3.1. Vehicle Ownership Projection
Previous studies show that there is obvious positive correlation between vehicle ownership rate and GDP per capita, and the growth rate of vehicle ownership rate with GDP per capita growth is not stable, but follows an S-shape upward trend [
12,
13,
14,
15]. The internal logic is as follows: When the income level is very low, the increase in income for the residents will be preferentially spent on daily necessities. As resident income rises, together with the social transportation infrastructure improved, the demand for automobiles will rise rapidly because residents have extra money after solving the problem of food and clothing. Then, the growth of vehicle ownership rate will slow down and gradually approach saturation when resident income reaches a certain level and most residents have their traffic needs met. Finally, at an extremely high income level, residents will not have a larger number of cars, but replace the old cars with new ones when necessary.
The S-shape curves for demand forecasting can be fit using different models, such as the Bass model, the Logistic model, and the Gompertz model. All three curve models indicate that as the independent variable increases, the growth rate of the dependent variable first has an increasing growth, and then slows down, and finally approaches a saturation level. The Bass model is usually used to describe the diffusion trend of a technological innovation. The Logistic model is applicable to describe the life cycle of a consumer product, with a curve symmetrical about the inflexion point and time as the independent variable. The Gompertz model has similar features to the Logistic model, with excellent applicability and general characteristics of the growth curve. However, its corresponding S-shape curve is asymmetrical about the inflection point, and the independent variable may not be time. Compared with the Bass model and the Logistic model, the Gompertz model is more suitable for the prediction of vehicle ownership rate. The existing research also verifies that. Based on the historical data of vehicle ownership in the United Kingdom, Muraleedharakurup et al. [
17] confirmed that the Gompertz model is better than the Logistic model and the Bass model in terms of forecasting future hybrid vehicle adaptation. Similarly, Huo and Wang [
18] performed regression analysis using data of vehicle sales and stocks in China. The results also showed that the Gompertz model fit best among the three models.
We draw on and expand the Gompertz model established by Dargay and Gately [
20] to forecast the vehicle ownership of the 31 provinces of China in 2035. We assume that the relationship between vehicle ownership rate and GDP per capita can be expressed as the following:
where
and
denote province and time, respectively;
is the vehicle ownership rate (measured in vehicles per 1000 people) of province
at time
t;
is the real GDP per capita (measured in GDP per 1000 people) of province
at time
t;
is the saturation level of the vehicle ownership rate (measured in vehicles per 1000 people) of province
at time
t;
and
are two parameters to be estimated that determine the shape or curvature of the function. (Let the second derivative of Equation (1) be equal to 0, and we can get the per capita GDP and the exact year of each province at the inflexion point.) This model takes into account the provincial differences both in the saturation level of vehicle ownership and in the time required to reach the saturation level in China.
Equation (1) can be mathematically transformed as:
In order to predict the vehicle ownership rate of each province in 2035, we use the data of 31 provinces in the past 20 years to establish the regression model to estimate the parameters
and
. The model is as follows:
where
,
,
,
,
. The random error term
satisfies the assumption of independence, zero conditional mean, and homoscedasticity. As it can be seen from Figure 3, most provinces in China have not yet reached the level of vehicle saturation, so it is necessary to set
, the saturation level of vehicle ownership rate in each province. Regarding the setting of
, there is no unified and standard method for that by now. Gu et al. [
21] divided China’s 31 provinces into three groups by their urbanization rate in 2007 and assigned different saturation levels to different groups in their prediction of China’s vehicle ownership. Based on the saturation level of the US vehicle ownership rate, Dargay et al. [
22] used the data on urbanization rates and population densities to adjust the saturation levels of different countries when predicting the vehicle ownership in 45 countries around the world. According to the domestic and foreign research results, GDP per capita, urbanization rate, and population density are important factors affecting the growth of the vehicle ownership rate in a region [
23,
24]. Considering the heterogeneity of different provinces in China, we estimate the saturation levels of the vehicle ownership rate in different provinces separately. For province
, the saturation level of its vehicle ownership rate at year
can be expressed as:
In Equation (4),
represents the real GDP per 1000 people;
indicates the urbanization rate;
is the population density. Besides,
,
,
, and
are parameters of the model;
is the error term. As
,
, and
change over time, the maximum potential value of the vehicle ownership rate in each province also changes with time. The descriptions of model parameters are shown in
Table 1.
It can be demonstrated from Equation (4) that the parameters (
,
,
,
) in the above model must be obtained first to obtain the vehicle saturation level of each province in 2035. China’s vehicle ownership rate has not yet reached the saturation level, and it is impossible to use China’s historical data to estimate these parameters. This paper uses the historical data of EU15 to measure the parameters in the model. This is mainly for two reasons: Firstly, countries or regions to be chosen must have already reached or approached the saturation level of vehicle ownership rate in order to meet the requirements in Equation (4). Around the world, countries and regions with a high vehicle ownership rate include countries in North America and some other developed countries in Europe. As it can be seen from
Figure 2, the vehicle ownership rate in EU15 is relatively stable between 2005 and 2015. Secondly, to more accurately estimate the saturation level of China’s vehicle ownership rate, it is necessary to select countries and regions with similar population distribution and geographical structure to China to minimize the error. The population density of the United States and Canada in North America is far less than China, while EU15 are more similar to China in terms of population distribution and regional structure. (In 2016, China, the United States, Canada, and EU15 had a population density of 143.1 peo./km
2, 35.3 peo./km
2, 4 peo./km
2, and 125.6 peo./km
2 respectively.) Therefore, we finally chose the historical data of EU15 to measure the parameters in Equation (4). After determining the parameters in Equation (4), the predicted real GDP per capita (2010 RMB), urbanization rate, and population density of each province in 2035 need to be estimated to obtain the saturation level of vehicle ownership rate. This paper assumes that the total population and GDP per capita of each province increases at the average annual growth rate between 2013 and 2016. The urban population grows linearly at the average number between 2013 and 2016. The land area of each province remains constant until 2035.
After determining the saturation level of the vehicle ownership rate of each province, we can estimate the parameters and in the Gompertz model by the regression model, using the historical data of the vehicle ownership rate and real GDP per capita (2010 RMB) of the 31 provinces from 1997 to 2016. After that, we can get the forecast results of the vehicle ownership rate of each province in 2035. On the basis of the forecast vehicle ownership rate, this paper assumes that the total population of each province increases at the average growth rate between 2013 and 2016, and obtains the forecast results of vehicle ownership in each province in 2035.
In the vehicle ownership forecasting model, the data involved includes real GDP per capita of each province, the vehicle ownership rate of each province, and the saturation level of the vehicle ownership rate of each province. Among them, real GDP per capita of each province over the years comes from the China Statistical Yearbook from 1996 to 2017, deflated by the CPI, with 2010 as the base year. The vehicle ownership rate is the ratio of vehicle ownership to total population, from the China Automotive Market Yearbook and the China Statistical Yearbook over the years, respectively.
In the setting of the saturation level of the vehicle ownership rate, the data involved includes vehicle ownership, the real GDP per capita (2010 RMB), the urbanization rate, and the population density in EU15 and in the 31 provinces of China. Among them, the data of vehicle ownership in EU15 comes from the International Organization of Motor Vehicle Manufacturers (OICA). The real GDP per capita (2010 RMB), urbanization rate, and population density are from the World Bank database. The historical data of vehicle ownership, real GDP per capita (2010 RMB), urbanization rate, and population density of the 31 provinces over the years are from the provincial statistical yearbooks.
3.2. Fuel Demand Projection
Fuel demand is determined by vehicle population, average miles traveled, and fuel consumption rates [
18]. Since the average mileage and fuel economy of different types of vehicles vary greatly, we further categorize them into eight types. Fuel demand of each type can be expressed as follows:
where
is the fuel consumption of province
in the year
;
denotes the vehicle type
ownership of province
in the year
, and
, in million;
is the annual miles traveled by vehicle type
of province
in the year
, in kilometers;
is the fuel consumption rate of vehicle type
of province
in the year
, in L/100 km;
indicates the density of the fossil fuel, and the unit is kg/L.
The National Bureau of Statistics divides vehicles into passenger vehicles and trucks. The passenger vehicles are further divided into large passenger vehicles (LPVs), medium passenger vehicles (MPVs), small passenger vehicles (SPVs), and mini cars (MCs). Trucks are further divided into heavy-duty trucks (HDTs), medium-duty trucks (MDTs), light-duty trucks (LDTs), and mini trucks (MTs). Based on the type of fuel consumed by vehicles, each type is subdivided into petrol ones and diesel ones. Since the population of diesel vehicles in MTs and MCs, and gasoline vehicles in LPVs and HDTs is extremely small, it is feasible in our calculation to assume that all mini vehicles consume gasoline and all heavy vehicles consume diesel.
The number of each vehicle type in each province is determined both by the total vehicle population in the province and by the proportion of the vehicle type. In the past three years, the proportion of each type of automobile in China has changed little [
2]. Therefore, we assume that the proportion of each vehicle type in each province remains constant from 2015 to 2035.
is predicted by the Gompertz model;
and
come from the Annual Report on Automobile Energy-saving in China (2015). The statistics show that the average annual mileage of each type of vehicle changed little in recent years [
25,
26]. Hence we assume that
for each vehicle type is constant until 2035.
reduces by the average speed between 2004 and 2014.
is based on National VI Standard (the fifth phase of the national gasoline and diesel national standard). Involved parameters above are summarized in
Table 2.