代写assignment之尼日利亚的石油产品需求的实证分析

发布时间：2016-12-02 07:53

本研究的主要目的是估计石油产品的需求，使用随机动态的方法来达到获得改进和更加稳定估计的价格和收入弹性的目的。这项研究作为一个两步的随机过程指定随机趋势模型的石油产品的需求。通过与卡尔曼滤波应用最大似然在一起得到每个石油产品在尼日利亚的模型参数的估计。研究表明，引入随机趋势减少了相对于没有趋势模型的三个石油产品滞后的因变量的系数的估计。因此，，石油产品需求的价格和收入弹性较高，在短期和长期相对于变截距模型。引入随机趋势导致内样本的预测均方误差的改进。

Key words: Elasticity, Kalman filter, Maximum likelihood and Energy Demand.

引言——INTRODUCTION

It is widely accepted among analysts that the quantity demanded of a good or service has an inverse relationship with the price. This general perception derives as much from common sense as from economic theory and basic data observation. Given the significance of this phenomenon, economists have developed a specific concept called price elasticity which measures the relative change (%) in quantity demanded for a good or a service, in response to a relative change (%) in price. Price elasticities can be useful for studying the expected demand growth of a good or service, and for analysing the impact of different government actions with respect to prices such as tariffs, taxes or consumption-related subsidies. The positive link between the consumption of a good or service and the income is also widely acknowledged. That is the relative change (%) in quantity demanded which results from a relative change (%) in the income.

The total energy demand, either with respect to the whole economy or to a specific sector, has received widespread attention in the last thirty five years as a result of the international oil crises of 1973 and 1979. Today, this topic is still of interest due to global warming, associated with greenhouse gases and their link to energy consumption. Previous studies which present a synthesis of previous works on total energy demand models are Ziemba et al (1980), Donnelly (1987) and Hawdon(1992)


The quest for more accurate estimates of such key energy parameters is critical importance in the projection of future energy demand in particular, the energy market trends in general. Second is the role of these parameters in the design of policies for dealing with the negative environment externalities of the energy sector. Third is the fact that understanding energy demand dynamic through improve and robust estimates of energy demand parameters is essential for more informed and successful energy policy decision making and implementation. (Iwayemi, et 2007).


The objective of this paper is to estimate petroleum products demand in Nigeria using random trend approach. Specifically compare the result of modelling the intercept as random trend with constant intercept model. To achieve this objective, this study applied the approach introduced by Hunt et al (2003) to model the intercept in petroleum product demand function as random trend. The last fifteen years or so there has been an over-reliance on the co-integration technique, which is not always the right tool for the job of estimating energy demand function. Harvey (1997) states in general, the emphasis on unit roots, vector auto regression and co-integration has focused too much attention on tackling un-interesting problems by flawed methods. But this study will not dwell on that due to scope constraint. The structural time series model used to represent the random shift in demand relies only on a few parameters and yet it is quite general in the sense that it rests several well known models such as random walks, fixed trends or trends at all (Andrews 1999; Khalaf and Kichian, 2005).


The random trend model will be used to estimate price and income elasticity for petroleum products using aggregates and disaggregates approach using annual data covers 1977-2005. The specific products that will be considered are automotive gas oil (Diesel), premium motor spirit (petrol) and dual purpose kerosene (household kerosene) measured in tonnes per capita. Other econometric tests will be performed. In section two, the estimation of the demand equation is described. Section three discusses empirical results. Our findings are summarized in section four.


研究方法——RESEARCH METHODOLOGY


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.  

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 ï32ï￥.

Following Hunt et al. (2003) the random trend is assumed to evolve according to the following stochastic process:

and nt ~ NID (0, ï32n.) (6)

and ~ NID (0, ï32ï￥.) (7)

Equation (6) represents the level of the trend and equation (7) represents its stochastic slope. This is a general and yet parsimonious parametric specification of an evolving random trend. Several well known cases are subsumed under equation (6) and (7) according to the values that are taken by .

If we have random walk. If Î20 a‰  0, ï32ï￥=0 and ï32ï￥a‰ 0, we get constant trend. Once the influence of fundamental variables such as energy price, income and other explanatory variables have been taken into account, which is known about how energy intensity is evolving over time as a result of technological change in particular. The model specified here is quite flexible and impose no constraint on the speed and the level of adjustment as we encounter in models with a constant trend as no trend at all.

The log linear model with lag dependent variables with or without a constant trend has been used extensively to model petroleum product demand. The introduction of the lag structure is an ad hoc way of taking into account the fact that stock of energy using equipments is adjusting slowly overtime in response to various factors including energy prices. For previous application, see Walkers and Wirl (1993), Arsenault et al (1995), Gately and Huntington (2002) and Griffin and Schulman (2005).

The solution to equation (7), for example is

Where ï￠o is initial value of this parameter.

The important point to note is that random shocks have a permanent effect on slope parameter. A similar interpretation can be given to equation (6) where random shocks have permanent effects on the level of trend. Note that both parameters evolve over time and capture the cumulative effects of the two random shocks n and . If the variances of these error terms one zero i.e. ï3n2 = 0 and ï32 = 0, they are no more stochastic shock and the trend becomes deterministic.

The equation to be estimated therefore consist of equation (3) with (4) (5) (6) and (7). All the disturbance term are assumed to be independent and mutually uncorrelated with each other. The hyper parameters have an important role to play and govern the basic properties of the model. The hyper parameters, along with the model are estimated by maximum likelihood and from these the optimal estimates of ï￠t and Ut are estimated by the Kalman filters which represent the latest estimates of the level and slope of the trend.

The optimal estimates of the trend over the whole sample period are further calculated by the smoothing algorithm of the Kalman filters. For model evaluation, equation residuals are estimated (which are estimates of the equation disturbance term, similar to those from ordinary regression) plus a set of auxiliary residuals include smoothened estimates of the equation disturbances (known as the level residuals) and smoothened estimates of the slope disturbance (known as the slope residuals).

Further, to avert the problem of 'spurious regression', the time series characteristics of the variables using the Dickey-Fuller (DF), Augmented Dickey-Fuller (ADF) and Phillips-Perron (P-P) tests were first examined. Basically, the idea is to ascertain the order of integration of the variables as to whether they are stationary I(0) or non-stationary; and, therefore, the number of times each variable has to be differenced to arrive at stationarity.

The standard DF test is carried out by estimating the following;

After subtracting from both sides of the equation:

Where =

The null and alternative hypotheses may be written as:

H0 : = 0

H1 : < 0

The simple Dickey-Fuller unit root test described above is valid only if the series is an AR(1) process. If the series is correlated at higher order lags, the assumption of white noise disturbances is violated. The Augmented Dickey-Fuller (ADF) test constructs a parametric correction for higher-order correlation by assuming that the y series follows an AR(P) process and adding P lagged difference terms of the dependent variable y to the right-hand side of the test regression:

The usual practice is to include a number of lags sufficient to remove serial correlation in the residuals and for this; the Akaike Information Criterion is employed.

Phillips and Perron (1988) propose a non-parametric alternative method of controlling for serial correlation when testing for a unit root. The P-P method estimates the non-augmented DF test equation (9), and modifies the t-ratio of the coefficient so that serial correlation does not affect the asymptotic distribution of the test statistic. The PP test is based on the statistic:

Where is the estimate, and the t-ratio of, is the coefficient standard error, and s is the standard error of the test regression. In addition, is a consistent estimate of the error variance in equation (9) (calculated as (T - K)s2 where k is the number of regressors). The remaining term, f0, is an estimator of the residual spectrum at frequency zero.

3. RESULTS
Source: Author computation using E-view 7(CBN bulletin 2007)
FIGURE 2:Trend of Per Capita Dual Purpose Kerosine Consumption
Source: Author computation using E-view 7(CBN bulletin 2007)
FIGURE 3:Per Capita Consumption of Automotive Gas Oil
Source: Author computation using E-view 7(CBN bulletin 2007)
It can be seen that the trend of per capita consumption of PMS rose for the period 1977 to 1980, after which it fell to up to 1999 and an upward drift is noted for the remaining period. This is coherent with the fact that epileptic power supply has made a lot of people to purchase power generating plant that is using petrol engine since cost of diesel is high. It can also be as a result of rising income which led to massive importation of fairly used vehicles with high consumption of fuel. Overall, the per capita consumption of dual purpose kerosene (DPK) is decreasing over the sample period. This decrease in consumption could be as a result of substituting household gas (LPO) for kerosene due to increase in income of the consumers. It can also be linked to fact a lot of low income earners that can not afford the high cost of kerosene have changed to traditional fuels like charcoal, fuel wood, sawdust. Finally, improved industrialisation activities have led to increased per capita consumption of automatic gas oil due to incessant power supply.

The effect of modelling the intercept as a random trend is to lower the estimate of the coefficient of the lagged dependent variable and to enhance the effects of economic variables this is particularly the case for the income effect. The random trend has some in-built effects and it can vary from year to year, this reduces the role played by the lagged dependent variable and leaves more room for the fundamental economic variables. The p-values of the co-efficient estimates of lagged dependent variable are lowerthan 5% in all petroleum products except for kerosene in while they are all very small for income and product prices, except for per capita real income of diesel in the long-run.

The Short Run And Long Run Elasticity Of The Estimates For The Random And No Trend
Table 5 shows the short run and long run price and income elasticities estimates for the random trend and the no trend models.

The above figures (4 to 6) show within sample forecasts on the basis of parameter estimates of random trend and no trend model. It can be seen that the random trend model parameter estimates yield a closes fit in all the three petroleum products, this is also corroborated by its lower Root Mean Square Error (RMSE) in all the forecasts. The estimated model is mainly used for forecasting. To evaluate the model's forecasting ability. This study considers trend and no trend model of random approach and estimate the root mean square error (RMSE). The random trend model parameter estimate yield a closes fit in all the three petroleum products. This is also corroborated by its lower root mean square error (RMSE) in all forecasts. For forecasting purposes, in an ideal forecasting model, RMSE would be the smallest possible, i.e. the relative forecasting error should be the lowest possible. The estimates of this co-efficient are extremely small in random trend model for all the three petroleum products. This mean the random trend model forecast well.

The price and income elasticity estimates of the random trend model are statistically different from zero at the 5% significance level in long-run and short-run. For the no trend model, the price elasticity estimates of premium motor spirit (PMS) and automotive gas (AGO) are statistically different from zero at 5%. In the long-run, only the income of automotive gas oil (AGO) is not statistically different from zero. All the income and price elasticities estimate of random trend model are larger than those of no trend model.

It can be observed in the random trend model that, the long run price elasticities for diesel is -0.1270 while corresponding long-run income elasticities is 4.0180. Also, the long-run income elasticity for gasoline is 2.0138. These estimates are higher than those reported by Iwayemi et al (2007). They found long-run income elasticity (0.100) and long-run price elasticity of 0.108. In Onwiodukit and Adenuga (1998), diesel has the highest long-run income of 1.96 and gasoline has the highest long-run price elasticity (-0.86).

In this study, Diesel has the highest long-run price elasticity (-0.1270) and income elasticity (4.0780). This really different from results obtained in the study conducted by Iwayemi et al (2007) in which diesel has lowest long-run income elasticity of -0.100.

The long-run income elasticity for kerosene estimated in this study is very close to those reported in Iwayemi et al (2007). The differences recorded in the magnitude of these studies may be attributed to differences in the methodology adopted. The random trend process has memory and this tend to decrease the role of lagged dependent variable and give more room for fundamental economic variable especially income. This may account for high income elasticities obtained in this study.

The price elasticities for gasoline and kerosene are lower than those reported in Iwayemi et al (2007). This can also be attributed to methodology adopted (STSM) which incorporate "Technical progress". The higher price elasticities reported in Iwayemi et al (2007) and Onwiodukit and Adenuga (1999) can be attributed to failure to incorporate technical progress in their model. According to Hunt et al (2003), the failure to incorporate technical progress will results to an over estimation of the price elasticity.

结论——SUMMARY AND CONCLUSIONS

The major findings of the study can be summarized as follows: modelling the intercept as a random trend reduces the role of the lagged dependent variable and augments the effects of fundamental economic variables such as price and income. As a result, price and income elasticities of petroleum products demands are higher in the short run and long run relative to constant intercept model. The random trend displays an upward drift in the consumption of premium motor spirit (PMS), and automotive gas oil (AGO) but a downward one in the consumption of dual purpose kerosene (DPK). The random trend process has memory and this tend to decrease the role played by the lagged dependent variable and leave more room for the fundamental variables, which are price and income. The introduction of a random trend leads to improvement in the mean square error of within sample forecasts.

本文编号：201417