1. Coping with Prosperity: The Response of Parents’ Child Care Time Use to Rising Earnings James M. Payne Calhoun Community College 1 November 23, 2015 Coping with Prosperity: A Double Hurdle Approach to Parents’ Earnings and Child Care Time Use in the ATUS

2. 2 Demand for human capital in children But where is the... Coping with Prosperity Demand for human capital in children Higher earnings More time spent with children

3. 3 ? Coping with Prosperity The unobserved substitution effect market services a b { I own-time services

4. Data American Time Use Survey (ATUS) & Current Population Survey (CPS) 2003 – 2010 n = 45,716 parents 4 Coping with Prosperity Data & model Model Cragg’s (1971) Double Hurdle

5. 15.6% missing earnings data 5 Coping with Prosperity Missing data Challenge # 1: Missing Data — Biased Census hot-deck imputation — Single-imputation methods underestimate uncertainty

6. 6 Coping with Prosperity Multiple imputation Multiple Imputation (MI) (Rubin 1987) Fill blanks with “neutral” values Repeat m times → m data sets Preserve variation in the data Model each set (imputation) separately Combine estimates using Rubin’s Rule

7. 7 Coping with Prosperity Sample selection and endogeneity Challenge # 2: Sample Selection Bias Challenge # 3: Endogeneity

8. Coping with Prosperity 8 Concurrent approach * Concurrent Heckman-IV approach 1 st step probit (Heckman) for WORKING = 1 2 nd step OLS (Heckman) for earnings Double hurdle model with x = earnings *Millimet, 2001; Amemiya, 1985

9. 9 Coping with Prosperity Heteroscedasticity with zeroes Challenge # 4: Heteroscedasticity with zero values in the data

10. 10 Coping with Prosperity Inverse hyperbolic sine Inverse Hyperbolic Sine transformation sinh -1 ln Burbidge, et al. (1988) Defined for all real numbers Equivalent to a log-linear model

11. 11 Coping with Prosperity Time use definitions market services a b { I own-time services Purchases + BEHALFTIME FACETIME }

12. Coping with Prosperity The issue: How will a higher hourly wage ( w ) affect input prices and time use? p facetime : FACETIME consists only of time, so p facetime = w & = 1 p services = γ p purchases + τ p behalftime (weighted average of components) = 0 (prices of purchases are orthogonal to w ) = τ (since = 1, if p behalftime = p facetme ) So = τ < 1 < a higher wage reduces p services relative to p facetime, and thus BEHALFTIME will be substituted for FACETIME 12 Theoretical model

13. Higher wages will lead to: higher levels of FACETIME greater use of market services and hence of BEHALFTIME a higher level of BEHALFTIME relative to FACETIME 13 Propositions Coping with Prosperity Propositions Greater demand for human capital in children substitution effect }

14. Coping with Prosperity 14 Substitution of BEHALFTIME for FACETIME Sensitivity analysis—marginal effects from bivariate probit model Cell contents:n = 26,963 women

15. Coping with Prosperity 15 Double hurdle results Double hurdle estimates: Salient results, 1 st hurdle probit (n = 26,963 women) *at means of regressors