學術發表 ---(2002 NTU 財務金融國際研討會 )

(( 國立台灣大學財務金融系 ))Regime-Switching Analysis for the Impacts of the

Exchange Rate Uncertainty on the Taiwan’s Corporate Values

Chien-Chung Nieh 聶建中淡江大學財務金融系副教授

Regime-Switching Analysis for the Impacts of the Exchange Rate Uncertainty on the Taiwan’s Corporate Values

Key Words: Exchange rate uncertainty, Corporate values, GARCH, Markov switching model

I. Introduction II. Data III. GARCH modeling for ERU IV. The OLS and the CUSUM V. Markov Switching VI. Concluding remark Appendix: theoretical model Based on the controversies between more opportunities to achieve the corporate

goals when exchange rates fluctuate and the harmful experiences of the large movements of exchange rates, this paper attempts to investigate the impacts of the ERU on the CVs for the industries concerned in Taiwan. A regime-switching regression is applied. To allow for variance to be drawn from different states, this paper extends the first-moment switching model to a second-moment one.

Contribution

Extends the first-moment switching model to a second-moment one.

A theoretical model which shows the relationship between the ERU and the CVs is derived.

A two-state first-order MS model is appropriate to describe the relationship between the ERU and the CVs.

動機Three drastic changes in the NTD against the USD since

1979.

(1)The regime of managed floating exchange rates was adopted by the government of Taiwan in February of 1979. (2) After the "Plaza Accord", the NTD followed the Japanese yen to appreciate within six months from June to November, 1986. (3) The drastic depreciation a few months after the Asian financial crisis happened in July 1997.

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28

32

36

40

44

75 80 85 90 95 00

TWEXR

Figure-1 the exchange rate movement of NTD/USD

文獻回顧 Negative relationship between the ERU and the exporting

flows: Arize (1995), Chowdhury (1993), Hassan (1998), Smith (1999), Arize, Osang and Slottje (2000), and Nieh (2002)

Negative relationship between the ERU and the trading volume: Gupta (1980), Rana (1981), Coes (1981), Cushman (1983), Akhtar and Hilton (1984), Kenen and Rodrik (1986), Chowdhury (1993), Arize (1997), Broll, Wong and Zilcha (1999), and Arize, Osang and Slottje (2000).

Positive relationship between the ERU and the trading volume: Gotur (1985), De Grauwe (1988), Per"ee and Steinherr (1989), Franke (1991), Viaene and Vries (1992), and Broll and Eckwert (1999)

文獻回顧 (Markov-switching (MS) ) Hamilton (1988): two-state first-order Markov-switching (MS)

model was first citedand. (The probability switching mechanism by Goldfelt and

Quandts (1973) for the heteroscedasticity.) Shen (1994) tests the hypothesis the efficiency of the Taiwan-

US forward exchange market Ho (2000a) and Ho (2000b) tests the hypothesis for the

international capital mobility and the Phillips curve trade-off. Huang (2000) employ the same technique to examine the

Sharpe-Lintner CAPM. Engel and Hamilton (1990), Garcia and Perron (1993), Engle

(1994), Kim and Yoo (1995), and Schaller and van Norden (1997): The applications of the MS mechanism.

各產業經濟變數之代號化學 (Y1) ；電子 (Y2) ；食品 (Y3) ；玻璃 (Y4) ；機電

(Y5) ；造紙 (Y6) ；塑膠 (Y7) ；橡膠 (Y8) ；鋼鐵(Y9) ；紡織 (Y10) ；

出口比例在 50% 以上之產業 (Y11) ； 出口比例在 30% 以下之產業 (Y12) ； 出口比例在 30%~50% 之產業 (Y13) ；匯率不確定性 ( 匯率波動 ) ： RX樣本頻率 ：月資料， 資料期間：七十七年一月至八十九年二月

理論與實證理論模型： .Cobb-

Douglas 型函數

推導得匯率之不確定性與企業盈餘之關係式：

GARCH effectThe OLSCUSUM and

CUSUM of squaresMarkov Switching

22

12

11

2

22 )(

)()1())((),(

r

bbbr

bK

KVttt

tt

tt

1),( tttttt KLAKLFQ

GARCH modeling

A GARCH(1,1) modeling

ht , the hetroscedastic variance, implies the EXU(2) in this paper . 。

Pozo(1992), Arize(1995) and Arize(1997)

ttt ee 110

112110 ttt hh

Table-1 )1,1(GARCH modeling for the exchange rate volatilityLM – test

F-statistic 8.8105 P-value 0.00352TR 8.3961 P-value 0.0038

Variance equation： 112110 ttt hh

Coefficient Estimator S.D. Z-statistic P-value0 0.0205 0.0081 2.5444 0.01091 0.6313 0.1422 4.4385 0.00011 0.3545 0.1069 3.3138 0.0009

GARCH effect

0

1

2

3

4

5

6

88 89 90 91 92 93 94 95 96 97 98 99

RX

F ig u re -1 )1,1(GARCH m o d e lin g fo r th e e x c h a n g e ra te v o la tility

The OLS

Table-2 OLS estimationY1Y2Y3Y4Y5Y6Y7Y8Y9Y10Y11Y12Y13

0.214*0.488*0.351*0.343*0.473*0.546*0.951*0.206*1.011*0.350*0.439*0.513*0.600*0.062*0.283*-0.030*0.0020.0070.0270.057*0.028*0.0110.0230.212*0.057*0.058*2R0.13050.13820.03850.00010.00520.01140.04720.09860.00010.01740.13790.06470.0820

note：* indicates significant at the 5% critical value

The goodness-of-fit type testsBrown, Durbin, and Evans (1975)

CUSUM (cumulative sum of residuals) and CUSUM of squares tests:

m

kttm TkmwW

1

,...,1ˆ1

T

ktt

m

ktt

m Tkmwss

wS

1

2221

2

,...,1,

Fifure-2.1 Plot of Y1 against RX Fifure-2.2 Plot of Y2 against RX

-50

0

50

100

150

200

89 90 91 92 93 94 95 96 97 98 99

CUSUM 5% Significance

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

89 90 91 92 93 94 95 96 97 98 99

CUSUM of Squares5% Significance

-50

0

50

100

150

89 90 91 92 93 94 95 96 97 98 99

CUSUM 5% Significance

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

89 90 91 92 93 94 95 96 97 98 99

CUSUM of Squares5% Significance

Fifure-2.3 Plot of Y3 against RX Fifure-2.4 Plot of Y4 against RX

-60

-40

-20

0

20

40

89 90 91 92 93 94 95 96 97 98 99

CUSUM 5% Significance

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

89 90 91 92 93 94 95 96 97 98 99

CUSUM of Squares5% Significance

-80

-60

-40

-20

0

20

40

89 90 91 92 93 94 95 96 97 98 99

CUSUM 5% Significance

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

89 90 91 92 93 94 95 96 97 98 99

CUSUM of Squares5% Significance

Markov switching (Stuctural break)

the OLS model

the MS setting

ittisisit VRtt

),0(~ 2tisit N

ttt VR

21

2

1

ti

tiiS sif

sift

21

2

1

ti

tiiS sif

sift

21

2

1

ti

tiiS sif

sift

122211211 pppp , where )/Pr( 1 isjsp ttij

Estimation

T

tttttjtt XYspxxy

1

0);|()ˆ'( , j = 1,2 (10)

T

XYspxyT

t jtttjt

1

2

12

);|()ˆ'(ˆ

(11)

T

tTTt

T

tTTtt

ij

XYisp

XYisjspp

21

21

);|(

);|,(

Table 3. Maximum likelihood estimates for state-transition estimation of Markov switchingParameters

1

2

1

2

1

2 p11 p22

RX to Y1 0.173 0.292(39.50)* (61.40)*

-0.029 0.021(-1.09) (3.64)*

0.029 0.031(11.92)* (10.44)*

0.993 0.992(5.76)* (5.35)*

RX to Y2 0.256 0.717(62.39)* (22.78) *

0.034 0.151(1.61) (3.41)*

0.023 0.253(9.06)* (12.62)*

0.992 0.993(5.28)* (5.81)*

RX to Y3 0.246 0.365(41.69) * (58.44) *

0.014 0.039(2.93)* (1.16)

0.024 0.046(6.90)* (12.33)*

0.872 0.963(3.20)* (6.39)*

RX to Y4 0.299 0.425(60.78)* (43.55)*

0.019 0.027(2.46)* (0.52)

0.044 0.053(13.85)* (9.33)*

0.994 0.991(6.07)* (4.75)*

RX to Y5 0.445 0.503(105.80)* (77.42)*

0.015 0.053(3.30)* (1.88)

0.028 0.030(11.92)* (9.84)*

0.978 0.970(6.40) * (5.39)*

RX to Y6 0.482 0.643(53.72)* (55.83)*

-0.057 -0.018(-1.09) (-1.31)

0.057 0.076(11.88)* (11.21)*

0.979 0.977(6.42)* (6.20)*

RX to Y7 1.038 0.842(120.3)* (70.17)*

0.015 0.156(1.47) (2.30)***

0.056 0.064(11.04)* (10.65)*

0.963 0.945(6.61) (6.21)*

RX to Y8 0.035 0.245(66.09)* (105.5)*

0.023 0.013(1.27) (4.19)*

0.017 0.015(10.08)* (8.65)*

0.990 0.988(5.93)* (5.51)*

RX to Y9 0.796 1.523(86.76)* (22.23)*

0.08184 0.3214(5.63)* (1.00)

0.084 0.3201(14.12)* (8.31)*

0.994 6.234(0.99) (4.49)*

RX to Y10 0.392 0.327(24.22)* (51.79)*

-0.0004 0.03565(-0.02) (0.77)

0.097 0.036(9.10)* (10.77)*

0.981 0.9858(2.47)** (3.12)*

RX to Y11 0.290 0.651(61.76)* (25.63)*

0.0141 0.09276(0.52) (2.83)*

0.030 0.184(11.26)* (11.53)*

0.993 0.9927(5.58)* (5.50)*

RX to Y12 0.577 0.420(103.0)* (22.66)*

0.017 0.213(2.30)*** (1.36)

0.042 0.078(12.25)* (10.47)*

0.991 0.9770(6.03) * (5.72)*

RX to Y13 0.797 1.527(83.06)* (23.03)*

0.088 0.318(4.84)* (0.96)

0.087 0.316(14.16)* (8.42)*

0.994 0.9898(6.24)* (4.55)*

Note: 1 The numbers in the parentheses are the values of t-statistic.2. *, ** and *** denote significant at 1%, 5% and 10% level, respectively.

3. The 1%, 5%, and 10% significant level of t-statistics are 2.61, 2.35, and 1.98, respectively.

Figure-3.1 RX and Y1 Figure-3.2 RX and Y2 Figure-3.3 RX and Y3 Figure-3.4 RX and Y4

0.0

0.2

0.4

0.6

0.8

1.0

888990919293949596979899

P1_Y1 0.0

0.2

0.4

0.6

0.8

1.0

888990919293949596979899

P1_Y2 0.0

0.2

0.4

0.6

0.8

1.0

888990919293949596979899

P1_Y3 0.0

0.2

0.4

0.6

0.8

1.0

888990919293949596979899

P1_Y4

Figure-3..5 RX and Y5 Figure-3.6 RX and Y6 Figure-3.7 RX and Y7 Figure-3.8 RX and Y8

0.0

0.2

0.4

0.6

0.8

1.0

888990919293949596979899

P1_Y5 0.0

0.2

0.4

0.6

0.8

1.0

888990919293949596979899

P1_Y6 0.0

0.2

0.4

0.6

0.8

1.0

888990919293949596979899

P1_Y7 0.0

0.2

0.4

0.6

0.8

1.0

888990919293949596979899

P1_Y8

Specification tests

)1(:;:;:;: 22114021

3021

2021

10 ppHHHH

)1(~)ˆ,ˆ(2)ˆ()ˆ(

)ˆˆ( 2

2121

221

CovVarVar

)1(~)ˆ,ˆ(2)ˆ()ˆ(

)ˆˆ( 2

2121

221

CovVarVar

)1(~)ˆ,ˆ(2)ˆ()ˆ(

)ˆˆ( 2

2121

221

CovVarVar

)1(~)ˆ,ˆ(2)ˆ()ˆ(

)]ˆ1(ˆ[ 2

22112211

22211

ppCovpVarpVarpp

Wald test statistics

Table 4. Specification tests

Null hypothesis :10H 1 = 2 :2

0H 1 = 2 :30H 1 = 2 :4

0H p11 = p22

RX to Y1 368.3* 3.391*** 0.3387 3.729***

RX to Y2 214.6* 5.707** 127.9* 3.717***

RX to Y3 233.5* 0.5437 18.21* 5.255**

RX to Y4 214.6* 5.707** 127.9* 3.717***

RX to Y5 132.9* 0.02467 1.833 3.507***

RX to Y6 135.5* 0.5179 5.539** 5.307**

RX to Y7 227.3* 7.341* 1.059 6.531**

RX to Y8 347.9* 0.3069 0.603 4.022**

RX to Y9 111.5* 0.5566 36.43* 3.308***

RX to Y10 12.79* 0.4701 26.59* 4.126**

RX to Y11 197.4* 3.466*** 3.740*** 3.740***

RX to Y12 70.03* 1.560 19.37* 4.152**

RX to Y13 119.6* 0.484 36.06* 3.354***

Note: 1 The number is the Wald statistic2. *, ** and *** denotes significant at 1%, 5% and 10% level, respectively.

3. The 1%, 5%, and 10% significant level of 2(1) are 6.63, 3.84, and 2.72,respectively.

ConclusionOLS approach find that the ERU has the

significantly positive impacts on the values among the industries of chemistry, electron, plastic and rubber, but has the negative impacts on that of food industry.

The structural unstable phenomena from the CUSUM and CUSUM of squares tests reduce the explaining power of the ERU affecting the CVs when the OLS regression is applied.

Using GARCH(1, 1) modeling to extract the value of exchange rate volatility is appropriate.

ConclusionTwo different regimes of a strong-impact and a weak-

impact are identified by the values of impact coefficients. the influence level of the ERU on the CVs is dominated

by the weak impact regime: industries of chemistry, food, electricity, plastic, and rubber .

the influence level of the ERU on the CVs is dominated by the strong impact regime: industries of electron, glass, and steel.

the effects of the ERU on the CVs are all dominated by the strong impact regime for all three export ratio.

the industries of paper and textile show that the impact level is undetermined.

ConclusionThe Wald statistics for the null of equality are mixed. It is hard to conclude that data are drawn from two

different states since the null of no strong-weak impact switching can only be rejected for three industry categories of electron, glass, and plastic. This implies that if the MS model is appropriate, the ERU may not be the major factor but other factors, which could switch the CVs of Taiwan’s industries.

The data of eight industries are shown to fit a two-state model when the volatility is stimulated.

ConclusionTesting for the transition probability, only six

out of thirteen industries are rejected at 5% significance level. However, when based on the 10% level, we are able to reject the null of "no regime change," and then conclude that a two-state first-order MS model is appropriate for the "goodness of fit" analysis.