Harutaka Takahashi

DOES THE CAPITAL INTENSITY MATTER? EVIDENCE FROM THE POSTWAR JAPANESE ECONOMY AND OTHER OECD COUNTRIES

The capital intensity takes an important role in two-sector and multisector growth models. Surprisingly very few empirical studies have been conducted so far except by Kuga (1967). This fact implies that few people have ever tried to perform any empirical research to study whether the two-sector and multisector optimal growth models could explain the economic development properly based on the empirical data. Although we witnessed fairly active theoretical research on two-sector and multisector growth models in the 1990s and recent years, R. M. Solow has thrown doubt on the capital intensities [in Philippe Aghion and Steven Durlauf (eds.), Handbook of Economic Growth , Vol. 1A (2005, pp. 3–10)]. Our purpose is to measure the capital intensities of the consumption good and the investment good sectors mainly in the postwar Japanese economy, and also in other OECD countries. By so doing, we will demonstrate that the capital intensity does matter and our empirical evidence will strongly support the common assumption that the consumption goods sector is more capital-intensive than the capital goods sector.

Comparing Open-Loop with Markov Equilibria in a Class of Differential Games

We consider a class of differential games with transition equations that are homogeneous of degree one. For any game G with a discount rate r, consider a Markov perfect equilibrium (MPE) with strategies that are linear in the state variables. We show that the time paths of the control variables of this equilibrium constitute an open-loop equilibrium of a corresponding game Classification-JEL: C72; C73; Q30

Turnpike Properties And Comparative Dynamics Of General Capital Accumulation Games

Publisher Summary This chapter discusses the solutions for a general class of capital accumulation games with stability properties of Nash equilibrium. It focuses on the application of turnpike theory to dynamic games. The turnpike results known from the theory of optimal economic growth can be used to derive a general convergence result. They also yield comparative statics and dynamics properties. The key result is the global convergence of the Nash trajectories to a unique steady state provided that the matrix of second order derivatives of the profit functions has a dominant diagonal. This result implies that the block diagonal assumption introduced by Araujo and Scheinkman is satisfied. Thus, comparative statics and dynamics analyses are possible. The chapter presents a model, which is very general in nature and can be applied to various market situations. The chapter discusses the relationship between the equilibrium path of the finite and infinite-horizon games. The finite horizon eqilibrium path stays within a closed neighborhood of the stationary equilibrium.

On the saddle-point stability for a class dynamic games

In this paper, we study the stability properties of the class of capital accumulation games introduced by Fershtman and Muller (Ref. 1). Both discrete and continuous time versions are discussed. It is shown that the open-loop Nash equilibrium solutions for both games are characterized by a general saddle-point property, a result best known from the turnpike literature in optimal growth theory. In the case of zero discount rates, an even stronger result can be derived: As long as the Hessian matrix of the instantaneous profit functions has a quasidominant diagonal, no pure imaginary roots are possible.

Further turnpike properties for general capital accumulation games

Abstract We consider a class of finite and infinite horizon discrete-time N -player capital accumulation games. Three turnpike results for the case of open-loop Nash equilibrium solutions are derived under fairly weak conditions.

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.

Transitional dynamics of economic integration and endogenous growth

Abstract Rivera-Batiz and Romer have demonstrated some comparative dynamic analysis, namely comparing pre- and post-economic integration balanced growth paths and have derived interesting economic results. Even though these results are interesting, their analysis has a serious shortcoming. Namely, the balanced growth path studied by them exhibits a knife-edge property and is unstable. This clearly implies that their results are not robust. In this paper, we propose a modified knowledge driven model based on their model. Then we give a comparative dynamic analysis and show different results of economic integration from theirs.

Global Externalities, Endogenous Growth and Sunspot Fluctuations

We consider a two-sector economy with Cobb-Douglas technologies,labor-augmenting global external effects and increasing social returns. We prove the existence of a normalized balanced growth path and we give conditions for the occurrence of sunspot fluctuations that are compatible with both types of capital intensity configuration at the private level provided the elasticity of intertemporal substitution in consumption admits intermediary values. We finally show that the existence of period-two cycles requires the consumption good to be physical capital intensive at the private level.

Nonbalanced Growth in a Neoclassical Two-Sector Optimal Growth Model

For a neoclassical two-sector optimal growth model with Cobb-Douglas technologies and sector specific technical progress, we examine three properties: (i) each sector has an optimal path by which it will grow at a constant growth rate (an optimal constant growth path); (ii) the optimal constant growth paths satisfy saddle path stability; (iii) the elasticity of substitution between total labor and total capital is less than one along the optimal constant growth paths. These results, presented by Acemoglu and Guerrieri in their model with two intermediate good sectors and one final good sector, will give a firm theoretical base for establishing the Kaldor and Kuznets facts, and are proven herein for a neoclassical growth model.

A Turnpike Theorem with Public Capital

Most of the literature on global stability of optimal public capital often treats private and public capital as physically identical goods. As a result, one important characterlistic of public capital,”non-rivalness,” will be neglected. This is clearly a serious analytical defect. To tackle the problem, a three-sector optimal growth model, where one of the sectors is a public sector and produces public capital, is set up, and the global stability of the optimal path of public capital will be demonstrated.