Creator: Hopenhayn, Hugo Andres and Prescott, Edward C. Series: Working paper (Federal Reserve Bank of Minneapolis. Research Department) Number: 374 Abstract:
The existence of fixed points for monotone maps on spaces of measures is established. The case of monotone Markov processes is analyzed and a uniqueness and global stability condition is developed. A comparative statics result is presented and the problem of approximation to the invariant distribution is discussed. The conditions of the theorems are verified for the cases of Optimal Stochastic Growth and Industry Equilibrium.
Keyword: Stochastic dynamic programming, Stochastic growth theory, Monotone functions, Investment theory, Stationay distributions, and Fixed points Subject (JEL): C61 - Optimization Techniques; Programming Models; Dynamic Analysis
Creator: Hosseini, Roozbeh, Jones, Larry E., and Shourideh, Ali Series: Working paper (Federal Reserve Bank of Minneapolis. Research Department) Number: 674 Abstract:
We use an extended Barro-Becker model of endogenous fertility, in which parents are heterogeneous in their labor productivity, to study the efficient degree of consumption inequality in the long run. In our environment a utilitarian planner allows for consumption inequality even when labor productivity is public information. We show that adding private information does not alter this result. We also show that the informationally constrained optimal insurance contract has a resetting property—whenever a family line experiences the highest shock, the continuation utility of each child is reset to a (high) level that is independent of history. This implies that there is a non-trivial, stationary distribution over continuation utilities and there is no mass at misery. The novelty of our approach is that the no-immiseration result is achieved without requiring that the objectives of the planner and the private agents disagree. Because there is no discrepancy between planner and private agents' objectives, the policy implications for implementation of the efficient allocation differ from previous results in the literature. Two examples of these are: 1) estate taxes are positive and 2) there are positive taxes on family size.
Subject (JEL): H21 - Taxation and Subsidies: Efficiency; Optimal Taxation, D30 - Distribution: General, D63 - Equity, Justice, Inequality, and Other Normative Criteria and Measurement, D64 - Altruism; Philanthropy; Intergenerational Transfer, H23 - Taxation and Subsidies: Externalities; Redistributive Effects; Environmental Taxes and Subsidies, H43 - Project Evaluation; Social Discount Rate, and C61 - Optimization Techniques; Programming Models; Dynamic Analysis
Creator: Boldrin, Michele and Levine, David K. Series: Staff report (Federal Reserve Bank of Minneapolis. Research Department) Number: 301 Abstract:
We study a simple model of factor saving technological innovation in a concave framework. Capital can be used either to reproduce itself or, at additional cost, to produce a higher quality of capital that requires less labor input. If higher quality capital can be produced quickly, we get a model of exogenous balanced growth as a special case. If, however, higher quality capital can be produced slowly, we get a model of endogenous growth in which the growth rate of the economy and the rate of adoption of new technologies are determined by preferences, technology, and initial conditions. Moreover, in the latter case, the process of growth is necessarily uneven, exhibiting a natural cycle with alternating periods of high and low growth. Growth paths and technological innovations also exhibit dependence upon initial conditions. The model provides a step toward a theory of endogenous innovation under conditions of perfect competition.
Keyword: Choices and consequences, Technological change, Aggregate productivity, Processes and incentives, Innovation and invention, One, two and multisector growth models, and Measurement of economic growth Subject (JEL): C61 - Optimization Techniques; Programming Models; Dynamic Analysis, D41 - Market Structure, Pricing, and Design: Perfect Competition, O30 - Innovation; Research and Development; Technological Change; Intellectual Property Rights: General, O40 - Economic Growth and Aggregate Productivity: General, and D24 - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity