Estimating fecundability from data on waiting times to first conception

"This article tests assumptions invoked in the demographic literature to estimate the population distribution of fecundability from data on waiting times to first conception. In continuous time, the key assumption is that waiting times are realizations from a mixture of exponentials distribution. In discrete time, the key assumption is that waiting times are realizations from a mixture of geometrics distribution. The [U.S.] Hutterite data analyzed by Sheps (1965) are consistent with this assumption. Various models, however, have one representation in mixture of exponentials form. A fundamental identification problem plagues the conventional estimation procedure. Our analysis calls into question the conventional practice of checking model specification by using goodness-of-fit tests. The practical importance of the identification problem in duration models is demonstrated."