Proceedings of the Institute of Statistical Mathematics Vol. 57, No. 2, 203-219

## Hash Property of an Ensemble of Sparse Matrices and Multi-terminal Source Codes

(NTT Communication Science Laboratories, NTT Corporation)
(NTT Network Innovation Laboratories, NTT Corporation)

The aim of this paper is to construct codes for basic multi-terminal coding problems by using sparse matrices. These problems are the Slepian-Wolf problem, the Wyner-Ziv problem, and the One-helps-one problem. To this end, the notion of a hash property for an ensemble of functions is introduced and asymptotically optimal codes are constructed by using this property. Since an ensemble of \$q\$-ary sparse matrices satisfies the hash property, we can construct asymptotically optimal codes by using sparse matrices.

Key words: Information theory, hash property, codes using sparse matrices, Slepian-Wolf problem, Wyner-Ziv problem, one-helps-one problem.

Proceedings of the Institute of Statistical Mathematics Vol. 57, No. 2, 221-232

## Statistical Mechanics of Sensing and Coding

(NTT Communication Science Laboratories, NTT Corporation)

Today very many and small sensing devices are produced and connected to the computer network. This can be considered as a new kind of information infrastructure. Therefore the potential demand for advanced and robust communication techniques for such systems seems to be increasing. In particular, the theoretical bound for such communications has crucial importance. In this paper, we consider a new approach to the problem, based on notions and techniques of information theory and statistical mechanics.

Key words: Sensor networks, coding, statistical mechanics.

Proceedings of the Institute of Statistical Mathematics Vol. 57, No. 2, 233-251

## Information Sensing and Multiterminal Source Coding

(Department of Information Science and Intelligent Systems, University of Tokushima)

Construction of a theoretical framework to treat sensor networks has a close connection with multiterminal information theory. In this paper we explain how a process of signal sensing in a sensor network is formulated as a coding problem of multiterminal information theory. We further explain previous results on the formulated coding problem.

Key words: Sensor network, multiterminal information theory, distributed source coding, many-help-one problem, CEO problem.

Proceedings of the Institute of Statistical Mathematics Vol. 57, No. 2, 255-275

## Developments of “Establishment and Enterprise Statistical Survey” and “Financial Statement Statistical Survey of Japanese Enterprises” and Creation of New Statistical Information through Combining Two Statistical Surveys Using Micro-data Linkage Techniques

(Aomori Public College)
(The Institute of Statistical Mathematics)
(Policy Research Institute, Ministry of Finance Japan)
(Policy Research Institute, Ministry of Finance Japan)

The Japanese industrial statistical survey system mainly depends on a survey operation based on an establishment concept since its beginning in the twentieth century. However, the current economic system requires a survey system based on enterprise-based statistics supported by firm accounting practice. This paper reviews the development of the two important statistical surveys “Establishment and Enterprise Statistical Survey” and “Corporate Financial Statement Statistical Survey” and then describes a recent research project compiling a database through exact-matching techniques of these two statistical surveys. The review covers the main findings of the project.

Key words: Establishment, corporate company, business enterprise, longitudinal data, integration of establishment data and corporate data, multinational enterprise, micro data, exact matching.

Proceedings of the Institute of Statistical Mathematics Vol. 57, No. 2, 277-303

## Integrated Enterprise Database of “Financial Statements Statistics of Corporations by Industry” and “Establishment and Enterprise Census”: 1983–2005

(Library and Academic Information Center, Kobe Gakuentoshi, University of Hyogo)
(School of Economics, University of Hyogo)
(Faculty of Economics, Keio University)

We construct an Enterprise Database from microdata of two sets of statistics: “Financial Statements Statistics of Corporations by Industry” (1983–2005) and “Establishment and Enterprise Census” (1991–2004) , permitted by the law of statistics. We make two panel datasets of these statistics and connect them to each other. We explain how to make this panel dataset and integrated enterprise database.

Key words: Financial statement statistics, estabilishment and enterprise census, exact matching, regional economic indicators.

Proceedings of the Institute of Statistical Mathematics Vol. 57, No. 2, 305-329

## An Attempt to Compile Regional Indicators UsingFinancial Statistics of Japan

(Faculty of Economics, Aoyama Gakuin University)
(Graduate School of Economics, Hitotsubashi University)
(School of Economics, University of Hyogo)

We propose a new regional economic indicator derived by combining two major statistical surveys, Establishment and Enterprise Census and Financial Statistics of Japan. The former survey is conducted every five years by the Statistics Bureau and covers all establishments and firms, while the latter is conducted quarterly for incorporated companies by the Ministry of Finance.

Currently, almost no regional statistics are provided by Financial Statistics, because major firms have a number of local establishments throughout the country, so allocating the economic activity of a firm to the region of its headquarter does not make much sense. On the other hand, regional information concerning business activity is often requested by economists as well as policy-makers, reflecting the recent tendency of expanding power of local governments.

Since Establishment and Enterprise Census provides information on structures of firms and their local establishments, we can create a conversion table through which establishments are connected to their headquarters. Then we can allocate quarterly economic activities of a firm obtained from Financial Statistics to its local establishments, by utilizing the conversion table. Thus we introduce a new indicator which we call Regional Economic Activity Indicator.

Based on this indicator, we compare regions in Japan, and find some interesting results. For example, the regional disparity based on headquarters has increased lately, because of the moves of many headquarters to metropolitan areas. In contrast, our indicator shows relatively stable regional disparity, reflecting the fact that not so many local establishments have moved across regions.

After presenting some other results, we also comment on the future role and implications of our indicator to Japanese official statistics.

Key words: Regional economic indicator, micro data, exact matching, Financial Statistics of Japan, Establishment and Enterprise Census.

Proceedings of the Institute of Statistical Mathematics Vol. 57, No. 2, 331-355

## An Essay on the Relation between Rate of Dispatched or Subcontracted Employees in the Work Force of Enterprises and Transition of Wage Cost Proportions

(Faculty of Economics, Keio University)

Enterprises decide the proportion of labor service by dispatched or subcontracted employees they should input to their production activities, generally, based on their wage cost proportions. The wage cost does not include the cost to employ labor service by dispatched or subcontracted employees, so we hypothesize that the ratio of dispatched or subcontracted employees is negatively correlated with wage cost proportion, and determine if this is supported by observations. Thus, we merged microdata records of the Financial Statements of Corporation by Industry with those of the Establishment and Enterprise Census of Japan by an exact matching method. We found that the rate of dispatched or subcontracted employees in the work force in the year 2001 is negatively and significantly correlated with the trend of wage cost proportion in some industries, especially the manufacture of transportation equipment; the industry of electricity, gas, heat supply and water; other services of transport and communications, accommodations, cinemas and services for amusement; and miscellaneous business services.

Key words: Financial statements of corporation by industry, establishment and enterprise census of Japan, wage cost, dispatched or subcontracted employees.

Proceedings of the Institute of Statistical Mathematics Vol. 57, No. 2, 357-369

## E-commerce among Corporate Groups

(Faculty of Economics, Keio University)

This paper describes an analysis of the relationship between the conditions of corporate e-commerce and affiliation to a corporate group. For the analysis, we used micro-data of the Establishment and Enterprise Census of Japan (2001). As a complete nationwide enumeration, this census was the first used to investigate e-commerce in Japan. Since the names of parent companies were also included in the census form, a corporate group could be formed by linking the parent company and its subsidiaries. Using this information on corporate groups, we devised classifications such as affiliation to a corporate group or position within a corporate group. The analysis results revealed that those classifications could be used to explain the conditions of e-commerce.

Key words: Establishment and Enterprise Census, corporate group, e-commerce.

Proceedings of the Institute of Statistical Mathematics Vol. 57, No. 2, 371-392

## Debt Maturity Structure of SMEs in Japan

(Department of Management and Economics, Aomori Public College)
(The Institute of Statistical Mathematics)

The financial structure of Japanese SMEs' is characterized by a high debt ratio reflecting their low profitability. Since the availability of long-term funds is one of the crucial factors for survival and growth of SMEs, several models have been proposed to explain the maturity structure of debt. This paper examines empirically the debt maturity of SMEs in Japan by testing hypotheses incorporating the asymmetric information between lenders and SMEs.

We run two types of regressions: firstly, a cross-section analysis for samples of each year; secondly, an analysis for samples pooled into three periods, based on micro data from the Financial Statements Statistics of Corporations by Industry, compiled by the Ministry of Finance. From the results of these regressions, we have found that the long-term borrowing ratio mostly responds positively to increases in a firm's profitability. This finding is consistent with the hypothesis that as a firm's profit increases it becomes more sensitive to the liquidity risks that terminate its projects than to the flexibility of borrowing conditions that reflect the arrival of favorable news at the time of refinancing.

Key words: SMEs, debt maturity structure, asymmetric information, financial statements statistics of corporations by industry.

Proceedings of the Institute of Statistical Mathematics Vol. 57, No. 2, 393-411

## Measurement Methodology of Disparity Ratio between Executive Officer's Average Payroll and Worker's Average Payroll by Using the Financial Statements Statistics of Corporations by Industry

(Faculty of Economics, Tokyo International University)

The disparity ratio between executive officer's average payroll and worker's average payroll is often used to analyze the allocation of corporate earnings, or to estimate the macro personal income. However, this ratio is not the official figure of the Ministry of Finance (MOF), and researchers calculate it from published data of Financial Statements Statistics of Corporations by Industry (FSSCI). This paper examines the measurement methodology of disparity ratio. I find that the disparity ratio calculated by the published data of FSSCI is possibly understated for two reasons. First, the executive officer's average payroll (numerator) mainly reflects the payroll of small corporations. On the other hand, the worker's average payroll (denominator) mainly reflects the payroll of large corporations. Second, both an executive officer's payroll and a worker's payroll are higher for larger corporations. Based on these findings, I propose a new disparity ratio calculated from micro data of FSSCI in the following manner. First, I calculate an executive officer's average payroll and a worker's average payroll by company and observe its distribution. Second, I calculate the disparity ratio in which the weight of each company is equal. I thus find that the disparity ratio calculated from published macro data is smaller than that calculated from micro data.

Key words: Financial Statements Statistics of Corporations by Industry, worker, executive officer, payroll, disparity ratio.

Proceedings of the Institute of Statistical Mathematics Vol. 57, No. 2, 413-424

## A Comparison of Estimators for the Survey of Corporation Statistics

(The Institute of Statistical Mathematics)
(Keio Economic Observatory, Keio University)
(Department of Management and Economics, Aomori Public College)

Several methods for estimating both population totals and their growth rates were compared by simulation with microdata from a survey of corporation statistics as a pseudo population. The conventional survey design basically replaces the whole samples with a new one, and the growth rates are estimated from the estimates of population totals of each year. The simulation study revealed that the rotating design, in which half the sample is kept in the panel until the next year, reduces standard errors of growth rates by almost two thirds that of the conventional design. The study also indicated that the estimating strategy, in which the growth rates are first estimated and then secondly used for estimating the population totals, decreases standard errors of population totals by one tenth to one third and growth rates by one tenth of the conventional design even if all the sample is replaced annually.

Key words: The survey of corporation statistics, sample rotation, growth rates.

Proceedings of the Institute of Statistical Mathematics Vol. 57, No. 2, 425-442

## Nonparametric Maximum Likelihood Estimation of Multi-population Size Indices—Application to Microdata Sets of Two Occasions—

(Faculty of Economics, Okayama Shoka University)

Population size indices estimated from observed sample size indices are often used to assess the disclosure risk of a microdata set sampled from a population. Parametric methods with superpopulation models such as the Poisson gamma model or the Pitman model are usually used to estimate population size indices. A restricted nonparametric maximum likelihood estimation method has also been proposed, and its problem of computing time is being improved.

Though most sample surveys of official statistics are repeated periodically, it is usual to carry out risk assessment for each microdata set independently. In order to assess the disclosure risk for several microdata sets simultaneously, the size indices are extended to those of the multi-indices, and a nonparametric method for estimating multi-population size indices from multi-sample size indices is proposed.

Restrictions for the estimates of multi-population size indices are expressed as penalty functions and are taken into a log likelihood function. To improve the estimation, a two-stage method is also proposed, in which the multi-population size indices are estimated under the condition that their marginal frequencies are fixed on the population size indices estimated in advance. These proposed methods are applied to 1990 and 2000 1-Percent Public Use Microdata Sample Files in the U. S.

Key words: Multi-indices, size indices, microdata, risk assessment, nonparametric estimation, official statistics.

Proceedings of the Institute of Statistical Mathematics Vol. 57, No. 2, 443-447

## A Sufficient Condition for Observation Noise Not to Affect the Extreme Value Distribution

(The Institute of Statistical Mathematics)
(The Institute of Statistical Mathematics)

In the usual context of extreme value theory, it is assumed that random variables \$ \{ X_i \} \$ can be observed exactly. On the other hand, real data are always exposed at risk of being perturbed by observation noise. We present a sufficient condition under which the extreme value distribution of a sequence \$ \{ X_{i} \} \$ is the same as that of data \$ \{ X_{i} + e_{i} \} \$ with observation noise \$ e_i \$. The condition is described in terms of the Orlicz norm. Our result gives a condition under which one may safely believe the extreme value theory which has been studied under the ideal situation that the data are exactly observed.

Key words: Extreme value statistics, observation noise, Orlicz norm.