1. 1 Dynamic Female Labor Supply Zvi Eckstein and Osnat Lifshitz December 27, 2010 Based on the Walras-Bowley Lecture to the American Econometric Society Summer meeting, June 2008

2. Why Do We Study Female Employment (FE)?

3. 3 Because they contribute a lot to US Per Capita GDP…

4. Central Question Why Did Female Employment (FE) Rise Dramatically?

5. 5 Because Married FE Rose…..!

6. 6 Who among the Married? The Educated (HSG-CG) Females!

7. 7 Why did Married Female Employment (FE) Rise Dramatically?

8. Main Empirical Hypotheses Schooling Level increase (Becker) Wage increase/Gender Gap decline Heckman and McCurdy(1980), Goldin(1990), Galor and Weil(1996), Blau and Kahn(2000), Jones, Manuelli and McGrattan(2003), Gayle and Golan(2007) Fertility decline Gronau(1973), Heckman(1974), Rosensweig and Wolpin(1980), Heckman and Willis(1977), Albanesi and Olivetti(2007) Attanasio at.al.(2008) Marriage decline/Divorce increase Weiss and Willis(1985,1997), Weiss and Chiappori(2006) Other – (unexplained)

9. Schooling Level Increase

10. 10 Wage increase – Gender Gap decline

11. 11 Fertility Decline Ref. by cohort

12. 12 Decrease in the Fertility of Married Women

13. 13 Marriage Declines – Divorce Increases

14. What are the Other Empirical Hypotheses? Social Norms Fernandez, Fogli and Olivetti(2004), Mulligan and Rubinstein(2004), Fernandez (2007) Cost of Children Attanasio, Low and Sanchez-Marcos(2008) Albanesi and Olivetti(2007) Technical Progress Goldin(1991), Greenwood et. al.(2002), Will show up as a cohort effects..

15. 15 Post baby-boomers Cohort’s FE stabilized Employment rates by Age

16. An Accounting Exercise Measure female’s employment due to:  Schooling Level increase  Wage increase/Gender Gap decrease  Fertility decline  Marriage decline/Divorce growth The “unexplained” is Others Lee and Wolpin, 2008

17. An Accounting Exercise Need an empirical model Use Standard Dynamic Female Labor Supply Model – Eckstein and Wolpin 1989 (EW): “old” model Later extensions (among others..): van der Klauw, 1996, Altug and Miller, 1998, Keane and Wolpin, 2006 and Ge, 2007.

18. Sketch of the Model Extension of Heckman (1974) Female maximizes PV utility  Chooses employment (p t = 1 or 0)  Takes as given: Education at age 22 Husband characteristics Processes for wages, fertility, marital status Estimation using SMM and 1955 cohorts from CPS Model

19. 19 The woman chooses employment in order to maximize:

20. 20 The household's budget constraint :

21. 21 The Mincer/Ben-Porath Female’s earning function Budget constraint and wage into utility imply: Employment: Unemployment:

22. 22 Probabilities Logistic form for: job offer probability, marriage and divorce probability and probability of having a new child Solution: Backward Solution following Eckstein and Wolpin (1989) and Keane and Wolpin (1997)

23. 23 Estimation: Structural DP model using CPS Estimation EW: SMM using 1955 cohort CPS data and choice of relevant cross-section moments. Joint estimation of the following equations :  Female Employment dynamic discrete choice model with cross equation restrictions and rational expectations internal consistency (Lucas, 1976, Sargent, 1983: Mix probit with logit FE offer rate)  Log wage with endogenous experience (not age).  MNL of Children, Marriage, Divorce  Random choice of husband conditional of characteristics; Female Alternative: Static Model (δ=0), Reduced Form Model – Heckman’s two steps.

24. Estimation Fit – 1955 cohort FE 24

25. Estimation Fit – 1955 cohort FE 25

26. Estimation Fit – 1955 cohort FE 26

27. Back to Accounting Exercise For the 1955 cohort we estimated: p 55 = P 55 (S, y w, y h, N, M) for each age Contribution of Schooling of 1945 cohort (S 45 ) for predicted FE of 1945 cohort is: predicted p 45 = P 55 (S 45, y w55, y h55, N 55, M 55 ) ….Schooling and Wage predicted p 45 = P 55 (S 45, y w45, y h45, N 55, M 55 ) ….Etc

28. FE by Age per Cohort

29. 1%Other 69%+ 4 Marital Status 69%+ 3 Children 69%1+ 2 Wage 71%1 - Schooling 68%Actual 1945 Age Group: 38-42 1955:Actual: 74% Fitted: 74% 12%Other 61%+ 4 Marital Status + 3 Children 63%1+ 2 Wage 63%1 - Schooling 49%Actual 1945 Age Group: 28-32 1955: Actual: 65% Fitted: 65% Accounting for changes in FE: 1945 cohort Dynamic Model Early age total difference 12% is Other 61%

30. 7%Other 61%+ 4 Marital Status 61%+ 3 Children 62%1+ 2 Wage 67%1 - Schooling 54%Actual 1935 Age Group: 38-42 1955:Actual: 74% Fitted: 74% 14%Other 50%+ 4 Marital Status + 3 Children 52%1+ 2 Wage 58%1 - Schooling 36%Actual 1935 Age Group: 28-32 1955: Actual: 65% Fitted: 65% Accounting for changes in FE: 1935 cohort Dynamic Model Early age total difference 10% is Other 50%

31. 31 Decomposition of the change in FE – Dynamic Model Schooling composition graph 1945Schooling composition graph 1965Schooling composition graph 1975

32. 32 Decomposition of the change in FE – Static Model

33. 33 Decomposition of the change in FE – Heckman Model

34. Goodness of Fit Tests for the Three Models 34

35. 35 Accounting for the change in FE: Cohorts of 1925, 30, 35 based on 1955

36. 36 Accounting for the change in FE: Cohorts of 1940, 45, 50: based on 1955

37. 37 Accounting for the change in FE: Cohorts of 1960, 65, 70, 75: based on 1955 What are the missing factors for “other”?

38. What is missing factor for early ages? Childcare cost if working Change 1 parameter (    – get perfect fit  1945 cohort childcare cost: $3/hour higher  1965 cohort childcare cost: $1.1/hour lower  1975 cohort childcare cost: $1.1/hour lower

39. What is missing factor for all ages? Childcare cost if working Value of staying at home Change 2 parameters (      – get perfect fit  1935,1925 cohorts childcare cost: $3.2/hour higher  1935 cohort leisure value: $4.5/hour higher  1925 cohort leisure value: $5/hour higher How can we explain results?

40. Actual and Predicted Employment Rates 1940 Cohort 40

41. Actual and Predicted Employment Rates 1930 Cohort 41

42. 42 How can we explain results? Change in cost/utility interpreted as:  Technical progress in home production  Change in preferences or social norms How do we fit the aggregate employment/participation?

43. Aggregate fit Simulation Simulate the Employment rate for all the cohorts: 1923-1978. Calculate the aggregate Employment for each cohort at each year by the weight of the cohort in the population. Compare actual to simulated Employment 1980-2007.

44. Predicted Aggregate Female Employment Rates Dynamic Model

45. Predicted Aggregate Female Employment Rates by Cohort and Age - Dynamic Model

46. Alternative Modeling for Explaining “Other Gap” Unobserved heterogeneity regarding leisure/cost of children Bargaining power of women changes Household game: a “new” empirical framework 46

47. 47 Concluding remarks We demonstrate the gains from using Stochastic Dynamic Discrete models:  Dynamic selection method, rational expectations, and cross-equations restrictions are imposed  Accounting for alternative explanations for rise in US Female Employment  Better fit than static models (new version) Education – 35% of increase in Married FE Other – 25-45% of increase in Married FE Change in two parameters close the Other Gap

48. Thanks!!