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經營管理研究所

博 士 論 文

No. 129

分類能源消費與價格衝擊對金融市場之影響

The Impacts of Disaggregated Energy Consumption and

Price Shocks on Financial Markets

研 究 生:林政勳

指導教授:胡均立 教授

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分類能源消費與價格衝擊對金融市場之影響

The Impacts of Disaggregated Energy Consumption and

Price Shocks on Financial Markets

研 究 生: 林政勳 Student: Cheng-Hsun Lin

指導教授: 胡均立 Advisor: Dr. Jin-Li Hu

國 立 交 通 大 學

經 營 管 理 研 究 所

博 士 論 文

A Dissertation

Submitted to Institute of Business and Management College of Management

National Chiao Tung University in Partial Fulfillment of the Requirements

for the Degree of Doctor of Philosophy

in

Business and Management October 2009

Taipei, Taiwan, Republic of China

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分類能源消費與價格衝擊對金融市場之影響

The Impacts of Disaggregated Energy Consumption and Price

Shocks on Financial Markets

研究生: 林政勳 指導教授: 胡均立 教授

國立交通大學經營管理研究所博士班

中文摘要

本篇論文以非對稱性的時間序列模型探討兩個與能源相關的議題。首先,近 年來台灣的能源消費成長高於經濟成長率,顯示過多的能源消費卻無法有效提升 國內產出,且隱含著能源效率持續惡化。能源消費與產出的脫鉤現象,在長期之 下是否會仍存在共整合關係? 對此,本研究利用非對稱性的門檻共整合檢定去探 討經濟成長與各類型能源消費的長期均衡關係。實證結果發現,除了原油消費與 經濟成長的組合之外,其他各類型能源消費與經濟成長之間存在非線性關係。此 外,透過兩狀態向量誤差模型則顯示,當達到一定的門檻水準之後,能源消費將 持續朝向長期均衡的調整。對此,決策者未來在進行經濟預測時,可考量能源消 費與經濟成長間的非對稱模型,並且應建立一套有效的能源需求管理,以改善能 源效率。 本篇論文的第二個議題,是探討原油價格衝擊對股價的影響。自從兩次能源 危機之後,過去三十年間油價變動及其對經濟活動衝擊的相關研究蓬勃發展。然 而,至今仍少有研究在探討油價變動與股票市場之間的動態關係。為了探究此議 題,我們將股價、油價、工業生產指數和利率等變數結合成一個多變量的線性架 構,探究六個已開發與開發中國家的股票市場中油價衝擊的傳遞行為。此外,我 們以原油價格變動當作一個門檻變數區分為油價上漲與下跌狀態,檢視在不同狀

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態之下油價衝擊對股價變動的影響。研究結果顯示,油價衝擊在解釋股票報酬的 調整行為中是一個重要的因子。此外,我們也發現加拿大、法國和台灣第一個月 的油價衝擊對股價變動具有規避效果,而對韓國股票市場則具有激勵效果,但這 些衝擊效果並不太大。當非對稱性的效果存在時,衝擊反應分析顯示,當油價變 動處於下跌狀態時,第一個月的油價衝擊對韓國的股價變動具有負向影響;然而, 當油價變動處於上漲狀態時,油價衝擊能增加股票報酬。根據此發現,對於跨國 投資機構而言,當油價變動增加時,可調整其投資組合成分,將資金轉投入低通 膨、正報酬的新興股票市場中,以避免損害其投資績效。 關鍵詞:分類能源消費、油價衝擊、門檻共整、兩狀態誤差修正模型、衝擊反應 分析、變異數分解、非對稱性

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The Impacts of Disaggregated Energy Consumption and Price

Shocks on Financial Markets

Student: Cheng-Hsun Lin Advisor: Dr. Jin-Li Hu

Institute of Business and Management

National Chiao Tung University

Abstract

The dissertation considers the time series model with an asymmetric framework to investigate two energy issues. Firstly, energy consumption growth is much higher than economic growth for Taiwan in recent years, worsening its energy efficiency. It reveals that consuming more energy cannot effectively enhance domestic output. Do there still exist a long-run co-integrating relationship as energy-output behaves a decoupling phenomenon? We provide a solid explanation by examining the equilibrium relationship between disaggregated energy consumption and GDP with the threshold co-integration test. The empirical results indicate that there is asymmetric co-integration relationship between disaggregated energy consumption and GDP, except for oil consumption nexus. The two-regime vector error-correction models show that the adjustment process of energy consumption toward equilibrium is highly persistent when an appropriately threshold is reached. There is mean-reverting behavior when the threshold is reached, making aggregated and disaggregated energy consumptions grow faster than GDP in Taiwan. Based on these results, there would progressively get into the insight to the possibility of asymmetric effects, and policy-makers as a result

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may be interested in identifying the asymmetric expected mechanisms of energy dependencies of economic growth as concerning future policy actions. Policy-makers should also establish an effective energy demand side management (EDSM) to improve energy efficiency.

Secondly, since the global energy crises of the 1970s and their effects on the world economy, the impact of an oil price change and its shock on economic activities have been a focus of research over the past three decades. So far, few studies explore the relationship between oil price and stock market, particularly in the impacts of oil shocks on equity returns. In order to address this issue, we incorporate stock price, oil price, industrial production and interest rate into a multivariate system, highlighting the transmission channels of oil price shocks on six developed and developing stock markets. The asymmetric effects are detected when the oil price changes separated into decrease and increase regimes. The empirical results show that oil price shock plays a significant role in explaining adjustments in stock market returns. Moreover, oil price shocks lead to initial an adverse effect on stock returns for Canada, France, and Taiwan. However, the magnitude of these effects proves small. When the asymmetric effects exist, the impulse response analysis in Korea indicates that an oil price shock will decrease the stock price changes under oil price changes decrease regime, while stimulate the stock returns as oil price changes increase. Hence, institutional investors should promptly re-adjust their global portfolio flowing to those stock markets with low inflation and positive returns when oil prices strikingly increasing that can prevent harming their performance.

Keywords: Disaggregated Energy Consumption; Oil Price Shocks; Threshold Co-integration; Two-regime Error Correction Model; Impulse Response Analysis; Variance Decomposition; Asymmetry

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Acknowledgements

I would first and foremost like to express my deeply and sincere gratitude to my thesis advisor, Professor Jin-Li Hu, for his warm encouragement and fruitful guidance throughout my academic work. His wide knowledge and logical thinking have been of great value for me. I feel very fortune to have an opportunity work under his patient advisor.

I would express special thanks to other members of my thesis committee: Professor Cherng G. Ding and Professor Chieh-Peng Lin, whose helpful suggestions increased readability and reduced ambiguity. Sincere thanks are extended to Professor Hsien-Chang Kuo, Professor Chin-Tsai Lin, Professor Chung-Shu Wu, and Professor Jui-Kou Shang, on behalf of devoting their precious time and provided many valuable suggestions that improved the quality of this thesis. I am very grateful for meeting Professor Nai-Fong Kuo and Dean-Ming Wu, my master advisors, and thank them for providing research data and sharing their valuable ideas. My debt to them is incalculable. For the administrative assistance, I would like to thank the Ms. Hsiao in the Ph.D. program for her patience dealing the process throughout my graduate studies.

During my Ph.D. program, I met my dearest fiancee, Fang-Yu. Your patience, love and encouragement have upheld me. Falls in love with you, I ultimately understand the meanings of love covered. Meeting with you, I find a warm harbor which can be resident. Someday, time will take away our youth but our love will never be changed. For now and future, I will try to live for you and for me. I will try to keep all lovely time in my memories forever.

Finally, I want to give my gratitude to my family, especially my parents and brother, without whose emotional and financial support the completion of my thesis would be merely impossible. I want to share this thesis with them.

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Table of Contents

中文摘要 ... i Abstract...iii Acknowledgements ... v Table of Contents ... vi List of Tables...viii List of Figures... ix Chapter 1 Introduction... 1 1.1 Research Background ... 1 1.2 Research Purpose ... 4

1.3 Organization of the Dissertation ... 6

Chapter 2 Literature Review ... 8

2.1 Issues on Energy Consumption and Economic Growth... 8

2.2 Issues on Oil Shocks and Economic Activity ... 10

Chapter 3 Methodology ... 16

3.1 Unit Root Tests... 17

3.1.1 Augmented Dickey Fuller (ADF) Test ...17

3.1.2 The Kwiatkowski, Phillips, Schmidt and Shin (KPSS) Test ...19

3.2 Cointegration Analysis... 20

3.3 Threshold Co-integration with Asymmetric Adjustment ... 22

3.4 Impulse Response Analysis... 26

3.5 Variance Decomposition ... 29

Chapter 4 Empirical Results... 32

4.1 The Asymmetric Behavior of Disaggregated Energy Consumption and GDP in Taiwan... 32

4.1.1 Data Sources...32

4.1.2 Results of the Asymmetric Threshold Co-integration Tests ...35

4.1.3 Results of the Two-Regime Error Correction Models...37

4.2 The Impacts of Oil Price Shocks on Stock Markets ... 44

4.2.1 Data Sources...44

4.2.2 Results of the Variance Decomposition and Impulse Response Analysis in the One-Regime VAR ...48 4.2.3 Results of the Variance Decomposition and Impulse Response Analysis

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in the Two-Regime VAR ...52

Chapter 5 Conclusions and Policy Implications ... 61

References ... 66

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List of Tables

Table 2.1 A Comparison of Earlier Studies about Causality and Co-integration Analysis

Between Energy Consumption and GDP... 11

Table 2.2 An Overview of Previous Studies of the Impacts of Oil Price Shocks on Stock Markets and Macroeconomics Activities ...14

Table 4.1 Tests for the Presence of Seasonality ...33

Table 4.2 Tests for Unit Root ...34

Table 4.3 Results of the Asymmetric Threshold Co-integration Tests...36

Table 4.4 Sample Sources and Research Periods...45

Table 4.5 Results of Unit Root Tests...46

Table 4.6 Results of the Johansen Co-integration Tests...48

Table 4.7 Variance Decomposition of Forecast Error Variance in One-Regime VAR model (12 periods forward) ...50

Table 4.8 Testing for Asymmetric Effects of Oil Price Changes ...55

Table 4.9 Variance Decomposition of Forecast Error Variance in Two-Regime VAR model (12 periods forward) ...57

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List of Figures

Figure 1.1 Historical Series of GDP and Energy Consumption Growth in Taiwan...3

Figure 1.2 Research Flow Chart ...7

Figure 3.1 Methodology Flow Chart ...16

Figure 4.1 Response of GDP and Energy Consumption to Error Correction ...39

Figure 4.2 Response of GDP and Coal Consumption to Error Correction ...40

Figure 4.3 Response of GDP and Natural Gas Consumption to Error Correction ...42

Figure 4.4 Response of GDP and Electricity Consumption to Error Correction...43

Figure 4.5 Impulse Responses to Oil Price Shock in the One-Regime VAR Model (12 Forward Periods) ...51

Figure 4.6 Impulse Responses to Oil Price Shock in the Two-regime VAR model for France (12 periods forward). ...59

Figure 4.7 Impulse Responses to Oil Price Shock in the Two-regime VAR model for Korea (12 periods forward) ...60

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Chapter 1 Introduction

1.1 Research Background

Energy is one of the critical determinants in economic development process. To maintain higher economic growth, rapid growing developing economies are confronted with substantial demand of various energy sources. Since the early 1980s, energy demand on a national and international basis has been extensively analyzed, initially motivated by concerns about security due to energy supply in view of the twin oil price shocks in 1970s and later because concerns about climate change. Due to the growing pressure exerted on governments to reduce carbon dioxide (CO2)

emissions in order to ease up the rate of climate change, many countries worry about the negative impact on economic growth caused by the restricted use of fossil fuels. Hence, various economic policies and options have been studied to practice energy conservation without harming on economic growth.

Growing concerns over the effects of greenhouse gas emissions for global warming have placed pressure on the world’s leading economies to improve their efficiency of energy use. In June 2005, the National Energy Conference in Taiwan took place and the objective was to establish an applicable energy policy that can conform to the newly developing trends under the Kyoto Protocol. The conference has given some directions for macro strategies of energy policy that have to be implemented in the future. First, carbon dioxide emissions are expected to reduce to levels of 38 million tons of oil equivalent (MTOE) in 2015 and to 78 MTOE in 2025, respectively. Second, the structures of energy allocation percentage in 2025 are expected to drop as follows: fuel 41% to 45%, oil 32% to 31%, natural gas 16% to 19%, nuclear energy to 4%, and renewable energy 5% to 7%. Third, Taiwan’s

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government regulatory authority should establish a market mechanism to promote the rationalization of energy prices and consolidate the management of efficient energy use. Although economists have long argued that pricing policies are an effective instrument to improve the efficiency of energy use, the effectiveness of a pricing policy to promote the efficient use of energy depends on the price elasticity of energy demand. Finally, the legislative body should create energy enterprising laws that can accomplish energy market liberalization progressively.

Beginning in the 1980s, an enormous amount of change in Taiwan’s economic structure took place. Financial liberalization and an internationalization policy were carried out in the middle part of the 1980s. The country’s average annual economic growth was 7.59% and the average growth rate of energy consumption was 5.84% starting from 1980 until the end of 1996. This signifies that domestic output consumes a relative lower level of energy. However, some economic incidents have caused a substantial decline in economic growth, including military tension across the Taiwan Strait, Asian financial crisis (1997-1999), and recessions in the global business cycle in 2001. As shown in Figure 1.1, during the period from 1997 to 2002, the average annual economic growth dropped to 3.63%, while energy consumption still sustained at 5.58%, worsening Taiwan’s energy efficiency. Energy over-consumption cannot effectively enhance economic growth and may generate disequilibrium between energy consumption and economic growth. Actions toward energy-saving and value-added promotion are needed to improve energy efficiency.

Among the most severe supply shocks hitting the world economies since World War II are sharp increases in the price of oil and other energy products. Since 1973, many researchers are focused on studying the oil prices-macroeconomy relationship. There is a consensus between economists that oil price shock reduces economic activity and increases inflation simultaneously.

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-5 0 5 10 15 20 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 G DP growth (EG )

Energy Consumption growth (EC)

(1980~1997) EG=7.59% EC=5.84% (1998~2002) EG=3.63% EC=5.58% %

Figure 1.1 Historical Series of GDP and Energy Consumption Growth in Taiwan

The transmission mechanisms through which oil prices have impact on real economic activity include both supply and demand channels. Some studies explain this recession by the supply side as the principal channel by which the effects of the rising oil price are transmitted. In this case, the rise of the price affects the potential production in an economy. Indeed, oil price rising is interpreted as an indicator of increase in the scarcity and that means that oil will be less available on the market. Since oil is an input for the production, this latter and the labor productivity slow down.

In sharp contrast to the volume of studies investigating the link between oil price shocks and macroeconomic variables, there have been relatively few analyses on the relationship between oil price shocks and financial markets such as the stock market. Market participants want a framework that identifies how oil-price changes affect stock prices or stock market returns. On theoretical grounds, oil-price shocks affect stock market returns or prices through their effect on expected earnings.

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1.2 Research Purpose

Because oil and various energy sources play critical role in determining economic growth, the main interest of this dissertation is therefore to address the issues of energy consumption and oil price fluctuation on financial markets with linear and asymmetric framework. There are two reasons to take into account asymmetric adjusting behavior between energy consumption and economic growth. The first one is that the topic of asymmetric properties of the adjustment process has been paid scant attention, while large numbers of recent studies provide evidence of the asymmetric adjustment of most macroeconomic variables (e.g., Ewing et al., 2006; Maki and Kitasaka, 2006). Neglecting an asymmetric adjustment among macroeconomic variables may lead to biased inferences and hence misleading results. As discussed by Balke and Fomby (1997), movement toward the long-run equilibrium is not necessarily constant, implying that the convergence to equilibrium may be faster under positive deviations than under negative ones (or vice versa). Therefore, if asymmetric co-integration is evident, then the conventional vector error-correction models (VECM) will be a mis-specification.

Another one is that several renowned recent studies have found an asymmetric relationship between energy consumption and economic growth in Taiwan. Lee and Chang (2005) argue that neglecting the structural break problem means being unable to uncover whether or not parameters are unstable within each of the sub-periods. They provide evidence that the co-integration relationship between energy consumption and GDP is unstable in Taiwan, and some economic events such as the oil crisis and Asian financial crisis significantly affect stability. Lee and Chang (2007) consider the possibility of both a linear and nonlinear effect of energy consumption on economic growth for Taiwan based on the conventional neoclassical one-sector aggregate production function. By conducting the threshold regression

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model during the two energy crisis periods, they indicate that the structural change due to the existence of an energy consumption threshold should be considered when constructing estimation and prediction models of economic growth. In addition, they also provide evidence that the relationship between energy consumption and economic growth in Taiwan can be characterized by an inverse U-shape. Most of these previous contributions suggest that there seems have an asymmetric relationship between energy consumption and economic growth in Taiwan.

Furthermore, Taiwan’s economy faces scarcity in domestic energy resources and has to rely heavily on imports of energy. Yang (2000), Sari and Soytas (2004) and Wolde-Rufael (2004) employ disaggregate energy consumption data with respect to different energy sources; whereas, Hondroyiannis et al. (2002) distinguish between residential and industrial energy consumption. Moreover, Yang (2000) indicates that one shortcoming with the use of aggregated energy data is that countries may depend on different energy sources. Therefore, it is not possible to identify the impact of a specific type of energy with aggregated data. These concerns have encouraged us to investigate the relationship between disaggregated energy consumption and economic growth in order to identify the impact of different energy sources on GDP in Taiwan. Based on the aforementioned argument, the first purpose of this dissertation is to examine the asymmetric behavior between disaggregated energy consumption and GDP in Taiwan, using a threshold co-integration model proposed by Hansen and Seo (2002).

Oil prices do not affect asset prices in isolation, but through the perceived effect on the macroeconomy. An analysis of the linkages between oil and stock markets therefore requires a through examination of macroeconomic linkages. Hence, the second purpose of this dissertation is to assess the effects of oil price shocks on stock prices with the linear and asymmetric perspective for six developed and developing

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stock markets. We incorporate the four relevant variables (including stock returns, oil price, industrial production and interest rate) as a multivariate framework in the vector autoregression (VAR) model. Applying the impulse response analysis (IRF) can capture the effects of oil price shocks on stock market. Besides, due to the differences in the degree of economic development, energy dependence, and the efficiency of energy use, the speed of economic response in each country as a result of the impact of a positive oil price change and its shock are expected to be different. Therefore, we separate the oil price changes as a decrease (down) and increase (up) band to analyze the impacts of oil shock on equity returns.

1.3 Organization of the Dissertation

The dissertation is organized in the following manner as Figure 1.2 shows: Chapter 1 presents the motivations and purposes of the study. Chapter 2 reviews the related literature. Chapter 3 gives a brief introduction of research methods. Chapter 4 presents the empirical results. Chapter 5 concludes this dissertation and proposes policy implications.

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Chapter 1 Introduction

Research Background Research Purpose

Chapter 2 Literature Review

Issue on Energy Consumption and Economic Growth

Issue on Oil Price Shocks and Economic Activity

Chapter 3 Methodology

Unit Root Tests Cointegration Analysis Threshold Cointegration Impulse Response Analysis Variance Decomposition

Chapter 4 Empirical Results

Asymmetric Behavior Between Disaggregated Energy Consumption and GDP

Oil Price Shocks and Stock Price Changes

Chapter 5 Conclusions

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Chapter 2 Literature Review

2.1 Issues on Energy Consumption and Economic Growth

Ever since 1970s numerous studies have examined the relationship between energy consumption and economic growth. A major question concerning this issue is which variable leads to the other: Is energy consumption a stimulus for economic growth or does economic growth lead to energy consumption? One of the time series methodologies to employ is the concept of Granger causality. Following Kraft and Kraft (1978) who provide pioneering evidence in support of causality from GNP to energy consumption in the United States, many empirical studies later extend to cover other industrial countries such as the United Kingdom, Canada, Germany, Italy, Japan, and France (e.g., Yu and Choi, 1985; Erol and Yu, 1987). However, the related literature on developed and developing countries, with diverse methodologies, and using various time periods fails to reach a unanimous conclusion.

Because of the critical role played by energy in the economic growth, an energy conservation policy (whether or not it can successfully be propagated within an individual country) has been a striking topic widely explored. The directions of the causal relationship between energy consumption and economic growth can be categorized into four types and evidence on either direction has important implications for an energy policy. First, if there is a unidirectional causality from economic growth to energy consumption, then policies for reducing energy consumption may be implemented with only little adverse or no effect on economic growth, such as in a less energy-dependent economy (Lise and Montfort, 2007; Oh and Lee, 2004; Yoo and Kim, 2006). Second, if there is unidirectional causality from energy consumption to economic growth, then restrictions on the use of energy

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may have significantly adverse effects on economic growth, while an increase in energy consumption may contribute to economic growth (Altinay and Karagol, 2005; Lee, 2005; Narayan and Singh, 2007; Shiu and Lam, 2004; Wolde-Rufael, 2004; Yuan et al., 2007). Third, if there is a bidirectional causal relationship, then economic growth may demand more energy whereas more energy consumption may also induce economic growth. Energy consumption and economic growth complement each other such that radical energy conservation measures may significantly hinder economic growth (Jumbe, 2004; Yang, 2000; Yoo, 2005). Finally, if there is no causality in either direction, which is known as the ‘neutrality hypothesis’, then neither conservative nor expansive energy consumption has any effect on economic growth (Asafu-Adjaye, 2000; Wolde-Rufael, 2005).

Another time series methodology explaining the relationship between energy consumption and economic growth is the co-integration technique with a bivariate (e.g., Yang, 2000; Zachariadis, 2007; Zamani, 2007) or multivariate (e.g., Masih and Masih, 1997; Oh and Lee, 2004; Soytas and Sari, 2007) framework. Stern (1993) adopts a multivariate vector autoregression (VAR) model to explore the causal relationship between GDP, energy use, capital, and labor inputs in the United States, where using a quality-adjusted index of energy input in place of gross energy use. Compared to the bivariate VAR analysis, the multivariate context is important because changes in energy inputs are more frequently countered by the substitution of other production factors, resulting in an insignificant overall impact on output. Stern (2000) further extends his previous analysis by incorporating the co-integration analysis with some relevant variables. The results show that there is co-integration in a relationship among GDP, capital, labor, and energy.

Ghali and El-Sakka (2004) employ the Johansen co-integration technique to analyze the relationship among output, capital, labor, and energy use in Canada on the

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basis of neo-classical one-sector aggregate production technology. Their results indicate that the long-run movements of output, capital, labor, and energy use are related by two co-integrating vectors.

Lise and Montfort (2007) undertake a co-integration analysis not only to explore the link between energy consumption and GDP, but also to take into account environmental protection and economic development for Turkey. Co-integration is found between energy consumption and GDP, while the energy Kuznets curve (EKC) hypothesis is rejected.

The aforementioned literature strengthens Stern’s conclusions that energy can be considered a limiting factor in economic growth. Shocks to the energy supply tend to reduce output. Table 2.1 summarizes more details about these studies of causality and co-integration analysis between energy consumption and economic growth.

2.2 Issues on Oil Shocks and Economic Activity

The important role of crude oil in the global economy has attracted a great deal of attention among politicians and economists. Since the first oil shock in 1973-74, many studies have been undertaken into the oil price-macroeconomy relationship. These studies have reached different conclusions over time. As such, Hamilton (1983), Burbidge and Harrison (1984), Gisser and Goodwin (1986), Mork (1989), Hamilton (1996), Bernanke et al. (1997), Hamilton (2003), and several others have concluded that there is a negative correlation between increases in oil prices and the subsequent economic downturns in the United States. Nevertheless, the relationship seems to lose significance as data from 1985 onwards are covered. In fact, the declines in oil prices occur over the second half of the 1980s are found to have smaller positive effects on economic activity than predicted by linear models

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Table 2.1 A Comparison of Earlier Studies about Causality and Co-integration Analysis Between Energy Consumption and GDP

Authors Countries Study period Causality Co-integration relationship

Cheng and Lai (1997) Taiwan 1955-1993 GDP→ EC No co-integration Ghali and El-Sakka

(2004)

Canada 1961-1997 GDP↔ EC Co-integration Hondroyiannis et al.

(2002)

Greece 1960-1996 No causality Co-integration Hwang and Gum (1992) Taiwan 1955-1993 GDP↔ EC

Lee (2005) 18 developing countries

1975-2001 EC→ GDP Co-integration Lee and Chang

(2005)

Taiwan 1954-2003 GDP↔ EC No co-integration Lise and Montfort

(2007)

Turkey 1970-2003 GDP→ EC Co-integration Masih and Masih

(1997)

South Korea Taiwan

1955-1991 EC→ GDP No causality

Two co-integrating vector One co-integrating vector Oh and Lee (2004) South Korea 1961-1990 No causality Co-integration

Soytas and Sari (2003) 16 countries 1950-1992 EC→ GDP in Turkey

Co-integration for 7 out of 16 countries

Stern (2000) U.S. 1948-1994 EC→ GDP Co-integration Yang (2000) Taiwan 1954-1997 GDP↔ EC

Zamani (2007) Iran 1967-2003 GDP→ EC

considered up to then. After taking into account the role of the breakdate 1985-1986, some researchers argue that the instability observed in this relationship may be due to a mis-specification of the functional form used. The linear specification might mis-represent the relationship between economic growth and oil prices.

The mis-specification of linear function form has led to different attempts to reestablish the measures of the relationship between oil price changes and output. On the one hand, Mork (1989) separates out oil price changes into negative and positive oil price changes, concluding that the decreases are not statistically significant. Thus, the results confirm that the negative correlation between GDP

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growth and oil price increases remain when data from 1985 onwards are included. Mory (1993) follow Mork’s (1989) measures and separated the oil price into negative and positive oil price changes. He finds that the positive oil price shocks Granger-caused the macroeconomic variables, but that negative shocks do not. Mork et al. (1994) also find the asymmetric effects for seven industrialized countries.

On the other hand, Lee et al. (1995) report that the response to an oil price shock by the economic growth depends on the environment of oil price stability. An oil shock in a price stability environment is more likely to have larger effects on GDP growth than those occur in a price volatile environment. These researchers propose a measure that takes the volatility into account through a GARCH-based on oil price transformation. This transformation scales estimated oil price shocks by their conditional variance. They find asymmetry in the effects of positive and negative oil price shocks, but they also reestablish the significance of the above-mentioned negative correlation. Using the same way, Hamilton (1996) shows that it seems more appropriate to compare the prevailing oil price with what it is during the previous year, rather than the previous quarter. Finally, Hamilton (2003) provides evidence of a non-linear representation and states that the functional form that relates GDP growth to oil price changes is similar what has been suggested in earlier studies. He specially analyzes the three non-linear transformations of oil prices proposed in the literature (i.e., Mork, 1989, Lee et al., 1995 and Hamilton, 1996), indicating that the formulation of Lee et al. (1995) has the best work of summarizing the non-linearity.

Afterwards, there are several works to study the impacts of oil price shocks, and the related issues can be divided into two parts. The first one part is related to macroeconomic level. Papapetrou (2001) analyzes the dynamic interactions among interest rates, real oil prices, real stock returns, industrial production and the

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employment for Greece. The evidence suggests that oil price changes affect real economic activity and employment. Cunado and Pérez de Gracia (2003) analyze the oil price-macroeconomy relationship by analyzing the impact of oil prices on inflation and industrial production for European countries. Using the transformation of oil price data, they find that oil prices have permanent effects on inflation and short run with asymmetric effects on production growth. More recently, Farzanegan and Markwardt (2009) find a strong positive relationship between positive oil price changes and industrial output growth in the Iranian economy.

As to the Asian developing countries studies, Cunado and Pérez de Gracia (2005) find that oil prices have a significant effect on both economic activity and price indexes, although the impact is limited to the short run and more significant when oil price shocks are measured in local currencies. Moreover, they find evidence of asymmetries in the oil price-macroeconomy relationship across some of the Asian countries. Chang and Wong (2003) suggest that the impact of an oil price shock on the Singapore economy is marginal and small.

Another part involves in stock markets. Asset prices are determined on the stock market depending on information about future prospects as well as current economic conditions facing firms. Jones and Kaul (1996) examine stock market efficiency, focusing on the extent to which stock prices change in response to oil price changes, (i.e., whether changes in stock prices reflect current and future real cash flows). By using a cash-flow/dividend valuation model, they find that oil prices can predict stock returns and output on their own. Sadorsky (1999) identifies that oil price shocks and its volatility play an important part in explaining US stock returns and the movements of oil price explained more than interest rates for the forecasting variance. Cong et al. (2008) find that oil price shocks do not show statistically significant impact on the real stock returns of most Chinese stock market indices.

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Park and Ratti (2008) show that oil price shocks have s statistically significant impact on real stock returns contemporaneously and within the following month in US and 13 European countries. Besides, they show that there is little evidence of asymmetric effects on stock returns of positive and negative oil price shocks. Apergis and Miller (2009) also show that different oil market structural shocks play significant role in explaining the adjustment in stock returns. However, the magnitude of such effects proves small. Bjørnland (2009) analyzes the effect of oil price shocks on stock returns in Norway. He finds that following a 10% increase in oil prices, stock returns increase by 2.5%. Table 2.2 summarizes the aforementioned and existing literature about the effects of oil price changes on macroeconomic activities and stock markets.

Table 2.2 An Overview of Previous Studies of the Impacts of Oil Price Shocks on Stock Markets and Macroeconomics Activities

Authors Periods Countries Variables Methodology Main Conclusions Apergis and Miller

(2009) 1981-2007 Australia Canada France Germany Italy Japan UK US Oil Price; Stock Price; CPI; Global economic activity Unit Root; Co-integration; VDC International stock market returns do no respond in a large way to oil market shocks

Bjørnland (2009) 1993-2005 Norway Oil Price; Stock Price; Interest rate; Unemployment CPI; Exchange rate VDC; IRF Following a 10% increase in oil prices, stock returns increase by 2.5%, after which the effect gradually dies out.

Chang and Wong (2003)

1978-2000 Singapore Oil price; GDP; COI; Unemployment Unit Root; Co-integration; VDC; IRF

The impact of an oil price shock on the Singapore economy is marginal.

Cunado and Pérez de Gracia (2005) 1960-1999 European countries Oil price; Inflation rate; Industrial Production Unit Root; Co-integration; Granger Causality; Nonlinear Transformation

Oil prices have permanent effects on inflation and

asymmetric effects on production growth rates

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Table 2.2 An Overview of Previous Studies of the Impacts of Oil Price Shocks on Stock Markets and Macroeconomics Activities (Continued)

Authors Periods Countries Variables Methodology Main Conclusions Cunado and Pérez

de Gracia (2005) 1975-2002 Japan Singapore Korea Malaysia Thailand Philippines Oil Price; CPI; Economic Activity Unit Root; Co-integration; Granger Causality; Nonlinear Transformation There is evidence of asymmetries in the oil prices-macroeconomy relationship for some of the Asian countries Farzanegan and

Markwardt (2009)

1975-2006 Iran Oil Price; GDP; Public Consumption Expenditures; Imports; Exchange Rate; Inflation VDC; IRF; Nonlinear Transformation There is a strong positive relationship between positive oil price changes and industrial output growth.

Jbir and Zouari-Ghorbel (2009)

1993-2007 Tunisia Oil price; Inflation rate; Exchange rate; Government spending; Industrial Production Unit Root; Granger Causality; IRF; VDC There is no direct impact of oil price shock on the economic activity.

Papapetrou (2001) 1989-1999 Greece Oil Price; Stock Return; Industrial production; Industrial Employment; Unit Root; Co-integration; VDC; IRF

Oil price changes affect economic activity and employment. Huang et al. (2005) 1970-2002 US Canada Japan Oil Price; Stock Return; Interest Rate; Industrial Production Unit Root; Co-integration; VDC; IRF; Multivariate Threshold Tests

An oil price change or its volatility has a limited impact on the economies if the change is below the threshold levels. Jiminez-Rodriguez (2008) 1975-1998 France Germany Italy Spain US UK Oil price; Manufacturing industry; Eight individual manufacturing industries IRF Evidence on cross-industry heterogeneity of oil shock effects within the EMU countries is found. Jiminez-Rodriguez (2009) 1947-2005 US Oil Price; GDP; Unemployment; Interest Rate; Federal Fund Rate; Wage; CPI Granger Causality; Nonlinear Transformation There is evidence of existence of non-linearity with the use of data earlier than 1984

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Chapter 3 Methodology

In this chapter the threshold co-integration and multivariate threshold autoregrresive models will be introduced to address two issues. To more clearly express the utilization of methods, we outline the research process with respect to each issue in Figure 3.1.

Unit Root Test

ADF Test KPSS Test

Threshold Cointegration

Threshold Cointegration Tests Threshold VECM

Issue Two

Stock Market Returns Oil Price

Industrial Production Interest Rate

Impulse Response Analysis Variance Decomposition One-Regime VAR

Cointegration Test

Maximum Eigenvalues Test Trace Test

Issue One

Disaggregated Energy Consumption GDP

Two-Regime VAR

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3.1 Unit Root Tests

A time series is a set of y observations, each one being record at a specific t

time t with stochastic process. To aid in identification, we know that a covariance stationary series need to be satisfied:

(1) Exhibits mean reversion in that it fluctuates around a constant long-run mean. (2) Has a finite variance that is time-invariant.

(3) Has a theoretical correlogram that diminishes as lag length increases.

On the other hand, a non-stationary series necessarily has permanent components. The mean and variance of non-stationary series are time-dependent. To aid in identification of a non-stationary series, we know that:

(1) There is no long-run mean to which the series returns.

(2) The variance is time-dependent and goes to infinity as time approaches infinity. (3) Theoretical autocorrelations do not decay, but the sample correlogram dies out

slowly in finite samples.

Although the traditional OLS approach often assumes the time series are stationary and its disturbances all white noise. If we assume the non-stationary time series as stationary, it may cause spurious regression proposed by Granger and Newbold (1974). Its result may have higher coefficient of determinant and much significant t value, implying non-reject the null hypothesis and though meaningless under spurious regression. Before proceeding analysis, we should test whether these variables have the stationarity property. If the time series variable is stationary with

d-times differencing, it can be called the integrated of order d and denoted as I(d).

We adopt two applicable unit root methods for examining the existence of unit roots.

3.1.1 Augmented Dickey Fuller (ADF) Test

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1 1

t t t

yy + , where the disturbances are white noise. Begin by subtracting ε yt1

from each side of the equation in order to write the equivalent from: ∆ =yt γyt1+ , εt where γ α= 1− . Certainly, testing the hypothesis 1 α1= is equivalent to testing 1 the hypothesis γ = . 0

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

{ }

yt follows an AR(p) process and adjusting the test methodology, the general form can be expressed as follows:

0 1 1 2 2

t t t p t p t

y =α α+ yy + +α y + (1) ε

To best understand the methodology of the augmented Dickey-Fuller test, add

and subtract αp t py− +1 to obtain:

0 1 1 2 2 2 2 ( 1 ) 1 1

t t t p t p p p t p p t p t

y =α α+ yy + +α y− + + α y− + − ∆α y− + + (2) ε Next, add and subtract (αp1p)yt p− +2 to obtain:

0 1 1 2 2 ( 1 ) 2 1

t t t p p t p p t p t

y =α α+ yy + − α +α ∆y− + − ∆α y− + + (3) ε Continuing in this fashion, we get:

0 1 1 2 p t t i t i t i y α γ y β y− + ε = ∆ = + +

∆ + (4) where 1 1 p i i γ α = ⎛ ⎞ = − −

and 1 p i j j β α =

=

. The selection of lag order of ∆yt i can

be used by the Akaike information criterion (AIC):

AIC=T ln(residual sum of squares)+2n (5) where n is the number of parameters estimated and T is the number of usable

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Three ADF test actually consider three different regression equations that can be used to test for the presence of a unit root:

1 1 2 p t t i t i t i y γy β y− + ε = ∆ = +

∆ + (6) 0 1 1 2 p t t i t i t i y α γ y β y− + ε = ∆ = + +

∆ + (7) 0 1 2 1 2 p t t i t i t i y α γ y α t β y− + ε = ∆ = + + +

∆ + (8)

The differences between the three regressions concerns the presence of the deterministic elements α0 and α2t. The first considers a pure random walk plus lagged dependent variables, the second adds an intercept (or drift term), and the third includes an additional linear time trend. The parameter of interest in all the regression equations is γ. If the null hypothesis γ = cannot be rejected, then the 0 {yt} sequence contains a unit root; otherwise, this sequence is stationary.

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

The standard conclusion that is drawn from this empirical evidence is that many or most aggregate economic time series contain a unit root. However, it is important to note that in this empirical work the unit root is the null hypothesis to be tested, and the way in which classical hypothesis testing is carried out ensures that the null hypothesis is accepted unless there is strong evidence against it. Therefore, an alternative explanation for the common failure to reject a unit root is simply that most economic time series are not very informative about whether or not there is a unit root, or equivalently, that standard unit root tests are not very powerful against relevant alternatives.

Kwiatkowski et al. (1992) use a parameterization which provides a plausible representation of both stationary and non-stationary variables and which leads naturally to a test of the hypothesis of stationarity. Specifically, they choose a

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component representation in which the time series under study is written as the sum of a deterministic trend, a random walk, and a stationary error. The KPSS test differs from the other unit root tests described here in that the {yt} sequence is assumed to be (trend) stationary under the null. The KPSS statistic is based on the residuals from the OLS regression of yt on the exogenous variables xt:

t t t

y =x′δ ε+

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

2 2

( ) /( o)

t

LM =

S t T f

where ( )S t is a cumulative residual function (i.e.,

1 ˆ ( ) t i, 1, 2, , i S t ε t T = =

= ), and o

f is an estimator of the residual spectrum at frequency zero. We point out that the

estimator of δ used in this calculation differs from the estimators for δ used by detrended GLS since it is based on a regression involving the original data and not on the quasi-differenced data.

3.2 Cointegration Analysis

Co-integration theory is definitely the innovation in theoretical econometrics that has created the most interest among economists in the last decade. Co-integration is an econometric property of time series variables. If two or more time series variables are non-stationary, but a linear combination of them is stationary, then the series are said to be co-integrated.

The Johansen co-integration method is provided by Johansen (1988) and Johansen and Juselius (1990). This procedure applying maximum likelihood to the vector autoregressive (VAR) model, and consider the relationships among more than two variables. Let yt denotes an (n× vector. The maintained hypothesis is that 1)

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addition, the errors are Gaussian.

1 1 2 2

+ + + + + , 1, 2, ,

t t t p t p t

y =µ Π x Π x Π x ε t= T (9) where μis constant term and εti i d. . .∼ N(0, )Ω . Moreover, VAR(p) in levels can be

written as: 1 1 2 2 1 1 1 t t t p t p t t y µ ς y ς y ς y− + ςy ε ∆ = + ∆ + ∆ + + ∆ + + (10) where ς = −(In − Π − Π − − Π = −Π1 2 p) (1) 1 2 ( ) 1, 2 , 1 i In i i p ς = − − Π − Π − − Π = −

Suppose that each individual variable yit is I(1) and linear combinations of yt are stationary. That implies ς can be showed as

ς = −αβ′

whereβis the cointegrating matrices, and α is the adjustment coefficients for both α and β (r n× matrices. The number of cointegrating relations relies on the ) rank of ς , and the rank of ς is :

(1) rank( )ς = , n ς is full rank means that all components of yt is a stationary process.

(2) rank( ) 0ς = , ς is null matrix meaning that there is no co-integration relationships.

(3) 0 rank( )< ς = < , the variables for yr n t are co-integrated and the number of cointegrating vectors is r.

To determine the number of co-integrating vectors, Johansen proposes two different likelihood ratio tests of the significance of these canonical correlations and thereby the reduced rank of the Π matrix: the trace test and maximum eigenvalue test, shown as follows:

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0: rank( )

H ς ≤ , i.e., there are at most r cointegrating vectors r

1: rank( )

H ς > r

The test statistic is

1 ˆ ln(1 ) n trace i i r T λ λ = + = −

− ,

where r is the cointegrating vector, T is the sample size, and λˆi is the ith largest

canonical correlation. The statistic has a limit distribution which can be expressed in terms of a (n-r)-dimensional Brownian motion.

(2) Maximum eigenvalues test:

0

H : there are r co-integrating vectors

1

H : there are r+ co-integrating vectors 1

The test statistic is λmax = −Tln(1−λˆr+1). If the absolute value of eigenvalue,

ˆ i

λ , is larger, then the test statistic will be higher and tend to reject the null hypothesis.

Neither of these test statistics follows a chi-square distribution in general; asymptotic critical values can be found in Johansen and Juselius (1990). Since the critical values used for the maximum eigenvalue and trace test statistics are based on a pure unit-root assumption, they will no longer be correct when the variables in the system are near-unit-root processes. Thus, the real question is how sensitive Johansen’s procedures are to deviations from the pure-unit root assumption.

3.3 Threshold Co-integration with Asymmetric Adjustment

The rationale behind threshold co-integration was introduced by Balke and Fomby (1997) as a feasible means to combine both non-linearity and co-integration. As pointed out by Balke and Fomby (1997), it is necessary to analyze the long-run equilibrium relationship by a co-integration test while assuming the feature of asymmetric adjustment. As is well known, variables are co-integrated to be

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characterized by an error correction model (ECM), which describes how the variables respond to deviations from the equilibrium. Therefore, it is possible that an asymmetric adjustment leads to poor results of the equilibrium relationship, because traditional approaches only take into account a tendency to move towards the long-run equilibrium for every time period.

Several studies have discussed co-integration with its corresponding ECM as the assumption of such a tendency to move toward a long-run equilibrium. Balke and Fomby (1997) emphasize the possibility that movement towards the long-run equilibrium need not occur in every period, because of the presence of some adjustment cost for the economic agent. In other words, there could be a discrete adjustment to equilibrium only when the deviation from the equilibrium exceeds a critical threshold, do the benefits of adjustment are higher than the costs. Therefore, economic agents act to move the system back to equilibrium. Threshold co-integration could characterize the discrete adjustment in terms of the case where the co-integrating relationship does not hold inside a certain band, but then remains active if the system gets too far from the equilibrium.

One of the most important statistical issues for threshold models in the econometric literature is testing for the presence of a threshold effect. Balke and Fomby (1997) propose applying several univariate tests (e.g., Hansen, 1996 and Tsay, 1989) to the known co-integrating residual (i.e., the error-correction term). Further related studies include Forbes et al. (1999), who develop a Bayesian estimation procedure for financial arbitrage, while Lo and Zivot (2001) extend Balke and Fomby’s approach to a multivariate threshold co-integration model with a known co-integration vector, employing Tsay (1998) and multivariate extensions of Hansen’s (1996) test. Hansen and Seo (2002) contribute further to the literature by examining the case of an unknown co-integration vector. In particular, these authors propose a

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vector error-correction model with one co-integrating vector and a threshold effect based on the error-correction term, and they develop a Lagrange Multiplier (LM) test for the presence of a threshold.

Hansen and Seo (2002) consider a two-regime threshold co-integration model, which can be treated as a non-linear VECM of order l+1 as the following form:

1 1 1 2 1 1 ( ) , if ( ) ( ) , if ( ) t t t t t t t A X u w x A X u w β β γ β β γ − − − − ⎧ ′ + ⎪ ∆ = ⎨ ′ + > ⎪⎩ (11) with 1 1 1 2 1 ( ) ( ) t t t t t l w x X x x β β − − − − − ⎛ ⎞ ⎜ ⎟ ⎜ ⎟ ⎜ ∆ ⎟ = ⎜ ⎟ ∆ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠

where xt is a p-dimensional I(1) time series which is co-integrated with one p×1 co-integrating vector β , ( )wt β =β′xt denotes the I(0) error-correction term, the coefficients matrices of A1 and A2 describe the dynamics in each of the regimes, γ is

the threshold parameter, and u is an error term. This may alternatively be written t

as:

1 1( ) ( , )+1 2 1( ) 2 ( , )

t t t t t t

x A X β d β γ A X β d β γ u

∆ = +

(12)

where d1t( , )β γ =I w( t1( )β ≤γ) , d2t( , )β γ =I w( t1( )β >γ) and ( )I ⋅ denotes the indicator function. The parameters of model (11) are estimated by maximum likelihood, under the assumption that the errors ut are i.i.d. Gaussian.

As can be seen, the threshold model (11) or (12) composes two regimes, and the non-linear mechanism depends on deviations from the equilibrium below or above the threshold parameter, where A1 and A2 describe the dynamics in each of the regime.

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there is only one co-integrating vector, a convenient choice is to set one element of β equal to unity that has no cost in the bivariate system (p = 2). The condition of

2

p> only imposes the restriction that the corresponding element of xt goes into the co-integrating relationship. Accordingly, there is no tendency for the variables xt to revert to an equilibrium state (i.e., the variables are not co-integrated); on the contrary condition, there is a tendency for xt to move towards the equilibrium states in another regime (i.e., the variables are co-integrated).

Hansen and Seo (2002) propose two heteroskedastic-consistent LM test statistics to test whether there is linear co-integration (i.e., the form of model (11)) under the null against the alternative threshold co-integration. This means that there is no threshold under the null, so that model (11) reduces to a conventional linear VECM. The first testing statistic would be used when the true co-integrating vector is known a priori and is denoted as:

(

)

0 0 Sup LM Sup LM , L U γ γ γ≤ ≤ β γ = , (13)

where β0 is the known value at fixed β (i.e., set β0 at unity), while the second case can

be used when the true co-integrating vector is unknown, and the test statistic is denoted as:

( )

Sup LM Sup LM , L U γ γ γ≤ ≤ β γ = (14)

where β is the null estimate of β.

In both tests,

[

γ γL, U

]

is the search region so that γL is the π0 percentile of

1

t

w , and γU is the

(

1−π0

)

percentile. Andrews (1993) suggests that setting π0 between 0.05 and 0.15 is a typically good choice. Finally, the bootstrap methods proposed by Hansen and Seo (2002) calculate the asymptotic critical values and

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3.4 Impulse Response Analysis

Impulse response analysis is used widely in the empirical literature to uncover the dynamic relationship between macroeconomic variables within VAR models. Impulse responses measure the time profile of the effect of a shock, or impulse, on the (expected) future values of a variable. By imposing specific restrictions on the parameters of the VAR model the shocks can be attributed an economic meaning.

Consider a bivariate structural VAR(1) system,

10 12 11 1 12 1 t t t t yt y =bb zyz +ε (15) 20 21 21 1 22 1 t t t t zt z =bb yyz +ε (16) where it assumed that both yt and zt are stationary, εyt and εzt are white-noise disturbances with standard deviations of σy and σz, respectively. {εyt} and {εzt} are uncorrelated white-noise disturbances. Equations (15) and (16) are not reduced-form equations since yt has a contemporaneous effect on zt and zt has a contemporaneous effect on yt. Using matrix algebra, we can write the system in the compact form: 10 1 12 11 12 12 20 21 22 1 1 1 yt t t t t zt y b y b b z b z ε γ γ γ γ ε − − ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ = + + ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦⎣ ⎦ ⎣ ⎦ ⎣ ⎦⎣ ⎦ ⎣ ⎦ or 1 1 t o t t Bx = Γ + Γ x + ε where 12 12 1 1 b B b ⎡ ⎤ = ⎢ ⎥ ⎣ ⎦, t t t y x z ⎡ ⎤ = ⎢ ⎥ ⎣ ⎦, 10 0 20 b b ⎡ ⎤ Γ = ⎢ ⎥ ⎣ ⎦, 11 12 1 21 22 γ γ γ γ ⎡ ⎤ Γ = ⎢ ⎥ ⎣ ⎦, yt t zt ε ε ε ⎡ ⎤ = ⎢ ⎥ ⎣ ⎦.

Pre-multiplication by B-1 allows us to obtain the VAR model in standard form:

1 1 t o t t x =A +A x + (17) e where 1 0 o A =BΓ , 1 1 1 A =BΓ , and 1 t t

e =B−ε . Using the brute force method to

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1 1 2 1 2 1 1 2 1 1 ( ) ( ) t o o t t t o t t t x A A A A x e e I A A A x A e e − − − − = + + + + = + + + +

where 2 2I = × identity matrix. After n iterations,

1 1 1 1 1 1 0 ( n) n i n t o t i t n i x I A A A A e A x+ − − − = = + + + +

+

The stability requires that the roots of 2 11 22 12 21

(1−a L)(1−a L) (− a a L ) lie outside the unit circle. For the time being, assume that the stability condition exist is net, so that we can write the particular solution for x as: t

1 0 µ i t t i i xA e = = +

(18) where µ=

[

y z ′

]

, y =

[

a10(1−a22)+a a12 20

]

/∆ , z =

[

a20(1−a11)+a a21 10

]

/∆ , and 11 22 12 21 (1 a )(1 a ) a a

∆ = − − − . In addition, if equation (18) can be performed as matrix form, we obtain: 1 11 12 0 21 22 2 i t t i i t t i y y a a e z z a a e ∞ − = − ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ = + + ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦

⎣ ⎦ (19) Equation (19) express yt and zt in terms of the {e1t} and {e2t} sequences.

However, it is insightful to rewrite equation (19) in terms of {εyt} and {εzt} sequences. According to the error terms in standard form of VAR(1), the vector of errors can be written as:

[

]

1 12 12 21 2 21 ε 1 1/(1 ) 1 ε yt t t zt e b b b e b − ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ = − ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ (20) so that (19) and (20) can be combined to form

[

]

11 12 12 12 21 0 21 22 21 ε 1 1/(1 ) 1 ε i yt t i t zt y y a a b b b z z a a b ∞ = − ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ = + − ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦

⎣ ⎦

Since the notion is getting unwieldy, we can simplify by defining the 2 2× matrix φi with elements φjk( )i :

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12 1 12 21 21 1 /(1 ) 1 i i b A b b b φ =⎡ − ⎤⎦ − − ⎤ ⎣ ⎦

Hence, the moving average representation of (19) and (20) can be written in terms of the {εyt} and {εzt} sequences:

11 12 0 21 22 ε ( ) ( ) ( ) ( ) ε yt t t i t zt i y y i i z z i i φ φ φ φ ∞ − = − ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ = + ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦

⎣ ⎦ or more compactly, 0 µ ε t i t i i x ∞ φ = = +

. (21) The coefficients of φi can be used to generate the effects of εyt and εzt shocks on the entire time paths of the {yt} and {zt} sequences. It should be clear that four elements (0)φjk are impact multiplier. For instance, the coefficient φ12(0) is the instantaneous impact of a one-unit change in εzt on yt. In the same way, the elements

11(1)

φ and φ12(1) are the one period responses of unit changes in εyt-1 and εzt-1 on yt, respectively. Updating by one period indicates that φ11(1) and φ12(1) also represent the effects of unit changes in εyt and εzt on yt+1.

The accumulated effects of unit impulses in εyt or εzt can be obtained by the appropriate addition of the coefficients of the impulse response functions. Note that after n periods, the effect of εzt on the value of yt+n is φ12( )n . Thus, the cumulated sum of the effects of εzt on the {yt} sequence is:

12 0 ( ) n i i φ =

.

Letting n approach infinity yields the long-run multiplier. Since the {yt} and {zt} sequences are assumed to be stationary, it must be the case that for all j and k,

2 0 ( ) jk i i φ ∞ =

is finite. The four sets of coefficients, φ11( )i , φ12( )i , φ21( )i , and φ22( )i , are called the impulse response functions. We can plot the impulse response

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functions (i.e., plotting the coefficients of φjk( )i against i) is a practical manner to visually present the behavior of the {yt} and {zt} series in response to the various shocks.

Knowledge of the various aij and variance/covariance matrix Σ is not sufficient to identify the primitive system. Hence, the econometricians have to impose an additional restriction on the two-variable VAR system in order to identify the impulse responses. One Possible identification restriction is to use Choleski decomposition. For example, it is possible to constrain the system such that the contemporaneous value of yt, does not have a contemporaneous effect on zt.

Formally, such restriction is represented by setting b21=0 in the primitive system.

In terms of (20), the error terms can be decomposed as:

1t εyt 12εzt

e = −b (22)

2t εzt

e = (23) Thus, if we use (23), all the observed errors from the {e2t} sequence are

attributed to εzt shocks. Although the Choleski decomposition constrains the system such that an εyt shock has no direct effect zt, there is an indirect effect in that lagged values of yt affect the contemporaneous value of zt. The critical point is that the decomposition forces a potentially important asymmetry on the system since an εzt shock has contemporaneous effects on both yt and zt. Given this reason, (22) and (23) are said to imply an ordering of the variables. An εzt shock directly affect e1t and e2t

but on εyt shock does not affect e2t. Hence, zt is prior to yt.

3.5 Variance Decomposition

If we use the equation (21) to conditionally forecast xt+1, the one-step ahead forecast error is φ0εt+1. In general,

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0 µ ε t n i t n i i x+ ∞ φ + − = = +

,

such that the n-period forecast error xt n+E xt t n+ is

1 0 ε n t n t t n i t n i i x+ E x+ − φ + − = − =

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

11 11 1 11 1 12 12 1 12 1 (0)ε (1)ε ( 1)ε (0)ε (1)ε ( 1)ε t n t t n yt n yt n yt zt n zt n zt y E y n n φ φ φ φ φ φ + + + + − + + + − + − = + + + − + + + + −

Denote the variance of the n-step ahead forecast error variance of yt n+ as

2 ( ) y n σ : 2 2 2 2 2 2 2 11 11 12 12 ( ) (0) ( 1) (0) ( 1) . y n y n z n σ =σ φ⎡ + +φ − ⎤+σ φ⎡ + +φ − ⎤

Since all values of ( )2

jk i

φ are necessarily nonnegative, the variance of the

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. The proportions of ( )2

y n

σ due to shocks in the {εyt} and {εzt} sequences are:

2 2 2 2 11 11 11 2 (0) (1) ( 1) ( ) y y n n σ φ φ φ σ ⎡ + + + − ⎤ ⎣ ⎦ (24) and 2 2 2 2 12 12 12 2 (0) (1) ( 1) ( ) z y n n σ φ φ φ σ ⎡ + + + − ⎤ ⎣ ⎦ (25) Equations (24) and (25) are the forecast error variance decomposition (VDC), showing the proportion of the movements in a sequence due to its own shocks versus shocks to the other variable. If εzt shocks explain none of the forecast error variance of {yt} at all forecast horizons, we can say that the {yt} sequence is exogenous. In such a circumstance, the {yt} sequence would evolve independently of the εzt shocks and {zt} sequence. At the other extreme, εzt shocks could explain all the forecast error variance in the {yt} sequence at all forecast horizons, so that {yt} would be

數據

Figure 1.1 Historical Series of GDP and Energy Consumption Growth in Taiwan
Figure 1.2 Research Flow Chart
Table 2.1 A Comparison of Earlier Studies about Causality and Co-integration  Analysis Between Energy Consumption and GDP
Table 2.2 An Overview of Previous Studies of the Impacts of Oil Price Shocks on  Stock Markets and Macroeconomics Activities
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