OGY
Since Hunt and Manning (1989) Cointegration has become the accepted approach for estimating energy demand relationships. Despite the advances explained by Hendry and Juseius (2000) the Cointegration approach can only accommodate a deterministic trend and deterministic seasonal dummies.
Therefore Harvey's Structural Time Series Model (STSM) is adopted in this study, since it is consistent with interpretation of the underlying Energy Demand Trend (UEDT). In particular, it allows for time estimation of a non-linear UEDT that can be negative, positive or zero over the estimation period. Moreover, the use of the simple deterministic time trend is not ruled out in the STSM, instead it becomes a limiting case that is admissible only if statistically accepted by the data. Similar arguments apply to the treatment of seasonality in the STSM. The STSM allows for stochastic or evolving seasonal over the estimation period. Therefore deterministic seasonal dummies are not excluded from this approach's they are encompassed within the stochastic seasonal and are admissible, provided they are statistically accepted by the data.
Another advantage of using this approach to estimate petroleum products demand model is in forecasting, at least in the short-term, imposing a linear trend throughout the sample period results in a UEDT represented by an average trend for the whole estimation period.
模型——THE MODEL
Let us consider the following petroleum products demand model which can be derived from the partial adjustment framework.
(1)
Where e = limit of as n approaches infinity and all other variables are as defined below. The log transformation of equation (1) gives
(2)
Following from equation (2) we generate equation (3), (4) and (5) for the three petroleum products, therefore we have
MODEL I: Automotive Gas Oil (AGO)
lnAGOCt = Ut + a1lnAGOCt-1 + a2lnPtAGO + a3lnYt+ ï￥t. (3)
MODEL 2: Premium Motor Spirit (PMS)
lnPMSCt = Ut + a1lnPMSCt-1 + a2lnPtPMS + a3lnYt+ ï￥t. (4)
MODEL 3: Dual Purpose kerosene (DPK)
lnDPKCt = Ut + a1lnDPKCt-1 + a2lnPtDPK + a3lnYt+ ï￥t. (5)
The variables are defined as follows:
Xt = aggregate petroleum products consumption
XPt = Weighted average petroleum product real price. Â
Yt = Real GDP per Capita
PMSC = Premium Motor Spirit Consumption
AGOC = Automotive gas oil consumption
DPKC = Dual purpose kerosene consumption.
PAGO = Real Price of automotive gas oil
PPMS = Real Price of premium motor spirit
PDPK = Real Price of dual purpose kerosene
Ut = random trend
t.= random error term
a1, a2, a3 are structural parameters of interest.
The random error term ï￥t is assumed to be normally and independently distributed (NID) with mean 0 and variance ï32ï￥.
Following Hunt et al. (2003) the random trend is assumed to evolve according to the following stochastic process:
and nt ~ NID (0, ï32n.) (6)
and ~ NID (0, ï32ï￥.) (7)
Equation (6) rep
