Least squares calibration of the gravity model when intrazonal flows are unknown

Some very fast least-squares based calibration procedures for the gravity model have been presented in earlier papers. Since these procedures are inconvenient or impossible to use when diagonal elements of the base period origin - destination (O - D) matrix are unavailable, one of the procedures has been modified to handle such situations. This modified procedure is described in this paper and then applied to two O - D tables -- one for food grains and the other for coal. For these two data sets the procedure yields estimates which are virtually identical to corresponding maximum likelihood estimates.