U.S. births and limit cycle Models

Lee’s (1974) formal demographic feedback models summarize the implications for births and age-structure of neo-Malthusian theories of baby booms such as those of Easterlin. For some parameter values, such models imply sustained cycles, so-called “limit cycles,” in births. Frauenthal and Swick recently reestimated a continuous-age version of Lee’s basic cohort model with U.S. series and, contrary to Lee’s original findings, concluded that “limit cycles oscillations have been occurring in U.S. births.” This article disputes their conclusion, ascribing it to an inconsistency in detrending procedures. Furthermore, it corrects Lee’s original conclusion by showing that his alternative period labor-force feedback model, estimated from U.S. series, leads to cycles of implausibly long period. This article thus reopens the question of whether any feedback model could account for the observed cycles in U.S. births.