A Study of SD National Model Based on Revised SNA

Conceptual, Institutional and Operational

Saburo Kameyama*

Department of Commerce, Chuo University

Higashinakano Hachioji, Tokyo, 192-03 Japan

Tomofumi Sumita

The University of Electro-Communications

Takayuki Toyama

Management Systems Technology Inc.


So far it has been paid a great deal of efforts to develop national models using System Dynamics. We would like to join these efforts with a new approach. Our approach is characterized by the following two points: (1) To be based on the SNA (System of National Accounts) as a framework to grasp a national economy comprehensively. (2) To be supported by the structured matrix as a basic core technology.

Our effort to develop SD national model is expected to be enhanced further by fusing above both points. A new approach to SD national model will be shown with the collaborated discussions.


System Dynamics is one of the most powerful modeling and simulation tool for social systems. We, however, can scarcely say that the full potentiality of SD has been utilized so far in policy making. Social systems are essentially institutional being. So the model for social systems should have real institutions as its model structure. The simulation of such model will be able to provide the most effective means for institutional policy making.

The SNA (System of National Accounts) is a consistent, coherent and integrated set of macroeconomic accounts based on institutional sectors. In fact the SNA statistics have played an important role in policy making of governmental agencies. But the SNA is still in the stage of a static framework as ex post statistics of national economy. System Dynamics approach will make the SNA more operational and powerful for the prediction and policy making of the national economy.

We will discuss how to build SD National model based on the revised SNA (1993) and how to simulate the model.

The SNA As a National Model

The SNA is a coherent, consistent and integrated set of macro-economic accounts of a country. It is internationally established, comprehensive framework of national economy and has been implemented over a quarter of century in many countries including OECD affiliates. Indeed the SNA represents substantially an unquestionably evident national model. It can be said that the SNA is the most accessible and institutionally ongoing national model. Furthermore there are many affinities between the SNA and SD model as follows.

Closed Boundary The economic territory of a country is defined as the geographic territory administered by a government within which persons, goods, and capital circulate freely. Within this territory, the SNA records all the transactions between the different economic agents, and groups of agents, taking place on market or elsewhere. In these context, the SNA has a closed boundary as the national model.

In the SNA, all the transactions are recorded in account form and there is a sequence of accounts which builds a feedback loop structure within a closed boundary of the model. Accounts consist of flow accounts and stock accounts. Stock accounts construct balance sheet and represent level variables. Flow accounts relate to a particular kind of activity such as production, or generation, distribution and use of income and imply rate variables.

Nested Account Structure Closed boundary, feedback loop structure of sequence of accounts, and level and rate substructure of stock and flow accounts, all these satisfy the requirements of SD model structure. But depending upon analytical purposes, the SNA has to be implemented at different level of aggregation: at the level of total economy of a country, for groups of institutional units, individual institutional units, or economic agents. In turn, it follows that each accounts has its sub-accounts and each sub-accounts has its sub-sub-accounts and so on.

Therefore, there must exist a nested accounts structure in the SNA. And a tool must be available which can describe such a hierarchical structure of accounts. We introduced a new technology of structured matrix which deal with such a structure of accounts.

Micro-macro Links Micro-macro links is one of the most critical issues of the national model. As mentioned above, the sequence of accounts has to be compiled at any level of aggregation in the model. So there must be micro-database that is fully compatible with corresponding macro-economic accounts for the total economy and it is also necessary to breakdown macro-accounts into micro-accounts at any level in order to meet the specific analytical purpose. These process can be conducted easily by structured matrix.

In addition to aggregation and disaggregation problem of data, a variety of analytical purposes of the national economy also necessitates the special type of information for solving the specific problem which derive from cross-sectional relevant database. To solve most environmental issues, for example, relevant data have to be assembled from various kinds of accounts which are belonged to different classifications. The account which relevant data are assembled is called "satellite account" in the revised SNA. It is also easier tobuild and operate the satellite accounts through the matching technique of structured matrix.

The Model Structure and Institutional Sectors

The SNA is designed to provide information for economic analysis, policy-making and decision-taking through monitoring the behavior of the national economy. Our purposes of modeling and simulation of the national model are in the same context of those of the SNA. As Forrester said, macroeconomic behavior derives from microstructure (Forester, 1989). In fact most policy-making and decision-taking are undertaking by individual micro institutional units.

The institutional sectors The SNA defines the total economy in terms of institutional units. Here, the institutional units are defined as economic entities which are capable of owing assets and incurring liabilities on their own behalf and can engage in the full range of transactions.

In the revised SNA, the institutional units are grouped together to form institutional sectors, on the basis of their principal functions, behavior, and objectives. They are as follows;

  1. Non-financial corporations, (2) Financial corporations, (3) General government,

(4) Households, (5) Non-profit institutions serving households.

It should be emphasized that in our SD national model, sectors are entirely identical with the institutional sectors in the SNA. This mechanism will provide the simulation results of our model with a strong qualification as supporter to institutional policy making.

Accounting Rule Each sector and sub-sector has the sequence of accounts which consists of current accounts, accumulation accounts and balance sheets. Current accounts consists of production account and distribution and use of income accounts. The production account records the activity of producing goods and services and its balancing item, value added, is carried forward into the distribution and use of income accounts. The balancing item of income accounts is saving and it is carried forward into the capital account in accumulation accounts.

The balance sheets record assets, liabilities and net worth. The closing balance sheets are fully determined by the opening balance sheets and transaction flow in the sequence of accounts.

The structure of our model, as well as the SNA, is built around the sequence of interconnected accounts.

A Technology for Model Operations: Structured Matrix

Our cherishing desire is to express complicated phenomenon in more easily understandable way without loosing their integrity. An idea of structured matrix was first proposed by German scholar Otto Pichler who was stimulated by the early stage of W. Leontief's model. We had independently reached same idea in Japan, before the time we heard of German development. Through introducing German nuance into Japan and expanding our idea, we got practical progress in modeling of various areas. Now our technology can be addressed toward new SD paradigm. By space limitation, only a few principles are introduced briefly.

Basic Principle of Structured Matrix Vector and matrix multiplication: inner product (a) can be rewritten introducing Vertically Multiply and Horizontally Add (VMHA) as in (b), if A ~ E, M1~ M4, are scalar values as in Figure 1. Also calculating relations can be read out as in (c).Then those symbols, A ~ E, and M1 ~ M4, can be expanded to vectors and matrices as in (d). Figure 2. illustrates example of structured matrix in a flat table (a) and set of tables hierarchically developed (b). By this hierarchically developed tables (b), we can handle very large model, keeping visibility and transparency. This mechanism implies Linear I / O Models with native operators: +, -, x and Mutual Causal Relations. Matrices in Center Part can be stretched to versatile operators. (Ex. Sum of Matrix Series, Bit Map for bundling of related matters, capsulated operations of nonlinear relations, etc.) Also this structure can handle looped models. Through these, Modeling of Input-Process-Output systems, are realizing on the packages of Table-Driven-Tables-Processing.

Figure 2. Principle of Structured Matrix II

This technology is bringing following capabilities. 1) Macro and Microscopic Views for complex modeling, 2) Common communication tools through models for collaborators. 3) Modeling of Value Chains of multiple items, their mutual relations with different dimensions like monetary and non-monetary values. This is common problems of modeling in the Satellite Accounting of the revised SNA. 4) Large scale modeling with visibility avoiding million formulas, if approached by scalar oriented simulation languages.

Matching Function Depending upon data attribution, picking up certain data and transferring them to appropriate cell in another table is matching function shown in Figure 3. Matching function contributes for Turning Inside-Out mechanism. This mechanism makes it possible to across various functional areas and to bundle the data with similar attributions.

Chaining Structure Transparency and visibility with bird's eye-view are essential for collaboration in chaining models. Easy combination and recombination of models are possible with chaining mechanism of hierarchically nested tables as in Figure 4. Turning of Inside-Out concomitant factors are usually left behind deeply in the bottom of hierarchical organizations. Such problems like budgeting models for common factors and influential analysis of environmental influences, can be processed on this chaining structure by synchronizing the use of Matching in individual models.

With the sophisticated modeling ideas, Structured Matrix Technology will be the strong vehicles for studying fairly large complex systems like national economy, world economics and global environmental project.


The System Dynamics national Model should have the capacity to provide institutionally feasible support to policy making. For this reason, our approach was built on the basis of the SNA. We introduced in our approach the structured matrix with matching technique. The structured matrix will make possible our approach a variety of sourcing beyond the SNA.

In our study, the following points were confirmed:

1) The model structure reflects real institutional aspects of national economy.

2) The model has hierarchical and recursive structure while keeping holonic causal relations from macroscopic and microscopic view points.

3) The model keeps transparency of nested account structures.

4) The structured matrix as a basic core technology is supporting our modeling and simulation.


  1. United Nations, Commission of the European Communities, International Monetary Fund, Organization for Economic Co-operation and Development. And World Bank, System of National Accounts 1993, Prepared under the auspices of the Inter-Secretariat Working Group on National Accounts, New York, Brussels / Luxemburg, Paris, Washington, D. C., 1993.
  2. Forrester, J. W. , "The System Dynamics National Model: Macrobehavior from Microstructure", PP.3-12. In Milling P.M and Zahn, E.O.K. Eds., Computer-Based Management of Complex Systems, Springer-Verlag, 1989.
  3. Pichler, O., 1953: "Anwedung der Matrizenrechnung auf betriebswirtschaftlihe Aufgaben", Ingenier Arcchiiv, PP.131-150. Goettingen
  4. Toyama, T. and Endoh, K.,: 1996:"Table-Driven-Tables-Processing for DSS beyond spread sheet", Journal of Decision Systems, PP.80, Vol. 5-n 3-4/1996, Paris

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