Volatility - New York University Stern School of Businesspages.stern.nyu.edu/~dbackus/3386/2004/Paper drafts... · Web viewUnfortunately, in East Asian countries, the volatility appears

Draft Term Paper for PhD course International Finance and MacroeconomicsProfessor David BackusNew York University

Foreign Capital in Emerging Economies

Junhua Qin

Draft Paper

Introduction

Since the1990s, Eastern Asian countries have gradually opened capital accounts1. 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 data2, 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

1 See the degree of openness discussed by Edision and Warnock (2003)2 The data I discussed here is dominated in local currency, excluded the exchange rate volatility.3 He provided more supportive evidence in his article.

- 1 -


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.

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’

- 2 -


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.

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)

- 3 -


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

- 4 -


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 is5

(6)

Where .

4 I used here because the investment decision is made at period t but get paid on period t+1.5 Please see Bacchetta and Wincoop (1998) for details

- 5 -


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)

- 6 -


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

- 7 -


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.

- 8 -


-2 0 2 4 6 8 10 120

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

lambda

Kt+

1Dynamic of K and lambda

K0

K1 KS

Curve K

Curve lambda

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

- 9 -


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

- 10 -


reaches the new steady state with higher capital stock and output level comparing to the

closed state.

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 10

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

lambda

Kt+

1

Dynamic of K and lambda with productivity improvement

K0

KS K1

Curve K

Curve lambda

Figure 6 Simulation to the total capital stock and portfolio share with productivity

improvement

Numerical simulation

Use the numerical calibration in Bacchetta and Wincoop’s (1998) paper. I set the model

parameters as follows. First is the average standard deviation on a broad measure of

capital return for the four industrialized countries in Baxter and Jermann (1996). I set

. W*=4 and the initial value of K=1, this reflects the fact that per capita stock in

industrialized countries is on average about four times that of emerging markets.6 is the

risk-aversion. The adjustment cost parameter b is set at 0.05. The average consumption ratio

6 This is based on the 1992 capital stock data

- 11 -


is lower in the emerging market, so I set it at 0.7. The depreciation rate and discounter is

calibrated with the steady state variables. Further more, to ensure the initial portfolio share

, I set at a very high level

Figure 7 and 8 shows the dynamics of the variables. These two curves, during the inflow

of foreign capital, there is no big turmoil in capital and output, that’s because the self-

adjustment mechanism of the foreign capital. The capital price gradually decreased but still on

a normal track. However, the volatility increased as the rental price of emerging economy

cannot attract foreign capital and they keep on moving out. To sustain output growth, the

domestic investment begins to rise, suppress the consumption; after foreign capital completely

moves out, the domestic investment increases sharply, causing big volatility in capital rental

prices and consumption. However, this is unsustainable, the GDP growth stops at a tough

way.

Figure 9 and 10 shows the dynamics of the variables with productivity spillover effect.

We can see a bigger cycles but the economy finally stabilized at a higher output level.

Conclusion

In this paper, I argued that foreign capital inflow without promoting the productivity to

the emerging economy would cause big volatility to the economy rather than significant

output growth. That’s because foreign investors are “return chasers”, the expected rate of

return affects their investment decisions so that there is a self-management ‘move-out’

mechanism that’s not controlled by an agent of an emerging economy. Under the

decreasing rate of return on capital pushing the expanding economy off the steady state

further and further and lower the attractiveness of the host country. As the foreign capital

begins to flow out, the GDP growth becomes unsustainable, a sudden stop in capital

formation will occur. This will cause the marginal product of capital to rise again, and a

new cycle will begin. I suggest that increasing productivity is the best way to hold

foreign capital and maintain long-term growth.

- 12 -


Reference:

Bacchetta, Philippe and Wincoop, Eric van, (1998), “Capital Flows to Emerging Markets:

Liberalization, Overshooting and Volatility,” NBER Working Paper N0.6530

Bekaert, Geert and Campbell R. Harvey (2003), “Emerging markets finance,” Journal of

Empirical Finance 10 (2003) 3-55

Edison, Hali J. and Warnock, Francis E. (2003), “A simple measure of the intensity of capital

controls,” Journal of Empirical Finance 10 (2003) 81-103

Mendoza, Enrique.G, (2001), “Credit, Prices, and Crashes: Business Cycles with a Sudden

Stop,” NBER Working Paper N0.8338

Neumeyer, Pablo A. and Perri, Fabrizio, (2001), “Business Cycles in Emerging Economies:

The Role of Interest Rates,” NBER Working Paper N0.w10387

Stiglitz, Joseph E. (2000), “Capital Market Liberalization, Economic Growth, and Instability,”

World Development Vol.28, No.6, pp. 1075-1086, 2000

Data source:

DSI data services and information: IMF statistics

- 13 -


Table 1 Volatility of East Asia economyA. Level data

Std.Dev Lny Lnc ykratioCountry 1974-1989 1990-2003 1974-1989 1990-2003 1974-1989 1990-2003Indonesia 0.288 0.151 0.359 0.272 0.451 0.475Korea 0.354 0.233 0.352 0.276 0.079 0.976Malaysia 0.300 0.247 0.283 0.209 0.411 0.440Thailand 0.334 0.183 0.244 0.165 0.544 0.675US 0.146 0.131 0.124 0.122 0.131 0.238

B. Growth Data

Year by year growth

Y C KCountry 1974-1989 1990-2003 1974-1989 1990-2003 1974-1989 1990-2003Indonesia Mean 0.058557 0.040347 0.064909 0.066222 0.080995 0.022444

Std. Dev. 0.023875 0.05569 0.059176 0.054425 0.102298 0.144374Korea Mean 0.075712 0.056723 0.075239 0.066945 0.085344 -0.01225

Std. Dev. 0.03204 0.041749 0.036606 0.073616 0.100763 0.238661Malaysia Mean 0.060803 0.061747 0.057374 0.053968 0.022404 0.046587

Std. Dev. 0.03411 0.051975 0.062656 0.064753 0.143029 0.211652Thailand Mean 0.071923 0.048675 0.053552 0.045405 0.101031 0.023464

Std. Dev. 0.027236 0.055531 0.031092 0.054072 0.072926 0.195443C. Growth Data with 1997 and 1998 omitted

Year by year growth

Y C KCountry 1974-1989 1990-2003 1974-1989 1990-2003 1974-1989 1990-2003Indonesia Mean 0.058557 0.054253 0.064909 0.066743 0.080995 0.054067

Std. Dev. 0.023875 0.020669 0.059176 0.056611 0.102298 0.086103Korea Mean 0.075712 0.066574 0.075239 0.08382 0.085344 0.045557

Std. Dev. 0.03204 0.020404 0.036606 0.039395 0.100763 0.104991Malaysia Mean 0.060803 0.072422 0.057374 0.06838 0.022404 0.095139

Std. Dev. 0.03411 0.034616 0.062656 0.037312 0.143029 0.113035Thailand Mean 0.071923 0.060967 0.053552 0.057393 0.101031 0.06755

Std. Dev. 0.027236 0.032389 0.031092 0.031431 0.072926 0.109105

Notes: Statistics are based on Hodrick-Prescott filtered annually data, from 1974 to 2003. Variables are: y, real

output; c, real consumption; ykratio, real output over real fixed capital formation. Lny and lnc refers to

logarithms of variables. All variables are dominated in local currencies.

- 14 -


Figure 1 Real GDP-Capital Ratio

3.0

3.5

4.0

4.5

5.0

86 88 90 92 94 96 98 00 02

GDP_INDO/RK_INDO

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

86 88 90 92 94 96 98 00 02

GDP_KOREA/RK_KOREA

2.0

2.5

3.0

3.5

4.0

4.5

5.0

86 88 90 92 94 96 98 00 02

GDP_MALA/RK_MALA

2.0

2.5

3.0

3.5

4.0

4.5

5.0

86 88 90 92 94 96 98 00 02

GDP_THAI/RK_THAI

- 15 -


Figure 2 Real fixed capital formation

100000

150000

200000

250000

300000

350000

400000

450000

86 88 90 92 94 96 98 00 02

RK_INDO

100000

150000

200000

250000

300000

350000

400000

450000

86 88 90 92 94 96 98 00 02

RK_KOREA

20000

40000

60000

80000

100000

120000

140000

86 88 90 92 94 96 98 00 02

RK_MALA

400

800

1200

1600

2000

2400

86 88 90 92 94 96 98 00 02

RK_THAI

- 16 -


Figure 3 Consumption-GDP ratios

.45

.50

.55

.60

.65

.70

.75

86 88 90 92 94 96 98 00 02

RC_INDO/GDP_INDO

.42

.44

.46

.48

.50

.52

.54

.56

86 88 90 92 94 96 98 00 02

RC_KOREA/GDP_KOREA

.40

.42

.44

.46

.48

.50

.52

86 88 90 92 94 96 98 00 02

RC_MALA/GDP_MALA

.55

.56

.57

.58

.59

.60

.61

.62

.63

.64

86 88 90 92 94 96 98 00 02

RC_THAI/GDP_THAI

- 17 -


Figure 4 The pattern of Net Financial Account

-12000

-8000

-4000

0

4000

8000

12000

86 88 90 92 94 96 98 00 02

Net Financial Account_INDO

-10000

-5000

0

5000

10000

15000

20000

25000

86 88 90 92 94 96 98 00 02

Net Financial Account_KOREA

-8000

-4000

0

4000

8000

12000

86 88 90 92 94 96 98 00 02

Net Financial Account_MALA

-20000

-10000

0

10000

20000

30000

86 88 90 92 94 96 98 00 02

Net Financial Account_THAI

- 18 -


Figure 7 Dynamic of marginal capital product and portfolio share

0 2 4 6 8 10 12 14 16 18 20-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

Time

r

Dynamic of r

rlambda

Figure 8 Dynamics of all variables

0 2 4 6 8 10 12 14 16 18 200

0.5

1

1.5

2

2.5

Time

OutputCapitalrforeign investment

- 19 -


Figure 9 Dynamic of marginal capital product and portfolio share with

productivity improvement

0 2 4 6 8 10 12 14 16 18 20-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

Time

r

Dynamic of r

rlambda

Figure 10 Dynamics of all variables with productivity improvement

0 2 4 6 8 10 12 14 16 18 200

0.5

1

1.5

2

2.5

Time

OutputCapitalforeign investmentConsumption

- 20 -

Documents

Volatility - New York University Stern School of Businesspages.stern.nyu.edu/~dbackus/3386/2004/Paper drafts... · Web viewUnfortunately, in East Asian countries, the volatility appears