Estimating the Threshold Levels and the Delay of Threshold Variables. 48

Before employing the MVTEC model, it is necessary to test the existence of the non-linear relationship in terms of the threshold variables (i.e., oil price, coal price, and natural gas price) during these two periods. The C(d) statistic based on the arranged regression (Tsay, 1998) can be used to test the linear relation. Table 4.5 displays the tests results.

Table 4.5 Results of Threshold Effect Tests

Threshold variable Delay (d) C(d) p-value Threshold value (c^*) Regime one Regime two

Oil 1 354.36 (0.04) 2.48% 326 68

Coal 1 180.52 (0.00) 0.22% 223 128

Natural Gas 1 397.87 (0.00) 0.87% 239 41

Note: Regime one refers to Zt-d≤c and Regime two Zt-d≥c. c^* is the optimal threshold value determined by the location of the minimum log det|∑|, and ∑ is the variance–covariance matrix for the corresponding multivariate VECM models.

Based on Table 4.5, we can reject the null hypothesis of the linear model using oil price as a threshold variable. It means that the result favors the MVTEC model. By the same token, we find a similar result when coal price or natural gas price is used as a threshold variable. There is a non-linear relationship between energy price and industrial production. The delay (d) of the threshold variable reflects the speed of response based on the economic impact of a positive energy price change and its shock.

Results about the length of delay are similar to Huang’s (2008) result: when a country has a higher energy import ratio, it will have a shorter delay in terms of its economic response from the positive impact of an energy price change. In this study the impact of energy price changes (i.e., oil price, coal price, and natural gas price) on production is rapid (one month).

The threshold value (c) reflects the critical level of the impact. In order to estimate the optimal threshold value c^*, we search procedure targets at the middle 60%

to 80% of the arranged dataset. From the estimated results of threshold effect tests in Table 4.5, the optimal threshold levels c are as follows: the highest level is oil price at 2.48%, the next highest is natural gas price at 0.87%, and the lowest level is coal price at 0.22%. When the oil price change (1 month before) exceeds 2.48%, its impact is significantly different from that if the price change is less than 2.48%. Similarly, when the coal price change (1 month before) exceeds 0.22%, its impact is significantly different from that if the price change is less than 0.22%. The impact on industrial production is different from when the natural gas price change (1 month before) exceeds 0.87%.

4.3.2 Results of the Variance Decomposition in the MVTEC Model

In order to depict the response of macroeconomic activities in regime one (energy price changes are less than or equal to c^*) and regime two (energy price changes exceed

c^*), we employ the VDC and the IRF analyses for each regime. Table 4.6 reports proportions of impacts emanating from an oil price change in terms of VDC. When an oil price change is below the threshold value c^*, an oil price change explains about 7.12% of industrial production change (greater than 1.98% explained by an interest rate change). Similarly, the proportions of the explanatory power of oil price and interest rate on unemployment change are roughly the same: 2.09% vs. 2.06%. On the other hand, when an oil price change exceeds the threshold value c^*, it explains much more on industrial production than does the interest rate (17.22% vs. 4.39%). However, oil price changes explain less significantly on stock prices (7.45% vs. 14.85%) and unemployment (6.87% vs. 14.11%) than the interest rate.

Table 4.6 Variance Decomposition Results Using Oil Price Changes as Threshold Variable (12 Periods Forward)

Shock sources

ε^y ε^ep ε^sp ε^r ε^un ε^ex ε^im

Panel A. Regime one

y 79.60 7.12 3.53 1.98 3.38 1.62 2.77 ep 2.16 89.71 2.62 0.65 2.05 1.23 1.59 sp 0.81 1.01 90.38 1.38 3.57 0.96 1.90 r 2.97 1.09 4.63 79.64 4.78 4.67 2.21 un 13.62 2.09 2.50 2.06 73.74 0.89 5.09 ex 34.81 2.98 2.08 0.39 1.00 57.53 1.22 im 28.36 4.12 3.68 0.68 3.63 22.72 36.79 Panel B. Regime two

y 51.86 17.22 7.79 4.39 3.61 8.14 6.99 ep 4.85 30.93 4.63 17.89 4.88 18.28 18.53 sp 18.11 7.45 34.99 14.85 10.98 4.74 8.88 r 9.91 17.84 8.01 33.91 6.59 9.55 14.18 un 13.12 6.87 10.17 14.11 37.27 9.83 8.64 ex 34.28 15.60 12.75 6.50 10.09 16.67 4.13 im 36.28 21.16 13.75 6.68 5.51 7.70 8.93 Note: Regime one pertains to Zt-d≤c^* while regime two pertains to Zt-d>c^*.

Given these results, the oil price change in Taiwan significantly explains industrial production. In the one-regime model, an oil price change has rather limited explanatory power on industrial production in comparison to the real interest rate (1.94% vs. 1.95%). In the two-regime model, however, an oil price change significantly explains macroeconomic activities especially for Taiwan’s industrial production. This phenomenon perhaps is due to the fact that the explanatory power of oil price changes is less than that of the interest rate being attributed to the use of the one-regime model.

Table 4.7 illustrates the impact of coal price changes on macroeconomic variables in terms of the VDC. When a coal price change is below the threshold value, it explains a significant portion of change in industrial production (4.11%), unemployment Table 4.7 Variance Decomposition Results Using Coal Price Changes as Threshold

Variable (12 Periods Forward)

Shock sources

ε^y ε^ep ε^sp ε^r ε^un ε^ex ε^im

Panel A. Regime one

y 87.78 4.11 3.53 0.26 0.69 2.30 1.32 ep 0.98 91.53 0.14 0.87 1.23 4.87 0.38 sp 0.37 0.53 93.26 0.96 2.22 1.61 1.05 r 2.85 0.93 0.65 91.45 3.18 0.42 0.52 un 11.45 3.19 0.53 0.40 81.65 2.30 0.50 ex 37.91 4.29 0.83 0.37 0.69 54.55 1.36 im 34.42 5.82 0.79 1.04 1.93 17.74 38.26 Panel B. Regime two

y 82.71 4.20 1.46 3.44 1.03 3.85 3.32 ep 2.66 83.08 2.30 1.11 7.34 1.66 1.86 sp 4.28 3.88 77.08 2.23 4.49 2.90 5.15 r 3.55 4.60 5.78 75.03 3.27 3.93 3.84 un 6.50 2.75 4.44 4.01 76.10 4.64 1.56 ex 31.57 8.02 6.20 7.42 3.64 36.98 6.18 im 23.01 10.22 8.80 3.60 2.81 21.76 29.80 Note: Regime one pertains to Zt-d≤c^* while regime two pertains to Zt-d>c^*.

(3.19%), exports (4.29%), and imports (5.82%). When a coal price change exceeds the threshold value c^* (regime two), the coal price change explains about 3.88% of the stock price change (greater than 2.23% explained by the interest rate change). Within the linear model, a coal price change exerts less significant impact than an interest rate change (0.22% vs. 0.91%). This is strikingly different from the results of the two -regime model, which displays significant responses from stock markets when the coal price change is modest or more. Furthermore, a coal price change has higher explanatory power on unemployment in comparison to the one-regime model. It also explains a significant portion of export change (8.02%) and import change (10.22%).

Table 4.8 presents the VDC results from natural gas price changes. As can be seen from the table (regime one in which a natural gas price change is below the threshold value c^*), a natural gas price change has significant explanatory power. It indicates that a natural gas price change (1) explains more on industrial production change than does an interest rate change (6.49% vs. 1.42%); (2) accounts more on stock price change than does an interest rate change (3.89% vs. 1.91%); (3) accounts more on unemployment in comparison to the interest rate (6.06% vs. 3.17%) and (4) explains more on exports (4.26%) and imports (6.20%) than other macroeconomic variables. In regime two, it indicates that a natural gas price change can explain more on unemployment than does an interest rate change (25.15% vs. 4.68%). Furthermore, a natural gas price change has significant explanatory power on exports (11.42% vs.

4.26%) and imports (18.16% vs. 6.20%) in comparison to regime one. In particular, the explanatory power of a natural gas price change is greater than the interest rate under two regimes. This result is consistent with findings by Park and Ratti (2008) in that the contributions from energy price shocks are greater than that of interest rates on the stock market.

The results of variance decomposition of energy price change are summarized: (1) an oil price change has significant explanatory power on industrial production in regime one. (2) When an oil price change exceeds the threshold value (regime two), an oil price change not only reports maximum proportions of industrial production, but the explanatory power rises in comparison to regime one. (3) A coal price change has significant explanatory power on industrial production in regime one. (4) A coal price change has higher explanatory power on stock price than the interest rate in regime one.

(5) A natural gas price change has significant explanatory power on industrial production in regime one. (6) A natural gas price change has higher explanatory power on stock prices than the interest rate in regime one.

Table 4.8 Variance Decomposition Results Using Natural Gas Price Change as Threshold Variable (12 Periods Forward)

Shock sources

ε^y ε^ep ε^sp ε^r ε^un ε^ex ε^im

Panel A. Regime one

y 76.64 6.49 4.71 1.42 3.54 4.95 2.26 ep 2.58 84.70 0.92 1.76 2.15 2.16 5.73 sp 0.47 3.89 80.22 1.91 3.37 8.11 2.03 r 1.27 1.12 2.79 85.42 5.21 2.66 1.52 un 11.82 6.06 2.34 3.17 63.82 7.36 5.43 ex 42.72 4.26 2.74 1.67 1.89 43.08 3.64 im 35.74 6.20 1.90 5.15 1.78 21.40 27.83 Panel B. Regime two

y 73.87 4.82 3.56 13.18 1.65 0.65 2.27 ep 10.96 52.03 9.11 8.82 3.14 9.50 6.44 sp 4.37 5.37 77.60 7.09 1.86 3.01 0.70 r 14.19 8.84 18.19 47.99 7.60 2.17 1.02 un 6.51 25.15 16.96 4.68 37.65 2.48 6.57 ex 23.81 11.42 25.43 3.49 2.35 31.38 2.12 im 30.26 18.16 24.66 5.25 1.07 10.60 9.99 Note: Regime one pertains to Zt-d≤c^* while regime two pertains to Zt-d>c^*.