Acknowledgments Firstly, I would like to express my profound gratitude towards Professor Pierre Giot of the University of Namur for accepting the role of being my thesis supervisor. His regular feedback, pertinent guidelines and straightforward explanations made the realization of this thesis possible.

His valuable knowledge and insights put me back on the right track when necessary. Besides, I am grateful that he introduced me to classic car auctions as beforehand I was unfamiliar with this specific subject and that this “new world” offered me the possibility to apply theoretical methods and concepts in a real live situation. Subsequently, I would like to warmly thank Professor Luc Bauwens of the Université Catholique de Louvain for taking the time to answer each and every one of my questions thoroughly. His expertise helped me put together all the different elements in order to comprehend the underlying details. Additionally, I would like to thank Benjamin Maquet for his support, encouragements and constructive suggestions. Last but not least, I would like to thank my parents for standing by me during my five years of university.

Throughout the last couple of months their support was a continuous source of energy. Table of contents TOC o “1-3” h z u Acknowledgments PAGEREF _Toc515448793 h 1Introduction PAGEREF _Toc515448794 h 3Chapter 1: The Mechanics of Auctions PAGEREF _Toc515448795 h 6Chapter 2: Literature Review PAGEREF _Toc515448796 h 8Chapter 3: The Data PAGEREF _Toc515448797 h 11Chapter 4: Unbiasedness of Presale Estimates PAGEREF _Toc515448798 h 15Econometric Models PAGEREF _Toc515448799 h 15Empirical Results PAGEREF _Toc515448800 h 18Chapter 5: Uncertainty of Experts in Presale Estimates PAGEREF _Toc515448801 h 21Econometric Models PAGEREF _Toc515448802 h 21Empirical Results PAGEREF _Toc515448803 h 24Chapter 6: Prediction PAGEREF _Toc515448804 h 27Econometric Models PAGEREF _Toc515448805 h 27Empirical Results PAGEREF _Toc515448806 h 29Conclusion PAGEREF _Toc515448807 h 31Bibliography PAGEREF _Toc515448808 h 33Annexes PAGEREF _Toc515448809 h 36IntroductionThe most expensive car ever sold at an auction was the 1962 Ferrari 250 GTO. It was sold for an astonishing amount of $38.12 million! Nowadays, this car is valued at $38.56 million. It was the second 250 GTO to be made and no more than 40 were ever manufactured (MarketWatch). In a world evolving towards driverless vehicles, it might seem odd to invest in a piece of automobile history. However, several explanations can be found to why a person would buy a classic car: joy of ownership, capital appreciation, status amongst peers, investment portfolio diversification, the automotive art and history, the iconic design, the high performance history or even a childhood dream.

There are several factors pushing this demand even higher: growth of wealth globally, an augmentation in the collecting lifestyle, advancement of the internet, the fact that classic cars are a finite group and that more collectors’ magazines exist nowadays (InvestmentNews).Indeed, a recent tendency emerged to pursuit higher returns in alternative investments, away from the traditional financial investments. The recent consistently strong performance of this asset class against alternative investment classes, such as wine and fine art, has made classic cars a more appealing investment (The Telegraph). Especially the outperformance of high-quality classic cars over recent years was impressive (The Financial Times). As those investments are considered alternatives, they offer an additional benefit of portfolio diversification from traditional asset classes. Besides, in the UK for example, the classic cars are considered “wasting assets” and are exempted from UK capital gains tax (The Telegraph). Many examples exist to illustrate the important role of nostalgia and childhood dreams in the classic car market.

The Aston Martin DB6 and DB5 are functionally equivalent, yet a DB5 will likely be sold for twice the price of a DB6. This difference can mainly be explained by the “James Bond” factor. The car was present in the James Bond movie “Goldfinger”, had many cinematic outgoings and little toys were made from the DB5 model.

As the managing director of the Artcurial Motorcars auction house explained: “The market is a question of generation. You want to own the car that was a dream for you when you were a child” (The Financial Times). Nevertheless, an important statement was made by Simon Marsh, a partner at wealth manager Killik ; Co. He highlighted that recent sellrates remain strong but the number of vehicles not reaching their presale valuation has risen. “However, this might have more to do with overambitious pricing by sellers, aided and abetted by the auction houses”, he said (The Financial Times). This brings us closer to the topic of this thesis.

Classic cars are mainly sold in auctions. Auction markets are characterized by the problem of information asymmetry. It is difficult for buyers to estimate the true value of an item.

The circumstances for asymmetric information arise because of two features of the items put up for sale. The items are heterogeneous (the exact same item is rarely sold twice) and they do not change hands very often (infrequent trading) (Mei and Moses 2001). The amount and the quality of the information available are thus pertinent for potential buyers (Bruno and Nocera 2008). The catalogues that salerooms publish before an auction contain relevant information about the object as well as experts’ presale estimations. Those predictions can be a crucial informative tool for the market participants and the quality of the accessible information is thus extremely relevant (Ekelund, Ressler and Watson 1998). Following the reasoning of Bruno and Nocera (2008), the informational content of presale estimates can be illustrated around two axes: uncertainty and accuracy.

The width of the estimation range is considered the uncertainty factor. The number of times hammer prices fall into the estimation window and the distance between the prediction and the final price represent the accuracy. Systematic over- or underestimation of the ex-ante valuations would be prove of bias (Bruno and Nocera 2008).

Existing literature has deeply examined the question of bias in presale estimates in art markets. The evidence is ambiguous and not conclusive. The aim of this thesis is to use a whole new and alternative data set. The data will be retrieved from classic car auctions. To my knowledge, this has never been done before. Since previous studies have focussed on the art market, some interesting insights might be found when analysing the same two axes but for a different kind of collectible.

Will previously established findings be contradicted? This thesis will thus focus on two main questions. The first question will investigate the accuracy of presale estimates: “Are presale estimates good predictors of realized prices? And is there a difference between auction houses?” The second question will analyse the uncertainty: “Which factors affect the experts’ uncertainty when defining presale estimates?”. A third part is added to investigate which factors will predict the ‘no sale’ of an item and which characteristics are important to predict a sale below the minimum estimated price and a sale above the maximum estimated price. To do so, we will use the well-known Heckman sample selection model and several logit regressions. We find that experts do not provide good predictors of realized prices and that there is indeed a difference between auction houses. However, the bias stays relatively small for each auction house. Concerning the uncertainty factors, we find that the characteristics single owners, well-identified owner, famous owners, Ferrari 250 and cabriolet increase the experts’ uncertainty.

More expensive cars, however, increases the experts’ confidence in setting presale estimates. Moreover, a large relative spread and famous owners decrease the probability of ‘no sale’. Whereas more expensive cars seem to be harder to sell. For cars sold below the minimum estimated price, we found that a larger relative spread, famous owners and a certificate of Ferrari Classiche reduce the probability of being sold below the minimum estimated price. On the other hand, more expensive cars increase the probability of being sold below the minimum estimated price. Additionally, cars having a certificate, famous owners or just a single owner increase the probability of selling above the experts’ high presale estimate. Conversely, more expensive cars and larger spreads reduce this probability.

The remainder of this paper is organized as follows. The next section will briefly introduce the mechanics of auctions. In segment two we discuss the existing literature concerning the accuracy of presale estimates and the uncertainty in auction markets. Section three will describe the data and the summary statistics.

Section four will elaborate the first part of our research question: “Does there exists a bias in the presale estimates of auction experts compared to the hammer price? And is there a difference between auction houses?” Section five will focus on identifying the factors that influence the experts’ uncertainty. Finally, section six will try to predict if a car is hold-in, sold below the low presale estimate or sold above the high presale estimate. Segment seven concludes.Chapter 1: The Mechanics of AuctionsAuction systems give uninformed sellers the opportunity to receive approximately the market value of the item they put up for sale (Ashenfelter 1989). All objects sold during auctions have two characteristics in common: heterogeneity and infrequent trading (Mei and Moses 2001).

Those features will induce uncertainty for both sellers and buyers and will make it challenging to price the object. Auctions are supposed to resolve a large fragment of this information asymmetry for the market participants by making information publicly available. Louargand and McDaniel (1991) went even further, by saying: “The process of public price-setting will tend to drive the market towards efficiency while making it deeper and wider.”Here’s where the experts’ knowledge about the object and the current state of the market comes in handy.

Before every auction, a catalogue is published by the auction house. The catalogue contains on-topic information about the auctioned objects and presale estimates established by the experts. Those presale estimates are affected by inconstant and intangible factors. That’s why experts usually constitute an estimation range (Bruno and Nocera 2008). Each item will have a high and low estimate which makes up the range in which the expert believes the item might sell. The estimates are based on the examination of the object and recent auction data on comparable prices (Sotheby’s Glossery). Presale estimates can be a crucial informative tool for the market participants and the quality of the accessible information is thus extremely relevant (Ekelund, Ressler and Watson 1998).

Classic cars are most commonly auctioned through English auctions, also known as ascending-bid auctions. The price of an item is contiguously raised until strictly one bidder remains (McAfee and McMillan 1987). Once this happens, the item is said to be “knocked down” or “hammered down”.

The final price will be called the “hammer price” (Ashenfelter and Graddy 2011). It is part of the auctioneers’ job to try and maximize this hammer price.Beware, not all items that have been “knocked down” are sold. If there are no bids or the secret reserve price is not reached, the item will not be sold and will be “bought in” (Ashenfelter 1989).

An unsold item may be taken off the market, put up for sale at a later auction or may be bought by the auction house (Ashenfelter and Graddy 2002). Note that the latter is very seldom. The probability that an item is sold in an auction depends on the height of the reserve price (Ashenfelter and Graddy 2011). However, sale rates change considerably through time and auction categories (Ashenfelter and Graddy 2002).

The “reserve price” previously mentioned, is agreed before the auction by the seller and the auction house. The “reserve” or “reservation price” is a confidential price for which the seller is indifferent between waiting to sell and selling now (Ashenfelter and Graddy 2002). Most auction houses comply with setting the secret reserve price at or below the experts’ low estimate (Ashenfelter and Graddy 2011).

The reservation price is indeed kept secret to make sure it does not affect the bidding. Auctioneers will thus have to get the bidding started without disclosing the reservation price (Abowd and Ashenfelter 2002). To do this, the auctioneer may have to accept and declare fictitious bids, called “off the wall” or “from the chandelier”. Nevertheless, the bidding “off the wall” may never exceed the reserve price.

Legally the auctioneer is making offers on behalf of the seller (Abowd and Ashenfelter 2002). The purpose of this practice is not to let bidders pay more, but to give them the opportunity to buy the product, knowing that if the reserve price is not made, nobody will get the item (Ashenfelter 1989). Chapter 2: Literature ReviewThe information content of presale estimates and hammer prices has been thoroughly researched before, especially in the art market. As explained above, the two main components of information content are accuracy and uncertainty (Bruno and Nocera 2008).

The aspect of accuracy in the literature often appears under the form of efficiency or the biasedness of presale estimates. Uncertainty is reflected in the presale estimation range.Let us start by discussing the existing literature on the first topic, the accuracy of presale estimates. The following foreseeable question is: “Are presale estimates biased?” Milgrom and Weber (1982), perhaps known as “the” reference in the theoretical literature, argue that “honesty is the best policy” for auction houses. Revealing information would increase revenues. By providing truthful information, they would remove uncertainty and induce low bidders to be more committed and driven. This will generate upward pressure on the bids and probably result in a higher hammer price (Ashenfelter 1989).

Underestimation of presale estimates would attract bidders but discourage sellers and overestimation of predictions would attract sellers but scare away bidders. Common sense would favour a middle ground, meaning no bias (Sproule and Valsan 2007). Besides that, auction houses have a reputation to defend. An image of accurate expertise is important to keep and attract clientèle. This argument would thus also favour the unbiasedness of ex-ante estimates (Sproule and Valsan 2007).

Once we focus on the empirical literature, the evidence is more ambiguous. Ashenfelter (1989) was the first one to show that presale estimates were very highly correlated with hammer prices and stated that “auctioneers do seem to provide genuine expertise in predicting prices”. Abowd and Ashenfelter (1989), Louargand and McDaniel (1991), Agnello and Pierce (1996) and McAndrew, Smith and Thompson (2009) all find that auction house price estimates are efficient predictors of hammer prices in a “Martingale sense”. This means that on average the actual price will be equal to the expected price (Louargand and McDaniel 1991). Remark, that the findings of McAndrew, Smith and Thompson (2009) need to be more nuanced since they find evidence of unbiasedness in estimates after controlling for the impact of reservation prices. In their paper on anchoring effects, Beggs and Graddy (2009) also emphasize that they do not find prove of bias of presale estimates relative to final prices. The bias they found should exist given the state of the market and the characteristics of the paintings and was labelled as anchoring. Bruno and Nocera (2008) also detect this anchoring effect.

The results of Czujack and Martins (2004) are less general. They found that for the items that were bought in, Sotheby’s and Christie’s could have given better estimates, meaning closer to the market value of the item. This probably would have strengthened the sale rates. However, the salerooms gave good predictions for the works that were sold.Contradicting results, evidence of bias, has been found as well. Ekelund, Ressler and Watson (1998) detected that the value of Latin-American art was overestimated by 2.7 percent between 1977 and 1996.

By including the unsold items, the overestimation rose to one third. Bauwens and Ginsburgh (2000) found that the more expensive the collectible, the lower the ex-ante valuations. They implied that auction houses try to make the items more attractive to potential bidders. In their paper on declining values and the afternoon effect, Beggs and Graddy (1997), also found proof of bias. Experts overestimated the value of recent art works and undervalued longer and wider paintings. Besides, a study on jewels exposes that on average the presale estimates of the experts were lower than the hammer prices for most types of jewellery (Chanel, Gérard – Varet and Vincent 1996).

Bruno and Nocera (2008) found that presale estimates of a data set of Italian paintings were no good predictors of the realized prices. The proportion of hammer prices falling within the presale estimate range was only 37%. Moreover, they introduced the “country effect”. This effect is defined as an increase in accuracy (price prediction) when an Italian painting is auctioned in Italy and the uncertainty (estimation range) decreases. Nevertheless, it’s important to emphasize that the biases found were most of the time relatively small compared to the hammer price (Ashenfelter and Graddy 2002).The question that comes to mind is: “What would induce experts to over- or underestimate the presale price?” Is it a purposeful strategy or are they unaware of the bias? Previously some auction professionals testified that their predictions were intentionally undervalued in order to encourage bidders to join the game.

As explained above, more bidders increase the probability to sell the artwork and to obtain higher prices through the laws of competition. This could be one of the strategic reasons for the bias downward (Louagrand and McDaniel 1991). It is also possible that experts provide ex-ante undervalued estimates in order to positively surprise the sellers once a higher hammer price is obtained. This could motivate sellers to continue doing business with the saleroom in question (Agnello & Pierce 1996). Nevertheless, this strategic temptation will be altered by the need to satisfy sellers’ desires, meaning that an acceptable hammer price has to be achieved.Tactics related to the ex-ante overvaluation are mostly influenced by the sellers’ hopes.

Indeed, higher predictions could persuade potential sellers to go ahead with the decision to sell (Sproule and Valsan 2007). Additionally, sellers have the right to set a reservation price. Intuitively, they want this reserve price to be as high as possible.

The low estimate of the expert will thus be increased because of the high reservation price (Ekelund, Ressler and Watson 1998). Besides, independent of the sellers’ desires, auction houses want to maximize their revenues. Both sellers and buyers own a commission to the saleroom. The commission paid is proportional to the hammer price of the item. This may induce salerooms to overestimate the items’ value. For this argument to hold, we need to believe that higher estimates will lead to higher prices.

Bidders would make bids based on the so believed accurate indication of the experts (Sproule and Valsan 2007).All arguments discussed above are established on the assumption that auction houses induce bias for strategic reasons. However, Ashenfelter and Graddy (2002), claimed that it is also possible that auction experts make systematic errors because they, the auction experts, are less “capable” or “efficient” than linear regressions.

This hypothesis could be confirmed by finding biases that vary in sign and amplitude, which seems to be the case (Ashenfelter and Graddy 2002). The second component of informational content is uncertainty. Its impact on the probability of sale has, for example, been studied by Ekeland, Ressler and Watson (1998). Indeed, an item will only be sold if the highest bid reaches the seller’s reserve price. Does the width of the estimation range (also called “the window”) influence the probability of sale? The researchers found that the probability of no sale increases when the window is narrowed because of a high reservation price. If the seller wants a higher reserve price, the experts will likely review their low estimate upward, which will narrow the estimation range. Buyers may discern this and become less willing to participate in the bidding process. This will then likely result in a lower probability of sale (Ekeland, Ressler and Watson 1998).

The “reserve hypothesis” thus states that a narrow range indicates a higher reserve price (Kells 2003). However, we can ask ourselves: “What motivates experts when they determine the spread?” The estimation window is often connected to the auctioneers’ uncertainty or the possible variance in the price. A large estimation rate would thus indicate a lot of uncertainty and an elevated price variance (Ashenfelter and Graddy 2002). Kells (2003) defines the previous statement as the “information hypothesis”: a wider window reflects greater uncertainty. The window may be based on the predictability of bidders’ behaviours, characteristics of the item or extra information regarding the collectible.

Auction houses may also play a role in the definition of the estimation range. They can have different policies to set the prediction window and their previous experience in valuing the same kinds of collectibles could also be a determinant (Bruno and Nocera 2008). As previously explained, the spread may also be influenced by the sellers’ wishes to set a high reserve price. It is thus not just a reflexion of the experts’ uncertainty (Ashenfelter and Graddy 2002).

Chapter 3: The DataThe source of the data is Professor P. Giot of the University of Namur and Professor L. Bertinelli of the University of Luxembourg. They assembled this dataset based on information included in the “Classic Car Auction Yearbooks” from 2006 until 2016. The cleaned dataset contains 1497 unique observations of auctioned Ferraris. Indeed, only Ferraris were included to try to obtain a homogeneous product. About 73% of the 1497 items were sold and 400 items remained unsold.The dataset is composed of two main categories of facts, namely information included in presale catalogues and information about the price.

Let us start by discussing the latter one (the price). As explained above, auction houses publish a window for presale estimates. The dataset will thus contain a high and low estimate for each observation. Besides, when an item is sold, the hammer price will be included as well. Table 1 indicates the number of hammer prices that fall within the experts estimated range (so a correct presale estimation), the number of times it did not fall into the estimation window and if not, how many times was the estimation over- or undervalued. This was done for the whole sample, as well as each auction house.

Let us note that this information is only available for items that reached the reserve price and that were sold. For 47% of the items, the hammer prices fell within the experts estimated range. For the remaining 53% that were not correctly estimated, 37% fell below the minimum estimated price (presale overestimation) but above the seller’s reserve price and 63% obtained a higher price than the maximum estimate (presale underestimation). RM Auction, Bonhams and Gooding & Company are the most represented auction houses in our dataset. We will thus focus our attention on these auction houses and created an additional category called ‘other’ to include the rest of the auction houses. The proportion of hammer prices that fell within the estimated range varies between 46% for Bonhams and 58% for Gooding & Company. The fraction of hammer prices that were wrongly estimated varies between 42% for Gooding & Company and 54% for Bonhams.

63% and 70% of the sold items at RM Auctions and Gooding & Company were underestimated (e.g. having a hammer price that fell above the estimation range).

The proportion of overestimated items (e.g. obtained a hammer price lower than the minimum estimate) varies between 30% for Gooding & Company and 37% for RM Auctions.

Those fractions are high since the percentages are calculated only for items that reached the sellers’ reserve price. The estimation windows and hammer prices are stated in different currencies according to the country in which they have been auctioned. Since we could not maintain the dates of the auctions (due to dataset manipulations), we will be unable to determine the exact exchange rate and obtain a description of the average prices. Nevertheless, table 2 shows descriptive statistics for the relative spread and the relative distance to estimate. The relative spread is defined as the difference between the high and low estimate, divided by the mean price estimate. The relative distance to the estimate is the difference between the hammer price and the mean estimated price, divided by the mean estimated price.

Note that the relative distance to estimate will only be available if the item was sold during the auction. For both the relative spread and the relative distance to estimate, the mean and the standard deviation are calculated. The difference between the high and low estimate corresponds on average to 20% of the presale estimation mean. The average of the relative distance to estimate is 0,0554.The following section explains the information included in presale catalogues. Determining the value of a classic car is a very daunting task. An impeccable appearance is no indication of unexisting mechanical problems.

That is why a lot of information is accessible for potential buyers. The cars’ model number is available combined with additional information about the body of the car, the serie digit, the number of seats and doors, the fabrication year (varying between 1948 and 1990), if it is a cabriolet or not, the chassis number, if the steering wheel is left or right and the color of the car. Table 3 reports the number and frequency of each model and characteristics such as cabriolet, left-hand driving or right hand driving.

The Ferrari 365, 250, 330 and Dino’s 246 are most present in our data. Their selling ratio varies between 67% for the Ferrari 365 and 79% for the Ferrari 250. All those elements are included in the catalogues to be able to correctly identify the model of the car, its originality, its rareness and the evolvement in mechanics of later models.Further information involves characteristics that will likely increase the value of a classic car. Is the car certified by Ferrari Classiche or not? Ferrari stores archives with technical records of all cars produced since 1947. As a result, Ferrari Classiche offers a unique service that enables owners to obtain an official document confirming the full authenticity of the car.

The benefits of having such a certificate for a classic car owner are that it will increase the sale value and give access to prestigious official events organized by the Prancing Horse (Auto.Ferrari). Only 13% of the whole dataset was in possession of such a certificate; almost 80% of those cars were sold and 21% did not reach the sellers’ reserve price. In addition, answers can be found to the following questions, namely, “Are previous owners well identified?” and “Has only one person been in possession of the car?” If it is the case, those previous owners will be able to give you the service history of the car. Full-service history lets you know when and where previous services have been performed and if the car ever had an accident.

This is important to know since it might give you an idea of the future maintenance costs. Besides, it is also fun to know the full history of a car and previous owners might give you some extra explanations or answer some of your questions. If the car only had one previous owner, you are more likely to obtain all the correct information. Only 11 cars of the 1497 had a single owner. 18% of those cars were not sold, all the rest were. The variable “well-identified owners” was a bit more present, 23 observations but this still only corresponds to 2% of the dataset.

The distribution between sold and unsold is quite similar to the one of the variable “single owner”.Were some of those previous owners famous? This question is again very likely to increase the value of the car if answered positively. Desirability and charisma are the primary explanations for this higher valuation. 175 cars having had a famous owner were sold and the other 41 cars were not sold. In total, the 216 cars owned by famous people correspond to 14% of the dataset.

Another important element is the condition of the classic car. The condition of a vehicle refers to the shape of the car and is based on a ranking system from 0 until 2. A condition of two means that the car is in a very good condition and a condition of zero indicates that the car is in a less good condition. More or less two fifth of the cars were defined as having condition number two.

The remaining cars were equally divided between condition number one and zero. The selling ratio of the cars, ranked by category, varies between 68% and 77%. Also, the matching engine is a crucial element in the valuation process.

A classic car purist might talk about the matching numbers of a car, which means that the vehicle still has all the parts it was manufactured with. Nevertheless, there are varying levels of strictness and commitment. Therefore, a more lenient definition for numbers matching was introduced. Nowadays, it generally means that the engine and transmission of the car are marked with the same chassis number (ThoughtCo.). This variable is a key part of assessing the authenticity of the car. Not less than 85% of the dataset still has the engine it was manufactured with.

Moreover, the dataset holds information about the cars’ memorable participation and/or victory in one or several historic races. Nostalgia, desirability and rareness explain the added value of owning one of the cars that participated in a prestigious, historic race and increases the enjoyment of ownership. Only 6% of the dataset has this added value and four fifth of them were sold. The descriptive statistics of the variables mentioned above can be found in table 4. In addition, the name of the designer was also incorporated in the data. Ferraris are instantly recognisable through their mix of innovation and continuity with their past.

The designer will design each car with unique characters and shapes (Auto.Ferrari). Ownership of a rare car designed by one of the most famous Ferrari designers might add fame to the car. Designers might be known for their way of styling, fine tuning and adding elements of innovation in the design of the cars. As a matter a fact, Pininfarina and Scaglietti are the dominating designers in the data. 85% of the cars in the dataset have been designed by Pininfarina or both.Last but not least, the auction house, auction country and auction city are other components of the dataset. In the art market, considerable evidence was found that art prices vary across auction houses and geographic areas (Ashenfelter and Graddy 2002).

Indeed, auction houses may behave differently in setting presale estimates and art will often be sold at a much higher price in the United States than in either London or Europe (Bruno and Nocera 2008). It may thus be important to consider those variables as well. The classic car auctions were spread over 20 auction houses, 11 countries and 70 cities. The number and frequency of each auction house and country is characterized in tables 5 and 6. To obtain clean data, several manipulation were made to the original dataset. Indeed, unnecessary spaces after models or country names were removed, incorrect year numbers were deleted and identical models and city names were substituted to acquire an identical spelling. Moreover, extreme values that seemed unlikely and that would impact the averages too much were erased.

Once all duplicates were removed, 1497 unique values persisted. To finish, for all categorical variables such as model, country or auction house, dummy variables were created.Chapter 4: Unbiasedness of Presale EstimatesThis section will test the unbiasedness of presale estimates. Do experts provide good predictors of realized prices and is there a difference between auction houses? Strategic reasons for biased or unbiased estimates have already been discussed in the literature review. We will start by explaining the econometric model and then afterwards the empirical results will be analysed.

Econometric Models The hammer price Yi obtained for a lot i will be defined according to the following equation: Yi=Xi+ui(4.1) Let Xi be the presale estimate of the price. This presale estimate will be calculated as the average of the high and low presale estimate, following intuition and existing literature.Xi=Xmax,i+Xmin,i2 (4.2)For presale estimates to be unbiased, Xi=EYi?) needs to be fulfilled, where ? is the information set available to the expert. ui is a random disturbance term that has zero mean and Eui?) should be equal to zero. The latter implies that the experts’ predictions take into account all the information available to them, the random disturbance is thus orthogonal to every variable contained in the information set ?.

To test whether Xi is an unbiased estimator of Yi, we could run the following regression by ordinary least squares (OLS): Yi=?+?Xi+vi(4.3)The null hypotheses would then be: H0:{?=0, ?=1}. If this hypothesis is not rejected, we can assume the unbiasedness of the presale estimates. However, we would like to do the test for every major auction house in the database since auction houses may behave differently in fixing predicted prices. As explained before the major auction houses are RM Sotheby’s (r), Bonhams (b), Gooding & Company (g) and an extra category ‘Other’ (o) was created to gather all the other auction houses. Equation 4.3 will thus be transformed into: Yi=?r?ri+?b?bi+?g?gi+?o?oi+?r?riXri+?b?biXbi+?g?giXgi+?o?oiXoi+vi (4.

4)Where ?ri=1 if the lot i was sold by the auction house RM Sotheby’s. ?bi, ?gi and ?oi are indeed all dummy variables that will indicate which auction house sold the item. The same logic is applied to the parameters and the presale estimates.

Every auction house has their own ?, ? and their corresponding Xi’s.Nevertheless, our dependent variable Yi is truncated. Indeed the hammer price, Yi, is only observed for items that were sold and not for items that were hold in. The observations that were not sold will thus not be taken into account in this regression. Hence, we would expect regression 4.4 to undergo a problem of selection bias that arises because we nonrandomly decided to only use the observations that reached the reserve price. The OLS coefficients would then yield biased and inconsistent estimates of ? and ? (Marinellei and Palomba 2008). We are thus led to consider an alternative model, the Heckman or Heckit model (Heckman 1979).

This model corrects for the selection bias, eliminates the specification error and will thus provide consistent estimates (Marinellei and Palomba 2008). This model has been widely used in the literature to solve for nonrandomly selected samples that suffer from selection bias. The model can be written as: si*= ?Zi+?i (4.5)Yi*=?r?ri+?b?bi+?g?gi+?o?oi+?r?riXri+?b?biXbi+?g?giXgi+?o?oiXoi+vi si*>0 (4.6)Equation 4.5 is the “selection equation” in which si* is a latent variable that will be positive if the auction price is superior to the reservation price. Zi is a vector that contains the variables influencing the selling decision.

? is a vector of unknown parameters and ?i is the random disturbance term. Since si* is not observed, a dichotomic variable si is introduced: si= 1 if si*>0, 0 otherwisesi will be equal to one if the car is sold and zero otherwise. The “price equation” (equation 4.6) illustrates the relationship between the price and presale estimates, such as in equation 4.4. Besides, we assume that (vi, ?i) in equations 4.

5 and 4.6 are jointly normally distributed and independent of (Zi,Xi) with zero mean and that E(vi2)=?, E(?i2)=1, cov(vi, ?i)=??. The parameters can then be estimated by maximum likelihood or by the Heckman two-step procedure. This procedure is based on the fact that the “pricing equation” can be calculated as (Hall 1999): EYi*si=1,Zi= ?Xi+???(?Zi)(4.7)Where ?. is defined as the inverse of Mill’s ratio: ?.

=?(.)/?(.) with ?(.) and ?(.) being, respectively, the density and distribution function for a standard normal variable. If the correlation (?) between (vi, ?i) is positive, equation 4.7 will be biased upwards since the inverse of Mill’s ratio will always be positive. The size of the bias will depend on the importance of the correlation, the variance of the disturbance term vi and the severity of truncation.

If there is no correlation, there is no selectivity bias and we may proceed using OLS (Hall 1999). Heckman (1979) proposes the following method. Step one consists of a Probit model that will predict if an item goes sold or not and will be used to obtain estimates ? of the parameters in the “selection equation”. With this information, ?(?Zi) can be defined as a proxy for ??Zi. In the second step, this additional regressor will be included in the “pricing equation” to correct for the potential sample selection bias. This equation can be estimated via the OLS method. The coefficient on ? will be a measure for ??, the covariance between (vi, ?i).

The ordinary t-statistic of this coefficient can be used to test the hypothesis ?=0 since ??0 (Hall 1999). These estimators obtained using the Heckman two-step method are consistent but not asymptotically efficient (Czujack and Martins 2004). Assuming the assumptions mentioned above still hold, the maximum likelihood estimation does yield consistent and efficient estimators. Those estimates can be obtained by maximizing the following function with respect to its arguments (Hall 1999, Czujack and Martins 2004): logL ?,?,?,??=S=0log1-??Zi+ S=1-log?+log?Yi-?Xi?+log?(?Zi+??Yi-?Xi1-?2)(4.

8)Two important notes need to be made before discussing the empirical results. Firstly, instead of using the hammer price Yi and the mean estimated price Xi, we will use the natural logarithm of both variables. Indeed, auction prices are often strongly skewed due to the presence of a very few expensive works (Vosilov 2015). This technique, of taking the logarithm, will re-center the observations and reduce the heteroscedasticity in the residuals of the model, meaning that the model will become a better fit. From now on, Yi and Xi will correspond to the natural logarithm of the hammer price and the mean estimated price. Subsequently, the variables Z in the “selection equation” 4.

5 include three dummy variables for the auction countries, three dummies for the auction houses and two dummy variables for the designers. Each time, we define dummies for the most important categories and add one additional dummy for the rest of the categories. Next, two dummies for the car models and a dummy indicating if the car has been owned by a famous person or not, were also included. The natural logarithm of the minimum estimated price multiplied by a dummy variable indicating which auction house sold the car was also inserted and the same was done for Xi. For the divisions of auction houses, auction countries and designers, one dummy variable representing a certain group has been dropped. This was done to avoid exact collinearity in the data and by consequence circumvent erratic estimates of the coefficients (Dougherty 2011).

Indeed all dummies were constructed as to equal one if all subcategories were summed. The dropped category will become the reference group. This “selection equation” still includes a large number of coefficient estimations and will not be discussed. We will focus on the “price equation”. However, table 7 in the annexes gives the results for the “selection equation” in the sample selection models.

Remember that these coefficients have no direct interpretation. Empirical ResultsThe estimation results of the “price equation”, explained in the subsection “econometric models”, are reported in table 8. Both sample selection models (two-step method and maximum likelihood) are included as well as the case of no correlation (?=0).

Table 8 is again included in the annexes. The first thing we notice is that the coefficients and the standard errors do not differ that much across the different approaches. The Heckman two-step method estimates the value of the lambda coefficient at -0.1027. As explained previously, the latter depends upon the covariance between (vi, ?i), defined as ??.

This implies that the disturbance term of the “selection equation” and “pricing equation” are negatively correlated. Which suggests that cars that go sold are more likely to be those with a lower price. Indeed, cheaper cars are likely to be bought by a wider group of potential buyers (Marinelli and Palomba 2008). Note that this coefficient is statistically different from zero at a 10% level, suggesting that some correction for the sample selection bias is needed.

The Heckman two-step method will thus be superior to using an ordinary least squares regression (assuming ?=0). Nevertheless, as previously explained the two-step method yields consistent but inefficient estimates. The maximum likelihood method, giving consistent and efficient estimates, will thus also be discussed. For technical reasons, the correlation between (vi, ?i), ?, is estimated through atanh ? (displayed as athrho in table 8). However, the null hypothesis H0: atanh ?=0 is equivalent to the null of ?=0. The coefficient of athrho is significantly different from zero at a 1% level and hence strongly rejecting the hypothesis of absence of correlation.

The same test can be performed by analysing the Wald test of independent equations. The chi-squared test statistic of 14.38 also rejects the null hypothesis of independent equations since the critical value of ?21 6.63 at the 1 percent level (Dougherty 2011). We can thus conclude by saying that the regression results are quite similar, despite the presence of selection bias.

Consequently, we will continue by using the regression results of the maximum likelihood method as our basic result since these estimates are consistent and efficient. The next step in our empirical analysis is to assess if presale estimates are unbiased predictors of realized prices. To do so, we will test several hypotheses regarding the behaviour of auction houses: starting by examining the most restrictive hypotheses and gradually slacken the assumptions.Since we use a composite or multiple equation model to obtain the coefficient estimates, we perform a Wald test and a Likelihood Ratio test to analyse the hypotheses with multiple restrictions. Indeed, we will perform the two tests to double check our conclusions, as has often been done in existing literature. Both tests compare the models’ likelihood to assess their fit and assume that the test statistic has an asymptotic chi-squared distribution with degrees of freedom equal to the number of restrictions being tested (Wooldridge 2013). All test results for the hypotheses (1) until (6) are displayed in table 9 in the annexes.

The first joint hypothesis tested is whether all auction houses behave identically and provide unbiased presale estimates (1). This is indeed a very restrictive hypothesis. As can be seen in table 9, both the test statistics of the Wald test and the likelihood ratio test are far superior to the critical value of the chi-squared distribution at a 1% level, meaning that the assumption of identical behaviour and unbiased predictors for all auction houses is rejected. Next, we verify if the null of all auction houses behaving identically in predicting prices (2) is rejected or not. This hypothesis can indeed be rejected since the critical value of the chi-squared distribution is inferior to the test statistics. The subsequent hypotheses will test the unbiasedness of presale estimates of each auction house separately: RM Sotheby’s (3), Bonhams (4), Gooding & Company (5) and ‘Other’ (6). Once again, we don’t accept the four preceding assumptions due to a superior test statistic compared to the chi-squared critical value at a 1% level. In summary, we can say that all hypotheses were rejected.

This suggests that auction houses have not given good predictors of realized prices for the cars. Looking at the estimation results of table 8, we can rewrite equation 4.4 as: Y=0.9931 XFor RM Sotheby’s(4.9)Y=0.7520+0.9498 X For Bonhams(4.10)Y=0.

9896 XFor Gooding & Company (4.11)Y=1.0218 XFor the category ‘Other’ (4.12) None of the equations 4.9, 4.

11 or 4.12 have an intercept since the results of table 8 indicated that none of them were significantly different from zero. The above equations help us determine if predictors are systematically over- or undervalued. Both RM Sotheby’s and Gooding & Company overestimated their predictions. On the contrary, the ‘Other’ category had the tendency to underestimate their predictions of realized prices. For the auction house Bonhams the results are less straightforward. Bonhams undervalues inexpensive cars, and overvalues expensive cars. Unfortunately, we are not able to identify exactly where the transition point is situated since we are dealing with different currencies.

However, notice that the bias is never really large. To conclude, we can say that auction houses do not provide good predictors of realized prices and that there is a difference between auction houses but the bias stays small. However, the question still remains if the estimation error is caused by unpredictable market forces (e.g. high ‘secret’ values) or if the experts didn’t use all the available information to correctly predict the auction prices (Bauwens and Ginsburgh 2000). Chapter 5: Uncertainty of Experts in Presale Estimates The “information hypothesis”, introduced by Kells (2003), proposes that wider estimate ranges reflect greater uncertainty from the experts in setting presale valuations.

This section will investigate which factors affect the uncertainty of experts in predicting presale prices.Econometric ModelsSince uncertainty cannot be observed directly, a proxy called ‘RELATIVE_SPREAD’ was defined. The relative spread is defined according to following equation: RELATIVE_SPREAD= Xmax,i-Xmin, iXi(5.1)Xi being the average estimated price for lot i and Xmax, i and Xmin, i being the high and low presale estimate for the same lot i.The greater the auctioneer’s prediction uncertainty, the higher the relative spread will be. The average relative spread over the whole sample is 20%. More than 95% of the observations have a relative spread between 5 and 35%. Auction cars with a relative spread inferior to 5% or superior to 35% are thus extremely rare in our dataset.

Figure 1, in the annexes, illustrates the relationship between the relative spread and the logarithm of the mean estimated price of the classic cars. There appears to be no clear relationship between both. The average relative spread for each auction house does not vary that much. It fluctuates between 21% for RM Sotheby’s and 18% for the category ‘Other’. To obtain a more formal relationship between the uncertainty proxy and the explanatory variables, we will regress the relative spread against the variables included in auction catalogues and variables giving information about the auction itself. Those variables can be categorized into subjective and objective variables (Bruno and Nocera 2008). The subjective variables will be dummy variables for auction houses since a difference in price setting may exist. The objective variables, corresponding to the information available to experts, will be composed of features describing the car and the conditions in which the car will be auctioned.

We use an ordinary least squares regression to estimate the following model: RELATIVE_SPREAD=f(CONSTANT,MODEL, CERTIFIED_BY_FERRARICLASSICHE, SINGLE_OWNER, WELL_IDENTIFIED_OWNERS,MATCHING_ENGINE,FAMOUS_OWNERS,RACEUSE,CABRIOLET,DESIGNER, AUCTION_HOUSE,log?(meanestimatedprice))+?(5.2)A few words about the independent variables and our assumptions about the coefficient outcomes. The objective variables are, amongst others, composed of four dummy variables representing the model of the car (MODEL).

Those variables were included to control for any difference in predicting the value of a car. Indeed, it might be more difficult to predict the selling price of a specific car model. According to Professor P. Giot, the car models Ferrari 330 and Ferrari 365 are more ordinary models and on the contrary, the Ferrari 250 is a rarer model. The Ferrari Dino 246 is also one of the first cars that was manufactured in high numbers in partnership with Fiat (Bloemendaalcs). We thus expect the Ferrari 330, the Ferrari 365 and Dino 246 to reduce the uncertainty and the Ferrari 250 to increase the experts’ uncertainty. Cars that are more common and ordinary might be easier to valuate.

‘CERTIFIED_BY_FERRARICLASSICHE’ is a dummy indicating if the car was certified by Ferrari Classiche or not. We expect this variable to have a negative coefficient sign since a certificate is prove of authenticity and might reduce uncertainty. The same can be said about the dummy used to point out if the car only had one owner (SINGLE_OWNER). Since the current owner can answer questions and provide all the necessary information to the auction expert, it will likely reduce the pricing uncertainty. The identical reasoning can be made for the dummy variable indicating if the car has well-identified owners (WELL_IDENTIFIED_OWNERS).

‘MATCHING_ENGINE’ is a dummy variable that shows if the car still has the engine it was originally manufactured with. As before, we expect this variable to have a negative coefficient sign since it illustrates the authenticity of the car and might reduce the uncertainty in valuation. Next a dummy indicating if the car had famous owners or not was added (FAMOUS_OWNERS). Besides a binary variable expressing if the car participated in a renowned race was introduced (RACEUSE). The additional amount a buyer is willing to pay for a car previously owned by a famous person or a car that participated in a prestigious race is very hard to define since it is so personal. We thus expect the signs of both coefficients to be positive and to add uncertainty for the expert. ‘CABRIOLET’ is a dummy for the car being cabriolet or not. This variable will control for any difference in fixing presale estimates for cars that are cabriolet.

Besides, two dummies for the designers will control for any difference in predicting presale estimates when it comes to who designed the car (DESIGNER). A specific designer might make it easier for an expert to define a probable selling price. Additionally, it may be easier to predict selling prices for more expensive items – having a higher mean estimated price – then cheaper ones (Bruno and Nocera 2008). The variable ‘log(meanestimatedprice)’ was thus included to indicate the price level and a negative coefficient sign is thereby awaited.

Finally, as briefly pointed out above, the prediction uncertainty may vary across auction houses. They may have different policies for setting presale estimates or their experts might have different opinions about how to value a classic car. By including three dummy variables for the auction houses (AUCTION_HOUSE), we may control for differences in auction houses’ confidence in setting presale estimates.

Larger auction houses probably rely upon more information to fix predictions and might thus have a negative coefficient sign that reduces the uncertainty in estimations (Bruno and Nocera 2008). As explained in chapter 4, a dummy variable of each one of the variables representing categories (being the model, the designer and the auction house) was randomly dropped to avoid exact multicollinearity. The dropped category will become the reference category.

Hence, the coefficients of the dummies in the regression thus represent an increase or decrease in the intercept relative to the reference category composed of several dimensions.In the model developed here above, the dependent variable is considered as continues. This method has already been applied in existing literature: Bruno and Nocera (2008) and Kells (2003). However, since the relative spread in our dataset only takes certain values between 0 and 0.

5, we could consider this variable as an unordered categorical variable with several discrete outcomes. The relative spread is then composed of 6 classes:Category 0 being all observations with a relative spread < 5%Category 0.1 being all observations with a relative spread > 5% and < 15%Category 0.2 being all observations with a relative spread > 15% and < 25%Category 0.3 being all observations with a relative spread > 25% and < 35%Category 0.4 being all observations with a relative spread > 35% and < 45%Category 0.5 being all observations with a relative spread > 45% and < 55%To estimate equation 5.2 with ‘RELATIVE_SPREAD’ as a categorical variable, we use a multinomial logistic regression instead of an ordinary least squares.

To my knowledge, this has never been done before. Regression 5.2 can thus be rewritten as: Pr?(RELATIVE_SPREAD =outcome)=f(CONSTANT,MODEL, CERTIFIED_BY_FERRARICLASSICHE, SINGLE_OWNER, WELL_IDENTIFIED_OWNERS,MATCHING_ENGINE,FAMOUS_OWNERS,RACEUSE,CABRIOLET,DESIGNER, AUCTION_HOUSE,log?(meanestimatedprice))+?(5.

3)With Pr being the probability of a certain outcome: one of the 6 relative spread classes. The main advantage of using this kind of regression is that it will provide insights for the different uncertainty categories in the dependent variable. A certain feature could be significant for a specific uncertainty category and insignificant for another. For purpose of illustration, we created 2 typical cars that were most represented in our dataset. We predicted the probability of obtaining each one of the uncertainty categories (called base probability) for both cars.

Afterwards, we add a certain feature (‘CERTIFIED_BY_FERRARICLASSICHE’, ‘FAMOUS_OWNERS’, ‘WELL_IDENTIFIED_OWNERS’, ‘RACEUSE’, ‘CABRIOLET’ or ‘SINGLE_OWNER’) and estimated how the probability of obtaining a specific uncertainty category has changed. The results are reported in table 10 but will not be discussed here as there is no significant difference as to what will be discussed below. Table 13 compares the expected results to the obtained ones. Our hypotheses regarding the coefficients of the variables do not change. Nevertheless, their formulation does change. We expect the variable ‘CERTIFIED_BY_FERRARICLASSICHE’ to have a positive coefficient sign for the lower uncertainty groups. Indeed a certificate is prove of authenticity and might thus increase the probability of observing a low relative spread.

The same reasoning can be made for the dummy variables ‘SINGLE_OWNER’ and ‘WELL_IDENTIFIED_OWNERS’. For the dummy variable ‘MATCHING_ENGINE’ we also expect a positive coefficient sign for low uncertainty categories since it illustrates the authenticity of the car and might thus increase the probability of finding a low uncertainty in valuation.’FAMOUS_OWNERS’ and ‘RACEUSE’ are expected to both have a coefficient that is positive for the large uncertainty categories and thus increase the probability of obtaining high relative spread. Besides, the two dummies included for the designers will again control for any difference in predicting presale estimates. So will the dummies for the car models. We believe that the model Ferrari 250 will increase the probability of obtaining a larger relative spread and decrease the probability of obtaining a small uncertainty range.

Next, we presume that coefficients of the variable ‘log(meanestimatedprice)’ will show a positive coefficient sign for low uncertainty levels and a coefficient smaller than zero for the higher categories of the relative spread. Finally, larger auction houses are expected to increase the probability of obtaining lower uncertainty levels. Empirical ResultsWe will start by discussing the regression results of equation 5.2, reported in table 11. Afterwards we will qualify our statements by analysing the estimation results of the multinomial logistic regression 5.3 displayed in table 12. For ease of exposition, tables 11 and 12 are included in the appendix.

The regression results summarized in table 11 show that the coefficients of the car models Ferrari 250 and the category ‘Other’ are significantly different from the reference category which indicates that those two models impact the dependent variable differently. The positive coefficient sign for the Ferrari 250 confirms our hypothesis that this model is harder to estimate since it is scarcer. The dummy variables ‘SINGLE_OWNER’ and ‘WELL_IDENTIFIED_OWNERS’ are significantly different from zero and both have positive signs. This contradicts our expectations.

The positive coefficients indicate that experts’ uncertainty increases when they have to value cars that only had one owner or a car whose previous owners are all well identified. A possible explanation could be that it is harder to give a monetary value to those characteristics since it might be preferred by some and unnecessary for others. The significant positive coefficient of the indicator variable ‘FAMOUS_OWNERS’ confirms our expectation that this feature increases the difficulty for the expert to predict the presale estimates, and thus increases the estimation range. The same conclusion can be made for a car that is a cabriolet.

Besides, the designer category ‘Pininfarina & Scaglietti’ has a significant negative coefficient indicating that experts’ uncertainty decreases when they are determining the value of a car designed by this duo. The significant negative coefficient of the logarithm of the mean estimated price is consistent with our assumption that it is easier for experts to determine presale estimates for more expensive classic cars. Finally, the auction house category ‘Other’, constructed of smaller auction houses, has a significant negative coefficient.

This result contradicts our belief that larger auction houses would give more precise presale estimates since they have access to bigger sets of information.To summarize, the dummy variables ‘SINGLE_OWNER’, ‘WELL_IDENTIFIED_OWNERS’, ‘FAMOUS_OWNERS’, ‘CABRIOLET’ and ‘Ferrari 250′ all increase the experts’ uncertainty. Nonetheless, the dummy variables for the designers ‘Pininfarina & Scaglietti’ and the auction house group ‘Other’ all decrease the presale spread compared to the reference group. Besides, the more the auctioned cars are expensive, the more the expert’s confidence increases. We are now turning to the results obtained by estimating equation 5.3.

We notice again that the car models impact the relative spread differently than the reference category. However, the models Ferrari 365 and Ferrari 330 also became significant for the categories 0 and 0.2. The statistically significant negative coefficients of the categories 0.1 and 0.

2 confirm that the model Ferrari 250 decreases the probability of obtaining a smaller spread. Nevertheless, the same model increases the probability of obtaining a relative spread inferior to 5%, which contradicts our hypothesis. The coefficient for the dummy variable ‘CERTIFIED_BY_FERRARI_CLASSICHE’ becomes negatively significant for the category 0.5, meaning that the owning such a certificate reduces the probability of obtaining a relative spread superior to 45 percent. This implies that our assumption is confirmed for the highest uncertainty category and not for the lower uncertainty levels. The dummies ‘SINGLE_OWNER’ and ‘WELL_IDENTIFIED_OWNERS’ both have significant negative coefficients for the largest uncertainty category (relative spread superior to 45 percent). This suggests that our hypothesis – stating that those two variables should reduce the uncertainty – cannot be fully rejected as was the case with equation 5.2. Nevertheless, those two characteristics also reduce the probability of obtaining a relative spread inferior to 5%. Next, the feature of having famous owners significantly decreases the probability of having a low relative spread (category 0.1) and significantly increases the chances of having a higher uncertainty category (0.3 and 0.4). Again, endorsing our expectations. The dummy for ‘CABRIOLET’ reduces the probability of obtaining a relative spread between 5 and 15%. A classic car that participated in a renowned race reduces the probability of obtaining a relative spread situated in category 0. Subsequently, the designer category ‘Pininfarina and Scaglietti’ again increases the probability of obtaining a lower relative spread and decreases the probability of obtaining an uncertainty level corresponding to the category 0.3 or 0.4. The significantly negative coefficient of the variable ‘log(meanestimatedprice)’ points out that the higher the mean estimated price, the lower the probability of obtaining a high uncertainty level. Finally, the significant coefficient signs of the auction house category ‘Other’, being composed of smaller auction houses, forces us to reject our hypotheses that larger auction houses should be more confident in setting presale estimates. However, we notice that RM Sotheby’s is indeed more confident in setting presale estimates than the reference category, being Bonhams.To improve the understanding of the empirical results, two additional tables were made to compare our expectations about the coefficient sign and the obtained results. Table 14 illustrates this for equation 5.2 and table 15 for equation 5.3. To conclude, we can say that some of our assumptions were confirmed for certain categories. However, some hypotheses could only be validated when using the multinomial logistic regression which enabled us to have a more precise view. Chapter 6: Prediction This section will deal with three different questions. The first question we ask ourselves is: “Would it be possible to predict if a car will go unsold?” 73% of the classic cars put up for auction were bought. However, the remaining 27% did not reach the seller’s reserve price and were by consequence not sold. Which factors influence this ‘no sale’?The second question regarding the possible prediction and influencing factors is related to hammer prices that did not reach the minimum predicted price but did make the seller’s reserve price. One fifth of the cars that were sold, ended up in this situation. Besides, 33% of the cars sold were bought above the high presale estimate. By the same token, the third question thus analyses the hammer prices that were superior to the expert’s high estimate. We investigate if it is possible to predict those cases and which characteristics of the cars or the auctions are more likely to influence those results. With this intention, we will start by discussing the econometric models that were used and our assumptions regarding the explanatory variables. Afterwards the empirical results will be examined.Econometric ModelsTo predict whether a car will go unsold or not, we use a logit regression that fits the model by maximum likelihood estimation. The following regression is estimated:Pr?(NOSALE)=f(CONSTANT,MODEL, CERTIFIED_BY_FERRARICLASSICHE, SINGLE_OWNER, WELL_IDENTIFIED_OWNERS,MATCHING_ENGINE,FAMOUS_OWNERS,RACEUSE,CABRIOLET,DESIGNER, AUCTION_HOUSE,log?(meanestimatedprice),RELATIVE_SPREAD)+?(6.1)NOSALE is a dummy variable that equals one when the reserve price is not reached and zero when the car is sold at the auction. We use the information listed in the auction houses’ catalogues as independent variables. Typically, this is all the information that is available to the potential buyers (Ekelund, Ressler and Watson 1998). All those independent variables (indicator and continues) have been explained in section 5 and will not be redefined. Additionally, to avoid exact multicollinearity, one category of the car models, designers and auction houses was randomly left out. This dropped category will become the reference category. We expect that all the coefficients of the binary variables RACEUSE, SINGLE_OWNER, CERTIFIED_BY_FERRARICLASSICHE, FAMOUS_OWNERS, MATCHING_ENGINE and WELL_IDENTIFIED_OWNERS will have a negative sign. Indeed, we believe that those variables should increase the probability of sale and thus decrease the probability of ‘no sale’. Besides, the indicator variable CABRIOLET will test for any difference in probability of ‘no sale’ when the car is a cabriolet. Several dummy variables for the different groups of models, auction houses and designers were also incorporated into equation 6.1 to control for any difference between categories on the probability of ‘no sale’. We expect the car model Ferrari 250 to increase the probability of ‘no sale’ since they are way more expensive and can thus only be bought by a smaller group of investors. Next, we believe that the coefficient of the variable ‘log(meanestimatedprice)’ will be larger than zero since more expensive items are harder to sell due to a smaller number of potential buyers. This would be consistent with our findings of section 4 that suggest that cars that go sold are more likely to be those with a lower price. To argument for the expected coefficient sign of the variable ‘RELATIVE_SPREAD’, we need to go back to the literature. The “reserve hypothesis” states that a narrow estimation spread indicates a higher reserve price (Kells 2003). Obtaining a negative coefficient, indicating that a larger relative spread reduces the probability of obtaining a ‘no sale’, would thus confirm this hypothesis. Ekelund, Ressler and Watson (1998) already found evidence to support the “reserve hypothesis” using a dataset of Latin-American Art Auctions from 1977-1996. Furthermore, to analyse our second question – predicting whether a car will be sold below the minimum estimated price or not – we also use a logit regression to fit the model by maximum likelihood estimation. The following regression is estimated: Pr?(BELOWMIN)=f(CONSTANT,MODEL, CERTIFIED_BY_FERRARICLASSICHE, SINGLE_OWNER, WELL_IDENTIFIED_OWNERS,MATCHING_ENGINE,FAMOUS_OWNERS,RACEUSE,CABRIOLET,DESIGNER, AUCTION_HOUSE,log?(meanestimatedprice),RELATIVE_SPREAD)+?(6.2)Where BELOWMIN is a dummy variable that equals one when the price obtained at the auction is inferior to the expert’s minimum estimated price and zero otherwise. The third regression that is estimated, will explore our third question and analyse if it is possible to predict that a car will be sold above the maximum estimated price. We again use a logit regression to do so. The regression is specified as:Pr?(ABOVEMAX)=f(CONSTANT,MODEL, CERTIFIED_BY_FERRARICLASSICHE, SINGLE_OWNER, WELL_IDENTIFIED_OWNERS,MATCHING_ENGINE,FAMOUS_OWNERS,RACEUSE,CABRIOLET,DESIGNER, AUCTION_HOUSE,log?(meanestimatedprice),RELATIVE_SPREAD)+?(6.3)ABOVEMAX is a binary variable that equals one when the price achieved is superior to the experts’ maximum estimated price and zero otherwise. We will not formulate assumptions for the variables of the equations 6.2 and 6.3. The situation of ABOVEMAX and BELOWMIN combined with the explanatory variables become too specific to anticipate general trends. The results of all three equations (6.1-6.3) will be discussed in the empirical part of this section and are summarized in table 16. Table 17 compares the expected and obtained coefficient signs of equation 6.1. For ease of exposition, both tables are included in the annexes. Empirical ResultsFirst the regression results of the ‘no sale’ equation 6.1 will be discussed, followed by an analysis of the outcomes of equation 6.2 regarding the sales below the minimum estimated price. We will finish this section by considering the prediction results of equation 6.3 that studies the sales above the maximum estimated price. We notice from table 16, regarding the prediction of NOSALE, that the Ferrari model 365 has a higher probability of not getting sold than the reference category. Besides, when the dummy variable ‘FAMOUS_OWNERS’ is equal to one, the probability that the car will not be sold, reduces. This is consistent with our expectation. The auction houses RM Sotheby’s and Gooding & Company seem to decrease the probability of not selling a car compared to the reference group, being the auction house Bonhams. On the contrary, the auction house category ‘Other’ increases this probability. Additionally, the coefficient of the variable ‘log(meanestimatedprice)’ has a positive sign, which indicates that more expensive cars – cars having a higher mean estimated price – are indeed harder to sell and hence it corroborates our assumption. To finish, the greater the relative spread, the more the probability of not selling an auctioned car reduces. This result is consistent with the idea that smaller spreads are prove of higher, inflated reserve prices and consequently a lower probability of sale. The “reserve hypothesis” can thus be sustained.After analysing the regression results of equation 6.2, we concluded that following features were significant to predict if a car would be sold below the expert’s minimum estimated price or not. The characteristics of having a certificate of Ferrari Classiche or having proven famous owners reduces the probability of obtaining a hammer price that is inferior to the minimum predicted price. Unfortunately, we have insufficient additional information to explain the negative coefficient of the dummy variable ‘CERTIFIED_BY_FERRARICLASSICHE’. However, for the indicator variable ‘FAMOUS_OWNERS’, we can refer to our previous findings to obtain a plausible explanation. From section 5, we know that the variable ‘FAMOUS_OWNERS’ increases the relative spread. Since the relative spread is more likely to be larger, it seems plausible that the probability of obtaining a price below this larger spread reduces. This explanation is confirmed by the negative coefficient sign of the variable ‘RELATIVE_SPREAD’. The lager the relative spread, the smaller the probability that the hammer price will fall below the minimum estimated price. Bruno and Nocera (2008) made similar findings: “… the wider the PRICERANGE, the higher the probability that the hammer price will fall into the presale estimate range.” Moreover, both designer categories ‘Pininfarina’ and ‘Pininfarina & Scaglietti’ seem to reduce the probability of obtaining a hammer price inferior to the minimum estimated price. No persuasive explanation was found to justify those results. Finally, the positive coefficient sign of the variable ‘log(meanestimatedprice)’ indicates that cars with a higher mean estimation are more likely to be sold below the minimum estimated price.To finish, we analyse which factors are important for predicting if a car will be sold above the maximum estimated price or not. All dummy variables ‘CERTIFIED_BY_FERRARICLASSICHE’, ‘FAMOUS_OWNERS’ and ‘SINGLE_OWNERS’ have a significantly positive coefficient, meaning that those features increase the probability of observing a hammer price above the high presale estimate. The only plausible explanation was already briefly mentioned in section 5. Those characteristics could have a large personal ‘secret’ value to some potential buyers. It seems acceptable to assume that certain buyers attach way more importance to possess a car that was certified by Ferrari Classiche, once previously owned by a famous person or even only owned by a single person. The increased personal value could induce them to take the auction bidding a notch higher. This would have a surprise effect that the auction experts could not have incorporated in their estimations. Even though, the indicator variable ‘FAMOUS_OWNERS’ increases the relative spread and thus reduces the probability of obtaining a hammer price above the high presale estimate (this is confirmed by the negative coefficient of the variable ‘RELATIVE_SPREAD’) the surprise effect seems to be larger, and thus increases the probability of reaching a price superior to the maximum predicted price. The same reasoning can be made for the ‘SINGLE_OWNER’ variable since it also increases the relative spread. Nevertheless, still no answer can be found to justify the increased probability of obtaining a higher hammer price than the maximum estimate when it comes to the designer ‘Pininfarina’. To finish, the more expensive the car, the more the probability of surpassing the maximum estimated price, reduces. This result could be defended by the idea that bidders’ uncertainty increases once they exceed the maximum estimated price. Potential buyers will thus become more careful during the bidding procedure. The effect is likely to increase when the mean estimated prices are higher.To conclude, we know that a larger relative spread and famous owners decrease the probability of ‘no sale’. Whereas more expensive cars increase to probability of not selling. For cars sold at a hammer price inferior to the minimum estimate, we found that more expensive cars increase the probability of being sold below the minimum estimated price. On the other hand, the features of a larger relative spread, famous owners and a certificate of Ferrari Classiche reduce the probability of being sold below the minimum estimated price. Additionally, cars having the certificate, famous owners or just a single owner increase the probability of selling above the experts’ high presale estimate. Conversely, more expensive cars and larger spreads reduce this probability. ConclusionThe main use of auction house catalogues is to provide information to potential buyers and help them overcome the difficulties faced in auction markets, namely heterogeneity and infrequent trading of the auctioned lots. The presale estimates that experts define play an important role in this clarification. However, we find that experts do not seem to provide good predictors of realized prices. RM Sotheby’s and Gooding & Company overestimated predicted prices. Bonhams, on the other hand, seems to undervalue inexpensive cars and to overvalue expensive classic cars. There thus exists a difference between auction houses in setting presale estimates. However, the bias stays relatively small for each auction house. This thesis provides further evidence supporting the biasedness of presale estimates and contradicts existing literature stating that “honesty is the best policy” (Milgrom and Weber 1982) and that experts do provide good predictors of realized prices (Ashenfelter 1989, Abowd and Ashenfelter 2002, Louargand and McDaniel 1991). Besides, we found that the uncertainty of experts increased when following characteristics were present: single owner, well-identified owners, famous owners and cabriolet. Those features could be harder to value since they are more related to the personal ‘secret’ value than objective features such as the model of the car. Indeed, some potential buyers may attribute an increased value to these characteristics compared to others. However, experts’ confidence in setting presale estimates increases for more expensive cars and decreases for Ferraris 250. Moreover, a larger relative spread and famous owners decrease the probability of ‘no sale’. Whereas more expensive cars seem to be harder to sell. The “reserve hypothesis”, stating that a narrow estimation range indicates higher reservation prices, can thus be sustained. For cars sold below the minimum estimated price, we found that a larger relative spread, famous owners and a certificate of Ferrari Classiche reduced the probability of being sold below the minimum estimated price. On the other hand, more expensive cars increase the probability of being sold below the minimum estimated price. Additionally, cars having the certificate, famous owners or just a single owner, increase the probability of selling above the experts’ high presale estimate. This is again likely related to the ‘secret’ value attributed by the potential buyer and can thus induce a surprise effect during the auction. Conversely, more expensive cars and larger spreads reduce the probability of obtaining a hammer price superior to the high presale estimate. To obtain those results, several hypotheses were made regarding the value of the presale estimate and the distribution of the disturbance terms in the Heckman sample selection model. Verifying those hypotheses would have increased the robustness of this thesis but would have made us deviate too much into the econometric aspects and would have led us to far from the initial focus, being the informational content of presale estimates and hammer price in classic car auctions. This paper thus provides new insights into the questions of accuracy and uncertainty of experts’ presale estimates in classic car auctions. However, we did not focus on finding an explanation for the biasedness of presale estimates or the factors increasing the experts uncertainty. We chose to focus on the two main axes of the informational content of presale estimates and hammer prices. Further research might deal with this part of the subject and hopefully this thesis will be a helpful starting point for such a new initiative. Bibliography ABOWD, J. M., ASHENFELTER, O. (2002), “Using Price Indices and Sale Rates to Assess Short Run Changes in Market for Impressionist and Contemporary Paintings”, G. Mosetto and M. Vecco, The Economics of Art Auctions, F. Angeli, Milan (Italie). AGNELLO, R. J., PIERCE, R. K. (1996), ” Financial Returns, Price Determinants, and Genre Effects in American Art Investment.”, Journal of Cultural Economics 20, pp. 359-383. ASHENFELTER, O. (1989), ” How Auctions Work for Wine and Art”, Journal of Economic Perspectives, Volume 3, Number 3, pp. 23-26. ASHENFELTER, O., GRADDY, K. (2002), “Art Auctions: A Survey of Empirical Studies”, NBER Working Paper No. 8997. ASHENFELTER, O., GRADDY, K. (2011), “Sales Rates and Price Movements in Art Auctions.”, CEPS Working Paper No. 214. BAUWENS, L., GINSBURGH, V. (2000), “Art experts and auctions. Are pre-sale estimates unbiased and fully informative?”, Recherches Economiques de Louvain – Louvain Economic Review 66(1). BEGGS, A., GRADDY, K. (1997), “Declining Values and the Afternoon Effect: Evidence from Art Auctions.”, The RAND Journal of Economics, Vol. 28, No. 3, pp. 544-565. BEGGS, A., GRADDY, K. (2009), “Anchoring Effects: Evidence from Art Auctions”, American Economic Review, Volume 99:3, pp. 1027-1039. Best Of Money: the classic car is the investment star. See website: https://www.ft.com/content/fc2a08b8-f824-11e5-96db-fc683b5e52db BRULS, A. (2017), “Creation of a Classic Car Index: investment considerations, opportunities and challenges.”BRUNO, B., NOCERA, G. (2008), “Investing in Art: the Informational Content of Italian Painting Pre-Sale Estimates.”CHANEL, O., GERARD-VARET, L.-A., VINCENT, S. (1996), “Auction Theory and Practice: Evidence from the Market for Jewellery.”, GREQAM, Economics of the Arts –Selected Essays, V.A. Ginsburgh and P.-M. Menger, 1996. Classic car prices have surged but investing in them is another story. See website: http://www.investmentnews.com/article/20150702/FREE/150709968/classic-car-prices-have-surged-but-investing-in-them-is-another-story Classic cars top alternative investment classes. See website: https://www.telegraph.co.uk/investing/news/classic-cars-top-alternative-investment-asset-classes-192pc/ CZUJACK, C., MARTINS, M. F. O. (2004), “Do art specialists form unbiased pre-sale estimates? An application for Picasso paintings.”, Applied Economics Letters, Vol. 11, pp. 245-249.Definition Certification Ferrari Classiche. See website: https://auto.ferrari.com/en_EN/sports-cars-models/past-models/ Definition Estimate. See website: http://www.sothebys.com/en/Glossary.html/Definition Homoscedasticity. See website: https://www.statisticssolutions.com/homoscedasticity/ Definition Matching Numbers. See website: https://www.thoughtco.com/what-is-numbers-matching-classic-car-726148 DOUGHERTY, C. (2011), Introduction to Econometrics, 4th edition, Oxford University Press (USA). EKELUND, R. B. JR., RESSLER, R. W., WATSON, J. K. (1998), “Estimates, Bias and “No Sales” in Latin-American Art Auctions, 1977-1996.”, Journal of Cultural Economics 22, pp. 33-42. Ferrari Dino 246 GT. See website: https://www.bloemendaalcs.nl/autos/ferrari-246-gt-dino/ HALL, B. H. (1999), “Notes on Sample Selection Models”, Econometrics Laboratory, University of California, Berkeley (USA). HANSSENS, T., KARURANGA, D. (2017), “Price setting in Art Auction Markets.”HECKMAN, J. J., (1979), “Sample Selection Bias as a Specification Error”, Econometrica, Vol. 47, No. 1, pp. 153-161. KALMYKOVA, A., (2010), “Auction Houses and Contemporary Art: A Study of Outstanding Sales in 2007 and 2009”. KELLS, S., (2003), “Explaining the breadth of expert estimate ranges in auctions of rare books”, Research paper number 873, Department of Economics, University of Melbourne. Likelihood tests. See website: https://stats.idre.ucla.edu/other/mult-pkg/faq/general/faqhow-are-the-likelihood-ratio-wald-and-lagrange-multiplier-score-tests-different-andor-similar/ LOUARGAND, M.A., MCDANIEL, J.R., (1991), “Price efficiency in the Art Auction Market”, Journal of Cultural Economics, Vol. 15(2), pp. 53-65. MARINELLI, N., PALOMBA, G., (2008), “A Model for Pricing the Italian Contemporary Art Paintings at Auction”, EHUCHAPS, Universidad del Pais Vasco – Facultad de Ciencias Economicas y Empersariales.MCAFEE, R. P., MCMILLAN, J. (1987), “Auctions and Bidding”, Journal of Economic Literature, Vol. XXV (June 1987), pp. 699-738. MCANDREW, C., SMITH, J.L., THOMPSON, R., (2009), “The Impact of Reservation Prices on the Perceived Bias of Expert Appraisals of Fine Art.”, Journal of Applied Econometrics, Vol. 27, Issue 2, pp. 235-252. MEI, J., MOSES, M. (2001), “Art as an Investment and the Underperformance of Masterpieces.”, NYU Working Paper No. FIN-01-012. MILGROM, P. R., WEBER, R.J., (1982), “A Theory of Auctions and Competitive Bidding.”, Econometrica, Vol. 50, Issue 5, pp. 1089-1122. Official Auction of the Amelia Island Concours d’Elegance (2018). See website: http://www.sothebys.com/en/auctions/2018/rm-sothebys-amelia-island.html RAVIV, Y., (2009), ” Uncertainty and Auction Outcomes: Evidence from Used Car Auctions.”, Robert Day School of Economics and Finance. Selectivity & Treatment – Heckman 2-step Correction. See website: http://personal.rhul.ac.uk/uhte/006/ec5040/Selectivity.pdf Top Sales Classic Cars. See website: https://www.marketwatch.com/story/this-385-million-ferrari-tops-the-list-of-worlds-most-expensive-classic-cars-2017-07-18 VALSAN, C., SPROULE, R. (2007), ” Reservation Prices and Pre-Auction Estimates: A Study in Abstract Art.” Journal of Economic Literature, D440, G120, Z110. VOSILOV, R. (2015), “Uncertainty, Disagreement and Expert Price Estimates in Art Markets.”, Umea School of Business and Economics. WOOLDRIDGE, J. M. (2013), Introductory Econometrics: A Modern Approach, 5th edition, South-Western, Mason (USA). AnnexesTable 1: Number and Frequency of observations for each auction houseAuction HousesRM Sotheby’sBonhamsGooding & Company OtherTotalTotal 569 288 266 374 1497 100,00%38,01% 19,24% 17,77% 24,98% Sold476 189 227 205 1097 73,28%83,66% 65,63% 85,34% 54,81% Not Sold93 99 39 169 400 26,72%16,34% 34,38% 14,66% 45,19% BelowMin109 32 47 28 216 37,05%43,25% 31,37% 43,12% 23,33% AboveMax143 70 62 92 367 62,95%56,75% 68,63% 56,88% 76,67% Outside252 102 109 120 583 53,14%52,94% 53,97% 48,02% 58,54% Inside 224 87 118 85 514 46,86%47,06% 46,03% 51,98% 41,46% Table 2: Mean relative spread and relative distance to estimate for each auction houseAuction HousesTotal RM Sotheby’sBonhamsGooding & Company OtherRelative spread mean0.1987(0.0711) 0.2059(0.0663) 0.2062(0.0757) 0.1974(0.0649) 0.1827(0.0760)Relative distance to estimatemean0.0554(0.2204) 0.0343(0.2176) 0.0957(0.2469) 0.0343(0.1939) 0.0904(0.2203)Standard errors in parentheses Table 3: Number and Frequency of models for each auction houseTotal SoldNot soldAuction HousesModel RMSotheby’sBonhamsGooding &Company OtherFerrari 365 460 308 152 141 99 66 15430,73% 28,08% 38,00% 24,78% 34,38% 24,81% 41,18%Ferrari 250 307 241 66 153 44 67 4320,51% 21,97% 16,50% 26,89% 15,28% 25,19% 11,50%Ferrari 330 224 172 52 69 57 29 6914,96% 15,68% 13,00% 12,13% 19,79% 10,90% 18,45%Dino 246 213 153 60 51 47 30 8514,23% 13,95% 15,00% 8,96% 16,32% 11,28% 22,73%Other293 223 70 155 41 74 2319,57% 20,33% 17,50% 27,24% 14,24% 27,82% 6,15%Cabriolet 99 71 28 6,61% 71,72% 28,28% Steering LHD 1241 915 326 82,90% 73,73% 26,27% Steering RHD 256 182 74 17,10% 71,09% 28,91% Table 4: Number and Frequency of several variablesNumber and Frequency of Certified_by_FerrarischeTotal Sold Not Sold 191 13% 150 79% 41 21%Number and Frequency of ownersTotal SoldNot SoldFamous216 14% 175 81% 41 19%Single 11 1% 9 82% 2 18%Well Identified23 2% 18 78% 5 22%Number and Frequency of conditionConditionTotal SoldNot Sold0 436 29% 297 68% 139 32%1 426 29% 313 73% 113 27%2 635 42% 487 77% 148 23%1497 1097 400 Number and Frequency matching_engineTotal SoldNot Sold1279 85% 934 73% 345 27%Number and Frequency raceuseTotal SoldNot Sold91 6% 73 80% 18 20%Table 5: Number and Frequency of the Auction HousesAuction HousesTotal FrequencyS&F Auction 1 0,07%RM Sotheby’s569 38,01%Bonhams288 19,24%Coys146 9,75%H&H Classics 17 1,14%Historia14 0,94%Gooding & Company 266 17,77%Silverstone Classic 21 1,40%Artcurial94 6,28%AA Auction20 1,34%Aguttes3 0,20%Christie’s9 0,60%Cleveland Cowan’s5 0,33%Dorotheam2 0,13%Mecum22 1,47%Osenat16 1,07%PBA Galleries1 0,07%R&S Auction3 0,20%Table 6: Number and Frequency of Auction CountriesAuction CountryTotal FrequencyAustria 2 0,13%Belgium 8 0,53%Canada 2 0,13%France 186 12,42%Germany 32 2,14%Greece 2 0,13%Italy 112 7,48%Monaco 101 6,75%South Africa1 0,07%UK 264 17,64%US 787 52,57%Table 7: The “selection equation” in the sample selection models2-step method Maximum LikelihoodAuction countries United States 0.2310** 0.1401(0.1082) (0.1084)United Kingdom 0.1232 0.0794(0.1233) (0.1202)France 0.3162** 0.2927**(0.1366) (0.1322)Log(minimumestimatedprice)RM Sotheby’s -5.677*** -4.6315**(1.9760) (1.8170)Bonhams-3.7879** -4.1295**(1.9060) (1.8943)Gooding & Company -2.5337 -3.3073(2.6698) (2.6443)Other -3.5038** -3.3490**(1.6418) (1.5198)Auction housesRM Sotheby’s 0.2895 0.6018(1.0908) (1.0942)Bonhams0.9646 0.8285(1.1576) (1.1715)Gooding & Company 2.3779 1.4479(2.6694) (1.3940)Log(meanestimatedprice)RM Sotheby’s 5.5736*** 4.5166**(1.9838) (1.8251)Bonhams3.5932* 3.9442**(1.9143) (1.8933)Gooding & Company 2.3779 3.1433(2.6694) (2.6418)Other 3.3648** 3.2129**(1.6443) (1.5217)Car modelsFerrari 365 -0.2766*** -0.2641***(0.0841) (0.0780)Other -0.0544 -0.0549(0.1096) (0.1054)DesignersPininfarina0.2045* 0.2707**(0.1189) (0.1205)Pininfarina & Scaglietti0.1440 0.1801(0.1128) (0.1128)Famous owners 0.2452** 0.3792***(0.1170) (0.1265)Constant 1.2347 1.1901(0.8152) (0.8394)Standard errors in parentheses , ***,**,* indicate statistical significance at the 1%, 5% and 10% level respectively.Table 8: Estimation results for the models 4.4 – 4.82-step method Maximum likelihood OLS (?=0)Coeff. S.E. Coeff. S.E. Coeff. S.E.?r0.1394 0.1032 0.1369 0.1126 0.1557 0.1099?b0.7552*** 0.1563 0.7520*** 0.1812 0.8069*** 0.1754?g0.1927 0.1730 0.1898 0.1477 0.2216 0.1420?o-0.1230 0.1661 -0.1180 0.1964 -0.1208 0.1929?r0.9927*** 0.0079 0.9931*** 0.0085 0.9893*** 0.0081?b0.9492*** 0.0131 0.9498*** 0.0143 0.9407*** 0.0137?g0.9892*** 0.0127 0.9896*** 0.0107 0.9851*** 0.0102?o1.0216*** 0.0140 1.0218*** 0.0166 1.0155*** 0.0159Athrho-0.6157*** 0.1599 lnsigma-1.5756*** 0.0579 rho-0.5020 -.0.5481 0.1119 sigma 0.2046 0.2068 0.0120 lambda-0.1027* 0.0537 -0.1134 0.0290 ***,**,* indicate statistical significance at the 1%, 5% and 10% level respectively.Table 9: Test results of the hypotheses (1) until (6)H0Wald-test LR-test d.f.?2-critical value (1%) Result(1) Auction houses behave identically and are unbiased( ?r=?b=?g=?o=0 , ?r=?b=?g=?o=1)76.63 50.77 8 20.1 Rejected(2) Auction houses behave identically(?r=?b=?g=?o, ?r=?b=?g=?o)30.96 33.93 6 16.82 Rejected(3) Unbiasedness of RM Sotheby’s(?r=0, ?r=1)13.19 13.45 2 9.2 Rejected(4) Unbiasedness of Bonhams(?b=0, ?b=1)43.78 41.08 2 9.2 Rejected(5) Unbiasedness of Gooding & Company(?g=0, ?g=1)11.73 11.50 2 9.2 Rejected(6) Unbiasedness of “Other”(?o=0, ?o=1) 55.30 12.03 2 9.2 RejectedFigure 1: Scatterplot of Relative Spread and Log(meanestimatedprice)Table 10: Probability of obtaining a car with those characteristicsBase prob. Certified by Ferrari Famous owners Well identified owners Single owner RaceuseCabrioletCAR 1 Category 0 0.5054*** 0.5171*** 0.5118*** 0.1211** 0.0816*** 0.1033*** 0.5353***(0.0042) (0.0138) (0.0098) (0.0542) (0.1566) (0.0292) (0.0354)Category 0.1 0.1240*** 0.1168*** 0.0912*** 0.1555 0.1301 0.2143*** 0.0859***(0.0193) (0.0226) (0.0204) (0.1082) (0.1101) (0.0612) (0.0247)Category 0.2 0.2616*** 0.2747*** 0.2356*** 0.4756*** 0.3688** 0.5216*** 0.2737***(0.0225) (0.0272) (0.0292) (0.1149) (0.1508) (0.0716) (0.0367)Category 0.3 0.0993*** 0.0799*** 0.1415*** 0.2138** 0.3812*** 0.1432*** 0.0930***(0.0202) (0.0217) (0.0304) (0.0842) (0.1387) (0.0513) (0.0293)Category 0.4 0.0093 0.0113 0.0192 0.0377 0.0381 0.0134 0.0082(0.0059) (0.0078) (0.0128) (0.0366) (0.0512) (0.0133) (0.0072)Category 0.5 0.0003 2.86e-100.0006 3.62e-101.31e-100.0041 0.0036(0.0002) (4.35e-10) (0.0012) (4.42e-10) 1.42e-10(0.0033) (0.0042)CAR 2 Category 0 0.5986*** 0.0076*** 0.6028*** 0.1379*** 0.1379*** 0.1600*** 0.6230***(0.0080) (0.0179) (0.0153) (0.0207) (0.0424) (0.0532) (0.0565)Category 0.1 0.1138*** 0.1085*** 0.0834*** 0.1527 0.1233 0.2161*** 0.0803***(0.0218) (0.0244) (0.0220) (0.1033) (0.1036) (0.0682) (0.0281)Category 0.2 0.1796*** 0.1910*** 0.1591*** 0.3705*** 0.2743** 0.4246*** 0.1929***(0.0225) (0.0265) (0.0262) (0.1063) (0.1295) (0.0765) (0.0410)Category 0.3 0.0962*** 0.0783*** 0.1321*** 0.2476 0.4109*** 0.1765*** 0.0928***(0.0207) (0.0219) (0.0293) (0.0922) (0.1352) (0.0606) (0.0313)Category 0.4 0.0117* 0.0145 0.0226 0.0543 0.0536 0.0227 0.0108(0.0069) (0.0097) (0.0139) (0.0522) (0.0698) (0.0209) (0.0091)Category 0.5 1.89e-101.76e-163.56e-102.19e-167.14e-172.80e-092.48e-09(1.56e-10) (0.0008) (6.09e-10) (0.0001) (1.73e-15) (2.38e-09) (3.04e-09)Car 1 has following characteristics: Ferrari 365, auctioned by RM Sotheby’s, designed by Pininfarina & Scaglietti and having a matching engine. Car 2 has following characteristics: Ferrari 330, auctioned by RM Sotheby’s, designed by Pininfarina and having a matching engine.Standard errors in parentheses, ***,**,* indicate statistical significance at the 1%, 5% and 10% level respectively.Table 11: Results of OLS Regression 5.2 relative spread on subjective and objective variablesVARIABLES RELATIVE_SPREADCar modelsF250 0.0133*(0.00723)F365 0.00741(0.00626)Other0.0159**(0.00754)Dino 246 0.00339(0.00787)Cabriolet 0.00484(0.00763)Certified_by_ferrariclassiche-0.00483(0.00533)Famous_owners0.0174***(0.00614)Single_owner0.0447*(0.0242)Well_identified_owners0.0297*(0.0159)Matching_engine-0.000554(0.00515)Raceuse0.00504(0.00809)Designers Pininfarina-0.00496(0.00650)Pininfarina & Scaglietti-0.0265***(0.00619)Auction housesRM Sotheby’s0.00143(0.00524)Gooding & Company -0.00290(0.00588)Other-0.0240***(0.00597)Log(meanestimatedprice) -0.00761***(0.00230)Constant 0.305***(0.0308)Observations1,496R-squared0.076Standard errors in parentheses, ***,**,* indicate statistical significance at the 1%, 5% and 10% level respectively.Table 12: Marginal effects of Multinomial Logistic Regression 5.3VARIABLES Category 0 Category 0.1 Category 0.2 Category 0.3 Category 0.4 Category 0.5Car modelsF330 0.357*** -0.0218 -0.301*** -0.0165 -0.00639 -0.0122(0.0270) (0.0371) (0.0382) (0.0355) (0.0189) (0.00986)F250 0.294*** -0.0708** -0.223*** -0.00658 0.0156 -0.00902(0.0158) (0.0345) (0.0401) (0.0361) (0.0267) (0.00935)F365 0.217*** -0.0411 -0.180*** 0.0153 0.00105 -0.0123(0.00795) (0.0305) (0.0372) (0.0330) (0.0191) (0.0114)Other0.0169 -0.00224 -0.159*** 0.0951* 0.0531 -0.00346(0.0155) (0.0460) (0.0526) (0.0566) (0.0464) (0.00433)Cabriolet 0.0240 -0.0807* 0.0335 -0.00928 -0.00355 0.0361(0.0238) (0.0442) (0.0549) (0.0403) (0.0212) (0.0270)Certified_by_ferrariclassiche0.0119 -0.0166 0.0379 -0.0385 0.00970 -0.00441**(0.0122) (0.0352) (0.0408) (0.0283) (0.0194) (0.00178)Famous_owners0.00542 -0.0785** -0.0653 0.0881*** 0.0465* 0.00377(0.00657) (0.0317) (0.0402) (0.0339) (0.0248) (0.00770)Single_owner-0.00268** -0.129 -0.114 0.211 0.0396 -0.00403**(0.00127) (0.108) (0.156) (0.129) (0.0834) (0.00161)Well_identified_owners-0.00268** -0.100 0.0221 0.0497 0.0354 -0.00404**(0.00127) (0.104) (0.115) (0.0793) (0.0547) (0.00161)Matching_engine-0.00879 0.00772 0.0204 -0.0261 0.00656 0.000296(0.00970) (0.0322) (0.0374) (0.0285) (0.0128) (0.00326)Raceuse-0.00274** -0.0501 0.0621 -0.0324 -0.00953 0.0327(0.00130) (0.0511) (0.0580) (0.0382) (0.0182) (0.0226)Designers Pininfarina-0.00674 -0.00693 0.0562 -0.0293 -0.0188 0.00558(0.00643) (0.0409) (0.0440) (0.0283) (0.0152) (0.00465)Pininfarina & Scaglietti0.00308 0.0985** 0.0271 -0.0865*** -0.0380*** -0.00420(0.00484) (0.0416) (0.0441) (0.0286) (0.0140) (0.00272)Auction HousesRM Sotheby’s0.174*** -0.0978*** -0.0570* -0.00256 -0.0120 -0.00447(0.00136) (0.0259) (0.0310) (0.0244) (0.0102) (0.00430)Gooding & Company -0.000424 0.0357 -0.0311 -0.0150 0.0159 -0.00503**(0.00109) (0.0386) (0.0444) (0.0323) (0.0192) (0.00220)Other0.232*** 0.0445 -0.157*** -0.114*** -2.98e-05 -0.00631(0.00438) (0.0288) (0.0314) (0.0205) (0.0125) (0.00406)Log(meanestimatedprice) -0.00161 0.0134 0.0241 -0.0156 -0.0171*** -0.00313(0.00150) (0.0135) (0.0155) (0.0120) (0.00613) (0.00267)Observations1,496 1,496 1,496 1,496 1,496 1,496Standard errors in parentheses, ***,**,* indicate statistical significance at the 1%, 5% and 10% level respectively.Table 13: Comparison of expected and obtained results for the two different cars of table 10. EXPECTED OBTAINEDCategory Category0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5CAR 1 Certified by FerrariClassiche+ + + – – – + – + – + -Famous Owners – – – + + + + – – + + +Well_identified_owners+ + + – – – – + + + + -Single_owners+ + + – – – – + + + + -Raceuse- – – + + + – + + + + +Cabriolet NHM NHM NHM NHM NHM NHM + – + – – +CAR 2 Certified by FerrariClassiche+ + + – – – – – + – + -Famous_owners- – – + + + + – – + + +Well_identified_owners+ + + – – – – + + + + -Single_owners+ + + – – – – + + + + -Raceuse- – – + + + – + + + + +Cabriolet NHM NHM NHM NHM NHM NHM + – + – – +Car 1 has following characteristics: Ferrari 365, auctioned by RM Sotheby’s, designed by Pininfarina & Scaglietti and having a matching engine. Car 2 has following characteristics: Ferrari 330, auctioned by RM Sotheby’s, designed by Pininfarina and having a matching engine.*NHM = No hypothesis made.*The highlighted signs indicate statistical significance at the 10% level.Table 14: Comparison of expected and obtained results for equation 5.2RELATIVE_SPREAD (5.2)VARIABLES EXPECTED SIGN OBTAINED SIGN SIGNIFICANT? (at 10% level) HYPOTHESIS CONFIRMED?Car ModelsF250 + + YES YESF365 NHM + NO OtherNHM + YES Dino 246 NHM + NO Cabriolet NHM + NO Certified_by_ferrariclassiche- – NO Famous_owners+ + YES YESSingle_owner- + YES Well_identified_owners- + YES Matching_engine- – NO Raceuse+ + NO Designers PininfarinaNHM – NO Pininfarina & ScagliettiNHM – YES Auction housesRM Sotheby’sNHM + NO Gooding & Company NHM – NO Other+ – YES Log(meanestimatedprice) – – YES YES*NHM = No hypothesis made Table 15: Comparison of the expected and obtained results of equation 5.3EXPECTED OBTAINEDCategory Category0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5Car ModelsF330 NHM NHM NHM NHM NHM NHM + – – – – -F250 – – – + + + + – – – + -F365 NHM NHM NHM NHM NHM NHM + – – + + -OtherNHM NHM NHM NHM NHM NHM + – – + + -Cabriolet NHM NHM NHM NHM NHM NHM + – + – – +Certified_by_ferrariclassiche+ + + – – – + – + – + -Famous_owners- – – + + + + – – + + +Single_owner+ + + – – – – – – + + -Well_identified_owners+ + + – – – – – + + + -Matching_engine+ + + – – – – + + – + +Raceuse- – – + + + – – + – – +Designers PininfarinaNHM NHM NHM NHM NHM NHM – – + – – +Pininfarina & ScagliettiNHM NHM NHM NHM NHM NHM + + + – – -Auction housesRM Sotheby’sNHM NHM NHM NHM NHM NHM + – – – – -Gooding & Company NHM NHM NHM NHM NHM NHM – + – – + -Other- – – + + + + + – – – -Log(meanestimatedprice) + + + – – – – + + – – -*NHM = No hypothesis made.*The highlighted signs indicate statistical significance at the 10% level.Table 16: Marginal Effects of the logit regressions 6.1-6.3NOSALE (6.1) BELOWMIN (6.2) ABOVEMAX (6.3)VARIABLES Predicted prob. Predicted prob. Predicted prob.Car ModelsF330 -0.0162 0.0583 0.0860(0.0500) (0.0541) (0.0620)F250 -0.00132 -0.0373 0.0437(0.0493) (0.0513) (0.0599)F365 0.0734* 0.0292 0.0479(0.0377) (0.0438) (0.0491)Other0.0257 -0.0562 0.0474(0.0464) (0.0539) (0.0600)Cabriolet 0.0398 0.00779 0.0273(0.0477) (0.0461) (0.0620)Certified_by_ferrariclassiche-0.0411 -0.111*** 0.126***(0.0358) (0.0404) (0.0418)Famous_owners-0.0754** -0.0832** 0.137***(0.0371) (0.0362) (0.0393)Single_owner-0.0175 0.0633 0.281*(0.144) (0.135) (0.148)Well_identified_owners0.0301 -0.0118 -0.0223(0.0934) (0.111) (0.112)Matching_engine-0.00622 -0.0524 0.0413(0.0329) (0.0320) (0.0421)Raceuse-0.0571 0.00566 -0.00579(0.0561) (0.0535) (0.0661)Designers Pininfarina-0.0605 -0.0843** 0.0899*(0.0376) (0.0393) (0.0498)Pininfarina & Scaglietti-0.0466 -0.0970** 0.0748(0.0377) (0.0382) (0.0511)Auction housesRM Sotheby’s-0.202*** 0.0499 -0.0382(0.0298) (0.0374) (0.0395)Gooding & Company -0.240*** 0.0142 -0.0569(0.0374) (0.0430) (0.0469)Other0.0736** -0.0625 0.0577(0.0288) (0.0434) (0.0445)Log(meanestimatedprice) 0.0401*** 0.0316** -0.0506***(0.0127) (0.0143) (0.0173)Relative spread -0.716*** -0.681*** -0.742***(0.161) (0.184) (0.207)Observations1,496 1,096 1,096Standard errors in parentheses, ***,**,* indicate statistical significance at the 1%, 5% and 10% level respectively.Table 17: Comparison of expectations and results of equation 6.1 ‘NOSALE’NOSALE (6.1)VARIABLES EXPECTED SIGN OBTAINED SIGN SIGNIFICANT? (at 10% level) HYPOTHESIS CONFIRMED?Car ModelsF330 NHM – F250 + – F365 NHM + YES OtherNHM + Cabriolet NHM + Certified_by_ferrariclassiche- – Famous_owners- – YES YESSingle_owner- – Well_identified_owners- + Matching_engine- – Raceuse- – Designers PininfarinaNHM – Pininfarina & ScagliettiNHM – Auction housesRM Sotheby’sNHM – YES Gooding & Company NHM – YES OtherNHM + YES Log(meanestimatedprice) + + YES YESRelative spread – – YES YES*NHM = No hypothesis made