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Coping with Prosperity: The Response of Parents’ Child Care Time Use to Rising Earnings

Coping with Prosperity: The Response of Parents’ Child Care Time Use to Rising Earnings. Coping with Prosperity: The Response of Parents’ Child Care Time Use to Rising Earnings. James M. Payne. Friday Afternoon Research Group November 15, 2013. Defining the dependent variables.

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Coping with Prosperity: The Response of Parents’ Child Care Time Use to Rising Earnings

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  1. Coping with Prosperity: The Response of Parents’ Child Care Time Use to Rising Earnings Coping with Prosperity: The Response of Parents’ Child Care Time Use to Rising Earnings James M. Payne Friday Afternoon Research GroupNovember 15, 2013

  2. Defining the dependent variables Defining the dependent variables • FACETIME—direct child care time • Physical & medical care • Reading, playing, sports, arts & crafts • Schooling & homework • Conversing • BEHALFTIME—indirect child care time • Organizing and planning • Attending events, conferences, etc. • Dropping off/picking up/waiting • Obtaining medical care • Using child care services Coping with Prosperity

  3. Coping with Prosperity Propositions • Parents seek to accumulate human capital in their children,with household production function: human capital = f (FACETIME, Market services) where market services = f (Purchased services, BEHALFTIME)An increase in parents’ wage rates raises: • nominal incomes, and thus demand for human capital in children • absolute prices of both own time and market services, and the relative price of own time Propositions

  4. Coping with Prosperity Propositions • Expectation: Rising wages will lead to • an increase in FACETIME (probably) • an increase in market services (unambiguously) and hence in BEHALFTIME • an increase in BEHALFTIME relative to FACETIME Propositions

  5. Coping with Prosperity Challenges • Wages   child care time use  is well established, but . . . • no studies have separated the income and price effects Challenges (1)

  6. Coping with Prosperity Challenges • Zeroes in time use data • A. 4 sources of zeroes1. measurement error • 2. the individual will not participate in the activity3. corner solution4. diary window is shorter than the consumption period • B. Log transformation cannot be used to reduce heteroscedasticity • C. Tobit models common, but generate biased estimatesGould (1992), Keen (1986), Daunfeldt and Hellström (2007), Stewart (2009), Frazis and Stewart (2010) Challenges (2)

  7. Coping with Prosperity Challenges • Wage variable problems--endogeneity--sample selection bias Challenges (3)

  8. Coping with Prosperity Challenges Missing income data in the Current Population Survey (CPS)A. 34% missing wage data (2003) with negative selectionHeckman and LaFontaine (2006); 15.6% in my parents-only ATUS sampleB. Census’ modified hot deck imputation produces match biasHirsch and Macpherson (2004), Bollinger and Hirsch (2006, 2010) Challenges (4)

  9. Coping with Prosperity Data • American Time Use Survey (ATUS) 2003 – 2010 Data • Initiated by Bureau of Labor Statistics (BLS), 2003 • One-day time use diaries • Linked to CPS demographic and labor force data • n = 45,716

  10. Two dependent variables Descriptive statistics(minutes on diary day) Coping with Prosperity

  11. Theoretical model Theoretical model • Two inputs for producing human capital in children: • Own time, which is FACETIME with price pf • Market services (S) • Two components: • Purchases (P) with share γand price pp • BEHALFTIME with shareτand price pb= pf • γ+τ= 1 Coping with Prosperity

  12. Theoretical model • Key point: How will a change in hourly earnings (w) affect input prices? • pf: FACETIME consists only of time, so pf = w, = 1 • ps = γpp + τpb (weighted average of component prices) • = 0 (prices of services are orthogonal to w) • = τ (since pb = pf and = 1) • So = τ < 1: an increase in earnings reduces the price of market services S relative to FACETIME, and . . . • predicts that BEHALFTIME will be substituted for FACETIME Coping with Prosperity

  13. ATUS earnings data • Challenges (4): Estimating earnings from CPS • Use updated ATUS earnings data • If available and valid, use hourly wage rate (TRERNHLY) • If not, use weekly earnings (TRERNWA) divided by usual weekly work hours (TEHRUSLT) • If topcoded, use estimates from Hirsch and Macpherson (2011) • If not available, set to missing and impute later • Adjust to 2003 constant dollars using CPI-U-SL to createrEARNHR Coping with Prosperity

  14. Coping with Prosperity Multiple imputation • Rubin (1987) • Process is intended to . . . • Fill blanks with “neutral” values • Preserve variation in the data • Use EM/MCMC multiple imputation method • Create several (m)different data sets, and • Model each set (imputation) separately • Combine estimates using Rubin’s Rule Challenges (4): Multiple imputation (MI) of missing data

  15. Multiple imputation • Multiple imputation • Impute all missing covariates • Create m = 10 imputed data sets Coping with Prosperity

  16. ATUS earnings data • Challenges (3): Endogeneity and sample selection in real hourly earnings (rEARNHR) • Two problems—rEARNHR is: • Endogenous with child care time (Heckman r = 0.14, p-value < 0.001) • Unobserved for nonworking parents Coping with Prosperity

  17. ATUS earnings data • Two-step solution—Millinet (2001) from Amemiya (1985):Heckman (1979) sample selection model, with • 1st step: probit model—estimate probability of being employed (WORKING = 1) • 2nd step: Include instrument (METRO) in OLS model for estimated real hourly earnings • Result: one estimated earnings variable, rEARNHRhat, accommodating both endogeneity and sample selection bias Coping with Prosperity

  18. ATUS earnings data • Two-step solution Coping with Prosperity double hurdle models with x = rEARNHRhat 1st step probit (Heckman) for WORKING = 1 2nd step OLS (Heckman) for rEARNHRhat Instrument for endogeneity(METRO*)

  19. Inverse hyperbolic sine • Challenges (2): Inverse hyperbolic sine transformation of dependent variablessinh-1y = ln(y + √ y2 + 1 ) Coping with Prosperity 4 3 2 1 0 -1 -2 -3 -4 sinh-1 • Burbidge, et al. (1988) • Defined for all real numbers • Equivalent of a log-linear model • Predicted values can be returned to levels by taking sinh ln -10 0 10 y

  20. Coping with Prosperity Double-hurdle model • Cragg (1971), Lin & Schmidt (1984) • Assumes a corner solution • Zero time use observations arise because some people never do the activity • Two hurdles to engaging in the activity: • 1st hurdle: choosingwhether to do the activity • 2nd hurdle: choosing how much to do the activity Challenges (2): Double hurdle model

  21. Estimation—Double hurdle Estimation—Double hurdle Two-part model—estimate, separately for both FACETIME and BEHALFTIME A. First-hurdle probit models for all observations B. Second-hurdle truncated normal models using OLS for nonzero observations of FACETIME and BEHALFTIME Coping with Prosperity

  22. Estimation—Double hurdle Double hurdle results--FACETIME Coping with Prosperity Boldface effects are significant at α = .05 *Marginal effects at means of regressors

  23. Estimation—Double hurdle Double hurdle results--BEHALFTIME Coping with Prosperity Boldface effects are significant at α = .05 *Marginal effects at means of regressors

  24. Theoretical model • Challenges (1): Testing the hypothesis • Construct a ratio of BEHALFTIME and FACETIME and observe the effect of earnings on this • Due to zeroes in the data, I construct the ratio of the marginal effects (ME) in the probit model Coping with Prosperity

  25. Substitution of BEHALFTIME for FACETIME • Substitution of BEHALFTIME for FACETIME • 1st hurdle probit model—strong results for both variables for women • Fit a bivariate probit model for women for each imputed data set, and combine results using Rubin’s Rule • For both variables, calculate marginal effects at: • P10Q1MedianQ3P90P95of rEARNHRhat • P10Q1MedianQ3P90of CHILDAGE • Medians of WORKHRS (30 hrs.) and SPOUSEHRS (40 hrs.) • Means of other continuous variables • White, female, college graduate, US citizen, married, homeowner, not a student, employed by a private firm, for a Monday in January, 2009 Coping with Prosperity

  26. Substitution of BEHALFTIME for FACETIME Sensitivity analysis—marginal effects from bivariate probit model Coping with Prosperity *Earnings shown are the means of the 10 imputations; models were estimated using imputation-specific means

  27. Substitution of BEHALFTIME for FACETIME • Comparisons from bivariate probit model • Substitution of BEHALFTIME for FACETIME occurs as earnings rise • Effect is similar but: • smaller for blacks • smaller for high school graduates • larger for single parents Coping with Prosperity

  28. Conclusions • Conclusions • Primary hypothesis • Parents substitute BEHALFTIME for FACETIME as earnings rise • Secondary hypotheses • Substitution effect is larger for single parents • For women, schooling positively affects the likelihood of engaging in both FACETIME and BEHALFTIME as well as the amount of time; for men, it affects the likelihoods only Coping with Prosperity

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