30

Total
0.20

0.10

0.00
25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75
Core
-0.10

-0.20
What Does it Mean?

• Aguiar and Hurst (2009)

Write down a model where households maximize utility with three
consumption goods (and leisure) with the following constraints:

one good (food) is amenable to home production
one good (transport, clothes) are complements to market work
there is a time budget constraint

Assumptions:

o    conditional on work, income process is uncertain
o    take the lifecycle process of work as exogenous
o    assume that individual receives no utility for the lifecycle component
of work related expenses.
Implications

When use disaggregated consumption data to match moments of model, get:

• The estimated uninsurable/unanticipated permanent income volatility gets
reduced by more than half (increases transitory volatility)

Reason:        The consumption volatility of “core nondurables” increases
by roughly 50% less than “total nondurables”

• The estimated importance of precautionary savings due to income
fluctuations in explaining the wealth holdings of individuals is reduced.

Reason:        Permanent income volatility is lower

• Agents are estimated to be significantly more patient

Reason:        Mean spending on core nondurables does not fall over the
back half of the lifecycle.
Conclusions

• Beckerian model of consumption is important for explaining not only
lifecycle profile of mean expenditures but also lifecycle profile of cross
sectional dispersion in expenditures.

-     Explains decline in mean during back half of the lifecycle.

-     Explains increase in cross sectional dispersion post middle age.

• The assumption that consumption (expenditure) and leisure are non-
separable is not a valid assumption.
Part 4:
Homework Part 2
and Time Series of Consumption
Inequality
Average Consumption in CEX
9.8500

9.8000

9.7500

9.7000

9.6500

9.6000

9.5500

84
Percent Change in Consumption in CEX (from 1981)
0

-0.02

-0.04

-0.06

-0.08

-0.1

-0.12

-0.14

-0.16
85
Income and Consumption Inequality
• Large literature documenting the increase in income inequality within the
U.S. during the last 30 years (Katz and Autor, 1999)

• Consumption is a better measure of well being than income (utility is U(C)
not U(Y)).

• Does income inequality imply consumption inequality?

Depends on whether income inequality is “permanent”
Depends on insurance mechanisms available to households
Depends on other margins of substitution (home production, female
labor supply, etc.).

• Topic taken up by Attanasio and Davis (1994, JPE), Krueger and Perri
(2006, ReStud), and Attanasio, Battistin, and Ichimura (2004, orazio’s web
page).
86
Kevin Murphy’s Web Page

87
Kevin Murphy’s Web Page

88
Consumption Inequality (Time Series)
0.5600

0.5500

0.5400

0.5300

0.5200

0.5100

0.5000

0.4900

89
Consumption Inequality: Adjusting For Family Size
0.06

0.05

0.04

0.03

0.02

0.01

0

-0.01

-0.02

No Controls   Family Size Dummies   Family Size Adjustment
90
Trends in CEX Consumption (Attanasio et al, 2004)

“What really happened to consumption inequality in the US?”
91
Trends in CEX Consumption Inequality
(Attanasio et al, 2004)

“What really happened to consumption inequality in the US?”
92
Aguiar and Hurst (2009)
Change in the Cross Sectional Variance of Log Expenditure Over Different
Time Ranges

I.                        II.                       III.
1981-    1990-    1981-    1981-    1990-   1981-    1981-    1990-   1981-
Log Expenditure Measure   1990     2003     2003     1990     2003    2003     1990     2003    2003

Log Total Non Durable
Expenditures              0.055    0.039    0.094    0.042    0.045   0.087    0.036    0.037   0.073

Log Core Non Durable
Expenditures              0.063    0.027    0.090    0.037    0.031   0.068    0.034    0.023   0.058

Log Work Related
Expenditures              0.104    0.041    0.145    0.076    0.038   0.114    0.052    0.020   0.072

Log Food at Home
Expenditures              -0.047   -0.020   -0.066   -0.005   0.003   -0.002   -0.004   0.000   -0.003

First Stage Controls      None     None     None      Full    Full     Full     Full    Full     Full

Second Stage Controls     None     None     None     None     None    None      Age     Age      Age
93
Part 5:
Consumption and Insurance
Consumption Insurance
•   The Broad Question of Interest:

Are households “insured” against “shocks” to their income process?

•   The Problem at Hand:

How does one measure a “shock” from the household’s perspective? What we
(the econometricians) label as a shock may be anticipated from the household’s
perspective. Given that, households may react little to our identified “shocks”.

•   The Methodology:

Use the joint distributions of income and consumption (and sometimes
expectations) to analyze the extent of consumption insurance.

95
The Conceptual Issue: Uncertain Income

Income

Time
t                T

96
Uncertain Income

Income
Shock (as identified by econometrician)

Time
t                          T

Suppose, from individual perspective, the household truly did receive an
unexpected permanent shock to income.

97
No Insurance

Consumption (dotted line)
Income

Time
t                           T

Household consumption responds completely to permanent shock to
income.

98
Complete Insurance

Income
Consumption

Time
t                       T

Household consumption will not respond to the permanent income shock.

99
The Conceptual Issue: Deterministic Income

Income

Time
t                        T

Suppose, from individual perspective, the income process is completely
deterministic.

100
The Conceptual Issue: Deterministic Income

Income
Shock (as identified by econometrician only)

Time
t                         T

Suppose, from individual perspective, the income process is completely
deterministic.

101
The Conceptual Issue: Deterministic Income

Income
Consumption

Time
t                       T

Forward looking consumers will incorporate the expected change in
income into their current consumption decisions.

102
The Conceptual Issue: Deterministic Income

Income
Consumption

No change in consumption growth

Time
t                       T

Forward looking consumers will incorporate the expected change in
income into their current consumption decisions.

103
The Conceptual Issue: Deterministic Income

Income
Consumption

No change in consumption growth

Time
t                        T

From the perspective of the econometrician, households appear to be
completely insured against permanent “shocks” to income.

104
The Conceptual Issue: Deterministic Income

Income
Consumption

No change in consumption growth

Time
t                        T

From the perspective of the econometrician, households appear to be
completely insured against permanent “shocks” to income.

Results from not properly identifying unanticipated changes in income.
105
Blundell, Pistaferri, and Preston (AER, 2008)
•   Write down and estimate an econometric model to uncover the extent to which
households are insured against both transitory and permanent income shocks.

•   They use data on actual income and consumption data.

•   Using data on only observed income and consumption does not allow the
econometrician to separately identifying unanticipated changes in income from
anticipated changes in income. (Akin to the simplified example above).

•   Blundell, Pistaferri and Preston made the implicit assumption that variance of
anticipated permanent changes in income and the variance of the anticipated
transitory changes in income were zero (i.e., there was no uncertainty over the
anticipated changes in income).

•   As seen above, if that assumption fails to hold, the estimated extent of
household insurance would be over stated (change in consumption
understated).                                                               106
Kaufmann and Pistaferri (AER P&P, 2009)

•   Use data on:

Actual income realizations
Actual consumption data
Expected income changes

•   Use the moments of these three series to identify how consumption responds to
the unexpected permanent and transitory innovations in income.

•   The key is using data on expected income changes to better isolate income
“shocks” from the perspective of the household.

107
Some More Preliminaries

•   Data is from the Italian Survey of Household Income and Wealth

•   Survey questions on individual expectations of future income.

•   With a tad bit of structure, can compute the expected future income for all
households who report answers to the survey questions.

•   Strong correlation between expected income and actual income (~0.5).

108
Key Results

•   As theory predicts, the amount of insurance is OVERSTATED with
respect to permanent income shocks when econometricians ignore the fact
that individuals have superior information about their own income
process.

-   Some of our identified “shocks” are expected by the household resulting in
a muted consumption response.

•   Key results from these paper:
BPP               KP
Response to Transitory Income Shocks                0.14              0.31
(0.05)            (0.43)

Response to Permanent Income Shocks                 0.69              0.94
(0.27)            (0.51)
109
Benefits of Risk Sharing
•   An important implication of complete markets, full insurance model is that
allows the construction of a “representative” consumer.

•   Good for aggregating individuals

•   Aggregate consumption moves as if it were determined by a representative
consumer who only responds to aggregate risk (no need to worry about
idiosyncratic risk).

Formalize the test:

 ln ( C        )  k  vt    yt  
i                             i       i
t                                     t

w h e r e f u ll r i s k s h a r i n g i m p li e s t h a t  = 0

110
Important Earlier Empirical Papers Testing Full Risk
Sharing
•    Townsend (1994) “Risk and Insurance in Village India” (Econometrica)

•    Cochrane (1991) “A Simple Test of Consumption Insurance” (JPE)

•    Attanasio and Davis (1996) “Relative Wage Movements and the Distribution
of Consumption” (JPE)

All papers reject perfect risk sharing. Some limited evidence of partial risk sharing
(government transfers, self insurance for transitory shocks, family transfers).

111

Job Market Paper from Greg Kaplan (out of NYU – now at Penn Economics
Department)

“Moving Back Home: Insurance Against Labor Market Risk”

Had offers from Booth, Wharton, Penn Econ, Berkeley Econ, Sloan, Michigan, and
6 others.

Dissertation looked at the role families play (particularly the ability to move back
home) in insuring labor market risk for young low educated workers.

http://homepages.nyu.edu/~gwk210/Greg_Kaplan/Home.html

All of you could have written this dissertation.
112
Conclusions on Risk Sharing

•   There is some risk sharing (within families).

•   However, we are far from perfect risk sharing.

•   Permanent idiosyncratic shocks have permanent effects on household
consumption.

113
Part 6

“Conspicuous Consumption and Race”

Charles, Hurst, and Roussanov
QJE 2009
Racial Differences in Economic Outcomes
•   Large literature documenting differences in wealth holdings, savings rates, and
portfolio allocation between Blacks and Whites. (e.g., Barsky et al. (2002), Hurst et
al. (1998), Charles and Hurst (2001), etc.)

Question: Why do Blacks save less (hold less wealth) than otherwise similar
Whites?

•   Likewise, there is some work documenting racial differences in individual
consumption categories such as education and health insurance.

Question:    Why do Blacks spend less on health insurance and education
than similar Whites?

•   Related Question:      What are Blacks spending more on?

•   Question:    Can racial differences in spending patterns on these goods explain
(at least partially) racial differences in savings rates or racial
differences in education or health spending?
Conspicuous (Visible) Consumption

•       Veblen (1899) :      Consumption communicates information about
economic status.

“Consumption is evidence of wealth, and thus becomes honorific,
and…failure to consume a mark of demerit.”

o      The argument does not necessarily apply to “total consumption” – only
the portion of consumption that is observable by others.

•       Theoretically, models of conspicuous consumption have been explored by
many.

•       Empirically, the signaling value of consumption is relatively unexplored in
economics.
Some Preliminaries: An Overview of Main Data Set
•       Use data from Consumer Expenditure Survey (CEX)

o      Use data from 1986 – 2002 (pooled).

o      Include one observation per household (collapse multiple observations
throughout the year into a single observation).

o      Restrict the primary analysis sample to households with a head aged 18
to 49 (inclusive).

o      Include households with a head being either Black, Hispanic, or White
(we also look at Asians in some cuts of the data).

Sample includes roughly 37,300 Whites; 6,800 Blacks; 5,300 Hispanics

Will use other data (PSID) to confirm the CEX findings
An Overview of the Data (continued)

•       Summary: We define visible goods to include expenditures on:

o      Clothing and Jewelry
o      Personal Care
o      Spending on vehicles (excluding maintenance)

•       Treat housing separately

o      Hard to separate the quantity from the price effect.
o      Evidence of discriminatory practices.

•       Note: Racial differences in visible spending get slightly LARGER if we
include housing as a visible good.
Some Descriptive Statistics (Tables 1 and A2)
All     White    Black    Hispanic

Total Annual Income             57,800   63,800   38,400   39,800
(Conditional Inc > 0 )

Total Expenditure (Quarterly)   10,700   11,600   7,700     8,400

Visible Expenditures            2,029    2,176    1,538     1,681
(Quarterly)

Vis Expend/Total Expend          0.12     0.12     0.12      0.12

All in 2005 dollars
Part 1: Documenting the Facts
Estimate:

ln(Visible Exp) = βo + β1 Black + β2 Hispanic + φ Permanent Income + θ X + η

o        Year dummies ;
o        Sex dummy ;
o        Family structure dummies (number of adults, number of children,
married) ;
o        Location dummies (urban dummy, MSA dummy, census region
dummies, city size dummies (post-1996)) ;
o        Wealth controls (in some specifications)
Measuring Permanent Income
Approach 1:

Use current income controls (current income, education dummies, and
occupation dummies) to proxy for permanent income.

CEX current income data is notoriously bad (27% of sample had missing
income – no imputations).

Racial gaps in income using CEX data do not match the racial gaps in
income using CPS data (although the CEX expenditure gaps match the CPS
income gaps).

Approach 2:

Use CEX total expenditure as a proxy for permanent income.
Potential Issues with Approach 2

Potential problems with using total expenditure as a proxy for permanent income:

1.   Total expenditure is not exogenous (expenditure components are jointly
determined).

2.   Measurement error in visible expenditure will cause a correlation between
visible expenditures and total expenditures.

Solution:

Instrument total expenditure with our current income controls (either current
income or current income, education and occupation dummies).

Verify our results in the PSID where we can use panel aspect to create a
better measure of permanent income.
Preferred Specification
Estimate:

ln(Visible Exp) = βo + β1 Black + β2 Hispanic + φ ln(Total Exp) + θ X + η

Notes:

Instrument Total Expenditure with: a dummy for whether current income
was zero, a cubic in current income (or the log of current income) if income
was positive, education and occupation dummies.

Included non-linear total expenditure controls as a robustness.

Similar to standard “consumption demand system” model.

Will estimate separately by race and plot the visible expenditure Engel
curves.
Table 2: Base Regression Results
Black         Hispanic
Regression Controls Included                      Coefficient    Coefficient

1.   No Additional Controls                       -0.38 (0.04)   -0.23 (0.04)

2. Specification 1 plus current income controls   -0.03 (0.03)   0.14 (0.04)

3. Specification 1 plus ln(Total Expenditure)     0.31 (0.03)    0.26 (0.06)

4. IV Regression of Specification 3               0.23 (0.03)    0.20 (0.05)

5. Specification 4 plus time dummies              0.24 (0.03)    0.21 (0.05)

6. Specification 5 plus rest of X vector          0.26 (0.02)    0.23 (0.05)
Magnitudes

•   Blacks Hispanics spend roughly 26% (23%) more on visible consumption
than comparable whites.

•   Average household in sample spends roughly \$2,100 per quarter on visible
consumption.

•   Blacks (Hispanics) spend roughly \$2,200 (\$1,900) a year more on visible
goods than comparable Whites.

•   The level is likely an under estimate (research shows that the CEX under
reports total expenditures relative to NIPA).

•   Mean total pre-tax family income for Blacks (Hispanics) during the 1990s
(March CPS):         \$42,500 (\$48,300)
Estimated Engel Curves (Figure 1)
8
6
4
2

7                   8                      9         10
Log Quarterly Total Expenditure

Black             White

Estimated Difference at sample mean income ~ 0.3
Separately Analyzing Visible Components (Table 3)
I. Full Sample        II. Positive Car
Spending
Visible Consumption Sub-    Black       Hispanic    Black    Hispanic
Category                   Dummy        Dummy      Dummy     Dummy

Clothing/Jewelry            0.38          0.41      0.36       0.37
(0.03)        (0.03)    (0.04)     (0.02)
Personal Care               0.73          0.43      0.81       0.42
(0.05)        (0.03)    (0.06)     (0.05)
Cars (Limited)              -0.43        -0.29      0.12       0.09
(0.07)        (0.10)    (0.04)     (0.06)
Cars (Expanded)             -0.46        -0.34      0.09       0.04
(0.10)        (0.17)    (0.03)     (0.05)
Separately Analyzing Visible Components (Table 3)
I. Full Sample        II. Positive Car
Spending
Visible Consumption Sub-    Black       Hispanic    Black    Hispanic
Category                   Dummy        Dummy      Dummy     Dummy

Clothing/Jewelry            0.38          0.41      0.36       0.37
(0.03)        (0.03)    (0.04)     (0.02)
Personal Care               0.73          0.43      0.81       0.42
(0.05)        (0.03)    (0.06)     (0.05)
Cars (Limited)              -0.43        -0.29      0.12       0.09
(0.07)        (0.10)    (0.04)     (0.06)
Cars (Expanded)             -0.46        -0.34      0.09       0.04
(0.10)        (0.17)    (0.03)     (0.05)
Table 4: Racial Differences in All Spending Categories
Log Expenditure        Black    Hispanic
Log Expenditure      Black    Hispanic

Housing                 0.03      0.13
(0.02)    (0.03)    Entertain Services   -0.29     -0.36
Utilities               0.09     -0.02                          (0.03)    (0.05)
(0.03)    (0.02)    Entertain Durables   -0.35     -0.17
Food                    -0.06     0.06                          (0.05)    (0.05)
(0.02)    (0.02)    Health               -0.51     -0.48
Other Transport.        -0.15    -0.02                          (0.05)    (0.06)
(0.03)    (0.04)    Alc./Tobacco         -1.04     -1.04
Home Furnishings        -0.18     0.09                          (0.05)    (0.05)
(0.04)    (0.05)
Other                -0.08     -0.38
Education               -0.16    -0.30
(0.04)    (0.08)
(0.10)    (0.12)
Table 5: Robustness Exercise Using PSID
Log Expenditure                                             Black

Clothing Expenditures, No Controls                          -0.07
(0.07)
Clothing Expenditures, Full Controls                        0.24
(0.07)
Price of Recent Car Purchase, Full Controls                 0.12
(0.09)

Food Expenditures, Full Controls                            -0.12
(0.03)
Entertainment Expenditures, Full Controls                   -0.33
(0.08)
Other Transportation, Full Controls                         -0.09
(0.06)
Summary of the Facts
•       Large evidence that relative to economically similar Whites, both Blacks and
Hispanics consume considerably more “visible” goods.

o      The magnitudes are large: roughly 26% more which translates to about
\$2,100 more per year in visible spending for blacks.

o      The findings are very robust – within different sub-groups of the
population, across different time periods, across different specifications.

o      The percentage differences are much smaller for older Black households
(off a much smaller base).

o      Aside from housing, all other consumption categories are lower for
Blacks and Hispanics (including health spending and education)
Part 2 – A Model of Conspicuous Consumption
•   Preference differences could explain the differences in consumption patterns
across races.

•   Question 1:

Is there any model that does not rely on differences in preferences between
races that can explain the documented consumption patterns?

•   Question 2:

If so, can the predictions of this model be distinguish from a model of
preference differences?
Part 2 – A Signaling Model of Conspicuous Consumption

•    Glazer and Konrad (1996) study the signaling value of observable charitable
giving.

•    Other models include Mailath (1987) and Ireland (1994).

•    Similar in implications to the classic Spence model (1973) of job market
signaling.

•    Our goal is to draw on the implications of these theoretical models.
Part 2 – Model Components
•        Preferences (household i drawn from group k)

 ( yi  ci )  u (ci )  w ( si )
k     k          k            k

where:        ci is consumption of all visible goods
yi is the total household income endowment
y-c is consumption of all non-visible goods (static model)

•        Income is not observable (only c is observable to others)
•        Income is drawn from known distribution fk(y) with support [ykmin, ykmax]

•        Define:       Status (sik) is society’s inference about i’s income based upon

s i  E  y i | c i , k  , w h e re c i
k             k   k*                   k*
is e q u ilib riu m v is ib le c o n s u m p tio n
               
Part 2 – Model Components

Notes:

•    All preferences are constant across all groups.
•    v(.), u(.), and w(.) are each concave and twice continuously differentiable.
•    We do not take a stand on the benefits of “status” .

Focus on separating equilibrium such that:

s i ( c i ( y i ))  y i
k    k*     k         k

•    Similar spirit to Glazer and Konrad (1996).
Signaling Predictions
1.    cik* is strictly increasing in yi (relationship can be concave or convex
depending on the relative concavity of w(.) with u(.) and v(.)).

2.    In equilibrium, the poorest individual in group k has no incentive to signal
(cik* will be the same regardless of whether or not w(.) = 0).

How does cik* relate with moments of the income distribution, f(.)?

3.    The relationship between group income dispersion and cik* is
theoretically ambiguous (holding own income constant).

Depends on curvature of ∂c*/∂y

4.    If poorer persons are added to the group such that the support of the
group’s income distribution becomes [ymin – θ, ymax] and average group
income falls, then cik* increases at every level of income.
•    Framework is quite general. Reference groups k represent, in theory, any
type of groupings into which the population can be sorted.

•    Depending on the situation, observers will know more or less about the
distribution from which other individual’s unobserved income is drawn.

•    Key insight: Information about one’s reference group influences
observer’s inferences about one’s income and thus interacts with the
optimal choice of signaling expenditures.

A leftward shift in the distribution of reference group income:

cik* ↑ (holding yi constant)

An increase in dispersion of reference group income:

cik* ? (holding yi constant)
.00001 .00002 .00003   Black vs. White Permanent Income Distribution (Fig 2a)
Density

0

0   20000   40000    60000    80000 100000 120000 140000 160000
Total Expenditure (Annual)

White
Black

Permanent Income Measured by Total Expenditure (CEX data)
Black vs. White Permanent Income Distribution (Fig 2b)
.00002
Density
.00001

0

0   25000   50000   75000 100000 125000 150000 175000 200000
Average Family Income

White
Black

Permanent Income Measured by Average Income (PSID data)
Relevant Questions at Hand
•   Are moments of the reference group income distribution (mean and
variance) systematically related to visible consumption?

Can we see such a relationship within a race?

For example, do Whites from poorer reference groups consume more
visible goods than otherwise similar Whites from richer reference
groups?

Note:    Use mean as proxy for the leftward shifting of the income
distribution.

•   Does controlling for moments of the reference group income
distribution explain the racial differences in visible consumption?

As seen above, the black distribution of income is, on average, to the left of
the white income distribution.
How Do We Define Reference Group Income Distribution
•     Main approach (when assessing CEX data)

Define reference group at the state/race level
States is the lowest level of geographic location available in the CEX.

•     Robustness approach (when assessing PSID data)

Define reference group at the MSA/race level
Use PSID confidential geo-code data to get MSA info for each household.

For the state/race moments of the income distribution, we use CPS data from
1990-2002 (total income of men aged 18-49).

For the MSA/race moments of the income distribution, we use census data from
2000 (total income of men aged 18-49).

We explored many different income measures as a robustness exercise.
An Important Caveat

•   Throughout our analysis, we are taking the choice of reference group as
being “exogenous”.

•   We believe that there are many interesting potential implications that may
arise if we endogenize residential choice patterns (i.e., allow people to
choose their reference group).

•   We are thinking about these implications in future work.
Reference Group Income Distribution and Visible Spending
•       How do moments of the reference group income distribution interact with
visible spending?

ln ( v is ib le isr )   0   sr (  s g r )   ln ( T o ta lE x p e n d itu r e i )   X i   i

where Γs and Γr are vectors of state and race fixed effects, respectively.

•       Regression estimated via IV (as described above) where current income,
education and occupation controls are used as instruments for total
expenditure.

•       Figure 3 plots the estimated δsr against the mean state income for the
particular race/state cell (from the CPS as described above).

Key results:          Systematic negative relationship between mean income of state
and the propensity to consume visible goods (all else equal).
Figure 3

1
AL

KY

MANVNV
NJ
.5

AR         KS SC
AR               IL     VA
TX
OH OK WI KS
TX
WA
AL
MI
DC
OR NYDC CA
MA           MD CO MD
PA           CO CA                    AK
IATN
WI FL
SC NY AZINNJHI AK
AZ
LA           MN CT IL
NC MN KY
NC           OH
MO
OK IN GA        CT MI IA
FL         VA
WA
0

PA OR HI    AL
AR KY        PA
IA            MO           SC
LA
IN OH
KS
TN                 NC
GA LA TN MO WI MI MA TX
IL
AZ GA
OR MNWA     CT   DC
OK   FL NVVA CA NJ
NY
COAK

HI           MD
-.5

9.6                10              10.4             10.8              11.2
Log of Mean Income of Race-State Cell

White      Black       Hispanic
Examining Within Race Regressions

ln ( v is ib le is )   0   1 (  k )   2 ( D k )   ln ( T o ta lE x p e n d itu r e i )
y              y

  X i  i

where:

μ is the log of the mean income for persons race/state cell (from CPS)

D is the dispersion of income in a race/state measured by the coefficient of
variation (from CPS).

Note:      We also control directly for “housing” costs (which are location
specific).
Table 6: Within White Results

Dependent Variable
Log All
Less
Visible
Log Visible Expenditure         Log Food      and
Housing
(1)         (2)          (3)           (4)     (5)

Log of Mean Income of Own         -0.60       -0.70         -0.58      0.23       -0.01
Race in State                     (0.14)     (0.14)        (0.13)     (0.06)     (0.05)

Coefficient of Variation of                   -0.72        -0.63       0.59      -0.06
Income for Own Race in State                 (0.30)        (0.28)     (0.10)     (0.03)

Log of Individual Housing                                   -0.13      0.01       -0.15
Expenditures *                                             (0.06)     (0.03)     (0.02)

* We also instrument individual housing expenses with state housing prices (from 1990
and 2000 census)
Table 7: Within Black and Hispanic Results

Dependent Variable
Log All
Less
Visible
and
Log Visible Expenditure            Log Food Housing
(1)         (2)        (3)         (4)        (5)     (6)

Log of Mean Income of Own          -0.44       -0.51     -0.45        -0.64     0.12     -0.02
Race in State                     (0.13)      (0.12)    (0.13)       (0.15)    (0.08)   (0.03)

Coefficient of Variation of                    0.25      0.26         0.26      -0.14    -0.02
Income for Own Race in State                  (0.17)    (0.18)       (0.17)    (0.07)   (0.04)

Log of Individual Housing                                -0.09        -0.16     0.16     -0.14
Expenditures *                                          (0.08)       (0.09)    (0.04)   (0.03)

Log Mean Income of All in State                                       0.60
(0.31)
Explaining the differences across races
How much of the race gap can be explained by differences in reference
group income?

Specifically, compare:

ln(Visible Expenditure) = βo + β1 Black + β2 Hispanic
+ φ ln(Total Expenditure) + θ X + η

with

ln(Visible Expenditure) = βo + β1 Black + β2 Hispanic + β3 Mean Incomeik
+ β4 Coefficient of Variationik + γ ln(Total Expenditure) + δ X + η
Table 8 (The Payoff)
Variable                         1         2         3         4       5

Black Coefficient                0.26     0.28     -0.03   -0.005     -0.04
(0.02)   (0.02)   (0.07)   (0.07)    (0.07)

Hispanic Coefficient             0.23     0.26     -0.01   -0.01      -0.04
(0.03)   (0.03)   (0.08)   (0.06)    (0.07)

Log of Mean Own Group                              -0.53     -0.51   -0.52
State Income                                      (0.12)    (0.11)   (0.11)

Coefficient of Variation                                               0.17
(0.12)

State Fixed Effects              No       Yes     No        Yes        Yes
Table 8 (The Payoff)
Variable                         1         2         3         4       5

Black Coefficient                0.26     0.28     -0.03   -0.005     -0.04
(0.02)   (0.02)   (0.07)   (0.07)    (0.07)

Hispanic Coefficient             0.23     0.26     -0.01   -0.01      -0.04
(0.03)   (0.03)   (0.08)   (0.06)    (0.07)

Log of Mean Own Group                              -0.53     -0.51   -0.52
State Income                                      (0.12)    (0.11)   (0.11)

Coefficient of Variation                                               0.17
(0.12)

State Fixed Effects              No       Yes     Yes       Yes        Yes
Table 8 (The Payoff)
Variable                         1         2         3         4       5

Black Coefficient                0.26     0.28     -0.03   -0.005     -0.04
(0.02)   (0.02)   (0.07)   (0.07)    (0.07)

Hispanic Coefficient             0.23     0.26     -0.01   -0.01      -0.04
(0.03)   (0.03)   (0.08)   (0.06)    (0.07)

Log of Mean Own Group                              -0.53     -0.51   -0.52
State Income                                      (0.12)    (0.11)   (0.11)

Coefficient of Variation                                               0.17
(0.12)

State Fixed Effects              No       Yes     Yes       Yes        Yes
Table 8 (The Payoff)
Variable                         1         2         3         4       5

Black Coefficient                0.26     0.28     -0.03   -0.005     -0.04
(0.02)   (0.02)   (0.07)   (0.07)    (0.07)

Hispanic Coefficient             0.23     0.26     -0.01   -0.01      -0.04
(0.03)   (0.03)   (0.08)   (0.06)    (0.07)

Log of Mean Own Group                              -0.53     -0.51   -0.52
State Income                                      (0.12)    (0.11)   (0.11)

Coefficient of Variation                                               0.17
(0.12)

State Fixed Effects              No       Yes     Yes       Yes        Yes
Summary

•   Document a set of facts that both Blacks and Hispanics spend a considerable
more on visible consumption items than similar Whites.

•   This behavior is persistent within all sub groups and exists in the data since
1984. There is some evidence that this behavior dissipates with age.

•   A model of conspicuous consumption and signaling fits the data very well.

•   Controlling for the mean income of the group from which the individual
is drawn explains the majority of the racial gap in visible consumption.

•   Moreover, the model is race blind. The model is supported when looking at
behavior within races (either Whites or Blacks).
Part 4. Potential Implications

•       How does the propensity to spend on visible goods effect the spending on
other categories?

o      If we wish to promote Black spending on items such as education or
health care, we need to understand the incentives to purchase status by
investing in visible consumption.

o      May effect they way we design social programs.

o      Question: To what extent is visible spending differences correlated with
spending differences in spending on other categories, like health care
and education?

o      Question: Can conspicuous consumption be a potential explanation for
observed saving/wealth differences across races?
Unresolved Questions

•   How does conspicuous consumption affect saving in a dynamic model?

Need to take a stance on why people value the “status”

•   Can any of the observed “saving” gaps between blacks and whites be
explained by differences in spending on conspicuous spending?

•   How do people signal status in different settings? Do these finer models of
signaling and status matter for anything “bigger”.

•   How are residential sorting patterns affected by conspicuous
consumption motives? The reference groups – along some dimension –
is endogenous!

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