Automobile Prices in Market Equilibrium with Automobile Prices in Market Equilibrium with Unobserved

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Text of Automobile Prices in Market Equilibrium with Automobile Prices in Market Equilibrium with Unobserved

  • Automobile Prices in Market Equilibrium with Unobserved Price Discrimination∗

    Xavier D’Haultfœuille† Isis Durrmeyer‡ Philippe Février§

    December 24, 2014


    In markets where sellers are able to price discriminate, or the buyers to bargain,

    individuals receive discounts over the posted prices that are usually not observed

    by the econometrician. This paper considers the structural estimation of a demand

    and supply model à la Berry et al. (1995) when only posted prices are observed.

    We consider that heterogeneous discounts occur due to price discrimination by firms

    on observable characteristics of consumers. Within this framework, identification is

    achieved by assuming that the marginal costs of producing and selling the goods do

    not depend on the characteristics of the buyers. We also require a condition relating

    the posted prices to the prices actually paid. For instance, we can assume that at

    least one group of individuals pays the posted prices. Under these two conditions,

    the demand and supply parameters, as well as the exact discounts corresponding to

    each type of consumers, can be identified. We apply our methodology to estimate the

    demand and supply in the new automobile market in France. Results suggest that

    discounting arising from price discrimination is important. The average discount is

    estimated to be 10.5%, with large variation depending on the buyers’ characteristics

    and cars’ specifications. Our results are in line with discounts generally observed in

    European and American automobile markets.

    ∗We would like to thank Steven Berry, Juan Esteban Carranza, Rob Clark, Pierre Dubois, Philippe Gagnepain, Gautam Gowrisankaran, Alessandro Iaria, John Morrow, Kathleen Nosal, Mario Pagliero, Philipp Schmidt-Dengler, Michelle Sovinsky, Hidenori Takahashi, Yuya Takahashi, Frank Verboven, Naoki Wakamori and the participants of various seminars and conferences for their valuable comments. We also thank Pierre-Louis Debar and Julien Mollet from the CCFA for providing us with the data. Isis Durrmeyer acknowledges financial support from the Deutsche Forschungsgemeinschaft through SFB-TR 15. †CREST. E-mail: ‡University of Mannheim. E-mail: §CREST. E-mail:


  • 1 Introduction

    The standard aggregate-level estimation of demand and supply models of differentiated products relies on the observation of the market shares and the characteristics of the products, in particular prices (see Berry 1994). Because of price discrimination and price negotiation, transaction prices for an identical product may differ from one individual to another. Sellers can practice third degree price discrimination according to observable demographic characteristics such as age, gender or city of residence. There may also be room for individual negotiation: the sellers are willing to offer discounts to the consumers that aggressively negotiate the prices. Automobiles, furniture, kitchens or mobile phone contracts are examples for which there is either documented or anecdotal evidence that consumers receive some discounts (on new automobiles, see, e.g. Ayres & Siegelman 1995, Goldberg 1996, Harless & Hoffer 2002, Morton et al. 2003, Langer 2012, Chandra et al. 2013).1 Loans and insured mortgages have also proved to be negotiable (see Charles et al. 2008, Allen et al. 2014). Such phenomena also exist in vertical relationships between producers and retailers. Producers are required to edit general terms and conditions of sale. These conditions are then the starting point for individual negotiation with each retailer.

    In all these cases, precise data on transaction prices may be hard to obtain. One typically observes either transaction prices on a small sample issued from a survey, or only posted prices on a large sample. In the first case, price discrimination can be studied but policy exercises cannot be performed. With large data, on the other hand, policy simulations are usually done without taking the issue of limited observation of prices into account. Because the instrumental variables approach used in Berry et al. (1995, henceforth, BLP) to control for price endogeneity does not solve this nonclassical measurement error problem (namely, observing posted prices instead of transaction prices), ignoring it generally results in an inconsistent estimation of the structural parameters and biases in policy exercises.

    This paper proposes a method to estimate a structural demand and supply model with unobserved discounts. Our rationale for the existence of discounts over the posted prices is that discounts allow firms to price discriminate between heterogeneous consumers and thus extract more surplus than they would with a uniform price.2 Sellers edit only one

    1In France, it is also commonly admitted that negotiation is possible when purchasing a new car. An article published in October 2011 by Le Figaro, which is the second largest French national newspaper, suggests that discounts up to 26% can be obtained.

    2In some cases, all profits could be higher if all firms did not price discriminate (see, e.g. Holmes 1989, Corts 1998). But without any commitment devise against price discrimination, price discrimination occurs for each firm at equilibrium.


  • price, namely the posted price, since it is usually legally forbidden to price discriminate between consumers and difficult to implement, but in practice the transaction prices differ from one individual to another. We suppose that sellers use observable characteristics of the buyers to price discriminate and set an optimal discount over the posted price. Importantly, we assume that the sellers do not have more information about consumers than the econometrician. This assumption may be problematic in settings where there are few buyers, such as vertical relationships between producers and retailers. But in markets where sellers do not know the buyers before the transaction, it seems plausible to assume that price discrimination is based only on a few easily observable characteristics, such as sex, age and the city of residence.

    We therefore extend the random coefficient discrete choice model of demand popularized by BLP to allow for unobserved price discrimination. BLP exploit the exogeneity of observed product characteristics, apart from price, to yield moment conditions involving the param- eters of interest. Their method does not apply directly to our framework, yet, because the moment conditions are not valid anymore if we replace the unobserved transaction prices with posted prices. Instead, we rely on structural assumption from the supply side, and replace the unobserved prices by their expression stemming from the first-order condition of profit maximization.

    These first-order conditions have identifying power under two assumptions. First, the marginal cost of a product is supposed to be identical for all buyers. This amounts to neglecting differences in selling costs to different consumers in the total cost of a product. This assumption is likely to be satisfied in many markets, such as the automobile market, where the major part of the marginal cost is production, not sale, and the cost of selling is probably not very different from one consumer to another. The second condition states, basically, that there is a known relationship between observed and transaction prices. In our application, we suppose that the prices posted by the sellers correspond to the highest discriminatory price, so that some consumers actually pay these observed posted prices. In other words, we normalize the optimal discount for one group of consumers to be zero. Such an assumption is necessary since otherwise, we could shift all discounts by an arbitrary constant. It is also consistent with empirical evidence reported by several surveys, such as the one made by Cetelem in 2012 in France (L’Automobile en Europe: 5 Leviers pour Rebondir 2013).

    The ideas underlying our approach can be applied to various settings where the information on prices is limited, with different assumptions on observed prices. This is the case in particular if we observe the average transaction prices paid by all consumers. In this setting,


  • there is a direct link between observed and transaction prices and no further assumption on prices is needed. Our methodology could also be implemented in a setting where demand is observed in different markets, while the prices are observed only in a subset of markets, as could be the case for example with the automobile market in Europe or supermarket chains in different municipalities. Two recent papers have used similar ideas in different settings. Miller & Osborne (2014) adopt a similar methodology to analyze the cement industry. They only observe average price and the total quantity of cement purchased in the US. They allow as well for price discrimination across US counties. They compute the optimal prices and quantities for each location using the equilibrium conditions. Then they compare the corresponding average prices and total quantities with the observed ones. Apart from this similarity, their model and estimation strategy is very different from ours. In particular, due to data limitations, they cannot account for observed and unobserved differences in preferences across counties. Also related is the paper by Dubois & Lasio (2014), which estimates marginal costs when observed prices are regulated and, therefore, no longer related to the marginal cost. They use the first-order conditions of the firms on other countries that do not regu

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