On the role of labor supply for the optimal size of Social Security

Bubbly Markov equilibria

“…Potential extensions of the previous framework include non-additive utility, non-multiplicative and correlated production shocks, and non-classical production technologies. Models with these features were employed, e.g., in Wang (1994), Morand & Reffett (2007), McGovern, Morand & Reffett (2013), or Hillebrand (2014 to study the existence and properties of bubbleless ME. Since all these papers rely on methods similar to those employed in this paper, we believe that the previous construction of a BME should be amendable to these extensions.…”

“…One can also interpret a BME as an equilibrium with a social security system in which p t > 0 represents the transfers from young to old consumers in period t ≥ 0. A particular appealing feature that follows from the Euler equation ( 3b) is that such a system is time consistent in the sense that no generation has an incentive to change it (see Hillebrand (2011) for an application of this concept). Thus, a BME directly implies the existence of a time-consistent Social Security system.…”

“…It is shown in Hillebrand (2014) that property (U) from Assumption 1 is already sufficient for the benchmark economy E to possess a unique bubbleless ME. In this case, the equilibrium mappings are given by P E 0 ≡ 0 and K E 0 = K 0 • W where K 0 : R ++ −→ R ++ determines the unique solution k = K 0 (w) to the implicit condition…”

“…For this reason, the following sections develop a more general approach which is based on methods from functional analysis similar to Morand & Reffett (2007). It is shown in Hillebrand (2014) that this approach is equivalent to the pointwise construction in Wang (1993) in the bubbleless case. Our method permits to construct ME of the general class of economies E d , d ≥ 0 introduced in the previous section.…”

“…The stochastic OLG model with production has been studied in Wang (1993Wang ( , 1994 and, more recently, in Morand & Reffett (2007), McGovern et al (2013), andHillebrand (2014). These studies focus on a particular class of equilibria in which the equilibrium variables are determined by time-invariant mappings on the minimal or 'natural' state space.…”