Auto insurance premiums in Ghana: An Autoregressive Distributed Lag model approach to risk exposure variables

Abstract

This study examined risk exposure and auto insurance premium determinants in Ghana. We analysed an existing data set of 23 434 policies (without claims = 84.1%, policies with claims = 15.9%; comprehensive policies = 48.0%, third-party policies = 52.0%) applying the Autoregressive Distributed Lag (ARDL) model, controlling for driver demographics, value of car, and car usage variables. Findings indicate policyholders’ age significantly determine premiums charges. Additionally, auto seating capacity significantly influenced third-party rather than comprehensive premiums, and auto’s cubic capacity had no significant impact on premium charges. Pricing system impact premiums were influenced by policyholders’ characteristics more than variables from the insured vehicle. These findings suggest that policyholders’ age (novice drivers) and vehicles with many occupants increases auto insurers risk exposure.

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Journal of Psychology in Africa
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Auto insurance premiums in Ghana: An
Autoregressive Distributed Lag model approach to
risk exposure variables
Jacob Azaare, Zhao Wu, Bernard Gumah, Enock Mintah Ampaw & Socrates
Modzi Kwadwo
To cite this article: Jacob Azaare, Zhao Wu, Bernard Gumah, Enock Mintah Ampaw & Socrates
Modzi Kwadwo (2021) Auto insurance premiums in Ghana: An Autoregressive Distributed Lag
model approach to risk exposure variables, Journal of Psychology in Africa, 31:4, 362-368, DOI:
10.1080/14330237.2021.1952668
To link to this article: https://doi.org/10.1080/14330237.2021.1952668
Published online: 24 Aug 2021.
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Journal of Psychology in Africa is co-published by NISC (Pty) Ltd and Informa UK Limited (trading as Taylor & Francis Group)
Journal of Psychology in Africa, 2021
Vol. 31, No. 4, 362–368, https://doi.org/10.1080/14330237.2021.1952668
© 2021 Africa Scholarship Development Enterprize
Introduction
Driving comes with risk exposure, necessitating insurance
protections (Isotupa et al., 2019) to mitigage possible
losses that may arise due to the usage of automobiles
(Boucher et al., 2009; Lemaire, 2006). The introduction of
automobile insurance is intended to protect policyholders
from possible enormous financial loss and loss to others
(third parties). However, the decision to buy a policy
sometimes partially depends on the premium, which is
calculated based on the policyholder’s risk (Alhassan
& Biekpe, 2016; Isotupa et al., 2019). Premium is the
monetary amount charged by the insurer and paid by
the policyholder for an insurance contract. Most studies
examine premium calculations from the classical point
of view based on the frequency and severity of the
policyholders’ claims (Denuit et al., 2007) and by driver’s
age, experience, career, marital status, sex, the age of the
vehicle, cubic capacity (horsepower), mileage, and garage
location (Ayuso et al., 2019; Bolancé et al., 2007; Jacob
& Wu, 2020) . However, approaches that consider the
distance covered each year by a policyholder (Ferreira &
Minikel, 2012), the policyholder’s driving speed records,
the most frequent ply roads, type of such roads, and the
time of day they are mostly on the roads are increasingly
employed by auto insurance companies when determining
the pricing system (Langford et al., 2008; Litman, 2005;
Paefgen et al., 2014; Sivak et al., 2007). We aimed to
examime risk exposure and auto insurance premuims
relationships for policyholders in the developing country of
Ghana, applying Autoregressive Distributed Lag (ARDL).
The Ghananian auto insurance industry sector
The Ghanaian auto insurance market, which constitudes the
lagest share of the non-life policies, is one of the fastest-
growing in Sub-Saharan African region (Alhassan et al.,
2015; Osei-Bonsu, 2021). The Ghanaian auto insurance
market considers the vehicle’s age, cubic capacity, type of
use for third party policy, and the inclusion of a vehicle’s
cost (sum insured) in the comprehensive (C) premium
case (Awunyo-vitor, 2012; Ghana National Insurance
Commission [NIC], 2015; Laryea, 2016). The tariff
structure from the Ghana National Insurance Commission
(NIC, 2015) does not charge any age loading for autos less
than five years old; but those from 5-10 and more than 10
years are charged with 5% and 7.5%, respectively, of the
basic premium as age loadings. Additionally, policyholders
pay 5% and 10% of the basic premium on vehicles with
1601-2000 and > 2000 cubic capacity (CC), respectively.
Further, an insured auto’s seating capacity in Ghana
plays an influential role in final premium determination
even though there is no clear evidence in the literature
to support its inclusion (National Insurance Commission
[NIC], 2015). This is with the exception of the proportional
relationship between vehicle’s size and mass reduction and
accident occurence (Mela,1974; Kahane, 2012;Puckett &
Kindelberger, 2016). Prior research (Mela,1974; Kahane,
2012;Puckett & Kindelberger, 2016) indicates that when
the size of a vehicle is increased, the probability of being
involved in an accident is much lower; yet, the nature of
the claims particularly to third parties are always severe
anytime it occurs.
The standard number of seats captured in the at-
rate system for both third-party and comprehensive seats
is ve. In this case, for example, any auto with seating
capacity > 5 pays 5 (US$ 0.85) and 8 (US$1.35) Ghana
cedis per seat, respectively, for private and commercial
use (NIC, 2015). This leaves an open question regarding
the relationship between risk exposure and auto insurance
premiums for policyholders in the developing country of
Ghana.
Auto insurance premiums in Ghana: An Autoregressive Distributed Lag model approach to
risk exposure variables
Jacob Azaare1* , Zhao Wu1, Bernard Gumah2a, Enock Mintah Ampaw2b and Socrates Modzi Kwadwo2c
1,2aSchool of Management and Economics, University of Electronic Science and Technology of China, Chengdu, China
2bDepartment of Mathematics, Koforidua Technical University, Koforidua, Ghana
2cFaculty of Business, Economics and Social-Sciences, University of Hamburg, Germany
*Correspondence: azaarejacob@yahoo.com
This study examined risk exposure and auto insurance premium determinants in Ghana. We analysed an existing data set
of 23 434 policies (without claims = 84.1%, policies with claims = 15.9%; comprehensive policies = 48.0%, third-party
policies = 52.0%) applying the Autoregressive Distributed Lag (ARDL) model, controlling for driver demographics,
value of car, and car usage variables. Findings indicate policyholders’ age significantly determine premiums charges.
Additionally, auto seating capacity significantly influenced third-party rather than comprehensive premiums, and auto’s
cubic capacity had no significant impact on premium charges. Pricing system impact premiums were influenced by
policyholders’ characteristics more than variables from the insured vehicle. These findings suggest that policyholders’ age
(novice drivers) and vehicles with many occupants increases auto insurers risk exposure.
Keywords: auto insurance market, auto insurance premiums, dynamic stability, long-run equilibrium, policyholders, risk
exposure variables

Risk exposure permutations 363
Frequency, severity of claims, and usage effects
Higher claims usually lead to higher premiums (Boucher
et al., 2009; Jacob & Wu, 2020; Lemaire, 1995; Mert &
Saykan, 2005; Sarabia et al., 2004). Thus, in the classical
insurance rate making system, premiums for policyholders
are charged considering the number and severity of their
reported claims. In this case, policyholders pays less
premiums for not reporting claims in a policy year (bonus)
and pay more depending on the number and severity of
reported claims (malus). Additionally, vehicles’ cubic
capacity/horsepower (CC) is associated with high speed
and claims/accident occurrence (McCartt & Hu, 2017).
Individual policyholders driving longer distances and faster
speedings are more exposed and likely to be involved in
an accident compared to shorter distance drives (Boucher
et al., 2013). Therefore, faster speed and distance covered
influence premiums. Hence, to understand the actual
rating variables that affect policyholders’ premium, it is
necessary to employ an agglomerative predictive model
that considers the level relationships between dependent
and explanatory variables (Alhassan & Fiador, 2014;
Bahmani-Oskooee & Brooks, 2003; Nkoro & Uko, 2016;
Narayan, 2005; Pesaran et al., 2001), such as the ARDL
model.
The autoregressive distributed lag model
The autoregressive distributed lag model (ARDL) is an
econometric infinite lag distributed model used to unravel
long-run relationships from short-run situations(Adu et al.,
2013; Pesaran et al., 2001). The major advantage of the
ARDL model is that, along with the dependent variable
being explained by the independent variable(s), the
dependent variable gets explained by its lag. In examining
whether the relationship exists between premium and our
explanatory variables, we define our ARDL in general
terms as:
(1) 0 11 2 1
11
nn
t i ti i ti t t t
ii
Y y XyX
   
  
 
       

From (1), we can have its expansion form as:
(2)
In Equation 2,
i

and
i

are short-run coefcients
for respectively premium and the independent variables
towards equilibrium. Further
1

, 2

,… 7

are the
autoregressive distributed lag long-run coefcients for
premium and the six independent variables. Lastly,
t

is the white noise of the model. In both Equation 1 and
Equation 2, we indicate the difference between the change
in Premium (Y) on the left side and its lag components
on the right side (y) for both the short-run and long-run
coefcients. The model’s independent variables are also
denoted by the
23 7
, ...
XX X
for comprehensive policy and
is reduced to ve in the third-party case. Additionally, in
both equations, represent the optimal model lags, which is
one for comprehensive and three for the third-party. The
model for the long run (LRM) association and their lag
residuals (LR) are respectively dened as:
(3) 01
1 10 11
...
t t nt t
tt t
LR y X X
LR Z y b b X

 
 

  
Thus in Equation 3, the error correction term is
replaced with
1t
y

and
1t
X
. To estimate the error
correction model (ECM), we replaced the long
run term (
1 1 221 771
...
tt
yX X
 
 

) with its residual
(
1
t
Z

). Nevertheless, the lagged residual remains
1 10 11tt t
Z
y b bX
 
 
. Thus, in this ARDL model, we
include the same lagged levels as in the ECM, but their
coefcients have not been restricted. Therefore, our ARDL
model is a form of unrestricted ECM, implying that all
our long-run relationship variables (
1it
X

) are specied.
The model speed of adjustment from short-run towards
long-run equilibrium is estimated as:
(4)
1
1
n
i
i


  
Further, the estimated long-run coefficients are given by:
(5)
1
1
1
n
i
i
n
i
i
i
















Table 1. Descriptive statistics by claims and variables categories (quantitative variables)
Variable Total sample
n = 23 434
Policies with no claims
n = 19 703 (84.1%)
Policies with claims
n = 3 731 (15.9%)
Comprehensive policies
from claims
n = 1 791 (48.0%)
Third-party policies
from claims
n = 1 940 (52.0%)
Mean Std Mean Std Mean Std Mean Std Mean Std
X1 854 1915 813 1 815 842 1 666 1 512 2 216 224 105
X2 27 784 – 26 270 58 505 29 648 61 105 66 747 222 965 – –
X3 11 7 11 7 12 6 9 6 14 24
X4 6 5 6 33 5 4 5 3 7 45
X5 1522 9799 – – 9 547 22 941 10 659 27 203 8 481 18 043
X6 2 456 1 077 2 461 1 078 2 442 1 068 2 466 1 097 2 419 1 040
X7 49 16 49 16 48 16 48 16 48 16
Note. See Table 2 for descrptions of each model.
0 1 2 6 6 1 1 2 2 1 ... 7 6 1
11 1
...
nn n
t i ti ti ti yt t t t
ii i
Y y X X XX
      
      
  
       
 

Azaare et al.
364
Goal of the study
Our study goal was to test the utility of the the ARDL
model in determining the effects of rating variables on
auto insurance premuiums in Ghana. Our specific research
question was: What are the risk exposure effects on auto
insurance premiums in Ghana?
Methods
Data collection
Data were collected from a leading insurance company in
Ghana. Table 1 depicts the information on risk exposure
and premiums payment for 23 434 vehicle insurance
policyholders for 2018, while Table 2 provides the model
descriptions. The sample is composed of drivers who
underwrote both third-party and comprehensive policies.
Out of the total sample, n = 3 731 (15.9%) drivers
reported claims with their mean age of 48 years for both
comprehensive (C) and Third-Party (TP). In turn, the mean
age of drivers for the total portfolio and those with no
reported claims was 49 years. We grouped the data based
on TP n = 1 940 (52.0%) and comprehensive n =1 791
(48.0%). Each category was analysed separately because
of the explanatory variable’s differentials. We included
the following explanatory variables: the policyholder age,
age of the insured vehicle, cubic capacity, claims size, and
vehicle’s seating capacity (Awunyo-vitor, 2012; Laryea,
2016; NIC, 2015).
Data analysis
As indicated in Table 3, we developed our original ARDL
models applying the Augmented Dickey-Fuller (Dickey &
Fuller, 1981) unit root test.
Further, we applied the Breusch-Pagan-Godfrey
Heteroskedasticity Test. The results are shown in Table 4
and Figure 1, supporting homoscedasticity of the data and
it being normally distributed.
As indicated in Table 5, our tests for lag effects were
also supported. Lag effects refer to the suggestion that
information is well retained when there is a longer time
spacing in repeating such information (Arjun, 2018). Thus,
the optimal delay times (lag 1 for comprehensive, lag 3 for
third party) for our dependent variable to respond to the
changes in the explanatory variables for robust estimates
were considered.
Table 2. Description of the model variables
X1(Premium) Premium paid by the policyholder to the insurer measured in Ghana cedi
X2(Sum insured) The value of the insured vehicle for comprehensive policies measured in Ghana cedi
X3(Vehicle age) The age of the insured vehicle measured in years
X4(Seat) The seating capacity of the insured vehicle measured in numbers
X5(Claims) Claims reported/paid to the policyholder by the insurer measured in Ghana cedi
X6(Cubic capacity) The cubic capacity or the horsepower of the insured vehicle measured in Watts.
X7(Policyholder age) The age of the policyholder or the driver measured in years
Note. *** In our models, C is for comprehensive and TP is for third-party whiles X1 is Premium (Ys)
Table 3. Augmented Dickey-Fuller unit root test showing stationarity for variables in both models
Comprehensive t-statistics p-value
Null hypothesis: The variables have unit root
Augmented Dickey-Fuller test statistic −40.3524 < 0.000
Test critical values: 1% −3.4338
5% −2.8630
10% −2.5676
Third Party t-statistics p-value
Null hypothesis: The variables have unit root
Augmented Dickey-Fuller test statistic −37.4524 < 0.000
Test critical values: 1% −3.4335
5% −2.8628
10% −2.5675
Table 4. Breusch-Pagan-Godfrey Heteroskedasticity test
Comprehensive
Null hypothesis: Homoscedasticity Dependent variable: RESID^2
F-statistic 1.1413 Prob.F(8,1779) 0.3321
Obs*R-Squared 9.1300 Prob.Chi-Square (8) 0.3314
Scaled explained SS 9.1289 Prob.Chi-Square (8) 0.3315
Third Party
Null hypothesis: Homoscedasticity Dependent variable: RESID^2
F-statistic 0.6688 Prob.F(18,1917) 0.8446
Obs*R-Squared 12.0823 Prob.Chi-Square (18) 0.8430
Scaled explained SS 286.2912 Prob.Chi-Square (18) 0.0000

Risk exposure permutations 365
Results
In Figure 2, we applied the Commutative Sum of recursive
residuals (CUSUM) test to show the graph of Stability for
comprehensive(C) and third-party (TP) policy premiums.
The blue lines of these CUSUM (Commutative Sum of
recursive residuals) plots lie between the two red lines (5%
signicant levels). This indicates that all the coefcients of
the explanatory variables are reliable in making decision
on premiums.
Using Equation 4, we developed the Error Correction
Terms (ECTs) to show the short run coefcients between
our dependent and the independent variables. There was a
signicant speed of adjustment of these models towards
a long-run equilibrium for both C and TP at 81.29% and
79.17%, respectively. This shows that the explanatory
variables are a bit faster in predicting comprehensive
premiums as compared to third party premiums. In order
to accept these models, we utilised the CUSUM test
once again at 5% level to check for stability. As depicted
Figure 3, the lag one of our independent variables caused
the model instability, which was removed to ensure
stability.
The CUSUM plots with the blues line between the
two red lines (5% signicant levels) are indications of
stability of the ECTs of our model. The stable ECTs
(Error Correction Terms) are indications of how easily
our model is adjusted from disequilibrium towards long
-run equilibrium states with the unstable model indicating
otherwise.
Figure 1. Normality test for comprehensive in red and third-party in black
Figure 2. Graph of Stability test for comprehensive (C) on the left and third-party (TP) policy premiums on the right
Table 5. Statistics for selecting model optimal lag
Comprehensive policies Third party
Lag AIC SIC AIC SIC
1 18.14 18.19 12.14 12.18
2 18.15 18.21 12.14 12.19
3 18.14 18.23 12.13 12.21
4 18.15 18.26 12.13 12.22
5 18.15 18.28 12.14 12.24
6 18.15 18.30 12.14 12.26
Note. ***Comprehensive lag 1 is optimal; lag 3 is optimal for third
party
-
150
-
100
-50
0
50
100
150
250 500 7 50 1000 1250 1500 1 750
CUSUM 5% Signi ficance
-
150
-
100
-50
0
50
100
150
250 500 750 1000 1250 1500 1750
CUSUM 5% Significanc e

Azaare et al.
366
Discussion
The findings indicate policyholders’ age significantly
determine premium charges. This is in line with previous
research that reported the influence of policyholders’ age
on their auto insurance premium (Ayuso et al., 2019;
Bolancé et al., 2007). In a typical insurance pricing
system, policyholders’ driving speed profile, the type of
roads they frequently plied, and the timing are mostly
considered. These pricing systems are usually targeted at
novice drivers within certain age brackets (Ayuso et al.,
2019). This indicates a significant difference in terms of
risk exposures between older and younger policyholders.
In this case, premiums are personalised based on the
policyholder’s age. To ensure optimally pricing systems,
individual policyholders pay premiums based on their
demographics on individual risk levels (Jacob & Wu,
2020).
Additionally, we found that auto seating capacity
signicantly inuence third party premiums, but not
comprehensive premiums. Vehicles with more seating
capacities are denitely bigger in size and mass with
low accident rate (Kahane, 2012; Mela, 1974; Puckett &
Kindelberger, 2016) Our inconsistent nding might be as
a result of the fact that comprehensive policies are mostly
limited to constant 5 seats which practically would not
impact premiums. On the other hand, with the third party
policies, our nding is consistent with previous studies
that reported the direct relationship between the severity
of claims and premiums increment (Boucher et al., 2009;
Jacob & Wu, 2020; Lemaire, 1995; Mert & Saykan, 2005;
Sarabia et al., 2004). This nding is likely explained by the
size and mass nature of third party vehicles (bigger in sizes
for commercial purposes), which causes severe impact
during accidents leading to high claims and premiums
(Mela,1974; Kahane, 2012;Puckett & Kindelberger, 2016).
Further, auto’s cubic capacity (horsepower) does not
impact premiums. This nding is in line with previous
reports (Boucher et al., 2013) that a non-linear relationship
exists between auto’s cubic capacity and accident
frequencies. The likely explanation to these ndings is that
the more the horsepower a car has, the better the accelation
and its performance and the longer the distance it travels.
Undoutedly, longer distance drivers are more exposed to
risk. However, they become more skillful and experienced
for being in their cars for longer periods. This skill and
experience eventually lower their risk of having accidents
(Isotupa et al., 2019). Contrary to our ndings, Ayuso and
colleagues (2019) demonstrate a proportional relationship
between the distance traveled by policyholders and the
expected number of accidents. However, this result might
be an effect of the method employed where the classical
variables used in this paper was giving a frequent update
with telematics information.
Implications for risk exposure mitigation practices
Auto insurance rating variables such as claims,age, gender,
experience, location are risk-based and depends on the
individual policyholder. Globally, several efforts have
been realised and insurers now involve variables that are
purely characteristics of the driver and other information
such as Global Positioning System technologically coming
from the insured car (Ayuso, Guillén, & Pérez Marín,
2016). However, despite all these efforts, the Ghanaian
auto insurance market is still strictly based on vehicle age,
cubic capacity, the type of vehicle use, and the sum insured
inclusion in the comprehensive policy. Consequently,
there are mixed feelings from policyholders on variables
considered because of the high nature of premiums.
Limitations of the study and suggestions for future
research
This study was limited to only one insurer because of
data constraints. Future research should endeavor to
be longitudinal and use data from several insurance
Figure 3. Graph of Unstable dynamic ECT (C) model on the top
left, dynamic stable ECT model(C) on the top right and dynamic
stability ECT model (TP) on the left bottom.
-
150
-
100
-50
0
50
100
150
250 500 750 1000 1250 1500 1750
CUSUM 5% Signi ficance
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-
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-50
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CUSUM 5% Signi ficance
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Risk exposure permutations 367
companies. We also acknowledge that the use of data from
a company based on convenience can result in selection
bias which can influence the reliability of the findings. We
therefore limit our findings to the company from which the
data was obtained.
Conclusion
In the Ghanaian insurance market, explanatory variables
for premium calculations include policyholders’ age, age
of the insured vehicle, cubic capacity, claims size, and the
vehicle’s seating capacity. Applying ARDL modelling
shows that not all these variables used in the pricing
system impacts premiums. Hence the market needs to
revise the rating factors (to include the policyholder’s age,
re-examined autos cubic capacity) to obtain an optimal and
financially balanced pricing model for policyholders.
Authors’ note
The authors declare no conflict of interest. This research was
supported by the National Science foundation of China (project
No: 71871044)
ORCID iD
Jacob Azaare – http://orcid.org/0000-0001-5547-3786
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