Transcript Two Applications of Infrequency of Purchase and Double

Coping with Prosperity: The Response of Parents’
Coping
Prosperity:
ThetoResponse
of Parents’
Childwith
Care
Time Use
Rising Earnings
Child Care Time Use to Rising Earnings
James M. Payne
Friday Afternoon Research Group
November 15, 2013
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Coping with Prosperity
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
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Coping with Prosperity
Propositions
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
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Coping with Prosperity
Propositions
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
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Coping with Prosperity
Challenges
Challenges (1)
Wages   child care time use  is well established, but . . .
no studies have separated the income and price effects
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Coping with Prosperity
Challenges
Challenges (2)
Zeroes in time use data
A. 4 sources of zeroes
1. measurement error
2. the individual will not participate in the activity
3. corner solution
4. diary window is shorter than the consumption period
B. Log transformation cannot be used to reduce
heteroscedasticity
C. Tobit models common, but generate biased estimates
Gould (1992), Keen (1986), Daunfeldt and Hellström (2007),
Stewart (2009), Frazis and Stewart (2010)
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Coping with Prosperity
Challenges
Challenges (3)
Wage variable problems
--endogeneity
--sample selection bias
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Coping with Prosperity
Challenges
Challenges (4)
Missing income data in the Current Population Survey (CPS)
A. 34% missing wage data (2003) with negative selection
Heckman and LaFontaine (2006); 15.6% in my parents-only
ATUS sample
B. Census’ modified hot deck imputation produces match bias
Hirsch and Macpherson (2004), Bollinger and Hirsch (2006, 2010)
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Coping with Prosperity
Data
Data
American Time Use Survey (ATUS) 2003 – 2010
•
Initiated by Bureau of Labor Statistics (BLS), 2003
•
One-day time use diaries
•
Linked to CPS demographic and labor force data
•
n = 45,716
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Coping with Prosperity
Two dependent variables
Descriptive statistics
(minutes on diary day)
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Theoretical model
Coping with Prosperity
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 γ and price pp
• BEHALFTIME with share τ and price pb = pf
•γ + τ =1
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Theoretical model
Coping with Prosperity
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
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Coping with Prosperity
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 create
rEARNHR
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Coping with Prosperity
Multiple imputation
Challenges (4): Multiple imputation (MI) of
missing data
•
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
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Multiple imputation
Coping with Prosperity
Multiple imputation
• Impute all missing covariates
• Create m = 10 imputed data sets
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Coping with Prosperity
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
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Coping with Prosperity
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
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ATUS earnings data
Coping with Prosperity
• Two-step solution
1st step probit
(Heckman) for
WORKING = 1
2nd step OLS
(Heckman) for
rEARNHRhat
double hurdle
models with
x = rEARNHRhat
Instrument
for
endogeneity
(METRO*)
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Coping with Prosperity
Inverse hyperbolic sine
Challenges (2): Inverse hyperbolic sine
transformation of dependent variables
sinh-1y = ln( y + √ y2 + 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
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sinh-1
3
2
ln
1
0
-1
-2
-3
-4
-10
0
10
y
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Coping with Prosperity
Double-hurdle model
Challenges (2): 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: choosing whether to do the activity
• 2nd hurdle: choosing how much to do the
activity
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Estimation—Double hurdle
Coping with Prosperity
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
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Estimation—Double hurdle
Coping with Prosperity
Double hurdle results--FACETIME
Boldface effects are significant at α = .05
*Marginal effects at means of regressors
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Estimation—Double hurdle
Coping with Prosperity
Double hurdle results--BEHALFTIME
Boldface effects are significant at α = .05
*Marginal effects at means of regressors
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Coping with Prosperity
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
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Coping with Prosperity
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:
• P10 Q1 Median Q3 P90 P95 of rEARNHRhat
• P10 Q1 Median Q3 P90 of 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
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January, 2009
Substitution of BEHALFTIME for FACETIME
Coping with Prosperity
Sensitivity analysis—marginal effects from bivariate probit model
Age of youngest
child
(CHILDAGE )
0
P 10
2
Q1
6
Median
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Q3
15
P 90
Cell contents:
Hourly earnings (2003$) (rEARNHRhat)*
$2.69
$5.92
$9.61
$15.18
$18.55
$21.73
P 10
Q1
Median
Q3
P 90
P 95
-0.0798 1.4760 -0.0029 1.5610
-0.0541
-0.0019
-0.0955 1.3589 -0.0185 1.4439
-0.0702
-0.0128
-0.1580 0.8907 -0.0811 0.9757
-0.1774
-0.0831
0.0853
1.6583
0.0514
0.0696
1.5413
-0.4078
1.0731
0.0066
-5.2482
-0.1456
MEBEHALFTIME
MEFACETIME
MEBEHALFTIME /MEFACETIME
-0.8631
1.6880
0.1399
1.2198
0.1147
0.0618
0.6346
0.0973
-0.2831 -0.0457 -0.2061 0.0393 -0.1179 0.1367
†
0.2024
0.1199
-0.2362 0.3054 -0.1592 0.3904 -0.0710 0.4878
-0.7732
1.8051
0.1208
0.0452
0.0071
0.2181
0.0149
0.2834
0.0524
0.2977
1.8930
0.1572
0.2820
1.7759
0.1588
0.2195
1.3077
0.1679
0.1413
0.7225
0.1956
0.0944
0.3713
0.2543
0.3742
1.9776
0.1892
0.3586
1.8606
0.1927
0.2960
1.3923
0.2126
0.2179
0.8071
0.2700
0.1710
0.4559
0.3750
*Earnings shown are the means of the 10
imputations; models were estimated using
imputation-specific means
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Coping with Prosperity
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
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Conclusions
Coping with Prosperity
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
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