**3. Methodology**

There are generally two ways to achieve the desired goal in this paper. The engineering simulation method could simulate the relationship between FCR and the influencing factors. Based on engineering simulation analysis, the FCR can also be predicted based on the change of influencing factors. However, the simulation method requires high quantity and quality of input data, and the simulation results for certain models may not represent the nationwide fleet. A linear regression method based mainly on the methodology of Knittel [19] and MacKenzie [13] was adopted in this study to analyze the relationship between official tested FCR and observable variables such as power, curb weight, fuel-efficient technology and other unobservable variables, such as vehicle brand, build year, etc., as shown in Equation (1):

$$
\ln{FC\_{it}} = \beta\_0 + \beta\_1 \ln{C} \\
\dot{W}\_{it} + \beta\_2 \ln{acc\_{it}} + \mathbf{X}\_{it}' \mathbf{B} + \tau\_t + \mu\_i + \varepsilon\_{it} \tag{1}
$$

where *FCit* represents the FCR of passenger vehicle model *i* in year *t* in the unit of L/100 km. β<sup>0</sup> is a constant. *CWit* is the curb weight in kg. *accit* is the 0 to 100 km/h acceleration time in seconds. **Xit** is a vector of dummy variables including whether the vehicle has a manual transmission, whether the vehicle is an SUV, or whether the vehicle has a turbocharge. τ*<sup>t</sup>* is the year fixed effects to estimate the technological progress by year *t*. μ*<sup>i</sup>* represents the difference by vehicle brands. We chose the vehicle brand rather than the manufacturer as a variable because the same manufacturer often produces more than one brand, and the vehicle characteristics of different brands vary widely. For instance, Changan Ford Mazda Corporation has four brands: the brand Ford of Sino-U.S., the brand Mazda of Sino-Japan, the brand Volvo of Sino-EU, and the local brand Changan. ε*it* is the random error term.

As τ*<sup>t</sup>* is a set of variables to estimate the annual technological growth, if **Xit** does not include any fuel-efficient technology, then τ*<sup>t</sup>* will capture all the technological growth in year *t*. If vehicle attributes do not change, *e*τ*<sup>t</sup>* represents the potential FCR improvement in year *t* compared with the FCR in the base year due to the fuel-efficient technology deployment, as shown in Equation (2):

$$\frac{F\mathcal{C}\_t}{F\mathcal{C}\_{\text{huc}}} = \mathcal{e}^{\tau\_t} \tag{2}$$

where, *FCt* represents FCR in year *t*. *FCbase* represents FCR in the base year. For small values of τ*t*, *<sup>e</sup>*τ*<sup>t</sup>* <sup>≈</sup> <sup>1</sup> + <sup>τ</sup>*t*.

#### **4. Results Analysis**

#### *4.1. Model Estimation Results*

Table 1 shows the estimation results of the regression models for passenger vehicle FCRs as a function of curb weight, power, acceleration time, and other attributes based on Equation (1). The products of joint venture brands and local brands showed great differences in both FCR and other attributes from 2009 to 2016. In this paper, we estimated the joint venture brands and local brands separately and compared them with each other. In each case, we estimated four models with different sets of control variables to explore the technological progress and effects of vehicle attributes on the FCR from 2009 to 2016. The estimated coefficients represent the elasticity coefficients of corresponding variables to FCR. The variables of all models include vehicle types, year fixed effect, vehicle brand, and curb weight. We captured the annual technological growth by using the year fixed effect while holding other variables constant. The estimate results are shown in Table 1. We also explored the effects of curb weight, acceleration time, power, drive type, turbocharging, GDI, and advanced transmissions on the official tested FCR.

Model 1 controlled the curb weight, power, vehicle type, year fixed effect, and brands. The fuel-efficient technologies, such as turbocharging, GDI, and advanced transmissions (Continuously Variable Transmission (CVT), Dual-clutch Transmission (DCT), etc.), were not controlled in Model 1, so that we could capture the technological progress for 2009–2016 through the year fixed effects while holding curb weight, power, vehicle type, and brand constant. The estimation results of Model 1 show that a 1% increase in curb weight results in a 0.86% and 0.85% increase in FCR for local brands and joint venture brands, respectively. A 1% increase in power leads to a 0.061% decrease in FCR for local brands in Model 1. The coefficient of power is negative, which is opposite to similar studies [13,14] but consistent with the results of Figures 4 and 5. Figures 4 and 5 show the linear regression result of power and FCR when holding curb weight constant (actually in a relatively small interval). The effect of power on FCR in Model 1 is because models with larger power are always more expensive and equipped with more fuel-efficient technologies, resulting in lower FCR. The coefficients of curb weight and power will be more reasonable if the model controls more variables of fuel-efficient technologies. More details of the results will be discussed in Model 3 and Model 4. The year fixed effect of local and joint venture brands between 2009 to 2016 are 16.1% and 20.3%, respectively, which means that if the controlling variables were kept constant in the base year of 2009, the local and joint venture brands could achieve the FCR improvement rate of 16.1% and 20.3% in 2016, respectively. We can also conclude that joint venture vehicles showed faster technological progress than that of local brands.

**Figure 4.** Regression results of power and fuel consumption rate of models in the 1200–1300 kg curb weight class.

**Figure 5.** Regression results of power and fuel consumption rate of models in the 1300–1400 kg curb weight class.

Model 2 is similar to Model 1 but replaces power with vehicle acceleration time. The coefficients of FCR to curb weight decrease, which is inconsistent with the findings of MacKenzie and Heywood. It is expected that the increase in weight at a constant power will result in both higher FCR and slower acceleration, but our results show this is not the case. The explanation is that power and acceleration time are both related to fuel-efficient technologies. In Model 2, the decreasing acceleration time may be accompanied by the deployment of fuel-efficient technologies. A comparison of the effects of power and acceleration time on the sensitivity of FCR to curb weight after controlling more variables will be discussed in Models 4 and 5.

Model 3 further calls for fuel-efficient technologies, such as turbocharging, GDI, advanced transmissions, drive type, and specific power deciles based on Model 1. Like the Model 5 proposed by MacKenzie and Heywood, it calls for specific power deciles as dummy variables to reflect the technical level of the engine and to make this model more robust and explanatory. The results show that compared with Model 1, the sensitivity of FCR to curb weight increases to 0.164 for local brands and 0.263 for joint venture brands after controlling more attributes. The sensitivities of the dummy variables automatic transmission (AT) and CVT to the FCR for local brands are 7.8% and 5.0%, which means that, compared with manual transmission (MT), AT and CVT could increase the passenger vehicle FCR by 7.8% and 5.0%, respectively, when other variables are constant. For the joint venture carmakers, the coefficients of AT and CVT are 4.5% and −4.4%. From the above, we can conclude that, compared with joint venture brands, the effectiveness of AT and CVT for local brands needs to be improved. The sensitivities of GDI to FCR are −3.1% for local brands and −6.5% for joint venture brands, which means the GDI of joint venture brands has a better effect than that of local brands.

Compared with Model 3, Model 4 replaces power with vehicle acceleration time. Instead of decreasing the sensitivity of FCR to curb weight in Model 1 and Model 2, this change increases it. After calling for more fuel-efficient technologies, especially those related with power and acceleration time, the change of sensitivity of FCR to curb weight is consistent with the findings of MacKenzie and Heywood and can be explained by the increase in weight at a constant acceleration time, which requires a higher FCR for both weight change and power change.




GDI

AT CVT DCT Vehicle types

Year fixed e

Brand Specific power decile a

Number of

observations

*R*2 *R*2

 8516 0.821

 8516

 0.823

 8516

 0.878

 8516

 0.876

 5667

 0.756

 5667

 0.756

 5667

 0.874

 5667

 0.871

ffect

–0.014

0.078 \*\*\*

–0.006

0.050 \*\*\*

–0.013

–0.022 \*

–0.009

 –0.015

 0.030 \*\*

 –0.011

 0

 –0.018

 –0.118 \*\*\*

 –0.018 √√√√√√√√

√√√√√√√√

√√√√√√√√

√√

√√

 –0.015

 0.045 \*\*\*

 –0.005

 –0.044 \*\*\*

 –0.009

 –0.007

 –0.012

 –0.107 \*\*\*

 –0.022

 –0.016

 –0.013

 –0.009

 –0.117 \*\*\*

 –0.011
