1Class 26Age-Period-Cohort EffectDefinition of Cohorts• According to Norman Ryder (1965), acohort is "the aggregate of individualswho experienced the same event withinthe same time interval."• E.g, all individuals born at the same time(say within a given calendar year) makeup a birth cohort.• Similarly defined are marriage cohortsand school cohorts.Time Series Effects• Age effects are effects related to aging or the life-cycle. E.g., individuals tend to become less healthyas they age.• Period effects are effects affecting all cohorts in agiven historical period. E.g., effects of famine onmortality.• Cohort effects are effects which reflect the uniquereaction of a cohort to an historical event, or whichwere experienced uniquely by the cohort. E.g.,Post-WWII cohort who reached draft age duringthe Vietnam War experienced unique issues.2Cohorts and Social Change• Many social scientists believe that realsocial change comes about only whenchanges are across cohorts, sincemost events are fixed over life course.• Examples: educational attainment,career, completed fertility, and death.Easterlin Hypothesis (CohortEffect)• Richard Easterlin conjectured that people bornin large cohorts (e.g., baby boomers) aresocially and economically disadvantaged, dueto crowding.• Economic disadvantage leads to low fertility.• Individuals growing up in small cohorts (suchas children of the Great Depression) areeconomically advantaged and thus have higherfertility.• Thus, the next generation of a large (small)cohort will be a small (large) cohort. Easterlin Cycle.Cohort Analysisyear19941993199219911990c1994c1993c1992c1991c19900c1993c1992c1991c1990c19891c1992c1991c1990c1989c19882c1991c1990c1989c1988c19873c1990c1989c1988c1987c19864Age3Linear Dependency amongAge, Period, and Cohort• Cohort + Age = Period– E.g., birth cohort = 1985, age = 20, period (year)= 1985 + 20 = 2005.• Therefore, age, period, and cohort arelinearly dependent, meaning that if weknow two of them, we know the value ofthe third.• In cross-sectional data (i.e., period isfixed), age effect and cohort effect areconfounded and indistinguishable.Linear Dependency amongAge, Period, and Cohort• In general, the effects of linearly-dependent independent variables cannotbe estimated in a multiple regressionequation. That is, we cannot estimate thefollowing regression equation:Y = a + b*age +c*cohort + d*year + e.• The above model involving age, period,and cohort is said to be “not identified.”Intercohort Decline in VerbalAbility• Why might verbal score change over time?– Word obsolescence– Instrument effect (easier tests in some years)– Less newspaper reading– Vocabulary growth– Cognitive decline– Expansion of education and educationalselectivity (i.e., over time, it has become easierto go to college)– Declining quality of education?4Intercohort Decline in VerbalAbility• Identify the previous potential causesof changing verbal scores as ageeffect, period effect, and/or cohorteffect.• Which factors are real effects? Whichfactors are measurement errors?Which factors should be controlled?wordsum1.log 12/4/2006. table cohort_rec age_rec, content(mean wordsum)-------------------------------------------------------------------------RECODE of | RECODE of age (age of respondent)cohort | 18/24 25/34 35/44 45/54=4 55/64 65/74 75/89----------+--------------------------------------------------------------min/1914 | 6.37576 5.66174 5.42151915/1924 | 6.04036 6.03485 5.91226 5.8751925/1934 | 6.24227 6.07525 5.93896 6.2556 6.521741935/1944 | 6.27208 6.16667 6.14828 6.40967 6.96251945/1954 | 5.58576 6.10897 6.41183 6.56882 6.312981955/1964 | 5.33628 5.85256 6.17736 61965/1974 | 5.22261 5.80788 6.078951975/max | 5.43459 5.97093-------------------------------------------------------------------------. table cohort_rec age_rec, content(mean educ)-------------------------------------------------------------------------RECODE of | RECODE of age (age of respondent)cohort | 18/24 25/34 35/44 45/54=4 55/64 65/74 75/89----------+--------------------------------------------------------------min/1914 | 10.5375 9.91509 9.881371915/1924 | 11.2668 11.1805 11.2339 11.53581925/1934 | 12.0698 11.9181 11.9069 12.3416 12.33331935/1944 | 12.6284 12.6539 12.9136 13.1515 13.21071945/1954 | 12.5376 13.1698 13.6846 13.9192 13.77951955/1964 | 12.3649 13.4304 13.7632 13.96451965/1974 | 12.6474 13.7912 13.79881975/max | 12.6438 13.8499-------------------------------------------------------------------------. label list newsnews:0 nap1 everyday2 few times a week3 once a week4 less than once wk5 never8 dk9 na. table cohort_rec age_rec, content(mean news)-------------------------------------------------------------------------RECODE of | RECODE of age (age of respondent)cohort | 18/24 25/34 35/44 45/54=4 55/64 65/74 75/89----------+--------------------------------------------------------------min/1914 | 1.39735 1.6288 1.894631915/1924 | 1.43081 1.58937 1.66121 1.767181925/1934 | 1.51376 1.58898 1.68679 1.67459 1.666671935/1944 | 1.70524 1.7366 1.77432 1.85036 1.744441945/1954 | 2.10731 1.99841 1.8642 2.04202 2.253731955/1964 | 2.29884 2.21615 2.23743 2.314611965/1974 | 2.45308 2.51042 2.550261975/max | 2.60797 2.72021-------------------------------------------------------------------------.. generate age2 = age * age(166 missing values generated). regress wordsum age cohortSource | SS df MS Number of obs = 21625-------------+------------------------------ F( 2, 21622) = 17.69Model | 165.655435 2 82.8277174 Prob > F = 0.00001wordsum1.log 12/4/2006Residual | 101264.575 21622 4.68340464 R-squared = 0.0016-------------+------------------------------ Adj R-squared = 0.0015Total | 101430.23 21624 4.69063219 Root MSE = 2.1641------------------------------------------------------------------------------wordsum | Coef. Std. Err. t P>|t| [95% Conf. Interval]-------------+----------------------------------------------------------------age | .0108136 .0018758 5.76 0.000 .0071369 .0144902cohort | .0076177 .0017022 4.48 0.000 .0042813 .0109542_cons | -9.299238 3.384331 -2.75 0.006 -15.93278 -2.665698------------------------------------------------------------------------------. regress wordsum age age2 cohortSource | SS df MS Number of obs = 21625-------------+------------------------------ F( 3, 21621) = 147.12Model | 2029.07189 3 676.357295 Prob > F = 0.0000Residual | 99401.1586 21621 4.59743576 R-squared =
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