Price determination for a collectible good: the case of rare U.S. coins.

• Author: Dickie, Mark

1. Introduction

   Researchers investigating markets for collectible goods such as paintings [1; 2; 6; 12], antique furniture [7], Stradivarius violins [14], wine [8; 10] and postage stamps [15] often report rates of return to holding collectibles that are both low [2; 6; 7; 8; 12] and volatile [6; 7; 8; 12]. Baumol [2] argues that the market for paintings of noted, deceased artists has no long-run equilibrium price, because the market is characterized by infrequent trades of

   unique assets which are available in fixed supply. His empirical analysis supports the idea that paintings experience unpredictable price changes and highly dispersed rates of return with a mean near zero. In contrast Anderson [1) reports estimated equations explaining approximately 60 percent of the variation in (log) prices of paintings based on the size of painting, date of sale, and a constructed measure of repute of the artist. Other researchers have examined markets with more frequent transactions and greater substitutability among the goods traded. Schnitzel [15) finds that year-to-year changes in prices of postage stamps are predictable based on age of the stamp and quantity printed. Ross and Zondervan [14) report that variations in quality affect prices, but not rates of return, of Stradivarius violins, a result which is consistent with user benefits' being invariant with respect to quality.

   Among markets for collectibles, the market for rare U.S. coins is active and well organized, and faces the potential for increased federal regulation. Annual sales are estimated at $5 billion [16]. Two Wall Street brokerages recently have formed multimillion-dollar limited partnerships to invest in rare coins, and some coins now are traded on electronic exchanges [5]. These innovations have come amid calls for increased regulation to guard against fraudulent grading of coins [5; 16]. A major determinant of the price of a collectible coin is its "grade," a measure of condition reflecting qualities such as sharpness of features. Regulators accuse coin dealers of defrauding collectors of millions of dollars annually by assigning higher-than-warranted grades to the coins dealers sell while downgrading coins they buy. For example, the Federal Trade Commission (FTC) filed a complaint against one dealer alleging $40 million in fraud and ordered another to return $400,000 to customers [5]. Independent, third-party grading firms claim to reduce the potential for fraud, yet the FTC recently obtained consent decrees from two of the three largest grading services, charging one with making "numerous false and misleading claims" [13].

   Despite the growth of the coin industry and the potential for fraud and increased regulation, there has been no systematic investigation of price determination for collectible coins. This paper extends the literature on collectibles markets to examine price determination for rare U.S. coins. Specifically, we address three issues. First, we note that if the coin market attains an equilibrium, then coin prices should be predictably related to the characteristics of coins valued by collectors. There is general agreement among coin dealers and collectors on the characteristics of coins which affect price, and data are available on all relevant characteristics.(1) We use eight years' data on over 1300 coins of five denominations to quantify the relationship between price and characteristics and find that coin prices are largely predictable. We then compare conditions in the coin market with those in the market for paintings to offer additional insight on Baumol's explanations for the absence of a long-run equilibrium price in the market for a collectible good. Second, we examine the effect of grade on price by testing whether the market process generating prices is identical across two grades. We reject the hypothesis that the relationship between prices and characteristics is identical across grades, and make illustrative calculations of the effect of a change in grade on price, holding other characteristics equal. Results are interpreted in light of potential for fraudulent grading and increased regulation. Finally, we test whether coin characteristics affect rates of return. After correcting for unequal variances in rates of return, we find that rates vary with characteristics, suggesting that some coins provide collectors with greater user benefits than others.

2. The Coin Market: Background and Data

   Collectors identify coins based on the following characteristics: (1) denomination, whether cent, nickel, dime, quarter- or half-dollar, or dollar; (2) vintage, or the date struck on the coin, which at least approximates the year minted; (3) type, or the image struck on the face of the coin; (4) the mint where the coin was produced; (5) the value of the silver contained in the coin; and (6) the condition or grade of the coin. An unusual feature of coins as heterogeneous goods is that the characteristics suffice to identify a coin uniquely, in the sense that two coins of the same denomination, vintage, type, mint and condition are essentially perfect substitutes.

   These characteristics are expected to influence price because they affect the relative values collectors attach to different coins. While motives for collecting may vary, coin dealers distinguish two broad classes of numismatists, which we term "general" and "type" collectors. Other things equal, both classes prefer coins preserved in better condition, but the classes differ in how they value the other characteristics of coins.

   The "general" collector chooses a particular type of coin, such as Barber quarters, and assembles a complete set of vintages and mints of Barber quarters. The "type" collector, on the other hand, assembles one specimen of each type of coin minted within some category, or one specimen of each type-mint or type-vintage combination. For example, a type collector might choose a denomination such as quarter and assemble one specimen from each mint for each type of quarter minted, without regard to vintage.

   In any event, numismatists choose a manner of collecting based on individual tastes and budgets, and thus exert demands differentiated by denomination, type, vintage and mint. The market value of embodied silver may also influence the price of a coin, since coins may be preserved as collectibles while held jointly as stores of silver.

   Data on coin prices and characteristics are taken from 1984 through 1991 editions of Yeoman, A Guide Book of United States Coins [19]. These publications list the quantities minted of various coins by denomination, vintage, type, and mint, as well as the silver content of coins and the previous year's prices for each coin by condition. The prices, which are estimated based on auction prices as well as data supplied by numismatic experts, thus pertain to the years 1983-90. Vintages used in this study range from the first regular U.S. mint issues of each denomination through 1964 for cents, nickels, dimes, quarter- and half-dollars. The final vintage (1964) was chosen as the last year prior to a major change in the metallic composition of U.S. coins: the silver content of the half-dollar was reduced by 50 percent in 1965, when silver was entirely eliminated from both the dime and quarter. Dollar coins are excluded because their metallic composition was changed 30 years before the other denominations: silver dollars were not minted for general circulation after 1935.

   We include prices for two grades of coins in our data: "mint state" MS-60 and "extremely fine" EF-40. The MS-60 grade was chosen because it represents the average condition of newly minted coins. Although higher-grade coins exist, their price series are generally much less complete than the MS-60 series. The EF-40 grade in contrast represents a coin with all features sharp and well-defined but lightly worn on all surfaces.

   Each denominational data set was assembled into cross sectional-time series format, where the year in which price is observed defines a point in time and the unique combination of denomination, vintage, type and mint defines a cross sectional unit. Table I reports the number of observations as well as sample means and standard deviations by denomination of all variables used in the empirical analysis. P refers to the price of the coin, while...