Adjusting Period Tempo Changes 269 Demography, Volume 39-Number 2, May 2002: 269–285 269 I ADJUSTING PERIOD TEMPO CHANGES WITH AN EXTENSION OF RYDER’S BASIC TRANSLATION EQUATION* ZENG YI AND KENNETH C. LAND 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 speci- fied assumptions. t is well known in the field of demography that the observed period total fertility rate (quantum) is biased 1 if the timing of childbearing (tempo) is changing; Ryder (1956, 1959, 1964, 1980, 1983) and others (see, for example, Keilman 1994; Keilman and Van Imhoff 1995) have made substantial contributions on this topic. Bongaarts and Feeney (1998) proposed a simple and effective method (hereafter denoted the B-F method) for adjusting the period quantum for the bias that has received much attention (Kim and Schoen 2000; Kohler and Philipov 2001; Van Imhoff and Keilman 2000; Zeng and Land 2001). Another important question, however, remains unanswered: are the observed changes in period tempo biased when the tempo is changing? If they are, how should they be adjusted? Answering this question would enable us to gain a better understanding of demographic relationships and thus deepen our knowledge of the classic, and currently relevant, tempo- quantum debate and analysis. In this article, we show that observed changes in the period tempo of fertility are also biased under conditions of changing tempo. We derive a new formula for adjusting bias in observed changes in the period tempo of fertility and present some numerical applica- tions of our proposed method to adjust bias in the observed changes in period fertility tempo in the United States and Taiwan. We also discuss the relevance of adjustments of observed changes in period fertility tempo to the evaluation of family planning programs that are aimed at reducing and delaying births to slow down population growth in devel- oping countries. Finally, we generalize the derivation of our new formula (which focuses *Zeng Yi, Center for Demographic Studies and Department of Sociology, Duke University, Durham, NC 27708-0408; E-mail: zengyi@Duke.edu. Kenneth C. Land, Department of Sociology and Center for Demo- graphic Studies, Duke University. Zeng Yi also is affiliated with the Institute of Population Research, Peking University, Beijing, China, and the Max Planck Institute for Demographic Research, Rostock, Germany. We thank John Bongaarts for sending us the U.S. and Taiwan data sets. Comments on a previous draft by John Bongaarts, Griffith Feeney, Norman Ryder, Elwood Carlson, Nico Keilman, Evert van Imhoff, Young Kim, Hans-Peter Kohler, Mimiter Philipov, Carl Schmertmann, and Robert Schoen are highly appreciated. We also thank the editor and three anonymous referees for their invaluable comments. We thank Zhenglian Wang and Yongyi Li for their excellent research assistance. Research reported in this article is supported by the NIA center grant awarded to the Center for Demographic Studies at Duke University. 1. The term bias, as used in this article, refers to distortions of observed fertility quantum and changes in tempo caused by changing tempo, which has no statistical implications. Downloaded from http://read.dukeupress.edu/demography/article-pdf/39/2/269/909262/269yi.pdf by guest on 05 June 2022