micro data for macro models topic 2: consumption inequality and lifecycle consumption

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Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

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Page 1: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Micro Data For Macro Models

Topic 2:

Consumption Inequality and

Lifecycle Consumption

Page 2: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Part A:Background on Household Surveys

(Jonathan Covered This in TA Sessions)

Page 3: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Micro Expenditure Data: Household Surveys

• Consumer Expenditure Survey (U.S. data)

Starts in 1980

Broad consumption measures

Some income and demographic data

Repeated cross-sections

• Panel Study of Income Dynamics (U.S. data)

Starts in late 60s

Only food expenditure consistently

Housing/utilities (most of the time)

Broader measures (recently)

Very good income and demographics

Panel nature

Page 4: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Micro Expenditure Data: Household Surveys

• British Household Panel (British Data)

o Panel data including income and expenditure

• Family Expenditure Survey (British Data)

• Bank of Italy Survey of Household Income and Wealth (Italian Data)

o Panel data including income and expenditure

• There are others….many Scandinavian countries, Japan, Canada, etc.

• Even some developing economies have detailed household surveys that track some measures of consumption (e.g., Mexico, Taiwan, Thailand)

Page 5: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Micro Expenditure Data: Scanner Data

• Nielsen Homescan Data

o Large cross-section of households

o Very detailed level transaction data (at the level of UPC code)

o Some demographics

o Some panel component

o Matches quantities purchased with prices paid

o Covers most of the large MSAs

o Measurement error?

o Selection?

o Coverage of goods?

Page 6: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Micro Income Data: Household Surveys

• Current Population Survey (CPS)

o Usual data set used within U.S. to track labor supply and earnings.

o Has panel component.

o Can be found at www.ipums.org/cps/

• PSID Can be found at http://psidonline.isr.umich.edu/

• Survey of Income and Program Participation (SIPP)

o Four year rotating panel

o Large sample sizes

o Over samples poor

• Census/American Community Survey

o Can be found at www.ipums.org

Page 7: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Part B:Trends in Consumption Inequality (Part 1)

Page 8: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

8

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; Autor, Katz, Kearney, 2008)

• 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.).

Page 9: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

9

Kevin Murphy’s Web Page

Page 10: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

10

Kevin Murphy’s Web Page

Page 11: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

11

Autor, Katz, Kearney (2008)

Page 12: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Why Do We Care About Consumption Inequality?

• Why is it important?

o Learn about well being over time (economic growth, standard of livings, inequality, etc.).

o Learn about insurance mechanisms available to households (public insurance, private insurance, etc.)?

o Learn about the nature of income processes (more on this in the next set of lecture notes).

Page 13: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

A Classic: Attanasio and Davis (1996)

Page 14: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

A Classic: Attanasio and Davis (1996)

A Short Discussion: The innovation of the Attanasio and Davis technique.The creation of synthetic cohorts from cross sectional data.

Page 15: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Krueger and Perri (2006)

• What they do:

o Use data from the Consumer Expenditure Survey (CEX) to track the evolution of consumption inequality.

o CEX is includes a nationally representative sample of households.

- Designed to compute consumption weights for CPI

- Short panel dimension (4 quarters)

- Mostly used as repeated cross sections.

- Includes detailed spending measures on expenditures by categories.

o Use repeated cross sections to track consumption inequality.

Page 16: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Krueger and Perri (2006): What They Find

Page 17: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Krueger and Perri (2006): What They Find

Page 18: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Krueger and Perri (2006): What They Find

Page 19: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Krueger and Perri (2005): What They Conclude

• Conclusions

o Income inequality is much greater than consumption inequality

o If some of the increase in income inequality is idiosyncratic, households can self insure (or public sector can provide insurance) making consumption inequality respond less than income inequality.

o Write down a model where insurance is endogenously provided. Increasing idiosyncratic shocks to income can increase demand

for insurance (leading to more insurance). Consistent with their model, credit card access increased during this period.

o Bottom line: Use the consumption data to learn about the nature of income processes and insurance mechanisms.

Page 20: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Part C:A Caveat – Some Data Issues

Page 21: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

21

A Data Problem: Average Real Consumption in CEX

Page 22: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

22

A Data Problem: Average Real Consumption in CEX

Page 23: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

23

Percent Change in Consumption in CEX (from 1981)

Page 24: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

24

Trends in Real NIPA Aggregate Consumption

Page 25: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Part D:Revisiting Trends in Consumption Inequality Accounting for Measurement Error in Data

Page 26: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Can Measurement Error Alter Inequality Findings?

• Yes

• Depends on whether measurement error differs across the consumption (income) distribution.

• Suppose richer households have been underreporting their income to a greater extent in recent periods (relative to the past).

• The rich could be increasing their expenditure more (relative to other parts of the distribution). However, the systematic measurement error could also be increasing.

• How to test for group specific differences in measurement error?

Page 27: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Aguair and Bils (2011)

• Try to account for differential measurement error over different “income-demographic” groups to get a sense of changing consumption inequality.

• Some particulars:

Define xijt = average expenditure on good j, by group i, at time t

j goods = food at home, clothing, utilities, entertainment, etc.

i groups = cells based on income (5) and demographics (18)

Define Xit = average total expenditure for group i at time t.

Formally: 1

J

it ijtjX x

Page 28: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

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

Inferred2006

The Essence of the Exercise (From a Discussion by Jonathan Parker; NBER EFG 2011)

Inferred adjustment to ln X90

ln X10

Page 29: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Aguair and Bils (2011)

• Assume measurement error in expenditure……

• represents a good specific error (common across all groups)

• represents a group specific error (common across all goods)

*j i

t t ijtvijt ijtx x e

jtit

Page 30: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Aguair and Bils (2011): Some Intuition

• Difference-in-Difference Estimates (2 good case, 2 group case)

• Goods = e (entertainment) and f(food)

• Groups = high (rich) and low (poor)

(difference out good specific error)

(difference out good specific error)

*, ,

*, ,

high lowhigh e high e

low e low e

x xe

x x

*, ,

*, ,

high lowhigh f high f

low f low f

x xe

x x

Page 31: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Aguair and Bils (2011): Some Intuition

• Take differences across goods to eliminate group specific error

• Obtain an unbiased estimate of relative consumption inequality.

• Need to map into units of total expenditure. Want to recover:

* *, , , ,

* *, , , ,

ln ln ln ln (1)high e high f high e high f

low e low f low e low f

x x x x

x x x x

* *, ,ln lnhigh t low tX X

Page 32: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Aguair and Bils (2011): Some Intuition

* * * *

* *, , ,

* *, , ,

* *, , ,

* *, , ,

* * * *, , , , , , , ,

Define: ln ; ln

.....

.....

.....

.....

( ) ( ) (

ijt ijt it it

high e t e high t

low e t e low t

high f t f high t

low f t f low t

high e t low e t high f t low f t e f

x X

* *, ,)( )high t low t

Page 33: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Aguair and Bils (2011): Some Intuition

* * * * * *, , , , , , , , , ,

Using (1), we know that we can express:

( ) ( ) ( )( ) high e t low e t high f t low f t e f high t low t

* *, , , , , , , , , ,as: ( ) ( ) ( )( ) high e t low e t high f t low f t e f high t low t

Page 34: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Aguair and Bils (2011)

• Suppose for true expenditures, x* :

• Can estimate the following using actual data in some period 0 where systematic measurement error is less of an issue:

• If there is no measurement error in the data, can uncover:

• Assumes income elasticities are constant over time (and can be locally estimated). Assume measurement error is zero in period 0.

* * *ln lnijt jt j ijt j i ijtx X Z

0 0 0 0ln lnij j j i j i ijx X Z u

ˆj j

Page 35: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Aguair and Bils (2011): Some Intuition

Substituting in the estimated β’s, we get:

* * * * * *, , , , , , , , , ,

Using (1), we know that we can express:

( ) ( ) ( )( ) high e t low e t high f t low f t e f high t low t

* *, , , , , , , , , ,as: ( ) ( ) ( )( ) high e t low e t high f t low f t e f high t low t

* *, , , , , , , , , ,( ) ( ) ( )( ) high e t low e t high f t low f t e f high t low t

Page 36: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

36

Aguiar and Bils (2011) Findings

Page 37: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

37

Aguiar and Bils (2011) Findings

Page 38: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

38

Aguiar and Bils (2011) Findings

Relative Spending Differences Between High and Low Income Groups

Page 39: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

39

Aguiar and Bils (2011) Findings

Page 40: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

40

Aguiar and Bils (2011) Findings

Different Saving Rates From the CEX

Page 41: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Attanasio, Hurst, and Pistaferri (2012)

• Also show that measurement error likely results in the underestimation of changes in consumption inequality within the U.S.

• Like Aguiar and Bils, find that consumption inequality and income inequality have moved essentially one-for-one over the past thirty years.

• Use other empirical approaches and data sets.

• You can find a copy of the paper on my web page (under working papers).

Page 42: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Attanasio, Hurst, and Pistaferri (2012)

• Use CE Diary Data (a separate survey) as opposed to CE Interview Data (which wasused by Krueger/Perri and Aguiar/Bils.

• Diary data found to have less measurement error (better matches NIPA trends).

Page 43: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Attanasio, Hurst, and Pistaferri (2012)

• Imputed PSID Consumption matches income inequality nearly identically.• Food PSID Consumption also matches income inequality trends (need to scale by

food income elasticity which is about 0.5).

Page 44: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Conclusions: Part 1 (A – D)

• Measurement error is important in Consumer Expenditure Survey!

• Even though there is measurement error, can still measure consumption inequality.

• Without controlling for measurement error, looks like small increases in consumption inequality.

• Much of that is due to the rich reporting less and less of their expenditures.

• Controlling for the systematic recent underreporting of the rich increases the estimated consumption inequality in the U.S. to levels that match the changing income inequality.

Page 45: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Part E:Overview of Lifecycle Expenditures

Page 46: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Why Do We Care About Lifecycle Expenditure?

• Why is it important?

- Learn about household preferences broadly

C.E.S. vs. log vs. other / Habits? / Status?

- Estimate preference parameters

intertemporal elasticity of substitution/ risk aversion/ discount rate

- Learn about income process

permanent vs. transitory shocks / expected vs. unexpected

- Learn about financial markets/constraints

liquidity constraints / risk sharing arrangements

- Learn about policy responses

spending after tax rebates, fiscal multipliers, etc.

Page 47: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Why Do We Care (continued)?

• The big picture with consumption:

- Use estimated parameters to calibrate models

- Understand business cycle volatility

- Conduct policy experiments (social security reform, health care reform, tax reform, etc.)

- Estimate responsiveness to fiscal or monetary policy

- Broadly understand household behavior

Page 48: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

How We Will Proceed

• The outline of the next part of the lecture:

- Understand lifecycle consumption movements

o Illustrative of how one fact can spawn multiple theories.

o Show how a little more data can refine the theories

o Illustrate the empirical importance of the Beckerian consumption model (i.e, incorporating home production and leisure).

Page 49: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Fact 1: Lifecycle Expenditures

Plot: Adjusted for cohort and family size fixed effects

Page 50: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Define Non-Durable Consumption (70% of outlays)

• Use a measure of non-durable consumption + housing services

• Non-durable consumption includes:

Food (food away + food at home) Entertainment Services

Alcohol and Tobacco Utilities

Non-Durable Transportation Charitable Giving

Clothing and Personal Care Net Gambling Receipts

Domestic Services Airfare

• Housing services are computed as:

Actual Rent (for renters)

Imputed Rent (for home owners) – Impute rent two ways

• Exclude: Education (2%) , Health (6%), Non Housing Durables (16%), and Other (5%) <<where % is out of total household expenditures>>

Page 51: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Empirical Strategy: Lifecycle Profile of Expenditure

• Estimate:

(1)

where is real expenditure on category k by household i in year t.

Note: All expenditures deflated by corresponding product-level NIPA deflators.

Cohortit = year-of-birth (5 year range – i.e., 1926-1930)

Dt = Vector of normalized year dummies (See Hall (1968))

Family Composition Controls:

Household size dummies, Number of Children Dummies

Marital status dummies , Detailed Age of Children Dummies

kitC

0ln( )k kit age it c it t t fs it itC Age Cohort D Family

Page 52: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Fact 2: Hump Shaped Profile – By Education

From Attanasio and Weber (2009)

Page 53: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Fact 3: Retirement Consumption Dynamics

From Bernheim, Skinner and Weinberg (AER 2001)

Page 54: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

The Puzzle? (Friedman, Modigliani, Hall, etc.)

( )

1

1max ( , ) ( , )

1t

s tT

t t t s sC

s t

u C E u C

1 1 1(1 )( )t t t t tX r X C Y

t t tY PV

1t t tP g P N

{Nt, Vt} are permanent and transitory mean zero shocks to income with underlying variances equal to σ2

N and σ2V

Page 55: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Preferences

1

( , ) exp( ), 11

(1/ ) intertemporal elasticity of consumption

real interest rate

time discount rate

vector of taste shifters

tt t t

Cu C Θ

r

Page 56: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Euler Equation

*1 11 1

1 1

*

ln(1 ) ( )ln(1 )

ln ln

if (in all periods) or if they are constant and

if the forecast error of future consumption (embedded in ) is constant

then cons

t t tt t

t t t

rC

where C C C

r

umption growth only depends on changes in tastes ( )

or changes in the real interest rate.

Page 57: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

What Are Potential Taste Shifters Over Life Cycle

1. Family Size

o Makes some difference

o Hump shaped pattern still persists

o See Facts 1 and 3 (above) – these were estimated taking out detailed family size controls.

2. Other Taste Shifters (that change over the lifecycle – for a given individual)?

Page 58: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

58

Fact 4: 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 researchers about:

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

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

Page 59: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

59

Deaton and Paxson Methodology (U.S. Application)

• Variance of Residual Variation

• Compute variance of εkit at each age and cohort

• Regress variance of εkit on age and cohort dummies

• Plot age coefficients (deviation from 25 year olds)

Note: This is my application of the Deaton/Paxson Methodology (very similar in spirit to theirs).

0ln k k k k k kit age it cohort it t t fs it itC Age Cohort D Family

Page 60: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Fact 4: Deaton-Paxson Cross Sectional Dispersion: With and With Out Housing Services

Page 61: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Fact 4: Deaton-Paxson Cross Sectional Dispersion: With and With Out Housing Services

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

Page 62: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Fact 4: Deaton-Paxson Cross Sectional Dispersion: With and With Out Housing Services

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

Page 63: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Questions:

1. What Else Drives the Hump Shaped

Expenditure Profile?

2. Why Does Expenditures (on food)

Fall Sharply At Retirement?

3. Why Does Cross Sectional Consumption Inequality Increase Over the Lifecycle?

Page 64: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Explanations for Questions (1) and/or (2)

• Liquidity Constraints and Impatience - Gourinchas and Parker (2002)

• Myopia - Keynes (and others)

• Time Inconsistent Preferences (with liquidity constraints) - Angeletos et al (2001)

• Habits and Impatience

• Non-Separable Preferences Between Consumption and Leisure - Heckman (1974)

• Home Production/Work Related Expenses - Aguiar and Hurst (2005, 2008)

Page 65: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Part F:Gourinchas and Parker (2002)

Page 66: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Gourinchas and Parker (2002)

“Consumption Over the Lifecycle” (Econometrica)

You should read this paper.

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).

Page 67: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Gourinchas and Parker Structure

11 1

1

1

1

1

max ( , ) ( )

(1 )( )

( , ) ( )1

Nt N

t N Nt

t t t t

t t t

t t t t

E u C V W

W r W Y C

Cu C Z v

Y PV

P G P N

Impose some liquidity constraints on model: Wt > some exogenous level

Page 68: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Goal of Gourinchas-Parker: Estimate Utility Parameters

• Intertemporal elasticity of substitution (I.E.S.) (1/ρ)

• Risk Aversion (ρ)

• Time Discount Factor (β = 1/(1+ δ))

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

Page 69: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Why is the I.E.S. (1/ρ) 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

Page 70: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Graphical Illustration – No Substitution Effect

1 2 period

C

Low interest rate

High interest rate

ΔC2 = X

ΔC1 = X

With only an income effect – consumption growth rate will not respond to interestrate changes. Estimate of (1/ρ) = 0.

Page 71: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Graphical Illustration – With Substitution Effect

1 2 period

C

Low interest rate

High interest rate

ΔC2 > X

ΔC1 < X

As the substitution effect gets stronger, the growth rate of consumption increases more as interest rates increase. Estimate of (1/ρ) > 0.

Page 72: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

One Way to Estimate I.E.S.

1

0

11

1 1 1 1

( )1max

1 1

(1 ) 1

1ln ln(1 )

t jT tt j

tj

tt t

t

t t t t

CE

CE r

C

C r

Page 73: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Issues With Estimating I.E.S.

• 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 affect consumption).

• Hall (1988) “Intertemporal Substitution in Consumption” (JPE; 1/ρ = 0)

• Attanasio and Weber (1993) “Consumption Growth, the Interest Rate and Aggregation” (ReStud; 1/ρ = 0.60-0.75).

• Vissing-Jorgensen (2002) “Limited Asset Market Participation and the Elasticity of Intertemporal Substitution” (JPE; 1/ρ = 0.3 (stockholders) and 1/ρ = 0.8 (bondholder).

1 1 1 1

1ln ln(1 )t t t tC r

Page 74: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Gournichas-Parker Methodology: Calibration

Choose preference parameters that match the lifecycle profiles of consumption given the mean and variance of income process.

Use synthetic individuals (based on education and occupation)

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)

Page 75: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Intuition

No Uncertainty:

No “Buffer Stock Behavior” (uncertainty coupled with liquidity constraints)

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

Page 76: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

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.

Page 77: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Gourinchas-Parker Conclusions

• Optimizing model of household behavior with income risk can match the lifecycle profile of household consumption

• Liquidity constraints can explain early life patterns.

• Impatience explains the late lifecycle patterns.

• Households face significant labor earnings risk (holding assets early in lifecycle even though they are impatient).

Take Away: Households are sufficiently impatient

Households face non-trivial income risk (even in middle age).

Page 78: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Part G:

The Beckerian Model

of Consumption

Page 79: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Ghez and Becker (1975); Aguiar, Hurst and Karabarbounis (2011)

subject to:

( , , ) max U( ,..., ) ( ', ', 1)ti NV a t C C E V a t

( , ), i 1,...,

1

' (1 ) (1 )

0, ' .

i i i i

ii

i ii

C F H X N

H L

a r a wL T p X

L a a

Let μ, λ, θ, and κ be the respective multipliers on the time budget constraint, the money budget constraint, the positive hours constraint and the positive assets constraint.

Assume U(.) is additively separable across time and across goods.

ψ= is vector of wages, commodity prices (p), taxes and transfers

(assume C.E.S., CRS)

Page 80: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

First Order Conditions

'

: ,

: ,

:

' : ( ', ', 1) .

ii i

i i

ii

i i

ta

U FX p i

C X

U FH i

C H

L w

a E V a t

If θ = 0 (L > 0), price of time (in permanent income units) (μ/λ = w)

More generally (given L often = 0), μ/λ = ω

Page 81: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

First Order Conditions

Intra-period tradeoff between time and goods:

(if L > 0)i i

i i i i

wF FH X p p

(1)

Marginal rate of transformation between time and goods in production of n is equated to the relative price of time.

Page 82: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

First Order Conditions

A few assumptions:

o Fi is constant elasticity of substitutiono pi’s are constant over time

Some algebra

ln ln

ln

ln

i i ii

i i i

i

ii

X F Fd d

H H X

Xd H

d

(2)

(3)

Note: To get (3), sub (2) into (1)

Page 83: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Static First Order Condition

The static F.O.C. pins down expenditure relative to time inputs.

If we know σ and the change in the opportunity cost of time, we should be able to pin down the relative movement in expenditures relative to time.

%ΔXi -%ΔHi =σi %Δω

Notice, this equation does not require us to make any assumptions about borrowing or lending, perfect foresight, etc.

Page 84: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

More Intuition (Assume separability in cn’s)

Differentiate FOC for xn with respect to ω holding λ constant. Get:

2 20

ln ;

ln ( )Hi ii i i i

d i i

d X U Cs

d C U C

ii

H ii

i

FH

Hs

C

This is just Ghez and Becker (1975)

Need to compare the intra-elasticity of substitution between time and goods (σ) to the elasticity of substitution in utility across consumption goods (γ).

Note: Complicates mapping of expenditures into permanent income in general and the estimation of Engel curves in particular.

Page 85: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Different Than Standard Predictions

Differentiate FOC for xn with respect to ω holding λ constant. Get:

Spending should fall the most (with declines in the marginal value of wealth) for goods that have high elasticities of substitution (high income elasticities).

0

ln

ln

n

i

d

d c

d

Page 86: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Implications• For given resources (λ):

– As the price of time increases, consumers substitute market goods for time (Xi increases) – depends on σi

– As the price of time increases, consumers substitute to goods (periods) in which consumption is “cheaper” (Xi falls) – depends on γi

• What goods have high/low σ:

- High σ: goods for which home production is an available margin of substitution (e.g., food)

- Low σ: goods for which time and spending are complements (e.g., entertainment goods)

• What goods have high/low γ:

- High γ: goods which have a high income elasticity (luxuries)

- Low γ: goods which have a low income elasticity (necessities)

Page 87: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Predictions: Lifecycle Movements

Gourinchas and Parker model (and most other models)

o Luxuries (entertainment) should decline more late in life relative to necessities (food)

o No importance of changing opportunity cost of time over lifecycle

Beckerian Model

o Goods for which home production is important can move over the lifecycle in ways that are different than goods for which

expenditure and time are complements.

o If opportunity cost of time declines after middle age, food may decline more than entertainment later in life.

Page 88: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Part H:

Tests for Beckerian Model of Consumption

Page 89: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Test 1: Aguiar and Hurst “Consumption vs. Expenditure” (JPE 2005)

Page 90: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

90

Question

• What causes the decline in spending for households at the time of retirement?

• Bernheim, Skinner, and Weinberg (AER 2001) “What Accounts for the Variation in Retirement Wealth Among U.S. Households”

o People do not plan for retirement (myopic)

• Banks, Blundell, and Tanner (AER 1998) “Is There a Retirement Savings Puzzle”

o People get bad news (on average) at retirement (shock to λ)

• Hundreds of other papers documenting similar patterns for different countries.

• Do not think about the cost of time changing with retirement.

Page 91: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Fact 3: Retirement Consumption Dynamics

From Bernheim, Skinner and Weinberg (AER 2001)

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92

Our Approach: Measuring Consumption Directly

• Main Data Set: Continuing Survey of Food Intake of Individuals (CSFII)

– Conducted by Department of Agriculture– Cross Sectional / Household Level Survey– Two recent waves: Wave 1 (1989 -1991) ; Wave 2 (1994-1996)– Nationally Representative– Multi Day Interview– All individuals within the household are interviewed (C at individual level)– Tracks final food intake (not intermediate goods --- think about a cake)

• Detailed food expenditure, demographic, earnings, employment, and health measures

• Large sample sizes:

– 6,700 households in CSFII-91– 8,100 households in CSFII-96

• Focus on intake NOT expenditure!

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93

Actual Consumption Data (CSFII)

• The key to the data:

24 hour food intake diaries (asked for all days in the survey)

• Diaries are detailed:

– Amount of food item consumed (detailed 8 digit food codes)– Brand of food item (often unusable by researchers)– Cooking method– Condiments added

• Dept of Agriculture converts the total day’s food intake into several nutritional measures (calories, protein, saturated fat, total fat, vitamin C, riboflavin, etc.).

– The conversion is made using all food diary data (i.e., brand, whether cooked with butter).

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94

8 digit food codes: Cheese• Example 18 of the 100 8-digit codes for cheese.

14101010 CHEESE, BLUE OR ROQUEFORT

14102010 CHEESE, BRICK

14102110 CHEESE, BRICK, W/ SALAMI

14103020 CHEESE, BRIE

14104010 CHEESE, NATURAL, CHEDDAR OR AMERICAN TYPE

14104020 CHEESE, CHEDDAR OR AMERICAN TYPE, DRY, GRATED

14104200 CHEESE, COLBY

14104250 CHEESE, COLBY JACK

14105010 CHEESE, GOUDA OR EDAM

14105200 CHEESE, GRUYERE

14106010 CHEESE, LIMBURGER

14106200 CHEESE, MONTEREY

14106500 CHEESE, MONTEREY, LOWFAT

14107010 CHEESE, MOZZARELLA, NFS (INCLUDE PIZZA CHEESE)

14107020 CHEESE, MOZZARELLA, WHOLE MILK

14107030 CHEESE, MOZZARELLA, PART SKIM (INCL ""LOWFAT"")

14107040 CHEESE, MOZZARELLA, LOW SODIUM

14107060 CHEESE, MOZZARELLA, NONFAT OR FAT FREE

Page 95: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

95

Changes in “Spending” At Retirement

Run: ln(xi) = γ0 + γ1 Retiredi + γ2 Zi + errori

• Retiredi is a dummy variable equal to 1 if the household head is retired.

• Instrument Retiredi status with age dummies (potential endogeneity)

• Z includes: race, sex, health, region, time, family structure controls

• Sample: Relatively “young” older households: Heads aged 57-71

• Total food expenditure (x) falls by 17% for retired households (γ1), p-value < 0.01

• Other results:

– Food expenditure at home falls by 15%

– Food expenditure away from home falls by 31%

Page 96: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

96

Changes in “Consumption” at Retirement

• How do we turn these food diaries into meaningful measures of consumption?

• Our approach:

1. Examine Nutritional Quality of Diet (vitamins, cholesterol, fat, calories, etc.)

2. Examine individual goods with strong income elasticities (hotdogs, fruit, yogurt, shellfish, wine)

3. Luxury/Quality goods (e.g. brands vs generics, lean vs. fatty meat)

4. Use structural model to aggregate food consumption data and perform formal PIH test.

Page 97: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

97

Nutritional Measures• Regress: ln(ci) = α0 + α1 ln(yperm) + demographics <<sample: heads 25-55>>

• Regress: ln(ci) = β0 + β1 Retired + demographics <<sample: heads 57-71>>

Consumption Measure (in logs) Estimated Elasticity (α1) Retirement Effect (β1)

Calories -4% (2%) -2% (4%)

Protein * -1% (1%) -3% (2%)

Vitamin A * 44% (5%) 36% (9%)

Vitamin C * 34% (5%) 33% (9%)

Vitamin E * 18% (3%) 11% (4%)

Calcium * 10% (2%) 13% (4%)

Cholesterol * - 26% (3%) -9% (5%)

Saturated Fat * - 9% (2%) -7% (3%)

• * Includes log calories as an additional control ; Include supplements as an additional control.

• Instrument for retirement status with age; Examined non-linear specifications (not reported)

• No evidence of any deterioration in diet quality

Page 98: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

98

Some Specific Consumption Measures• Regress: ci = α0 + α1 ln(yperm) + demographics <<sample: heads 25-55>>

• Regress: ci = β0 + β1 Retired + demographics <<sample: heads 57-71>>

Consumption Measure (Dummy) Estimated Semi-Elasticity Retirement Effect

Eat Fruit 0.25 (0.03) <<59%> 0.14 (0.04)

Eat Yogurt 0.14 (0.02) <<8%>> 0.01 (0.03)

Eat Shellfish 0.05 (0.01) <<6%>> -0.02 (0.02)

Drink Wine 0.15 (0.02) <<8%>> -0.03 (0.03)

Eat Oat/Rye/Multigrain Bread 0.10 (0.02) <<9%>> 0.06 (0.04)

Eat Hotdog/Sausage -0.16 (0.03) <<51%>> -0.06 (0.05)

Eat Ground beef -0.10 (0.03) <<22%>> -0.01 (0.04)

• Sample means in << >>

• Instrument for retirement status with age

• Drawback: Tastes could differ across income types

• Drawback: Categories are broad and do not allow for differences in quality

Page 99: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

99

Luxury Goods/Quality: My Favorite….

• Examine some dimensions of quality:

– Eating at restaurants with Table Service

– Eating Branded vs. Generic Goods

– Eating Lean vs. Fattier Cuts of Meat

• Restaurants, Brands, and Eating Lean Meat have very STRONG income elasticities in the cross section of working households.

• If households are unprepared for retirement, we should see them switching away from such consumption goods.

• No evidence of that in the data.

Page 100: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

100

,0 1 1, ,ln( ) .... ln( )perm i i i i i

t J J t X t t ty c c X

• Where

c1, ….. cJ are quantities of individual consumption categories consumed

X is monthly expenditure on food

θ is a vector of demographic and health controls (including education, sex,

race, family composition, ect.)

yperm is the household’s predicted permanent income

• Estimated on a sample of 40 – 55 year old household heads where the head is

working full time.

Creating a Food Intake Aggregate

Page 101: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

101

• Permanent income is our numeraire – one unit increase in our consumption index maps into a one percent increase in permanent income.

– What are we doing: We project permanent income of household i onto household i’s consumption (controlling for taste shifters).

• Basically, in a statistical sense, if you tell me what you eat, I can predict your permanent income. Our consumption index is in permanent income dollars!

• We also did this for households aged 25-55 who are working fulltime (results did not change).

• We want to ask if households act like their permanent income has changed once they become retired.

Thought Experiment

Page 102: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

102

Is Our Permanent Income Measure Predictive?

• Projection of income on consumption and expenditure patterns

• How well does consumption forecast income?

– Split sample into odd and even years (again focusing only on prime age household heads working full time).

– Focus only on odd years of our sample (in sample):

• In sample R-square 0.53

• Food consumption on its own explain 21% of variation in income

• Incremental R-square is 0.12

– Focus on even years (test out of sample):

• Out of sample R-square: 0.42

• Food consumption and expenditure a fairly good predictor of income

Page 103: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

103

Page 104: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

104

A Note on the Unemployed

• Unemployed, on average, should experience some decline in expenditure.

• Labor studies find that the unemployed (from exogenous plant closings) have earnings that are 5-10 percent lower during the subsequent decade.

• Can our methodology detect a decline in expenditures for the unemployed?

• Our study is imperfect – we only have cross sectional data.

• Using the panel dimension of the PSID, the unemployed experience a reduction in expenditures of about 8 percent (Stephens, 2002). We find a decline of about 15 percent (in expenditures) using our data.

• In terms of actual consumption intake, we find the unemployed reduce their intake by about 6 percent.

Page 105: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

105

Conclusions

• No “Retirement Consumption Puzzle”

• Technically, preferences between “consumption” and leisure are not substitutes.

– Leisure goes up dramatically in retirement (we will show this in a few weeks).

– Food consumption (as measured by intake) remains roughly constant (if anything it increases slightly).

• However, “expenditures” and leisure could still be non-separable.

– Non-separability enters through “home production”

Page 106: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Test 2: Aguiar and Hurst (2009)“Deconstructing Life Cycle Expenditure”

Page 107: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Question

• What about the lifecycle patterns of consumption more broadly?

o Can a Beckerian model explain the declining expenditures post middle age with relying on either:

- really impatient consumers?

- myopia (or time inconsistent preferences)?

• Use the disaggregated consumption data by category?

• Estimate a model on the disaggregated data.

- estimate time preference rate

- estimate the amount of risk households face

Page 108: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Entertainment Spending

Page 109: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

All Non Decreasing Categories

-0.50

0.00

0.50

1.00

1.50

2.00

2.50

3.00

25 30 35 40 45 50 55 60 65 70 75

Log

Dev

iati

on fr

om A

ge 2

5

Entertainment Utilities Housing Services Other ND Domestic Svcs

Page 110: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Decreasing Categories

-1.20

-1.00

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

25 30 35 40 45 50 55 60 65 70 75

Log

Dev

iati

on f

rom

Age

25

Age

Clothing Transportation Food at Home Food Away

Page 111: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Summary (in Log Differences)

Consumption Category Share

Log Change Between

25 and 44

Log Change Between

45 and 59

Log Change Between 60 and 68

Decreasing Categories Food at Home 0.17 0.24 -0.07 -0.04 Transportation 0.13 0.25 -0.20 -0.17 Clothing/Personal Care 0.08 0.04 -0.36 -0.20 Food Away from Home 0.06 0.13 -0.55 -0.29 Alcohol and Tobacco 0.03 -1.35 -1.69 -1.22

Non-Decreasing Categories Housing Services 0.33 0.73 0.23 0.14 Utilities 0.11 0.72 0.28 0.11 Entertainment 0.04 0.80 0.07 0.17 Other Non-Durable 0.03 1.44 0.16 0.17 Domestic Services 0.02 1.52 0.30 0.32

Page 112: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

112

What About Deaton-Paxson Fact?

• 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 incomeo Insurance mechanisms available to households

Page 113: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Dispersion of Propensity to Work Over Life Cycle

Page 114: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Cross Sectional Dispersion Over Lifecycle

Page 115: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Cross Sectional Dispersion Over Lifecycle

Page 116: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Cross Sectional Dispersion Over Lifecycle: Figure 6b

Core

Page 117: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Cross Sectional Dispersion Over Lifecycle: Figure 6b

Core

Page 118: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Food, Transportation and Clothing

• Food is amenable to “Beckerian” home production (see Aguiar and Hurst 2005, 2007)

No evidence of any decline in food intake over the lifecycle despite declining food expenditures.

As opportunity cost of time declines later in life, households substitute towards home production of food (including more intense shopping for bargains).

Data (and calibrated model) actual show food intake increases over the back half of the lifecycle

Page 119: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Work Related Expenses

• Transportation, Clothing and Food Away From Home are work related expenses:

Lazear and Michael (1980) – Net out work related expenses (clothing and transportation) when making welfare calculations across people

Banks et al (1998) and Battistin et al (2008) when measuring consumption changes of retirees

Nelson (1989) and DeWeese and Norton (1991) comprising models of “clothing demand”

Page 120: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Level of Work Hours Over the Lifecycle

Page 121: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

New Facts About Food, Clothing, and Transport

• Look at food away patterns at different types of establishments

• Look at changes in different amounts of transportation patterns using time use data

• Estimate “simple” demand systems and control directly for work status

Page 122: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Propensity To Eat Away At Home

Page 123: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Propensity To Eat Away At Home

Page 124: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Propensity To Eat Away At Home

Page 125: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Travel Times and Employment Status

Page 126: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Travel Times and Employment Status

Page 127: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Travel Times and Employment Status

Page 128: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Control Directly For Work Status

• Estimate a demand system

• Control for labor supply (conditional on total expenditures)

• Estimate:

1) what consumption categories where spending is positively associated with market work

2) to what extent is the decline in spending on clothing, transportation and food away from home attributable to employment status.

Page 129: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Estimate Simple Demand System

Xit is total nondurable expenditures (less alcohol and tobacco, plus housing) for household i in year t.

sitk is the share of expenditures in consumption category k out of Xit

Ptk is the price index for consumption category k in year t

Lit is a vector of work status controls for household i in year t.

Note: Instrument lnXit with household total income and education controls

0 ln ln

ln ,

k k kit age it c it t t fs it p t p t

k

kX it L it it

s Age Cohort D Family P P

X L

Page 130: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

1. Simple Demand System Results

• Restrict sample to married households between age 25 and 50

• Use two work status controls: Husband working? Wife working?

Page 131: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Simple Demand System Results

• Restrict sample to married households between age 25 and 50

• Use two work status controls: Husband working? Wife working?

Consumption Category Husband Work? Wife Work?

Transportation (0.13) 0.014 (0.002) 0.014 (0.002)

Clothing/P. Care (0.08) 0.003 (0.001) 0.001 (0.001)

Food Away From Home (0.06) 0.008 (0.001) 0.005 (0.001)

Page 132: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Simple Demand System Results

• Restrict sample to married households between age 25 and 50

• Use two work status controls: Husband working? Wife working?

Consumption Category Husband Work? Wife Work?

Transportation (0.13) 0.014 (0.002) 0.014 (0.002)

Clothing/P. Care (0.08) 0.003 (0.001) 0.001 (0.001)

Food Away From Home (0.06) 0.008 (0.001) 0.005 (0.001)

Housing Services (0.34) -0.009 (0.003) -0.012 (0.002)

Utilities (0.12) -0.005 (0.001) -0.003 (0.001)

Food At Home (0.18) -0.016 (0.002) -0.013 (0.001)

Entertainment (0.04) 0.000 (0.001) 0.000 (0.001)

Page 133: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

2. Adding Work Controls To the Lifecycle Profile

• Married Sample, 25 – 75

• Work Status Controls:7 Dummies for Husband Weeks Worked7 Dummies for Wife Weeks Worked9 Dummies for Hours per week Husband Worked9 Dummies for Hours per week Wife Worked

• Three Categories:Food (food at home and food away)Work Related Expenses (transportation and clothing)Core Non Durables (everything else)

• Ask: “How do work status controls effect lifecycle profiles?”

Page 134: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Demand Estimates, Transportation

-0.045-0.040-0.035-0.030-0.025-0.020-0.015-0.010-0.0050.0000.0050.010

25 30 35 40 45 50 55 60 65 70 75

Sh

are

of E

xpen

dit

ure

:

Dif

fere

nce

fro

m A

ge 2

5

Age

Page 135: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Demand Estimates, Food Away

-0.020

-0.015

-0.010

-0.005

0.000

0.005

25 30 35 40 45 50 55 60 65 70 75

Sh

are

of E

xpen

dit

ure

:

Dif

fere

nce

fro

m A

ge 2

5

Age

Page 136: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Demand Estimates, Clothing

-0.040-0.035-0.030-0.025-0.020-0.015-0.010-0.0050.0000.005

25 30 35 40 45 50 55 60 65 70 75

Shar

e of

Exp

endi

ture

: D

iffe

renc

e fr

om A

ge 2

5

Age

Page 137: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Level of Lifecycle Expenditure

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

25 30 35 40 45 50 55 60 65 70 75

Log

Dev

iati

on f

rom

Age

25

Work Related Core Nondurables Food at Home

Page 138: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Level of Lifecycle Expenditure (Older Version)

Page 139: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

What Does it Mean?

• 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 productionone good (transport, clothes) are complements to market workthere is a time budget constraint

Assumptions:

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

• Other from the disaggregated consumption data (and home production functions), very similar procedure to Gourinchas and Parker.

Page 140: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Model: Household

Income Risk While Working:

Retirement/Disability Shock (Rt)

Conditional on Rt = 0, there is an age dependent hazard that next period Rt+1 = 1.

Page 141: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Model: Household

• Close the model with a standard representative competitive firm.

• Calibrate the model to match: average labor supply of prime age workers, lifecycle profile of spending on “core” and “home-production”/ “work-related” goods, the variance of spending on those goods and the coviariance.

Page 142: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Findings

• Households face much less risk than estimated by Gourinchas and Parker

o Cross sectional variation in core consumption is much less than cross sectional variance in total.

o Find that permanent variance of income risk is 35% lower (0.047 vs. 0.073).

Page 143: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Findings: Lifecycle Profiles

Page 144: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Findings: Lifecycle Profiles

Page 145: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Findings: Lifecycle Profiles

Page 146: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Home Production vs. Non-Separable Preferences

A Question:

• Does one need to model the home production sector formally?

• There is always a mapping between home production (non-separability between X and N through home production technology) and preferences (non-separability between X and N through preferences).

o X = expenditureso N = labor

• However, to match the data, may need to have preference parameters change over time (or states).

• We will talk more about this in Topic 4.

Page 147: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Heckman (1974): Non-Separable Consumption and Leisure

( )

,1

1 1

*1 0 1 1 2 1 1

1max ( , ) ( , )

1

1( , ) ( (1 ) )

1

ln(1 ) (1 )

t t

s tT

t t t s sC N

s t

t t t t

t t t t

u C N E u C N

u C N C N

C r N

Page 148: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

Big Picture Wrap Up: 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).

Page 149: Micro Data For Macro Models Topic 2: Consumption Inequality and Lifecycle Consumption

A Short Summary

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.

Show a situation (with labor supply) where it may be useful to separate the home production sector separately from preferences.