1. Estimating the Causal Effect of Children on Parents’ Well-being
Strengths and Weaknesses of an Instrumental Variable Approach
Gerrit Bauer
Thorsten Kneip
Dominik Steinbeißer

2. Motivation
“The belief that parenthood makes people happier seems to be rather pervasive across the world” (Hansen, 2012, p33)
“[…] adding virtually nothing to life, apart from perpetual difficulty and worry” (Donath, 2015, p359)
“As well as providing reasons to expect the more satisfied to have higher fertility, the literature also provides other reasons which might lead one to expect lower fertility among the more satisfied” (Parr, 2010, p639)
“[…] there is no reason to expect that parents will have better or worse lives than nonparents” (Deaton & Stone, 2014, p1328)
“One of the central questions in the analysis of subjective well-being is whether people adapt to conditions. If this is the case, then […] conditions or circumstances may not matter, in the long run at least. ” (Clark et al., 2008, p222)

3. Different Research Questions & Methods
Cross sectional
Twin-FE FE IV
Parenthood
Deaton & Stone (2014)
Kohler et al. (2005)
Myrskylä & Margolis (2014) ?
Higher parities
Margolis & Myrskylä (2011)
# of children
Stutzer & Frey (2006)
(In-)direct effects
Alesina et al. (2004)
Pollmann-Schult (2014)
Dynamic effects
Frijters et al. (2011)
Reverse effect
Aassve et al. (2016)

4. Better Methods or Data?
“Unfortunately, even the most advanced statistical approaches that have been used in this research fail to handle all […] problems, so reported results should be interpreted very cautiously” (Kravdal, 2014, p263)

5. Different Research Questions & Methods
Cross sectional
Twin-FE FE IV
Parenthood
Deaton & Stone (2014)
Kohler et al. (2005)
Myrskylä & Margolis (2014) ?
Higher parities
Margolis & Myrskylä (2011)
# of children
Stutzer & Frey (2006)
(In-)direct effects
Alesina et al. (2004)
Pollmann-Schult (2014)
Dynamic effects
Frijters et al. (2011)
Reverse effect
Aassve et al. (2016)

6. Distinguishing Causal Structures
#kids
happy
#kids
happy
#kids
happy
#kids
happy
#kids
happy

7. Distinguishing Causal StructuresIV
#kids
happy IV
#kids
happy IV
#kids
happy IV
#kids
happy IV
#kids
happy

8. Distinguishing Causal StructuresIV
#kids
happy IV
#kids
happy X IV
#kids
happy IV
#kids
happy X IV
#kids
happy X

9. Distinguishing Causal Structures
twins
#kids
happy
twins
#kids
happy X
twins
#kids
happy
twins
#kids
happy X
twins
#kids
happy X

10. Identifiability of the Total Causal Effect

11. Assuming Conditional Exogeneity
twins
#kids
happy
age
infertility
child mortality
education
+ FE

12. Estimated Effects
Men
Women
POLS + controls FE
FE + controls IV
IV + controls
FE-IV
FE-IV + controls -1
-.75
-.5
-.25
.25 .5
.75 1
1.25
1.5 -1
-.75
-.5
-.25
.25 .5
.75 1
1.25
1.5
Source: pairfam 7.0 W1-W7; own calculations 3,495 obs. in 11,823 obs. years; 321 twin years
POLS

13. Identifiability of the Direct Effect

14. Mediation or Confoundedness?
Men
Women
.25 .5
.75 1
1.25
-.75
-.5
-.25
.25 .5
basic IV
+ hh income
+ income
+ workload
+ housework
+ pregnant
+ sleep
+ health
+ marrdur
+ cohabdur
+ reldur
+ relsat
+ socsat
+ sexsat

15. Identifiability of the Direct Effect

16. Identifiability of the Indirect Effect

17. Lessons Learned
IV can help identify total causal effects in the presence of
confounders
reverse causality
mediatiors correlated to the error of the treatment

18. Lessons Learned IV
non-IV

19. Lessons Learned
IV can help identify total causal effects in the presence of
confounders
reverse causality
mediators correlated to the errors of treatment or oucome
In case of doubt:
Do not control variables that might be mediators or confounders of the treatment and outcome
IV hardly relaxes the assumptions for identifying direct & indirect causal effects (unless the mediator is also instrumented)

20. Lessons Learned IV
non-IV

21. Thank you

22. Example
labour orientation
income
twins
#kids
happy
family orientation

23. Costs of Children Women Men Effect on Happiness Effect on Happiness1 1
0,5
0,5
Effect on Happiness
Effect on Happiness
-0,5
-0,5
-12 -6 6 12 18 24 30
36+
-12 -6 6 12 18 24 30
36+
Months before and after birth
Months before and after birth
Note: 4025 Respondents in Observations
Note: 4318 Respondents in Observations
total effect
direct effect

24. Discussion of findings
According to the IV estimator, more children lead to an increase in happiness for men, but not women.
OLS and FE estimates are insignificant for both men and women.
Results substantially consistent over models for women, but not for men
Possible reasons:
OLS/FE: Ommitted variable bias
OLS/FE: Over-control
IV: Exclusion restriction does not hold
Comparability of estimates across different model types?
(N)ATE vs. ATT vs. LATE vs. LATT
FE Models exploit different sample: those begetting children/twins (i.e. have young children)
Result transferable to transition into parenthood?
What if effects were only transitory?