The Determinants of Used Rental Car Prices

Sung Jin Cho / Journal of Economic Research 10 (2005) 277 304 277 The Determinants of Used Rental Car Prices Sung Jin Cho 1 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) sungjcho@hanyang.ac.kr, (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 The Determinants of Used Rental Car Prices 1 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) 277 304 279 2 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.

280 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 Number of Renal Cars Compact Below 1500cc A-company, B-company, 548 C-company Mid-Size 1500cc 2000cc A-company, B-company, 1260 C-company, D-company Large-Size 2000cc 2500cc A-company, B-company, 429 D-company Luxury Above 2500cc A-company, B-company, 619 E-company SUV 2000cc A-company, E-company 485 RV 2000cc A-company, B-company, 239 E-company Imported 1500cc BMW, Land Rover, etc. 12 2.2.1 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.

Sung Jin Cho / Journal of Economic Research 10 (2005) 277 304 281 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 B- company 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) (won/years) Type Purchasing Price Selling Price Residual Value 3 Age Compact 4,790,094.9 2,083,311.1 43.5% 2.9 Mid-Size 12,812,685.0 5,846,904.8 45.6% 2.8 Large-Size 20,370,819.0 11,105,233.1 54.5% 2.9 Luxury 32,051,431.2 15,188,731.8 47.4% 3.0 SUV 18,925,117.3 7,996,917.5 42.3% 2.8 RV 15,834,581.7 6,935,230.1 43.8% 2.8 Imported 72,361,595.9 28,365,166.7 39.2% 3.6 2.2.2 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.

282 The Determinants of Used Rental Car Prices Table 3 Type Band Average Residual Value A-company 0.528240 Compact B-company 0.494596 C-company 0.469074 A-company 0.454247 Mid-Size B-company 0.417115 D-company 0.510264 C-company 0.441861 A-company 0.551550 Large-Size B-company 0.434544 D-company 0.558578 A-company 0.469115 Luxury B-company 0.422173 E-company 0.506755 SUV A-company 0.416325 E-company 0.465593 A-company 0.461173 RV 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. Table 4 (All values are averages) Type Kilometers Ages Number of Cost Per Accidents Accident Compact 78,600 Km 2.9 years 0.8 times 794,337.3 Won Mid-Size 82,500 Km 2.8 years 0.8 times 707,610 Won Large-Size 77,600 Km 2.9 years 0.7 times 715,156.4 Won Luxury 88,800 Km 3.0 years 0.8 times 953,597.3 Won SUV 93,800 Km 2.8 years 0.7 times 1,159,387.2 Won RV 104,100 Km 2.8 years 0.6 times 712664.6 Won Imported 89,400 Km 3.6 years 1.1 times 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 Models 3.1.1 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) 277 304 285 3.2.1 Pooled Estimation Estimated parameters We find very interesting point from these estimation results of all models. For one thing, the Age and Age 2 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 Age 2 variable, and the whole effect of the two age variables (Age and Age 2 ) 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 Kilometer 2. 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 Kilometer 2 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

286 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 A- company 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 C- company, whose effect is pronouncedly negative. Both A-company and

288 The Determinants of Used Rental Car Prices B-company brand do not affect the devaluation of rental cars. As we expected, the Age 2 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 Kilometer 2 has a positive sign significantly different from zero. In fact, the Kilometer 2 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 Kilometer 2 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 A- company 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, Age 2 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 Age 2 exceed those of the Age variable, the total effect of both the Age and Age 2 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) 277 304 291 3.3.3 Large-Size Car Estimation The manufacturers that produce large-size cars are A-company, D- company, 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.

292 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, E- company, 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 Age 2 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

294 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 Age 2 variables, only the Age 2 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 Kilometer 2 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 Kilometer 2 in the case of Model C, the signs of Kilometer 2 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 Age 2 variable affects rental RV resale prices negatively, as expected, but, the Age itself has a positive effects. Age 2 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 shows very high R 2 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) 277 304 297 4 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, Age 2, 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) 277 304 299 5 Appendix A 5.1 Explanation of All Independent Variables. Variable Age Age 2 Kilometer Kilometer 2 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 Table 1 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 The Determinants of Used Rental Car Prices 6 Appendix B 6.1 Pooled Estimation Model A Model B Model C Constant -0.7072**(0.1158) -0.7242**(0.1163) -0.7353**(0.1177) Age 0.1104**(0.0431) 0.1099**(0.0431) 0.0182**(0.0186) Age 2-0.0357**(0.0072) -0.0355**(0.0072) -0.0356**(0.0071) Kilometer -0.0013**(0.0002) -0.0012**(0.0002) -0.0031**(0.0002) Kilometer 2 0.00004**(0.00001) 0.00004**(0.00001) 0.00004**(0.00001) Total Accident costs -0.00007**(0.00001) -0.00007**(0.000009) -0.000073**(0.00001) Number of accidents 0.0014(0.0038) 0.0015(0.0038) -0.0081(0.0184) Compact A-company 0.1337(0.0962) 0.1375(0.0962) 0.1328(0.0959) Compact B-company -0.0160(0.1029) -0.0127(0.1029) -0.1026(0.1026) Midsize A-company -0.0131(0.0960) -0.0104(0.0960) -0.0177(0.0958) Midsize B-company -0.1121(0.0972) -0.1054(0.0973) -0.1118(0.0970) Midsize R-Samsung 0.1032(0.0971) 0.1066(0.0971) 0.1040(0.0968) Midsize GM-Dawoo -0.0535(0.0991) -0.0513(0.0991) -0.0640(0.0989) Large-size A-company 0.189**(0.0963) 0.1919**(0.0963) 0.1823*(0.0960) Large-size B-company -0.0791(0.1031) -0.0775(0.1031) -0.0960(0.1029) Large-size R-Samsung 0.1798**(0.1008) 0.1831*(0.1009) 0.1742*(0.1005) Luxury A-company 0.0533(0.0962) 0.0569(0.0962) 0.0474(0.0959) Luxury B-company -0.0884(0.1086) -0.0847(0.1086) -0.0853(0.1083) Luxury E-company 0.1410(0.0981) 0.1443(0.0981) 0.1359(0.0978) SUV A-company -0.1048(0.0963) -0.1022(0.0963) -0.1090(0.0960) SUV E-company 0.0188(0.0991) 0.0223(0.0991) 0.0671(0.0989) RV A-company -0.0185(0.0974) -0.0148(0.0974) -0.0206(0.0971) RV B-company -0.0291(0.0985) -0.0260(0.0985) -0.0308(0.0982) RV E-company -0.2748**(0.1002) -0.2734**(0.1002) -0.2789**(0.0999) Foreign -0.0143(0.118) -0.0094(0.1109) -0.0117(0.1106) *Significant at 10% Level; **Significant at 5% Level

Sung Jin Cho / Journal of Economic Research 10 (2005) 277 304 301 6.2 Continued on the Pooled Estimation Model A Model B Model C Seasonality -1 (January) 0.0195 (0.0184) Seasonality -1 (February) -0.0397** (0.0186) Seasonality -1 (March) 0.0414** (0.0185) Seasonality -1 (April) 0.0434** (0.0180) Seasonality -1 (May) -0.0081 (0.0184) Seasonality -1 (June) 0.1084 (0.0187) Seasonality -1 (July) 0.0132 (0.0192) Seasonality -1 (August) 0.0911** (0.0231) Seasonality -1 (September) 0.0207 (0.0211) Seasonality -1 (October) -0.0098 (0.0192) Seasonality -1 (November) -0.0155 (0.02211) Seasonality -2 (Decreasing Period) 0.0204(0.0127) Seasonality -2 (Decreasing Period) 0.1031(0.0117) Seasonality -2 (Decreasing Period) 0.0092(0.0124) R 2 0.2848 0.2849 0.2926 F 60.5911 53.9840 43.4411 *Significant at 10% Level; **Significant at 5% Level 6.3 Compact Car Estimation Model A Model B Model C Constant -0.5659**(0.2176) -0.5833**(0.2224) -0.6489**(0.2278) Age 0.0499(0.1291) 0.0503(0.1301) 0.0547(0.1322) Age 2-0.0399*(0.0214) -0.0343(0.0216) -0.0351*(0.0218) Kilometer -0.0010**(0.0004) -0.0010**(0.0004) -0.0010**(0.0004) Kilometer 2 0.000023**(0.00001) 0.000023**(0.00001) 0.000021**(0.00001) Total Accident costs -0.000019*(0.000009) -0.000017*(0.00001) -0.00002*(0.000009) Number of accidents -0.0118(0.0095) -0.0140(0.0096) -0.0163*(0.0098) Brand dummy (A-company) -0.0194(0.1067) 0.1453(0.0999) 0.1406(0.1026) Brand dummy (B-company) -0.1482*(0.0997) -0.0205(0.1068) -0.0045(0.1099) Seasonality -1 (January) -0.0105(0.0463) Seasonality -1 (February) 0.0270(0.0477) Seasonality -1 (March) 0.0676(0.0477) Seasonality -1 (April) 0.0322(0.0458) Seasonality -1 (May) 0.0194(0.0470) Seasonality -1 (June) 0.0523(0.0482) Seasonality -1 (July) 0.0525(0.0575) Seasonality -1 (August) 0.0515(0.0698) Seasonality -1 (September) 0.0095(0.0535) Seasonality -1 (October) 0.0571(0.0460) Seasonality -1 (November) 0.0191(0.0490) Seasonality -2 (Decreasing Period) -0.0072*(0.0016) Seasonality -2 (Recovering Period) 0.0300(0.0270) Seasonality -2 (Increasing Period) 0.0329(0.0298) R 2 0.1448 0.1461 0.1992 F 12.5736 9.5097 5.6919 *Significant at 10% Level; **Significant at 5% Level

302 The Determinants of Used Rental Car Prices 6.4 Mid-Size Car Estimation Model A Model B Model C Constant -0.5953**(0.1224) -0.5956**(0.1231) -0.5913**(0.1230) Age 0.0142(0.0776) 0.0131(0.0777) 0.0035(0.0777) Age 2-0.0136(0.0131) -0.0131(0.0131) -0.0129*(0.0031) Kilometer -0.0027**(0.0007) -0.0027**(0.0007) -0.0027**(0.0007) Kilometer 2 0.00002**(0.00001) 0.000019*(0.00001) 0.000019(0.00001) Total Accident costs -0.000033**(0.00001) -0.000039**(0.00001) -0.000036**(0.00001) Number of accidents 0.0044(0.0063) 0.0043(0.0063) 0.005(0.0063) Brand dummy (A-company) 0.0481*(0.0267) 0.0469*(0.0267) 0.0492*(0.0266) Brand dummy (B-company) -0.0434*(0.0290) -0.0392(0.0313) -0.0387(0.0314) Brand dummy(re-samsung) 0.1644**(0.0308) 0.1633**(0.0308) 0.1704**(0.0309) Seasonality -1 (January) 0.0384(0.030) Seasonality -1 (February) 0.0024(0.0297) Seasonality -1 (March) 0.0452*(0.0304) Seasonality -1 (April) 0.0237(0.0290) Seasonality -1 (May) -0.0453(0.0292) Seasonality -1 (June) -0.0046(0.0311) Seasonality -1 (July) -0.0346(0.0316) Seasonality -1 (August) 0.0246(0.0387) Seasonality -1 (September) 0.0110(0.0347) Seasonality -1 (October) -0.040(0.0318) Seasonality -1 (November) 0.003(0.0352) Seasonality -2 (Decreasing Period) 0.0167(0.0216) Seasonality -2 (Recovering Period) 0.0007(0.0199) Seasonality -2 (Increasing Period) -0.0206(0.0211) R 2 0.1305 0.1321 0.144 F 22.0006 16.9662 11.6139 *Significant at 10% Level; **Significant at 5% Level 6.5 Large-Size Car Estimation Model A Model B Model C Constant -0.5269**(0.1303) -0.6075**(0.1319) -0.6726**(0.1361) Age -0.0824(0.0855) -0.0820(0.0847) -0.0704(0.0845) Age 2-0.0043(0.0142) -0.0042(0.0141) -0.0053(0.0140) Kilometer -0.0007(0.0005) -0.0008(0.0005) -0.0004(0.0002) Kilometer 2 0.00007(0.0001) 0.00008(0.0001) 0.000012(0.00001) Total Accident costs 0.0000(0.0000) -0.000001(0.00001) -0.00001(0.00001) Number of accidents -0.0150**(0.0076) -0.0146*(0.006) -0.0141**(0.0075) Brand dummy (A-company) 0.2587**(0.0246) 0.2633**(0.0244) 0.2723**(0.0247) Brand dummy (Re-Samsung) 0.2444**(0.0309) 0.2521**(0.0307) 0.2627**(0.0308) Seasonality -1 (January) -0.1021*(0.0557) Seasonality -1 (February) -0.1479**(0.0552) Seasonality -1 (March) 0.1330**(0.0550) Seasonality -1 (April) 0.1451**(0.0536) Seasonality -1 (May) 0.1436**(0.0548) Seasonality -1 (June) 0.1197**(0.0541) Seasonality -1 (July) 0.1000*(0.0555) Seasonality -1 (August) 0.1927**(0.0590) Seasonality -1 (September) 0.0846(0.0578) Seasonality -1 (October) 0.0953*(0.0544) Seasonality -1 (November) 0.0623(0.0598) Seasonality -2 (Decreasing Period) -0.0791**(0.0289) Seasonality -2 (Recovering Period) 0.0884**(0.0267) Seasonality -2 (Increasing Period) 0.0934**(0.0279) R 2 0.3379 0.3528 0.3653 F 28.2999 22.2093 13.9622 *Significant at 10% Level; **Significant at 5% Level

Sung Jin Cho / Journal of Economic Research 10 (2005) 277 304 303 6.6 Luxury Car Estimation Model A Model B Model C Constant -1.0539**(0.1855) -1.0816**(0.1876) -1.1462**(0.1886) Age 0.2781**(0.1165) 0.2835**(0.1165) 0.2792**(0.1166) Age 2-0.0600**(0.0185) -0.0611**(0.0185) -0.0596**(0.0185) Kilometer -0.0015**(0.0007) -0.0015**(0.0007) -0.0012*(0.0007) Kilometer 2 0.00001(0.00001) 0.00009(0.0001) 0.00006(0.0001) Total Accident costs -0.00004**(0.00001) -0.00004**(0.00001) -0.00004**(0.00001) Number of accidents 0.0159(0.0098) 0.0147(0.0098) 0.0138(0.0098) Brand dummy (A-company) 0.1328**(0.0566) 0.1349**(0.0566) 0.1185**(0.0563) Brand dummy (E-company) 0.2174**(0.0603) 0.2196**(0.0603) 0.2053**(0.060) Seasonality -1 (January) 0.0555(0.0461) Seasonality -1 (February) -0.1055**(0.0461) Seasonality -1 (March) 0.0699(0.0462) Seasonality -1 (April) 0.0728*(0.0458) Seasonality -1 (May) 0.0645(0.0476) Seasonality -1 (June) 0.0748*(0.0454) Seasonality -1 (July) 0.0926**(0.0460) Seasonality -1 (August) 0.1886**(0.0505) Seasonality -1 (September) 0.0914*(0.0523) Seasonality -1 (October) 0.0556(0.0488) Seasonality -1 (November) -0.1341**(0.05457) Seasonality -2 (Decreasing Period) 0.0157(0.0332) Seasonality -2 (Recovering Period) 0.0065(0.0306) Seasonality -2 (Increasing Period) 0.0387(0.0316) Age*A-company Age*B-company R 2 0.1272 0.1272 0.1400 F 12.2525 9.1854 6.2931 *Significant at 10% Level; **Significant at 5% Level 6.7 SUV Estimation Model A Model B Model C Constant -0.6910*(0.1960) -0.6728**(0.2060) -0.6509**(0.2130) Age 0.0421(0.1365) 0.0441(0.1369) 0.0653(0.1377) Age 2-0.0357(0.0236) -0.0361(0.0236) -0.0409*(0.0238) Kilometer -0.0023(0.0017) 0.0022(0.0017) -0.00003(0.0003) Kilometer 2-0.000015(0.00001) -0.000015(0.00001) -0.000018*(0.00001) Total Accident costs -0.00004**(0.000009) -0.00004**(0.000009) -0.00005**(0.00001) Number of accidents 0.0018(0.0111) 0.0019(0.0111) -0.036(0.0112) Brand dummy (A-company) -0.1303**(0.0280) -0.1290**(0.0281) -0.1347**(0.0281) Seasonality -1 (January) -0.0862*(0.0502) Seasonality -1 (February) -0.0239(0.0547) Seasonality -1 (March) -0.0335(0.0534) Seasonality -1 (April) -0.0573(0.0522) Seasonality -1 (May) -0.0886(0.0542) Seasonality -1 (June) -0.0805(0.0545) Seasonality -1 (July) -0.0414(0.0522) Seasonality -1 (August) 0.0753(0.0687) Seasonality -1 (September) -0.0692(0.0709) Seasonality -1 (October) -0.1317*(0.0577) Seasonality -1 (November) -0.0748(0.0632) Seasonality -2 (Decreasing Period) -0.0258 (0.0359) Seasonality -2 (Recovering Period) -0.0251 (0.0346) Seasonality -2 (Increasing Period) -0.0136 (0.0363) R 2 0.1720 0.1681 0.1848 F 15.3679 10.7834 7.0961 *Significant at 10% Level; **Significant at 5% Level

304 The Determinants of Used Rental Car Prices 6.8 RV Estimation Model A Model B Model C Constant -1.4169*(0.1684) -1.5397**(0.1882) -1.4181**(0.1991) Age 0.3685**(0.1105) 0.3646**(0.1081) 0.3044**(01082) Age 2-0.0776**(0.0193) -0.0778**(0.0189) -0.0674**(0.0188) Kilometer -0.0009(0.0015) 0.0011(0.0015) 0.0009(0.0015) Kilometer 2-0.00001(0.00001) -0.000011(0.00001) -0.00001(0.00001) Total Accident costs -0.00003(0.0001) 0.00004(0.0001) 0.00001(0.0001) Number of accidents -0.0152(0.0180) -0.0141(0.0178) -0.0067(0.0177 Brand dummy (A-company) 0.2626**(0.0380) 0.2578**(0.0375) 0.2376**(0.0376) Brand dummy (B-company) 0.2469**(0.0408) 0.2439**(0.0401) 0.2330**(0.0402) Seasonality -1 (January) 0.1196(0.0894) Seasonality -1 (February) -0.1419*(0.0804) Seasonality -1 (March) -0.0017(0.0796) Seasonality -1 (April) 0.1493*(0.0782) Seasonality -1 (May) -0.0218(0.0786) Seasonality -1 (June) 0.0452(0.0798) Seasonality -1 (July) -0.0293(0.0839) Seasonality -1 (August) 0.0681(0.1980) Seasonality -1 (September) 0.0647(0.0845) Seasonality -1 (October) -0.0559(0.0815) Seasonality -1 (November) -0.0162(0.0879) Seasonality -2 (Decreasing Period) -0.1479**(0.0548) Seasonality -2 (Recovering Period) 0.0577(0.0482) Seasonality -2 (Increasing Period) 0.0044(0.0514) R 2 0.3619 0.3921 0.4226 F 17.8693 14.9544 10.1693 *Significant at 10% Level; **Significant at 5% Level