Silviase/jgov_v1.4_full_ann huggingface dataset:
countries with the capital stock less than $ k_{T} $ . Emerging markets are those countries that converge to the high capital equilibrium ( $ k_{H} $ ) while non-emerging markets are those that converge to the low capital equilibrium ( $ k_{L} $ ). Developed countries may be defined as those countries that have already achieved a high level of capital accumulation ( $ k_{HH} \gg \overline{k} $ ) where diminishing returns dominate.

### I II. Comparative Statics of Return and Risk Factors

This section studies the comparative static properties of the high and low capital equilibrium with respect to the return and risk factors.

### A. Expected exchange rate, expected productivity, and the world interest rate

The return factors in the model are expected exchange rate $ (E(d)) $ , expected productivity $ (E(\varepsilon)) $ , and the world interest rate $ (R) $ . Expected currency depreciation shifts the excess return curve downward by its magnitude (Figure 8). Expected currency depreciation therefore reduces the equilibrium capital stock, inducing capital outflows. Conversely, expected currency appreciation shifts the excess return curve upward by its magnitude. Expected currency appreciation therefore increases the equilibrium capital stock, inducing capital inflows.

Those results are confirmed by the following derivative at $ k = k_{H} $ , $ k_{L} $ :

$$ \frac{dk}{dE(d)}=\frac{1}{f^{^{\prime \prime}}(k)-\beta(\sigma^{2}_{\varepsilon}+\sigma^{2}_{d})}<0 $$

At $ k = k_{H}, k_{L} $ , the slope of the risk premium line is larger than the slope of
the excess return curve: that is, $ \beta\left(\sigma_{\varepsilon}^{2}+\sigma_{d}^{2}\right)>f^{\prime\prime}(k) $ . This makes the sign of the denominator strictly negative.

Similarly, expected productivity increase shifts the excess return curve upward by its magnitude. It increases the equilibrium capital stock, inducing capital inflows. Expected productivity decline, on the other hand, reduces the equilibrium capital stock, inducing capital outflows. A fall in the world interest rate shifts the excess return curve upward by its magnitude. It increases the equilibrium capital stock, inducing capital inflows. A rise in the world interest rate, on the other hand, reduces the equilibrium capital stock, inducing capital outflows.

These results are confirmed by the following derivatives at $ k = k_{H}, k_{L} $ :

$$ \frac{d k}{d E(\boldsymbol{\varepsilon})}=\frac{-1}{f^{^{\prime \prime}}(k)-\beta(\boldsymbol{\sigma}_{\varepsilon}^{2}+\boldsymbol{\sigma}_{d}^{2})}>0 $$

$$ \frac{dk}{dR}=\frac{1}{f^{\prime \prime}(k)-\beta(\sigma^{2}_{\varepsilon}+\sigma^{2}_{d})}<0 $$

Again the sign of the denominator is strictly negative.

### B. Exchange rate risk, productivity risk, and risk aversion

The risk factors in the model are the exchange rate risk $ (\sigma_{d}^{2}) $ , the productivity risk $ (\sigma_{\varepsilon}^{2}) $ , and the risk aversion $ (\beta) $ of international investors. Increases in those risk factors rotate the risk premium line counter-clockwise. They reduce the equilibrium capital stock, inducing capital outflows (Figure 9). Decreases in the risk factors, on the other hand, rotate the risk premium line clockwise. They increase the equilibrium capital stock, inducing capital inflows. In short, increased risks reduce the equilibrium capital stock, inducing capital outflows while reduced risks increase the equilibrium capital.
stock, inducing capital inflows.

These results are confirmed by the following derivative at $ k = k_{H}, k_{L} $ :

$$ \frac{d k}{d[\beta(\boldsymbol{\sigma}_{\varepsilon}^{^{2}}+\boldsymbol{\sigma}_{d}^{^{2}})]}=\frac{k}{f^{^{\prime \prime}}(k)-\beta(\boldsymbol{\sigma}_{\varepsilon}^{^{2}}+\boldsymbol{\sigma}_{d}^{^{2}})}<0 $$

Again the sign of the denominator is strictly negative.

### I V. Mechanism of Economic Takeoff and Capital Flight

This section studies the mechanism of switching between two equilibria or the mechanism of economic takeoff and capital flight in modern economic development.

### A. Sudden capital inflows and outflows

The comparative static analyses in the previous section have revealed that the absolute values of derivatives become greater as the level of capital $ (k) $ moves closer to the high critical level $ (k_{CH}) $ from above (Figure 8 and 9). This is because the slope of the excess return curve $ f''(k) $ increases as k moves down to $ k_{CH} $ from above, decreasing the absolute value of the denominator and therefore increasing the absolute values of derivatives. In other words, the effect of a change in the basic factors is greater for the economy that is located closer to the high critical level of capital $ (k_{CH}) $ . It goes to infinity as the economy moves onto the high critical level $ (k_{CH}) $ . This corresponds to the moment of capital flight.

Likewise, the absolute values of derivatives become greater as the level of capital $ (k) $ moves closer to the low critical level $ (k_{CL}) $ from below (Figure 8 and 9). This is because the slope of the excess return curve $ f''(k) $
increases as k moves up to $ k_{CL} $ from below, decreasing the absolute value of the denominator and therefore increasing the absolute values of derivatives. In other words, the effect of a change in the basic factors is greater for the economy that is located closer to the low critical level of capital ( $ k_{CL} $ ). It goes to infinity as the economy moves up to the low critical level ( $ k_{CL} $ ). This corresponds to the moment of economic takeoff.

The high capital equilibrium will suddenly disappear if the risk factors overtake the return factors, bringing the economy below the high critical level $ (k_{CH}) $ . If the risk premium line and the excess return curve no longer intersect at $ k_{H} $ , capital outflows will suddenly occur. Conversely, the low capital equilibrium will suddenly disappear if the return factors overtake the risk factors, bringing the economy above the low critical level $ (k_{CL}) $ . If the excess return curve and the risk premium line no longer intersect at $ k_{L} $ , capital inflows will suddenly emerge.

Suppose the economy is initially at $ k = k_{H} > k_{CH} $ . Then expected currency depreciation will reduce the equilibrium level of capital and trigger capital flight when the excess return curve falls below ER(CH) (Figure 8). Then the economy will move from $ k_{H} = k_{CH} $ to $ k_{L} $ , inducing capital outflows. This represents capital flight. A similar situation will arise with expected productivity decline and a fall in the world interest rate.

In addition, a rise in productivity risk and exchange rate risk as well as the risk aversion of international investors reduces the equilibrium level of capital. They will trigger capital flight when the risk premium line rotates counter-clockwise beyond RP(CH) (Figure 9). The economy will move from $ k_{H}=k_{CH} $ to $ k_{L} $ with sudden capital outflows.

In contrast, expected currency appreciation, expected productivity increase, a fall in the world interest rate, as well as decreases in productivity risk, exchange rate risk, and the risk aversion of investors create an environment conducive to achieving economic takeoff with large capital inflows. They shift the excess return curve upward and rotate the risk
premium line clockwise (Figure 8 and 9). The economy will move from $ k_{L}=k_{CL} $ to $ k_{H} $ with the disappearance of the low capital equilibrium. This represents a takeoff with large capital inflows.

### B. Emerging economies and capital flight

The globalization of capital markets is associated with growth in the number of international investors. An increase in the number of investors implies an equi-proportionate shift of the excess return curve to the left from a viewpoint of international investors (Figure 10). In other words, the amount of foreign investment per investor declines to finance a given amount of total investment in a developing country. It means enhanced risk-sharing among investors and reduced risk for each investor. It helps trigger a takeoff into development. Thus the globalization of capital markets helps achieve the transformation of developing countries into emerging economies.

Emerging economies $ (k > k_{CH}) $ are more likely to face capital flight than developed countries $ (k >> \overline{k}) $ . The minimum shift in the risk premium line or the excess return curve that can trigger capital flight in a developing country cannot cause capital flight in a developed country (Figure 7). Only larger shifts can trigger capital flight in developed countries. This is because developed countries are operating their production at the level of diminishing returns and are located further away from the high critical level of capital $ (k_{CH}) $ .

The emerging economies that are located near the high critical level are susceptible to capital flight. Those marginal emerging economies $ (k_{H} \approx k_{CH}) $ exist if international capital markets are efficient and the number of emerging economies is large. To see this point, suppose there is an increasing number of emerging economies in the efficient global capital market. Then, their increasing demand for international capital will induce the world interest rate to go up until some of the emerging economies are
attacked by capital flight. A rise in the world interest rate shifts the excess return curve down until the supply and demand for international capital in developing countries are balanced. Therefore there are many emerging economies near the high critical level of capital $ (k_{CH}) $ . In short, a combination of an efficient global capital market and a large number of emerging economies make capital flight more likely to occur. A slight perturbation of the basic factors can trigger capital flight in marginal emerging economies.

The crisis of capital flight in one country will increase the perceived risks $ \left(\sigma^{2}\right) $ for investing in other developing countries. The increased risks can trigger capital flight in other emerging markets (Figure 9). Moreover, an increasing number of crises will have adverse effects on the risk aversion of investors ( $ \beta $ ). Like increased risks, a rise in the risk aversion of investors can trigger capital flight. Therefore the crisis contagion of capital flight can spread among emerging economies through the increased risks as well as the increased risk aversion of international investors.

### C. Economic takeoff and coordination failure

The existence of the high capital equilibrium is a necessary condition for capital inflows and economic development. Is it also a sufficient condition? The answer is no. When there exist multiple equilibria, the high capital equilibrium is not necessarily selected over the low capital equilibrium. In other words, coordination failures can arise. The reason for coordination failures in the model is the stability of both high and low capital equilibria. History matters and the phenomenon of hysteresis can arise.

Suppose that the economy is initially located at the unique low capital equilibrium $ k_{LL} $ (Figure 7). Now suppose that changes in the return and risk factors bring the excess return curve and the risk premium line into intersecting three times at $ k_{L} $ , $ k_{T} $ and $ k_{H} $ . Will the economy move from
the low capital equilibrium to the high capital equilibrium? In general, it will not move so long as the low capital equilibrium continues to exist. This is because the low capital equilibrium is stable. The economy will stay at the low capital equilibrium even if the high capital equilibrium exists.

There are two ways in which a developing country can achieve economic takeoff in this situation. First, the simplest case is that the expected excess return increases and the risks decline so that the excess return curve and the risk premium line intersect at the unique high capital equilibrium $ k_{HH} $ (Figure 7). If this happens, the economy will start economic takeoff with large capital inflows until it converges to the high capital equilibrium $ (k_{HH}) $ . Second, if international investors can coordinate their investments so that they invest in a developing country at the same time above the threshold level $ (k_{T}) $ . This possibility seems, however, to be small because of difficulties and costs associated with coordinating a large number of international investors in a decentralized global capital market in a way that is compatible with their individual incentives. $ ^{8} $

### V. Policy Implications

This section studies the policy implications of the model. We have seen in the previous sections how autonomous changes in the return and risk factors can bring about economic takeoff and capital flight. To the extent that the government can control those return and risk factors, it can influence the equilibrium selection of the economy. Therefore the developmental role of government can be well defined: It is to help achieve
the high capital equilibrium through policies that can affect the return and risk factors in the right directions. What are those policies?

With respect to exchange rate policy, a fixed exchange rate creates an economic environment conducive to large capital inflows and therefore economic development. It reduces the exchange rate risk $ \left(\sigma_{d}^{2}\right) $ and thus helps achieve the high capital equilibrium with capital inflows (Figure 9). This seems to be the main reason why many developing countries have pegged their local currencies to the currency of international investors. In contrast, a flexible exchange rate increases the exchange rate risk, and makes it difficult for a developing country to attract international capital. As the economy matures into a more advanced stage that is located away from the critical level $ \left(k_{CH}\right) $ and thus faces less risk of capital flight, the government can adopt a more flexible exchange rate. $ ^{9} $

Suppose that fixed exchange rate policy lost credibility and expected currency depreciation has triggered capital flight. In other words, the excess return curve has shifted from ER to below ER(CH) in Figure 8. In this case, the role of government is to bring the high capital equilibrium back into existence. This goal can be achieved, for example, if the government devalues the currency immediately and sufficiently so that investors expect future appreciation instead of depreciation. It will shift the excess return curve back to ER and beyond, restoring the high capital equilibrium.

As long as the initial fall in capital is small and capital remains close enough to the high critical level ( $ k_{CH} $ ), an immediate and sufficient
devaluation will bring the economy back to the high capital equilibrium even though the new equilibrium may be less than the previous level. It will stop capital flight because the high capital equilibrium is stable. The economy will move back to the high capital equilibrium so long as it stays near the equilibrium. $ ^{10} $

When combined with the immediate and sufficient devaluation, capital controls can play an important role in stopping capital flight. If capital controls can limit capital outflows to a minimum amount, the economy will return to the high capital equilibrium as soon as the devaluation brings the equilibrium back into existence. This is because the high capital equilibrium is stable (Figure 7). Capital controls can also prevent the economy from moving to the low capital equilibrium by increasing the costs of capital movements for international investors. $ ^{11} $ However, capital controls can be effective only if they are combined with other policies that help bring the high capital equilibrium back into existence. Without the re-emergence of the high capital equilibrium, capital controls will not be able to stop capital flight because the low capital equilibrium becomes the only equilibrium. Therefore, the appropriate policy response to capital flight is firstly to limit the amount of capital outflows, and secondly to bring the high capital equilibrium back into existence. Capital controls can accomplish the first objective while the immediate and sufficient devaluation can accomplish the second objective.
Government guarantee for foreign debts can be an effective means to achieve the high capital equilibrium. From the viewpoint of international investors, government guarantee is equivalent to purchasing a put option with the option fee paid by taxpayers. A put option transforms the payoff function into a convex shape. It has the same effect as an increase in the expected marginal product $ E(\varepsilon) $ and a reduction in the productivity risk $ \sigma_{\varepsilon}^{2} $ . It shifts the excess return curve upward and rotates the risk premium line clockwise. Therefore, government guarantee increases the probability that the economy will achieve economic takeoff (Figure 8 and 9). $ ^{12} $

The model suggests the two-stage development strategy of domestic capital accumulation and capital market liberalization. The accumulation of domestic capital has the effect of shifting the risk premium line to the right by that amount (Figure 11). Therefore the following two-stage development strategy becomes an effective means of achieving the high capital equilibrium: In the first stage, domestic capital $ (k_{D}) $ should be accumulated sufficiently above the level of $ k_{DC} $ . In the second stage, capital market liberalization should be implemented. Then, as Figure 11 shows, the high capital equilibrium $ (k_{H}) $ becomes a unique Nash equilibrium and the optimal response of international investors is to increase their investment in the developing country. The country will thus achieve economic takeoff through the autonomous inflows of international capital $ (k_{H} - k_{D}) $ .

The capital market liberalization should be implemented only after a sufficient accumulation of domestic capital is achieved. There are two
reasons: First, capital market liberalization will not help the economy to achieve the high capital equilibrium if domestic capital is less than $ k_{DC} $ . Second, capital market liberalization will bring about some outflows of domestic capital. Therefore, it becomes necessary for achieving the high capital equilibrium that domestic capital ( $ k_{D} $ ) remains above the critical level ( $ k_{DC} $ ) after some outflows of domestic capital due to the liberalization. Otherwise the country will be trapped in the low capital equilibrium.

The role of government must change with the stages of economic development. During the stage of increasing returns and complementarity, the government can help achieve the high capital equilibrium through policies that affect the return and risk factors in the right directions. However, after the high capital equilibrium is achieved and the risk of capital flight is reduced, the role of government must change. Those interventional policies become distortionary for the economy that is characterized by decreasing returns and substitutability. Therefore, they must be abolished after the economy has achieved a successful takeoff.

### V I. Conclusion

I have presented a model of economic takeoff and capital flight with free international capital flows. In the early stage of development, investments are complementary and aggregate production exhibits increasing returns to capital. The increasing returns lead to strategic complementarity between the optimal portfolio decisions of international investors. The result is multiple Nash equilibria: a high capital equilibrium and a low capital equilibrium. The model has shown how changes in the return and risk factors can trigger switches between two equilibria. Switches between two equilibria correspond to the economic takeoff and capital flight of a developing country.

At the high capital equilibrium, the interest rate parity with risk
premium holds and international capital allocation is efficient. If the risk factors dominate the return factors, the high capital equilibrium will disappear. Then, capital flight becomes inevitable. Conversely, if the return factors dominate the risk factors, the low capital equilibrium will disappear. Then, autonomous capital inflows will bring about the economic takeoff of the developing country.

To the extent that the government can influence the return and risk factors, it can affect the selection of the equilibrium in the economy. Therefore the role of government is to help achieve the high capital equilibrium through policies that affect the return and risk factors. Fixed exchange rate policy, government guarantee, and capital control potentially help achieve the high capital equilibrium. However, after the economy is sufficiently developed to the level of decreasing returns, those policies become distortionary and therefore should be abolished.

The globalization of capital markets helps achieve the high capital equilibrium through risk-sharing among the increasing number of investors. The two-stage development strategy of domestic capital accumulation and capital market liberalization can also help achieve the high capital equilibrium. It enables the economy to achieve economic takeoff with autonomous capital inflows from the global capital market. However, the economy may be trapped in the low capital equilibrium if the liberalization is implemented before the sufficient accumulation of domestic capital.
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