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

Rising Earnings

James M. PayneCalhoun Community College

November 23, 2015

Coping with Prosperity: A Double Hurdle Approach to Parents’ Earnings

and Child Care Time Use in the ATUS

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Demand for human capital in children

But where is the . . .

Coping with Prosperity Demand for human capital in children

Higher earnings

More timespent withchildren

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?

Coping with Prosperity The unobserved substitution effect

marketservices

a

b

{I

own-time services

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DataAmerican Time Use Survey (ATUS)

&Current Population Survey

(CPS)2003 – 2010

n = 45,716 parents

Coping with Prosperity Data & model

ModelCragg’s (1971) Double Hurdle

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15.6% missing earnings data

Coping with Prosperity Missing data

Challenge # 1: Missing Data

— Biased Census hot-deck imputation

— Single-imputation methodsunderestimate uncertainty

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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

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Coping with Prosperity Sample selection and endogeneity

Challenge # 2: Sample Selection Bias

Challenge # 3: Endogeneity

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Coping with Prosperity

Concurrent approach*

Concurrent Heckman-IV approach

1st step probit (Heckman) for WORKING = 1

2nd step OLS (Heckman) for

earnings

Instrument for

endogeneity

(METRO)

Double hurdle model with x = earnings

† �̂�𝑀𝐸𝑇𝑅𝑂=2.838 ;𝑡=20.32*Millimet, 2001; Amemiya, 1985

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Coping with Prosperity Heteroscedasticity with zeroes

Challenge # 4: Heteroscedasticity with zero

values in the data

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Coping with Prosperity Inverse hyperbolic sine

Inverse Hyperbolic Sine transformation

sinh-1

ln

𝒔𝒊𝒏𝒉−𝟏(𝒚 )=𝒍𝒏 (𝒚+√𝒚𝟐+𝟏 )

• Burbidge, et al. (1988)

• Defined for all real numbers

• Equivalent to alog-linear model

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Coping with Prosperity Time use definitions

marketservices

a

b

{I

own-time services

Purchases +

BEHALFTIME

FACETIME

}

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Coping with Prosperity

The issue: How will a higher hourly wage (w ) affect input prices and time use?

• pfacetime : FACETIME consists only of time, so pfacetime = w & = 1

• pservices = γppurchases + τpbehalftime (weighted average of components)

• = 0 (prices of purchases are orthogonal to w )• = τ (since = 1, if pbehalftime = pfacetme )

• So = τ < 1 <

a higher wage reduces pservices relative to pfacetime , and thus BEHALFTIME will be substituted for FACETIME

Theoretical model

𝜕 (𝛾𝑝 h𝑝𝑢𝑟𝑐 𝑎𝑠𝑒𝑠 )𝜕𝑤

𝜕 (𝜏 𝑝 h𝑏𝑒 𝑎𝑙𝑓𝑡𝑖𝑚𝑒 )𝜕𝑤

𝜕 (𝑝𝑠𝑒𝑟𝑣𝑖𝑐𝑒𝑠 )𝜕𝑤

𝜕𝑝 𝑓𝑎𝑐𝑒𝑡𝑖𝑚𝑒

𝜕𝑤

𝜕𝑝 𝑓𝑎𝑐𝑒𝑡𝑖𝑚𝑒

𝜕𝑤𝜕𝑝 𝑓𝑎𝑐𝑒𝑡𝑖𝑚𝑒

𝜕𝑤

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• 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

Propositions

Coping with Prosperity Propositions

Greaterdemand forhumancapital inchildren

substitutioneffect

}

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Coping with Prosperity Substitution of BEHALFTIME for FACETIME

Sensitivity analysis—marginal effects from bivariate probit model

-0.080 1.476 -0.003 1.561 0.085 1.658 0.218 1.805 0.298 1.893 0.374 1.978

-0.095 1.359 -0.019 1.444 0.070 1.541 0.202 1.688 0.282 1.776 0.359 1.861

-0.158 0.891 -0.081 0.976 0.007 1.073 0.140 1.220 0.220 1.308 0.296 1.392

-0.236 0.305 -0.159 0.390 -0.071 0.488 0.062 0.635 0.141 0.722 0.218 0.807

-0.2831 -0.0457 -0.2061 0.0393 -0.1179 0.1367 0.0149 0.2834 0.0944 0.3713 0.1710 0.4559

Hourly earnings (2003$) (rEARNHRhat)*

$2.69 $5.92 $9.61 $15.18 $18.55 $21.73

P 95

-0.05 0.00 0.05 0.12 0.16 0.19

P 90P 10 Q 1 Median Q 3

0.21

-0.07 -0.01 0.05 0.12 0.16 0.19

-0.18 -0.08 0.01 0.11 0.17

0.38

-0.77 -0.41 -0.15 0.10 0.20 0.27

† -5.25 -0.86 0.05 0.25

Age of youngest child

(CHILDAGE )

Q 3

P 90

P 100

2

6

11

15

Q 1

Median

MEBEHALFTIME MEFACETIME

MEBEHALFTIME/MEFACETIMECell contents: n = 26,963 women

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Coping with Prosperity Double hurdle results

Double hurdle estimates: Salient results, 1st hurdle probit

(n = 26,963 women)

*at means of regressors

VARIABLE p-value p-value

EARNINGS 0.010 <0.001 0.010 <0.001

CHILDAGE -0.041 <0.001 -0.006 <0.001

SINGLEPARENT -0.033 0.168 0.057 0.031

WORKHOURS -0.003 <0.001 -0.001 0.005

FACETIME BEHALFTIMEmarginal

effect*

marginal

effect*