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Dynamic Female Labor Supply

This study investigates the factors behind the dramatic rise in female employment rates, including schooling level, wage increase, fertility decline, and marriage decline. The findings suggest that factors such as social norms, cost of children, and technical progress may also play a role in explaining the increase in female employment.

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Dynamic Female Labor Supply

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  1. Dynamic Female Labor Supply Zvi Eckstein and Osnat Lifshitz November 5, 2010, CBC Based on the Walras-Bowley Lecture to the American Econometric Society Summer meeting, June 2008

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

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

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

  5. Because Married FE Rose…..! 5

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

  7. 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)

  8. Schooling Level Increase

  9. Wage increase – Gender Gap decline 10

  10. Fertility Decline Ref. by cohort 11

  11. Marriage Declines – Divorce Increases 13

  12. 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..

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

  14. An Accounting Exercise • Measure female’s employment due to: • Schooling Levelincrease • Wageincrease/Gender Gap decrease • Fertilitydecline • Marriagedecline/Divorcegrowth • The “unexplained” is Others Lee and Wolpin, 2008

  15. 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.

  16. Sketch of the Model • Extension of Heckman (1974) • Female maximizes PV utility • Chooses employment (pt = 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

  17. Estimation Fit – 1955 cohort FE 24

  18. Estimation Fit – 1955 cohort FE 25

  19. Back to Accounting Exercise • For the 1955 cohort we estimated: p55= P55(S, yw, yh, N, M) for each age • Contribution of Schooling of 1945 cohort (S45) for predicted FE of 1945 cohort is: predicted p45= P55(S45, yw55, yh55, N55, M55) • ….Schooling and Wage predicted p45= P55(S45, yw45, yh45, N55, M55) • ….Etc

  20. FE by Age per Cohort

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

  22. Accounting for the change in FE:Cohorts of 1925, 30, 35 based on 1955 • Schooling:~36% of the change in FE • Wages:~24% • Fertility:~3% • Marriage: ~0% • Other:~37% • 45% at the early ages • 34% for older ages

  23. Accounting for the change in FE:Cohorts of 1940, 45, 50: based on 1955 Cohort • Schooling :~ 33% of the change in FE • Wages:~22% • Fertility:~8% • Marriage:~1% • Other:~36% • 55% at the early ages • 18% for older ages

  24. Accounting for the change in FE: Cohorts of 1960, 65, 70, 75: based on 1955 Cohort Schooling :~ 39% of the change in FE Wages:~16% Fertility:~2% Marriage:~1% Other:~43% 44% at the early ages almost no data after age of 40 What are the missing factors for “other”? 33

  25. What is missing factor for early ages? • Childcare cost if working • Change 1 parameter (a4) – get perfect fit • 1945 cohort childcare cost: $3/hour higher • 1965 cohort childcare cost: $1.1/hourlower • 1975cohort childcare cost: $1.1/hourlower

  26. What is missing factor for all ages? • Childcare cost if working • Value of staying at home • Change 2 parameters (a1,a4) – get perfect fit • 1935,1925 cohorts childcare cost: $3.2/hour higher • 1935 cohort leisure value: $4.5/hourhigher • 1925cohort leisure value: $5/hourhigher How can we explain results?

  27. 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?

  28. 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.

  29. Predicted Aggregate Female Employment Rates

  30. Alternative Modeling for Explaining “Other Gap” • Unobserved heterogeneity regarding leisure/cost of children • Bargaining power of women changes • Household game: a “new” empirical framework 39

  31. Concluding remarks We demonstrate the gains from using Stochastic Dynamic Discretemodels: 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% ofincrease in Married FE Other – 25-45% ofincrease in Married FE Change in two parameters close the Other Gap 40

  32. Labor Supply of Couples:Classical and Modern Households –”new” Model • Internal family game(McElroy,1984, Chiappori, 1998) • New empirical dynamic models of household labor supply: Lifshitz (2004), Flinn (2007), Tartari (2007)

  33. The Model: Household Dynamic Game • Two types ofhousehold (unobserved) • Classical (C): Husband is Stackelberg leader. Every period after state is realized the husband makes the decision before the wife, and then she responds. • Modern (M): Husband & Wife play Nash. Husband & wife are symmetric, act simultaneously after state is realized, taking the other person actions as given. • Both games are solved as sub-game perfect.

  34. Sketch of Model: Choices • Employment; Unemployment; Out of LF • Initially UE or OLF - two sub-periods • Period 1: Search or OLF • Period 2: Accept a potential offer E or UE • Initially E – one period • Quit to OLF • Fired to UE • Employment in a “new” wage.

  35. Sketch of Model: Dynamic program • Max Expected PV as in EW • Utilityfunctions are identical for both C and M • Characteristics of husband and wife different • Game solved recursively backwards to wedding

  36. Sketch of model: Budget constraint The household budget constraint

  37. Sketch of model: Wage and probabilities (EW) • Mincerian wage functions for each j = H, W • Endogenous experience • Logistic form for job offer probability, divorce probability and probability of having a new child (like EW model).

  38. Sketch of Model: Main Result • Wives work more in M than C family because: • Husband earnings and offer rates are larger • In M family she faces more uncertainty (Husband employment and earnings are uncertain when she makes the decision independently)

  39. Estimation: SMM Data • PSID – Panel - 863 couples who got married between 83-84 - Cohort of 1960 • 10 years (40 quarters) sample (at most) 2 sets of moments: • Mean individual choice of (E; UE; OLF) by duration since marriage. • Average predicted and actual wage for men and women by duration since marriage.

  40. Estimation Results • 90% of choices are correctly predicted • 61% is estimated proportion of C families • Husbands in C & M have similar labor supply • Wives work 10% more in M families

  41. Fit: Employment rate 52

  42. Probability of Family type • Posterior probability of M family is: • Negatively correlated with: husband age at wedding, number of children, husband is black or Baptist. • Positively correlated with: couples education, wife age at wedding; husband is white, Catholic; potential divorce.

  43. Counterfactual: 100% of Families are Modern • Increase of female employment ~ 6% • No impact on males • Employment difference from males ~ 11%.

  44. Counterfactual: Full Equality - 100% of Families are Modern; Equal Wages & Job Offers for Males and Females • Males employment decreases by 1.4% • Females employment increases by 12.9%. • Difference between males & females employment (3.2%) due to higher risk aversion and higher cost/utility from home for females 57

  45. Summary of results • Education – 35% ofincrease in Married FE • Other – 25-45% ofincrease in Married FE • Householdgame model for change in Social Norms (C and M families) can account to large change in Married FE – 5% to 10%

  46. Concluding remarks • The two examples demonstrate the gains from using Stochastic Dynamic Discretemodels: • Dynamic selection method, rational expectations, and cross-equations restrictions are imposed • Accounting for alternative explanations for rise in US Female Employment • Dynamic couples game models are the framework for future empirical labor supply

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