Hye-Jin Cho

ECONOMIC SIZE AND DEBT SUSTAINABILITY AGAINST PIKETTY'S "CAPITAL INEQUALITY"

Keywords: capital-labor split, factors of production, capital/income ratio, Thomas Piketty, capitalism, economic size, debt sustainability, Latin America, import substitution industrialization (ISI) model, insolvent external debt, openness, external debt to exports ratio JEL Classifications: E01, E22, G00, G01, H63

This article presents a methodology designed to facilitate alternative variables measuring economic growth. A capital-labor split of Cobb-Douglas function is adapted for use in the context of economic growth.

A capital/income ratio and two fundamental laws of capitalism originated by Thomas Piketty illustrate capital inequality undervalued with respect to labor inequality. In addition, the article includes export and external debt as strong alternatives. Empirical data of the World Bank are analyzed to demonstrate broad differences in economic sizes. The case analysis on Latin America as an example of different sized economy is also discussed.

Introduction

Questions about stability of the capital-labor split " …..in the 2000s several official reports published by the Organization for Economic Cooperation and Development (OECD) and the International Monetary Fund (IMF) took note of the phenomenon (a sign that the question was being taken seriously). The novelty of this study is that it is to my knowledge the first attempt to place the question of the capital-labor split and the recent increase of capital's share of national income in a broader historical context by focusing on the evolution of the capital/income ratio from the eighteenth century until now. ….. "

Ref: Thomas [START_REF] Piketty | Capital in the Twenty-First Century[END_REF] Capital in the Twenty-First Century

Until when, can we use the Cobb-Douglas function with the mindset to believe the stability of the Capital-Labor split? A rational answer with alternative solutions should be pursued to this question. At the first step, we may comment on weakness of this method.

Firstly, the Solow residual which is a number describing empirical productivity growth in an economy from year to year and decade to decade is hard to be calculated because of its "residual" which is the part of growth that cannot be explained through capital accumulation or the accumulation of other traditional factors, such as land or labor.

The equation in Cobb-Douglas form is: Y=A K  L  where total output Y is as a function of total-factor productivity A, Capital input K, Labor input L and two input's respective shares of output. ( and  are the capital input share of contribution for K and L respectively)

Even though Robert Solow defined rising productivity as rising output with constant capital and labor input perfectly, he left undefined part as the Solow residual. The problem is that Solow residual has pro-cyclicality. Traditionally, total output is measured by inputs of labor and capital. TFP (TFP) called multi-factor productivity (MFP) accounting for all inputs cannot be measured directly and accounts for effects in total output not caused by inputs. Indeed, there are two sided directions to analyze the economy.

Especially, Multifactor Productivity (MFP) is measured as below:

MFP i = Y i - i where Y i denotes actual output and  i denotes predicted output (1a) Log e (Y) =  0 +  I log e ( i ) +  I log e (L i )

So we get, MFP = (ln)/t = (lnY)/ts L (lnL)/t -s K (lnK)/t where  is the global production function: Y is output, t is time, S L is the share of input costs attributable to labor expenses, S K is the share of input costs attributable to capital expenses, L is a dollar quantity of labor, K is a dollar quantity of capital, M is a dollar quantity of materials, S is a dollar quantity of (business) services, E is energy or exergy (available energy), only used in some models.

Secondly, like Total Factor Productivity (TFP), Growth accounting exercises are open to the Cambridge Critique. The aggregation problem is the major part of this debate. The style that the representative agent solves the decision problem in the function assuming the entire economy cannot be from the debate about the collection problem of different inputs, sudden shocks, rate of profit and a large number of heterogeneous workplaces. Hence, some economists believe that the method and its results are invalid.

Otherwise, we can indirectly establish the model to find determinants of TFP. Neoclassical economics started with the classical factors of production of land, labor and capital. Further distinctions from classical and neoclassical microeconomics include capital-the result of investment, fixed capital, working capital, financial capital and technological progress.

Additionally, entrepreneurship, human capital, intellectual capital, social capital, natural resources and energy can be considered. So we need to think "Weightiness" on Labor, Capital and other factors at the next step. I agree with the opinion of Thomas Piketty that structure of inequality with respect to both labor and capital has actually changed since the ninetieth century.

"To what extent are inequalities of income from labor moderate, reasonable, or even no longer an issue today? It is true that inequalities with respect to labor are always much smaller than inequalities with respect to capital. It would be quite wrong, however, to neglect them, first because income from labor generally accounts for two-thirds to three-quarters of national income, and second because there are quite substantial differences between countries in the distribution of income from labor, which suggests that public policies and national differences can have major consequences for these inequalities and for the living conditions of large numbers of people."

Ref: Thomas [START_REF] Piketty | Capital in the Twenty-First Century[END_REF] Capital in the Twenty-First Century Dynamics of the capital/income ratio of Thomas Piketty: r > g "…If, moreover, the rate of return on capital remains significantly above the growth rate for an extended period of time (which is more likely when the growth rate is low, though not automatic), then the risk of divergence in the distribution of wealth is very high..."

"…This fundamental inequality, which I will write as r > g (where r stands for the average annual rate of return on capital, including profits, dividends, interest, rents, and other income from capital, expressed as a percentage of its total value, and g stands for the rate of growth of the economy, that is, the annual increase in income or output), will play a crucial role in this book. In a sense, it sums up the overall logic of my conclusions.…."

Ref: Thomas Piketty (2014) Capital in the Twenty-First Century

Thomas Piketty put emphasis on capital inequality. This is the similar viewpoint of boom and bust. Boom and bust are periods of a severe business cycle over time.

Several economic indicators are denoted as sustained increases followed by a sharp and rapid contraction. Times of increased business and investment have collapsed leaving widespread poverty such as the depression of 1837 and 1857 in the United States. For example, in the early 1800s in Ohio people were buying land on credit to sell at twice the price but land became too expensive to buy. At the same time, wheat prices became too low to transport wheat to market. Wheat was $1.50 per bushel in 1816; by 1821, 20 cents. The automaker Paul Hoffman said "we cannot live with a crash with 26 depressions over 100 years including the burst of the 1930s."

The dynamics of the capital/income ratio adds a new perspective to the debate on capital and wealth.

Previous study provides an overview of economic development. The direction of economic growth rate should increase to the top. However, the new viewpoint offers an alternative framework to demonstrate how the society actually moves. It examines different meanings of changes and directions with regard of economic growth. The attempt to be escaped by the required bilateral choice between capital and labor re-illuminates on alternative factors to research economic growth.

The First Fundamental Law of Capitalism α = r × β

With the aid of exploration of capital induced from national income, the first law of capitalism attempts to show visible motion of dynamics. It requires the fully-fledged account of global data because the formula produces the global interpretation without constraints. In the left side of formula, α can be added and in the right side of formula, r × β can be added. Hence, broader context with global empirical data is somewhat limited.

"In order to illustrate the difference between short-term and long-term movements of the capital/income ratio, it is useful to examine the annual changes observed in the wealthiest countries between 1970 and 2010, a period for which we have reliable and homogeneous data for a large number of countries. To begin, here is a look at the ratio of private capital to national income, whose evolution is shown in Figure 5.3 for the eight richest countries in the world, in order of decreasing GDP: the United States, Japan, Germany, France, Britain, Italy, Canada, and Australia." " Figure 5.3 (figure 1 in the paper as below) displays annual series and shows that the capital/income ratio in all countries varied constantly in the very short run. " "…. can now present the first fundamental law of capitalism, which links the capital stock to the flow of income from capital. The capital/income ratio β is related in a simple way to the share of income from capital in national income, denoted α. The formula is α = r × β, where r is the rate of return on capital. …"

Ref: Thomas [START_REF] Piketty | Capital in the Twenty-First Century[END_REF] Capital in the Twenty-First Century

The first law of capitalism offers a subjective view of capital to focus on deviation of bilateral choice between capital and labor. Further evidence of the authenticity of the text is needed.

In the figure 1 (as below), the slope is upward in the end. It implies i nterpretation whether long-run or short-run economy is possible. However, dep ending on the date of the World Bank as below, it's impossible to explain abo ut capital formation except for data of China. China has the highest gross cap ital formation (% of gross domestic production (GDP)) from 2004 to 2013. Indeed, this level is higher than the world's one. France, Germany, United Sta tes and Japan's graphs are similar except for China's one. In the figure 2 (as below), gross capital formation (formerly gross domestic investment) consists of outlays on additions to the fixed assets of the economy plus net changes in the level of inventories. Fixed assets include land improvements (fences, ditches, drains, and so on); plant, machinery, and equipment purchases; and the construction of roads, railways, and the like, including schools, offices, hospitals, private residential dwellings, and commercial and industrial buildings. Inventories are stocks of goods held by firms to meet temporary or unexpected fluctuations in production or sales, and "work in progress." According to the 1993 SNA, net acquisitions of valuables are also considered capital formation. The first law of capitalism gives fresh impetus to emphasize the role of capital to promote economic growth. It should be elaborated to describe the main features of dynamics related to global data for the possibility of wide cross-country comparison.

The Second Fundamental Law of Capitalism: β = s / g "….In the long run, the capital/income ratio β is related in a simple and transparent way to the savings rate s and the growth rate g according to the following formula: β = s / g….."

Ref: Thomas [START_REF] Piketty | Capital in the Twenty-First Century[END_REF] Capital in the Twenty-First Century.

Gauging the general applicability related to the income rate to the growth rate is investigated by similarity between each gross domestic production (GDP) motion of different countries and world average motion.

As below, there are graphs of correlation between countries' gross domestic production (GDP) growths and the world's one. China has very different shapes of correlation with respect to the world's one from other's. This example is to test the hypothesis of the second law of capitalism. With the panoramic viewpoint of figure 3, the argument is evidently to make explicit cross-sectional data of different countries and thus contrast various interpretations upon which to different approaches to the contemporary management of past built environments are based. In addition, in the long run, can the capital/income ratio β be reflected by the volatility of the savings rate s and the growth rate g ? Within the context not to divide into countries depending on their economic sizes, then, we face aggregation problem. This brief empirical test here is intended to provoke the case that outstanding values than averaged value in the long run can exist. The second law of capitalism encapsulates the capital concern in general. However, it initiates a discussion of the stabilization of dynamics and boundary of optimal values by the end. Hence, in this paper, I will endeavor to explore new variables which can affect the left side and right side in the law of capitalism by absorption.

Economic Size and Debt Sustainability

Trade condition

Judging from stability of the capital-labor split, in the paper, attention was directed to the weightiness of capital and labor. Two laws of Piketty's capitalism have centered on the capital inequality within national income. The main objective of arguments is to investigate the validity of global application because an idea of capital inequality takes economic growth as focal point. In what follows, I explore key signifying variables. I hope to look most closely at familiar economic variables from a global angle.

I shall start by an attempt to check the correlation between average value of world and each value of each country with regard to exports of goods and services, gross domestic production (GDP) growth, GDP per capital, gross national income (GNI) per capital purchasing power parity (PPP), Gross capital formation, Gross savings, foreign direct investment (FDI) and inflation consumer price. What I propose to do here is to examine structural importance of key economic variables except for capital within world variables. I will use these empirical data as a framework against which to understand the capital within national income. I will concentrate on more rational way to address economic growth and capital inequality offering the global interpretation beyond the capital inequality framework within national income of Thomas Piketty.

Depend on data of World Bank, from 1970 to 2013, the correlation between world's one and countries' exports of goods and services is positive. (Observation 43) From 1970 to 2012, the correlation between world's one and countries' FDI is no observation. Among the correlation with the world's one, exports of goods and services, GDP per capital and gross capital formation have positive correlation value. This is the reason why we need to focus on trade condition beyond no trade condition and complete market condition. The attempt to identify the law of capitalism by Thomas Piketty draws together the bulk of the published neoclassical papers mainstreamed by French Economists. I wish to flesh this out to take a highly microscopic approach to the question of economic growth. I begin with a case analysis of Latin America animated by a curiosity about impact of export and debt problematizing sovereign credit to affect the sustainability of each country and the whole economy in general.

To deal with the global framework of capital inequality and economic growth, I turn to state export and debt sustainability in a series of ratio analysis of Thomas Piketty. I may say that capital inequality within national income will be articulated with ideas about external debt to export. Having discussed empirical data, it is now time to focus on global activities beyond the domestic activities concerning sustainability of economic society.

Export and Debt sustainability

In case of debt sustainability, the debt to export criterion should be considered with the size of countries. [START_REF] Roubini | Debt Sustainability: How to assess whether a country is insolvent[END_REF]) Suppose you have two countries, A and B that are identical. Their GDP is 100 each, their external debt is 50 each and their exports are 20 each. Then the debt to GDP ratio is 50% for each and the debt to export ratio is 250% each. Assume that, at this ratio, both countries are solvent. Now take the two countries and merge them. Total GDP will be 200, total debt will be 100 and total exports will be 20. [START_REF] Roubini | Debt Sustainability: How to assess whether a country is insolvent[END_REF] mentioned this is because exports among each other are now inter-regional rather than international trade. Hence, economic problems with no trade cannot be solved in reality.

By the end of this case, the combined A+B economy has a debt to GDP ratio that is still 50% but now the debt to export ratio is 500%, a figure that is clearly unsustainable and would suggest default.

Indeed, using the debt to export criterion, same two economies look solvent if they are a separate country and insolvent if they are joined in one country. This suggests that the debt to export ratio may be a faulty measure of solvency; larger countries with greater intra-regional, rather than international trade, would look insolvent while smaller countries with similar fundamental would look solvent just because their export to GDP ratio is higher. However, in the example, the export to GDP ratio is lower for a larger country with greater amount of inter-regional, rather than international trade. But a small open economy, like Argentina, is usually more open than a larger economy; thus, low export to GDP ratio may reflect currency overvaluation, high degrees of trade protection and other policy restrictions to openness rather than structural factors that explain lower openness. Thus, an economy that should be more open than it is and has a large debt to export ratio may find it harder to service its external debt. For example, if export ratios are low, even a large real depreciation may not improve exports and trade balance enough to reduce a resource (trade balance) gap necessary to prevent insolvency. So, the degree of openness (export to GDP ratio) within countries or beyond countries does affect country's ability to service its debt.

As below, through the dickey fuller test -examines a unit root is present in an autogressive model, validity of variables can be detected more. These data arranged yearly from 1970 to 2012 can be distinguished whether it has a unit root, a feature of processes that evolve through time that can cause problems in statistical inference. A clear understanding of empirical data about economic data requires reliability of raw data. In supporting the assumption that export and debt sustainability are keys to get to the heart of questions relating to the economic growth, I mentioned them with the empirical angle because it provides the necessary background for discussing capital to GDP and further GDP analysis related to capital inequality.

Debt management of Latin America

Debt-driven capital

In the 1960s and 1970s, Latin American countries, notably Brazil, Argentina, and Mexico, borrowed huge sums of money from international creditors for industrialization; especially infrastructure programs. After 1973, private banks had an influx of funds from oil-rich countries and believed that sovereign debt was a safe investment. Between 1975 and[START_REF] Street | Structuralism, and Dependency in Latin America[END_REF], Latin American debt to commercial banks increased at a cumulative annual rate of 20.4 percent. This heightened borrowing led Latin America to quadruple its external debt from $75 billion in 1975 to more than $315 billion in 1983, or 50 percent of the region's gross domestic product (GDP). Debt service (interest payments and the repayment of principal) grew even faster, reaching $66 billion in 1982, up from $12 billion in 1975.

Failure of debt-driven capital

As interest rates increased in the United States of America and in Europe in 1979, debt payments also increased, making it harder for borrowing countries to pay back their debts. Deterioration in the exchange rate with the US dollar meant that Latin American governments ended up owing tremendous quantities of their national currencies, as well as losing purchasing power. The contraction of world trade in 1981 caused the prices of primary resources (Latin America's largest export) to fall.

Argentina has until midnight on July 30, 2014 to avoid going into default for eight times in its history. Most creditors exchanged their defaulted debt for new securities in two restructurings in 2005 and 2010 but a few creditors led by a hedge fund called NML Capital scooped up the cheap defaulted debt in order to chase payment of full principal plus interest. If Argentina defaults, its outstanding debt under foreign law amounts will be $29 billion.

Why capital cannot be simply explained within gross domestic production (GDP) : Attention to GDP replacing foreign imports -Import substitution industrialization (ISI)

Import substitution industrialization (ISI) is a trade and economic policy that advocates replacing foreign imports with domestic production. ISI policies were enacted by countries within the Global South with the intention of producing development and self-sufficiency through the creation of an internal market. ISI works by having the state leading economic development through nationalization, subsidization of vital industries (including agriculture, power generation, etc.), increased taxation, and highly protectionist trade policies. Import substitution industrialization was gradually abandoned by developing countries in the 1980s and 1990s due to structural indebtedness from ISI related policies on the insistence of the IMF and World Bank through their structural adjustment programs of market-driven liberalization aimed at the Global South.

ISI was most successful in countries with large populations and income levels which allowed for the consumption of locally produced products. Latin American countries such as Argentina, Brazil, Mexico, and (to a lesser extent) Chile, Uruguay and Venezuela, had the most success with ISI. This is so because while the investment to produce cheap consumer products may pay off in a small consumer market, the same cannot be said for capital intensive industries, such as automobiles and heavy machinery, which depend on larger consumer markets to survive. Thus, smaller and poorer countries, such as Ecuador, Honduras, and the Dominican Republic, could implement ISI only to a limited extent. Peru implemented ISI in 1961, and the policy lasted through to the end of the decade in some forms.

By the early 1960s, domestic industry supplied 95% of Mexico's and 98% of Brazil's consumer goods. Between 1950 and 1980, Latin America's industrial output went up six times, keeping well ahead of population growth. Infant mortality fell from 107 per 1,000 live births in 1960 to 69 per 1,000 in 1980 and life expectancy rose from 52 to 64 years. In the mid of 1950s, Latin America's economies were growing faster than those of the industrialized West.

More to the immediate point why the GDP is not just the GDP to consider the capital inequality: example of Export-oriented industrialization (EOI)

Export-oriented industrialization (EOI) sometimes called export substitution industrialization (ESI), export led industrialization (ELI) or export-led growth is a trade and economic policy aiming to speed up the industrialization process of a country by exporting goods for which the nation has a comparative advantage.

From the Great Depression to the years after World War II, under-developed and developing countries started to have the hard time economically. During this time, many foreign markets were closed and the danger of trading and shipping in wartime waters drove many of these countries to look for another solution to development. The initial solution to this dilemma was called import substitution industrialization.

Both Latin American and Asian countries used this strategy at first. However, during the 1950s and 1960s, Asian countries, like Taiwan and South Korea, started focusing their development outward, resulting in an export-led growth strategy. Most of Latin American countries continued with import substitution industrialization, just expanding their scopes. Some have pointed that out because of the success of Asian countries, especially Taiwan and South Korea.

Insolvent external debt of Latin America

Since the 1980 several countries in the region have experienced a surge in economic development and have initiated debt management programs in addition to debt relief and debt rescheduling programs agreed to by their international creditors. The following is a list of external debt for Latin America based on a 2012 report by The World Factbook. The ratio of gross external debt to exports provides a quick indicator of the capability of an economy to repay external debt with enhanced revenue from sales to foreign countries. A ratio below 1 suggests that debt can be repaid rapidly, theoretically in less than one year. Conversely, the higher the ratio is the lower the country's capability to finance the debt with revenue from exports.

Having discussed the capital inequality issue, attention to the export variable and need of comprehensive ratio analysis: debt to export ratio and capital to income ratio, we will now proceed to investigate the risk management status of Latin America.

Risk management in major Latin America countries: (Mexico, Argentina, Brazil, Chile) Among Latin America, the adoption of solvency II which is EU directive -codifies and harmonizes the EU insurance regulation primary concerning the amount of capital that EU insurance companies must hold to reduce the risk of insolvency-is realistic in Mexico. In the second half of 2008, the Mexican regulator (Comisión Nacional de Seguros y Fianzas, or CNSF) shared with the Mexican association of insurance companies (Asociación Mexicana de Instituciones de Seguros, or AMIS) a draft of a project of insurance law (the proposed law) in which a Solvency II-type regime was incorporated. The draft considered an initial date for this proposed law of January 2012. Since that time (end of 2008) through 2009 and the beginning of 2010, the proposed law was discussed and reviewed between CNSF and AMIS. The actual initial date is January 2014. However, the proposed law did not approved by the Mexican Congress.

If the strong solvency regulation is existed like Argentina, the conflict of two regulations between local solvency regulation and international one should be considered for the stable adoption. The current framework does not seem to indicate that an extended application of the Solvency II methodology will be feasible in the near future, except for offices and branches of European-based insurance companies.

The regulatory agency, SSN (Superintendencia de Seguros de la Nación) only mentioned the adoption of Solvency II without clear criteria. Actually, the insurance industry is tightly regulated in Argentina. SSN resolutions cover most aspects of insurance company activities, including unearned premiums and methods of mathematical reserve valuation. The agency establishes minimum valuation methods arising from formulas used to value out-of-court, mediation and lawsuit payables, as well as incurred but not reported (IBNR) claims reserves. Most insurance companies use these mechanisms to value their payables. As of 30 June 2011 (last fiscal year-end), all insurance companies in the market calculated their capital to be credited based on the issued premiums indicator. Of 155 insurers, only 4 carried minimum capital deficit as of this date. In recent months, the SSN announced the launch of a strategic plan of insurance, inviting all industry participants to bring their vision to define the insurance policy to be used during the period 2012-2020.

The existence of many solvency regulations can be analyzed with the conflict inside rules in Brazil so the Own Risk and Solvency Assessment (ORSA) is needed to integrate them. Brazil has adopted international regulations at each pillar. For Pillar I, the adoption of International Financial Reporting Standards (IFRS) as Brazilian generally accepted accounting principles (GAAP) in 2010. Detailed monthly reporting requirements of individual policy and claims data for the Insurance Supervisory Authority (Superintendência de Seguros Privados, SUSEP) were introduced in 2004 at the level of Pillar II. In 2004, the Supervisory Authority introduced the requirement that each insurance company should produce an annual actuarial valuation report proper to Pillar III.

In Chile, A new law that would require insurance companies to withhold risk-based capital was sent to Congress for approval on 30 September 2011. The methodology for calculating risk-based capital in Chile has yet to be made public. It is expected that the Chilean regulator will publish a consultative white paper with details around the calculation of risk-based capital in the third quarter of 2012. The SVS (Superintendencia de Valores y Seguros) has demonstrated interest in performing the first Quantitative Impact Study (QIS) by the end of 2012.

Conclusion

A capital-labor split of Cobb-Douglas function which continues to be widely used by economists, has little empirical support. Even though neo-classical economists have proposed mathematical and theoretical realisms of economic growth by using the function, it was never empirically validated as the appropriate model for economic growth. Indeed, Thomas Piketty, a French economist, brought up this debated topic about capital inequality in his book, Capital in the Twenty-First Century in 2014. I agree with him in that there is the structure of inequality with respect to both labor and capital actually changed since the ninetieth century of the chapter: Beyond Cobb-Douglas "The Question of the Stability of the Capital-Labor Split. Some research questions like "Did the Increase of inequality cause the financial crisis?", "The illusion of marginal productivity", "The Question of Time Preference" and "Is there an equilibrium distribution?" are fresh and fancy to break old fixed ideas.

I feel the solution is weak to support his brilliant idea enoughly. At the part4, the talk is suddenly changed to tax and pension (PAYGOs) without connection with previous capital inequality. Tax issues on Capital and Chinese millionaires are far from the real data of capital formation because it is very high value in China. We cannot see any empirical data of China's one in his book even though the major capital part is by China. It seems hard to accept a solution of redistribution by immigration and an opinion about the central bank just as a loan deal before redistribution of wealth.

In the article, the most recent data shows that export and external debt may be correlated to explain economy growth. In the paper, Latin America history pervades the claim that capital within GDP of Thomas Piketty should be enhanced by conceptual capital related to debt and export beyond GDP. In addition, to point out miscalculation of ratio analysis depending on economic size, the example by [START_REF] Roubini | Debt Sustainability: How to assess whether a country is insolvent[END_REF] is demonstrated. To conclude, through the case analysis of Latin America, in detail, economic size and debt sustainability as economic growth indicators are emphasized by empirical data.

Figure 1 :

 1 Figure 1 : Private Capital in Rich Countries, 1970-2010

Figure 2 :

 2 Figure 2 : Gross Capital Formation (% of gross domestic production (GDP))

Figure 3 :

 3 Figure 3 : Graphs of Correlation between Countries' gross domestic production (GDP) Growths and the World's One

  From 1971 to 2012, among the correlation between world's one and countries' GDP growth, China and Argentine's ones have negative values. (Observation 42) Table 3.2 : Correlation between World's One and Countries' GDP Growth From 1970 to 2013, the correlation between world's one and countries' GDP per capital is positive. (Observation 43)

  From 1980 to 2012, the correlation between world's one and countries' GNI per capital ppp is positive. (Observation 27) Table 3.4 : Correlation between World's One and Countries' GNI per Capital PPP From 1970 to 2013, the correlation between world's one and countries' gross capital formation is positive. (Observation 27)

  From 1970 to 2012, the correlation between world's one and countries' gross savings have negative value. (Observation 14) Table 3.6 : Correlation between World's One and Countries' Gross SavingsFrom 1961 to 2013, the correlation between world's one and countries' inflation consumer prices have negative value. (Observation 3)

  Openness and External debt to exports ratioDebt burden indicators include the (a) Debt to gross domestic production (GDP) ratio, (b) External debt to exports ratio, (c) Government debt to current fiscal revenue ratio etc. This set of indicators also covers the structure of the outstanding debt including the (d) Share of foreign debt, (e) Short-term debt, and (f) Concessional debt in the total debt stock.

Table 1 :

 1 Methodology about Factors of Production

	Inputs: Three Factors of Production
	Classical economics Adam Smith, David Ricardo: Labor, Capital Stock, Land (Natural Resource)
	Marxism Labor, The subject of labor, The instruments of labor
	Neoclassical microeconomics different format: Capital, Fixed Capital, Working Capital,
	Financial Capital, Technological progress
	+add: Entrepreneurs (Frank Knight), Human Capital, Intellectual Capital, Social Capital (Pierre
	Bourdieu), Natural resources (Ayres-Warr), Energy
	Output: Finished Goods (National Income)
	Factor Payments: Rent, Wage, Interest, Profit
	Ref: author, 2014

Table 3 .

 3

1 : Correlation between World's One and Countries' Exports of Goods and Services

Table 3 .

 3

3 : Correlation between World's One and Countries' GDP per Capital

Table 3 .

 3

5 : Correlation between World's One and Countries' Gross Capital Formation

Table 3 .

 3 8 : Correlation between World's One and Countries' Inflation Consumer Prices

Table 3 .

 3 7 : Correlation between World's One and Countries' FDIno observation

Table 4 :

 4 Validity of Detectable Variables Checked by the Dickey Fuller Test

	dickey fuller test	p-value	Mexicogniperc	0.298
	Worldinfconsumerp	0.3432	Argentinagniperc	0.3281
	Chinainfconsumerp	0.0997	Brazilgniperc	0.3169
	United Kingdominfconsumerp	0.0351	Chilegniperc	0.267
	United Statesinfconsumerp	0.0279	Greecegniperc	0.0641
	Franceinfconsumerp	0.046	Irelandgniperc	0.2209
	Germanyinfconsumerp	0.0676	Italygniperc	0.0459
	Japaninfconsumerp	0.241	Portugalgniperc	0.5748
	Korea, Rep.infconsumerp	0.0657	Spaingniperc	0.115
	Mexicoinfconsumerp	0.0459	Worldgdpperc	0.5265
	Argentinainfconsumerp	0.0061	Chinagdpperc	0.1349
	Brazilinfconsumerp	0.1299	United Kingdomgdpperc	0.0888
	Chileinfconsumerp	0.4592	United Statesgdpperc	0.0062
	Greeceinfconsumerp	0.5022	Francegdpperc	0.3853
	Irelandinfconsumerp	0.3117	Germanygdpperc	0.5728
	Italyinfconsumerp	0	Japangdpperc	0.1964
	Portugalinfconsumerp	0.3045	Korea, Rep.gdpperc	0.0356
	Spaininfconsumerp	0.2629	Mexicogdpperc	0.298
	Worldgsaving	0.4606	Argentinagdpperc	0.2843
	Chinagsaving	0.7955	Brazilgdpperc	0.3086
	United Kingdomgsaving	0.2142	Chilegdpperc	0.267

Ref : author made by the Dickey fuller test of countries' variables extracted from the World

Bank, 2014

Table 5

 5 External Debt for Latin America

	Rank	Country -Entity	External Debt (million US$)	Date of information
	26	Brazil	405,300	31 December 2012.
	35	Argentina	130,200	31 December 2012.
	40	Mexico	125,700	31 December 2012
	45	Chile	102,100	31 December 2012.
	49	Colombia	73,410	31 December 2012.
	51	Venezuela	63,740	31 December 2012.
	63	Peru	4,200	31 December 2012.
	77	Cuba	22,160	31 December 2012.
	78	Ecuador	20,030	31 December 2012.
	81	Dominican Republic	16,580	31 December 2012.
	82	Guatemala	16,170	31 December 2012.
	83	Uruguay	15,900	31 December 2012.
	85	Panama	14,200	31 December 2012.
	86	El Salvador	12,840	31 December 2012.
	88	Costa Rica	12,040	31 December 2012.
	112	Nicaragua	5,228	31 December 2012.
	114	Honduras	4,884	31 December 2012.
	123	Bolivia	4,200	31 December 2012.
	139	Paraguay	2,245	31 December 2012.
				Ref: author, 2014

Table 6 :

 6 External Debt to Exports Ratio

	Country -Entity (million$)	external debt	exports	Ratio (External debt/Exports)
	Brazil	405,300	242,000	1.674793388
	Argentina	130,200	85,360	1.525304592
	Mexico	125,700	370,900	0.338905365
	Chile	102,100	83,660	1.220415969
	Colombia	73,410	59,960	1.224316211
	Venezuela	63,740	96,900	0.657791538
	Peru	4,200	47,380	0.088644998
	Cuba	22,160	5,600	3.957142857
	Ecuador	20,030	23,770	0.842658814
	Dominican Republic	16,580	9,467	1.751346784
	Guatemala	16,170	9,864	1.639294404
	Uruguay	15,900	9,812	1.620464737
	Panama	14,200	17,970	0.790205899
	El Salvador	12,840	5,804	2.212267402
	Costa Rica	12,040	11,470	1.049694856
	Nicaragua	5,228	4,160	1.256730769
	Honduras	4,884	6,946	0.703138497
	Bolivia	4,200	11,770	0.356839422
	Paraguay	2,245	4,700	0.477659574
				Ref: world fact book, 2012


recapitalization cost to the government was 6% of GDP (Gross Domestic product). Fiscal costs associated with crisis management were averaged 13% for GDP (16% of GDP if expense recoveries are ignored), and economic output losses were averaged about 20% of GDP during the first four years of the crisis. Otherwise, if the government decides to adopt the Basel capital regulation framework, the adoption cost will influence the economy of countries. Either households or banks, related parties to economy should pay for the Basel capital regulation as the preventive method in the banking business cycle. An OECD (The Organization for Economic Cooperation and Development) study released on 17 February 2011, estimated that the medium-term impact of the Basel III implementation on GDP growth would be in the range of 0.05% to 0.15% per year. Economic output would be mainly affected by increase in banks' lending spreads, as banks pass a rise in bank funding costs, due to higher capital requirements, to their customers. Therefore, the situation is that banks are struggling to manage the regulation cost and the government wants to defend about nationwide contagion of other banks.

Part II The macro-prudential approach to financial regulation covering onbalance-sheet and off-balance-sheet (OBS)

Insofar as systemic risk is concerned, risks that firms, households and reserve banks and commercial banks face are highly linked to each other. Seen from this point of view, the banking industry and the monetary policy have particular relevance to systemic risk. Undoubtedly, it goes without saying that financial contagion problems through international banks should be measured in the manner of systemic risk management. With the macro-prudential approach, it is highly probable that systemic risk is explained by the static model of the general equilibrium. Because on-balancesheet and off-balance-sheet (OBS) risks are structurally segmented annually or periodically by financial statements containing the balance sheet. Even though domino effects or contagions can be understood as movements having the future tendency to figure out solutions toward the future, scope of regulation should be articulated by categorization of on-balance-sheet and off-balance-sheet (OBS) risks in the static model. Thus the macro-prudential approach to financial regulation covering on-balance-sheet and off-balance-sheet (OBS) risks is intimately linked with the general equilibrium (GE) approach.

On-balance-sheet risks are presented in a fourfold manner and are divided into credit risk, market risk, liquidity risk and systemic risk. Assets of banks have credit risk and market risk. Credit risk is the risk that a borrower will default on any type of debt by failing to make required payments. Market risk is the risk of losses in positions arising from movements in market prices. In case of liquidity risk, there are two major situations. One is emergency capacity of banks. When an illiquidity event takes place, an affected bank typically must borrow funds at interest rates exceeding those paid by other institutions. Another is about the stability of the banking system in case of inducing a large number of depositors to seek withdrawals. I would say liquidity risk in regard of demand deposit is on-the-balance-sheet risks of banks. Credit, market and liquidity risk are portrayed in considerable individual details but systemic risk is negative externality or adverse spillover effect stemming from transaction in which they were not participants. Distinguished from credit risk containing sovereign risk (government risk), counterparty risk (unincorporated entities' risk exposed to financial risk, usually referring to governments, national banks), systemic risk is the risk of collapse of an entire financial system or the entire market, as opposed to risk associated with any individual entity, group or component of a system. George G. Kaufman and Kenneth E. Scott (2003) define "systemic risk" in imprecise terms as below:

"Systemic risk refers to the risk or probability of breakdowns in an entire system, as opposed to breakdowns in individual parts or components, and is evidenced by comovements (correlations) among most or all the parts."

Darryll [START_REF] Hendricks | Defining Systemic Risk[END_REF], who is a practitioner, suggests a more theoretical definition from sciences in which the term originated:

"A systemic risk is the risk of a phase transition from one equilibrium to another, much less optimal equilibrium, characterized by multiple self-reinforcing feedback mechanisms making it difficult to reverse."

Banks engage in a number of activities that yield income, entail expenses and manage risks from on-balance-sheet risks to off-balance-sheet risks. Depending on bank characteristics, Banks extend loan commitments, security loans and trade derivative securities. Through extended loan commitments, the borrower has a guarantee of All of these figures are emphasized by capital circulation of the Freixas-Rochet model (1999) in the figure II.2. In conjunction with the Freixas-Rochet model, the equilibrium is detected with the general equilibrium approach with direct relevance to circulation of securities and stability of deposits. In the paper, the general equilibrium approach is upgraded with an adroit mixture of the balance sheet concept evaluating the value of economic entities and the income statement concept considering the profit to support the existence of financial entities.

Part III Model

Saving preference of Consumers

A microeconomic theory of banks had not been existed before the microeconomic foundation related to banks in the early 1970s. I would suggest add a banking sector at the Arrow general equilibrium model (1953) under the complete financial market assumption. The main purpose of the model has been to explore solutions about the problem of households, firms, banks and regulation bodies.

The two-period model (t=0,1,2) with a unique physical good initially owned by consumers in the economy in which a continuum of ex-ante identical agents is each endowed with one unit of goods at the period t=0, and this good is to be consumed at each period of t=1 and t=2. The consumer chooses her consumption profile (C 1, C 2 ) and the allocation of her savings S between bank deposits D h and securities  s P s B s h , in a way that maximize her utility function  under her budget constraints:

Max (C 1, C 2 ) C 1 +  s P s B s h + D h + S h - s P s B s h -D h = W 1 C 2 =  f + b +(1+r)  s P s B s h + (1+r D )D h + (1+r h )S h -(1+r)  s P s B s h -(1+r D )D h
Where W 1 for her initial endowment of the consumption good,  f + b for respectively profits of the firm and of the bank (distributed to the consumer-stockholder at t=2). B h denotes for securities, D h for bank deposits. S h denotes for savings. r, r D , r h are interest rates paid by securities, deposits and savings. For each future state of the world s (s) one can determine the price P s the contingent claim that pays one unit of accounts in state s and nothing otherwise.

The consumer has a well-defined set of desires ("preference"), which can be represented by a numerical utility function. In addition, we assume that the consumer chooses optimally, in the sense that they choose the option with the highest utility of those available to them. It implies that a consumer is solving an optimization problem. An optimization problem has three key components.

a. Selected object The consumer chooses her consumption profile (C 1 , C 2 ) and allocation of her savings S h between bank deposits D h and securities B h . If real assets S h - s P s B s h -D h is non-negative, it implies real assets are sufficient to support the household economy.

b. The objective function The consumer maximizes her utility function .  is assumed to be increasing and concave. Notice that preferences are contingent states and do not fit the standard Von Neumann-Morgenstern representation. Incompleteness of preference becomes apparent that decision makers cannot make a decision in the ambiguous situation. However, even though one individual or one factor doesn't decide, the regulator decides the policy with a foretaste of what is to come after annual closing accounts.

c. Constraints

Cash-in-advance 0D h W 1 , The paper will be based on the Cash-in-advance constraint. This approach that was introduced by Clower (1967) is the requirement that each consumer or firm must have sufficient available cash before they can buy goods.

Price of security h under

d. Arguments

There are concerns about savings that are substituted into consumption by the household like Covas-Fujuta (2010). [START_REF] Diaz | General Equilibrium Implications Of The Capital Adequacy Regulation For Banks[END_REF] adds no capital requirement at basics to reduce consumption and increase savings by the household. [START_REF] Haslag | On Fed Watching And Central Bank Transparency In An Overlapping Generations Model[END_REF] assumed that return to money is positively related to the money growth rate that is a random variable, gross real returns to savings are random. His realized gross real return to savings indicates that the gross real return to savings is a weighted sum of capital and fiat money (which derives its value from government regulation or law, so called as 'fiat currency'). The weight is the share of agent's asset.

In the Waller model ( 2004), Savings are very passively selected by the household depending upon decisions at the previous period. Middle-aged agents have already earned their wage income, as the wage during period t was determined by the previous period's interest rates (a level of the capital stock). Also, they have already decided how much to consume and save (since savings are a fixed fraction of wage income), but they

have not yet decided how to allocate their savings between capital and fiat currency. What these middle aged agents want at this point is just the highest possible interest rate between period t and t + 1, so that they can obtain the best possible return on their savings and can thus consume as much as possible during their period of old age. In the third period of life, retired agents consume their savings and exit the model.

Practically, Christensen-Meh-Moran (2011, Bank of Canada) mentioned, at the timing of events, households deposit savings at banks that use these funds as well as their own net worth to finance the entrepreneur's projects. In the investment frame, exiting (failing to return from the project) agents sell their capital for consumption goods and surviving agents buy this capital as part of their consumption-savings decision.

However, in reality, even though the agent has a house, they need to spend expenditure for renting, maintenance and extension of houses. Savings and real asset portion are large enough to make the loan from banks. It is hard to explain price fluctuation of houses and savings on the economy by depending upon the interest rate of capital stock and deposit, or perfect substitution of consumption. For households, the preference of savings is the matter about existence of household economy making future benefits and directly affecting to the welfare of any individual.

House-price appreciation by the model of Goodhart-Kashrap-Tsomocos ( 2012) is impressive. Reducing deposit defaults induces more savings circulated by the bank and less self-insurance and by the end, the reduction in self-insurance reduces the number of houses for sale in a good state, which means that house-price appreciation in the boom is higher than otherwise. Most of all, the market incompleteness with deadweight costs of default distorts the housing market. Wealthy agents endowed with houses make their saving decisions accounting for the possibility that deposits will not be fully repaid. When default penalties for banks are low, then households internalize risks putting less wealth into the banking system and hold more in the form of houses. This choice increases the supply of houses that is available in boom, which lowers house prices and raise welfare for agents entering the housing market at that time. To insure that house price reduction in the bad state of the world, households P and F are also presumed to have lower wealth. Likewise, the non-bank is endowed with lower capital in period 1 as well as in the bad state of the world. This model describes the house bubble phenomenon interestingly.

In the model of [START_REF] Lucas | Comment on Financial Intermediation and Monetary Policy in a General Equilibrium Banking Model[END_REF], to support the incompleteness of markets, he pointed out savings that the young split their savings between bank deposits, which promise a fixed nominal return, and a bank equity, which yields an uncertain real dividend. In addition, because a constant fraction of initial wealth is saved, there is no distortion due to fixed nominal interest payments on deposits. Hence regardless of deposits, the bank equity is related to the real effect of monetary policy.

In the paper, at the framework of securities, deposits and real assets with savings, firstly, the relation between savings and real assets (especially houses) can be much more attached. Secondly, deposits included in the total saving amount which are escaped from the one-sided thinking that deposits are equal to savings and can be perfectly substituted to consumption. Thirdly, Securities at uncertainty are affecting to the investment portfolio of households. These dynamics are explained by the following academical detail.

Households choose (C 1 , C 2 , S 1 , S 2 , R 1 ) taking prices (W 1 , W 2 ) as given. Formally, if we consider the 4-factor model containing banks, because banks have the special financial structure having deposits as liabilities and loans as assets, we need to have the different mindset from generally accepted accounting principles about debit and credit accounts. The general equilibrium (GE) diagram is similar with the balance sheet. Distinguishably, the money flow in the paper starts at the bank transaction which is "deposits and borrowings" as liabilities and "claims to corporate" as assets.

Then, deposits of household are the amount to be accumulated in banks. Conveniently, riskier investments than deposits for household are categorized as securities.

Savings are moving in the real household economy by capital circulation of securities, deposits and real assets. In addition, the welfare of each household is moving from dynamics of accumulated savings. In the overlapping generation model, wealth is always given and manages the household economy easily by each generation. In reality, one who didn't get a house as a legacy, she should spend quite a long time to have a house or rent a house. Attention about fundamental wealth related to non-working capital of a household economy should be emphasized. If the consumer spends his income entirely, the total amount W 1 may be spent totally and can be bounded. In this manner, the household always has their fundamental welfare to manage the household economy and consumption can be naturally deduced from the framework of household economy. That is, W 1 is the budget constraint and the market information is incomplete so we cannot deduce the real variable of consumption in reality. W 1 and incompleted market information are not enough to deduce the real variable of consumption. In terms of the working capital, we are not so surprised to know that capital has various liquidities. For example, a household wants to spend money on a daily basis but should reduce the amount of money by spending it to have fundamental living basis like houses. In the paper, the financial budget constraint is bounded within the W 1 except for S 1 because S 1 is the summation of securities, deposits and real assets. These are vital factors to operate household economy related to financial markets. The working capital concept at the household economy is evoked within the general equilibrium in the paper. In the perspective that the industrial characteristics of banks mainly operated by capital, it makes sense to us that consideration about the household economy should be balanced with the working capital concept of banks.

Then, why we need to define return R 1 in this model? Simply, we think of three variables of W for endowment, S for savings and C for consumption. We assume that the concept of the golden-rule saving rate in Chapter 1 of Barro and Sala-i-Martin, n denotes for the constant exogenous population growth rate, and d is for the constant exogenous rate of depreciation of capital. We know the house saving rate is 5% (usually 2-11%, OECD, Economic Outlook n.91, June 2012). The amount of savings in the economy should grow as population grows. To support this insured saving amount caused by population growth, the return should be enough to make profits to cover the insurance expense in the economy with the general equilibrium (GE) perspective. Then, we can assume the worst scenario like a bank-run case. Even though the fix amount of saving deposits is secured, the loss amount induced from total savings by the endinsured savings will go to the consumption part. In this overall perspective of an equilibrium, insuring savings of households seems plausible to support the economy of households, yet it requires further understanding about the profitable dynamic mechanism to operate the economic cycle. I would say the original form is mainly based on the BCR general equilibrium model diagram presenting as the balance-sheet format as it can be because on-balance-sheet factors are reflected by two regards -the money flow perspective (profit) and the economic status perspective (net present value).

Original form (savings containing real assets)

Max (C 1, C 2 ) C 1 +  s P s B s h + D h + S h - s P s B s h -D h = W 1 C 2 =  f + b +(1+r)  s P s B s h + (1+r D )D h + (1+r h )S h -(1+r)  s P s B s h -(1+r D )D h
Simplified form for calculation (savings containing real assets)

Max (C 1, C 2 ) C 1 =W 1 -S 1 C 2 =R 1 +W 2 -(1+r)S 1 -S 2
We have the first order condition of consumption at period 1 and 2 as below.

𝐿 C1 = '(C 1, C 2 ) - = 0 𝐿 C2 = '(C 1, C 2 ) - = 0
We know the Lagrange multiplier is 0 as  = 0, by the 𝐿 S1

, the first order condition of savings at period 1 and by the 𝐿 𝑅1

, the first order condition of return from initial investment. In addition, we get (1+r 1 ) = 0 by the 𝐿 S1

, the first order conditon of savings at period 1.

Therefore, what is get from checking the first order condition of household problem is that households consume today or tomorrow regardless of a banking money flow and it is not affected by the return of initial savings. '(C 1, C 2 ) = 0 denotes as time indifference about consumption preference. Households operate the household economy related to banks regardless of consumption for today or tomorrow. We conclude consumption choice is not affected by return of initial savings r 1 at the frame of banking money flow related to household.

The house expense portion in deposits held with MFIs (Monetary Financial Institutions) is the asset that can induce the future benefit and considered as priority to invest for a long time. For example, among loans to households of MFIs (5231 billion euros), loans for house purchase are 74%, 3858.1 billion euros in 2013. Note that we focus on the money transaction started from the bank balance sheet, in the concept of savings, House fee is deduced from S h - s P s B s h -D h Where h is the period of household. If we suppose the house fee is not contained in savings as below.

Simplified form for calculation (savings without real assets)

Max (C 1, C 2 ) = 0 C 1 +  1 P 1 B 1 h + D 1 = W 1 R 1 +C 2 +(1+r)  1 P 1 B 1 h + (1+r 1 )D 1 -(1+r) - 2 P 2 B 2 h -D 2 =W 2 Also, C 1 = (W 1 -S 1 )+(S 1 - 1 P 1 B 1 h + D 1
The first-order condition

𝐿 C1 = '(C 1, C 2 ) - = 0 𝐿 C2 = '(C 1, C 2 )- = 0 𝐿 D1  = 0 𝐿 D1 - (1+r 1 ) = 0 𝐿 D2  = 0 '(C 1, C 2 )=0 𝐿  1P1B1h - (1+r 1 ) = 0 𝐿  1P1B1h  = 0 𝐿 r1 =  ( 1 P 1 B 1 h + D 1 ) = 0
In conclusion, '(C 1, C 2 )=0 (time indifference about consumption preference) is the same condition regardless of real assets whether it is contained in savings or not.

Consumption choice is not affected by the interest rate r 1 for initial savings (same condition regardless of real assets whether is contained in savings or not) and summation of securities and deposits  1 P 1 B 1 h +D 1 . Evidently, this condition appears in this banking model when we ignore real assets which is most stable in the household economy and can be interpreted as the big portion expense and the intangible asset producing future benefits. Therefore, with the condition that real assets are contained in savings, we can explain the house economy affected by the proportion of securities and deposits.

First intention to choose the general equilibrium model in the paper is to offer understandable method to the academic field and professional field. In the practice, the reserve bank has many methods and even they want more methods together in the weighted way. As I can do, I am intending to use real variables than random variables and a lot of Lagrange methods which is very general way to use the general equilibrium. The saving composition matter is more specifically supported by the following empirical data.

The deposit amount traded is different depending upon factor composition of economic models. For example, the European Central Bank announces the Euro areas' deposit amounts for the 4th quarter in 2013 in the Euro areas. Gross saving amount of households is 2521.3 billion euros (growth rate: 2.4). Deposits by non-financial corporations are 1870.7 billion euros. (growth rate: 6.7). Deposits by Insurance corporations and pension funds (financial intermediaries) are 653.2 billion euros. (growth rate: -5.3). Deposits by other financial intermediaries are 1854.1 billion euros (growth rate -3.1). Deposits by government are 440.8 billion euros (growth rate: -1.8). Deposits by non-euro area residents are 2522.9 billion euros (growth rate: -11.2). Therefore, without consideration about deposits by non-financial corporations (1870.7), the comparison between deposits by household (2521.3) and deposits by financial intermediaries (653.2+1854.1=2507.3) is naive explanation.

Loans for house purchase is 3858.1 billion euros. (growth rate: 0.7). It is Longterm liability affecting the existence of household economy. In addition, the total (7341.7) of deposits by insurance corporations, pension funds (653.2, -5.3), other financial intermediaries (1854.1, -3.1), non-financial corporations (1870.7), government (440.8), non-euro area residents (2522.9) are. Also, total (7752.2) of deposits by household (2521.3, 2.4) and Loans for house purchase (3858.1, 0.7) and other loans (796.7, -1.6), consumer credit (576.1, -3.0) are. Savings S h are the sum of Securities  s P s B s h , Deposits D h , Real assets S h - s P s B s h -D h . Households try to control the balance of assets and liabilities because in the situation of uncertainty, to maintain enough Deposits D h for the economic existence of households, households need to invest on securities as of  s P s B s h posed on uncertainty conditions. Mainly, real assets imply the budget for houses which can afford to manage the residence and invested real assets. For example, if the household has an apartment and there is the redundancy after spending the investment on securities and deposits, it can be the maintenance fee for house decoration or big furniture purchases.

The importance of portion for houses is considerable. Otherwise, if real assets are negative, hence, savings of households are less than the amount of securities and deposits. Even though, the amount of operation in the household is enough with securities and deposits. In the conservatism on the house budget, we can consider the effect on housing. In the paper, Houses of households is considered as future economic assets that support each member of households to make productions.

Through the general equilibrium approach, the link from the bank problem to the household problem is naturally connected. Also, the following technical finding by usage of same accounts at the household problem induces direction of regulation on banks like the portfolio analysis and initial GDP consideration. The following are technical findings with saving preference.

Suppose that  s G, B, G=Good, B=Bad. In the case 1, risk aversion is a s below. (resp. risk-taking case)

= G, B, C 1 + s P s=B B s=B h +D h +S h - s P s=G B s=G h -D h =W 1
In this case, portfolio analysis should be detected by regulation because the situation can be changed depending on the status.

In the case 2, incompleteness preference can be considered.

= G, B, no choice, no choice can be selected by the choquet expectation CE((x)) = min core() E  ((x)) where core() = S :

(A)  (A) for all AS C 1 +0+D h +S h -0-D h =W 1 and D h offset, hence C 1 + 𝐶2 1+𝑟ℎ

=W

Initial GDP is caused by partition of initial endowment that is combination of consumption set. Hence, regulation direction is originated from initial GDP in this case.

Borrowing composition of Firms -Additional session is in the Part IV.6

The firm chooses its investment level I and its financing (through Real Assets  s P s B s h + D h , Liabilities to banks  s P s B s h + D h -L fr (Or Liabilities to central banks L fr ) in a way that maximizes its profit:

Max  f (P f )  f =(I)+r f ( s P s B s h + D h )-r L bank (D h +  s P s B s h -L fr )-r L fr L fr I=S h =D h + s P s B s h
Where  denotes the production function of the representative firm. r  is the premium of firm's real assets. r L bank , r L fr are interest rates on bank loans and federal reserve bank loan. D h denotes for bank deposits. B h denotes for securities. Especially B fr denotes for securities of federal reserve banks. L fr are loans claimed by the firm to the federal reserve bank. For each future state of the world s (s), one can determine the price P s of the contingent claim that pays one unit of accounts in a state s and nothing otherwise. I is the investment level and S h denotes for savings.

Interior Solution P  has an interior solution only when: r = r L bank =r L fr

The Modigliani-Miller (MM) theorem projects a theme of a theorem on capital structure. The basic theorem states that, under a certain market price process (the classical random work) and an efficient market, in the absence of taxes, bankruptcy costs, agency costs and asymmetric information, the value of a firm is unaffected by how that firm is financed. Firms are indifferent about the composition of borrowings. Given the proposition II of the Modigliani-Miller (MM) theorem, a higher debt-to-equity ratio leads to a higher required return on equity because of the higher risk involved for equity-holders in a company with debt. r E =r 0 + 𝐷 𝐸 (r 0 -r D ) where r E is the required rate of return on equity or cost of equity, r 0 is the company unlevered cost of capital (ie. Assume no leverage, r D is the required rate of return on borrowings or cost of debt and 𝐷 𝐸 is the debt-to-equity ratio under two assumptions: (1) no transaction costs exist. (2) individuals and corporations borrow at the same rates. However, on the surface, given same ratios of 𝐷 𝐸 , two different sized banks are distortly intepreted. Even though this proposition is induced in the absence of the bankruptcy costs, merges of banks like "too big to fail", so called "the size game among big banks, are considerable. Thus it is certainly worth inquiring D+E behind it's apparent dynamics of 𝐷 𝐸 .

The BCR model provides a key with which to unlock riddles of firms' borrowing compositions. The borrowing composition of firms imparted dynamics with the preference to maintain Real Assets  s P s B s h + D h. Regardless of equilibrium, firms prefer to loan from central banks (so called as bonds) than commercial banks. Among the D h and  s P s B s h , Firms prefer to have D h because of financial stability and preference about certainty. The model reflects the tendency of banks toward the big size with Real Assets. In the economic existence respect of banks, banks have responsibility to operate the dynamics of the debt-to-equity ratio 𝐷 𝐸 and maintain the economic entity of Real Assets D+E in the economy of countries.

Given the firm's problem, we have ambiguity about change of firms because of investments or loan status. Precise explanation about the relation with commercial banks and central banks should be offered. In the general equilibrium (GE), firms choose labor cost and manage the capital for production or business process but labor effect is hard to be clarified with certain connection of commercial banks and federal banks. Hence, the transaction like loan movements (i.e. liabilities to banks, liabilities to central banks, investments) can be selected to explain in this paper. Additionally, Investments is regarded as Real assets to support existence of business entities. It implies firms want to acquire investment budget to maintain real assets that can be requisite for existence of firms. Therefore, by having borrowing preference to have much more stability between liabilities to banks and central banks (so called as bonds), firms pursue to obtain stability to acquire the investment up to the stability of Investments which can be equal to Real Assets. Thus, we can explain dynamics of investments and loans with the firm's property.

There are many arguments to explain the ambiguity of firms with informational asymmetry, shock absorbed by effective capitals, securities, technical shocks, and interest rates on loans and borrowing constraints.

Boyd-Chang-Smith ( 2004) points out two informational asymmetry problems of firms: The moral hazard problem arises because any borrower's project choice is not observable. Also, the costly state verification (CSV) problem arises because, for either type of projects, the return of investments cannot be freely observed by any agent other than the project owner.

In the [START_REF] Nelson | Macroprudential Capital Regulation In General Equilibrium[END_REF] model, at the production function of cobb-douglas standard form, there is a shock variable to the quality of physical capitals. When we face the unanticipated exogenous declines in the productive capacity of physical capitals, available "Effective capitals" for use in the production is diminished. This intends to consider the effect on banks since banks hold claims on physical capitals directly on their balance sheets, this will be loss for banks, which must be absorbed or passed on to outside creditors.

In the Dewatripont-tirole (2012) model, he argues that securities are characterized not only by income rights but also by control rights. Optimal corporate choices are t h e time-inconsistency. Investors in control of corporate choices must face an incentive that differs from firm-value maximization. So a banking manager has no financial resources to cover an investment cost and turns to investors for financing. The capital structure -that is, the allocation among investors of contingent cash-flow and control rights -is designed at this financial stage.

Covas Fujita (2010) mentioned that the technology shock is distributed as standard normal distribution. Labor and capital rental markets are assumed to be competitive. [START_REF] Diaz | General Equilibrium Implications Of The Capital Adequacy Regulation For Banks[END_REF] thinks that since interest rates on loans are greater or equal than the discount rate, firms prefer to use internal sources (i.e. cash flows) rather than external financing. In addition, he induces that capital depreciation is paid out of firm's cash flow and net investment is entirely financed with debting. In the model of [START_REF] Nuno | Bank Leverage Cycles. P.7. H6.Money Stock Measures[END_REF], they assumed that the firm can only borrow from banks located on the same island.

In the static model of general equilibrium (GE), if we know the GDP endowment as the exogenous factor, we can calculate more at the firm's problem. Indeed, the analysis about GDP like Consumption to GDP, Government Expenditure to GDP, Fixed Capital Formation to GDP, Export to GDP, Net Export to GDP, Money to GDP except for inflation rate and nominal interest rate are used with the general equilibrium (GE) approach.

The effort to figure out ambiguity of firms and overall perspective analysis display a coherent structural and compositional understanding. Then, how we can measure the firm's productivity relating to the banking area in general equilibrium (GE)? The classical viewpoint that there are three basic factors of production, (land, labor and capital) at the production function. Total-factor productivity (TFP) is different from the traditional calculation measured by inputs of labor and capital. The TFP calculation is measured as a Solow residual affecting in total output and not caused by inputs. The equation Y = A × K α × L β in Cobb-Douglas form represents total output (Y) as a function of total-factor productivity (A), capital input (K), labor input (L), and the two inputs' respective shares of output (α and β are the capital input share of contribution for K and L respectively). The problem is that units of A do not admit a simple economic interpretation. We have two ways to calculate TFP (Chen, 2011). Firstly, we obtain the TFP measurement by estimating a production function. Secondly, we establish a model to find the determinant of TFP and uncover whether financial factors exert any effects on TFP. Materials and energy are secondary factors because they are from land, labor and capital.

It can be puzzled whether duplicated or missed amounts are existed in the general equilibrium (GE). The equity portion as capitals is in the liabilities of firms and the wage portion as expense is in the eliminated account of firms. With this production function measure, we are talking about the exact asset amount of firms that is the part of equity at the same time. Let's go back to the definition of the production function. Factors of production are inputs to the production process. Finished goods are the output and the relationship of input and output is the production function. The important point is that we cannot exaggerate too much about money. Indeed, the classical viewpoint is that money is not contained in capital because it is not directly produce any good so it is hard to be related to consumptions of goods at the problem of household.

In the paper, firstly, we are focusing on "capital" including the "financial capital." Financial capital is raised to operate and expand a business and it is net worth (assets minus liabilities) including money borrowed from others. Originally, "Capital" means goods that can help produce other goods in the future, the result of investment. Considering a labor is not realistic because the number of employees at the firm is hard to be considered at the banking problem. Already we consider equity (asset-liability) is the result after considering labor cost. Redundant firm size variable can evoke the biased information if we pursue obtain the general equilibrium (GE) in this model. It's true that wage is the large portion of input at the firm and should be considered distinguishably. However, for the special industry like banking, we need to clarify needed variables to figure out the problem in the academic field for future and in the realistic world for present.

If we contain banks and federal banks in the banking model, we add the real asset variable. It implies the capital concept is naturally inducing the working capital concept. Adding the shock variable to the quality of physical capital [START_REF] Nelson | Macroprudential Capital Regulation In General Equilibrium[END_REF], Gertler-Karadi 2011, Gertler-Kiyotaki 2010) is hard to be measured and needed to be predicted with a lot of unexpected uncertain situation.

Also, the conservative business cycle is deduced. If we assume that multiplier µ exists, (D h +B h )D h +B h -L fr L fr . This assumption exactly reflects the preference of safetier capital type like real assets > a government bond (lower interest rate on a bond than a loan) > a loan.

Demand Deposit of Bank

Scope of Bank Domestically chartered commercial banks, country branches and agencies of foreign banks, Edge Act corporation.

The bank chooses its supply of loans to firms D h +B fr +L fr , its demand for deposits D h , and the borrowing B fr -L fr in a way that maximized its profit:

Max  b (P b )  b = r L Bank (D h + s P s B s h -L fr ) -r Lfr ( s P s B s fr -L fr ) -r D D h
where r L Bank , r Lfr are interest rates on bank loans and federal reserve bank loan. D h denotes for bank deposits. R D is the interest rate paid by deposits. B s h denotes for securities. Especially B s fr denotes for securities of federal reserve banks. L fr are loans claimed by the firm to the federal reserve bank.

The bank maximizes the profit by choosing its supply of loans L + , its demand for deposits D -and the issuance

 s P s B s b. Max  b (P b )  b = r L L + + r  s P s B s b -r D D -L + =  s P s B s b +D -
The part of banks' problem provides a context which capital circulation within banks is required by other main factors of economy. The problem of banks is presented without equities of banks in fairly balanced debits and credits of banks. This main issue has been to handle the demand deposit in the banking area and it related to the money supply closely. In the data of Board of Governors of the Federal Reserve System, demand deposit and money stock data have been collected from Demand Deposit, Currency and Related items (J.3, Semi monthly) in 1960 to Money Stock Measures in 2012.

Under the fractional reserve banking, deposit is important indicator for economy because of money multiplier effect. In the formula of moneysupply=currency+deposits, demand deposit which has highest liquidity among deposits on the balance sheet of banks is directly related to the M1 of central banks. Diamond and Dybvig model (1983) explains why bank runs occur at an undesirable equilibrium and why banks issue demand deposits that are more liquid than their assets by providing better risk sharing among people who need to consume at different random times. The key to describe the rationality both for the existence of banks and for their vulnerability to runs is the illiquidity of assets, especially by the demand deposit. His conclusion on the bank runs as better indicator of economic distress than money supply is too quick because there is the duplicated section of deposits and money supply. A bank run is the sudden withdrawal of deposits of just one bank and money supply contains the currency section.

In case of bank runs, the government of country should prepare the recovery solution for economy. Regularly, given information about money supply, the government can figure out about both moving of currency and deposits. [START_REF] Krugman | Economics[END_REF] points this out that deposits are usually considered part of the narrowly defined money supply, as they can be used, via checks and drafts, and a means of payment for goods and services and to settle debts. The money supply of a country is usually held to consist of currency plus demand deposits. In most countries, demand deposits account for a majority of the money supply. To explain the correlation between deposit (demand deposit) and money supply, bank runs can be interpreted as the sudden constraint of deposit and money supply. We research on indicators of economic crisis so economic crisis is not the indicator to analyze the status of economy. [START_REF] Gorton | Financial Intermediaries and Liquidity Creation[END_REF] assume that the uniqueness of demand deposits roles as a desirable medium of exchange so the existence of demand for privately produced riskless trading securities induces issuing demand deposits by banks. Actually, under the fractional reserve banking, a bank deposit is not a bailment that implies physical possession of personal property. It moves safely upon the banking revenue process.

Firstly, the property of customer was deposited. In turn, the customer receives an asset called the deposit account. Finally, the deposit account is the liability of the bank on its balance sheet. On the balance sheet of Liabilities of all commercial banks in the United States (2014.01), 70% is the deposit account. The circulation of deposits is important in economy. David [START_REF] Vanhoose | The industrial organization of banking[END_REF] categories the deposit into three sections like transaction deposit, large-denomination time deposit, saving deposits and smalldenomination time deposits, at the United States commercial bank liability and equity capital. Transaction deposit contains non-interest-bearing demand deposits. Transaction deposit is 6% among total liabilities and equity capital of bank balance sheet. [START_REF] Dewatripont | Macroeconomic Shocks and Banking Regulation[END_REF] points out that deposit insurance is the prevention of banks runs following the [START_REF] Diamond | Bank Runs, Deposit Insurance, and Liquidity[END_REF]. In the model of [START_REF] Boyd | Deposit insurance and bank regulation in a monetary economy: a general equilibrium exposition[END_REF], even though project return is safe because of a large number of borrowers, he assumes possibility for banks to fail.

Regardless of a single borrower and aggregate of borrower, potential bankers can suggest needless to operate the bank.

In the model of [START_REF] Covas | Procyclicality Of Capital Requirements In a General Equilibrium Model of Liquidity Dependence[END_REF], the bank can raise funds through either deposits or equity so holding equity involves the equity issuance cost.

Diaz model ( 2005) also tries to select the considerable sources. For example, firms only source of financing is bank lending the bank can claim the full amount of firm's cash flow. T h e equity of banks moves under upper limit of dividend (under the hypothesis that the bank can turn equity into dividend with restriction) because of balance sheet constraint.

Goodhart-Kashrap-Tsomocos ( 2012) mentioned shadow banking. The securitized loans, called mortgage backed securities (MBS) can be sold to the non-bank and the non-bank will finance the purchase with a repo loan from the bank (that will have the MBS as collateral)

Federal Reserve Banks and general equilibrium (GE)

The Federal Reserve Bank chooses its investment level I and its financing (through real assets D h + s P s B s h , Liabilities to bank D h + s P s B s h -L fr (or Liabilities to central bank L fr ) in a way that maximizes its profit:

Max  b (P b )  f = f (I) + r f (D h + s P s B s h ) -r L Bank (D h + s P s B s fr -L fr )r L fr L fr I=S h Where  denotes the production function of the representative firm. r f is the premium of firm's real assets. r L Bank , r L fr are interest rates on bank loans and federal reserve bank loan. D h denotes for bank deposits. B h denotes for securities. Especially B fr denotes for securities of federalreserve banks. L fr are loans claimed by the firm to the federal reserve bank. For each future state of the world s (s ∈ ω), one can determine the price P s of the contingent claim that pays one unit of account in state s and nothing otherwise. I is the investment level and S h denotes for savings.

Interior Solution P f has an interior solution only when: r f = r L Bank = r L fr

General Equilibrium (GE)

General equilibrium (GE) is characterized by a vector of interest rates (r, r D, r h , r f, , r L Bank , r L fr ) and three vectors of demand and supply levels (C 1, C 2,  s P s B s h , D h ) for the consumer, (I,  s P s B s h , D h , L fr ) for the firm, (L fr,  s P s B s h , D h,  s P s B s fr ) for the bank and (D h ,  s P s B s h , L fr ) for federal reserve banks. Each agent behaves optimally. (i.e., his or her decisions solve P h , P f or P b respectively. If firms and households have unrestricted access to perfect financial markets, then at the competitive equilibrium, banks make zero profit and the size and composition of balance sheet (banks) have no impact on other economic agents.

(result) Cho (2014) If some accumulated variables are not negative, for example, the components Investment I, Savings S h , L fr are not negative, there is the equilibrium in the economy and the existence of each factors like firms, Househoulds, Banks, Federal Reserve Banks is fulfilled. The size of banks is affecting on each agent because equity capitals depend on previous deposits (additional explanation in Part IV, 7). Depending the change of bank size influencing on total deposits D h , the liability of firms is affected by liabilities to banks D h + s P s B s fr -L fr , deposits of household D h and real assets of households and firms. This is supported by the following the process of equity capital multiplication.

Figure II. 1

 1 Figure II.1 Vanhoose 2008 -Asset/Liability of banks

Figure

  FigureII.2 Freixas-Rochet (1999)

  s

  Firm) -D h (Firm) + D h (Household) -D h (Household) + D h (Bank) -D h (Bank) (Deposit market) L fr (Firm) -L fr (Firm) -L fr (Bank) + L fr (Firm) + L fr (FR:Federal Reserve Banks) -L fr (FR) (Credit Market) in this model that the only possible equilibrium is such that all interest rates are equal: r = r L = r D (result)Arrow (1953)

Part IV Effects of Equity Capital Regulation 6. Additional explanation about the borrowing composition of firm's problem -The portfolio composition effected by the minimum equity capital regulation.

In the model of [START_REF] Kahane | Capital adequacy and the regulation of financial intermediaries[END_REF], the minimum capital requirement causes an unintended result: it worsened, rather than improved the intermediary's condition and increases its probability of ruin. He checks this calculation with the ruin constraint and given standard deviation of rate of return at the portfolio composition of liability, stock and bonds.

In this paper, with the portfolio of risky portfolio and stable portfolio, explanation will be easier to be understood why minimum equity regulation induces for banks to operate riskier portfolio. In addition, it intends to reduce pro-cyclicality (to the financial shocks) and promote the countercyclical buffer.

If we assume that the bank manages a risky portfolio with an expected rate of return of 17% and a standard deviation of 27%. The expected rate of return on equity is 7% and even though, there is pressure to raise the required equity every period, liability is same every period. The bank tries to meet the bank capital condition regulated by financial intermediaries so the bank should operate much more risky portfolio comparing to the previous period as following. To calculate the portfolio composition, we calculate the expected value (Mean).

Mean 0.12(12/100) × 0.07 + 0.88 × 0 = 0.0084 0.1287(13/101) × 0.07 + 0.8712 × 0 = 0.0090 0.1372(14/102) × 0.07 + 0.8672 × 0 = 0.0096

Suppose that the bank decides to invest in the portfolio having a proportion Y of the total investment budget so that the overall portfolio will have an expected rate of return as above.

We know an expected rate of return of a risky portfolio R p is 17% and an expected rate of return of a stable portfolio is 7%. Hence, we get the risky portfolio proportion Y.

Thus, in order to obtain a mean return of 0.84%, 0.90%, 0.96%, the bank must invest -61.6%, -61%, -60.4 of total funds in the risky portfolio and 161.6%, 161%, 160.4% in stable portfolio.

Standard deviation that implies the probability, to get mean of returns, is also increasing. Hart and Jaffee (1974) analyzed the properties of the feasible and efficient set with the assumption that the initial equity capital is zero (i.e. K=0). However, it is possible that the intermediary's equity is zero in the substantial degree of leverage (high liabilities to equity ratios

𝐸𝑞𝑢𝑖𝑡𝑦𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝐷ℎ+𝐵𝑓𝑟+𝐿𝑓𝑟

). Then, we should assume that the equity is negliglible.

In the paper as the same as [START_REF] Kahane | Capital adequacy and the regulation of financial intermediaries[END_REF], we assume the equity is positive (K  0) so that the opportunity set does not pas through the origin (i.e. the vector of Deposit D, Borrowing B, Optimized Equity Capital = 0 give an infeasible solution).

Then theoretical superior limit for deposits is defined by the following:

Theoretically, superior limit for the equity capital by the firm is defined by the following: OptimizedEquityCapital = K × Deposit = 𝐾 𝐾+ And the theoretical superior limit for total borrowings in banks is defined by the following: Borrowings = (1-) × Deposits =

1-

𝐾+

The process described above by the geometric series can be represented, where Borrowings at stage k are a function of deposits at the precedent stage:

Optimized Equity Capital at stage k is a function of the deposits at the precedent stage:

Hence, if the optimized equity capital depends on the initial deposit and assume the terminal condition of bank is liquidation of bank deposits.

(result) Hence, Optimized Equity Capital depends on the previous deposit. In addition, deposit insurance cost also increases because deposit insurance depends on the number of household.

Deposits at stage k are the difference between additional borrowings and optimized equity capital relative to the same stage: D k = B k -OEC k

In the model of Gorton-Winton (1995), bank size is given. In the theorem of Modigliani-Miller, the size and composition of banks' balance sheets have no impact on other agents. However, as population grows, insured deposits will increase. Then, the bank size should grow so bank size growth concern should be measured.

K index for the indicator of risk taking

Define the equity capital ratio with respect to total liabilities and equity capital, 𝐸𝑞𝑢𝑖𝑡𝑦𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝐷ℎ+𝐵𝑓𝑟-𝐿𝑓𝑟 , K(0,1), the borrowing (from federal banks) ratio 𝐵𝑓𝑟-𝐿𝑓𝑟 𝐷ℎ+𝐵𝑓𝑟-𝐿𝑓𝑟 , (0,1).

Suppose the demand for funds is unlimited, by summing up two quantities, the theoretical equity capital multiplier is defined as:

where the equity capital ratio with respect to total liabilities and equity capital, 𝐸𝑞𝑢𝑖𝑡𝑦𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝐷ℎ+𝐵𝑓𝑟+𝐿𝑓𝑟 k is the index to decline to increase the risk at the portfolio of commercial banks. The deposit is fixed at total 1 and borrowings have the constraint cannot be negative value beyond the minimum borrowings . For example, if deposit=1, the minimum of required equity = 10%, borrowings = 0.3. To increase the k index, the bank should increase the deposit beyond the initial deposit level (1 in this simulation) or allocate the borrowing portfolio.

Conclusion

The minimum capital requirement is a necessary condition for banking sector stability to raise the quality, consistency and transparency of the capital base. However, it has friction with the portfolio management. By using effects of increasing the equity at the portfolio composition, reducing pro-cyclicality (to the financial shocks) and promoting the countercyclical buffer are pursued.

In the Basel 3 system, the risk coverage framework intends to capture all material risks by using counterparty credit risk formula weighted on the external rating of the counter party. Exposure measures contain on-balance sheet, repurchase agreements and securities finance, derivatives and off-balance sheet (OBS) items. In the paper, rather than enlarging the risk contagion, related factors and risk affection scope are detected without overstatement by using the general equilibrium (GE) model and deposit affection to the optimized equity capital. Deposits are in the large portion at the household, firm and banks. To explain risk coverage, by proving correlation of optimized equity capital upon the previous deposit level, the paper aims to ensure that banking-sector-capital requirements take account of the macro-financial environment in which each substantial economic entity operates.

Basel 3 introduced a minimum leverage ratio. The leverage ratio was calculated by dividing Tier1 capital by the bank's average total consolidated assets. In the paper, k index is suggested as the indicator of risk taking. Within the liability, three major fractions like deposits, borrowings and optimized equity capital are considered as the complementary of minimum capital requirement. Assets of commercial banks are mainly consisted with loans and securities. Because the optimized equity capital grows and deposits is restricted by change. Borrowings that are the difference between asset and deposit+equity capital should be checked whether borrowings cover the optimized equity by k index or not.

The combination of portfolio composition test, deposit-equity optimization and k index enables bounding the bank capital regulation problems.