1. Micro Data For Macro Models
Topic 3: Home Production 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. Model: Consumers

12. Model: Production

13. Model: Constraints

14. 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.

15. Aguiar, Hurst and Karabarbounis (2013)
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 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

16. Naïve Analysis

17. Look at the Pre-Trends

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

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

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

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

22. Cross State Estimates (Pooled Sample)

23. 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).

24. 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.