“License Plate Lottery”: Why Are People So Keen to Participate in It?

Abstract

Vehicle purchase restriction policies greatly influence people’s behavior, especially their participation in the license plate lottery. This paper focuses on the socioeconomic characteristics and psychological factors of citizens participating in the license plate lottery, which can serve as a reference for policy makers aiming to guide rational participation in the lottery. A Multi-Index and Multi-Causal model were established based on social psychology, combined with the Theory of Planned Behavior (TPB). Perceived car necessity, perceived behavioral control, car ownership attitude and subjective norms were regarded as four latent psychological variables. Furthermore, the behaviors of license plate lottery participants in cities with purchase restriction policies were statistically analyzed from the perspectives of personal socioeconomic characteristics and psychological factors. The empirical research results reveal that the socioeconomic attributes of citizens have different degrees of influence on latent variables. Perceived car necessity is observed to have a significant direct impact on a citizen’s behavioral intention to participate in the lottery, which is also affected by perceived behavioral control. Car ownership attitude has the strongest impact on citizen behavior towards participating in the license plate lottery, followed by subjective norms, perceived behavioral control, and perceived car necessity. More specifically, the economic benefit associated with perceived behavioral control is identified as the critical factor in further promoting participation in the license plate lottery.

1. Introduction

To address a series of environmental and transportation problems caused by the rapid growth of motorization [1], Singapore, Mexico City, Shanghai, Guangzhou, Shenzhen, and Tokyo have implemented restriction policies on vehicle purchases. In 2011, Beijing launched the license plate lottery policy (LPLP) for citizens wanting to purchase passenger vehicles, limiting the number of the number of new issued license plate registrations to 100,000 vehicles per year [2]. Since the implementation of the LPLP, the number of lottery participants has increased, while the winning rate has gradually decreased due to the total volume control of issued license plate. The benchmark winning rate dropped from 1:10.6 in the first period of 2011 to 1:3120 in the sixth period of 2020 [3].

In addition, in 2014, the Beijing Municipal Government launched the license plate queuing policy for new energy vehicles (NEVs) as an alternative approach to registering license plates without participating in the lottery [4]. With the government’s policy incentivizing the purchase of NEVs, large numbers of license plate applications have shifted to the NEV program, which has led to rapid growth in the queuing time for NEV plate registration. In November 2019, new applications for NEVs had to wait for over 9 years to be issued [3]. The increasing difficulty of acquiring plates has led to a series of social issues, such as irregular trading of plates among individuals [5].

It is acknowledged that the implementation of the license plate restriction policy has made it increasingly difficult to attain license plate registration. The awareness of queuing and uncertainty has encouraged a large number of people to participate in the lottery even if they do not have an immediate need for registration [6]. As a result, promoting rational participation in the lottery and stabilizing the winning rate have become critical issues for policy makers. Therefore, this study aims to analyze the psychological factors affecting citizens’ participation in the lottery (queuing), which can serve as a reference for refining the LPLP to establish a rational vehicle purchase environment. Since Singapore took the lead in implementing the license plate restriction policy in the 1990s, scholars have conducted a series of studies in this field. Feiqi Liu introduced license plate restriction policies in Beijing, Tianjin, Shanghai, and Guangzhou, and analyzed the impact of these policies on the local private car stock. The results show that despite economic growth, the policy has maintained a relatively stable car ownership per thousand people in these cities [7]. Yang analyzed the impact of the LPLP on energy consumption [8]. Meisi Su evaluated the Beijing lottery restriction policy [9]. After studying the motor vehicle purchase restriction policy in Guangzhou, Shenhao Wang concluded that the lottery policy had become a means of speculation for the rich, rather than a solution for the poor [10]. Sandel reported that lotteries and auctions are common methods for allocating limited public resources [11]. Jianwei Ma analyzed the impact of the LPLP on consumers’ car purchase choices from an economic perspective [12], and Tao Li proposed optimization and improvement methods for the current LPLP in terms of the quota allocation plan [13]. Zhichun Li conducted a theoretical analysis on car ownership allocation plans, based on lottery, auction and hybrid of the two; based on model analysis, the best share of each scheme in the implementation plan was proposed [14]. Liwei Gao found that not all plate winners had an immediate demand for a car. The shortage caused by the existing policy has shifted the demand for car purchasing indicator from elastic to rigid. Aiming to address the problems of the lottery policy, he provided three measures to improve the vehicle purchase restriction policy in Beijing [6]. Focusing on the LPLP in Beijing, Chengxiang Zhuge investigated the impact of the policy on individual EV users over time by applying an agent-based spatially integrated urban model [15]. Yang et al. evaluated the impact of Beijing’s plate lottery policy. They found that the policy reduced the total stock of cars in Beijing by 14%. It also caused large reductions in vehicle distance traveled, and rush hour traffic in both the morning and evening [16]. Yang combined the information of whether a family member had won the lottery with the individual’s travel diary to study how the acquisition of the car affected travel behavior. The study found that the lottery policy in Beijing did not significantly increase the total travel distance or commuting time [17]. Zhang assessed the influences of the license plate lottery and subsidy policies, together with other influential factors, on consumers’ intention to purchase EVs. Based on a large sample of data collected in Beijing, they found that both the license plate lottery and subsidy policies were among the most influential factors in promoting EVs in Beijing [18]. In the past, research on the vehicle lottery policy has mostly focused on policy evaluation, the adjustment of the index allocation scheme, the impact of the policy on the mode of transportation and the impact of the policy on the willingness to buy electric vehicles. Under the vehicle lottery restriction policy, the behavior of citizens can be divided into two steps according to the lottery rules: the first step is deciding whether to participate in the lottery, and the second step is the vehicle purchase choice after winning the lottery. However, previous research on the influence of the vehicle purchase restriction policy on citizens’ car ownership and traveling choice behavior has only considered the effect of objective factors (socioeconomic attributes, purpose of travel, travel mode and so on) after winning the lottery. Few scholars have studied the role of the vehicle purchase restriction policy in citizens’ participation in the lottery. In addition, to objective factors, psychological factors significantly affect people’s choice behavior in decision making. As an important tool in the research of traffic psychology, the theory of planned behavior has been widely used to study vehicle use and purchase intentions, green intentions and so on. Lars examines the variables driving the intention to reduce car use by modeling the structure of a phase of change with mechanisms from the Theory of Planned Behavior (TPB) and the Normative Activation Model (NAM) [19]. Based on the TPB, Wang explored people’s willingness to adopt hybrid electric vehicles (HEVs) on their behavior [20]. Peng Ju integrated the psychological factors influencing car-sharing behavior into the traditional discrete choice model. A mixed choice model was then used to study travelers’ choice of car-sharing behavior. The results showed that latent psychological variables such as travelers’ perception of the usefulness of car-sharing, positively influenced their choice behavior, and the mixed choice model had a better fit than the traditional model without latent variables [21]. Peng Jing proposed an extended theory of planned behavior (ETPB) to thoroughly study the psychological factors caused by the influence of adult cognition and behavior habits. The study explored the relationship paradigm between these factors by constructing the theoretical framework of the choice behavior of students’ travel mode in China [22]. Based on an online survey in Sweden, Haustein used the TPB to compare electric vehicle user groups with traditional vehicle user groups, and the results showed that the acceptance attitude of electric vehicles was the most important factor influencing citizens to choose electric vehicles [23]. Oretiz-Peregrina used the TPB to study the influencing factors of distracted driving [24]. Mingyu Huo used the TPB to study the behavior of Chinese people using mobile phones when crossing the road [25]. Based on the TPB, Huiling Wang explored the relationship between willingness and environmental behavior in new garbage classification policy of China [26].

Previous studies have shown that socioeconomic attributes and psychological factors have an important impact on citizens’ choice behavior. However, the analysis of the existing research literature shows that few scholars have considered the impact of psychological factors, especially the effect on citizens’ participation in the license plate lottery. Therefore, this study focuses on the following three points:

• Based on the theory of planned behavior, the perceived car necessity is expanded, and the various psychological factors that affect citizens’ participation in the lottery are divided into several variables;
• Social attributes and psychological factors are combined in this study to establish a model of citizens’ willingness to participate in the LPLP;
• The purpose of this study is to investigate the impact of these factors on citizens’ participation in the car lottery, which can provide a reference basis for refining the license plate lottery policy and guiding the rational participation in the lottery. Resulting in the improved vehicle demand management.

The rest of this paper is arranged as follows: Section 2 presents the MIMIC model, which is used as a behavior model of citizen’s participation in LPLP based on the TPB and its influencing factors. Section 3 describes the collection data and preliminary statistical analysis of data from Beijing, which is used as an example. The reliability of the latent variables and the estimation results of the model are discussed in Section 4. Section 5 presents conclusions and recommendations for future research and makes suggestions for optimizing and adjusting the current LPLP.

2. Methods

2.1. Theory of Planned Behavior

Social psychology is a theoretical system that focuses on the psychology of people in a social environment. In this field, the psychological and behavioral patterns of individuals and groups in social interaction are studied. The representative theory is the Theory of Planned Behavior (TPB), firstly proposed by Ajzen et al., which can explain general behavior in the decision-making progress. The theory asserts that individual behavioral decisions are determined by their behavioral intentions, which in turn are jointly influenced by a combination of attitudes, subjective norms, and perceived behavioral control [27].

Haustein addressed Perceived Mobility Necessity (PMN), determined by actual demand of people according to the TPB, as people’s perception of the impact of mobility in their personal living environment, which then affect the choice of travel [28]. Many subsequent studies have extended PMN to the TPB in the analysis of travel behavior [29,30,31]. In this article, the focus is on whether the demand for cars affects the willingness to participate in the LPLP [5]. Therefore, this study extends Perceived Car Necessity (PCN), latent variable based on the TPB by incorporating the perceived mobility necessity.

We constructed an extended theoretical model of the TPB that includes perceived car necessity, psychological factors, behavioral intention to participate in the lottery, and participation behavior. The ETPB model is shown in Figure 1, where the behavioral intention to participate in the lottery (BI) is used as an intermediary variable, and the result of BI is the decision of whether to participate in the lottery (Behavior). The following hypothesis are proposed for the model:

Hypothesis 1 (H1).

Citizens’ car ownership attitude (ATT) is positively correlated with their behavioral intention to participate in the lottery (BI);

Hypothesis 2 (H2).

Citizens’ subjective norms (SN) are positively related to their behavioral intention to participate in the lottery (BI);

Hypothesis 3 (H3).

Citizens’ perceived behavioral control (PBC) is positively correlated with their behavioral intention to participate in the lottery (BI);

Hypothesis 4 (H4).

Citizens’ perceived behavioral control (PBC) is positively related to their choice of participation in the lottery (Behavior);

Hypothesis 5 (H5).

Citizens’ perceived car necessity (PCN) is positively correlated with their behavioral intention to participate in the lottery (BI);

Hypothesis 6 (H6).

Citizens’ perceived car necessity (PCN) is positively correlated with their choice of participation in the lottery (Behavior);

Hypothesis 7 (H7).

Citizens’ behavioral intention to participate in the lottery (BI) is positively correlated with their choice of participate in the lottery (Behavior).

Based on the above theory, a structural equation model of willingness to participate in the LPLP to analyze the influencing factors of willingness to participate in the lottery and the impact of psychological factors on citizens’ participation behavior in the lottery was estimated by analyzing the parameters in the model. The model includes 5 latent variables: perceived car necessity (PCN), subjective norm (SN), perceived behavioral control (PBC), car ownership attitude (ATT), and behavioral intention to participate in the lottery (BI). Twenty-six measurement variables were analyzed to interpret the defined latent variables.

Table 1. Description of each latent variable and its measurement variable.

Latent Variable	Measurement Variable	Variable Description
Perceived Car Necessity (PCN)	PCN1	Holiday driving demand
	PCN2	The demand for driving when taking children to and from school
	PCN3	Demand for commuting by private vehicle
	PCN4	Other driving demand
Car Ownership Attitude (ATT)	ATT1	Owning a car can improve the flexibility of travel.
	ATT2	Owning a car can improve the comfort of travel.
	ATT3	Owning a car can improve the convenience of travel.
	ATT4	Owning a car can improve the safety of travel.
	ATT5	Owning a car can improve the quality of life.
Subjective Norm (SN)	SN1	Influenced by friends/colleagues/classmates
	SN2	Influenced by relevant news or social media
	SN3	Other people who participate in the lottery will affect your participation
	SN4	Influenced by family
Perceptual Behavior Control (PBC)	PBC1	Participate in the lottery with a “try and see” mentality out of opportunism
	PBC2	The degree of difficulty of successfully applying for the license plate (winning rate)
	PBC3	You can participate in the lottery at no cost
	PBC4	The license plates can be leased and sold at a profit, and the results of the application for license plates are equivalent to invisible property
Intention to Participate in Lottery Behavior (BI)	BI1	I have a strong desire to participate in the lottery
	BI2	I would like to encourage people around me to participate in the lottery
	BI3	Even if I have a car, I will still participate in the lottery

provides a detailed description of each latent variable and its measurement variable. On the basis of the related literature on the TPB, a Likert-five-level scale was applied for the evaluation of the measurement variables [27].

2.2. Multiple Indicators and Multiple Causes Model (MIMIC)

Psychological factors, also called psychological latent variables, are variables that cannot be directly and precisely observed and are obtained by corresponding observed variables using measurement equations.

In the MIMIC model, the exogenous and endogenous variables of the latent variable are expressed through a structural model and the relationship between the latent variable and its related measurement variable is obtained. The MIMIC model can not only clearly express the exogenous causes and endogenous indicators of latent variables through a rigorous structural model, obtaining the degree of influence of all measurement variables on the latent variables, but also conveniently apply a formal statistical test on the relationship. Schneider asserted that the MIMIC model does not need to be based on strict constraints and assumptions. The model can handle multiple latent variables and endogenous indicators and allows exogenous causes and endogenous indicators to contain measurement errors. Therefore, its theoretical framework is more flexible than other indirect measures and can potentially incorporates all other indirect measures [32]. Multi-indicator multi-causal models can integrate both causal and indicator variables affecting latent variables through a rigorous structural model hierarchy. In addition, it determined the influence coefficient between measurement and latent variables. The MIMIC model has been widely used in theoretical studies by scholars [22,33,34].

A multi-index and multi-causal model is essentially a form of structural equation model, including two sub-models: the measurement model is used to describe the relationship between latent variables and measurement variables; the structural model describes the relationship between latent variables and variables that do not explain the variation.

The measurement equation is shown in Equation (1):

$$y=\Lambda \eta +\epsilon$$

(1)

The structural equation is shown in Equation (2):

$$\eta =\mathrm{\Gamma }x+\zeta$$

(2)

In the formula: $\eta$ is a latent variable vector;

• $x$ is an exogenous observable variable vector with causality to $\eta$;
• $y$ is an observable index variable vector of $\eta$;
• $\epsilon$ and $\zeta$ are the error terms of endogenous and exogenous variables, respectively;
• $\Lambda$ and $\mathrm{\Gamma }$ are coefficient matrices with estimated parameters.

Formula (1) is substituted into Equation (2):

$$y=\mathrm{\Lambda }(\mathrm{\Gamma }x+\zeta )+\epsilon =\mathrm{\Pi }x+v$$

(3)

$$\mathrm{\Pi }=\mathrm{\Lambda }\mathrm{\Gamma }, v=\mathrm{\Lambda }\zeta +\epsilon$$

(4)

In the Formula (3), Π, v is show as Equation (4).

The objective of Equation (3) for the structural equation model is to minimize the difference between the sample covariance matrix S and the covariance matrix ∑. The elements in the covariance matrix ∑ are assumed to be the function ∑ = ∑(θ) of the parameter vector θ. The difference function F = F (S, ∑(θ)) can be used to measure the difference between the sample covariance matrix S and ∑(θ) on $\stackrel{⌢}{\theta }$. Assuming that ζ and ε obey the normal distribution and are independent of each other, $E(\zeta \epsilon ’)=0$, $E({\zeta }^2)={\sigma }^2$, $E(\epsilon {\epsilon }^2)={\Theta }^2$, ${\Theta }^2$ are the lower triangular matrices about v, then the covariance matrix can be obtained, as in the Equation (5) Once the model is identified, various parameters can be estimated.

$${\displaystyle \sum (\stackrel{⌢}{\theta })}=E(vv’)={\sigma }^2\mathrm{\Lambda }\mathrm{\Lambda }’+{\Theta }^2$$

(5)

The Multiple Indicator (MI) part of the MIMIC model is equivalent to confirmatory factor analysis of the variables of the ETPB. The Multiple Causes (MIC) part of the model can be expressed by the following formula:

$$\begin{array}{l}{\eta }_{li}={\gamma }_{l1}mal{e}_i+{\gamma }_{l2}ag{e}_i+{\gamma }_{l3}educatio{n}_i\\ +{\gamma }_{l4}ca{r}_i+{\gamma }_{l5}commut{e}_i+{\gamma }_{l6}tim{e}_i\\ +{\gamma }_{l7}numbe{r}_i+{\gamma }_{l8}qualifactio{n}_i+{\zeta }_i\end{array}$$

(6)

In the equation: $l$ is car ownership attitude, subjective norms, perceived car necessity, perceived behavioral control, behavioral intention and other latent variables that represent the theoretical elements of the ETPB; $i$ is observed individual.

The multi-index and multi-causal model was established to test the internal mechanism among the latent variables in the theory of planned behavior, as well as the relationship between the latent variables and the individual economic and social attributes of citizens. The model is based on latent variables, and socio-economic attribute variables are introduced to the structural model to analyze the correlation between latent variables of travelers and measurement indicators. The measurement model with information on socio-economic attributes is used to analyze the relationship between the individual characteristics of travelers and latent variables. The conceptual framework diagram of the multi-index and multi-causal model is shown in Figure 2.

3. Questionnaire Survey and Inspection

Empirical data were obtained through a questionnaire survey. The respondents were mainly people with lottery qualifications (holding a motor vehicle driver’s license without vehicle under their name). To ensure the reliability and richness of the sample, the questionnaire described the current LPLP scenario in Beijing so that all respondents successfully understood the policy and responded according to their actual situation under different scenarios. The content of the questionnaire mainly includes information about the respondent’s personal and family socioeconomic attributes and willingness to participate in the lottery.

The design of the questionnaire is mainly based on the latent psychological variable scale of the TPB. A corresponding adjustment was made according to practical problems of the vehicle purchase restriction policy, and the RP survey method was adopted.

The online questionnaires were distributed on 13 August 2019 through Questionnaire Star, an online commercial survey platform widely used in China. Using the sample service function of Questionnaire Star, questionnaires were randomly distributed to users who lived in Beijing and were over 18 years old. A total of 528 questionnaires were collected, after excluding obvious contradictions and incomplete answers, 430 valid datasets were obtained, accounting for 81.4%.

For a finite population, the sample sampling size formula is as follow [35]:

$$n\ge \frac{N}{{(\frac{\alpha }{k})}^2\frac{N-1}{P(1-P)}+1}$$

(7)

In the formula: n is the sample demand;

• N is the population;
• α is the significance level;
• k is quantile;
• P is usually set to 0.05. Because a setting of 0.50 yields the most plausible sample size.

Generally, the significant level α was set to 0.05, and the quantile k was 1.96, the number of participants in the shake was 3.3 million, and the minimum sample size n was calculated to be about 384. The number of valid questionnaires was 430 over 384, so it met the requirement.

For SEM analysis, the desirable ratio of the number of samples to the observed variables is usually between 10:1 and 15:1 [36]. The structural equation model constructed in this research has 26 observed variables, so the desired sample size is at least 260. The survey resulted in more than 260 valid questionnaires, so the sample size of respondents is adequate.

3.1. Descriptive Statistics Analysis

This section provides descriptive statistics on the socioeconomic attributes of individuals in the sample. The sample contained slightly more males (58.14%) than female. The education of respondents was mostly undergraduate, and 36.98%; 32.56% of respondents had an annual family income of 50,000–100,000 yuan; 74.65% of people were qualified to participate in the lottery (legally holding a driver’s license with no registered motor vehicle). The majority of households had 3 people. The personal socio-economic information is shown in

Table 2. Personal socioeconomic attributes of respondents.

Variables		Percentage	Variables		Percentage
Age	18–25 years old	26.51%	Gender	Male	58.14%
	26–30 years old	27.67%		Famale	41.86%
	31–40 years old	25.81%	The number of household members who need to commute by car	0	19.77%
	41–50 years old	16.51%		1	38.6%
	51–60 years old	3.26%		2	30.23%
	Older than 60 years old	0.23%		3	7.91%
Occupation	Staff in governmentor or public institution	33.02%		4	1.86%
	Professional and technical personnel such as lawyers/doctors/teachers/engineers	15.12%		≥5	1.63%
	Private/self-employed	3.26%	The number of household members who are eligible for participating in the lottery	0	25.35%
	Corporate Staff	20.93%		1	37.21%
	Freelance	4.65%		2	29.53%
	Retired	0.47%		3	6.05%
	Full-time student	13.72%		≥4	1.86%
	other	8.84%	Famliy annual income (CNY)	≤50,000	21.63%
Education level	Senior high school and under	7.91%		50,000–100,000	32.56%
	Technical secondary school/junior college	24.88%		100,000–200,000	25.12%
	University	36.98%		200,000–300,000	10.47%
	Master degree or above	30.23%		300,000–500,000	6.74%
Number of household members	1	10.7%		500,000–1,000,000	2.09%
	2	17.44%		≥1,000,000	1.4%
	3	34.65%	The main mode of transportation for daily travel	Private car	38.84%
	4	23.72%		Public transportation (subway, bus)	31.16%
	≥5	13.49%		Walking/cycling	21.4%
Number of Vehicles in the household	0	29.77%		Taxi/online car-hailing	5.58%
	1	49.53%		other	3.02%
	2	18.14%
	≥3	2.56%

Note: CNY 1000 ≈ USD 156.8.

. The survey results of the seventh national census in Beijing in 2020 show that there are slightly more males than females in Beijing at present, and a higher proportion has an education level of university or above. Therefore, the survey data in this paper are consistent with the data of the seventh census in Beijing and are representative of the population. Thus, the data can represent the overall circumstances of participation in the lottery among permanent residents of Beijing and can be used for the analysis described in the subsequent chapters.

3.2. Model Inspection

Cronbach’s alpha coefficient was used to test the reliability of the scale. Mallery and George stated that a reliability coefficient α greater than 0.9 indicates excellent reliability; 0.8 or greater is good, 0.7 or greater is acceptable, greater than 0.6 is basically recognized, greater than 0.5 is borderline, and less than 0.5 is unacceptable [37].

Table 3. Reliability test of latent variables.

Variables	Items	Loadings	Cronbach’s Alpha	AVE
PCN	PCN1	0.731	0.889	0.644
	PCN2	0.807
	PCN3	0.780
	PCN4	0.711
ATT	ATT1	0.827	0.914	0.691
	ATT2	0.859
	ATT3	0.864
	ATT4	0.649
	ATT5	0.713
SN	SN1	0.790	0.884	0.680
	SN2	0.803
	SN3	0.843
	SN4	0.565
PBC	PBC1	0.866	0.946	0.612
	PBC2	0.856
	PBC3	0.890
	PBC4	0.870
BI	BI1	0.673	0.825	0.612
	BI2	0.717
	BI3	0.653

shows that the Cronbach’s alpha coefficient of each variable is greater than the standard value of 0.7, and the overall Cronbach reliability coefficient is 0.922. The strong internal consistency indicates that the variables have good reliability.

The average variance extracted value (AVE) is used to evaluate the convergent validity of the questionnaire, that is, the amount of variation explained by each factor from all of the items contained in the factor. An AVE value greater than 0.5 [38] indicates that the indicator variables can effectively explain the latent variables, and the latent variables have good reliability and validity. Table 3 shows that the AVE of each latent variable is greater than 0.5, which shows that the questionnaire has ideal convergent validity and can be used for further research and analysis.

Based on the TPB, the latent variables of perceived car necessity (PCN), and the factor analysis was required. SPSS was used to conduct exploratory factor analysis on the samples. The results of Kaiser-Meyer-Olkin (KMO) and Bartlett’s sphericity test are shown in

Table 4. Results of KMO and Bartlett’s spherical test.

Kaiser-Meyer-Olkin Value		0.905
Bartlett’s Sphericity Test	Approximate chi-square	7007.652
	Df	190
	Sig.	0.000

. KMO = 0.905, greater than 0.7, Bartlett’s sphericity test value is significant (Sig. < 0.001), which shows that there is a strong correlation between the observed variables and the prerequisite of factor analysis is satisfied. The total explanatory power of perceived car necessity (PCN), subjective norms (SN), perceived behavioral control (PBC), car ownership attitude (ATT), and behavioral intention to participate in the lottery (BI), which is higher than 50%, indicating that the scale has a good internal consistency reliability.

The maximum variance method was used to orthogonally rotate the factor loading matrix, and the loading value is greater than 0.5. The results in

Table 5. Factor loading matrix after rotation.

Item	Rotated Component Matrix
	ATT	PBC	SN	PCN	BI
ATT1	0.866
ATT2	0.852
ATT3	0.898
ATT4	0.711
ATT5	0.613
PBC1		0.901
PBC2		0.894
PBC3		0.924
PBC4		0.920
SN1			0.879
SN2			0.866
SN3			0.898
SN4			0.609
PCN1				0.813
PCN2				0.750
PCN3				0.738
PCN4				0.662
BI1					0.791
BI2					0.702
BI3					0.691

show that the scale has good structural validity.

Then, confirmatory factor analysis was applied to test the model fit. The chi-square degree of freedom ratio (${\chi }^2/df$), goodness of fit index (GFI), adjusted goodness of fit index (AGFI), root mean square residual (RMR), root mean square error of approximation (RMSEA), normed fit index (NFI), incremental fit index (IFI), and comparative fit index (CFI) were used as the evaluation indicators in this study. Among them, ${\chi }^2/df$ is a statistic that directly tests the similarity between the sample covariance matrix and the estimated covariance matrix. The closer the value of ${\chi }^2/df$ to 0, the better the observation data fits the model. Generally, when the ${\chi }^2/df$ value is less than 3, the model fits well, and when the ${\chi }^2/df$ value is between 3 and 5, the model has an acceptable fit. A value greater than 5 means that the observation data do not fit the model well, but the indicator is affected by sample size [39]. The results are shown in

Table 6. Fitness results.

Evaluation Index	Test Results	Fit Criteria
Chi-Square/degrees of freedom (${\chi }^2/df$)	3.155	1–5
Goodness of fit index (GFI)	0.891	>0.80
Adjusted goodness of fit index (AGFI)	0.855	>0.80
Root mean square residual (RMR)	0.066	<0.08
Root mean square error of approximate (RMSEA)	0.071	<0.08
Normed fit index (NFI)	0.924	>0.80
Incremental fit index (IFI)	0.947	>0.80
Comparative fit index (CFI)	0.936	>0.80

. The results in the table below indicate that fitness indicators of the model meet the criteria, and the overall model fit is good.

4. Multiple Indicators and Multiple Causes Model Analysis

Through the estimation of the MIMIC model, the relationship between the individual socioeconomic attributes of lottery participants and the latent variables of the extended theory of planned behavior was determined, as was the mutual causal relationship between the latent variables.

4.1. Analysis of the Relationship between Individual Socioeconomic Attributes and the Latent Variables of Extended Theory of Planned Behavior Model

Table 7. The influence of individual socio-economic attributes on latent variables.

Items	ATT	SN	PBC	PCN	BI
Age	−0.118 *	−0.142 **	−0.022	0.191 **	−0.061
Education level	0.095	0.046	0.013	0.062	−0.205 **
The number of people in a household who need to commute by car	0.041	0.035	0.228	0.067	0.158 *
The number of people in a household who are eligible for participating in the lottery	−0.03	−0.086	0.19 **	−0.011	0.067
The number of family members in a household participating in the lottery	0.174	0.025	0.157 **	0.086	−0.061
Time spent participating in the lottery	−0.092	0.019	0.075 ***	0.024	0.105
Household annual income	0.183 ***	−0.059	0.076	0.091	0.085
Vehicle ownership in a household	−0.171 **	0.004	0.068	−0.086	0.077

Note: *: p < 0.05; **: p < 0.01; ***: p < 0.001.

shows the influence of individual socio-economic attributes on the latent variables of in the ETPB. The results show that not all personal soci-economic attributes have a significant impact on the latent variables in the MIMIC model, and the number of households and daily travel patterns have no significant impact on any of the latent variable. Individual socio-economic attributes have a greater impact on “car ownership attitude” and “perceived behavioral control”.

Age, family income, and vehicle ownership in a household have a significant impact on citizens’ attitudes towards car ownership, and the path coefficients are −0.118, 0.183, and −0.171, respectively. The household annual income and ATT have a significant positive effect, while age has a significant negative effect on ATT. Older citizens are relatively reluctant to own motor vehicles because people are becoming more fitness conscious and tend to choose green transportation such as walking and bicycling. The number of motor vehicles in the household also has a significant negative impact on car ownership attitudes, that is, the more motor vehicles owned by people in an individual’s households, the less inclined to own new motor vehicles. This may be due to the difficulty finding parking, and the increase in the cost of car ownership. As a result, these citizens are not inclined to own motor vehicles.

Age has a significant negative impact on SN, and the path coefficient is −0.142. SN describes the particular influence of other people’s and society’s expectations on an individual [40]. The data show that older citizens are less likely to be affected by others or by the outside world in their choice of to participate in the lottery.

The number of people in the household who are eligible for the lottery, the number of household member participating in the lottery, and the time spent participating in the lottery have a significant positive effect on the PBC. The path coefficients are 0.19, 0.157, and 0.075, respectively. This shows that the greater the number of household members who are eligible for the lottery, the greater the number of household members participating in the lottery, and the longer that citizens have participated in the lottery, the smaller the expected obstacle to lottery participation, and the more optimistic the public will be about winning the lottery.

Age has a significant positive impact on PCN, and the path coefficient is 0.191. This shows that the perceived car necessity for activities such as commuting and holiday travel gradually increase with age.

Education level has a significant negative impact on BI, and its path coefficient is −0.205. From the perspective of its relationship with education level and motor vehicle ownership, citizens are less likely to participate in the lottery if they have higher education levels and fewer individuals in their households without vehicles. The number of household members who need to commute by private vehicle has a significant positive impact on the behavioral intention to participate in the lottery, and its path coefficient is 0.158. This shows that the greater the number of people in the family who need to commute by car, the stronger the behavioral intention of citizens to participate in the lottery.

4.2. Analysis of the Relationship between the Latent Variables of the Expanded Theory of Planned Behavior

Based on valid sample data, AMOS software was used to establish a structural equation model. The output result of the model is shown in Figure 3. The standardized path coefficient between the variables reflects the magnitude of the direct influence between variables. Figure 3 shows that ATT, SN, PBC, and PCN have significant positive effects on BI, and the path coefficients are 0.366, 0.262, 0.218, 0.213, respectively. The significance level of ATT, SN and PBC is p < 0.001, and the significance level of PCN is p < 0.01. This indicates that the behavioral intention to participate in the lottery affected by ATT, SN, PBC and PCN, and thus the hypotheses H1, H2, H3 and H5 are proven.

BI and PBC have a significant positive effect on behavior, and their path coefficients are 0.324 and 0.110, respectively. The significance level of BI is p < 0.001 and the significance level of PBC is p < 0.05. This shows that BI and PBC influence citizens’ behavior towards participating in the lottery. Therefore, hypotheses H4 and H7 hold. The influence of PCN on behavior did not pass the significance test, so hypothesis H6 does not hold.

4.3. Analysis of the Relationship between Latent Variables and Corresponding Observed Variables

Table 8. Estimation results for relationships between latent variables and observed variables.

Path	Estimate	Standard Deviation	Critical Ratio	p
ATT → ATT1	0.849	0.071	16.480	***
ATT → ATT2	0.93	0.070	17.920	***
ATT → ATT3	0.927	0.070	17.763	***
ATT → ATT4	0.693	—	—	—
ATT → ATT5	0.727	0.070	14.247	***
SN → SN1	0.849	0.105	14.056	***
SN → SN2	0.889	0.107	13.738	***
SN → SN3	0.922	0.109	14.056	***
SN → SN4	0.599	—	—	—
PBC → PBC1	0.869	0.036	27.224	***
PBC → PBC2	0.857	0.039	26.450	***
PBC → PBC3	0.943	0.031	33.599	***
PBC → PBC4	0.916	—	—	—
PCN → PCN1	0.698	0.061	15.377	***
PCN → PCN2	0.775	0.057	17.832	***
PCN → PCN3	0.886	0.049	22.040	***
PCN → PCN4	0.838	—	—	—
BI → BI1	0.812	—	—	—
BI → BI2	0.79	0.061	17.832	***
BI → BI3	0.744	0.063	15.377	***

Note: ***: p < 0.001.

shows the estimated relationships between the latent and observed variables based on the MIMIC model of citizens’ willingness to participate in the lottery.

Among ATT variables, ATT2 (path coefficient of 0.93) and ATT3 (path coefficient of 0.927), are the two largest coefficient values. This shows that the travel comfort and convenience that comes with owning a motor vehicle motivates citizens to participate in the lottery. Among SN variables, SN3 has the largest standardized path coefficient of 0.922, which indicates that citizens are vulnerable to the influence of other citizens around them who participate in the lottery. Among PBC variables, the standardized path coefficient of PBC3 is 0.943, and the path coefficient of PBC4 is also high 0.916, which indicates the ability to participate in the lottery no cost and the potential economic benefits associated with a successful license plate application are the main factors that attract citizens to participate in the lottery. Among PCN variables, the path coefficient of PCN3 is 0.886, which shows that the demand for commuting by private vehicle is the main factor that motivates citizens to participate in the lottery.

5. Conclusions

This article explores the high enthusiasm of citizens participating in the lottery under license plate restriction policies. Under the current LPLP, many people who have an urgent demand for vehicles have difficulty obtaining vehicle license plates in a short time frame. The aim of this study is to evaluate citizens’ behavior towards participating in the lottery and conduct an in-depth exploration of the influencing mechanisms underlying this behavior. The perceived car necessity (PCN) was assessed using the theoretical research framework of the TPB, and the MIMIC model was constructed to verify the relationship between personal socio-economic attributes and latent psychological variables. The results of relationship between potential psychological latent variables and citizens participation behavior in the lottery are listed as follows:

Car ownership attitude (ATT) subjective norm (SN) perceived behavioral control (PBC) and perceived car necessity (PCN) are four latent variables that have an important influence on behavioral intention to participate in the lottery (BI).

(1) The individual social and economic attributes of citizens have a significant impact on the latent variables in the MIMIC model. Among them, age has a significant negative impact on car ownership attitude, subjective norms, and behavioral intention to participate in the lottery, while age has a significant positive impact on perceived car necessity. Education level has a significant negative impact on behavioral intention to participate in the lottery. The number of household members with need a car for commuting has a significant positive impact on behavioral intention to participate in the lottery. The number of households members who are eligible to participate in the lottery, the number of household members participating in the lottery, and the overall time spent in the lottery have a significant positive impact on perceived behavioral control. Family annual income has a significant positive impact on car ownership attitude. The number of household motor vehicles has a significant negative impact on car ownership attitude. This shows that policy makers can classify lottery participants according to their social and economic attributes and establish management practices based on these classifications.

(2) Perceived car necessity, perceived behavioral control, car ownership attitude, and subjective norms have a significant positive impact on behavioral intention to participate in the lottery.

• Car ownership attitude has the greatest impact on behavioral intention to participate in the lottery. The main attraction of motor vehicle ownership is the increased comfort and convenience of travel. Therefore, policy makers can learn from cities with advanced transit development experiences such as Portland, to reduce citizens’ reliance on motor vehicle travel by restricting the car use environment and improving the quantity of public transportation services [41], thereby reducing citizens’ perception of the convenience and comfort of car travel.
• The impact of subjective norms on behavioral intention to participate in the lottery indicates that the behavior of relatives and friends plays the strongest subjective normative role. Messages delivered through the news media can also play a strong subjective normative role. Based on this finding, rational participation in the lottery can be strengthened by providing public and green transportation, which can help in eliminating non-essential car purchases.
• Perceived behavioral control has a stronger impact on behavioral intention to participate in the lottery than perceived car necessity. The ability to participate in the lottery at no cost and the potential economic benefits of the license plate registration are the main factors that attract citizens to participate in the lottery. At present, citizens can easily participate in the lottery at no cost, and the economic benefit from the secondary trading of license plate is growing increasingly significant. Therefore, a considerable number of citizens who lost the lottery seek to rent or purchase the use of license plates from others. In response to this phenomenon, policy makers can consider increasing the participation threshold to discourage the participation of individuals who profit from the lottery and those with flexible demand lacking an immediate need for a car.
• Perceived car necessity has the least impact on behavioral intention to participate in the lottery. Among the associated variables, the demand for commuting by private vehicle is the main factor that motivates citizens to participate in the lottery. Policy makers can increase the investment and promotion of customized buses, carpooling and other transport modes to supplement the comfort freedom and flexibility that comes with commuting by the private vehicle. The government can set up relevant indicators to evaluate the necessity of car use among citizens and adopt different lottery policies according to the vehicle needs of different citizens, thus ensuring that citizens in urgent need of a car will have a better chance of winning the lottery.

In future research, other psychological influencing factors can be further introduced to the TPB framework. Furthermore, other psychological behavior models combining effective adjustment measures for lottery participants can be designed and verified to further enhance the understanding of the lottery participation behavior of citizens with different socio-economic statistical attributes.