Optimal Growth Model Research Articles

Competitive equilibrium cycles for small discounting in discrete-time two-sector optimal growth models

Abstract We study the existence of endogenous competitive equilibrium cycles under small discounting in a two-sector discrete-time optimal growth model. We provide precise concavity conditions on the indirect utility function leading to the existence of period-two cycles with a critical value for the discount factor that can be arbitrarily close to one. Contrary to the continuous-time case where the existence of periodic-cycles is obtained if the degree of concavity is close to zero, we show that in a discrete-time setting the driving condition does not require a close to zero degree of concavity but a symmetry of the indirect utility function’s concavity properties with respect to its two arguments.

Hopf bifurcation and the existence and stability of closed orbits in three-sector models of optimal endogenous growth

Abstract The present paper constructs a family of three-sector models of optimal endogenous growth, and conducts exact bifurcation analysis. In so doing, original six-dimensional equilibrium dynamics is decomposed into five-dimensional stationary autonomous dynamics and one-dimensional endogenously growing component. It is shown that the stationary dynamics thus decomposed undergoes supercritical Hopf bifurcation. It is inferred from the convex structure of our model that the dimension of a stable manifold of each closed orbit thus bifurcated in this five-dimensional dynamics should be two.

Power-law distribution in the external debt-to-fiscal revenue ratios: Empirical evidence and a theoretical model

This paper provides evidence that the external debt-to-fiscal revenue ratio in emerging countries follows a power-law distribution. Such a distribution reflects the fact that external debt distress or debt crises correspond to extreme events that have been found to happen fairly often. We formally test the hypothesis of a power-law, going further than the usual visual inspection of the distribution of the variable of interest on a doubly logarithmic scale. We also show that such a distribution can be derived from a theoretical model in which uncertainty comes from tax evasion and corruption. Using the framework of an optimal stochastic growth model, we model the external debt-to-fiscal revenue ratio as a diffusion process for which the stochastic steady state distribution is derived using the properties of Itô diffusion processes.

Machine learning for high-dimensional dynamic stochastic economies

We present a novel computational framework that can compute global solutions to high-dimensional dynamic stochastic economic models on irregular state space geometries. This framework can also resolve value and policy functions’ local features and perform uncertainty quantification, in a single model evaluation. We achieve this by combining Gaussian process machine learning with active subspaces; we then embed this into a parallelized discrete-time dynamic programming algorithm. To demonstrate the broad applicability of our method, we compute solutions to stochastic optimal growth models of up to 500 continuous dimensions. We also show that our framework can address parameter uncertainty and can provide predictive confidence intervals for policies that correspond to the epistemic uncertainty induced by limited data. Finally, we propose an algorithm that, based on combining this framework with Bayesian Gaussian mixture models, is capable of learning irregularly shaped ergodic sets as well as performing dynamic programming on them.

Georgescu-Roegen versus Solow/Stiglitz: Back to a controversy

Within the framework of an optimal growth model with a non renewable resource, this paper seeks to answer the question of whether a production function that ignores the constraints of physics on the production process (such as the Cobb-Douglas) can generate a good medium-term approximation of the trajectory of the economy obtained with a “true” production function, which takes these constraints into account. Two functions that respect these constraints are considered: (i) the CES function and (ii) a function called ATF, designed specifically for the purposes of this paper and which has the property of being closer to the Cobb-Douglas than is the CES.The approximation generated by the Cobb-Douglas can be rough, at least for some variables. When the “true” production function is the CES, this is explained by two effects: (i) the difference in technologies and (ii) the fact that the Cobb-Douglas totally changes the long-term path of the economy compared to that induced by the CES. In the case of the ATF, only the second effect acts. If accuracy is a concern, then whatever the “true” function the obtained results do not argue in favour of a positive answer to the above question. The Cobb-Douglas is only acceptable when the constraints of physics act weakly, which unfortunately is not always empirically verified (especially in the case of energy). If accuracy is not the first concern, then the answer seems positive, to the extent that the medium term paths generated by the Cobb-Douglas and the “true” function have a similar shape and the orders of magnitude are preserved.

Optimal Growth in Two-Sided Markets

We develop a theoretical model of optimal growth in two-sided markets. The model posits that market output (number of transactions) is a function of the stock of supply and demand. This market output is modeled using a homogeneous function, which can have increasing or decreasing returns to scale. The supply and demand stock levels follow a growth model in which the rate of growth at each point in time is a function of both the surplus each side of the market receives and the attrition of supply and demand (supply and demand lifetimes). The surplus can be apportioned between the two sides of the market by changing the price paid to sellers and the price charged to buyers, which we assume the platform controls. Through these price levers, the platform can pay subsidies to one or both sides of the market. We investigate the behavior of optimal market growth, including the point at which the market becomes self-sustaining and the long-run optimal size of the market. We characterize the optimal balance between supply and demand as the market size grows and determine optimal policies that maximize discounted total profit. For the case of both increasing and decreasing returns without price constraints, we show the optimal policy is to grow using an impulse of spending (a subsidy shock'') to move the market immediately to its optimal long-run size. This result is consistent with the ``race to growth'' observed in many two-sided markets like ride-sharing.

Exploitation status of Squaliobarbus curriculus in the Xijiang River based on the analysis of the yield per recruit and spawning biomass per recruit models

PDF HTML阅读 XML下载 导出引用 引用提醒 基于单位补充量模型的西江赤眼鳟种群资源利用现状评价 DOI: 作者: 作者单位: 1. 中国水产科学研究院珠江水产研究所, 广东 广州 510380;2. 上海海洋大学海洋科学学院, 上海 201306;3. 农业农村部珠江中下游渔业资源环境科学观测实验站, 广东 广州 510380 作者简介: 李策(1993-),男,硕士研究生,从事渔业资源研究.E-mail:lice930811@aliyun.com 通讯作者: 中图分类号: S931 基金项目: 广东省自然科学基金项目（2016A030313147）；中国水产科学研究院中央级公益性科研院所基本科研业务费专项资金（2017HY-ZD0103）. Exploitation status of Squaliobarbus curriculus in the Xijiang River based on the analysis of the yield per recruit and spawning biomass per recruit models Author: Affiliation: 1. Pearl River Fisheries Research Institute, Chinese Academy of Fishery Sciences, Guangzhou 510380, China;2. College of Marine Sciences, Shanghai Ocean University, Shanghai 201306, China;3. Scientific Observing and Experimental Station of Fishery Resources and Environment in the Middle and Lower Reaches of Pearl River, Ministry of Agriculture and Rural Affairs, Guangzhou 510380, China Fund Project: 摘要 | 图/表 | 访问统计 | 参考文献 | 相似文献 | 引证文献 | 资源附件 | 文章评论 摘要:赤眼鳟（）是珠江中下游最重要的经济鱼类之一，本研究利用2009—2014年西江肇庆江段渔业捕捞调查监测数据，分析了其生长和死亡参数历史变化，利用单位补充量渔获量（yield per recruitment，YPR）模型、单位补充量产卵群体生物量（spawning biomass per recruitment，SBR）和生物学参考点评估了赤眼鳟资源利用状况。结果表明，赤眼鳟体长（R2=0.9595，+0.613）]。目前西江的捕捞强度（=0.86）远超种群可持续开发水平，赤眼鳟种群处于生长型捕捞过度状态。根据实际情况，建议将西江赤眼鳟开捕年龄提高至3龄（或开捕体长增大至238 mm），则预计单位补充量渔获量可增加175%，在珠江禁渔期制度的协同保护下，种群实际保护效果可能更好。 Abstract:The Pearl River, the largest river in southern China, historically harbors abundant fishery resources. However, the fishery resources have severely declined in recent decades owning to dam cascade development, overfishing, water pollution, and so on. Therefore, it is necessary to evaluate fishery resource utilization and exploitation, which provides scientific guidance for fishery resource conservation in the Pearl River. Generally, the per recruitment model has been widely applied to the dynamics of single fish populations. The per recruitment models mainly consist of the yield per recruitment model (YPR) and the spawning biomass per recruitment models (SBR). The YPR model prevents overgrowth overfishing and is usually used to determine the fishery management parameters (e.g. mesh size and catch rate). This model could provide management guidance for the development and utilization of fish stocks. The spawning biomass per recruitment model prevents supplemental overfishing. This model is utilized to assess whether parental biological residues and spawning stock are sufficient to maintain the stock of larvae supplementation, and then it estimates the status of resource utilization. The barbel chub () is an important economic fish inhabiting the middle and lower reaches of the Pearl River. An assessment of the current status of utilization is important for reasonable resource exploitation and maintenance. The data of the present study were collected in the Zhaoqing section of the Xijiang River (an important stem of the Pearl River) between 2009 and 2014. We analyzed the growth and mortality characteristic parameters and evaluated the resource exploitation status by the YPR model, SBR model, and biological reference points. The relationship between standard length and weight was expressed as:=0.9595, =2346). The von Bertalanffy growth equation was selected as the optimal growth model and was expressed as ]. The present fishing intensity (=0.86) have far exceeded the level of sustainable population development. The stock of was overfished in its vegetative form. We suggest to increase the catch age to 3 years old (or to a standard length of 238 mm) for the stock conservation of in the Xijiang River; the yield per recruitment could thus be increased by 175%. The protective efficacy could increase with a fishing moratorium in the Pearl River, and relevant fishery management measurements should be improved at the same time. 参考文献 相似文献 引证文献

Savings and growth in neoclassical growth models: A comment on “Is Piketty’s “second law of capitalism” fundamental?”

This note explores the response of saving rates to the rate of income growth in models of optimal growth. Contrary to the claims in Krusell and Smith (2015) the sign of this response depends on the consumption intertemporal elasticity of substitution.

Parametric Analysis of the Sensitivity of a Functional on the Basis of the Non-Classical Model of Optimal Economic Growth

We study the sensitivity of a functional on the basis of the macroeconomic model. This analysis is a calculation of the derivative with respect to the parameters of the functional characterizing the optimal trajectory. To solve this problem, we apply an approach using conjugate functions and bring the results down to concrete computations. As the model we use a neoclassical model of optimal economic growth and estimate the sensitivity with the growth rate of civilian labor force of national economies in three European countries. Our results can be recommended for analysis and practical use by the relevant authorities. Since the ultimate goal of modeling is to consider feasible alternatives when making decisions, such analysis can be useful.

Regional Climate Change Policy Under Positive Feedbacks and Strategic Interactions

The surface albedo feedback, along with heat and moisture transport from the Equator to the Poles, is associated with polar amplification which is a well-established scientific fact. The present paper extends (Brock and Xepapadeas in Eur Econ Rev 94:263–282, 2017) to a non-cooperative framework with polar amplification, where regions decide emissions by maximizing own welfare. This can be regarded as a case of regional non-cooperation regarding climate change. Open loop and feedback solutions are derived and compared, in terms of temperature paths and welfare, with the cooperative solution. Carbon taxes which could bridge the gap between cooperative and non-cooperative emissions path are also derived. Finally, the framework is extended to a Ramsey set-up in which it is shown how the regional climate model can be coupled with standard optimal growth models. Numerical simulations confirm the theoretical results and provide insights about the size and the direction of deviations between the cooperative and the non-cooperative solutions.

Parametric Analysis of the Sensitivity of a Functional on the Basis of the Non-Classical Model of Optimal Economic Growth

Parametric Analysis of the Sensitivity of a Functional on the Basis of the Non-Classical Model of Optimal Economic Growth

Stochastic optimal growth model with risk sensitive preferences

This paper studies a one-sector optimal growth model with i.i.d. productivity shocks that are allowed to be unbounded. The utility function is assumed to be non-negative and unbounded from above. The novel feature in our framework is that the agent has risk sensitive preferences in the sense of Hansen and Sargent (1995). Under mild assumptions imposed on the productivity and utility functions we prove that the maximal discounted non-expected utility in the infinite time horizon satisfies the optimality equation and the agent possesses a stationary optimal policy. A new point used in our analysis is an inequality for so-called associated random variables. We also establish the Euler equation that incorporates the solution to the optimality equation.

Optimality of Ramsey–Euler policy in the stochastic growth model

For the canonical one sector stochastic optimal growth model, we outline a new set of conditions for a policy function that satisfies the Ramsey–Euler equation to be optimal. An interior Ramsey–Euler policy function is optimal if, and only if, it is continuous or alternatively, if, and only if, both consumption and investment are non-decreasing in output. In particular, we show that under these conditions, the stochastic paths generated by the policy must satisfy the transversality condition; the implication is that in applying our result, one does not need to verify the transversality condition when checking for optimality of a policy function.

On the Political Economy of Deficit Bias and Immigration

How much can governments shift the cost of their expenditure from today’s voters to tomorrow’s generations of immigrants, without resorting to taxation that is explicitly discriminatory? I demonstrate that if their societies are absorbing continuous flows of new immigrants, we should expect governments that represent the interests of today’s population to choose policies that shift some portion of the tax burden to the future, even if that population is altruistically linked to future generations. To measure the deficit bias, I analyse the dynamic behaviour of an optimal growth model with overlapping dynasties and factor taxation, calibrated for the US economy, and consider the welfare implications for today’s population and their descendants of intertemporal shifts in the tax rates on labour and asset income as well as transfer payments. Models with overlapping infinite-lived dynasties allow for a very clear distinction between natural population growth (an increase in the size of existing dynasties) and immigration (the addition of new dynasties). They also provide an alternative to the strict dichotomy between models with overlapping generations, where agents disregard the impact of their choices on future generations, and the quasi-Ricardian world of infinite-lived dynasties with representative agents that fully participate in both the economy and the political system in every period. The trajectory of the debt burden predicted by the model is a good match for the rise in US Federal Government debt since the early 1980’s, as well as the increases in debt projected by the Congressional Budget Office over the next few decades.

Optimal modes in a multidimensional model of economic growth

An n-dimensional problem of optimal economic growth in a multifactor model with the Cobb–Douglas production function and an integral-type functional with discounting is investigated. The model is studied by assuming that all amortization coefficients are equal. A constructive description of an optimal solution for a sufficiently large planning horizon and a sufficiently small discount coefficient is obtained. The extremal solution is described in analytical form. The studied problem with other production functions has a biological interpretation in an optimal growth model of agricultural plants with n vegetative organs during a specific finite time interval.

Machine Learning for High-Dimensional Dynamic Stochastic Economies

We present the first computational framework that can compute global solutions to very-high-dimensional dynamic stochastic economic models on arbitrary state space geometries. This framework can also resolve value and policy functions' local features and perform uncertainty quantification, in a self-consistent manner. We achieve this by combining Gaussian process machine learning with the active subspace method; we then embed this into a massively parallelized discrete-time dynamic programming algorithm. To demonstrate the broad applicability of our method, we compute solutions to stochastic optimal growth models of up to 500 continuous dimensions. We also show that our framework can address parameter uncertainty and can provide predictive confidence intervals for policies that correspond to the epistemic uncertainty induced by limited data. Finally, we propose an algorithm, based on this framework, that is capable of learning irregularly shaped ergodic sets as well as performing dynamic programming on them.

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Non-existence of optimal programs for undiscounted growth models in continuous time

We report an example of a two-dimensional undiscounted convex optimal growth model in continuous time in which, although there is a unique “golden rule”, no overtaking optimal solutions exists in a full neighborhood of the steady state. The example proves, for optimal growth models, a conjecture advanced in 1976 by Brock and Haurie that the minimum dimension for non-existence of overtaking optimal programs in continuous time is 2.

Existence and uniqueness of equilibrium in a distorted dynamic small open economy

We provide a set of sufficient conditions for existence and uniqueness of recursive equilibrium for a class of small open economies with distortion. The second welfare theorem is not available in this framework and usual approach for studying optimal neoclassical growth models is also not applicable.

Cycles and chaos in the one-sector growth model with elastic labor supply

It is shown that the discrete-time version of the neoclassical one-sector optimal growth model with elastic labor supply and standard monotonicity and convexity assumptions on technology and preferences can have periodic solutions of any period as well as chaotic solutions. The optimality of these non-monotonic solutions is traced back to strong income effects. When technology and preferences are parameterized as it is commonly done in quantitative macroeconomic studies, these phenomena cannot occur.