Understanding the Income Gradient in College Attendance in Mexico: The Role of Heterogeneity in Expe

1
Understanding the Income Gradient in College
Attendance in Mexico The Role of Heterogeneity
in Expected Returns to College

• Katja Maria Kaufmann
• Stanford University

2
Motivation

• Empirical fact
• Strong positive correlation between parental
  income and childrens college enrollment in
  Mexico.

3
Motivation
College Enrollment Students of Different Income
Quintiles in of Student Body
Richest 20
Poorest 40
4
Motivation
College Enrollment Students of Different Income
Quintiles in of Student Body
Richest 20
Poorest 40
Enrollment Rates 16 20
23 39 55
TA
5
Questions of Interest

• College attendance decision
• Why are enrollment rates so low among poor
  Mexicans, and what explains the large differences
  between the poor and the rich?
• 2. Implications for the design of policies to
  improve college access
• What are potential welfare gains of policies such
  as student loans?

6
Challenge

• Educational Choice under Uncertainty
• Earnings Expectations
• Preferences
• Credit Constraints

Sources of unobserved heterogeneity
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Challenge

• Educational Choice under Uncertainty
• Earnings Expectations
• Preferences
• Credit Constraints
• There is a fundamental identification problem
  concerning the separation of preferences, market
  structures and agent information sets.
• (See Manski (2004) and Cunha and Heckman (2007).)

Sources of unobserved heterogeneity
8
Challenge

• Educational Choice under Uncertainty
• Earnings Expectations
• Preferences
• Credit Constraints
• There is a fundamental identification problem
  concerning the separation of preferences, market
  structures and agent information sets.
• (See Manski (2004) and Cunha and Heckman (2007).)

Sources of unobserved heterogeneity
9
Earnings Expectations Conventional Approach

• Example Simple school choice rule
• Problems
• Counterfactual earnings are unobserved.
• Information sets at time of decision are
  unobserved.

Conventional Approach Infer earnings
expectations from earnings realizations.
10
Earnings Expectations Subjective Expectations
Approach

• Example Simple school choice rule

Subjective Expectations Approach Elicit
information on individuals expected earnings for
both scenarios of college attendance choice,
and .
11
Literature on Subjective Expectations

• Subjective expectations of earnings/income
• Overview Manski (2004)
• Schooling Dominitz and Manski (1996), Attanasio
  and Kaufmann (2007), Jensen (2007).
• Income expectations Guiso, Jappelli and
  Pistaferri (2002), Attanasio, Meghir and
  Vera-Hernandez (2005) on income expectations in
  Colombia.

12
Literature on Income Gradient in College
Enrollment

• Earnings Expectations Expected gross returns
• Preferences Costs
• Credit Constraints (direct, financing,
  psychic)

13
Literature on Income Gradient in College
Enrollment

• Earnings Expectations Expected gross returns
• Preferences Costs
• Credit Constraints (direct, financing,
  psychic)
• Large literature in the US Examples

Carneiro and Heckman (2002), Cameron and Taber
(2004) Low enrollment among the poor due to
lack of college readiness ? Low returns to
college.
Card (2001) Low enrollment among poor due to
high marginal costs and not to low marginal
returns.
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Subjective Expectations and the Questions of
Interest

• Data on subjective expectations help
• To address why college enrollment rates are so
  low among poor Mexicans and why differences
  between the poor and the rich are large.
• ? Driven by differences in expected (monetary)
  returns or in college attendance costs?
• 2. To take into account that peoples beliefs
  about future earnings based on their information
  set (ex ante expected returns) matter for their
  choice.
• ? Particularly important in developing country
  context with large unpredictable income shocks.

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Policy Implications

• Are there individuals with high expected returns
  at the margin of attending college, who would
  decide to attend in response to certain policies?
• ? Scope for policy interventions if this is due
  to
• Credit constraints, which would imply
  underinvestment in human capital and thereby
  impede economic development and growth.
• Psychological costs/time preferences, if there
  are important externalities and external returns
  are correlated with private returns.

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Preview of Results

• Low college enrollment among poor Mexicans and
  differences between poor and rich individuals
• Primarily driven by higher costs for the poor.
• Poor individuals are significantly more
  responsive to changes in direct costs (consistent
  with poor households being credit constrained).
• The introduction of policies such as a student
  loan program could lead to large welfare gains
• A sizeable fraction of poor Mexicans would change
  their college attendance decision in response to
  such a policy.
• Individuals at the margin of attending have
  higher expected returns than those who are
  already attending.

17
Outline

• Data Description
• Household survey data with information on
  subjective expectations
• Data on educational costs
• Model of College Attendance Choice
• Model set-up and use of subjective expectations
• Test 1 Do the poor and the rich differ in their
  cost distributions?
• Test 2 Do the poor exhibit excess sensitivity
  w.r.t. changes in direct costs?
• Counterfactual Policy Experiments
• Introduction of a student loan program
• Comparison Average expected return of
  individuals at the margin versus average expected
  return of individuals attending college.
• Conclusion

18
Outline

• Data Description
• Household survey data with information on
  subjective expectations
• Data on educational costs
• Model of College Attendance Choice
• Model set-up and use of subjective expectations
• Test 1 Do the poor and the rich differ in their
  cost distributions?
• Test 2 Do the poor exhibit excess sensitivity
  w.r.t. changes in direct costs?
• Counterfactual Policy Experiments
• Introduction of a student loan program
• Comparison Average expected return of
  individuals at the margin versus average expected
  return of individuals attending college.
• Conclusion

19
Survey Data

• 2005 Survey Jovenes con Oportunidades (cash
  incentive program for high school completion in
  Mexico).
• Eligibility criteria individuals in grade 9 to
  12, whose families are Oportunidades
  beneficiaries.
• Sample used here 3,680 high school graduates.

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Survey Data

• 2005 Survey Jovenes con Oportunidades (cash
  incentive program for high school completion in
  Mexico).
• Eligibility criteria individuals in grade 9 to
  12, whose families are Oportunidades
  beneficiaries.
• Sample used here 3,680 high school graduates.

Sample representative of about the poorest third
of the HS grad population.
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Survey Data

• Information
• High School Graduate present and past schooling,
  GPA of junior high school, and demographic
  background.
• Household parental education, labor earnings and
  income, household assets and transfers.
• Module on subjective expectations of earnings for
  both scenarios of college attendance choice.

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Data Subjective Expectations

• Probability of working
• Assume that you finish High School (College)
  and that this is your highest schooling degree.
  From zero to one hundred, how certain are you
  that you will be working at the age of 25?

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Data Subjective Expectations

• Probability of working
• Assume that you finish High School (College)
  and that this is your highest schooling degree.
  From zero to one hundred, how certain are you
  that you will be working at the age of 25?
• Earnings distribution
• Assume that you finish High School (College)
  and that this is your highest degree. Assume that
  you have a job at age 25.
• (a) What do you think is the maximum amount you
  can earn per month at that age?
• (b) What do you think is the minimum amount you
  can earn per month at that age?
• (c) From zero to one hundred, how certain are
  you that your earnings at that age will be at
  least x (midpoint)?

Scale
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Individual Earnings Distribution
Assumption triangular distribution (compare
Guiso, Jappelli, Pistaferri (2002) and Attanasio
and Kaufmann (2007))

• Compute moments for each individual for both
  high school and
• college degree

25
Deriving Expected Returns

• For each individual
• Compute expected log earnings
• Compute expected (gross) returns to college

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Is the Data on Subjective Expectations of
Earnings Informative?

• First Check
• Are Expected Returns Important Determinants (and
  thus Good Predictors) of College Attendance
  Choices?
• ? Probit of College Attendance on Expected Returns

Real
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Probit Attend College or not
28
Probit Attend College or not
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Data on College Attendance Costs

• Tuition and enrollment costs
• Median costs per year are 700 pesos (around 14
  of median yearly per capita parental income).
• (data source National Association of Univ. and
  Institutes of Higher Education (2004))

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Data on College Attendance Costs

• Tuition and enrollment costs
• Median costs per year are 700 pesos (around 14
  of median yearly per capita parental income).
• (data source National Association of Univ. and
  Institutes of Higher Education (2004))
• Distance to closest university
• Costs of living vary depending on the distance
  to university.
• ? Economies of scale of living with family
  versus costs for room and board (see Card
  (1993)).
• (data source Dep. of Education (SEP) for
  location of universities and geocode data from
  the National Institute of Statistics, Geography
  and Information (INEGI))

JUMP
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Timing of the Survey and Attendance Decision
July/August Individuals with HS degree Decide
about College Attendance
Mid August/Sept Classes start
Oct/Nov Survey eliciting information on
subjective expectations.
32
Timing of the Survey and Attendance Decision
July/August Individuals with HS degree Decide
about College Attendance
Mid August/Sept Classes start
Oct/Nov Survey eliciting information on
subjective expectations.
Assumption Expectations elicited in Oct/Nov are
the same as the ones people use in July/Aug to
decide whether to attend college or not.
33
Timing of the Survey and Attendance Decision
July/August College Attendance Decision
Mid August/Sept Classes start
Oct/Nov Survey eliciting Information on
subjective expectations.

• Feb to June
• Entrance exams
• Updating information
• about skills compared
• to peers.

• December
• First exams
• at college
• Additional
• info updating

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Robustness concerning Timing of the Survey

• Would want to observe expected earnings of the
  High School Graduates
• two/three months earlier before their college
  decision
• ? Comparison of cross-sections of expected
  earnings
• of High School Graduates who are at college or
  work, i.e. after their college choice
• with the following counterfactual
• 2) individuals who are one year younger (begin
  grade 12) before their college choice.

35
Robustness concerning Timing of the Survey

• Would want to observe expected earnings of the
  High School Graduates
• two/three months earlier before their college
  decision
• ? Comparison of cross-sections of expected
  earnings
• of High School Graduates who are at college or
  work, i.e. after their college choice
• with the following counterfactual
• 2) individuals who are one year younger (begin
  grade 12) before their college choice.

• No evidence
• of ex-post
• justification
• of college choice

36
Outline

• Data Description
• Household survey data with information on
  subjective expectations
• Data on educational costs
• Model of College Attendance Choice
• Model set-up and use of subjective expectations
• Test 1 Do the poor and the rich differ in their
  cost distributions?
• Test 2 Do the poor exhibit excess sensitivity
  w.r.t. changes in direct costs?
• Counterfactual Policy Experiments
• Introduction of a student loan program
• Comparison Average expected return of
  individuals at the margin versus average expected
  return of individuals attending college.
• Conclusion

37
Model of College Attendance Choice

• An individual chooses to go to college (S1) at
  age 18, if
• Assumptions
• Individuals face an interest rate which is
  unobserved.
• Individuals enter the labor market with zero
  experience and then experience evolves
  deterministically. Return to experience is the
  same in both schooling states and for every
  individual.

lt__
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Generalized Roy Model and Subjective Expectations

• Potential outcome equations for high school and
  college degree
• where denotes the anticipated part of the
  unobservable
• and denotes the unanticipated part.

39
Generalized Roy Model and Subjective Expectations

• Potential outcome equations for high school and
  college degree
• where denotes the anticipated part of the
  unobservable
• and denotes the unanticipated part.
• ? Individuals base their decision on ,
  which is unobserved for the researcher, but
  predictable by the individual. Can be captured by
  subjective expectations.

40
Generalized Roy Model and Subjective Expectations

• Individuals base their decision on ,
  which is unobserved for the researcher. Can be
  captured by subjective expectations
• Use in model of college attendance using the
  approximation
• together with assumptions on experience.

MO
2-PM
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Model of College Attendance Choice

• An individual decides to attend college or not
  based on the following decision rule
• where the expected gross return is given by

42
Outline

• Data Description
• Household survey data with information on
  subjective expectations
• Data on educational costs
• Model of College Attendance Choice
• Model set-up and use of subjective expectations
• Test 1 Do the poor and the rich differ in their
  cost distributions?
• Test 2 Do the poor exhibit excess sensitivity
  w.r.t. changes in direct costs?
• Counterfactual Policy Experiments
• Introduction of a student loan program
• Comparison Average expected return of
  individuals at the margin versus average expected
  return of individuals attending college.
• Conclusion

43
Test 1 Comparison of Cost Distributions

• Participation equation (as derived from model of
  college attendance) is additively separable
  between expected return and overall costs of
  college attendance

K(C,r,)
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Test 1 Comparison of Cost Distributions

• Derive a distribution of overall costs of college
  attendance making use of data on
• Individuals expected returns
• Individuals college attendance choice
• And the assumption
• Implementation Locally weighted linear
  regression of S on expected return
• ? Compare cumulative distribution function of
  costs, , for different income groups.

ReDis
45
Test 1 Comparison of Cost Distributions
46
Test 1 Comparison of Cost Distributions
47
Test 1 Comparison of Cost Distributions
SL
48
Test 1 Comparison of Cost Distributions
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Test 1 Comparison of Cost Distributions -
Conclusions

• The poor face significantly higher overall costs
  of college attendance.
• ? Is this driven by higher financing costs for
  the poor?

50
Outline

• Data Description
• Household survey data with information on
  subjective expectations
• Data on educational costs
• Model of College Attendance Choice
• Model set-up and use of subjective expectations
• Test 1 Do the poor and the rich differ in their
  cost distributions?
• Test 2 Do the poor exhibit excess sensitivity
  w.r.t. changes in direct costs?
• Counterfactual Policy Experiments
• Introduction of a student loan program
• Comparison Average expected return of
  individuals at the margin versus average expected
  return of individuals attending college.
• Conclusion

51
Test 2 Credit Constraints

• Prediction of the model in the case of credit
  constraints
• Intuition People facing a high interest rate are
  more sensitive to changes in direct costs.
• Robustness of Test
• Prediction not specific to my model (see Cameron
  and Taber (2004)).
• Concern in conventional approaches
• the expected return is an omitted variable and
  potentially correlated with direct costs or
  interest rate.
• ? Test is more robust using subjective
  expectations.

2-P M
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Test 2 Credit Constraints

• Conventional approach
• Using subjective expectations

Expected gross returns
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Test 2 Credit Constraints

• Conventional approach
• Using subjective expectations
• Implementation
• a) Use proxies for being credit constrained.
• Parental income (and wealth), as it determines
  the ability to collateralize and to receive loans
  from a bank.
• b) Use distance to college and tuition as
  measures of direct cost

Expected gross returns
54
Attend College or not
Direct costs
55
Attend College or not
Proxy for Credit Constraints
56
Attend College or not
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Test 2 Credit Constraints

• Additional advantage of subjective expectations
  based on the following
• idea
• Being poor does not necessarily mean being credit
  constrained.
• It is a combination of being poor and having high
  returns that generates binding credit
  constraints.
• ? Subjective expected returns allows to test the
  prediction of the model for individuals who are
  more likely to face binding credit constraints.

58
Attend College or not (Full Sample)
59
Attend College or not (Adol. Sample)
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Test 2 Credit Constraints - Conclusions

• Results show excess responsiveness of poor
  high-expected return individuals to changes in
  direct costs, which is consistent with credit
  constraints playing an important role in
  affecting college attendance.
• Use of subjective expectations allows for a more
  robust test. My results suggest that omitting
  expected returns could lead to underestimating
  the importance of credit constraints.

61
Outline

• Data Description
• Household survey data with information on
  subjective expectations
• Data on educational costs
• Model of College Attendance Choice
• Model set-up and use of subjective expectations
• Test 1 Do the poor and the rich differ in their
  cost distributions?
• Test 2 Do the poor exhibit excess sensitivity
  w.r.t. changes in direct costs?
• Counterfactual Policy Experiments
• Introduction of a student loan program
• Comparison Average expected return of
  individuals at the margin versus average expected
  return of individuals attending college.
• Conclusion

62
Counterfactual Policy Experiments

• Counterfactual Policy Experiments
• Change in direct costs (distance to college), and
• Change in interest rate ? simulate introduction
  of student loan program.
• Derive the average expected returns of
  individuals changing their attendance decision in
  response to the policy (average marginal
  return), and compare it to the average return of
  those attending.
• ? Apply LIV methodology (see, e.g., Carneiro,
  Heckman and Vytlacil (2005) and Heckman and
  Vytlacil (2005)) to model of college attendance
  as introduced before.

RDist
Real
63
Counterfactual Policy Experiments

• There are individuals with high expected returns
  who do not attend
• college, but who would change attendance in
  response to the policy.

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Conclusion

• Low college enrollment rates among poor Mexicans
• Not mainly driven by low expected returns
• sizeable fraction of individuals with high
  expected returns are not attending college
• Policies such as student loans could increase the
  poors access to college and could lead to
  important welfare improvements.
• 2. Subjective expectations
• Direct information on one important determinant
  of school choice (relax assumptions about
  individuals information sets).
• ? Help to address the concern that correlation
  between income and enrollment is driven by
  systematic differences in beliefs/information
  sets.

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Extensions/Future Work

• Model of school choice allowing for risk aversion
  (using subjective measures from lotteries) and
  taking into account perception of earnings and
  employment risk ? subjective expectations allow
  to distinguish between true risk and unobserved
  heterogeneity.
• Intra-household allocation in terms of human
  capital investment Data on subjective
  expectations for all children in the family
  allows to address the question, whether parents
  invest more in the children with higher returns
  or in a compensatory manner and whether this
  behavior differs between rich and poor families.
• College drop-out behavior Data on subjective
  expectations allows to control for changes in
  expectations about future earnings when trying to
  understand the determinants of dropping out of
  college.

66
Thanks!
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Motivation
College Enrollment Rates by Parental Income
Quartile as a fraction of the relevant age group
(18-24 years old) (MxFLS, 2003)
68
Financing of Higher Education in Latin America
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Data Subjective Expectations
Explanation of the concept of probabilities
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Robustness concerning Timing of the Survey

• Compare cross-sections of expected earnings of
  two cohorts
• that are one school year apart
• High school graduates two/three months after
  college decision
• Individuals now at beginning of grade 12 of High
  school

Second Comparison Expected High School Earnings
? Distributions not significantly different
71
Test 1 Comparison of Cost Distributions
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Test 1 Comparison of Cost Distributions
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Is the Cost-Cdf of Low and Middle Income People
Statistically Different?
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Is the Cost-Cdf of Low and Middle Income People
Statistically Different?
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Is the Slope for Low Income People Statistically
Different from Zero?
76
Is the Slope for Low Income People Statistically
Different from Zero?
77
Is the Slope for Middle Income People
Statistically Different from Zero?
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Illustration Two period model

• Two period model to illustrate testable
  implication of credit constraints

79
Illustration Two period model

• Two period model to illustrate testable
  implication of credit constraints
• where
  assuming U0 is
  orthogonal
• to observables
• ? In model use

80
Illustration Two period model

• Two period model to illustrate testable
  implication of credit constraints
• With

T2
Mo
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Cdf
Cou
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Expected Return Distance Scatter Plot
Adolescent Sample
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Survey Data Potential Sample Selection Problem

• Interviews
• If the HS graduate was not at home when the
  interviewer visited, the mother answered the
  questionnaire (including subjective
  expectations).
• I address the potential sample selection problem
  in two ways
• 1) using the full sample
• 2) using only the sample for which the HS
  graduate answers herself correcting for potential
  sample selection (exclusion restriction -timing
  of the interview- is highly significant).
• ? Results are very similar in both cases (in fact
  selection on unobservables does not seem to be a
  problem).

SU
85
Summary statistics of the two groups of
respondents
86
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87
Coun
Probit
88
Internal Validity Determinants of Expected
Returns
Probit