Dynamic inefficiency in an overlapping generations economy with production

Abstract

Reichlin (JET, 1986) has shown in an OLG model with productive capital that whenever the steady state is locally indeterminate and undergoes a Hopf bifurcation, it is Pareto-optimal. While these results were established under the assumption of Leontief technology, the author has partially extended them to show that the Hopf bifurcation is robust with respect to the introduction of capitallabor substitution. In this note, we prove that the Pareto-optimality of the steady state does not extend to technologies with capital-labor substitution. When the steady state is a sink or undergoes a Hopf bifurcation, it is characterized by over-accumulation with respect to the Golden Rule -the interest rate is negative -hence not Pareto-optimal. Most importantly, it follows that stabilization policies targeting the steady state leave room for welfare losses associated with productive inefficiency, apart from the very special case of Leontief technology.

Endogenous Business Cycles in Overlapping-Generations Economies With Multiple Consumption Goods

“…In contrast, when local indeterminacy occurs under dynamic inefficiency, stabilization policies targeting the steady state leave room for welfare losses. Although Reichlin (1986) has shown that locally indeterminate dynamically efficient equilibria can occur in an aggregate model with a Leontief technology, Cazzavillan and Pintus (2007) have recently proved that this result is not robust to the introduction of any positive capital-labor substitution.…”

Controlling Bifurcations in an OLG Economy with PAYG Pension Schemes

“…The OLG model, which has become an engine for economic analysis, can exhibit complicated dynamic behavior involving oscillations, chaos and bifurcations (see [5], [18], [24]). It is demonstrated that there are many causes of bifurcation in the OLG system, such as pollution perception ( [22]), different utility functions ( [15]), markup variability ( [10]), productive externalities ( [4]), exponentially fading memory ( [2]) and increasing returns to scale ( [1]).…”