Modelling the Asymmetric Volatility in Hog Prices in Taiwan: The Impact of Joining the WTO

Transcription

1 Modelling he Asymmeric Volailiy in Hog Prices in Taiwan: The Impac of Joining he WTO Chia-Lin Chang Deparmen of Applied Economics Naional Chung Hsing Universiy Biing-Wen Huang Deparmen of Applied Economics Naional Chung Hsing Universiy Meng-Gu Chen Deparmen of Applied Economics Naional Chung Hsing Universiy Michael McAleer Deparmen of Quaniaive Economics Compluense Universiy of Madrid Revised: March 2009 * Corresponding auhor: Chia-Lin Chang, Deparmen of Applied Economics Naional Chung Hsing Universiy Taichung, 250 Kuo Kuang Road, Naional Chung Hsing Universiy Taichung 402, Taiwan, changchialin@nchu.edu.w, Tel: +886 (04) ex 309. Fax: +886(04)

2 Absrac The hog indusry, where prices are deermined according o an aucion sysem, is of vial imporance o he agriculural indusry in Taiwan by providing significan producion and employmen. In paricular, here were significan impacs on daily hog prices in he periods before, during and afer joining he WTO, which we will refer o as periods of anicipaion, adjusmen and selemen. The purpose of he paper is o model he growh raes and volailiy in daily hog prices in Taiwan from 23 March 1999 o 30 June 2007, which enables an analysis of he effecs of joining he WTO. The paper provides a novel applicaion of financial volailiy models o agriculural finance. The empirical resuls have significan implicaions for risk managemen and policy consideraions in he agriculural indusry in Taiwan, especially when significan srucural changes, such as joining he WTO, are concerned. The hree sub-samples relaing o he period before, during and afer joining he WTO display significanly differen volailiy persisence, namely symmery, asymmery bu no leverage, and leverage, respecively, whereby negaive shocks increase volailiy bu posiive shocks of a similar magniude decrease volailiy. Keywords and phrases: Hog prices, joining he WTO, condiional volailiy models, asymmery, leverage, momen condiions. JEL Classificaions: Q14, G18,G32 2

3 1. Inroducion Time-varying volailiy in agriculural commodiy prices, such as hog prices, usually accompanies riskiness in he raes of growh (or reurns). How o capure he paern or characerisics of volailiy is of concern o farmers. Under he World Trade Organizaion (WTO) regulaions, direc price suppor programs of agriculural auhoriies have had o be progressively eliminaed, so ha farm prices are essenially deermined by he marke. Therefore, he volailiy associaed wih prices imposes significan pressures on agriculural producers. Price changes are associaed wih volailiy and risk. If agriculural commodiy prices have predicable ime-varying volailiy, hey can be analysed using recenly developed financial economeric mehods ha incorporae imporan aspecs of opimal porfolio managemen. McAleer (2008) explains why ime-varying volailiy can be useful in areas such as environmenal finance and ourism finance. Similar argumens can be used for applicaions in agriculural finance. Volailiy from high frequency daa can be aggregaed, whereas aggregaed daa a low frequencies ypically display no volailiy, hereby enabling he predicion of risk associaed wih he imposiion of agriculural axes. Dynamic confidence inervals can also be compued. Moreover, modelling volailiy permis an analysis of he asymmeric and leveraged responses of prices and associaed commodiy inflaion raes o posiive and negaive shocks of equal magniude. In his way, commodiy prices behave like financial sock prices, so ha he heory of finance can be applied direcly o agriculural commodiy prices. In order o assis farmers o predic he volailiy in prices, several relaed issues need o be invesigaed. This paper focuses on he asymmeric response of volailiy o posiive and negaive shocks o prices and reurns because he sochasic propery of agriculural commodiy prices migh no be symmeric. The empirical models examined in his paper will evaluae hog prices, heir reurns and associaed volailiy in Taiwan. 3

4 The hog indusry is he bigges indusry in he livesock secor in Taiwan. According o he Agriculural Saisics Yearbook in Taiwan, he quaniy of producion was 930,609 ons in 2006, and is value amouned o NT$ 55.5 billion, which is 14.72% of oal agriculural producion. There were 12,508 hog farms in 2006 and here were around 7 million hogs on farms a he end of he year. Furhermore, he feed indusry is closely relaed o he hog indusry as 45.5% of feed producs, namely 7.7 million ons, were provided for hog producion in The raw maerial for feed comes from grain impors. For example, he impored quaniy of corn was around 5 million ons in 2006, wih he main source of impors being he USA. Thus, he hog indusry no only plays an imporan role in Taiwan s agriculural secor, bu i is also closely relaed o he grain expors counry. Wih regard o he developmen of he hog indusry in Taiwan, farmers ypically raised hogs as a secondary source of income prior o he 1960s, where he number of hogs a he end of he year was around 3 million heads. Since producion echnology has gradually improved over ime and agriculural auhoriies encouraged farmers o raise hogs, he hog indusry became more commercialized in he 1970s and hereafer developed quickly. The oal number of hogs increased from 2.9 million heads o 4.8 million heads, bu he number of hog farms decreased from 583,127 o 175,178 during he period In he 1980s, he indusry prospered, expors expanded rapidly, and he oal number of hogs a he end of he year increased o hisorical higher levels of around 10 million heads in Unil he mid-1990s, he hog indusry was sill developing seadily and expors were increasing, wih a peak of around US$ 1.5 billion being reached in The indusry was also he larges exporer of agriculural commodiies. Unforunaely, in 1997 he oubreak of foo and mouh disease caused significan damage o his indusry and resuled in resricion of expors. The oal number of hogs a he end of he year decreased o 8 million heads in 1997, and he value of hog producion decreased dramaically from NT$ 88.6 billion o NTS 44.7 billion in Subsequenly, he 4

5 producion of hogs has adjused o concenrae on he domesic marke from he lae 1990s o he presen. Afer Taiwan applied o join he WTO in he 1990s, impor resricions on pork, excep for pork bellies and some offal, were gradually deregulaed for purposes of meeing rade liberalizaion requiremens. Pork impors are primarily from he USA and he quaniy impored annually flucuaes significanly, such as 19,507 ons in 2002, 40,150 ons in 2004, and 18,546 ons in 2006, depending on marke facors. Afer Taiwan joined he WTO in 2002, pork bellies and some offal were deregulaed, based on he quoa sysem during , and free impors were permied from In order o confron he serious siuaion, paricularly in he planning sages of Taiwan s joining he WTO, he governmen encouraged inefficien farmers o move away from hog producion by providing subsidies. Consequenly, he oal number of hog farms decreased from 20,454 o during However, he average raising scale was enlarged from 390 o 520 heads during he same period, and was hen increased o 565 heads in This implies ha he compeiiveness of he hog indusry in Taiwan was srenghened during he period ha Taiwan was applying o join he WTO. The hog farm price is deermined by an aucion sysem in he local wholesale markes. There are 23 local hog wholesale markes in Taiwan. Farmers may ranspor heir hogs o any markes according o he price in each marke, which is accordingly very similar o a perfecly compeiive marke. As he consumpion of pork in Taiwan has no changed markedly over ime, having sabilized a around 40 kg per capia per year over he las decade, his indicaes ha he demand side for hogs is relaively seady. Therefore, hog farm prices are primarily affeced by domesic supply and by hog impors. The liberalizaion of pork impors has complicaed he analysis of he facors ha deermine hog farm prices. Hog farm prices have displayed significan flucuaions, varying from NT$ per kg in 1999 o NT$ per kg in 2001, and hen o NT$ per kg in The volailiy of hog farm prices is of serious concern o farmers because i is direcly relaed o reurns and heir associaed risk. 5

6 Despie farmers aking noice of he volailiy in daily hog prices, he agriculural auhoriies in Taiwan also pay srong aenion o hog farm price informaion. In order o assis farmers o overcome he impacs of impored livesock producs, he agriculural auhoriies esablished he Naional Animal Indusry Foundaion (NAIF) in One of he main asks of he NAIF is o evaluae hog price informaion as he basis for sraegic guidance and operaional assisance. When he price is higher han he hisorical average, he NAIF will announce an early warning o urge farmers no o raise oo many pigs. On he oher hand, when he price is considerably lower han he hisorical average, he NAIF will provide some indirec suppor programs o raise prices o an accepable level. For example, he NAIF migh provide subsidies for framers o encourage hem o sop raising pigs emporarily, or for processing plans o sock pork in warehouses. Such measures will reduce he supply of pork, so ha hog farm prices would be expeced o recover. Consequenly, he volailiy in hog farm prices would be affeced. Imporanly, he volailiy in such prices migh be expeced o be ime-varying, in which case hey can be modelled and prediced using financial economeric mehods. Wih regard o he volailiy in he prices of agriculural commodiies, Langley e al. (2000) analyzed he relaionship beween inernaional financial volailiy in 1997 and agriculural commodiy rade in Thailand. The GARCH(1,1) condiional volailiy model was used o esimae he variance of he exchange rae as a measure of financial risk (or volailiy), and i was found ha here were srong impacs of exchange rae risk on poulry, hough no on aggregae, expors. Lence and Hayes (2002) examined he significan volailiy in U.S. corn, soybean and whea prices during and is connecion o he Federal Agriculural Improvemen and Reform (FAIR) Ac of A dynamic hree-commodiy raional expecaions sorage model was used o simulae he scenarios of he pre-fair and FAIR regimes, and i was deermined empirically ha he grain price volailiy was no due o FAIR. Shively (2001) invesigaed he price hreshold and volailiy in an African maize marke. The resuls from he ARCH and hreshold 6

7 ARCH condiional volailiy models suggesed ha he price volailiy was subjec o a hreshold, such ha larger price increases produced greaer subsequen volailiy. Oher research has concenraed on he volailiy in agriculural fuures prices. Jin and Frechee (2004) analysed he presence of fracional inegraion o explain he volailiy of U.S. agriculural fuures prices, and showed ha he FIGARCH(1,d,1) fracional inegraion model was superior empirically o GARCH (1,1). Koekebakker and Lien (2004) analyzed he U.S. whea fuures prices for ime-varying volailiy wih a jump diffusion process, and found ha he price volailiy of whea opions was affeced differenially by seasonal, mauriy and jump effecs. Egelkrau e al. (2007) examined he erm srucure of volailiy and showed ha he implied forward volailiy was successful in explaining he realized volailiy in he corn opions marke. ARCH and GARCH condiional volailiy models have been applied widely o accommodae he ime-varying heeroskedasiciy ha is associaed wih he riskiness in price movemens in he hog marke. For example, Chang (1999) applied he ARCH model using monhly daa in Taiwan o examine changes in hog farm prices. The empirical resuls showed ha hog farm prices displayed ime-varying condiional heeroskedasiciy, which implies ha hog farmers face price volailiy during he producion process. Lien and Hennessy (2007) used he AR (1)-GARCH(1,1) model wih weekly daa for Saskachewan, Canada, o esimae he hog spo price sochasic process and generae simulaed prices. These prices were used o evaluae wheher farmers received benefis from he shor run hog loan program of Schroeer and Azzam (1991) analyzed he effecs of U.S pork price uncerainy on farm wholesale margins. The ARCH(2) model was used o esimae he condiional forecas variance, and he resuls indicaed ha he oupu price risk componen significanly affeced he markeing margins. Yang and Brorsen (1992) esed daily cash prices wih daily daa for nine commodiies, including pork bellies, for normaliy and nonlinear independence. Their conclusions showed ha he GARCH model was superior 7

8 o he alernaive considered, hereby forming he basis for heoreical and applied work in agriculural finance. To dae, any discussions in he agriculural finance lieraure regarding he shor and long run persisence of shocks, and he possibly asymmeric effecs of posiive and negaive shocks of similar magniude on he volailiy in agriculural prices, has been scarce. This suggess ha he issue of asymmeric volailiy remains relaively unexplored. If hog farmers and he hog indusry could undersand he informaion conen in models of hog prices, growh raes and heir associaed volailiy, hey could underake profiable and opimal risk managemen sraegies. The purpose of he paper is o model he prices, growh raes and heir respecive volailiies in daily hog prices in Taiwan from 23 March 1999 o 30 June A novel applicaion of financial volailiy models o agriculural finance is given, which should be relevan for he analysis of oher agriculural commodiies in differen counries. The empirical resuls show ha he ime series of hog prices and heir logarihms are nonsaionary, bu ha heir log differences (or growh raes) are saionary. In addiion, he esimaed symmeric and asymmeric condiional volailiy models, specifically he GARCH, GJR and EGARCH models, all fi he daa exremely well. The empirical second momen and log-momen condiions also suppor he saisical adequacy of boh he esimaed symmeric and asymmeric condiional volailiy models. The remainder of he paper is organized as follows. Secion 2 presens he daa for daily hog prices in Taiwan, performs a es of srucural change across hree regimes associaed wih he planning, adjusmen and selemen sages of joining he WTO, and discusses he ime-varying volailiy. Secion 3 performs uni roo ess on he levels, logarihms and growh raes of daily hog prices. Secion 4 discusses alernaive condiional mean and condiional volailiy models for daily hog prices. The esimaed models and empirical resuls are discussed in Secion 5. Finally, some concluding remarks are given in Secion 6. 8

9 2. Daa The daa se comprises daily hog prices in Taiwan from 23 March 1999 o 30 June 2007, giving a oal of 2,024 observaions. The daa were obained from he websie of he Naional Animal Indusry Foundaion (NAIF) in Taiwan. Figures 1-3 plo he rends in daily hog prices (Y), he logarihm of daily hog prices (LY), and he firs difference (ha is, he log difference or growh rae) of daily hog prices (DLY), as well as he volailiy of he hree variables, where volailiy is defined as he squared deviaion from he sample mean. As shown in Figures 1 and 2, here has been a large decrease in daily hog prices, as well as in he logarihm of daily hog prices, during he period 23 June 1999 o 27 December 2001, a large increase in prices and log prices during he period 28 December 2001 o 6 Augus 2004, and hen a significan reducion in prices and log prices during he period 7 Augus 2004 o 30 June Furhermore, he series in levels and logarihms migh be saionary or nonsaionary, bu he log difference series is clearly saionary. As shown in Figure 3, here is clear volailiy persisence in daily hog prices for he log difference series. However, hog prices display volailiy ha would seem o be differen in various sub-sample periods. In paricular, here would seem o be greaer volailiy in hog prices for subsample 2 for 2001 o 2004 as compared wih sub-sample 1 for 1999 o 2001 and subsample 3 for 2004 o As described above, here would seem o be significan increasing and decreasing rends in he daily hog price and logarihmic hog price hroughou he sample period. These variaions in daily hog prices are likely o have been caused by Taiwan s decision o join he World Trade Organizaion (WTO) in 2002, whereby rade liberalizaion led o srikes in he domesic hog marke in Taiwan. Prominenly, he hree sub-samples described above correspond o he hree sages in erms of Taiwan joining he WTO. For 9

10 his reason, we will inerpre sub-sample 1 as he planning sage of Taiwan joining he WTO, sub-sample 2 as he adjusmen period immediaely afer Taiwan joined he WTO, and sub-sample 3 as he selemen sage. Table 1 presens he resuls of he Chow breakpoin ess of he null hypohesis of no srucural change across he hree regimes, namely 1999/3/ /12/27, 2001/12/ /8/6 and 2004/8/7-2007/6/30. As he iming of he srucural change is presumed o be known, i is no necessary o esimae he daes of he breakpoins (for furher deails, see Bai and Perron (1998, 2003)). Boh he F and likelihood raio ess rejec he null hypohesis a he 5% level of significance, which lends suppor o he view ha joining he WTO led o srucural change. In he nex secion, we analyze he presence of a sochasic rend by applying uni roo ess before modelling he ime-varying volailiy ha would seem o be presen in he levels, logarihms and log differences (or growh raes) in he respecive series. 3. Uni Roo Tess I is well known ha radiional uni roo ess, primarily hose based on he classic mehods of Dickey and Fuller (1979, 1981) and Phillips and Perron (1988), suffer from low power and size disorions. However, hese shorcomings have been overcome by modificaions o he esing procedures, such as he mehods proposed by Perron and Ng (1996), Ellio, Rohenberg and Sock (1996), and Ng and Perron (2001). The modified uni roo ess given by MADF GLS and MPP GLS were applied o he ime series of daily hog prices in Taiwan. In essence, hese ess use GLS de-rended daa and he modified Akaike informaion crierion (MAIC) o selec he opimal runcaion lag. The asympoic criical values for boh ess are given in Ng and Perron (2001). The resuls of he uni roo ess are obained from he economeric sofware package EViews 5.0, and are repored in Tables 2a-2d. Table 1 shows he resuls of uni 10

11 roo ess for he full sample period, while Tables 2b-2d show he resuls for each of he hree sub-sample periods, respecively. As shown in Table 1, he null hypohesis of a uni roo is no rejeced for he levels of daily hog prices in he models wih a consan and wih a consan and rend as he deerminisic erms. A similar resul holds for he logarihms of daily hog prices, where boh he MADF GLS and MPP GLS ess do no rejec he null hypohesis of a uni roo for he models wih a consan and wih a consan and rend. However, for he series in log differences (or growh raes), he null hypohesis of a uni roo is rejeced for boh specificaions using boh he MADF GLS and MPP GLS ess. Overall, he null hypohesis of a uni roo is no rejeced for he levels or logarihms of daily hog prices, bu is rejeced for he growh rae of daily hog prices. Similar resuls of he uni roo ess are found in each of he hree sub-samples. As shown in he uni roo ess, he empirical resuls srongly sugges he use of growh raes in daily hog prices in Taiwan o esimae alernaive univariae condiional mean and condiional volailiy models simulaneously. For his reason, condiional mean and condiional volailiy models will be esimaed in Secion 5 using only he growh rae of daily hog prices in Taiwan for various sub-samples of he daa. 4. Condiional Mean and Condiional Volailiy Models The alernaive ime series models o be esimaed for he condiional means of he daily hog prices, as well as heir respecive condiional volailiies, are discussed below. As Figures 1-3 illusrae, daily hog prices and he logarihm of daily hog prices do no show persisence in volailiy, whereas he firs differences (ha is, he log difference or growh rae) of daily hog prices in Taiwan show periods of persisen high volailiy from 23 June 1999 o 27 December 2001, followed by relaively low volailiy from 23 June 1999 o 27 December 2001, and hen by relaively high volailiy from 28 December 2001 o 6 Augus One implicaion of his persisen ime-varying volailiy is ha he assumpion of condiionally homoskedasic residuals would seem o be inappropriae for sensible empirical analysis. 11

12 For a wide range of financial daa series, ime-varying condiional variances can be explained empirically hrough he auoregressive condiional heeroskedasiciy (ARCH) model of Engle (1982). When he ime-varying condiional variance has boh auoregressive and moving average componens, his leads o he generalized ARCH(p,q), or GARCH(p,q), model of Bollerslev (1986). The lag srucure of he appropriae GARCH model can be chosen by informaion crieria, such as hose of Akaike and Schwarz, alhough i is very common o impose he widely esimaed GARCH(1,1) specificaion in advance. In he seleced condiional volailiy model, he residual series should follow a whie noise process. Bollerslev e al. (1992) documen he adequacy of he GARCH(1,1) specificaion. Li e al. (2002) provide an exensive review of recen heoreical resuls for univariae and mulivariae ime series models wih condiional volailiy errors. McAleer (2005) reviews a wide range of univariae and mulivariae, condiional and sochasic, models of financial volailiy. McAleer e al. (2007) discuss recen developmens in modeling univariae asymmeric volailiy, while McAleer e al. (2008) develop he regulariy condiions and esablish he asympoic properies of a general model of imevarying condiional correlaions. As shown in Figure 3, he log difference daily hog price daa display ime-varying volailiy persisence, so i is naural o esimae alernaive condiional volailiy models. Consider he saionary AR(1)-GARCH(1,1) model for daily hog prices in Taiwan (or heir growh raes, as appropriae), y : y = φ + φ + ε φ 1 (1) 1 2 y 1, 2 < for = 1,..., n, where he shocks (or movemens in daily hog prices) are given by: ε = η h, h = ω + αε η ~ iid (0,1) βh 1, (2) 12

13 and ω > 0, α 0, β 0 are sufficien condiions o ensure ha he condiional variance h > 0. The AR(1) model in equaion (1) can easily be exended o univariae or mulivariae ARMA(p,q) processes (for furher deails, see Ling and McAleer (2003a)). In equaion (2), he ARCH (or α ) effec indicaes he shor run persisence of shocks, while he GARCH (or β ) effec indicaes he conribuion of shocks o long run persisence (namely, α + β ). The saionary AR(1)-GARCH(1,1) model can be modified o incorporae a non-saionary ARMA(p,q) condiional mean and a saionary GARCH(r,s) condiional variance, as in Ling and McAleer (2003b). In equaions (1) and (2), he parameers are ypically esimaed by he maximum likelihood mehod o obain Quasi-Maximum Likelihood Esimaors (QMLE) in he absence of normaliy of η, he condiional shocks (or sandardized residuals). The condiional log-likelihood funcion is given as follows: n l = 1 = 1 n 2 log h + ε 2 = 1 h. The QMLE is efficien only if η is normal, in which case i is he MLE. When η is no normal, adapive esimaion can be used o obain efficien esimaors, alhough his can be compuaionally inensive. Ling and McAleer (2003b) invesigaed he properies of adapive esimaors for univariae non-saionary ARMA models wih GARCH(r,s) errors. The exension o mulivariae processes is complicaed. As he GARCH process in equaion (2) is a funcion of he uncondiional shocks, he momens of ε need o be invesigaed. Ling and McAleer (2003a) showed ha he QMLE for GARCH(p,q) is consisen if he second momen of ε is finie. For GARCH(p,q), Ling and Li (1997) demonsraed ha he local QMLE is asympoically normal if he fourh momen of ε is finie, while Ling and McAleer (2003a) proved ha he global QMLE is asympoically normal if he sixh momen of ε is finie. The well 13

14 known necessary and sufficien condiion for he exisence of he second momen of ε for GARCH(1,1) is α + β < 1. As discussed in McAleer e al. (2007), Elie and Jeanheau (1995) and Jeanheau (1998) esablished ha he log-momen condiion was sufficien for consisency of he QMLE of a univariae GARCH(p,q) process (see Lee and Hansen (1994) for he proof in he case of GARCH(1,1)), while Boussama (2000) showed ha he log-momen condiion was sufficien for asympoic normaliy. Based on hese heoreical developmens, a sufficien condiion for he QMLE of GARCH(1,1) o be consisen and asympoically normal is given by he log-momen condiion, namely 2 E (log( αη + β)) < 0. (3) The log-momen condiion for he GARCH(1,1) model involves he expecaion of a funcion of a random variable and unknown parameers. Alhough he sufficien momen condiions for consisency and asympoic normaliy of he QMLE for he univariae GARCH(1,1) model are sronger han heir log-momen counerpars, he second momen condiion is more sraighforward o check in pracice. In pracice, he log-momen condiion in equaion (3) would be esimaed by he sample mean, wih he parameers α and β, and he sandardized residual, η, being replaced by heir QMLE counerpars. The effecs of posiive shocks (or upward movemens in daily hog prices) on he condiional variance, h, are assumed o be he same as negaive shocks (or downward movemens in daily hog prices) of a similar magniude in he symmeric GARCH model. In order o accommodae asymmeric behaviour, Glosen, Jagannahan and Runkle (1992) proposed he GJR model, for which GJR(1,1) is defined as follows: h = ( ω + α + γi( η )) ε βh, (4) where ω > 0, α 0, α + γ 0, β 0 are sufficien condiions for h > 0, and I η ) is an indicaor variable ha is defined by: ( 14

15 1, I( η ) = 0, ε < 0 ε 0 as η has he same sign as ε. The indicaor variable differeniaes beween posiive and negaive shocks of equal magniude, so ha asymmeric effecs in he daa are capured by he coefficien γ. For financial daa, i is ypically expeced ha γ 0 because negaive shocks increase risk by increasing he deb o equiy raio, bu his inerpreaion need no hold for hog price daa in he absence of a similar inerpreaion in erms of risk. The asymmeric effec, γ, measures he conribuion of shocks o boh shor run γ γ persisence, α +, and o long run persisence, α + β Ling and McAleer (2002a) showed ha he regulariy condiion for he exisence of he second momen for GJR(1,1) under symmery of η is given by: 1 α + β + γ < 1, (5) 2 while McAleer e al. (2007) showed ha he weaker log-momen condiion for GJR(1,1) was given by: 2 E (ln[( α + γi( η )) η + β ]) < 0, (6) which involves he expecaion of a funcion of a random variable and unknown parameers. An alernaive model o capure asymmeric behaviour in he condiional variance is he Exponenial GARCH (EGARCH(1,1)) model of Nelson (1991), namely: log h ω, β < 1 (7) = + α η 1 + γη 1 + β log h 1 where he parameers α, β and γ have differen inerpreaions from hose in he GARCH(1,1) and GJR(1,1) models. 15

16 As noed in McAleer e al. (2007), here are some imporan differences beween EGARCH, on he one hand, and GARCH and GJR, on he oher, as follows: (i) EGARCH is a model of he logarihm of he condiional variance, which implies ha no resricions on he parameers are required o ensure h > 0 ; (ii) momen condiions are required for he GARCH and GJR models as hey are dependen on lagged uncondiional shocks, whereas EGARCH does no require momen condiions o be esablished as i depends on lagged condiional shocks (or sandardized residuals); (iii) Shephard (1996) observed ha β < 1 is likely o be a sufficien condiion for consisency of QMLE for EGARCH(1,1); (iv) as he sandardized residuals appear in equaion (7), β < 1 would seem o be a sufficien condiion for he exisence of momens; and (v) in addiion o being a sufficien condiion for consisency, β < 1 is also likely o be sufficien for asympoic normaliy of he QMLE of EGARCH(1,1). Furhermore, EGARCH capures asymmeries differenly from GJR. The parameers α and γ in EGARCH(1,1) represen he magniude (or size) and sign effecs of he sandardized residuals, respecively, on he condiional variance, whereas α and α + γ represen he effecs of posiive and negaive shocks, respecively, on he condiional variance in GJR(1,1). Asymmeric effecs are capured by he coefficien γ, hough in a differen manner, in he EGARCH and GJR models. The EGARCH model is also capable of capuring leverage hrough he deb o equiy raio, whereby negaive shocks increase volailiy bu posiive shocks decrease volailiy. 5. Esimaed Models I is well known ha he esimaes of volailiy will depend on he adequacy of he specificaion of he condiional mean equaion, which yields he sandardized residuals. A relaed issue is he effec of ignoring srucural change in he condiional mean of he esimaes of he condiional variance (see, for example, Bai and Perron (1998, 2003)). The effecs of misspecifying he condiional mean on he esimaes of he condiional volailiy will be analyzed below. Boh he asympoic sandard errors, as well as he 16

17 robus sandard errors of Bollerslev and Wooldridge (1992), are presened. In virually all cases, he asympoic sandard errors are smaller han heir robus counerpars. The esimaed condiional mean and condiional volailiy models are given in Tables 3-6. As shown in he uni roo ess, he levels and logarihms of daily hog prices are no saionary, bu he log differences (or growh raes) are saionary. For his reason, only he growh raes and heir associaed volailiy will be modelled for he full sample period, which is given in Table 3, and for he hree sub-samples, which are given in Tables 4-6. These empirical resuls are suppored by he esimaes of he lagged dependen variables in he esimaes of equaion (1), wih all he coefficiens of he lagged dependen variable being less han one in each of he esimaed hree models for he growh raes of daily hog prices. This is consisen wih he empirical finding ha he log difference (or growh rae) is saionary. As he second momen condiion is less han uniy in all cases, i follows ha he weaker log-momen condiion is less han zero in all cases (see Tables 3-6). Thus, he regulariy condiions are saisfied, he QMLE are consisen and asympoically normal, and inferences are valid. The EGARCH(1,1) model is based on he sandardized residuals, so he regulariy condiion is saisfied if β < 1, and hence he QMLE would seem o be consisen and asympoically normal (see, for example, McAleer a al. (2007)). As shown in Table 3, in he full sample esimaion, he GARCH(1,1) esimaes for he log differen (or growh rae) of daily hog prices in Taiwan sugges ha he shor run persisence of shocks is 0.274, while he long run persisence is As he second momen condiion, α + β < 1, is saisfied, he log-momen condiion is also saisfied. Therefore, he symmeric GARCH(1,1) esimaes are saisically significan. 17

18 If posiive and negaive shocks of a similar magniude o daily hog prices in Taiwan are reaed asymmerically, his can be evaluaed using he GJR(1,1) model. The asymmery coefficien is found o be posiive and significan for daily hog prices, namely 0.434, which indicaes ha decreases in prices increase volailiy. This is a consisen empirical oucome o ha found in virually all cases in empirical finance, where he negaive shocks increase risk (or volailiy). Moreover, he shor run persisence of posiive and negaive shocks are esimaed o be and 0.538, respecively, and he long run persisence of shocks is esimaed o be for he log difference in daily 1 prices of hogs. As he second momen condiion, α + β + γ < 1, is saisfied, he logmomen condiion is also saisfied, and he asymmeric GJR(1,1) esimaes are 2 saisically significan. The inerpreaion of he EGARCH model is in erms of he logarihm of volailiy. As shown in Table 3, each of he EGARCH(1,1) esimaes is saisically significan. The coefficien of he lagged dependen variable, β, is esimaed o be and significan, which suggess ha all momens exis, wih he esimaes likely o be consisen and asympoically normal. Overall, he size effecs of he sandardized residuals, α, have a posiive and significan impac on he condiional variances. However, he sign effec of he sandardized residuals, γ, is negaive and significan. Furhermore, he absolue vale of γ is lower han for he corresponding α esimaes, which suggess ha he sign effecs have smaller impacs han he size effecs on he condiional variances. However, as he esimae of γ is significan, asymmery is eviden, as in he case of he GJR model, bu here is no leverage effec, whereby negaive shocks increase volailiy bu posiive shocks of a similar magniude decrease volailiy. These empirical resuls are similar o a wide range of financial sock marke prices, so ha he heory of finance is direcly applicable o hog prices. As given in Figures 1-3, he rends and volailiies in daily hog prices (as well as in heir logarihms) seem o have experienced wo noiceable srucural changes during 18

19 he sample period. As has already been menioned, hese changes would seem o have arisen from Taiwan s decision o join he World Trade Organizaion (WTO) in 2002, when he naional governmen delegaed effors o proec domesic hog producers agains lower impored hog prices. These acions may have alered he rends in he hog prices, as well as heir associaed volailiy, in hose periods. In order o invesigae he effecs of joining he WTO, alernaive models of he growh raes and heir associaed volailiy were esimaed for hree sub-samples before, during and afer Taiwan joined he WTO, namely sub-sample 1 from 23 June 1999 o 27 December 2001, sub-sample 2 from 28 December 2001 o 6 Augus 2004, and sub-sample 3 from 7 Augus 2004 o 30 June 2007, respecively. The esimaes for he hree sub-sample periods are given separaely in Tables 4-6. Table 4 shows he saisical resuls for he GARCH(1,1), GJR(1,1) and EGARCH(1,1) models for sub-sample 1. Regarding he condiional mean esimaes of he growh rae of daily hog prices, he esimaes are predicable for he AR(1) condiional mean models associaed wih he GARCH (1,1) and GJR (1,1) volailiy models, bu no for he EGARCH (1,1) model. This is slighly differen from he esimaes for he full sample period, in which he growh raes were predicable for all hree models. Regarding he condiional volailiy esimaes for sub-sample 1, i is clear from he esimaes ha volailiy has ime-varying persisence, wih an esimaed shor run persisence of shocks of and he esimaed long run persisence of shocks of for he symmeric GARCH (1,1) model As he second momen condiion, α + β < 1, is saisfied, he log-momen condiion is also saisfied, and he symmeric GARCH(1,1) esimaes are saisically significan. For he GJR(1,1) model, boh he second momen and log-momen condiions are saisfied. The asympoic -raio for he γ esimae is posiive bu no significan, suggesing ha a negaive shock will no affec risk (or volailiy) any differenly from a posiive shock of equal magniude. Furhermore, he shor run persisence of posiive shocks 0.275, while he shor run persisence of negaive shocks is These resuls 19

20 for GJR(1,1) sugges ha boh posiive and negaive shocks have significanly and similarly posiive impacs on volailiy. The inerpreaion of he EGARCH model is in erms of he logarihm of volailiy in sub-sample 1. As shown in Table 4, each of he EGARCH(1,1) esimaes is saisically significan. Moreover, he coefficien of lagged log volailiy, β, is esimaed o be and significan, which suggess ha all momens exis, wih he esimaes likely o be consisen and asympoically normal. Overall, he size effecs of he sandardized residuals, α, have posiive and significan impacs on he condiional variances, bu he sign effec of he sandardized residuals, γ, is negaive bu no significan. However, he absolue vale of γ, a 0.005, is considerably lower han for he corresponding α esimae (0.490), which indicaes ha he sign effecs have a much smaller, if any, impac han he size effecs on he condiional variances. Overall, on he basis of he hree condiional volailiy models, here is a symmeric effec on volailiy wih regard o posiive and negaive shocks of equal magniude. Table 5 shows he saisical resuls for he GARCH(1,1), GJR(1,1) and EGARCH(1,1) models for sub-sample 2. Wih regard o he condiional mean esimaes of he growh rae of daily hog prices, he esimaes are significanly predicable for each of he hree models. Moreover, he condiional means for he hree models in sub-sample 2 are much sronger as compared wih hose in sub-sample 1. Indeed, he magniudes of he condiional means in sub-sample 2 are very similar o hose of he full sample. These resuls would seem o sugges ha sub-sample 2 may play a dominan role for predicing he growh rae of daily hog prices in Taiwan. Regarding he condiional volailiy esimaes for sub-sample 2, he second momen condiion, α + β < 1, is saisfied and hence he log-momen condiion is also saisfied. Furhermore, he esimae for he shor run persisence of shocks, α, is 0.363, which is larger han he corresponding esimae for sub-sample 1, whereas he long run 20

21 persisence of for he GARCH (1,1) model is relaively smaller for sub-sample 2 han for sub-sample 1. The β esimae is significan and posiive, bu is magniude is now considerably smaller. These resuls for GARCH(1,1) sugges ha he shor run persisence of shocks has a more significan impac on he condiional variance in he adjusmen sage (sub-sample 2), whereas he impac of long run persisence has a more significan effec on he condiional variance in he planning sage (sub-sample 1). These oucomes are he opposie of hose given in Table 4, in which here is a sronger long run persisence of shocks bu a weaker shor run persisence of shocks in sub-sample 1. Wih regard o he asymmeric effec, namely he γ coefficien for he GJR(1,1) model in sub-sample 2, Table 5 shows ha he esimae is posiive and significan. Moreover, he magniude of is much larger han he corresponding esimae in subsample 1 a These resuls suggess ha negaive shocks have a much sronger impac on he condiional variance han do posiive shocks of a similar magniude, and ha his effec is also sronger in sub-sample 2 han in sub-sample 1. Owing o he srong effec of negaive shocks in sub-sample 2, he shor run persisence of negaive shocks on he condiional variance, a 0.480, is much greaer han for posiive shocks of a similar magniude, a However, he shor run persisence of posiive shocks on he condiional variance is no as srong for sub-sample 2 as compared wih he corresponding effec for sub-sample 1. Furhermore, he long run persisence of shocks, a 0.662, in sub-sample 2 is much lower han ha in sub-sample 1, a Moreover, in comparison wih subsample 1, he magniude of he long run persisence of shocks is similar o ha for he full sample period. These resuls sugges ha he daa for sub-sample 2 can play a dominan role in evaluaing he effec of he long run persisence of shocks. Moreover, boh he second momen and log-momen condiion are saisfied for he GJR(1,1) model. The inerpreaion of he EGARCH model is in erms of he logarihm of volailiy for sub-sample 2. As shown in Table 5, each of he EGARCH(1,1) esimaes is 21

22 saisically significan. Moreover, he coefficien of he lagged dependen variable, β, is esimaed o be and significan, which suggess ha all momens exis. Furhermore, he size effecs of he sandardized residuals, α, have posiive and significan impacs on he condiional variances, and he sign effec of he sandardized residuals, γ, on he condiional variances is negaive and significan. Moreover, in comparison wih sub-sample 1, he impac of γ is larger in sub-sample 2, which suggess ha negaive shocks have a more significan impac in his period on he condiional variance. Overall, on he basis of he hree condiional volailiy models, here is an asymmeric effec on volailiy wih regard o posiive and negaive shocks of equal magniude. However, here is no leverage effec, whereby negaive shocks increase volailiy bu posiive shocks of a similar magniude decrease volailiy. Table 6 shows he saisical resuls for he GARCH(1,1), GJR(1,1) and EGARCH(1,1) models for sub-sample 3. In a comparaive perspecive, i is clear ha he condiional means, as well as he condiional volailiy for he growh raes of daily hog prices in he sub-sample 3, are vasly differen from he corresponding esimaes for subsamples 1 and 2. The condiional mean esimaes are only predicable for he GARCH (1,1) model, bu he effec of he condiional mean model for he GARCH(1,1) model is even lower han he esimaes for sub-sample 3. Regarding he condiional volailiy for sub-sample 3, he esimaes make i clear ha volailiy is persisen, wih a relaively small value of α, a 0.079, and a relaively large value of β, a 0.602, which are he esimaes of he conribuions of he shocks o long run persisence in he GARCH (1,1) model. However, in comparison wih he magniude of he coefficien of shor run persisence of shocks among he hree subsamples, sub-sample 3 shows he weakes impac of shor run persisence on he condiional variance. As he second momen condiion, α + β < 1, is saisfied, he logmomen condiion is also saisfied, and he symmeric GARCH(1,1) esimaes are saisically significan. 22

23 For he GJR(1,1) model, boh he second momen and log-momen condiions are boh saisfied. The asympoic -raio for he γ esimae in Table 6 is highly significan, suggesing ha negaive shocks increase risk (or volailiy) significanly in sub-sample 3 as compared wih posiive shocks of a similar magniude. Moreover, he magniude of he asymmeric effec, γ, a 0.473, is now much larger and more prominen han was observed in he oher sub-samples. These resuls imply ha negaive shocks sill have a srong impac on he condiional variance in he selemen period. The β esimae is significanly posiive, while he esimae of α is now negaive, hough insignifican. Overall, he shor run persisence of negaive shocks on he condiional variance is and he long run persisence of shocks is 0.563, which indicaes he weakes impac on he condiional variance among he various sub-samples. Furhermore, he second momen and log-momen condiions are saisfied for he GJR(1,1) model. The inerpreaion of he EGARCH model is in erms of he logarihm of volailiy for sub-sample 3. As shown in Table 6, each of he EGARCH(1,1) esimaes is saisically significan, and he coefficien of he lagged dependen variable, β, is esimaed o be and significan, which suggess ha all momens exis. Again, he size effecs of he sandardized residuals, α, have posiive and significan impacs on he condiional variances, while he sign effec of he sandardized residuals, γ, on he condiional variances is now negaive and significan. I is worh emphasizing ha he condiions for leverage in he EGARCH(1,1) model are saisfied, which suggess ha negaive shocks increase volailiy bu posiive shocks of a similar magniude decrease volailiy in he selemen period, namely sub-sample 3. Consequenly, he selemen sage of WTO enry has alered hog prices o behave jus like some financial sock marke prices. In a comparison of he esimaes for he hree sub-samples, i may be concluded ha he long run persisence of shocks in he planning period (ha is, sub-sample 1) 23

24 suggess a more significan impac on he condiional variance han in he oher wo subsamples. In addiion, he shor run persisence of shocks in he selemen period (ha is, sub-sample 3) suggess he weakes impac on he condiional variance among he hree sub-samples. Overall, he asymmeric effec is found o be significan for he GJR (1,1) model in wo of he hree sub-samples, while he effec of negaive shocks has ended o increase over he full sample period. However, in he asymmeric EGARCH(1,1) model, a leverage effec is observed only in he selemen period (ha is, sub-sample 3), whereas i is no significan in sub-period 1 and is significan, bu does no sugges he exisence of leverage effecs, in sub-sample 2. In summary, he adjusmen period (ha is, subsample 2) implies a dominan conribuing role for esimaing he impac of he shor run and long run persisence of shocks for he full sample period. In general, he QMLE for he GARCH(1,1), GJR(1,1) and EGARCH(1,1) models for he log differences (or growh rae) in daily hog prices in Taiwan are saisically adequae and have sensible inerpreaions. For he full sample period, in which any srucural changes are ignored, here is asymmery in volailiy for he GJR(1,1) and EGARCH(1,1) models, bu here is no presence of leverage effecs, whereby negaive shocks increase volailiy bu posiive shocks of a similar magniude decrease volailiy. The hree sub-samples exhibi differen ypes of symmery or asymmery, wih he period prior o joining he WTO showing symmery, he period of joining displaying asymmery bu no leverage, and he period afer joining indicaing leverage. This enables an empirical analysis of he effecs on he prices of he hog producion indusry of joining he WTO by Taiwan, whereby hog prices behave very much like financial commodiy prices. 6. Concluding Remarks The paper presened a novel applicaion of financial volailiy models o agriculural finance, and should be relevan for he analysis of oher agriculural commodiies in differen counries. Specifically, he paper modelled he growh raes and volailiy (or variabiliy in he growh rae) in daily hog prices in Taiwan from 23 March 24

25 1999 o 30 June 2007, which enables an analysis of he effecs of joining he WTO. The empirical resuls show ha he ime series of daily hog prices and heir logarihms were non-saionary, bu ha heir log differences (or growh raes) were saionary. In addiion, he esimaed symmeric and asymmeric condiional volailiy models, specifically he widely used GARCH, GJR and EGARCH models, for he growh raes all fi he daa exremely well. The esimaed models were able o accoun for he volailiy persisence ha was observed in hree sub-samples for he log difference (or growh rae) in daily hog prices, namely 23 June 1999 o 27 December 2001 (sub-sample 1), 28 December 2001 o 6 Augus 2004 (sub-sample 2), and 7 Augus 2004 o 30 June 2007 (sub-sample 3). The empirical second momen and log-momen condiions also suppored he saisical adequacy of he esimaed symmeric and asymmeric condiional volailiy models. These empirical resuls have significan implicaions for risk managemen and policy consideraions in he agriculural indusry in Taiwan, especially when significan srucural changes such as joining he WTO are concerned. The hree sub-samples relaing o he period before, during and afer joining he WTO displayed significanly differen volailiy persisence, namely symmery, asymmery bu no leverage, and leverage, respecively, whereby negaive shocks increase volailiy bu posiive shocks of a similar magniude decrease volailiy. As hog prices behave very similarly o financial sock marke prices, he heory of finance and opimal risk managemen can be applied direcly o he analysis of agriculural commodiy prices. 25

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