Yuichi Ikeda

International Comparison of Labor Productivity Distribution for Manufacturing and Non-Manufacturing Firms

Labor productivity was studied at the microscopic level in terms of distributions based on individual firm financial data from Japan and the US. A power-law distribution in terms of firms and sector productivity was found in both countries data. The labor productivities were not equal for nation and sectors, in contrast to the prevailing view in the field of economics. It was found that the low productivity of the Japanese non-manufacturing sector reported in macro-economic studies was due to the low productivity of small firms.

Distribution of Labour Productivity in Japan Over the Period 1996 - 2006

The distribution of labour productivity is investigated by analyzing the longitudinal micro-level data set which contains the detailed financial conditions of large numbers of Japanese companies over the period 1996-2006. The authors show that the distribution of labour productivity in both the high and low productivity ranges follows a power law distribution. The generalized beta function of the second kind, which asymptotically reproduces a power law function, is applied to explain the distribution of labour productivity. By comparing the power law exponents that characterize high and low productivity ranges, the authors show that for manufacturing industries, inequality in the low productivity range is larger than that in the high productivity range. For the manufacturing industries, the authors also clarify that the change of inequality in the low productivity range has strong correlation with GDP. In addition, by comparing the power law exponents of the high productivity range in the manufacturing and non-manufacturing industries, the authors show that the inequality of the non-manufacturing industry is higher than that of the manufacturing industry.

Community structure in a large-scale transaction network and visualization

We analyze a transaction network of about 800 thousand Japanese firms to elucidate its community structure. Finding community in networks means the appearance of dense connected groups of vertices and sparse connections between groups. We adopt modularity as a quality function of communities introduced by Newman. The modularity optimization is one of effective approaches to find community. We first use a bottom-up algorithm, which makes the optimization fast by using a greedy algorithm. For the community extraction, the greedy algorithm is widely used, however, may not sufficiently optimize modularity because the optimization tends to be trapped by a local maximum especially for large-scale networks. Alternatively we propose a top-down algorithm with implementation of an annealing method and compare effectiveness of the two algorithms. We also compare the results of the community analysis with images of network structure visualized by molecular dynamics method. The vertices belonging to the same community are spatially located close to each other. The community structure determined by the modularity optimization is well reproduced in the network structure obtained by molecular dynamics.

Superstatistics of Labour Productivity in Manufacturing and Nonmanufacturing Sectors

Labour productivity distribution (dispersion) is studied both theoretically and empirically. Superstatistics is presented as a natural theoretical framework for productivity. The demand index e is proposed within this framework as a new business index. Japanese productivity data covering small-to-medium to large firms from 1996 to 2006 is analyzed and the power-law for both firms and workers is established. The demand index e is evaluated in the manufacturing sector. A new discovery is reported for the nonmanufacturing (service) sector, which calls for expansion of the superstatistics framework to negative temperature range.

Agent-Based Model Approach to Complex Phenomena in Real Economy

An agent-based model for firms dynamics is developed. The model consists of firm agents with identical characteristic parameters and a bank agent. Dynamics of those agents is described by their balance sheets. Each firm tries to maximize its expected profit with possible risks in market. Infinite growth of a firm directed by the profit maximization principle is suppressed by a concept of going concern. Possibility of bankruptcy of firms is also introduced by incorporating a retardation effect of information on firms decision. The firms, mutually interacting through the monopolistic bank, become heterogeneous in the course of temporal evolution. Statistical properties of firms dynamics obtained by simulations based on the model are discussed in light of observations in the real economy.

A paradigm shift from production function to production copula: statistical description of production activity of firms

The heterogeneity of economic agents is emphasized in a new trend in macroeconomics. Accordingly, the new emerging discipline requires one to replace the production function, one of the key ideas in conventional economics, by an alternative that can take explicit account of the distribution of firms production activities. In this paper we propose a new idea referred to as a production copula; a copula is an analytic means for modeling the dependence among variables. Such a production copula predicts the value added by firms with given capital and labor in a probabilistic way. It is thereby in sharp contrast to the production function, where the output of firms is completely deterministic. We demonstrate the empirical construction of a production copula using financial data of listed Japanese firms. Analysis of the data shows that there are significant correlations among capital, labor and value added, and confirms that the values added are too widely scattered to be represented by a production function. We employ four models for the production copula, that is trivariate versions of Frank, Gumbel and survival Clayton and non-exchangeable trivariate Gumbel. The latter was found to be the best.

Structure analyses of a large-scale transaction network through visualization based on molecular dynamics

We shed light on industrial structure of the economic system in Japan by combining visualization technique and community analysis in this and an accompanying paper. Here we focus on visualization of a production network comprising submillion nodes (firms) and three million links (transaction relations). A network structure is optimized through molecular dynamics simulation with a spring-electrical model in a three-dimensional space. The lowest-energy state in the model, corresponding to a crystalline state in a physical system, is expected to give a comprehensible view on the network. Then we discuss how firms are distributed in the optimized network structure by classifying them according to sectors, sizes or regions. The distributions of firms reflect characteristics of individual classifications. Also propagation of the shock due to a recent economic scandal over the network is visualized.

Firm Dynamics Simulation Using Game-theoretic Stochastic Agents

Decision-making is a crucial task for the business planning of industrial firms, in order to cope with uncertainties in the business environment. A method of firm dynamics simulation, i.e. the game-theoretic stochastic agent, was developed by applying game theory to a stochastic agent model in order to analyze the uncertain business environment. Each stochastic agent is described by a Langevintype equation with an additional term for rational decision-making. In this paper, the dynamics of firms in computer related industries, which consist of three industrial sectors, i.e. the large scale integrated circuit sector, the personal computer sector, and the liquid crystal display sector, are simulated using the game-theoretic stochastic agents model. Then, the importance of the herding behavior of firms is demonstrated to reproduce the formation and collapse of the bubble in the Japanese computer related industry markets during the late 90s.

Response of Firm Agent Network to Exogenous Shock

This paper describes an agent-based model of interacting firms, in which interacting firm agents rationally invest capital and labor in order to maximize payoff. Both transactions and production are taken into account in this model. First, the performance of individual firms on a real transaction network was simulated. The simulation quantitatively reproduced the cumulative probability distribution of revenue, material cost, capital, and labor. Then, the response of the firms to a given exogenous shock, defined as a sudden change of gross domestic product, is discussed. The longer tail in cumulative probability and skewed distribution of growth rate are observed for a high growth scenario.

A Game-theoretic Stochastic Agents Model for Enterprise Risk Management

A model of business scenario simulation is developed by applying game theory to the stochastic agents described by the Langevin equations for enterprise risk management (ERM). Business scenarios of computer-related industries are simulated using the developed model, and are compared with real market data. Economic capital was calculated based on the business scenario, as the most basic requisite of ERM.