WHAT INFLUENCES THE PRICE OF USED CAR: A critical study into what determines the price of a used car in internet auctions?

Financial Econometrics Data Analysis

Raza Ghulam Mujtaba Sean O’ Moley

Zhou Yang

Introduction

This project analyses, how the price of a used car is affected by a change in model, engine size, colour,

age, etc. In an attempt to form an educated conclusion this project investigated the results in the light of

the findings by other academics. A total of 188 cars from different models, age, colour etc. were taken as

a sample. The essay will explain the methodology involved in analysing the results and at the same time

data will be analysed with the help of the models and assumptions explained in the methodology. The

main auction website used for the project is www.carzone.ie which contains more than fifty thousand

used cars data, internet auctions are probably the best source to buy a used car and the data available is

probably the most credible source of information. Although traditionally the trading if a used car has

involved an advert in the newspaper followed a one on one meeting between the prospective buyer and

seller however internet has eased the process a great deal. Hence, this essay will begin by providing some

information about how the internet has brought the evolution to the businesses and to what level has it

impacted the used car trading business.

Since the introduction of the World Wide Web the way to do business has changed for the better and

continues to do so. The number of internet users has risen from 40.3% in the year 2000 to almost 75% in

2009 in the developed world as seen in the table below.

YEAR Population Users % Penet. Usage Source

2000 31,496,800 12,700,000 40.3 % ITU

2003 32,050,369 20,450,000 63.8 % C.I.Almanac

2005 32,440,970 21,900,000 67.5 % C.I.Almanac

2008 33,212,696 28,000,000 84.3 % I.T.U.

2009 33,487,208 25,086,000 74.9 % I.T.U.

The Ecommerce industry has been around for more than a decade now and has seen growth of an

unprecedented size. Retail has been the biggest beneficiary of this growth in the Ecommerce Industry.

Online retail reached $5 trillion in 2007 and is set to reach $12 trillion by 2012 according to recent survey

by the Verdict Research and the percent of total retail sales has been rising at a rapid pace, reaching at

about five percent only in the United Sates as seen in the figure below depicting the data from the US

Census Bureau. From groceries to clothing everything can be found online. The trade of cars and

particularly the used cars is still a novelty relative to the retail online shopping, but is becoming a major

part faster then anyone expected.

Subject Motivation:

The financial crisis of the late 2000s have had a profound effect for the worse on the developed world, the

residents and the Governments has been involved in the spending cuts. This is one of the major reasons

why there has been a surge in the activity in the used car market and at the same time new car sales has

been decreasing for some time as the figure below explains. Hence, used cars market was more attractive

subject for the essay than the new cars because diversity in the probable determinants of the price for a

used car.

According to the European Automobile Manufacturers' Association (EAMA) the registration of the new

cars in Europe decreased by 9.6% in 2010 compared to 2009 on a month by month basis as seen in the

diagram above. The EAMA has cited the uncertain economic conditions for the decrease in the sales of

the new cars because the consumers are unwilling to commit funds to the purchase at the same time it has

become more difficult to get a mortgage on a car from financial institutions.

Source: ACEA

Maintenance:

Another reason for the increase in the sales of used cars is the cost of maintaining a used car. According

to RAC cost of motoring Index, the costs of maintaining a used car were found to be less than the cost of

maintaining a new car as seen in the table below:

As might be expected, used car owners save on finance costs, but pay more maintenance. Used car

owners also spend more on fuel; partly because there has been a small gain in fuel efficiency in newer

cars (the “average” gain in fuel efficiency in 2010 is estimated by the RAC to be 2.7%).

Literature Review

A used car, also referred to as a pre-owned vehicle, or a second hand car, is any vehicle that has

previously had one or more retail owners. Like all industries out there, the motor industry has seen a

dramatic decline in recent years. This has led to plant closures, and in extreme cases, government

bailouts. As new car sales have fallen, it has ultimately led to a rise in used car demand. In 2009, the

European used car market was valued at $246.4 billion, with an estimated 24.5 million cars. Due to the

global financial distress, it’s estimated to reach $260.11 billion (an increase of 5.6%) or 24.8 million cars

(an increase of 1.4%) by 2014. (Used Cars Industry Profile: Europe 2010) It is only natural that a cheaper

alternative is likely to be sought instead of new car purchases.The market can be affected in many ways.

Below are some of the factors that have consequences on the realizable market value that are out of the

customer’s control, yet can have dramatic role in sales numbers.

UK new UK used

Fuel 1958 2102

Insurance 727 776

Maintenance 574 1232

Miscellaneous fees 383 364

Depreciation 4626 1566

Finance 571 648

Total 8839 6688

Depreciation:

Although the motor industry faces unprecedented times, the wise consumer has always opted for a second

hand vehicle. It is widely reputed that on buying a new car, its value will depreciate by approximately

20% as soon as it’s driven off the forecourt. Charlie Vogelheim, executive editor of the Kelly Blue Book,

a tracker of used-car values once stated that the depreciation rate of a particular vehicle is dependent upon

market conditions, supply and demand. A highly popular or desirable car with limited availability will

depredate slower than a car that is in excess supply or less desirable. On average, a vehicle will only

retain about 35% of its original value after five years, with ones in high demand as used cars will retain

closer to 50%. (Finlay 2004) Any car that does hold its value well usually has a premium when it is

purchased new, meaning it is difficult for a consumer to try and “outplay” the market.

VRT:

According to www.Revenue.ie, Vehicle Registration Tax is chargeable on the registration of motor

vehicles (including motor-cycles) in the State. All motor vehicles in the State, other than those brought in

temporarily by visitors, must be registered with the Revenue Commissioners. Prior to 2008, in the case of

cars and small vans, the tax was a percentage of the expected retail price, including all taxes in the State.

This price is known as the Open Market Selling Price (OMSP). Based on the vehicle details forwarded to

Revenue by the NCT centre following examination of the vehicle.

Category “A” vehicles include cars (saloons, estates, hatchbacks, convertibles, coupés, MPVs, Jeeps etc.)

and minibuses with less than 12 permanently fitted seats including the driver's seat. Today the rate of tax

chargeable is based on the level of CO2 emissions for the vehicle at the time of manufacture. The rates

and associated minimum amounts are as follows:

CO2 Emissions (g CO2/km) VRT Rates Minimum VRT

0 - 120g 14% of OMSP €280

121 - 140g 16% of OMSP €320

141 - 155g 20% of OMSP €400

156 - 170g 24% of OMSP €480

171 - 190g 28% of OMSP €560

191 - 225g 32% of OMSP €640

226g and over 36% of OMSP €720

The VRT that is charged during the purchase of the car when new will undoubtedly affect the cars resale

value as this tax (or at least a percentage of it) will be passed onto the consumer buying the car second

hand.

Incentives:

One incentive that should have a positive effect on resale cost for the consumer will be the newly

introduced VRT exemptions for electric vehicles. This exemption which was meant to run until 31 st

December 2012 has now been changed to a rebate of up to €5,000 on the VRT due on new electric

vehicles sold from May onwards. Even with this change however the VRT due on these vehicles is less

than the exemption limit, meaning that any person who does purchase a new electric car will end up

paying no VRT. So what does this mean for the second hand market? If the VRT is not being charged

when the car is newly purchased, the cost associated with it will not be passed onto the customer who

wishes to purchases the car second hand sometime in the future. While this incentive should increase the

purchase of new cars it is important to note that this passing on in savings is one reason why used car

sales are expected to increase in the coming years.

According to www.revenue.ie, the government scrappage scheme provides for VRT relief when a new

passenger car with CO2 emissions of not more than 140g/km (i.e. CO2 band A or B) is purchased and

registered and another passenger car, over ten years old is scrapped. The scheme has been extended and

will run until 30 June 2011. Although the VRT relief that is now available has been reduced from €1,500

down to €1,250 for qualifying vehicles, it is still a good incentive. Figures released by SIMI show that

17,272 reclaims were made under the government Scrappage Scheme in 2010. Although this is directly

applicable to new car sales, the SIMI have reported that “the real benefit of the Scheme is the positive

knock-on effect it has had on the overall new and used car sectors”.

Finance:

As the banks and financing institutions tighten their lending, the average used car consumer is finding it

more and more difficult to borrow. While most franchised dealers selling new cars have agreements in

place for customers, several used car outlets have found it more difficult. To combat this The Society of

the Irish Motor Industry (SIMI) has joined forces with the Credit Union to create the Direct Access Credit

Union (DACU), an online application process for dealers. (McAleer 2011) Through this scheme,

customers can apply online for financing, regardless of whether it’s a new or used car purchase. This

should result in further activity in the car market.

While the various factors mentioned above are directly out of the control of a consumer, the following are

variable that directly impact the value of a used car in the market. Studies indicate that consumers should

purchase car models that are cheaper, have lower variable and service costs, have a longer life and higher

performance than cars made by a different production technology. The problem that a car buyer faces,

however, is that some of these factors (such as driving features, design, safety, reliance) are not

objectively measured. A car buyer must either rely on car manufacturers who claim that their models are

superior to those of their competitors, on professional car magazines, or on the objective and measurable

characteristics (Pingjun 2009).

Data Analysis

R 2 and Adjusted R

R2 is the simplest commonly used way of measuring the fit between the estimated regression

equation and the sample data. According to Studenmund (2011), the closer the R2 is to 1, the

closer the estimated regression fits the sample data. However, a value near 0 indicates a failure of

the estimated regression equation to explain the values of Y i. In this model the R2 is 0.7505,

which means that approximately 75% of the independent variables explain the dependent

variable (used car price).

Studentmund(2011) states that a major problem with R2 is that adding another independent

variable to a particular equation can never decrease R2. In order to solve this problem, the

degrees of freedom are introduced into the calculation of R2 which have developed the adjusted

R2. The highest possible adjusted R2 is 1, the same as for R2, while the lowest possible adjusted

R2 can be slightly negative. The result of adjusted R2 for this model is 0.7135, which is less than

the original R2.

Multicollinearity

Multicollinearity is a situation in which two or more variables in a multiple regression model are

highly correlated. According to Studenmund(2011) the major consequences of multicollinearity

are:

1. Estimates will remain unbiased.

2. The variances and standard errors of the estimates will increase.

3. The computed t-scores will fall.

4. Estimates will become very sensitive to changes in specification.

5. The overall fit of the equation and the estimation of the coefficients of non-muticollinear

variables will be largely unaffected.

In order to detect whether multicollinearity existed in the model, the variance inflation factor

(VIF) test is used. The VIF is a method of detecting the severity of multicollinearity by looking

at the extent to which a given explanatory variable can be explained by all the other explanatory

variables in the equation. There is a VIF for each explanatory variable in an equation. The higher

the VIF, the more severe the effects of muticollinearity. In general, if VIF >5, the

multicollinearity is severe. The VIF results of this model that Stata produced is an average score

of 2.18 which is less than 5. Therefore, multicollinearity is not a big problem in this model.

Specification

According to Studenmund(2011), one of the most used formal specification criteria other than R2

is the Ramsey Regression Specification Error Test (RESET). It is a general test that determines

the likelihood of an omitted variable or some other specification error by measuring whether the

fit of a given equation can be significantly improved by the addition of Y2, Y3 and Y4.

Yi = β0 + β1X1i + β2X2i + β3X3i + … + β23X23i + β24X24i +єi

Yi = β0 + β1X1i + β2X2i + β3X3i + … + β23X23i + β24X24i + β25Y25i2 + β26Y26i

3 + β27Y27i4 + єi

Compare the fits of these two equations using the ovtest.

H0: β25= β26 = β27 = 0

HA: Specification Error

The F-test result from Stata is 48.98, while the critical value acquitted from table is 2.60.

Therefore, the null hypothesis is rejected, there are omitted variables exist in this model. This

conclusion is not surprising because there are a number of determinants that could be considered

when analysing the price of used cars, for example, number of previous owners and services. In

addition, the Ramsey RESET test can prove that a specification error is likely to exist but it does

not specify the details of that error.

Serial Correlations

Studenmund(2011) states serial correlation or autocorrelation is the observations of the error

term are correlated with each other. Usually, econometricians focus on first-order serial

correlation, in which the current observation of the error term is assumed to be a function of the

previous of the error term and a not serially correlated error term: єt = pєt-1 + ut (-1< p <1)

The major consequence of serial correlation is the bias in the OLS estimates which leads to

unreliable hypothesis testing. The most common method of detecting serial correlation is the

Durbin-Watson d test; it uses the residuals of an estimated regression to test the possibility of

serial correlation in the error term.

The null and alternative hypotheses are set up as follows;

H0: No serial correlation.

HA: serial correlation.

The appropriate decision rule is reached by comparing the test statistic against critical values (d l

and du) from the Durban- Watson tables. The decision rule is;

If d < dl reject H0

If d > du Do not reject H0

If dl ≤ d ≤ du Inconclusive

Stata produced a figure of 1.364915 for the Durban- Watson d test. There are 188 observations in

the model with 8 explanatory variables. However, in the tables it only accommodates for 7

explanatory variables and 100 observations. The closest critical values obtained from the tables

were: dl =1.53, du =1.83. And 1.36 < 1.53, therefore reject H0. It means serial correlation do exist

in the model.

The Classical Assumptions of OLS

As Studenmund( 2011) states the assumptions blow:

Assumption 1: The regression model is linear, is correctly specified, and has an additive error

term.

The regression model does not have to be linear in the variables, however, it is assumed

to be linear in the coefficients. There are two addition requirement must be held. First, the

equation is correctly specified, it cannot work if it has an incorrect functional form or an

omitted variable. Second, a stochastic error term which is additive and cannot be

multiplied or divided by another variable.

Assumption 2: The error term has a zero population mean.

A stochastic error term is added to the regression equations to account for the variation in

the independent variable that cannot be explained by the model. The average value of the

entire population of the stochastic error term is assumed to be zero. In order to allow for

the possibility that the population error will not be zero a constant term is added to the

equation and it forces the mean of the error term to be zero.

Assumption 3: All explanatory variables are uncorrelated with the error term.

If an independent variable was correlated with the error term, the variation in Y would

actually come from the error term instead of X.

Assumption 4: Observations of the error term are uncorrelated with each other.

It would be very difficult for OLS to accurately estimate the standard errors of the

coefficients, if there is a systematic correlation exists in the observation of the error

term. This assumption is most important in time series models. An increase in the error

term in one time period, such as a random shock, does not affect the error term in

another time period. But this assumption is sometimes unrealistic as the impact of a

random shock may last after the time period.

Assumption 5: The error term has a constant variance.

This assumption is the way to eliminate heteroscedasticity, it is a key factor in the cross

sectional data sets. According to Studenmund (2011), if it is assumed that all error term

observations are drawn from a distribution with a constant variance when in reality they

are drawn from distributions with different variances, then the relative important variance

in Y is difficult to estimate. Although the actual values of the error term are not directly

observable, the lack of a constant variance for the distribution of the error causes OLS not

able to generate accurate estimates of the coefficients.

Assumption 6: No explanatory variable is a perfect linear function of any other explanatory

variables.

Perfect collinearity or muticollinearity means two or more independent variables are

closely interrelated. It would cause the OLS estimation procedure being incapable of

distinguishing the different variables. While perfect muticollinearity is unusual in reality,

even multicollinearity can also cause problems for estimations.

Assumption 7: The error term is normally distributed.

According to Stundenmund ( 2011), this assumption of normality is not a requirement

for OLS estimation. It is majorly used is in hypothesis testing, which uses the estimated

regression statistics to accept or reject hypothesis about economic behaviour. Without

the normality assumption most hypothesis testing would be invalid.

Actual vs. Estimated/Fitted Values

The adjusted R2 value as calculated by Stata for the model was obtained as 0.7135. R 2 measures the

percentage of the variation of Y around Y that is explained by the regression equation. Studenmund

(2006). The greater the value or R2 the closer the estimated regression equation fits the sample data. R2 is

always between 0 and 1. With 0 indicating the OLS has predicted no match between the actual and the

predicted values of the model. At the same time, R2 value of 1 indicates that the OLS has explained the

model perfectly. Therefore our result of 0.7135 indicates that 71.35% of the change in the price of the

used cars is explained by OLS while 28.65% of the change in the price of the used cars does not depend

upon the determinants that are used in the model. The actual values were plotted against the fitted values

and found that it shows that OLS has explained the model quite accurately.

1 9 17 25 33 41 49 57 65 73 81 89 97 105 113 121 129 137 145 153 161 169 177 185

-10000.00

0.00

10000.00

20000.00

30000.00

40000.00

50000.00

Actual vs Estimated Price

Actual Price Estimated Price

Hypothesis Testing

The regression equation:

Price=166.69 + 8559.19x1 + 1235.065x2 + 1858.221x3 + 339.72x4 - 782.2815x5 - 0.0435x6 + 969.852x7

+865x8 + 1633.95x9 + 916.65x10 + 1592.517x11 + 5779.01x12 + 2568.36x13 - 1202.78x14 + 6415x15 -

1842.80x16 - 280.78x17 - 302.10x18 + 372.98x19 - 935.02x20 - 2396.353x21 -3806.80x22 + 1427.822x23 +

801.73x24

X1 Engine Size

X2 Type of sell(Dummy Variable)

X3 Fuel Type(Dummy Variable)

X4 Dublin(Dummy Variable)

X5 Age

X6 Mileage

X7 Blue(Dummy Variable)

X8 Silver(Dummy Variable)

X9 Grey(Dummy Variable)

X10 Red(Dummy Variable)

X11 Black(Dummy Variable)

X12 Gold(Dummy Variable)

X13 3-Series(Dummy Variable)

X14 Golf(Dummy Variable)

X15 Polo(Dummy Variable)

X16 Megane(Dummy Variable)

X17 C5(Dummy Variable)

X18 Peugeot(Dummy Variable)

X19 Micra(Dummy Variable)

X20 Corolla(Dummy Variable)

X21 Avensis(Dummy Variable)

X22 Almera(Dummy Variable)

X23 Focus(Dummy Variable)

X24 Fiesta(Dummy Variable)

T-Test

Variable Coefficient Standard Error T CI

Engine Size 8559.19 694.10 12.32 (7186.77,9931.61)

Type Of Sell 1235.10 702.50 1.76 (-152.18,2622.31)

Fuel Type 1858.22 712.35 2.61 (451.54,3264.90)

Age -782.28 143.54 -5.45 (-1065.73,-498.83)

Mileage -0.04 .007 -6.11 (-0.06,-.03)

Gold 5779.01 2186.73 2.64 (1460.85,10097.18)

A total of 24 variables were used in the research in order to reach best possible solution. However, some

variables, initially thought to be significant were found to be not significant enough to conduct a

hypothesis test. Hence only the variables that were found to be significant are short listed in the table

below and will be investigated in detail, the rest of the variables will be discussed briefly.

Engine Size:

For every unit increase in the engine size the miles per gallon decreases, at the same time the cost of

insuring a vehicle increases with the size of the engine size. Hence, it can be expected that there will be a

negative relationship between the engine size and the price of the car. However, the result obtained by the

research finds that there is a direct relationship between the engine size and the price of the used car. The

result indicated that for every unit increase in the engine size which in the case of cars is 0.1, the price of

the car is expected to increase by €8559.19.

Engine Size:

H0: β1≤ 0

HA: β1>0

T critical= 1.645

i. β1=12.32, >1.645

ii. β1>0

Enough Evidence to reject the Null Hypothesis.

Type of Sell:

This is a dummy variable where value of the variable is one when the used car is being sold at a Motor

Showroom. The research found that there is positive relationship between the car being sold at a Garage

and the price charged for the car. This positive relationship can be explained by the profit margin that a

Motor showroom is expected to charge a consumer. The result obtained concluded that a car being sold at

a motor showroom is expected to cost €1235.07 more than a private sell.

Type of sell: (Dummy variable with the value of 1 for Garage sale)

H0: β2≤ 0

HA: β2>0

T critical= 1.645

i. β2=1.76, >1.645

ii. β2>0

Enough Evidence to reject the Null Hypothesis.

Fuel Type:

This is a dummy variable where the value of the variable is one when the fuel type of the car is petrol.

The result concluded a direct relationship between the type of fuel and the price of the vehicle. The result

found that the price of the vehicle is expected to increase by €1858.22 if the fuel type is petrol. This

relationship seems logical considering the fact that the maintenance of a petrol car is relatively lower than

that of a diesel car. At the same time a diesel car allows a car owner to VAT refund as per UK and Irish

Tax systems which is expected to offset the relative advantage of the petrol cars but the results found in

the research do not coincide with that.

Fuel Type: (Dummy variable with the value of 1 for a petrol car)

H0: β3≤ 0

HA: β3>0

T critical= 1.645

i. β3=2.61, >1.645

ii. β3 >0

Enough Evidence to reject the Null Hypothesis.

Dublin:

This is a dummy variable where the value of the variable is one when the car being sold is located and

registered in Dublin. It is often believed that the cars registered in the urban area are likely to be pricier

than those registered in a county. The results concluded that the price of a car is expected to increase by

€339.72 if the car is registered in Dublin. However, the results in the research found that the level of

significance of the results is only 0.60 which is not significant. If the null hypothesis H0: β≤0 estimates no

relationship between the location and the price than the research did not find a significant evidence to

reject the null hypothesis.

Age:

The research found that there is strong negative relationship between the age of a car and the price. The

results obtained concluded that for every year increase in the age of the car, its price decreases by

€782.30. The level of significance of this relationship was also found to be very significant at 5.45. The

price of a car is expected to decrease considering a direct relationship between price of a car and the cost

of maintenance including insurance which increase with the increase in the age of a vehicle.

Age:

H0: β4≥ 0

HA: β4< 0

T critical= 1.645

i. β4=5.45, >1.645

ii. β4 < 0

Enough Evidence to reject the Null Hypothesis

Mileage:

For the mileage as expected the research found that there is negative relationship between the price of a

car and the miles driven. The results concluded that for every mile driven the price of the car is expected

to fall by approximately €.40cents.

Mileage:

H0: β5≥ 0

HA: β5< 0

T critical= 1.645

i. β5=6.11, >1.645

ii. β5 < 0

Enough Evidence to reject the Null Hypothesis.

Gold :( Dummy variable with a value of 1 for a Gold coloured car)

H0: β6≤ 0

HA: β6 >0

T critical= 1.645

i. β6=2.64, >1.645

ii. β6 > 0

Enough Evidence to reject the Null Hypothesis

Black:

This is a dummy variable where the value of the variable is one when the colour of the car is black. The

research found that the price of the car increase by €1592.52 when the colour of the car is black. This

finding is consistent with the findings of one of the biggest supplier of the Automotive paints “DuPont

Automotive Color” which in 2008 colour popularity report found that most Europeans prefer black, the

detail analysis is found in the table below. However, enough evidence was not found to support this

claim.

New Vehicles Colour Popularity % of regional totals Source: DuPont Automotive Color Popularity

Report, 2008

Colour Bra

z

Mex EU Russ China Indi

a

Japan Kore

a

Black 17 25 20 26 14 31 7 13 25

Blue/Turquoise 13 3 12 13 12 9 8 7 2

Brown/Beige 5 3 1 4 2 0 4 2 0

Green/Olive 3 2 2 2 13 2 1 3 0

Grey,

medium/dark

12 16 13 18 3 15 4 7 3

Red/Pink/Purple 11 8 11 7 14 5 12 3 1

Silver 17 31 17 20 30 32 27 28 50

White 20 11 20 10 10 1 28 32 18

Yellow/Gold 2 1 3 0 2 2 7 0 1

Silver:

This is a dummy variable where the value of the variable is one when the colour of the car being sold is

silver. The research found that the price of the car increases by almost €865when it is a silver car.

According to “DuPont Automotive Color” silver is the second most favoured colour in Europe as seen in

the table above. However, the hypothesis test concluded that there is no significant evidence to suggest

that the price of the car increases by an extra €865 for silver coloured car.

Japanese car:

All the Japanese cars selected for the model except Nissan Micra were found to be negatively related to

the price of the used cars. It was found by model that on average a Japanese car is likely to be €1691.30

less expensive than a European car with same characteristics. However, as mentioned earlier Nissan

Micra was expected to make a gain on the price of €372.98.