1. Micro Data For Macro Models
Topic 3: Home Production, Leisure and Labor Supply

2. Home Production and Labor Supply Elasticities

3. Simple Labor Supply Example: No Home Production
Look at static model:

4. Simple Labor Supply Example: No Home Production

5. How Do Things Change With Home Production?

6. How Do Things Change With Home Production?

7. 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….

8. Home Production and The Business Cycle

9. 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.

10. 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).

11. 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.

12. Aguiar, Hurst and Karabarbounis (2013)
How does home production actually evolve during recessions?
Until recently, 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 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

13. Naïve Analysis

14. Look at the Pre-Trends

15. A Cross State Analysis: Home Production (Pooled Years)

16. A Cross State Analysis: Leisure (Pooled Years)

17. A Cross State Analysis: Home Production (Separate Years)

18. A Cross State Analysis: Leisure (Separate Years)

19. Cross State Estimates (Pooled Sample)

20. 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).

21. 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.

22. “Leisure Luxuries and the Labor Supply of Young Men”
Aguiar, Bils, Charles and Hurst
Fall 2017

23. How Does Technology Affect Labor Markets?
Labor Demand (Relatively Large Literature):
o Skill biased technological change
o Most real business cycle models
o Automation in manufacturing/routine occupations
o “Robots”
Labor Supply (Much Smaller Literature):
o Home production technology and female labor supply
o Leisure technology and long run trend in hours worked

24. How Does Technology Affect Employment/Hours?
Simplified intuition
o Individuals compare market wage relative to reservation wage.
Technological change and labor markets:
o Market wage effects (perhaps lowering market wages for lower skilled workers in recent periods).
o Reservation wage effects (perhaps raising reservation wages during recent periods).
Note: If technology raises market wages and reservation wages at similar rates, little effect on labor supply.

25. What This Paper is About
Methodological:
Create a methodology (a leisure demand system) which uses data on how time is allocated to different leisure activities to infer innovations to leisure technology.
Application 1:
Use the methodology and detailed time use data to estimate changes in leisure technology for recreational computer activities during the 2000s (video games, social media, etc.).
Application 2:
Use our framework to assess how innovations in recreational computer leisure technologies increased the marginal value of leisure for different demographic groups and contributed to declining market hours during the 2000s.

26. Major Innovations in Computer Leisure Technology
Starting in Mid-2000s
Able to engage in leisure activities easily with others at different locations.
Social media – Facebook started in 2004; grew from 12 million to 360 million users between 2006 and 2009.
Video games – Sony, Microsoft and Nintendo all released consoles in 2005/2006 that allowed online capabilities. Video game revenues increased by 50 percent (were flat between 2000 and 2006).
Large multiplayer online video games developed over same time period. World of Warcraft started around 2005 and had 10 million monthly users by 2009.
iPhone released in Smart phones take off.
Time series trends in leisure technologies occurred around same time as Great Recession. Need theory to tease the two apart.

27. What We Actually Do: Part 1
Describe changing nature of broad time use for various groups during 2000s
o Examine trends in schooling, home production, leisure, etc.
o Finding: Change in work ≈ change in leisure for most groups (younger men, older men, etc.)
Document shifts in the nature of leisure for various groups during the 2000s
o Finding: During this time, market work fell and leisure increased by about 130 hours per year in ATUS (from )
o Finding: Young men increased their computer leisure activities by hours per year between 2004 and 2015
o Finding: No comparable shift for other demographic groups

28. What We Actually Do: Part 2
Heart of the paper: Introduce a leisure demand system
o Estimate Leisure Engel Curves
o Demonstrate importance of “leisure luxuries”
- Leisure luxuries are not subject to strong diminishing returns
- Very responsive to technological improvements
- Finding: Computer/Gaming is a strong leisure luxury
o Show how Leisure Engel Curves can be used to infer relative changes in leisure technology for different leisure goods.
- Finding: Large estimated increase in computer/video game technology during the 2000s (consistent with BLS price data)
o Key: movement along a Leisure Engel Curve vs. a shift in Leisure Engel Curve

29. What We Actually Do: Part 3
Use leisure demand system and time use data to estimate change in the marginal return to leisure.
o Findings: Increased computer/video game technology resulted in a shift in of the labor supply curve by about 1.5 to 3.0 percent for young men during
o Translates to about 20 – 40 hours per year.
o No effect on older men.
o Explains about 38% to 79% of the differential trends in labor supply for young vs older men during the period.
o Absent the innovations in leisure technology, younger men would have had hours trends that were more similar to older men.

30. Part I: The Changing Allocation of Time

31. Time Use Data American Time Use Survey (ATUS)
24-hour recall time diaries, one diary per individual
Samples from the exiting rotation of the CPS
Examine patterns for 4 demographic groups based on age and gender:
o Younger:
o Older:
Exclude full time students from sample
Examine broad time use categories in Aguiar, Hurst and Karabarbounis (2013).
Pool data across years , , and

32. Changing Time Allocation of Men (Hours Per Week):
Changes Between and
Men
21-30
31-55
Market Work
-2.7
-1.1
Job Search
0.4
0.1
Home Production
-0.6
-0.9
Child Care
-0.4
Education
0.7
0.0
Leisure
2.5
1.2
Younger and older women increased leisure by 1.6 and 1.9 hours per week,
respectively, over this time period.

33. Leisure Categories 1. Adjusted Sleep, Eating and Personal Care
o Subtract off 49 hrs./week for biological needs
o 5th percentile of the distribution
o At state-time cell, no negative values
Computer Usage
o Includes video/computer games, , time surfing the web, time surfing on smart phones, Facebook, etc.
o Caveat on video/computer games.
3. TV/Movies/Netflix
o Includes time watching YouTube, streaming services, etc.
Socializing
Other Leisure

34. Hours per Week of Leisure Time, Young MenYM
(n = ~2,200/sample)
Pooled
Total Leisure
61.1
63.6
Adj. Eating/Sleeping/P. Care
24.3
24.9
Total Computer Time
3.3
5.2
(Video Game Sub Component)
(2.0)
(3.4) TV
17.3
17.2
Socializing
7.8
8.0
Other Leisure
8.3
8.2
+2.5
+1.9
(+1.4)

35. Hours per Week of Leisure Time, By Employment Status
04-07
12-15
Change
Employed Young Men
Total Computer Time
3.0
4.3
1.3
Video Game
(1.9)
(2.9)
(1.0)
Non-Employed Young Men
5.5
9.7
4.2
(3.5)
(5.9)
(2.4)

36. Distribution of Computer Time, Non-Working Young Men
Only one day of data for each individual
(1)
Pooled
(2)
Percent w/ positive computer time
30%
40%
Hours per day, conditional on positive
2.6
3.4
Percent at least 4 hours per day
5.0%
11.1%
Percent at least 5 hours per day
2.5%
7.5%
Percent at least 6 hours per day
1.5%
4.3%

37. Computer Time By Adjusted Leisure Quartile: Men 21-30

38. Time Use (Hours Per Week) from ATUS, By Sex-Age-Skill Group
(1)
Pooled
(2)
(3)
Diff
(2)-(1)
Men, 31-55, Ed = All
Total Leisure
57.0
58.1
1.1
Total Computer
2.1
2.2
0.1
Video Games Sub Component
(0.9)
(0.8)
(-0.1)
Women, 21-30, Ed = All
58.4
60.0
1.6
1.5
0.7
(0.0)
Women, 31-55, Ed = All
56.1
58.0
1.9
0.5
(0.6)
(0.7)
(0.1)

39. Part II: A Leisure Demand System

40. Static Model Preferences: c = spending on consumption good
hi = time input into leisure activity I
I = number of leisure activities
θ = {θi,….θI} = vector of leisure technology shifters
= aggregator over leisure activities
Key assumption 1: Weak separability between consumption and leisure aggregator (conditional on θ).

41. Static Model Leisure Aggregator:
ηi = governs diminishing returns to spending time in activity i.
Goal: Estimate the ηi’s from the ATUS micro data
Allow the ηi’s to differ by demographic groups
Key assumption 2: Linear separability across leisure activities

42. Implication of Linear Separability Assumption, Young Men
Note: Engel Curve Adjusted (more details later)

43. Two Stage Budgeting: Allocation of Leisure Across Activities
Given (weak) separability between consumption and leisure, can break the problem in two parts.
1. Chose time allocation on leisure categories given total leisure
2. Chose consumption, total leisure (market work), and technology
Given separability:
FOC:
ηi = elasticity of activity i w.r.t. the shadow value of leisure time (μ)

44. Leisure Engel Curves
Leisure Engel Curve: relationship between time spent on leisure activity i and total leisure time (H).
Define βi as the slope of leisure Engel curve:
Define:
βi > 1 is a “leisure luxury” - time is very responsive to technological changes in activity

45. Leisure Engel Curves
Leisure Engel Curve: relationship between time spent on leisure activity i and total leisure time (H).
Define βi as the slope of leisure Engel curve:
Define:
βi > 1 is a “leisure luxury” - time is very responsive to technological changes in activity

46. Overview Using Leisure Engel Curve to Uncover Relative ΔθI
ln hI
(time spent
on leisure
good I)
Slope = βI
(Drawn for a given θI)
ln H (total leisure time)

47. Overview Using Leisure Engel Curve to Uncover Relative ΔθI
ln hI
(time spent
on leisure
good I)
Slope = βI
(Drawn for a given θI)
ln H (total leisure time)
Estimate the βi’s for different groups using cross-region variation during the
period. (Discuss this in a few slides).
Estimate βcomputer ≈ 2.0 for young men.

48. Overview Using Leisure Engel Curve to Uncover Relative ΔθI
ln hI
(time spent
on leisure
good I)
Slope = βI
(Drawn for a given θI)
ln H2005
ln H (total leisure time)

49. Overview Using Leisure Engel Curve to Uncover Relative ΔθI
ln hI
(time spent
on leisure
good I)
Slope = βI
(Drawn for a given θI)
ln H2005
ln H2015
ln H (total leisure time)
Do individuals slide along a given “Leisure Engel Curve”?
Lose a job – take more leisure and spend more time on
computer/video game?

50. Overview Using Leisure Engel Curve to Uncover Relative ΔθI
Slope = βI
(Drawn for a higher θI)
ln hI
(time spent
on leisure
good I)
Slope = βI
ln H2005
ln H2015
ln H (total leisure time)
Is there a shift up in the Leisure Engel Curve?
Implies a relative increase in leisure technology for good I.

51. Measuring Leisure Technology Changes (θi’s)
Define I as computer leisure activity
Define:
Then:
Note: Procedure estimates relative θ’s. Need a normalization assumption about change in θ for another leisure activity.

52. Part III: Estimating β’s and θ’s

53. Estimating βi’s, Group Specific
Collapse data to state-time observations. Use cross-state variation to estimate βi’s . k denotes state.
Use three time periods pooling data across years: , 08-11, 12-15
Estimate the following (for different groups):
Identifying assumption: Variation over time in Hkt at state level is orthogonal to εikt.
Robustness, use state level labor demand “instruments” for Hkt.
(AIDS Specification)

54. Identification Concerns
Estimate the following (for different groups):
States with increasing Hkt are states with increasing εikt
The increasing computer leisure taste is causing employment to fall (leisure to rise)
This will bias up our estimates of β (via higher γ).
Note – this will bias down our estimates of θ!
Robustness, use state level labor demand “instruments” for Hkt.
(AIDS Specification)

55. Raw Cross State Variation: 2004/07

56. Raw Cross State Variation: 2012/15

57. Raw Cross State Variation: 2004/07 vs 2012/15

58. Engel Curve Estimates (s.e.’s in parentheses): Sample Young Men
AIDS Specification
Estimated γi
Implied βi
Total Computer
0.08 (0.04)
0.12 (0.05)
2.07 (0.66)
Video Games
0.06 (0.03)
2.40 (0.99) TV
0.08 (0.03)
0.06 (0.08)
1.29 (0.27)
Socializing
0.01 (0.03)
0.03 (0.04)
1.06 (0.26)
Eat/Sleep/P. Care (adjusted)
-0.16 (0.10)
-0.22 (0.12)
0.59 (0.37)
Other Leisure
(0.06)
0.004 (0.06)
0.98 (0.43)
Time Fixed Effects
Yes
State Fixed Effects No
Number of Obs.
153
150
Standard Errors
OLS
Bootstrap

59. Estimates of β1: Other Groups
Women
21-30
Ed = All
Men
31-55
Total Computer (γi)
-0.02
(0.02)
-0.01
-0.005
(0.01)
Total Computer (imp. βi)
0.50
0.80
0.86

62. Relative Price of Computer and Games
Our estimated increase in recreational computer technology consistent with price data.
Can get price data for games from 2008 onward
Both computers and games declined by about 13 log points per year during the sample period.
Relative price decline (compared to full CPI) is about 15 percent per year.
Hard to quality adjust price evolution. However, our methodology yields results consistent with price data.

63. Part IV: Leisure Innovations and Labor Supply

65. Annual Hours Index Relative to Year 2000, March CPS
Men, 31-55
(160 Hours/Year)
Men, 21-30
(200 hours/year)

66. Fraction Reporting Working Zero Weeks in Prior Year, Excluding Students (March CPS)
Men, 21-30

67. CPS Annual Hours By Sex-Skill-Age, March CPS
Ed < 16
Δ Annual Hours
Percent Change
Men: 21-30
-242
-14.4%
Men: 31-50
-190
-10.2%
Women: 21-30
-144
-11.7%
Women: 31-50
-139
-10.5%
Ed ≥ 16
Δ Annual Hours
Percent Change
Men: 21-30
-122
-6.6%
Men: 31-50
-145
Women: 21-30
-68
-4.2%
Women: 31-50 35
2.1%

68. Real Wage Series 1: Raw Data
No relative decline in wages of young men relative to older men

69. Real Wage Series 2: Demographic Adjusted
No relative decline in wages of young men relative to older men

70. Individual First Stage Problem

71. Frisch Elasticity
Define “Frisch elasticity of leisure” and curvature of total leisure in utility.
ε depends on Uv as well as v’(H;θ) w.r.t. H
Given above:
Summary:

72. Increasing Leisure Technology and Total Leisure
How does leisure respond to changes in θi? (Shifts in leisure demand curve – maps to shifts in labor supply curve)
Scenario 1: Consumption Constant (Full Insurance)
Scenario 2: Hand-to-Mouth c=w(1-h) (No Insurance)
(assume ε/ρ = 1; ρ = -Uccc/Uc)

73. Increasing Leisure Technology and Total Leisure

74. Computing Shifts in Leisure Demand Curve/
Labor Supply Curve (Baseline)

75. Summary of Results Men 21-30 -1.52% -3.05% (0.54%) (1.08%) Men 31-50
Shift in Labor Supply
Reference = Sleep
Hand to Mouth
Full Insurance
Men 21-30
-1.52%
-3.05%
(0.54%)
(1.08%)
Men 31-50
-0.03%
-0.06%
(0.13%)
(0.3%)
Women 21-30
-0.48%
-0.96%
(0.22%)
(0.44%)
Bootstrapped standard errors in parenthesis.

76. Magnitudes (Base Parameterization)
Rising computer technology can explain between 1.5 and 3.0 percent decline in young men hours between
Explains none of older men hour decline.
ATUS: Hours decline of young men = 6.7 percent.
CPS: Hours decline of young men = 8.0 percent.
Hours decline of young men = 12 percent.
Both: Gap in decline between young and old men = 4 percent
Results: Can explain between 38 and 76 percent of differential declines.

78. Robustness: Young Men Shifts in Labor Supply
Holding marginal utility of consumption fixed
0.75 1
1.25
ε = 0.75
-3.0%
-1.6%
-1.1%
ε = 1.0
-5.8%
-2.1%
ε = 1.25
-8.5%
-4.5%

79. Part V: Bonus (if time allows)

80. Reported Happiness From General Social Survey, By Sex-Age-Skill Group
Fraction Reporting “Very Happy” or “Pretty Happy”
(1)
Pooled
(2)
Pooled
(3)
(4)
Diff
(3)-(1)
(5)
p-value of difference
Men, Ed = All, 21-30
0.839
0.854
0.892
0.053
0.060
(n=249)
(n=507)
(n=343)
Men, Ed = All, 31-55
0.886
0.847
-0.039
0.031
(n=630)
(n=1,528)
(n=903)
Men, Ed < 16, 21-30
0.813
0.828
0.881
0.068
0.048
(n=193)
(n=372)
(n=244)
Men, Ed < 16, 31-55
0.883
-0.069
0.023
(n=426)
(n=1,043)
(n=594)

81. Employment Rate Young and Older Men,
OECD Country Average, (OECD Statistics)

82. U.S. Cohabitation With Parent or Close Relative,
American Community Survey
21-30 Year Olds, All Education Groups
 Men
Women
2000
0.30
0.20
2007
0.35
0.26
2010
0.39
0.29
2014
0.44
0.33
Change 00-14
0.14
0.13

83. U.S. Cohabitation Patterns By Employment Status, Men 21-30, Ed = All
American Community Survey
Pooled
Employed
Non-
Living w/Parent or Close Rel.
0.37
0.67
Head: Single
0.23
0.12
Head: Spouse/Partner
0.28
Living w/ Others
0.09

84. Summary
Technology and trade likely have had an effect on labor demand.
o Particularly for those with lower levels of education
Technology may have also had an effect on labor supply – by raising a worker’s reservation wage.
o Particularly for younger men
Innovations in computer technology – particularly the ability to simultaneously connect with others – occurred around the time of the Great Recession.
Need structure to tease out time series effects of labor demand and labor supply (given they were occurring around the same time)
Estimate increased computer leisure technology explains between 38% and 76% of differential decline of young relative to old during 2000s.

85. Employment Rates Young and Older Men, Excluding Students (March CPS)