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Vehicle Ownership Analysis Based on GDP per Capita in China: 1963–2050

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This paper presents the Gompertz function of per capita GDP and vehicle stock to forecast the vehicle ownership of China through to 2050 against a background of increasing energy use and CO2 emissions associated with the potential demands of on-road vehicles. We forecast the level of vehicle stock in China based on the extant patterns of vehicle development in Organisation for Economic Co-operation and Development (OECD) countries, Europe, the United States and Japan. The results show that the OECD pattern and European pattern are more suitable for describing China's vehicle stock growth when compared with Japanese and U.S. patterns. The study finds that China's vehicle stock has developed as an S-shaped curve. During the forecast period, the inflection point of the increasing curve appears around the year 2030, with the annual growth of vehicle ownership increasing from 6.13% to 9.50% in the prior period prior and subsequently dropping to 0.45% in 2050. Based on the sensitivity analysis and robustness check, the impact of different Gompertz curve parameters and GDP growth rates on vehicle stock projection are analyzed.
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Sustainability 2014, 6, 4877-4899; doi:10.3390/su6084877
sustainability
ISSN 2071-1050
www.mdpi.com/journal/sustainability
Article
Vehicle Ownership Analysis Based on GDP per Capita in
China: 1963–2050
Tian Wu 1, Hongmei Zhao 2 and Xunmin Ou 3,4,*
1 School of Economics and Management, Tsinghua University, Beijing 100084, China;
E-Mail: wut.11@sem.tsinghua.edu.cn
2 Institute of Econometrics and Statistics, School of Economics, Nankai University,
Tianjin 300071, China; E-Mail: hongmeizhao@nankai.edu.cn
3 Institute of Energy, Environment and Economy, Tsinghua University, Beijing 100084, China
4 China Automotive Energy Research Center, Tsinghua University, Beijing 100084, China
* Author to whom correspondence should be addressed; E-Mail: ouxm@mail.tsinghua.edu.cn;
Tel.: +86-10-6279-7376; Fax: +86-10-6279-6166.
Received: 21 May 2014; in revised form: 16 July 2014 / Accepted: 25 July 2014 /
Published: 4 August 2014
Abstract: This paper presents the Gompertz function of per capita GDP and vehicle stock
to forecast the vehicle ownership of China through to 2050 against a background of
increasing energy use and CO2 emissions associated with the potential demands of on-road
vehicles. We forecast the level of vehicle stock in China based on the extant patterns of
vehicle development in Organisation for Economic Co-operation and Development
(OECD) countries, Europe, the United States and Japan. The results show that the OECD
pattern and European pattern are more suitable for describing China’s vehicle stock growth
when compared with Japanese and U.S. patterns. The study finds that China’s vehicle stock
has developed as an S-shaped curve. During the forecast period, the inflection point of the
increasing curve appears around the year 2030, with the annual growth of vehicle
ownership increasing from 6.13% to 9.50% in the prior period prior and subsequently
dropping to 0.45% in 2050. Based on the sensitivity analysis and robustness check, the
impact of different Gompertz curve parameters and GDP growth rates on vehicle stock
projection are analyzed.
Keywords: vehicle ownership; per capita GDP; Gompertz function; MARMA model
OPEN ACCESS
Sustainability 2014, 6 4878
1. Introduction
In recent years, the Chinese vehicle fleet has experienced rapid growth (Figure 1). Data from the
China Association of Automobile Manufacturers show that the production and sales of vehicles both
exceeded 20 million units in 2013 in China, and that China has been ranked first in the world for
production and sales of vehicles for five consecutive years.
Figure 1. Vehicle production and sales in China, 19922013 (Data source: [1,2]).
This result comes with an attendant problem. The increasing energy use and carbon dioxide (CO2)
emissions associated with on-road vehicles are a major challenge in China [3]. The rapid development
of the automotive industry inevitably brings an emission increase. Simonsen and Walnum [4] showed
that its high energy consumption means that transportation accounts for nearly 30% of CO2 emission in
the Organisation for Economic Co-operation and Development (OECD) countries and is one of the
main sources of regional and local air pollution. Similarly, He et al. [5] estimated that energy use and
carbon emissions in the transportation sector will comprise roughly 30% of total Chinese emissions by
2030. There is widespread concern in China at the levels of haze and PM2.5 (fine particulate matter: up
to 2.5 micrometers in size) pollution [6]. As Lang et al. [7] state, a new National Ambient Air Quality
Standard (NAAQS) was proposed in China in early 2012, introducing PM2.5 controls for the first time.
Since then, the first thing Chinese residents do each morning is check the Air Pollution Index.
It is therefore necessary to obtain an in-depth understanding of China’s automobile manufacturing
developments, particularly in relation to the environmental impacts of Chinese vehicles and to the
relationship between vehicle ownership and economic factors. Rather than using per capita income (or
per capita disposable income) as an economic factor as previous studies did [3,8–11], we use per capita
gross domestic product (GDP) to represent the economic factors. This paper is directly related to
Meyer et al. [12]. They use the real GDP growth rate of China (Taken from Leimbach and TÒch [13])
that differ from those mentioned in this paper and develop scenarios for global passenger car stock
0.00
5.00
10.00
15.00
20.00
25.00
199920002001200220032004200520062007200820092010201120122013
Vehicles/million
Year
Production of Vehicle
Sales of Vehicle
Sustainability 2014, 6 4879
until 2050. In this paper, we use the GDP index instead of real GDP to do the analysis. The reason is
that the GDP index published by China’s National Bureau of Statistics (NBS) is constructed by setting
last year’s GDP at 100. Thus, the GDP index can eliminate some effects of inflation on nominal GDP.
The real GDP data used in Meyer et al. [12] is not available for the public and we cannot find out the
reliable real GDP data for China from the current official data source.
Previous studies assumed an annual Chinese GDP growth rate of 6.0%, 4.7%, 4.0%, and 3.0%
during each decade from 2011 to 2050 [14]. Here, we use a multiple autoregressive moving average
(MARMA) model to forecast China’s annual GDP growth rate, then undertake the empirical analysis
based on this forecast results. The MARMA model is a combination of the regression and
autoregressive moving average (ARMA) models. The regression part of the MARMA model can
capture the long-term characteristics of the behaviors of GDP growth rate. The ARMA part of the
MARMA model can capture the short-term characteristics of the behaviors of GDP growth rate. The
tobustness checks and sensitivity analysis for the vehicle stock forecast are subsequently performed to
support our research findings.
Our analysis contributes to several literature strands. First, the existing Gompertz curve analyses are
successful in specifying features of the vehicle market to explain how to use economic factors to
estimate vehicle ownership. Huo and Wang [3] show that the Gompertz function fits the historical
data better than the Logistic or Richards functions. Dargay and Gately [15] tested several functional
forms, and showed that the Gompertz function is somewhat more flexible than the Logistic model,
particularly in allowing different curvatures at low- and high-income levels. They also illustrated
the characteristics of the Gompertz function for long-run vehicle ownership. Huo et al. [14] used
the Gompertz function to estimate the 2011–2050 Highway Vehicles (HWVs) stocks in China and
projected three vehicle stock scenarioshigh-growth, mid-growth and low-growthby HWV
saturation level. Zheng et al. [16] used the Gompertz function to calculate county level vehicle
ownership and found it to be reliable for simulating city-level vehicle growth patterns in China.
However, there are econometric problems in estimating the Gompertz function parameters in these
empirical works. A well-known advantage of the Gompertz function is its log-linearization ability [17].
Thus, previous studies treat it as a linear regression and use Ordinary Least Square (OLS) regression to
get the parameters, and focus on the mean value of R-square (R2) of the linear regression. This ignores
the panel data feature. Panel data have two dimensions: time series and cross-section. To apply the
usual OLS statistics from the pooled OLS regression across i and t, we need to add homoscedasticity
and no serial correlation assumptions [18]. The pooled OLS treat the data as cross sectional and
ignores the individual-specific effects [19]. Zhao [17] discussed the difference between pooled OLS,
Fixed Effects (FE), and the Random Effects (RE), but did not use the Hausman specification test
(details in [20]) to test whether the RE model is resoundingly rejected.
Second, this paper is directly related to Huo and Wang [3] and Dargay et al. [21] for Chinese
vehicle stock estimations. Huo and Wang [3] focus on the country level and estimate Chinese vehicle
stocks by the Gompertz, Logistic and Richards functions. They assume two scenarios for the growth of
private car ownership in Chinaa low-growth scenario and a high-growth scenariowhere the
saturation level of private car ownership per 1000 people is 400 and 500, respectively. Dargay et al. [21]
found that China has by far the greatest growth in vehicle ownership10.6% annuallyof non-OECD
countries. Further, they project that China will have nearly 20 times as many vehicles in 2030 as it had
Sustainability 2014, 6 4880
in 2002. This expansion is associated with both China’s rapid income growth and its per capita income
during this period being related with vehicle ownership growing at over twice the rate of income.
There are several important differences between this paper and those of Huo and Wang [3] and
Dargay et al. [21]. First, we use per capita GDP as an economic factor and estimate the annual GDP
growth based on the MARMA model regression. Second, we run regression on the Gompertz function
by FE and RE, and use the Hausman specification test to confirm the advantage of the FE or RE over a
pooled OLS. Third, sensitivity analysis is undertaken, one is that varies the saturation level of vehicle
ownership at the same rate of change for each country, and another one is with different GDP growth
rate. Fourth, we use a scenario analysis to discuss OECD, Europe, United States (U.S.), and Japan
patterns. Finally, we investigate a large sample: 1963–2011 per capita GDP and vehicle ownership in
21 countries and regions.
The remainder of the paper is organized as follows: Section 2 introduces the methodology and data.
Section 3 presents the empirical model and forecast the annual 2012–2050 vehicle ownership in China.
Section 4 presents the sensitivity analysis and robustness check, and Section 5 concludes and lays
down several implications in terms of sustainability policies.
2. Methodology and Data
In the short term, the variation of supply and price, using cost and consumption policy, may have an
impact on vehicle demand and increase short-term fluctuations in the vehicle market. However, in the
longer term, vehicle demand shows a highly significant correlation with the level of economic
development [22]. For instance, the Chinese consumption policies differ from the market approach of
OECD countries. (1) Bidding to drive: Car License Auction Policy in Shanghai. Shanghai had
approximately two million motor vehicles in 2004, increasing to 3.1 million in 2010. As a result,
Shanghai has promulgated a vehicle control policy, which uses monthly license auctions to limit the
number of new cars [23]; (2) Beijing’s Vehicle Lottery. Beijing is first and unique in restricting license
plates via a random lottery rather than using an auction system. Following Beijing’s lottery and
Shanghai’s auction experience, other Chinese cities are considering the similar policies to restrict the
vehicle demand and improve the air pollution caused by the high vehicle stock growth [24].
There are many reasons for relating the vehicle stock to GDP growth in China. At the macro level,
with the rapid growth of GDP, labor mobility and capital mobility between different regions should be
accelerated. This would cause an obvious increase of the vehicle stock. Also the GDP growth drives
the energy consumption up [25–27], which gives a chance to increase the vehicle stock for exploring
the energy and transferring the energy. At the individual level, for instance, motor vehicles are
considered more as necessities than luxury items as income levels transfer from poor to wealthy.
Under normal circumstances, strong growth in demand for motor vehicles is consistent with the growth
of wealth.
As Figure 2 shows, there is a highly significant correlation between vehicle ownership per 1000
people and per capita GDP (e.g., U.S., Germany, Japan and the United Kingdom).
Sustainability 2014, 6 4881
Figure 2. Annual vehicle ownership and economic development (Data source: [28]).
(a) United States (b) Germany
(c) Japan (d) United Kingdom
Based on such findings, earlier studies used the historical growth trends in developed countries and
employed the S-shaped growth curve [3,15,16,21,22]. Zhao [17] points out that vehicle ownership in
most OECD countries has reached the ultimate saturation level and that there is a Gompertz curve
function between vehicle stock and GDP per capita; other emerging countries also follow a
Gompertz curve pattern and present an upward trend. China is in the primary stage of the Gompertz
curve. The Development Research Center of the State Council [22] provides a theoretical analysis
explaining why vehicle demand has an S-shaped growth curve. Without government intervention or
vehicle market regulatory policies, vehicle demand changes are influenced by market factors (e.g.,
consumer income and vehicle price). Vehicle demand clearly increases with a consumer income
increase (income effect) or with a vehicle price decrease (price effect). Both conditions may occur
simultaneously to give an integrated effect. Historical evidence shows that increasing vehicle demand
levels can experience three stages: high-income, middle-income and low-income. Therefore, the
vehicle demand growth curve presents a non-linear growth pattern in developed countries that is
similar to the S-shape curve (Figure 3).
In relation to the particularity in China: China’s economic development has two primary
characteristics. Firstly, both Chinese GDP and the production and sales of vehicles have experienced
tremendous growth in recent years. Secondly, the China’s per capita GDP and vehicle ownership per
1000 people are still well behind advanced countries. As highlighted by Zhao [17], there is a large
population base and the income gap between urban and rural households in China. Thus, we were
unable to use Chinese historical data to estimate the Gompertz function. China is still at the start of the
0
200
400
600
800
1000
0
10,000
20,000
30,000
40,000
50,000
1963
1968
1973
1978
1983
1988
1993
1998
2003
2008
Vehicle/1000 people
Per c apita GDP
/constant 2000 U.S.$
Year
Per capita GDP Vehicle per 1000 people
0
200
400
600
800
0
10,000
20,000
30,000
1970
1974
1978
1982
1986
1990
1994
1998
2002
2006
2010
Vehicle/1000 people
Per ca pita GDP
/constant 2000 U.S.$
Year
Per capita GDP Vehicle per 1000 people
0
100
200
300
400
500
600
700
0
10,000
20,000
30,000
40,000
50,000
1963
1967
1971
1975
1979
1983
1987
1991
1995
1999
2003
2007
Veh icl e/1000 peopl e
Per capita GDP
/constant 2000 U.S.$
Year
Per capita GDP Vehicle per 1000 people
0
100
200
300
400
500
600
0
10,000
20,000
30,000
40,000
1963
1968
1973
1978
1983
1988
1993
1998
2003
2008
Veh icl e/1000 people
Per capita GDP
/constant 2000 U.S.$
Year
Per capita GDP Ve hicle per 1000 peopl e
Sustainability 2014, 6 4882
Gompertz curve: the orange circle in Figure 3 (at the lower left corner of the first quadrant) shows
China’s current position, close to the origin.
Figure 3. Worldwide vehicle ownership trends and per capita GDP (Data source: [28,29]).
Therefore, this study proceeds as follows. Firstly, we study the vehicle development trends of other
developed countries and choose an appropriate data to estimate the key parameters in the Gompertz
function. Secondly, we use Chinese GDP historical data to predict the annual 2012–2050 per capita
GDP. Finally, we use the parameters estimated in step one and the annual per capita GDP data
estimated in step two to predict the annual vehicle ownership in China. This process has an important
assumption that the development of China’s vehicle will follow the Gompertz curve path. This
assumption is reasonable because (1) vehicle development trends generally follow the Gompertz curve
in other countries; and (2) the success of China’s economic development shows that its industry
development is imitating the mature experience of other developed countries.
2.1. Economic Factor
The speed of vehicle ownership expansion in developed countries is mainly driven by the demand
side of the market; this means that vehicle ownership increases are decided mainly by consumers’
wealth level and purchase intention. The income variable usually better reflects the aggregate demand.
Therefore, researchers can use per capita income (or per capita disposable income) as an economic
factor in the Gompertz function in developed countries. It is important to note that there are two main
differences between China and other developed countries, which lead us to using per capita GDP as an
economic factor for China.
Sustainability 2014, 6 4883
First, the statistics relating to Chinese income levels are biased. Microeconometrics has a sizeable
volume of literaturestatistical deviationrelating to the income levels of Chinese residents.
Reported earnings may not fully reflect the actual income of individuals in the state sector, which may
result in an underestimation of earnings [30]. Li and Luo [31] claim that both disguised subsidies (such
as public housing, social insurances) and regional living costs should be considered when estimating
income in China.
Second, the balance between vehicle supply and demand is affected by the government’s
intervention (e.g., energy efficiency standards, car licensing regulations etc.) However, the case of
China’s vehicle market regulatory policies is much more unique. In recent years, the government
introduced several policies to address air pollution and exacerbated congestion. Aside from the
aforementioned policies, Car License Auction Policy in Shanghai and Beijing’s Vehicle Lottery, there
are some other policies: (1) Odd–Even Day Vehicle Prohibition (OEDVP) where vehicles with odd
license plate numbers can only be used on odd days. If the increase of vehicle ownership is decided
by consumer wealth and use levels, consumers with high income levels may be incentivized to
owning more vehicles under this policy, thus increasing market friction; (2) Other related policies.
On 25 February 2014, Xi Jinping, General Secretary of the Communist Party of China’s Central
Committee, State President and Chairman of the Central Military Commission, set five development
and management requirements, specifically referring to the increasing air pollution control, tackling
heavy haze, and improving air quality priorities, including strictly controlling vehicle market
sizes [32].
We use microeconomics to further explain why vehicle ownership is affected by government
intervention and regulatory policies: they may dampen consumer behavior. In the view of general
equilibrium models of consumers, producers and government, the constraints imposed on consumers
by government intervention and regulatory policies is equivalent to restrictions on producers:
the government can shift the market distortions to the producers. Therefore, we consider a
Government-Producers model, and take the partial equilibrium into account. The vehicle is good with
negative externality; it may produce air pollution during its production and use. The government’s
objective differs to the firm’s objective. The firm seeks profit maximization, while the Government is
concerned with both profit and the negative externality. The government aims for social welfare
maximization and reaching the social optimal. Therefore, the optimal investment is IG from the
government’s social welfare maximization objective and is IF > IG from the firm’s profit maximization
objective. This means that the firm is over-invested in the view of the government. As a result, the
government may restrict the production behavior of the firm: this is equivalent to placing restrictions
on consumers (e.g., Car License Auction Policy in Shanghai or Beijing’s Vehicle Lottery).
In conclusion, in China, buying a vehicle is not only a self-selection process but also subject to the
government intervention and vehicle market regulatory policies. Taking Beijing’s Vehicle Lottery as
an example, the difficulty of winning the lottery suggests that many entrants with a high willingness to
pay for a vehicle were unable to buy a car [24]. Affected by such policies, consumers cannot make the
decision to buy a vehicle according to their wealth level and purchase intention. We believe that GDP
is a typical indicator representing the aggregate economy. It reflects both the aggregate demand and
aggregate supply of an economy. The vehicle ownership is not only affected by the demand factor,
Sustainability 2014, 6 4884
but also by the supply factor and government intervention and regulatory policies. Therefore, GDP
rather than income should be used as the economic factor.
2.2. Gompertz Function
The Gompertz function is widely applied to establish the relationship between vehicle ownership
and economic factors [3,15,16,21]. The Gompertz function is used here to estimate country-level
vehicle ownership as follows:
,
*
,
EFit
e
it i
VVe
 (1)
where i denotes different countries and t denotes different years; Vi,t represents the vehicle ownership
(vehicles per 1000 people) of country i in year t; Vi* represents the ultimate saturation level of vehicle
ownership (vehicles per 1000 people) of country i. Given the parameters of α and β, Vi,t changes in
proportion to the change of Vi*; EFi,t represents the economic factor (per capita GDP) of country i in
year t; α and β are two negative parameters that determine the shape of the S-curve. The increase of α
and β would lead to a steep S-shape curve against the economic factors.
Log-linearization, then Equation (2) is converted from Equation (1)

*
,
,
ln ln ln
i
it
it
VEF
V





 (2)
As shown by Equation (2), ln (α) and β were linearly related and could be regressed as OLS for
time series data in country i.
In this study, we construct a panel data, including data from 1963–2011 within 21 countries and
regions. For panel data, based on the books by Baltagi [33], the Fixed-Effects estimator that amounts
to using OLS to estimate Equation (3)

**
,,
,
ln ln ln ln
iii
it it
it i
VVEF EF
VV













(3)
Additionally, the Hausman specification test should be used for clarity in identifying which model
(e.g., FE or RE) is the best tool for the Gompertz function.
2.3. Multiple Autoregressive Moving Average (MARMA) Model
We use a MARMA model to forecast China’s GDP growth. The MARMA model is actually an
application of the Box-Jenkins methodology. It is the combination of regression model and ARMA
model. The regression part captures the long-term characteristics of the behavior of GDP growth and
the ARMA part captures the short-term characteristics. The MARMA model is constructed first by
running a regression of GDP growth on population growth, and then taking the regression residual.
Next, we apply the Box-Jenkins methodology [34] to the regression residual, then forecast GDP
growth up until 2050. The reason for doing this is that the classical growth theory such as the Solow
model considers the population as the most important factor affecting the economic growth. To
forecast the long-term GDP growth, we would like to control the affected population. Also, as a time
series variable, the GDP growth always shows the cyclical moving pattern, which can be described by
Sustainability 2014, 6 4885
the ARMA process. Therefore, the MARMA model we use to forecast GDP growth has the
following expression:
ttttt
D
GDP T Dpop A L DGDP u B L u
   (4)
Define DGDP in Equation (4) as the annual GDP growth rate in period t, which is the dependent
variable. μ is the mean of DGDP process. T can be considered to be the time trend. A (L) is the
coefficient of lagged DGDP, where L is lag operator and the sum of lagged DGDP is called the
autoregressive part of DGDP process. B (L) is the coefficients of disturbance term u and lagged
disturbance term, where the sum of disturbance term and lagged disturbance term is called the moving
average part of the DGDP process.
2.4. Data
Four sources of data are used in the main empirical work: country-level vehicle ownership data
from 1963 to 2011 from the International Road Federation (IRF) world road statistics [29]; country-level
annual GDP data from 19632011 from the World Bank open data; country-level annual population
data for 19632011 from the World Bank open data [28]; and annual Chinese population prediction
data sets for 20122050 collected from National Population Development Strategy Research [35].
Vehicle ownership data includes full vehicles in use for 1963–2011 for different countries. The
variables include total vehicles, passenger cars, buses, lorries and vans, and motorcycles. We collected
such data for 21 countries and regions, including Australia, Austria, Belgium, Canada, Switzerland,
Germany, Denmark, Spain, Finland, France, Ireland, Italy, Japan, Netherlands, United Kingdom, U.S.,
Republic of Korea, Malaysia, Singapore, China and Hong Kong. The first 17 are OECD countries, and
Malaysia, Singapore and Hong Kong are emerging regions.
World Bank open data provided annual GDP and population data. We matched these two datasets
with vehicle ownership by year to get a panel data for 1963–2011: this was used in estimating the
Gompertz function. Annual GDP data was converted to constant 2000 US$. However, there is a great
impact of the China’s reform and opening-up policies on the Chinese economy, and China has pursued
sweeping economic changes in an officially sponsored transition. Furthermore, China’s National
Bureau of Statistics (NBS) has revised its estimates of nominal GDP from 1978 to 2004 on the basis of
nationwide economic censuses in 2004 [36]. Therefore, we used the the post-1978 data.
National Population Development Strategy Research [35] provided 38 prediction results of
population from 2012 to 2050 in China, which are based on different levels of birth rate, death rate, sex
ratio and other factors. Although the annual GDP growth fluctuates, it is a regulatory government
economic index. According to the series of reports about the National People’s Congress (NPC) and
Chinese People’s Political Consultative Conference (CPPCC) [37], the annual GDP growth must be
stabilized at a suitable level, and the annual GDP growth will be below 8.0% in the long run. The
annual population size has an impact on predicting the annual GDP growth when using the MARMA
model. The seven results we select are those based on the medium level of birth rate, death rate, sex
ratio and other factors. Among these, we choose the average one to do the forecast for GDP growth in
the next section and the other six results to do the robustness check. From the above discussion, the
Sustainability 2014, 6 4886
independent Gompertz function variable is the economic factor rather than demographic indicators.
This implies robust estimation results by using different results of predicting population.
3. Results and Analysis
To estimate the annual 2012–2050 vehicle ownership in China, we need to determine the
parameters α, β, and Vi* and the annual per capita GDP in China for the period.
The ultimate saturation level of Chinese vehicle ownership VChina* was determined through the
literature surveys [3,14,16], and we assumed a middle-growth scenario where the saturation level of
vehicle ownership per 1000 people is 500. Sensitivity analysis on different ultimate saturation levels of
vehicle ownership is undertaken in Section 4.
For parameters α and β derived from the Gompertz curve, we run regressions based on the OECD
(full sample), Europe (including all European countries), U.S., and Japan patterns. The first two
samples are panel data that run regressions as in Equation (3); the others are time-series data.
For the annual 20122050 Chinese per capita GDP, we use the MARMA model to get the
independent variable EFChina,t in the Gompertz function.
The estimations that give us all of the variables are required in estimating the annual vehicle
ownership per 1000 people in China by Equation (1).
3.1. Parameters in the Gompertz Function
We use the Hausman specification test to establish whether the FE or the RE model is the best tool
to be used in the Gompertz function.
The null hypothesis states that the random effects model is preferable (Table 1).
Table 1. Hausman Test in the Gompertz function.
Coefficients
(b) (B) (bB) Sqrt (diag(V_bV_B))
Fixed Random Difference Standard Error
it
EF 0.0001382 0.0001349 3.33×106 7.46×107
Notes: chi2 (1) = (bB)’[(V_bV_B)^(1)](bB) = 19.93; Prob > chi2 = 0.0000.
The empirical results are shown in Table 2. The first two columns show the regression results for
the OECD pattern by pooled OLS and FE: the results are significantly different. The middle column
shows the European pattern regression results, and the last two columns show the American and
Japanese patterns.
Decision: under the current specification, since p-value = 0.0000 < 0.05, reject H0. This means
the two models are different enough to resoundingly reject the RE model, and we should choose the
FE model.
Sustainability 2014, 6 4887
Table 2. Regression in the Gompertz function.
OECD Pattern Europe Pattern U.S. Pattern Japan Pattern
Pooled OLS Fixed Effects Fixed Effects OLS OLS
*
,
ln ln i
it
V
V








*
,
ln ln i
it
V
V








*
,
ln ln Europe
Europe t
V
V




*
,
ln ln US
US t
V
V




*
,
ln ln Japan
Japan t
V
V








,it
EF 0.000110 *** 0.000138 *** 0.000130 *** 0.000207 *** 0.000177 ***
(29.84) (40.14) (32.75) (8.63) (9.25)

ln
0.671 *** 1.169 *** 1.121 *** 2.882 *** 3.343 ***
(10.82) (17.67) (14.35) (5.70) (8.35)
N 971 971 625 42 44
t statistics has shown in parentheses: * p < 0.05; ** p < 0.01; *** p < 0.001.
We derived the parameters
,
from the Gompertz curve (Table 3).
Table 3. Parameter estimation in the Gompertz function.
Saturation Level of Vehicle Ownership per 1000 People
OECD pattern Saturation level of vehicle ownership for each country 3.21877 0.000138
Europe pattern Saturation level of vehicle ownership for each country 3.06792 0.000130
U.S. pattern 800 17.8499 0.000207
Japan pattern 590 28.3039 0.000177
Table 3 shows that the absolute value of parameter
in the U.S. or Japan is larger than those in
OECD or European countries; the absolute value of parameter β shows a similar pattern. There is no
significant difference between the absolute value of parameter α and β within the OECD and European
pattern, because the European sample has dominated (see the last row in Table 2).
We set the parameter substitution into Chinese data from historical data, comparing real data (Figure 4).
Figure 4. Simulated vehicle ownership data in China in different patterns (1990–2011).
Note: the saturation level of vehicle ownership per 1000 people is 500 in China.
0
10
20
30
40
50
60
70
80
0 500 1000 1500 2000 2500 3000
Veh icl e/1000 peopl e
Per capi ta GDP/c onstant 2000 U .S.$
Real data (1990-2011)
Calculated in OECD pattern
Calculated in Europe pattern
Calculated in U.S. pattern
Calculated in Japan pattern
Sustainability 2014, 6 4888
Figure 4 clearly shows that the OECD and Europe patterns fit the real vehicle ownership data best,
particularly in the high level of per capita GDP in recent years. In fact, the level of vehicle ownership
in the U.S. was 437 per 1000 people in 1963; this approaches the saturation level of vehicle ownership
per 1000 people of China. Therefore, we use the parameters α and β estimated in the OECD and
European patterns to forecast the growth pattern of vehicle ownership in China for 20122050.
Furthermore, the reason why Japanese and U.S. vehicle ownership patterns are at zero along the
different per capita GDP levels shown is due to the large absolute value of parameter α for Japan and
U.S., in contrast to a low level of per capita GDP and low level of development of automotive industry
for China.
Figure 5 illustrates why the OECD and Europe patterns best fit the real vehicle ownership data
of China.
Figure 5. Simulated vehicle ownership projection to 2050 of China in different patterns.
Note: Saturation of vehicle ownership per 1000 people is 500 in the OECD and Europe patterns.
In Figure 5, given per capita GDP, the larger absolute value of parameters α and β depict the
extremely low value of vehicle ownership per 1000 people in the low level of per capita GDP, with a
higher value in the high level of per capita GDP. As mentioned in Section 2, China is in the primary
stage of the Gompertz curve, experiencing tremendous growth in vehicle production and sales and with
the Chinese per capita GDP still well behind advanced countries. In the Gompertz curve, the smaller
absolute value of parameters α and β best fits the case of lower levels of per capita GDP.
Sustainability 2014, 6 4889
3.2. GDP Growth in China
We built the MARMA model based on the annual GDP growth from 1979 to 2012 (the base period
is 1978). We followed Zhao [17], controlling the annual population growth that may have an impact on
the growth of GDP in the channel of the change of labor supply and productivity of labor.
3.2.1. Augmented Dickey–Fuller Unit-Root Test
When the autoregression includes lagged changes, tests for a unit root are described as augmented
Dickey–Fuller (ADF) tests [38].
Figure 6 shows the annual GDP growth time series from 1979 to 2012.
Figure 6. The annual GDP growth (19792012) (Data source: [39]).
The ADF test for the annual GDP growth from 1979 to 2012 shows that the t-statistic for
ADF = 4.66 > 2.79 (critical value under the 5% significance level); this rejects H0, and means the
annual GDP growth time series is a stationary process. Therefore, we can use these series to build the
MARMA model.
3.2.2. Estimation in MARMA Model
According to the analysis by correlation diagram and partial correlation diagram, the order of
MARMA process has been determined. Then, we get the estimated function
  
1
2
ˆ
22.07 0.29 0.55 0.47
- 3.49 1.83 1.80 2.73
0.3566, 1.60, 30
tttt
DGDP T DPOP v
t Statistic
RDWT
 


(5)
where t
DPOP is the growth of total population in period t; ˆt
is an AR (1) process.
Therefore, we have
2
4
6
8
10
12
14
16
GDP growth
Year
Sustainability 2014, 6 4890

1
11
ˆ
22.07 0.29 0.55 0.47
22.07 0.29 0.55
0.47 22.07 0.29 1 0.55
ttt
t
tt
DGDP T DPOP
TDPOP
DGDP T DPOP

 



(6)
3.2.3. Forecasting the Annual GDP Growth Rate
Based on Equation (6), we can estimate the 20132050 annual GDP growth rate.
In Figure 7, the annual GDP growth is in the moderate range, with a slow growth from 2013 to
2029, then a gradual reduction to nearly 6.0% in 2046 followed by a recovery until 2050. The forecast
error bands around the forecasted value are calculated, which shows that the forecasted value stays
within the bands with the probability of 68%. Compared with the literature, Huo et al. [14] assume
China’s annual GDP growth rate to be 6.0%, 4.7%, 4.0%, and 3.0% during each decade from 2011 to
2050. Meyer et al. [12] uses real GDP growth rate of China for the analysis, which decreases rapidly
from 9% in 2010 to 2% in 2050. Their forecasted values for China’s GDP growth rate lie within the
forecast error bands we present here. However, these values are close to the lower band of our results.
It must nevertheless be pointed out that the GDP definition varies in different studies. We use the GDP
index to do the forecast, resulting in possible discrepancies with other studies. In view of this
uncertainty about the forecasted GDP growth rate, we do the sensitivity analysis using different
forecasted values of GDP growth in the next section.
Figure 7. The annual GDP growth rate (2013–2050).
Note: the DGDP_LOW and DGDP_UP are derived from the DGDP and standard error (S.E).
In period t, the annual per capita GDP is calculated as
11100
t
t
t
t
DGDP
GDP
per capita GDP POP



(7)
0
2
4
6
8
10
12
GDP growth
Year
DGDP DGDP_LOW DGDP_UP
Sustainability 2014, 6 4891
where t
POP is total population in period t.
Figure 8 shows the 2013–2050 annual per capita GDP.
Figure 8. Annual Chinese per capita GDP (2013–2050).
3.3. Vehicle Ownership Projection in China
All parameters needed for the Gompertz function are now estimated, including the parameters α and
β estimated by the OECD pattern and the annual per capita GDP in China for 20122050. Therefore,
according to Equation (1), we estimate the vehicle ownership per 1000 people in China from 2013 to
2050 (Figure 9).
Figure 9. Annual vehicle ownership per 1000 people in China (20122050).
Note: the saturation level of vehicle ownership per 1000 people is 500.
0
10,000
20,000
30,000
40,000
50,000
2012
2014
2016
2018
2020
2022
2024
2026
2028
2030
2032
2034
2036
2038
2040
2042
2044
2046
2048
2050
Per capita GDP
Year
0
100
200
300
400
500
600
2012
2014
2016
2018
2020
2022
2024
2026
2028
2030
2032
2034
2036
2038
2040
2042
2044
2046
2048
2050
vehicle ownership/1000 people
Year
Sustainability 2014, 6 4892
The results show that the growth pattern of vehicle ownership in China depicts an S-shape curve
with rapid growth from 2012 to 2027 that then gradually reduces annually, reaching the inflection
point of the increasing curve around the year 2030. Figure 10 shows the growth of annual vehicle
ownership per 1000 people in China.
Figure 10. Growth of annual vehicle ownership per 1000 people in China (2013–2050).
Figure 11 compares the projections on Chinese vehicle ownership per 1000 people made in
various studies.
Figure 11. Comparison of vehicle ownership projections per 1000 people made in
various studies.
0
1
2
3
4
5
6
7
8
9
10
Growth rate of vehicle ownership
Year
0
100
200
300
400
500
600
2010
2012
2014
2016
2018
2020
2022
2024
2026
2028
2030
2032
2034
2036
2038
2040
2042
2044
2046
2048
2050
Vehicle ownership/1000 people
Year
This study
Zhao[17]:scenariohigh-growth
Zhao[17]:scenariomedium-growth
Zhao[17]:scenariolow-growth
Huo et al.[14]:scenariohigh-growth
Huo et al.[14]:scenariomedium-growth
Huo et al.[14]:scenariolow-growth
Wang et al.[40]
Sustainability 2014, 6 4893
As was the case for the vehicle ownership projections shown in Figure 11, most of the earlier study
projections of vehicle ownership per 1000 people are lower than those of this study. The three
scenarios applied in Zhao [17] generated the lowest vehicle ownership levels because the ultimate
saturation level of vehicle ownership of China was set at 315 per 1000 people; this may have caused
the absolute value of vehicle ownership projection by the Gompertz function in Equation (1). The
assumptions of Huo et al. [14] on the Chinese annual average GDP growth were overly pessimistic,
resulting in lower vehicle ownership projections. However, Wang et al. [40] generated a much higher
vehicle ownership result than our results from 2010 to 2024. They assumed and mapped a higher GDP
growth onto China based on historical growth patterns of a set of countries with comparable growth
dynamics; however, they ignored the particularities of China (e.g., the low levels of Chinese per capita
GDP and vehicle ownership per 1000 people) and that vehicle stock conforms to the general Gompertz
S-shape curve.
4. Sensitivity Analysis and Robustness Check
4.1. Sensitivity Analysis
4.1.1. Changing the Ultimate Saturation Level
Sensitivity analysis investigates the effects of changing the ultimate saturation level on vehicle
ownership projections, based on the parameters reported in Table 4. To be clear, it would multiply the
level of vehicle ownership in China if we adjust the ultimate saturation level for China alone.
Table 4. Gompertz function parameter estimations for different multipliers in the pattern for OECD.
Saturation Level of Vehicle Ownership per 1000 People
0.8
*
0.8
i
V 3.05567 0.000170
0.9
*
0.9
i
V 2.80948 0.000144
1.0
*
i
V 3.21877 0.000138
1.1
*
1.1
i
V 2.23223 0.0000915
1.2
*
1.2
i
V 2.05033 0.0000735
We set the same multiplier δ to the ultimate saturation for each country. Therefore, the parameters
α and β derived from the Gompertz curve may change with the different value of the multiplier δ.
δ > 1 means there is a global automotive industry boom, while 0 < δ < 1 implies a automotive
industry contraction.
The changes are relative to the original value ranging from 0.8
to 1.2
, the interval 0.1
 .
The changes are shown in Figure 12.
The following insights are derived:
(1) The vehicle ownership per 1000 people is increasing, with the multiplier
increasing in the
two extreme levels of per capita GDP, particularly in the low economic development level. This
result is intuitive as purchasing power derives mainly from the early stage of economic
development. When the market has reached saturation, the purchasing power shrinks in the
vehicle market.
Sustainability 2014, 6 4894
(2) The inflection point lagged as the multiplier
increased; this means that market size
contractions may restrain the growth of vehicle ownership.
Figure 12. Sensitivity analysis for annual vehicle ownership per 1000 people in China
(20122050).
4.1.2. Different GDP Growth Rates
As discussed in the former section, sensitivity analysis on GDP growth rates may be an interesting
additional feature of analysis with respect to potential future vehicle stock development in China.
Following the result in Section 3.2.3, we do sensitivity analysis for the DGDP_LOW and
DGDP_UP, which are derived from the DGDP forecasted value plus and minus one standard error (S.E).
The other parameter set in the pattern for OECD as α = 3.21877, β = 0.000138, Vchina* = 500.
The results are shown in Figure 13.
Figure 13. Sensitivity analysis for different GDP growth rates in China (20122050).
0
100
200
300
400
500
600
2013
2015
2017
2019
2021
2023
2025
2027
2029
2031
2033
2035
2037
2039
2041
2043
2045
2047
2049
vehicle ownership/1000 people
Year
DGDP
DGDP_LOW
DGDP_UP
Sustainability 2014, 6 4895
The following insights are derived:
(1) The smaller the variation between the Chinese per capita GDP with the role model
(e.g., OECD pattern), the more similar the trend of vehicle ownership per 1000 people becomes
to the mature stage of the Gompertz curve, thus forming an S-curve (see the green line in
Figure 13).
(2) If the Chinese per capita GDP is far less than the role model (e.g., OECD pattern), the trend of
vehicle ownership per 1000 people is much more similar to the primary stage of the Gompertz
curve, with an increasing growth rate, and never reaches the inflection point (see the red line in
Figure 13).
4.2. Robustness Check
This section varies the methods of population estimation for a robustness check (Figure 14).
Figure 14. Robustness check for annual vehicle ownership per 1000 people in China
(20122050).
Note: R-C is an abbreviation for robustness check.
The check reveals that the increase of vehicle ownership per 1000 people follows a very similar
pattern for varied population estimation methods from 2012 to 2050; this indicates that economic
factors rather than demographic indicators are the drivers.
5. Conclusions
(1) Based on inter-external experiences and considering the future energy development and
resource constraints in China, we believe that China’s vehicle stock will follow the OECD or
Europe patterns in the long run, forming an S-shape curve. The U.S. and Japan patterns are not
complementary matches for the Chinese vehicle industry features. Although the geographical
and topographical features match more between U.S. and China than between Europe and
50
100
150
200
250
300
350
400
450
500
vehicle ownership/1000 people
Year
Basic R-C 1 R-C 2 R-C 3 R-C 4 R-C 5 R-C 6
Sustainability 2014, 6 4896
China, the key points of the Gompertz function are two factors, which are the level of
economic development and the development in automotive industry. However, the level of per
capita GDP for China is far less than U.S., and China is in the primary stage of the Gompertz
function (the growth rate is increasing, and never reaches the inflection point), whereas the
U.S. is in the mature stage (the growth rate is decreasing, and closer to the saturation level), due
to the difference of the development in automotive industry.
(2) The growth of vehicle ownership in China shows a rapid, three-fold increase from 2012 to
2030, and a subsequent gradual annual reduction. The inflection point of the increasing curve is
around the year 2030.
(3) Specific aspects of China’s economic development mean that the economic factor is per capita
GDP rather than per capita income. GDP annual growth projections suggest that it is
appropriate to follow the MARMA model in the moderate range.
(4) Using the same vehicle stock and per capita GDP historical data while varying the vehicle
ownership saturation level value could result in significant differences in projections on vehicle
ownership per 1000 people.
Based on the presented vehicle stock estimations, China is in the primary stage of the
Gompertz function today, and we trust that we are very early in what will be a boom of the
automotive industry over the next fifteen years, which may bring a great challenge to the air
pollution, energy consumption and CO2 emissions. Therefore, we present some sustainability
suggestions as follows:
In terms of energy for conventional Internal Combustion Engine Vehicles (ICEVs): increase
the energy efficiency standards, and encourage the production and consumption of light-duty
vehicles for the conventional ICEVs.
In terms of energy for New Energy Vehicles: rapid development of New Energy Vehicles (e.g.,
Electric Vehicles), due to their advantage in energy-saving and emission-reduction.
In terms of automotive industrial development: focus on the value chain or vertical structure
in the automotive industry. In recent years, it has focused on the vehicle manufacturers and
vehicle consumers, in order to decrease the air pollution, energy consumption and CO2
emissions. In fact, both vehicle manufacturers and vehicle consumers are downstream in the
value chain in the automotive industry. We should also focus on the upstream industries. For
instance, although there are advantages to energy-saving and emission-reduction in view of
vehicle use, the material consumption, process energy type and amount for the battery
manufacturing is always neglected in the Life Cycle Analysis [41].
Acknowledgments
The project was co-sponsored by the National Natural Science Foundation of China (71103109,
71203119, and 71373142), the Beijing Special Fund for Joint Construction with State Owned
Universities (Excellent Ph.D Degree Thesis Tutor Fund 20111000301), and the Beijing Higher
Education Young Elite Teacher Project (YETP0160).
Sustainability 2014, 6 4897
Author Contributions
Xunmin Ou contributed to design the research framework. Tian Wu and Hongmei Zhao developed
the analysis methods. Tian Wu performed research and analyzed the data and wrote the paper.
All authors have read and approved the final manuscript.
Conflicts of Interest
The authors declare no conflict of interest.
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... Wu et al.'s Gompertz function approach [32] is adopted here to predict China's passenger vehicle ownership, with curve parameters consistent with the OECD patterns. And the saturation level of vehicle ownership per 1000 people is assumed to be 400. ...
... In the third stage, along with the popularization of passenger vehicles, the vehicle ownership rate becomes close to its saturation level and grows slowly again. In the case of China, researches [38,46] also proved that similar to the mentioned developed countries, the development of passenger vehicle ownership in China also fits the positive correlation with income level and a slow-rapid-slow pattern with a saturation level in the later stage. However, since the automobile society in China is still in the beginning stage, such a trend cannot be observed as clear as in developed countries [39]. ...
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