Pierre-Carl Michaud (RAND) Frederic Vermeulen (Tilburg University)

1. A collective labor supply model with externalitiesIdentification and estimation by means of panel data Pierre-Carl Michaud (RAND) Frederic Vermeulen (Tilburg University)

2. Introduction • Household labor supply usually rationalized by standard unitary model • Households assumed to behave as single decision makers • Utility function maximized subject to a budget constraint • Implies well-known theoretical restrictions • Unique preference ordering if restrictions are satisfied • Unitary model suffers from methodological and empirical shortcomings • Does not fit in methodological individualism • Unitary restrictions usually rejected when tested on multi-person households

3. Introduction • Collective approach to household behaviour • Chiappori (1988, 1992) • Multi-person households consist of different individuals with own rational preferences • Intra-household allocations are Pareto-efficient • Theoretical restrictions that fit the data better than unitary restrictions

4. Introduction • Crucial issue: can we identify individual preferences and the intra-household bargaining process on couples’ labor supply data alone? • No, if there are leisure externalities and consumption is public • Yes, if leisure is exclusive • Yes, if individual preferences are egoistic or of the Beckerian caring type • Allows analyzing policy reforms in terms of individual preferences • But restrictive assumptions

5. Introduction • Novel approach to obtain identification when individual preferences allow for general externalities with respect to leisure • Idea: make use of individuals who are observed as member of a couple and as a single (widows and widowers) • Core assumption: preferences can only change via observable characteristics when somebody is widowed • Preferences are individual specific: can only change via clear channel when spouse dies • Obvious candidate: mental health shocks that can in principle be controlled for

6. Introduction • Application to sample of older Americans drawn from the Health and Retirement Study • HRS allows identification strategy: substantial number of initial couples dissolved over time due to death of one of the spouses • Evidence for joint retirement: complementarities in leisure • Social security simulations by collective model and related unitary model • What is value added of collective model?

7. Overview • Identifying a collective labor supply model with leisure externalities • Empirical specification • Data • Estimation results • Simulation results • Conclusion

8. Overview • Identifying a collective labor supply model with leisure externalities

9. Identifying a collective labor supply model with leisure externalities • Ingredients of a collective labor supply model • Individual preferences • Pareto-efficient intra-household bargaining process • Observed allocations result from the maximization of a weighted sum of spouses’ utilities subject to a household budget constraint • Pareto weights depend on wages and non-labor income

10. Household maximization problem

11. Identifying a collective labor supply model with leisure externalities • Individual preferences and Pareto weights are not identifiable without additional assumptions • Continuum of utility functions and Pareto weights yield same observed behavior • Chiappori and Ekeland (2005) propose restrictions on marginal utilities to secure identifiability • Marginal utility of exclusive goods set to zero in other individual’s utility function

12. Identifying a collective labor supply model with leisure externalities • Approach not immediately applicable: • We only observe leisure and consumption of Hicksian aggregate good in labor supply data sets • Evidence that there are leisure externalities • Our identification strategy: make use of individuals who are observed as member of a couple and as a single (panel data) • Core assumption: preferences can only change via observable characteristics when somebody becomes a widow(er) • Allows to pin one (and only one) structural model from the continuum of structural models

13. Identifying a collective labor supply model with leisure externalities • Recall: single’s optimization problem • Assumption regarding preferences implies • Unidentified constant: leisure level associated with deceased spouse

14. Identifying a collective labor supply model with leisure externalities • ‘Household’ utility function: • Three cases can be distinguished: couple, widows and widowers • Compare to Chiappori and Ekeland (2005): marginal utility of partner’s leisure equals zero only when that spouse died

15. Overview • Identifying a collective labor supply model with leisure externalities • Empirical specification

16. Empirical specification • Discrete choice framework • Spouses choose between a limited number of working hours choices • Husbands: 0, 25, 40 and 50 hours • Wives: 0, 15, 30 and 40 hours • Nonlinear budget sets

17. Empirical specification • Preferences are of a modified Cobb-Douglas type • Discrete unobserved heterogeneity in marginal utility of own leisure

18. Empirical specification • Pareto weight • Fixed costs of participation taken into account via monetary costs subtracted from after-tax income if one returns to work (state dependence) • Part-time specific utility costs • Estimation in conditional logit framework with discrete heterogeneity

19. Empirical specification • Unitary model’s specification • Also discrete heterogeneity, fixed costs of participation and part-time specific utility costs taken into account

20. Overview • Identifying a collective labor supply model with leisure externalities • Empirical specification • Data

21. Data • Health and Retirement Study • Longitudinal survey that follows a cohort of individuals who were born between 1931 and 1941, and their partners • We use first six biennial waves (1992-2002) • Sample selection • Married or cohabiting couples where both individuals were alive in 1992 • Sample of 2342 households that are potentially 6 times observed (487 widows and 138 widowers in 2002)

22. Overview • Identifying a collective labor supply model with leisure externalities • Empirical specification • Data • Estimation results

23. Estimation results

24. Estimation results

25. Overview • Identifying a collective labor supply model with leisure externalities • Empirical specification • Data • Estimation results • Some simulations

26. Some simulations • Simulation 1: Elimination of earnings test • Social security benefits are reduced if one has earnings above a threshold if one is younger than the normal retirement age • Reimers and Honig (1996), Friedberg (2000): men are deterred from working by this rule, while women are not affected • Gruber and Orszag (2000): no influence on husbands, while there are disincentive effects for women

27. Simulation 1

28. Some simulations • Simulation 2: Elimination of spouse allowance • Spouse is entitled to the maximum of the own benefit and half of the spouse’s benefit given eligibility • Blau (1997): elimination of allowance with replacement by earnings sharing has negative impact on husbands’ participation and positive impact on wives’ participation

29. Simulation 2

30. Welfare effects

31. Overview • Identifying a collective labor supply model with leisure externalities • Empirical specification • Data • Estimation results • Some simulations • Conclusion

32. Conclusion • Collective labor supply model • Identification strategy in the presence of leisure externalities • Application to Health and Retirement Study • Strong rejection of unitary model • Better fit of collective model • Simulations: depending on simulation and criterion (participation/welfare) qualitatively different results obtained