Introduction
GSOEP Data
Econometric Model
Preliminary Results
Separating the Effects of Risk Attitudes, Cognitive
and Non-Cognitive Skills, Social Preferences and
Financial Aid in Schooling Decisions
Mathias ANDRÉ (École Polytechnique, CREST), Christian BELZIL
(École Polytechnique, ENSAE, IZA), François POINAS (Toulouse
School of Economics), Konstantinos TATSIRAMOS (IZA)
EALE Conference, Cyprus 2011
September 24, 2011
M. André, C. Belzil, F. Poinas, K. Tatsiramos
Separating Effects in Schooling Decisions
EALE Conference 2011
Introduction
GSOEP Data
Econometric Model
Preliminary Results
Outline
1 Introduction
2 GSOEP Data
Background Variables and Psychometric Questionnaire
3 Econometric Model
(Static) Factors Model
Modeling the Lottery
Behavioral Model : Likelihood and Identification
4 Preliminary Results
M. André, C. Belzil, F. Poinas, K. Tatsiramos
Separating Effects in Schooling Decisions
EALE Conference 2011
Introduction
GSOEP Data
Econometric Model
Preliminary Results
Motivation
Context
Decision to access higher education is multi-dimensional :
Cognitive skills
Preferences such as risk aversion :
Achievments are uncertain and one may lose investment
Future earnings distribution (e.g. variance) may depend on
schooling
Smoothing consumption vs. smoothing earnings
Personality traits such as Motivation (Locus of Control), "Big
Five" measures.
Economic context and financial opportunities
Human Capital : parental education, early childhood
investments, etc.
→ Difficulty to have direct measures of all these mechanisms
in practice and no unified framework.
M. André, C. Belzil, F. Poinas, K. Tatsiramos
Separating Effects in Schooling Decisions
EALE Conference 2011
Introduction
GSOEP Data
Econometric Model
Preliminary Results
Motivation
Objectives
Separating those determinants is challenging :
correlated with parental background
may have an individual specific component
identification issues
Separating those determinants is our primary objective
Such a deep analysis is "data hungry"
Cannot realistically be achieved without
factor analysis : Carneiro, Hansen and Heckman (2003)
a framework where Risk Aversion is directly measured : Belzil
and Leonardi (2007)
Our approach is tied to both Psychometrics (self-reported
measurements) and to Microeconomics (real life economic
choices)
M. André, C. Belzil, F. Poinas, K. Tatsiramos
Separating Effects in Schooling Decisions
EALE Conference 2011
Introduction
GSOEP Data
Econometric Model
Preliminary Results
Literature
At the “Cross-Roads” of several literatures
1
Non-Cognitive vs. Cognitive Skills/Schooling
Piatek, Pinger (2010), Bowles, Gintis, Osborne (2001)
Carneiro, Hansen, Heckman (2003), Heckman, Stixrud and
Urzua (2006), Cunha, Heckman, Schennach (2010)
2
Risk Aversion and Schooling
Lehvari, Weiss (1974), Dohmen et al. (2005), Belzil and
Leonardi (2007) with SHIW data (Bank of Italy) from a
Special Issue of Labour Economics
Sociological litterature : Holm, Jäger (2006)
3
Trust and Risk Taking
4
Liquidity and Borrowing Constraints
Fehr (2009), Bohnet and Zeckhauser (2004)
Keane and Wolpin (2001), Cameron and Heckman (1998),
Keane (2002)
M. André, C. Belzil, F. Poinas, K. Tatsiramos
Separating Effects in Schooling Decisions
EALE Conference 2011
Introduction
GSOEP Data
Econometric Model
Preliminary Results
What do we do ?
Overview
We estimate a “semi-structural” model of Schooling decisions
of German youth (from age 17)
We use German Socio Economic Panel (GSOEP) between
2000 and 2009 with scolarity trajectory and labor income.
We have data on choices, parental background, covariates and
26 measurements on :
Skills : Cognitive and Non-Cognitive
Preferences : Social Pref. and Risk Aversion
3 Financial Opportunities : Parental Income and Grant
1
2
Measurements are collected at age 17, and their
distribution is conditional on history and covariates.
M. André, C. Belzil, F. Poinas, K. Tatsiramos
Separating Effects in Schooling Decisions
EALE Conference 2011
Introduction
GSOEP Data
Econometric Model
Preliminary Results
What do we do ?
Methodology
Application of Factors Models as Carneiro, Hansen, Heckman
(2003) by maximum likelihood with measurement errors and a
simulated random part for factors.
Two parts in the likelihood : Extraction of the distribution of
Factors and Estimation of the discrete choice model.
German schooling system is particular with two main tracks :
academic (Gymnasium) and professional (early tracking at 11).
With a simple behavioral model, we study the probability of
entering Higher Education separately for academic and non
academic.
M. André, C. Belzil, F. Poinas, K. Tatsiramos
Separating Effects in Schooling Decisions
EALE Conference 2011
Introduction
GSOEP Data
Econometric Model
Preliminary Results
What do we do ?
Structure of the Model
Factors decomposed as a sum of
individual specific (random) term
a component that depends on
parental background and covariates,
Early-Tracking/High-school status (academic track or not)
Determinants of education function of 6 distinct elements :
1
2
3
4
5
6
cognitive skills
non-cognitive skills
risk aversion (Lottery and Risk Attitudes questions)
social preferences (Trust and positive Reciprocity)
parental income
government financial aid
We want to compare parameters for academic individuals to
the non academic version of the model : early tracking policy.
M. André, C. Belzil, F. Poinas, K. Tatsiramos
Separating Effects in Schooling Decisions
EALE Conference 2011
Introduction
GSOEP Data
Econometric Model
Preliminary Results
Outline
1 Introduction
2 GSOEP Data
Background Variables and Psychometric Questionnaire
3 Econometric Model
(Static) Factors Model
Modeling the Lottery
Behavioral Model : Likelihood and Identification
4 Preliminary Results
M. André, C. Belzil, F. Poinas, K. Tatsiramos
Separating Effects in Schooling Decisions
EALE Conference 2011
Introduction
GSOEP Data
Econometric Model
Preliminary Results
Background Variables and Psychometric Questionnaire
Measuring Risk Attitudes
Lottery question :
"Imagine you had won 100,000 Euros in a lottery. Almost
immediately after you collect, you receive the following
financial offer from a reputable bank, the conditions of which
are as follows: There is the chance to double the money within
two years. It is equally possible that you could lose half of the
amount invested."
Individuals decide on a share sh that must be chosen among :
0%, 20%, 40%, 60%, 80%, 100%.
3 Risk attitudes Likert-type scale questions in specific context :
General, Financial and Occupation
M. André, C. Belzil, F. Poinas, K. Tatsiramos
Separating Effects in Schooling Decisions
EALE Conference 2011
Introduction
GSOEP Data
Econometric Model
Preliminary Results
Background Variables and Psychometric Questionnaire
Measuring Skills and Social Preferences
13 Questions on Non-cognitive skills (Locus of control and
Conscientiousness from the Big Five dimensions) :
7 points Likert scale (from “strongly agree” to “strongly
disagree”)
Examples : “Life depends on me”, “I have not what I deserve”,
“Need to work hard to succeed”...
6 Questions on Social preferences (Trust and Reciprocity)
7 points Likert scale
Example: “On the whole, one can trust people”
3 Cognitive skills scores of the Amthauer’s test
Verbal abilities
Numerical abilities
Figural abilities
−→ K = 26 measurement questions
M. André, C. Belzil, F. Poinas, K. Tatsiramos
Separating Effects in Schooling Decisions
EALE Conference 2011
Introduction
GSOEP Data
Econometric Model
Preliminary Results
Background Variables and Psychometric Questionnaire
Financial Aid to go to University
Means-tested transfer scheme (depends on parental income
and taxes), called Bafög.
Half of the financial aid is a grant and the other half is a loan.
The maximum amount is 585 monthly euros and it depends on
parental income :
585
if PInc ≤ 1, 440
Grant =
Max(0; 585 − (PInc − 1, 440)/2) if PInc > 1, 440
M. André, C. Belzil, F. Poinas, K. Tatsiramos
Separating Effects in Schooling Decisions
EALE Conference 2011
Introduction
GSOEP Data
Econometric Model
Preliminary Results
Background Variables and Psychometric Questionnaire
Covariates and Parental Background
The 8 other Covariates are :
Indicators of being in the Gymnasium track (at age 17),
gender, indicator if individual is born in former East Germany
Indicators if father and mother has attended Gymnasium,
Household size, Number of siblings between 0-14 when
individual is aged 17
M. André, C. Belzil, F. Poinas, K. Tatsiramos
Separating Effects in Schooling Decisions
EALE Conference 2011
Introduction
GSOEP Data
Econometric Model
Preliminary Results
Background Variables and Psychometric Questionnaire
Structure of the Sample
Missing data are supposed random : distribution of factors may be
"extrapolated" accross calendar years :
Data \ Year
Questions type :
lottery (1q)
risk attitudes (2q)
general risk (1q)
non cognitive (13q)
cognitive (3q)
social preferences (6q)
Sample size
2004
2005
2006
2007
X
X
X
X
310
X
X
307
X
X
X
X
254
X
X
X
X
291
Choices are measured since 2000. Because of selection issues, we
keep only individuals more than 23 years old. Sample size is 2276.
M. André, C. Belzil, F. Poinas, K. Tatsiramos
Separating Effects in Schooling Decisions
EALE Conference 2011
Introduction
GSOEP Data
Econometric Model
Preliminary Results
Background Variables and Psychometric Questionnaire
Composition of the Sample and Choices
Academic Status at age 17
Track
Frequency
Percentage
Professional (P)
1455
64%
Academic (G)
821
36%
Total
2276
100%
Choices by Group Likelihood
Choices \ Group
Academic
Non Academic
Other
60% (487)
92% (1345)
40% (334)
8% (110)
Higher Education
Total
100% (821)
100% (1455)
Other : Apprenticeship, Vocational School, Work or Inactivity.
M. André, C. Belzil, F. Poinas, K. Tatsiramos
Separating Effects in Schooling Decisions
EALE Conference 2011
Introduction
GSOEP Data
Econometric Model
Preliminary Results
Outline
1 Introduction
2 GSOEP Data
Background Variables and Psychometric Questionnaire
3 Econometric Model
(Static) Factors Model
Modeling the Lottery
Behavioral Model : Likelihood and Identification
4 Preliminary Results
M. André, C. Belzil, F. Poinas, K. Tatsiramos
Separating Effects in Schooling Decisions
EALE Conference 2011
Introduction
GSOEP Data
Econometric Model
Preliminary Results
(Static) Factors Model
Modeling Factors : Motivation, Social Preferences and
Cognitive Skills
Each Fj is the sum of two orthogonal parts : a deterministic
and a random (unobserved to the econometrician) component :
Fj = Fj + Fj∗ with Fj∗ ∼ N(0, σF2j )
The deterministic part is linear in parental background :
Fj =
10
X
φrj · xr
r =1
where xr covariates and φrj estimated parameters.
M. André, C. Belzil, F. Poinas, K. Tatsiramos
Separating Effects in Schooling Decisions
EALE Conference 2011
Introduction
GSOEP Data
Econometric Model
Preliminary Results
(Static) Factors Model
Measurement Equations
Psychometric questions are discrete ordered variable Mk ,
driven by a continuous latent variable Mk∗
Latent variables are linear in factors :
Mk∗ = αk +
4
X
αjk · Fj +εk for k = 1, 2, ...K
j=1
|
{z
mk∗
}
where εk ∼ N(0, σk ) is the measurement error term.
These apply to Risk (not Lottery), Non-cognitive skills, Social
Preferences, and Cognitive tests.
We need to impose some constraints on the α’s (restrictions).
M. André, C. Belzil, F. Poinas, K. Tatsiramos
Separating Effects in Schooling Decisions
EALE Conference 2011
Introduction
GSOEP Data
Econometric Model
Preliminary Results
Modeling the Lottery
Extracting the Structural Risk Aversion
From the lottery question, six possible responses for the
amount invested : individuals decide on a share sh of
x = 100, 000 invested in the lottery that goes from
0%, 20%, 40%, 60%, 80%, 100%.
Assuming CRRA utility function, expected utility is :
U(sh , x) =
((1 − sh )x)1−RAi
β 2 (2sh x)1−RAi
β 2 (0.5sh x)1−RAi
+
+
1 − RAi
2 1 − RAi
2
1 − RAi
where RAi = exp{
10
X
2
φrj · xr + RA∗i } and RA∗ ∼ N(µra , σra
)
r =1
M. André, C. Belzil, F. Poinas, K. Tatsiramos
Separating Effects in Schooling Decisions
EALE Conference 2011
Introduction
GSOEP Data
Econometric Model
Preliminary Results
Modeling the Lottery
Modeling the Lottery
We represent the probabilistic optimal choice (from the
perspective of the econometrician) as a multi-variate probit
model.
Ui∗ (.) = U(sh ; RAi ) + κih
with {κih=0.0 , κih=0.2 , κih=0.4 , κih=0.6 , κih=0.8 , κih=1.0 } ∼ N(0, Σ)
The probability that individual i chooses fraction h, is given by :
Pr(∀k 6= h, Ui∗ (sh ; RAi ) > Ui∗ (sk ; RAi ))
= Pr(∀k 6= h, U(sh ; RAi ) − U(sk ; RAi ) > κik − κih )
M. André, C. Belzil, F. Poinas, K. Tatsiramos
Separating Effects in Schooling Decisions
EALE Conference 2011
Introduction
GSOEP Data
Econometric Model
Preliminary Results
Behavioral Model : Likelihood and Identification
Behavioral Model : logit specification
Two distinct set of parameters for each probability of entering
Higher Education.
(Binary) Logit specification for g ∈ {A, NA}:
P(HE | i ∈ g ) =
where Ui∈g
e Ui ∈g
1 + e Ui ∈g
= α0g + αRA,g · RAi + αNC ,g · NCi
+ αCO,g · COi + αSP,g · SPi + αX ,g · Xi
M. André, C. Belzil, F. Poinas, K. Tatsiramos
Separating Effects in Schooling Decisions
EALE Conference 2011
Introduction
GSOEP Data
Econometric Model
Preliminary Results
Outline
1 Introduction
2 GSOEP Data
Background Variables and Psychometric Questionnaire
3 Econometric Model
(Static) Factors Model
Modeling the Lottery
Behavioral Model : Likelihood and Identification
4 Preliminary Results
M. André, C. Belzil, F. Poinas, K. Tatsiramos
Separating Effects in Schooling Decisions
EALE Conference 2011
Introduction
GSOEP Data
Econometric Model
Preliminary Results
Estimation results
Estimates of Probabilities
Marginal impacts of factors and covariates :
Variable/Proba.
Cognitive Ability
Non Cognitive
Risk Aversion
Social Pref.
Income
Financial Aid
Academic
0.044(0.0136)???
0.009(0.001)???
0.008(0.0036)??
0.025(0.0031)???
−0.010(0.0113)
0.069(0.0140)???
Non Academic
0.014(0.0113)?
0.003(0.001)???
−0.018(0.003)???
0.007(0.0022)???
−0.003(0.003)
−0.063(0.0161)???
In st. dev. unit and 10 ke for monetary variables (standard errors with 1%, 5% and 10 % stars).
Fit with simulated and observed trajectories :
Probabilities
Observed Choices
Simulated Choices
Estimated Mean Prob.
M. André, C. Belzil, F. Poinas, K. Tatsiramos
Separating Effects in Schooling Decisions
Academic
0.645
0.602
0.642
Non Academic
0.091
0.091
0.090
EALE Conference 2011
Introduction
GSOEP Data
Econometric Model
Preliminary Results
Estimation results
Estimates of Factors
Average value of factors for each track :
Factor/Track
Cognitive Ability
Non Cognitive
Risk Aversion
Social Pref.
Sample Size
Academic
2.709
0.0002
3.876
0.004
352
Non Academic
-0.629
-0.131
3.855
-0.042
761
Factors’ moments :
Factor/Moment
Cognitive Ability
Non Cognitive
Risk Aversion
Social Pref.
M. André, C. Belzil, F. Poinas, K. Tatsiramos
Separating Effects in Schooling Decisions
Mean
0.635
-0.077
3.822
-0.030
St. Dev. FA
1.888
0.109
0.524
0.137
St. Dev. FR
0.016
0.010
0.016
0.018
FA+FR
1.888
0.109
0.528
0.138
EALE Conference 2011
Introduction
GSOEP Data
Econometric Model
Preliminary Results
Estimation results
Estimates of Probabilities : Auxiliary model
Marginal impacts of factors and covariates only academic :
Variable/Proba.
Cognitive Ability
Non Cognitive
Risk Aversion
Social Pref.
Income
Financial Aid
Abitur
0.114(0.0185)???
0.004(0.0007)???
0.029(0.0061)???
0.001(0.0005)?
0.029(0.0050)???
−0.044(0.0105)???
Higher Ed.
0.004(0.0202)
0.002(0.0009)??
0.008(0.0083)
.011(0.0020)???
0.019(0.0071)??
0.197(0.0326)???
In st. dev. unit and 10 ke for monetary variables (standard errors with 1%, 5% and 10 % stars).
Fit with simulated and observed trajectories :
Probabilities
Observed Choices
Simulated Choices
Estimated Mean Prob.
M. André, C. Belzil, F. Poinas, K. Tatsiramos
Separating Effects in Schooling Decisions
Abitur
0.788
0.733
0.696
H. Ed.
0.748
0.725
0.753
Uncond. H. Ed.
0.589
0.531
0.521
EALE Conference 2011
Introduction
GSOEP Data
Econometric Model
Preliminary Results
Final Comments
Conclusion
We implemented a Factors model of schooling choices taking
into account various of dimensions : skills, preferences and
financial ressources.
Distribution of factors :
Same risk aversion but different for other factors (less for NA)
Standard deviations driven by non orthogonal part
Distinct effects of factors :
Non cognitive skills significant but less than 1%.
Risk Aversion : education as an insurance (+) for academics
and as a risky asset (-) for non academics.
Social Preferences positive for entering higher education :
2.5% for Acad. but 0.7% for Non Acad.
M. André, C. Belzil, F. Poinas, K. Tatsiramos
Separating Effects in Schooling Decisions
EALE Conference 2011
Introduction
GSOEP Data
Econometric Model
Preliminary Results
Final Comments
The End
Thank you.
M. André, C. Belzil, F. Poinas, K. Tatsiramos
Separating Effects in Schooling Decisions
EALE Conference 2011
Introduction
GSOEP Data
Econometric Model
Preliminary Results
Final Comments
Appendix : Two Parts of the Likelihood
Choices ci of individual i in group g (G1 or G2) : Choices
Y Y
e Uk,i ∈g
P(k|i ∈ g )1(ci =k) with P(ci = k|i ∈ g ) = X
e Uk 0 ,i ∈g
i=1 1≤g ≤2 k∈Cg
| {z } |{z}
k 0 ∈Cg
n
Y
groups choices
Measurements mk,i of individual i of question 1 ≤ k ≤ K
(nk modalities)
n
Y
K
Y
nk
Y
i=1
k=1
|{z}
|{z}
P(Mk,j )1(mk,i =Mk,j ) with
j=1
measures modalities
∗
∗
P(mk,i = Mj,k ) = Φ(αj+1,k − mk,i
) − Φ(αj,k − mk,i
)
M. André, C. Belzil, F. Poinas, K. Tatsiramos
Separating Effects in Schooling Decisions
EALE Conference 2011