Patience and Altruism of Parents: Implications for Children’s Education Investment Jinghao Yang Thesis Advisor: Professor Steven N. Durlauf Department of Economics, University of Wisconsin - Madison
March 29, 2015
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Overview
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Motivation • Parents care about their children, and they invest in their
children, in particular human capital. • Human capital investment is an intergenerational problem faced by households • Patience and altruism are two possible important factors involved in this problem • It is difficult to empirically estimate these parameters.
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Literatures on Household Intergenerational Investment • Fundamental works on intergenerational investment, such as
Aiyagari et al. (2002); Becker and Tomes (1979, 1986), do not capture the multi-period feature of childhood, and thus cannot distinguish the effect of parents’ patience. • There are sensitive periods for child investment (Cunha and
Heckman, 2007, 2008). • Borrowing constraints for investment decisions (Cunha et al.,
2010; Lochner and Monge-Naranjo, 2011). • Recent works, such as Caucutt and Lochner (2012); Lee and
Seshadri (2014), have taken multi periods of investments into account. 4 / 31
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Goals of this Paper • Investigate the comparative static effects of parents’ patience
and altruism in multi-period childhood investment. • To achieve this, we need to estimate a simplified model of
intergenerational investments with credit constraints. • Uncover the corresponding policy implications.
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Outline of this Paper • Model • Estimation • Calibration • Discussion & Conclusion
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Model
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Set-ups • Two generations of agents: parents and children. • No borrowing and no saving: credit constraint is zero. • A representative household facing their investment problem in
their children.
ߠ
ܫଵ Early Childhood
ߠଵ
ܫଶ
ߠଶ
Parents
Later Childhood
Figure 1: Two-period investment model illustration 8 / 31
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Object Function
Ua = ln ca,1 + β ln ca,2 + ρβ ln θ2 , s.t. ca,t + It = Yt where subscript a denotes adult and subscript t denotes period t, t ∈ {1, 2}. β – parental patience, ρ – parental altruism. Yt refers to income in period t, It refers to child investments in period t, c refers to parental consumption, and θ2 refers to skill level of children at the end of period 2.
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Skill Production Technology Production technologies for children’s skill levels (θ1 and θ2 ) are: θ1 = α0 I1α1 θaα2 θ2 =
γ0 I2γ1 θaγ2 θ1γ3
(1) (2)
Then, we take the logarithm: ln θ1 = ln α0 + α1 ln I1 + α2 ln θa
(3)
ln θ2 = ln γ0 + γ1 ln I2 + γ2 ln θa + γ3 ln θ1
(4)
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Skill Production Technology Functions Solving for FOCs and plugging credit constraints of two periods give the following: ρβγ3 α1 Y1 1 + ρβγ3 α1 ργ1 Y2 I2∗ = 1 + ργ1
I1∗ =
(5) (6)
Taking the ratio of eq.(5) and (6) gives: I2∗ γ1 + ρβγ3 α1 γ1 Y2 = ∗ I1 βργ3 α1 γ1 + βγ3 α1 Y1
(7)
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Estimation
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Data • Los Angeles Family and Neighborhood Survey (LAFANS) • A longitudinal survey with two waves of data (2000 & 2006) • Child skills (cognitive and non-cognitive) and parental skills
(cognitive) • cognitive: Woodcock Johnson Achievement Scores • non-cognitive: Behavioral Problems Index
• Proxies for parental investment • material investments: magazines, newspapers, PC’s, books • emotional investments: hugging and praising the child • Background controls
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Measures investments
wjr
bpi
human capital
weekly homework
letter word index
anxiety
expulsion
reading books
passage comprehension
headstrong
applied problems
anti-social
outdoor activities classroom volunteer attend school events magazines
grade repeitition school misbehavior
hyperactive
skipping school
peer influence
trouble with teacher
depression
daily newspaper number of books computer
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Regression Model To estimate the parameters in eq.(7) I2∗ γ1 + ρβγ3 α1 γ1 Y2 = , I1∗ βργ3 α1 γ1 + βγ3 α1 Y1 we will need to recall eq.(3)-(4): ln θ1 = ln α0 + α1 ln I1 + α2 ln θa ln θ2 = ln γ0 + γ1 ln I2 + γ2 ln θa + γ3 ln θ1 Plugging (3) into (4) gives: ln θ2 = γ3 α1 ln I1 + γ1 ln I2 + (γ2 + γ3 α2 ) ln θa + ln γ0 + γ3 ln α0
(8) 15 / 31
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Regression Model We create an investment index to contain all the investment proxies, and then we jointly estimate the factor model with the following production functions: ln childskill1 = ln α0 + α1 ln invind1 + α2 ln PCGskill + α3 childage1 + α4 PCGage1 + ε1 ln childskill2 = ln γ0 + γ1 ln invind2 + γ2 ln PCGskill + γ3 ln childskill1 + γ4 childage2 + γ5 PCGage2 + ε2 To capture the heterogeneities of skill production across ages, we divide the children into two age groups based on their ages in 2000: • Age 2-6 in 2000 (i.e. Wave I) • Age 7-11 in 2000 (i.e. Wave I) 16 / 31
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Figure 2: Table of Regression Results Dependent Variable
Letter-Word Identification score Age 2-6
Age Group
Inverted Behavioral Problem Index
Age 7-11 II
I
Age 2-6
Wave Number
I
II
I
Investment in Wave 1
0.158**
0.062
0.12
(0.075)
(0.048)
(0.079)
Age 7-11 II
I
II
0.176*** (0.055)
Investment in Wave 2
0.103**
0.129***
0.166**
(0.049)
(0.039)
(0.074)
(0.053)
Child Skill Level in Wave 1
0.325***
0.423***
0.389***
0.459***
(0.093)
(0.053)
0.219***
(0.082)
(0.075)
0.255***
0.072
0.238***
0.189***
0.09
-0.007
0.035**
-0.064
(0.080)
(0.065)
(0.050)
(0.048)
(0.079)
(0.061)
(0.049)
(0.044)
PCG Skill Level
Sample Size
421
461
433
460
Significance Levels: *** 1%, ** 5% Age group refers to the child age in the Wave 1 of LAFANS.
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Calibration
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Calibration Model To we have estimated the parameters in eq.(7) I2∗ γ1 + ρβγ3 α1 γ1 Y2 = , ∗ I1 βργ3 α1 γ1 + βγ3 α1 Y1 we will need to recall eq.(8): ln θ2 = γ3 α1 ln I1 + γ1 ln I2 + (γ2 + γ3 α2 ) ln θa + ln γ0 + γ3 ln α0
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Table 1: Rate of Return of Parental Investments across Periods
Parameter
LWI Score Age 2-6 Age 7-11
Inverted BPI Age 2-6 Age 7-11
Rate of Return in Wave I
γ3 α1
0.051
0.026
0.046
0.081
Rate of Return in Wave II
γ1
0.103
0.129
0.166
0.219
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Estimated Ranges of Patience and Altruism By Frederick et al. (2002); Nishiyama (2000), we have: Variable
Range
β ρ Y2 /Y1
[0.8, 1.0] [0.5, 0.7] [0.4, 2.0]
Patience β is in annual term. Y2 is derived based on LAFANs dataset, and we assume 6-year where Y 1 interest rates is about r = 5%.
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0
.2
Density .4
.6
.8
Figure 3: Histogram of Family Annual Income Ratio - Most observations 2 fall into the interval of [0.4, 2.0], which gives range of Y Y1 for calibration.
0
1
2 family annual income ratio
3
4
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Figure 4: Investment Ratio - Income Ratio (Letter Word Identification Score, age 2-6) Simulated I /I with lwi score, β=∈[0.8, 1], ρ∈[0.5, 0.7] 2 1
Investment Ratio I2/I1
15
10
optimal level β=0.8 ρ=0.5 β=0.8 ρ=0.6 β=0.8 ρ=0.7 β=0.9 ρ=0.5 β=0.9 ρ=0.6 β=0.9 ρ=0.7 β=1.0 ρ=0.5 β=1.0 ρ=0.6 β=1.0 ρ=0.7
5
0 0.4
0.6
0.8
1 1.2 1.4 Family Earn Ratio Y /Y 2
1.6
1.8
2
1
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Figure 5: Investment Ratio - Income Ratio (Letter Word Identification Score, age 7-11) Simulated I2/I1 with lwi score, β=∈[0.8, 1], ρ∈[0.5, 0.7] 40 35
Investment Ratio I2/I1
30 25 20
optimal level β=0.8 ρ=0.5 β=0.8 ρ=0.6 β=0.8 ρ=0.7 β=0.9 ρ=0.5 β=0.9 ρ=0.6 β=0.9 ρ=0.7 β=1.0 ρ=0.5 β=1.0 ρ=0.6 β=1.0 ρ=0.7
15 10 5 0 0.4
0.6
0.8
1 1.2 1.4 Family Earn Ratio Y /Y 2
1.6
1.8
2
1
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Figure 6: Investment Ratio - Income Ratio (Inverted Behavioral Problems Index, age 2-6) Simulated I2/I1 with bpi score, β=∈[0.8, 1], ρ∈[0.5, 0.7] 30
Investment Ratio I2/I1
25
20
15
optimal level β=0.8 ρ=0.5 β=0.8 ρ=0.6 β=0.8 ρ=0.7 β=0.9 ρ=0.5 β=0.9 ρ=0.6 β=0.9 ρ=0.7 β=1.0 ρ=0.5 β=1.0 ρ=0.6 β=1.0 ρ=0.7
10
5
0 0.4
0.6
0.8
1 1.2 1.4 Family Earn Ratio Y /Y 2
1.6
1.8
2
1
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Figure 7: Investment Ratio - Income Ratio (Inverted Behavioral Problems Index, age 7-11) Simulated I /I with bpi score, β=∈[0.8, 1], ρ∈[0.5, 0.7] 2 1
20 18 16
Investment Ratio I2/I1
14 12 10
optimal level β=0.8 ρ=0.5 β=0.8 ρ=0.6 β=0.8 ρ=0.7 β=0.9 ρ=0.5 β=0.9 ρ=0.6 β=0.9 ρ=0.7 β=1.0 ρ=0.5 β=1.0 ρ=0.6 β=1.0 ρ=0.7
8 6 4 2 0 0.4
0.6
0.8
1 1.2 1.4 Family Earn Ratio Y /Y 2
1.6
1.8
2
1
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Discussion & Conclusion
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Discussion • The horizontal blue line is the optimal investment ratio without ∗
credit constraints, i.e.
I2 I1∗
=
γ1 (1+r ) . α1 γ3
• The comparative static effect of patience β is much larger than
that of altruism ρ. • Given a household’s income ratio: • holding altruism ρ constant, as parental patience rises, the optimal investment ratio falls. • holding patience β constant, as parental altruism increases, the
optimal investment ratio decreases.
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Conclusion • Ideally, childhood investment programs would include parents’
patience and altruism to determine the optimal subsidization level to the disadvantaged households. • An alternative is to raise the credit availability to low-income
families up to a level that credit availability is no longer binding their children’s investment. • Lastly, intervention programs can cover the whole childhood of
the participants to avoid the high cost to remedy a lack of investment in the early childhood period.
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Future Research • Investment index versus latent investment via factor analysis • Zero credit constraints versus non-zero credit constraints • Skill formation versus human capital accumulation
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Acknowledgements I am immensely grateful to my advisor, Prof. Steven Durlauf, for his invaluable guidance and support and to the insightful discussions with Prof. Kenneth West and Prof. Noah Williams. I also thank Kegon Tan for his great help and comments to my writing of this paper. The Honors Summer Senior Thesis Research Grant funded by the University of Wisconsin-Madison L&S Honors Program is gratefully acknowledged.
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References
Aiyagari, S., J. Greenwood, and A. Seshadri (2002). Efficient investment in children. Journal of Economic Theory 102 (2), 290 – 321. Becker, G. S. and N. Tomes (1979, December). An equilibrium theory of the distribution of income and intergenerational mobility. Journal of Political Economy 87 (6), 1153–1189. Becker, G. S. and N. Tomes (1986). Human capital and the rise and fall of families. Journal of Labor Economics 4 (3), pp. S1–S39. Caucutt, E. M. and L. Lochner (2012, October). Early and late human capital investments, borrowing constraints, and the family. Department of Economics, University of Western Ontario. Cunha, F. and J. Heckman (2007). The technology of skill formation. American Economic Review 97 (2), 31–47. Cunha, F. and J. J. Heckman (2008). Formulating, identifying and estimating the technology of cognitive and noncognitive skill formation. Journal of Human Resources 43 (4), 738–782. 31 / 31
References
Cunha, F., J. J. Heckman, and S. M. Schennach (2010). Estimating the technology of cognitive and noncognitive skill formation. Econometrica 78 (3), pp. 883–931. Frederick, S., G. Loewenstein, and T. O’Donoghue (2002). Time discounting and time preference: A critical review. Journal of Economic Literature 40 (2), 351–401. Lee, S. Y. and A. Seshadri (2014, January). On the intergenerational transmission of economic status. Department of Economics, University of Wisconsin - Madison. Lochner, L. J. and A. Monge-Naranjo (2011). The nature of credit constraints and human capital. American Economic Review 101 (6), 2487–2529. Nishiyama, S. (2000, October). Measuring time preference and parental altruism. Technical Paper Series 2000-7, Congressional Budget Office. 31 / 31
