examples of fixed-effect models

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Examples of Fixed-Effect Models

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Almond et al.

• Babies born w/ low birth weight(< 2500 grams) are more prone to– Die early in life– Have health problems later in life– Educational difficulties

• generated from cross-sectional regressions

• 6% of babies in US are low weight• Highest rate in the developed world

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• Let Yit be outcome for baby t from mother I

• e.g., mortality

• Yit = α + bwit β + Xi γ + αi + εit

• bw is birth weight (grams)

• Xi observed characteristics of moms

• αi unobserved characteristics of moms

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• Terms

• Neonatal mortality, dies in first 28 days

• Infant mortality, died in first year

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• Many observed factors that might explain health (Y) of an infant– Prenatal care, substance abuse, smoking,

weight gain (of lack of it)

• Some unobserved as well– Quality of diet, exercise, generic

predisposition

• αi not included in model

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• Cross sectional model is of the form

• Yit = α + bwit β + Xi γ + uit

• where uit =αi + εit

• Cov(bwit,uit) < 0

• Same factors that lead to poor health lead to a marker of poor health (birth weight)

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• Solution: Twins

• Possess same mother, same environmental characterisitics

• Yi1 = α + bwi1 β + Xi γ + αi + εi1

• Yi2 = α + bwi2 β + Xi γ + αi + εi2

• ΔY = Yi2-Yi1 = (bwi2-bwi1) β + (εi2- εi1)

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Questions to consider?

• What are the conditions under which this will generate unbiased estimate of β?

• What impact (treatment effect) does the model identify?

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Large changeIn R2

Big Drop in Coefficient onBirth weight

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Teenage pregnancy

• 40% of teen women become pregnant before the age of 20

• 25% will be a mother by age 20• Most of these pregnancies end in a live

birth• About 4 million children born each year,

1/8 are to teen mothers• 8% of teen women, aged 15-19 give birth

n a given year

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• Teen birth rates have changed considerably over time

• Most of these births are out of wedlock

• Rates differ considerably across race

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1991 1993 1995 1997 1999 2001 2003 2005

All Students 37.5 37.6 37.9 34.8 36.3 33.4 34.3 33.9

Race/Ethnicity2  

White, non-Hispanic 33.9 34.0 34.8 32.0 33.0 31.3 30.8 32.0

Black, non-Hispanic 59.3 59.1 54.2 53.6 53.0 45.6 49.0 47.4

Hispanic 37.0 39.4 39.3 35.4 36.3 35.9 37.1 35.0

Grade  

9 22.4 24.8 23.6 24.2 26.6 22.7 21.2 21.9

10 33.2 30.1 33.7 29.2 33.0 29.7 30.6 29.2

11 43.3 40.0 42.4 37.8 37.5 38.1 41.1 39.4

12 50.6 53.0 49.7 46.0 50.6 47.9 48.9 49.4

% Students, Grades 9-12 who have hadIntercourse in the past 3 months

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Outcomes of teen mothers

• Teen mothers are– Twice as likely to not complete high school– 90% less likely to attend college

• At age 28 – teen mothers– 50% more likely to be on poverty in their 20s– Have lower wages– Have more children– Have lower labor supply– Less likely to be married

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• Bill Clinton’s State of the Union Address, 1995

• “We've got to ask our community leaders and all kinds of organizations to help us stop our most serious social problem: the epidemic of teen pregnancies and births where there is no marriage. “

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Are poor economic outcomes ‘caused’ by early childbearing?

• Teen mothers are not a random sample of the population

• Teen mothers are more likely to come from situations that would predict poorer economic outcomes anyway

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• On average, teen mothers are more likely to come from:– families with lower income and education– poorer neighborhoods and lower quality

schools– Families with a teen mother– Have Lower test scores– Racial and ethnic minorities

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• Consider an alternative explanation of results– Women with lowest opportunity cost of having

children have more children– Women from poorer backgrounds lower opportunity

cost of having children because they have lower economic prospects

• In this example, teen motherhood does not ‘cause’ poor outcomes, but instead, is a signal of the same problem – poor future prospects

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