Micro Data For Macro Models

Topic 2:

Lifecycle Consumption

Part A:Overview of Lifecycle Expenditures

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.

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

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).

Fact 1: Lifecycle Expenditures

Plot: Adjusted for cohort and family size fixed effects

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>>

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

Fact 2: Hump Shaped Profile – By Education

From Attanasio and Weber (2009)

Fact 3: Retirement Consumption Dynamics

From Bernheim, Skinner and Weinberg (AER 2001)

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

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

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.

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)?

15

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

16

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

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

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

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

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?

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)

Part B:Gourinchas and Parker (2002)

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).

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

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

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

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.

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.

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

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

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)

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

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.

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).

Part C:

The Beckerian Model

of 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)

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

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.

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)

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.

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.

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

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)

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.

Part D:

Tests for Beckerian Model of Consumption

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

47

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.

Fact 3: Retirement Consumption Dynamics

From Bernheim, Skinner and Weinberg (AER 2001)

49

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!

50

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).

51

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

52

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%

53

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.

54

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

55

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

56

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.

57

,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

58

• 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

59

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

60

61

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.

62

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”

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

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

Entertainment Spending

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

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

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

69

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

Dispersion of Propensity to Work Over Life Cycle

Cross Sectional Dispersion Over Lifecycle

Cross Sectional Dispersion Over Lifecycle

Cross Sectional Dispersion Over Lifecycle: Figure 6b

Core

Cross Sectional Dispersion Over Lifecycle: Figure 6b

Core

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

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”

Level of Work Hours Over the Lifecycle

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

Propensity To Eat Away At Home

Propensity To Eat Away At Home

Propensity To Eat Away At Home

Travel Times and Employment Status

Travel Times and Employment Status

Travel Times and Employment Status

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.

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

1. Simple Demand System Results

• Restrict sample to married households between age 25 and 50

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

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)

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)

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?”

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

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

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

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

Level of Lifecycle Expenditure (Older Version)

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.

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.

Model: Household

• Close the model with a standard representative competitive firm.

• Calibrate the model to match: real interest rate of 4%, aggregate wealth to income ratio of 3.1, average labor supply of prime age workers (of 1/3 time endowment), lifecycle profile of spending on “core” and “home-production”/ “work-related” goods the variance of spending on those goods and the co-variance between the two goods.

Findings

Findings: Lifecycle Profiles

Findings: Lifecycle Profiles

Findings: Lifecycle Profiles

Findings: Lifecycle Profiles

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.

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

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).

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.