“Demand for Rarity: Evidence from a Collectible Good”, 2022-02-28 ():
Markets for art, coins and other collectibles, culinary delicacies and eco-tourism suggest that consumers value the rarity of many goods. While empirical evidence supports higher prices for rare goods, isolating the value of rarity has proven difficult.
I analyze prices for a collectible card game [Magic: The Gathering] and show that:
goods that are designated as rare trade at higher prices than functionally equivalent substitutes. Importantly, I use novel features of this market to account for scarcity, observed and unobserved product characteristics and separately identify rarity effects.
These results have important implications for markets ranging from luxury goods to conservation of endangered species.
…In this market, the manufacturer labels goods according to 4 different rarity categories that approximate relative rarity. However, changes in product design combined with manufacturing technology constraints affect the market supply within and across rarity categories over time. Using these changes, I calculate the odds of obtaining a particular card in a retail pack, a proxy for quantity. Then, using 2 different empirical strategies, I non-parametrically estimate the effect of odds on prices and separately identify the effect of rarity. To do this, I collect secondary market prices on thousands of unique goods (cards) from a popular online marketplace [TCGplayer]. I combine these data with detailed product-level information where I observe every characteristic appearing on each card. By comparing functionally equivalent and, in some cases otherwise identical cards, I isolate the effect of rarity designation from other factors such as scarcity and unobserved quality.
The 2 empirical approaches form upper and lower bounds on the rarity values.
The first strategy leverages variation in prices and odds across different cards in each of the rarity categories. I collect data on ~3,600 recently-printed cards over a 6-week period in 2019. I employ a cross-sectional hedonic framework using fixed-effects for observed product characteristics to flexibly model functional differences across cards. I show prices are inversely related to the odds of obtaining a particular card in a retail pack. However, conditional on these odds and product characteristics, prices are substantially higher for cards with rare designations. On average, prices for cards in the highest rarity category are 70–90× higher than cards in the common category, all else equal. I present several robustness checks investigating the salience of scarcity and the possibility of unobserved (to the econometrician) product differences across rarity categories. To the extent that remaining unobserved quality differences are not captured by the model, these estimates are an upper bound on the true rarity values.
The second strategy uses variation in rarity designation within individual cards that are reprinted, many times more than once, at different rarity categories. I collect prices for ~600 cards that experienced these ‘rarity shifts.’ I account for observable and unobservable card characteristics with individual card fixed-effects. Since the rarity-shifted cards are identical other than the change in rarity designation, I attribute observed price differences to rarity value. I find prices are substantially higher for cards printed with rare designations relative to the same cards with common designations. For reasons discussed below, rarity values measured by these rarity shifts are likely biased downwards and therefore represent a lower bound on the true rarity values.
In both empirical approaches, I can easily rule out cost-based explanations for the observed price differences because manufacturing costs are equivalent across rarity categories. The observed price effects are also independent of scarcity value, as captured by the odds of obtaining a particular card in a retail pack, and do not seem to be driven by functional differences across cards. Since both empirical approaches yield large positive rarity values, these results are perhaps the best evidence to date in support of a demand for rarity.
…Moving from common to rare increases log price by 0.445 or about 56 per cent. Moving from common to mythic rare increases log price by 0.726 or about 107 per cent. The effect for foil cards is similar in magnitude. These results, namely that variation in rarity designation within-card yields large price effects, are quite remarkable and provide further evidence of rarity effects.