Economic Waves: The Effect of the U.S. Economy on World Economy

This paper shows how the inter-connections of the U.S. economy with five major economic regions in the world: Japan, China, ASEAN, Latin America, and the European Union can be captured through use of the inter-linkage coordinate space, and how such connections can be represented graphically with the U.S. economy placed in the center and with these regions plotted along the rays (axes) that are drawn from the center, each ray having as many windows as are required at the predetermined perimeter levels. Hence, this paper evaluates the way in which an economic recession or financial crisis from the U.S. economy can simultaneously affect five different markets economic hotspots viz. Japan, China, ASEAN, Latin America and the European Union. Finally, this paper proposes the use of computer graphical animation to generate the real time effect of these economic waves into the same graphical space.


The Evolution of Graphical Modeling in Economics from 2-Dimensional to Multi-Dimensional
Academics and scholars have long been limited to 2-dimensional graphical modeling (Shchepin, 1976), but advancement in computer technology now allows the development of multi-dimensional graphical models. This paper illustrates a novel type of economic modeling for studying market behavior as a whole. This method combines new multidimensional graphical modeling tools with to display the propagation of effects in real time. Two-Dimensional graphical models are only able to display historical and forecasting data in the same graphical space within a limited space of time. In contrast, multidimensional real-time graphical modeling can display all possible changes among a large number of variables. By producing a multidimensional graph that displays simultaneous changes in many variables, this type of modeling allows observers to clearly see cause and effect among the different variables. Here, we demonstrate that 2-dimensional (X,Y) and 3-dimensional space (X,Y,Z) can only illustrate a micro-slice of complex and dynamic economic phenomena. The hypothesis of this paper is that 2-dimensional and 3-dimensional spaces are a micro-slice of the huge mega-space or universe of a fixed period of time and common space. To test this hypothesis, this paper applies an alternative, multi-dimensional graphical modeling method called "Inter-Linkage Coordinate Space" to a set of economic variables. Economists have long attempted to visualize simple (static)  (dynamic) economic phenomena across a specific period of time in the same graphical space through the application of 2-dimensional (X,Y) or 3-dimensional spaces (X,Y,Z). Given their widespread use, this paper also investigates why economists continue to use 2-dimensional (X,Y) or 3-dimensional (X,Y,Z) graphical representations of complex and dynamic economic phenomena; some possible explanations are as follows: • The application of 2-dimensional and 3-Dimensional spaces in the economic graphical analysis is simply an ingrained tradition.
• 2-dimensional and 3-Dimensional spaces are simple and easy methods for visualizing basic trends or values in the same graphical space. • Alternative and suitable multi-dimensional graphical models are not readily available.
The main hypothesis of this paper is that 2-dimensional and 3-dimensional spaces are inadequate for modeling complex economic behavior. The real world is constantly changing along nearly unlimited measures, spaces and times (Inselberg and Dimsdale, 1994). Therefore, this paper proposes a type of multi-dimensional economic modeling that can dynamically display a large number of variables in the same graphical space in both real time and slow motion and that can be used to study the behavior of complex and dynamic economic phenomena.

An Introduction to the Inter-Linkage Coordinate Space
The inter-linkage coordinate space (Ruiz Estrada, 2011a) is formed by an infinite number of general axes (A 0, A 1, …, A n …), perimeter levels (L 0, L 1, …, L n …) and window refractions (W 0, W 1,…, W n… ) (see Figure 1 and Prototype 1). Each window refraction is produced by joining its sub-x axis (X A-L ) with its sub-y axis (Y A-L ); therefore, each window refractions (W 0, W 1… W n… ) has its own coordinate space (X A-L ,Y A-L ). All window refractions on the same general axis (A 0, A 1, …, A n …) are joined together under the application of the inter-linkage connectivity of windows refraction, represented by "®"; this inter-connects all window refractions (W 0, W 1, …, W n …) on the same general axis (A 0, A 1, …, A n …) but in different perimeter levels (L 0, L 1, …, L n …). The inter-linkage coordinate system is represented by Expression 1: (1.) Perimeter level P 0 ® Perimeter level P 1 ® … ® Perimeter level P n General Axis 0 (A 0 ): . . .

General Axis n (A ∞ ): W
The inter-linkage coordinate space is available to fix a large number of different functions located in different windows refraction (W 0, W 1, …, W n …), perimeter levels (L 1, L 2, …, L n …) and general axes (A 1, A 2, …, A n …) (see

Economic Waves
In this section, we describe economic waves, which are generated from a large surface plotted in the same graphical space. The large surface is formed by different parts that represent different markets (countries/ regions), all of which are connected directly to a single epicenter. For the case studied in this paper, this epicenter is fixed by the GDP growth rate of the U.S. This paper assumes that each market (country/region) has a large number of windows refraction (or quadrants), each of which is formed by its X-axis, which represents time (days, weeks, months, years and decades), and its Y-axis, which represents the main variable(s) under consideration. The main variables in our model of each window refraction for different market(s) are the growth rates GDP US , exports (X), foreign direct investment (FDI), the stock market (SM) and unemployment (U). Thus, each market (country/ region) possesses five windows refraction within the same coordinate space (see Table 1 and Figure 2).
Second, we assume that the economic wave in each market (country/region) propagate at different speeds and sizes. The size and speed of the economic waves depend on uncontrolled forces of the market, such as economic speculation(s), economic bubbles and imaginary markets (Issing, 2011). The main objective in modeling these economic waves is to evaluate the global negative impact that comes from a deep economic recession in the U.S. economy. To do so, we use multi-dimensional graphical modeling that can illustrate the movement of economic waves in real time. Latin America). We assume that the epicenter that is connected to all markets (country/region) is the GDP growth rate of the U.S.; at the same time, each market has a large number of windows refraction. Economic waves are generated first by plotting a single value (growth rate) in each window refraction and joining each single value located in each window refraction by straight lines from the epicenter to the last window refraction in each market (see Figure 2); we call this concept "windows refraction links (╬)". Windows refraction links (╬) facilitates the connection of all windows refraction in the same market and other markets simultaneously, from the epicenter to the last window refraction in the same market. Therefore, the epicenter is going to affect different countries simultaneously in the same graphical space but at different magnitudes and speeds. We assume that these countries maintain a high international trade volume and investment mobility relationship with the U.S. (Ruiz Estrada & Yap, 2006). In this paper, the economic waves originate  Latin America (12%) (see Figure 3 and Table 3). These  goods sub-market, money sub-market, social submarket, financial sub-market, international trade sub-market, labor sub-market, government submarket, transport and energy sub-market and technological sub-market (see Table 3 and Figure 3). For the purposes of this study, we will not deeply analyze the U.S. economy, as we explore it only to display the U.S. economy within a multi-dimensional coordinate space under the use of different databases in different sub-markets (windows refraction). The application of the multi-dimensional coordinate space method offers a novel and useful multi-dimensional graphical modeling technique for economists, policy makers, students and academics.

Comments and Remarks (from the reviewer)
This paper shows how the interactions of the U.S. economy with five major economic regions, namely, Japan, China, ASEAN, Latin America, and the European Union, can be captured through use of the inter-linkage coordinate space. Such connections are graphically represented by placing the U.S. economy in the center and the other regions plotted along the rays (axes) that are drawn from the center, each ray having as many windows as are required at the predetermined perimeter levels. Each window has its own coordinate system, and all windows at each perimeter level are interconnected. Thus, variations within each economic region for each of the dimensions under scrutiny are plotted in the coordinate system of the refraction-windows. This scheme allows one to see the impact of the U.S. economy on other major economic regions as wave-like motions that originate in an epicenter that represents variation of the GDP growth rate of the U.S. economy.
Because the economic data from the world as a whole are enormous in dimension, representing such data in a single visual graph may seem impossible; however, this can be accomplished if one draws rays from the origin, each for a given region, with as many refraction-windows as are required plotted on such rays in order to show the movement of the economy of each region. This method allows one to graph a complex set of data that cannot be represented in the conventional way, eliminating the worry of running out of axes or windows, as there is no limit to the number of rays and windows in this method. Thus, this paper demonstrates, through a particular example, that an inter-linkage coordinate space coupled with an accompanying graphing method of Econographicology is a powerful apparatus for representing complex sets of data.