Optimal Growth Model Research Articles

Bridging the barriers: knowledge connections, productivity and capital accumulation

The paper contributes to the explanation of the large differences in cross-country productivity performance by modelling and testing the effects of social barriers to communication on productivity and capital accumulation. In an optimal growth model, social barriers to com- munication, which impede the formation of knowledge connections, are shown to reduce both transitory and steady-state levels of total factor productivity (TFP), per capita consumption and reproducible capital. Empirical testing yields a robust and theoretically consistent result: linguistic barriers to communication reduce productivity and capital accumulation. The findings provide an expla- nation for cross-country differences in TFP, and fresh insights into how productivity 'catch up' may be initiated.

A NOTE ON THE CONSEQUENCES OF AN ENDOGENOUS DISCOUNTING DEPENDING ON THE ENVIRONMENTAL QUALITY

Our intention is to study, in the framework of a very simple optimal growth model, the consequences on the optimal paths followed by consumption and the environmental quality of an endogenous discounting. Consumption directly comes from the use of environmental services and so is a direct cause of environmental degradation. The environment is valued both as a source of consumption and as an amenity. For a sustainability concern, we introduce an endogenous discount rate growing with the environmental quality, and compare the optimal growth paths with the ones obtained in the usual case of exogenous and constant discounting. We show that the convergence of the environmental quality toward a steady state occurs only for a very special configuration of the parameters in the exogenous discounting case, whereas it occurs generically in the endogenous discounting one. This happens for a utility discount rate becoming sufficiently high when the environmental quality is high and sufficiently low when the environmental quality is poor. In this case, then, endogenous discounting with a positive marginal discount rate allows us to avoid the depletion of the environment.

Beyond the Ramsey model for climate change assessments

The Ramsey optimal growth model contains a class of ethical frameworks popular among economists for assessing climate change. This essay critiques the Ramsey model, highlighting shortcomings in it and describing how to go beyond it towards more nuanced assessments through more accurate utility approximation and more diverse climate change mitigation strategies. This essay also critiques the 2 popular approaches for defining the model's ethics, prescriptivism and descriptivism, both in and beyond the Ramsey model context. The descriptive approach is found to hold serious flaws and should be rejected. Despite the model's various shortcomings, the climate change assessments using it provide a valuable applied ethics tool and bolster the case for climate change mitigation.

Invariance in growth theory and sustainable development

This paper analyzes the general concept of sustainability from a different point of view than that generally found in the literature. If sustainability is defined as the requirement to keep something constant or at least non-decreasing throughout time, the choice of the thing to be preserved is controversial. Neo-classical models mainly assume that sustainability requires that consumption or a utility level has to be preserved. In this paper, we object to this a priori conception of sustainability and define all the quantities that can be preserved in neo-classical optimal growth models. We thus wonder if invariant quantities can be found along the optimal paths defined by a classical representation of an economy with an exhaustible resource. We use the Noether theorem to determine the conservation laws of dynamic systems. We examine under which conditions there is such invariance and how it could be interpreted as a sustainability indicator. We emphasize the limits of the economic growth theory for coping with the sustainability issue.

Ronald W. Jones and Two-Sector Growth: Ramsey Optimality in the RSS and Leontief Cases

In this essay, we interpret the value-loss line, familiar in models of undiscounted optimal growth, as delineating the cone of diversification, familiar in models of international trade. This interpretation allows an embedding of the 2-sector Robinson-Solow-Srinivasan (RSS) model in the 2-sector Leontief model, and clarifies situations when the Leontief case offers additional insights into transition dynamics. The geometry underlying this embedding extends an earlier construction due to Khan-Mitra, and it has independent interest.

WITCH - A World Induced Technical Change Hybrid Model

The need for a better understanding of future energy scenarios, of their compatibility with the objective of stabilizing greenhouse gas concentrations, and of their links with climate policy, calls for the development of hybrid models. Hybrid because both the technological detail typical of Bottom Up (BU) models and the long run dynamics typical of Top Down (TD) models are crucially necessary. We present WITCH - World Induced Technical Change Hybrid model - a neoclassical optimal growth model (TD) with energy input detail (BU). The model endogenously accounts for technological progress, both through learning curves affecting prices of new vintages of capital and through R&D investments. In addition, the model captures the main economic interrelationships between world regions and is designed to analyze the optimal economic and environment policies in each world region as the outcome of a dynamic game. This paper provides a detailed description of the WITCH model, of its baseline, and of the model calibration procedure.

Quantitative comparison of photoacclimation models for marine phytoplankton

Photoacclimation models for marine phytoplankton describe the changes in their composition (typcially C, N and chlorophyll) and growth in response to changing light and nutrient environment. We compared two such models: that of Geider et al. (Geider, R.J., MacIntyre, H.L., Kana, T.M., 1998. A dynamic regulatory model of phytoplankton acclimation to light, nutrients, and temperature. Limnol. Oceanogr. 43, 679–694), hereafter the G model, and that of Pahlow (Pahlow, M., 2005. Linking chlorophyll-nutrient dynamics to the redfield N:C ratio with a model of optimal phytoplankton growth. Mar. Ecol. Prog. Ser. 287, 33–43), hereafter the P model. Using the Monte Carlo Markov Chain method, we fitted both models to the data set from an incubation experiment by Flynn et al. (Flynn, K.J., Davidson, K., Leftley, J.W., 1994. Carbon–nitrogen relations at whole-cell and free amino-acid levels, during batch growth of isochrysis galbanna (prymnesiophyceae) under conditions of alternating light and dark. Mar. Biol. 118, 229–237). Data consisted of measured concentrations for particulate organic N, particulate organic C, chlorophyll and ammonium. The authors of the G model began their simulation from day 5 for this experiment, claiming that their model could not reproduce the initial lag phase (slow growth during the first few days of the experiment). The author of the P model claimed that its ability to reproduce this initial lag phase (starting from the beginning of the experiment) was a significant improvement over previous models. Our fitting revealed that the G model can reproduce this initial lag phase as well as the P model, and that both models simulate the data set well. In the best-fits of both models, chlorophyll synthesis during the initial lag phase was limited by the rate of carbon assimilation, even though the G model was designed to have chlorophyll synthesis limited only by the rate of N assimilation. The requirement of organic carbon for energy to assimilate nitrogen results in this indirect limitation of chlorophyll synthesis by C assimilation in the G model, whereas chlorophyll synthesis is explicitly limited by the rate of C assimilation in the P model. This suggests that chlorophyll synthesis is in fact limited by the rate of C assimilation during the initial lag phase. As in the hand-tuned simulations previously published, the P model simulated the initial decrease in Chl:N ratio (as observed) whereas the G model simulated an initial increase in this ratio (contrary to the observations). We also discuss the relative merits of the two models for applications at large scales. Although data assimilation is not perfectly objective, because it requires certain choices such as weights for various data types and which data to include when fitting, our results show the advantage of mathematically rigorous fitting as opposed to hand-tuning of models. Our best-fits were significantly better than the hand-tuned fits originally published, especially for the G model, and this yielded insight into the mechanism responsible for the initial lag in phytoplankton growth.

Capital Maintenance versus Technology Adoption under Embodied Technical Progress

We study an optimal growth model with one-hoss-shay vintage capital, where labor resources can be allocated freely either to production, technology adoption or capital maintenance. Technological progress is partly embodied. Adoption labor increases the level of embodied technical progress. First, we are able to disentangle the amplification-propagation role of maintenance in business fluctuations: in the short run, the response of the model to transitory shocks on total factor productivity in the final good sector are definitely much sharper compared to the counterpart model without maintenance but with the same average depreciation rate. Moreover, the one-hoss shay technology is shown to reinforce this amplification-propagation mechanism. We also find that accelerations in embodied technical progress should be responded by a gradual adoption effort, and capital maintenance should be the preferred instrument in the short run.

Endogenous Fluctuations in Two-Sector Models: Role of Preferences

We consider a discrete-time two-sector CES (constant elasticity of substitution) economy with sector specific external effects and nonlinear preferences. Our goal is to examine carefully the influence of the utility curvature on the occurrence of multiple equilibria. We show that local indeterminacy depends on an interplay between factor substitutability and the elasticity of intertemporal substitution in consumption. Moreover, considering that, when the external effects are set equal to zero, we get a two-sector optimal growth model, we study also the role of the utility curvature on the occurrence of competitive equilibrium cycles. We show that persistent endogenous fluctuations and macroeconomic volatility require a strong enough elasticity of intertemporal substitution in consumption.

On unbounded growth with heterogenous consumers

This paper studies unbounded growth with infinite-horizon consumers whose discount factors and instant utility functions are not assumed to be identical. The Negishi-type planner becomes non-homogenous and as a consequence, different consumer types may end up holding all wealth in the far future for different initial distributions of income. The main technical contribution is a turnpike theorem which generalizes the global stability results of [Kaganovich, M., 1998. Sustained endogenous growth with decreasing returns and heterogenous capital. Journal of Economic Dynamics and Control 22, 1575–1603] and [Jensen, M.K., 2003. On the global stability of unbounded optimal growth models. Mimeo].

Stochastic optimal growth with bounded or unbounded utility and with bounded or unbounded shocks

This paper studies a one-sector stochastic optimal growth model with i.i.d. productivity shocks in which utility is allowed to be bounded or unbounded, the shocks are allowed to be bounded or unbounded, and the production function is not required to satisfy the Inada conditions at zero and infinity. Our main results are three-fold. First, we confirm the Euler equation as well as the existence of a continuous optimal policy function under a minimal set of assumptions. Second, we establish the existence of an invariant distribution under quite general assumptions. Third, we show that the density of optimal output converges to a unique invariant density independently of initial output under the assumption that the shock distribution has a density whose support is an interval, bounded or unbounded. In addition, we provide existence and stability results for general one-dimensional Markov processes.

An application of expert information to win betting on the Kentucky Derby, 1981–2005

The Kentucky Derby features top three-year-old thoroughbred horses. Run at miles, it is typically at least 1/8 mile longer than any of the horses has raced before. This extra distance, usually combined with a large field, makes the race a difficult test of stamina for horses this young. Bettors, because there is no direct evidence of whether a horse has the stamina to compete effectively at miles, are also challenged. The informational content of one publicly available, pedigree-based measure of stamina, the Dosage Index, is used with simple performance measures to identify a semi-strong-form inefficiency, and to create a betting scheme based on the optimal capital growth model that merges these criteria with the public’s opinion. Statistically significant profits, net of transaction costs, could have been achieved during the period 1981 to 2005.

A World Induced Technical Change Hybrid Model

The need for a better understanding of future energy scenarios, of their compatibility with the objective of stabilizing greenhouse gas concentrations, and of their links with climate policy, calls for the development of hybrid models. Hybrid because both the technological detail typical of Bottom Up (BU) models and the long run dynamics typical of Top Down (TD) models are crucially necessary. We present WITCH - World Induced Technical Change Hybrid model - a neoclassical optimal growth model (TD) with energy input detail (BU). The model endogenously accounts for technological progress, both through learning curves affecting prices of new vintages of capital and through R&D investments. In addition, the model captures the main economic interrelationships between world regions and is designed to analyze the optimal economic and environment policies in each world region as the outcome of a dynamic game. This paper provides a detailed description of the WITCH model, of its Baseline, and of the model calibration procedure.

Optimal Control in Infinite Horizon Problems: A Sobolev Space Approach

In this paper, we make use of the Sobolev space W1,1(R+, Rn) to derive at once the Pontryagin conditions for the standard optimal growth model in continuous time, including a necessary and sufficient transversality condition. An application to the Ramsey model is given. We use an order ideal argument to solve the problem inherent to the fact that L1 spaces have natural positive cones with no interior points.

Stochastic optimal economic growth model with natural resources

The paper examines an economic growth problem how social planners reasonably open up and retain natural resources. The objective is to maximize the total expected discounted utility of comsumption. Social planners' optimal devision and optimal expected rates at the steady state are derived. At last, how productivity and productivity shock affect on the expected growth rate, consumption-resources ratio and the fraction of exploited resources, are analyzed.

Relative Wealth, Consumption Taxation, and Economic Growth

This paper examines the role of the relative wealth-induced status motive in affecting the neutrality of consumption taxation in an optimizing growth model. It is found that a key factor determining the validity of the neutrality of consumption taxation in both the level sense and the growth rate sense is the desire for relative wealth-induced social status. When individuals care about their relative wealth, a rise in consumption tax enhances the steady-state level of capital stock and consumption. Furthermore, if the production function takes a linear technology form as the engine of sustained growth, then increases in consumption taxation raise the economy's long-run growth rate. In addition, an optimal consumption tax policy provides full subsidies to consumption so as to induce the economy to achieve the social optimum and the optimal growth rate.

On optimal growth models when the discount factor is near 1 or equal to 1

The aim of this paper is to fill the gap between intertemporal growth models when the discount factor is close to one and when it equals one. We show that the value function and the policy function are continuous with respect both to the discount factor, β, and the initial stock of capital, x0. We prove that the optimal policy gβ(x0) is differentiable and that Dgβ(x0) is continuous with respect to (β, x0). As a by-product, a global turnpike result is proved.

Optimal cycles and social inequality: What do we learn from the Gini index?

One of the plausible explanations for macroeconomic fluctuations relies on the occurrence of endogenous deterministic cycles. In the last three decades, most of the relevant literature has rested on the assumption of a representative agent but, recently, a few papers have investigated the role of consumers' heterogeneity on endogenous fluctuations. Our article aims at taking a step forward in order to give a more suitable interpretation. To keep things as simple as possible, we introduce heterogeneous households in a two-sector optimal growth model and we study how wealth heterogeneity affects the occurrence of endogenous cycles. In contrast to previous results, we relate the existence of such cycles to the most commonly used inequality measure, the Gini index, and analyze the impact of consumers' heterogeneity on this index.

The Development Problem under Embodiment

This paper studies technology adoption in an optimal growth model with embodied technical change. The economy consists of the final good sector, the capital sector, and the technology sector which role is the imitation of exogenous innovations. Scarce labor resources are allocated to the technology and final good sectors. The final good is allocated to consumption and to the capital sector. The authors analytically characterize the long run optimal allocations. Using a calibrated version of the model, they find that an acceleration in the rate of embodied technical change should not be responded by an immediate and strong adoption effort. Instead, adoption labor should decrease in the short run, and the optimal technological gap is shown to increase either in the short or in the long run. The state of the institutions and policies around the technology sector is key in the design of the optimal adoption timing.

Impatience and equilibrium indeterminacy

This paper extends the neoclassical one-sector optimal growth model by postulating that individual agents’ time preference (impatience) depends on the economy-wide average consumption and average income, which are social factors taken as external by individual agents. The paper shows that with the socially determined individual time preference local equilibrium indeterminacy can arise. Moreover, local indeterminacy can also be associated with global indeterminacy in many cases. The results hold in models with bounded and unbounded growth.