Research Motivation and Purpose

As energy prices play a critical role in influencing economic growth and economic activities, this phenomenon excites the research interest of this dissertation to address a linkage analysis of international energy prices and macroeconomic variables in Taiwan with linear and non-linear frameworks. Our research is motivated by the following reasons.

First, most studies (e.g., Burbidge and Harrison, 1984; Gisser and Goodwin, 1986; Mork, 1989; Hooker, 1996; Hamilton, 1996; Bernanke et al., 1997; Hamilton, 2003; Hamilton and Herrera, 2004) show that oil price shocks have a significantly negative impact on industrial production. However, little is known about the relationship between other energy prices and economy activities. For this reason, researchers may refocus their attention on the issue of natural gas price and coal price and their impact on economic activities.

Second, some of the related research (e.g., Mork, 1989; Mork et al., 1994;

Sadorsky, 1999; Papapetrou, 2001; Hu and Lin, 2008) already consider the asymmetrical relation in terms of the impact of an oil price change or its volatility on industrial production and stock returns. However, these studies arbitrarily use zero as a cutoff point and distinguish oil price changes into up (increase) and down

(decrease). This shows that the traditional approaches using predetermined value(s) as a demarcation point are rather unreasonable. They neglect the asymmetrical relation to accurately gauge varying degrees of impacts of energy price change (or volatility) on macroeconomy. To solve the neglected phenomenon, we implement rigorous econometric methods to refine the true relation.

Third, early studies about the macroeconomic consequences of energy price shocks focus on developed economies. Recent studies examine other research samples such as European countries (e.g., Mork et al, 1994; Papapetrou, 2001;

Cunado and Pérez de Gracia, 2003; Jiménez-Rodríguez, 2008; Bjørnland, 2009) and Asian countries (e.g., Chang and Wong, 2003; Cunado and Pérez de Gracia, 2005;

Huang et al., 2005). However, few studies investigate the relationship between energy price and macroeconomy for Taiwan. In contrast to these studies, this dissertation assesses the dynamic effect of energy price shocks on the macroeconomy in Taiwan.

Based on the aforementioned argument, the purposes of this dissertation contain two parts: The first purpose is to examine the effects of energy price shocks (including crude oil, natural gas and coal) on Taiwan’s industrial production from a linear perspective. Energy prices do not affect industrial production in isolation, but through the perceived effect on the macroeconomy. Therefore, we further analyze the dynamic relationship between energy price shocks and major macroeconomic variables (including stock price, interest rate, unemployment rate, exports and imports) by applying a vector error correction (VECM) model. Next, the variance decomposition (VDC) and the impulse response functions (IRF) are employed to capture the effects of energy price shocks on the macroeconomy. The results find how each variable responds to shocks by other variables of the system and explore the response of a variable to a shock immediately or with various lags.

The second purpose focuses on the impacts of an energy price change and the shock on the macroeconomy from an asymmetric perspective. According to Sadorsky (1999), the energy price adjustment may not immediately impact macroeconomic variables. An economic threshold for an energy price impact is the amount of price increase beyond which an economic impact on industrial production and stock prices is palpable. Huang et al. (2005) propose that a change in oil price explains the macroeconomic variables better than the shock caused by the oil price if an oil price change exceeds the threshold levels. Therefore, we apply the multivariate threshold error correction model by Tsay (1998) to analyze the relevant data. By separating energy price changes into decrease (down) and increase (up), the energy price changes as the threshold variable can analyze different impacts of energy price changes on industrial production. In particular, we assess the impact of energy price fluctuations on the Taiwan economy. The impulse response and the variance decomposition analysis now follow.

2 Literature Review

Since the 1970s many studies have examined the relationship between energy prices and the macroeconomy especially for oil price shocks. However, there is an inconsistent conclusion in the literature with different estimation procedures and data.

According to the different energy prices used by researchers, previous studies can be divided into three streams of research: the impact of oil price on GDP, the impact of oil price on other macroeconomic variables, and the natural gas and coal price effect.

Hamilton (1983) using Granger causality examines the impact of oil price shocks on the United States economy, indicating that oil price increases partly account for every United States recession. Many researchers extend and reinforce Hamilton’s basic findings using different estimation procedures on new data (e.g., Burbidge and

Harrison, 1984; Gisser and Goodwin, 1986; Mork, 1989; Hooker, 1996; Hamilton, 1996; Bernanke et al., 1997; Hamilton, 2003; Hamilton and Herrera, 2004). These studies conclude that there is a significant negative correlation between increases in oil prices and the subsequent recessions in the United States, but that oil price changes have different impacts on economies over time.

By separating oil price changes into negative and positive, Mork (1989) finds that there is an asymmetrical relationship between oil price and real output. When the oil price is increasing, the increase in the cost of production and the decrease in the cost of resource allocation often offset each other. Mory (1993) follows Mork’s (1989) measures and presents that positive oil price shocks Granger-cause the macroeconomic variables. Mork et al. (1994) again confirm that oil price shock induced inflation reduces real balances for seven industrialized countries. Lee et al.

(1995) find that an oil shock in a price stable environment is more likely to have greater effects on GDP growth than those occurring in a price volatile environment.

Jiménez-Rodríguez and Sánchez (2005) find that oil price increase has a larger impact on GDP growth than oil price declines.

In addition to exploring the relationship between oil price shocks and GDP, some economists have emphasized the relationship between oil price shocks and other macroeconomic variables. The first part is related to the macroeconomic level.

Several models (e.g., Rasche and Tatom, 1981; Bruno and Sachs, 1982, Hamilton, 1983) and diverse episodes for oil price shocks (e.g., Davis, 1986; Carruth et al., 1998;

Ferderer, 1996) present that an oil shock is one of the important influences on the macroeconomy. The directions for the causal relationship between oil price and macroeconomy can be concluded in four parts. First, oil price changes significantly impact economic activity (e.g., Papapetrou, 2001; Ewing et al., 2006; Jiménez-Rodrí guez, 2008; Farzanegan and Markwardt, 2009). Second, there is an asymmetric

correlation between oil price and the macroeconomy (e.g., Loungani, 1986; Mork, 1989; Lee et al., 1995; Hamilton, 2003; Cunado and Pérez de Gracia, 2003; Cunado and Pérez de Gracia, 2005; Jiménez-Rodríguez, 2009). Third, some researchers show effects of oil price shocks at a disaggregate level.

The second part is related to stock markets. Kaneko and Lee (1995) find that Japanese stock prices are affected by oil price shocks. Jones and Kaul (1996) further investigate the reaction of stock prices to oil price shocks and what may justify these movements. By using a cash-flow/dividend valuation model (i.e., Campbell, 1991), they find that oil prices can predict stock returns and output on their own. Sadorsky (1999) discovers that oil price movements can explain more of the forecast error variance of stock returns than can interest rates. Some studies (e.g., Lo and MacKinlay, 1990; Kaul and Seyhum, 1990; Sadorsky, 2003; Park and Ratti, 2008) propose that an increased volatility of oil prices significantly depresses real stock returns. Bjørnland (2009) indicates that following a 10% increase in oil prices, Norway’s stock returns increase by 2.5%. Apergis and Miller (2009) also find that different oil market structural shocks play a significant role in explaining the adjustments in stock returns.

The third part involves the labor market. A clear negative relationship between oil prices and employment is reported by Rasche and Tatom (1981), Hamilton (1983), Keane and Prasad (1996), Uri (1996), Raymond and Rich (1997), among others.

Keane and Prasad (1996) further indicate that oil price increases reduce employment in the short run, but tend to increase total employment in the long run. An oil price decrease depresses demand for some sectors, and unemployed labor is not immediately shifted elsewhere (Hamilton, 2003). However, oil price changes impact unemployment when the changes in oil prices persist for a long time as adjustments in employment (Keane and Prasad, 1996). Carruth et al. (1998) present an

asymmetrical relationship among unemployment, real interest rates, and oil prices, meaning that oil price increases cause employment growth to decline more than oil price decreases cause employment growth to increase. Davis and Haltiwanger (2001) find an oil price shock can explain 25% of the cyclical variability in employment growth from 1972 to 1988.

Most studies show the effect of oil price shocks, but rarely consider the effect of natural gas or coal price shocks. Coal and natural gas are the two main alternative sources of energy. There are three effects of changing natural gas price controls:

on regional economic activity (e.g., Leone, 1982), on inflation (e.g., Ott and Tatom, 1982), and on the distribution of income between households and suppliers (e.g., Stockfisch, 1982). Hickman et al. (1987) examine the correlation between natural gas price and industrial production. They indicate that a 10% increase in natural gas price affects the same effect on real GDP growth. Jin et al. (2009) find that energy prices have significant negative effects on real economic growth and oil price shocks are greater than other resources. Lutz and Meyer (2009) observe that a stabilizing effect via international trade and domestic structural change on the GDP of oil importing countries with a permanent oil price increase occurs.

Researchers have begun to analyze the causality relationship between coal consumption and economic growth in recent years. Yang (2000) shows a causality relationship between coal consumption and economic growth in Taiwan. Yoo (2006) finds that bidirectional causality running from GDP to coal consumption exists in South Korea. Both Li et al. (2008) and Li et al. (2009) cover that there is unidirectional causality between coal consumption and GDP in China and Japan.

However, there are few studies specifically addressing coal price with economic growth.

3 Methodology 3.1 Unit Root Tests

3.1.1 Augmented Dickey Fuller (ADF) Test

Dickey and Fuller (1979) consider a autoregressive process AR(1) model

1 1

t t t

y  a y

_

 

, where the disturbances,



_t , are assumed to be white noise, conditional on past

y

_t, and the first observation,

y

₁, is assumed to be fixed. By subtracting

y

_t1 from both sides of the equation, we can rewrite the model as follows:

1

t t t

y  y

_



  

, where

   a

₁

1

. The unit root test is equivalent to testing

 

0, that is, that there exists a unit root. The standard t-statistic for ˆ



can be used to test

 

0, but with the Dickey-Fuller critical values.

However, simple unit root test described above is valid only if the series is an

AR(1) process. If the series is correlated at higher order lags, the assumption of

white noise disturbances is violated. Dickey and Fuller (1981) make a parametric correction for higher order correlation by assuming that the

  y

t follows an AR(p) process and extending model as follows:

0 1 1 2 2 1 1 Continuing in this fashion, we get:

0 1 1

where different regression equations that can be used to test for the presence of a unit root:

1 1

3.1.2 The Kwiatkowski, Phillips, Schmidt, and Shin (KPSS) Test

Kwiatkowski et al. (1992) propose a test of the null hypothesis that an observable series is stationary around a deterministic trend. The series is expressed as the sum of deterministic trend, random walk, and stationary error, and the test is the LM test of the hypothesis that the random walk has zero variance. The KPSS statistic is based on the residuals from the OLS regression of

y

_t on the exogenous variables

x

_t:

t t t

y  x    

The Lagrange Multiplier (LM) statistic can be defined as:

2 2

where

S

_t is a cumulative residual function (i.e.,

1

ˆ , 1, 2, ,

t

t i

i

S  i T



  

^{). We}

point out that the estimator of



used in this calculation differs from the estimators for



used by detrended GLS since it is based on a regression involving the original data and not on the quasi-differenced data. Finite sample size and power are considered in a Monte Carlo experiment.

Prior to performing the Johansen co-integration method, we need to determine the appropriate number of lag length of the VAR model. The Bayesian information criterion (BIC) (Schwarz, 1978) is employed. The test criteria to determine appropriate lag lengths and seasonality are the multivariate generalizations of the BIC.

The BIC criterion is a purely statistical technique and allows data themselves to select optimal lags. Given any two estimated models, the model with the lower value of BIC is the one to be preferred. The selection of lag order of

 y

_{t i} can be used by the Bayesian information criterion (BIC):

BIC=-2*ln(L)+k*ln(n) (8)

where n is the number of observations, k is the number of free parameters to be estimated and L is the maximized value of the likelihood function for the estimated model. The BIC penalizes free parameters more strongly than does the Akaike information criterion (AIC) (Akaike, 1969).

3.2 Cointegration Analysis

The Johansen co-integration method is provided by Johansen (1988) and Johansen and Juselius (1990). This procedure applying maximum likelihood estimators circumvent the low-power of using Granger two-step estimators and can estimate and test for the presence of multiple cointegrating vectors. Moreover, this test allows the researcher to test restricted versions of the cointegrating vectors and

speed of adjustment parameters. Continuing in this fashion, we obtain:

1

Suppose that each individual variable

y

_it is I(1) and linear combinations of

y

_t are stationary. That implies



can be shown as

   ^

where β is the matrix of cointegrating parameters, and



is the matrix of the speed of adjustment parameters. The number of cointegrating relations relies on the rank of



, and the rank of



is:

(1) rank( )

  n

,



is full rank means that all components of

y

_t is a stationary process.

(2) rank( )

 

0 ,



is null matrix meaning that there is no cointegration relationships.

(3) 0



rank( )

   r n

, the variables for

y

_t are cointegrated and the number of cointegrating vectors is r.

The test for the number of characteristic roots that are insignificantly different from unity can by conducted using the following two test statistics:

(1) Trace test:

1

( ) ln(1 ˆ )

n

trace i

i r

r T

 

 

   

^,

0

: rank( ) H   r

,

1

: rank( )

H   r

where

 ^ˆ

_i is the estimated values of the characteristic roots (also called eigenvalues) obtained from the estimated



matrix, r is the cointegrating vector, and T is the number of usable observations. The statistic tests the null hypothesis that the number of distinct cointegrating vectors is less than or equal to r against a general alternative. If there is no cointegrating vector, it should be clear that



_trace equals zero when all

 ^ˆ

_i

 0

. The further the estimated characteristic roots are from zero, the

more negative is

ln(1   ^ˆ

_i

)

and the larger the



_trace statistic.

(2) Maximum eigenvalues test:

max

( , r r 1) T ln(1 ˆ

_r 1

)

     

_

H

0: there are r cointegrating vectors



and



_max statistics follows a chi-square distribution in general.

3.3 Multivariate Threshold Error Correction (MVTEC) Model

At the beginning, we consider the univariate TAR model which is also referred to as SETAR (self-exciting TAR). The SETAR(1) can be formed as:

0,1 1,1 1 1 0,2 1,2 1 1 and can be expressed as:

1 1 1 ,1

z

t d_ .

Given observations

 y

t

^{, z}

t



, where

t  

1, ,

n

, we have to detect the threshold nonlinearity of

y

_t. Assuming p and d are known, the Eq. (14) can be re-written as:

X

_t



_t

, t h 1, , n



_t

      

y

(15) where

h 

max( , )

p d

, X_t



(1, y ,_t



_1 y



_{tt p} ,



_t1)



is a (

pk 

1)-dimensional regressor, and Φ denotes the parameter matrix. If the null hypothesis holds, then the least squares estimates of (15) are useful. On the other hand, the estimates are biased under the alternative hypothesis. Eq. (15) remains informative under the alternative hypothesis when rearranging the ordering of the setup. For Eq. (15), the threshold variable

z

_{t d} assumes values in

S   z

_{h }1 _d

, z

_{n d}



. Consider the order statistics

of S and denote the ith smallest element of S by

z . Then the arranged regression

_{( )i} based on the increasing order of the threshold variable

z

_{t d} is

( ) ( )

X_{t id}



_{t id},

i

1, ,

n h



_t(i)+d

     

y Φ

, (16)

where ( )

t i is the time index of z . Tsay (1998) use the recursive least squares

_{( )i} method to estimate (16). If

y

_t is linear, then the recursive least squares estimator of the arranged regression (16) is consistent, so the predictive residuals approach white noise. Consequently, predictive residuals are uncorrelated with the regressor

X_{t i}( )_d.

Let Φm be the least squares estimate of Φ of Eq. (16) with

i 

1, ,

m

; i.e., the estimate of the arranged regression using data points associated with the m smallest values of

z

_{t d} . Tsay (1998) suggests a range of m (between

3 n

and

5 n

).

Different values of m can be used to investigate the sensitivity of the modeling results with respect to the choice. It should be noted that the ordered autoregressions are

sorted by the variable

z

_{t d} , which is the regime indicator in the MVTEC model. Let by the recursive least squares algorithm. Next, consider the regression

( ) ( ) ( ) 0

ˆ_{t l d} X_{t l d}

w

_{t l d},

l m

1, ,

n h



_

 

_

  

_

  

, (19) where

m

₀ denotes the starting point of the recursive least squares estimation. The problem of interest is then to test the hypothesis

H

₀

:   0

versus the alternative where the delay d implies the test depends on the threshold variable

z

_{t d} , and

0

where

ˆw

_t is the least squares residual of regression (19). Under null hypothesis the

y

_t is linear and some regularity conditions, C(d) is asymptotically a chi-squared random variable with

k pk

(



1) degree of freedom.

3.4 Impulse Response Analysis

Consider the first-order structural VAR model with 7-variables:

12 13 17 1 10 11 12 13 17 1 1 1

We can write the system in the compact form:

  

rewrite (21) in the equivalent form:

1 10 11 1 1 12 2 1 17 7 1 1

1 10 11 12 17 1 1 1 value. Using the backward method to iterate model (21), we can obtain:

0 1 0 1

Using model (24), model (23) can be re-written as:

1 1 11 12 17 1

sequences. However, it is insightful to rewrite (26) in terms of

Since the notation gets unwieldy, we can simplify by defining the 7×7 matrix



_i with elements



_jk( )

i

:

the same way, the elements



₁₁

(1)

,



₁₂

(1)

,…,



₁₇

(1)

are the one period responses of

The accumulated effects of unit impulses in

1

,

2

, ,

7

the cumulated sum of the effects of

y t2 plotting the coefficients of



_jk( )

i

against i) is a practical manner to visually present the behavior of the

  y

1t ,

  y

2t ,…,

  y

7t series in response to the various shocks.

1

Forecasting solely on the {x_1t} sequence, the n-step ahead forecast error is:

11 11 11 forecast error increases as the forecast horizon n increases. Note that it is possible to decompose the n-step ahead forecast error variance due to each one of the shocks. (VDC), showing the proportion of the movements in a sequence due to its own shocks versus shocks to the other variable. If

  

y t2 ,

  

y t3 ,…,

  

y t7 shocks explain none

of the forecast error variance of

  y

1t at all forecast horizons, we can say that the

  y

1t sequence is exogenous. In applied research, it is typical for a variable to

explain almost all its forecast error variance at short horizons and smaller proportions at longer horizons.

However, impulse response analysis and variance decompositions can be useful tools to examine the relationships among economic variables. If the correlations among the various innovations are small, the identification problem is not likely to be particularly important. The alternative orderings should yield similar impulse response and variance decompositions.

4 Empirical Results 4.1 Data Description

A total of nine time series datasets, including three energy prices and six macroeconomic variables, are applied in this study. The oil price (oil) data are collected from the West Texas Intermediate (WTI) crude oil spot price index in the commodity prices section. The gas price (gas) data are collected from the Russian Federation natural gas spot price index. The coal price (coal) data are collected from the Australia coal spot price index. Following Sadorsky (1999), we employ the six macroeconomic variables: industrial production index (ip), stock prices (sp), interest rate (r), unemployment rate (un), exports (ex) and imports (im). The industrial production index represents the level of output produced within an economy in a given year. In order to test for the impact in the labor market, the unemployment rate is chosen as a desirable proxy.

All data used in this study are monthly frequencies. Since the VAR or VECM model is used to estimate the non-linear relation, at least 200 data points are needed

for a delay of 12 periods as suggested by Hamilton and Herrera (2004). The length of the available data is different and covers the period from 1975:M7-2008:M5 (oil price), 1979:M2-2008:M5 (coal price), and 1985:M1-2008:M5 (natural gas price).

The energy price data are obtained from International Financial Statistics (IFS) CD-ROM. The macroeconomic variables are obtained from Taiwan Economic Journal (TEJ) and Advanced Retrieval Econometric Modeling System (AREMOS).

All variables are deflated by the base year 2006 consumer price index (CPI) and a natural logarithm (except for interest rate and unemployment rate) is taken before conducting the analysis. Table 4.1 summarizes a description of all variables.

Table 4.1 Definitions of Variables

Variables Definitions of variables Source

oil Logarithmic transformation of monthly real West Texas Intermediate

oil Logarithmic transformation of monthly real West Texas Intermediate

在文檔中 國際能源價格與台灣總體經濟變數之關聯性分析 (頁 7-0)