What is the Counterfactual

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What is the Counterfactual?
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Predicated CounterfactualAlternative 1 -
Contracting Differences 1. School Interaction -
Those Who Are Not So Smart Gain From Schooling2.
Age Interaction - Those Who Are Not So Smart
Catch up With Age
Projected
Observed
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Predicated CounterfactualAlternative 2 -
Widening Differences1. School Interaction -
Those who are not so smart gain from schooling2.
Age Interaction - Those who are not so smart
catch up with age
Observed
Projected
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Predicted CounterfactualAlternative 3 - Parallel
Change1. No School or Age Interaction2.
Interactions Cancel Each Other Out
Projected
Observed
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Projected Counterfactual OutcomeUsing Additional
Data forTreatment Group
Observed
Projected
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Confirming DataUsing Additional Data
forTreatment Group
Observed
Projected
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Confirming DataUsing Additional Data forControl
Group
Observed
Projected
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Projected Counterfactual OutcomeUsing Additional
Data forTreatment and Control Group
Observed
Projected
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What Have We Learned?

• Need for multiple waves of data
• In our context, multiple waves of pretest data
  will be needed to estimate the combined effects
  of age and schooling
• Multiple waves of post-test data are needed to
  estimate the effects of age

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• School effect (combined school and age effect)
  (age effect)
• Multiple waves of pretest and post-test data
  needed to both identify effects and to test
  assumptions about the evolution of mental ability
  with age and schooling
• Pretest and post-test data on both treatment and
  control groups can be used for this purpose

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Where Do We Find Multiwave Data?

• Long term panels of individual data can be
  difficult to find. I know of no national sample
  that contains repeated measures of mental
  ability.
• Heckman and Robb (1985) point out that cohort
  data are often sufficient.

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Where Do We Find Multiwave Data?

• Claim in some contexts even synthetic cohort
  data will work.
• Synthetic cohortseparate samples of
  individuals at successive ages.
• Age pattern across groups indicates changes
  any cohort/individual would go through as it
  aged.
• Strong assumptionthere are no cohort effects
  and/or they can be adjusted out.

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Data SetNational Longitudinal Survey of Youth

• Sample of 12,686 individuals ages 14 to 21 in
  1979 including military oversample
• In 1980 all individuals are given the armed
  services vocational aptitude battery
  (ASVAB)lengthy test with 10 different components

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• I will use four components of the ASVAB known as
  the Armed Forces Qualifying Test (AFQT) which
  measures quantitative and verbal ability.
  Generally considered an IQ test.
• Restrict sample to individuals that are age grade
  normal who are continually in school before
  exiting n 6692

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Focus

• Comparison between individuals who eventually
  complete either twelve (high school) or fourteen
  years of school (some college)
• Logit transformation of combined test score in
  order to deal with ceiling effectsthe fact that
  an individual cant get better than 100 on the
  overall test

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Raw Data
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Synthetic Cohort Data
Years of Schooling
AGE - 6
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Regression Model
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Are My Data Nearly Linear?

• Pro Adjusted R2 for Model (13 parameters) is
  .523. Adjusted R2 for Saturated Model (120
  parameters) is .530
• Con F(99, 6579) 2.9, because of the sample
  size is significant at the .001 level.
• Here, I assume I have the correct model.

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Projected Mental Ability for Those in School
Increasing Schooling by One Year
Total Sch Est (12) F - H 0.208 In Sch Est
(12) F - G 0.120 Out Sch Est (12) G - H
0.088
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Projected Mental Ability for Those in School
Increasing Schooling by One Year
Total Sch Est (14) B - D 0.253 In Sch Est
(14) B - C 0.189 Out Sch Est (14) C - D
0.064
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Projected Mental Ability for Both Groups
Increasing Schooling by One Year
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What Have We Learned About the Effects of
Schooling on Mental Ability?

• An additional year of schooling appears to
  modestly increase mental ability post-schooling.
• The effect is greater for individuals who stop
  schooling earlier.
• Being in school, per se, makes one smarter.
• This effect is greater for individuals who
  complete more years of schooling.

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• 3. Individuals mental ability increases modestly
  with age even when individuals are out of school.
• This effect is greater for individuals who
  complete more years of schooling.

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THE END
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Predicted Counterfactual Outcome Using Additional
Data for Treatment and Control Group
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Confirming Data Using Additional Data for Control
Group
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Predicted Counterfactual Outcome Using Additional
Data for Treatment Group
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Predicted Counterfactual Reversing Treatment and
Control Groups
Observed
Projected
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Projected Mental Ability for Those Out of School
Reducing Schooling by One Year
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Projected Mental Ability for Those In School
Increasing Schooling by One Year
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Projected and Observed Mental Ability for Those
Out of School
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Projected Mental Ability for Those Out of School
Reducing Schooling by One Year
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Projected Mental Ability for Those in School
Increasing Schooling by One Year
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Projected Mental Ability for Both Group
Increasing Schooling by One Year
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Projected and Observed Mental Ability for Those
Out of School