Age-period-cohort (APC) analysis has a long, controversial history in sociology and related fields. Despite the existence of hundreds, if not thousands, of articles and dozens of books, there is little agreement on how to adequately analyze APC data. This article begins with a brief overview of APC analysis, discussing how one can interpret APC effects in a causal way. Next, we review methods that obtain point identification of APC effects, such as the equality constraints model, Moore-Penrose estimators, and multilevel models. We then outline techniques that entail point identification using measured causes, such as the proxy variables approach and mechanism-based models. Next, we discuss a general framework for APC analysis grounded in partial identification using bounds and sensitivity analyses. We conclude by outlining a general step-by-step procedure for conducting APC analyses, presenting an empirical example examining temporal shifts in verbal ability.
The political liberalism of professors-an important occupational group and anomaly according to traditional theories of class politics-has long puzzled sociologists. This article sheds new light on the subject by employing a two-step analytic procedure. In the first step, we assess the explanatory power of the main hypotheses proposed over the last half century to account for professors' liberal views. To do so, we examine hypothesized predictors of the political gap between professors and other Americans using General Social Survey data pooled from . Results indicate that professors are more liberal than other Americans because a higher proportion possess advanced educational credentials, exhibit a disparity between their levels of education and income, identify as Jewish, non-religious, or non-theologically conservative Protestant, and express greater tolerance for controversial ideas. In the second step of our article, we develop a new theory of professors' politics on the basis of these findings (though not directly testable with our data) that we think holds more explanatory promise than existing approaches and that sets an agenda for future research.
For more than a century, researchers from a wide range of disciplines have sought to estimate the unique contributions of age, period, and cohort (APC) effects on a variety of outcomes. A key obstacle to these efforts is the linear dependence among the three time scales. Various methods have been proposed to address this issue, but they have suffered from either ad hoc assumptions or extreme sensitivity to small differences in model specification. After briefly reviewing past work, we outline a new approach for identifying temporal effects in population-level data. Fundamental to our framework is the recognition that it is only the slopes of an APC model that are unidentified, not the nonlinearities or particular combinations of the linear effects. One can thus use constraints implied by the data along with explicit theoretical claims to bound one or more of the APC effects. Bounds on these parameters may be nearly as informative as point estimates, even with relatively weak assumptions. To demonstrate the usefulness of our approach, we examine temporal effects in prostate cancer incidence and homicide rates. We conclude with a discussion of guidelines for further research on APC effects.
The intrinsic estimator (IE) has become a widely used tool for the analysis of age-periodcohort (APC) data in sociology, demography, and other fields. However, it has been recently recognized that the IE is a subtype of a larger class of estimators based on the Moore-Penrose generalized inverse (MP estimators) and that different estimators can lead to radically divergent estimates of the true, unknown APC effects. To clarify the differences and similarities of MP estimators, we introduce a canonical form of the linear constraints imposed on the true temporal effects. Using this canonical form, we compare the IE to related MP estimators, examining the conditions under which they recover the true temporal effects, the impact of the size and sign of nonlinearities on the estimated linear effects, and their sensitivity to the number of age, period, and cohort categories. We show that two MP estimators, which we call the difference estimator (DE) and the orthogonal estimator (OE), impose constraints that are both less sensitive and easier to interpret than those of the IE. We conclude with practical guidelines for researchers interested in using MP estimators to estimate temporal effects.
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