Taking Stock

This chapter has continued our investigation of the mechanics of capital accumulation in dynamic equilibrium models. The main departure from the baseline neoclassical growth model of the last section has been the relaxation of the representative household assumption.

All of these models fall outside the scope of the First Welfare Theorem. As a result, there is no guarantee that the resulting equilibrium path will be Pareto optimal. In fact, the extensive study of the baseline overlapping generations models were partly motivated by the possibility of Pareto suboptimal allocations in such models. We have seen that these equilibria may be “dynamically inefficient” and feature overaccumulation—a steady-state capital-labor ratio greater than the golden rule capital-labor ratio. We have also seen how an unfunded Social Security system can reduce aggregate savings and thus ameliorate the overaccumulation problem.

Our analysis of perpetual youth models, especially Yaari and Blanchard’s continuous-time perpetual youth model, further clarified the roles of the path of labor income, finite horizons and arrival of new individuals in generating the overaccumulation result. In particular, this model shows that the declining path of labor income is important for the overaccumulation result (in the Samuelson-Diamond model there is an extreme form of this, since there is no labor income in the second period of the life of the individual). But perhaps the more important insight generated by these models is that what matters is not finite horizons per se, but the arrival of new individuals. Overaccumulation and Pareto suboptimality arise because of the pecuniary externalities created on individuals that are not yet in the marketplace.

While overaccumulation and dynamic inefficiency have dominated much of the discussion of overlapping generations models in the literature, one should not overemphasize the impor­tance of dynamic inefficiency. As emphasized in Chapter 1, the major question of economic growth is why so many countries have so little capital for their workers and why the process of economic growth and capital accumulation started only over the past 200 years. It is highly doubtful that overaccumulation is a major problem for most countries in the world.

The models presented in this chapter are very useful for another reason, however. They significantly enrich our arsenal in the study of the mechanics of economic growth and capital accumulation. All three of the major models presented in this chapter, the baseline overlap­ping generations model, the overlapping generations model with impure altruism, and the perpetual youth model, are tractable and useful vehicles for the study of economic growth in a variety of circumstances.

In summary, this chapter has provided us with new modeling tools and new perspectives on the question of capital accumulation, aggregate saving and economic growth. It has not, however, offered new answers to questions of why countries grow (for example, technological progress) and why some countries are much poorer than others (related to the fundamental causes of income differences). Of course, its purpose was not to provide such answers in the first place.

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