Optimal Growth Model Research Articles

On Lipschitz continuity of the iterated function system in a stochastic optimal growth model

This paper provides qualitative properties of the iterated function system (IFS) generated by the optimal policy function for a class of stochastic one-sector optimal growth models. We obtain, explicitly in terms of the primitives of the model (i) a compact interval (not including the zero stock) in which the support of the invariant distribution of output must lie, and (ii) a Lipschitz property of the iterated function system on this interval. As applications, we are able to present parameter configurations under which (a) the support of the invariant distribution of the IFS is a generalized Cantor set, and (b) the invariant distribution is singular.

Development and application of the theory of parametric regulation of evolution of economic systems based on a neoclassical model of optimal growth

Presented were some results on roughness of the mathematical model of the neoclassical theory of optimal growth with and without parametric regulation, selection of the optimal law of parametric regulation, and the optimal law of parametric regulation vs. the uncontrollable parameters of this mathematical model based on the parametric regulation theory.

Emissions corridors for reducing the risk of a collapse of the Atlantic thermohaline circulation

In this paper, we present the integrated assessment model dimrise (dynamic integrated model of regular climate change impacts and singular events). This model is designed to investigate the stability of the Atlantic thermohaline circulation (THC) and to derive related climate policy recommendations. It is written in GAMS and comprises a dynamic model of the THC coupled to a climate model and a global economy model for assessing the monetary cost of climate protection. The THC model is a dynamic four-box interhemispheric extension of the classic Stommel model calibrated against results obtained using the CLIMBER-2 climate model. The reduced-form climate model used to drive the THC model is the ICLIPS multi-gas climate model, which is a computationally efficient, globally aggregated model able to mimic the response of more sophisticated carbon cycle and atmosphere-ocean general circulation models. The THC and climate modules are coupled to a globally aggregated Ramsey-type optimal growth model of the world economy derived from the Nordhaus DICE model. Together, these components create a novel dynamic fully coupled computationally efficient integrated assessment model. Illustrative applications demonstrate that dimrise is able to derive (constrained) economically optimal emissions paths that comply with prescribed bounds on admissible THC weakening imposed in order to avoid an irrevocable breakdown. In addition, emissions corridors are presented which contain all possible emissions paths that do not endanger the stability of the THC and that simultaneously obey restrictions on welfare loss arising from mitigation efforts. The presented results show that, under worst-case conditions, the stability of the THC may be threatened within two decades if global emissions would not deviate from the business-as-usual trajectory.

Solving optimal growth models with vintage capital: The dynamic programming approach

This paper deals with an endogenous growth model with vintage capital and, more precisely, with the AK model proposed in [R. Boucekkine, O. Licandro, L.A. Puch, F. del Rio, Vintage capital and the dynamics of the AK model, J. Econ. Theory 120 (1) (2005) 39–72]. In endogenous growth models the introduction of vintage capital allows to explain some growth facts but strongly increases the mathematical difficulties. So far, in this approach, the model is studied by the Maximum Principle; here we develop the Dynamic Programming approach to the same problem by obtaining sharper results and we provide more insight about the economic implications of the model. We explicitly find the value function, the closed loop formula that relates capital and investment, the optimal consumption paths and the long run equilibrium. The short run fluctuations of capital and investment and the relations with the standard AK model are analyzed. Finally the applicability to other models is also discussed.

An algorithm for construction of optimal timing solutions in problems with a stochastic payoff function

A dynamic model of optimal timing is applied to the problem of optimization of an innovation process in a competitive market environment. The basic element of the model is a block for optimization of the stopping time of the investment process. The problem of optimal timing is solved in parallel with adjoint problems of assessment of the market potential innovation and optimal control synthesis of the investment process. For construction of the optimal control synthesis the basic elements of models of optimal economic growth are used. In the econometric block, a probabilistic model is applied for design of market trajectories described by distribution functions. These distribution functions determine a market share of commercialized projects and probability of presence of competitors on the market at the current moment of time. Stochastic models for specification of the price formation mechanism are constructed for a series of distribution functions. An algorithm for construction of the optimal commercialization time and optimal investment plan is proposed. The algorithm is based on qualitative analysis of extremal points of the utility function which correspond to intersection points of a market distribution function and marginal costs of the innovation process. The algorithms are realized in the program software for simulation of optimal investment plans.

Biphasic growth in fish I: Theoretical foundations

We develop the theory of biphasic somatic growth in fish using models based on the distinction between pre- and post-maturation growth and an explicit description of energy allocation within a growing season. We define a ‘generic biphasic’ (GB) model that assumes post-maturation growth has a von Bertalanffy (vB) form. For this model we derive an explicit expression for the gonad weight/somatic weight ratio ( g) which may either remain fixed or vary with size. Optimal biphasic models are then developed with reproductive strategies that maximise lifetime reproductive output. We consider two optimal growth models. In the first (fixed g optimal), gonad weight is constrained to be proportional to somatic weight. In the second (variable g optimal) model, allocation to reproduction is unconstrained and g increases with size. For the first of these two models, adult growth in a scaled measure of length has the exact vB form. When there are no constraints on allocation, growth is vB to a very good approximation. In both models, pre-maturation growth is linear. In a companion paper we use growth data from lake trout ( Salvelinus namaycush) to test the bioenergetics assumptions used to develop these models, and demonstrate that they have advantages over the vB model, both in quality of fit, and in the information contained in the fitted parameters.

Non-convex aggregate technology and optimal economic growth

This paper examines a model of optimal growth where the aggregation of two separate well behaved and concave production technologies exhibits a basic non-convexity. First, we consider the case of strictly concave utility function: when the discount rate is either low enough or high enough, there will be one steady state toward which the convergence of the optimal path is monotone and asymptotic. When the discount rate is in some intermediate range, we will find sufficient conditions for having either one equilibrium or multiple equilibria steady state. Depending to whether the initial capital per capita is located with respect to a critical value, we show that the optimal paths monotonically converge to one single appropriate equilibrium steady state. Second, we consider the case of linear utility and provide sufficient conditions to have either unique or two steady states when the discount rate is in some intermediate range. In this range, we give conditions under which the above critical value might not exist, and the economy attains one steady state in finite time, then stays at the other steady state afterward.

On the dynamics of capital accumulation across space

We solve an optimal growth model in continuous space, continuous and bounded time. The optimizer chooses the optimal trajectories of capital and consumption across space and time by maximizing an objective function with both space and time discounting. We extract the corresponding Pontryagin conditions and prove their sufficiency. We end up with a system of two parabolic differential equations with the corresponding boundary conditions. We propose a simple numerical set-up to simulate PDE systems which we employ to study the roles of initial capital and technology distributions over space in various scenarios.

OPTIMAL DISCOUNTING OF BENEFITS FROM CLEANUP AT WASTE SITES

Abstract This paper uses a general equilibrium optimal growth model to discuss the role of optimal discounting of future benefits from cleanup at high‐level toxic waste sites. Cleanup simultaneously generates two streams of benefits. One of these is directly from utility and the other is indirectly from the added productivity of workers. We note that the optimal discount rate is different for these two types of benefits. Along the optimal path, the former are discounted at the rate of time preference and the latter at the market rate of interest. We achieve this by identifying four components of the shadow value of the stock of toxic waste. These are the utility, productivity, cost, and abundance effects.The distinction between discount rates appears to have been overlooked in the literature but has significant implications for environmental cost‐benefit analysis due to the growing interest in applying zero time preference to environmental problems, (like waste cleanup) whose consequences extend many generations into the future. A numerical example is included to illustrate these concepts.

Economists, value judgments, and climate change: A view from feminist economics

A number of recent discussions about ethical issues in climate change, as engaged in by economists, have focused on the value of the parameter representing the rate of time preference within models of optimal growth. This essay examines many economists' antipathy to serious discussion of ethical matters, and suggests that the avoidance of questions of intergenerational equity is related to another set of value judgments concerning the quality and objectivity of economic practice. Using insights from feminist philosophy of science and research on high reliability organizations, this essay argues that a more ethically transparent, real-world-oriented, and flexible economic practice would lead to more reliable and useful knowledge.

Can interaction contribute to the explanation of business cycles?

Purpose – Recent literature has been able to include into standard optimal growth models some hypotheses that allow for the generation of endogenous long‐run fluctuations. This paper aims to contribute to this endogenous business cycles literature by considering social interactions.Design/methodology/approach – The paper is essentially theoretical and it develops a growth/cycles model, in which social interactions play a relevant role. In the proposed model, individuals can choose, under a discrete choice rule, to which social group they prefer to belong. This selection process is constrained essentially by the dimension of the group, which is the main determinant regarding the utility individuals withdraw from social interaction. The proposed set‐up implies the presence of cycles and chaotic motion describing the evolution of group dimension over time.Findings – Because being a member of a group involves costs to households, the inclusion of these costs in a standard Ramsey growth model will imply that e...

Existence of solutions in continuous-time optimal growth models

This paper studies the existence of solutions in continuous time optimization problems. It provides a theorem whose conditions can be easily checked in most models of the optimal growth theory, including those with increasing returns and multi-sector economies.

Loss aversion in aggregate macroeconomic time series

Prospect theory has been the focus of increasing attention in many fields of economics. However, it has scarcely been addressed in macroeconomic growth models—neither on theoretical nor on empirical grounds. In this paper we use prospect theory in a stochastic optimal growth model. Thereafter, the focus lies on linking the Euler equation obtained from a prospect theory growth model of this kind to real macroeconomic data. We will use generalized method of moments (GMM) estimation to test the implications of such a non-linear prospect utility Euler equation. Our results indicate that loss aversion can be traced in aggregate macroeconomic time series.

The Short-Run Dynamics of Optimal Growth Models with Delays

Differential equations with advanced and delayed time arguments may arise in the optimality conditions of simple growth models with delays. Models with delayed adoption of new technologies, habit formation or learning-by-using lie in this category. In this paper we present new insight on the role of advanced time arguments to mitigate the echo effects induced by lag structures. In so doing we use optimal control theory with delays, and we propose a shooting method to deal with leads and lags in the Euler system associated to dynamic general equilibrium models in continuous time. We implement these methods to solve for the short-run dynamics of a neoclassical growth model with a simple time-to-build lag.

Equilibrium Selection in an Experimental Macroeconomy

In this paper we report the results of an experiment designed to study the behavior of a laboratory macroeconomy with two stable steady states. The economy has the structure of an optimal growth model in which resources are allocated between consumption and investment over a sequence of time periods. The economy is decentralized, with a market for capital in operation. We find that the economy often falls into the Pareto‐inferior steady state, which can be viewed as a poverty trap. The initial endowment of capital stock is varied as a treatment variable in the experiment, and the economy is more likely to reach the optimal steady state when its initial endowment is high than when it is low. Organizing the economy with a central planner directing economic activity fails to induce it to reach the optimal steady state.

International passenger transport and climate change: A sector analysis in car demand and associated [formula omitted] emissions from 2000 to 2050

The paper provides global regionalized projections of passenger car demand, use and associated CO 2 emissions from 11 world regions. The study is based on empirical data that have been originally collated from international sources for the purpose of modeling region-specific car stock demand. Derived demands serve as indicator of car related fuel consumption and associated CO 2 emissions, which are calculated on the basis of behavioral and technological scenarios. The obtained CO 2 emission paths are sectoral baseline scenarios that identify region-specific potentials of growth in car induced CO 2 emissions assuming that current trends continue to prevail. The study adopts a multi-model approach to car demand by applying two methodologies rooted in the economics of consumption: utility maximization and single equation models. The utility maximization method for modeling car demand is driven by the preferences of the representative consumers of each world region, subject to exogenous price and income trajectories. The latter is adopted from an optimal growth model. This is a novel approach to projecting global regionalized sectoral car demands. The study is complemented by the application of single equation income–consumption models based on logistical Gompertz functions and non-linear regression techniques to compare model results.

The Spenders-Hoarders Theory of Capital Accumulation, Wealth Distribution and Fiscal Policy

This paper proposes a simple OLG model which is consistent with the essential facts about consumer behavior, capital accumulation and wealth distribution, and yields some new and surprising conclusions about fiscal policy. By considering a society in which individuals are distinguished according to two characteristics, altruism and wealth preference, we show that those who in the long run hold the bulk of private capital are not so much motivated by dynastic altruism as by preference for wealth. Two types of social segmentation can result with different wealth distribution. To a large extent our results seem to fit reality better than those obtained with standard optimal growth models in which dynastic altruism (or rate of impatience) is the only source of heterogeneity: overaccumulation can appear, public debt and unfunded pensions are not neutral, estate taxation can improve the welfare of the top wealthy.

The American frontier: Technology versus immigration

How important was international immigration for the US and its demography during the nineteenth century? This paper investigates, quantitatively, its effect on the westward movement of population and the regional and secular changes in fertility. Beside immigration, two alternative forces are considered: technological progress and the land policy (the Homestead Act). An optimal growth model with endogenous fertility and migration is calibrated, and counterfactual experiments reveal that the main driving forces were productivity growth and the declining cost of transportation. International immigration played a lesser role.

Animal spirits in cash-in-advance economies

Résumé La pertinence empirique des modèles avec indétermination de l’équilibre et fluctuations “à taches solaires” a souvent été remise en cause, notamment parce que de tels modèles exigeraient des rendements d’échelle fortement croissants ou des calibrations relativement controversées des fondamentaux de l’économie. Dans cet article, nous étudions l’apparition de tels phénomènes dans un modèle standard de croissance optimale avec offre de travail endogène lorsqu’une contrainte d’encaisses préalables partielle porte sur les dépenses de consommation des ménages. Nous montrons, sous des préférences usuelles et des rendements d’échelle constants, que de tels phénomènes émergent en présence d’une contrainte de liquidité arbitrairement faible . Nous étudions également les propriétés cycliques de cette économie en présence de chocs portant simultanément sur la technologie et les croyances, et analysons nos résultats au regard de modèles comparables proposés dans la littérature. Classification JEL : D90, E32, E41.

Animal spirits in cash-in-advance economies

Resume La pertinence empirique des modeles avec indetermination de l’equilibre et fluctuations “a taches solaires” a souvent ete remise en cause, notamment parce que de tels modeles exigeraient des rendements d’echelle fortement croissants ou des calibrations relativement controversees des fondamentaux de l’economie. Dans cet article, nous etudions l’apparition de tels phenomenes dans un modele standard de croissance optimale avec offre de travail endogene lorsqu’une contrainte d’encaisses prealables partielle porte sur les depenses de consommation des menages. Nous montrons, sous des preferences usuelles et des rendements d’echelle constants, que de tels phenomenes emergent en presence d’une contrainte de liquidite arbitrairement faible. Nous etudions egalement les proprietes cycliques de cette economie en presence de chocs portant simultanement sur la technologie et les croyances, et analysons nos resultats au regard de modeles comparables proposes dans la litterature.Classification JEL : D90, E32, E41.