Introduction to Cohort Analysis

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Introduction to Cohort Analysis

• PRI SUMMER METHODS WORKSHOP
• June 16, 2008
• Glenn Firebaugh

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Cohort Analysis

• Objective -- To separate the effects of
• Age (aging/maturation, life cycle status)
• Period (historical conditions that affect
  everyone)
• Birth Cohort (each cohort experiences a
  distinctive slice of history - Ryder)
• - key notion of imprinting during
  impressionable years imprinting may result in
  period-age interaction effects that create cohort
  differences which persist over time

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Cohort Analysis

• Problem Linear dependence
• Age (years since birth) Period (current year)
  Cohort (year of birth)
• So you cannot estimate the linear equation
• Y a ßAAge ßPPeriod ßCCohort e

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Cohort Analysis

• There are various ways to think about the
  problem.
• One useful way -- as a problem of
  multicollinearity
• rAC.P -1.0
• rAP.C 1.0
• rPC.A 1.0

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Cohort Analysis

• rAC.P -1 At a given point in time, everyone
  lies on the diagonal line for age by birth year

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Cohort Analysis

• What to do? Replace A with A, then rAC.P ? -1

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Cohort Analysis

• In effect, we have replaced A with A, a
  nonlinear function of A, where rAC.P ? -1.
• The correlation rAC.P still is close to 1.0 ?
  large standard errors, unless N is large
• What we are assuming is that, for the Y of
  interest, A captures the age effect as well as
  does actual age A.
• Possible example age and voting. Voting
  increases with age until some age threshold where
  it levels off due to declining health and
  mobility. In this approach, some set of
  parameters constrained to be equal.

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Cohort Analysis

• Strategy 1 Transformed Variables Method
  Identification by assuming equivalence of
  adjacent categories of A, C, or P to create A,
  C, or P, respectively. Example
• A (age in years) ? A (collapsed/recoded A) ? Y
• Because A has no direct effect on Y, net of A,
  to get the age effect we can simply estimate
  effect of A on Y (and A is not linearly
  dependent with P and C).

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Cohort Analysis

• Observations about Transformed Variables Method
• Often C is the variable that is collapsed (e.g.
  depression cohort, baby boomers, etc.)
• Extreme case collapse all the categories of A,
  P, or C. Thats what researchers do in effect
  when they omit A, P, or C (i.e., assume no
  effect for one of them).
• Collapsing adjacent categories to create A, P
  and C all goes back to moving cases off the
  linear regression line for rAC.P etc.

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Cohort Analysis

• Age by cohort figure where cohort categories are
  collapsed (rAC.P ? -1)

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Cohort Analysis

• Strategy 2 Proxy Variables Method Avoid linear
  dependence by substituting A, P or C for A,
  P, or C, where measures capture what it is
  about age, period, or cohort that matters.
• Common example Cohort size for C. Used in labor
  market studies where, e.g., wage is thought to
  depend on ones age (hump-shaped), period, and
  the size of ones birth cohort (C).
• Unlike A-P-C measures, A-P-C measures
  are not recoded functions of A, P and C

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Same underlying assumption for both strategies

• Assumption That A has no effect on Y net of A,
  or that C has no effect on Y net of C, or P has
  no effect on Y net of P. Similarly for the proxy
  variables A, C and P. The idea in both
  cases is that at least one or variable must
  mediate all the effect. (Note parallels with
  Winship-Harding approach for both and
  methods.)
• For example, C Are we capturing all the cohort
  effect when we assume no effect within some range
  of birth years? Or, by collapsing birth years,
  are we simply identifying by adding measurement
  error?
• C Are we capturing all the cohort effect when
  we use cohort size?

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Natural experiments as a promising method (where
possible)

• Are there instances in nature where, say, age
  and cohort effects are uncoupled? Consider voting
  19th Amendment (enduring effect of
  disenfranchisement)
• Best predictor of voting at time t is whether you
  voted at t-1, so learning to vote early matters.
• But women couldnt vote in most states before
  1920 ? different cohort experiences than men the
  same age
• Sex is randomly assigned by family SES, etc.
• A natural experiment compare sex differences
  in voting rates for men and women who came of age
  pre- and post-19th Amendment (Firebaugh-Chen AJS
  1995)