The elasticity of demand for wagering in an unregulated market

Abstract

The literature estimating the take-out rate (price) elasticity of horse race wagering has consistently found values far above one. The persistence of these apparently inefficiently high prices can be attributed to institutional factors of the US market where federal taxes are imposed on the total amount wagered, and not on the bookmakers’ revenue. By investigating all horse races in New Zealand from August 1993 to April 2009, our article is the first one to consider price setting for wagering in an unregulated market where taxes for a monopolistic betting agency are based on revenues. In such a setting, one would expect elasticities close to one, but in all econometric specifications, we find values well below one. We identify two reasons why higher prices could nevertheless reduce profits: cross price elasticities are negative and, due to the specific features of parimutuel betting, international competitors may only be attracted when take-out rates are above a critical threshold.

Keywords:

• demand elasticity
• market structure
• market efficiency
• price regulation
• wagering

JEL Classification::

• A10
• A19

Acknowledgements

We are grateful to an anonymous referee for very helpful comments.

Notes

¹ See Suits (1979), Thalheimer and Ali (1995a, b) and the literature review as follows.

² To see this, suppose the handle is 100, tax on handle is 6%, and the take-out rate is 10%. Then, pre-tax revenues are 100 · 10% = 10, and after-tax revenues are 100 · 10%−100 · 6% = 4. If the price elasticity is 2, then lowering the take-out rate by 1% (i.e. from 10% to 9.9%) would increase the handle to 102 and pre-tax revenues to 102 · 0.099 = 10.098, but after-tax revenues would decrease from 10 to 10.098–102 · 6% = 3.978.

³ Taking small variable costs per bet into account, elasticities should be slightly above one.

⁴ We will discuss in the forthcoming text, however, that such a simple conclusion is only valid when potential competition and spill-over effects between products measured by cross price elasticities are neglected.

⁵ This is different in betting markets for soccer, for instance, where bettors can be sure to receive the quota currently offered. Then, comparing quota of different agencies is easy, and the difference in quota is consistently shrinking over time due to market transparency provided by internet betting.

⁶ See our numerical example in footnote 2.

⁷ Less closely related, Gramm et al. (2007) analyse which individual race aspects encourage increased wagering spending and draw conclusions for the risk-attitude of punters. Using data from 12 major racetracks in 2002, they find evidence for two types of customers, risk-averse informed and basically uninformed bettors.

⁸ We abbreviate take-out rate with TOR in all tables.

⁹ We also include a time index in the regressions to control for a possible growth trend after adjusting for inflation and after controlling for seasonality.

¹⁰ The superscript ‘d’ expresses ‘direct’ product elasticity to distinguish from the cross price elasticity considered later.

¹¹ See, e.g., the seminal paper by Woodland and Woodland (1994).

¹² As a robustness check we ran our calculations also with two, four, six and 12 months lags. Our results remain qualitatively the same.

¹³ Based on information provided by the NZRB, average income of betters is similar to the national average earnings of employees. As a robustness check we ran all calculations without the hourly earnings control variable. Our results remain qualitatively identical.

¹⁴ Unemployment figures were obtained from the Organization for Economic Co-operation and Development (OECD) data base.