1. automotive and vehicles
2. cars

Sung Jin Cho / Journal of Economic Research 10 (2005) 277–304
277
The Determinants of Used Rental
Car Prices
Sung Jin Cho1
Hanyang University
Received 23 August 2005; accepted 18 October 2005
Abstract
This paper presents several important factors affecting the resale
prices of used rental cars. In fact, this paper empirically shows
and proves several conjectures regarding the determinants for used
rental car resale values through the use of detailed micro data from
one of the biggest rental car companies. Specifically, the age of a
used car has two composite effects on its resale value, even though
overall the two effects work negatively with a concavity, as rental
cars ages. On the other hand, two mileage variables interact with
each other and produce overall decreasing effects on the resale
prices with the opposite interactions. In terms of the effects of
brand image, Hyundai and Renault-Samsung have positive effects
on resale values generally. Ssangyong has a positive effect on the
resale values in the SUV category, and Kia and GM-Daewoo are
generally inferior to the other brands in terms of resale values in all
categories. In terms of seasonal effects, we can conclude that this
paper confirms the general perception regarding seasonal effects
on resale values. In details, from November to February, resale
values are affected negatively, and March is the recovering month
of increasing demand in the used car market. August seems to
be the highest season for the used car market due to several demand increases. As a result, this paper plays an important role
in providing a substantial amount of information on the factors
affecting the resale prices of rental cars.
Keywords : Rent a car; Used car; Rental Market; Average Residual Values; Seasonality.
JEL classification : D4, L1, L8
1
Correspondence : (e-mail) [email protected], (phone) 82-2-2220-1019,
(fax) 82-2-2296-9587
I am indebted to the provider of the rental data who wishes to remain anonymous.
All errors are my own.
278
1
The Determinants of Used Rental Car Prices
Introduction
Car rental companies invest tremendous sums of money to maintain their rental fleets, as they must constantly purchase and replace
their rental cars. Until now, there has been no detailed research conducted on this area, because of the difficulty of data collection at the
micro level. In fact, a research area to find out the determinants of used
rental car pricing and to estimate used rental car’s price has not been
examined completely. As a result, only guesses and hypothesis have
been widely spread. For this paper, I have collected a rich data set from
the biggest rental car company. I will examine the important explanatory facts of the data and significant factors affecting the resale value of
the company’s fleets. Then, I will show how these factors can be used to
estimate the actual resale values of used rental cars. This research will
provide a foundation and basics for further research to be titled “The
Optimal Retirement Decision for Car Rental Companies.”2 To achieve
the objective of this paper, I first investigate state variables that represent the condition of used rental cars. These state variables can be
either internal or external state variables of used rental cars. In order to
obtain information regarding the variables, I examine several regression
models. In these regressions, I want to show which states variables are
more important factors in determining the actual depreciation of used
rental car values - between the cars’s own state or external states. To
achieve this, I use the depreciation ratio between new purchasing price
and selling price as a dependent variable in the first regression. I then
predict the prices of used rental cars and compare the predicted values
with the actual resale values.
This paper is constructed as follows. Chapter 2 explains the data set
and its explanatory factors. Chapter 3 explains several models. Chapter
4 shows the estimation results. The paper ends with the Conclusion and
future research.
2
Sungjin Cho and John Rust, 2005
Sung Jin Cho / Journal of Economic Research 10 (2005) 277–304
2
279
The Data
2.1
Summary of the Data
I obtained a data set from one of the largest car rental companies in
the region in which I am interested. The company currently possesses
over 12,000 cars. The rental cars in the company are used for either
long-term or short-term rental. Long-term rental fleets account for 70%
of the company’s entire rental fleet. However, short term rental fleets
usually dominate in tourist areas or at large airports. In contrast, the
rental locations in large cities tend to specialize in long term rentals
generally. I have all data for the company’s rental fleets that were sold
from the beginning of 2003 through July 2004. The data include 2376
sold cars during 2003, and 1225 sold cars in 2004. These cars were
originally from 1999 to 2002.
The data consist of four parts: (1). Registration data, which includes the name of each car, the brand name, car registration number,
purchasing price, sale price, registration date, selling date, fuel type,
engine displacement (CC); (2). Rental contract data for each car, including rental contract dates, revenue from each contract’s, in-and-out
kilometer readings, and in-and-out dates and times; (3). Maintenance
data, which includes all maintenance data such as dates, details of maintenance, etc., for each rental car; and (4). Accident data, which contains
all accidents records for all of the company’s rental fleets during the relevant periods. I am continuously updating data from the company. I
also obtained used car prices from several websites.
2.1.1
Classification
Table 1 shows the classification of the company’s rental fleets. I
follow the company’s own system of classification. The rental cars are
classified as compact, mid-size, large-size, luxury, SUV (Sports Utility Vehicle), and RV (Recreational Vehicle). Generally speaking, the
car types are classified by engine displacement from compact to luxury.
But, for the classification of SUVs and RVs, the characteristics of the
cars are more important in classification than is engine displacement.
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The Determinants of Used Rental Car Prices
Some of the automakers, such as A-company and B-company, manufacture all types of cars, whereas other manufacturers, such as C-company,
D-company, and E-company only produce limited types of cars.
2.2
The Explanatory Facts of the Data
Usually, the company sells its rental cars when they reach three years
of age or 100,000 km of mileage. Wherever any car reaches one of two
thresholds, the manager may decide at will to sell the car. However, I
found out many exceptions regarding this rule.
Table 1
Type
Displacement
Brand Name
Compact
Below 1500cc
Mid-Size
1500cc∼2000cc
Large-Size
2000cc∼2500cc
Luxury
Above 2500cc
SUV
RV
2000cc ∼
2000cc ∼
Imported
1500cc ∼
A-company, B-company,
C-company
A-company, B-company,
C-company, D-company
A-company, B-company,
D-company
A-company, B-company,
E-company
A-company, E-company
A-company, B-company,
E-company
BMW, Land Rover, etc.
2.2.1
Number of
Renal Cars
548
1260
429
619
485
239
12
Used Car Price.
Table 2 summarizes average purchasing prices, average selling prices,
average ages before resale at used car markets, and average residual values of the rental cars in my data set in terms of the seven types of cars.
First, the table shows that large-size cars retain the highest residual
values at time of selling, followed by luxury cars. Table 3 shows the average residual values in terms of brand and car type. In the compact-car
category, A-company cars retains the highest residual values on average,
followed next by B-company, then C-company.
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Sung Jin Cho / Journal of Economic Research 10 (2005) 277–304
Second, in the mid-size category, D-company retains the highest
residual value, while Bcompany retains the lowest residual value. Third,
in the large-size category, A-company and Dcompany cars retain similar residual values, and B-company once again retains again the lowest
residual value. Fourth, E-company cars retain slightly higher residual
values than A-company cars. Fifth, E-company SUVs retain higher
residual values than A-company SUVs. Sixth, unlike the case of SUVs,
A-company RVs retain the highest residual values, followed by Bcompany RVs. In fact, E-company RVs retain the lowest residual values
at the time of resale. All of these facts should be confirmed in the sections on estimation to follow.
Table 2 (All values are averages)
Type
Compact
Mid-Size
Large-Size
Luxury
SUV
RV
Imported
2.2.2
Purchasing Price
4,790,094.9
12,812,685.0
20,370,819.0
32,051,431.2
18,925,117.3
15,834,581.7
72,361,595.9
Selling Price
2,083,311.1
5,846,904.8
11,105,233.1
15,188,731.8
7,996,917.5
6,935,230.1
28,365,166.7
(won/years)
Residual Value3
43.5%
45.6%
54.5%
47.4%
42.3%
43.8%
39.2%
Age
2.9
2.8
2.9
3.0
2.8
2.8
3.6
Average Ages and Kilometer Readings of Rental Fleets
Prior to Resale
Table 3 presents average kilometer readings, average number of accidents at the time of resale, and average repair costs per accidents, in
terms of cars type. First, we can see that SUVs and RVs have the highest operating ratios, when we compare their average kilometer readings
and average ages before resale. This phenomenon results in the lowest
residual values, especially in case of SUVs from Table 2. Imported cars
seems to have the lowest operating ratio. This is because the rental
price of these imports are relatively high, and thus, these cars are less
frequently rented than the other types of cars. In terms of average number of accidents, imported cars have the most frequent accidents. This
suggested renters of imported cars may be overconfident with their
3
Residual values in terms of percentage at the time of resale.
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The Determinants of Used Rental Car Prices
Type
Compact
Mid-Size
Large-Size
Luxury
SUV
RV
Table 3
Band
Average Residual Value
A-company
0.528240
B-company
0.494596
C-company
0.469074
A-company
0.454247
B-company
0.417115
D-company
0.510264
C-company
0.441861
A-company
0.551550
B-company
0.434544
D-company
0.558578
A-company
0.469115
B-company
0.422173
E-company
0.506755
A-company
0.416325
E-company
0.465593
A-company
0.461173
B-company
0.449881
E-company
0.337380
rental cars and drive carelessly. Excluding the imports, the average
number of accidents are similar for all types of cars except for RVs,
which have the lowest accident rate.
Type
Compact
Mid-Size
Large-Size
Luxury
SUV
RV
Imported
Table 4 (All values are averages)
Kilometers
Ages
Number of
Accidents
78,600 Km 2.9 years
0.8 times
82,500 Km 2.8 years
0.8 times
77,600 Km 2.9 years
0.7 times
88,800 Km 3.0 years
0.8 times
93,800 Km 2.8 years
0.7 times
104,100 Km 2.8 years
0.6 times
89,400 Km 3.6 years
1.1 times
Cost Per
Accident
794,337.3 Won
707,610 Won
715,156.4 Won
953,597.3 Won
1,159,387.2 Won
712664.6 Won
1,133,889.2 Won
As for average costs incurred per accident, compact cars have the
highest repair costs per accident, even though the purchase prices of
Sung Jin Cho / Journal of Economic Research 10 (2005) 277–304
283
compact cars are the lowest among the others. We can conjecture that
compact cars tend to get into more severe accidents than other types
of cars, i.e., compacts cars are, on average, damaged most seriously per
accident. The SUV appears to be the next most severely damaged per
accident. This is because SUVs are frequently overturned in accidents,
because of their high center of gravity. This is currently a very important safety issue.
2.2.3
Seasonality Comparison
According to several used-car market reports, the seasonality of the
used car markets can be defined as follows (assuming one year can be
divided into four categories): (1). The semi-decreasing 6 period (5 percent price drop on average) includes November and December; (2). The
decreasing period (10 percent price drop on average) includes January
and February. During these periods, car manufacturers tend to hold
large sales events, hence consumers are inclined to buy brand new cars
rather than used cars. Thus, it is natural that used rental cars become undersold in terms of prices; (3). The recovering period includes
March, April, May and June. During this period, because the conditions for purchasing brand new cars become worse from the consumers
point of view, used car prices recover somewhat, i.e., the demand for
cars starts to move toward used cars; and (4). The increasing period
includes July, August, September and October. During this period,
because of increasing mobility and other seasonal needs arising from
summer holidays, etc., used car prices increase in response to the increasing demand for used cars. These seasonality factors, in addition to
monthly effects, will be examined in the next section.
3
The Estimation
3.1
3.1.1
Models
Model A
In order to find out the determinants of used rental car price, I estimate using a log linear model. This model explains how several factors
284
The Determinants of Used Rental Car Prices
affect in depreciation of each rental car value. This is very important
because this model will provide the elements that affect the resale value
of rental cars.
The dependent variable of the model is the log of the ratio between
new purchase price and selling price of all rental cars. The independent
variables of the model are as follows: kilometer reading, age of each car
at time of resale, accident record (number of accidents and total repair
costs for all accidents). I also want to see how many accidents make the
manager indifferent toward resale value, whether or not each car has
had any accidents. This model can also easily provide an elasticity for
each determinant.
The reason why I let the coefficient of the log of purchase price one
is that I primarily wanted to find out important factors affecting the
depreciation of the selling price relative to the purchasing price.
3.1.2
Models B and C
In addition to Model A, I assume that there are other elements
which affect resale values, elements representing the external states of
rental cars. According to several interviews with top managers from
the company, one of the most important factors would be the period
when each used rental car is sold. These can be inserted into the model
as monthly or quarterly dummies. Model B includes the quarterly seasonal dummies mentioned above. Model C includes monthly dummies.
Therefore, in this model, I want to investigate whether this monthly
division provides better results than just the separated twelve months.
3.2
Estimation
First, I estimate all rental cars as a whole without separating them
based on car-type. Then, I estimate each model after separating the
renal cars based on car-type. These estimations are based on the ratio
estimation. The level estimation follows each ratio estimation. Table 1
in Appendix A explains all important independent variables.
Sung Jin Cho / Journal of Economic Research 10 (2005) 277–304
3.2.1
285
Pooled Estimation
Estimated parameters We find very interesting point from these
estimation results of all models. For one thing, the Age and Age2 variables carry different signs. According to our expectation, Age must
affect rental car resale values negatively. But, for estimations of these
three models exhibit Age variable, rental car resale values are affected
positively. However, this positive effect is offset by the negative effect of
the Age2 variable, and the whole effect of the two age variables (Age and
Age2 ) affects rental car resale values negatively, which meets our conventional expectations. However, an interesting point should be noted
here. As a renal car gets older, its resale value does decrease but, the
rate of decrease of resale value is small when the car is relatively new,
but increase the car ages. In other words, as the older a rental car, the
more rapidly its resale value falls. In fact, the age function for resale
values is a concave function. This is because the second derivative is
negative and the parameter value is more than twice as much as the
parameter of the Age variable itself. This phenomenon is a result of the
characteristics of rental cars. In fact, any cars that are used for rental
purposes are usually exploited excessively and carelessly. In fact, rental
users exhibit certain kinds of moral hazard, since rental cars are not
owned, but just rented and considered as a sort of public good. Therefore, if there were two used cars in the market with the similar ages,
but from different previous owners - one a private owner and the other
a rental company - it is only natural that the former would definitely
be preferred to the latter in the market.
We can also find out another interesting point from the two Kilometer variables, Kilometer and Kilometer2 . In fact, their interaction is
the opposite that of the two Age variables. Again, we expect the overall
effects of the two Kilometer variables to be negative to the resale values of rental cars. At first, the Kilometer variable itself affects rental
cars resale prices negatively. But, the Kilometer2 variable has a positive parameter. This can be explained as follows: The overall effects of
the two Kilometers variables are negatively related to the resale value
of rental cars. But, as the kilometer reading of a renal car increases,
the negative effect decreases because of the positiveness of the second
derivative. Thus, as the kilometer reading of a rental car grows, the
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The Determinants of Used Rental Car Prices
car’s resale value decreases at a decreasing rate. Thus, the kilometer
function for the resale values of cars is convex.
The Total Accident Costs variable has a negative sign which coincides with our conventional expectation. On the other hand, the number
of accidents variable does not have any significant signs for all models.
This means that the resale values of rental cars are determined not by
the frequency of total accidents, but by the total severity of accidents
that particular rental cars have experienced during their lives.
In terms of types and brand name of rental cars, large-size Acompany and D-company have significantly positive effects on resale
values. This means that A-company and D-company appear to have
built strong brand images in large-size category of the used car market.
In fact, Acompany has about a 10% more favorable brand image than
D-company in this category. The other important category is RV. In
this category, E-company has a strong negative effect on the resale value
of rental RVs.
Next, we should examine the effects of seasonality for two models,
B and C. Four divisions of the seasonal effect do not provide accurate
information through Model B. According to Model C, February has a
negative effect on the resale value of rental cars. Thus, it appears that
the car rental company tends not to sell its rental cars during the month
of February. However, market conditions begin to recover in March.
This positive effects seems to be the highest in the month of August,
when demand for used cars seems to be highest due to several factors,
including summer holidays, increasing mobility, etc.
However, since these pooled regressions can’t provide better and
more accurate informations regarding car brands and type, we should
investigate these facts further in separate regressions for each type of
rental cars.
Price Estimation Based on Model C, which of the three models
has the most comprehensive, I estimated the resale prices of the rental
cars that had been sold between the beginning of 2003 and July 2004 and
regressed them against actual resale values. Figure 1 shows the pooled
regression result. In fact, it seems that the predicted resale prices are
accurate estimates of actual resale prices. Compared to the estimation
result of the log ratio, the fit is much better than that of the previous
estimation. This is because the former values of dependent variables
are represented by ratios in order to measure the devaluation of the
Sung Jin Cho / Journal of Economic Research 10 (2005) 277–304
287
Figure 1: Regression of estimated resale prices against actual resale
prices
cars. On the other hand, the latter dependent variables are represented
by actual levels. It would seem that level estimation provides better
estimation results.
3.3
Separate Regressions
In this section, I separate all types of cars - compact, mid-size, largesize, luxury, SUV, and RV and estimate them separately. Due to the
lack of data in the imported car category, a separate estimation of imported rental cars has been omitted intentionally.
3.3.1
Compact Car Estimation
In this category, the A-company, B-company, and C-company manufacture compact cars.
Estimated parameters Through separate estimations of compacts
cars, we can obtain several key bits of information. First, brand name
does not affect the resale values of rental cars except in case of Ccompany, whose effect is pronouncedly negative. Both A-company and
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The Determinants of Used Rental Car Prices
B-company brand do not affect the devaluation of rental cars. As we
expected, the Age2 variable has a negative sign. This tells us that as a
car gets older and older, its resale value falls. However, the Age variable
itself does not show any significant sign. The Kilometer variable has a
significantly a negative sign, which coincides with my expectation. This
is because as a rental car runs more and more, its kilometer reading affects its resale value negatively. On the other hand, the Kilometer2 has
a positive sign significantly different from zero. In fact, the Kilometer2
variable functions in the opposite direction of the Kilometer variable.
This means that higher kilometer readings speed down the depreciation
of its resale value, when the car has a very high kilometer reading. That
is, the resale values of a car decreases at a decreasing rate, as its kilometer reading increases. The effect of Kilometer2 is unable to reverse
the effect of Kilometer, since the estimated parameter from the former
is much smaller than that of the latter, i.e., when considering both the
first derivative and the second derivative, the values are still negative.
Total Accident Costs affects used car resale values negatively, because this variable seems to represent how cars get experienced with
severe accidents. I think that this variable is more important than the
“number of accidents” variable. In fact, “number of accidents” variable
can be misleading because it ignores accident “severity.” Some cars that
experience several accidents can have lower total accident costs, since
some accidents do not require any repair costs, i.e., some accidents may
involve only human injuries. Thus, the “total accidents costs” variable
seems to present a car’s status more accurately than does the “number
of accidents” variable. In the case of compact cars, both the Total Accident Costs and the Number of Accidents variables in Model C affect
resale values negatively. In Models A and B, however, only the Total
Accidents Costs variable has a significant negative sign.
Estimating the Price of Used Rental Cars The Table 2 shows
a regression of the predicted resale values of compact cars against their
actual selling prices. The predicted resale values are calculated based
on Model C. The result are better than the results of the depreciation
ratio regression. In fact, our determinants are explanatory enough to
predict the actual resale values of compact cars.
Sung Jin Cho / Journal of Economic Research 10 (2005) 277–304
289
Figure 2: Regression of estimated resale prices against actual resale
prices
3.3.2
Mid-Size Car Estimation
This separate estimation is for mid-size cars only. The manufacturers that produce mid-size cars are A-company, B-company, D-company,
and C-company.
Estimated parameters In the case of mid-size cars, the Acompany brand image has a positive effect on the resale value of its cars,
but its impact is not as great as D-company’s. C-company’s brand image
has a negative impact on the resale value of its cars, and the B-company
has a neutral effect. Therefore, we can conclude that D-company has
established a very strong brand image in this category.
In terms of age variables, similar to our expectation, Age2 does affect
resale values of used cars negatively. On the other hand, Age variable
itself has a positive sign but is not significant. Since the estimated parameters of Age2 exceed those of the Age variable, the total effect of
both the Age and Age2 variables is negative. This can be explained as
follows: When a car is relatively new, its age does not have a significant
impact on its resale value, but as the ages, the negative effect on its
resale value increases. Put simply, as a rental car gets older and older,
290
The Determinants of Used Rental Car Prices
Figure 3: Regression of estimated resale prices against actual resale
prices
its resale values continue to decrease. This is the opposite of used cars
that have been privately owned. We should note that we are dealing
with rental cars. Thus, normally speaking, older rental cars mean that
the cars have been severely exploited with high rental frequency.
Again, the total number of accidents variable, which can tell people
the current condition of a car, has a negative effects on resale values.
The severity of accidents variable has a significantly negative impact on
the resale values of rental cars.
In terms of seasonal effects, in Model C, only March has a positive
sign. This shows that the company particularly likes to sell its mid-size
rental cars in March. Other than the month of March, resale prices
seem to be neutral in all other months.
Estimating the Price of Used Rental Cars Table 3 shows a
regression of predicted resale values of mid-size cars against the actual
selling prices of mid-size cars. The predicted resale values are calculated
based on Model C. Compared to the other categories of cars, the fit are
relatively poor.
Sung Jin Cho / Journal of Economic Research 10 (2005) 277–304
3.3.3
291
Large-Size Car Estimation
The manufacturers that produce large-size cars are A-company, Dcompany, and B-company.
Estimated parameters In these estimations, both the A-company
and D-company brands have a strong positive effects on the resale values
of their used rental cars. However, we can guess that the B-company
brand has a strong negative effect on resale values for all models - A,
B, and C. In terms of the seasonal effects from Models B and C, almost
all seasonal dummies have the expected signs and are significant. As
expected, January and February in Model C which correspond to the
decreasing period in Model B, have negative signs, and the signs are all
significant. This coincides with other reports from used car websites.
However, the other months in Model C, with the exception of November, have a positive effect on the resale values of large-size cars. This
phenomenon can be seen in Model B as well. The dummies from both
the recovering period and the increasing period have positive parameters. This tell us that, in these periods, the resale values are affected in
relatively positive ways. Specifically, we notice that the increasing period has larger estimated parameters than the recovering period. This
coincides with our hypothesis.
This brings us to a very interesting point. Unlike the other types of
cars, both Age variables and both Kilometer variables are not significant at all. Even the Total Accident Costs variable is not significantly
different from zero. However, the Number of Accidents variables for
Models A, B, and C have the expected negative signs and are significant. Thus, we can conclude that unlike the other types of cars, the
resale values of large-size cars are more influenced by their number of
accidents than by their total accident costs. This means that customers
wanting to by used large-size cars pay more attention to the frequency
of a cars accidents than the severity of the accidents themselves.
Price Estimation of Used Large-Size Rental Cars Table 4
shows a regression of predicted resale values of large-size cars against
their actual selling prices. The predicted resale values are calculated
using Model C. The results seem fairly good compared with the other
categories of cars. The determinants from this study can explain the
actual resale values of large-size rental cars fairly well.
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The Determinants of Used Rental Car Prices
Figure 4: Regression of estimated resale prices against actual resale
prices
3.3.4
Luxury Car Estimation
The manufacturers that produce luxury cars are A-company, Ecompany, and B-company.
Estimated parameters In this estimation, the Age variables for
all models have positive signs as expected, like the other types of cars.
However, the Age2 variables for all three models have negative signs,
similar to the case of mid-size cars estimation. This can be explained
as follows. The resale values of luxury cars decrease as cars ages, and
the rate of decrease increases, as the car gets older, as a result of the
negative effects of the second derivatives. Like the other car types, the
total effect of age variables is negative.
In case of Kilometer parameters, the signs are significant and coincide with our expectation, which is that they are negative. The resale
values decrease in proportion to the increase in Kilometers.
The estimated parameters for total accident costs for all models tell
us that the resale values of Luxury cars depend on severity of accidents,
but not on accident frequency.
In terms of brand power, both A-company and E-company’s brand
Sung Jin Cho / Journal of Economic Research 10 (2005) 277–304
293
Figure 5: Regression of estimated resale prices against actual resale
prices
images have positive effects on the resale values of used luxury cars,
whereas B-company’s brand has a negative effect. The reason for this is
A-company and E-company control over 90% of the luxury rental cars,
and B-company has recently retreated from the luxury car market.
In terms of seasonal effects, February has a negative effect on the
resale value of luxury rental cars, so that the company is unwilling to
sell its rental fleet during that particular month. However, April, June,
July, August, and September affect resale prices of luxury rental cars
positively. August, in particular, has the biggest value of parameters.
This is because the demand for used cars increases to its highest during
this month because of increase in demand. February, November, and
December affect the resale prices of used rental cars negatively, since
the demand for used cars drops during these months because of special
new cars sales event put on by car manufacturers.
However, according to Model B, none of the seasonality variables are
not significantly different from zero, except for the last period, which
includes November and December. The last period seems to have a
negative sign. This is why we call this period as the “decreasing period.”
Price Estimation of Used Luxury Rental Cars The Table 5
shows a regression of the predicted resale values of luxury cars against
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The Determinants of Used Rental Car Prices
their actual selling prices. The predicted resale values are calculated
using Model C. The fit is accurate compared with the other categories
of cars. The determinants from this study can explain over 80% of the
actual resale values of luxury rental cars.
3.3.5
SUV Estimation
In this category, there are only two companies in my data set that
produce SUVs; A-company and E-company.
Estimated Parameters According to the estimations of Models,
A, B, and C, we can note that the A-company brand has a negative
effect on its SUV’s resale values. E-company also has a negative effect.
E-company’s image has a greater negative effect on the devaluation of
its SUVs than does A-company’s. Of the Age and Age2 variables, only
the Age2 variable is significant, and in the case of Model C, it has a
negative effect on the resale value of used luxury rental cars. The Age
variable has a positive sign, but it is not significant. Thus, the resale
values of SUVs can be affected by their age when the cars are very old,
but. they devaluate relatively slowly when they’re still relatively new.
For the Kilometer and Kilometer2 variables, the results are different from what I obtained for the other types of cars. Even though
the estimated parameters are not significant for all models, except for
the parameters of Kilometer2 in the case of Model C, the signs of
Kilometer2 are in fact negative. Therefore, the function of kilometer
variables for resale values of SUV is concave rather than convex.
In the case of the Total Accident Costs variable, all of the signs are
significantly negative. Thus, the resale values of SUVs strongly depend
on accident severity.
In terms of seasonal effects, only January, October, and December
have significant signs in Model C. According to the sign of the October
dummy, we can guess that the price drop starts from October in the
case of SUVs, earlier than the other types of cars. In Model B, the
last decreasing period, which includes November and December, shows
a negative sign. Therefore, in this period, the company is unwilling to
sell its used SUV fleets.
Price Estimation of Used Rental SUVs Table 6 shows a regression of predicted SUV resale values against their actual selling prices.
Sung Jin Cho / Journal of Economic Research 10 (2005) 277–304
295
Figure 6: Regression of estimated resale prices against actual resale
prices
The predicted resale values are calculated based onModel C. The fit
seems to be fairly good compared with the other categories of cars. The
determinants from this study can explain about 50% of the actual resale
values of rental SUVs.
3.3.6
RV Estimation
The manufacturers that produce RVs are A-company, E-company,
and B-company.
Estimated parameters In RV estimations from Models A, B, and
C, the E-company brand image has a negative effect on its resale price,
whereas the A-company and B-company brands have a positive impact
on their resale prices. These situations coincide with the current market
situation of RVs. We observed very few RVs from E-company.
According to the results of the two age variables, the Age2 variable
affects rental RV resale prices negatively, as expected, but, the Age itself
has a positive effects. Age2 has a very significant t ratio. Therefore, the
resale values of RVs depreciate at an increasing rate, as they get older,
thus implying concavity of the function.
296
The Determinants of Used Rental Car Prices
Figure 7: Regression of estimated resale prices against actual resale
prices
Compared with the estimations for the other cars, neither Total Accident Costs nor Number of Accidents affects rental cars’ resale values.
Therefore, accident history seems to never affect choice of used RVs in
the used car markets. Even the two kilometer variables do not play any
role in the depreciation of resale values of used RVs.
In terms of seasonal effects, the decreasing period has an expected
sign in Model B. This is because the demand for used cars falls down
because of the increasing demand for brand new cars resulting from seasonal new car sales event put on by car manufacturers. Also, in Model
C, only February and April have significant signs, which are negative
and positive, respectively. This is because used car sales drop in February as a result of the special new cars sales events of car manufacturers.
On the other hand, the demand for used cars gradually recovers in the
month of April.
Price Estimation of Used Rental RVs Table 7 shows a regression of predicted RV resale values against actual selling prices. The
predicted resale values are calculated based on Model C. The result
2
shows very high R compared with the other categories of cars. The
determinants from this estimation can explain about 80% of the actual
resale values of rental RVs.
Sung Jin Cho / Journal of Economic Research 10 (2005) 277–304
4
297
Conclusion
This paper identifies several important factors that affect the resale
prices of used rental cars. In fact, this paper empirically shows and
proves several conjectures regarding the determinants for used car resale
values through the use of detailed micro data from one of the biggest
rental car companies. To be more specific, the Age of used cars has
two composite effects on resale values. The first Age variable has a
positive effect, whereas the square of Age, Age2 , has a negative effect
on the resale values of used rental cars. Overall, the two effects work
negatively, at an increasing rate, as a rental car ages. On the other
hand, two mileage variables, Kilometer and the square of Kilometers,
also interact with each other and produce an overall negative effect on
the resale prices of used cars. But, the mode of interaction is different
from that of the two Age variables. As the Kilometers of a rental cars
grows, the cars residual value decreases at a decreasing rate.
In terms of brand image, A-company and D-company generally have
positive effects on the resale values of used rental cars. E-company has
a positive effect on the resale values in the SUV category, and a negative
effect on the resale values in the RV category. Generally, B-company
and C-company are inferior to the other brands in terms of resale values
across all categories.
With regard to seasonal effects, we can conclude that this paper
confirms the general perception regarding seasonal effects on resale values. Usually, from November to February, the resale values are affected
negatively and thus the company is normally unwilling to sell its used
rental cars during these months. March is the month of stretching in
the used car market, and it has a positive effect on resale values. August seems to be the highest season for the used car market because of
several factors that increase demand. Thus, August has a more positive
impact on resale values than any other month.
However, due to the tremendous variations in the data, general estimation efficiency should be improved. In fact, this paper plays an
important role in providing an important information regarding factors
affecting the resale prices of rental cars. In this regard, this paper has
achieved its objective.
298
The Determinants of Used Rental Car Prices
Reference
Billingsley, Patrick, Probability and Measure, New York, John Wiley,
1979, 309-310; 320.
Greene, William C., Eonometric Analysis, Prentice-Hall, 2000.
House, Christoper L., and Leahy, John V, “An sS model with Adverse
Selection,” NBER Working Paper 8030, December, 2000.
Hedel, Igal. and Lizzeri, Alessandro, “Adverse Selection in Durable
Goods Markets,” NBER Working Paper 6194, September, 1997.
Korea Automobile Manufacturers Association, Korea Automobile Manufacturers Association Reports, Korea Automobile Manufacturers
Association.
Korea Used Car Industry Development Association Inc, Used Car market Monthly Report, Korea Used Car Industry Development Association Inc.
The Korean Used Car Dealers Association, Used Car, October,
1998.∼March, 2002.
www.naver.com
www.yahoo.co.kr
Sung Jin Cho / Journal of Economic Research 10 (2005) 277–304
5
5.1
299
Appendix A
Explanation of All Independent Variables.
Table 1
Variable
Age
Age2
Kilometer
Kilometer2
Total Accident costs
Number of accidents
Compact C-company
Compact A-company
Compact B-company
Midsize A-company
Midsize B-company
Midsize R-Samsung
Midsize GM-Dawoo
Large-size A-company
Large-size B-company
Large-size R-Samsung
Luxury A-company
Luxury B-company
Luxury E-company
SUV A-company
SUV E-company
RV A-company
RV B-company
RV E-company
Foreign
Explanation
Age of car at time of selling
Age is squared
Kilometer reading recorded at time of selling
Kilometer is squared
Sum of all repair costs from all accidents for each car
Total number of accidents for each car
Compact car from C-company
Compact car from A-company
Compact car from B-company
Mid size car from A-company
Mid size car from B-company
Mid size car from Renault Samsung
Mid size car from C-company
Large size from A-company
Large size from B-company
Large size from Renault Samsung
Luxury car from A-company
Luxury car from B-company
Luxury car from E-company
Sport Utility Vehicle from A-company
Sport Utility Vehicle from E-company
Recreational Vehicle from A-company
Recreational Vehicle from B-company
Recreational Vehicle from E-company
Imported cars
300
6
6.1
The Determinants of Used Rental Car Prices
Appendix B
Pooled Estimation
Constant
Age
Age2
Kilometer
Kilometer 2
Total Accident costs
Number of accidents
Compact A-company
Compact B-company
Midsize A-company
Midsize B-company
Midsize R-Samsung
Midsize GM-Dawoo
Large-size A-company
Large-size B-company
Large-size R-Samsung
Luxury A-company
Luxury B-company
Luxury E-company
SUV A-company
SUV E-company
RV A-company
RV B-company
RV E-company
Foreign
Model A
-0.7072**(0.1158)
0.1104**(0.0431)
-0.0357**(0.0072)
-0.0013**(0.0002)
0.00004**(0.00001)
-0.00007**(0.00001)
0.0014(0.0038)
0.1337(0.0962)
-0.0160(0.1029)
-0.0131(0.0960)
-0.1121(0.0972)
0.1032(0.0971)
-0.0535(0.0991)
0.189**(0.0963)
-0.0791(0.1031)
0.1798**(0.1008)
0.0533(0.0962)
-0.0884(0.1086)
0.1410(0.0981)
-0.1048(0.0963)
0.0188(0.0991)
-0.0185(0.0974)
-0.0291(0.0985)
-0.2748**(0.1002)
-0.0143(0.118)
Model B
-0.7242**(0.1163)
0.1099**(0.0431)
-0.0355**(0.0072)
-0.0012**(0.0002)
0.00004**(0.00001)
-0.00007**(0.000009)
0.0015(0.0038)
0.1375(0.0962)
-0.0127(0.1029)
-0.0104(0.0960)
-0.1054(0.0973)
0.1066(0.0971)
-0.0513(0.0991)
0.1919**(0.0963)
-0.0775(0.1031)
0.1831*(0.1009)
0.0569(0.0962)
-0.0847(0.1086)
0.1443(0.0981)
-0.1022(0.0963)
0.0223(0.0991)
-0.0148(0.0974)
-0.0260(0.0985)
-0.2734**(0.1002)
-0.0094(0.1109)
*Significant at 10% Level; **Significant at 5% Level
Model C
-0.7353**(0.1177)
0.0182**(0.0186)
-0.0356**(0.0071)
-0.0031**(0.0002)
0.00004**(0.00001)
-0.000073**(0.00001)
-0.0081(0.0184)
0.1328(0.0959)
-0.1026(0.1026)
-0.0177(0.0958)
-0.1118(0.0970)
0.1040(0.0968)
-0.0640(0.0989)
0.1823*(0.0960)
-0.0960(0.1029)
0.1742*(0.1005)
0.0474(0.0959)
-0.0853(0.1083)
0.1359(0.0978)
-0.1090(0.0960)
0.0671(0.0989)
-0.0206(0.0971)
-0.0308(0.0982)
-0.2789**(0.0999)
-0.0117(0.1106)
301
Sung Jin Cho / Journal of Economic Research 10 (2005) 277–304
6.2
Continued on the Pooled Estimation
Model A
Seasonality -1 (January)
Seasonality -1 (February)
Seasonality -1 (March)
Seasonality -1 (April)
Seasonality -1 (May)
Seasonality -1 (June)
Seasonality -1 (July)
Seasonality -1 (August)
Seasonality -1 (September)
Seasonality -1 (October)
Seasonality -1 (November)
Seasonality -2 (Decreasing Period)
Seasonality -2 (Decreasing Period)
Seasonality -2 (Decreasing Period)
2
R
F
Model B
Model C
0.0195 (0.0184)
-0.0397** (0.0186)
0.0414** (0.0185)
0.0434** (0.0180)
-0.0081 (0.0184)
0.1084 (0.0187)
0.0132 (0.0192)
0.0911** (0.0231)
0.0207 (0.0211)
-0.0098 (0.0192)
-0.0155 (0.02211)
0.0204(0.0127)
0.1031(0.0117)
0.0092(0.0124)
0.2848
60.5911
0.2849
53.9840
0.2926
43.4411
*Significant at 10% Level; **Significant at 5% Level
6.3
Compact Car Estimation
Constant
Age
Age2
Kilometer
Kilometer 2
Total Accident costs
Number of accidents
Brand dummy (A-company)
Brand dummy (B-company)
Seasonality -1 (January)
Seasonality -1 (February)
Seasonality -1 (March)
Seasonality -1 (April)
Seasonality -1 (May)
Seasonality -1 (June)
Seasonality -1 (July)
Seasonality -1 (August)
Seasonality -1 (September)
Seasonality -1 (October)
Seasonality -1 (November)
Seasonality -2 (Decreasing Period)
Seasonality -2 (Recovering Period)
Seasonality -2 (Increasing Period)
2
R
F
Model A
-0.5659**(0.2176)
0.0499(0.1291)
-0.0399*(0.0214)
-0.0010**(0.0004)
0.000023**(0.00001)
-0.000019*(0.000009)
-0.0118(0.0095)
-0.0194(0.1067)
-0.1482*(0.0997)
Model B
-0.5833**(0.2224)
0.0503(0.1301)
-0.0343(0.0216)
-0.0010**(0.0004)
0.000023**(0.00001)
-0.000017*(0.00001)
-0.0140(0.0096)
0.1453(0.0999)
-0.0205(0.1068)
Model C
-0.6489**(0.2278)
0.0547(0.1322)
-0.0351*(0.0218)
-0.0010**(0.0004)
0.000021**(0.00001)
-0.00002*(0.000009)
-0.0163*(0.0098)
0.1406(0.1026)
-0.0045(0.1099)
-0.0105(0.0463)
0.0270(0.0477)
0.0676(0.0477)
0.0322(0.0458)
0.0194(0.0470)
0.0523(0.0482)
0.0525(0.0575)
0.0515(0.0698)
0.0095(0.0535)
0.0571(0.0460)
0.0191(0.0490)
-0.0072*(0.0016)
0.0300(0.0270)
0.0329(0.0298)
0.1448
12.5736
*Significant at 10% Level; **Significant at 5% Level
0.1461
9.5097
0.1992
5.6919
302
6.4
The Determinants of Used Rental Car Prices
Mid-Size Car Estimation
Constant
Age
Age2
Kilometer
Kilometer 2
Total Accident costs
Number of accidents
Brand dummy (A-company)
Brand dummy (B-company)
Brand dummy(Re-Samsung)
Seasonality -1 (January)
Seasonality -1 (February)
Seasonality -1 (March)
Seasonality -1 (April)
Seasonality -1 (May)
Seasonality -1 (June)
Seasonality -1 (July)
Seasonality -1 (August)
Seasonality -1 (September)
Seasonality -1 (October)
Seasonality -1 (November)
Seasonality -2 (Decreasing Period)
Seasonality -2 (Recovering Period)
Seasonality -2 (Increasing Period)
2
R
F
Model A
-0.5953**(0.1224)
0.0142(0.0776)
-0.0136(0.0131)
-0.0027**(0.0007)
0.00002**(0.00001)
-0.000033**(0.00001)
0.0044(0.0063)
0.0481*(0.0267)
-0.0434*(0.0290)
0.1644**(0.0308)
Model B
-0.5956**(0.1231)
0.0131(0.0777)
-0.0131(0.0131)
-0.0027**(0.0007)
0.000019*(0.00001)
-0.000039**(0.00001)
0.0043(0.0063)
0.0469*(0.0267)
-0.0392(0.0313)
0.1633**(0.0308)
Model C
-0.5913**(0.1230)
0.0035(0.0777)
-0.0129*(0.0031)
-0.0027**(0.0007)
0.000019(0.00001)
-0.000036**(0.00001)
0.005(0.0063)
0.0492*(0.0266)
-0.0387(0.0314)
0.1704**(0.0309)
0.0384(0.030)
0.0024(0.0297)
0.0452*(0.0304)
0.0237(0.0290)
-0.0453(0.0292)
-0.0046(0.0311)
-0.0346(0.0316)
0.0246(0.0387)
0.0110(0.0347)
-0.040(0.0318)
0.003(0.0352)
0.0167(0.0216)
0.0007(0.0199)
-0.0206(0.0211)
0.1305
22.0006
0.1321
16.9662
0.144
11.6139
*Significant at 10% Level; **Significant at 5% Level
6.5
Large-Size Car Estimation
Constant
Age
Age2
Kilometer
Kilometer 2
Total Accident costs
Number of accidents
Brand dummy (A-company)
Brand dummy (Re-Samsung)
Seasonality -1 (January)
Seasonality -1 (February)
Seasonality -1 (March)
Seasonality -1 (April)
Seasonality -1 (May)
Seasonality -1 (June)
Seasonality -1 (July)
Seasonality -1 (August)
Seasonality -1 (September)
Seasonality -1 (October)
Seasonality -1 (November)
Seasonality -2 (Decreasing Period)
Seasonality -2 (Recovering Period)
Seasonality -2 (Increasing Period)
2
R
F
Model A
-0.5269**(0.1303)
-0.0824(0.0855)
-0.0043(0.0142)
-0.0007(0.0005)
0.00007(0.0001)
0.0000(0.0000)
-0.0150**(0.0076)
0.2587**(0.0246)
0.2444**(0.0309)
Model B
-0.6075**(0.1319)
-0.0820(0.0847)
-0.0042(0.0141)
-0.0008(0.0005)
0.00008(0.0001)
-0.000001(0.00001)
-0.0146*(0.006)
0.2633**(0.0244)
0.2521**(0.0307)
Model C
-0.6726**(0.1361)
-0.0704(0.0845)
-0.0053(0.0140)
-0.0004(0.0002)
0.000012(0.00001)
-0.00001(0.00001)
-0.0141**(0.0075)
0.2723**(0.0247)
0.2627**(0.0308)
-0.1021*(0.0557)
-0.1479**(0.0552)
0.1330**(0.0550)
0.1451**(0.0536)
0.1436**(0.0548)
0.1197**(0.0541)
0.1000*(0.0555)
0.1927**(0.0590)
0.0846(0.0578)
0.0953*(0.0544)
0.0623(0.0598)
-0.0791**(0.0289)
0.0884**(0.0267)
0.0934**(0.0279)
0.3379
28.2999
*Significant at 10% Level; **Significant at 5% Level
0.3528
22.2093
0.3653
13.9622
Sung Jin Cho / Journal of Economic Research 10 (2005) 277–304
6.6
303
Luxury Car Estimation
Constant
Age
Age2
Kilometer
Kilometer 2
Total Accident costs
Number of accidents
Brand dummy (A-company)
Brand dummy (E-company)
Seasonality -1 (January)
Seasonality -1 (February)
Seasonality -1 (March)
Seasonality -1 (April)
Seasonality -1 (May)
Seasonality -1 (June)
Seasonality -1 (July)
Seasonality -1 (August)
Seasonality -1 (September)
Seasonality -1 (October)
Seasonality -1 (November)
Seasonality -2 (Decreasing Period)
Seasonality -2 (Recovering Period)
Seasonality -2 (Increasing Period)
Age*A-company
Age*B-company
2
R
F
Model A
-1.0539**(0.1855)
0.2781**(0.1165)
-0.0600**(0.0185)
-0.0015**(0.0007)
0.00001(0.00001)
-0.00004**(0.00001)
0.0159(0.0098)
0.1328**(0.0566)
0.2174**(0.0603)
Model B
-1.0816**(0.1876)
0.2835**(0.1165)
-0.0611**(0.0185)
-0.0015**(0.0007)
0.00009(0.0001)
-0.00004**(0.00001)
0.0147(0.0098)
0.1349**(0.0566)
0.2196**(0.0603)
Model C
-1.1462**(0.1886)
0.2792**(0.1166)
-0.0596**(0.0185)
-0.0012*(0.0007)
0.00006(0.0001)
-0.00004**(0.00001)
0.0138(0.0098)
0.1185**(0.0563)
0.2053**(0.060)
0.0555(0.0461)
-0.1055**(0.0461)
0.0699(0.0462)
0.0728*(0.0458)
0.0645(0.0476)
0.0748*(0.0454)
0.0926**(0.0460)
0.1886**(0.0505)
0.0914*(0.0523)
0.0556(0.0488)
-0.1341**(0.05457)
0.0157(0.0332)
0.0065(0.0306)
0.0387(0.0316)
0.1272
12.2525
0.1272
9.1854
0.1400
6.2931
*Significant at 10% Level; **Significant at 5% Level
6.7
SUV Estimation
Constant
Age
Age2
Kilometer
Kilometer 2
Total Accident costs
Number of accidents
Brand dummy (A-company)
Seasonality -1 (January)
Seasonality -1 (February)
Seasonality -1 (March)
Seasonality -1 (April)
Seasonality -1 (May)
Seasonality -1 (June)
Seasonality -1 (July)
Seasonality -1 (August)
Seasonality -1 (September)
Seasonality -1 (October)
Seasonality -1 (November)
Seasonality -2 (Decreasing Period)
Seasonality -2 (Recovering Period)
Seasonality -2 (Increasing Period)
2
R
F
Model A
-0.6910*(0.1960)
0.0421(0.1365)
-0.0357(0.0236)
-0.0023(0.0017)
-0.000015(0.00001)
-0.00004**(0.000009)
0.0018(0.0111)
-0.1303**(0.0280)
Model B
-0.6728**(0.2060)
0.0441(0.1369)
-0.0361(0.0236)
0.0022(0.0017)
-0.000015(0.00001)
-0.00004**(0.000009)
0.0019(0.0111)
-0.1290**(0.0281)
Model C
-0.6509**(0.2130)
0.0653(0.1377)
-0.0409*(0.0238)
-0.00003(0.0003)
-0.000018*(0.00001)
-0.00005**(0.00001)
-0.036(0.0112)
-0.1347**(0.0281)
-0.0862*(0.0502)
-0.0239(0.0547)
-0.0335(0.0534)
-0.0573(0.0522)
-0.0886(0.0542)
-0.0805(0.0545)
-0.0414(0.0522)
0.0753(0.0687)
-0.0692(0.0709)
-0.1317*(0.0577)
-0.0748(0.0632)
-0.0258 (0.0359)
-0.0251 (0.0346)
-0.0136 (0.0363)
0.1720
15.3679
*Significant at 10% Level; **Significant at 5% Level
0.1681
10.7834
0.1848
7.0961
304
6.8
The Determinants of Used Rental Car Prices
RV Estimation
Constant
Age
Age2
Kilometer
Kilometer 2
Total Accident costs
Number of accidents
Brand dummy (A-company)
Brand dummy (B-company)
Seasonality -1 (January)
Seasonality -1 (February)
Seasonality -1 (March)
Seasonality -1 (April)
Seasonality -1 (May)
Seasonality -1 (June)
Seasonality -1 (July)
Seasonality -1 (August)
Seasonality -1 (September)
Seasonality -1 (October)
Seasonality -1 (November)
Seasonality -2 (Decreasing Period)
Seasonality -2 (Recovering Period)
Seasonality -2 (Increasing Period)
2
R
F
Model A
-1.4169*(0.1684)
0.3685**(0.1105)
-0.0776**(0.0193)
-0.0009(0.0015)
-0.00001(0.00001)
-0.00003(0.0001)
-0.0152(0.0180)
0.2626**(0.0380)
0.2469**(0.0408)
Model B
-1.5397**(0.1882)
0.3646**(0.1081)
-0.0778**(0.0189)
0.0011(0.0015)
-0.000011(0.00001)
0.00004(0.0001)
-0.0141(0.0178)
0.2578**(0.0375)
0.2439**(0.0401)
Model C
-1.4181**(0.1991)
0.3044**(01082)
-0.0674**(0.0188)
0.0009(0.0015)
-0.00001(0.00001)
0.00001(0.0001)
-0.0067(0.0177
0.2376**(0.0376)
0.2330**(0.0402)
0.1196(0.0894)
-0.1419*(0.0804)
-0.0017(0.0796)
0.1493*(0.0782)
-0.0218(0.0786)
0.0452(0.0798)
-0.0293(0.0839)
0.0681(0.1980)
0.0647(0.0845)
-0.0559(0.0815)
-0.0162(0.0879)
-0.1479**(0.0548)
0.0577(0.0482)
0.0044(0.0514)
0.3619
17.8693
*Significant at 10% Level; **Significant at 5% Level
0.3921
14.9544
0.4226
10.1693