Micro Data For Macro Models

Micro Data For Macro Models

Topic 3: More Home Production

2

What More Do I Want To Do

• We already looked at the importance of home production in explaining lifecycle patterns of consumption

• What else do I want us to think about?

1) How do we estimate the parameters of the home production function?

2) What are the long run trends in home production (and time use more generally)?

3) Is home production an important margin of substitution at business cycle frequencies?

Part A:

Estimating Parameters of Home Production Function:

Using Micro Data

4

Micro Estimates of Home Production Elasticities

• Hard to do….

• Need data on both home production inputs and consumption.

• Consistently measured home production data is difficulty to find.

• Often missing measures of the opportunity cost of time for people who do a lot of the home production (those out of labor force, the retired, etc.).

• See Rogerson, Rupert and Wright (1995 Economic Theory) “Estimating Substitution Elasticities in Household Production Models”

• Use PSID data.

• Estimate the elasticity of substitution between time and goods in home production to be about 1.8 for single women, about 1.0 for single men, and about 1.5 for married households.

Aguiar and Hurst (AER 2008)

Lifecycle Prices and Production

6

Available Margins of Substitution: Shopping and Home Production

• Expenditure is price (p) * quantity (q)

• Shopping is time intensive but it may affect prices paid (holding quantities constant)

• Given that time is an input into shopping, the opportunity cost of one’s time should determine how much an individual shops.

– Those whose time is less valuable should shop more and, all else equal, pay lower prices (holding quantities constant)

• Both shopping and home production should respond to changes in the opportunity cost of time.

7

What We Do in This Paper

• Use new scanner data (on household grocery packaged goods) to document:

– Prices paid differs across individuals for the same good

– Price paid varies with proxies for cost of time.

• Use this micro data to actually estimate household shopping functions which relate prices paid to shopping intensity.

– This shopping function will give us the implied opportunity cost of time for the shopper

• Given margin conditions, we can use the shopping function and time use data on home production to estimate the home production technology.

• Show empirically that the ratio of consumption to expenditure varies over the lifecycle.

8

Scanner Data on Prices

• Note: In this data part of the paper, we will only be talking directly about food consumptions and expenditures (in model, we will extend the implications)

• Data is from AC Nielson HomeScan

– Panel of households

– Random sample within the MSA of households

• The survey is designed to be representative of the Denver metropolitan statistical area and summary demographics line up well with the 1994 PSID

– Coverage at several types of retail outlets

9

Scanner Data (continued)

• Each household is equipped with an electronic home scanning unit

• Each household member records every UPC-coded food purchase they make by scanning in the UPC code

• After each shopping trip, household records:

– What was purchased (i.e. scan in UPC code)

– Where purchase was made (specifically)

– Date of purchase

– Discounts/coupons (entered manually)

• AC Nielson collects the price data from all local shopping outlets.

• Data has decent demographics (income categories, household composition, employment status, sex, race, age of members, etc.). Collected annually.

10

• We have access to the Denver data for the years 1993-1995.

– Short panel

• Sample:

– 2,100 households (focus on age of shopper between 24 and 75)

– 950,000 transactions

– 40,000 household/month observations.

Sample

11

• Derive a price index using the scanner data

• Show some unconditional means of how this price index varies across differing income and demographic groups

• Think about measurement issues relating to our estimate of the price index

• Goal is to get estimate shopping and home production functions that I could import into our model

How We Use the Data

12

Potential Measurement Issue 1: Underreporting

• Average monthly expenditure in the data set: $176/month (1993 dollars)

• Average total food “at home” in the PSID for similarly defined sample (1993 dollars) is $320 (55% coverage rate in the HomeScan Data)

• Differences between the coverage due to:

– Omission of certain grocery expenditures due to lack of UPC code (some meat, diary, fresh fruit and vegetables).

– Omission of expenditures due to household self-scanning.

• Explore underreporting by different age/education/year cells (forming a ratio by comparing homescan data to PSID). The gap does not vary with age – however, it does vary with education levels (only 42% of expenditures for high educated vs 55% for low educated).

• Underreporting not a problem for our analysis if random.

13

Potential Measurement Issue 2: Attrition

• Cannot observe on the extensive margin (homescan only releases data for households who participated consistently over the sample)

• Can observe attrition on intensive margin

– Compare average expenditures in Homescan between 1993, 1994, and 1995

– first quarter of 1994 had 1% less expenditures than first quarter of 1993

– first quarter of 1995 had 5% less expenditures than first quarter of 1993

• No difference in expenditure declines by age or education

• For completeness, we redid our whole analysis only including 1993 – no differences found

14

Potential Measurement Issue 3: Store Effects

• Price of a good may be associated with better (unmeasured) services

– 83.6% of purchases made at grocery stores

– 4.1% at discount stores

– 3.1% at price clubs

– 1.7% at convenient stores

– 1.5% at drug stores

– remainder from vending machines, liquor stores, gas stations, pet stores, etc.

– Of the grocery stores, essentially all came from Albertsons, King Sooper, Safeway or Cubs Food

• For robustness, we computed everything with store chain fixed effects (identify off of price differences at a given chain during a given period of time)

15

Aggregation over Prices

• We want a summary of the price a household pays

– Relate to cost of time

• Households buy many goods and basket varies over time

– Look at one popular good (milk)

– Define an index that answers: For its particular basket of goods, does this household pay more or less than other households?

16

Definition: Price Index

Household j, good i, month m, day t

• Expenditure for household j

• Average price for good i

• Average quantity of good i

• “Real” basket of goods (at average price)

17

Price Index

18

Notes on Price Index

• Controls for quality. Same UPC code.

– Low price does not mean low quality

– Does not reflect “bulk” purchases (those are a different UPC code)

• “Brand Switching” may occur

– robust to inclusion of control for brand switching.

• Like a traditional price index – hold quantities constant and vary prices.

• Unlike a traditional price index – not prices over time, but prices in the same market at the same time.

19

Simple “Hypothesis Tests”

• Households with high value of time will pay higher prices than households with low value of time. We would expect (all else equal – particularly amounts):

– Higher income households to pay higher prices than lower income households

– Households with larger families/children to pay higher prices than households with smaller families or no children

– Middle aged households (with high wages and lots of child commitments) to pay higher prices than both younger and older households. <<Lifecycle prediction>>

• Predictions consistent with data

20

Price and Income (Table 1)

0.95

0.96

0.97

0.98

0.99

1.00

1.01

1.02

1.03

1.04

Less than $30,000 $30,000 to $50,000 $50,000 to $70,000 Greater than $70,000

Pri

ce I

ndex

p-value of difference < 0.01

p-value of difference < 0.01

21

Price and Household Size (Table 1)

0.94

0.96

0.98

1.00

1.02

1.04

1.06

1 2 3 4 >4

Hosuehold Size

Pri

ce I

ndex

22

Price and Household Composition (Table 1)

0.94

0.96

0.98

1.00

1.02

1.04

1.06

Married withchildren

Unmarried femalewith children

Unmarried malewith children

Married w/ochildren

Unmarried femalew/o children

Unmarried malew/o children

Pri

ce I

ndex

27

Cost Minimization on Part of Household

subject to

Q = market expendituresh = home production time

s = shopping timeN = some measure of size of shopping basket

28

First Order Condition From Cost Minimization

Need to estimate shopping function: p(s,N)

Use Homescan data to estimate above equation

31

Figure A1: Wage Rates Over the Life Cycle, Married Males

0.000

5.000

10.000

15.000

20.000

25.000

Age

Wag

e

Conditional/Fixed Effect

Unconditional

Conditional

Note: PSID data

32

Estimation of Home Production Function

• Cost minimization: MRT between time and goods in shopping = MRT between time and goods in home production

• Independent of preferences and dynamic considerations.

• Caveat = assuming that the shopper is the home producer

• Note: We are allowing shopping functions to differ from home production functions

33

{ , , }

( , )

. . ( , )

mins Q h

p s Q Q s h

s t f h Q C

C

C

pQ

sp f

Q pQ Q

f

h

•First-order conditions:

f pQ

h sf p

Q pQ Q

34

• Home Production Function– Functional Form:

• MRT condition:

( , ) h Qf h Q h Q

ln / ln lnh

Q

p ph Q Q p

s Q

• σ= 1/(1-ρ) = elasticity of substitution between time and goodsin home production

35

• RHS variable can be constructed from shopping data.

• No measure of h in scanner data set

– Merge in from ATUS using cells based on

– 92 separate cells represented in data

• Run “between effects” regression over cells

38

• We estimate an elasticity of substitution between time and goods in home production between 1.5 and 2.1.

– Less aggregation leads to lower estimates

• With estimated home production parameters, can estimate actual consumption given observed inputs.

– Consumption/Expenditure varies over lifecycle

– Even if consumption and leisure are separable in utility, need to be careful in interpreting lifecycle expenditure.

40

Conclusions

• Fairly large elasticities between time and money due to shopping and home production.

• We find that households can and do alter the relationship between expenditures and consumption by varying time inputs.

• Household time use, prices, and expenditures vary in a way that is consistent with standard economic principles and the lifecycle profile of the relative price of time.

• Supports growing emphasis on importance of non-market sector in understanding household’s interaction in market

Long Run Trends in Time Use

Aguiar and Hurst (QJE 2007)

• Explore the changing nature of the allocation of time over the last 40 years.

– Focus on the aggregate trends.

– Examine the changing nature of “leisure inequality”.

• Ask a related question: Can changing educational differences in employment status explain changing leisure inequality?

• Why is that interesting? In terms of welfare implications, it is important to know whether low education individuals are taking more leisure because they are unable to find employment at their reservation wage. (Individuals will be off their labor supply curve).

• Help to understand labor supply elasticities and how they may evolve over time.

43

The Data (Table 1)

• 1965-1966: Americans’ Use of Time

2,001 individuals Aged 19-65

One household member must be working in last year

Only one person per household is surveyed

24 hour recall of previous day/ Lots of additional demographic information

• 1975-1976 Time Use in Economic and Social Accounts

2,406 adults (1519 households)

Interviews both husbands and wives (same household)

Interviews them four times (once per quarter)

Designed to be nationally representative

24 hour recall of previous day/ Lots of demographic and earnings data

Note: We only use first interview (fall 1975)

44

The Data (Table 1)

• 1985 Americans’ Use of Time

4,939 adults (over the age of 18)

One adult per household


24 hour recall of previous day

Limited demographics

• 1992-1994 National Human Activity Pattern Survey (sponsored by the EPA)

9,386 individuals (7,514 adults over the age of 18)

One person per household



Limited demographics

45

The Data (Table 1)

• 2003 American Time Use Survey (BLS)

Over 20,000 individuals

One person per household



Very detailed demographics

Sample is drawing from exiting CPS main sample (after survey month 8)

Only have time use linked to actual wages in 2003

Note: 2004 data is not available from BLS (discuss results throughout the talk)

Two problems? Much finer time use categories

One of goals is to create better measures of time spent with children.

Some comfort: 1993 data and 2003 data are very similar along many dimensions

46

Some Existing Work on Time Use

• Juster and Stafford (1985, 1991) and Robinson and Godbey (1997)

– Analyze 1965, 1975, and 1985 time diaries

– Present unconditional means (mostly)

– * Robinson and Godbey also analyze a small 1995 pilot time use survey in their last chapter of second edition of their 1997 book

– 1995 sample does not match well with either 85 or 03 survey.

– Focus on 65 – 85 trends

• What we do is:

– Extend through 03

– Harmonize the data in consistent manner

– Adjust for differences in sample composition between surveys

– Also show conditional means.

47

Creating consistent measures of Time Use

• For the 1965, 1975, 1985, and 1993 data, it was relatively easy

• Classifying activities in 2003 was a bit harder

Some codes for 1985 (time spent in):

Act10 Meal preparation, cooking, and serving food

Act11 Meal cleanup, doing dishes

Act12 Cleaning house (dusting, vacuuming, cleaning bathrooms, etc.)

Act14 Laundry, Ironing, Clothes Care (sewing, mending, etc.)

Some codes for 1993 (time spent in):

Act10 Meal preparation, cooking, and serving food

Act11 Meal cleanup, doing dishes

Act12 Cleaning house (dusting, vacuuming, cleaning bathrooms, etc.)

Act14 Laundry, Ironing, Clothes Care (sewing, mending, etc.)

48

Sample

• All non-retired individuals between the age of 21 and 65 (inclusive)

– 1965 time use survey excludes retired households.

– 1965 survey only includes individuals up until the age of 65

• Restrict individuals to have a “full” time use report (1440 minutes/day)

• Throughout the talk:

– All individuals

– By sex, education, marital status, and employment status

• All results are presented in units of “Hours per Week”

49

Are Time Use Samples Representative (Table A1)?• Compare males in time use data to males in PSID (weighting both data

sets). Restrict sample: Age 21 – 65, non-retired

1965 1975 1985 1993 2003

Time PSID Time PSID Time PSID Time PSID Time PSID

Age 20s 0.25 0.21 0.27 0.30 0.27 0.23 0.25 0.18 0.20 0.16

Age 30s 0.23 0.25 0.28 0.24 0.32 0.33 0.31 0.33 0.26 0.27

Age 40s 0.26 0.27 0.20 0.24 0.20 0.20 0.25 0.30 0.28 0.31

Age 50s 0.19 0.19 0.19 0.18 0.16 0.18 0.15 0.15 0.20 0.21

Age 60s 0.07 0.08 0.06 0.05 0.05 0.05 0.04 0.05 0.06 0.05

Ed > 12 0.30 0.28 0.30 0.39 0.46 0.49 0.58 0.54 0.55 0.59

Married 0.87 0.89 0.85 0.85 0.69 0.76 ---- 0.71 0.69 0.70

Have Kid 0.65 0.65 0.55 0.60 0.42 0.51 0.32 0.46 0.42 0.45

# of Kids

Employed

1.57

0.97

1.66

0.96

1.24

0.93

1.30

0.93

0.76

0.88

0.96

0.90

----

0.89

0.89

0.91

0.80

0.88

0.86

0.91

• Note: 30/40 year olds have increased 1965 to 2003• Note: Population is becoming more educated between 1965 and 2003

50

Are Time Use Samples Representative?

1965 1975 1985 1993 2003

Monday .115 .133

.151

.140

.139

.143

.137

.156

.154

.140

.149

.147

.130

.144

.135

.188

.129

.132

.123

.097

.152

.179

.140

.136

.151

.140

.142

.143

.148

Tuesday .169

.139

.164

.159

.128

.126

Wednesday

Thursday

Friday

Saturday

Sunday

• Data weighted using survey “weights” to make the sample representative by day of the week!

• If random, each cell should have a value equal to 0.142

Allocation of women with children by day of week

51

Definitions: Time Spent in Market Production (Table A2)

1. “Core Market Work” – Time spent working for pay on all jobs

(Main job, other jobs, overtime)

Analogous to measure of hours worked in PSID

2. “Total Market Work” - Direct market work, plus commuting to work, plus ancillary work activities

Ancillary work activities includes time at work “off the clock” (mandatory breaks, meals at work)

52

Figure 1: Comparison of Weekly Core Market Work Hours in PSID and Time Use Surveys: Sample: All Non-Retired Men Between Ages of 21 and 65

34.00

36.00

38.00

40.00

42.00

44.00

46.00

Year

Hou

rs P

er W

eek

PSID Work Hours Time Use Work Hours

Time Use Categories (Table A1)

• Market Work: Paid work in formal sector

Paid work in informal sector

Job search

• Non-Market Work: Home and vehicle maintenance

Shopping/Obtaining goods and services

All other home production (cooking, cleaning, laundry, house work)

• Child Care

• Gardening, Lawn Care, Pet Care

Note: All associated travel time is embedded in the time use category

Time Use Categories (continued)

• Leisure TV watching

Socializing

Exercise/Sport

Reading

Hobbies/Other Entertainment

Eating

Sleeping

Personal Care

• Other Medical Care

• Care of Other Adults

• Religious/Civic Activities

• Education

• Other

Trends in the Allocation of Time (Men): Table 1

Changes Over Time

(Adjusted for Demographics)

05-65 85-65 05-85

Total Market Work -11.7 -7.7 -4.0

Non Market Work 3.5 4.3 -0.8

Child Care 1.8 0.0 1.8

Leisure 4.7 4.3 0.4

Trends in the Allocation of Time (Women): Table 1

Changes

(Adjusted for Demographics)

05-65 85-65 05-85

Total Market Work 3.4 1.2 2.1

Non Market Work -10.4 -6.1 -4.3

Child Care 1.8 -0.8 2.6

Leisure 3.3 6.4 -3.1

Trends in Leisure by Sub-Aggregate: ALL

tv

socializing

entertainment

hobbies

reading

eating

sleeping + personal care

sports

gardening

leisure 2

-6

-4

-2

0

2

4

6

8

10

1965 1975 1985 1993 2003

Ho

urs

per

Wee

k

Time Allocation By Education (Leisure Dispersion): Men

Changes adjusted for demographics

65 85 03-05 05-65 85-65 05-85

< 12 104.3 104.9 113.0 8.7 0.5 8.1

12 101.2 107.3 107.9 6.7 6.1 0.6

13-15 98.6 104.1 104.4 5.8 5.5 0.3

16+ 101.9 105.8 99.7 -2.2 3.9 -6.1

<12 vs. 16+ 2.4 2.1 13.3

12 vs. 16+ -0.7 1.5 8.2



65 85 03-05 05-65 85-65 05-85

< 12 104.3 104.9 113.0 8.7 0.5 8.1

12 101.2 107.3 107.9 6.7 6.1 0.6

13-15 98.6 104.1 104.4 5.8 5.5 0.3

16+ 101.9 105.8 99.7 -2.2 3.9 -6.1

<12 vs. 16+ 2.4 2.1 13.3

12 vs. 16+ -0.7 1.5 8.2 (1)



65 85 03-05 05-65 85-65 05-85

< 12 104.3 104.9 113.0 8.7 0.5 8.1

12 101.2 107.3 107.9 6.7 6.1 0.6

13-15 98.6 104.1 104.4 5.8 5.5 0.3

16+ 101.9 105.8 99.7 -2.2 3.9 -6.1

<12 vs. 16+ 2.4 2.1 13.3 (2)

12 vs. 16+ -0.7 1.5 8.2



65 85 03-05 05-65 85-65 05-85

< 12 104.3 104.9 113.0 8.7 0.5 8.1

12 101.2 107.3 107.9 6.7 6.1 0.6

13-15 98.6 104.1 104.4 5.8 5.5 0.3

16+ 101.9 105.8 99.7 -2.2 3.9 -6.1

<12 vs. 16+ 2.4 2.1 13.3

12 vs. 16+ -0.7 1.5 8.2

(3)



65 85 03-05 05-65 85-65 05-85

< 12 104.3 104.9 113.0 8.7 0.5 8.1

12 101.2 107.3 107.9 6.7 6.1 0.6

13-15 98.6 104.1 104.4 5.8 5.5 0.3

16+ 101.9 105.8 99.7 -2.2 3.9 -6.1

<12 vs. 16+ 2.4 2.1 13.3

12 vs. 16+ -0.7 1.5 8.2

(4)



65 85 03-05 05-65 85-65 05-85

< 12 104.3 104.9 113.0 8.7 0.5 8.1

12 101.2 107.3 107.9 6.7 6.1 0.6

13-15 98.6 104.1 104.4 5.8 5.5 0.3

16+ 101.9 105.8 99.7 -2.2 3.9 -6.1

<12 vs. 16+ 2.4 2.1 13.3

12 vs. 16+ -0.7 1.5 8.2

(5)



65 85 03-05 05-65 85-65 05-85

< 12 104.3 104.9 113.0 8.7 0.5 8.1

12 101.2 107.3 107.9 6.7 6.1 0.6

13-15 98.6 104.1 104.4 5.8 5.5 0.3

16+ 101.9 105.8 99.7 -2.2 3.9 -6.1

<12 vs. 16+ 2.4 2.1 13.3

12 vs. 16+ -0.7 1.5 8.2

Question: Is the dispersion driven by the changing pool of individuals within each educational category?

General Increase in Leisure Dispersion

10th Percentile

50th Percentile

90th Percentile

25th Percentile

75th Percentile

-5

0

5

10

15

20

1965 1975 1985 1993 2003

Ho

urs

per

Wee

k

Summary of Trends

• Leisure increased dramatically since 1965 for average individual

• Most of the average increase occurred prior to the 1990s

• There is a large increase in leisure dispersion that also occurred during this period. Most of that occurred post 1985 (particularly for men).

• Note: The timing of the increase in leisure inequality matches the timing of the well documented increase in

consumption inequality and wage inequality.

Remaining Questions

• Can the increase in leisure for low educated men be interpreted as an increase in well being?

Set out to answer four new questions:

1. Conditional on working full time, is there an educational gap in leisure in either 1985 or 2003?

2. How do men who do not work, regardless of education, allocate their foregone market work hours?

3. Is there an educational gap in leisure for the unemployed? the disabled? other non-employed?

4. How much of the increased leisure dispersion across education groups can be explained by changes in employment status by education?

Employment Status By Education

Conditional

Low Ed High Ed Difference

1985 Share Employed 0.89 0.94 -0.04

1985 Share Non-Employed 0.11 0.06 0.04

Unemployed 0.04 0.02 0.02

Other Non-employed 0.07 0.04 0.02

03-05 Share Employed 0.83 0.92 -0.09

03-05 Share Non-Employed 0.17 0.08 0.09

Unemployed 0.05 0.04 0.02

Disabled 0.08 0.02 0.05

Other Non-employed 0.04 0.03 0.02

Note: From now on, we only focus on two education groups (because of small sample sizes in some cells).

Time Allocation By Education: All Men 2003-2005

Low Ed High Ed Difference*

Total Market Work 36.9 41.9 -4.6

Total Non-Market Work 10.9 11.7 -0.7

Child Care 2.7 3.4 -0.7

Gardening, Lawn Care, Pet Care 2.2 2.1 0.2

Total Leisure 109.8 102.3 7.1

T.V. 21.6 15.3 6.0

Own Medical Care 0.8 0.7 0.1

Care of Other Adults 1.7 1.4 0.2

Religious/Civic Activities 1.5 1.9 -0.4

Time Allocation By Education: Employed Men 2003-2005




Child Care 2.6 3.4 -0.7



T.V. 18.4 14.3 4.0

Own Medical Care 0.5 0.6 -0.1



* Conditional on Demographics

Time Allocation By Education: Unemployed Men 2003-2005



Job Search 2.4 5.5 -2.9

Education 0.9 2.1 -1.2


Child Care 4.4 4.2 -0.5

Gardening, Lawn Care, Pet Care 2.3 4.5 -2.2


T.V. 29.7 22.2 7.5



Religious/Civic Activities 2.4 2.6 0.1

Time Allocation By Education: Unemployed Men 2003-2005



Job Search 2.4 5.5 -2.9 -4.6



Child Care 4.4 4.2 -0.5



T.V. 29.7 22.2 7.5




Where Did the Foregone Work Hours Go (in percent)?

Low Ed High Ed

Total Market Work 6.7 8.4

Job Search 5.2 11.9

Education 0.0 4.0

Total Non-Market Work 19.6 17.8

Child Care 4.0 1.8

Gardening, Lawn Care, Pet Care 0.2 5.7

Total Leisure 53.5 47.0

T.V. 25.4 17.4

Socialization 12.6 8.4

Sleeping 12.6 10.1

Other Entertainment/Hobbies -0.7 8.6


Low Ed High Ed


Job Search 5.2 11.9

Education 0.0 4.0


Child Care 4.0 1.8



T.V. 25.4 17.4


Sleeping 12.6 10.1

Other Entertainment/Hobbies -0.7 8.6

24%

Time Allocation By Education: Disabled Men 2003-2005



Job Search 0.0 0.2 -0.2



Child Care 2.5 2.0 0.2



T.V. 43.2 36.0 7.5


Care of Other Adults 1.5 2.5 -1.4



Low Ed High Ed


Education -1.6 0.2

Total Non-Market Work -1.6 2.9

Child Care 1.3 3.7

Gardening, Lawn Care, Pet Care -0.2 -3.1


T.V. 55.7 47.7


Sleeping 19.1 24.8

Other Entertainment/Hobbies 5.6 4.2

Own Medical Care 8.5 8.8

Time Allocation By Education: Other Men 2003-2005



Job Search 0.0 0.3 -0.3



Child Care 4.0 4.5 -0.4



T.V. 32.9 24.6 8.5





Low Ed High Ed


Job Search -0.2 0.4

Education -0.2 1.3


Child Care 3.1 2.4



T.V. 32.6 22.6


Sleeping 18.7 14.7

Other Entertainment/Hobbies 5.8 2.9

2003-2005 Cross Sectional Decomposition

• How much of the difference in leisure between high and low educated men in 2003-2005 is due to differences in job status?

Perform a Blinder-Oaxaca Decomposition:

Define Wjk = probability of being in job status k for educational attainment j

Xjk = hours per week of leisure for individual in job status k and educational attainment j.

Conditional Difference: 7.5 Hours Per Week

(WL – WH) XH (vectors): 2.4 Hours Per Week

WL(XL – XH) (vectors): 5.1 Hours Per Week

• Roughly 30% of difference in leisure in 2003-2005 between low and high educated men can be attributed to employment status differences.

Perform Same Analysis for 1985

Leisure

Unconditional

Low Ed High Ed Difference

All 107.4 105.1 2.2

Employed Men 103.9 103.5 0.4

Non-Employed Men 134.6 130.0 4.6

Perform a similar Blinder-Oaxaca decomposition

• Roughly 60% of difference in leisure in 1985 between low and high educated men can be attributed to employment status differences.

Time Series Decomposition (85-05)

Percent

Change (W05-W85)X05 W85(X05-X85) Explained

Less Educated 2.5 2.0 0.4 0.82

More Educated -2.8 0.6 -3.4<0.00

• How much of the overall dispersion (combining cross section and time series) can be explained by changing employment status?

Answer: ~ 40%

• Conclusion: If all non-employment is involuntary for low educated men, 60% of the documented leisure dispersion remains.

• Low educated men are still “choosing” to take more leisure than high educated men over last 25 years.

Implications for Changing Inequality #1

• How does one value the additional leisure time?

If individuals are on their labor supply curve, we can use their wage to value their increased leisure time.

• Back of the envelop calculation:

Approximately 4 to 7 hour increase in leisure per week for low educated men relative to high educated men since the mid 1980s.

After tax low educated wage ~14 hours per hour.

Value of the additional leisure time: $3,000 - $5,000 a year.

• Is this large?

Implications for Changing Inequality #2

• Provides a caution for interpreting measures of consumption inequality.

Time can be allocated to “home production” which can cause expenditure to diverge from true consumption.

Examples: Shopping intensity

Take advantage of time dependent discounts

Cooking meals

Do their own home production

• The unemployed do allocate more time to home production/shopping than their employed counterparts.

• Changes in employment propensities over time can be expected to change the mix of market expenditures and time that enter the commodity production function. (Aguiar and Hurst 2005, 2007a, 2007b)

Broader Implications

• Why do low educated men choose higher leisure relative to higher educated men?

1) Do wages differences cause the leisure differences?

– Substitution effects are important?

2) Or are preference differences driving the leisure differences? There are stark differences in behavior among the non-employed.

- Perhaps those with a taste for leisure are sorting are the ones

sorting into the low educated category.

One Last Point: Within Education Dispersion

-10

-5

0

5

10

15

20

25

5 15 25 35 45 55 65 75 85 95

Percentile of Distribution

Ch

ang

e 19

65 -

200

3H

ou

rs p

er W

eek

<12 12 13-15 16+

Conclusions (Update)

• The allocation of time has changed dramatically over the last 40 years.

• The allocation differed dramatically by educational attainment with low educated individuals experiencing larger “leisure” increases than high educated individuals.

• Only about 40% of the dispersion can be explained by involuntary non-employment.

Home Production and The Business Cycle

A Diversion:Labor Supply and Home Production

95

Simple Labor Supply Example: No Home Production

Look at static model:

1 1

( , )1 1

. .

. . .

:

:

C

N

C NU C N d

s t C wN

F O C

U C

U dN w

96

Simple Labor Supply Example: No Home Production

:

Take Logs:

1 1 1ln( ) ln( ) ln( ) ln( )

:

ln( ) ln( ) ln( )

NU dN w

N w d

Estimate

N A w

= labor supply elasticity with respect to wages (holding constant)

= labor supply elasticity with respect to marginal utility of wealth (holding w constant)

How Do Things Change With Home Production?

1 1

1/

1 1

1 1

( )( , )

1 1

. . X

( )

. . .

:

: ( )

: ( )

H X

C X

H H

N

C N HU C N d

s t wN

C H X

F O C

U C X

U C H d N H

U d N H w

How Do Things Change With Home Production?

Similar in spirit to no-home production model

1 1 1ln( ) ln( ) ln( ) ln( )

But, the elasticity of market work changes:

1ln( ) ln( ) ln( ) ln

(1 ) (1 )H

X

N H w d

H N w

Interpretation

• Home production makes work hours more elastic to changes in wages (holding the marginal utility of wealth constant).

• Implications:

Women’s labor supply more elastic than men (if they do most of the home production) (Mincer 1962)

Labor supply is more elastic during temporary wage changes (recessions) with home production.

Expenditure (X) is more elastic during temporary wage changes (recessions) with home production.

Has business cycle implications….

Business Cycle Variation in Hours

• Standard business cycle models have trouble matching the business cycle patterns of hours worked, consumption, and wages.

• Wages do not move that much – yet, there are big movements in consumption (measured as expenditures) and hours worked (measured as time spent in the market sector).

• Trying to reconcile jointly the movements in expenditures, market hours worked and wages has spawned a large literature.

o For a recent attempt at reconciliation, see Hall (JPE 2009) “Reconciling Cyclical Movements in the Marginal Value of Time and the Marginal Product of Labor”

o Hall (2009) relies on non-separabilities in preferences between consumption and leisure.

Earlier Iterations

• Non-separabilities in preferences (as alluded to in previous lecture) can be thought of as a reduced form for a model with non-market production.

• Earlier models, tried to reconcile the joint movements of expenditures, hours worked and wages at business cycle frequencies by appealing to models of nonmarket production.

o At business cycle frequencies, individuals substitute toward home production when leave labor force.

o Small changes in wages can cause substitution of some households from the market sector to home sector.

o Big declines in expenditure does not imply big declines in expenditure.

o Home production shocks can drive business cycles!

• See work by Benhabib, Rogerson, and Wright (1991, JPE) and Greenwood and Hercowitz (1991, JPE).

Model: Consumers

00

11

1/

( , )

1( )

1

1 ( ) ( )

t tt

b bt t

t t

m ht t t

E U C L

C LU C L

C a C a C

Model: Production

11

11

1

1

exp( )( ) ( )

exp( )( ) ( )

(1 ) ; j=m,h

Z [ , ]'

~ (0, )

m m

m m

m m mt t t t

h h h ht t t t

j j jt t t

m ht t t

t t t

t

Y z K N

C z K N

K X K

z z

Z RZ

N

Model: Constraints

1

1

mt t t

m ht t t

m m mt t t t t

m ht t t

Y C X

X X X

C X wN r K

L N N

Benhabib, Rogerson, Wright Conclusions

• Business cycle models with home production offer individuals another margin of substitution when wages move:

o They can substitute market work hours for nonmarket work hours (when the opportunity cost of time falls).

o Even though market work hours fall a lot, the sum of market plus nonmarket work may not fall by as much.

• Models with home production generate much bigger labor market responses to change in market productivity (wages) at business cycle frequencies.

• Models with home production generate much bigger declines in market expenditures in response to changes in market productivity at business cycle frequencies.

• Can pick parameter values for home production technology and shock process for the market and home technologies that can come very close to matching the data.

Aguiar, Hurst and Karabarbounis (2011)

• How does home production actually evolve during recessions?

• Until this year, that question was not answerable given there were no major data sets that included time use during periods spanning a recession.

• What we do is use the 2003-2010 ATUS to explore how time use actually evolves during recessions.

• Potential problem:

- Low frequency trends in time use

- Need to distinguish business cycle effects from these low frequency trends

- Hard to do with short time series

Naïve Analysis

Look at the Pre-Trends

A Cross State Analysis: Home Production (Pooled Years)

A Cross State Analysis: Leisure (Pooled Years)

A Cross State Analysis: Home Production (Separate Years)

A Cross State Analysis: Leisure (Separate Years)

Cross State Estimates (Pooled Sample)

Implication 1: Do Estimates Match The Model?

Implication 2: Are Home Sector Shocks Important?

• Data only for this recession.

• No evidence of home sector shocks.

• Run this on individual level data. Ast is a measure of aggregate labor market conditions in state s during time t (we use unemployment rate as our proxy).

• Regression asks whether people do more or less home production when aggregate conditions change (at state level) holding their work hours constant.

• Coefficient on Ast was zero (tightly estimated).

Conclusions

• A non-trivial fraction of the movement of consumption and hours can be explained by movements into home production.

• Do not have measures of home production output, only measures of home production inputs.

• The change in home production time during recessions matches well the prediction of business cycle models of labor supply, wages and consumption during recessions with home production.

• Is the elasticity of substitution between time and goods in home production during recessions the same as during non-recessionary periods?

• Still need to take a stance on the correlation of shocks between home and market sector at business cycle frequencies. No evidence that home production shocks were important during last recession.

Micro Data For Macro Models

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