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Regime-Switching Analysis for the Impacts of the Exchange Rate ...

Regime-Switching Analysis for the Impacts of the Exchange Rate ...

IV. The OLS and

IV. The OLS and the CUSUMIn order to investigate the influence of the exchange rate uncertainty on each ofthe corporate values, the ordinary least squares (OLS) method is commonly used:Rt = α + βV t+ εt(2)where R t denotes the corporate values, Vtis the exchange rate volatility, and2ε ~ iid N(0, σ ) is a white noise.tThe OLS estimation presents in Table 2 shows that the ERU possesses a positiveeffect on the values of chemistry, electron, plastic, rubber industries, and all threecategories of the export ratios while it has a negative impact on that of food industry.However, for the rest of the industries considered, the exchange rate volatility doesnot show any significant explaining power.To assert the findings of the OLS regression analysis, the "stability" of the dataset seems critical. To examine this, the goodness-of-fit type tests of cumulative sum ofresiduals (CUSUM) and CUSUM of squares based on recursive residuals areemployed for the unknown structural break (see Brown, Durbin, and Evans (1975)).The equations for CUSUM and CUSUM of squares models are represented as follows,respectively:WSmm==1σˆm∑t = k+1m2∑ wtt = k+12swtm = k + 1,..., TT∑22, s = w m = k + 1,..., T(4)t = k + 1twhere w t denotes the recursive residual and is the estimated standard deviation.If the path of W m (Equation (3)) or S m (Equation (4)) crosses the boundary for somem, say, 5% significance level, we reject the null hypothesis of no structural break,which is the case of being unstable.Though we can analyze the impacts of the ERU on the CVs of industriesinvestigated from Table 2, the relatively lower R 2 seems as if the OLS results are notreliable. This can be answered through the results of the CUSUM and CUSUM ofsquares tests, which are presented in Figure 3. These figures show that, from all theplots, the paths of recursive residuals cross the boundary. The null of "stability" isthus rejected significantly at the 5% critical level. This evidential existence ofstructural breaks in the model provides the possibility of the relatively lower R 2 .(3)5

V. Markov SwitchingEven though we can analyze the parameters of the OLS formula to describe the2impacts of the ERU on the CVs, the realized lower R infers that the predictedpower of the OLS model seems inadequate. The two observed structural changeswithin the sample period of the exchange rate volatility (see Figure 1) and the"non-stationary" property for most of the series might be the reason for reducing the2values of R . 6 This can also be explained by the rejection of the null of "stability"from the CUSUM and CUSUM of squares plots, as described above (see Figure 2).Moreover, the constant estimated parameters from the OLS are not appropriate indescribing the time-varying relationships between variables considered. To remedyfor these problems, we employ the basic idea of the Hamilton’s (1988, 1989) settingsof the two-state first-order MS model by maximum likelihood and further extend toconsider the time-varying error variance as suggested in Ho (2000a, 2000b) andHuang (2000). The OLS model, R = α + β + ε , is thus transferred to thetX tfollowing MS setting with MS mean and variance.tRit2= α + β V + ε , εit~ N (0, σ ist)(5)ististtitwhere R itdenotes the CVs for industry i at time t. Vtis the ERU at time t. stis theunobserved state variable presumed to follow a two-state Markov chain withβis tis the influence parameter in state st, whichtransition probability ( p ).ijmeasures the impacts of the ERU on the CVs for industry i.deviations in states , which measures the risks from the CVs of industry i.tσis tis the standardEquation (5) is assumed to follow a regime-switching framework byquasi-maximum likelihood as described in Hamilton (1989). The testable scheme isexpressed as follows.αiSt⎧αi= ⎨⎩αi12ififsstt= 1= 2βiSt⎧ βi= ⎨⎩βi12ififsstt= 1= 2σiSt⎧σi= ⎨⎩σi12ififsstt= 1= 2where the two states represent two regimes. The coefficients are ( αi1 , βi1,σi1) inregime 1 and ( αi2 , βi2,σi 2) in regime 2, respectively. The evolution of theunobservable state variable is assumed to follow a two-state first-order Markov chainsatisfying p + p = p + p 1 , where p = Pr( s = j / s− 1i)gives the11 12 21 22=ij t t=6 The non-stationary property is obtained from the ADF (Dickey and Fuller, 1981) unit-root test, whichis omitted in this paper, however, those will be available upon request.6

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