Hirofumi Uzawa

Bio: Hirofumi Uzawa is an academic researcher from Doshisha University. The author has contributed to research in topics: Capital (economics) & Social reproduction. The author has an hindex of 29, co-authored 82 publications receiving 6856 citations. Previous affiliations of Hirofumi Uzawa include University of California, Berkeley & University of Tokyo.

Production Functions with Constant Elasticities of Substitution

Abstract: В статье рассматривается класс производственных функций с постоянной эластичностью замены безотносительно цен факторов, рассматривается случай, когда в процесс вовлекается больше чем два фактора.

Time Preference and the Penrose Effect in a Two-Class Model of Economic Growth

Abstract: In the theory of economic growth, we are concerned with the analysis of those economic factors which crucially determine the process of growth for a national economy. Our primary interest is in the mechanisms by which aggregate variables such as national income, aggregate stock of capital, and others are interrelated and in how they change as time passes. Since Harrod (1948) first laid down the fundamental theorems for a dynamic economics, we have seen the emergence of an increasing number of aggregate growth models to clarify and extend these theorems, as aptly described in Hahn and Matthews' (1964) survey article. These growth models, however, have been mostly built upon premises directly involving aggregate variables, without specifying the postulates which govern the behavior of individual units comprising the national economy. In particular, the specifications of aggregate savings are seldom based upon analysis of individual behavior concerning savings and consumption; instead, they have been merely hypothesized in terms of historical and statistical observations. Similarly, the aggregative behavior of investment has been either entirely neglected, as has been typically the case with the so-called neoclassical models, or it has been postulated in terms of somewhat ad hoc relations involving market rate of interest, rate of profit, and other variables. In the present paper, I should like to pay closer attention to the behavior of individual units concerning consumption, saving, and investment, and to build a formal model of economic growth for which the aggregate variables are described in terms of these macroeconomic analyses.

The mechanics of economic development

Abstract: This paper considers the prospects for constructing a neoclassical theory of growth and international trade that is consistent with some of the main features of economic development. Three models are considered and compared to evidence: a model emphasizing physical capital accumulation and technological change, a model emphasizing human capital accumulation through schooling, and a model emphasizing specialized human capital accumulation through learning-by-doing.

Increasing Returns and Long-Run Growth

Abstract: This paper presents a fully specified model of long-run growth in which knowledge is assumed to be an input in production that has increasing marginal productivity. It is essentially a competitive equilibrium model with endogenous technological change. In contrast to models based on diminishing returns, growth rates can be increasing over time, the effects of small disturbances can be amplified by the actions of private agents, and large countries may always grow faster than small countries. Long-run evidence is offered in support of the empirical relevance of these possibilities.

Distributed Optimization and Statistical Learning Via the Alternating Direction Method of Multipliers

Abstract: Many problems of recent interest in statistics and machine learning can be posed in the framework of convex optimization. Due to the explosion in size and complexity of modern datasets, it is increasingly important to be able to solve problems with a very large number of features or training examples. As a result, both the decentralized collection or storage of these datasets as well as accompanying distributed solution methods are either necessary or at least highly desirable. In this review, we argue that the alternating direction method of multipliers is well suited to distributed convex optimization, and in particular to large-scale problems arising in statistics, machine learning, and related areas. The method was developed in the 1970s, with roots in the 1950s, and is equivalent or closely related to many other algorithms, such as dual decomposition, the method of multipliers, Douglas–Rachford splitting, Spingarn's method of partial inverses, Dykstra's alternating projections, Bregman iterative algorithms for l1 problems, proximal methods, and others. After briefly surveying the theory and history of the algorithm, we discuss applications to a wide variety of statistical and machine learning problems of recent interest, including the lasso, sparse logistic regression, basis pursuit, covariance selection, support vector machines, and many others. We also discuss general distributed optimization, extensions to the nonconvex setting, and efficient implementation, including some details on distributed MPI and Hadoop MapReduce implementations.

Endogenous Technological Change

Abstract: Growth in this model is driven by technological change that arises from intentional investment decisions made by profit-maximizing agents. The distinguishing feature of the technology as an input is that it is neither a conventional good nor a public good; it is a nonrival, partially excludable good. Because of the nonconvexity introduced by a nonrival good, price-taking competition cannot be supported. Instead, the equilibrium is one with monopolistic competition. The main conclusions are that the stock of human capital determines the rate of growth, that too little human capital is devoted to research in equilibrium, that integration into world markets will increase growth rates, and that having a large population is not sufficient to generate growth.