Two-sector Optimal Growth Model Research Articles

A dynamic theory of the declining aggregated labor income share: Intangible capital vs. tangible capital

Reports of the literature documenting the declining labor share of income have increased greatly in the past few years, which is opposed to one of the famous “Kaldor's stylized facts” of growth. The declining labor income share has been observed since the 1980s in a number of countries, and especially in the United States. Recent studies have revealed the following five major driving forces of the declining labor share: (i) supercycles and boom-busts, (ii) rising and faster depreciation, (iii) superstar effects and consolidation, (iv) capital substitution and automation, and (v) globalization and labor bargaining power. We set up a two-sector optimal growth model with the R&D intermediate sectors producing intangible capital. By integrating driving factors (ii) through (iv) above into the model, we demonstrate the long-run decline of the aggregated labor income share.

A new route to the rapid growth of the service sector: rise of the standard of living

Abstract In the present study, we set up a continuous-time two-sector optimal growth model with services and manufacturing goods and then examine structural change: the rapid growth of the service sector. Earlier studies of structural changes can be separated into two categories: preference-driven and technology-driven. Here we introduce a new and distinct category of structural change: consumption externality identified as rise of the living standard. A key assumption is that (1) a representative consumer has a non-homothetic Stone–Geary type utility function with respect to manufacturing goods and that (2) its subsistence level will be regarded as the standard of living and will be affected by the average consumption of manufacturing goods, which also affects the consumption level of services. We also assume that the manufacturing sector is more capital-intensive than the service sector, which takes an important role in our proofs. Results show that a steady state equilibrium exists that is globally stable as well as saddle-point stable. Then, given certain production parameters in a steady state, there exists optimal steady state where the value-added and employment shares by service sector will dominate those of the manufacturing sector under the condition that external effects of the service sector dominates capital-intensity effect of the manufacturing sector. In other words, through the transition process, the service sector will dominate the manufacturing sector in the steady state.

STRUCTURAL CHANGE AND A CONSTANT GROWTH PATH IN A THREE-SECTOR GROWTH MODEL WITH THREE FACTORS

This study proposes the unified framework of a three-sector model with structural change where agriculture, manufacturing, and service sectors have different production technologies. All three sectors use the factors of capital, labor, and land as inputs. The constant-growth path (CGP), which is the trajectory along which the rental rate of capital remains constant, is used to reconcile the Kaldor and Kuznets facts, and plays a role in linking the wage rate and land rent in the three-factors model. Because the prices of agricultural goods and services are determined endogenously, the CGP condition is no longer the knife-edge condition. We find that the dynamic system along the CGP in the three-sector, three-factor model corresponds to the standard two-sector optimal growth model.

Nonbalanced Growth in a Neoclassical Two-Sector Optimal Growth Model

Nonbalanced Growth in a Neoclassical Two-Sector Optimal Growth Model

FRACTALS AND SELF-SIMILARITY IN ECONOMICS: THE CASE OF A STOCHASTIC TWO-SECTOR GROWTH MODEL

We study a stochastic, discrete-time, two-sector optimal growth model in which the production of the homogeneous consumption good uses a Cobb-Douglas technology, combining physical capital and an endogenously determined share of human capital. Education is intensive in human capital as in Lucas (1988), but the marginal returns of the share of human capital employed in education are decreasing, as suggested by Rebelo (1991). Assuming that the exogenous shocks are i.i.d. and affect both physical and human capital, we build specific configurations for the primitives of the model so that the optimal dynamics for the state variables can be converted, through an appropriate log-transformation, into an Iterated Function System converging to an invariant distribution supported on a generalized Sierpinski gasket.

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.

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.

Competitive equilibrium cycles with endogenous labor

In this paper, we study a two-sector optimal growth model with elastic labor supply. We show that the modified golden rule is saddle-point stable when the investment good is capital intensive. To characterize stability with a capital intensive consumption good, we focus on either additively separable or homothetic preferences. In the first specification, we show that optimal oscillations require the elasticity of intertemporal substitution in consumption to be high enough while the elasticity of labor needs to be low enough. At the same time, we prove that with a linear utility in leisure the modified golden rule is always saddle-point stable. In the second specification for preferences, we show that the local dynamic properties of the optimal path depend instead on the shares of consumption and leisure into total utility. We prove that endogenous fluctuations are even more likely with homothetic preferences.

Stable Optimal Cycles With Small Discounting in a Two-sector Discrete-time Model: A Non-bifurcation Approach

This paper presents a standard two-sector optimal growth model with general neoclassical production functions: strictly quasi-concave, twice continuously differentiable homogeneous of degree 1 functions. Instead of applying the standard local bifurcation theory, I exploit two well established properties in Turnpike Theory—“simple dynamics” and the Neighbourhood Turnpike— and, combining both results, I demonstrate that there exists an interval of the discount factor near 1 such that a corresponding optimal steady state is totally unstable and an optimal path converges asymptotically to a two-period cycle for a chosen discount factor in it. JEL Classification Numbers: O21, O41.

Consumption Externalities, Production Externalities and Indeterminacy

In this paper we show that consumption externalities reduce the degree of increasing returns needed to generate indeterminacy in a two-sector optimal growth model. In equilibrium, consumption externalities operate as if the utility function is (close to) linear. If these externalities are strong, the minimum necessary increasing returns approach zero. Therefore, this paper—in a stylized fashion—provides an example of how microbehavior, i.e. interactions at the household level, can generate aggregate instability. Consumption externalities also help to eliminate the counterfactual cyclical behavior of consumption in the two-sector model.

The von Neumann facet and a global asymptotic stability

We will study a multi-sector discrete-time optimal growth model with neoclassical non-joint technology and show that any path on ann-dimensional flat supported by the optimal steady state price will converge to the optimal steady state and is optimal. Burmeister and Graham have proved a similar result in a continuous-time setting. Although their result is limited, it is a first challenge to generalize the global stability result obtained by Uzawa and Srinivasan in a two-sector optimal growth model. One prominent advantage of our approach is that due to the discrete-time model setting, we can apply the duality approach and introduce the so called "von Neumann facet" intensively studied by McKenzie, which plays a very important role in proving the saddle point stability.

Green manure and nitrogenous fertilizer—a two-sector optimal-growth model

AbstractA continuous-time model of a two-sector trading economy with a finitely-saturating production function and constant population is constructed. To apply it to the farm-economy problem of optimal trading of cereal for chemical nitrogenous fertilizer and of optimal allocation of land for green manure the special assumptions are made of similar technologies in both sectors and of a nitrogen-capital loss proportional to the cereal production. Optimal-control theory is applied to get the pair of controls that maximizes an infinite-horizon integral of utility of consumption. The analysis of the model is shown to reduce to that of the Ramsey-Koopmans one-sector neoclassical model of optimal growth. Calculations of the feedback control and optimal time-paths for the standardized dimensionless model are tabulated for a range of 7 utility functions of constant elasticity of marginal utility of magnitude 1 to 4 and of production functions of degree 2 to 4. Two particular analytic solutions are given. The application of the results both to the farm-economy model and to the Ramsey-Koopmans model is illustrated.