high child dependency burden, are now beginning to worry instead about the costs of impending population aging.

This chapter develops an accounting framework for evaluating systems of interage transfers, and examines how such systems are affected by changing population age distributions. To understand the role of transfers in achieving a desirable allocation of consumption over the life-cycle, it is necessary to consider them in relation to the other forms of reallocation: credit and capital. There is a rich and controversial literature on the relation between transfer systems and capital accumulation: Does life-cycle saving account for the capital stock of industrial nations (Modigliani, 1988; Tobin, 1967)? Or is the desire to leave bequests responsible (Kotlikoff and Summers, 1981, 1988)? Do public sector pension systems undermine private saving (Feldstein, 1974)? Or do elderly parents simply increase their familial transfers to their children to offset the pensions (Barro, 1974)? Transfers may be used to achieve efficient allocations over the life-cycle that are unattainable via competitive market mechanisms (Samuelson, 1958), and if transfers upwards or downwards by age are needed to achieve efficient allocations, that fact tells us that the population growth rate is less than or more than the optimal rate (Samuelson, 1975, 1976; Willis, 1988; Lee, in press, b). These are issues that a coherent accounting framework may help to clarify.

The theoretical basis for a comprehensive framework for studying the reallocation of resources across age in general, and transfers in particular, has been laid by economic and demographic research over the past 35 years. Macroeconomic models with "overlapping generations" sprang from the seminal work of Samuelson (1958) and, later, Diamond (1965). The literature has developed to the point that there is now a textbook that teaches macroeconomic theory entirely from the point of view of a simple model of economies with overlapping generations (McCandless, 1991). The models have been used to explore such diverse topics as the existence of money, the rate of interest, aggregate savings rates, the Ricardian equivalence theorem, optimal population growth rates, economic fluctuations, and so on. These important developments in economic theory pave the way for a deeper integration of demography and macroeconomics than has yet proven possible. However, perhaps because of the wish to examine nonsteady-state situations, the demographic models used by most mainline economists are very simplistic: the life-cycle typically consists of two broad age groups, workers and retirees, or young and old, with perfect survival until the end of the second. Childhood is often ignored, and life really begins at labor market entry. This life-cycle incorporates only one period of dependency rather than two. In such a demographic world (used all the way through the McCandless textbook), some of the most basic questions cannot be properly posed or will receive misleading answers. This is true of most questions

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