Econometric Modelling and Forecasting of Freight ... - Green Logistics

9 downloads 0 Views 166KB Size Report
The diagnostic tests used in the study are as follows: the Lagrange Multiplier test for serial correlation (Breusch,. 1978 and Godfrey, 1978); the Jarque-Bera test ...
ECONOMETRIC MODELLING AND FORECASTING OF FREIGHT TRANSPORT DEMAND IN GREAT BRITAIN Shujie Shen, Tony Fowkes, Tony Whiteing and Daniel Johnson Institute for Transport Studies, University of Leeds, Leeds, UK, LS2 9JT 1. INTRODUCTION Empirically derived estimates of freight transport demand elasticities and accurate forecasts of future demand are important for freight planning and policy making. The sensitivity of freight transport demand to the changes of its determinants can help policy makers to evaluate alternative policy options in controlling future freight transportation growth, emissions reductions or modal shift. Accurate forecasts can provide information on future freight transport levels in the appraisal of freight transport related projects and transport policies. From the sustainability standpoint, it is important to be able to forecast future freight volumes, so that the impacts of any environmental policy initiatives can be compared against the do-nothing scenario. Econometric models can not only forecast future demand but can also explain economic or business phenomena and increase our understanding of relationships among variables. This study applies state of the art econometric models to the analysis of road plus rail freight transport demand in Great Britain (GB). This work has been carried out as part of the EPSRC-funded ‘Green Logistics’ project, which examines the sustainability of logistics systems and supply chains and is currently being undertaken by a consortium of 6 UK universities, supported and steered by a range of project partners including the Department for Transport and CILT (UK). The movement of goods around GB increased markedly over the period 19782007, from 178 billion tonne kilometres in 1978 to 255 billion tonne kilometres in 2007. Road and rail have taken a substantial share of total freight movements. In 2007, 76 percent of freight was moved by road and rail, only 24 percent by water and pipelines (DfT, 2008). Figure 1 shows the trend of the demand for road and rail freight transport over the past 30 years. It can be seen that the road freight demand has experienced sustained increases while rail freight demand decreased until 1993 and has recovered since. We will focus on the road plus rail freight demand in this study. Due to the dominant role of road and rail in the GB freight transport sector, modelling and forecasting GB road plus rail freight demand can provide useful information for both transportation planners and policy makers. Six econometric methods are applied to GB road plus rail freight transport demand modelling and forecasting, at both aggregate and disaggregate (commodity group) levels. The econometric models applied are: the traditional OLS regression model, the Partial Adjustment (PA) model, the reduced Autoregressive Distributed Lag model (ReADLM), the unrestricted Vector Autoregressive (VAR) model, the Time-Varying-Parameter (TVP) model, and the Structural Time Series model (STSM). Elasticity estimates with respect to measures of economic activity are provided and the relative forecasting accuracy of the alternative econometric models is evaluated.

Figure 1 Demand for Road and Rail Freight Transport in GB (Goods Moved) Source: DfT (2008) 2. BACKGROUND In the freight demand literature, most previous studies focus on freight demand modelling, examining elasticities or modal choice based on either cross-section data or time series data (see for example, the surveys by Zlatoper and Austrian, 1989; Graham and Glaister, 2004 and de Jong et al, 2004). Few studies of freight demand have employed the recent developments in multivariate dynamic econometric time series modelling, with notable exceptions being Bjørner (1999), Kulshreshtha, Nag and Kulshrestha (2001) and Ramanathan (2001). Bjørner (1999) carried out an empirical analysis on freight transport in Denmark in a cointegrating Vector Autoregressive (VAR) system. Kulshreshtha et al. (2001) also applied the cointegrating VAR model in modelling Indian railways freight transport demand. Ramanathan (2001) applied a Cointegration (CI) and Error Correction Model (ECM) in modelling and forecasting both passenger and freight transportation demand in India. As far as we know, other recent econometric models, such as the TVP model and the STSM, have not been applied in the freight demand literature. Furthermore, none of the studies has evaluated the forecasting performance of alternative models. This paper aims to fill this gap in the literature by applying state of the art econometric time series models to modelling the road plus rail freight demand in GB. It presents a relatively comprehensive comparison of the forecasting performance of these econometric forecasting models within the freight demand context. Although the Cointegration and ECM approaches can both illustrate the long-run equilibrium relationship between the freight demand and

its determinants and capture the short-run dynamic characteristics of freight demand, they are not applied in this study as the some of the data series under examination were considered to be unsuited to cointegration analysis. For GB freight demand econometric work, two major studies should be mentioned here: Fowkes et al. (1993) and the National Road Traffic Forecasts in DfT (1997). Fowkes et al. (1993) applied the traditional OLS regression model and the PA model to estimate road freight demand for 15 commodity groups using time series data, with the freight demand being measured both in tonnes lifted and tonne kilometres moved. Based on that work DfT (1997) used the OLS regression model and the PA model to generate the forecasts of tonnes lifted as the basis for forecasting vehicle kilometres over the period 1995-2031 at sector level. By applying state of the art econometric time series models we aim to update such earlier work, making use of the new methods to provide further empirical evidence for the freight literature.

3. METHODOLOGY In this paper we apply six econometric models to GB road plus rail freight transport demand forecasting. The econometric models applied are: the traditional OLS regression model, the PA model, the ReADLM, the VAR model, the TVP model and the STSM. Apart from the OLS regression model, the other econometric models have shown their advantages in previous empirical studies in other economic fields. Diagnostic checking is used in the study because of its importance in econometric modelling. Normally in model selection the functional form should be specified correctly and the final model should not exhibit autocorrelation, heteroscedasticity and non-normality. The diagnostic tests used in the study are as follows: the Lagrange Multiplier test for serial correlation (Breusch, 1978 and Godfrey, 1978); the Jarque-Bera test for non-normality (Jarque and Bera, 1980); the RESET test for mis-specification (Ramsey, 1969) and the White test for heteroscedasticity (White, 1980). The OLS Regression Model The traditional OLS regression model takes the form: I

y t = α + ∑ β i xit + ε t

(1)

i =1

where yt is the dependent variable, x it is the ith explanatory variable, I is the number of explanatory variables, α and β i are the coefficients that need to be estimated empirically, ε t is normally and independently distributed random error with zero mean and constant variance. The traditional regression model assumes that the data series are stationary. Hence when the data series are not stationary there may be a problem of spurious regression.

The Partial Adjustment (PA) Model The partial adjustment model has been extensively used in modelling macroeconomic data being interpretable as a lagged effect or an adaptive expectations process. It can be specified as follows: I

y t = α + ∑ β i xit + φy t −1 + ε t

(2)

i =1

where 0 ≤ φ < 1 , yt is the dependent variable, x it is the ith explanatory variable, I is the number of explanatory variables, α and β i are the coefficients that need to be estimated empirically, ε t is normally and independently distributed error term. The adjustment parameter, 1 − φ , measures the speed of adjustment. The closer it is to 1 the faster the speed of adjustment. For applications of the PA model see Dargay and Hanly (1999) and Dargay and Hanly (2002). The Reduced Autoregressive Distributed Lag Model (ReADLM) Following the modern econometric methodology ‘General-to-specific’ approach, the specification starts with a general autoregressive distributed lag model (ADLM). The original form of ADLM is as follows: I

J

J

y t = α + ∑∑ β ij xi ,t − j + ∑ φ j y t − j + ε t i =1 j =0

(3)

j =1

The equation incorporates as many explanatory variables as possible, supported by appropriate economic theory, where J is the lag length which is determined by the type of data used, I is the number of explanatory variables, and ε t is the error term as explained above. As a general guide J=1 for annual data, but the lag lengths may vary and are normally decided by experimentation (see Thomas, 1997). The reduction procedure of the Reduced ADLM is as follows. Insignificant variables, including dummy variables, are removed from the equation one by one. Usually the least significant variable (the one with the lowest t statistic) is deleted from the model, and the reduced model is re-estimated. This process is repeated until all the remaining coefficients of the variables are statistically significant at least at the 5% significance level and have the correct signs (see Song, Witt and Jensen, 2003). The Time Varying Parameter (TVP) Model The TVP model relaxes the constancy restriction on the parameters of a traditional econometric model by allowing them to change over time. The TVP model is normally specified in state space (SS) form: I

yt = β 0t + ∑ β it xit + ε t i =1

(4)

β it = β it −1 + u t i = 0,1, L , I

(5)

where yt is the dependent variable, x it is the ith explanatory variable, β it is assumed to be adaptive in nature and is modelled in Equation (4) as a random-walk. ε t and u t are normally and independently distributed random errors with zero mean and constant variances. Equation (4) is called the observation equation, and Equation (5) is known as the state equation. Once the SS model is formulated, it can be estimated using an algorithm known as the Kalman filter (Kalman, 1960). The Kalman filter algorithm is a recursive procedure for calculating the optimal estimator of the state vector given all the information available at time t. For applications of the TVP model refer to Li et al. (2006) and Song, Romilly and Liu (1998). The Vector Autoregressive (VAR) Model The VAR model is an equation system in which all variables are treated as endogenous. However, unlike the structural approach to simultaneousequation modelling that normally deals with endogenous variables, the VAR approach models every endogenous variable in the system as a function of the lagged values of all the variables in the system. The VAR model is specified as follows: J

I

J

y t = α 00 + ∑ β 0 j yt − j + ∑∑ φ0ij xi ,t − j + ε 0t j =1 J

i =1 j =1 I

J

x1t = α 10 + ∑ β1 j y t − j + ∑∑ φ1ij xi ,t − j + ε 1t j =1

i =1 j =1

M J

I

J

x It = α I 0 + ∑ β Ij y t − j +∑∑ φ Iij xi ,t − j + ε It j =1

(6)

i =1 j =1

where α , β and φ are coefficients and ε t are normally and independently distributed random errors. It is important to determine the lag length of the VAR model as too many lags will result in over-parameterisation while too few lags will result in loss of information in forecasting. Criteria such as the likelihood ratio (LR) statistic, Akaike Information Criterion (AIC) or Bayesian Information Criterion (BIC) are used to determine the lag length of the VAR model (see Song and Witt, 2006). The Structural Time Series Model (STSM) By including time-varying components in the regression equation, the STSM suggested by Harvey (1989) can capture movements not explained by explanatory variables. The model can be represented by the following form:

I

y t = µ t + ∑ β i x it + ε t

(7)

i =1

where yt is the dependent variable; µ t and ε t are the trend and irregular components, respectively; x it is the ith explanatory variable, and β i is its unknown parameter to estimate. The stochastic formulation for the trend component is following Harvey (1989), which includes level and slope:

µ t = µ t −1 + β t −1 + η t

(8)

β t = β t −1 + ξ t

(9)

where ηt and ξ t are normally and independently distributed. The extent to which the level and slope change over time is governed by the hyperparameters σ η2 and σ ξ2 (the variances of ηt and ξ t ). For applications see Dimitropoulos, Hunt and Judge (2005) and Thury and Witt (1998).

4. DATA The analysis presented in this paper is carried out based on annual data on the road plus rail freight demand in GB at both aggregate and commodity group level for the period 1974-2006. The freight demand is measured in billion tonne-kilometres moved. The time series data for both road and rail freight demand are presented in Johnson et al. (2008). They are available by the following commodity groups: A: Food, Drink and Agricultural Products B: Coal and Coke C: Petrol and Petroleum Products D: Metals and Ores E: Construction F: Chemicals and Fertiliser G: Others, including Machines, Manufactured Goods and Miscellaneous Mixed Loads etc. In this paper, we are particularly interested in the elasticity of freight demand with respect to the level of economic activity, of which the most appropriate proxy is industrial production. Hence the freight transport demand function can be written in the following general form: LZK kt = f ( LIIPkt , dummies )

(10)

where the prefix ‘L’ denotes that the data series are in logarithmic form, ‘ Z ’ for ‘road plus rail’, K for ‘tonne kilometres’, and the subscript k refers to the commodity group k and also for the total; IIPkt is the Index of Industrial Production (2003=100) for commodity group k (and total), a proxy for the

economic activity in that sector. The series on IIPkt are obtained from the Office for National Statistics (ONS, 2009a). As there are no exact production sectors matching the commodity group categories listed above, the closest sectors are chosen as proxies. In addition to the sector level IIPkt , other proxies of economic activity were tried in the models by way of comparison. These include: the Gross Domestic Product (GDP) of the UK in constant prices (2003=100), the total production output plus total imports ( IIPIM t measured in tonnes) and the aggregate IIPt . The series on GDP were obtained from the International Financial Statistics Yearbooks published by the International Monetary Fund (IMF). In the absence of a data series for IIPIM t , measured in tonnes, this was derived from an index of IIP and the known tonnes for one particular year, to which tonnes of imports for each year were then added. Dummy variables are included in the models to capture the effects of one-off events on the road plus rail freight demand in GB when appropriate. Among them DUM84 represents the UK miners’ strike in 1984 (DUM84=1 in 1984, 0 otherwise) and is included in the models for Commodity B (Coal and Coke). DUM81 and DUM86 represent oil price shocks of 1981 and 1986, respectively (DUM81=1 in 1981 and 0 otherwise; DUM86=1 in 1986 and 0 otherwise). They are included in the models for Commodity C (Petrol and Petroleum Products). DUM80 is included in the models for Commodity D (Metals and Ores) and Total to represent the steel workers’ strike in 1980 (DUM80=1 in 1980 and 0 otherwise). These events may have negative effects on the GB road plus rail freight demand. DUM88 is a level dummy variable, representing an upward shift in the data series of road plus rail freight demand for Commodity G (Others) since 1988 (DUM88=1 in 1988 and onwards, 0 otherwise). We also experimented with a price variable. In the absence of information on actual freight prices due to commercial confidentiality, an index of real road operating costs was used as a proxy. These were calculated using figures from the SOFTICE study (Gacogne et al, 1999) and then updated with more recent figures from the RHA (2009), all deflated by the Retail Prices Index (ONS, 2009b).

5. EMPIRICAL RESULTS 5.1 Estimation Results of the Econometric Models The six econometric models are used to model and forecast GB road plus rail freight demand at both aggregate and disaggregate levels. The STSM is estimated using STAMP 7.0, and the others using Eviews 6.0. Models were estimated using a range of proxies of economic activity (i.e. GDP, IIPIMt and IIPt) as well as those with IIPkt, and price variables were also included. Due to the space constraint the full estimation results are not presented in this paper but are available upon request. The estimation results of the models with IIPkt

are presented in Tables 1 to 6 respectively, based on the full sample period 1974-2006. OLS Regression Models Table 1 shows that industrial production is an important determinant of the road plus rail freight transport demand in GB, judged by the significance of the coefficient estimates in all the cases. For one-off events, the UK miners’ strike in 1984 had an adverse influence on the freight demand for Coal & Coke (B). The oil price shock in 1986 has been shown to affect the road plus rail freight demand for Petrol and Petroleum Products (C) adversely. The Steel workers’ strike in 1980 had negative effect on road plus rail freight demand for Metals and Ores (D) but is not significant in the model for Total demand. The level dummy variable DUM88 is significant in the model for Others (G), which confirmed that there is an upward shift in the road plus rail freight demand series for this sector. Table 1 Estimation Results of the OLS Regression Models ZKA

ZKB

ZKC

ZKD

ZKE

ZKF

ZKG

ZKTOT

Constant

-11.575** 1.555** -0.613 (0.575) (0.177) (0.712)

-1.863* (0.756)

0.281 1.619** (0.165) (0.275)

-0.709 (2.075)

-1.503** (0.278)

LIIPkt

3.388** 0.108** 0.562** (0.127) (0.031) (0.151)

0.924** (0.162)

0.701** 0.159* (0.038) (0.065)

0.964* (0.475)

1.467** (0.062)

-0.149* (0.083)

DUM80

-0.033 (0.048)

-0.111 (0.072)

DUM81 -0.461** (0.133)

DUM84

-0.248** (0.070)

DUM86

0.397** (0.115)

DUM88

R2

0.957

0.420

0.453

0.546

0.914

0.136

0.834

0.948

S.E.

0.057

0.131

0.068

0.080

0.044

0.103

0.138

0.047

NORM(2)

0.670

1.837

0.468

0.211

1.003

0.854

1.843

1.381

LMSC(2)

8.631* 17.881** 2.180

15.889**

7.843* 12.314** 21.635** 29.522**

HETRO(1)

0.005

9.657**

0.720

0.477

0.216

1.152

4.535*

1.692

RESET(1)

1.378

57.887** 1.821

6.112*

0.941 48.117** 18.001** 22.472**

Notes: * and ** indicate that the estimates are significantly different from 0 at 5% and 1% levels respectively. Values in parentheses are standard errors. NORM(2) is the Jarque-Bera normality test, LMSC(2) is the Lagrange multiplier test for serial correlation, HETRO(1) is the heteroscedasticity test, RESET(1) is Ramsey’s misspecification test.

Only in the case of commodity group C did the models pass all of the diagnostic tests at the 5% significance level. The models are subject to the problem of serial correlation in all of the other cases. The model for the Total demand failed the misspecification test at the 1% significance level. The fact that the models failed at least one diagnostic test in seven out of the eight cases is not surprising, as the disadvantage of the OLS regression model is that when the data series are not stationary a problem of spurious regression will occur. PA Models By including the demand in the previous period in the model, the PA model brings the dynamic partial adjustment process into the traditional regression model. Table 2 shows the estimated results.

Table 2 Estimation Results of the PA Models ZKA

ZKB

ZKC

ZKD

ZKE

ZKF

ZKG

ZKTOT

Constant

-3.330* (1.510)

0.868** (0.258)

-0.579 (0.704)

-0.912 (0.774)

0.167 (0.178)

0.811* (0.326)

-1.098 (0.752)

-0.511** (0.182)

LZKkt-1

0.699** (0.123)

0.477** (0.141)

0.360* (0.145)

0.571** (0.142)

0.256 (0.154)

0.610** (0.159)

0.840** (0.059)

0.670** (0.072)

LIIPkt

0.990* (0.432)

0.048 (0.032)

0.400* (0.171)

0.421* (0.211)

0.531** (0.109)

0.020 (0.062)

0.385* (0.182)

0.490** (0.110)

-0.237** (0.071)

DUM80

-0.092** (0.026)

-0.112 (0.066)

DUM81 -0.527** (0.117)

DUM84

-0.204** (0.068)

DUM86

0.019 (0.048)

DUM88

R2

0.977

0.566

0.548

0.699

0.917

0.387

0.979

0.986

S.E.

0.041

0.113

0.063

0.065

0.043

0.084

0.047

0.024

NORM(2)

6.108*

0.313

1.998

0.475

1.930

2.486

0.485

2.793

LMSC(2)

3.963

7.928*

2.598

1.059

5.744

3.397

1.419

14.511**

HETRO(1)

0.809

4.203*

0.510

0.207

0.155

0.699

2.599

0.293

RESET(1)

0.0003

5.543*

0.405

1.418

0.032

0.015

4.796*

0.521

Notes: Same as Table 1.

The estimated coefficients of the IIPkt are significant and have the expected sign for all commodity groups apart from B and F, which again confirms that industrial production is the key determinant of GB road plus rail freight demand at both aggregate and disaggregate level. The estimated coefficients for Coal & Coke (B) and Chemicals & Fertiliser (F) are not significant but have the anticipated sign. The lagged dependent variables are significant in all the cases except Construction (E). For one-off events, DUM84 is significant with right sign in the model for Coal & Coke (B), and the oil price shock in 1986 affected the road plus rail freight demand for Petrol and Petroleum Products (C) adversely. The Steel workers’ strike in 1980 had a negative effect on road plus rail freight demand for Metals and Ores (D) and on Total demand. The level dummy variable DUM88 is not significant in the model for Others (G). The PA models passed all the diagnostic tests in four out of the eight cases. The model for Coal & Coke (B) failed three diagnostic tests. The models passed all but one tests in the other three cases. Reduced ADLM The initial specification of the general ADLM includes all possible variables. The lag length of the ADLM is set to be one (J=1) as the data we used is annual data. The final models are achieved by dropping the variables with coefficients that are incorrectly signed and / or insignificant. Results for these reduced ADLMs are presented in Table 3. The estimates of the Reduced ADLM suggest that the industrial production in the current period shows its significant impact on the road plus rail freight demand in GB in all of the cases except commodity groups B and F. Moreover, the industrial production in the previous year has an influence on the road plus rail freight demand for commodity groups D and G. The lagged dependent variables are significant in all the cases except Construction (E). The oil price shock in 1986 had negative effect on the freight demand for commodity group C. The steel workers’ strike affected the total demand adversely. Only in four out of eight cases did the models pass all of the diagnostic tests. VAR Model The specification of the VAR model starts with an unrestricted form. Dummies are regarded as exogenous variables in VAR models. The maximum lag length of the VAR model is set to be 3 for the purpose of identifying the appropriate lag structure of the VAR models. The optimal lag structure of the VAR model is decided on the AIC and BIC with the adjusted Likelihood Ratio (LR) being considered as references. The estimates of the VAR models are presented in Table 4. The IIPkt −1 variable is only significant in the case of Construction (E). The lagged dependent variable features in all the cases. This suggests that the lagged dependent variable is the key determinant of road plus rail freight demand in GB. All of the dummy variables are significant and have expected

Table 3 Estimation Results of the Reduced ADLMs ZKA Constant LZKkt-1 LIIPkt

-3.330 (1.510)

ZKB

ZKC

ZKD

ZKE

ZKF

ZKG

ZKTOT

1.035** -0.905 (0.339) (0.700)

-0.718 (0.767)

0.281 0.838* (0.165) (0.311)

-0.669 (0.440)

-0.511** (0.182)

0.699** 0.517** 0.352* (0.123) (0.158) (0.150)

0.689** (0.151)

0.636** (0.135)

0.920** (0.049)

0.670** (0.072)

0.990* (0.432)

1.187** 0.701** (0.239) (0.038) -0.871** (0.239)

0.837** (0.168) -0.614** (0.180)

0.490** (0.110)

0.472* (0.171)

LIIPk,t-1

-0.092** (0.026)

DUM80 DUM81 DUM84 -0.206** (0.070)

DUM86 DUM88

R2

0.977

0.239

0.518

0.714

0.914

0.405

0.985

0.986

S.E.

0.041

0.150

0.065

0.063

0.044

0.082

0.040

0.024

NORM(2)

6.108* 23.319** 1.653

0.051

1.003

2.162

0.058

2.793

LMSC(2)

3.963

1.298

0.686

3.430

7.843*

1.478

2.429

14.511**

HETRO(1)

0.809

0.132

0.596

0.118

0.216

0.205

1.692

0.293

RESET(1)

0.0003

5.711*

0.575

0.313

0.941

0.072

3.869

0.521

Notes: Same as Table 1.

Table 4 Estimation Results of the VAR models

Constant LZKkt-1

ZKA

ZKB

-1.441 (1.688) 0.848** (0.139)

0.894** (0.265) 0.516** (0.155)

ZKC

ZKD

0.302 0.339 (0.696) (0.758) 0.447** 0.734** (0.158) (0.164)

ZKE

ZKF

ZKG

0.155 (0.217) 0.440* (0.217)

0.831* (0.328) 0.629** (0.159)

1.308 (0.746) 0.915** (0.066)

0.450 (0.485)

0.028 (0.038)

0.175 (0.171)

0.066 (0.218)

0.396* (0.159)

0.005 (0.064)

-0.226 (0.187)

LIIPkt-2 -0.293** (0.073)

DUM80

-0.559** (0.120)

DUM84

-0.160* (0.070)

DUM86 DUM88 S.E. LMSC(2) NORM(2) HETRO(1)

0.071 (0.249) 0.273 (0.264) -0.132** (0.027)

-0.141* (0.070)

DUM81

R2

-0.167 (0.237) 1.277** (0.200) -0.546** (0.197)

LZKkt-2 LIIPkt-1

ZKTOT

0.974 0.044 4.013 5.882 9.104

0.540 0.117 4.220 0.873 25.743*

0.477 0.068 3.308 3.356 12.783

0.658 0.069 3.421 2.235 13.202

0.875 0.053 2.972 1.967 17.209

0.113* (0.046) 0.385 0.977 0.084 0.050 5.325 1.944 10.495* 2.194 29.424** 25.610*

0.983 0.026 1.583 2.128 26.374

Notes: Same as Table 1.

Table 5 Estimation Results of the TVP Models ZKA

ZKB

Constant

-3.201 (2.050)

LIIPkt

1.569** (0.442)

ZKC

ZKD

ZKE

ZKF

ZKG

ZKTOT

1.924** (0.484)

0.678 -1.903* (0.857) (0.903)

0.775 (0.763)

0.764 (1.186)

0.751 (0.777)

0.927 (0.658)

0.099 (0.118)

0.310* 0.892** 0.599** (0.183) (0.194) (0.164)

0.296 (0.253)

0.761** (0.169)

0.958** (0.143)

DUM80

-0.105

DUM81

-0.035

-0.044

DUM84

-0.506

DUM86

-0.124

DUM88

0.108

Log likelihood

39.097

8.288

21.456

29.050

34.988

17.429

37.935

56.551

SC

-2.051

-0.078

-0.771

-1.337

-1.803

-0.738

-1.875

-3.003

Notes: Same as Table 1.

Table 6 Estimation Results of the STSMs ZKA

ZKB

ZKC

ZKD

ZKE

ZKF

ZKG

ZKTOT

0

0.001485

0

5.146e-5

0

0.000566

0.000334 0.003972 0.003189 0.001465 0.001757 0.004047

0

0

Hyperparameters Level Slope Irregular

0.00110 7.083e-5 0.00349 0.000354 6.155e-6 0

0.000313 2.692e-7 8.389e-5

0

Coefficients Level

0.079 (2.346)

0.714 (0.590)

-0.385 (0.770)

-2.940** (0.755)

-0.641 (0.518)

-2.614 (1.353)

1.381 (0.743)

2.025** (0.585)

Slope

0.017* (0.007)

0.120** (0.034)

0.003 (0.004)

-0.036 (0.018)

-0.004 (0.002)

-0.047** (0.017)

0.025** (0.007)

0.014 (0.024)

LIIPkt

0.862* (0.506)

0.383* (0.141)

0.528** (0.164)

1.126** (0.162)

0.897** (0.111)

1.028** (0.288)

0.628** (0.165)

0.720** (0.127) -0.042** (0.010)

-0.080 (0.047)

Dum80 -0.086 (0.063)

Dum81 -0.252* (0.135)

Dum84

-0.205** (0.065)

Dum86

0.087* (0.042)

Dum88 Diagnostic Tests Normality

3.759

4.756

0.518

2.318

1.833

3.981

3.567

10.084**

H(8)

0.646

9.440*

1.089

2.106

0.387

2.910

0.131

1.411

DW

2.068

2.019

2.003

1.912

1.360

1.727

1.366

1.837

Q -statistic

4.132

3.880

0.668

1.390

12.387**

5.336

2.214

6.305

Rd

0.086

0.720

0.378

0.596

0.392

0.226

0.481

0.613

Se

0.040

0.087

0.063

0.055

0.043

0.077

0.037

0.022

2

Note: * and ** indicate that the estimates are significant at the 5% and 1% levels, respectively. Values in parentheses are standard errors. HETRO is the heteroscedasticity test and Qstatistic is the Box-Ljung Q-statistic test for residual serial correlation.

signs. The models passed all the diagnostic tests in five out of the eight cases. TVP Models Results for the TVP models, estimated using the Kalman filter algorithm, are presented in Table 5. It should be noted that in TVP models dummy variables are treated as exogenous variables whose parameters do not vary with time. However, the significance of the dummy variables is not reported by the Eviews 6.0 programme. The parameters reported are the estimates at the end of the sample period. The coefficients of the IIPkt have the expected signs and are significant in all cases but two, i.e., Coal & Coke (B) and Chemicals & Fertiliser (F), which is consistent with the results from some of the fixed parameter models. This suggests that industrial production explains well the road plus rail freight demand in GB. STSM By including a stochastic trend component in the regression equation, one can capture movement in freight demand series which is not explained by the explanatory variables included and would otherwise be left in the residuals. Table 6 shows that IIPkt is significant in all of the cases. For one-off events, DUM84 is significant with right sign in the model for Coal & Coke (B), and the oil price shock in 1986 affected the road plus rail freight demand for Petrol and Petroleum Products (C) adversely. The steel workers’ strike in 1980 had negative effect on Total demand. The level dummy variable DUM88 is significant in the model for Others (G). The models passed all of the diagnostic tests in five out of the eight cases. 5.2 Long-run Elasticity Analysis The long-run elasticities from the OLS regression model, the TVP model and STSM are obtained directly from the estimated coefficients of the independent variables in the models. For the PA model, reduced ADLM and VAR model, the lagged variables are treated as the current values of the variables in the long-run and the elasticities are calculated using the estimated coefficients of the explanatory variables. Taking the PA model as an example, the long-run income elasticities are calculated as the estimated coefficient of the industrial production variable (IIP) divided by the adjustment coefficient (1 − φ ), where φ is the estimated coefficient of the lagged dependent variable. Estimates of long-run elasticities of road plus rail freight transport demand with respect to industrial production (economic activity) from alternative econometric models are compared. The results are presented in Table 7.

Table 7 Comparison of Estimated Elasticities with respect to Industrial Production

Model Type

Commodity Group A

B

C

D

E

F

G

Total

Static

3.388**

0.108**

0.562**

0.924**

0.701**

0.159*

0.964*

1.467**

PA

3.289*

0.092

0.625*

0.981*

0.714**

0.051

2.406*

1.485**

0.728*

1.016**

0.701**

2.788**

1.206**

ReADLM 3.289*

-

-

VAR

2.961

0.058

0.316

0.248

0.707*

0.013

-2.659

1.279

TVP

1.569**

0.099

0.310*

0.892**

0.599**

0.296

0.761**

0.958**

STSM

0.862*

0.383*

0.528**

1.126**

0.897**

1.028**

0.628**

0.720**

Note: * and ** indicate that the elasticities are based on estimated parameters significant at the 5% and 1% levels, respectively. ‘-‘ denotes that the variable is insignificant in the reduced ADLM and hence was deleted in the estimation procedure.

It can be seen that the estimated elasticity values vary across commodity groups, which indicates that the composition of the economy has an influence on income elasticities of the demand for road plus rail freight in GB. The OLS regression model, the PA model and the reduced ADLM are more consistent with each other in terms of the significance of variables and the magnitudes of estimated elasticity values, while the results from the TVP model and STSM are similar to each other. The elasticities of road plus rail freight demand with respect to economic activity (which is a form of income elasticity) vary across different commodity groups. This indicates different sensitivity to variations in industrial production for different market sectors. The actual magnitude of income elasticity estimates also vary due to the different models estimated. For Food Drink & Agricultural Products (Group A), the income elasticities from the OLS regression model and the PA model (the reduced ADLM collapses to the PA model in this case) are consistent but extremely high (3.388 and 3.289). The derived income elasticity from the VAR model is similarly high at 2.961. The values from the TVP model and the STSM are 1.569 and 0.862 respectively. This gives the range of income elasticity from 0.862 to 3.388 in this sector, which is rather wide. Excluding the results from the VAR model which are extremely variable and often insignificant, the ranges for elasticities for other commodity groups are as follows. For the Coal & Coke (B) sector, the estimated income elasticities

are dubiously low, ranging from 0.092 to 0.383. The ranges for Petrol & Petroleum Products (C) and Construction (E) are relatively narrow: 0.3100.728 and 0.599-0.897 respectively. For the Metals & Ores sector (D), the estimated elasticity values are close to 1, in the range 0.892-1.126. In the case of Others (G), the range is wider, between 0.628 and 2.788. As far as the total road plus rail freight demand is concerned, the range of the income elasticity is from 0.720 to 1.485. Close inspection of the data suggests that these elasticity estimates, whilst informative, are likely to be contaminated with other trend effects. We made many other attempts to disentangle these effects, but no better results were obtained. 5.3 Ex Post Forecasting Comparison The chosen models are used to generate forecasts of the GB road plus rail freight demand for each commodity group, as well as for total road plus rail freight demand, over the period 1999-2006. For each model, the recursive forecasting technique is used to generate forecasts, i.e., the models are estimated over the period 1974-1998 first, and the estimated models are used to forecast road plus rail freight demand over the period 1999-2006. Subsequently the models are re-estimated using the data from 1974 to 1999 and forecasts are generated for the period 2000-2006. Such a procedure is repeated until all observations are exhausted. As a result, 8 one-year-ahead forecasts, 6 three-year-ahead forecasts, and 4 five-year-ahead forecasts are generated. The ex post forecasting performances of the models are evaluated based on a measure of error magnitude: the mean absolute percentage error (MAPE). MAPE is defined as n

MAPE =

∑ Yˆ − Y t =1

t

t

n

/ Yt

× 100

(11)

where Yˆt and Yt are respectively the forecast and actual values and n the number of forecast observations. The smallest values of the MAPE indicate the most accurate forecasts. The forecasting performances of the alternative models are ranked based on MAPE and the results are reported in Table 8. One-year-ahead forecasts Table 8 shows that for one-year-ahead forecasts, the STSM is the most accurate forecasting model in five out of the eight cases. The TVP model performs best in two cases, followed by the Reduced ADLM and OLS regression model for one case each (the Reduced ADLM model collapses to the OLS regression model in the case of commodity group E). On the basis of the number of occasions when each model is either the most accurate or the second most accurate forecasting model, the STSM is ranked first followed by the TVP model.

Table 8 Forecasting Accuracy of Alternative Econometric Models based on MAPE Forecasting Method

Forecast Horizon 1-year-ahead

3-year-ahead

5-year-ahead

ZKA

ZKB

ZKC

ZKD

ZKE

ZKF

ZKG

ZKTOT

OLS Regression

1.472%(6)

10.348%(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)

OLS Regression

1.241%(2)

15.385%(5)

3.491%(5)

3.252%(1)

0.351%(2=)

9.412%(6)

5.623%(6)

1.364%(6)

PA

1.331%(3=)

15.265%(4)

3.206%(4)

3.571%(2)

0.345%(1)

7.692%(4)

1.222%(5)

0.641%(2=)

ReADLM

1.331%(3=)

13.552%(3)

3.784%(6)

3.786%(3)

0.351%(2=)

6.151%(2)

0.759%(3)

0.641%(2=)

VAR

1.806%(5)

19.996%(6)

2.068%(2)

5.505%(5)

1.473%(6)

8.229%(5)

0.676%(2)

0.759%(5)

TVP

0.716%(1)

12.224%(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)

OLS Regression

1.477%(2)

19.752%(5)

4.324%(5)

3.872%(1)

0.306%(2=)

11.654%(5)

6.433%(6)

1.752%(6)

PA

1.972%(3=)

19.643%(4)

4.041%(4)

4.177%(2)

0.265%(1)

10.555%(4)

2.027%(4)

0.793%(1=)

ReADLM

1.972%(3=)

17.804%(3)

4.632%(6)

4.757%(3)

0.306%(2=)

9.051%(3)

0.944%(1)

0.793%(1=)

VAR

3.207%(5)

31.903%(6)

2.148%(1)

7.131%(5)

3.094%(6)

11.732%(6)

1.286%(3)

0.908%(3)

TVP

0.987%(1)

16.679%(2)

3.671%(3)

5.999%(4)

1.040%(5)

8.630%(2)

2.049%(5)

1.226%(4)

STSM

3.641%(6)

11.169%(1)

2.759%(2)

9.757%(6)

0.331%(4)

7.981%(1)

1.035%(2)

1.254%(5)

Note: The figures in parentheses are rankings.

The least accurate forecasting model is the traditional OLS regression model, due to the fact that it performs worst in five out of the eight cases. The VAR model, the STSM and the TVP model generate the least accurate forecasts in one case each, but as stated above, the latter two otherwise perform well. When the criterion is based on the number of occasions when each model is either the least accurate or the second least accurate forecasting model, again the OLS regression model exhibits the worst forecast performance, followed by the PA model and the VAR model. Three-year-ahead forecasts At the three-year-ahead forecasting horizon, the STSM performs consistently well, being ranked top in five out of the eight cases, whilst the TVP, PA and OLS regression models generate the best forecasts in just one case each. Based on the criterion of ‘the most accurate or second most accurate’ forecasting model, the STSM is still the best. It is difficult to differentiate between the PA model, the reduced ADLM and the OLS regression models on this basis, but as the PA model never generates the worst forecasts, it is considered to be the second best forecasting model following the STSM. The OLS regression model is ranked bottom in three cases, followed by the VAR model and STSM in two cases each. The PA and ReADLM models are each better than the STSM model for three out of the seven commodity groups, and close for the total. Despite the fact that the STSM is ranked bottom in two cases, it is still considered the best performing model as it generates the most accurate forecasts in most of the cases. When the criterion is ‘the least accurate or second least accurate’ forecasting model, the VAR model seems to be the worst performing model followed by the OLS regression model. Five-year-ahead forecasts For five-year-ahead forecasts, the PA model, the reduced ADLM and STSM each generate the most accurate forecasts in two out of the eight cases. According to the ‘most accurate or second most accurate’ criterion, the STSM is in the lead (four cases), followed by the PA model and reduced ADLM (three cases each). However, the STSM is ranked bottom twice and the reduced ADLM generates the least accurate forecasts once, whereas the rank of the PA model never drops below fourth place. It can be concluded that the PA model is the best performing model for five-year-ahead horizon, followed by the STSM and the reduced ADLM. As far as the least accurate forecasting model is concerned, the VAR model performs worst in three cases, followed by the OLS model and STSM in two cases. If the criterion is the ‘least accurate or second least accurate’ forecasting model, the VAR model and the OLS regression model are ranked equal. On the basis that the VAR model is ranked bottom more often than the OLS regression model, the VAR model could be considered the worst performing model for five-year-ahead horizons. As might be expected, MAPE shows a tendency to rise as the forecast horizon increases. This can be seen for example in the case of total road and rail freight (the final column in Table 8). Moreover, the MAPE for the PA and

ReADLM models tends to rise less quickly than for the other model forms. We concluded that for long-term (i.e. 5+ years) forecasts, the PA or its generalisation ReADLM are to be preferred. 6. CONCLUSIONS In this study, six econometric time series models have been applied to modelling and forecasting the road plus rail freight demand in GB, based on annual time series data for the period 1974-2006. These models comprise: the traditional OLS regression model, the PA model, the reduced ADLM, the unrestricted VAR model, the TVP model and the STSM. The empirical analysis is carried out at both aggregate and disaggregate levels. The relative forecasting accuracy of alternative models has been evaluated based on MAPE in the context of freight demand. The estimation results show that industrial production generally offers a good explanation of road plus rail freight demand in GB. However, the sensitivity of road plus rail freight demand to the change in the industrial production varies across different commodity groups, as different commodities have different transport requirements and each estimate reflects particular circumstances for each commodity group. The actual magnitudes of income elasticity estimates also vary due to the different models estimated. The ranges of estimated income elasticity for different sectors have been provided. This information will be valuable for transport planners and policy makers. The forecasting performance comparison results show that no single model outperforms the others in all situations. Overall, it can be concluded that for short-term (one-year-ahead) forecasting, the STSM is the best forecasting model, followed by the TVP model. For medium-term (three-year-ahead) forecasting the STSM is superior to its competing models, followed by the PA model. For relatively longer horizons (five-year-ahead in this study), the PA model and reduced ADLM seem to perform best although the STSM is not far behind. Forecasting horizons do seem to have an effect on the forecasting performance of different models. The STSM seems to perform better for short to medium term horizons, whereas the PA model outperforms others for longer term horizons. The TVP model generally performs better in the shortterm (one-year-ahead) than for longer-term forecasting. This gives the policy makers useful information when they need to choose between different forecasting tools.

REFERENCES Bjørner, T. B. (1999). Environmental benefits from better freight transport management: freight traffic in a VAR model, Transportation Research, Part D, 4 45-64. Breusch, T. (1978). Testing for autocorrelation in dynamic linear models. Australian Economic Papers, 17 334-355.

Dargay, J. M. and Hanly, M. (1999). Bus fare elasticities: report to the Department of the Environment, Transport and the Regions, ESRC TSU, December. Dargay, J. M. and Hanly, M. (2002). The demand for local bus services in England, Journal of Transport Economics and Policy, 36 (1) 73-91. de Jong, G., Gunn, H. and Walker, W. (2004). National and international freight transport models: an overview and ideas for future development, Transport Reviews, 24 103-124. Department for Transport (DfT) (1997). National Road Traffic Forecast (Great Britain) 1997, Working paper 3, Non-car Traffic: Modelling and Forecasting. London: DfT. 1-69. Department for Transport (DfT) (2008). Transport Statistics Great Britain (TSGB) 2008, London: DfT. Dimitropoulos, J., Hunt, L. C. and Judge, G. (2005). Estimating underlying energy demand trends using UK annual data. Applied Economics Letters, 12 239-244. Fowkes, A. S., Nash, C. A., Toner, J. P. and Tweddle, G. (1993). Disaggregated approaches to freight analysis: a feasibility study; report for the Department of Transport, Working Paper 399, Institute for Transport Studies, University of Leeds. Gacogne, V. and Reynaud, C. (1999). SOFTICE Deliverable D2: Methodology for Freight Transport Costs in Europe. European Commission, DG VII, Brussels, Belgium. Godfrey, L. G. (1978). Testing for higher order serial correlation in regression equations when the regressors contain lagged dependent variables, Econometrica, 46 1303-1310. Graham, D. and Glaister, S. (2004). Road traffic demand elasticity estimates: a review. Transport Reviews, 24(3) 261-274. Harvey, A. C. (1989). Forecasting, structural time series models and the Kalman filter, Cambridge University Press. Jarque, C. M. and Bera, A. K. (1980). Efficient tests for normality, homoscedasticity and serial independence of regression residuals, Economic Letters, 6 255-259. Johnson, D., Fowkes, A. S., Whiteing, A. E., Maurer, H.H. and Shen, S. (2008). Emissions modelling with a simple transport model, refereed paper presented at the European Transport Conference, Leiden, the Netherlands, October 6-8, 2008. Kalman, R. E. (1960). A new approach to linear filtering and prediction problems. Transactions ASME Journal of Basic Engineering, 82 35-45.

Kulshreshtha, M., Nag, B. and Kulshrestha, M. (2001). A multivariate cointegrating vector auto regressive model of freight transport demand: evidence from Indian railways, Transportation Research Part A, 35 29-45. Li, G., Wong, K. F., Song, H., and Witt, S. F. (2006). Tourism demand forecasting: a time varying parameter error correction model, Journal of Travel Research, 45 175-185 Office for National Statistics (2009a). Index of Production. Available at URL: http://www.statistics.gov.uk/statbase/tsdtables1.asp?vlnk=diop. Office for National Statistics (2009b). Retail Prices Index. Available at URL: http://www.statistics.gov.uk/rpi. Ramanathan, R. (2001). The long-run behaviour of transport performance in India: a cointegration approach, Transportation Research Part A, 35 309-320. Ramsey, J. B. (1969). Test for specification errors in classical linear least squares regression analysis, Journal of the Royal Statistical Society, Series B, 31 350-371. Road Haulage Association (2009). RHA Cost Tables 2009, prepared by DFF International, http://www.rha.uk.net/ContentFiles/Cost_Tables_2009%5B1%5D.pdf Song, H., Romilly, P. and Liu, X. (1998). The UK consumption function and structural instability: improving forecasting performance using a time varying parameter approach, Applied Economics, 30 975-983. Song, H. and Witt, S. F. (2006). Forecasting international tourist flows to macau, Tourism Management, 27 (2) 214-224. Song, H., Witt, S. F., and Jensen, T. C. (2003). Tourism forecasting: accuracy of alternative econometric models, International Journal of Forecasting, 19 123-141. Thomas, R. L. (1997). Modern econometrics: an introduction, Wesley, Harlow.

Addison-

Thury, G. and Witt, S. (1998). Forecasting industrial production using structural time series models, Omega, 26 (6): 751-767. White, H. (1980). A heteroscedasticity-consistent covariance matrix estimator and a direct test of heteroscedasticity, Econometrica, 48 817-838. Zlatoper, T. J. and Austrian, Z. (1989). Freight transportation demand: a survey of recent econometric studies, Transportation, 16 27-46.