Coping with Prosperity: A Double Hurdle Approach to
Parents’ Earnings and
Coping with Prosperity: The Response of Parents’
Child
Care
Time
in the Earnings
ATUS
Child
Care
Time
UseUse
to Rising
James M. Payne
Calhoun Community College
November 23, 2015
1
Coping with Prosperity
Demand for human capital in children
Demand for human capital in children
Higher
earnings
More time
spent with
children
But where is the . . .
2
Coping with Prosperity
The unobserved substitution effect
?
market
services
b
a
{
I
own-time services
3
Coping with Prosperity
Data & model
Data
American Time Use Survey (ATUS)
&
Current Population Survey (CPS)
2003 – 2010
n = 45,716 parents
Model
Cragg’s (1971) Double Hurdle
4
Coping with Prosperity
Missing data
Challenge # 1: Missing Data
— Biased Census hot-deck imputation
15.6% missing earnings data
— Single-imputation methods
underestimate uncertainty
5
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
6
Coping with Prosperity
Sample selection and endogeneity
Challenge # 2: Sample Selection Bias
Challenge # 3: Endogeneity
7
Concurrent Heckman-IV approach
Coping with Prosperity
Concurrent approach*
1st step probit
(Heckman) for
WORKING = 1
Double hurdle
model with
x = earnings
2nd step OLS
(Heckman) for
earnings
Instrument
for
endogeneity
(METRO†)
*Millimet, 2001; Amemiya, 1985
†
𝛽𝑀𝐸𝑇𝑅𝑂 = 2.838; 𝑡 = 20.32
8
Coping with Prosperity
Heteroscedasticity with zeroes
Challenge # 4: Heteroscedasticity
with zero values in the data
9
Coping with Prosperity
Inverse hyperbolic sine
Inverse Hyperbolic Sine transformation
• Burbidge, et al. (1988)
sinh-1
• Defined for all
real numbers
ln
• Equivalent to a
log-linear model
𝒔𝒊𝒏𝒉−𝟏 (𝒚) = 𝒍𝒏 𝒚 + 𝒚𝟐 + 𝟏
10
Time use definitions
Coping with Prosperity
}
Purchases
+
BEHALFTIME
market
services
b
a
{
I
FACETIME
own-time services
11
Coping with Prosperity
Theoretical model
The issue: How will a higher hourly wage (w )
affect input prices and time use?
• pfacetime :
FACETIME
consists only of time, so pfacetime = w
𝜕𝑝𝑓𝑎𝑐𝑒𝑡𝑖𝑚𝑒
&
=1
𝜕𝑤
• pservices = γppurchases + τpbehalftime (weighted average of components)
𝜕 𝛾𝑝𝑝𝑢𝑟𝑐ℎ𝑎𝑠𝑒𝑠
•
= 0 (prices of purchases are orthogonal to w )
𝜕𝑤
𝜕 𝜏𝑝𝑏𝑒ℎ𝑎𝑙𝑓𝑡𝑖𝑚𝑒
𝜕𝑝𝑓𝑎𝑐𝑒𝑡𝑖𝑚𝑒
•
= τ (since
= 1, if pbehalftime = pfacetme )
𝜕𝑤
𝜕𝑤
𝜕𝑝𝑓𝑎𝑐𝑒𝑡𝑖𝑚𝑒
𝜕 𝑝𝑠𝑒𝑟𝑣𝑖𝑐𝑒𝑠
• So
= τ <1<
𝜕𝑤
𝜕𝑤
a higher wage reduces pservices relative to pfacetime , and thus
BEHALFTIME will be substituted for FACETIME
12
Coping with Prosperity
Propositions
Propositions
•
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
}
Greater
demand for
human
capital in
children
substitution
effect
13
Substitution of BEHALFTIME for FACETIME
Coping with Prosperity
Sensitivity analysis—marginal effects from bivariate probit model
Age of
youngest child
(CHILDAGE )
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
-0.080
0
P 10
1.476
-0.05
-0.095
2
Q1
1.359
Median
0.891
Q3
0.305
P 90
Cell contents:
-0.019
1.444
-0.081
0.976
-0.159
0.390
0.085
1.658
0.05
0.070
1.541
0.05
0.007
1.073
0.01
-0.071
0.488
-0.77 -0.41 -0.15
-0.2831
15
0.00
-0.18 -0.08
-0.236
11
1.561
-0.07 -0.01
-0.158
6
-0.003
-0.0457
†
-0.2061
0.0393
-0.1179
0.1367
-5.25 -0.86
MEBEHALFTIME
MEFACETIME
MEBEHALFTIME /MEFACETIME
0.218
1.805
0.12
0.202
1.688
1.220
0.635
0.220
1.308
0.141
0.722
0.20
0.2834
0.05
1.776
0.17
0.10
0.0149
0.282
0.16
0.11
0.062
1.893
0.16
0.12
0.140
0.298
0.0944
0.3713
0.25
0.374
1.978
0.19
0.359
1.861
0.19
0.296
1.392
0.21
0.218
0.807
0.27
0.1710
0.4559
0.38
n = 26,963 women
14
Double hurdle results
Coping with Prosperity
Double hurdle estimates:
Salient results, 1st hurdle probit
(n = 26,963 women)
FACETIME
marginal
marginal
VARIABLE
effect*
BEHALFTIME
p -value
effect*
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
*at means of regressors
15