This paper presents a new approach to the old problem of linear dependency of age, cohort and time effects. It is shown that second differences of the effects can be estimated without any normalization restrictions, providing information on the shape of the age-, cohort- and time-effect profiles, and enabling identification of structural breaks. A Wald test is provided to test the popular linear and quadratic specifications against a very general alternative. The method is illustrated through examples which show its ability to detect structural breaks in time effects as a result of the Mexican peso crisis, and to determine whether the age-effect profile in the variance of Taiwanese log consumption is concave or convex. Copyright 2006 Blackwell Publishing Ltd.