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Adoption of Autonomous Vehicles with Endogenous Safety Concerns:
A Recursive Bivariate Ordered Probit Model
Fatemeh Nazari (Corresponding author)
Ph.D. Student
Department of Civil and Materials Engineering
University of Illinois at Chicago
842 W. Taylor Street
Chicago, IL 60607-7023
Email: fnazar2@uic.edu
Mohamadhossein Noruzoliaee
Ph.D. Candidate
Department of Civil and Materials Engineering
University of Illinois at Chicago
842 W. Taylor Street
Chicago, IL 60607-7023
Email: mnoruz2@uic.edu
Abolfazl (Kouros) Mohammadian
Professor
Department of Civil and Materials Engineering
University of Illinois at Chicago
842 W. Taylor Street
Chicago, IL 60607-7023
Email: Kouros@uic.edu
Paper number 19-02998 (Extended Abstract)
98th Annual Meeting of Transportation Research Board (TRB)
Word Count: 1,621
Nazari, Noruzoliaee, and Mohammadian 1
ABSTRACT
It is generally believed that safer roads will be a major benefit of autonomous vehicles (AVs). Recent AV-
involved accidents in road tests and empirical evidence, however, suggest that travelers might still be
concerned about the safety of a ride in an AV. It is further unknown whether and to what extent the travelers’
safety concern will hinder or promote the adoption of AVs. This paper makes a rigorous attempt to ascertain
the causality between the travelers’ safety concern about the AV technology and their AV adoption
behavior, in addition to exploring the determinants thereof. To this end, a recursive bivariate ordered probit
model is estimated, which explicitly accounts for the endogeneity of safety concern in the AV adoption
behavior. Drawing from a stated preference survey in the state of California, we find a significant negative
association between safety concern and AV adoption. Important insights are also obtained into the impact
on shaping travelers’ behavior of several socioeconomic and demographic characteristics, current travel
behavior factors, and vehicle decision factors and attributes.
Keywords: autonomous vehicle, adoption behavior, safety concern, endogeneity, recursive bivariate
ordered probit
Nazari, Noruzoliaee, and Mohammadian 2
INTRODUCTION
1
It is envisaged that the emergence of autonomous vehicles (AVs) will transform transportation systems
2
through more efficient mobility and enhanced safety. In particular, AVs could remove the leading cause of
3
road crashes, which is human error in 90% of the U.S. road accidents (1). Even without full automation,
4
the economic benefits of partially automated vehicle collision avoidance technologies in the U.S. are
5
projected at up to $202 billion (2). Notwithstanding, the recent AV crashes in road tests (e.g., see (3)) could
6
cast doubts on the reliability of future transport safety with AVs in terms of fatalities and injuries. Such a
7
blurred picture of future road safety is even exacerbated by noting that car manufacturers and decision
8
makers cannot simply prove AV reliability through extensive road tests (4). As a consequence, consumers’
9
perceptions about the safety of a ride in an AV could be negatively affected (5-7). Despite the potentially
10
significant impact of consumers’ safety concern on their adoption of AVs, there is a dearth of behavioral
11
studies to explore the causality between the travelers’ safety concern about the AV technology and their
12
AV adoption behavior (8).
13
However, existing travel behavior studies on AVs mostly ignore safety concern about the AV
14
technology and mainly focus on socio-economic, built-environment, current travel behavior, and
15
instrumental variables. A main hypothesis in this paper is that AV adoption is controlled by, among various
16
factors, the safety concern of travelers, which is itself a function of exogenous factors. For instance, persons
17
who are more familiar with new technologies, especially vehicle technology, could be expected to have
18
lower concerns about AV safety and thus be more interested in AV adoption. In other words, we
19
simultaneously model AV adoption and safety concern while considering the endogeneity between the two
20
dependent variables. To do so, we estimate a recursive bivariate ordered probit (RBOP) model. In addition
21
to treating endogeneity, the model captures the cross-equation error correlation between the two dependent
22
variables. Ignoring the endogeneity could lead to inconsistent parameter estimates, inaccurate predictions,
23
and erroneous inferences (9).
24
25
METHODOLOGY
26
To address endogeneity in a bivariate probit model, Burnett (10) proposed the recursive bivariate probit
27
model, which jointly models two outcomes while addressing variable endogeneity. Later on, Sajaia (11)
28
extended the recursive bivariate probit to jointly model two ordinal outcomes while addressing endogeneity.
29
In this paper we estimate a recursive bivariate ordered probit model to simultaneously model AV adoption
30
and AV safety addressing endogeneity and cross-equation correlation of error terms.
31
32
FINDINGS
33
The majority of the existing studies on AV adoption behavior collect stated preference data sets, in which
34
respondents choose one of the alternatives presented as possible scenarios (see Becker and Axhausen (8)
35
for a recent review of these studies). Each scenario in a stated preferences survey presents one alternative
36
(e.g., AV, shared AV, and conventional vehicle) with specific features and a respondent could choose one
37
or multiple options. In this paper, we estimate a RBOP mode using the stated preference data set provided
38
by California Energy Commission (12), which does not contain features of AVs, but the respondents are
39
asked about their agreement level with AV adoption and AV safety. Specifically, the respondents answered
40
the following two questions by Likert scale ranging from 1 (strongly disagree) to 5 (strongly agree).
41
42
• AV adoption: “I would consider purchasing a vehicle that is fully self-driving (i.e., the vehicle drives
43
itself)”.
44
• AV safety concern: “I am concerned about the safety of self-driving vehicles”.
45
46
We assume that “considering AV as an option for future vehicle decision” could represent potential
47
for adopting an AV in the future. The data set contains Californians’ response to the mentioned questions
48
from five regions of California: San Francisco, Los Angles, San Diego, Sacramento, Central Valley, and
49
the rest of California. Based on the residential region of the respondents, the distribution of the response
50
Nazari, Noruzoliaee, and Mohammadian 3
variables is depicted in FIGURE 1. It is interesting to note that almost half of the respondents in all five
1
regions and the rest of California strongly or moderately disagree with adopting an AV. In addition, majority
2
of them strongly or moderately agree on safety concerns about AVs. Among the five regions, the residents
3
of San Francisco showed more agreement with AV adoption and more disagreement with its safety
4
concerns.
5
6
(a)
(b)
FIGURE 1. Response of the five regions of the state of California to: (a) AV adoption and (b) AV safety
7
concern (note: the numbers in the parenthesis are the number of observations for the
8
corresponding region)
9
10
0
5
10
15
20
25
30
35
40
45
50
San Francisco
(843) Los Angeles
(1,502) San Diego
(339) Sacramento
(273) Central Valley
(306) Rest of CA
(311)
Share of respondents (%)
Strongly disagree Moderately disagreeNeither agree nor disagree
Moderately agreeStrongly agree
0
5
10
15
20
25
30
35
40
45
50
San Francisco
(843) Los Angeles
(1,502) San Diego
(339) Sacramento
(273) Central Valley
(306) Rest of CA
(311)
Share of respondents (%)
Strongly disagree Moderately disagreeNeither agree nor disagree
Moderately agreeStrongly agree
Nazari, Noruzoliaee, and Mohammadian 4
TABLE 1 shows the estimation results of the recursive bivariate ordered probit model of people’s AV
1
adoption with endogenous AV safety while accounting for cross-equation correlation. The estimated model
2
has a fair prediction accuracy (indicated by R2 = 0.21). In addition, the ordered levels of both dependent
3
variables are separated by significant estimated thresholds.
4
5
TABLE 1. Estimation results of recursive bivariate ordered probit model
6
Variable description
AV adoption
AV safety concern
coef.
t-stat
coef.
t-stat
Constant
3.703
11.34
2.414
18.48
Endogenous variable
AV safety
-0.644
-8.79
—
—
Socio-economic characteristics
Gender
Female
-0.110
-2.62
0.156
4.14
Education
Level 2
—
—
-0.144
-1.83
Level 3
—
—
-0.205
-2.64
Level 4
—
—
-0.268
-3.39
Employment type
Full-time employed
0.065
1.70
—
—
Self-employed
0.107
1.50
—
—
Household income
Low level (less than 75K)
-0.086
-2.20
—
—
High level (equal or more than 200K)
0.191
3.02
—
—
Household structure
# kids (age < 6) and teenagers (6 ≤ age < 12)
0.083
3.25
—
—
# young children (12 ≤ age < 16)
0.139
2.85
—
—
# vehicles per # adults (in household)
-0.181
-4.54
—
—
Household has plug-in electric vehicle
Yes = 1
—
—
-0.468
-7.50
Household has/ plans to purchase solar panels
Yes = 1
—
—
-0.082
-2.01
Demographic factor
Residential region
San Francisco
0.190
4.01
—
—
Log Angeles
0.069
1.76
—
—
Travel behavior factors
Logarithm of annual VMT (individual-level)
-0.037
-3.49
-0.031
-2.88
Use of mobility-on-demand services
Car-sharing frequency
—
—
-0.064
-2.99
Ride-sharing frequency
—
—
-0.046
-3.69
Daily parking cost at residence (× 10-3)
0.724
2.54
—
—
Vehicle decision factors
Important attributes of a vehicle
Reliability
—
—
0.081
2.30
Brand
—
—
0.097
2.32
Vehicle history of household in the past 10 years
# vehicles purchased new
0.028
1.99
—
—
Nazari, Noruzoliaee, and Mohammadian 5
Variable description
AV adoption
AV safety concern
coef.
t-stat
coef.
t-stat
# vehicles leased
0.046
2.58
—
—
Involvement in future vehicle decisions
Sole decision maker
0.140
3.20
—
—
Shared equally with other household member(s)
-0.082
-1.76
—
—
Logarithm of price for replacing one of vehicles
-0.014
-1.49
—
—
Logarithm of price for adding a vehicle
0.014
3.59
—
—
Error correlations
AV adoption
1.00
—
0.394
3.84
AV safety concerns
1.00
—
Thresholds
Threshold 1
0.00*
—
0.00*
—
Threshold 2
0.486
18.88
0.504
14.55
Threshold 3
1.040
23.10
1.051
24.85
Threshold 4
1.735
25.49
1.953
45.06
Goodness-of-fit measures
No. of observations = 3,574
𝐿𝐿(𝛽) = -9,877, 𝐿𝐿(0) = -12,528, R2 = 0.21
*Threshold 1 is fixed at zero.
1
2
The estimated model captures the cross-equation error correlations, which appropriately absorb any
3
propensity for AV adoption and AV safety associated with omitted exogenous variables (or unobserved
4
factors). We find significant and positive correlations (𝜌 = 0.394) across the error components of the
5
equations which suggests same-sign association of the outcomes with the omitted exogenous variables. It
6
should be noted that the correlation between the two dependent variables, AV adoption and AV safety, is
7
negative. In fact, the cross-equation error correlation is different from the correlation between the two
8
outcome variables; the former captures the unobserved heterogeneity in the error terms, while the latter
9
shows the linear association between the two variables.
10
To test the hypothesis of zero correlation of the error terms (𝜌 = 0), we use the likelihood ratio test
11
by comparing the estimated model with a restricted model which corresponds to independent ordered
12
response estimation of each of the two outcomes (13). The likelihood ratio test with p-value << 0.0001
13
shows that in this particular empirical context, it cannot be rejected to model AV adoption and AV safety
14
accounting for the correlation across the error components of the equations.
15
Almost all estimated coefficients are statistically significant at the 0.05 level and intuitively signed.
16
The sign of each estimated coefficient is of particular interest: a positive sign means increase in the highest
17
agreement level (i.e., strongly agree) or decrease in the lowest disagreement level (i.e., strongly disagree)
18
of AV adoption and AV safety (13). However, analysis of the intermediate order levels of an ordered probit
19
model (i.e., the three middle agreement levels in this model) requires computing the associated marginal
20
effects, as illustrated in the methodology section. TABLE 2 presents the marginal effects of the exogenous
21
variables explaining each level of agreement with AV adoption and AV safety, which refer to the
22
approximate change in the probability of each agreement level with AV adoption and AV safety in response
23
to a unit change in the desired exogenous variable while other variables are held constant at their respective
24
population mean.
25
The estimated model further accounts for endogeneity of AV safety in the equation of AV adoption,
26
which is signified by the negative coefficient of AV safety in the equation of AV adoption. In fact, as a
27
person disagrees more with AV safety, he/she agrees less, strongly or moderately, with AV adoption. To
28
test the hypothesis of no endogeneity, we use the likelihood ratio test by comparing the estimated model
29
with a restricted model which corresponds to bivariate ordered probit model with no endogeneity (13). The
30
Nazari, Noruzoliaee, and Mohammadian 6
likelihood ratio test with p-value < 0.05 shows that in this particular empirical context, it cannot be rejected
1
to jointly model AV adoption and AV safety without endogenous AV safety.
2
3
TABLE 2. Marginal effects for recursive bivariate ordered probit model
4
Variable description
AV adoption
AV safety concern
Strongly
disagree
Moderately
disagree
Neither agree
nor disagree
Moderately
agree
Strongly
agree
Strongly
disagree
Moderately
disagree
Neither agree
nor disagree
Moderately
agree
Strongly
agree
Endogenous variable
AV safety
0.190
0.019
-0.019
-0.060
-0.131
—
—
—
—
—
Socio-economic characteristics
Gender
Female
0.033
0.003
-0.003
-0.010
-0.022
-0.013
-0.014
-0.019
-0.013
0.060
Education
Level 2
—
—
—
—
—
0.012
0.013
0.017
0.012
-0.055
Level 3
—
—
—
—
—
0.017
0.019
0.025
0.018
-0.079
Level 4
—
—
—
—
—
0.023
0.024
0.032
0.023
-0.103
Employment type
Full-time employed
-0.019
-0.002
0.002
0.006
0.007
—
—
—
—
—
Self-employed
-0.032
-0.003
0.003
0.010
0.022
—
—
—
—
—
Household income
Low level (less than 75K)
0.026
0.002
-0.002
-0.008
-0.018
—
—
—
—
—
High level (equal or more than 200K)
-0.056
-0.006
0.006
0.018
0.039
—
—
—
—
—
Household structure
# kids (age < 6) and teenagers (6 ≤ age < 12)
-0.024
-0.002
0.002
0.008
0.017
—
—
—
—
—
# young children (12 ≤ age < 16)
-0.041
-0.004
0.004
0.013
0.028
—
—
—
—
—
# vehicles per # adults (in household)
0.053
0.005
-0.005
-0.017
-0.037
—
—
—
—
—
Household has plug-in electric vehicle
Yes = 1
—
—
—
—
—
0.040
0.042
0.057
0.040
-0.179
Household has/plans to purchase solar panels
Yes = 1
—
—
—
—
—
0.007
0.007
0.010
0.007
-0.031
Demographic factor
Residential region
San Francisco
-0.056
-0.006
0.005
0.018
0.039
—
—
—
—
—
Log Angeles
-0.020
-0.002
0.002
0.006
0.014
—
—
—
—
—
Travel behavior factors
Logarithm of annual VMT (individual-level)
0.011
0.001
-0.001
-0.003
-0.007
0.003
0.003
0.004
0.003
-0.012
Use of mobility-on-demand services
Car-sharing frequency
—
—
—
—
—
0.005
0.006
0.008
0.006
-0.024
Ride-sharing frequency
—
—
—
—
—
0.004
0.004
0.006
0.004
-0.017
Daily parking cost at residence (× 10-2)
-0.214
-0.021
0.021
0.067
0.147
—
—
—
—
—
Vehicle decision factors
Important attributes of a vehicle
Reliability
—
—
—
—
—
-0.007
-0.007
-0.010
-0.007
0.031
Brand
—
—
—
—
—
-0.008
-0.009
-0.012
-0.008
0.037
Vehicle history of household in the past 10 years
Nazari, Noruzoliaee, and Mohammadian 7
Variable description
AV adoption
AV safety concern
Strongly
disagree
Moderately
disagree
Neither agree
nor disagree
Moderately
agree
Strongly
agree
Strongly
disagree
Moderately
disagree
Neither agree
nor disagree
Moderately
agree
Strongly
agree
# vehicles purchased new
-0.008
-0.001
0.001
0.003
0.006
—
—
—
—
—
# vehicles leased
-0.014
-0.001
0.001
0.004
0.009
—
—
—
—
—
Involvement in future vehicle decisions
Sole decision maker
-0.041
-0.004
0.004
0.013
0.028
—
—
—
—
—
Shared equally with other household member(s)
0.024
0.002
-0.002
-0.008
-0.017
—
—
—
—
—
Logarithm of price for replacing one of vehicles
0.004
0.0004
-0.0004
-0.001
-0.003
—
—
—
—
—
Logarithm of price for adding a vehicle
-0.004
-0.0004
0.0004
0.002
0.003
—
—
—
—
—
1
CONCLUSIONS
2
A main hypothesis in this paper is that AV adoption is controlled by, among various factors, the
3
safety concern of travelers, which is itself a function of exogenous factors. For instance, persons who are
4
more familiar with new technologies, especially vehicle technology, could be expected to have lower
5
concerns about AV safety and thus be more interested in AV adoption. In light of this, we simultaneously
6
model AV adoption and safety concern while considering the endogeneity between the two dependent
7
variables. To do so, we estimate a recursive bivariate ordered probit (RBOP) model. In addition to treating
8
endogeneity, the model captures the cross-equation error correlation between the two dependent variables.
9
Drawing from a stated preference survey in the state of California, we find a significant negative association
10
between safety concern and AV adoption. Important insights are also obtained into the impact on shaping
11
travelers’ behavior of several socioeconomic and demographic characteristics, current travel behavior
12
factors, and vehicle decision factors and attributes.
13
14
REFERENCES
15
16
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