Draft Term Paper for PhD course International Finance and Macroeconomics
Professor David Backus
New York University
Foreign Capital in Emerging Economies
Junhua Qin
Draft Paper
l Introduction
Since the1990s, Eastern Asian countries have gradually opened capital accounts[1]. Does capital liberalization generate more volatility to the economy or does it contribute to economic growth? To get an inkling of what’s going on lets first compare the four East Asian countries’ (Indonesia, Korea, Malaysia and Thailand) macro-data before (1974-1989) and after (1990-2003) capital liberalization (around 1990s). On level data[2], the real output and consumption become less volatile even experiencing financial crisis; however the output-capital stock ratio (YKratio) is more fluctuated (table 1 A). As to the growth data, after 1990, the standard deviations (s.d.) are much bigger but the mean growth is smaller, especially in capital formation (K) (table 1 B); Kick out the impact of financial crisis, the differences before and after financial liberalization in both mean and s.d. in GDP growth become insignificant, but still exhibit a lower speed in capital formation. In summary, the data shows that capital liberalization contributes instability, but not growth to the economy; and opening capital accounts does not promise a higher speed of capital formation. This is also the argument of Stiglitz (2000)[3] and he presents more evidence to this point.
Unfortunately, in East Asian countries, the volatility appears in the form of an abrupt interruption in capital inflows, a sharp cut in investment and later output. In many literatures, the East Asian financial crisis is featured by the phenomenon “Sudden Stop” labeled by Calvo (1998). In data we can see that after 1990, the Ykratio dropped steadily accompanied with the foreign capital inflow until the crisis (figure 1 & 4), the YKratio rose immediately after the crisis (more than twice) and there is no evidence that it will drop down to the pre-crisis levels in the short term. Looking at the fixed capital formation, it is clear that the sharp rise in YKratio is caused by the sharp decrease in capital (figure 2). In those countries, the actual consumption ratio (consumption over GDP) is low compared to the U.S., the average ratio from 1985 to 2003 are no more than 60% (figure 3) which implies a high savings rate; After the crisis, there is a pick up in consumption ratio with the exception of Indonesia. The aforementioned evidence indicates that the decrease in capital formation is not only caused by the interruption of foreign capital inflow but also by the contraction of domestic investment. On one hand, people are unwilling to save; on the other hand, the financial intermediates malfunction during the crisis, domestic investment decreases are expected.
My argument is that, under the assumption that foreign investors are “return chasers”, the only thing they are concerned about is the rate of return on capital; after capital liberalization, there is usually an overshoot in foreign capital inflow which supports a higher investment and GDP growth; however, without productivity spillover, the economic expansion is unsustainable. Under decreasing rate of return on capital, the foreign capital inflow lowers the capital marginal product and decreases the attractiveness of the host country to foreign capital quickly. As a result, the foreign capital flow cannot support a persistent output boom in the host country, however once foreign capital completely flows out, domestic investment cannot support such a high growth rate of output and the economy would collapse. That’s why foreign capital contributes to the volatility but not the growth. Further more, as the foreign investors are rational, they watch over the emerging countries’ rate of return on capital as a self-adjustment mechanism, the opening of capital accounts won’t promise a long term high speed rate of capital inflow.
l Literature
In most of the emerging economies’ business cycle literature, they adopt a small open economy RBC model with external shocks to explain the volatility of foreign capital flow fluctuations. Such as Mendoza’s (2001) paper, he explains the sudden stop as a result of real shocks making the credit constraint binding. I do not concur that the volatility of foreign capital flow can just be explained by the external shocks however it does reflect the foreign investors’ rational decisions and the instability of an open emerging economy. Volatility always exists even without a specific shock. Bacchetta and Wincoop (1998) discuss the capital flow overshooting and volatility with a simple model of international investors’ behavior. In their model, international capital flow depends on the rate of return discrepancy between emerging economy and the developed economy. This gives a rich dynamic of capital flow, but the rates of return in both economies are given.
In my paper, based on the assumption that foreign investors are “return chasers” (Bohn and Tesar (1996)), the investment decision of capital flow in or out depends on the marginal product of capital (YKratio); the foreign capital flow affects the domestic capital formation and capital marginal products directly, so that the foreign investors’ decision is endogenous. This gives a limit to the foreign capital inflow and introduces a “get-out” mechanism, and generates volatility in foreign capital flow even without external shocks. Furthermore, the persistent growth of the economy requires the support from a stable foreign capital inflow, however the growing capital stock this period will lower the Ykratio and the inflow of foreign capital next period. This conflict produces the instability of the economic system. I argue that it can be solved if foreign capital brings improvement in productivity to the host country, which generates increasing capital return to scale.
I first developed a small open economy model in which the foreign capital flow doesn’t generate a productivity spillover effect. I show that this is an unstable economic system; and then I modified the model in which the foreign capital inflow promotes productivity. I show that the existence of foreign capital flow amplifies the business cycle but is a more stable system.
l Model
Before capital liberalization,
Before liberalization, this is a closed economy run on deterministic state. The utility function is given as:
(1)
There is only one input capital and constant productivity, the decreasing rate of return technology function:
(2)
Under budget constraint:
Y = c + x (3)
X is the investment. The law of capital motion is:
(4)
The agents in this economy will maximize the aggregate consumption under budget constraint. Use Lagrange solve for the maximization problem.
(EC)
Solve for steady state,
, the marginal product of capital. After capital liberalization, capital becomes international mobile, allowing foreign capital inflow. Foreign investors can purchase the right claimed to the domestic output without restrictions. To be clear, I focus on the portfolio capital flows, it is also reasonable to assume that these capital flows do not promote productivity of the host country. In the following session I will describe an economy with two countries. For simplicity, only the developed economy makes investment in the emerging economy. I use Bacchetta and Wincoop (1998)’s structure to described the developed economy,
Developed country
There is only one capital good, which can be invested in both countries. At time 0, individual in developed economy owns W* capital goods. The depreciation rate is , each year individuals receive a new endowment of capital good . Thus, the endowment of capital goods in developed country remains constant overtime.
Assume that the agents in emerging economy only invest domestically, and the agents in developed economy can invest in both countries, making investment decision based on the portfolio optimization. The agents maximize their utility each period through the optimal investment allocation across countries. Assuming an exponential utility function , and given that consumption is equal to portfolio return R*t times W*, developed country investors’ optimization problem is:
Where and . ~ is the rate of return in developed country, the expected return on emerging economy is
(5)
and . [4] is the return from firms’ productions from period t to t+1. A tax imposed on foreign investors captures the various barriers or costs to investment faced by investors, we assume that it is deterministic which means the foreign invests know when the country open and the degree of openness. Liberalization is simply modeled by a decrease in . is the total investment in emerging country.
Here we consider the case where the correlation of returns across both countries is zero and . Solve for the investment share in emerging economy is[5]
(6)
Where .
Emerging Country
After liberalization, emerging country allows international capital inflow and under the shock of foreign capital. The economy is not deterministic. The budget constraint becomes
(2’)
xt is the domestic investment, at is the net foreign asset. Noted we assumed that the emerging economy agent only invests domestically, a ≥ 0 and the domestic capital market affect net foreign asset through the rate of return rt. The law of net foreign asset motion, which is decided by the foreign investors
(7)
The law of capital motion becomes
(3’)
Where is determined by the foreign investors, the domestic investor doesn’t know the decision formula, which means that domestic investors make decisions only based on the consumption optimization and does not take account to the foreign investment, so that when they differentiate equation (3’), just treat as given. Recalls equation (5) , assume the foreign investors look at the rental price for capital as the domestic return for production. To simplify our model, assuming that this is a one-time liberalization, the tax rate cut to zero immediate after liberalization. Now the return on emerging economy is endogenous. Incorporate equation (6) into (3’), the foreign investors need to solve this two equation to get the investment portfolio ratio in emerging economy. is endogenous.
(8)
The Bellman equation of this problem,
As noted before, the foreign capital inflow is determined by the foreign investor, so when we maximizing the domestic consumer’s utility, just treat as a constant term. The first order condition and envelope condition are,
(FOC)
(EC)
Incorporate equation (EC) and (FOC), we get
(8)
New Steady State
Endogenous rate of return on capital, I introduce a nonlinear form in capital motion function. Solve for steady state becomes more difficult. However, compare the Euler’s function in new steady state
(EC’)
and the Euler function under closed economy steady state, as long as a > 0, the new steady state YK ratio will be lower, and both output and capital stock increase.
Dynamic Problem
Defined the domestic real interest rate, and the pricing kernel Equation (8) is saying that . With the market data, we can reverse the time structure for the random variable logmt+1, and reveal the expected consumption ECt+1. However, I would like to do the simulation to track the economy. As the liberalization to the foreign capital gives a big shock to the domestic economy, use approximation for the economy is unrealistic. I assume that the economy is deterministic, so that equation (8) gives us the consumption-decision rule
(8’)
The timing of this model will be at the beginning of time 0, the emerging economy is closed to the foreign. It runs on steady state, with capital and net foreign asset a1=0; the output and pay out the rent to capital . At the beginning of time 1, it announces to open to foreign capital with the tax decreasing to 0. According to the consumption rule, domestic investment is determined; then the foreign investors decide its optimal portfolio shares by looking at the emerging country’s capital stock.
Figure 5 is a simulation curves of capital motion and optimal portfolio shares.
Figure 5 Simulation to the total capital stock and portfolio share
Initially, the economy is at the point K0; after capital liberalization, the capital stock jumps to point K1 with a positive (capital inflow). In each period, the capital stock Kt+1 and optimal portfolio share is determined by the intersection of two curves (the upward straight line with slope W*) and (the downward curve). The curve is always fixed but the is changing each period with a different intersection . From equation (EC’), in new equilibrium state, if there is positive foreign capital inflow, there will be more capital stock and higher output. However this equilibrium state is unsustainable, because under expansion, the curve will keep on moving up, lowering the capital marginal product and the speed of foreign capital inflow. Once foreign investors realize the marginal product has dropped to undesirable levels, and trigger the “sudden stop” in foreign capital, the economy will have a big contraction back to the initial levels. Thus foreign capital introduces volatility but not growth to the economy.
All the undesirable events are caused by the decreasing rates of return on capital. Without improvement in productivity, the economy has problems to accommodate the flood of capital inflow. It is common to find that before the crisis, a price hike in real estate indicates bubbles in the economy. If the capital inflow promotes the productivity in the emerging economy, it will amplify the volatility of output but greatly reduce the decreasing speed of the rate of return on capital. Assume the spillover effect
Thus in new steady state, it is possible that the capital stock K and YKratio increase together, or the economy expands with the injection of foreign capital.
The new dynamics of capital stock and portfolio share becomes
As long as higher than a certain number, the curve is an increasing function of capital. Using =0.7, x1=0.5,x2=66.67=1/3 and =0.106, I got the following simulation (figure 6). Now the curve becomes upward slope, the increase of foreign capital did not lower the marginal product of capital. It is possible that the foreign capital support the host country’s economic growth. Again, the economy stars at point K0, after liberalization, the foreign capital jumps to point K1 with an overshooting; after self-adjustment, the economy reaches the new steady state with higher capital stock and output level comparing to the closed state.