Bequests, Gifts, and Social Security

This paper analyses the very long run, or “stationary state,†impact of an unfunded social security system. We use an overlapping generations model framework. A key feature is that while parents care about their children and can leave non-negative bequests to them, children also care about their parents and can make non-negative “gifts†to them. We show that the possibility of negative “net bequests†may make social security less harmful to private wealth accumulation than would otherwise be the case. A subsidiary finding is that risk-loving behaviour may emerge for some households due to the nature of intergenerational transfers within family lines.Center for Research on Economic and Social Theory, Department of Economics, University of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/100825/1/ECON283.pd

Dynamic Determinancy and the Existence of Sunspot Equilibria

This paper relates the existence of stationary sunspot equilibria in the vicinity of a conventional stationary state to the phase diagram surrounding the latter. We find that the local condition required for a unique equilibrium path returning to the stationary state following any slight perturbation is also sufficient to exclude stationary sunspot equilibria in the state's immediate vicinity or (if the model includes predetermined variables) to exclude local sunspot outcomes which are not virtually indistinguishable from the stationary state itself. In that sense, an eigenvalue condition can tell us something about the possibilities of local sunspot activity.Center for Research on Economic and Social Theory, Department of Economics, University of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/100826/1/ECON284.pd

The Climate Imperative and Innovative Behavior: Encouraging Greater Advances in the Production of Energy-Efficient Technologies and Services

This white paper examines why a larger array of innovative institutions, behaviors, technologies, and servicesis needed – specifically in the context of what we call “the climate imperative.” We explore possible mechanisms that can encourage the more robust development of innovative programs and policies within the State of California, with special attention to the activities of the California Public Utilities Commission

Intergenerational preference differences and optimal national saving

This paper investigates the problem facing national planners who realize that their successors may employ different social welfare criteria for determining economic policies than they do. In such a situation, we show that the present planners may want to leave future generations a smaller capital stock than they would if they thought the stock would be managed in a way consistent with their own preferences. On the other hand, we also identify cases in which the opposite is true. We obtain the results by studying an optimal aggregate growth model the utility function of which changes randomly from one generation to the next. We analyze the model using a system of functional equations in place of the conventional Bellman equation from dynamic programming theory.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/23322/1/0000261.pd

Long-run equilibria with borrowing constraints and altruism

This paper adapts a nonstochastic overlapping generations model to include liquidity constraints and intergenerational altruism. Existing work indicates the importance of both but often considers them separately. This paper studies their interactions. First, it shows that they tend to conflict - the model only admits stationary equilibria with dynastic wealth accumulation but no binding liquidity constraints, or with binding constraints but no dynastic accumulation. Second, it examines the latter type of equilibrium closely. If liquidity constraints bind, quantitative examples imply that consequent utility losses may be small and that economywide wealth accumulation tends to be unrealistically low.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/31039/1/0000716.pd

Transition time paths for overlapping-generations models

This paper examines the transition stages between steady states for an overlapping-generations growth model. Our procedure is based on eigenvalues and eigenvectors. For marginal parameter changes, we can generate exact `multipliers' for the responses of state variables in each time period. Our solution technique is direct (rather than iterative), it yields an intermediate-stage test of stability, and it clearly reveals the need to interpret initial conditions carefully. We work several illustrative examples numerically.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/24825/1/0000251.pd

The definition of stability in models with perfect foresight

Frequently the stationary states of decentralized models with perfect foresight and more than one asset are saddlepoints. In this note we develop a distinction between "historical" and "nonhistorical" variables. Then we use the distinction to define economic concepts of "weak" and "strong" local asymptotic stability--which apply even for some saddlepoints. We conclude with three examples.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/23786/1/0000024.pd

Dynamic determinacy and the existence of sunspot equilibria

This paper relates the existence of stationary sunspot equilibria in the vicinity of a conventional stationary state to the phase diagram surrounding the latter. We find that the local condition required for a unique equilibrium path returning to the stationary state following any slight disturbance of initial conditions is also sufficient to exclude stationary sunspot equilibria in the stationary state's immediate vicinity. In that sense, an eigenvalue condition familiar from dynamic analysis can tell us something about the possibilities of local sunspot activity as well.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/28064/1/0000506.pd

The steady states of a stochastic decentralized growth model

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/24362/1/0000631.pd

Random earnings differences, lifetime liquidity constraints, and altruistic intergenerational transfers

This paper develops a model of private savings behavior in which households care about their descendants, cannot have negative net worth, and have lifetime earnings depending on random draws from an exogenous distribution of abilities. The elements interact: very lucky parents are likely to leave large estates; constrained children are unusually likely to receive intergenerational transfers. The paper proves the existence of a stationary cross-sectional distribution of wealth, endogenously determines where liquidity constraints will bind, and shows that the long-term interest rate must be such that Ricardian neutrality fails. Its last section generates several illustrative numerical simulations.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/29692/1/0000024.pd