Silviase/jgov_v1.4_full_ann huggingface dataset:
## コード番号について

## 1 コード番号設定の目的

コード番号設定の目的は、予算の内容について、その分析を多角的に行うため、経費の性質、分類等を明らかにすることにある。

## 2 コード番号の読み方

（１）各政府関係機関に付した４桁の数字は、左から１桁は公庫、株式会社及び独立行政法人別区分のコード番号であり、次の３桁は公庫、株式会社及び独立行政法人ごとに付したコード番号である。なお、この３桁のうち、末尾の１桁の１から始まる数字は株式会社に付した業務区分のコード番号である。

(2) 各政府関係機関(業務区分のあるものは業務。)の収入の款項目別区分の表及び収入支出予定額科目別表の収入に付した6桁の数字は、左から款(2桁)、項(2桁)、目(2桁)をあらわすコード番号である。

（３）支出の事項別内訳の表及び収入支出予定額科目別表の支出の各項に付した２桁の数字は、政府関係機関(業務区分のあるものは業務。)ごとに付した項のコード番号である。

（４）収入支出予定額科目別表の支出の各目に付した３桁の数字は、左から使途別(１桁)の分類を明らかにするコード番号及び従来の目の一連番号（２桁）である。

(5) 各種分類のコード番号は次のとおりである。

## (イ) 政府関係機関

2100	沖縄振興開発金融公庫	5014	信用保險等業務
5010	株式会社日本政策金融公庫	5017	危機対応円滑化業務
5011	国民一般向け業務	5018	特定事業等促進円滑化業務
5012	農林水産業者向け業務	5030	株式会社国際協力銀行
5013	中小企業者向け業務	6010	独立行政法人国際協力機構有償資金協力部門

## (口) 使途別分類

1	人 件 費	5	補 助 費・委 託 費
2	旅 費	6	他 会 計 へ 繰 入
3	物 件 費
4	施 設 費	9	そ の 他

(備考)

国民経済計算上の政府支出を算出する場合の便宜に供するため、損益計算書の固定資産の減価償却費に資本形成を明らかにするコード番号20を付し、また、貸借対照表の資本形成に該当する項目については、その全額が資本形成となるのではなく、前年度額に対する当該年度の増(減)額が資本形成となるので、これを明らかにするためコード番号20の上に・を付して20と表示した。
(参考) 収入支出予定額科目別表の支出の各目に付したコード番号の読み方の例
科目	平成27年度予定額(千円)	前年度予算額(千円)	比較増△減額(千円)
01 事業損金	13,730,032	15,360,150	△ 1,630,118
1-01 役員給	87,522	86,462	1,060
1 - 01(1) (2)
(1) 使途別→人件費(2) 従来の目の一連番号
ESRI Discussion Paper Series No.8

# Economic Takeoff and Capital Flight

by

Hiroshi Shibuya

December 2001

Economic and Social Research Institute

Cabinet Office

Tokyo, Japan
# Economic Takeoff and Capital Flight

by

Hiroshi Shibuya $ ^{*} $

December 2001

Office Address: Department of Economics, Otaru University of Commerce, Midori 3-5-21, Otaru, Hokkaido, Japan 047-8501.

E-mail: shibuya@res.otaru-uc.ac.jp
# Economic Takeoff and Capital Flight

by

Hiroshi Shibuya

## Abstract

This paper presents a model of economic takeoff and capital flight with free international capital flows. In the early stage of development, investments are complementary and production exhibits increasing returns to capital. The increasing returns give rise to strategic complementarity between the optimal portfolio decisions of international investors. It produces two stable Nash equilibria: a low and high capital equilibrium. Switches between two equilibria represent economic takeoff and capital flight. At the high capital equilibrium, the interest rate parity with risk premium holds and international capital allocation is efficient. The model identifies the return and risk factors that can trigger switches between two equilibria. The role of government is to achieve the high capital equilibrium through policies that affect the return and risk factors. The globalization of capital markets helps achieve economic takeoff through risk-sharing among the increasing number of investors. The development strategy of domestic capital accumulation and capital market liberalization can achieve economic takeoff. However, a developing country may be trapped in the low capital equilibrium if the liberalization is implemented before a sufficient accumulation of domestic capital.

JEL Classifications: F21, F43, O40

Keywords: Increasing returns; Strategic complementarity; Optimal portfolio; Multiple equilibria; Interest rate parity; Risk premium; Emerging economies; Capital market liberalization; Economic development.
### I. Introduction

One important development in the world economy during the last few decades has been the extended liberalization and globalization of capital markets. We now have a global capital market with free international capital flows. Facilitating an efficient allocation of capital, the global capital market has contributed to the remarkable transformation of many less developed countries into emerging economies. At the same time, however, we have witnessed a growing number of capital flights and economic crises. Asian developing countries are recent examples. Many Asian countries had gone through a stage of economic takeoff with large capital inflows, which was hailed as the “Asian miracle” in the early 1990s, and then suddenly faced capital flight and the turmoil of the “Asian crisis” in the late 1990s. $ ^{1} $

What characterized the “Asian miracle” and the “Asian crisis” was the sudden inflows and outflows of international capital. In the global economy with an integrated capital market, sudden capital inflows and outflows correspond to the economic takeoff and capital flight of developing countries. To understand the mechanism of modern economic development, we need to understand why and how the sudden inflows and outflows of international capital occur. Thus, we ask the following questions: What is the mechanism of sudden capital inflows and outflows? What triggers such capital inflows and outflows? What are the conditions for economic takeoff and capital flight? What is the role of government in economic development?

This paper presents a model of economic takeoff and capital flight with free international capital flows. The model emphasizes the importance of strategic complementarity between the optimal portfolio decisions of international investors. In the early stage of economic development,
investments are complementary and the aggregate production exhibits increasing returns to capital. The complementarity between investments or the increasing returns to capital give rise to strategic complementarity between the actions of international investors. The strategic complementarity produces two stable Nash equilibria: a low and high capital equilibrium. Switches between two equilibria represent economic takeoff and capital flight. Thus, economic takeoff and capital flight emerge from the same mechanism of modern economic development, which is characterized by increasing returns and multiple equilibria. It is not a coincidence, therefore, that capital flights are observed among those countries that have recently achieved a successful takeoff into development.

Many papers in development economics have argued that basic investments are complementary and aggregate production exhibits increasing returns in the early stage of development. They are known as the “big push” models. $ ^{2} $ The “big push” models emphasize the importance of various “economies of scale,” “linkages,” and “balanced growth” for economic development. The essential element behind all of those concepts is the idea of complementarity between investments. Lewis (1955: p.249), for example, has stated as follows: “If a new undertaking is to be started, the productivity of this undertaking depends not only upon itself, but also upon the efficiency of all other industries whose services the new undertaking would need to use---especially general engineering services, suppliers of components, transport, and other public utilities. This in turn depends partly upon how
highly capitalized these other services are. Hence the productivity of one investment depends upon other investments having been made before in many directions. At least up to a point, there are increasing rather than decreasing returns to capital investment.”

In fact, the assumption of decreasing returns to capital is inconsistent with the growth data of developing countries, while it is consistent with those of developed countries. The main implication of the conventional production function with decreasing returns is that the growth rate declines as the economy develops or equivalently that the marginal product of capital declines as the economy accumulates more capital (Figure 1). This implication is consistent with the growth data of developed countries. As Figure 2 shows, developed countries with higher income (capital) tend to have lower growth (marginal product) while developed countries with lower income (capital) tend to have higher growth (marginal product). As a result, the phenomenon of convergence is observed among developed countries.

However, the implication of the conventional production function is incompatible with the growth data of developing countries. No phenomenon of convergence is observed among developing countries (Figure 3). Most developing countries are characterized by low income (capital) and low growth (marginal product), while emerging economies are characterized by medium income (capital) and high growth (marginal product). This is the opposite of what decreasing returns to capital implies. Thus the conventional production function does not apply to developing countries. Furthermore, the lack of convergence suggests multiple equilibria.

What kind of a production function is consistent with the growth data of both developed and developing countries? It is a production function with increasing returns in the early stage and decreasing returns in the later stage of development (Figure 4). This production function is consistent with the inverted-U shaped growth pattern that countries initially move from the stage of low income and low growth to the stage of medium income and high
growth (economic takeoff), and then enter into the stage of high income and low growth (convergence). $ ^{3} $

Given the new production function with increasing and decreasing returns to capital, the optimal portfolio decisions of international investors and their non-cooperative interaction give rise to two stable Nash equilibria: a Pareto-inferior low capital equilibrium and a Pareto-superior high capital equilibrium. Switches between two equilibria correspond to the economic takeoff and capital flight of developing countries. They are triggered by changes in the basic return and risk factors: (i) expected exchange rate, (ii) expected productivity, (iii) the world interest rate, (iv) exchange rate risk, (v) productivity risk, and (vi) the risk aversion of international investors.

Now, given the Pareto-ranked multiple equilibria and the basic factors for equilibrium selection, the role of government can be well defined. It is to achieve the high capital equilibrium through policies that can affect the return and risk factors. Those policies potentially include fixed exchange rate policy, government guarantee, and capital control. The development strategy of domestic capital accumulation and capital market liberalization can also help achieve the high capital equilibrium. However, the economy may be trapped in the low capital equilibrium if the liberalization is implemented before the sufficient accumulation of domestic capital.

I will elaborate on those points, using a formal model. The rest of the paper is organized as follows: Section II presents a model of optimal portfolio decisions of international investors and Nash equilibria. Section III presents the comparative static analyses with respect to the return and risk factors. Section IV analyzes the mechanism of economic takeoff and capital flight or switching between two equilibria. Section V studies the role of government and development strategy. Section VI concludes the paper.
### I I. The Model of Optimal Portfolio and Nash Equilibria

The model assumes the following situation: Capital markets are integrated and form an efficient global capital market. There are no obstacles to international capital flows. The economic growth of a developing country depends on capital inflows from the global capital market. The aggregate production function exhibits increasing returns to capital in the early stage and decreasing returns in the later stage of development. There are a large number of international investors. Their portfolios consist of risk-free assets and risky investment in a developing country. Their optimal portfolio decisions and their non-cooperative interactions produce two stable Nash equilibria with high and low capital stocks. Switches between two equilibria represent economic takeoff and capital flight.

### A. Production function with increasing and decreasing returns

There are many reasons why increasing returns to capital arise in the early stage of development. The main argument is that many investments are complementary at the beginning of development. $ ^{4} $ Investments reinforce each other through positive feedback and build the infrastructure of the economy, which makes an efficient production possible. An investment may not be profitable by itself, but its effects on other investments and their
feedback effects on itself can make the investment profitable. Consequently, investments are complementary in the aggregate production process. However, as the economy develops into a more advanced stage, there emerge various opportunities for investments associated with a wider variety of substitutable products. Consequently, investments for new products are more likely to be substitutable and they compete for limited resources. As a result, the aggregate production function exhibits increasing returns in the early stage and decreasing returns in the later stage of development. $ ^{5} $

Thus we define the production function as follows: The production function is twice continuously differentiable with respect to capital k and takes the following form:

$$ F(k)=f(k)+\varepsilon k $$

where $ \varepsilon $ is a marginal productivity shock or a rate-of-return shock. It is distributed as $ \varepsilon\sim N(E(\varepsilon),\sigma_{\varepsilon}^{2}) $ , which represents a normal distribution with mean $ E(\varepsilon) $ and variance $ \sigma_{\varepsilon}^{2} $ . The production function satisfies that $ f(0)=0, f'(0)=1, f'(k)>1 $ for k>0 and also that

$$ f^{\prime \prime}(k)>0\quad for k<\overline{k}\quad and\quad f^{\prime \prime}(k)<0\quad for k>\overline{k} $$
where $ \bar{k} $ is the capital level at which the marginal product is maximal.

An important characteristic of this production function is that the expected marginal product of capital initially increases and then declines. It suggests that the marginal product of capital or the rate of return for capital exhibits an inverted-U shaped growth pattern with the accumulation of capital. The marginal product initially rises with a takeoff into development Then, after reaching a maximum rate, the marginal product begins to decline with a further accumulation of capital. This implication is consistent with the stylized fact that an economy tends to develop from a low-income low-growth stage to a medium-income high growth stage (takeoff), and then to a high-income low-growth stage (convergence).

### B. Optimal portfolio decision of international investors

There are many identical international investors $ (i = 1,2,3,\ldots,n) $ . Each investor has total wealth w available for investment. Their asset portfolios consist of risk free assets and risky foreign investment. The risk free assets yield the world interest rate R while the risky foreign investment yields the rate of return $ \tilde{r} $ . Investor i invests his wealth w either in risk free assets $ (w - k_{i}) $ at the world interest rate R or in a risky foreign country $ (k_{i}) $ at the rate of return $ \tilde{r} $ .

I assume that the global capital market is competitive so that each investor takes the rate of return as independent of one's own action. The rate of return on foreign investment ( $ \tilde{r} $ ) depends on the average investment of other investors (k) as follows:

$$ \tilde{r}=r(k)+\varepsilon $$

where $ r(k) = f'(k) - 1 $ (Figure 4). The rate of return ( $ \tilde{r} $ ) also depends on a
marginal productivity shock ( $ \varepsilon $ ). International investors thus face productivity risk.

In addition to the productivity risk, international investors face foreign exchange rate risk. Depreciation of foreign currency reduces the value of foreign investment. The rate of return for foreign investment is therefore reduced by the rate of the foreign currency depreciation $ \tilde{d} $ . The rate of depreciation is normally distributed as $ \tilde{d} \sim N(E(d), \sigma_{d}^{2}) $ .

To sum up, the return on the portfolio of international investor i can be written as follows:

$$ \tilde{\pi}=(1+r\left(k\right)+\varepsilon-\tilde{d})k_{i}+(1+R)\left(w-k_{i}\right) $$

where

$$ \varepsilon\sim N\left(E\left(\varepsilon\right),\sigma_{\varepsilon}^{2}\right)\mathrm{~a n d~}\tilde{d}\sim N\left(E\left(d\right),\sigma_{d}^{2}\right) $$

If $ (w - k_{i}) $ is positive (negative), it indicates net lending (borrowing) at the world interest rate R, which is the opportunity cost for investors. Stochastic variables $ \varepsilon $ and $ \tilde{d} $ are assumed to be independent for the sake of simplicity.

International investors maximize their expected utilities that depend on the return on their portfolio $ \tilde{\pi} $ . The utility function is given by the following form of constant absolute risk aversion (CARA):

$$ u(\tilde{\pi})\;=\;-\exp(-\beta\;\tilde{\pi}) $$

where $ \beta $ is the parameter of constant absolute risk aversion ( $ \beta > 0 $ ).

Then the expected utility maximization problem of investor i with respect to $ k_{i} $ is obtained as follows:

$$ \max_{k_{i}}\ E(u(\tilde{\pi}))\;=\;-\exp\{-\beta\;[E(\tilde{\pi})-\frac{1}{2}\;\beta\;\sigma_{\pi}^{2}]\} $$
where the equality is established by the calculation method that one uses to find the moment generating function for the normal distribution.

The above expected utility maximization problem is equivalent to the following maximization problem:

$$ \max_{k_{i}}\phi(k_{i},k)=\left(1+r(k)+E\left(\varepsilon\right)-E(d)\right)k_{i}+(1+R)(w-k_{i})-\frac{1}{2}\beta\sigma^{2}k_{i}^{2} $$

where $ \sigma^{2}\equiv\sigma_{\varepsilon}^{2}+\sigma_{d}^{2} $ . This involves only the means and variances of stochastic variables.

The first order condition for maximization is obtained as follows:

$$ k_{i}=\frac{r(k)+E\left(\varepsilon\right)-E\left(d\right)-R}{\beta\left(\sigma_{\varepsilon}^{2}+\sigma_{d}^{2}\right)} $$

This gives the optimal action $ (k_{i}) $ of investor i as a function of the average action $ (k) $ of other investors. It is the best response function of $ k_{i} $ with respect to k. The second order condition is satisfied because $ \beta(\sigma_{\varepsilon}^{2}+\sigma_{d}^{2})>0 $ .

The optimal portfolio solution clearly shows a tradeoff between risk and return. The numerator expresses the expected excess rate of return over the risk-free assets while the denominator expresses the risk factors associated with investing in a foreign country. The optimal investment level $ k_{i} $ is increasing with respect to the return in the numerator and decreasing with respect to the risk in the denominator. There is a clear tradeoff between risk and return in the optimal portfolio decision.

### C. Strategic complementarity and multiple Nash equilibria

We define strategic complementarity and strategic substitutability in terms of the function $ \phi_{12}(k_{i},k) $ . International investors face the situation of
strategic complementarity if $ \phi_{12}(k_{i},k)>0 $ . It means that the optimal investment of an investor increases if other investors increase their investment. It induces rational herd behavior among international investors Conversely, investors face the situation of strategic substitutability if $ \phi_{12}(k_{i},k)<0 $ . It means that the optimal investment of an investor decreases if other investors increase their investment. $ ^{6} $ Therefore, strategic substitutability makes capital flows stable while strategic complementarity makes capital flows unstable.

In the model, strategic complementarity exists ( $ \phi_{12} > 0 $ ) if and only if the production function exhibits increasing returns to capital ( $ f''(k) > 0 $ ). This proposition follows directly from the fact that

$$ \phi_{12}(k_{i},k)\;=\;r^{^{\prime}}(k)\;=\;f^{^{\prime \prime}}(k) $$

Therefore, strategic complementarity exists in the early stage of development with increasing returns while strategic substitutability exists in the later stage of development with decreasing returns. It follows that capital flows are unstable in the early stage of development while they become stable in the later stage of development.

Strategic complementarity among the optimal portfolio decisions of international investors produces multiple Nash equilibria: a low capital equilibrium and a high capital equilibrium. Figure 5 shows the response functions of investor i and j ( $ i \neq j $ ): that is, the response function of $ k_{i} $ with respect to k which includes $ k_{j} $ and the response function of $ k_{j} $ with respect to k which includes $ k_{i} $ . Nash equilibria are obtained at the intersection of those response functions. The Nash equilibria satisfy the condition that $ k_{i} = k_{j} = k $ for all i and j.
There are generally two stable Nash equilibria at $ k_{H} $ and $ k_{L} $ as well as one unstable Nash equilibrium at $ k_{T} $ , which is located between the two stable Nash equilibria (Figure 5). Both high and low capital equilibria are stable Nash equilibria because an investor i has no incentive to deviate from $ k_{i}=k_{H} $ if other investors choose $ k=k_{H} $ and also from $ k_{i}=k_{L} $ if other investors choose $ k=k_{L} $ . Although there is another equilibrium ( $ k_{T} $ ) between $ k_{L} $ and $ k_{H} $ , it turns out to be unstable. A small perturbation will trip the unstable Nash equilibrium ( $ k_{T} $ ), and the economy will move to either $ k_{H} $ or $ k_{L} $ . In other words, the unstable Nash equilibrium ( $ k_{T} $ ) represents the threshold level of capital.

The two stable Nash equilibria are Pareto-ranked. This follows directly from the relationship that

$$ \begin{array}{r}{\phi(k_{H},k_{H})-\phi(k_{L},k_{L})=\frac{1}{2}\beta\sigma^{2}\left\{\left(k_{H}\right)^{2}-\left(k_{L}\right)^{2}\right\}>0}\end{array} $$

It shows that the high capital equilibrium $ (k_{H}) $ is a Pareto-superior Nash equilibrium while the low capital equilibrium $ (k_{L}) $ is a Pareto-inferior Nash equilibrium. All investors prefer the high capital equilibrium to the low capital equilibrium. The Pareto-ranked multiple equilibria suggest a possibility of coordination failure that the economy gets stuck at a Pareto-inferior equilibrium.

If the return factors $ (E(\varepsilon)-E(d)-R) $ are sufficiently large or the risk factors $ (\beta(\sigma_{\varepsilon}^{2}+\sigma_{d}^{2})) $ are sufficiently small, the high capital equilibrium will exist. However, if the return factors are sufficiently small or the risk factors are sufficiently large, the high capital equilibrium does not exist and the low capital equilibrium becomes a unique equilibrium (Figure 6).
Therefore the high capital equilibrium will prevail if the risk factors dominate the return factors. In this sense, the high capital equilibrium may be called a Return-dominant equilibrium while the low capital equilibrium may be called a Risk-dominant equilibrium. There exists a tradeoff between risk and return for the equilibrium selection.

### D. Interest rate parity with risk premium

Substituting k into $ k_{i} $ in equation (9), we find that the Nash equilibria satisfy the following form of the interest rate parity with risk premium:

$$ \left\{\begin{array}{l}r(k)+E\left(\varepsilon\right)-E\left(d\right)\end{array}\right\}-R=\beta\left(\sigma_{\varepsilon}^{2}+\sigma_{d}^{2}\right)k $$

This interest rate parity equation is derived from the utility maximization of individual investors and the condition of the Nash equilibrium.

The left-hand-side of equation (12) represents the expected excess return (ER) of risky investment in a foreign county over risk-free assets. The right-hand-side represents the risk premium (RP), which is increasing with respect to k. Let us call the left-hand equation the excess return curve (ERC) and the right-hand equation the risk premium line (RPL). The Nash equilibria correspond to the intersections of the excess return curve and the risk premium line (Figure 7). The representation of Figure 7 corresponds to that of Figure 5. Figure 5 describes the Nash equilibria in terms of the game-theoretic response functions while Figure 7 describes the same Nash equilibria in terms of the excess return curve and the risk premium line.

Figure 7 suggests a natural way to distinguish between emerging markets and non-emerging markets among developing countries. Emerging markets may be defined as developing countries with the capital stock greater than $ k_{T} $ . Non-emerging markets may be defined as developing