Academic journal article Economic Inquiry

Testing for Efficiency in Lotto Markets

Academic journal article Economic Inquiry

Testing for Efficiency in Lotto Markets

Article excerpt

I. INTRODUCTION

When some agents behave irrationally or when some markets operate inefficiently, opportunities exist for others to profit. The profit motive tends to eliminate these opportunities so that markets will tend to be efficient. Interest in the efficiency of markets has led to much empirical testing. An enormous amount of work has been done in the field of finance investigating the efficiency of various financial markets.

Another area where individual rationality and market efficiency are prominent is wagering markets. While the economic significance of financial markets dwarfs that of wagering markets, gambling events offer excellent natural experiments for examining the same sort of economic behavior exhibited in financial markets. One gambling instrument, state-sponsored lotto games, is particularly interesting because of the way the mathematical expected value of a bet is determined.

Lotto differs from most other lottery products because the expected monetary value of a ticket depends on the behavior of other bettors. The expected value also depends on the amount of money rolled over (if any) from the previous drawing's jackpot. Repeated drawings of a lotto game thus present consumers with a range of betting opportunities, some more favorable than others. In deciding whether to purchase tickets, bettors must evaluate the expected monetary return, which requires them to forecast sales. A rational expectations equilibrium in the lotto market will not exist unless bettors' individual forecasts lead to an overall level of sales and ex post expected value that conform to their original expectations.

There are several aspects of lotto that make its study worthwhile. As with financial markets, a significant portion of the population participates. Just like investors, lotto players must formulate expectations about the return on their investment. Expected monetary return depends on the behavior of other players. Unlike investing in the stock market, however, the outcome of the purchase of a lotto ticket is based on objective probabilities. As Thaler and Ziemba [1988, 162] point out, the conditions for learning are optimal in lotto because there is quick and repeated feedback. If an efficient market equilibrium does not exist in lotto, we should not be optimistic about finding one in more complicated financial markets.

The next section introduces the notions of efficiency developed by Fama [1970] and applies them to wagering markets. The third section follows with an explanation of the lotto game and how the expected monetary value of a bet is determined. The fourth section contains tests of the weak form of market efficiency using data from the Kentucky, Massachusetts, and Ohio lotto games. Finally, in the fifth section strong-form efficiency is evaluated using these same games and applying the concept of a rational expectations equilibrium.

Unsurprisingly, we find that very rarely do lotto games offer a positive net expected return, thus meeting the requirements of weak-form efficiency. More importantly, we find general support for the existence of a rational expectations equilibrium in lotto markets. In most cases individual bettors' decisions to play generate a level of sales that conform to their original expectations of the expected value of a lotto ticket.

II. EFFICIENCY IN WAGERING MAVKETS

A capital market is efficient if there are no investment strategies that will yield abnormally high returns. Fama [1970] defines efficiency to mean that security prices reflect all the information contained in a given information set. If the information set is comprised of only historical prices, the market is weak-form efficient. If the information set includes all publicly available information, the market is semi-strong-form efficient. The inclusion of insider information as well makes the market strong-form efficient.

Interest in efficiency has led to much empirical testing of the efficiency of financial markets. …

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