JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.Many recent studies of the process of family accumulation in general and household response to social security in particular have revealed growing dissatisfaction with the life-cycle theory of saving (see, for example, Leimer and Lesnoy, 1982). An alternative to the life-cycle hypothesis is expressed by defining the preference of each family over its own consumption as well as the welfare of the generations that follow. Thus, each family consists of an infinite chain of generations who have interdependent preferences, and for this reason we shall call it the "Inter-Generational Hypothesis". It was recently used by Barro (1974Barro ( , 1978 to attack the conclusions of the life-cycle hypothesis.Our purpose in this paper is to start the long road of studying the structure of the private inter-generational transfer system with the aim of providing additional tests of the two competing hypotheses.