ECONOMETRIC MODELLING AND FORECASTING OF FREIGHT TRANSPORT DEMAND IN GREAT BRITAIN

Transcription

1 ECONOMETRIC MODELLING AND FORECASTING OF FREIGHT TRANSPORT DEMAND IN GREAT BRITAIN Shujie Shen, Tony Fowkes, Tony Whieing and Daniel Johnson Insiue for Transpor Sudies, Universiy of Leeds, Leeds, UK, LS2 9JT 1. INTRODUCTION Empirically derived esimaes of freigh ranspor demand elasiciies and accurae forecass of fuure demand are imporan for freigh planning and policy making. The sensiiviy of freigh ranspor demand o he changes of is deerminans can help policy makers o evaluae alernaive policy opions in conrolling fuure freigh ransporaion growh, emissions reducions or modal shif. Accurae forecass can provide informaion on fuure freigh ranspor levels in he appraisal of freigh ranspor relaed projecs and ranspor policies. From he susainabiliy sandpoin, i is imporan o be able o forecas fuure freigh volumes, so ha he impacs of any environmenal policy iniiaives can be compared agains he do-nohing scenario. Economeric models can no only forecas fuure demand bu can also explain economic or business phenomena and increase our undersanding of relaionships among variables. This sudy applies sae of he ar economeric models o he analysis of road plus rail freigh ranspor demand in Grea Briain (GB). This work has been carried ou as par of he EPSRC-funded Green Logisics projec, which examines he susainabiliy of logisics sysems and supply chains and is currenly being underaken by a consorium of 6 UK universiies, suppored and seered by a range of projec parners including he Deparmen for Transpor and CILT (UK). The movemen of goods around GB increased markedly over he period , from 178 billion onne kilomeres in 1978 o 255 billion onne kilomeres in Road and rail have aken a subsanial share of oal freigh movemens. In 2007, 76 percen of freigh was moved by road and rail, only 24 percen by waer and pipelines (DfT, 2008). Figure 1 shows he rend of he demand for road and rail freigh ranspor over he pas 30 years. I can be seen ha he road freigh demand has experienced susained increases while rail freigh demand decreased unil 1993 and has recovered since. We will focus on he road plus rail freigh demand in his sudy. Due o he dominan role of road and rail in he GB freigh ranspor secor, modelling and forecasing GB road plus rail freigh demand can provide useful informaion for boh ransporaion planners and policy makers. Six economeric mehods are applied o GB road plus rail freigh ranspor demand modelling and forecasing, a boh aggregae and disaggregae (commodiy group) levels. The economeric models applied are: he radiional OLS regression model, he Parial Adjusmen (PA) model, he reduced Auoregressive Disribued Lag model (ReADLM), he unresriced Vecor Auoregressive (VAR) model, he Time-Varying-Parameer (TVP) model, and he Srucural Time Series model (STSM). Elasiciy esimaes wih respec o measures of economic aciviy are provided and he relaive forecasing accuracy of he alernaive economeric models is evaluaed.

2 Figure 1 Demand for Road and Rail Freigh Transpor in GB (Goods Moved) Source: DfT (2008) 2. BACKGROUND In he freigh demand lieraure, mos previous sudies focus on freigh demand modelling, examining elasiciies or modal choice based on eiher cross-secion daa or ime series daa (see for example, he surveys by Zlaoper and Ausrian, 1989; Graham and Glaiser, 2004 and de Jong e al, 2004). Few sudies of freigh demand have employed he recen developmens in mulivariae dynamic economeric ime series modelling, wih noable excepions being Bjørner (1999), Kulshreshha, Nag and Kulshresha (2001) and Ramanahan (2001). Bjørner (1999) carried ou an empirical analysis on freigh ranspor in Denmark in a coinegraing Vecor Auoregressive (VAR) sysem. Kulshreshha e al. (2001) also applied he coinegraing VAR model in modelling Indian railways freigh ranspor demand. Ramanahan (2001) applied a Coinegraion (CI) and Error Correcion Model (ECM) in modelling and forecasing boh passenger and freigh ransporaion demand in India. As far as we know, oher recen economeric models, such as he TVP model and he STSM, have no been applied in he freigh demand lieraure. Furhermore, none of he sudies has evaluaed he forecasing performance of alernaive models. This paper aims o fill his gap in he lieraure by applying sae of he ar economeric ime series models o modelling he road plus rail freigh demand in GB. I presens a relaively comprehensive comparison of he forecasing performance of hese economeric forecasing models wihin he freigh demand conex. Alhough he Coinegraion and ECM approaches can boh illusrae he long-run equilibrium relaionship beween he freigh demand and

3 is deerminans and capure he shor-run dynamic characerisics of freigh demand, hey are no applied in his sudy as he some of he daa series under examinaion were considered o be unsuied o coinegraion analysis. For GB freigh demand economeric work, wo major sudies should be menioned here: Fowkes e al. (1993) and he Naional Road Traffic Forecass in DfT (1997). Fowkes e al. (1993) applied he radiional OLS regression model and he PA model o esimae road freigh demand for 15 commodiy groups using ime series daa, wih he freigh demand being measured boh in onnes lifed and onne kilomeres moved. Based on ha work DfT (1997) used he OLS regression model and he PA model o generae he forecass of onnes lifed as he basis for forecasing vehicle kilomeres over he period a secor level. By applying sae of he ar economeric ime series models we aim o updae such earlier work, making use of he new mehods o provide furher empirical evidence for he freigh lieraure. 3. METHODOLOGY In his paper we apply six economeric models o GB road plus rail freigh ranspor demand forecasing. The economeric models applied are: he radiional OLS regression model, he PA model, he ReADLM, he VAR model, he TVP model and he STSM. Apar from he OLS regression model, he oher economeric models have shown heir advanages in previous empirical sudies in oher economic fields. Diagnosic checking is used in he sudy because of is imporance in economeric modelling. Normally in model selecion he funcional form should be specified correcly and he final model should no exhibi auocorrelaion, heeroscedasiciy and non-normaliy. The diagnosic ess used in he sudy are as follows: he Lagrange Muliplier es for serial correlaion (Breusch, 1978 and Godfrey, 1978); he Jarque-Bera es for non-normaliy (Jarque and Bera, 1980); he RESET es for mis-specificaion (Ramsey, 1969) and he Whie es for heeroscedasiciy (Whie, 1980). The OLS Regression Model The radiional OLS regression model akes he form: y I = α + β i xi + ε i=1 (1) where y is he dependen variable, x i is he ih explanaory variable, I is he number of explanaory variables, α and β i are he coefficiens ha need o be esimaed empirically, ε is normally and independenly disribued random error wih zero mean and consan variance. The radiional regression model assumes ha he daa series are saionary. Hence when he daa series are no saionary here may be a problem of spurious regression.

4 The Parial Adjusmen (PA) Model The parial adjusmen model has been exensively used in modelling macroeconomic daa being inerpreable as a lagged effec or an adapive expecaions process. I can be specified as follows: y I = + β i xi + φy 1 i= 1 α + ε (2) where 0 φ < 1, y is he dependen variable, variable, I is he number of explanaory variables, α and x i is he ih explanaory β i are he ε is normally and coefficiens ha need o be esimaed empirically, independenly disribued error erm. The adjusmen parameer, 1 φ, measures he speed of adjusmen. The closer i is o 1 he faser he speed of adjusmen. For applicaions of he PA model see Dargay and Hanly (1999) and Dargay and Hanly (2002). The Reduced Auoregressive Disribued Lag Model (ReADLM) Following he modern economeric mehodology General-o-specific approach, he specificaion sars wih a general auoregressive disribued lag model (ADLM). The original form of ADLM is as follows: y I J J = α + β ij xi, j + φ j y j + ε (3) i= 1 j= 0 j= 1 The equaion incorporaes as many explanaory variables as possible, suppored by appropriae economic heory, where J is he lag lengh which is deermined by he ype of daa used, I is he number of explanaory variables, and ε is he error erm as explained above. As a general guide J=1 for annual daa, bu he lag lenghs may vary and are normally decided by experimenaion (see Thomas, 1997). The reducion procedure of he Reduced ADLM is as follows. Insignifican variables, including dummy variables, are removed from he equaion one by one. Usually he leas significan variable (he one wih he lowes saisic) is deleed from he model, and he reduced model is re-esimaed. This process is repeaed unil all he remaining coefficiens of he variables are saisically significan a leas a he 5% significance level and have he correc signs (see Song, Wi and Jensen, 2003). The Time Varying Parameer (TVP) Model The TVP model relaxes he consancy resricion on he parameers of a radiional economeric model by allowing hem o change over ime. The TVP model is normally specified in sae space (SS) form: y I 0 + β i xi ε (4) i=1 = β +

5 β + u i = 0,1, L, I (5) i = βi 1 where y is he dependen variable, xi is he ih explanaory variable, β i is assumed o be adapive in naure and is modelled in Equaion (4) as a random-walk. ε and u are normally and independenly disribued random errors wih zero mean and consan variances. Equaion (4) is called he observaion equaion, and Equaion (5) is known as he sae equaion. Once he SS model is formulaed, i can be esimaed using an algorihm known as he Kalman filer (Kalman, 1960). The Kalman filer algorihm is a recursive procedure for calculaing he opimal esimaor of he sae vecor given all he informaion available a ime. For applicaions of he TVP model refer o Li e al. (2006) and Song, Romilly and Liu (1998). The Vecor Auoregressive (VAR) Model The VAR model is an equaion sysem in which all variables are reaed as endogenous. However, unlike he srucural approach o simulaneousequaion modelling ha normally deals wih endogenous variables, he VAR approach models every endogenous variable in he sysem as a funcion of he lagged values of all he variables in he sysem. The VAR model is specified as follows: J I J y = α 00 + β 0 j y j + φ0ij xi, j + ε 0 j= 1 i= 1 j= 1 J I J x1 = α 10 + β1 j y j + φ1ij xi, j + ε1 j= 1 i= 1 j= 1 M x I J = α + β y + φ x + ε I J I 0 Ij j Iij i, j I (6) j= 1 i= 1 j= 1 whereα, β and φ are coefficiens and ε are normally and independenly disribued random errors. I is imporan o deermine he lag lengh of he VAR model as oo many lags will resul in over-parameerisaion while oo few lags will resul in loss of informaion in forecasing. Crieria such as he likelihood raio (LR) saisic, Akaike Informaion Crierion (AIC) or Bayesian Informaion Crierion (BIC) are used o deermine he lag lengh of he VAR model (see Song and Wi, 2006). The Srucural Time Series Model (STSM) By including ime-varying componens in he regression equaion, he STSM suggesed by Harvey (1989) can capure movemens no explained by explanaory variables. The model can be represened by he following form:

6 y I = + i=1 µ β x + ε i i (7) where y is he dependen variable; µ and ε are he rend and irregular componens, respecively; x i is he ih explanaory variable, and β i is is unknown parameer o esimae. The sochasic formulaion for he rend componen is following Harvey (1989), which includes level and slope: = µ 1 + β 1 η (8) µ + β = β 1 + ξ (9) where η and ξ are normally and independenly disribued. The exen o which he level and slope change over ime is governed by he hyperparameers σ and σ (he variances of η and ξ ). For applicaions 2 η 2 ξ see Dimiropoulos, Hun and Judge (2005) and Thury and Wi (1998). 4. DATA The analysis presened in his paper is carried ou based on annual daa on he road plus rail freigh demand in GB a boh aggregae and commodiy group level for he period The freigh demand is measured in billion onne-kilomeres moved. The ime series daa for boh road and rail freigh demand are presened in Johnson e al. (2008). They are available by he following commodiy groups: A: Food, Drink and Agriculural Producs B: Coal and Coke C: Perol and Peroleum Producs D: Meals and Ores E: Consrucion F: Chemicals and Feriliser G: Ohers, including Machines, Manufacured Goods and Miscellaneous Mixed Loads ec. In his paper, we are paricularly ineresed in he elasiciy of freigh demand wih respec o he level of economic aciviy, of which he mos appropriae proxy is indusrial producion. Hence he freigh ranspor demand funcion can be wrien in he following general form: LZK k = f ( LIIPk, dummies) (10) where he prefix L denoes ha he daa series are in logarihmic form, Z for road plus rail, K for onne kilomeres, and he subscrip k refers o he commodiy group k and also for he oal; IIP k is he Index of Indusrial Producion (2003=100) for commodiy group k (and oal), a proxy for he

7 economic aciviy in ha secor. The series on IIP k are obained from he Office for Naional Saisics (ONS, 2009a). As here are no exac producion secors maching he commodiy group caegories lised above, he closes secors are chosen as proxies. In addiion o he secor level IIP k, oher proxies of economic aciviy were ried in he models by way of comparison. These include: he Gross Domesic Produc (GDP) of he UK in consan prices (2003=100), he oal producion oupu plus oal impors ( IIPIM measured in onnes) and he aggregae IIP. The series on GDP were obained from he Inernaional Financial Saisics Yearbooks published by he Inernaional Moneary Fund (IMF). In he absence of a daa series for IIPIM, measured in onnes, his was derived from an index of IIP and he known onnes for one paricular year, o which onnes of impors for each year were hen added. Dummy variables are included in he models o capure he effecs of one-off evens on he road plus rail freigh demand in GB when appropriae. Among hem DUM84 represens he UK miners srike in 1984 (DUM84=1 in 1984, 0 oherwise) and is included in he models for Commodiy B (Coal and Coke). DUM81 and DUM86 represen oil price shocks of 1981 and 1986, respecively (DUM81=1 in 1981 and 0 oherwise; DUM86=1 in 1986 and 0 oherwise). They are included in he models for Commodiy C (Perol and Peroleum Producs). DUM80 is included in he models for Commodiy D (Meals and Ores) and Toal o represen he seel workers srike in 1980 (DUM80=1 in 1980 and 0 oherwise). These evens may have negaive effecs on he GB road plus rail freigh demand. DUM88 is a level dummy variable, represening an upward shif in he daa series of road plus rail freigh demand for Commodiy G (Ohers) since 1988 (DUM88=1 in 1988 and onwards, 0 oherwise). We also experimened wih a price variable. In he absence of informaion on acual freigh prices due o commercial confidenialiy, an index of real road operaing coss was used as a proxy. These were calculaed using figures from he SOFTICE sudy (Gacogne e al, 1999) and hen updaed wih more recen figures from he RHA (2009), all deflaed by he Reail Prices Index (ONS, 2009b). 5. EMPIRICAL RESULTS 5.1 Esimaion Resuls of he Economeric Models The six economeric models are used o model and forecas GB road plus rail freigh demand a boh aggregae and disaggregae levels. The STSM is esimaed using STAMP 7.0, and he ohers using Eviews 6.0. Models were esimaed using a range of proxies of economic aciviy (i.e. GDP, IIPIM and IIP ) as well as hose wih IIP k, and price variables were also included. Due o he space consrain he full esimaion resuls are no presened in his paper bu are available upon reques. The esimaion resuls of he models wih IIP k

8 are presened in Tables 1 o 6 respecively, based on he full sample period OLS Regression Models Table 1 shows ha indusrial producion is an imporan deerminan of he road plus rail freigh ranspor demand in GB, judged by he significance of he coefficien esimaes in all he cases. For one-off evens, he UK miners srike in 1984 had an adverse influence on he freigh demand for Coal & Coke (B). The oil price shock in 1986 has been shown o affec he road plus rail freigh demand for Perol and Peroleum Producs (C) adversely. The Seel workers srike in 1980 had negaive effec on road plus rail freigh demand for Meals and Ores (D) bu is no significan in he model for Toal demand. The level dummy variable DUM88 is significan in he model for Ohers (G), which confirmed ha here is an upward shif in he road plus rail freigh demand series for his secor. Table 1 Esimaion Resuls of he OLS Regression Models ZKA ZKB ZKC ZKD ZKE ZKF ZKG ZKTOT Consan ** (0.575) 1.555** (0.177) (0.712) * (0.756) (0.165) 1.619** (0.275) (2.075) ** (0.278) LIIP k 3.388** (0.127) 0.108** (0.031) 0.562** (0.151) 0.924** (0.162) 0.701** (0.038) 0.159* (0.065) 0.964* (0.475) 1.467** (0.062) DUM80 DUM81 DUM84 DUM86 DUM ** (0.133) (0.072) ** (0.070) * (0.083) 0.397** (0.115) (0.048) 2 R S.E NORM(2) LMSC(2) 8.631* ** ** 7.843* ** ** ** HETRO(1) ** * RESET(1) ** * ** ** ** Noes: * and ** indicae ha he esimaes are significanly differen from 0 a 5% and 1% levels respecively. Values in parenheses are sandard errors. NORM(2) is he Jarque-Bera normaliy es, LMSC(2) is he Lagrange muliplier es for serial correlaion, HETRO(1) is he heeroscedasiciy es, RESET(1) is Ramsey s misspecificaion es.

9 Only in he case of commodiy group C did he models pass all of he diagnosic ess a he 5% significance level. The models are subjec o he problem of serial correlaion in all of he oher cases. The model for he Toal demand failed he misspecificaion es a he 1% significance level. The fac ha he models failed a leas one diagnosic es in seven ou of he eigh cases is no surprising, as he disadvanage of he OLS regression model is ha when he daa series are no saionary a problem of spurious regression will occur. PA Models By including he demand in he previous period in he model, he PA model brings he dynamic parial adjusmen process ino he radiional regression model. Table 2 shows he esimaed resuls. Table 2 Esimaion Resuls of he PA Models ZKA ZKB ZKC ZKD ZKE ZKF ZKG ZKTOT Consan * (1.510) 0.868** (0.258) (0.704) (0.774) (0.178) 0.811* (0.326) (0.752) ** (0.182) LZK k ** (0.123) 0.477** (0.141) 0.360* (0.145) 0.571** (0.142) (0.154) 0.610** (0.159) 0.840** (0.059) 0.670** (0.072) LIIP k 0.990* (0.432) (0.032) 0.400* (0.171) 0.421* (0.211) 0.531** (0.109) (0.062) 0.385* (0.182) 0.490** (0.110) DUM80 DUM81 DUM84 DUM86 DUM ** (0.117) (0.066) ** (0.068) ** (0.071) (0.048) ** (0.026) 2 R S.E NORM(2) 6.108* LMSC(2) * ** HETRO(1) * RESET(1) * * Noes: Same as Table 1.

10 The esimaed coefficiens of he IIP k are significan and have he expeced sign for all commodiy groups apar from B and F, which again confirms ha indusrial producion is he key deerminan of GB road plus rail freigh demand a boh aggregae and disaggregae level. The esimaed coefficiens for Coal & Coke (B) and Chemicals & Feriliser (F) are no significan bu have he anicipaed sign. The lagged dependen variables are significan in all he cases excep Consrucion (E). For one-off evens, DUM84 is significan wih righ sign in he model for Coal & Coke (B), and he oil price shock in 1986 affeced he road plus rail freigh demand for Perol and Peroleum Producs (C) adversely. The Seel workers srike in 1980 had a negaive effec on road plus rail freigh demand for Meals and Ores (D) and on Toal demand. The level dummy variable DUM88 is no significan in he model for Ohers (G). The PA models passed all he diagnosic ess in four ou of he eigh cases. The model for Coal & Coke (B) failed hree diagnosic ess. The models passed all bu one ess in he oher hree cases. Reduced ADLM The iniial specificaion of he general ADLM includes all possible variables. The lag lengh of he ADLM is se o be one (J=1) as he daa we used is annual daa. The final models are achieved by dropping he variables wih coefficiens ha are incorrecly signed and / or insignifican. Resuls for hese reduced ADLMs are presened in Table 3. The esimaes of he Reduced ADLM sugges ha he indusrial producion in he curren period shows is significan impac on he road plus rail freigh demand in GB in all of he cases excep commodiy groups B and F. Moreover, he indusrial producion in he previous year has an influence on he road plus rail freigh demand for commodiy groups D and G. The lagged dependen variables are significan in all he cases excep Consrucion (E). The oil price shock in 1986 had negaive effec on he freigh demand for commodiy group C. The seel workers srike affeced he oal demand adversely. Only in four ou of eigh cases did he models pass all of he diagnosic ess. VAR Model The specificaion of he VAR model sars wih an unresriced form. Dummies are regarded as exogenous variables in VAR models. The maximum lag lengh of he VAR model is se o be 3 for he purpose of idenifying he appropriae lag srucure of he VAR models. The opimal lag srucure of he VAR model is decided on he AIC and BIC wih he adjused Likelihood Raio (LR) being considered as references. The esimaes of he VAR models are presened in Table 4. The 1 k IIP variable is only significan in he case of Consrucion (E). The lagged dependen variable feaures in all he cases. This suggess ha he lagged dependen variable is he key deerminan of road plus rail freigh demand in GB. All of he dummy variables are significan and have expeced

11 Table 3 Esimaion Resuls of he Reduced ADLMs ZKA ZKB ZKC ZKD ZKE ZKF ZKG ZKTOT Consan (1.510) 1.035** (0.339) (0.700) (0.767) (0.165) 0.838* (0.311) (0.440) ** (0.182) LZK k ** (0.123) 0.517** (0.158) 0.352* (0.150) 0.689** (0.151) 0.636** (0.135) 0.920** (0.049) 0.670** (0.072) LIIP k LIIP k,-1 DUM * (0.432) 0.472* (0.171) 1.187** (0.239) ** (0.239) 0.701** (0.038) 0.837** (0.168) ** (0.180) 0.490** (0.110) ** (0.026) DUM81 DUM84 DUM ** (0.070) DUM88 2 R S.E NORM(2) 6.108* ** LMSC(2) * ** HETRO(1) RESET(1) * Noes: Same as Table 1.

12 Consan LZK k-1 LZK k-2 LIIP k-1 LIIP k-2 DUM80 DUM81 DUM84 DUM86 DUM88 Noes: Same as Table 1. Table 4 Esimaion Resuls of he VAR models ZKA ZKB ZKC ZKD ZKE ZKF ZKG ZKTOT (1.688) 0.848** (0.139) (0.485) 0.894** (0.265) 0.516** (0.155) (0.038) ** (0.120) (0.696) 0.447** (0.158) (0.171) * (0.070) * (0.070) (0.758) 0.734** (0.164) (0.218) ** (0.073) (0.217) 0.440* (0.217) 0.396* (0.159) 0.831* (0.328) 0.629** (0.159) (0.064) (0.746) 0.915** (0.066) (0.187) (0.237) 1.277** (0.200) ** (0.197) (0.249) (0.264) ** (0.027) 0.113* (0.046) 2 R S.E LMSC(2) NORM(2) * HETRO(1) * ** * Consan (2.050) LIIP k 1.569** Noes: Same as Table 1. Table 5 Esimaion Resuls of he TVP Models ZKA ZKB ZKC ZKD ZKE ZKF ZKG ZKTOT (0.442) 1.924** (0.484) (0.118) (0.857) 0.310* (0.183) * (0.903) 0.892** (0.194) (0.763) 0.599** (0.164) (1.186) (0.253) (0.777) 0.761** (0.169) (0.658) 0.958** (0.143) DUM DUM DUM DUM DUM Log likelihood SC

13 Table 6 Esimaion Resuls of he STSMs ZKA ZKB ZKC ZKD ZKE ZKF ZKG ZKTOT Hyperparameers Level e e Slope e e e Irregular Coefficiens Level Slope LIIP k Dum (2.346) 0.017* (0.007) 0.862* (0.506) (0.590) 0.120** (0.034) 0.383* (0.141) (0.770) (0.004) 0.528** (0.164) ** (0.755) (0.018) 1.126** (0.162) (0.047) (0.518) (0.002) 0.897** (0.111) (1.353) ** (0.017) 1.028** (0.288) (0.743) 0.025** (0.007) 0.628** (0.165) 2.025** (0.585) (0.024) 0.720** (0.127) ** (0.010) Dum (0.063) Dum * (0.135) Dum ** (0.065) Dum * (0.042) Diagnosic Tess Normaliy ** H(8) * DW Q -saisic ** Rd Se Noe: * and ** indicae ha he esimaes are significan a he 5% and 1% levels, respecively. Values in parenheses are sandard errors. HETRO is he heeroscedasiciy es and Q- saisic is he Box-Ljung Q-saisic es for residual serial correlaion.

14 signs. The models passed all he diagnosic ess in five ou of he eigh cases. TVP Models Resuls for he TVP models, esimaed using he Kalman filer algorihm, are presened in Table 5. I should be noed ha in TVP models dummy variables are reaed as exogenous variables whose parameers do no vary wih ime. However, he significance of he dummy variables is no repored by he Eviews 6.0 programme. The parameers repored are he esimaes a he end of he sample period. The coefficiens of he IIP k have he expeced signs and are significan in all cases bu wo, i.e., Coal & Coke (B) and Chemicals & Feriliser (F), which is consisen wih he resuls from some of he fixed parameer models. This suggess ha indusrial producion explains well he road plus rail freigh demand in GB. STSM By including a sochasic rend componen in he regression equaion, one can capure movemen in freigh demand series which is no explained by he explanaory variables included and would oherwise be lef in he residuals. Table 6 shows ha IIPk is significan in all of he cases. For one-off evens, DUM84 is significan wih righ sign in he model for Coal & Coke (B), and he oil price shock in 1986 affeced he road plus rail freigh demand for Perol and Peroleum Producs (C) adversely. The seel workers srike in 1980 had negaive effec on Toal demand. The level dummy variable DUM88 is significan in he model for Ohers (G). The models passed all of he diagnosic ess in five ou of he eigh cases. 5.2 Long-run Elasiciy Analysis The long-run elasiciies from he OLS regression model, he TVP model and STSM are obained direcly from he esimaed coefficiens of he independen variables in he models. For he PA model, reduced ADLM and VAR model, he lagged variables are reaed as he curren values of he variables in he long-run and he elasiciies are calculaed using he esimaed coefficiens of he explanaory variables. Taking he PA model as an example, he long-run income elasiciies are calculaed as he esimaed coefficien of he indusrial producion variable (IIP) divided by he adjusmen coefficien ( 1 φ ), where φ is he esimaed coefficien of he lagged dependen variable. Esimaes of long-run elasiciies of road plus rail freigh ranspor demand wih respec o indusrial producion (economic aciviy) from alernaive economeric models are compared. The resuls are presened in Table 7.

15 Table 7 Comparison of Esimaed Elasiciies wih respec o Indusrial Producion Model Type Commodiy Group A B C D E F G Toal Saic 3.388** 0.108** 0.562** 0.924** 0.701** 0.159* 0.964* 1.467** PA 3.289* * 0.981* 0.714** * 1.485** ReADLM 3.289* * 1.016** 0.701** ** 1.206** VAR * TVP 1.569** * 0.892** 0.599** ** 0.958** STSM 0.862* 0.383* 0.528** 1.126** 0.897** 1.028** 0.628** 0.720** Noe: * and ** indicae ha he elasiciies are based on esimaed parameers significan a he 5% and 1% levels, respecively. - denoes ha he variable is insignifican in he reduced ADLM and hence was deleed in he esimaion procedure. I can be seen ha he esimaed elasiciy values vary across commodiy groups, which indicaes ha he composiion of he economy has an influence on income elasiciies of he demand for road plus rail freigh in GB. The OLS regression model, he PA model and he reduced ADLM are more consisen wih each oher in erms of he significance of variables and he magniudes of esimaed elasiciy values, while he resuls from he TVP model and STSM are similar o each oher. The elasiciies of road plus rail freigh demand wih respec o economic aciviy (which is a form of income elasiciy) vary across differen commodiy groups. This indicaes differen sensiiviy o variaions in indusrial producion for differen marke secors. The acual magniude of income elasiciy esimaes also vary due o he differen models esimaed. For Food Drink & Agriculural Producs (Group A), he income elasiciies from he OLS regression model and he PA model (he reduced ADLM collapses o he PA model in his case) are consisen bu exremely high (3.388 and 3.289). The derived income elasiciy from he VAR model is similarly high a The values from he TVP model and he STSM are and respecively. This gives he range of income elasiciy from o in his secor, which is raher wide. Excluding he resuls from he VAR model which are exremely variable and ofen insignifican, he ranges for elasiciies for oher commodiy groups are as follows. For he Coal & Coke (B) secor, he esimaed income elasiciies

16 are dubiously low, ranging from o The ranges for Perol & Peroleum Producs (C) and Consrucion (E) are relaively narrow: and respecively. For he Meals & Ores secor (D), he esimaed elasiciy values are close o 1, in he range In he case of Ohers (G), he range is wider, beween and As far as he oal road plus rail freigh demand is concerned, he range of he income elasiciy is from o Close inspecion of he daa suggess ha hese elasiciy esimaes, whils informaive, are likely o be conaminaed wih oher rend effecs. We made many oher aemps o disenangle hese effecs, bu no beer resuls were obained. 5.3 Ex Pos Forecasing Comparison The chosen models are used o generae forecass of he GB road plus rail freigh demand for each commodiy group, as well as for oal road plus rail freigh demand, over he period For each model, he recursive forecasing echnique is used o generae forecass, i.e., he models are esimaed over he period firs, and he esimaed models are used o forecas road plus rail freigh demand over he period Subsequenly he models are re-esimaed using he daa from 1974 o 1999 and forecass are generaed for he period Such a procedure is repeaed unil all observaions are exhaused. As a resul, 8 one-year-ahead forecass, 6 hree-year-ahead forecass, and 4 five-year-ahead forecass are generaed. The ex pos forecasing performances of he models are evaluaed based on a measure of error magniude: he mean absolue percenage error (MAPE). MAPE is defined as MAPE = n = 1 Yˆ Y n / Y 100 (11) where Ŷ and Y are respecively he forecas and acual values and n he number of forecas observaions. The smalles values of he MAPE indicae he mos accurae forecass. The forecasing performances of he alernaive models are ranked based on MAPE and he resuls are repored in Table 8. One-year-ahead forecass Table 8 shows ha for one-year-ahead forecass, he STSM is he mos accurae forecasing model in five ou of he eigh cases. The TVP model performs bes in wo cases, followed by he Reduced ADLM and OLS regression model for one case each (he Reduced ADLM model collapses o he OLS regression model in he case of commodiy group E). On he basis of he number of occasions when each model is eiher he mos accurae or he second mos accurae forecasing model, he STSM is ranked firs followed by he TVP model.

17 Forecas Horizon Table 8 Forecasing Accuracy of Alernaive Economeric Models based on MAPE Forecasing Mehod ZKA ZKB ZKC ZKD ZKE ZKF ZKG ZKTOT 1-year-ahead OLS Regression 1.472%(6) %(6) 3.506%(5) 3.033%(4) 0.629%(1=) 7.125%(6) 4.916%(6) 0.963%(6) PA 0.826%(2=) 8.904%(5) 3.016%(3) 2.021%(2) 0.699%(4) 5.192%(5) 0.525%(5) 0.321%(4=) ReADLM 0.826%(2=) 8.678%(3) 3.502%(4) 2.067%(3) 0.629%(1=) 4.760%(4) 0.363%(3) 0.321%(4=) VAR 0.958%(4) 8.784%(4) 2.974%(2) 3.103%(5) 0.841%(6) 4.728%(3) 0.327%(2) 0.290%(2) TVP 0.750%(1) 6.360%(2) 3.537%(6) 1.996%(1) 0.778%(5) 4.511%(2) 0.489%(4) 0.291%(3) STSM 0.994%(5) 6.056%(1) 2.686%(1) 3.258%(6) 0.678%(3) 4.404%(1) 0.304%(1) 0.211%(1) 3-year-ahead OLS Regression 1.241%(2) %(5) 3.491%(5) 3.252%(1) 0.351%(2=) 9.412%(6) 5.623%(6) 1.364%(6) PA 1.331%(3=) %(4) 3.206%(4) 3.571%(2) 0.345%(1) 7.692%(4) 1.222%(5) 0.641%(2=) ReADLM 1.331%(3=) %(3) 3.784%(6) 3.786%(3) 0.351%(2=) 6.151%(2) 0.759%(3) 0.641%(2=) VAR 1.806%(5) %(6) 2.068%(2) 5.505%(5) 1.473%(6) 8.229%(5) 0.676%(2) 0.759%(5) TVP 0.716%(1) %(2) 2.231%(3) 3.838%(4) 0.803%(5) 6.286%(3) 1.219%(4) 0.723%(4) STSM 2.214%(6) 9.240%(1) 1.441%(1) 5.865%(6) 0.501%(4) 5.595%(1) 0.669%(1) 0.617%(1) 5-year-ahead OLS Regression 1.477%(2) %(5) 4.324%(5) 3.872%(1) 0.306%(2=) %(5) 6.433%(6) 1.752%(6) PA 1.972%(3=) %(4) 4.041%(4) 4.177%(2) 0.265%(1) %(4) 2.027%(4) 0.793%(1=) ReADLM 1.972%(3=) %(3) 4.632%(6) 4.757%(3) 0.306%(2=) 9.051%(3) 0.944%(1) 0.793%(1=) VAR 3.207%(5) %(6) 2.148%(1) 7.131%(5) 3.094%(6) %(6) 1.286%(3) 0.908%(3) TVP 0.987%(1) %(2) 3.671%(3) 5.999%(4) 1.040%(5) 8.630%(2) 2.049%(5) 1.226%(4) STSM 3.641%(6) %(1) 2.759%(2) 9.757%(6) 0.331%(4) 7.981%(1) 1.035%(2) 1.254%(5) Noe: The figures in parenheses are rankings.

18 The leas accurae forecasing model is he radiional OLS regression model, due o he fac ha i performs wors in five ou of he eigh cases. The VAR model, he STSM and he TVP model generae he leas accurae forecass in one case each, bu as saed above, he laer wo oherwise perform well. When he crierion is based on he number of occasions when each model is eiher he leas accurae or he second leas accurae forecasing model, again he OLS regression model exhibis he wors forecas performance, followed by he PA model and he VAR model. Three-year-ahead forecass A he hree-year-ahead forecasing horizon, he STSM performs consisenly well, being ranked op in five ou of he eigh cases, whils he TVP, PA and OLS regression models generae he bes forecass in jus one case each. Based on he crierion of he mos accurae or second mos accurae forecasing model, he STSM is sill he bes. I is difficul o differeniae beween he PA model, he reduced ADLM and he OLS regression models on his basis, bu as he PA model never generaes he wors forecass, i is considered o be he second bes forecasing model following he STSM. The OLS regression model is ranked boom in hree cases, followed by he VAR model and STSM in wo cases each. The PA and ReADLM models are each beer han he STSM model for hree ou of he seven commodiy groups, and close for he oal. Despie he fac ha he STSM is ranked boom in wo cases, i is sill considered he bes performing model as i generaes he mos accurae forecass in mos of he cases. When he crierion is he leas accurae or second leas accurae forecasing model, he VAR model seems o be he wors performing model followed by he OLS regression model. Five-year-ahead forecass For five-year-ahead forecass, he PA model, he reduced ADLM and STSM each generae he mos accurae forecass in wo ou of he eigh cases. According o he mos accurae or second mos accurae crierion, he STSM is in he lead (four cases), followed by he PA model and reduced ADLM (hree cases each). However, he STSM is ranked boom wice and he reduced ADLM generaes he leas accurae forecass once, whereas he rank of he PA model never drops below fourh place. I can be concluded ha he PA model is he bes performing model for five-year-ahead horizon, followed by he STSM and he reduced ADLM. As far as he leas accurae forecasing model is concerned, he VAR model performs wors in hree cases, followed by he OLS model and STSM in wo cases. If he crierion is he leas accurae or second leas accurae forecasing model, he VAR model and he OLS regression model are ranked equal. On he basis ha he VAR model is ranked boom more ofen han he OLS regression model, he VAR model could be considered he wors performing model for five-year-ahead horizons. As migh be expeced, MAPE shows a endency o rise as he forecas horizon increases. This can be seen for example in he case of oal road and rail freigh (he final column in Table 8). Moreover, he MAPE for he PA and

19 ReADLM models ends o rise less quickly han for he oher model forms. We concluded ha for long-erm (i.e. 5+ years) forecass, he PA or is generalisaion ReADLM are o be preferred. 6. CONCLUSIONS In his sudy, six economeric ime series models have been applied o modelling and forecasing he road plus rail freigh demand in GB, based on annual ime series daa for he period These models comprise: he radiional OLS regression model, he PA model, he reduced ADLM, he unresriced VAR model, he TVP model and he STSM. The empirical analysis is carried ou a boh aggregae and disaggregae levels. The relaive forecasing accuracy of alernaive models has been evaluaed based on MAPE in he conex of freigh demand. The esimaion resuls show ha indusrial producion generally offers a good explanaion of road plus rail freigh demand in GB. However, he sensiiviy of road plus rail freigh demand o he change in he indusrial producion varies across differen commodiy groups, as differen commodiies have differen ranspor requiremens and each esimae reflecs paricular circumsances for each commodiy group. The acual magniudes of income elasiciy esimaes also vary due o he differen models esimaed. The ranges of esimaed income elasiciy for differen secors have been provided. This informaion will be valuable for ranspor planners and policy makers. The forecasing performance comparison resuls show ha no single model ouperforms he ohers in all siuaions. Overall, i can be concluded ha for shor-erm (one-year-ahead) forecasing, he STSM is he bes forecasing model, followed by he TVP model. For medium-erm (hree-year-ahead) forecasing he STSM is superior o is compeing models, followed by he PA model. For relaively longer horizons (five-year-ahead in his sudy), he PA model and reduced ADLM seem o perform bes alhough he STSM is no far behind. Forecasing horizons do seem o have an effec on he forecasing performance of differen models. The STSM seems o perform beer for shor o medium erm horizons, whereas he PA model ouperforms ohers for longer erm horizons. The TVP model generally performs beer in he shorerm (one-year-ahead) han for longer-erm forecasing. This gives he policy makers useful informaion when hey need o choose beween differen forecasing ools. REFERENCES Bjørner, T. B. (1999). Environmenal benefis from beer freigh ranspor managemen: freigh raffic in a VAR model, Transporaion Research, Par D, Breusch, T. (1978). Tesing for auocorrelaion in dynamic linear models. Ausralian Economic Papers,

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