Assessing the Significance of Cohort and Period Effects in Hierarchical Age-Period-Cohort Models: Applications to Verbal Test Scores and Voter Turnout in U.S. Presidential Elections

Abstract

In recently developed hierarchical age-period-cohort (HAPC) models, inferential questions arise: How can one assess or judge the significance of estimates of individual cohort and period effects in such models? And how does one assess the overall statistical significance of the cohort and/or the period effects? Beyond statistical significance is the question of substantive significance. This paper addresses these questions. In the context of empirical applications of linear and generalized linear mixed-model specifications of HAPC models using data on verbal test scores and voter turnout in U.S. presidential elections, respectively, we describe a two-step approach and a set of guidelines for assessing statistical significance. The guidelines include assessments of patterns of effects and statistical tests both for the effects of individual cohorts and time periods as well as for entire sets of cohorts and periods. The empirical applications show strong evidence that trends in verbal test scores are primarily cohort driven, while voter turnout is primarily a period phenomenon.

Another 'futile quest'? A simulation study of Yang and Land's Hierarchical Age-Period-Cohort model

“…However, the HAPC model is able to assess random variation in periods and cohorts, so long as any trends are absorbed in the fixed part of the model. These may well be of substantive interest, telling us, for example, that baby boomers have a higher level of literacy (a cohort effect), or that voter turnout in America was particularly high in the 1960 election between Kennedy and Nixon (a period effect): both of these results can be interpretations of the examples used by Frenk, Yang and Land (2013) 23 . In both of these cases it seems that the age terms in the fixed part of the model accounted for all APC trends 24 .…”

“…Glenn (2005, p. 6) This paper considers one of these solutions, proposed recently by Yang and Land (2006) with some additional methodological caveats discussed in subsequent papers (Frenk, Yang and Land 2013;Yang 2006;. The methodology has already been employed in a number of empirical applications, studying social trends in happiness (Yang 2008a), voter turnout (Dassonneville 2013), obesity (Reither, Hauser and Yang 2009), religious service attendance (Schwadel 2010), and cannabis use (Piontek et al 2012), to name a few.…”

“…8 It may be that it is unnecessary to include both period and cohort residuals in the model. As such, Yang and Land recommend comparing the cross-classified model to nested models of observations in periods and observations in cohorts, and comparing them on the basis of likelihood ratio tests (Frenk, Yang, and Land 2013).…”

Doing Less with More: Cohorts, Education, and Civic Participation in America

“…For example, social issues may provoke civic engagement independent of cohort changes (Caren, Ghoshal, and Ribas 2011;Frenk, Yang, and Land 2013). Contentious issues are period effects that could generate an outpouring of letters to the editor, contacting elected officials, petition signing, and attendance at public meetings.…”

“…Caren, Ghoshal, and Ribas (2011) also found cohort-level decreases in petition signing and protesting, although they found that the decline started with later cohorts. However, differences in voting behavior are primarily due to period rather than cohort changes (Smets and Neundorf 2014;Frenk, Yang, and Land 2013) ii .…”