Adjusting period tempo changes with an extension of Ryder's basic translation equation

We show that the observed changes in the period tempo of fertility are biased and derive a new formula for adjusting such bias. We present illustrative applications of our proposed method to the cases of the United States and Taiwan. We then describe the relevance of adjustments of observed period fertility tempo for evaluating family planning programs aiming at delaying and reducing births to slow down population growth in developing countries. The work reported in this article also can be regarded as an extension of Ryder's basic translation equation. The extension provides a set of formulas expressing relationships of quantum-tempo between cohorts and periods under specified assumptions.