SeparatingtheEﬀectsofRiskAttitudes,Cognitive andNon ... · Mathias ANDRÉ (École Polytechnique,...

Introduction Overview of Literature Data Econometric Model Very Preliminary Results

Separating the Effects of Risk Attitudes, Cognitiveand Non-Cognitive Skills, Trust and Financial Aid

in Schooling Decisions

Mathias ANDRÉ (École Polytechnique, CREST), Christian BELZIL

(École Polytechnique, ENSAE, IZA), François POINAS (ToulouseSchool of Economics), Konstantinos TATSIRAMOS (IZA)

Internal Seminar, CREST-LMI

January 12, 2011

Internal Seminar CREST-LMI

Separating Effects in Schooling Decisions


Outline

1 Introduction

2 Overview of Literature

3 DataGerman Socio Economic Panel and Background VariablesPsychometric questionnaire

4 Econometric ModelFactors Model à la Cunha & HeckmanLikelihood and Identification

5 Very Preliminary Results




Context and Framework

Motivation

Usual determinants of higher education : cognitive skills,parental backgrounds and other covariates, liquidityconstraints.Deeper in the individual usually unobserved heterogeneity(caracteristics or preferences) :

Non cognitive skills and personality traits (or socialpreferences),Risk aversion, risk perceptionSocial preferences, early childhood investments, etc.

Difficulty to have direct measures in practice (LC unmeasuredby definition) and no unified framework.





Remarks on Risk InfluenceRisky accumulation process of human capital : uncertainties onreturn to schooling

Risks of success/failure (imperfect information set)Uncertainty of finding a job after graduating, about the realquality of diploma (wage distribution unknown)Education can also be an insurance against risks on the labormarket and have an effect on risk exposure (incomefluctuations, unemployement, etc.).Imperfections on loan markets (no consensus about returns toschooling) can cause liquidity constraints and uncover therisks.

Can risk aversion influence schooling choices ?





Framework (1/2)

We use German Socio Economic Panel (GSOEP) between2000 and 2008 with personality questionnaire, risk attitudesand background variables. We have scolarity choices and laborincome.Our approach is tied to both Psychometrics (self-reportedmeasurements) and to Economics (real life economicoutcomes, not only tests).German schooling system is particular with two main tracks :academic (Gymnasium) and professional. It is called earlytracking because children are selected at age 11.





Framework (2/2)

With a simple behavioral model, we study different choices :Occupational choices for professionnal track (P)Drop out (G1) and continuation probability to university (G2)for academic.

Application of Factors Models as Carneiro, Hansen, Heckman(IER 2003) by maximum likelihood with measurement errorsand a simulated random part for factors.We will use Heckman & Singer’s framework for trueunobserved heterogeneity for the financial aid variable.Two parts in the likelihood : Extraction of the distribution ofFactors and Estimation of the discrete choice model.





Outline

1 Introduction








Related works

Factors Models and Noncognitive Skills

Cunha, Heckman (AER 2007, JHR 2008), Heckman, Stixrud,Urzua (JLE 2006)Cunha, Heckman, Schennach (Ecta 2010) :

Non linear dynamic factors (CS and NCS with endogenousparental investments) non parametrically identified (linearlyestimated on CNLSY) with additive measurement errors termsImportance of measurement errors, of timing of investments,of self-productivity effects (only cross for NCS on CS)

IZA Workshop (01/2011): Cognitive and Non-Cognitive Skills




Related works

Risk Aversion and Schooling Decisions

Lehvari, Weiss (AER 1974), Belzil, Hansen (2004), Brodaty,Gary-Bobo, Prieto (2010)Special Issue of Labour Economics (2007), Sociologicallitterature (Holm, Jäger (2006))Belzil, Leonardi (2007) :

Given high school completion, continuing to higher educationnegatively correlated with risk aversion.Individual differences in risk aversion almost as important asparents’ educational background and with good explanatorypower (e.g. resp. 30% against 55% of variance)But no direct measure of heterogeneity.

Dohmen et al. (2005) : good quality of the GSOEP.




Related works

Behavorial models and social preferences

Bohnet, Zeckhauser (2004), Fehr (2009) :Role of trust in social and market transactions (beliefs)Behavioral and statistical evidence that trust is not just aspecial case of risk taking (using GSOEP)If risky context, trust can be a critical ingredientImperfect measure and need of link it with risk behavior




Related works

The Liquidity constraints question

Leslie (1984), Keane (AER 2002)Keane, Wolpin (IER 2001) :

Methodological contribution (simulated likelihood withclassification errors, form of EMAX, terminal period).Structural estimation (dynamic school/work model withsavings decisions).LC exist but no impact on enrollment, substantial parentaltransfers increase attendance.




Outline

1 Introduction








German Socio Economic Panel and Background Variables

German schooling system and Choices diagramEarling tracking (age 11) : Professionnal (Apprenticeship,Vocational) versus Academic (Gymnasium). If Abitur iscompleted, one can enter higher education (University).

Initial Condition

Academic Track

AP

G1G1 VG1

W

IG1

Abitur

G2

AP

V

W

I

U

Professional Track

AP

PVP

WP

I

P

1





Covariates

The 10 Covariates are :Indicators of being in the Gymnasium track (at age 17),gender, indicator if individual is born in former East GermanyIndicators if father and mother has attended Gymnasium(cross product), Household size, Number of siblings between0-14 when individual is aged 17Yearly per capita income and Government-provided financialaid for higher education (in thousands of 2005 euros)

This Financial Aid Indicator is very useful (see below).





Financial Aid to go to University

It is a means-tested transfer scheme depending on parentalincome, taxes and social contributions.Half of the financial aid is paid as a grant and the other half asa loan that has to be repaid after completion of tertiaryeducation.The maximum monthly amount of financial aid is 585 Euros(fully granted if monthly parents’ income less than 1,440Euro). The part of parents’ income exceeding the threshold iswithdrawn at a rate of 50% :

Grant ={

585 if Inc ≤ 1, 440Max(0; 585− (Inc − 1, 440)/2) if Inc > 1, 440





Descriptive Statistics

Variables/Moda 1 Freq. Percent.Female 1238 49.6Mother Educ. 374 15.2Father Educ. 442 18.2Born in East G. 686 27.5

Table: Binary Covariates

Note : Education is indicator forfinishing Gymnasium

Variables Mean Std. Dev. MaxHousehold 4.1 1.23 13Siblings 0.5 0.83 7Income 10.5 6.13 99.03Grant 2.44 2.91 7.0

Table: Other Covariates

Note : Money amount are yearlyand in ’000 euros 2005.




Psychometric questionnaire

Measuring Attitudes and Skills (1/2)

Cognitive skills (3q) : Score based on the IST-2000R testdeveloped by Amthauer et al. (2001) with 3 components :verbal, numerical, and figural abilities.Non cognitive skills and Social preferences (10q+3q):Personality questionnaire based on the Big Five dimensionsfrom Psychology; Trust on other people, society etc.(motivation, social preferences, values, perception of outsideworld, etc.)General risk question (1q) :

"How do you see yourself: Are you generally a person who is fullyprepared to take risks or do you try to avoid taking risks?"





Measuring Attitudes and Skills (2/2)

Risk attitudes (6q) : Same question but in specific context(car driving, financial matters, leisure and sports, career, andhealth)Lottery (1q) :

"Imagine you had won 100,000 Euros in a lottery. Almostimmediately after you collect, you receive the following financialoffer from a reputable bank, the conditions of which are as follows:There is the chance to double the money within two years. It isequally possible that you could lose half of the amount invested."−→ K = 24 measurement questions





Structure of the Sample (1/2)

Timing of the model is :1 At age 11, children are distributed in Tracks : Professionnal

(P) or Academic (G). Everything will be conditional on it.2 At age 17 (or around for University), they have a distribution

for factors and make choices according to them and their X’s.

We have realized choices for ??? individuals.We only estimate factors distributions on 17-year oldindividuals (between ?? and ?? non missing questions).Three types of individuals in the data :

Only schooling choices ??Only psychometric questionnaire for factors ??In both parts of the likelihood ??





Structure of the Sample (2/2)

Missing data are supposed random, years of interview are :

Data \ Year 00-03 2004 2005 2006 2007 2008Questions type :lottery (1q) - X - - - -risk taking (6q) - X - - - -general risk (1q) - X - X X -non cognitive (10q) - - X X X -cognitive (3q) - - - X - -trust (3q) - - - X X -Choices X X X X X XSample size 1278 328 315 269 305 .

Note: Entries marked by an ”X ” denote a year over which aspecific set of questions has been administered.





Composition of the Sample : Choices

Academic Status at age 17Track Frequency PercentageProfessional (P) 1467 58.8%Academic (G) 1028 41.2%Total 2495 100%

Choices in Percentage by Group Likelihood Choices Tree

Choices \ Group Professional (P) Academic (G1) If completed Abitur (G2)Apprenticeship 45% 9% 4%Vocational 17% 7% 1%Work 13% 3% 10%Inactivity 25% 6% 16%Complete Abitur - 75% (G2) -Higher Education - - 69%Total 100% 100% 100%




Outline

1 Introduction








Factors Model à la Cunha & Heckman

Modeling FactorsWe define 4 factors Fj : risk aversion (denoted RA), cognitiveability (denoted CO), non cognitive skills or motivation(denoted MO) and social preferences or trust (denoted TR).Each Fj is the sum of two orthogonal parts : a deterministiccomponent and a random (unobserved to the econometrician)component which follows a Normal distribution :

Fj = Fj + F ∗j with F ∗j ∼ N(0, σ2Fj) for 1 ≤ j ≤ 4

The deterministic part is linear in covariates and writes :

Fj =10∑

r=1

φrj · xr

where xr covariates and φrj estimated parameters.





Measurement Equations

Psychometric questions are discrete ordered variable and notedMk , each driven by a continuous latent variable M∗kLatent variables are linear in factors :

M∗k = αk +4∑

j=1

αkj · Fj︸︷︷︸

m∗k

+εk for k = 1, 2, ...K

where εk ∼ N(0, σk) is the measurement error term.These measurements are extracted from four groups ofquestions (Risk, NCS, Social Preferences, tests) so that weimpose some constraints on the α’s (see exclusion restrictions).





Restrictions on Factors

Not a strictly statistial approach : limitation of number offactors (4) and exclusion constraints are imposed.Exclusion restrictions (on αk

j ’s) are :

type of question # of questions RA MO CO TRlottery 1 X . . .

risk taking 6 X X X Xgeneral risk 1 X X X X

non-cognitive 10 . X . Xtrust 3 . . . X

cognitive 3 . X X .





Extracting the Structural Risk AversionFrom the lottery question, six possible responses for theamount invested : sh = h

5 for h = 0, ..., 5 is the proportion ofx = 100, 000 invested in the lottery.Assuming CRRA utility function, payoff is :

U(sh, x) =((1− sh)x)1−RAi

1− RAi+0.5

(2shx)1−RAi

1− RAi+0.5

(0.5shx)1−RAi

1− RAi

With an additional randorm term N (0, σL) (expected utilityunobserved to the econometrician ex ante) and known fixedthresholds th, the likelihood of answering sh ∈ [th, th+1] is :

Φ(U(th+1, x)

σL)− Φ(

U(th, x)

σL)




Likelihood and Identification

Behavioral Model : logit specificationOccupational Choices :

1 Professional Track (group P) : k ∈ CP1 = {AP,V ,W , I}2 Gymnasium Track (group G1) : k ∈ CG1 = {AP,V ,W , I ,AB}

Continuation Probability (if Abitur, group G2) :k ∈ CG2 = {AP,V ,W , I ,HE}Logit specification for choice k in group g ∈ {P,G1,G2}:

P(k | i ∈ g) =exp(Uk,i∈g )∑

k ′∈Cgexp(Uk ′,i∈g )

for k ∈ Cg

where Uk,i∈g = α0kg + αRA,k,g · RAi + αMO,k,g ·MOi

+ αCO,k,g · COi + αTR,k,g · TRi + αX ,k,g · Xi





Two Parts of the LikelihoodChoices ci of individual i in group g (P, G1 or G2) : Choices

n∏i=1

∏1≤g≤3︸︷︷︸groups

∏k∈Cg︸︷︷︸choices

P(k |i ∈ g)1(ci=k) with P(ci = k |i ∈ g) =eUk,i∈g∑

k ′∈Cg

eUk′,i∈g

Measurements mk,i of individual i of question 1 ≤ k ≤ K(nk modalities)

n∏i=1

K∏k=1︸︷︷︸

measures

nk∏j=1︸︷︷︸

modalities

P(Mk,j)1(mk,i=Mk,j ) with

P(mk,i = Mj ,k) = Φ(αj+1,k −m∗k,i )− Φ(αj ,k −m∗k,i )





Identification

Theorems of Heckman and coauthors (2003, 2010) : nonparametric identification of non linear factors models withendogenous inputsWith constraints on parameters :

Identification for linear factors model : αk = 0, σk = 1 for1 ≤ k ≤ K and φi = 0 for 1 ≤ i ≤ 4 (resp. intercept andstandard errors in measurement equations and intercept indeterministic part of factors). Because we identify allthresholds in probit models of measurement equations.Identification of logit models in groups P, G1 and G2 :αi,I = 0 and βk,i,I = 0 for factor 1 ≤ i ≤ 4 and choice1 ≤ k ≤ 2 (I - inactivity- is the reference modality)




Outline

1 Introduction








Estimation results

Estimates of FactorsImportance of Factors with respect to measurement errors :

σk√V(Fj )

reported by type of measurement equations

Ratio/Q Risk NCS Cog. Sk. Trust<0.7 1 3 . 1[0.7;1.3] 5 1 . 1>1.3 2 6 3 1

Covariance between deterministic part of Factors :RA MO CO TR

RA 1506 . . .MO -1016 3016 . .CO -1403 -187 2325 .TR -2424 -704 3575 7484

Table: Covariances

Note : Sum of Variances is S =14330.54

RA MO CO TRRA 1 . . .MO -.48 1 . .CO -.75 -.07 1 .TR -.72 -.15 .12 1

Table: Correlation Matrix




Estimation results

Estimates of Probabilities

Effects on probabilities :Variable/Proba. Appr. (P) Appr. (G1) Univ. (G2)Risk Aversion 0.53 -8.89 5.66Cognitive ability 6.87 0.68 -9.91Motivation -6.42 -3.49 1.38Trust (Social P.) 0.33 -4.72 3.58Financial Aid -5.06 -1.86 -3.43Father’s Educ. -7.93 -2.83 -4.26

Standard errors still non reliable and may need to bebootstrappedWe will report marginal effects and percent correctly predicted




Final Comments

Conclusion

Optimization of the likelihood is currently running in Fortran,waiting for final and more reliable results (691-214=417estimated parameters).We implemented a Factors model of schooling choices takinginto account various of dimensions : cognitive and noncognitive skills, risk aversion and liquidity constraintsExtensions : with Gymnasium, personality may evolve(dynamic risk aversion) and additional unobservedheterogeneity in the Financial Aid variable.




Final Comments

The End

Thank you.




Final Comments

Some questions on personality

Do you agree with these statements ? (Pick boxes between"Totally agree" and "Totally disagree")

NCS (10) : Life depends on me, I have not what I deserve,Achievements in life is fate or luck, Social activity can affectsocial conditions, Others influence life, Work hard to succeed,etc.Trust (3) : one can trust people, one can’t rely on anyone,better to be careful with strangers.



SeparatingtheEﬀectsofRiskAttitudes,Cognitive andNon ... · Mathias ANDRÉ (École Polytechnique,...

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