Debt, deficits and finite horizons: The stochastic case

We introduce aggregate uncertainty and complete markets into Blanchard's (1985) perpetual youth model. We derive a simple expression for the pricing kernel that can be used to close a variety of equilibrium models in which the set of agents changes over time.     

ALLOCATION UNDER INCREASING AND DECREASING RETURNS

Abstract.  Efficient Allocation of labour among a set of machines (say) operating under initially increasing and then decreasing returns is studied first for identical machines and then for the case when machines can be ranked by their productivity. Essentially it is a question of the number of machines to be operated. At critical input levels this number jumps and the intensity of machine use is reduced discontinuously.     

An extension of the home-attachment criteria under dynamic tax competition

In this short note we extend the home attachment setting of Mansoorian and Myers (1993) and Ogura (2006) to allow the study of tax competition in a dynamic framework when international business relocation occurs over successive periods. The dynamic framework we propose also helps to understand why tax rates may change over time. Our modified home-attachment rule is illustrated by a simple model of dynamic tax competition in discrete time.     

Sustainable growth in a model with dual-rate discounting

In an important model of growth and pollution proposed by Stokey [Int. Econ. Rev. 39 (1998) 1] neither the rate of economic growth nor the rate of growth of emissions depends on the time preference of the representative agent, which seems somewhat paradoxical. To resolve this paradox, we introduce into Stokey's model the assumption of dual-rate discounting, prove the existence of a sustainable balanced growth optimal path, and show that the growth rates of output and emissions are increasing in the proportion between the consumption and the environmental discount factors of the representative agent.     

Research cycles

This paper studies the dynamics of fundamental research. We develop a simple model where researchers allocate their effort between improving existing fields and inventing new ones. A key assumption is that scientists derive utility from recognition from other scientists. We show that the economy can be either in a regime where new fields are constantly invented, and then converges to a steady state, or in a cyclical regime where periods of innovation alternate with periods of exploitation. Our analysis provides a rigorous foundation to the Kuhnian theory of scientific evolution. We show that scientists' care for reputation has a strong impact on research dynamics and tends to favor innovation. Especially, innovation fads may emerge. We also study welfare and find that the academic reputational reward system can help align scientists' short-term incentives with society's long-term interests.     

A closed-form solution to the transitional dynamics of the Lucas–Uzawa model

This paper studies how the intertemporal allocation determines the transitional dynamics to a given steady state and the long-term growth of an economy. Our main contribution consists in determining the solutions path for all the variables of the model, under fairly general conditions on σ and β.     

Stability of stochastic optimal growth models: a new approach

The paper proposes an Euler equation technique for analyzing the stability of differentiable stochastic programs. The main innovation is to use marginal reward directly as a Foster-Lyapunov function. This allows us to extend known stability results for stochastic optimal growth models, both weakening hypotheses and strengthening conclusions.     

Intertemporal price discrimination in infinite horizon

In infinite horizon, a credible durable-good monopolist may resort to intertemporal price discrimination. We provide an analytical characterization of his optimal price policy when consumers and the monopolist have different values for the trade because of distinct discount factors.     

On Ramseyʼs conjecture

Studying a one-sector economy populated by finitely many heterogeneous households that are subject to no-borrowing constraints, we confirm a conjecture by Frank P. Ramsey according to which, in the long run, society would be divided into the set of patient households who own the entire capital stock and impatient ones without any physical wealth. More specifically, we prove (i) that there exists a unique steady state equilibrium that is globally asymptotically stable and (ii) that along every equilibrium the most patient household owns the entire capital of the economy after some finite time. Furthermore, we prove that despite the presence of the no-borrowing constraints all equilibria are efficient. Our results are derived for the continuous-time formulation of the model that was originally used by Ramsey, and they stand in stark contrast to results that – over the last three decades – have been found in the discrete-time version of the model.     

Anticipation effects of technological progress on capital accumulation: a vintage capital approach

Due to embodied technological progress new generations of capital goods are more productive. Therefore, in order to study the effects of technological progress, a model must be analyzed in which different generations of capital goods can be distinguished. We determine in what way the firm adjusts current investments to predictions of technological progress. In the presence of market power we show that a negative anticipation effect occurs, i.e. current investments in recent generations of capital goods decline when faster technological progress will take place in the future, because then it becomes more attractive to wait for new generations of capital goods. In case that only investments in new machines are possible, actually a whole wave of anticipation phases arises.     

A nonsmooth, nonconvex model of optimal growth

This paper analyzes the nature of economic dynamics in a one-sector optimal growth model in which the technology is generally nonconvex, nondifferentiable, and discontinuous. The model also allows for irreversible investment and unbounded growth. We develop various tools to overcome the technical difficulties posed by the generality of the model. We provide sufficient conditions for optimal paths to be bounded, to converge to zero, to be bounded away from zero, and to grow unboundedly. We also show that under certain conditions, if the discount factor is close to 1, any optimal path from a given initial capital stock converges to a small neighborhood of the golden rule capital stock, at which sustainable consumption is maximized. If it is maximized at infinity, then as the discount factor approaches 1, any optimal path either grows unboundedly or converges to an arbitrarily large capital stock.     

Learning-by-doing,technology-adoption costs and wage inequality

In the dominant literature, the technological-knowledge bias that drives wage inequality is determined by the market-size channel. We develop an endogenous growth model with two technologies in which: a specific quality of labour, low or high-skilled, is combined with a specific set of quality-adjusted intermediate goods; the market-size channel is practically removed; adoption costs and learning-by-doing are linked with labour endowments. By solving transitional dynamics numerically, we show that changes in the supply of labour affect learning-by-doing and technology-adoption costs, which, in turn, influence the technological-knowledge bias and thus wage inequality. The proposed mechanisms can accommodate facts not explained by the previous literature.     

A percolation model of eco-innovation diffusion: The relationship between diffusion, learning economies and subsidies

An obstacle to the widespread adoption of environmentally friendly energy technologies such as stationary and mobile fuel cells is their high upfront costs. While much lower prices seem to be attainable in the future due to learning curve cost reductions that increase rapidly with the scale of diffusion of the technology, there is a chicken and egg problem, even when some consumers may be willing to pay more for green technologies. Drawing on recent percolation models of diffusion, we develop a network model of new technology diffusion that combines contagion among consumers with heterogeneity of agent characteristics. Agents adopt when the price falls below their random reservation price drawn from a lognormal distribution, but only when one of their neighbors has already adopted. Combining with a learning curve for the price as a function of the cumulative number of adopters, this may lead to delayed adoption for a certain range of initial conditions. Using agent-based simulations we explore when a limited subsidy policy can trigger diffusion that would otherwise not happen. The introduction of a subsidy policy seems to be highly effective for a given high initial price level only for learning economies in a certain range. Outside this range, the diffusion of a new technology either never takes off despite the subsidies, or the subsidies are unnecessary. Perhaps not coincidentally, this range seems to correspond to the values observed for many successful innovations.     

Structural shifts in the dynamics of the European income distribution

This paper aims to evaluate structural shifts in the regional per capita income distribution in Europe between the periods 1980–1993 and 1993–2005. After a brief analysis of several aspects of the distribution (inequality, external shape, polarisation and spatial dependence), we focus on intra-distribution dynamics by applying a novel causative matrix model that reveals strong structural shifts. In particular, increase in relative persistence during the second period has been the major change, especially for regions around the average and those at the upper end of the income distribution.     

Nonlinear economic growth: Some theory and cross-country evidence

This paper aims to test the existence of different growth regimes, that is of different relationships between growth rate and income level. We propose a simple nonlinear growth model and test its empirical implications by estimating Markov transition matrices and stochastic kernels. We show that growth is indeed nonlinear: a first phase of slow or zero growth is followed by a take-off and, finally, by a phase of deceleration. We discuss the relevance of these results with respect to the issue of convergence and reversibility of development, in the light of models of structural change and technological diffusion.     

The existence, uniqueness, and optimality of the terminal wealth depletion time in life-cycle models of saving under uncertain lifetime and borrowing constraint

In life-cycle models of saving under uncertain lifetime and borrowing constraint, the consumer's wealth must be depleted before the maximum lifetime. This paper investigates the existence, uniqueness, and optimality of the terminal wealth depletion time. It is proved that the optimal terminal wealth depletion time, if such exists, must be unique. If the equation that determines the optimal terminal wealth depletion has multiple solutions, then the location of the optimal solution will depend on the configuration of the solutions. An optimality test is developed to verify whether a candidate solution for the terminal wealth depletion time is indeed optimal. The paper introduces a method new to economics, the Dubovitskii-Milyutin adjoint equation, to analyze the properties of the optimal control problem.     

When does Learning by Doing generate current losses?

We study under which conditions a learning by doing effect in the industry causes a monopolist to operate at a loss for some initial periods. Those conditions involve a parameter of the learning process, the slope of inverse demand function and the discount parameter. In order to get results, we explore the analytical solution to a T-period learning by doing model, which is also a novelty. Numerical examples are presented.