Conclusion
Aggregate savings behavior in OLG models is not characterized by social efficiency, as it is in the representative household model. Besides, in economies where there is no representative household, comparing welfare across different households is largely arbitrary.
In any case, although the dynamic behavior of OLG models is largely similar to that of the representative household model, there is no guarantee of efficiency OLG models. Thus, in these models, there is scope for policy interventions that would result in greater social efficiency, as the competitive equilibrium does not necessarily lead to optimal results. Furthermore, in the Diamond model, it is theoretically possible to have dynamic inefficiency, although empirical considerations suggest that this possibility is unlikely.
Because the competitive equilibrium does not result in an optimal savings behavior in OLG models, such models also have different properties than the representative household model regarding both the short- and the long-run effects of budgetary (fiscal) policies and monetary policies that affect the rate of growth of the money supply. These are questions that we shall investigate in the next two chapters.
1. The model of two overlapping generations of Diamond [1965] is based on the two-period model of Fisher [1930] and bears many similarities to an earlier model put forward by Allais [1947]. It is also closely related to a model of three overlapping generations, first presented and analyzed by Samuelson [1958], to explain the demand for money as a store of value. OLG models are also known as Samuelson-Diamond models, because the important contribution of Allais was in French and was initially ignored. See Malinvaud [1987]. We will analyze the Diamond growth model in this chapter, a simplified version of the Samuelson OLG monetary model in chapter 12, where we analyze general equilibrium models with money, and a more general version of the Samuelson OLG monetary model in chapter 22, when we discuss multiple equilibria and sunspots.
Barro [1974] has extended the Diamond model to a model where households are also concerned about the welfare of their offspring, converting it effectively to a representative household model.2. See Weil [2008] for a relatively recent survey of OLG models and their policy implications.
3. The time period in the Diamond [1965] model, as in the Fisher [1930] model for that matter, can be thought of as being equal to one half of the life expectancy of an adult (i.e., about 30 years).
4. These conditions are the same as the conditions discussed in the Fisher and Ramsey models in chapters 2 and 4.
5. Moreover, the equilibrium that eventually prevails may, under some conditions, depend on self-fulfilling expectations, or sunspots, or the economy may be characterized by endogenous cyclical fluctuations, even though there are no exogenous random shocks. Balanced growth is therefore not guaranteed, and the balanced growth path, if it exists, may depend on initial conditions. We shall postpone our discussion of self-fulfilling expectations, sunspots, and endogenous cycles to chapter 22. See Azariadis [1993] for an extensive textbook treatment of these issues.
6. This model, augmented with a positive probability of death, was first presented by Blanchard [1985] and was based to some extent on the model of Yaari [1965].
7. There are variations of this model in which productivity and labor income is a negative function of the age of the household. The properties of these variants of the model are closer to some of the properties of the Diamond model, in the sense that the possibility of dynamic inefficiency may arise. See Blanchard and Fischer [1989].
8. In the perpetual youth model, accumulated savings depend on the date of birth of households. This causes differences in the savings behavior of households depending on their date of birth, because households of different generations have different accumulated stocks of nonhuman capital. This results in direct effects of the aggregate capital stock (and other assets, such as government bonds) on the behavior of aggregate consumption. Buiter [1988] has an extensive discussion of this point.
9. Compare the consumption function (5.30) with those for the representative household derived in chapter 4.