Academic journal article Economic Inquiry

A Bandwagon Effect in Personalized License Plates?

Academic journal article Economic Inquiry

A Bandwagon Effect in Personalized License Plates?

Article excerpt

A BANDWAGON EFFECT IN PERSONALIZED LICENSE PLATES?

The bandwagon effect is a consumption externality that exists when an individual's demand for a good is increased by his observation of other consumers using that good. This paper models a product demand curve with a bandwagon effect and, using data on sales of personalized license plates, estimates such a demand curve. Certain more conventional models of product demand, including information diffusion and habit formation models, are observationally similar to the bandwagon model, despite being conceptually different from it. I attempt to use the license plate data to discriminate between the bandwagon model and these other models.

In 1950, Harvey Leibenstein described the impact on product demand curves of what he called a "bandwagon effect." The bandwagon effect was said to exist if peoples' valuations of a good (and thus demand for that good) increased when they observed others consuming the good. No one to my knowledge has attempted to empirically verify the existence of or estimate the magnitude of a bandwagon effect in any product market. In this paper I attempt to do both by looking at the demand for personalized license plates, a good that could plausibly be subject to a bandwagon effect.

In the first section of the paper I develop a simple model of product demand in the presence of a bandwagon effect. The model is based on Leibenstein's treatment but is modified to fit the case of personalized license plates. In the second section, data on the sales of personalized plates are described and used to estimate a demand function. The results of this estimation are consistent with the theoretical model of the bandwagon effect.

The search for the bandwagon effect cannot end there, however. The bandwagon model, in which consumers are moved by considerations of fashion and status emulation, is observationally similar to other well-known but conceptually quite different models of product demand in which consumers are more sober and level-headed. In particular, models of information diffusion or habit formation imply patterns in the data very much like those that follow from the bandwagon model. Section III discusses this matter in more detail and presents statistical tests designed to differentiate between the bandwagon model and alternative models of product demand. In the final section I draw some conclusions from the empirical evidence.

I. THE BANDWAGON EFFECT

Consider a product that lasts for a single period of well-defined length. Each period, a consumer may purchase at most one of the product. The personalized license plate is a product of this sort, as are subscriptions to a particular magazine, hairstyles, club memberships, vacations to chic resorts, etc. Assume first that there is no bandwagon effect and let (1) [V.sub.it]([X.sub.it], [Z.sub.t]) represent the value of the product to individual i in period t, where [X.sub.it] is a vector of individual characteristics such as age or income, and [Z.sub.t] is a vector of product characteristics in period t. The function [V.sub.it] is a random variable defined over the population of potential buyers. Let [F.sub.t](V) = prob([V.sub.it] < V) in period t. Then, if [M.sub.t] is the population of potential consumers in period t, market level demand in period t is (2) [Q.sub.t] = [M.sub.t][1 - [F.sub.t]([p.sub.t])] where [p.sub.t] is the product price. Demand is a decreasing function of price. It also depends on product characteristics and the distribution of personal characteristics in the population.

Adding a bandwagon effect to this model involves allowing individuals' preferences to depend on aggregate behavior. Liebenstein assumed that in the presence of a bandwagon effect the quantity of a product demanded by each consumer at a given price depended on market level demand at that price. This creates a problem when moving from individual to market level demand functions, for the market level demand curve is no longer a lateral summation of individual demand curves. …

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