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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?

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micro data for macro models

Micro Data For Macro Models

Topic 2:

Lifecycle Consumption

why do we care about lifecycle expenditure

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

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

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
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
Empirical Strategy: Lifecycle Profile of Expenditure
  • Estimate:


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

fact 2 hump shaped profile by education

Fact 2: Hump Shaped Profile – By Education

From Attanasio and Weber (2009)

fact 3 retirement consumption dynamics

Fact 3: Retirement Consumption Dynamics

From Bernheim, Skinner and Weinberg (AER 2001)

the puzzle friedman modigliani hall etc

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

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

variances equal to σ2N and σ2V

what are potential taste shifters over life cycle

What Are Potential Taste Shifters Over Life Cycle

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)?

fact 4 deaton and paxson 1994

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 income

o Insurance mechanisms available to households.

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

deaton and paxson methodology u s application

Deaton and Paxson Methodology (U.S. Application)

Variance of Residual Variation

Compute variance of εkitat each age and cohort

Regress variance of εkiton 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).

fact 4 deaton paxson cross sectional dispersion with and with out housing services1
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 services2
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



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

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)

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

Gourinchas and Parker Structure

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

goal of gourinchas parker estimate utility parameters

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 important

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.


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


High interest rate

Graphical Illustration – No Substitution Effect

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


High interest rate

Graphical Illustration – With Substitution Effect

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

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).

gournichas parker methodology calibration

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)



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



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)


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

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
Part C:

The Beckerian Model

of Consumption

ghez and becker 1975 aguiar hurst and karabarbounis 2011
Ghez and Becker (1975); Aguiar, Hurst and Karabarbounis (2011)

subject to:

(assume C.E.S., CRS)

Let μ, λ, θ, andκbe 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

first order conditions
First Order Conditions

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 conditions1
First Order Conditions

Intra-period tradeoff between time and goods:


Marginal rate of transformation between time and goods in

production of n is equated to the relative price of time.

first order conditions2
First Order Conditions

A few assumptions:

o Fi is constant elasticity of substitution

o pi’s are constant over time

Some algebra



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

static first order condition
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 c n s
More Intuition (Assume separability in cn’s)

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

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
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).

  • For given resources (λ):
    • As the price of time increases, consumers substitute market goods for time (Xiincreases) – 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
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
Part D:

Tests for Beckerian Model of Consumption



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 dynamics1

Fact 3: Retirement Consumption Dynamics

From Bernheim, Skinner and Weinberg (AER 2001)

our approach measuring consumption directly

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!

actual consumption data csfii

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).

8 digit food codes cheese

8 digit food codes: Cheese

Example 18 of the 100 8-digit codes for cheese.


14102010 CHEESE, BRICK


14103020 CHEESE, BRIE



14104200 CHEESE, COLBY












changes in spending at retirement

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%

changes in consumption at retirement

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.

nutritional measures

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

some specific consumption measures

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-ElasticityRetirement 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

luxury goods quality my favorite

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.


Creating a Food Intake Aggregate

  • Where
  • c1, ….. cJare 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.

Thought Experiment

  • 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.
is our permanent income measure predictive
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
a note on the unemployed
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.
  • 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”
  • 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

what about deaton paxson fact

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 income

o Insurance mechanisms available to households

food transportation and clothing
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
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”

new facts about food clothing and transport
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
control directly for work 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
Estimate Simple Demand System

Xitis 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

1 simple demand system results
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
Simple Demand System Results
  • Restrict sample to married households between age 25 and 50
  • Use two work status controls: Husband working? Wife working?

Consumption CategoryHusband 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 results1
Simple Demand System Results
  • Restrict sample to married households between age 25 and 50
  • Use two work status controls: Husband working? Wife working?

Consumption CategoryHusband 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
2. Adding Work Controls To the Lifecycle Profile
  • Married Sample, 25 – 75
  • Work Status Controls:

7 Dummies for Husband Weeks Worked

7 Dummies for Wife Weeks Worked

9 Dummies for Hours per week Husband Worked

9 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?”
what does it mean
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 production

one good (transport, clothes) are complements to market work

there is a time budget constraint


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.

  • Other from the disaggregated consumption data (and home production functions), very similar procedure to Gourinchas and Parker.
model household
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 household1
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.
home production vs non separable preferences
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 = expenditures

o 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.
big picture wrap up non separabilities

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))


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

a short summary

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.