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Speculation and price volatility : the case of rice in United States Doroudian, Ali 2011

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 Speculation and Price Volatility: The Case of Rice in United States  by  Ali Doroudian  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  MASTER OF SCIENCE  in  The Faculty of Graduate Studies  (Agricultural Economics)   THE UNIVERSITY BRITISH COLUMBIA (Vancouver)  August 2011   © Ali Doroudian, 2011          ii  Abstract  In response to the rampant and high volatility in rice prices relative to other grains over the past few decades and calls by governments for tighter control and regulation on futures trading to limit speculation and curtail volatility, this work evaluates the performance of the rice futures market in United State in terms of its impact on the nation’s rice cash price volatility. This study presents a refined form of Milton Friedman’s original theory (1953) that speculation leads to less volatility unless it is carried out by irrational speculators. It will test this theory empirically using time series econometrics. Generalized autoregressive conditional heteroskedasticity (GARCH) is used to measure volatility of the price of rice. Vector autoregressive (VAR) models are deployed to measure the impact of trading activity on cash price volatility through Granger Causality test, forecast error variance decomposition (FEVD), and impulse response (IR) methods.  Results show that rice cash price volatility after the introduction of the rice futures market on the Chicago Board of Trade is lowered by 51%. The Granger Causality test also indicates that sudden changes in the futures market trading activity (proxy for the presence of irrational speculators) cause higher volatility in the cash market. The FEVD, and IR methods indicate that a sudden rise in non-commercial open interest has a larger impact on cash price volatility than changes in trading volume.      iii  Table of Contents Abstract ..................................................................................................................... ii Table of Contents ..................................................................................................... iii List of Tables ............................................................................................................ vi List of Figures ......................................................................................................... vii Acknowledgements ................................................................................................ viii Dedication ................................................................................................................ ix Chapter 1: Introduction and Objectives .................................................................... 1 1.1 Introduction ........................................................................................................................... 1 1.2 Objective ................................................................................................................................ 4 1.2.1 Specific Objectives ....................................................................................................................... 4 1.3 Study Plan .............................................................................................................................. 5 Chapter 2: Background .............................................................................................. 6 2.1 The Rice Market .................................................................................................................... 6 2.1.1 World Rice Market ....................................................................................................................... 6 2.1.2 United States’ Rice Market ........................................................................................................ 10 2.2 Futures Markets and the Impact of Speculation on Price Volatility.................................... 11 2.2.1 Futures Markets and Contracts ................................................................................................... 11 2.2.2 Speculation and Price Volatility ................................................................................................. 13 2.2.3 Speculation through Futures Markets and Cash Price Volatility ............................................... 16 2.2.4 Futures Market and Cash Price Volatility: Empirical Evidence ................................................. 19 2.2.5 Cash Price Volatility before and after the Introduction of Futures Market ................................ 20 2.2.6 Level of Futures Trading Activity and Cash Price Volatility ..................................................... 22 2.2.7 World and U.S. Rice Price: Pre and Post Introduction of Rice Futures on CBOT .................... 24 2.2.8 United States’ Rice Futures Market ........................................................................................... 25 2.3 Summary .............................................................................................................................. 27 Chapter 3: Theory .................................................................................................... 29 3.1 The General Theory and its Application to this Study ........................................................ 29 3.2 The Theoretical Model ........................................................................................................ 30 3.3 Summary .............................................................................................................................. 36 Chapter 4: Econometrics ......................................................................................... 37 4.1 Rice Cash Price Volatility ................................................................................................... 37 iv  4.2 Vector Autoregressive Models (VARs) .............................................................................. 42 4.2.1 Granger Causality Test ............................................................................................................... 43 4.2.2 Impulse Response Function (IR) ................................................................................................ 44 4.2.3 Forecast Error Variance Decomposition (FEVD) ...................................................................... 45 4.3 Detrending Futures Trading Volume and Open Interest ..................................................... 46 4.4 Summary .............................................................................................................................. 48 Chapter 5: Data and Results .................................................................................... 50 5.1 Data ...................................................................................................................................... 50 5.1.1 Data Source ................................................................................................................................ 50 5.1.2 Cash Price Data .......................................................................................................................... 51 5.1.3 World Prices ............................................................................................................................... 51 5.1.4 Open Interest Data ...................................................................................................................... 52 5.2 Results ................................................................................................................................. 52 5.2.1 Summary of Results ................................................................................................................... 52 5.2.2 Has Speculation Reduced Cash Price Volatility of Rice? .......................................................... 53 5.2.3 Have Irrational Speculators Increased Cash Price Volatility of Rice? ....................................... 57 5.3 Summary .............................................................................................................................. 59 Chapter 6: Conclusion ............................................................................................. 61 6.1 Limitations ........................................................................................................................... 62 Tables ...................................................................................................................... 63 Figures ..................................................................................................................... 65 Bibliography ............................................................................................................ 77 Appendices .............................................................................................................. 81 Appendix A: Derivation of Equations 3.7, 3.8 and 3.9 ............................................................. 81 Appendix B: Another GARCH Model ...................................................................................... 85 Appendix C: Another Form of Equation (4.7) .......................................................................... 86 Appendix D: Seasonality Test Results (Stata Output)............................................................... 87 Appendix E: Different Ordering of Variables in I.R. and FEVD Analysis ............................... 90 Appendix F: Choosing Separate Lags for each Variable of a VAR Model .............................. 93 Appendix G: Monthly Variance Generated by GARCH (1,1) Model ....................................... 94 Appendix H: Results of Estimating Volatility by GARCH Model (Stata Output) ................. 100 v  Appendix I: Correlation between the Change in US and World Rice Price before and after Rice Futures on the CBOT ............................................................................................................... 109 Appendix J: Results of Granger Causality, Impulse Response Analysis, and Forecast Error Variance Decomposition from Stata........................................................................................ 110                                         vi  List of Tables  Table 1: Rough Rice Price Volatility Estimation (equations 4.4 and 4.7) 1982-2011 ................................ 63  Table 2: Rough Rice Price Volatility before and after CBOT Rice Futures Market 1982-Sep1994 and Oct 1994-2011 (equation 5.1) ............................................................................................................................ 63  Table 3: Milled Rice Price Volatility Estimation (equations 4.4 and 4.7) 1979-2010 ................................ 63  Table 4: Milled Rice Price Volatility before and after Futures Market 1979-Sep1994 and Oct1994- 2007*(equation 5.1) .................................................................................................................................... 63  Table 5: Impact of Trading Activity on Cash Price Volatility: Granger Causality ..................................... 64  Table 6: Impact of Trading Activity on Cash Price Volatility: IR Analysis ............................................... 64  Table 7: Correlation between Detrended Price Change in Milled, Rough and Futures Rice Price ............. 64  Table 8: Impact of Trading Activity on Cash Price Volatility: FEVD Analysis ......................................... 64  Table I. 1: Rough Rice Price and World Price Correlation ....................................................................... 109 Table I. 2: Milled Rice Price and and World Price Correlation ................................................................ 109              vii  List of Figures Figure 1: Speculator with Perfect Foresight ................................................................................................ 65  Figure 2: Top Ten Rice Producers in the World and USA .......................................................................... 66  Figure 3: Total Rice, Wheat, and Maize Production in the World (1961-2009) Data Source: FAOSTAT (2009) Production/Crops ............................................................................................................................. 66  Figure 4: Top Ten Rice Exporting Countries .............................................................................................. 67  Figure 5: Top Ten Rice Importing CountriesNote: figures are tonnes of rice (milled equivalent) ............. 67  Figure 6: Rice Production in United States (1961-2009) ............................................................................ 68  Figure 7: World Price of Rice (1960-2011) *Thai 100% B Second Grade F.O.B Bangkok....................... 68  Figure 8: Rough Rice Futures Contract Specification ................................................................................. 69  Figure 9: Total non-commercial Futures Contract Long Positions (1994-2010) ........................................ 70  Figure 10: Rice Futures Contract Trading Volume (2000-2011) Data Source: Reuters Datastream CBOT Rough Rice Futures Trade Data .................................................................................................................. 70  Figure 11: Total non-commercial Rice Futures Open Interest (2000-2010) Data Source: US Commodity Futures Trading Commission ...................................................................................................................... 71  Figure 12: Detrended Futures Trading Volume and non-Commercial Open Interest-FD Method ............. 71  Figure 13: Detrended Futures Trading Volume and non-commercial Open Interest-P3 Method ............... 72  Figure 14: Detrended Futures Trading Volume and non-commercial Open Interest-CMA Method .......... 72  Figure 15: Rough Rice Price Return Variance (GARCH) pre Futures ....................................................... 73  Figure 16: Rough Rice Price Return Variance (GARCH) post Futures ...................................................... 73  Figure 17: Milled Rice Price Return Variance (GARCH) pre Futures ....................................................... 74  Figure 18: Milled Rice Price Return Variance (GARCH) post Futures ...................................................... 74  Figure 19: World Rice Price Volatility pre Zhengzhou Rice Futures Market ............................................. 75  Figure 20: World Rice Price Volatility post Zhengzhou Rice Futures Market ........................................... 75  Figure 21: World Price Volatility pre Rice Futures on the CBOT .............................................................. 76  Figure 22: World Price Volatility post Rice Futures on the CBOT ............................................................ 76   viii  Acknowledgements  I would like to thank my supervisor Professor James Vercammen for his unwavering support and invaluable input that opened doors for me in agricultural economics and made this study possible. I would also like to thank my thesis committee members, Professors Richard Barichello and Adlai Fisher for their guidance. I also thank Laval University for their financial support, which made research towards finishing this work possible. I would also like to thank Dr. David Dawe for his guidance and support during my stay at F.A.O. ix  Dedication          This Work is dedicated to Dr. Ahmad Doroudian  1  Chapter 1: Introduction and Objectives  Planting rice in never fun; Bent from morn till set of sun; Cannot stand and cannot sit; Cannot rest for a little bit. Oh, my back is like to break; Oh, my bones with dampness ache; And my legs are numb and set From the soaking in the wet  (Fowke & Glazer, 1973) a Filipino song  1.1 Introduction  Food prices have increased and become significantly more volatile during the past few years. Periods of rapid price increase have been followed by precipitous decline in prices. What separates the current period of high volatility in food prices from others in recent history is its persistence. This lingering high volatility in staple foods and agricultural commodity prices is particularly disastrous for the poor, who must rely on very few affordable sources of food for survival of which rice is one. Rice is a staple food for more than half of the world’s population, mainly in East and South East Asia. Relative to other grains, rice requires very little processing to reach consumption stage. Also unlike other grains, it is produced only for human consumption. These characteristics along with its high calorie content make it a valuable source of food for the poor. The price of rice has not been immune to the high rampant volatility in food prices over the past few years. The unprecedented high volatility in rice prices jeopardized the lives of millions and led to short term political and social unrest in some countries that depend on the grain as a major source of food. Therefore, understanding the sources of price volatility and seeking ways to avoid or navigate through it is important in ensuring food security and stability. The thinness in rice trade and geographical concentration of its production has always been a cause for concern about the supply of rice. In order to secure supplies and stabilize 2  domestic prices, the governments of many rice dependent countries have emergency policies in place that could stop trade and lead to high volatility in global rice prices in a very short period of time. Therefore other tools should be developed and promoted to prevent such price volatility in the rice market. The futures market could be one such tool, and by evaluating the rice futures market’s impact on cash price volatility some light could be shed on whether rice futures market could be used to stabilize cash prices. Several reasons have been put forward to explain the recent rise in food prices and high volatility. Amongst these is the rapid economic growth that developing economies have experienced over the past few decades. Economic growth in these economies has increased global demand for meat. As a result a significant amount of land that could be used for grain production is now used for livestock. This certainly puts constraint on supplies of grains and basic food items. Another reason cited for high price volatility is inconsistency of supplies caused by climate change. Recent droughts, floods, and other unusual weather patterns have disrupted the flow of grains and other agricultural products around the globe. Lastly, speculation has been widely blamed for the high volatility in food prices. The food market has attracted a relatively large sum of investment over the past several years. Most of this investment has been placed by entities that do not plan to be involved in any part of the food supply chain. Instead their objective has been to speculate on food prices. These entities are referred to as the non-commercial interest in the market. Their activities have come under great scrutiny by both the academic and political establishment. Speculation and its impact on price volatility has been a subject of many studies. However it seems that a clear answer as to whether speculation stabilizes or destabilizes prices in the market for a commodity has not yet been provided. Most studies acknowledge this and instead focus on presenting conditions under which speculation can lead to higher or lower volatility. 3  Almost all the speculation by non-commercial interest on food prices is carried out through futures markets. Agricultural commodities are widely traded on futures markets around the world. Futures contracts are a hedging tool for participants and traders in the physical commodity market (commercial interest)1. However, recently more than ever before futures contracts have become prominent tools for speculation in the commodities market by non- commercial interest. Speculation in the futures markets has been blamed for fuelling the sharp grain price increases of 2007. Many studies have been conducted to examine the role that futures markets play in the price volatility of the physical commodity (cash price). Some studies have concluded that the futures market was a contributing factor in destabilizing the markets in the short term (FAO, 2010), while others blame the futures markets and speculators entirely for the high volatility in commodity markets (Medlock & Myers, 2009). Rice futures market has not been included in any of these studies. The thinness of trade in both physical and futures market has prevented much attention to be drawn to the rice futures market. This market was permanently established on the CBOT in October of 1994. The rice futures contracts have much lower trading volume relative to futures contracts of other major grains and agricultural products. However, in the past decade speculative activity has clearly been on the rise in the rice futures market. Open interest and trading volume attributed to speculators (non-commercial interest) have been consistently increasing over the past several years. Therefore, it is time for the rice futures market to be scrutinized and its relationship with the rice cash market studied. The purpose of this study is to examine the impact of futures trading and changes in speculative positions in the futures market on the cash price volatility of rice in United States. This work builds on Friedman’s (1953) argument that speculation by rational (informed)  1  In this work commercial traders are defined as those who hold positions in both the underlying commodity and in the futures contract of that commodity. The source of this definition is the U.S. Commodity Futures Trading Commission (www.cftc.gov/oce/web/index.htm) 4  speculators leads to lower cash price volatility, whereas excessively speculative trading by irrational (misinformed) speculators would lead to the destabilization of the cash price. The theoretical model presented in this study shows that agents form price expectations and decide on storage levels by using the information they receive about the future demand levels. The model demonstrates how use of more accurate information leads to more efficient storage decisions and lower price volatility. Further, it illustrates how basing storage decisions on inaccurate information leads to less efficient storage of goods and higher price volatility. In order to test the prediction of the theoretical model, two types of empirical analysis are proposed. First Generalized Autoregressive Conditional Heteroskedasticity (GARCH) is used to measure cash price volatility before and after the introduction of the rice futures market. The second method makes use of Vector Autoregressives (VAR) and the Granger Causality Test to measure the impact of change in speculative positions in the futures market on the cash price volatility of rice. 1.2 Objective  The general objective of this work is to present and empirically test a refined form of Friedman’s (1953) theory on the impact of speculators on price volatility. This study uses rice futures market as a proxy for the presence of speculators in the rice market. 1.2.1 Specific Objectives  There are several specific objectives that need to be met in order to achieve the goal of this work specified above. The following line indicate these specific objectives. a) Develop an understanding of the world and US physical rice market. b) Explain the mechanics of the futures markets and how they are used for speculation in the physical market. 5  c) Establish a theoretical model to assess the impact of informed and irrational speculation on price volatility. d) Measure rice cash price volatility prior to and after the introduction of the rice futures market in United State. i. Measure international rice price volatility before and after the introduction of the rice futures market in China and on the CBOT. e) Measure the impact of a sudden rise in futures trading activity as a proxy for the presence of irrational (misinformed) speculators on rice cash price volatility. In addition to these objectives, the other goal of this work is to draw attention to the rice futures market and establish the ground for further research on the role that a viable rice future market can potentially play in stabilizing the world rice market 1.3 Study Plan   This chapter offers an introduction of the work along with the objectives that this project seeks to meet. Chapter 2 offers a background and a review of the global and U.S. rice markets. It provides a comprehensive literature review on the impact of speculation on price volatility through futures markets. Chapter 3 presents the theoretical model of this thesis. Chapter 4 describes the empirical methods and econometric tools used to test the theory. Chapter 5 discusses the data series used in this work and offers discussion and analysis of the results. Chapter 6 concludes this study by outlining the results and major findings of this work. It discusses possible directions for future studies.  6  Chapter 2: Background  This chapter is divided into two major sections. The first offers a review of the rice market. The second section presents a comprehensive review of the futures markets as well as the theoretical and empirical work that have been carried out to measure the impact of speculation on price volatility. 2.1 The Rice Market  It is important to understand the international and the U.S. rice markets before we engage in the analysis of the rice futures market in United States. A review of the world rice market dynamics helps one understand the high volatility that seems so embedded in the world price of rice. This global volatility in international prices could also be a major source of volatility in the cash market for rice in the U.S. given that for the most part United States is a price taker. United States produces only about 2% of the world’s rice (FAO 2007)2, and volatility of prices in United States could be greatly affected by the events on the world stage. Therefore, it is important to explore the dynamics of the world rice market before discussing the rice futures market on the CBOT. 2.1.1 World Rice Market  Rice is an important staple food for about half of the world’s population. It accounts for 30% of the total cereal production, and ranks second largest produced grain after maize (FAO 2007). However, unlike other important staple foods such as wheat and corn it does not trade in a free market environment. It has a weak connection to other commodities in that it is only produced for human consumption and not for animal feed or bio-fuel (Timmer, 2008). The market for rice is extremely thin as only about 5% of the rice produced in the world is traded. Therefore, rice has a high consumption to production ratio that has remained fairly  2  Figure 6 reports the total rice production in United States from 1961-2009 7  stable over the past few decades. This ratio is higher in South and South East Asian countries than other parts of the world where rice is produced. Approximately 80% of the traded rice is supplied by five countries, Thailand, Vietnam, United States, India, and Pakistan. For the most part rice is produced for domestic consumption. For instance China produces about 30% of world’s rice, yet her participation in the world market is close to zero (Timmer, 2009). Countries like Vietnam and India could be exceptions to this general rule, but even they stop exports of rice to secure supplies for domestic consumption3. Indeed the government of India’s policy of banning rice exports in 2007 is a testimony to how easily the world rice market could be left without any participants in it. Constant government intervention to control the supply and demand of rice does not allow world prices to play an important role in the decision making of market participants4. Siamwalla’s et al (1983) analysis of 55 countries showed that only 17 showed some degree of responsiveness to world prices. Therefore, world rice prices do not reflect the true supply and demand levels in the rice market. Government intervention in the market tends to be a sudden reaction to the current situation in the market, which could lead to higher price volatility. Indeed, in the six months between October 2007 and April 2008 the price of rice tripled to about $1000/tonne and reached unseen levels in nominal terms (Dawe & Slayton, 2009)5. This unpredictability in the price of rice discourages private participation in the rice market. The world rice market is one in which its participants for the most part are there to secure domestic supplies to avoid shortages and political instability, or to achieve self-sufficiency for largely domestic political reasons. They are not there to profit from price swings. This has been  3  Since the early 1980s Thailand has become a consistent exporter of rice with fluctuating quantities. It is now the biggest exporter of rice in the world. 4  It should be noted that the governments of South and South East Asian countries are the largest participants in the world rice market. Therefore, unless specified any reference to government policy or intervention in the rice market involves those governments. 5  The world price is the price of Thai 100% B second grade-Figure 7 8  the norm for decades in the rice market and has led to shortages and price volatility unseen in other major grains’ markets. High level of government involvement in the rice market may lead one to conclude that the rice market is the most regulated and stable of all grain markets. Despite the presence of governments and this degree of regulation, the rice market has experienced and continues to experience tremendous price fluctuations. The sharp price increase of 2007-08 mentioned earlier was followed by a fall of 40% from May to December 2008. A few decades earlier, rice prices increased by $200 per metric tonne per month in 1972 and 1973 after more than a decade of almost no change (Petzel & Monke, 1979). These price fluctuations did not reflect the true scale of shortages or abundance in the world rice market. It is now generally agreed that perception (rather than reality) about the immediate supply of rice and subsequent policies of some of the Asian governments played a significant role in rapid price increases of 2007 and 2008 (Timmer, 2009). To cite a few examples; the government of India (the second largest exporter in 2007 with 5 mmt6) imposed a ban on non-basmati rice in 2007 in order to secure domestic supply to prevent domestic prices from increasing. The government of Thailand, the largest exporter of rice with nearly 10 mmt in 2007 discussed the reduction of exports for the same purpose in March 2007. On the demand side, the Philippines (the largest importers of rice in the world)7 announced its plans to increase its rice stocks by two or three folds (Dawe & Slayton, 2009). According to Timmer’s (2009) supply and demand model, a 25% increase in short-run demand will lead to a 167% increase in rice prices. Panic led to both shortages and political instability in some countries that depend on rice as a major source for food, the very thing that the government policies intended to avoid.  6  mmt = million metric tonnes 7  The Philippines is expected to import more than 2.4 mmt in 2010 (Source: Food and Agricultural Organization) 9  Indeed studies show that the structure of the rice market results in such an outcome. Speculation is present in the rice market however, it is in the form of supply speculation and not price speculation. Another characteristic of the rice market is that rice is produced by smallholders and traded by a small group of traders. Unlike other grains rice is not always stored by commercial interest in the market. This characteristic makes collecting inventory data on rice difficult. According to Timmer (2009) short run price behaviour in commodities that have reliable and readily available inventory data depends on supply behaviour. However, short run price behaviour of commodities with scarce and unreliable inventory data, depends on changing price expectations reflected by hoarding and dishoarding the commodity. The scarcity of data on rice inventories, thinness of the rice trade, and absence of private agents in the market are all structural characteristics of the world rice market, which are the main contributors to the rampant volatility in the rice market. The world production of rough rice is approximately equal to the production of maize and wheat.  However, its trade quantity is much lower than the two. In 2007 the production of rice paddy (rough rice), wheat, and maize stood at 657, 611, and 788 million tonnes respectively. In the same year only 31 million tonnes of rice was traded compared to 110 and 133 million tonnes of maize and wheat respectively (FAO, 2010). Figure 3 provides a juxtaposition of total annual production for rice, wheat and maize over past five decades. Siamwalla et al (1983) suggest that the creation of the role of seller of last resort or a central market for rice alters these characteristics and reduces rice price volatility. They cite the wheat market as an example where the presence of the United States as a central market (where wheat futures contracts are traded) and a seller of last resort has been a stabilizing factor. It has also been suggested that United States can do the same for the rice market. 10  2.1.2 United States’ Rice Market   United States has traditionally played an important role in the world rice market. With the exception of the Civil War years It has always been a major exporter of rice since the 1700s (Cole, 1927). In the early 1800s U.S. was exporting more than 90% of its rice output which amounted to about 10% of the total trade (Coclanis, 1993). In present day nearly all the rice in the United States is grown in five states: California, Louisiana, Arkansas, Mississippi, and Texas. California produces the short grain high quality japonica type, and the other four produce the indica type given their hotter climates (USDA, 2007). United States is the only major rice exporting country that is not preoccupied with securing domestic supply. There are also a few other features that make the U.S. unique in world rice market. Only 2% of the annual world rice production belongs to the U.S, yet its share of trade in the global market is more than 10% (Childs & Balwin, 2009)8. United States has never put any restrictions on rice trade particularly on the quantity of exports, and it is one of the few major rice producing/exporting countries that respond to world price of rice9. However, pricing of rice in United States is done through cooperative pool pricing, and not competitive auctions (McKenzie, Jiang, Djunaidi, Hoffman, & Wailes, 2002). Government intervention in export of rice from the US is limited to export subsidies and quantity produced (Siamwalla & Haykin, 1983). The U.S. government has never implemented a policy to build rice stockpiles similar to other major rice producing countries. There have been policies that have indirectly affected exports of rice from the U.S. In response to rice price volatility and in order to lower it, the US government implemented the Rice Marketing Loan in 1985. This resulted in the U.S. rice prices  8  The US’ share of global rice trade was much higher.  From the early 1700s until the beginning of the civil war the United States was the largest exporter of rice in the world. It even exported to major rice producing countries such as China. Due to the civil war United States lost this status only to regain it in the beginning of the 1960s and maintaining it until the middle of 1980s (Coclanis, 1993). 9  Prices in Thailand’s domestic market also respond to world prices 11  being above the world price for almost two decades and effectively reduced U.S. rice exports while increasing government rice stocks (Taylor, Bessler, Waller, & Rister, 1996). Despite the relatively liberal policies toward rice exports, United States is still not a seller of last resort in the world rice market. Perhaps the only issue that has prevented the United States from acting as the seller of last resort in the rice market is that unlike wheat, U.S. is not a large enough producer of rice. Therefore, it can never build enough stocks to meet a sudden surge in demand from the major rice consuming countries (Siamwalla & Haykin, 1983). The world rice market needs “relevant stockholdings” which implies that stored rice can affect world prices. Many countries store rice, but this does not mean that they have the intention of releasing the rice in stock into the world market. Therefore, the existence of an offshore storage where storage of rice is done by speculators or private enterprise could be an important factor in stabilizing the market. This offshore storage should not be subjected to government policies of various countries. The speculators should be motivated to get involved in this market for profit. Only in the U.S. does such a central market exist for rice in the form of a futures market. The results of this study could shed some light on whether rice futures markets are a viable solution to reducing (even if not eliminating) the seemingly inherent volatility in the rice market. 2.2 Futures Markets and the Impact of Speculation on Price Volatility   Prior to describing the nature of the rice futures market in United States, it is important to have a broad understanding of the mechanics of futures markets in general and their impact on cash price volatility in particular by speculative behaviour. 2.2.1 Futures Markets and Contracts  Futures contracts are standardized contracts that oblige their holders to deliver or take delivery of a specified quantity of a specified commodity at a specified date in the future. These 12  contracts are traded on futures exchanges around the world. The most notable exchange is the Chicago Board of Trade (CBOT), which was founded in 1848 and listed the first futures contract in 1864. The agent who enters a futures contract to take delivery of a commodity in the future is said to be taking a “long” position. The one who is obliged to deliver the commodity at a specified date in the future is said to be taking a “short” position. The speculative agent with the “long” position expects prices to rise and the one with the short position expects prices to decline by the time the futures contract s/he has entered in matures. For example an agent who takes a “long” position in February 2012 rice futures contract believes that rice prices in February 2012 will be higher than what the market currently expects rice prices to be in February 2012. The agent with a “short” position anticipates the opposite. There is a “short” position for every “long” position. Therefore, all gains in a “long” or “short” position are offset by losses in the opposing “short” or “long” positions respectively. The role of the futures market in the economy extends beyond providing a platform for individuals to engage in a zero sum game. The presence of the futures contracts and markets allows for a more complete market. A complete market is one in which there exist enough investment instruments to allow investors to bet on or protect themselves against (either directly or indirectly by combining different existing instruments) all possible outcomes in the market. Transaction costs prevent the existence of a market that takes into account all states of the world. Yet uncertainty about the future state of the world concerns investors and they look for ways to be as prepared for any future state of the world as possible. They do this either by hedging their current position or speculating that a particular state of the world will materialize (Strong & Walker, 1987). 13  Futures market allows market participants (hedgers and speculators) to do that. Futures market and futures contracts provide a cost effective way for agents to prepare for anticipated or unanticipated states of the world that affect market outcomes. 2.2.2 Speculation and Price Volatility  Participants in the futures market can be divided into two groups: hedgers and speculators. Hedgers enter the futures market to lock the price of a commodity they plan to buy or sell in the future. Speculators enter the futures market to bet on the price movement of a particular commodity, and hence are in the futures market for profits. As hedgers go “long” or “short” in the futures market depending on whether they wish to buy or sell (respectively) a commodity in the future, speculators take the opposite side of the contract and bear the price risk that initially rested with the hedgers. In order to transfer the risk to speculators, hedgers are willing to pay a premium. The expectation of receiving this premium is one of the reasons that speculators enter the futures market and bear the price risk (Keynes, 1930)10. Therefore, speculators are a necessary part of the futures market, if it is to function as a place where traders of the physical commodity can hedge their positions. Despite the role they play in mitigating the risk to the physical market participants, futures contracts are viewed with concern as many believe they may also have negative impacts on the price and allocation of the underlying commodity. Futures contracts and markets have been a subject of controversy from their inception in Chicago in 1864, over their impact on the spot (cash) price of the physical commodity. Politicians and many traders in the physical (cash) market believe that speculation in the futures  10  Keynes asserts that the “short” position of hedgers requires the speculators to take a “long” position. The speculators take that position if the expected future price of the commodity in the futures contract is higher than the current future price specified in the contract (i.e. E(St+1) > Ft), where E(St+1) is the expected spot price in the future and Ft is the current future price reflected in the futures contract (Keynes, 1930). 14  market leads to volatility (destabilization) of the spot market (Antoniou & Holmes, 1995). The impact of speculation on the stability of the cash market has been a subject of numerous studies. Friedman (1953) asserts that there is no reason for speculation to lead to the destabilization of prices in the physical market, because speculators buy when prices are low (low demand and high supply) and sell when prices are high (high demand and low supply). This course of action by speculators causes prices to rise when they are low and decline when they are high (Friedman, 1953). In addition, Friedman argues that saying speculation is destabilizing is equivalent to saying that speculators lose money11. According to Friedman only irrational (misinformed) speculators destabilize prices. Hart et al. (1986)12 take an opposite view and argue that in a market where rational agents have access to identical information and history, speculation may increase price volatility. According to them, rational speculators base their decision to enter the market in this period on the probability of high demand level in the next period. In the Hart et al. model speculators buy and store a commodity if they receive the high demand signal for next period. It should be noted that the signal only indicates high probability and therefore the next period high demand may not materialize. False signal means that next period speculators will dump the commodity in the physical market leading to a further decrease in prices13. Therefore, when demand is low, the lowest price in the absence of speculators is higher than the lowest price in their presence. The presence of speculators widens the range over which prices fluctuate (Hart & Krept, 1986).  11  According to Friedman speculators would destabilize the market if they buy when prices are high, leading to further rise in prices, and if they sell when prices low, leading to further decline in prices. This action will lead to losses for speculators. 12  Although Hart and Kreps (1986) paper does not assess the impact of futures market on the spot market, it offers a comprehensive study of the impact of speculation on the spot price of the physical commodity. Therefore citing their work is warranted given that speculation is an essential component of the futures market. 13  The model assumes speculators can only store for one period, demand for the commodity is elastic, and every period a fresh fixed amount of the commodity is supplied to the market irrespective of consumers’ and speculators’ demands and actions. 15  This may not be true if speculators have foresight. In the extreme case of perfect foresight where next period’s prices are visible in this period, the presence of speculators does not lead to wider range of prices. There are two cases in perfect foresight: 1) Pt+1 > Pt or 2) Pt+1 < Pt. In the first case, there will be speculative demand in the market in period t given that speculators know that prices in the next period (t+1) will be higher. This extra demand by speculators means a higher price in period t than the lowest price without speculators in that period. In period t+1, when speculators sell their stored commodity, prices would be lower than what they would be without speculators. In the second case, speculators do not enter the market to buy the commodity at time t knowing that prices will be lower at t+1. In this case prices are not raised further in t relative to t+1 because there will not be an additional demand from speculators. Also, prices are not depressed further in t+1 because there are no additional supplies released into the market by speculators. In general Hart et al. assert that complete foresight is required for speculation to be stabilizing (Hart & Krept, 1986). Figure 1 demonstrates this. In both cases in figure 1 the width of price range (volatility) between the two periods is lower when speculators have foresight and are informed than when they are not. Further in their analysis, Hart et al. indicate that speculation could lead to stability from the production side. Current increase in speculative demand could also be a signal to producers that demand for their products will be higher in the future. As a result producers invest in increasing capacity in the current period in order to produce more in later periods. Under these circumstances prices would be lower in the future when demand is high than they would have been without the extra production. 16    2.2.3 Speculation through Futures Markets and Cash Price Volatility  Speculation through a futures market, where speculators do not necessarily store the physical commodity, may have additional and somewhat distinct ways of affecting the volatility of prices in the physical market. Miller (1991) points out that the interdependency of the physical (cash) and the futures market requires that price changes in one be transferred to the other. This could lead to volatility, which is exacerbated if markets are separated in terms of trading hours, speed with which trading can be done, and transactions costs etc (Miller, 1991). Valentine (1995) mentions that value of the futures contracts exceed the value of the physical underlying asset because there can be an unlimited number of futures contracts. This makes unlimited speculation possible, which can lead to higher or lower prices than otherwise would be possible in the physical market. However, this flexibility in the futures market can absorb the shocks in physical market. A supply shortage leads to higher prices in the physical market. However the futures market can mitigate the price increase in the physical market by allowing traders to take long positions and claim future supplies rather than seeking the goods now for later use (Valentine, 1995). Powers (1970) addresses the role that futures markets play in increasing information about the fundamentals (supply and demand) in the physical market. According to Powers a price series has a systematic and a random component (2.1). Therefore, variance and volatility in a price series also have a random and systematic component (2.2). Pt = St + Rt           (2.1) Pt = price time-series St = systematic component Rt = Random component V(Pt) = V(St) + V(Rt) V= variance        (2.2) 17  The systematic part of the price series reflects the changes in the fundamentals of the commodity such as supply and demand. The random part reflects the “noise” and movement in price that is not related to the fundamentals. This component distorts the message that prices (which are essential for further allocation of resources in the economy), send. The random component (disturbance) may arise from insufficient information and distorted price messages sent to the market. This disturbance may have several sources. Kawai (1983) points to the importance of the source of random disturbances in determining whether the introduction of futures market has any impact on cash price volatility. In Kawai’s model there are three types of agents in the physical market: consumers, producers, and inventory carriers (dealers). The introduction of the futures market could have a stabilizing or destabilizing effect depending on which of these agents is the source of volatility. For example, when dealers are infinitely risk averse, the introduction of a futures market increases price stability in the cash market if random disturbances are predominantly coming from the activities of consumers. However, the opposite would be true, if the disturbances were predominantly from the production or dealer side (Kawai, 1983)14. The more informed economic agents are about the fundamentals the more they will base their decisions on real changes in supply and demand. The futures market allows for a better and faster flow of information, hence reducing the variance in the random component of the price series. Prices in the futures contracts include information on production, storage, supplies, demand, current cash price etc. This information, available through numerous institutions and exchanges around the world is used by speculator and cash market participants alike (Powers, 1970)15.  14  Kawai’s model is applied to storable commodities 15  Although Powers’ analysis shows that the random component of price variance is reduced after the introduction of the futures market, it does not address the impact of the futures market on the variance of the systematic component of the price series. He acknowledges that the introduction of the futures market may have a different 18  Higher quantity of information does not necessarily imply higher quality of information. Cox (1976) addresses this issue by analyzing the influence that speculators could have on the allocation of storable goods in the cash market. Futures markets attract traders (speculators) who are only interested in the price movement of the underlying commodity, do not handle it, and would not be present in the market had it not been for the futures market. The speculators take net long or short positions, which implies that hedgers could be taking the opposite position. Therefore, speculators’ belief about the future price leads to the reallocation of some of the current physical stock hence changing the cash price16. By this analogy misinformed speculators can alter price expectations in the spot market that do not really reflect true market fundamentals17. Whether speculators who spend time and resources to acquire information about the underlying commodity have high quality information to bring efficiency to the market is still debated (Cox, 1976). However, Ross’ (1989) argument of the relationship between information flow volatility and price volatility renders the information quality argument somewhat immaterial. Ross’ model asserts that in the absence of arbitrage18, the volatility of prices should equal the volatility of information flow (Ross, 1989). This could imply that the introduction of futures markets, while increasing the volume of available information, also increases the volatility of information flow and lead to higher price volatility. It may not be possible to assert with certainty whether futures markets lead to volatility in cash prices or not. None of the literature reviewed in this section reach a general conclusion  effect on the variance of the systematic component of seasonally produced and storable commodities (Powers, 1970). 16  Hedgers here are not just producers of the commodity but also agents who may use the underlying commodity in the production of other goods. 17  This argument could perhaps be applied to when two speculators enter a futures contract (no hedgers involved). Participants in the physical market view this transaction from outside. Based on their belief about which speculator is better at predicting the future price, they can shift and reallocate the physical stock. 18  Ross’ assumption has two major assumptions: 1) markets are efficient (no arbitrage) 2) information for period t only becomes available in period t). 19  about the impact of the futures market on cash price volatility. However, collectively they lay the theoretical ground for a better understanding of the rice futures market in the U.S. and its impact on rice cash price volatility. 2.2.4 Futures Market and Cash Price Volatility: Empirical Evidence   In addition to theoretical works, there have been many empirical studies on the impact of futures trading on cash price volatility. Many agricultural and non-agricultural commodities have been the subject of these studies. These studies measure cash price volatility before and after the introduction of the futures market. The following paragraphs offer a review of several of these works. The U.S. congress banned the trading of onion futures contracts through the Onion Futures Act in August 1958 (U.S. Code, 1958). The implementation of this act ignited research on effect of futures trading on cash price volatility. Early works by researchers such as Gray 1959 concluded that onion futures contract trading reduced the seasonal spot price range in the onion market (Gray, 1959). Gray’s 1963 work suggested that after the banning of the futures trading in the onion market, the price range was increasing and going back to its pre futures trading years (Gray, 1963). Building on this, subsequent research was conducted to evaluate the impact of futures trading in other commodities’ markets. These early works concluded that the futures market: a) lowers seasonal price range due to the presence of speculative support at harvest time. Speculators are willing to take ownership of the harvest, hence prices do not drop, and this leads to more grain being stored by the farmer. More grain in store prevents prices from rising too high later in the year b) acts as a guide for better production planning and hence leads to less annual price fluctuations c) allows for better anticipation of price adjustments and rational storage decisions by commercial traders, which would lead to lower volatility (Powers, 1970), (Leuthold & Taylor, 1974), and (Morgan, 1999). 20  The futures market achieves the three points above by facilitating information flow through the actions of thousands of traders in the market. More information causes the market price to be closer to the equilibrium price which would signal the true level of supply and demand. Therefore, there will be less variability in cash price once the decision of suppliers and consumers are based on close to equilibrium prices (Powers, 1970).  There have only been a few studies on rough rice futures market in United States. These works have focused on market efficiency and estimating whether the rice futures market is biased19. In a 2002 paper, McKenzie et al used various methods (Johansen cointegration procedure and Error Correction Model) to analyse the ability of the current futures price to provide an unbiased estimate of cash price when the contract matures. They find that rice futures prices outperformed both of those methods in forecasting the future cash price of rice in short and long run (McKenzie, Jiang, Djunaidi, Hoffman, & Wailes, 2002). Taylor et al. (1996) study the relationship between US rough rice cash prices, Thai milled rice price and rough rice futures price (Taylor, Bessler, Waller, & Rister, 1996). A detailed review of this work will be offered in section 2.2.7. 2.2.5 Cash Price Volatility before and after the Introduction of Futures Market   Futures markets have allowed non-commercial interest and speculative money to enter the commodities market. This has given rise to the question of whether the presence of this speculative money and generally futures trading has increased cash price volatility. It is said that a well functioning futures market guides the commodity storage decision and smoothes its release into the market (Morgan, 1999). Majority of the analyses using various methodologies show that futures trading has indeed reduced cash price volatility.  19  Downward biased futures price means lower current futures price than what is expected to be received at maturity. Upward biased futures price means higher current futures price than what is expected to be received at maturity. 21  Powers (1970) used the Variate Difference Method to separate the random (noise) component of the time-series price from the systematic component20 for pork bellies and cattle before and after introduction of futures trading for these two commodities. He found that the variance of the random component was reduced after the introduction of the futures trading for both commodities (Powers, 1970). Leuthold et al (1974) simply used the variance of the monthly average cash price of cattle around two eight year period averages. They concluded that this variance was significantly lower in the second eight year period (during futures trading) than in the first eight year period (before futures trading). Morgan (1999) used standard deviation to measure cash price volatility of potato in Britain and concluded that after the introduction of futures trading in 1980, cash price volatility has been reduced. Antoniou et al (1992) used the GARCH model to represent the cash price return volatility of crude oil and their results strongly rejected the null of no change in volatility pre and post futures trading (Antoniou & Foster, 1992). In addition, the coefficient of their cash return volatility was less important in explaining cash returns after the introduction of futures trading. They tested both models for unit root to assess the persistence of the shocks in the crude market and found that the post future volatility model was stationary whereas that of pre-futures was not. Their results also indicated that post introduction of futures trading, ‘news’ becomes more relevant in explaining the conditional variance of cash return as information flow and hence reaction to news is faster because of the futures market. In contrast, lagged volatility becomes less important in explaining current period variance, and the authors attribute this to the fact that any risk posed by lagged volatility could be hedged away21.  20  Systematic component refers to fundamental economic conditions such supply and demand 21  The detailed model used by the authors will be discussed in the Model section of this thesis. 22  In this study the GARCH model will be used to measure the cash price volatility of rice before and after the introduction of rough rice futures trading on CBOT. The rice futures market is a thinly traded market. Therefore, trading frequency may play a part in determining whether a futures market is beneficial in allowing for better flow of information in the market for the underlying commodity. Using the GARCH volatility model Holmes (1996) demonstrate that a thinly traded futures market lowered the volatility in the cash price of the underlying asset22. By analysing the components of the GARCH volatility model, he shows that despite a low trading volume in the futures market, the information flow was improved and persistence of shocks (new information) in the market was reduced23. This implies that despite low frequency of trade, the futures market could still facilitate information flow and price discovery. 2.2.6 Level of Futures Trading Activity and Cash Price Volatility   More recent literature has focused on the question of how trading activity in an existing futures market affects spot price volatility. This section is concerned with the impact of change in futures trading volume and open interest (i.e. level of futures trading activity) on cash price volatility. The activity level of the futures market contributes to the volatility in the cash market in three ways: First is when manipulation and technical factors distort futures prices, and traders in the futures market act on false signals. Second, lack of speculation in the futures market and pure hedge trading in that market could lead to instability in the cash market. The hedging pressure in the futures market affects the cash market through dealers and market makers who are now bearing the risk from both the cash and the futures market. Finally, if traders in the futures market are not as well informed as the participants in the cash market, then the actions of the former lead to distortions in the cash price. The better  22  The futures contracts were written for FTSE Eurotrack 100 index which covers the largest capitalized companies in 12 European countries. 23  Please see “Model” section of this work for a detailed analysis of the GARCH volatility model. 23  informed commercial traders in the cash market will then use this distortion to generate profit (through arbitrage) and inadvertently stabilize the futures market at the expense of increasing volatility in the cash market (Figlewski, 1981). The last point implies that due to less friction and lower transaction costs, prices adjust much faster in the futures market. This price adjustment enters the underlying cash market through arbitrage and given that normally large transactions are required to generate profits from arbitrage, the cash market becomes more volatile (Antoniou & Foster, 1992). Harris (1989) found short run volatility in the stock price returns as trading volume in S&P 500 index futures contract increased. Large transactions in the futures market are normally accompanied by related transactions in the cash market. Therefore, lack of liquidity in the cash market (in terms of the volume of transaction) and higher trading volume (activity) in the futures market would lead to higher volatility in the cash market. He found no such relationship in the long run once liquidity has entered the market (Harris, 1989). Another interesting study done by Adrangi and Chatrath (1998) on exchange rates found no relationship between the open interest position of large hedgers and change in cash price volatility. However, they found such relationship between open interest and cash price volatility once there was an increase in open interest position of speculators in the market (Adrangi & Chatrath, 1998). Epps et al (1976) suggest that if traders disagree on the magnitude of the impact of new information on asset valuation, then both trading volume and price volatility would rise (Epps & Epps, 1976). Their study was not specifically directed at the interaction between futures trading volume and cash price volatility, but their result is applicable to that field. The rapid absorption of the information in the futures market and traders’ decision based on their interpretation of the new information could increase futures trading volume and in turn affect the cash price volatility as described earlier. 24  Bessembinder et al (1992) found that cash price volatility decreased after the introduction of equity futures market. However, they conclude that an increase in unexpected trading volume in equity futures market increased cash price volatility (BESSEMBINDER & SEGUIN, 1992). In addition, they found a reduction in cash price volatility as open interests position increased in the futures market.  There have been only a few empirical studies on the effect of the level of futures trading on cash price volatility for agricultural commodities. Yang et al (2005) study the lead-lag relationship between the futures trading level and cash price volatility for several agricultural commodities (not including rice). They used the Granger Causality test and the Generalized Forecast Error Variance Decomposition (GFEVD) to examine the effect of an increase in future trading volume and open interest positions on cash price volatility (which they modeled using GARCH 1,1). They concluded that an unexpected increase in futures trading volume of these commodities caused an increase in cash price volatility for most of the commodities under examination (Yang, Balyeat, & Leatham, 2005). 2.2.7 World and U.S. Rice Price: Pre and Post Introduction of Rice Futures on CBOT   The relationship between U.S. rice and world rice prices has come under scrutiny in the context of studying how integrated the world rice market is. In evaluating the degree of integration in the world rice market Petzel et al (1979) studied the reaction of rice prices in United States to changes in world prices. They used the Granger causality test and found that Thai prices from the previous month explained the current prices of US rice (Petzel & Monke, 1979). Understanding this relationship has become more interesting with the introduction of the rice futures trading in United States. Taylor et al (1996) concluded that there is a long run equilibrium price relationship between the rough rice futures market and Thai rice. Therefore, the rough rice futures market in 25  United States could be an important price discovery tool in the international rice market or at least it can be relied upon to convey new information in the international rice market (Taylor, Bessler, Waller, & Rister, 1996). This price discovery role by a central market has been sought by experts in international rice market for decades and was discussed in earlier sections. Similar studies in other areas may shed light on how a thinly traded futures market can link the larger world market to the domestic cash market. Martikainen et al (1994) show that the information from world’s stock markets is transmitted to the Finnish stock market through the Finnish stock index futures. They found that world stock market returns Granger cause changes in the Finnish index futures returns. Subsequently the Finnish index futures returns Granger cause the change in the returns of the Finnish stock market (Martikainen & Puttonen, 1994). Therefore, the presence of a futures market, however thin could be a communicator of information in a particular market. 2.2.8 United States’ Rice Futures Market   The first rice futures market was established in the Tokugawa period in the city of Osaka in Japan in 1730. Research shows that this futures market possessed all the characteristics of a modern futures market (Schaede, 1989)24. The New Orleans rice futures market which was established in the mid 1970’s and closed a few years later, was perhaps the first attempt at allowing in investors and speculators into the rice market in United States25. Rough Rice futures contracts began trading for a second time in U.S. on the Chicago Board of Trade in 199426. Each futures contract obliges the owner to purchase or sell  24  Same source claims that this market is the oldest modern futures market in the world. 25  The U.S. government policy of floor loan rate led to a domestic price higher than the world price, and little to no variation in the market price. Therefore, a central market with the desirable objective mentioned above could not exist. 26  Starting in 1986 rice futures resumed trading on the Chicago Rice & Cotton Exchange, which then merged with Mid American Exchange. Rice futures traded there until their move to CBOT in October 1994. The contract is for the delivery of No. 2 U.S. long grain or a better quality. Contracts size is for 2000 hundredweight of rough rice (200,000 pounds) (CBOT, Rough Rice Futures, 2008). 26  approximately 91 tons (or 2000 hundredweights) of long grain no. 2 rough rice with a milling yield of not less than 65% (CME, 2011)27. With the introduction of the futures market on the CBOT, the entrance of speculators and non-commercial interest into the rice market in the United States was facilitated, and there has been a steady growth of non-commercial interest in the market. For example, in 1994 non- commercial long positions (Figure 8) in the market as a percentage of total reported long positions was about 23% compared to 55% at end of 2009 (CFTC, 2009)28. However, the rice futures market is still considered a very thin market relative to the other grain futures market in United States namely maize and wheat. For instance, during the last trading week of 2009, the wheat futures market had 18 times and 117 times more non-commercial long and short open interest positions respectively than the rough rice futures market (CFTC, 2009). The trading volume of maize and wheat futures contracts expiring in May 2010 were 1183 and 2783 respectively, whereas that of rough rice was only 321 (CBOT, 2010)29. Despite the thinness of trade in the rice futures market, it would be interesting to evaluate its impact on the rice inventories and cash prices in United States and abroad. The CBOT may not be large enough to accommodate the speculative and hedging position of all rice market participants in the world but it can act as a launching pad for the creation and expansion of other such markets elsewhere in the world. Indeed in March 2009 Zhengzhou Commodity Exchange introduced rice futures, which could be the first step in establishing a large central market for rice where private speculation can take place (Forbes, 2011). It is therefore, essential to evaluate the 16 year performance of the rice  27  Figure 8 shows the complete specification of a rough rice futures contract 28  The share of non-commercial short position in total reported short positions has been consistently falling since 1994. At the end of 2009 it stood at 8%. This could be due to the usage of short contracts as hedging vehicles by farmers or the board, and the fact that the price of rice has not shown sign of decline since that time to motivate speculator to take short positions in the futures market. 29  March 18 th  2010 27  futures market on the CBOT in terms of affecting the volatility of the cash (spot) price of rice and its impact on world rice prices.  The impact of futures contract trading on cash prices of the underlying commodity has been a topic of discussion in agricultural economics for many years. Many studies have been done on various commodities’ futures trading. Futures contracts are used by hedgers to lock their profit/revenue from the crops they cultivate. They are also used by speculators to bet on the price direction of commodities. Futures contracts are the only vehicles that speculators (non- commercial traders) can use to profit from the price movement of a commodity, without having to take possession of the actual commodity30. It is the actions of the latter in the futures market that has given rise to numerous works on the impact of futures contract trading on the cash price of the underlying commodity. This study has been motivated by allegations that the activity of non-commercial interest in the futures market is responsible for cash price volatility. The rice futures market with all the unique characteristics that the rice market has will enable us to test theories relating speculation to price volatility. Almost all commodities with traded futures contracts on the CBOT have been analyzed, and the analysis has been focused on assessing the cash price volatility prior to and after the establishment of the futures market. More recent work has been focused on analysing the impact of the level of trading activity in the futures market on cash price volatility. In this work both analyses will be conducted to examine the theory that will be put forward in the next chapter. 2.3 Summary   The world rice market has experienced significant price volatility over the past few years. The mechanics of the rice market do not allow it to function and allocate the rice based on prices.  30  By owning exchange traded funds, investors trade futures contracts indirectly. 28  United States is a rice producer and in recent years has become a major supplier of rice to the world market. It hosts the only major rice futures market in the world.  Futures markets have played a key role in allowing market participants to hedge their positions. They have also attracted speculative non-commercial interests to the market. The actions of this group and their impact on cash price volatility have been a subject of many theoretical and empirical studies. These studies have failed to provide a clear answer on the impact of speculation on price volatility. However, they provide the necessary theoretical and empirical framework for studying the impact of futures trading on rice price volatility.  29  Chapter 3: Theory   This chapter presents the theoretical model of this study, which is built on Milton Friedman’s (1953) work on the impact of speculation on price volatility. It begins by presenting the general theory and describing how it applies to this thesis. The second part of this chapter discusses the details of the theoretical model that this thesis tests. 3.1 The General Theory and its Application to this Study  The general theory of this thesis is that speculation lowers price variation from one period to the next, unless it is carried out by irrational speculators. The following paragraphs explain how this theory could be applied to examine the impact of speculation in the rice futures market on its cash price volatility. In Friedman’s (1953) work, speculators buy and store the commodity, which makes them different from the speculators in the futures market. The latter do not take possession of the underlying commodity and simply close their positions by entering the opposite side of the futures contract. It may seem that speculators’ actions in the futures market do not have any impact on the physical market. On closer inspection however, the speculators’ actions and foresight in the futures market may entice the actors in the physical market to reallocate the commodity for sale or purchase to a later period. Therefore, the speculators in the futures market could have an indirect effect on the allocation of the commodity in the physical market, making Friedman’s theoretical work applicable to a situation where speculators act through the futures market. As described earlier the futures market increases the flow and quantity of information. The price of the underlying commodity indicated in the futures contract reveals market participants’ expectations about the future of supply and demand of that commodity. These expectations are formed through research done by many agents with commercial and non- 30  commercial interests. Needless to say, the non-commercial interest (speculators) would not be there without the existence of a futures market. Friedman (1953) asserts that only irrational speculators who act on misinformation destabilize the market. The proxy for the presence of irrational speculators in the futures market could be a sudden rise in the activity of speculators in the futures market. The unanticipated temporary presence of additional non-commercial interest in the futures market could lead (directly or indirectly) to higher price volatility. Friedman argues that irrational speculators lose money. They buy when prices are high and sell when prices are low, hence increasing the magnitude of the price variation. The sudden rise in the futures market activity is captured by a rise in volume and open interests in the futures contracts. Therefore, we will be looking at the impact of speculators’ trading activities in an established futures market on price volatility in the physical market. 3.2 The Theoretical Model   The following paragraphs explain the details of the theoretical model of this work. The model illustrates how speculation could lead to lower price volatility and how the presence of irrational speculators leads to higher price volatility (the full mathematical derivation of the results is available in appendix A) 31.  The first part of this section describes the parameters and assumptions of the theoretical model. It describes price volatility under the condition of certainty about the future. In the second part uncertainty about the future is added to the model. Under uncertainty, the model compares price volatility in a market with speculators to one without speculators.    31  I am forever grateful to my supervisor Professor James Vercammen for developing this section, which I call a refined form of Friedman’s theory. The theoretical framework of this study could not have been presented with such clarity had it not been for his input. 31  Parameters and Assumptions The theory is based on a two period model (t1 and t2). In the first period (t1), individuals are endowed with a fixed quantity of a good (Q1). Some of this good is consumed in the first period (t1) and some is stored (with a cost = m) for consumption in the second period (t2). Therefore, the quantity stored (S) in the first period dictates the level of prices in period 1 and period 2 (P1 and P2 respectively). 3.1 and 3.2 present P1 and P2 as a function of S. P1 = a – (Q1 – S)          (3.1) P2 =  – S            (3.2)  is the demand level in the t2 which could either be high or low  (S*) is the equilibrium quantity of the stored good. It is the amount of storage that minimizes the difference between P2 and P1. As (3.3) indicates the minimum difference between P2 and P1 should equal the storage cost (m) 32. P2 – P1 = m           (3.3) If (P2 – P1) > m, then more can be stored in t1 to be released in t2 and lower P2. Therefore, storage will continue until (3.3) is achieved. P2 – P1 < m, would signify that too much is stored in t1 and losses would occur carrying the goods from t1 to t2. Therefore, less should be stored to establish the equality in (3.3). It is worth mentioning that the storage cost (m) is expressed in terms of the good (i.e. it costs m goods to store the good in t1 for consumption in t2). The Model with Uncertainty The assumption so far, has been that demand levels for the endowed good are the same in both periods. However, demand levels (relative to supply levels) are subject to change from one period to another due to a number of factors. Indeed the reason for the existence of a futures market is to protect market participants from potential variation and change in the fundamentals.  32  This is the law of one price which indicates that the difference in price of a good between two periods must equal the cost of carrying that good from one period to the next. This assumes that all other factors such as demand level remain unchanged between the two periods. 32  The demand for the good in the second period (t2) of our model could be high or low ( or  respectively). This uncertainty in the demand level in the second period may cause more or less than the equilibrium level of stocks be carried over to t2 from t1. Therefore, with the element of uncertainty in second period demand level, the measure of price variability between the two periods, expressed as the expected squared price difference (ESPD) between t2 and t1 would become:  −   = 
 +   −          (3.4)  ESPD as a measure of volatility is higher when there is uncertainty about demand levels in the second period. Inequality (3.5) demonstrates that volatility is higher when there is uncertainty about next period’s demand level: 
 +   −  > 
          (3.5)  
 is the ESPD when demand level is certain in the second period (i.e 3.3 squared). In reality uncertainty is always present and there is always under or over allocation of goods to another period, which may cause prices to move away from the equilibrium point. The purpose of this study is to assess whether speculation could lower this under or over allocation of goods to another period. Could the presence of speculators in the market at least reduce the ESPD shown in (3.4) and bring its value closer to the m2? In other words, could speculation lower price volatility? The Model with Speculators  The two period model presented here makes the following assumptions to incorporate speculators. 1) There are two types of speculators 33  a. Speculators who act on information about the demand level in the second period. The quality of this information (), determines how likely it is for particular demand level to occur in the second period. b. Speculators who are convinced that demand level in the second period will be high, no matter what  indicates. These speculators either do not have access to the information that the first group has, or have some preconceived ideas of where the market is heading. Therefore, they are always bullish no matter what the information indicates. The degree of this bullishness is represented by . 2) There is an equal chance that the news regarding the demand level in t2 indicates either or . 3) The chances that one of or  materializes depends on which state  favours and its magnitude. Therefore, the expression for the expected squared price difference (ESPD) between the first and the second period in the market with speculators is as follows:  −   =  [  +  −   +   −  −  ] +    [  −  −   +   +  −  ]  (3.6) In state A, news in t1 indicates that demand in the second period will be low (i.e.  = ). In State B, news in t1 indicates that demand in the second period (t2) will be high (i.e.  = ). The probability of either news states A or B happening is 50%.  There are two possible outcomes once either state A or B is revealed. The actual demand level in the second period could be either low () or high (). In case of state A, the probability that demand will be low (i.e.  = ) in the second period is   +  and the 34  probability of  = is   − . In case of state B, the probability of  = is   −  and of  =  is   + .   indicates P2 in state A, where actual demand level in the second period is low.  signifies P2 in state B, where actual demand level in the second period is low. The other two notations ( and ) represent period two prices in states A and B, where actual demand level is high in the second period.  Equation (3.6) and the left hand side of inequality (3.5) are the ESPD for the markets with and without speculators respectively. The following sentences describe the dynamics and ESPD value in the market with speculators, and compare the results to the ones from the market without speculators. NS = without speculators WS = with speculators  −   = 
 +   −  = ESPDNS      (3.7)  −   =  −  + 2
 −  −  −  + 
 +   − = ESPDWS             (3.8)  Two immediate results emerge from equation (3.8). The first is that as  increases, ESPDWS falls. As indicated earlier,  signifies the quality of the information available in t1 about the level of demand in the t2 (i.e. ). As  increases there will be less uncertainty about the future demand, a more efficient allocation of goods for consumption in the second period takes place. ESPDWS, which captures the price difference between the two periods, falls. Speculation would be absent if  = 0. Therefore,  > 0 implies that speculators enter the market and act on this information regarding demand level in the next period. Therefore (3.8) demonstrates that speculation lowers the price volatility and leads to more stability. 35   The second result from (3.8) is that as  increases, ESPDWS (i.e. price volatility) also increases. As explained earlier,  represents the degree of irrationality (bullishness) of uninformed speculators. This result confirms Friedman’s argument that only irrational speculators destabilize the market. In the absence of irrational speculators ( = 0), and when speculators, who are acting on  > 0 are present, there is less volatility (ESPDWS < ESPDNS). However, as  increases for a given , the positive effects of informed speculation on stabilizing the market erode.  Further analysis of equation (3.8) indicates that there is a relationship between  and . For a given value of , there is a value for  (i.e. ∗ that neutralizes the stabilizing (i.e. volatility reducing) effects of  on lowering volatility. In other words, ∗ sets ESPDWS = ESPDNS. ∗ =  !"!#$#%!#$#%           (3.9) Equation (3.9) demonstrates that as the value of  rises, the value of ∗ also rises. As the quality of information increases, it takes more and more bullishness by irrational speculators to neutralize the stabilizing effects of speculation by informed speculators. There are three possible values for  for any given value of : 1)  < ∗: in this case ESPDWS < ESPDNS 2)  = ∗: in this case ESPDWS = ESPDNS 3)  > ∗: in this case ESPDWS > ESPDNS The three cases above indicate that the quality of information () should be sufficiently high to counter the destabilizing effects the presence of irrational speculators.  The model presented in this section confirms Friedman’s assertion that speculation leads to less price volatility, unless it is carried out by irrational (uninformed) speculators. The model indicates that the impact of uncertainty on price variability from one period to another is 36  mitigated once information based speculation is introduced into the market. As discussed earlier, the futures market is a conveyer of information about the fundamentals in the spot market. 3.3 Summary  This chapter describes the theoretical model of this study. The model shows that speculation reduces price volatility unless it is carried out by speculators who do not act on information. The action of these irrational speculators counters the stabilizing effect of speculation based on information. Higher quality of information leads to less price volatility and increases the level of misinformed speculation needed neutralize the stabilizing effect of speculation based on information.  37  Chapter 4: Econometrics  This chapter describes the econometric models used to test the theory that was discussed in chapter 3. It begins by describing the GARCH model, which is used to measure the rice price volatility before and after the introduction of the futures market on the CBOT. It then proceeds to specify vector autoregressive models (VAR) for the purposes of conducting the Granger Causality test and the impulse response function analysis. The latter two are performed to detect and measure any causality between futures trading activity and rice price volatility respectively33. Lastly, three detrending methods are proposed to capture sudden changes in futures trading activity. 4.1 Rice Cash Price Volatility   Generalized autoregressive conditional heteroskedasticity (GARCH) is used to model the volatility of the rice cash market in United States and the world. The GARCH model is commonly used when dealing with time series data. The use of GARCH as a model of volatility allows for the past shocks in the rice market to be included in the measure of current period volatility. More specifically, a GARCH (p,q) model would take the contribution from the lagged values of conditional variances into account (Bollerslev, 1986). Equation (4.3) represents a GARCH (p,q) model. '( =   + ) *+'(+,+-  + (         (4.1) ℎ( = /∘ +  ) /+,+-   (+                    (4.2)34 ℎ( = /∘ +  ) /+ (+ + ) 12ℎ(232- ,+-         (4.3)  33  Forecast error variance decomposition (FEVD) analysis will also be carried out along with the impulse response function analysis 34  Equation (4.2) represents the ARCH (Autoregressive Conditional Heteroskedasticity) process where the error variance is calculated only based on the lagged values of the error term. 38  '( represents the return on the asset over a period of time. *+ is the coefficient on the past values of asset returns. Equation (4.1) indicates that the current value of the return depends on the past values of the return plus an error term, represented by ( which has a zero mean and a conditional variance of ℎ(. The error term may not necessarily have a constant variance, ℎ( over time. This is due to the effect of shocks as they carry over to other periods in a time series data before they completely subside.  The error variance in the GARCH model depends on past variance (persistence effect of past information, ℎ(2 as well as exogenous shocks (new information, (+ . A reduction in the value of 12 implies that news from previous periods has a less persistent effect on current price changes. Similarly, an increase in the value of /+ implies that prices absorb new information more rapidly.  This quality makes the GARCH model applicable to the analysis of the volatility of the rice cash market before and after the introduction of the futures market. It allows the change in cash price volatility in the rice market to be dissected into two major components with different implications. For example, an increase in rice cash price volatility after the introduction of the futures market could imply a more rapid absorption of information (larger value of /+) by the market. Higher volatility could also indicate a higher persistence of the effect of past shocks and information (larger values of ℎ(2) in the market. The latter case implies that the futures market is not playing its roles as a conveyer of information and a market price discovery tool (Holmes, 1996).  The GARCH model is widely used in measuring price volatility in commodities, as it is superior to other volatility measures such as the simple standard deviation or the weighted average of historical price variance. The drawback with these methods is that they do not distinguish between the predictable components of error variance, namely past error terms (ℎ(2) 39  and the unpredictable ones ((+ ) as GARCH does. In the GARCH model, price risk and forecast are determined simultaneously where price risk is specified as a function of variance of the errors of prices (Jayne & Myers, 1994). In addition, as inferred above, the GARCH model accounts for the time-varying pattern of price volatility (Yang, Haigh, & Leatham, 1992).  To model the impact of futures trading on the volatility of the cash price of rice the following regression is proposed: 4( = *5 + * 67( + *8( + (         (4.4) Where 4( is the log return of cash price for rice at time t, CRB< and WP< are the log returns of the proxy variables (more below), and ( is the error term in estimating the cash price return. It should be mentioned that log return refers to the log of the ratio of next period’s price to the current one (i.e. log GHIJGH )35. The use of proxy variables in the model allows the impact of market wide changes on rice cash price returns to be isolated, leaving the error term to explain the sources of change specific to the rice market. The proxy variables should be commodities for which there are no trading futures contracts (Antoniou & Foster, 1992) or the price of which is not affected by the introduction of the rice futures market. In 2010 finding a commodity without an established trading futures market is a tedious task. Instead, the return on CRB Reuters Commodity Index (CRB) is used. CRB has been in existence since 1957 and provides a good reflection of the impact of shocks and new information in the commodity market in general36. Despite the fact that there have been futures trading on this index since 1986, similar studies have used it as a proxy variable in their models. It should also be noted that the values of 4( from previous periods (4(+)  35  It should be noted that log return and return are used interchangeably in this study and both mean log GHIJGH 36  The composition of CRBR index is as follows: Oil & Natural Gas: 17.6%, Grains (wheat, corn, and soybean): 17.6%, Industrials: 11.8%, Meats: 11.8%, Softs: 23.5%, Precious metals: 17.6% (Reuters, 2010) 40  are not included in the model specified by equation (4.4). The proxy variables specified in equation (4.4) contains all the information that (4(+) do and more, because they reflect the state of the wider commodity market. In addition to the CRB Index, the use of log return of the world price of rice in equation (4.4) controls for the exogenous events that solely impact the rice market and not other commodities. The volatility in the world price of rice has not been influenced by the introduction of the rice futures market on the CBOT (as will be shown in chapter 5).  All literature reviewed for this work pointed to the presence of heteroskedasticity in the price returns of various commodities. Therefore, it is assumed that rice is not an exception. The error term in equation (4.4) is estimated using a GARCH(1,1) model (equation (4.6)) ( = ℎ(K(           (4.5) ℎ( = /L + / (  + 1 ℎ(          (4.6) Most of the previous work on commodity market volatility have chosen the GARCH(1,1) specification (Antoniou & Foster, 1992) and (Yang, Balyeat, & Leatham, 2005). The frequency of the data used in this work is monthly, a GARCH(1,1) model should be adequate to fully account for the effect of past news on current volatility37. The entire cash price series is divided into two sub series belonging to pre and post rice futures market. The GARCH(1,1) model is used to estimate the volatility for each period and then volatility results from each period are compared. In addition, the volatility of the entire price series is measured with a dummy variable in the GARCH model to account for the introduction of rice futures contract trading on CBOT in October 1994. The significance of the coefficient on this dummy variable indicates whether the introduction of the futures market has affected cash price volatility or not. The rough rice price  37  There are several alterations of the classic GARCH model. Appendix B provides a detailed theoretical explanation of one of these alternative models. Choosing GARCH(1,1) over the other methods allows for better comparison of results with previous studies on other commodities. 41  level is also included in the model to control for the level effect. Several works have concluded that there is less volatility at higher price levels. Reilly et al (1978) examined several stocks after a split and conclude that prices are significantly more volatile post split than before the split when prices were at a higher level (Reilly & Drzycimski, 1978). The general conclusion is that there is less volatility when prices rise and more when prices fall. Therefore the final equation modelling volatility in this work is38: ℎ( = ∘ +    (  + ℎ(  + MN( +  (       (4.7) D takes the value of 0 to signify the era prior to the introduction of rice futures on the CBOT, and value of 1 for after. P is the price of rough rice (or milled rice when milled rice is examined). The log return of the rice price was also tested for seasonality. The coefficients on the dummy variables representing each month of the year were insignificant with p-values higher than 0.0539. 4( = O N  + ON + OMNM + ON + OPNP + OQNQ + ORNR + OSNS + OTNT + O LN L + O  N   + O N  (4.8) The joint null hypothesis failed to reject that O+ = 0 (p-value = 0.06)40. The same method was applied to wheat price series and strong seasonality was detected with the joint test of the hypothesis strongly rejecting the null of O+ = 0. Seasonal patterns in the price of wheat are well known and documented. Therefore, running the same regression as (4.8) with wheat price returns confirms validity of (4.8) in detecting the presence of seasonality in rough rice price returns. Seasonality test results are reported in Appendix D.  38  Another form of this equation is presented in Appendix C. The equation in appendix C controls for the effect of previous periods’ dummies on this period’s volatility. However since the structural break occurres once in our model and is permanent with the same value, it was decided that both forms would yield approximately the same result, therefore the simpler one was chosen for this study. 39  The coefficients for October and November were significant (p-values 0.033 and 0.003 respectively). However, given that the joint test was not significant, it was concluded that seasonality is not present in the series. 40  The same test was applied to the rough rice futures price series and seasonality was also rejected for that series. The value of the joint test was 0.55 42   4.2 Vector Autoregressive Models (VARs)  There are three forms of VARs: reduced form, recursive form, and structural. This study will use the reduced form and recursive forms for the Granger causality test. U( = /5 + ) +U(+ +3+-  ) *+VW(+ +,+-  ) O+XY(+ +Z+-  (      (4.9) VW( = 15 + ) *+VW(+ +,+-  ) O+XY(+ +Z+-  ) +U(+ + [(3+-       (4.10) XY( = \5 + ) O+XY(+ +Z+-  ) *+VW(+ +,+-  ) +U(+ +3+-  ](     (4.11) Where U( is the rice cash price volatility, VW is the detrended rice futures contract trading volume, and XY is the detrended non-commercial open interest position in the rice futures contract. (, [( , ]( are the error terms. TV and OI are expressed in percentage form and have no units as will be discussed in section 4.3.  The concern with using the reduced form VAR is that the errors may be serially correlated. In order to address this problem, recursive VAR analysis is proposed. The recursive form VAR has the following structure: U( = /5 + ) +U(+ +3+-  ) *+VW(+ +,+-  ) O+XY(+ +Z+-  _(     (4.12) VW( = 15 + ) *+VW(+ +,+-  ) O+XY(+ +Z+-  ) +U(+ + `U(3+-  + [(   (4.13) XY( = \5 + ) O+XY(+ +Z+-  ) *+VW(+ +,+-  ) +U(+ +3+-  `U( + aVW( + ](  (4.14) (, [( , /bc ]( are uncorrelated. The inclusion of the current value of volatility (σ) in equation (4.13) removes any correlation between the error terms in equations (4.12) and (4.13). Therefore, the impact of the error in estimating equation (4.13) on the future value of volatility (σ) will only come from shocks to VW and not other variables in the system. The drawback with the recursive method is that the results depend on the ordering of variables (Stock & Watson, 2001). This 43  work includes three variables in the VAR model. Therefore, the ordering of the variables will not alter the results significantly41. More recent literature has discussed the need to examine the level of trading activity in existing futures markets to understand their impact on cash price volatility. Granger causality test will be deployed to examine whether level of trading in the futures market causes changes in cash price volatility. 4.2.1 Granger Causality Test   The Granger causality test is used to determine whether past changes in variable X Granger cause (or explain) current changes in variable Y over and above past values of Y. Vector Autoregressive (VAR) techniques are used to carry out the Granger causality test. The first stage involves a regression in which variable Y is regressed on its own lagged values to determine how much of the current value of Y is explained by its lagged values. In the second stage lagged values of another variable (X) are included in the regression. If the lagged values of X have any explanatory power (i.e. statistically significant) then X is said to Granger cause Y. The Granger causality test makes use of the following specification: d( = 5 + ) *+d(+3+-  + (          (4.15) d( = 5 + ) *+d(+3+-  + ) O+e(+,+-  + [(        (4.16) X represents other factors that may Granger cause Y. ( and [( are white noise residuals respectively. The null hypothesis of the Granger Causality test indicates that: O  = O = ⋯ = O, = 0          (4.17) Therefore, failing to reject the null in the Granger causality test implies that X does not Granger cause Y.  41  Different ordering of variables mean that there will be six different combinations (n! Or 3!). The different combinations were examined but the results were similar as there are only three variables (Appendix E) 44  4.2.2 Impulse Response Function (IR)  Another advantage of the recursive VAR with uncorrelated errors is that it allows for an impulse response function analysis (IRF). The impact of one unit increase in error of estimating one of the variables on the current and future values of the other variables is purpose of the IR analysis. Increasing ]( by one unit in equation (4.14) and having the _( and [( from equations (4.12) and (4.13) constant allows one to observe the change in the current and future values of VW and U. This indicates the impact that a unit increase in XY will have on VWand U. The future horizon over which the impact is studied has to be chosen long enough so that the effect levels off or reverts to zero. An important aspect of working with VAR models is the choice for the lag length of the variable in the model. The following part addresses this issue. Akaike Information Criterion (AIC) After determining the appropriate variables to be included in the VAR model (in this case detrended futures trading volume and open interest), one also has to specify the number of lags from each of those variable to be included in the model. Akaike Information Criterion (AIC) is chosen to determine the lag length for the VAR model in this study (Akaike, 1974). Y6 = 2T − 2ln L           (4.18) Where T = number of parameters L = value of likelihood function (maximized) ln L = ibjk  lmn! o+-   −  ) pqnrst! mn! o+-         (4.19) Where yi = actual observation f(x) = estimated results U+ = conditional variance  45  The lag length associated with the lowest AIC value will be included in the VAR model. Choosing the right lag order is important in rejecting or failing to reject the null hypothesis for Granger causality. Granger chose all lags for all variables to be equal (Granger, 1969). For larger number of variables in the model, Atukeren (2005) suggests another methodology to choose different lag for each variable. There is a description of this methodology in appendix F. 4.2.3 Forecast Error Variance Decomposition (FEVD)   Another method of studying the impact of a sudden change in either trading volume or open interest on cash price volatility is Forecast Error Variance Decomposition (FEVD). This method indicates the percentage of error made in forecasting a variable that is due to shocks in another variable in the recursive VAR model over a specified forecast horizon42. The FEVD method indicates how a shock to one variable contributes to the unpredictability of the other variable in the VAR model. The IR analysis (described in 4.2.2) and FEVD point to the economic significance of a variable. These methods allow one to see the size of change in a variable caused by changes in another variable and not just whether the change is statistically significant or not (Abdullah & Rangazas, 1988). Therefore, variable A may fail the joint F-test of the Granger causality, indicating that it does cause changes in variable B, however variable A may explain a large percentage of the error variance when forecasting variable B. Therefore, it is important use the FEVD method as a supplement to the Granger Causality test to realize the magnitude of the effect of change in one variable on another.  42  This study uses 100 steps ahead in order to have a long enough horizon. The effect of a current shock in one variable will have a long term impact on the error of forecasting another variable. This effect levels off after a few periods and becomes the long term effect. Therefore, in order to avoid the short term and intermediate fluctuations in the impact of shock to one variable on another, it is important to choose a long enough time horizon in this study to detect the long term impact of the shock to one variable (for example futures trading volume) on another variable (for example rice cash price volatility) 46  4.3 Detrending Futures Trading Volume and Open Interest   Level of futures trading is divided into two parts: trading volume and open interests. The goal of this section is to isolate the unexpected changes from long term trends in trading volume and open interests and estimate whether they cause changes in rice cash price volatility. The unexpected change in trading volume and open interest could be attributed to the sudden entrance of speculators into the futures market. The term speculation is referred to the activity of non-commercial interest in the rice market. Individuals whose sole purpose is to draw profits from the rice price fluctuations using futures contracts, without assuming position of any amount of rice.  In order to obtain the data pertaining to unexpected rise in trading volume and open interest, one has to detrend the data. The trading volume and open interest data of non- commercial interests has to be detrended to account for secular trends in trading volume and open interest numbers in the futures market43. Indeed both non-commercial open interest and trading volume demonstrate an increasing trend over time (Figures 10 and 11). Three detrending methods are proposed: one period percent change, polynomial of third degree, and centre moving average44. Percent Change (or First Difference Method-FD)  The percent change (represented by equation 4.20) of open interest and trading volume from one period to another is calculated. The Granger causality method tests whether change in percentage change of open interest or trading volume causes change in cash price volatility. The  43  Unlike open interests the U.S. Commodity Futures Trading Commission does not provide non-commercial trading volume. This data could not be obtained from another source either. The detrending methods used in this study are adequate to ensure that only sudden momentary changes in the series are captured. General assumption of this study is that sudden changes in trading volume are attributable to the presence of non- commercial agents who are not normally present in the market. Therefore, lack of separate data on trading volume from non-commercial agents should not alter the results of this study. 44  Please refer to the DATA section of this work for explanation on data selection. 47  advantage of using a one-period percent change is that one period change does not contain the long term trend in the time series. uHuH_J uHwJ              (4.20) X = Open interest or trading volume Figure 12 demonstrates the trading volume and open interest data after be detrended by the first difference method. Polynomial of Third Degree (P3)  This method takes into account of the possibility that open interest and trading volume may increase in a cubic function form (figures 10 and 11). The open interest or trading volume number is regressed on time in the following format: e(xy( =  *L + * z + *z + *MzM + {(       (4.21) Where e = open interest or trading volume, z = time and {( is the error term at time t. The difference between observed e and estimated e (i.e. {() is then divided by estimated e (i.e. e(xy() to yield:  xH uH |}H                      (4.22) The value of this ratio should be very close from one period to the next unless there are shocks to open interest and trading volume numbers during a period. Increase in the ratio for indicates a sudden jump in trading volume or open interest (figure 13). The Granger Causality method tests to determine whether change in the ratio specified by (4.22) causes a change in cash price volatility. Centre Moving Average (CMA) This method subtracts the current period trading volume or open interest from a five week average and then divides it by the average. The result clearly eliminates the long term trend in the data (figure 14) 48  uH~xZ~€xuHw!,uHwJ,uH,uHIJ,uHI! ~xZ~€xuHw!,uHwJ,uH,uHIJ,uHI!                       (4.23) Where is X is trading volume or open interest. The Granger Causality test analyzes the effect of change in the value of this ratio (i.e. 4.23) on cash price volatility.  The three detrending methods specified above, eliminate the long term trend in the data set used in this work (figures 12-14). The Granger causality test will be conducted using the detrended trading volume and non-commercial open interest from each of the methods specified above. Detrended open interest and trading volume may Granger cause rice cash price volatility under one detrending method and not another. For example, trading volume may Granger cause cash price volatility after being detrended by the FD method and not cause volatility under P3 method. Therefore, a rule needs to be established for a final verdict (on whether sudden changes in trading volume and open interest Granger cause change in cash price volatility) while considering the results from the three detrending method. In order for a sudden change in trading volume or/and open interest to Granger cause a significant change in cash price volatility two of the three detrending methods have to indicate so and at 5% level (i.e. P-values ≤ 0.05). This is referred to as the two-out-of-three rule. 4.4 Summary  Rice cash price volatility from before the introduction of the rice futures market is compared the one after. In addition, a dummy variable is introduced in the volatility model to mark the era of pre and post rice futures market. The significance of this dummy variable would be a strong indication that the presence of the futures market impacts cash price volatility. 49   GARCH(1,1) model is used to measure volatility and Vector Autoregressive models (VARs) are used to carry out the Granger Causality test, impulse response analysis, and forecast error variance decomposition. In order to capture the sudden change in trading activity and to eliminate the long term trends in volume and open interest data, the two are detrended using three methods of rate of change (first difference-FD), third degree polynomial (P3), and centre moving average (CMA). The impact of trading activity on cash price volatility is measured three times, with one of these detrending methods being used each time. These detrending methods clearly removed the long term trend present in the open interest and trading volume data.  50  Chapter 5: Data and Results  This chapter is divided into two parts. The first part reveals the sources of data and the way they were used in the empirical analysis. The second part of this chapter offers an analysis of the results. 5.1 Data   The following sections describe the sources of the data that this study used to carry out the empirical analysis. In addition, they describe any operation done on the data series prior to use in the analysis. 5.1.1 Data Source  Two sets of prices are used as cash prices in our analysis. One is price of rough rice, which is the price received by farmers. The other is milled price of rice, which is the price received at milling stations by their operators. The volatility of the price of rough rice is the main focus of this study as it is underlying commodity of the rice futures contract on the CBOT. Both sets of prices are received from USDA’s Rice Yearbook45 (USDA, 2010). The price for rough rice was available from September 1982 to February 2011 on a monthly basis. The milled rice prices were available from September 1979 to February 201046. The futures contract trading volume data for rough rice is obtained from Datastream in a continuous stream format (Datastream, 2007)47 and on a monthly basis48. Although rough rice  45  2010 and earlier versions 46  The 2010 version of rice yearbook only included prices up to February 2010. The price of rough rice from February 2010 to February 2011 was found in recent reports published by USDA (http://www.ers.usda.gov/briefing/rice/data.htm). However no such reports were found for milled rice 47  Datastream provides a few continuous stream formats.  The one that was chosen takes the closing price of the nearest contract. Once the delivery month is reached (on the first trading day of the delivery month), the data stream then switches over to the next nearest contract to obtain closing prices. 48  Datastream provides trading volume data with daily and weekly frequencies. The monthly data is simply a sum of the daily trading volume 51  contracts were introduced to the CBOT in October 1994, the trading volume data were available only from February 2000. Non-commercial open interest data were obtained from the U.S. Commodity Futures Trading Commission49. CRB Reuters Commodity Index numbers were obtained with monthly frequency from Datastream. The price of Thai 100% B second grade, which represents the world price of rice, was partially obtained from the Food and Agricultural Organization (F.A.O) International Commodity Price data base (please refer to 5.1.3 for more details)50. 5.1.2 Cash Price Data  Milled rice prices are the average price of long grain no. 2 from three milling centres in United States (Louisiana, Arkansas, and Texas). Milled rice prices were divided into two sub series. The first series is from September 1979 to November September 1994. The second series is from October 1994 to February 2010. These two series fall before and after the introduction of the futures market on the CBOT and are equal in the number of observations. The same process was applied to rough rice prices. They were divided into two series one spanning from September 1982 to September 1994 and the other from October 1994 to February 2011 (145 and 197 observations for each period respectively). The price data reported in USDA publications are expressed in US dollars/hundredweight (CWT). These figures are converted to metric tonne (1 cwt = 0.045352 tonnes). 5.1.3 World Prices  World rice prices (Thai 100% B second grade, Bangkok) are obtained from USDA rice year book from January 1960 to January 2010. From February 2010 to February 2011 prices are  49  http://www.cftc.gov/MarketReports/CommitmentsofTraders/HistoricalCompressed/index.htm 50  http://www.fao.org/es/esc/prices/PricesServlet.jsp?lang=en 52  obtained from the Food and Agricultural Organization’s (FAO) International Commodity Prices database51. The FAO database contains price data with weekly frequency. The futures market in Zhengzhou was established in April 2009. Therefore, there were 104 weekly observations of world prices after the introduction of the futures market52. The volatility of this series was compared to 104 weekly world price observations from 2003 to 2005 signifying the period before the introduction of the rice futures market in Zhengzhou53. 5.1.4 Open Interest Data  The non-commercial open interest data were available from October 1994 with weekly frequency, and were converted to monthly by taking the average of the open interest values of the four (or five) weekly data in each month. As indicated in 5.1.1, trading volume data were only available from February 2000, and therefore open interest data are also used from February 2000. 5.2 Results  This section presents and analyzes the results of the empirical analysis. It also offers an assessment of the empirical results in testing the theory that was presented in Chapter 3. In general the empirical results confirm the theory that the introduction of the futures market reduces cash price volatility. 5.2.1 Summary of Results   Results indicate that rice cash price volatility is lower after the introduction of the rice futures market.  In addition, Granger Causality tests reveal that sudden changes in futures trading activity lead to higher volatility in cash prices. This indicates that the presence of irrational  51  http://www.fao.org/es/esc/prices/PricesServlet.jsp?lang=en 52  April 2009 to April 2011 53  The era of 2007 to 2009, which would have been a natural choice for the period without the futures market was left out because of the crisis and the extraordinary circumstances in the rice market. Therefore, a random period that is far from this crisis and not too far from the realities of the current rice market was chosen. 53  speculators (represented by sudden and temporary changes in futures trading volume and open interest) leads to higher cash price volatility. 5.2.2 Has Speculation Reduced Cash Price Volatility of Rice?  The monthly cash price return variance, measured by the GARCH (1,1), is lower after the introduction of the futures market on the CBOT in October 1994. The average monthly log return variance of the price received by farmers (rough rice) from September 1982 to September 1994 was 0.0076, whereas from October 1994 to February 2011, the variance was 0.0019. This is also despite the world rice market crisis of 2007-2008. The results of the same analysis on milled rice prices indicated that the variance was higher in the period prior to the introduction of the futures market (0.0051 versus 0.0009). Figures 15 to 18 demonstrate this higher volatility for both rough and milled rice during the period before the introduction of the rice futures market. Appendix G reports the monthly variance generated by the GARCH(1,1) model for both rough and milled rice. Rough Rice Price Volatility  The estimation of equation 4.7 (ℎ( = ∘ +    (  + ℎ(  + MN( +  () reveals that the coefficient on the dummy variable (M) is significant (p-value = 0.000) and the introduction of the rice futures market has reduced cash price volatility by about 51%. The coefficient on the price level () is also significant (p-value = 0.046) and confirms that an increase in price level lowers the volatility and vice versa by 0.5%. Therefore, controlling for the price level in the volatility model is important as price changes generate different magnitude of volatility at different price levels. Estimation of equation 4.4 (4( = *5 + * 67( + *8( + () reveals that the monthly return on world price has a positive and significant effect on the price return of rough rice in Unite States (8.8% and p-value= 0.00). This result demonstrates the link between the world and 54  U.S. rice market and justifies controlling for the impact of return on world rice price on the US rough rice price. The coefficient on the CRB Index return was not significant (p-value = 0.64), which is an indication that wider commodity events in the world do not have a significant effect on rough rice price returns in Untied States. Table 1 summarizes the results discussed above. The following equation was estimated separately for each period before and after the introduction of the rice futures market to compare the characteristics of the price volatility from each period. The purpose of this analysis is to see how sources and characteristics of volatility in the rough rice price change in the presence and absence of the rice futures market. ℎ( = ∘ +    (  + ℎ(  + M(        (5.1) It is interesting to note that none of the coefficients ( , and M) are significant in the period after the introduction of the futures market. This indicates that news from previous periods has a less persistent effect on current price changes and that prices absorb new information more rapidly. This confirms the earlier theoretical discussion about the effect of the futures market on increasing information flow, which seems to apply to the rice market in United States. The coefficients in equation (5.1) were all significant when the analysis was done for the period prior to the introduction of the rice futures market (Table 2). This indicates that before the rice futures market, shocks were more persistent and took longer to show their full effect on the market. In addition, price level effect discussed earlier was significant in the period prior to the futures market, whereas it was not after the introduction of the futures market. This result could be due to the fact that the futures market creates the possibility of hedging hence price level movement in either direction does not have as pronounced asymmetric effect as it would in the absence of the futures market. 55  The coefficient on the world price return is also significant and has positive effect on rough rice price return in United State before the rice futures market (unlike after the introduction of the futures market). The hedging effect made possible by the futures market perhaps makes the rough rice market in United States less susceptible to high volatility due to temporary shocks to the world rice market. Milled Rice Price Volatility  This study is mainly concerned with the volatility of the price of rough rice. However, for reasons cited earlier, the volatility of milled rice prices are also investigated. The dummy variable specified by equation (4.7) was significant (p-value = 0.00) and indicated that the introduction of the futures market has led to a 47% reduction in the volatility of milled rice. As in the case of rough rice the world price returns also have a significant impact on the milled rice price returns (p-value = 0.00). However, unlike rough rice, milled rice price returns are linked with the CRB index return (p-value=0.02). Rice millers maybe more exposed the wider commodity spectrum where the prices of other commodities have a more direct impact on the price they charge than rice farmers. Table 3 summarizes the results of monthly volatility estimation for milled rice.  The volatility characteristics of milled rice price before and after the introduction of the futures market were compared by estimating equation (5.1). Table 4 presents a summary of the results. Change in world price return has a significant effect on the price return of milled rice both before and (unlike rough rice) after the introduction of the futures market. Also, change in price level has an impact on change in price volatility both before and after the futures market. The rice futures market seems to have had a more significant impact on the volatility of rough rice than milled rice. Perhaps this is expected given that the underlying rice futures contract is rough rice.  56  Rice Futures Market in China and Global Rice Price Volatility The volatility of world rice prices prior to and after the introduction of rice futures market in Zhengzhou is measured using GARCH (1,1). Comparing the two volatility series shows that the weekly volatility is lower for most of the months in the period prior to the introduction of the futures (Figures 19 and 20). However, as statistics show (below), one cannot conclude that the world price is affected by the introduction of the rice futures in Zhengzahou. The coefficients of equation (5.3) are estimated to determine the volatility of the world price of rice: 4( = *5 + * 67( + (          (5.2) ℎ( = ∘ +    (  + ℎ(  + MN(        (5.3) 4( is the world price return and 67( is the return on the CRB index. The CRB index controls for the events that affect the commodity markets and also have an impact on the world rice market. Therefore ( captures the shocks exclusive to the rice market54. The estimate of the coefficient on the dummy variable in equation (5.3) is not significant (p-value = 0.73). Therefore, one cannot claim that the newly established futures market in China has led to less volatility in world rice prices. Rice Futures on the CBOT and Global Rice Price Volatility   The volatility of world rice prices prior to and after the introduction of rice futures market on the CBOT was measured using GARCH (1,1). Juxtaposing the two price series volatilities (January 1978 to September 1994 and October 1994 to April 2011) does not show a higher or lower volatility of world prices prior to or after the introduction of the rice futures market on the CBOT (Figures 21 and 22). The estimate of the coefficient (M) on the dummy variable in equation (5.3) is not significant (p-value = 0.24). Therefore, one cannot claim that the  54  The CRB coefficient is significant (p-value =0.00) post establishment of rice futures market in Zhengzhou and not before. This could be due to the general volatility that commodity markets have been experiencing since 2006 and is continuing today. This condition did not exist prior to 2006, therefore the return on CRB index does not have a significant (p-value=0.56) explanatory power for the world rice price return. It should be noted that the pre Zhengzhou rice futures period spans from 2003 to 2005 in this study 57  establishment of the rice futures market on the CBOT has led to less volatility in world rice prices55. 5.2.3 Have Irrational Speculators Increased Cash Price Volatility of Rice?  The impact of trading volume and open interest on cash price volatility at both farm level and after milling is analyzed. The results of the Granger Causality test indicate that change in detrended trading volume and non-commercial open interest Granger cause a positive change in the variance of the cash price return of rice at both farm (rough rice) and milled rice level. The results are significant with p-values of less than 0.05 for all three detrending methods in case of rough rice, and for P3 and CMA in case of milled rice (two-tailed joint test), hence satisfying the two-out-of-three rule that was established in 4.3. Table 5 reports the p-values of the two-tailed test for causality in the rough rice market. The results of the IR analysis indicate that errors in estimating the changes in the values of volume and open interest do not have a large impact on predicting the future changes in cash price variance. One unit increase in error of estimating the change in the detrended trading volume only leads to a 0.06% (using the first difference detrending method) change in variance estimation of the cash price. This value was 0.03% and 0.07% when the same analysis was done with P3 and CMA as detrending methods respectively. One unit increase in error of estimating the change in the detrended open interest leads to 0.1%, 0.08%, and 0.1% change in variance estimation of the cash price when deploying FD, P3, and CMA methods respectively. The results of the IR analysis indicate that sudden changes in detrended volume and open interest do not have a significant (not statistically speaking) on the change in the volatility of the cash price at the farm level.  55  Appendix I offers a brief discussion on the correlation between the price of rough rice in United States and the world before and after the introduction of the rice futures market on the CBOT. This could shed further light on the impact that the introduction of this market may have had on the way the US rice market interacts with the world rice market. 58  The error in estimating changes in rice futures trading volume and open interest using their lagged values explained more (although not significatnly more) of the change in the volatility of the price of milled rice than rough rice. One unit increase in the trading volume error leads to a 0.3%, 0.03%, and -0.5% change in the volatility of the milled rice price using FD, P3, and CMA methods respectively56. These values are 0.02%, 0.4%, and 0.9% for open interest for each of the methods specified above (these figures are summarized in Table 6). The futures trading volume and non-commercial open interest seem to have a larger impact on the price volatility of milled rice than rough rice. Indeed studying the correlation between the change in rough rice and futures price, and milled rice and futures price reveals that the futures price is more correlated with milled than rough rice (Table 7)57. This could partially explain why futures trading activity has a larger impact on milled rice price volatility in the IR analysis. The results of the FEVD analysis paint a different picture than those from the IR analysis. In the case of rough rice, sudden changes in trading volume contributes 3.3%, 2.3%, (using FD and P3 detrending methods) and 2.7% (using CMA detrending method) to the error in forecasting the volatility of the rough rice price. Therefore, it could be concluded that sudden changes in trading volume does not have a significant (not in statistical sense) impact on the rough rice price volatility. In case of non-commercial open interest these values were 18.9%, 15.2%, and 7.4%. Therefore, shocks to futures open interest numbers contribute significantly (in an economic sense) to the error in forecasting rough rice price volatility. In case of milled rice, shocks to trading volume have a larger contribution to changes in price volatility than rough rice. Using the three detrending methods specified earlier, a shock to  56  The negative value (-0.5%) obtained from the CMA detrending method indicates that positive sudden change in futures trading volume could lead to a decrease in volatility. However, given that this figure is small and that the other two numbers from FD and P3 methods (two-out-of-three rule) are positive, this negative value is ignored 57  The results from the P3 method should be viewed with skepticism as all three values generated by this method are the highest and far off the other two values 59  trading volume number leads to 3.8%, 6.2%, and 9.5% (FD, P3, CMA respectively) change in milled price volatility. The values of these shocks were 0.1%, 7.8%, and 3.0% in case of open interest. The results are summarized in Table 8. The results above indicate that shocks to futures open interest have a larger impact on rough rice (farm) price volatility than trading volume. Change in non-commercial open interest numbers could be a signal to farmers that speculators are anticipating higher or lower prices in the future and hence farmers allocate their harvest accordingly. For instance, a surge in the number of non-commercial short positions could be a signal prices will fall in the future. Farmers58 may decide to sell all they can today (including what they store) as they perceive today’s prices to be higher than tomorrow. This surge in supply in the market, while lowering the price that farmers receive, could also lead to higher volatility.  Shocks to futures trading volume seem to have a larger impact on milled rice price volatility than rough rice according to the FEVD analysis. Milling operations could be more engaged in the trading of the rice futures contracts than farmers. They are constantly buying and selling the physical rice stocks (they do not wait for harvest etc.). Therefore, sudden changes in rice futures trading volume which reflects the temporary conditions in the rice market affects rice millers more than rice farmers. Higher futures trading volume and the presence of more (irrational) speculators may be inviting for rice millers to adjust the price of milled rice to take advantage of the temporary market conditions, leading to higher volatility in the price milled rice59. 5.3 Summary  The rice market seems to be less volatile after the introduction of the rice futures market on the CBOT, hence confirming the theory presented in chapter 3. In addition, the tests reveal  58  or other agents who carry rice inventories 59  Stata output for section 5.2 is available in appendix J 60  that sudden increase in rice futures trading activity, which is a proxy for the presence of irrational speculators, causes higher rice cash price volatility. The cash price of rice shows more volatility prior to the introduction of the rice futures market on the CBOT than afterwards. The dummy variable, which distinguishes the pre and post futures periods in the GARCH(1,1) volatility equation, is significant. The same analysis on the impact of the introduction of the rice futures market in China produced insignificant results. Sudden change in trading activity which is a proxy for the presence of irrational speculators in the market Granger caused the cash price volatility (farm and milled prices). The IR analysis indicated that a change in detrended open interest or trading volume data has a minor effect on cash price volatility of rough rice. These effects are more pronounced when the same analysis is carried out using milled rice prices. The FEVD method indicates that sudden changes in futures trading volume affect the volatility of milled rice prices more than rough rice prices. The reverse is true when the impact of temporary shocks to non-commercial open interest on milled and rough rice price volatility is examined. The Granger Causality test indicates that the trading activity in the rice futures market has a significant impact on cash price volatility of rice. However, this should be viewed with caution as Granger Causality points to statistical significance of the results. The magnitude of this impact, measured by IR and FEVD methods, indicates that the price volatility of rough rice is not affected by futures trading volume as much as milled rice. This could be attributed to the higher correlation between milled rice and futures price than rough rice and futures price. However, sudden change to futures open interest had a higher impact on rough rice price volatility than milled rice. Perhaps better understanding of the structure of rice market in United States could shed more light on this matter, and why open interest matters more to rough rice price volatility than milled rice price volatility  61  Chapter 6: Conclusion  This work presents and tests Friedman’s original statement that speculators stabilize the market (reduce price volatility) unless they are irrational. The first part of this theory asserts that the presence of speculators in the market and better foresight about the future price of the commodity does lead to less volatility. The second part indicates that only the presence of irrational (uninformed) speculators lead to increase price volatility. This study proposes the use of the futures market as a proxy for the presence of speculators in the market. Sudden changes in futures trading activity figures such as trading volume and open interest is set as a proxy for the presence of irrational speculators. The rice futures market on the CBOT is chosen for this project. Rice is an important staple food for about half the world’s population, yet it does not have a viable global market like wheat and maize. The intention is that the empirical testing of the impact on speculation on price volatility using the rice futures market could provide a direction for further research in forming a more functional and less volatile global rice market. Based on the results of the empirical analysis, the introduction of rice futures market has led to lower cash price volatility in the rice market in United States. This indicates that the presence of speculators with enhanced foresight through futures market has led to more stability in the rice market in United States. GARCH(1,1) model was used to measure the volatility of rice prices. In addition, a dummy variable was added to the GARCH(1,1) model to separate the two periods of pre and post introduction of rice futures market on the CBOT. Using the Granger Causality method, modeled by a recursive VAR reveals that trading activity in the futures market increases cash price volatility. However, Granger Causality test only points out the statistical significance of one variable explaining another. FEVD and IR analysis are proposed to measure the effect of futures trading activity on cash price volatility. 62  The latter tests reveal that a sudden change in trading volume and open interest lead to higher degree of volatility in the cash price of milled rice than rough rice (farm price). Sudden entrance of speculators in the futures market destabilizes the rice cash market. However, understanding the market for a commodity is important in determining where this irrational speculative presence is most destabilizing. This study could be applied to another more global rice futures market in the future to assess its impact on world price volatility. The same assessment in this work revealed no impact on world prices by rice futures market on the CBOT. Future research could focus more directly on how a viable global rice futures market and private speculative presence in that market could lead to more stability in world rice prices. 6.1 Limitations   The more prominent impact of rice futures trading activity on the volatility of milled rice prices may be an indication that rice milling operators use the futures market more than farmers. However, data on futures trading and open interest do not distinguish between the two. Therefore, obtaining separate data on farmer’s and milling operators’ activities in the futures market could shed light on the reason for the different degree of interaction between rough rice (farm), milled rice, and rice futures market.  The thinness of trade in the rice market, illiquidity in futures market and a relatively low number of monthly observations make it an inherently volatile market in terms of trading activity. As a result the rice futures market may not be a good proxy for the presence of speculation in the market to test the theory put forward in chapter 3. However, the importance of rice as a global staple food makes the current study using the rice futures market relevant. Never the less, these results should be revisited a few years from now once there is longer time series on rice futures trading activity and when the rice futures market is more active. 63  Tables Table 1: Rough Rice Price Volatility Estimation (equations 4.4 and 4.7) 1982-2011  *5 *  * ∘    M  0.0089 0.0352 0.0890 -5.8528 0.4226 0.3277 -0.5124 -0.0050 0.76 0.64 0.00 0.00 0.00 0.00 0.00 0.05 *note: last row report the p-value  Table 2: Rough Rice Price Volatility before and after CBOT Rice Futures Market 1982-Sep1994 and Oct 1994-2011 (equation 5.1) 60   *5 *  * ∘    M 1982-Sep94 -0.0146 0.0306 0.2338 -0.0682 0.2401 0.5111 -0.0472 p-value 0.67 0.84 0.00 0.92 0.02 0.00 0.00 Oct94-2011 0.0007 0.0679 0.0784 -7.5920 0.2230 0.4786 0.0007 p-value 0.83 0.48 0.14 0.00 0.09 0.06 0.76   Table 3: Milled Rice Price Volatility Estimation (equations 4.4 and 4.7) 1979-2010 *5 *  * ∘    M  -0.0103 0.1298 0.0821 -7.7117 1.1916 0.0042 -0.4716 0.0012 0.00 0.02 0.00 0.00 0.00 0.85 0.00 0.10 *note: last row report the p-value  Table 4: Milled Rice Price Volatility before and after Futures Market 1979-Sep1994 and Oct1994- 2007*(equation 5.1) 61  *5 *  * ∘    M 1979-Sep94 -0.0014 0.1213 0.1724 -0.2889 0.8998 0.3776 -0.0239 p-value 0.34 0.06 0.00 0.84 0.00 0.00 0.00 Oct94-2007 -0.0020 0.1532 0.1201 -4.9863 0.0143 0.9494 -0.0180 p-value 0.35 0.10 0.00 0.00 0.21 0.00 0.013 *note: Stata encountered problems estimating the GARCH(1,1) with data running to 2010 for the post futures period. Therefore, data series to study the post futures for milled rice were chosen to December 2007          60  Stata results of estimating equations (4.4), (4.7) and (5.1) are presented in Appendix H 61  Stata results of estimating equations (4.4), (4.7) and (5.1) are presented in Appendix H 64  Table 5: Impact of Trading Activity on Cash Price Volatility: Granger Causality  Detrending Method TV→ σ OI → σ TV& OI → σ (Joint Test) FD 0.078 0.000 0.001 P3 0.399 0.002 0.006 CMA 0.068 0.012 0.003 *note: → signifies direction of causality. TV → σ change in trading volume (TV) Granger causes cash price volatility OI → σ change in open interest (OI) Granger causes cash price volatility   Table 6: Impact of Trading Activity on Cash Price Volatility: IR Analysis   Rough Rice Milled Rice Detrending Method Open Interest Trading Volume Open Interest Trading Volume FD 0.1% 0.06% 0.02% 0.3% P3 0.08% 0.03% 0.4% 0.03% CMA 0.1% 0.07% 0.9% -0.5%   Table 7: Correlation between Detrended Price Change in Milled, Rough and Futures Rice Price  Detrending Method Futures- Rough Futures- Milled Rough- Milled FD 0.18 0.33 0.57 P3 0.80 0.81 0.85 CMA 0.0007 0.13 0.42 Note: Price series is from February 2000 to February 2010   Table 8: Impact of Trading Activity on Cash Price Volatility: FEVD Analysis   Rough Rice Milled Rice Detrending Method Open Interest Trading Volume Open Interest Trading Volume FD 18.9% 3.3% 0.1% 3.8% P3 15.2% 2.3% 7.8% 6.2% CMA 7.4% 2.7% 3.0% 9.5%   65  Figures  Figure 1: Speculator with Perfect Foresight  Case 1: price in t+1 > price in t     Case 2: Price in t+1< price in t         At time (t) Speculator enters the market and buys the commodity Prices rise at time (t) due to extra demand from speculators At time (t+1) speculator enters the market and sells the commodity Prices fall at time (t+1) due to extra supply from speculators  At time (t) speculator does not enter the market to buy the commodity Prices do not rise at time (t) because there is no extra demand At time (t+1) speculator is not in the market to sell the commodity Prices do not fall at time (t) because there is no extra supply  Prices at time (t) are lower than if speculator had been in the market Prices at time (t+1) are higher than if speculator had been in the market Prices in time (t) are higher than if speculator had not been in the market Prices in time (t+1) are lower than if speculator had not been in the market  Figure 2: Top Ten Rice Producers in the World Data Source: FAOSTAT (2009) Production/Crops Figure 3: Total Rice, Wheat, and Maize Produ Data Source: FAOSTAT (2009) Production/Crops USA China India 0.00E+00 1.00E+07 2.00E+07 3.00E+07 4.00E+07 5.00E+07 6.00E+07 7.00E+07 8.00E+07 9.00E+07 1.00E+08 1.10E+08 1.20E+08 1.30E+08 1.40E+08 1.50E+08 1.60E+08 1.70E+08 1.80E+08 1.90E+08 2.00E+08 T o n n e s o f P a d d y  R ic e 0.00E+00 1.00E+08 2.00E+08 3.00E+08 4.00E+08 5.00E+08 6.00E+08 7.00E+08 8.00E+08 9.00E+08 1961 1966 1971 T o n n e s and USA  ction in the World (1961-2009)  Indonesia Bangladesh Viet Nam Myanmar Thailand Philippines Top 10 Rice Producers & United States 2009 1976 1981 1986 1991 1996 2001 Total World Production Quantity Maize Rice Wheat 66  Brazil Japan 2006 Maize Rice Wheat  Figure 4: Top Ten Rice Exporting Countries Note: figures are tonnes of rice (milled equivalent) Data Source: USDA Rice Yearbook (20 Figure 5: Top Ten Rice Importing Countries Note: figures are tonnes of rice (milled equivalent) Data Source: USDA Rice Yearbook (2011) Table 23  Pakistan, 4,000 United States, 3,856 India, 2,052 Cambodia Uruguay China Top Ten Rice Exporters  2010 (1000 tonnes) Saudi Arabia, 1,069 Iran, 1,000 Malaysia, 907 Cote d'Ivoire, 840 Brazil, 774 Top Ten Rice Importers  2010 (1000 tonnes)  11) Table 23   Thailand, 9,047 Vietnam, 6,734 Egypt Argentina Philippines, 2,400 Nigeria, 2,000 Indonesia, 1,150 Iraq, 1,140 South Africa, 733 67  68  Figure 6: Rice Production in United States (1961-2009)  Data Source: FAOSTAT (2009) Production/Crops  Figure 7: World Price of Rice (1960-2011) *Thai 100% B Second Grade F.O.B Bangkok Data Source: USDA Rice Yearbook Table 20 and Food and Agricultural Organization (F.A.O) International Commodity Price data base 0 2,000,000 4,000,000 6,000,000 8,000,000 10,000,000 12,000,000 1 9 6 1 1 9 6 3 1 9 6 5 1 9 6 7 1 9 6 9 1 9 7 1 1 9 7 3 1 9 7 5 1 9 7 7 1 9 7 9 1 9 8 1 1 9 8 3 1 9 8 5 1 9 8 7 1 9 8 9 1 9 9 1 1 9 9 3 1 9 9 5 1 9 9 7 1 9 9 9 2 0 0 1 2 0 0 3 2 0 0 5 2 0 0 7 2 0 0 9 to n n e s Total Rice Production in USA 0 200 400 600 800 1000 1200 Ja n -6 0 Ja n -6 2 Ja n -6 4 Ja n -6 6 Ja n -6 8 Ja n -7 0 Ja n -7 2 Ja n -7 4 Ja n -7 6 Ja n -7 8 Ja n -8 0 Ja n -8 2 Ja n -8 4 Ja n -8 6 Ja n -8 8 Ja n -9 0 Ja n -9 2 Ja n -9 4 Ja n -9 6 Ja n -9 8 Ja n -0 0 Ja n -0 2 Ja n -0 4 Ja n -0 6 Ja n -0 8 Ja n -1 0 U S  D o ll a rs Monthly World Rice Price 1960-2011 69  Figure 8: Rough Rice Futures Contract Specification Source: Chicago Mercantile Exchange (CME Group) http://www.cmegroup.com/trading/agricultural/grain-and-oilseed/rough-rice_contract_specifications.html Contract Size 2,000 hundredweights (CWT) (~ 91 Metric Tons) Deliverable Grade U.S. No. 2 or better long grain rough rice with a total milling yield of not less than 65% including head rice of not less than 48%. Premiums and discounts are provided for each percent of head rice over or below 55%, and for each percent of broken rice over or below 15%. No heat-damaged kernels are permitted in a 500-gram sample and no stained kernels are permitted in a 500-gram sample.  A maximum of 75 lightly discolored kernels are permitted in a 500-gram sample. Pricing Unit Cents per hundredweight Tick Size (minimum fluctuation) 1/2 cent per hundredweight ($10.00 per contract) Contract Months/Symbols January (F), March (H), May (K), July (N), September (U) & November (X) Trading Hours CME Globex (Electronic Platform) 6:00 pm - 7:15 am and 9:30 am - 1:15 pm Central Time, Sunday - Friday Open Outcry (Trading Floor) 9:30 am - 1:15 pm Central Time, Monday - Friday Daily Price Limit $0.50 per hundredweight expandable to $0.75 and then to $1.15 when the market closes at limit bid or limit offer. There shall be no price limits on the current month contract on or after the second business day preceding the first day of the delivery month. Settlement Procedure Physical Delivery Last Trade Date The business day prior to the 15th calendar day of the contract month. Last Delivery Date Seventh business day following the last trading day of the month. Product Ticker Symbols CME Globex (Electronic Platform) ZR 14=Clearing Open Outcry (Trading Floor) RR Exchange Rule These contracts are listed with, and subject to, the rules and regulations of CBOT. 70  Figure 9: Total non-commercial Futures Contract Long Positions (1994-2010)  Data Source: US Commodity Futures Trading Commission  Figure 10: Rice Futures Contract Trading Volume (2000-2011) Data Source: Reuters Datastream CBOT Rough Rice Futures Trade Data 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 Weekly Non-commercial Long Position 0 10000 20000 30000 40000 50000 60000 70000 80000 90000 Ja n -0 0 M a y- 0 0 S e p -0 0 Ja n -0 1 M a y- 0 1 S e p -0 1 Ja n -0 2 M a y- 0 2 S e p -0 2 Ja n -0 3 M a y- 0 3 S e p -0 3 Ja n -0 4 M a y- 0 4 S e p -0 4 Ja n -0 5 M a y- 0 5 S e p -0 5 Ja n -0 6 M a y- 0 6 S e p -0 6 Ja n -0 7 M a y- 0 7 S e p -0 7 Ja n -0 8 M a y- 0 8 S e p -0 8 Ja n -0 9 M a y- 0 9 S e p -0 9 Ja n -1 0 M a y- 1 0 S e p -1 0 Ja n -1 1 Rice Futures Trading Volume on the CBOT 71  Figure 11: Total non-commercial Rice Futures Open Interest (2000-2010) Data Source: US Commodity Futures Trading Commission Figure 12: Detrended Futures Trading Volume and non-Commercial Open Interest-FD Method  Data Source: Datastream and US Commodity Futures Trading Commission  0 2000 4000 6000 8000 10000 12000 14000 Ja n -0 0 M a y- 0 0 S e p -0 0 Ja n -0 1 M a y- 0 1 S e p -0 1 Ja n -0 2 M a y- 0 2 S e p -0 2 Ja n -0 3 M a y- 0 3 S e p -0 3 Ja n -0 4 M a y- 0 4 S e p -0 4 Ja n -0 5 M a y- 0 5 S e p -0 5 Ja n -0 6 M a y- 0 6 S e p -0 6 Ja n -0 7 M a y- 0 7 S e p -0 7 Ja n -0 8 M a y- 0 8 S e p -0 8 Ja n -0 9 M a y- 0 9 S e p -0 9 Ja n -1 0 M a y- 1 0 S e p -1 0 Total Non-commercial Rice Futures Open Interest -1.00 -0.50 0.00 0.50 1.00 1.50 2.00 2.50 F e b -0 0 Ju l- 0 0 D e c- 0 0 M a y- 0 1 O ct -0 1 M a r- 0 2 A u g -0 2 Ja n -0 3 Ju n -0 3 N o v- 0 3 A p r- 0 4 S e p -0 4 F e b -0 5 Ju l- 0 5 D e c- 0 5 M a y- 0 6 O ct -0 6 M a r- 0 7 A u g -0 7 Ja n -0 8 Ju n -0 8 N o v- 0 8 A p r- 0 9 S e p -0 9 F e b -1 0 Ju l- 1 0 D e c- 1 0 Trading Volume Open Interest 72  Figure 13: Detrended Futures Trading Volume and non-commercial Open Interest-P3 Method  Data Source: Datastream and US Commodity Futures Trading Commission    Figure 14: Detrended Futures Trading Volume and non-commercial Open Interest-CMA Method  Data Source: Datastream and US Commodity Futures Trading Commission  -1.00 -0.50 0.00 0.50 1.00 1.50 F e b -0 0 Ju l- 0 0 D e c- 0 0 M a y- 0 1 O ct -0 1 M a r- 0 2 A u g -0 2 Ja n -0 3 Ju n -0 3 N o v- 0 3 A p r- 0 4 S e p -0 4 F e b -0 5 Ju l- 0 5 D e c- 0 5 M a y- 0 6 O ct -0 6 M a r- 0 7 A u g -0 7 Ja n -0 8 Ju n -0 8 N o v- 0 8 A p r- 0 9 S e p -0 9 F e b -1 0 Ju l- 1 0 D e c- 1 0 Trading Volume Open Interest -0.80 -0.60 -0.40 -0.20 0.00 0.20 0.40 0.60 0.80 1.00 A p r- 0 0 S e p -0 0 F e b -0 1 Ju l- 0 1 D e c- 0 1 M a y- 0 2 O ct -0 2 M a r- 0 3 A u g -0 3 Ja n -0 4 Ju n -0 4 N o v- 0 4 A p r- 0 5 S e p -0 5 F e b -0 6 Ju l- 0 6 D e c- 0 6 M a y- 0 7 O ct -0 7 M a r- 0 8 A u g -0 8 Ja n -0 9 Ju n -0 9 N o v- 0 9 A p r- 1 0 S e p -1 0 Trading volume open int 73  Figure 15: Rough Rice Price Return Variance (GARCH) pre Futures  Figure 16: Rough Rice Price Return Variance (GARCH) post Futures  0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040 0.045 0.050 S e p -8 2 F e b -8 3 Ju l- 8 3 D e c- 8 3 M a y- 8 4 O ct -8 4 M a r- 8 5 A u g -8 5 Ja n -8 6 Ju n -8 6 N o v- 8 6 A p r- 8 7 S e p -8 7 F e b -8 8 Ju l- 8 8 D e c- 8 8 M a y- 8 9 O ct -8 9 M a r- 9 0 A u g -9 0 Ja n -9 1 Ju n -9 1 N o v- 9 1 A p r- 9 2 S e p -9 2 F e b -9 3 Ju l- 9 3 D e c- 9 3 M a y- 9 4 Pre Futures Rough Rice Volatility Sep82-Sep94 0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040 0.045 0.050 O ct -9 4 A p r- 9 5 O ct -9 5 A p r- 9 6 O ct -9 6 A p r- 9 7 O ct -9 7 A p r- 9 8 O ct -9 8 A p r- 9 9 O ct -9 9 A p r- 0 0 O ct -0 0 A p r- 0 1 O ct -0 1 A p r- 0 2 O ct -0 2 A p r- 0 3 O ct -0 3 A p r- 0 4 O ct -0 4 A p r- 0 5 O ct -0 5 A p r- 0 6 O ct -0 6 A p r- 0 7 O ct -0 7 A p r- 0 8 O ct -0 8 A p r- 0 9 O ct -0 9 A p r- 1 0 O ct -1 0 Post Futures Rough Rice Volatility Oct94-Feb2011 74  Figure 17: Milled Rice Price Return Variance (GARCH) pre Futures  Figure 18: Milled Rice Price Return Variance (GARCH) post Futures   0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 S e p -7 9 M a r- 8 0 S e p -8 0 M a r- 8 1 S e p -8 1 M a r- 8 2 S e p -8 2 M a r- 8 3 S e p -8 3 M a r- 8 4 S e p -8 4 M a r- 8 5 S e p -8 5 M a r- 8 6 S e p -8 6 M a r- 8 7 S e p -8 7 M a r- 8 8 S e p -8 8 M a r- 8 9 S e p -8 9 M a r- 9 0 S e p -9 0 M a r- 9 1 S e p -9 1 M a r- 9 2 S e p -9 2 M a r- 9 3 S e p -9 3 M a r- 9 4 S e p -9 4 Pre Futures Milled Rice Volatility Sep79-Sep94 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 O ct -9 4 M a r- 9 5 A u g -9 5 Ja n -9 6 Ju n -9 6 N o v- 9 6 A p r- 9 7 S e p -9 7 F e b -9 8 Ju l- 9 8 D e c- 9 8 M a y- 9 9 O ct -9 9 M a r- 0 0 A u g -0 0 Ja n -0 1 Ju n -0 1 N o v- 0 1 A p r- 0 2 S e p -0 2 F e b -0 3 Ju l- 0 3 D e c- 0 3 M a y- 0 4 O ct -0 4 M a r- 0 5 A u g -0 5 Ja n -0 6 Ju n -0 6 N o v- 0 6 A p r- 0 7 S e p -0 7 Post Futures Milled Rice Volatility Oct94-Dec2007 75  Figure 19: World Rice Price Volatility pre Zhengzhou Rice Futures Market   Figure 20: World Rice Price Volatility post Zhengzhou Rice Futures Market  0.0000 0.0002 0.0004 0.0006 0.0008 0.0010 0.0012 0.0014 0.0016 2 1 .0 2 .2 0 0 3 1 4 .0 3 .2 0 0 3 0 4 .0 4 .2 0 0 3 2 5 .0 4 .2 0 0 3 1 6 .0 5 .2 0 0 3 0 6 .0 6 .2 0 0 3 2 7 .0 6 .2 0 0 3 1 8 .0 7 .2 0 0 3 0 8 .0 8 .2 0 0 3 2 9 .0 8 .2 0 0 3 1 9 .0 9 .2 0 0 3 1 0 .1 0 .2 0 0 3 3 1 .1 0 .2 0 0 3 2 1 .1 1 .2 0 0 3 1 2 .1 2 .2 0 0 3 0 2 .0 1 .2 0 0 4 2 3 .0 1 .2 0 0 4 1 3 .0 2 .2 0 0 4 0 5 .0 3 .2 0 0 4 2 6 .0 3 .2 0 0 4 1 6 .0 4 .2 0 0 4 0 7 .0 5 .2 0 0 4 2 8 .0 5 .2 0 0 4 1 8 .0 6 .2 0 0 4 0 9 .0 7 .2 0 0 4 3 0 .0 7 .2 0 0 4 2 0 .0 8 .2 0 0 4 1 0 .0 9 .2 0 0 4 0 1 .1 0 .2 0 0 4 2 2 .1 0 .2 0 0 4 1 2 .1 1 .2 0 0 4 0 3 .1 2 .2 0 0 4 2 4 .1 2 .2 0 0 4 1 4 .0 1 .2 0 0 5 0 4 .0 2 .2 0 0 5 World Price Volatitliy before Rice Futures in Zhengzhou 2003-05 -0.0002 0.0000 0.0002 0.0004 0.0006 0.0008 0.0010 0.0012 0.0014 0.0016 2 4 .0 4 .2 0 0 9 1 5 .0 5 .2 0 0 9 0 5 .0 6 .2 0 0 9 2 6 .0 6 .2 0 0 9 1 7 .0 7 .2 0 0 9 0 7 .0 8 .2 0 0 9 2 8 .0 8 .2 0 0 9 1 8 .0 9 .2 0 0 9 0 9 .1 0 .2 0 0 9 3 0 .1 0 .2 0 0 9 2 0 .1 1 .2 0 0 9 1 1 .1 2 .2 0 0 9 0 1 .0 1 .2 0 1 0 2 2 .0 1 .2 0 1 0 1 2 .0 2 .2 0 1 0 0 5 .0 3 .2 0 1 0 2 6 .0 3 .2 0 1 0 1 6 .0 4 .2 0 1 0 0 7 .0 5 .2 0 1 0 2 8 .0 5 .2 0 1 0 1 8 .0 6 .2 0 1 0 0 9 .0 7 .2 0 1 0 3 0 .0 7 .2 0 1 0 2 0 .0 8 .2 0 1 0 1 0 .0 9 .2 0 1 0 0 1 .1 0 .2 0 1 0 2 2 .1 0 .2 0 1 0 1 2 .1 1 .2 0 1 0 0 3 .1 2 .2 0 1 0 2 4 .1 2 .2 0 1 0 1 4 .0 1 .2 0 1 1 0 4 .0 2 .2 0 1 1 2 5 .0 2 .2 0 1 1 1 8 .0 3 .2 0 1 1 0 8 .0 4 .2 0 1 1 World Price Volatility Post  Rice Futures in Zhengzhou 2009-11 76  Figure 21: World Price Volatility pre Rice Futures on the CBOT  Figure 22: World Price Volatility post Rice Futures on the CBOT  0.000 0.005 0.010 0.015 0.020 0.025 0.030 Ja n -7 8 Ju l- 7 8 Ja n -7 9 Ju l- 7 9 Ja n -8 0 Ju l- 8 0 Ja n -8 1 Ju l- 8 1 Ja n -8 2 Ju l- 8 2 Ja n -8 3 Ju l- 8 3 Ja n -8 4 Ju l- 8 4 Ja n -8 5 Ju l- 8 5 Ja n -8 6 Ju l- 8 6 Ja n -8 7 Ju l- 8 7 Ja n -8 8 Ju l- 8 8 Ja n -8 9 Ju l- 8 9 Ja n -9 0 Ju l- 9 0 Ja n -9 1 Ju l- 9 1 Ja n -9 2 Ju l- 9 2 Ja n -9 3 Ju l- 9 3 Ja n -9 4 Ju l- 9 4 World Price Volatility before Rice Futures on CBOT 1978-1994 0.000 0.005 0.010 0.015 0.020 0.025 0.030 O ct -9 4 A p r- 9 5 O ct -9 5 A p r- 9 6 O ct -9 6 A p r- 9 7 O ct -9 7 A p r- 9 8 O ct -9 8 A p r- 9 9 O ct -9 9 A p r- 0 0 O ct -0 0 A p r- 0 1 O ct -0 1 A p r- 0 2 O ct -0 2 A p r- 0 3 O ct -0 3 A p r- 0 4 O ct -0 4 A p r- 0 5 O ct -0 5 A p r- 0 6 O ct -0 6 A p r- 0 7 O ct -0 7 A p r- 0 8 O ct -0 8 A p r- 0 9 O ct -0 9 A p r- 1 0 O ct -1 0 A p r- 1 1 World Price Volatility after Rice Futures Market on CBOT 1994-2011 77  Bibliography Abdullah, D. 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Applied Economics Letters , 593-598.   81  Appendices  Appendix A: Derivation of Equations 3.7, 3.8 and 3.9  Two periods: t1 and t2 State A:  =   State B:  =  ‚  = t1 news of Demand in (t2) Q1 = first period endowment a = intercept value S = quantity stored in the first period S*= equilibrium quantity of storage m= storage cost P1 = a – Q1 + S = price in t1         (A.1) P2 =  – S = price in t2         (A.2) P2 – P1 = m            (A.3) Solving for S*: P2 – P1 = m   – S – a + Q1 – S = m ƒ∗ =   + „  − / − 
          (A.4)  A. Expected Squared Price Difference (ESPDNS) (Derivation of 3.7)  =  = 0  =   +   → equal probability for either high or low demand in second period  −   =  [ − 2ƒ∗ − / + „ … +  [ − 2ƒ∗ − / + „ … = 12 ‡ − ˆ12 ‚ + 12  + „1 − / − 
‰ − / + „1Š 2 + 12 ‡‚ − ˆ12 ‚ + 12  + „1 − / − 
‰ − / + „1Š 2  =  ‡
 −   − Š  + ‡
 +   − Š   =    
 −  
 −  + S  −  +  
 +  
 −  + S  −  = 
 +   −  = ESPDNS = (T.7)       (A.5) End  B. Expected Squared Price Difference with Speculation (ESPDWS) (Derivation of 3.8)  State A:  = ˆ  +  − ‰  + ˆ  −  + ‰  State A indicates that t1 news points to low demand in period 2 State B:  = ˆ  −  − ‰  + ˆ  +  + ‰  State B indicates that t1 news points to high demand in period 2 Equal probability of each state happening  Two possible S* (please see A. for derivation of S*):  ƒ‹∗ =  ‡ ˆ  +  − ‰ +  ˆ  −  + ‰ − / + „  − 
Š 82   ƒŒ∗ =  ‡ ˆ  −  − ‰ +  ˆ  +  + ‰ − / + „  − 
Š    −   =  ‡ˆ  + ‰ p −  t  + ˆ  − ‰ p −  t Š +   ‡ˆ  − ‰ p −  t  + ˆ  + ‰ p −  t Š (A.6)  Begin Aside: Recall  −   =  − 2ƒ∗ + Therefore: p −  t =  − [ −  −  −  + 
…     (A.7) p −  t =  − [ −  −  −  + 
…     (A.8) p −  t =  − [ +  +  −  + 
…      (A.9) p −  t =  − [ +  +  −  + 
…     (A.10)  Rearrange (A.7): (I.7) =  − [ −  +  +  −  + 
… = ˆ −   −   +  −  −  +  − 
‰  = ˆ   −   +  −  −  +  − 
‰  = ˆ −  −  −  −   −  − 
‰   = ‡ˆ −  − ‰  −  − 
Š  = ‡ˆ −  − ‰  −  − 
Š ‡ˆ −  − ‰  −  − 
Š  =  − 
 − 
 =  − 
  Rearrange (A.8): (I.8) = ˆ −  −  −  +   −  − 
‰   =‡ˆ −  + ‰  −  − 
Š  = d − 
  Rearrange (A.9): (I.9) = ˆ− −  −  −  −   −  − 
‰   ‡ˆ− −  − ‰  −  − 
Š  = 8 − 
  Rearrange (A.10): (I.10) = ˆ− −  −  −  +   −  − 
‰   = ‡ˆ− −  + ‰  −  − 
Š  = Ž − 
  End Aside  (A.6) =    ‡ˆ  + ‰  − 
 + ˆ  − ‰ d − 
Š +  ‡ˆ  − ‰ 8 − 
 + ˆ  + ‰ Ž − 
Š =    ‡ˆ  + ‰  − 
 + ˆ  − ‰ d − 
 + ˆ  − ‰ 8 − 
 + ˆ  + ‰ Ž − 
Š = 12 ‡2
2 − 
 + d + 8 + Ž + 2 − d2 − 82 + Ž2 + 12 2 + d2 + 82 + Ž2 − 2
 − d − 8 + ŽŠ (A.11)     83  Aside  +  + ‘ + ’ = “ −  − 12”  −  + “ −  + 1 2”  −  + “− −  − 1 2”  −  + “− −  + 12”  −  =  −  • −  − 12 +  −  + 1 2 −  −  − 1 2 + 1 2 −  − –= −4 −              (A.12)   ˜ − ˜ − ‘˜ + ’˜ = “ −  − 12”   −  − “ −  + 12”   −  − “− −  − 12”   −  + “− −  + 12”   −  =  −  • − 2 −  +  +  + 14 −  + 2 −  −  +  − 1 4 −  − 2 −  −  −  − 14 + 1 4 −  −  +  + 2 + – = −4 −              (A.13)  ˜ + ˜ + ‘˜ + ’˜ =  −  • − 2 −  +  +  + 14 +  − 2 +  − + 1 4 +  + 2 +  +  +  + 14 + 1 4 −  −  +  + 2 + – = 4 + 4 + 1 −              (A.14)   −  − ‘ + ’ =  −  ‡ −  −  −  +  −  +  +  +  +  −  − Š = 0             (A.15)  End Aside  Going back to (A.6) deriving (3.8):  −   = 12 •2
 − 
p−4 − t + −4 −  + 12 4 + 4 + 1 −  − 2
0– = 12 •2
 + 4
 −  −  −  “2 − 2 − 1 2”– = 
 + 2
 −  −  −  +  −  + 14  − = 3.8 (A.16)  84  (A.16) is the ESPDWS. As the value of  increases, ESPDWS falls. As the value of  increases, ESPDWS rises.  Value of œ∗ Derivation of 3.9 In order to derive the value of δ∗, (3.7) has to be set equal to (3.8)  ƒN = ƒN → 
 +   −  = 
 + 2
 −  −  −  +  −  +   −   2
 −  −  −  +  −  = 0  Use quadratic formula to solve for :   = −2  −  ± jp2
 − t − 4 − − −  2 −  = −2
 −  ±  4
 −  + 4 −  − 2 −  = −2
 −  ± 2 −  
 +  − 2 −  = −
 ±  
 +  −  −    =  !"!#$#%!#$#% = b{ /z¡]{ ]/i[{  ∗ =  !"!#$#%!#$#%  = (3.9)   85  Appendix B: Another GARCH Model  The GARCH-in-mean (GARCH-M) model is one of those which may allow for a better estimation of the rice spot returns. The general equation for the GARCH-M model is: '( =   + ) *+'(+,+-  + ℎ( + (          (B.1) GARCH-M allows the conditional variance to provide an explanation for the dependent variable, and equation (4.4) becomes: 4( = *5 + * 67( + *8( + ℎ( + (        (B.2) Where ℎ( is defined by equation (4.3). The GARCH-M model is a general form of the GARCH model which adds the current period conditional variance (ℎ() as an exogenous variable to the model estimating the current period returns (4(). GARCH-M has a few advantages over the conventional GARCH model. The GARCH-M model allows for the spot price return to be expressed directly as a function of conditional variance. Two other characteristics which are thought to be appealing to the rice market are discussed here. First, excluding the error variance (ℎ() from equation (B.2) when price fluctuation is high during the sample period, may ignore the problems of heteroskedasticity. Second, GARCH-M model explains how much of the return is due to the current period volatility (Brewer, Carson, Elyasiani, Mansur, & Scott, 2007).  86  Appendix C: Another Form of Equation (4.7)  This section presents another form of equation (4.7), which controls for the past values of the dummy variable while determining the current period’s volatility.  For simplicity Pt from equation (4.7) is ignored and that equation is takes the following form.  ℎ( = ∘ +    (  + ℎ(  + MN(        (C.1)  In order to remove the effect of last period’s dummy on current period’s volatility (J.1) has to take the following form:  ℎ( = ∘ +    (  + ℎ(  − MN(  + MN(       (C.2)  h< = α∘ +  α  ϵ<  + αh<  − αMD<  + αMD<= α∘ +  α  ϵ<  + α[α∘ +  α  ϵ< + αh< − αMD< + αMD< … − αMD<  + MN(= α∘ +  α  ϵ<  + αα∘ +  α  ϵ< + αh< − αMD< + MN(= α∘ +  α  ϵ<  + αα∘ +  α  ϵ< + αα∘ +  α  ϵ<M + αh<M − αMD<M + αMD< − αMD<+ MN( = α∘ +  α  ϵ<  + αα∘ +  α  ϵ< + αα∘ +  α  ϵ<M + αh<M − αMD<M + MN(  Repeating this process to infinity:  ℎ( = α∘ +  α  ϵ<  + αα∘ +  α  ϵ< + αα∘ +  α  ϵ<M + αα¥ + α  ϵ< + … . . +αα∘ +  α  ϵ<∞ + αh<∞ − αMD<∞ + MN(           (C.3)  Expanding (C.3)  ℎ( =  α∘ + α  ϵ<  + αα∘ +  αα  ϵ< + αα∘ +  αα  ϵ<M + αMα¥ + αMα  ϵ< + ⋯ + α§ α¥ + α§ ϵ<§ +α§ h<§ − αMD<§ + αMD<          (C.4)   < 1 because volatility from periods further in the past contributes less to the volatility in the current period. Therefore,  α§  ≈ 0            (C.5)  and (C.4) becomes:  ℎ( =  α∘ + α  ϵ<  + αα∘ +  αα  ϵ< + αα∘ +  αα  ϵ<M + αMα¥ + αMα  ϵ< + ⋯ + α§ α¥ + α§ ϵ<§ + D< (C.6) Therefore, the only dummy value that is left is D<. The dummy variable in each period explains the volatility ℎ( in that period and not the volatility in future periods. Not subtracting previous period dummy variable values yields the following result.  ℎ( = ∘ +    (  + ℎ(  + MN( = ∘ +    (  + ∘ +    ( + ℎ( + MN(  + MN(  (C.7)  Repeating this process to infinity, it becomes evident that dummy variables from all previous periods are explanatory variables for the current volatility ℎ(. Therefore, (C.7) becomes:  ℎ( = ∘ +    (  + ∘ +    ( + ⋯ + α∘ +  α  ϵ<∞ + αh<∞ + MN(∞  + ⋯ + MN(  + MN(             (C.8)  87  Appendix D: Seasonality Test Results (Stata Output)  Wheat Seasonality Test  . tabulate month, gen(m)        month |      Freq.     Percent        Cum. ------------+-----------------------------------         Apr |         23        8.13        8.13         Aug |         24        8.48       16.61         Dec |         24        8.48       25.09         Feb |         23        8.13       33.22         Jan |         24        8.48       41.70         Jul |         24        8.48       50.18         Jun |         23        8.13       58.30         Mar |         23        8.13       66.43         May |         23        8.13       74.56         Nov |         24        8.48       83.04         Oct |         24        8.48       91.52         Sep |         24        8.48      100.00 ------------+-----------------------------------       Total |        283      100.00  . reg rtrnw m1 m2 m3 m4 m5 m6 m7 m8 m9 m10 m11 m12, noconstant        Source |       SS       df       MS              Number of obs =     283 -------------+------------------------------           F( 12,   271) =    3.87        Model |  .104940799    12  .008745067           Prob > F      =  0.0000     Residual |  .612487282   271  .002260101           R-squared     =  0.1463 -------------+------------------------------           Adj R-squared =  0.1085        Total |  .717428081   283  .002535082           Root MSE      =  .04754  ------------------------------------------------------------------------------        rtrnw |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval] -------------+----------------------------------------------------------------           m1 |  -.0022488   .0099129    -0.23   0.821    -.0217648    .0172673           m2 |   .0165187   .0097042     1.70   0.090    -.0025865    .0356238           m3 |   .0101389   .0097042     1.04   0.297    -.0089662    .0292441           m4 |  -.0039844   .0099129    -0.40   0.688    -.0235005    .0155316           m5 |   .0005898   .0097042     0.06   0.952    -.0185153    .0196949           m6 |  -.0310489   .0097042    -3.20   0.002     -.050154   -.0119437           m7 |  -.0397279   .0099129    -4.01   0.000     -.059244   -.0202119           m8 |   .0000231   .0099129     0.00   0.998    -.0194929    .0195392           m9 |  -.0112847   .0099129    -1.14   0.256    -.0308007    .0082314          m10 |   .0086941   .0097042     0.90   0.371    -.0104111    .0277992          m11 |   .0284294   .0097042     2.93   0.004     .0093243    .0475346          m12 |   .0222267   .0097042     2.29   0.023     .0031215    .0413318 ------------------------------------------------------------------------------  Rice Seasonality Test . tabulate month, gen(m)        month |      Freq.     Percent        Cum. ------------+-----------------------------------         Apr |         28        8.19        8.19         Aug |         28        8.19       16.37         Dec |         29        8.48       24.85         Feb |         29        8.48       33.33         Jan |         29        8.48       41.81         Jul |         28        8.19       50.00         Jun |         28        8.19       58.19         Mar |         28        8.19       66.37         May |         28        8.19       74.56         Nov |         29        8.48       83.04       month |         Freq.     Percent     Cum.         Oct |         29        8.48       91.52         Sep |         29        8.48      100.00 ------------+----------------------------------- 88        Total |        342      100.00  . reg spot m1 m2 m3 m4 m5 m6 m7 m8 m9 m10 m11 m12, noconstant        Source |       SS       df       MS              Number of obs =     342 -------------+------------------------------           F( 12,   330) =    1.72        Model |  .063835781    12  .005319648           Prob > F      =  0.0616     Residual |  1.02154456   330   .00309559           R-squared     =  0.0588 -------------+------------------------------           Adj R-squared =  0.0246        Total |  1.08538034   342  .003173627           Root MSE      =  .05564  ------------------------------------------------------------------------------         spot |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval] -------------+----------------------------------------------------------------           m1 |  -.0102574   .0105146    -0.98   0.330    -.0309415    .0104267           m2 |   -.001397   .0105146    -0.13   0.894    -.0220811    .0192871           m3 |   .0108695   .0103317     1.05   0.294    -.0094548    .0311939           m4 |   .0025304   .0103317     0.24   0.807    -.0177939    .0228548           m5 |   .0095848   .0103317     0.93   0.354    -.0107396    .0299091           m6 |  -.0101483   .0105146    -0.97   0.335    -.0308324    .0105358           m7 |  -.0089429   .0105146    -0.85   0.396     -.029627    .0117412           m8 |  -.0072255   .0105146    -0.69   0.492    -.0279096    .0134586           m9 |  -.0144594   .0105146    -1.38   0.170    -.0351435    .0062247          m10 |   .0308802   .0103317     2.99   0.003     .0105559    .0512046          m11 |   .0221058   .0103317     2.14   0.033     .0017814    .0424301          m12 |   -.003188   .0103317    -0.31   0.758    -.0235124    .0171363 ------------------------------------------------------------------------------  Rice Futures Price Seasonality Test (Stata output) . tabulate month, gen(m)        month |      Freq.     Percent        Cum. ------------+-----------------------------------         Apr |         12        8.96        8.96         Aug |         11        8.21       17.16         Dec |         11        8.21       25.37         Feb |         11        8.21       33.58         Jan |         11        8.21       41.79         Jul |         11        8.21       50.00         Jun |         11        8.21       58.21         Mar |         12        8.96       67.16         May |         11        8.21       75.37         Nov |         11        8.21       83.58         Oct |         11        8.21       91.79         Sep |         11        8.21      100.00 ------------+-----------------------------------       Total |        134      100.00  . reg futspot m1 m2 m3 m4 m5 m6 m7 m8 m9 m10 m11 m12, noconstant        Source |       SS       df       MS              Number of obs =     134 -------------+------------------------------           F( 12,   122) =    0.89        Model |  .077935625    12  .006494635           Prob > F      =  0.5588     Residual |  .890072269   122  .007295674           R-squared     =  0.0805 -------------+------------------------------           Adj R-squared = -0.0099        Total |  .968007894   134   .00722394           Root MSE      =  .08541  ------------------------------------------------------------------------------      futspot |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval] -------------+----------------------------------------------------------------           m1 |  -.0081064   .0246571    -0.33   0.743    -.0569176    .0407048           m2 |  -.0000467   .0257535    -0.00   0.999    -.0510283    .0509349           m3 |   .0119898   .0257535     0.47   0.642    -.0389919    .0629714      futspot |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]            m4 |  -.0057409   .0257535    -0.22   0.824    -.0567225    .0452408           m5 |  -.0024888   .0257535    -0.10   0.923    -.0534704    .0484928           m6 |  -.0406545   .0257535    -1.58   0.117    -.0916361    .0103272           m7 |   -.011686   .0257535    -0.45   0.651    -.0626677    .0392956           m8 |   .0474054   .0246571     1.92   0.057    -.0014058    .0962167 89       futspot |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]           m9 |   .0463902   .0257535     1.80   0.074    -.0045915    .0973718          m10 |   .0168421   .0257535     0.65   0.514    -.0341396    .0678237          m11 |   .0108874   .0257535     0.42   0.673    -.0400943     .061869          m12 |  -.0059414   .0257535    -0.23   0.818     -.056923    .0450403 ------------------------------------------------------------------------------    90  Appendix E: Different Ordering of Variables in I.R. and FEVD Analysis  Different ordering of variables in a VAR model could yield different results. However, as indicated in section 4.2.1, different ordering of variables do not change the results of this study, because there are only two explanatory variables (trading volume and open interest) other than dependent variable (price volatility). Therefore the following two VAR models, where the position of trading volume (TV) and open interest (OI) have been changed in the second model are tested and the results compared. The CMA method is used to detrend the futures trading volume and open interest. The first VAR model, used in this study and indicated by equations (4.12-4.14) in section 4.2, is represented by the following set of equations here: U( = /5 + ) +U(+ +3+-  ) *+VW(+ +,+-  ) O+XY(+ +Z+-  _(    (E.1) VW( = 15 + ) *+VW(+ +,+-  ) O+XY(+ +Z+-  ) +U(+ + `U(3+-  + [(  (E.2) XY( = \5 + ) O+XY(+ +Z+-  ) *+VW(+ +,+-  ) +U(+ +3+-  `U( + aVW( + ]( (E.3) The second VAR model with changing of the order of the explanatory variables (TV and OI) is represented by the following set of equations: U( = /5 + ) +U(+ +3+-  ) *+XY(+ +,+-  ) O+VW(+ +Z+-  _(    (E.4) XY( = 15 + ) *+XY(+ +,+-  ) O+VW(+ +Z+-  ) +U(+ + `U(3+-  + [(  (E.5) VW( = \5 + ) O+VW(+ +Z+-  ) *+XY(+ +,+-  ) +U(+ +3+-  `U( + aXY( + ]( (E.6) The results of the Granger Causality Test, IR, and FEVD analyses are reported in the following tables (Stata outputs). There is clear indication that different ordering of variables in the VAR did not alter the results of this study. The VAR model that is used in this study (equations E.1 to E.3) is referred to as Model 1 and the one represented by equations E.4 to E.6 is referred to as Model 2. Granger Causality Test Model 1    Granger causality Wald tests 91    +------------------------------------------------------------------+   |          Equation           Excluded |   chi2     df Prob > chi2 |   |--------------------------------------+---------------------------|   |            garchm             cmavol |  13.418     3    0.004    |   |            garchm              cmaoi |  3.6074     3    0.307    |   |            garchm                ALL |  17.423     6    0.008    |   |--------------------------------------+---------------------------|   |            cmavol             garchm |  2.4016     3    0.493    |   |            cmavol              cmaoi |  21.101     3    0.000    |   |            cmavol                ALL |  25.187     6    0.000    |   |--------------------------------------+---------------------------|   |             cmaoi             garchm |  12.257     3    0.007    |   |             cmaoi             cmavol |  .54747     3    0.908    |   |             cmaoi                ALL |  13.089     6    0.042    |   +------------------------------------------------------------------+ Model 2    Granger causality Wald tests   +------------------------------------------------------------------+   |          Equation           Excluded |   chi2     df Prob > chi2 |   |--------------------------------------+---------------------------|   |            garchm              cmaoi |  3.6074     3    0.307    |   |            garchm             cmavol |  13.418     3    0.004    |   |            garchm                ALL |  17.423     6    0.008    |   |--------------------------------------+---------------------------|   |             cmaoi             garchm |  12.257     3    0.007    |   |             cmaoi             cmavol |  .54747     3    0.908    |   |             cmaoi                ALL |  13.089     6    0.042    |   |--------------------------------------+---------------------------|   |            cmavol             garchm |  2.4016     3    0.493    |   |            cmavol              cmaoi |  21.101     3    0.000    |   |            cmavol                ALL |  25.187     6    0.000    |   +------------------------------------------------------------------+  Impulse Response Analysis (IR) Model 1:             Model 2: Step garch-garch TV-garch OI-garch Step garch-garch OI-garch TV-garch 1 0.655796 -0.00477 0.008841 1 0.655796 0.008841 -0.00477 2 0.267846 -0.00663 0.004279 2 0.267846 0.004279 -0.00663 3 0.09384 -0.00272 -0.00086 3 0.09384 -0.00086 -0.00272 4 0.06486 0.002445 -0.00469 4 0.06486 -0.00469 0.002445 5 0.064405 0.000698 -0.00231 5 0.064405 -0.00231 0.000698 6 0.070075 -0.00159 0.001726 6 0.070075 0.001726 -0.00159 7 0.042706 -0.00149 0.003159 7 0.042706 0.003159 -0.00149 8 0.001602 0.000463 -0.00044 8 0.001602 -0.00044 0.000463 9 -0.01762 0.000623 -0.00225 9 -0.01762 -0.00225 0.000623 10 0.004971 1.90E-06 -0.00066 10 0.004971 -0.00066 1.90E-06     Note: - garch-garch indicates the impact of a shock in the current volatility of cash price on future volatility of the cash price of rice (garch) - TV-garch indicates the impact of a shock in detrended futures trading volume (TV) on future volatility of the cash price of rice (garch) 92  - OI-garch indicates the impact of a shock in detrended futures open interest (OI) on future volatility of the cash price of rice (garch) - Ten steps are chosen as beyond 10th period the effect of the shocks become very small in magnitude  Forecast Error Variance Decomposition (FEVD)  Model 1     Model 2 Step garch-garch TV-garch OI-garch Step garch-garch OI-garch TV-garch 1 1 0 0 1 1 0 0 2 0.953134 0.017641 0.029225 2 0.953134 0.02848 0.018386 3 0.902067 0.019605 0.078327 3 0.902067 0.077195 0.020737 4 0.894453 0.019573 0.085975 4 0.894453 0.084897 0.020651 5 0.884734 0.023701 0.091564 5 0.884734 0.090321 0.024944 98 0.874527 0.028739 0.096735 98 0.874527 0.095336 0.030137 99 0.874527 0.028739 0.096735 99 0.874527 0.095336 0.030137 100 0.874527 0.028739 0.096735 100 0.874527 0.095336 0.030137  Note: - garch-garch indicates the impact of a shock in the current volatility of cash price on future unpredictability (error) in estimating future volatility of the cash price of rice (garch) - TV-garch indicates the impact of a shock in detrended futures trading volume (TV) on future unpredictability (error) in estimating future volatility of the cash price of rice (garch) - OI-garch indicates the impact of a shock in detrended futures open interest (OI) on unpredictability (error) in estimating future volatility of the cash price of rice (garch) - 100 steps are chosen to have long enough horizon and assess the long term impact of current shocks to TV and OI on cash price volatility   93  Appendix F: Choosing Separate Lags for each Variable of a VAR Model  Choosing all lags for all variables to be equal could lead to rapid loss of degrees of freedom in the model. Granger causality test is sensitive to the selection of lag orders. Including insignificant lags could lead to rejecting the null hypothesis of the Granger causality test where one should fail to reject it. Atukeren (2005) suggests a few steps to identify the appropriate lag orders and these steps are adopted in this work. First, the following autoregressions are estimated based on lag orders ©=1 to 8. The autoregression with the lowest AIC value identifies the appropriate value of ©.  U( = /5 + ) `+U(+3+-  + ](         (F.1) Second, lagged values of VW are added to equation (F.1), and several autoregressions based lag orders ª = 1 to 8 are estimated. The estimation with the lowest AIC identifies the appropriate value for ª and of course © was determined in the first step.  U( = /5 + ) +U(+ +3+-  ) *+VW(+ +,+-   [(       (F.2) Same process is continued in step three to find the appropriate lag order for OI (4 value). U( = /5 + ) +U(+ +3+-  ) *+VW(+ +,+-  ) O+XY(+ +Z+-  _(     (F.3) OI and TV are detrended values of futures contract trading volume and open interest After each stage if the AIC from estimating the bivariate (equation F.2) or the trivariate (equation F.3) models is lower than that obtained from estimating the autoregression in (F.1), then that is an indication that TV (alone) and TV and OI Granger cause U (Atukeren, 2005). However, this work uses Granger’s original method of choosing all variable lengths the same. There are only three variables in the current VAR model, and given the low frequency of the data, it is believed that the lag lengths are fairly close to one another.  94  Appendix G: Monthly Variance Generated by GARCH (1,1) Model  Rough Rice   Before the Introduction of Rice Futures Contracts on the CBOT Date GARCH(1,1) Date GARCH(1,1) Date GARCH(1,1) Date GARCH(1,1) Sep-82 0.0035257 Oct-85 0.0012828 Dec-88 0.0021625 Jan-92 0.000996 Oct-82 0.0034043 Nov-85 0.0010716 Jan-89 0.0021096 Feb-92 0.0008484 Nov-82 0.0020686 Dec-85 0.0009073 Feb-89 0.002052 Mar-92 0.0007816 Dec-82 0.0012752 Jan-86 0.0009489 Mar-89 0.0020352 Apr-92 0.000912 Jan-83 0.001083 Feb-86 0.0007734 Apr-89 0.0019288 May-92 0.0014334 Feb-83 0.0007312 Mar-86 0.0007493 May-89 0.0018112 Jun-92 0.0016538 Mar-83 0.0006734 Apr-86 0.0041169 Jun-89 0.001542 Jul-92 0.0016014 Apr-83 0.0009526 May-86 0.0381241 Jul-89 0.0013556 Aug-92 0.0017977 May-83 0.0008804 Jun-86 0.0395468 Aug-89 0.001553 Sep-92 0.0026311 Jun-83 0.0007085 Jul-86 0.0401789 Sep-89 0.0011611 Oct-92 0.0026041 Jul-83 0.0008541 Aug-86 0.0348185 Oct-89 0.00128 Nov-92 0.0025331 Aug-83 0.0006628 Sep-86 0.0349172 Nov-89 0.0012968 Dec-92 0.0025127 Sep-83 0.000912 Oct-86 0.0352923 Dec-89 0.0013947 Jan-93 0.0025482 Oct-83 0.0005857 Nov-86 0.0341708 Jan-90 0.0011198 Feb-93 0.0030201 Nov-83 0.0008894 Dec-86 0.0365883 Feb-90 0.0015763 Mar-93 0.0045487 Dec-83 0.0005787 Jan-87 0.0421163 Mar-90 0.0011661 Apr-93 0.0059408 Jan-84 0.0004301 Feb-87 0.0395152 Apr-90 0.001025 May-93 0.0070729 Feb-84 0.0003172 Mar-87 0.0426977 May-90 0.0010139 Jun-93 0.0087642 Mar-84 0.0006228 Apr-87 0.0443778 Jun-90 0.0010496 Jul-93 0.0106368 Apr-84 0.0006022 May-87 0.0423127 Jul-90 0.0011577 Aug-93 0.0104125 May-84 0.0005588 Jun-87 0.0433015 Aug-90 0.0015778 Sep-93 0.0102445 Jun-84 0.0006348 Jul-87 0.0469157 Sep-90 0.0030803 Oct-93 0.0070498 Jul-84 0.0005183 Aug-87 0.0416929 Oct-90 0.0044404 Nov-93 0.0063384 Aug-84 0.0005017 Sep-87 0.0328997 Nov-90 0.0041711 Dec-93 0.0155953 Sep-84 0.00046 Oct-87 0.0197929 Dec-90 0.0044109 Jan-94 0.0108309 Oct-84 0.0004857 Nov-87 0.0400088 Jan-91 0.0035307 Feb-94 0.0055906 Nov-84 0.0004576 Dec-87 0.0303825 Feb-91 0.0026551 Mar-94 0.0057207 Dec-84 0.0006381 Jan-88 0.015819 Mar-91 0.0023552 Apr-94 0.0044096 Jan-85 0.0005317 Feb-88 0.0081527 Apr-91 0.0024345 May-94 0.0024258 Feb-85 0.0005747 Mar-88 0.0101805 May-91 0.0028439 Jun-94 0.0017808 Mar-85 0.0008636 Apr-88 0.0052967 Jun-91 0.0018627 Jul-94 0.0036936 Apr-85 0.0014131 May-88 0.0031177 Jul-91 0.0014682 Aug-94 0.0072898 May-85 0.0009728 Jun-88 0.0036462 Aug-91 0.0016388 Sep-94 0.0089007 Jun-85 0.0010597 Jul-88 0.0026187 Sep-91 0.0011557  Jul-85 0.0009211 Aug-88 0.0019172 Oct-91 0.0023271  Aug-85 0.0008429 Sep-88 0.0022867 Nov-91 0.0014767  Sep-85 0.0012485 Oct-88 0.0032191 Dec-91 0.0011865   Nov-88 0.0024818  95   After the Introduction of Rice Futures Contracts on the CBOT Date GARCH(1,1) Date GARCH(1,1) Date GARCH(1,1) Date GARCH(1,1) Date GARCH(1,1) Oct-94 0.0018912 Mar-98 0.0012772 Aug-01 0.0017247 Jan-05 0.0019226 Jun-08 0.0030854 Nov-94 0.0019446 Apr-98 0.0012178 Sep-01 0.002197 Feb-05 0.0014812 Jul-08 0.0027426 Dec-94 0.0015305 May-98 0.0013978 Oct-01 0.0027032 Mar-05 0.0023664 Aug-08 0.0020652 Jan-95 0.0013015 Jun-98 0.0012644 Nov-01 0.0025524 Apr-05 0.0017029 Sep-08 0.002828 Feb-95 0.0013622 Jul-98 0.0012623 Dec-01 0.0019913 May-05 0.0013768 Oct-08 0.0026464 Mar-95 0.001273 Aug-98 0.0011863 Jan-02 0.0014944 Jun-05 0.0012206 Nov-08 0.0044376 Apr-95 0.0011948 Sep-98 0.0019934 Feb-02 0.0012546 Jul-05 0.001145 Dec-08 0.0046119 May-95 0.001164 Oct-98 0.0020115 Mar-02 0.001422 Aug-05 0.0011776 Jan-09 0.0034507 Jun-95 0.0011686 Nov-98 0.0015511 Apr-02 0.001618 Sep-05 0.0013949 Feb-09 0.0026734 Jul-95 0.0011764 Dec-98 0.001429 May-02 0.0013417 Oct-05 0.001358 Mar-09 0.0057531 Aug-95 0.0011639 Jan-99 0.0012779 Jun-02 0.0011848 Nov-05 0.0014525 Apr-09 0.0034934 Sep-95 0.0025309 Feb-99 0.0012127 Jul-02 0.0011949 Dec-05 0.0025857 May-09 0.0026372 Oct-95 0.0019365 Mar-99 0.0011593 Aug-02 0.001311 Jan-06 0.0018091 Jun-09 0.0020675 Nov-95 0.0034145 Apr-99 0.0011304 Sep-02 0.0014493 Feb-06 0.0016403 Jul-09 0.0016183 Dec-95 0.0027348 May-99 0.0015519 Oct-02 0.0015486 Mar-06 0.0014681 Aug-09 0.0018196 Jan-96 0.0020494 Jun-99 0.0016387 Nov-02 0.0013306 Apr-06 0.0012775 Sep-09 0.0016851 Feb-96 0.0016117 Jul-99 0.0013573 Dec-02 0.001725 May-06 0.0012093 Oct-09 0.0014375 Mar-96 0.0014332 Aug-99 0.0012126 Jan-03 0.0018928 Jun-06 0.0012549 Nov-09 0.0013879 Apr-96 0.0012688 Sep-99 0.0084033 Feb-03 0.0017399 Jul-06 0.0011929 Dec-09 0.0014402 May-96 0.001302 Oct-99 0.0072155 Mar-03 0.0033988 Aug-06 0.0011522 Jan-10 0.0014104 Jun-96 0.0014755 Nov-99 0.0043431 Apr-03 0.0022258 Sep-06 0.0026616 Feb-10 0.0016487 Jul-96 0.0012932 Dec-99 0.0026368 May-03 0.0026267 Oct-06 0.0019172 Mar-10 0.0014414 Aug-96 0.0012086 Jan-00 0.0018283 Jun-03 0.0022861 Nov-06 0.0031357 Apr-10 0.001552 Sep-96 0.0014034 Feb-00 0.0014597 Jul-03 0.0044193 Dec-06 0.0023618 May-10 0.0013706 Oct-96 0.0012717 Mar-00 0.0013796 Aug-03 0.0027668 Jan-07 0.0017736 Jun-10 0.0014633 Nov-96 0.0013808 Apr-00 0.0013975 Sep-03 0.0046311 Feb-07 0.0014391 Jul-10 0.0017517 Dec-96 0.001371 May-00 0.001328 Oct-03 0.0048044 Mar-07 0.0015015 Aug-10 0.00191 Jan-97 0.0016339 Jun-00 0.0012605 Nov-03 0.0043453 Apr-07 0.001362 Sep-10 0.0032675 Feb-97 0.0013715 Jul-00 0.0011929 Dec-03 0.0042834 May-07 0.0013123 Oct-10 0.0027736 Mar-97 0.0013003 Aug-00 0.0011561 Jan-04 0.0045203 Jun-07 0.0013175 Nov-10 0.0019364 Apr-97 0.0012583 Sep-00 0.001239 Feb-04 0.0027404 Jul-07 0.0012235 Dec-10 0.0021999 May-97 0.0012538 Oct-00 0.0013719 Mar-04 0.0023181 Aug-07 0.0011856 Jan-11 0.0026927 Jun-97 0.0012538 Nov-00 0.0012078 Apr-04 0.0017363 Sep-07 0.0011578 Feb-11 0.0019216 Jul-97 0.0013962 Dec-00 0.0012968 May-04 0.0014753 Oct-07 0.0011717  Aug-97 0.001284 Jan-01 0.0011803 Jun-04 0.0013858 Nov-07 0.0026609  Sep-97 0.0012027 Feb-01 0.0012865 Jul-04 0.0019337 Dec-07 0.0025626  Oct-97 0.0011652 Mar-01 0.0012966 Aug-04 0.0015176 Jan-08 0.0018805  Nov-97 0.0011596 Apr-01 0.0011888 Sep-04 0.0018827 Feb-08 0.0021238  Dec-97 0.001192 May-01 0.0011386 Oct-04 0.0021944 Mar-08 0.0016418  Jan-98 0.0011618 Jun-01 0.001735 Nov-04 0.0041748 Apr-08 0.0018902  Feb-98 0.0013026 Jul-01 0.0019792 Dec-04 0.0028229 May-08 0.0018693   96  Milled Rice Before the Introduction of Rice Futures Contracts on the CBOT Date GARCH(1,1) Date GARCH(1,1) Date GARCH(1,1) Date GARCH(1,1) Date GARCH(1,1) Sep-79 0.0041226 Jan-83 0.0009458 May-86 0.0041575 Sep-89 0.0016349 Jan-93 0.0012684 Oct-79 0.0022628 Feb-83 0.0007354 Jun-86 0.036585 Oct-89 0.000916 Feb-93 0.0039818 Nov-79 0.0016281 Mar-83 0.0018097 Jul-86 0.01485 Nov-89 0.000674 Mar-93 0.00227 Dec-79 0.0006763 Apr-83 0.0007826 Aug-86 0.0075986 Dec-89 0.0005043 Apr-93 0.0015416 Jan-80 0.0047892 May-83 0.0008809 Sep-86 0.0073544 Jan-90 0.0004774 May-93 0.0014353 Feb-80 0.0039536 Jun-83 0.0004892 Oct-86 0.0045009 Feb-90 0.0005524 Jun-93 0.0017151 Mar-80 0.0108331 Jul-83 0.0003965 Nov-86 0.0033739 Mar-90 0.0003865 Jul-93 0.0023065 Apr-80 0.0093283 Aug-83 0.000379 Dec-86 0.0029258 Apr-90 0.0004569 Aug-93 0.0021293 May-80 0.0036639 Sep-83 0.0001817 Jan-87 0.0035244 May-90 0.0004991 Sep-93 0.0017912 Jun-80 0.0035218 Oct-83 0.0001171 Feb-87 0.0073282 Jun-90 0.000497 Oct-93 0.0014032 Jul-80 0.0047081 Nov-83 0.0002113 Mar-87 0.0064847 Jul-90 0.0003671 Nov-93 0.023621 Aug-80 0.0028749 Dec-83 0.0001745 Apr-87 0.0050383 Aug-90 0.0004159 Dec-93 0.1208422 Sep-80 0.0011458 Jan-84 0.0001324 May-87 0.0044472 Sep-90 0.0016238 Jan-94 0.0515679 Oct-80 0.0029271 Feb-84 0.0001994 Jun-87 0.0041388 Oct-90 0.0040535 Feb-94 0.0198445 Nov-80 0.0045622 Mar-84 0.0001333 Jul-87 0.0041213 Nov-90 0.0023601 Mar-94 0.0082164 Dec-80 0.004785 Apr-84 0.0000889 Aug-87 0.0037908 Dec-90 0.0015729 Apr-94 0.0031664 Jan-81 0.0056222 May-84 0.0000774 Sep-87 0.0023785 Jan-91 0.001084 May-94 0.002716 Feb-81 0.0021546 Jun-84 0.0001433 Oct-87 0.0105829 Feb-91 0.0009222 Jun-94 0.0054772 Mar-81 0.000876 Jul-84 0.0000928 Nov-87 0.1337221 Mar-91 0.0055773 Jul-94 0.015007 Apr-81 0.0009394 Aug-84 0.0001268 Dec-87 0.059164 Apr-91 0.0024726 Aug-94 0.0184427 May-81 0.0007564 Sep-84 0.0003746 Jan-88 0.0224998 May-91 0.0017754 Sep-94 0.0195466 Jun-81 0.0003682 Oct-84 0.000194 Feb-88 0.0085009 Jun-91 0.0020385  Jul-81 0.0002902 Nov-84 0.0001513 Mar-88 0.0219036 Jul-91 0.0018853  Aug-81 0.0002389 Dec-84 0.0005594 Apr-88 0.0084103 Aug-91 0.0009004  Sep-81 0.0017248 Jan-85 0.0003178 May-88 0.0032112 Sep-91 0.0006381  Oct-81 0.0028472 Feb-85 0.0001709 Jun-88 0.0102441 Oct-91 0.0003706  Nov-81 0.0022725 Mar-85 0.0001518 Jul-88 0.0090346 Nov-91 0.0002318  Dec-81 0.001589 Apr-85 0.0001107 Aug-88 0.0056405 Dec-91 0.0016624  Jan-82 0.0010574 May-85 0.0001208 Sep-88 0.006261 Jan-92 0.0010336  Feb-82 0.0009077 Jun-85 0.0001132 Oct-88 0.0092338 Feb-92 0.0004966  Mar-82 0.0023142 Jul-85 0.0001369 Nov-88 0.0101021 Mar-92 0.0002845  Apr-82 0.0022632 Aug-85 0.0001486 Dec-88 0.0041441 Apr-92 0.0004903  May-82 0.0011041 Sep-85 0.0001307 Jan-89 0.0019776 May-92 0.0003532  Jun-82 0.0005081 Oct-85 0.0001614 Feb-89 0.0011535 Jun-92 0.0011864  Jul-82 0.0003094 Nov-85 0.0001313 Mar-89 0.0007983 Jul-92 0.0013699  Aug-82 0.001178 Dec-85 0.0001266 Apr-89 0.0008051 Aug-92 0.0008543  Sep-82 0.0016561 Jan-86 0.0002144 May-89 0.0005843 Sep-92 0.0005796  Oct-82 0.0009194 Feb-86 0.0004949 Jun-89 0.0023709 Oct-92 0.0004338  Nov-82 0.0004175 Mar-86 0.0003108 Jul-89 0.0010919 Nov-92 0.0004399  Dec-82 0.000359 Apr-86 0.0004554 Aug-89 0.0034928 Dec-92 0.0005828    97  After the Introduction of Rice Futures Contracts on the CBOT Date GARCH(1,1) Date GARCH(1,1) Date GARCH(1,1) Date GARCH(1,1) Date GARCH(1,1) Oct-94 0.0009861 Jan-98 0.000476 Apr-01 0.000617 Jul-04 0.001376 Oct-07 0.000409 Nov-94 0.0010032 Feb-98 0.000456 May-01 0.000623 Aug-04 0.001311 Nov-07 0.000402 Dec-94 0.0009904 Mar-98 0.000437 Jun-01 0.000637 Sep-04 0.001269 Dec-07 0.000409 Jan-95 0.0009792 Apr-98 0.000434 Jul-01 0.000642 Oct-04 0.001333  Feb-95 0.0009596 May-98 0.000417 Aug-01 0.00065 Nov-04 0.0013  Mar-95 0.0009425 Jun-98 0.0004 Sep-01 0.000674 Dec-04 0.001255  Apr-95 0.0009239 Jul-98 0.000385 Oct-01 0.000761 Jan-05 0.001211  May-95 0.0008981 Aug-98 0.000371 Nov-01 0.0008 Feb-05 0.001166  Jun-95 0.0009175 Sep-98 0.000358 Dec-01 0.000847 Mar-05 0.001129  Jul-95 0.0010802 Oct-98 0.000357 Jan-02 0.00092 Apr-05 0.001092  Aug-95 0.0010498 Nov-98 0.000345 Feb-02 0.000983 May-05 0.00106  Sep-95 0.0010025 Dec-98 0.000345 Mar-02 0.001066 Jun-05 0.001025  Oct-95 0.0009632 Jan-99 0.000333 Apr-02 0.001143 Jul-05 0.000993  Nov-95 0.0010896 Feb-99 0.000327 May-02 0.001214 Aug-05 0.000965  Dec-95 0.0010378 Mar-99 0.000319 Jun-02 0.001293 Sep-05 0.000939  Jan-96 0.0010022 Apr-99 0.000314 Jul-02 0.001375 Oct-05 0.000911  Feb-96 0.0009696 May-99 0.000309 Aug-02 0.00144 Nov-05 0.000885  Mar-96 0.0009299 Jun-99 0.000326 Sep-02 0.00149 Dec-05 0.000869  Apr-96 0.0008892 Jul-99 0.000335 Oct-02 0.001565 Jan-06 0.000838  May-96 0.0008665 Aug-99 0.000334 Nov-02 0.001654 Feb-06 0.000877  Jun-96 0.000853 Sep-99 0.000346 Dec-02 0.001723 Mar-06 0.000853  Jul-96 0.0008126 Oct-99 0.000351 Jan-03 0.001777 Apr-06 0.000822  Aug-96 0.0007732 Nov-99 0.000355 Feb-03 0.001817 May-06 0.000787  Sep-96 0.0007915 Dec-99 0.000366 Mar-03 0.001859 Jun-06 0.000753  Oct-96 0.0007552 Jan-00 0.000377 Apr-03 0.001838 Jul-06 0.000722  Nov-96 0.0008003 Feb-00 0.000404 May-03 0.002057 Aug-06 0.00069  Dec-96 0.0008017 Mar-00 0.000421 Jun-03 0.002062 Sep-06 0.000693  Jan-97 0.0007639 Apr-00 0.000442 Jul-03 0.002008 Oct-06 0.000711  Feb-97 0.0007269 May-00 0.000467 Aug-03 0.001943 Nov-06 0.000678  Mar-97 0.0007219 Jun-00 0.0005 Sep-03 0.001955 Dec-06 0.000647  Apr-97 0.0006946 Jul-00 0.000532 Oct-03 0.001899 Jan-07 0.000617  May-97 0.0006641 Aug-00 0.000556 Nov-03 0.00183 Feb-07 0.000588  Jun-97 0.0006339 Sep-00 0.000579 Dec-03 0.001774 Mar-07 0.000561  Jul-97 0.0006037 Oct-00 0.000592 Jan-04 0.001726 Apr-07 0.000537  Aug-97 0.0005775 Nov-00 0.000608 Feb-04 0.001649 May-07 0.000514  Sep-97 0.0005515 Dec-00 0.000609 Mar-04 0.001573 Jun-07 0.000491  Oct-97 0.0005316 Jan-01 0.000611 Apr-04 0.0015 Jul-07 0.000469  Nov-97 0.0005179 Feb-01 0.000612 May-04 0.001432 Aug-07 0.000448  Dec-97 0.0004981 Mar-01 0.000614 Jun-04 0.001417 Sep-07 0.000428     98  World Rice (Thai 100% B Second Grade) Date GARCH(1,1) Date GARCH(1,1) Date GARCH(1,1) Date GARCH(1,1) Date GARCH(1,1) Jan-78 0.0038039 May-81 0.0015619 Sep-84 0.0017814 Jan-88 0.0053109 May-91 0.0056669 Feb-78 0.0032594 Jun-81 0.0013632 Oct-84 0.0031604 Feb-88 0.0082689 Jun-91 0.0040759 Mar-78 0.0050708 Jul-81 0.0014306 Nov-84 0.0024427 Mar-88 0.0063135 Jul-91 0.0030758 Apr-78 0.0044706 Aug-81 0.0014389 Dec-84 0.0043256 Apr-88 0.0049808 Aug-91 0.0028018 May-78 0.0035989 Sep-81 0.0019821 Jan-85 0.003293 May-88 0.0037601 Sep-91 0.0024007 Jun-78 0.0027178 Oct-81 0.001799 Feb-85 0.0025018 Jun-88 0.0064208 Oct-91 0.0021468 Jul-78 0.0021793 Nov-81 0.0028374 Mar-85 0.0021444 Jul-88 0.0050636 Nov-91 0.0023672 Aug-78 0.0025218 Dec-81 0.0032813 Apr-85 0.0017423 Aug-88 0.0037388 Dec-91 0.0019368 Sep-78 0.0026003 Jan-82 0.0065978 May-85 0.0014764 Sep-88 0.0029128 Jan-92 0.0016833 Oct-78 0.0020449 Feb-82 0.007477 Jun-85 0.0013005 Oct-88 0.0022891 Feb-92 0.0015368 Nov-78 0.0018732 Mar-82 0.0062121 Jul-85 0.0011849 Nov-88 0.0018387 Mar-92 0.0013452 Dec-78 0.0064945 Apr-82 0.0044313 Aug-85 0.0021511 Dec-88 0.0015494 Apr-92 0.0012229 Jan-79 0.0058551 May-82 0.0037185 Sep-85 0.0017474 Jan-89 0.0019532 May-92 0.0011376 Feb-79 0.0042269 Jun-82 0.0033635 Oct-85 0.0014805 Feb-89 0.0016578 Jun-92 0.0011889 Mar-79 0.0031186 Jul-82 0.0027309 Nov-85 0.0013039 Mar-89 0.001568 Jul-92 0.0013853 Apr-79 0.0028792 Aug-82 0.0021528 Dec-85 0.0011872 Apr-89 0.0014597 Aug-92 0.0017824 May-79 0.002231 Sep-82 0.0017915 Jan-86 0.0022838 May-89 0.0020536 Sep-92 0.0019082 Jun-79 0.0018023 Oct-82 0.0025858 Feb-86 0.0028567 Jun-89 0.0025485 Oct-92 0.0023077 Jul-79 0.0015844 Nov-82 0.003112 Mar-86 0.0027544 Jul-89 0.00296 Nov-92 0.0020331 Aug-79 0.0013827 Dec-82 0.0024266 Apr-86 0.0032823 Aug-89 0.0031192 Dec-92 0.0016754 Sep-79 0.0022798 Jan-83 0.0021364 May-86 0.0037827 Sep-89 0.0032883 Jan-93 0.0014775 Oct-79 0.0020468 Feb-83 0.0019074 Jun-86 0.0028664 Oct-89 0.0028477 Feb-93 0.0014134 Nov-79 0.0016791 Mar-83 0.0019142 Jul-86 0.0022979 Nov-89 0.0030708 Mar-93 0.0015579 Dec-79 0.0014358 Apr-83 0.0020352 Aug-86 0.0058186 Dec-89 0.0062638 Apr-93 0.0041141 Jan-80 0.0016538 May-83 0.0016708 Sep-86 0.0043335 Jan-90 0.0044716 May-93 0.0064303 Feb-80 0.0018176 Jun-83 0.001453 Oct-86 0.0046875 Feb-90 0.0033189 Jun-93 0.0078027 Mar-80 0.0015402 Jul-83 0.0017681 Nov-86 0.0034443 Mar-90 0.0042579 Jul-93 0.0055777 Apr-80 0.0017016 Aug-83 0.0018489 Dec-86 0.0026192 Apr-90 0.0035632 Aug-93 0.0068266 May-80 0.0014616 Sep-83 0.0023091 Jan-87 0.002562 May-90 0.0033081 Sep-93 0.0048394 Jun-80 0.0015344 Oct-83 0.0034609 Feb-87 0.0023029 Jun-90 0.0035438 Oct-93 0.0036499 Jul-80 0.0014243 Nov-83 0.0028479 Mar-87 0.0033547 Jul-90 0.0027953 Nov-93 0.0154693 Aug-80 0.0012668 Dec-83 0.0024005 Apr-87 0.0033357 Aug-90 0.0021722 Dec-93 0.0241592 Sep-80 0.0011626 Jan-84 0.002306 May-87 0.0025307 Sep-90 0.0018043 Jan-94 0.0165033 Oct-80 0.0010937 Feb-84 0.0029036 Jun-87 0.0020121 Oct-90 0.0015273 Feb-94 0.0147085 Nov-80 0.0010482 Mar-84 0.002332 Jul-87 0.0016968 Nov-90 0.0029941 Mar-94 0.0101855 Dec-80 0.0015287 Apr-84 0.001867 Aug-87 0.00166 Dec-90 0.0026315 Apr-94 0.0285152 Jan-81 0.0013754 May-84 0.0015805 Sep-87 0.0024878 Jan-91 0.0023431 May-94 0.0192977 Feb-81 0.0012344 Jun-84 0.0014232 Oct-87 0.0127057 Feb-91 0.0072285 Jun-94 0.0181338 Mar-81 0.0012306 Jul-84 0.001287 Nov-87 0.0097905 Mar-91 0.0061954 Jul-94 0.0143248 Apr-81 0.0017561 Aug-84 0.0021894 Dec-87 0.007531 Apr-91 0.0050771 Aug-94 0.0102819   99  Date GARCH(1,1) Date GARCH(1,1) Date GARCH(1,1) Date GARCH(1,1) Date GARCH(1,1) Sep-94 0.0097 Jan-98 0.0032564 May-01 0.0036926 Sep-04 0.0023876 Jan-08 0.0024496 Oct-94 0.0070773 Feb-98 0.0054281 Jun-01 0.0027955 Oct-04 0.001908 Feb-08 0.0023193 Nov-94 0.0050104 Mar-98 0.0039358 Jul-01 0.0022632 Nov-04 0.0015881 Mar-08 0.0123589 Dec-94 0.0036532 Apr-98 0.002949 Aug-01 0.001842 Dec-04 0.0016388 Apr-08 Jan-95 0.0028234 May-98 0.0029462 Sep-01 0.0015601 Jan-05 0.0022736 May-08 Feb-95 0.002875 Jun-98 0.002392 Oct-01 0.0014882 Feb-05 0.002109 Jun-08 Mar-95 0.0026181 Jul-98 0.002249 Nov-01 0.0013668 Mar-05 0.0017508 Jul-08 Apr-95 0.0021065 Aug-98 0.0020049 Dec-01 0.0012426 Apr-05 0.0014921 Aug-08 0.0280304 May-95 0.0017327 Sep-98 0.0016508 Jan-02 0.0018418 May-05 0.0013444 Sep-08 0.0207093 Jun-95 0.0015693 Oct-98 0.0014233 Feb-02 0.0025287 Jun-05 0.0012768 Oct-08 0.0141608 Jul-95 0.0053413 Nov-98 0.002934 Mar-02 0.0020487 Jul-05 0.00142 Nov-08 0.0155558 Aug-95 0.0046856 Dec-98 0.004972 Apr-02 0.001901 Aug-05 0.0015356 Dec-08 0.0135458 Sep-95 0.003498 Jan-99 0.0040694 May-02 0.0015808 Sep-05 0.001394 Jan-09 0.0094476 Oct-95 0.0033549 Feb-99 0.0040747 Jun-02 0.0018573 Oct-05 0.0012785 Feb-09 0.0096885 Nov-95 0.0034697 Mar-99 0.004601 Jul-02 0.001619 Nov-05 0.0011895 Mar-09 0.0069312 Dec-95 0.0063976 Apr-99 0.0055902 Aug-02 0.0014495 Dec-05 0.0016219 Apr-09 0.0049789 Jan-96 0.004554 May-99 0.0060269 Sep-02 0.0018204 Jan-06 0.0014154 May-09 0.0054255 Feb-96 0.0043946 Jun-99 0.0046153 Oct-02 0.0016087 Feb-06 0.0014002 Jun-09 0.0051381 Mar-96 0.0032348 Jul-99 0.0037916 Nov-02 0.0014791 Mar-06 0.0016459 Jul-09 0.0037585 Apr-96 0.0025215 Aug-99 0.002831 Dec-02 0.001313 Apr-06 0.0014126 Aug-09 0.006945 May-96 0.0051722 Sep-99 0.0023162 Jan-03 0.0012355 May-06 0.0012573 Sep-09 0.0066445 Jun-96 0.003821 Oct-99 0.0034328 Feb-03 0.0025458 Jun-06 0.0011664 Oct-09 0.0049147 Jul-96 0.0030152 Nov-99 0.0040398 Mar-03 0.0020218 Jul-06 0.001131 Nov-09 0.004235 Aug-96 0.0028476 Dec-99 0.0035268 Apr-03 0.0016963 Aug-06 0.0011732 Dec-09 0.0031255 Sep-96 0.0034186 Jan-00 0.0026985 May-03 0.0014807 Sep-06 0.0010991 Jan-10 0.0035254 Oct-96 0.0027366 Feb-00 0.0032833 Jun-03 0.0013313 Oct-06 0.0010545 Feb-10 0.0027214 Nov-96 0.0028361 Mar-00 0.0026108 Jul-03 0.0013983 Nov-06 0.0010657 Mar-10 0.0022888 Dec-96 0.0022044 Apr-00 0.0030991 Aug-03 0.001393 Dec-06 0.0013044 Apr-10 0.0032974 Jan-97 0.0017932 May-00 0.0031932 Sep-03 0.0013303 Jan-07 0.0013655 May-10 0.0041315 Feb-97 0.0056064 Jun-00 0.0046044 Oct-03 0.0014371 Feb-07 0.0012578 Jun-10 0.0044761 Mar-97 0.004242 Jul-00 0.0033819 Nov-03 0.001276 Mar-07 0.0011633 Jul-10 0.0032887 Apr-97 0.0045474 Aug-00 0.002941 Dec-03 0.0012166 Apr-07 0.0013163 Aug-10 0.0025991 May-97 0.0050307 Sep-00 0.0024119 Jan-04 0.001313 May-07 0.0012501 Sep-10 0.0020753 Jun-97 0.005278 Oct-00 0.0026267 Feb-04 0.0018344 Jun-07 0.0011659 Oct-10 0.0024449 Jul-97 0.003825 Nov-00 0.0025885 Mar-04 0.0017029 Jul-07 0.0011542 Nov-10 0.0020065 Aug-97 0.0028943 Dec-00 0.0020774 Apr-04 0.0050999 Aug-07 0.0011585 Dec-10 0.0026044 Sep-97 0.0059701 Jan-01 0.0017213 May-04 0.0043711 Sep-07 0.0010981 Jan-11 0.0024354 Oct-97 0.005103 Feb-01 0.0014626 Jun-04 0.0032396 Oct-07 0.0010625 Feb-11 0.002393 Nov-97 0.0037956 Mar-01 0.0012907 Jul-04 0.0027411 Nov-07 0.0010735 Mar-11 0.0020067 Dec-97 0.0036887 Apr-01 0.0017599 Aug-04 0.002229 Dec-07 0.0019524 Apr-11 0.0025868   100  Appendix H: Results of Estimating Volatility by GARCH Model (Stata Output)  Estimation of (4.4 and 4.7) 4( = *5 + * 67( + *8( + (         (4.4) ℎ( = ∘ +    (  + ℎ(  + MN( +  (       (4.7)  Rough Rice . tsset time         time variable:  time, 1 to 342  . arch spot crb wprtrn, het(dum cash) arch(1) garch(1)  (setting optimization to BHHH) Iteration 0:   log likelihood =  524.67564 Iteration 1:   log likelihood =  534.30804 Iteration 2:   log likelihood =  541.34092 Iteration 3:   log likelihood =  542.63938 Iteration 4:   log likelihood =  542.81027 (switching optimization to BFGS) Iteration 5:   log likelihood =  547.41497 Iteration 6:   log likelihood =  548.90147 Iteration 7:   log likelihood =  549.15428 Iteration 8:   log likelihood =  549.15428  (backed up) Iteration 9:   log likelihood =  549.24244 Iteration 10:  log likelihood =  549.42047 Iteration 11:  log likelihood =  549.44315 Iteration 12:  log likelihood =  549.48556 Iteration 13:  log likelihood =  549.53128 Iteration 14:  log likelihood =  549.53425 (switching optimization to BHHH) Iteration 15:  log likelihood =   549.5346 Iteration 16:  log likelihood =  549.63989 Iteration 17:  log likelihood =  549.65658 Iteration 18:  log likelihood =  549.66548 Iteration 19:  log likelihood =  549.66933 (switching optimization to BFGS) Iteration 20:  log likelihood =  549.67367 Iteration 21:  log likelihood =  549.68119 Iteration 22:  log likelihood =   549.6815 Iteration 23:  log likelihood =  549.68178 Iteration 24:  log likelihood =  549.68232 Iteration 25:  log likelihood =  549.68387 Iteration 26:  log likelihood =  549.68389  (backed up) Iteration 27:  log likelihood =  549.68414 Iteration 28:  log likelihood =  549.68419 Iteration 29:  log likelihood =  549.68424 (switching optimization to BHHH) Iteration 30:  log likelihood =  549.68426 Iteration 31:  log likelihood =  549.68431 Iteration 32:  log likelihood =  549.68431 Iteration 33:  log likelihood =  549.68433 Iteration 34:  log likelihood =  549.68433 (switching optimization to BFGS) Iteration 35:  log likelihood =  549.68433  (backed up) Iteration 36:  log likelihood =  549.68433  (backed up) Iteration 37:  log likelihood =  549.68433 Iteration 38:  log likelihood =  549.68433  (backed up) Iteration 39:  log likelihood =  549.68433 Iteration 40:  log likelihood =  549.68433  (backed up) Iteration 41:  log likelihood =  549.68433  (backed up) Iteration 42:  log likelihood =  549.68433 Iteration 43:  log likelihood =  549.68433  (backed up) Iteration 44:  log likelihood =  549.68433  (backed up) (switching optimization to BHHH) Iteration 45:  log likelihood =  549.68433  (backed up) Iteration 46:  log likelihood =  549.68433  (backed up) Iteration 47:  log likelihood =  549.68433  (backed up) Iteration 48:  log likelihood =  549.68433  (backed up) Iteration 49:  log likelihood =  549.68433  (backed up) (switching optimization to BFGS) 101  Iteration 50:  log likelihood =  549.68433  (backed up) Iteration 51:  log likelihood =  549.68433  (backed up) Iteration 52:  log likelihood =  549.68433  (backed up) Iteration 53:  log likelihood =  549.68433  (backed up) Iteration 54:  log likelihood =  549.68433  (backed up) Iteration 55:  log likelihood =  549.68433  (backed up) Iteration 56:  log likelihood =  549.68433  (backed up) Iteration 57:  log likelihood =  549.68433  (backed up) Iteration 58:  log likelihood =  549.68433  (backed up) Iteration 59:  log likelihood =  549.68433  (backed up) (switching optimization to BHHH) Iteration 60:  log likelihood =  549.68433  (backed up) Iteration 61:  log likelihood =  549.68433  (backed up) Iteration 62:  log likelihood =  549.68433  (backed up) Iteration 63:  log likelihood =  549.68433  (backed up) Iteration 64:  log likelihood =  549.68433  (backed up) (switching optimization to BFGS) Iteration 65:  log likelihood =  549.68433  (backed up) Iteration 66:  log likelihood =  549.68433  (backed up) Iteration 67:  log likelihood =  549.68433  (backed up) Iteration 68:  log likelihood =  549.68433  (backed up) Iteration 69:  log likelihood =  549.68433  (backed up) Iteration 70:  log likelihood =  549.68433  (backed up) Iteration 71:  log likelihood =  549.68433  (backed up) Iteration 72:  log likelihood =  549.68433  (backed up) Iteration 73:  log likelihood =  549.68433  (backed up) Iteration 74:  log likelihood =  549.68433  ARCH family regression -- multiplicative heteroskedasticity  Sample:  1 to 342                               Number of obs      =       342                                                 Wald chi2(2)       =     12.92 Log likelihood =  549.6843                      Prob > chi2        =    0.0016  ------------------------------------------------------------------------------              |                 OPG         spot |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval] -------------+---------------------------------------------------------------- spot         |          crb |    .035179   .0750278     0.47   0.639    -.1118727    .1822308       wprtrn |   .0889872   .0258457     3.44   0.001     .0383306    .1396438        _cons |  -.0008927   .0029301    -0.30   0.761    -.0066356    .0048502 -------------+---------------------------------------------------------------- HET          |          dum |  -.5124324   .1382895    -3.71   0.000    -.7834748     -.24139         cash |  -.0049808   .0024909    -2.00   0.046    -.0098629   -.0000986        _cons |  -5.852786   .3187265   -18.36   0.000    -6.477479   -5.228094 -------------+---------------------------------------------------------------- ARCH         |         arch |          L1. |   .4225579   .0860238     4.91   0.000     .2539543    .5911615        garch |          L1. |   .3277246   .0848441     3.86   0.000     .1614333     .494016 ------------------------------------------------------------------------------  Milled Rice . tsset time         time variable:  time, 1 to 366  . arch milled crb wprtrn, het(dum cash) arch(1) garch(1)  (setting optimization to BHHH) Iteration 0:   log likelihood =  636.30661 Iteration 1:   log likelihood =  659.23383 Iteration 2:   log likelihood =  668.41137 Iteration 3:   log likelihood =  673.11275 Iteration 4:   log likelihood =  678.05973 (switching optimization to BFGS) Iteration 5:   log likelihood =  679.60549 Iteration 6:   log likelihood =  680.39368 Iteration 7:   log likelihood =  683.12243 Iteration 8:   log likelihood =   686.7832 Iteration 9:   log likelihood =  688.90191 102  Iteration 10:  log likelihood =  690.50595 Iteration 11:  log likelihood =   691.5507 Iteration 12:  log likelihood =  691.79982 Iteration 13:  log likelihood =  692.21058 Iteration 14:  log likelihood =  692.31443 (switching optimization to BHHH) Iteration 15:  log likelihood =  692.38653 Iteration 16:  log likelihood =  692.43812 Iteration 17:  log likelihood =  692.44464 Iteration 18:  log likelihood =   692.4486 Iteration 19:  log likelihood =  692.45113 (switching optimization to BFGS) Iteration 20:  log likelihood =   692.4533 Iteration 21:  log likelihood =  692.47041 Iteration 22:  log likelihood =  692.47697 Iteration 23:  log likelihood =  692.48118 Iteration 24:  log likelihood =   692.4826 Iteration 25:  log likelihood =   692.4828 Iteration 26:  log likelihood =  692.48282 Iteration 27:  log likelihood =  692.48282 Iteration 28:  log likelihood =  692.48282  ARCH family regression -- multiplicative heteroskedasticity  Sample:  1 to 366                               Number of obs      =       366                                                 Wald chi2(2)       =     31.37 Log likelihood =  692.4828                      Prob > chi2        =    0.0000  ------------------------------------------------------------------------------              |                 OPG       milled |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval] -------------+---------------------------------------------------------------- milled       |          crb |   .1297854    .055997     2.32   0.020     .0200332    .2395375       wprtrn |   .0820868   .0192359     4.27   0.000     .0443851    .1197884        _cons |  -.0102783    .001563    -6.58   0.000    -.0133417   -.0072149 -------------+---------------------------------------------------------------- HET          |          dum |  -.4716149   .1608746    -2.93   0.003    -.7869234   -.1563064         cash |   .0012217   .0007337     1.67   0.096    -.0002162    .0026597        _cons |  -7.711668   .3227048   -23.90   0.000    -8.344158   -7.079178 -------------+---------------------------------------------------------------- ARCH         |         arch |          L1. |    1.19158   .1427916     8.34   0.000     .9117134    1.471446        garch |          L1. |   .0041671   .0220867     0.19   0.850    -.0391219    .0474562 ------------------------------------------------------------------------------  World Rice (Impact of Rice Futures on the CBOT) . arch wprtrn crbrtrn, het(dum) arch(1) garch(1)  (setting optimization to BHHH) Iteration 0:   log likelihood =  592.80672 Iteration 1:   log likelihood =  597.14604 Iteration 2:   log likelihood =  605.37951 Iteration 3:   log likelihood =  610.32706 Iteration 4:   log likelihood =  611.18809 (switching optimization to BFGS) Iteration 5:   log likelihood =  611.32873 Iteration 6:   log likelihood =  611.40914 Iteration 7:   log likelihood =  611.41736 Iteration 8:   log likelihood =  611.41796 Iteration 9:   log likelihood =  611.41799    ARCH family regression -- multiplicative heteroskedasticity  Sample:  1 to 400                               Number of obs      =       400                                                 Wald chi2(1)       =      1.06 Log likelihood =   611.418                      Prob > chi2        =    0.3023  ------------------------------------------------------------------------------ 103               |                 OPG       wprtrn |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval] -------------+---------------------------------------------------------------- wprtrn       |      crbrtrn |    .123953   .1201777     1.03   0.302     -.111591     .359497        _cons |   .0016475   .0025046     0.66   0.511    -.0032614    .0065564 -------------+---------------------------------------------------------------- HET          |          dum |  -.2818254   .2436502    -1.16   0.247    -.7593709    .1957202        _cons |   -7.96268   .3273619   -24.32   0.000    -8.604298   -7.321063 -------------+---------------------------------------------------------------- ARCH         |         arch |          L1. |   .2537816   .0420329     6.04   0.000     .1713985    .3361646        garch |          L1. |   .6770279   .0425368    15.92   0.000     .5936573    .7603985  Estimation of Volatility before and after the Introduction of the Rice Futures on the CBOT Estimation of (5.1) ℎ( = ∘ +    (  + ℎ(  + M(        (5.1)  Rough Rice pre Futures . tsset time         time variable:  time, 1 to 145  . arch spot crb wprtrn, het(cash) arch(1) garch(1)  (setting optimization to BHHH) Iteration 0:   log likelihood =   185.7151 Iteration 1:   log likelihood =  189.85806 Iteration 2:   log likelihood =  189.85806  (backed up) Iteration 3:   log likelihood =   195.8655 Iteration 4:   log likelihood =  202.94261 (switching optimization to BFGS) Iteration 5:   log likelihood =  209.38516 Iteration 6:   log likelihood =  212.02512 Iteration 7:   log likelihood =  212.02512  (backed up) Iteration 8:   log likelihood =  213.90129 Iteration 9:   log likelihood =  214.93967 Iteration 10:  log likelihood =  216.52912 Iteration 11:  log likelihood =  217.11542 Iteration 12:  log likelihood =  217.47106 Iteration 13:  log likelihood =  217.67165 Iteration 14:  log likelihood =  217.78075 (switching optimization to BHHH) Iteration 15:  log likelihood =  218.08447 Iteration 16:  log likelihood =   219.3064 Iteration 17:  log likelihood =  220.73756 Iteration 18:  log likelihood =   221.6741 Iteration 19:  log likelihood =   222.1615 (switching optimization to BFGS) Iteration 20:  log likelihood =  222.50483 Iteration 21:  log likelihood =  222.72384 Iteration 22:  log likelihood =  222.88762 Iteration 23:  log likelihood =  222.95527 Iteration 24:  log likelihood =  222.96176 Iteration 25:  log likelihood =  222.98784 Iteration 26:  log likelihood =  222.98817 Iteration 27:  log likelihood =  223.00069 Iteration 28:  log likelihood =  223.00459 Iteration 29:  log likelihood =  223.00476 (switching optimization to BHHH) Iteration 30:  log likelihood =  223.00494 Iteration 31:  log likelihood =  223.00979 Iteration 32:  log likelihood =  223.00989 Iteration 33:  log likelihood =  223.01261 Iteration 34:  log likelihood =  223.01328 (switching optimization to BFGS) Iteration 35:  log likelihood =  223.01349 Iteration 36:  log likelihood =  223.01412 Iteration 37:  log likelihood =  223.01415 Iteration 38:  log likelihood =  223.01418 104  Iteration 39:  log likelihood =  223.01419 Iteration 40:  log likelihood =  223.01419 Iteration 41:  log likelihood =  223.01419 Iteration 42:  log likelihood =  223.01419  ARCH family regression -- multiplicative heteroskedasticity  Sample:  1 to 145                               Number of obs      =       145                                                 Wald chi2(2)       =     13.91 Log likelihood =  223.0142                      Prob > chi2        =    0.0010  ------------------------------------------------------------------------------              |                 OPG         spot |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval] -------------+---------------------------------------------------------------- spot         |          crb |   .0306101   .1520313     0.20   0.840    -.2673658     .328586       wprtrn |   .2337961   .0638407     3.66   0.000     .1086707    .3589216        _cons |  -.0014647    .003421    -0.43   0.669    -.0081697    .0052402 -------------+---------------------------------------------------------------- HET          |         cash |  -.0472173   .0057529    -8.21   0.000    -.0584927   -.0359418        _cons |  -.0682407   .7121321    -0.10   0.924    -1.463994    1.327513 -------------+---------------------------------------------------------------- ARCH         |         arch |          L1. |   .2400776   .1074041     2.24   0.025     .0295695    .4505857        garch |          L1. |   .5111449   .0800673     6.38   0.000     .3542158     .668074 ------------------------------------------------------------------------------  Rough Rice post Futures . tsset time         time variable:  time, 1 to 197  . arch spot crb wprtrn, het(cash) arch(1) garch(1)  (setting optimization to BHHH) Iteration 0:   log likelihood =  342.04218 Iteration 1:   log likelihood =   345.2133 Iteration 2:   log likelihood =  346.35268 Iteration 3:   log likelihood =  346.39511 Iteration 4:   log likelihood =  346.39695 (switching optimization to BFGS) Iteration 5:   log likelihood =  346.40034 Iteration 6:   log likelihood =  346.41561 Iteration 7:   log likelihood =  346.42034 Iteration 8:   log likelihood =  346.42188 Iteration 9:   log likelihood =  346.42222 Iteration 10:  log likelihood =  346.42225 Iteration 11:  log likelihood =  346.42226  ARCH family regression -- multiplicative heteroskedasticity  Sample:  1 to 197                               Number of obs      =       197                                                 Wald chi2(2)       =      3.50 Log likelihood =  346.4223                      Prob > chi2        =    0.1740  ------------------------------------------------------------------------------              |                 OPG         spot |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval] -------------+---------------------------------------------------------------- spot         |          crb |   .0678762   .0954526     0.71   0.477    -.1192076    .2549599       wprtrn |   .0783801   .0527498     1.49   0.137    -.0250076    .1817679        _cons |   .0007341   .0034416     0.21   0.831    -.0060113    .0074794 -------------+---------------------------------------------------------------- HET          |         cash |   .0006997   .0022743     0.31   0.758    -.0037578    .0051573        _cons |  -7.592031   .6729529   -11.28   0.000    -8.910995   -6.273068 -------------+---------------------------------------------------------------- ARCH         |         arch |          L1. |   .2230368    .130504     1.71   0.087    -.0327463    .4788198 105               |                 OPG         spot |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]         garch |          L1. |   .4785565   .2545573     1.88   0.060    -.0203666    .9774796 ------------------------------------------------------------------------------  Milled Rice pre Futures . tsset time         time variable:  time, 1 to 181  . arch milled crb wprtrn, het(cash) arch(1) garch(1)  (setting optimization to BHHH) Iteration 0:   log likelihood =  269.79774 Iteration 1:   log likelihood =  287.79507 Iteration 2:   log likelihood =  289.86851 Iteration 3:   log likelihood =  291.48128 Iteration 4:   log likelihood =  295.17766 (switching optimization to BFGS) Iteration 5:   log likelihood =  305.20887 Iteration 6:   log likelihood =  316.58162 Iteration 7:   log likelihood =  318.18448 Iteration 8:   log likelihood =  321.56573 Iteration 9:   log likelihood =  329.03388 Iteration 10:  log likelihood =  332.02454 Iteration 11:  log likelihood =  332.57227 Iteration 12:  log likelihood =  333.26637 Iteration 13:  log likelihood =  333.69829 Iteration 14:  log likelihood =  334.00653 (switching optimization to BHHH) Iteration 15:  log likelihood =  334.90762 Iteration 16:  log likelihood =   337.7614 Iteration 17:  log likelihood =  339.19864 Iteration 18:  log likelihood =  340.06857 Iteration 19:  log likelihood =  340.31456 (switching optimization to BFGS) Iteration 20:  log likelihood =  340.39954 Iteration 21:  log likelihood =  340.47101 Iteration 22:  log likelihood =   340.4889 Iteration 23:  log likelihood =  340.49219 Iteration 24:  log likelihood =  340.49277 Iteration 25:  log likelihood =  340.49281 Iteration 26:  log likelihood =  340.49281  ARCH family regression -- multiplicative heteroskedasticity  Sample:  1 to 181                               Number of obs      =       181                                                 Wald chi2(2)       =     71.84 Log likelihood =  340.4928                      Prob > chi2        =    0.0000  ------------------------------------------------------------------------------              |                 OPG       milled |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval] -------------+---------------------------------------------------------------- milled       |          crb |   .1213094   .0633392     1.92   0.055    -.0028332     .245452              |                 OPG       milled |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval] milled       wprtrn |   .1723618   .0265672     6.49   0.000      .120291    .2244327        _cons |  -.0014053   .0014687    -0.96   0.339    -.0042839    .0014733 -------------+---------------------------------------------------------------- HET          |         cash |  -.0238578   .0043449    -5.49   0.000    -.0323736    -.015342        _cons |  -.2889215   1.397403    -0.21   0.836    -3.027781    2.449938 -------------+---------------------------------------------------------------- ARCH         |         arch |          L1. |    .899769   .1372182     6.56   0.000     .6308262    1.168712        garch |          L1. |   .3775949   .0549957     6.87   0.000     .2698053    .4853844 ------------------------------------------------------------------------------ 106   Milled rice post Futures *****POST FUTURES**** October 1994 to December 2007 . tsset time         time variable:  time, 1 to 159  . arch milled crb wprtrn, het(cash) arch(1) garch(1)  (setting optimization to BHHH) Iteration 0:   log likelihood =   322.5688 Iteration 1:   log likelihood =   325.6554 Iteration 2:   log likelihood =  327.42804 Iteration 3:   log likelihood =  329.07989 Iteration 4:   log likelihood =  330.97627 (switching optimization to BFGS) Iteration 5:   log likelihood =  332.54269 Iteration 6:   log likelihood =  332.77856 Iteration 7:   log likelihood =  333.74915 Iteration 8:   log likelihood =  334.92089 Iteration 9:   log likelihood =  335.12921 Iteration 10:  log likelihood =  335.34701 Iteration 11:  log likelihood =  335.69087 Iteration 12:  log likelihood =  335.98004 Iteration 13:  log likelihood =  336.30806 Iteration 14:  log likelihood =  336.35333 (switching optimization to BHHH) Iteration 15:  log likelihood =  336.52425 Iteration 16:  log likelihood =  336.67211 Iteration 17:  log likelihood =  336.68899 Iteration 18:  log likelihood =   336.6908 Iteration 19:  log likelihood =   336.6911 (switching optimization to BFGS) Iteration 20:  log likelihood =   336.6912 Iteration 21:  log likelihood =  336.69124 Iteration 22:  log likelihood =  336.69124 Iteration 23:  log likelihood =  336.69124  ARCH family regression -- multiplicative heteroskedasticity  Sample:  1 to 159                               Number of obs      =       159                                                 Wald chi2(2)       =     15.16 Log likelihood =  336.6912                      Prob > chi2        =    0.0005  ------------------------------------------------------------------------------              |                 OPG       milled |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval] -------------+---------------------------------------------------------------- milled       |          crb |    .153215   .0936955     1.64   0.102    -.0304248    .3368548       wprtrn |   .1201143   .0415242     2.89   0.004     .0387284    .2015001        _cons |  -.0020257     .00218    -0.93   0.353    -.0062984    .0022471 -------------+---------------------------------------------------------------- HET          |         cash |  -.0179978   .0072617    -2.48   0.013    -.0322304   -.0037652               |                 OPG       milled |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval] HET        _cons |  -4.986346   1.676782    -2.97   0.003    -8.272778   -1.699915 -------------+---------------------------------------------------------------- ARCH         |         arch |          L1. |   .0142886   .0113278     1.26   0.207    -.0079135    .0364906        garch |          L1. |   .9494134   .0199533    47.58   0.000     .9103057    .9885211 ------------------------------------------------------------------------------  World Price before Zhengzhou Rice Futures Market Estimation of equations (5.2) and (4.6): 4( = *5 + * 67( + (          (5.2) ℎ( = /L + / (  + 1 ℎ(          (4.6) 107   **********************2003-2005******************************         time variable:  time, 1 to 104  . arch wp crb, arch(1) garch(1)  (setting optimization to BHHH) Iteration 0:   log likelihood =  269.87445 Iteration 1:   log likelihood =  270.98982 Iteration 2:   log likelihood =  273.94391 Iteration 3:   log likelihood =  274.43796 Iteration 4:   log likelihood =   274.5061 (switching optimization to BFGS) Iteration 5:   log likelihood =  274.58357 Iteration 6:   log likelihood =  274.78988 Iteration 7:   log likelihood =  274.82075 Iteration 8:   log likelihood =  274.85599 Iteration 9:   log likelihood =  274.87199 Iteration 10:  log likelihood =  274.87245 Iteration 11:  log likelihood =  274.87247  ARCH family regression  Sample:  1 to 104                               Number of obs      =       104                                                 Wald chi2(1)       =      9.71 Log likelihood =  274.8725                      Prob > chi2        =    0.0018  ------------------------------------------------------------------------------              |                 OPG           wp |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval] -------------+---------------------------------------------------------------- wp           |          crb |   .5410251   .1736509     3.12   0.002     .2006755    .8813747        _cons |   .0035222   .0016648     2.12   0.034     .0002593    .0067852 -------------+---------------------------------------------------------------- ARCH         |         arch |          L1. |   .3643266   .1116529     3.26   0.001      .145491    .5831622        garch |          L1. |   -.096395   .1908426    -0.51   0.613    -.4704396    .2776496        _cons |    .000254   .0000726     3.50   0.000     .0001118    .0003962 ------------------------------------------------------------------------------  World Price after Zhengzhou Rice Futures Market Estimation of equations (5.2) and (4.6): 4( = *5 + * 67( + (          (5.2) ℎ( = /L + / (  + 1 ℎ(          (4.6)  . tsset time         time variable:  time, 1 to 104  . arch wp crb, arch(1) garch(1)  (setting optimization to BHHH) Iteration 0:   log likelihood =  259.76399 Iteration 1:   log likelihood =  260.68565 Iteration 2:   log likelihood =  261.00538 Iteration 3:   log likelihood =  261.06492 Iteration 4:   log likelihood =  261.08911 (switching optimization to BFGS) Iteration 5:   log likelihood =  261.26828 Iteration 6:   log likelihood =  261.34244 Iteration 7:   log likelihood =  261.34577 Iteration 8:   log likelihood =  261.34602 Iteration 9:   log likelihood =  261.34604  ARCH family regression  Sample:  1 to 104                               Number of obs      =       104                                                 Wald chi2(1)       =      0.33 Log likelihood =   261.346                      Prob > chi2        =    0.5647 108   ------------------------------------------------------------------------------              |                 OPG           wp |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval] -------------+---------------------------------------------------------------- wp           |          crb |    .097071   .1685686     0.58   0.565    -.2333174    .4274594        _cons |  -.0027701   .0026134    -1.06   0.289    -.0078922     .002352 -------------+---------------------------------------------------------------- ARCH         |         arch |          L1. |    .190394   .1413746     1.35   0.178    -.0866952    .4674832        garch |          L1. |   .4661546   .3549539     1.31   0.189    -.2295423    1.161851        _cons |   .0001372   .0001164     1.18   0.238    -.0000909    .0003654 ------------------------------------------------------------------------------    109  Appendix I: Correlation between the Change in US and World Rice Price before and after Rice Futures on the CBOT  Table I. 1: Rough Rice Price and World Price Correlation FD P3 CMA Pre Post Pre Post Pre Post 0.419 0.101 0.738 0.727 0.280 0.098  Table I. 2: Milled Rice Price and and World Price Correlation FD P3 CMA Pre Post Pre Post Pre Post 0.455 0.495 0.708 0.703 0.290 0.361  The prices are detrended using the three methods outlined in chapter 4. Change in rough rice prices are clearly less correlated with the world price after the introduction of the rice futures market on the CBOT. It seems that the change in world prices has less effect on the US rough rice prices and is not transmitted to the US market post introduction of the futures market. This could be another factor contributing to the reduction of rough rice price volatility post futures market. The rice futures market in United States reduces the transmission of world price volatility to the domestic market. Therefore, reducing the part of rice price volatility in United States that is attributable to the volatility in world prices. The correlation between changes in milled rice price and the world price of rice shows a slight increase post futures market. This could be an indication that rice futures market in United States does not isolate the milled rice market from the world market. The higher correlation value could be due to the recent (2007-08) high volatility in world rice prices that have been transmitted to the milled rice market. More frequent and larger changes in world rice prices imply more action and changes in the milled rice prices and hence the higher correlation post futures.  110  Appendix J: Results of Granger Causality, Impulse Response Analysis, and Forecast Error Variance Decomposition from Stata  Rough Rice  Granger Causality (FD Method) . var garchr fdvol fdoi, lags(1/5)  Vector autoregression  Sample:       6      130                           No. of obs      =       125 Log likelihood =  675.5257                         AIC             = -10.04041 FPE            =  8.79e-09                         HQIC            = -9.599197 Det(Sigma_ml)  =  4.06e-09                         SBIC            = -8.954338  Equation           Parms      RMSE     R-sq      chi2     P>chi2 ---------------------------------------------------------------- garchr               16     .001191   0.4989   124.4592   0.0000 fdvol                16     .406959   0.5256   138.5008   0.0000 fdoi                 16     .162957   0.1252   17.88271   0.2689 ---------------------------------------------------------------- ------------------------------------------------------------------------------              |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval] -------------+---------------------------------------------------------------- garchr       |       garchr |          L1. |   .4421465   .0884207     5.00   0.000      .268845    .6154479          L2. |     .11995    .094697     1.27   0.205    -.0656527    .3055527          L3. |   .0718118   .0945208     0.76   0.447    -.1134456    .2570692          L4. |   .1539765     .09102     1.69   0.091    -.0244194    .3323725          L5. |  -.1333496    .083307    -1.60   0.109    -.2966283    .0299291        fdvol |          L1. |   .0006245   .0002588     2.41   0.016     .0001172    .0011318          L2. |   .0002142   .0002328     0.92   0.357     -.000242    .0006704          L3. |  -.0004403   .0002161    -2.04   0.042    -.0008639   -.0000167          L4. |  -.0001529   .0002189    -0.70   0.485    -.0005819    .0002761          L5. |  -.0001456   .0002237    -0.65   0.515    -.0005841    .0002928         fdoi |          L1. |   .0009826   .0006464     1.52   0.128    -.0002843    .0022496          L2. |   -.002444   .0006716    -3.64   0.000    -.0037603   -.0011277          L3. |   .0001443   .0007024     0.21   0.837    -.0012324    .0015209          L4. |  -.0018699   .0007134    -2.62   0.009    -.0032682   -.0004717          L5. |  -.0004695   .0007266    -0.65   0.518    -.0018937    .0009547        _cons |   .0009197   .0002589     3.55   0.000     .0004123    .0014271 -------------+---------------------------------------------------------------- fdvol        |       garchr |          L1. |   2.945676   30.21383     0.10   0.922    -56.27233    62.16369          L2. |   .0243947   32.35846     0.00   0.999    -63.39701     63.4458          L3. |  -30.36615   32.29826    -0.94   0.347    -93.66957    32.93727          L4. |   11.71073   31.10201     0.38   0.707    -49.24809    72.66955          L5. |   4.323115   28.46643     0.15   0.879    -51.47006    60.11629        fdvol |          L1. |  -.3311274   .0884356    -3.74   0.000     -.504458   -.1577967          L2. |   .0808125   .0795422     1.02   0.310    -.0750874    .2367124          L3. |  -.0594888   .0738542    -0.81   0.421    -.2042403    .0852627          L4. |   .3010099   .0747993     4.02   0.000      .154406    .4476139          L5. |   .1279558   .0764412     1.67   0.094    -.0218662    .2777778         fdoi |          L1. |   .7372156   .2208781     3.34   0.001     .3043025    1.170129          L2. |  -.2682684    .229489    -1.17   0.242    -.7180587    .1815219          L3. |   .7555426   .2400088     3.15   0.002     .2851341    1.225951          L4. |  -.5269109   .2437731    -2.16   0.031    -1.004698   -.0491243          L5. |  -.1492747   .2482953    -0.60   0.548    -.6359246    .3373752        _cons |   .1440533    .088469     1.63   0.103    -.0293427    .3174493       111                      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval] -------------+---------------------------------------------------------------- fdoi         |       garchr |          L1. |  -12.30073   12.09839    -1.02   0.309    -36.01313    11.41168          L2. |   23.19322   12.95715     1.79   0.073    -2.202331    48.58877          L3. |   5.454734   12.93305     0.42   0.673    -19.89357    30.80304          L4. |  -24.43042   12.45404    -1.96   0.050    -48.83989   -.0209507          L5. |   11.50206   11.39869     1.01   0.313    -10.83895    33.84308        fdvol |          L1. |  -.0294766   .0354119    -0.83   0.405    -.0988826    .0399294          L2. |  -.0057484   .0318507    -0.18   0.857    -.0681747    .0566779          L3. |   .0035379   .0295731     0.12   0.905    -.0544243    .0615001          L4. |  -.0454095   .0299516    -1.52   0.129    -.1041134    .0132945          L5. |   .0122882    .030609     0.40   0.688    -.0477043    .0722808         fdoi |          L1. |   .1670226   .0884452     1.89   0.059    -.0063269    .3403721          L2. |   -.015609   .0918933    -0.17   0.865    -.1957166    .1644985          L3. |  -.0997128   .0961056    -1.04   0.299    -.2880764    .0886508          L4. |   .1864804    .097613     1.91   0.056    -.0048375    .3777984          L5. |  -.0440031   .0994238    -0.44   0.658    -.2388702    .1508639        _cons |   .0253242   .0354252     0.71   0.475     -.044108    .0947563 ------------------------------------------------------------------------------  . vargranger     Granger causality Wald tests   +------------------------------------------------------------------+   |          Equation           Excluded |   chi2     df Prob > chi2 |   |--------------------------------------+---------------------------|   |            garchr              fdvol |  9.8948     5    0.078    |   |            garchr               fdoi |   22.75     5    0.000    |   |            garchr                ALL |  30.791    10    0.001    |   |--------------------------------------+---------------------------|   |             fdvol             garchr |   1.068     5    0.957    |   |             fdvol               fdoi |  25.246     5    0.000    |   |             fdvol                ALL |  28.329    10    0.002    |   |--------------------------------------+---------------------------|   |              fdoi             garchr |   6.709     5    0.243    |   |              fdoi              fdvol |  4.1229     5    0.532    |   |              fdoi                ALL |  10.362    10    0.409    |   +------------------------------------------------------------------+  Impulse Response and FEVD (FD Method) . irf ctable (fdr garchr garchr fevd, noci) (fdr fdvol garchr fevd, noci) (fdr fdoi garchr fevd, noci) (fdr > garchr garchr irf, noci) (fdr fdvol garchr irf, noci) (fdr fdoi garchr irf, noci)  +--------------------------------------------------------------------------------+ |        |    (1)    |    (2)    |    (3)    |    (1)    |    (2)    |    (3)    | |  step  |   fevd    |   fevd    |   fevd    |   irf     |   irf     |   irf     | |--------+-----------+-----------+-----------+-----------+-----------+-----------| |0       | 0         | 0         | 0         | 1         | 0         | 0         | |1       | 1         | 0         | 0         | .442146   | .000624   | .000983   | |2       | .945951   | .039631   | .014418   | .305196   | .000255   | -.001385  | |3       | .921734   | .039602   | .038664   | .300381   | -.000154  | -.000863  | |4       | .916231   | .038918   | .044851   | .319591   | -.000023  | -.002187  | |5       | .874264   | .034565   | .091171   | .108821   | .000104   | -.001816  | |6       | .845378   | .033267   | .121355   | .118747   | .00016    | -.002154  | |7       | .808108   | .03205    | .159842   | .072154   | -.000102  | -.000906  | |8       | .801674   | .0326     | .165726   | .0535     | .000065   | -.001253  | |9       | .790149   | .0321     | .177752   | .013269   | .000013   | -.000538  | |10      | .788029   | .032006   | .179966   | .031058   | .000118   | -.000868  | |11      | .782204   | .032275   | .185521   | .001031   | -.000043  | -.000108  | |12      | .782023   | .032391   | .185586   | .002025   | .000064   | -.000425  | |13      | .780577   | .032498   | .186925   | -.008094  | -.000023  | .000058   | |14      | .78054    | .032521   | .186939   | .006292   | .000074   | -.000319  | |15      | .77961    | .032732   | .187657   | -.008154  | -.000029  | .00013    | |16      | .779465   | .032765   | .187771   | -.00163   | .000046   | -.000168  | |17      | .779177   | .032856   | .187967   | -.007803  | -.00003   | .000165   | |18      | .778958   | .032884   | .188157   | .00262    | .000045   | -.00015   | |19      | .778718   | .032974   | .188308   | -.005391  | -.000026  | .000142   | |20      | .778554   | .032994   | .188452   | .000745   | .000033   | -.000107  | |21      | .77843    | .033041   | .188529   | -.004706  | -.000027  | .000137   | |22      | .778274   | .033065   | .188661   | .002332   | .000029   | -.0001    | |23      | .77817    | .033101   | .188729   | -.00305   | -.000022  | .000108   | |24      | .778071   | .033118   | .188811   | .001795   | .000023   | -.000086  | |25      | .777998   | .033141   | .188862   | -.002779  | -.000021  | .000096   | |26      | .777916   | .033157   | .188927   | .002005   | .00002    | -.000077  |      112               |    (1)    |    (2)    |    (3)    |    (1)    |    (2)    |    (3)    | |  step  |   fevd    |   fevd    |   fevd    |   irf     |   irf     |   irf     |  |27      | .777858   | .033174   | .188968   | -.001948  | -.000017  | .000078   | |28      | .777805   | .033185   | .18901    | .001754   | .000017   | -.000069  | |29      | .777761   | .033197   | .189043   | -.001811  | -.000016  | .000068   | |30      | .777719   | .033206   | .189075   | .001562   | .000015   | -.000059  | |31      | .777686   | .033215   | .1891     | -.00141   | -.000013  | .000057   | |32      | .777657   | .033222   | .189122   | .001393   | .000013   | -.000053  | |33      | .777631   | .033228   | .189141   | -.001282  | -.000012  | .000049   | |34      | .777609   | .033233   | .189158   | .001171   | .000011   | -.000045  | |35      | .77759    | .033238   | .189172   | -.001068  | -.00001   | .000042   | |36      | .777574   | .033242   | .189184   | .00104    | 9.4e-06   | -.000039  | |37      | .77756    | .033245   | .189195   | -.000943  | -8.7e-06  | .000036   | |38      | .777547   | .033248   | .189204   | .000872   | 8.0e-06   | -.000034  | |39      | .777537   | .033251   | .189212   | -.000809  | -7.5e-06  | .000031   | |40      | .777528   | .033253   | .189219   | .000767   | 7.0e-06   | -.000029  | |41      | .77752    | .033255   | .189225   | -.000701  | -6.5e-06  | .000027   | |42      | .777513   | .033257   | .18923    | .00065    | 6.0e-06   | -.000025  | |43      | .777507   | .033258   | .189235   | -.000608  | -5.6e-06  | .000023   | |44      | .777502   | .033259   | .189238   | .000567   | 5.2e-06   | -.000022  | |45      | .777498   | .03326    | .189242   | -.000523  | -4.8e-06  | .00002    | |46      | .777494   | .033261   | .189244   | .000486   | 4.5e-06   | -.000019  | |47      | .777491   | .033262   | .189247   | -.000454  | -4.2e-06  | .000017   | |48      | .777488   | .033263   | .189249   | .000421   | 3.9e-06   | -.000016  | |49      | .777486   | .033263   | .189251   | -.00039   | -3.6e-06  | .000015   | |50      | .777484   | .033264   | .189252   | .000363   | 3.3e-06   | -.000014  | |51      | .777482   | .033264   | .189254   | -.000338  | -3.1e-06  | .000013   | |52      | .77748    | .033265   | .189255   | .000313   | 2.9e-06   | -.000012  | |53      | .777479   | .033265   | .189256   | -.000291  | -2.7e-06  | .000011   | |54      | .777478   | .033265   | .189257   | .000271   | 2.5e-06   | -.00001   | |55      | .777477   | .033265   | .189258   | -.000252  | -2.3e-06  | 9.7e-06   | |56      | .777476   | .033266   | .189258   | .000233   | 2.2e-06   | -9.0e-06  | |57      | .777475   | .033266   | .189259   | -.000217  | -2.0e-06  | 8.4e-06   | |58      | .777475   | .033266   | .189259   | .000202   | 1.9e-06   | -7.8e-06  | |59      | .777474   | .033266   | .18926    | -.000187  | -1.7e-06  | 7.2e-06   | |60      | .777474   | .033266   | .18926    | .000174   | 1.6e-06   | -6.7e-06  | |61      | .777473   | .033266   | .18926    | -.000162  | -1.5e-06  | 6.2e-06   | |62      | .777473   | .033266   | .189261   | .00015    | 1.4e-06   | -5.8e-06  | |63      | .777473   | .033267   | .189261   | -.00014   | -1.3e-06  | 5.4e-06   | |64      | .777472   | .033267   | .189261   | .00013    | 1.2e-06   | -5.0e-06  | |65      | .777472   | .033267   | .189261   | -.000121  | -1.1e-06  | 4.6e-06   | |66      | .777472   | .033267   | .189261   | .000112   | 1.0e-06   | -4.3e-06  | |67      | .777472   | .033267   | .189262   | -.000104  | -9.6e-07  | 4.0e-06   | |68      | .777472   | .033267   | .189262   | .000097   | 8.9e-07   | -3.7e-06  | |69      | .777471   | .033267   | .189262   | -.00009   | -8.3e-07  | 3.5e-06   | |70      | .777471   | .033267   | .189262   | .000083   | 7.7e-07   | -3.2e-06  | |71      | .777471   | .033267   | .189262   | -.000078  | -7.1e-07  | 3.0e-06   | |72      | .777471   | .033267   | .189262   | .000072   | 6.6e-07   | -2.8e-06  | |73      | .777471   | .033267   | .189262   | -.000067  | -6.2e-07  | 2.6e-06   | |74      | .777471   | .033267   | .189262   | .000062   | 5.7e-07   | -2.4e-06  | |75      | .777471   | .033267   | .189262   | -.000058  | -5.3e-07  | 2.2e-06   | |76      | .777471   | .033267   | .189262   | .000054   | 5.0e-07   | -2.1e-06  | |77      | .777471   | .033267   | .189262   | -.00005   | -4.6e-07  | 1.9e-06   | |78      | .777471   | .033267   | .189262   | .000046   | 4.3e-07   | -1.8e-06  | |79      | .777471   | .033267   | .189262   | -.000043  | -4.0e-07  | 1.7e-06   | |80      | .777471   | .033267   | .189262   | .00004    | 3.7e-07   | -1.5e-06  | |81      | .777471   | .033267   | .189262   | -.000037  | -3.4e-07  | 1.4e-06   | |82      | .777471   | .033267   | .189262   | .000035   | 3.2e-07   | -1.3e-06  | |83      | .777471   | .033267   | .189262   | -.000032  | -3.0e-07  | 1.2e-06   | |84      | .777471   | .033267   | .189262   | .00003    | 2.8e-07   | -1.2e-06  | |85      | .777471   | .033267   | .189262   | -.000028  | -2.6e-07  | 1.1e-06   | |86      | .777471   | .033267   | .189262   | .000026   | 2.4e-07   | -9.9e-07  | |87      | .777471   | .033267   | .189262   | -.000024  | -2.2e-07  | 9.2e-07   | |88      | .777471   | .033267   | .189262   | .000022   | 2.0e-07   | -8.6e-07  | |89      | .777471   | .033267   | .189262   | -.000021  | -1.9e-07  | 8.0e-07   | |90      | .777471   | .033267   | .189262   | .000019   | 1.8e-07   | -7.4e-07  | |91      | .777471   | .033267   | .189262   | -.000018  | -1.6e-07  | 6.9e-07   | |92      | .777471   | .033267   | .189262   | .000017   | 1.5e-07   | -6.4e-07  | |93      | .777471   | .033267   | .189262   | -.000015  | -1.4e-07  | 5.9e-07   | |94      | .777471   | .033267   | .189262   | .000014   | 1.3e-07   | -5.5e-07  | |95      | .777471   | .033267   | .189262   | -.000013  | -1.2e-07  | 5.1e-07   | |96      | .777471   | .033267   | .189262   | .000012   | 1.1e-07   | -4.8e-07  | |97      | .777471   | .033267   | .189262   | -.000011  | -1.1e-07  | 4.4e-07   | |98      | .777471   | .033267   | .189262   | .000011   | 9.8e-08   | -4.1e-07  | |99      | .777471   | .033267   | .189262   | -9.9e-06  | -9.1e-08  | 3.8e-07   | |100     | .777471   | .033267   | .189262   | 9.2e-06   | 8.5e-08   | -3.5e-07  | +--------------------------------------------------------------------------------+  Granger Causality (P3 Method) . tsset time         time variable:  time, 1 to 131  . irf set p3r (file p3r.irf created) (file p3r.irf now active)  . var garchr p3vol p3oi, lags(1/5)  Vector autoregression 113   Sample:       6      131                           No. of obs      =       126 Log likelihood =  713.0889                         AIC             = -10.55697 FPE            =  5.24e-09                         HQIC            =   -10.118 Det(Sigma_ml)  =  2.44e-09                         SBIC            = -9.476478  Equation           Parms      RMSE     R-sq      chi2     P>chi2 ---------------------------------------------------------------- garchr               16     .001211   0.4788   115.7411   0.0000 p3vol                16     .361363   0.3705   74.15863   0.0000 p3oi                 16     .139196   0.8481   703.6929   0.0000 ---------------------------------------------------------------- ------------------------------------------------------------------------------              |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval] -------------+---------------------------------------------------------------- garchr       |       garchr |          L1. |   .4592553   .0848247     5.41   0.000     .2930019    .6255086          L2. |   .1200236    .092667     1.30   0.195    -.0616003    .3016476          L3. |   .0748445   .0906909     0.83   0.409    -.1029063    .2525953          L4. |   .1517996   .0893151     1.70   0.089    -.0232548     .326854          L5. |  -.1434951    .083025    -1.73   0.084    -.3062211     .019231        p3vol |          L1. |   .0003001   .0002301     1.30   0.192     -.000151    .0007511          L2. |  -.0000803   .0002135    -0.38   0.707    -.0004986    .0003381          L3. |  -.0003536   .0002088    -1.69   0.090    -.0007628    .0000556          L4. |   .0001756   .0002062     0.85   0.394    -.0002285    .0005797          L5. |   .0000819   .0002003     0.41   0.683    -.0003106    .0004744         p3oi |          L1. |   .0007723   .0007485     1.03   0.302    -.0006947    .0022394          L2. |  -.0032015    .001138    -2.81   0.005    -.0054318   -.0009711          L3. |   .0033311   .0011786     2.83   0.005      .001021    .0056411          L4. |  -.0030876    .001197    -2.58   0.010    -.0054337   -.0007415          L5. |   .0024727   .0008136     3.04   0.002     .0008781    .0040673        _cons |   .0008287    .000228     3.63   0.000     .0003818    .0012756 -------------+---------------------------------------------------------------- p3vol        |       garchr |          L1. |  -10.13995    25.3214    -0.40   0.689    -59.76899     39.4891          L2. |   11.94606   27.66244     0.43   0.666    -42.27134    66.16345          L3. |  -20.44368   27.07254    -0.76   0.450    -73.50489    32.61752          L4. |   19.69729   26.66186     0.74   0.460      -32.559    71.95357          L5. |   12.22666   24.78418     0.49   0.622    -36.34944    60.80276        p3vol |          L1. |   .2186745   .0686925     3.18   0.001     .0840396    .3533094          L2. |   .1697336    .063719     2.66   0.008     .0448466    .2946206          L3. |  -.0012202   .0623223    -0.02   0.984    -.1233696    .1209293          L4. |   .1425515   .0615483     2.32   0.021      .021919     .263184          L5. |  -.0069046    .059784    -0.12   0.908    -.1240791    .1102699         p3oi |          L1. |    .781757   .2234439     3.50   0.000     .3438149    1.219699          L2. |  -.7696456    .339696    -2.27   0.023    -1.435437   -.1038537          L3. |   1.107517   .3518303     3.15   0.002      .417942    1.797091          L4. |  -1.378116    .357322    -3.86   0.000    -2.078454   -.6777781          L5. |   .6119483   .2428741     2.52   0.012     .1359239    1.087973        _cons |  -.0285156    .068066    -0.42   0.675    -.1619226    .1048913 -------------+---------------------------------------------------------------- p3oi         |       garchr |          L1. |   -9.98707   9.753724    -1.02   0.306    -29.10402    9.129878          L2. |   11.85343   10.65549     1.11   0.266    -9.030938     32.7378          L3. |   3.010599   10.42826     0.29   0.773    -17.42841    23.44961          L4. |  -19.53252   10.27006    -1.90   0.057    -39.66148    .5964313          L5. |   7.517569   9.546788     0.79   0.431    -11.19379    26.22893        p3vol |          L1. |   -.057965   .0264601    -2.19   0.028    -.1098259    -.006104          L2. |  -.0217965   .0245444    -0.89   0.375    -.0699026    .0263095          L3. |   .0039916   .0240064     0.17   0.868      -.04306    .0510432          L4. |  -.0018267   .0237082    -0.08   0.939     -.048294    .0446405          L5. |   .0143088   .0230286     0.62   0.534    -.0308265     .059444     114                            Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]         p3oi |          L1. |    1.10643   .0860699    12.86   0.000     .9377363    1.275124          L2. |  -.2211061   .1308498    -1.69   0.091     -.477567    .0353548          L3. |  -.1107649   .1355239    -0.82   0.414    -.3763869     .154857          L4. |   .4242464   .1376393     3.08   0.002     .1544784    .6940145          L5. |  -.3219079   .0935543    -3.44   0.001     -.505271   -.1385447        _cons |   .0129296   .0262188     0.49   0.622    -.0384583    .0643176 ------------------------------------------------------------------------------  . vargranger     Granger causality Wald tests   +------------------------------------------------------------------+   |          Equation           Excluded |   chi2     df Prob > chi2 |   |--------------------------------------+---------------------------|   |            garchr              p3vol |   5.143     5    0.399    |   |            garchr               p3oi |  18.516     5    0.002    |   |            garchr                ALL |  24.738    10    0.006    |   |--------------------------------------+---------------------------|   |             p3vol             garchr |  1.7031     5    0.889    |   |             p3vol               p3oi |  36.944     5    0.000    |   |             p3vol                ALL |  41.157    10    0.000    |   |--------------------------------------+---------------------------|   |              p3oi             garchr |  4.9598     5    0.421    |   |              p3oi              p3vol |  5.6614     5    0.341    |   |              p3oi                ALL |  10.705    10    0.381    |   +------------------------------------------------------------------+  Impulse Response and FEVD (P3 Method) . irf ctable (p3r garchr garchr fevd, noci) (p3r p3vol garchr fevd, noci) (p3r p3oi garchr fevd, noci) (p3r > garchr garchr irf, noci) (p3r p3vol garchr irf, noci) (p3r p3oi garchr irf, noci)  +--------------------------------------------------------------------------------+ |        |    (1)    |    (2)    |    (3)    |    (1)    |    (2)    |    (3)    | |  step  |   fevd    |   fevd    |   fevd    |   irf     |   irf     |   irf     | |--------+-----------+-----------+-----------+-----------+-----------+-----------| |0       | 0         | 0         | 0         | 1         | 0         | 0         | |1       | 1         | 0         | 0         | .459255   | .0003     | .000772   | |2       | .988175   | .005446   | .006378   | .320183   | .000078   | -.001758  | |3       | .958458   | .006132   | .03541    | .30651    | -.000141  | -.000177  | |4       | .959816   | .00684    | .033344   | .344863   | .000113   | -.002077  | |5       | .927508   | .00796    | .064532   | .145095   | .000288   | -.00046   | |6       | .922235   | .012732   | .065033   | .139785   | .000178   | -.000792  | |7       | .916533   | .014718   | .068749   | .091939   | .000078   | .00087    | |8       | .911544   | .014676   | .073779   | .093974   | .000081   | .000164   | |9       | .911539   | .014889   | .073572   | .040372   | .000036   | .001073   | |10      | .903728   | .014742   | .08153    | .048993   | -.000014  | .000813   | |11      | .899333   | .014732   | .085935   | .013053   | -.000064  | .001604   | |12      | .881739   | .015138   | .103123   | .018453   | -.00009   | .001127   | |13      | .872931   | .01579    | .111279   | -.001037  | -.000121  | .001412   | |14      | .859286   | .01692    | .123794   | .002255   | -.000124  | .001012   | |15      | .852011   | .017988   | .130001   | -.017731  | -.000132  | .001224   | |16      | .841842   | .019208   | .13895    | -.013192  | -.00013   | .000831   | |17      | .836809   | .020269   | .142923   | -.021863  | -.000127  | .000849   | |18      | .831702   | .021274   | .147024   | -.018047  | -.000109  | .000504   | |19      | .829637   | .021968   | .148395   | -.02557   | -.000097  | .000519   | |20      | .82763    | .022526   | .149844   | -.020576  | -.000081  | .000254   | |21      | .82698    | .02288    | .15014    | -.022696  | -.000068  | .00023    | |22      | .826499   | .023125   | .150375   | -.017585  | -.00005   | .000021   | |23      | .826424   | .023238   | .150338   | -.018591  | -.000036  | .000017   | |24      | .826399   | .023297   | .150305   | -.013732  | -.000023  | -.000116  | |25      | .826326   | .023308   | .150366   | -.013007  | -.000013  | -.000111  | |26      | .82627    | .023308   | .150423   | -.008533  | -2.1e-06  | -.000199  | |27      | .826052   | .023301   | .150647   | -.007652  | 5.0e-06   | -.000177  | |28      | .825877   | .023301   | .150822   | -.004173  | .000011   | -.000219  | |29      | .825595   | .023309   | .151096   | -.003232  | .000015   | -.000185  | |30      | .825384   | .023324   | .151292   | -.000514  | .000018   | -.000203  | |31      | .825128   | .023345   | .151527   | .000081   | .000019   | -.000164  | |32      | .824952   | .023369   | .151679   | .001826   | .00002    | -.000163  | |33      | .824778   | .023393   | .151829   | .002052   | .000019   | -.000123  | |34      | .824672   | .023415   | .151913   | .003123   | .000018   | -.000114  | |35      | .824582   | .023434   | .151984   | .003015   | .000016   | -.000079  | |36      | .824534   | .023448   | .152018   | .003476   | .000014   | -.000067  | |37      | .8245     | .023459   | .152041   | .00311    | .000011   | -.000038  | |38      | .824486   | .023466   | .152047   | .003203   | 9.3e-06   | -.000027  | |39      | .824479   | .023471   | .15205    | .002709   | 7.0e-06   | -5.7e-06  | |40      | .824477   | .023473   | .152049   | .002561   | 5.0e-06   | 1.4e-06   | |41      | .824477   | .023474   | .152049   | .002021   | 3.1e-06   | .000016   | |42      | .824476   | .023475   | .15205    | .001776   | 1.6e-06   | .000019   | 115  |43      | .824474   | .023474   | .152052   | .00128    | 1.8e-07   | .000027   | |44      | .82447    | .023474   | .152056   | .001023   | -8.5e-07  | .000027   | |45      | .824466   | .023474   | .15206    | .000607   | -1.7e-06  | .000031   |          |        |    (1)    |    (2)    |    (3)    |    (1)    |    (2)    |    (3)    | |  step  |   fevd    |   fevd    |   fevd    |   irf     |   irf     |   irf     | |46      | .82446    | .023475   | .152065   | .000394   | -2.3e-06  | .000028   | |47      | .824455   | .023475   | .15207    | .000087   | -2.7e-06  | .000028   | |48      | .82445    | .023475   | .152074   | -.000057  | -2.8e-06  | .000024   | |49      | .824446   | .023476   | .152078   | -.000259  | -2.8e-06  | .000023   | |50      | .824443   | .023476   | .152081   | -.000333  | -2.7e-06  | .000018   | |51      | .824441   | .023477   | .152082   | -.000442  | -2.5e-06  | .000016   | |52      | .824439   | .023477   | .152084   | -.000455  | -2.3e-06  | .000011   | |53      | .824438   | .023477   | .152084   | -.000493  | -2.0e-06  | 9.0e-06   | |54      | .824437   | .023478   | .152085   | -.000462  | -1.6e-06  | 5.5e-06   | |55      | .824437   | .023478   | .152085   | -.000452  | -1.3e-06  | 3.4e-06   | |56      | .824437   | .023478   | .152085   | -.000396  | -9.9e-07  | 8.2e-07   | |57      | .824437   | .023478   | .152085   | -.000359  | -7.0e-07  | -5.8e-07  | |58      | .824437   | .023478   | .152085   | -.000294  | -4.3e-07  | -2.3e-06  | |59      | .824437   | .023478   | .152085   | -.000247  | -2.0e-07  | -3.0e-06  | |60      | .824437   | .023478   | .152085   | -.000184  | -9.0e-09  | -3.9e-06  | |61      | .824437   | .023478   | .152085   | -.000139  | 1.4e-07   | -4.1e-06  | |62      | .824437   | .023478   | .152085   | -.000087  | 2.6e-07   | -4.4e-06  | |63      | .824437   | .023478   | .152085   | -.00005   | 3.4e-07   | -4.1e-06  | |64      | .824436   | .023478   | .152086   | -.000011  | 3.9e-07   | -4.0e-06  | |65      | .824436   | .023478   | .152086   | .000013   | 4.1e-07   | -3.5e-06  | |66      | .824436   | .023478   | .152086   | .000038   | 4.1e-07   | -3.2e-06  | |67      | .824436   | .023478   | .152086   | .000051   | 3.9e-07   | -2.6e-06  | |68      | .824436   | .023478   | .152086   | .000064   | 3.7e-07   | -2.2e-06  | |69      | .824436   | .023478   | .152086   | .000068   | 3.3e-07   | -1.6e-06  | |70      | .824436   | .023478   | .152086   | .000071   | 2.8e-07   | -1.2e-06  | |71      | .824436   | .023478   | .152086   | .000068   | 2.3e-07   | -7.7e-07  | |72      | .824436   | .023478   | .152086   | .000065   | 1.9e-07   | -4.4e-07  | |73      | .824436   | .023478   | .152086   | .000057   | 1.4e-07   | -1.0e-07  | |74      | .824436   | .023478   | .152086   | .000051   | 9.7e-08   | 1.2e-07   | |75      | .824436   | .023478   | .152086   | .000042   | 5.8e-08   | 3.4e-07   | |76      | .824436   | .023478   | .152086   | .000035   | 2.6e-08   | 4.6e-07   | |77      | .824436   | .023478   | .152086   | .000026   | -1.3e-09  | 5.7e-07   | |78      | .824436   | .023478   | .152086   | .000019   | -2.3e-08  | 6.0e-07   | |79      | .824436   | .023478   | .152086   | .000012   | -3.9e-08  | 6.3e-07   | |80      | .824436   | .023478   | .152086   | 6.5e-06   | -5.0e-08  | 6.0e-07   | |81      | .824436   | .023478   | .152086   | 1.3e-06   | -5.7e-08  | 5.7e-07   | |82      | .824436   | .023478   | .152086   | -2.5e-06  | -6.0e-08  | 5.1e-07   | |83      | .824436   | .023478   | .152086   | -5.7e-06  | -6.0e-08  | 4.5e-07   | |84      | .824436   | .023478   | .152086   | -7.8e-06  | -5.7e-08  | 3.8e-07   | |85      | .824436   | .023478   | .152086   | -9.3e-06  | -5.3e-08  | 3.1e-07   | |86      | .824436   | .023478   | .152086   | -9.9e-06  | -4.7e-08  | 2.3e-07   | |87      | .824436   | .023478   | .152086   | -.00001   | -4.0e-08  | 1.7e-07   | |88      | .824436   | .023478   | .152086   | -9.8e-06  | -3.3e-08  | 1.1e-07   | |89      | .824436   | .023478   | .152086   | -9.3e-06  | -2.6e-08  | 5.8e-08   | |90      | .824436   | .023478   | .152086   | -8.3e-06  | -1.9e-08  | 1.2e-08   | |91      | .824436   | .023478   | .152086   | -7.2e-06  | -1.3e-08  | -2.2e-08  | |92      | .824436   | .023478   | .152086   | -6.0e-06  | -7.9e-09  | -5.1e-08  | |93      | .824436   | .023478   | .152086   | -4.9e-06  | -3.3e-09  | -6.9e-08  | |94      | .824436   | .023478   | .152086   | -3.7e-06  | 5.7e-10   | -8.3e-08  | |95      | .824436   | .023478   | .152086   | -2.7e-06  | 3.6e-09   | -8.9e-08  | |96      | .824436   | .023478   | .152086   | -1.7e-06  | 5.9e-09   | -9.1e-08  | |97      | .824436   | .023478   | .152086   | -8.5e-07  | 7.4e-09   | -8.8e-08  | |98      | .824436   | .023478   | .152086   | -1.3e-07  | 8.4e-09   | -8.2e-08  | |99      | .824436   | .023478   | .152086   | 4.2e-07   | 8.7e-09   | -7.4e-08  | |100     | .824436   | .023478   | .152086   | 8.7e-07   | 8.7e-09   | -6.4e-08  | +--------------------------------------------------------------------------------+ (1) irfname = p3r, impulse = garchr, and response = garchr (2) irfname = p3r, impulse = p3vol, and response = garchr (3) irfname = p3r, impulse = p3oi, and response = garchr  Granger Causality (CMA Method) . tsset time         time variable:  time, 1 to 127  . irf set cmar (file cmar.irf created) (file cmar.irf now active)  . var garchr cmavol cmaoi, lags(1/4)  Vector autoregression  Sample:       5      127                           No. of obs      =       123 Log likelihood =  814.5507                         AIC             = -12.61058 FPE            =  6.71e-10                         HQIC            = -12.24839 Det(Sigma_ml)  =  3.55e-10                         SBIC            = -11.71891  Equation           Parms      RMSE     R-sq      chi2     P>chi2 116  ---------------------------------------------------------------- garchr               13     .001225   0.4633   106.1758   0.0000 cmavol               13     .205039   0.4629   106.0187   0.0000 cmaoi                13     .089736   0.2961   51.74788   0.0000 ----------------------------------------------------------------        ------------------------------------------------------------------------------              |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval] -------------+---------------------------------------------------------------- garchr       |       garchr |          L1. |   .4618128   .0883253     5.23   0.000     .2886984    .6349273          L2. |   .1641758    .095624     1.72   0.086    -.0232438    .3515954          L3. |  -.0147788   .0933951    -0.16   0.874    -.1978298    .1682723          L4. |   .0759585   .0861658     0.88   0.378    -.0929235    .2448404       cmavol |          L1. |   .0006823    .000535     1.28   0.202    -.0003662    .0017309          L2. |   -.000106   .0005496    -0.19   0.847    -.0011832    .0009712          L3. |  -.0006775   .0005352    -1.27   0.206    -.0017265    .0003714          L4. |   .0005415     .00048     1.13   0.259    -.0003993    .0014822        cmaoi |          L1. |    .001004   .0012217     0.82   0.411    -.0013904    .0033984          L2. |  -.0044146   .0012945    -3.41   0.001    -.0069517   -.0018774          L3. |   .0016207   .0012944     1.25   0.211    -.0009162    .0041576          L4. |  -.0033623   .0013603    -2.47   0.013    -.0060285   -.0006962        _cons |   .0007372   .0002274     3.24   0.001     .0002915     .001183 -------------+---------------------------------------------------------------- cmavol       |       garchr |          L1. |  -2.228709   14.78319    -0.15   0.880    -31.20323    26.74581          L2. |   17.66916   16.00479     1.10   0.270    -13.69965    49.03796          L3. |  -12.97091   15.63173    -0.83   0.407    -43.60854    17.66672          L4. |   3.229754   14.42176     0.22   0.823    -25.03637    31.49588       cmavol |          L1. |   -.569982   .0895406    -6.37   0.000    -.7454783   -.3944857          L2. |  -.4352594    .091988    -4.73   0.000    -.6155525   -.2549663          L3. |   -.402937   .0895757    -4.50   0.000    -.5785021    -.227372          L4. |   -.038156   .0803388    -0.47   0.635     -.195617    .1193051        cmaoi |          L1. |   .7193535   .2044723     3.52   0.000     .3185952    1.120112          L2. |  -.0061372   .2166605    -0.03   0.977     -.430784    .4185096          L3. |   .8606314   .2166428     3.97   0.000     .4360192    1.285244          L4. |  -.3498513   .2276798    -1.54   0.124    -.7960955    .0963929        _cons |  -.0399838   .0380643    -1.05   0.294    -.1145885    .0346209 -------------+---------------------------------------------------------------- cmaoi        |       garchr |          L1. |  -12.62009   6.469875    -1.95   0.051    -25.30081    .0606301          L2. |   5.419212   7.004507     0.77   0.439    -8.309369    19.14779          L3. |   8.769677   6.841239     1.28   0.200    -4.638905    22.17826          L4. |  -4.076669   6.311693    -0.65   0.518    -16.44736    8.294022       cmavol |          L1. |  -.0063094   .0391875    -0.16   0.872    -.0831155    .0704967          L2. |  -.0484954   .0402586    -1.20   0.228    -.1274008      .03041          L3. |  -.0354125   .0392029    -0.90   0.366    -.1122486    .0414237          L4. |  -.0513326   .0351603    -1.46   0.144    -.1202455    .0175804        cmaoi |          L1. |   .1303332   .0894874     1.46   0.145     -.045059    .3057253          L2. |  -.4547085   .0948216    -4.80   0.000    -.6405555   -.2688615          L3. |   -.053399   .0948139    -0.56   0.573    -.2392308    .1324328          L4. |   .0609506   .0996442     0.61   0.541    -.1343485    .2562497        _cons |   -.004572   .0166589    -0.27   0.784    -.0372228    .0280788 ------------------------------------------------------------------------------  . vargranger     Granger causality Wald tests   +------------------------------------------------------------------+ 117    |          Equation           Excluded |   chi2     df Prob > chi2 |   |--------------------------------------+---------------------------|   |            garchr             cmavol |  8.7208     4    0.068    |   |            garchr              cmaoi |  12.895     4    0.012    |   |            garchr                ALL |  23.446     8    0.003    |   |--------------------------------------+---------------------------|   |            cmavol             garchr |  1.6345     4    0.803    |   |            cmavol              cmaoi |  24.116     4    0.000    |   |            cmavol                ALL |  27.613     8    0.001    |   |          Equation           Excluded |   chi2     df Prob > chi2   |--------------------------------------+---------------------------|   |             cmaoi             garchr |  4.7754     4    0.311    |                Equation           Excluded |   chi2     df Prob > chi2 |    |             cmaoi             cmavol |  3.5158     4    0.475    |   |             cmaoi                ALL |  7.7272     8    0.461    |   +------------------------------------------------------------------+  Impulse Response and FEVD (CMA Method)  . irf ctable (cmar garchr garchr fevd, noci) (cmar cmavol garchr fevd, noci) (cmar cmaoi garchr fevd, noci) > (cmar garchr garchr irf, noci) (cmar cmavol garchr irf, noci) (cmar cmaoi garchr irf, noci)  +--------------------------------------------------------------------------------+ |        |    (1)    |    (2)    |    (3)    |    (1)    |    (2)    |    (3)    | |  step  |   fevd    |   fevd    |   fevd    |   irf     |   irf     |   irf     | |--------+-----------+-----------+-----------+-----------+-----------+-----------| |0       | 0         | 0         | 0         | 1         | 0         | 0         | |1       | 1         | 0         | 0         | .461813   | .000682   | .001004   | |2       | .984545   | .011135   | .00432    | .363256   | -.000186  | -.003329  | |3       | .94548    | .010541   | .043978   | .288723   | -.000697  | -.001082  | |4       | .936173   | .018991   | .044836   | .255937   | .000723   | -.002522  | |5       | .913341   | .025368   | .061291   | .178665   | .000223   | -.001454  | |6       | .90879    | .025284   | .065926   | .177345   | .000283   | -.001271  | |7       | .905348   | .025706   | .068946   | .111515   | -.000215  | .000466   | |8       | .904756   | .026185   | .069059   | .087097   | .000196   | -.000897  | |9       | .902672   | .02649    | .070838   | .070925   | -.000014  | -.00076   | |10      | .90149    | .026365   | .072145   | .080068   | .000155   | -.000817  | |11      | .899909   | .026502   | .073589   | .048407   | -.000055  | .000204   | |12      | .899881   | .026508   | .073611   | .034728   | .000097   | -.00022   | |13      | .899712   | .026615   | .073673   | .024759   | -.000031  | -.000203  | |14      | .899629   | .026618   | .073753   | .031995   | .000062   | -.000431  | |15      | .899183   | .026631   | .074187   | .021459   | -.000027  | .000024   | |16      | .899196   | .026635   | .07417    | .015779   | .00005    | -.00008   | |17      | .899162   | .026665   | .074173   | .008918   | -.000015  | -.000021  | |18      | .899162   | .026667   | .07417    | .012085   | .000028   | -.000184  | |19      | .899078   | .026671   | .074251   | .008779   | -.000016  | -1.0e-05  | |20      | .899078   | .026674   | .074247   | .007269   | .000022   | -.000047  | |21      | .89907    | .02668    | .07425    | .003562   | -7.3e-06  | .000011   | |22      | .899069   | .026681   | .07425    | .004612   | .000014   | -.000072  | |23      | .899055   | .026682   | .074262   | .003364   | -8.6e-06  | -5.9e-06  | |24      | .899055   | .026683   | .074262   | .003217   | 9.7e-06   | -.000028  | |25      | .899052   | .026684   | .074263   | .001499   | -4.1e-06  | 9.3e-06   | |26      | .899052   | .026685   | .074263   | .001835   | 7.1e-06   | -.000029  | |27      | .89905    | .026685   | .074265   | .001252   | -4.1e-06  | -1.2e-06  | |28      | .899049   | .026685   | .074265   | .001376   | 4.4e-06   | -.000015  | |29      | .899049   | .026686   | .074266   | .000629   | -2.4e-06  | 5.3e-06   | |30      | .899049   | .026686   | .074266   | .000756   | 3.4e-06   | -.000012  | |31      | .899048   | .026686   | .074266   | .000461   | -1.9e-06  | 4.8e-07   | |32      | .899048   | .026686   | .074266   | .000579   | 2.1e-06   | -7.3e-06  | |33      | .899048   | .026686   | .074266   | .000258   | -1.3e-06  | 2.7e-06   | |34      | .899048   | .026686   | .074266   | .000319   | 1.6e-06   | -5.0e-06  | |35      | .899048   | .026686   | .074266   | .000169   | -9.4e-07  | 7.3e-07   | |36      | .899048   | .026686   | .074266   | .000242   | 1.0e-06   | -3.5e-06  | |37      | .899048   | .026686   | .074266   | .000104   | -6.7e-07  | 1.4e-06   | |38      | .899048   | .026686   | .074266   | .000137   | 7.6e-07   | -2.2e-06  | |39      | .899048   | .026686   | .074266   | .000061   | -4.7e-07  | 5.8e-07   | |40      | .899048   | .026686   | .074266   | .000101   | 4.9e-07   | -1.7e-06  | |41      | .899048   | .026686   | .074266   | .000041   | -3.4e-07  | 6.7e-07   | |42      | .899048   | .026686   | .074266   | .000059   | 3.6e-07   | -1.0e-06  | |43      | .899048   | .026686   | .074266   | .000022   | -2.3e-07  | 3.8e-07   | |44      | .899048   | .026686   | .074266   | .000042   | 2.4e-07   | -7.8e-07  | |45      | .899048   | .026686   | .074266   | .000015   | -1.7e-07  | 3.3e-07   | |46      | .899048   | .026686   | .074266   | .000026   | 1.7e-07   | -4.7e-07  | |47      | .899048   | .026686   | .074266   | 7.5e-06   | -1.2e-07  | 2.2e-07   | |48      | .899048   | .026686   | .074266   | .000018   | 1.2e-07   | -3.6e-07  | |49      | .899048   | .026686   | .074266   | 5.5e-06   | -8.4e-08  | 1.6e-07   | |50      | .899048   | .026686   | .074266   | .000011   | 8.1e-08   | -2.2e-07  | |51      | .899048   | .026686   | .074266   | 2.5e-06   | -5.7e-08  | 1.2e-07   | |52      | .899048   | .026686   | .074266   | 7.5e-06   | 5.6e-08   | -1.7e-07  | |53      | .899048   | .026686   | .074266   | 1.8e-06   | -4.2e-08  | 8.2e-08   | |54      | .899048   | .026686   | .074266   | 5.0e-06   | 3.9e-08   | -1.1e-07  | |55      | .899048   | .026686   | .074266   | 7.9e-07   | -2.9e-08  | 6.2e-08   | |56      | .899048   | .026686   | .074266   | 3.2e-06   | 2.7e-08   | -7.8e-08  | |57      | .899048   | .026686   | .074266   | 5.4e-07   | -2.0e-08  | 4.2e-08   | |58      | .899048   | .026686   | .074266   | 2.2e-06   | 1.9e-08   | -5.1e-08  | |59      | .899048   | .026686   | .074266   | 2.0e-07   | -1.4e-08  | 3.2e-08   | 118  |60      | .899048   | .026686   | .074266   | 1.4e-06   | 1.3e-08   | -3.7e-08  | |61      | .899048   | .026686   | .074266   | 1.2e-07   | -1.0e-08  | 2.1e-08   | |62      | .899048   | .026686   | .074266   | 9.8e-07   | 9.1e-09   | -2.5e-08  | |63      | .899048   | .026686   | .074266   | 2.7e-08   | -7.0e-09  | 1.6e-08   | |64      | .899048   | .026686   | .074266   | 6.3e-07   | 6.4e-09   | -1.7e-08  | |65      | .899048   | .026686   | .074266   | 6.3e-10   | -4.9e-09  | 1.1e-08   | |66      | .899048   | .026686   | .074266   | 4.3e-07   | 4.4e-09   | -1.2e-08  | |67      | .899048   | .026686   | .074266   | -1.7e-08  | -3.5e-09  | 8.0e-09   | |68      | .899048   | .026686   | .074266   | 2.8e-07   | 3.1e-09   | -8.2e-09  | |69      | .899048   | .026686   | .074266   | -2.3e-08  | -2.4e-09  | 5.5e-09   | |70      | .899048   | .026686   | .074266   | 1.9e-07   | 2.2e-09   | -5.7e-09  | |71      | .899048   | .026686   | .074266   | -2.1e-08  | -1.7e-09  | 3.9e-09   | |72      | .899048   | .026686   | .074266   | 1.3e-07   | 1.5e-09   | -3.9e-09  | |73      | .899048   | .026686   | .074266   | -2.0e-08  | -1.2e-09  | 2.7e-09   |           |        |    (1)    |    (2)    |    (3)    |    (1)    |    (2)    |    (3)    | |  step  |   fevd    |   fevd    |   fevd    |   irf     |   irf     |   irf     | |74      | .899048   | .026686   | .074266   | 8.7e-08   | 1.0e-09   | -2.8e-09  | |75      | .899048   | .026686   | .074266   | -1.6e-08  | -8.4e-10  | 2.0e-09   | |76      | .899048   | .026686   | .074266   | 5.8e-08   | 7.3e-10   | -1.9e-09  | |77      | .899048   | .026686   | .074266   | -1.3e-08  | -5.8e-10  | 1.4e-09   | |78      | .899048   | .026686   | .074266   | 4.0e-08   | 5.1e-10   | -1.3e-09  | |79      | .899048   | .026686   | .074266   | -1.0e-08  | -4.1e-10  | 9.6e-10   | |80      | .899048   | .026686   | .074266   | 2.7e-08   | 3.6e-10   | -9.1e-10  | |81      | .899048   | .026686   | .074266   | -7.9e-09  | -2.9e-10  | 6.8e-10   | |82      | .899048   | .026686   | .074266   | 1.8e-08   | 2.5e-10   | -6.4e-10  | |83      | .899048   | .026686   | .074266   | -5.8e-09  | -2.0e-10  | 4.8e-10   | |84      | .899048   | .026686   | .074266   | 1.2e-08   | 1.7e-10   | -4.4e-10  | |85      | .899048   | .026686   | .074266   | -4.4e-09  | -1.4e-10  | 3.4e-10   | |86      | .899048   | .026686   | .074266   | 8.4e-09   | 1.2e-10   | -3.1e-10  | |87      | .899048   | .026686   | .074266   | -3.2e-09  | -9.8e-11  | 2.3e-10   | |88      | .899048   | .026686   | .074266   | 5.7e-09   | 8.4e-11   | -2.1e-10  | |89      | .899048   | .026686   | .074266   | -2.4e-09  | -6.9e-11  | 1.7e-10   | |90      | .899048   | .026686   | .074266   | 3.9e-09   | 5.9e-11   | -1.5e-10  | |91      | .899048   | .026686   | .074266   | -1.7e-09  | -4.8e-11  | 1.2e-10   | |92      | .899048   | .026686   | .074266   | 2.7e-09   | 4.1e-11   | -1.0e-10  | |93      | .899048   | .026686   | .074266   | -1.3e-09  | -3.4e-11  | 8.1e-11   | |94      | .899048   | .026686   | .074266   | 1.8e-09   | 2.9e-11   | -7.3e-11  | |95      | .899048   | .026686   | .074266   | -9.1e-10  | -2.4e-11  | 5.7e-11   | |96      | .899048   | .026686   | .074266   | 1.3e-09   | 2.0e-11   | -5.1e-11  | |97      | .899048   | .026686   | .074266   | -6.5e-10  | -1.6e-11  | 4.0e-11   | |98      | .899048   | .026686   | .074266   | 8.6e-10   | 1.4e-11   | -3.5e-11  | |99      | .899048   | .026686   | .074266   | -4.7e-10  | -1.2e-11  | 2.8e-11   | |100     | .899048   | .026686   | .074266   | 5.9e-10   | 9.8e-12   | -2.5e-11  | +--------------------------------------------------------------------------------+ (1) irfname = cmar, impulse = garchr, and response = garchr (2) irfname = cmar, impulse = cmavol, and response = garchr (3) irfname = cmar, impulse = cmaoi, and response = garchr  Milled Rice  Granger Causality (FD Method) . tsset time         time variable:  time, 1 to 120  . irf set fdm (file fdm.irf created) (file fdm.irf now active)  . var garchm fdvol fdoi, lags(1/5)  Vector autoregression  Sample:       6      120                           No. of obs      =       115 Log likelihood =  478.6809                         AIC             = -7.490102 FPE            =  1.13e-07                         HQIC            = -7.025064 Det(Sigma_ml)  =  4.87e-08                         SBIC            = -6.344391  Equation           Parms      RMSE     R-sq      chi2     P>chi2 ---------------------------------------------------------------- garchm               16     .004994   0.3765   69.44455   0.0000 fdvol                16     .396152   0.5627   148.0039   0.0000 fdoi                 16      .15315   0.2370   35.72984   0.0019 ---------------------------------------------------------------- ------------------------------------------------------------------------------              |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval] -------------+---------------------------------------------------------------- garchm       | 119        garchm |          L1. |   .6015071   .0969926     6.20   0.000     .4114051    .7916092          L2. |  -.2259989   .1123941    -2.01   0.044    -.4462873   -.0057105          L3. |   .0986694   .1165051     0.85   0.397    -.1296764    .3270151          L4. |   .0427477   .1177078     0.36   0.716    -.1879554    .2734508          L5. |  -.0079704   .0990377    -0.08   0.936    -.2020807    .1861398        fdvol |          L1. |   .0029578   .0011989     2.47   0.014      .000608    .0053075          L2. |   .0007833   .0010488     0.75   0.455    -.0012722    .0028388          L3. |  -.0002661   .0009606    -0.28   0.782    -.0021489    .0016168          L4. |   .0000573   .0009521     0.06   0.952    -.0018087    .0019233          L5. |   -.001671   .0009541    -1.75   0.080     -.003541    .0001991         fdoi |          L1. |  -.0001995   .0029038    -0.07   0.945    -.0058907    .0054918              |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]          L2. |  -.0017896   .0029642    -0.60   0.546    -.0075993    .0040201          L3. |   .0001287   .0028759     0.04   0.964     -.005508    .0057654          L4. |   -.004657   .0029638    -1.57   0.116    -.0104659    .0011519                 |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]           L5. |   .0034567   .0029767     1.16   0.246    -.0023775    .0092909        _cons |   .0010793   .0007157     1.51   0.132    -.0003234     .002482 -------------+---------------------------------------------------------------- fdvol        |       garchm |          L1. |   4.111851   7.693498     0.53   0.593    -10.96713    19.19083          L2. |  -12.96071   8.915149    -1.45   0.146    -30.43408    4.512662          L3. |     1.0064   9.241234     0.11   0.913    -17.10609    19.11889          L4. |  -23.64914   9.336638    -2.53   0.011    -41.94862    -5.34967          L5. |   11.46207   7.855712     1.46   0.145    -3.934843    26.85898        fdvol |          L1. |  -.3622938   .0950967    -3.81   0.000    -.5486799   -.1759077          L2. |    .085714   .0831881     1.03   0.303    -.0773317    .2487598          L3. |  -.0454688   .0761988    -0.60   0.551    -.1948156    .1038781          L4. |   .3507932   .0755177     4.65   0.000     .2027812    .4988052          L5. |    .182665   .0756821     2.41   0.016     .0343308    .3309992         fdoi |          L1. |    .786835   .2303278     3.42   0.001     .3354009    1.238269          L2. |  -.4439489   .2351192    -1.89   0.059     -.904774    .0168762          L3. |   .6367667   .2281195     2.79   0.005     .1896607    1.083873          L4. |  -.6385815   .2350888    -2.72   0.007    -1.099347   -.1778158          L5. |  -.0782563   .2361113    -0.33   0.740    -.5410259    .3845134        _cons |   .1582295   .0567667     2.79   0.005     .0469687    .2694902 -------------+---------------------------------------------------------------- fdoi         |       garchm |          L1. |  -4.409868   2.974262    -1.48   0.138    -10.23931    1.419579          L2. |  -7.119328   3.446546    -2.07   0.039    -13.87443   -.3642227          L3. |   7.791849   3.572608     2.18   0.029     .7896658    14.79403          L4. |  -.4143495   3.609491    -0.11   0.909    -7.488821    6.660122          L5. |  -7.893384   3.036973    -2.60   0.009    -13.84574   -1.941026        fdvol |          L1. |  -.0294575   .0367638    -0.80   0.423    -.1015133    .0425983          L2. |   .0159736   .0321601     0.50   0.619     -.047059    .0790061          L3. |   .0170748    .029458     0.58   0.562    -.0406619    .0748114          L4. |   -.055605   .0291947    -1.90   0.057    -.1128256    .0016155          L5. |  -.0039654   .0292583    -0.14   0.892    -.0613105    .0533798         fdoi |          L1. |   .1040251   .0890434     1.17   0.243    -.0704968    .2785469          L2. |   .0251048   .0908957     0.28   0.782    -.1530476    .2032571          L3. |  -.0846315   .0881897    -0.96   0.337    -.2574801    .0882171          L4. |   .0689379    .090884     0.76   0.448    -.1091915    .2470672          L5. |   -.156481   .0912793    -1.71   0.086    -.3353851    .0224231        _cons |   .0678421   .0219457     3.09   0.002     .0248293    .1108548 ------------------------------------------------------------------------------  . vargranger     Granger causality Wald tests   +------------------------------------------------------------------+   |          Equation           Excluded |   chi2     df Prob > chi2 | 120    |--------------------------------------+---------------------------|   |            garchm              fdvol |  7.4866     5    0.187    |   |            garchm               fdoi |  3.5262     5    0.619    |   |            garchm                ALL |  8.9019    10    0.541    |   |--------------------------------------+---------------------------|   |             fdvol             garchm |  12.913     5    0.024    |   |             fdvol               fdoi |  27.755     5    0.000    |   |             fdvol                ALL |   42.86    10    0.000    |   |--------------------------------------+---------------------------|   |              fdoi             garchm |  25.687     5    0.000    |   |              fdoi              fdvol |  5.4421     5    0.364    |   |              fdoi                ALL |  29.776    10    0.001    |   +------------------------------------------------------------------+   Impulse Response and FEVD (FD Method) . irf ctable (fdm garchm garchm fevd, noci) (fdm fdvol garchm fevd, noci) (fdm fdoi garchm fevd, noci) (fdm > garchm garchm irf, noci) (fdm fdvol garchm irf, noci) (fdm fdoi garchm irf, noci)    +--------------------------------------------------------------------------------+ |        |    (1)    |    (2)    |    (3)    |    (1)    |    (2)    |    (3)    |   |  step  |   fevd    |   fevd    |   fevd    |   irf     |   irf     |   irf     | |--------+-----------+-----------+-----------+-----------+-----------+-----------| |0       | 0         | 0         | 0         | 1         | 0         | 0         | |1       | 1         | 0         | 0         | .601507   | .002958   | -.000199  | |2       | .969521   | .030455   | .000024   | .148853   | .001497   | .000397   | |3       | .962615   | .03727    | .000115   | .019755   | .000342   | -.001077  | |4       | .961711   | .037499   | .000789   | .065691   | -.000023  | -.003447  | |5       | .955171   | .037206   | .007622   | .020555   | -.000357  | -.000912  | |6       | .954213   | .037694   | .008092   | .020304   | .00022    | -5.1e-06  | |7       | .954081   | .037832   | .008087   | .005258   | .00008    | .000503   | |8       | .953909   | .037859   | .008231   | .005474   | .000223   | -.000486  | |9       | .953657   | .037979   | .008364   | .038843   | -.00022   | .001072   | |10      | .952957   | .038031   | .009012   | .020214   | .000165   | -.000175  | |11      | .952882   | .038093   | .009025   | -.002454  | .000021   | .000359   | |12      | .952808   | .038095   | .009098   | -.004397  | .000129   | -.000553  | |13      | .952606   | .038123   | .009271   | .011623   | -.000155  | .000283   | |14      | .952499   | .038185   | .009316   | -.003309  | .000046   | -.000403  | |15      | .952407   | .038184   | .009408   | -.004906  | -.000044  | .000286   | |16      | .952361   | .038184   | .009454   | -.003767  | .000079   | -.000316  | |17      | .952293   | .038196   | .009511   | .005606   | -.000078  | .000254   | |18      | .952244   | .038208   | .009547   | .000543   | .000034   | -.000159  | |19      | .952228   | .03821    | .009562   | .0008     | -.000028  | .000236   | |20      | .952197   | .03821    | .009593   | -.002275  | .000057   | -.000201  | |21      | .952167   | .038216   | .009616   | .002514   | -.000043  | .000148   | |22      | .952151   | .03822    | .009629   | .000128   | .00002    | -.000133  | |23      | .952141   | .03822    | .009639   | .000189   | -.000025  | .000128   | |24      | .952131   | .038221   | .009648   | -.002093  | .000033   | -.00013   | |25      | .95212    | .038223   | .009657   | .001139   | -.000026  | .000096   | |26      | .952113   | .038224   | .009663   | .000031   | .000014   | -.000085  | |27      | .952109   | .038224   | .009667   | .000471   | -.000017  | .000089   | |28      | .952104   | .038225   | .009671   | -.00104   | .000021   | -.000075  | |29      | .9521     | .038226   | .009674   | .000662   | -.000014  | .000062   | |30      | .952098   | .038226   | .009676   | -.000062  | 9.9e-06   | -.000056  | |31      | .952096   | .038226   | .009678   | .000402   | -.000012  | .000055   | |32      | .952094   | .038226   | .00968    | -.000634  | .000012   | -.000048  | |33      | .952092   | .038227   | .009681   | .000291   | -8.8e-06  | .000039   | |34      | .952091   | .038227   | .009682   | -.000119  | 6.7e-06   | -.000037  | |35      | .95209    | .038227   | .009683   | .000302   | -7.9e-06  | .000035   | |36      | .95209    | .038227   | .009684   | -.000356  | 7.5e-06   | -.00003   | |37      | .952089   | .038227   | .009684   | .00017    | -5.4e-06  | .000025   | |38      | .952089   | .038227   | .009684   | -.000098  | 4.6e-06   | -.000024  | |39      | .952088   | .038227   | .009685   | .00021    | -5.1e-06  | .000022   | |40      | .952088   | .038227   | .009685   | -.000202  | 4.6e-06   | -.000019  | |41      | .952088   | .038227   | .009685   | .0001     | -3.4e-06  | .000016   | |42      | .952087   | .038227   | .009685   | -.000086  | 3.1e-06   | -.000015  | |43      | .952087   | .038227   | .009685   | .000134   | -3.2e-06  | .000014   | |44      | .952087   | .038227   | .009686   | -.000116  | 2.8e-06   | -.000012  | |45      | .952087   | .038227   | .009686   | .000063   | -2.2e-06  | .000011   | |46      | .952087   | .038227   | .009686   | -.000064  | 2.1e-06   | -9.8e-06  | |47      | .952087   | .038227   | .009686   | .000085   | -2.0e-06  | 8.8e-06   | |48      | .952087   | .038227   | .009686   | -.000066  | 1.7e-06   | -7.5e-06  | |49      | .952087   | .038227   | .009686   | .000042   | -1.4e-06  | 6.8e-06   | |50      | .952087   | .038227   | .009686   | -.000045  | 1.3e-06   | -6.2e-06  | |51      | .952087   | .038227   | .009686   | .000052   | -1.3e-06  | 5.5e-06   | |52      | .952087   | .038227   | .009686   | -.00004   | 1.1e-06   | -4.8e-06  | |53      | .952087   | .038227   | .009686   | .000028   | -9.1e-07  | 4.3e-06   | |54      | .952087   | .038227   | .009686   | -.000031  | 8.7e-07   | -4.0e-06  | |55      | .952087   | .038227   | .009686   | .000032   | -8.1e-07  | 3.5e-06   | |56      | .952087   | .038227   | .009686   | -.000024  | 6.8e-07   | -3.1e-06  | |57      | .952087   | .038227   | .009686   | .000019   | -5.9e-07  | 2.8e-06   | |58      | .952087   | .038227   | .009686   | -.00002   | 5.6e-07   | -2.5e-06  | |59      | .952087   | .038227   | .009686   | .00002    | -5.1e-07  | 2.2e-06   | |60      | .952087   | .038227   | .009686   | -.000015  | 4.3e-07   | -2.0e-06  | |61      | .952087   | .038227   | .009686   | .000013   | -3.8e-07  | 1.8e-06   | |62      | .952087   | .038227   | .009686   | -.000013  | 3.6e-07   | -1.6e-06  | |63      | .952087   | .038227   | .009686   | .000012   | -3.2e-07  | 1.4e-06   | |64      | .952087   | .038227   | .009686   | -9.4e-06  | 2.7e-07   | -1.3e-06  | 121  |65      | .952087   | .038227   | .009686   | 8.4e-06   | -2.5e-07  | 1.1e-06   | |66      | .952087   | .038227   | .009686   | -8.5e-06  | 2.3e-07   | -1.0e-06  | |67      | .952087   | .038227   | .009686   | 7.5e-06   | -2.0e-07  | 9.0e-07   | |68      | .952087   | .038227   | .009686   | -6.0e-06  | 1.7e-07   | -8.0e-07  | |69      | .952087   | .038227   | .009686   | 5.5e-06   | -1.6e-07  | 7.2e-07   | |70      | .952087   | .038227   | .009686   | -5.4e-06  | 1.4e-07   | -6.5e-07  | |71      | .952087   | .038227   | .009686   | 4.6e-06   | -1.3e-07  | 5.7e-07   | |72      | .952087   | .038227   | .009686   | -3.8e-06  | 1.1e-07   | -5.1e-07  | |73      | .952087   | .038227   | .009686   | 3.6e-06   | -1.0e-07  | 4.6e-07   | |74      | .952087   | .038227   | .009686   | -3.4e-06  | 9.2e-08   | -4.1e-07  | |75      | .952087   | .038227   | .009686   | 2.9e-06   | -8.1e-08  | 3.7e-07   | |76      | .952087   | .038227   | .009686   | -2.5e-06  | 7.2e-08   | -3.3e-07  | |77      | .952087   | .038227   | .009686   | 2.3e-06   | -6.5e-08  | 2.9e-07   | |78      | .952087   | .038227   | .009686   | -2.1e-06  | 5.8e-08   | -2.6e-07  | |79      | .952087   | .038227   | .009686   | 1.8e-06   | -5.1e-08  | 2.3e-07   | |80      | .952087   | .038227   | .009686   | -1.6e-06  | 4.6e-08   | -2.1e-07  | |81      | .952087   | .038227   | .009686   | 1.5e-06   | -4.1e-08  | 1.9e-07   | |82      | .952087   | .038227   | .009686   | -1.4e-06  | 3.7e-08   | -1.7e-07  | |83      | .952087   | .038227   | .009686   | 1.2e-06   | -3.3e-08  | 1.5e-07   | |84      | .952087   | .038227   | .009686   | -1.0e-06  | 2.9e-08   | -1.3e-07  | |85      | .952087   | .038227   | .009686   | 9.5e-07   | -2.6e-08  | 1.2e-07   |              |        |    (1)    |    (2)    |    (3)    |    (1)    |    (2)    |    (3)    | |  step  |   fevd    |   fevd    |   fevd    |   irf     |   irf     |   irf     | |86      | .952087   | .038227   | .009686   | -8.5e-07  | 2.4e-08   | -1.1e-07  | |87      | .952087   | .038227   | .009686   | 7.4e-07   | -2.1e-08  | 9.5e-08   | |88      | .952087   | .038227   | .009686   | -6.6e-07  | 1.9e-08   | -8.5e-08  | |89      | .952087   | .038227   | .009686   | 6.1e-07   | -1.7e-08  | 7.6e-08   | |90      | .952087   | .038227   | .009686   | -5.4e-07  | 1.5e-08   | -6.8e-08  | |91      | .952087   | .038227   | .009686   | 4.7e-07   | -1.3e-08  | 6.0e-08   | |92      | .952087   | .038227   | .009686   | -4.2e-07  | 1.2e-08   | -5.4e-08  | |93      | .952087   | .038227   | .009686   | 3.9e-07   | -1.1e-08  | 4.8e-08   | |94      | .952087   | .038227   | .009686   | -3.4e-07  | 9.5e-09   | -4.3e-08  | |95      | .952087   | .038227   | .009686   | 3.0e-07   | -8.5e-09  | 3.9e-08   | |96      | .952087   | .038227   | .009686   | -2.7e-07  | 7.6e-09   | -3.4e-08  | |97      | .952087   | .038227   | .009686   | 2.5e-07   | -6.8e-09  | 3.1e-08   | |98      | .952087   | .038227   | .009686   | -2.2e-07  | 6.1e-09   | -2.7e-08  | |99      | .952087   | .038227   | .009686   | 1.9e-07   | -5.4e-09  | 2.5e-08   | |100     | .952087   | .038227   | .009686   | -1.7e-07  | 4.9e-09   | -2.2e-08  | +--------------------------------------------------------------------------------+ (1) irfname = fdm, impulse = garchm, and response = garchm (2) irfname = fdm, impulse = fdvol, and response = garchm (3) irfname = fdm, impulse = fdoi, and response = garchm  Granger Causality (P3 Method) . tsset time         time variable:  time, 1 to 121  . irf set p3m (file p3m.irf created) (file p3m.irf now active)  . var garchm p3vol p3oi, lags(1/5)  Vector autoregression  Sample:       6      121                           No. of obs      =       116 Log likelihood =  530.6909                         AIC             = -8.322257 FPE            =  4.90e-08                         HQIC            = -7.859719 Det(Sigma_ml)  =  2.13e-08                         SBIC            =  -7.18284  Equation           Parms      RMSE     R-sq      chi2     P>chi2 ---------------------------------------------------------------- garchm               16      .00477   0.4260    86.0969   0.0000 p3vol                16     .359254   0.4193   83.77463   0.0000 p3oi                 16     .135435   0.8612    719.497   0.0000 ---------------------------------------------------------------- ------------------------------------------------------------------------------              |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval] -------------+---------------------------------------------------------------- garchm       |       garchm |          L1. |   .5911772    .100337     5.89   0.000     .3945203    .7878341          L2. |   -.233564   .1139331    -2.05   0.040    -.4568688   -.0102591          L3. |   .1389206   .1176557     1.18   0.238    -.0916804    .3695216 122           L4. |  -.0046484   .1165485    -0.04   0.968    -.2330791    .2237824          L5. |   .0273461   .0957494     0.29   0.775    -.1603192    .2150114        p3vol |          L1. |   .0003317   .0010109     0.33   0.743    -.0016497     .002313          L2. |  -.0012912    .000907    -1.42   0.155    -.0030689    .0004865          L3. |  -.0011858   .0008888    -1.33   0.182    -.0029279    .0005562          L4. |  -.0010621   .0008692    -1.22   0.222    -.0027657    .0006416          L5. |  -.0009183   .0008523    -1.08   0.281    -.0025887    .0007521         p3oi |          L1. |   .0042469    .003303     1.29   0.199    -.0022268    .0107207          L2. |  -.0043713   .0050075    -0.87   0.383    -.0141859    .0054433          L3. |   .0041125    .004901     0.84   0.401    -.0054934    .0137184          L4. |  -.0062348   .0048285    -1.29   0.197    -.0156985    .0032288          L5. |   .0082588   .0034289     2.41   0.016     .0015383    .0149793        _cons |   .0015171   .0005583     2.72   0.007     .0004227    .0026114 -------------+---------------------------------------------------------------- p3vol        |       garchm |          L1. |   13.56663   7.556793     1.80   0.073    -1.244409    28.37768          L2. |  -7.503612   8.580774    -0.87   0.382    -24.32162    9.314395          L3. |   12.98333   8.861139     1.47   0.143     -4.38418    30.35084          L4. |  -20.56606   8.777745    -2.34   0.019    -37.77012   -3.361991                     Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]          L5. |   12.37189   7.211281     1.72   0.086    -1.761956    26.50575        p3vol |          L1. |   .1813719   .0761361     2.38   0.017      .032148    .3305959                 |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]           L2. |   .1662555   .0683102     2.43   0.015       .03237     .300141          L3. |  -.0099347   .0669403    -0.15   0.882    -.1411353    .1212658          L4. |   .1829413   .0654653     2.79   0.005     .0546317    .3112509          L5. |  -.0060709   .0641869    -0.09   0.925    -.1318749     .119733         p3oi |          L1. |   1.068023   .2487623     4.29   0.000     .5804576    1.555588          L2. |  -1.120376   .3771378    -2.97   0.003    -1.859552   -.3811995          L3. |   1.252971   .3691181     3.39   0.001     .5295125    1.976429          L4. |  -1.528619   .3636529    -4.20   0.000    -2.241366   -.8158724          L5. |   .6767306   .2582444     2.62   0.009     .1705809     1.18288        _cons |  -.0179049   .0420512    -0.43   0.670    -.1003237    .0645139 -------------+---------------------------------------------------------------- p3oi         |       garchm |          L1. |  -2.134806   2.848826    -0.75   0.454    -7.718403    3.448791          L2. |   -5.60574   3.234856    -1.73   0.083    -11.94594    .7344606          L3. |   6.599546    3.34055     1.98   0.048     .0521881     13.1469          L4. |  -1.287298   3.309112    -0.39   0.697    -7.773038    5.198441          L5. |  -3.685058   2.718572    -1.36   0.175    -9.013362    1.643245        p3vol |          L1. |  -.0383016   .0287024    -1.33   0.182    -.0945573    .0179542          L2. |   .0004541   .0257522     0.02   0.986    -.0500192    .0509274          L3. |  -.0044454   .0252357    -0.18   0.860    -.0539066    .0450157          L4. |  -.0146685   .0246797    -0.59   0.552    -.0630398    .0337028          L5. |    .014683   .0241977     0.61   0.544    -.0327437    .0621097         p3oi |          L1. |   1.067046   .0937806    11.38   0.000     .8832392    1.250852          L2. |  -.1418135   .1421767    -1.00   0.319    -.4204748    .1368477          L3. |  -.0798038   .1391534    -0.57   0.566    -.3525394    .1929319          L4. |   .2061639   .1370931     1.50   0.133    -.0625335    .4748614          L5. |  -.1574802   .0973552    -1.62   0.106     -.348293    .0333326        _cons |   .0103994   .0158528     0.66   0.512    -.0206716    .0414703 ------------------------------------------------------------------------------  . vargranger     Granger causality Wald tests   +------------------------------------------------------------------+   |          Equation           Excluded |   chi2     df Prob > chi2 |   |--------------------------------------+---------------------------|   |            garchm              p3vol |  7.3055     5    0.199    |   |            garchm               p3oi |  17.858     5    0.003    |   |            garchm                ALL |  19.679    10    0.032    | 123    |--------------------------------------+---------------------------|   |             p3vol             garchm |  8.7342     5    0.120    |   |             p3vol               p3oi |  44.358     5    0.000    |   |             p3vol                ALL |  50.517    10    0.000    |   |--------------------------------------+---------------------------|   |              p3oi             garchm |  11.612     5    0.041    |   |              p3oi              p3vol |  2.3111     5    0.805    |   |              p3oi                ALL |  16.849    10    0.078    |   +------------------------------------------------------------------+  Impulse Response and FEVD (P3 Method) . irf ctable (p3m garchm garchm fevd, noci) (p3m p3vol garchm fevd, noci) (p3m p3oi garchm fevd, noci) (p3m > garchm garchm irf, noci) (p3m p3vol garchm irf, noci) (p3m p3oi garchm irf, noci)  +--------------------------------------------------------------------------------+ |        |    (1)    |    (2)    |    (3)    |    (1)    |    (2)    |    (3)    | |  step  |   fevd    |   fevd    |   fevd    |   irf     |   irf     |   irf     | |--------+-----------+-----------+-----------+-----------+-----------+-----------| |0       | 0         | 0         | 0         | 1         | 0         | 0         | |1       | 1         | 0         | 0         | .591177   | .000332   | .004247   | |2       | .989346   | .000433   | .010221   | .11136    | -.001198  | .003025   | |3       | .980727   | .004017   | .015256   | .017675   | -.002188  | .002976   | |4       | .964199   | .016059   | .019742   | .050238   | -.002632  | -.002387  | |5       | .943578   | .034093   | .02233    | .026893   | -.002436  | .000465   | |6       | .92965    | .048352   | .021998   | .021779   | -.001831  | .004368   | |7       | .91377    | .054952   | .031278   | -.036675  | -.001468  | .005924   | |8       | .89486    | .057578   | .047562   | -.075488  | -.001305  | .00437    |            |        |    (1)    |    (2)    |    (3)    |    (1)    |    (2)    |    (3)    | |  step  |   fevd    |   fevd    |   fevd    |   irf     |   irf     |   irf     | |9       | .885194   | .059453   | .055353   | -.050223  | -.001196  | .004022   | |10      | .877048   | .061138   | .061814   | -.035825  | -.000899  | .003574   | |11      | .871176   | .061911   | .066913   | -.056849  | -.000622  | .003344   | |12      | .866949   | .061854   | .071198   | -.069514  | -.000401  | .002429   | |13      | .86521    | .061571   | .073219   | -.060226  | -.000265  | .001558   | |14      | .864686   | .061378   | .073936   | -.047754  | -.000111  | .000728   | |15      | .864723   | .061265   | .074012   | -.039316  | .000034   | .000341   | |16      | .864802   | .061207   | .073991   | -.033257  | .000161   | -.000111  | |17      | .864801   | .061235   | .073964   | -.02559   | .000228   | -.000523  | |18      | .864615   | .061321   | .074064   | -.015598  | .000267   | -.000892  | |19      | .864186   | .061429   | .074384   | -.006095  | .000285   | -.001051  | |20      | .863637   | .061539   | .074824   | .000186   | .000292   | -.001141  | |21      | .863025   | .061641   | .075334   | .004678   | .000276   | -.001153  | |22      | .862434   | .061718   | .075848   | .00883    | .000245   | -.001135  | |23      | .861898   | .061761   | .076341   | .01224    | .000206   | -.001042  | |24      | .861476   | .061776   | .076748   | .01403    | .000165   | -.00091   | |25      | .861174   | .061772   | .077053   | .01445    | .000123   | -.000747  | |26      | .860986   | .06176    | .077254   | .01405    | .000082   | -.000587  | |27      | .860881   | .061745   | .077374   | .013161   | .000043   | -.000425  | |28      | .860835   | .061731   | .077434   | .011772   | 9.5e-06   | -.000272  | |29      | .860822   | .061722   | .077456   | .00994    | -.000018  | -.000129  | |30      | .860823   | .061719   | .077458   | .007867   | -.000039  | -.00001   | |31      | .860823   | .061721   | .077456   | .005811   | -.000055  | .000086   | |32      | .860815   | .061726   | .077458   | .003875   | -.000064  | .000159   | |33      | .860799   | .061733   | .077468   | .002097   | -.000069  | .00021    | |34      | .860774   | .06174    | .077485   | .000522   | -.000068  | .00024    | |35      | .860746   | .061747   | .077508   | -.000778  | -.000065  | .000251   | |36      | .860717   | .061751   | .077532   | -.001775  | -.000058  | .000246   | |37      | .860691   | .061755   | .077554   | -.002479  | -.00005   | .000229   | |38      | .86067    | .061756   | .077574   | -.00292   | -.00004   | .000203   | |39      | .860655   | .061756   | .077589   | -.003123  | -.000031  | .000171   | |40      | .860644   | .061756   | .077599   | -.003117  | -.000021  | .000136   | |41      | .860639   | .061755   | .077606   | -.002942  | -.000012  | .0001     | |42      | .860636   | .061755   | .077609   | -.002642  | -4.6e-06  | .000066   | |43      | .860635   | .061754   | .07761    | -.002259  | 2.0e-06   | .000035   | |44      | .860635   | .061754   | .077611   | -.001829  | 7.1e-06   | 7.5e-06   | |45      | .860635   | .061754   | .077611   | -.001381  | .000011   | -.000015  | |46      | .860635   | .061754   | .077611   | -.000945  | .000013   | -.000032  | |47      | .860634   | .061755   | .077611   | -.000542  | .000015   | -.000044  | |48      | .860633   | .061755   | .077612   | -.000188  | .000015   | -.000052  | |49      | .860632   | .061755   | .077613   | .000109   | .000014   | -.000055  | |50      | .86063    | .061756   | .077614   | .000343   | .000013   | -.000055  | |51      | .860629   | .061756   | .077615   | .000514   | .000011   | -.000051  | |52      | .860628   | .061756   | .077616   | .000624   | 9.3e-06   | -.000046  | |53      | .860627   | .061756   | .077617   | .00068    | 7.2e-06   | -.000039  | |54      | .860627   | .061756   | .077617   | .000688   | 5.1e-06   | -.000032  | |55      | .860626   | .061756   | .077618   | .000658   | 3.1e-06   | -.000024  | |56      | .860626   | .061756   | .077618   | .000598   | 1.4e-06   | -.000016  | |57      | .860626   | .061756   | .077618   | .000518   | -1.4e-07  | -9.2e-06  | |58      | .860626   | .061756   | .077618   | .000425   | -1.3e-06  | -3.0e-06  | |59      | .860626   | .061756   | .077618   | .000327   | -2.2e-06  | 2.1e-06   | |60      | .860626   | .061756   | .077618   | .00023    | -2.8e-06  | 6.2e-06   | |61      | .860626   | .061756   | .077618   | .00014    | -3.2e-06  | 9.1e-06   | |62      | .860626   | .061756   | .077618   | .000059   | -3.3e-06  | .000011   | 124  |63      | .860626   | .061756   | .077618   | -9.3e-06  | -3.2e-06  | .000012   | |64      | .860626   | .061756   | .077618   | -.000064  | -2.9e-06  | .000012   | |65      | .860626   | .061756   | .077618   | -.000105  | -2.6e-06  | .000012   | |66      | .860626   | .061756   | .077618   | -.000132  | -2.2e-06  | .00001    | |67      | .860626   | .061756   | .077618   | -.000147  | -1.7e-06  | 9.0e-06   | |68      | .860626   | .061756   | .077618   | -.000151  | -1.2e-06  | 7.4e-06   | |69      | .860626   | .061756   | .077618   | -.000147  | -7.9e-07  | 5.6e-06   | |70      | .860626   | .061756   | .077618   | -.000135  | -3.9e-07  | 4.0e-06   | |71      | .860626   | .061756   | .077618   | -.000118  | -4.5e-08  | 2.4e-06   | |72      | .860626   | .061756   | .077618   | -.000098  | 2.3e-07   | 9.7e-07   | |73      | .860626   | .061756   | .077618   | -.000077  | 4.5e-07   | -2.2e-07  | |74      | .860626   | .061756   | .077618   | -.000056  | 6.0e-07   | -1.2e-06  | |75      | .860626   | .061756   | .077618   | -.000035  | 6.8e-07   | -1.9e-06  | |76      | .860626   | .061756   | .077618   | -.000017  | 7.2e-07   | -2.3e-06  | |77      | .860626   | .061756   | .077618   | -1.3e-06  | 7.1e-07   | -2.6e-06  | |78      | .860626   | .061756   | .077618   | .000011   | 6.6e-07   | -2.7e-06  | |79      | .860626   | .061756   | .077618   | .000021   | 5.9e-07   | -2.6e-06  | |80      | .860626   | .061756   | .077618   | .000028   | 5.0e-07   | -2.4e-06  | |81      | .860626   | .061756   | .077618   | .000032   | 4.0e-07   | -2.1e-06  | |82      | .860626   | .061756   | .077618   | .000033   | 2.9e-07   | -1.7e-06  | |83      | .860626   | .061756   | .077618   | .000033   | 2.0e-07   | -1.3e-06  | |84      | .860626   | .061756   | .077618   | .00003    | 1.1e-07   | -9.6e-07  | |85      | .860626   | .061756   | .077618   | .000027   | 2.7e-08   | -6.0e-07  | |86      | .860626   | .061756   | .077618   | .000023   | -3.8e-08  | -2.8e-07  | |87      | .860626   | .061756   | .077618   | .000018   | -8.8e-08  | -1.1e-08  | |88      | .860626   | .061756   | .077618   | .000013   | -1.2e-07  | 2.1e-07   | |89      | .860626   | .061756   | .077618   | 8.8e-06   | -1.5e-07  | 3.8e-07   | |90      | .860626   | .061756   | .077618   | 4.7e-06   | -1.6e-07  | 4.9e-07   | |91      | .860626   | .061756   | .077618   | 1.1e-06   | -1.6e-07  | 5.6e-07   | |92      | .860626   | .061756   | .077618   | -1.9e-06  | -1.5e-07  | 5.8e-07   | |93      | .860626   | .061756   | .077618   | -4.2e-06  | -1.3e-07  | 5.7e-07   | |94      | .860626   | .061756   | .077618   | -5.8e-06  | -1.1e-07  | 5.3e-07   | |95      | .860626   | .061756   | .077618   | -6.8e-06  | -9.2e-08  | 4.7e-07   | |96      | .860626   | .061756   | .077618   | -7.2e-06  | -7.0e-08  | 3.9e-07   | |97      | .860626   | .061756   | .077618   | -7.2e-06  | -4.8e-08  | 3.1e-07   | |98      | .860626   | .061756   | .077618   | -6.8e-06  | -2.8e-08  | 2.3e-07   | |99      | .860626   | .061756   | .077618   | -6.1e-06  | -9.8e-09  | 1.5e-07   | |100     | .860626   | .061756   | .077618   | -5.2e-06  | 5.2e-09   | 7.8e-08   | +--------------------------------------------------------------------------------+ (1) irfname = p3m, impulse = garchm, and response = garchm (2) irfname = p3m, impulse = p3vol, and response = garchm (3) irfname = p3m, impulse = p3oi, and response = garchm  Granger Causality (CMA Method) . tsset time         time variable:  time, 1 to 119  . irf set cmam (file cmam.irf created) (file cmam.irf now active)  . var garchm cmavol cmaoi, lags(1/3)  Vector autoregression  Sample:       4      119                           No. of obs      =       116 Log likelihood =  612.0589                         AIC             =  -10.0355 FPE            =  8.81e-09                         HQIC            = -9.746413 Det(Sigma_ml)  =  5.24e-09                         SBIC            = -9.323364  Equation           Parms      RMSE     R-sq      chi2     P>chi2 ---------------------------------------------------------------- garchm               10     .004676   0.4154   82.42696   0.0000 cmavol               10     .207052   0.4518   95.58593   0.0000 cmaoi                10     .087607   0.3007    49.8698   0.0000 ---------------------------------------------------------------- ------------------------------------------------------------------------------              |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval] -------------+---------------------------------------------------------------- garchm       |       garchm |          L1. |   .6557957    .092877     7.06   0.000     .4737603    .8378312          L2. |  -.1636187    .109394    -1.50   0.135     -.378027    .0507896          L3. |   .1089096   .0922027     1.18   0.238    -.0718043    .2896236       cmavol |          L1. |  -.0047655   .0017956    -2.65   0.008    -.0082847   -.0012462          L2. |  -.0064984   .0019412    -3.35   0.001    -.0103031   -.0026938          L3. |  -.0036996   .0016987    -2.18   0.029     -.007029   -.0003702        cmaoi |          L1. |    .008841   .0048596     1.82   0.069    -.0006836    .0183656          L2. |   .0007178   .0044381     0.16   0.872    -.0079807    .0094163          L3. |   .0055065   .0048803     1.13   0.259    -.0040586    .0150716        _cons |   .0009786    .000497     1.97   0.049     4.45e-06    .0019528 -------------+---------------------------------------------------------------- 125  cmavol       |       garchm |          L1. |   3.201407   4.112778     0.78   0.436     -4.85949     11.2623          L2. |   1.952684   4.844187     0.40   0.687    -7.541747    11.44712          L3. |   1.246162    4.08292     0.31   0.760    -6.756214    9.248537       cmavol |          L1. |  -.6280672   .0795119    -7.90   0.000    -.7839076   -.4722268          L2. |  -.4631388   .0859593    -5.39   0.000    -.6316159   -.2946618          L3. |  -.4243152   .0752212    -5.64   0.000     -.571746   -.2768844        cmaoi |          L1. |   .7433044   .2151925     3.45   0.001     .3215349    1.165074          L2. |    .244413   .1965277     1.24   0.214    -.1407743    .6296003          L3. |   .7969228   .2161073     3.69   0.000     .3733603    1.220485        _cons |  -.0387496   .0220099    -1.76   0.078    -.0818883     .004389 -------------+---------------------------------------------------------------- cmaoi        |       garchm |          L1. |    1.88354   1.740184     1.08   0.279    -1.527158    5.294238          L2. |  -6.895753   2.049655    -3.36   0.001      -10.913   -2.878504          L3. |   3.893586    1.72755     2.25   0.024     .5076492    7.279522       cmavol |          L1. |      .0006   .0336428     0.02   0.986    -.0653387    .0665386          L2. |   .0170802   .0363708     0.47   0.639    -.0542052    .0883656          L3. |   .0215352   .0318273     0.68   0.499    -.0408452    .0839156        cmaoi |          L1. |    .147642   .0910515     1.62   0.105    -.0308156    .3260996                     Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]          L2. |  -.4242101   .0831541    -5.10   0.000    -.5871891    -.261231          L3. |   .0067385   .0914385     0.07   0.941    -.1724777    .1859548        _cons |   -.008012   .0093128    -0.86   0.390    -.0262646    .0102407 ------------------------------------------------------------------------------  . vargranger     Granger causality Wald tests   +------------------------------------------------------------------+   |          Equation           Excluded |   chi2     df Prob > chi2 |   |--------------------------------------+---------------------------|   |            garchm             cmavol |  13.418     3    0.004    |   |            garchm              cmaoi |  3.6074     3    0.307    |   |            garchm                ALL |  17.423     6    0.008    |   |--------------------------------------+---------------------------|   |            cmavol             garchm |  2.4016     3    0.493    |   |            cmavol              cmaoi |  21.101     3    0.000    |   |            cmavol                ALL |  25.187     6    0.000    |   |--------------------------------------+---------------------------|   |             cmaoi             garchm |  12.257     3    0.007    |   |             cmaoi             cmavol |  .54747     3    0.908    |   |             cmaoi                ALL |  13.089     6    0.042    |   +------------------------------------------------------------------+  Impulse Response and FEVD (CMA Method) . irf ctable (cmam garchm garchm fevd, noci) (cmam cmavol garchm fevd, noci) (cmam cmaoi garchm fevd, noci) > (cmam garchm garchm irf, noci) (cmam cmavol garchm irf, noci) (cmam cmaoi garchm irf, noci)  +--------------------------------------------------------------------------------+ |        |    (1)    |    (2)    |    (3)    |    (1)    |    (2)    |    (3)    | |  step  |   fevd    |   fevd    |   fevd    |   irf     |   irf     |   irf     | |--------+-----------+-----------+-----------+-----------+-----------+-----------| |0       | 0         | 0         | 0         | 1         | 0         | 0         | |1       | 1         | 0         | 0         | .655796   | -.004765  | .008841   | |2       | .953134   | .02848    | .018386   | .267846   | -.006625  | .004279   | |3       | .902067   | .077195   | .020737   | .09384    | -.002716  | -.000863  | |4       | .894453   | .084897   | .020651   | .06486    | .002445   | -.004686  | |5       | .884734   | .090321   | .024944   | .064405   | .000698   | -.002307  | |6       | .883578   | .090473   | .025949   | .070075   | -.001594  | .001726   | |7       | .880782   | .092798   | .02642    | .042706   | -.001491  | .003159   | |8       | .876924   | .094739   | .028337   | .001602   | .000463   | -.000441  | |9       | .876681   | .094951   | .028368   | -.017616  | .000623   | -.002253  | |10      | .875423   | .09521    | .029367   | .004971   | 1.9e-06   | -.000656  | |11      | .875347   | .095201   | .029453   | .020703   | -.00045   | .001419   | |12      | .874824   | .095335   | .029841   | .00861    | -.000107  | .000725   | |13      | .874725   | .095331   | .029944   | -.009394  | .000091   | -.000569  | |14      | .874667   | .095327   | .030006   | -.006337  | .000138   | -.000661  | |15      | .874574   | .095334   | .030092   | .004306   | -.000019  | .000173   | |16      | .87457    | .095333   | .030098   | .005832   | -.000059  | .000377   | |17      | .874544   | .095331   | .030125   | -.00068   | -.000056  | .000059   | |18      | .87454    | .095334   | .030126   | -.003064  | .00003    | -.000199  | |19      | .874533   | .095333   | .030134   | -.000666  | .000039   | -.000086  | |20      | .87453    | .095335   | .030135   | .001544   | 9.1e-06   | .000052   | |21      | .87453    | .095335   | .030135   | .000844   | -.000034  | .000079   | 126  |22      | .874528   | .095336   | .030137   | -.000355  | -.000012  | 2.0e-06   | |23      | .874528   | .095336   | .030137   | -.000637  | .000012   | -.000037  | |24      | .874527   | .095336   | .030137   | -.000069  | .000016   | -.000028  | |25      | .874527   | .095336   | .030137   | .000291   | -5.6e-06  | .000014   | |26      | .874527   | .095336   | .030137   | .000236   | -9.0e-06  | .000022   | |27      | .874527   | .095336   | .030137   | -.000083  | -1.7e-06  | 3.8e-06   | |28      | .874527   | .095336   | .030137   | -.000182  | 6.1e-06   | -.000016  | |29      | .874527   | .095336   | .030137   | -.000045  | 1.9e-06   | -7.2e-06  | |30      | .874527   | .095336   | .030137   | .000116   | -1.7e-06  | 6.1e-06   | |31      | .874527   | .095336   | .030137   | .00007    | -2.4e-06  | 7.9e-06   | |32      | .874527   | .095336   | .030137   | -.000042  | 5.5e-07   | -1.7e-06  | |33      | .874527   | .095336   | .030137   | -.000065  | 1.1e-06   | -4.8e-06  | |34      | .874527   | .095336   | .030137   | 6.8e-06   | 5.4e-07   | -1.1e-06  | |35      | .874527   | .095336   | .030137   | .000039   | -6.5e-07  | 2.7e-06   | |36      | .874527   | .095336   | .030137   | .000012   | -4.2e-07  | 1.3e-06   | |37      | .874527   | .095336   | .030137   | -.00002   | 1.7e-08   | -8.3e-07  | |38      | .874527   | .095336   | .030137   | -.000013  | 4.1e-07   | -1.2e-06  | |39      | .874527   | .095336   | .030137   | 5.7e-06   | 7.3e-08   | 9.8e-08   | |40      | .874527   | .095336   | .030137   | .00001    | -1.5e-07  | 6.3e-07   | |41      | .874527   | .095336   | .030137   | 2.0e-07   | -1.8e-07  | 3.0e-07   | |42      | .874527   | .095336   | .030137   | -5.1e-06  | 7.5e-08   | -2.9e-07  | |43      | .874527   | .095336   | .030137   | -2.7e-06  | 1.0e-07   | -2.6e-07  | |44      | .874527   | .095336   | .030137   | 2.0e-06   | 2.2e-08   | 1.5e-08   | |45      | .874527   | .095336   | .030137   | 2.3e-06   | -7.7e-08  | 2.0e-07   | |46      | .874527   | .095336   | .030137   | 5.0e-08   | -2.5e-08  | 5.8e-08   | |47      | .874527   | .095336   | .030137   | -1.5e-06  | 2.3e-08   | -8.3e-08  | |48      | .874527   | .095336   | .030137   | -6.2e-07  | 3.4e-08   | -8.7e-08  | |49      | .874527   | .095336   | .030137   | 6.1e-07   | -8.7e-09  | 2.7e-08   | |50      | .874527   | .095336   | .030137   | 7.3e-07   | -1.6e-08  | 5.7e-08   | |51      | .874527   | .095336   | .030137   | -1.4e-07  | -6.5e-09  | 1.2e-08   |               |        |    (1)    |    (2)    |    (3)    |    (1)    |    (2)    |    (3)    | |  step  |   fevd    |   fevd    |   fevd    |   irf     |   irf     |   irf     | |52      | .874527   | .095336   | .030137   | -4.7e-07  | 1.1e-08   | -3.5e-08  | |53      | .874527   | .095336   | .030137   | -1.3e-07  | 5.1e-09   | -1.7e-08  | |54      | .874527   | .095336   | .030137   | 2.6e-07   | -1.5e-09  | 1.1e-08   | |55      | .874527   | .095336   | .030137   | 1.6e-07   | -5.6e-09  | 1.7e-08   | |56      | .874527   | .095336   | .030137   | -7.9e-08  | -1.0e-10  | -2.1e-09  | |57      | .874527   | .095336   | .030137   | -1.4e-07  | 2.2e-09   | -9.2e-09  | |58      | .874527   | .095336   | .030137   | 2.2e-09   | 1.9e-09   | -3.6e-09  | |59      | .874527   | .095336   | .030137   | 7.4e-08   | -1.2e-09  | 4.7e-09   | |60      | .874527   | .095336   | .030137   | 3.4e-08   | -1.2e-09  | 3.4e-09   | |61      | .874527   | .095336   | .030137   | -3.4e-08  | -1.7e-10  | -7.8e-10  | |62      | .874527   | .095336   | .030137   | -3.0e-08  | 9.9e-10   | -2.8e-09  | |63      | .874527   | .095336   | .030137   | 4.1e-09   | 2.5e-10   | -4.0e-10  | |64      | .874527   | .095336   | .030137   | 2.2e-08   | -3.1e-10  | 1.2e-09   | |65      | .874527   | .095336   | .030137   | 5.4e-09   | -4.3e-10  | 9.8e-10   | |66      | .874527   | .095336   | .030137   | -9.4e-09  | 1.4e-10   | -4.9e-10  | |67      | .874527   | .095336   | .030137   | -8.4e-09  | 2.2e-10   | -6.9e-10  | |68      | .874527   | .095336   | .030137   | 2.9e-09   | 7.7e-11   | -8.8e-11  | |69      | .874527   | .095336   | .030137   | 5.8e-09   | -1.5e-10  | 4.6e-10   | |70      | .874527   | .095336   | .030137   | 1.1e-09   | -6.3e-11  | 1.9e-10   | |71      | .874527   | .095336   | .030137   | -3.5e-09  | 3.0e-11   | -1.6e-10  | |72      | .874527   | .095336   | .030137   | -1.8e-09  | 7.6e-11   | -2.1e-10  | |73      | .874527   | .095336   | .030137   | 1.2e-09   | -6.5e-12  | 4.0e-11   | |74      | .874527   | .095336   | .030137   | 1.7e-09   | -3.2e-11  | 1.2e-10   | |75      | .874527   | .095336   | .030137   | -1.3e-10  | -2.2e-11  | 4.2e-11   | |76      | .874527   | .095336   | .030137   | -1.0e-09  | 1.9e-11   | -6.8e-11  | |77      | .874527   | .095336   | .030137   | -4.0e-10  | 1.4e-11   | -4.2e-11  | |78      | .874527   | .095336   | .030137   | 4.9e-10   | 2.8e-13   | 1.5e-11   | |79      | .874527   | .095336   | .030137   | 3.9e-10   | -1.3e-11  | 3.7e-11   | |80      | .874527   | .095336   | .030137   | -9.5e-11  | -2.0e-12  | 1.7e-12   | |81      | .874527   | .095336   | .030137   | -3.0e-10  | 4.3e-12   | -1.8e-11  | |82      | .874527   | .095336   | .030137   | -4.4e-11  | 5.2e-12   | -1.1e-11  | |83      | .874527   | .095336   | .030137   | 1.4e-10   | -2.2e-12  | 8.1e-12   | |84      | .874527   | .095336   | .030137   | 1.0e-10   | -2.7e-12  | 8.6e-12   | |85      | .874527   | .095336   | .030137   | -5.3e-11  | -8.2e-13  | 1.0e-13   | |86      | .874527   | .095336   | .030137   | -7.4e-11  | 2.1e-12   | -6.2e-12  | |87      | .874527   | .095336   | .030137   | -6.2e-12  | 7.2e-13   | -1.8e-12  | |88      | .874527   | .095336   | .030137   | 4.7e-11   | -4.8e-13  | 2.4e-12   | |89      | .874527   | .095336   | .030137   | 2.0e-11   | -1.0e-12  | 2.6e-12   | |90      | .874527   | .095336   | .030137   | -1.7e-11  | 1.7e-13   | -7.4e-13  | |91      | .874527   | .095336   | .030137   | -2.2e-11  | 4.4e-13   | -1.6e-12  | |92      | .874527   | .095336   | .030137   | 3.6e-12   | 2.6e-13   | -4.3e-13  | |93      | .874527   | .095336   | .030137   | 1.3e-11   | -2.9e-13  | 9.5e-13   | |94      | .874527   | .095336   | .030137   | 4.3e-12   | -1.7e-13  | 5.0e-13   | |95      | .874527   | .095336   | .030137   | -7.0e-12  | 2.0e-14   | -2.6e-13  | |96      | .874527   | .095336   | .030137   | -4.7e-12  | 1.7e-13   | -4.9e-13  | |97      | .874527   | .095336   | .030137   | 1.7e-12   | 1.0e-14   | 1.8e-14   | |98      | .874527   | .095336   | .030137   | 4.0e-12   | -6.1e-14  | 2.5e-13   | |99      | .874527   | .095336   | .030137   | 2.7e-13   | -6.3e-14  | 1.3e-13   | |100     | .874527   | .095336   | .030137   | -2.0e-12  | 3.5e-14   | -1.2e-13  | +--------------------------------------------------------------------------------+ (1) irfname = cmam, impulse = garchm, and response = garchm (2) irfname = cmam, impulse = cmavol, and response = garchm (3) irfname = cmam, impulse = cmaoi, and response = garchm 127    

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