How Do Financial Market Outcomes Affect Gambling?
Abstract
:1. Introduction
2. Prior Gambling Demand Literature
3. Data and Historical Background
4. Conceptual Framework
Explanatory Variables
5. Results
5.1. Robustness Analysis
5.2. The Dynamics of the Economic and Racing Industry Parameters
6. Conclusions and Directions for Future Research
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
1 | After a Supreme Court ruling that legalized sport betting in 2018, wagering has expanded across the U.S. Currently 34 states and the District of Columbia permit online and in-person sport wagering. According to the American Gaming Association, sport wagering generated $4.3B in revenues in 2021. For a detailed analysis of sport betting markets see Mosenhauer et al. (2021). |
2 | The history of gambling in the U.S. includes periods with no legal constraints on gambling, followed by episodes of stringent federal and state prohibitions (Schwartz 2013). In recent decades, firms within the gambling industry have become public companies. A move that has resulted in a flow of Wall Street investments and increased public scrutiny. The profitability of these firms is directly tied to consumers’ acceptance of gambling as a form of entertainment, and ubiquitous gaming advertisements attest to this fact. |
3 | Lottery-stocks are shares of unprofitable firms in financial distress, which have negative expected returns, high volatility, and highly skewed returns. |
4 | By the late 1800s, there were over 300 racetracks in operations across the U.S. Bookmaking was replaced with the regulated pari-mutuel betting system starting in 1908. Under the pari-mutuel wagering system, players bet on random outcomes and winners share, in proportion to their wagers, the pool of all bets net of the racetrack’s commissions and state taxes—the “take-out rate”. |
5 | Starting in the early 1980s, racetracks began offering Advance Deposit Wagering (ADW) accounts, which are similar to electronic brokerage accounts at financial institutions. The horse racing industry infrastructure supports betting from multiple states and internationally. For a detailed historical background see Liebman (2017). |
6 | Pari-mutuel betting institutions function in a similar manner as the financial system, fulfilling important services, as outlined in Merton (1995). Merton’s functional perspective framework rests on the premise that financial functions, such as fulfilling demand for games of chance, are stable over time and market institutions, including the gambling industry, evolve to serve such functions. |
7 | Relying on more recent data, Maggio et al. (2020) empirically demonstrate that consumption responds to changes in stock market returns. These authors suggest that households treat capital gains and dividends as separate sources of income and show that consumption is highly responsive to both. Furthermore, Chodorow-Reich et al. (2021) demonstrate that, in addition to consumption, changes in stock market wealth also affect employment and the real economy. |
8 | Kaplan (2002) notes that since the 1980’s, the racing industry has witnessed significant proliferation of such intermediaries, generating a large flow of funds into horse wagering. Apparently, these hedge funds rely on exotic wagers with low probability but high payouts, for instance, superfecta, and picking winners in multiple races. Such bets are similar to the purchase of deep out-of-the-money options. A successful strategy generates small steady losses with infrequent but large gains. It is important to note, however, that the ability of horse betting markets to absorb a large flow of funds is limited by the number of tracks and available races. There is also a long tradition of racetrack gamblers and handicappers, becoming traders and stock pickers, and vice versa. Warren Buffet and Charlie Munger are two prime examples of horse race handicappers that became stock pickers. |
9 | This is not surprising, as rising VIX likely signals higher volatility of lottery-stocks and more skewed returns. Rising realized stock market volatility is unlikely to impact gambling payoffs at racetracks. |
10 | Under cumulative prospect theory, gamblers may act in a risk-loving manner as a consequence of over weighting small probability outcomes. On the application of prospect theory to gambling, see Barberis (2012) and Barberis (2013) and for a survey of economic models of risk aversion, see O’Donoghue and Somerville (2018) and their references. |
11 | As Conlisk (1993) has shown, this perspective is also consistent with the expected utility model. All that is needed to adequately explain the individual’s demand for gambles is a tiny felicity of gambling appended to any proposed utility function. For an interesting application of felicity of gambling in the horse wagering context see Green et al. (2020). |
12 | It is impossible to incorporate illegal wagering among individuals or through bookmakers in our analysis. In any case, the magnitude of illegal wagering likely dwindled as telephone and simulcast betting were introduced, starting in 1980’s. |
13 | Detailed historical information about these tracks and their Media Guides are available at https://www.dmtc.com/ and https://www.santaanita.com/, both accessed on 29 May 2023. After the Pearl Harbor attack (1941), both racetracks were closed (1942–1945) and were used as temporary internment camps for Japanese Americans. |
14 | The data for Del Mar Racetrack is available starting in 1938, its first operating year, resulting in 79 observations. |
15 | Over the long span of time we study, the per capita wager in California has declined because the cumulative growth rate of the population, which is always positive with little variability, mostly exceeds the cumulative growth rate of aggregate wagers, which is subject to large positive and negative annual fluctuations. |
16 | History of gambling in California is detailed in Atkinson (1998) and California Legislative Analyst Office (2019). |
17 | Gramm et al. (2007) note similar trends across the United States: “From 1985 to 2002, the total wagered on Thoroughbred races in North America increased from $8.25 billion to $15.62 billion, despite the fact that the number of races dropped over 20 percent.” |
18 | In response to falling aggregate wagers, a host of new wagering products are introduced during this period. These include, exchange wagering (direct bettor to bettor wagers); futures wagering; track-subsidized and guaranteed wagering pools; wagering on the success rate of jockeys or trainers; take-out rebates to larger bettors; fantasy horse racing; wagering on previously-run races; and the ability to include fixed-odds wagering. |
19 | Surprisingly, during the COVID-19 pandemic, aggregate wagering on California races nearly matched its 2019 level, despite an 18% decline in the number of races. A similar phenomenon occurred for the U.S. as a whole. |
20 | Chiappori and Ekeland (2011) provide a detailed discussion of aggregate demand functions and the required assumptions for summing demand across individuals. |
21 | The specification in (1) and its logarithmic variants are popular in several areas of empirical economics; for example, estimation of CES-type production (utility, cost, other) functions. Following the introduction of the Box-Cox transformation, the search for “optimal variable transformation” has produced several useful methods to linearize Equation (1), as discussed in a recent survey by Atkinson et al. (2021). |
22 | See Grote and Matheson (2013) for a survey of the empirical literature and elasticity estimates for a variety of gambling activities, including horse wagering and lottery. |
23 | Modeling and interpreting linear and nonlinear interaction affects are discussed in Balli and Sørensen (2013) and Greene (2010). |
24 | While it is possible to model interaction effects by using the product of s and , our proposed specification provides better fits for the distribution of R. As Equation (3) shows, the term essentially acts as a weighting function that adjusts s over the range of . As seen below, this structure captures the dynamics of quite well. |
25 | We utilize the current realized excess returns, i.e., the current “premium” relative to the risk-free rate. In contrast, “equity risk premium” is typically estimated from long time series (Siegel 2017). We refrain from using the term “premium”, because it is often associated with expectations, rather than a single period of realized excess returns. |
26 | CRSP-VW and S&P-500 indexes are obtained from Wharton Research Data Services (https://wrds-www.wharton.upenn.edu/). Shiller’s total market returns are obtained from Yale University (http://www.econ.yale.edu/~shiller/data.htm). We also considered the Dow Industrial index. While we obtained similar results, we believe comparisons with the Dow is problematic because the Dow is a price-weighted index and has few constituents (30 stocks), and additions/deletions to this index are less reflective of the state of the economy. In any case, using the Dow will not change our results because it is highly correlated with the S&P 500 and CRSP indexes. The treasury bill data (https://fred.stlouisfed.org/series/TB3MS) and the monthly Aaa and Baa bond yields (https://fred.stlouisfed.org/series/AAA) are obtained from the Federal Reserve Bank of St. Louis. (These sources were last accessed on 29 May 2023). |
27 | Relative to a “recession dummy”, bond spread is more informative, as its magnitude captures the extent of recession or expansion. |
28 | Another measure of the credit market condition is the term spread, defined as the yield difference between corporate and treasury bonds with similar maturity. However, as Duca (1999) has shown, the term spread is a less informative measure due to the differences in the associated bonds’ covenants, for example callability provisions. The quality spread uses bonds with similar covenants and maturity, and is therefore subject to fewer complications arising from provisions that result in differential prepayment risk. Note that the quality spread is simply the difference between the term spreads of Baa and Aaa bonds relative to treasuries. |
29 | Under the current California law, at least 50% of the total sales revenues must be returned to the public in the form of prizes (take-out rate of 50%) and the remainder will be used to support public education (37%) and cover the lottery’s administrative costs (maximum of 13%). |
30 | We obtain the California annual per capita income from Federal Reserve Bank of St. Louis, https://fred.stlouisfed.org/series/CAPCPI, accessed on 29 May 2023. |
31 | We also considered the effect of the state unemployment rate. However, the coefficient is not significant and it is highly correlated with income. We therefore dropped unemployment rate from the estimation. |
32 | At off-track betting sites, races are simulcast from different tracks, allowing patrons to bet on a multitude of races. Nationwide, the ability to bet on horse races dramatically increased when off-track betting was legalized, first in New York (1970), and subsequently in other states. A second expansion of betting opportunities was brought about by inter-track wagering (simulcasts from one track to another). It is interesting to note that, Schwab implemented TeleBroker, the first trading application using the phone in 1989, nearly two decades after horse wagering by phone started in 1971. |
33 | Olmstead et al. (2007) estimate a water demand function in which price elasticity is conditional on the prevailing price structure, i.e., pricing is nonlinear such that higher marginal prices are charged for higher quantities consumed. Non-linearity arises from the fact the quantity consumed is conditional on individual’s “consumption block”, where different blocks have their own marginal pricing scheme. |
34 | Estimation results for the levels specification (Equation (1)) are consistent with the results for percent change specification (Equation (2)). However, the levels model suffers from major statistical shortcomings and biased coefficient estimates, as noted earlier. The results for levels specification are available upon request. |
35 | In the special case where errors in the nonlinear model are homoskedastic and orthogonal, NLS is efficient among estimators that only require the first two moments of residuals distribution (Cameron and Trivedi 2005). The percent change specification is more likely to be consistent with these requirements. |
36 | In the context of nonlinear models, the usefulness of adjusted has been a subject of debate. The row labeled “Fit” in the tables reports the squared correlation between the dependent variable and the model’s predicted values, and serves an alternative goodness-of-fit metric for nonlinear models. |
37 | For an interesting historical exposé regarding horse wagering during the Great Depression, see https://www.pbs.org/wgbh/americanexperience/features/seabiscuit-racing-depression/, accessed on 29 May 2023. |
38 | We included a dummy variable for each tail separately, but the estimated coefficients remained unchanged. We opted for a symmetrical “Tail Impact” to keep the models parsimonious and save degrees of freedom. |
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Dependent Variables | |
---|---|
(% Change in WRC) | Wager Per Race, (WRC, $) |
WRC = Aggregate Wagers/number of races, by year | |
Similarly defined for Del Mar and Santa Anita Tracks | |
Explanatory Variables | |
Financial Market Outcomes and Lottery | |
Bond Spread | Average of Moody’s Monthly Yield Spread (Baa-AAA) |
CRSP-VW Premium | Average of Monthly CRSP-VW Excess Returns |
CRSP-VW Volatility | Standard Deviation of Monthly CRSP-VW Returns |
S&P Premium | Average of Monthly S&P-500 Excess Returns |
S&P Volatility | Standard Deviation of Monthly S&P-500 Returns |
Shiller Premium | Average of Monthly Shiller’s Excess Returns |
Shiller Volatility | Standard Deviation of Shiller’s Monthly Returns |
Lottery | California Lottery Dummy Variable |
Economic and Racing Industry Variables | |
Price (Take-out Rate) | Fraction of Aggregate Wagers distributed to racetracks, |
horse owners and taxes. | |
Income, $ | California Income deflated by Population |
Purse per Race, $ | Purse Proceeds / number of races |
Off-Track Wager | Fraction of Aggregate Wagers originating from off-track facilities |
Purse Proceeds, $ | Aggregate Dollars distributed to horse owners, $ |
Track Proceeds, $ | Aggregate Dollars distributed to racetracks & affiliated businesses |
Relative Incentive | Purse Proceeds / Track Proceeds |
Relative Compensation Index | RCI = (Relative Incentive) × (number of operating racetracks) |
Mean | St. Dev. | Skewness | Kurtosis | Min | Max | |
---|---|---|---|---|---|---|
Dependent Variables | ||||||
Wager Per Race-California ($) | 309,383 | 268,865 | 0.93 | 2.40 | 18,627 | 866,227 |
(% Change in WRC) | 0.05 | 0.15 | 1.01 | 6.30 | −0.34 | 0.57 |
-Del Mar (N = 79) | 0.05 | 0.13 | 1.90 | 12.93 | −0.30 | 0.74 |
-Santa Anita | 0.04 | 0.13 | 0.84 | 8.30 | −0.42 | 0.61 |
Explanatory Variables | ||||||
Financial Market Outcomes and Lottery | ||||||
Bond Spreads—(Baa-AAA) | 0.01 | 0.00 | 1.35 | 4.46 | 0.00 | 0.03 |
CRSP-VW Excess Returns | 0.08 | 0.16 | −0.38 | 3.12 | −0.35 | 0.45 |
CRSP-VW Market Volatility | 0.04 | 0.02 | 1.84 | 8.16 | 0.02 | 0.13 |
S&P Excess Returns | 0.05 | 0.15 | −0.37 | 3.21 | −0.38 | 0.45 |
S&P Market Volatility | 0.04 | 0.02 | 2.17 | 9.96 | 0.02 | 0.14 |
Shiller Excess Returns | 0.03 | 0.17 | −0.37 | 2.94 | −0.36 | 0.40 |
Shiller Market Volatility | 0.03 | 0.02 | 1.36 | 4.61 | 0.01 | 0.08 |
Lottery Dummy | 0.44 | 0.50 | 0.22 | 1.05 | 0.00 | 1.00 |
Economic and Racing Industry Variables | ||||||
Price (Per $ of Wager) | 0.17 | 0.03 | −0.22 | 1.65 | 0.12 | 0.21 |
% Change in Price | 0.01 | 0.03 | 0.93 | 9.44 | −0.09 | 0.12 |
Income($) | 19,248 | 19,391 | 0.96 | 2.80 | 776 | 71,261 |
% Change in Income | 0.05 | 0.04 | 0.82 | 6.04 | −0.04 | 0.21 |
Purse (Per $ of Wager) | 0.04 | 0.01 | 0.08 | 2.26 | 0.02 | 0.06 |
Track (Per $ of Wager) | 0.08 | 0.04 | 0.58 | 1.62 | 0.03 | 0.16 |
Purse Proceeds/Track Proceeds | 0.60 | 0.29 | 0.89 | 3.06 | 0.25 | 1.47 |
Number of Tracks—California | 14 | 2.22 | −0.55 | 3.35 | 8 | 19 |
Relative Compensation Index (RCI) | 8.63 | 4.73 | 0.59 | 2.51 | 2.17 | 22.03 |
Purse Per Race (PRC) ($) | 13,790 | 12,327 | 0.73 | 2.02 | 585 | 39,068 |
% Change in PRC | 0.05 | 0.13 | 1.52 | 7.24 | −0.18 | 0.56 |
% Change in PRC—Del Mar (N = 79) | 0.05 | 0.11 | 1.00 | 9.47 | −0.37 | 0.56 |
% Change in PRC—Santa Anita | 0.05 | 0.17 | 0.78 | 5.89 | −0.46 | 0.62 |
Number of Races | 6107 | 2430 | 0.24 | 1.89 | 2113 | 10,590 |
% Change in Number of Races (NRC) | 0.01 | 0.11 | 0.92 | 9.91 | −0.33 | 0.47 |
% Change in NRC—Del Mar (N = 79) | 0.01 | 0.10 | 2.37 | 14.39 | −0.32 | 0.48 |
% Change in NRC—Santa Anita | 0.01 | 0.11 | 1.94 | 12.81 | −0.36 | 0.56 |
Off-Track Wager (Fraction of Wagers) | 0.31 | 0.39 | 0.55 | 1.41 | 0.00 | 0.93 |
% Change in Off-Track Wager | 0.01 | 0.03 | 5.35 | 35.48 | −0.00 | 0.25 |
Explanatory Variables | s (S&P) | and | s | Static | S&P | CRSP | Schiller |
---|---|---|---|---|---|---|---|
Financial Market Outcomes and Lottery | |||||||
Bond-Spread | 4.130 | 3.917 | 7.190 *** | 7.215 *** | 6.308 ** | ||
0.98 | 1.66 | 3.96 | 3.56 | 2.30 | |||
Excess Returns | 0.015 | −0.082 | −0.154 ** | −0.123 * | −0.092 | ||
0.13 | −0.93 | −2.23 | −1.87 | −1.22 | |||
Market Volatility | 0.128 | −1.231 | −1.793 *** | −1.679 ** | −1.814 *** | ||
0.13 | −1.52 | −2.80 | −2.50 | −2.81 | |||
California Lottery | −0.004 | −0.014 | −0.059 ** | −0.064 ** | −0.069 *** | ||
Dummy Var. | −0.12 | −0.79 | −2.55 | −2.59 | −2.73 | ||
Economic and Racing Industry Variables | |||||||
Price | −0.77 | −0.678 | −2.402 ** | −2.449 ** | −2.330 ** | ||
−1.28 | −1.17 | −2.34 | −2.38 | −2.01 | |||
Income | 1.00 *** | 0.877 ** | 2.593 *** | 2.646 *** | 2.689 *** | ||
3.07 | 2.18 | 4.52 | 4.40 | 3.99 | |||
Purse per Race | 0.653 *** | 0.543 *** | 0.921 *** | 0.927 *** | 0.880 *** | ||
5.83 | 4.87 | 3.68 | 3.42 | 3.32 | |||
Number of Races | −0.452 *** | −0.549 *** | −0.741 *** | −0.757 *** | −0.836 *** | ||
−4.57 | −6.16 | −7.86 | −7.78 | −7.04 | |||
Off Track Wager | 0.438 *** | 0.488 *** | 2.168 * | 2.223 * | 2.276 * | ||
4.38 | 2.83 | 1.96 | 1.91 | 1.69 | |||
Relative Comp. Index | −0.103 *** | −0.107 *** | −0.114 *** | ||||
RCI | −2.99 | −2.91 | −3.06 | ||||
Model Diagnostics | |||||||
Adj. R | 0.06 | 0.16 | 0.61 | 0.67 | 0.73 | 0.72 | 0.71 |
Fit | 0.02 | 0.09 | 0.59 | 0.67 | 0.74 | 0.73 | 0.72 |
Serial Correlation (p-value) | 0.89 | 0.58 | 0.17 | 0.34 | 0.63 | 0.57 | 0.46 |
Normality (p-value) | 0.00 | 0.00 | 0.00 | 0.04 | 0.32 | 0.16 | 0.25 |
Log-Likelihood | 42 | 45 | 77 | 87 | 96 | 95 | 93 |
AIC | −76 | −87 | −147 | −155 | −172 | −170 | −166 |
BIC | −67 | −82 | −140 | −134 | −148 | −146 | −142 |
Num. of Iterations | - | - | - | - | 19 | 22 | 30 |
Explanatory Variables | Del Mar | Santa Anita | ||||
---|---|---|---|---|---|---|
S&P | CRSP | Schiller | S&P | CRSP | Schiller | |
Financial Market Outcomes and Lottery | ||||||
Bond-Spread | 0.494 | 1.199 | 0.251 | 7.200 ** | 7.073 ** | 6.104 ** |
0.20 | 0.47 | 0.08 | 2.42 | 2.35 | 2.25 | |
Excess Returns | −0.103 | −0.062 | −0.052 | −0.06 | −0.067 | −0.042 |
−1.51 | −1.04 | −0.84 | −0.93 | −1.03 | −0.60 | |
Market Volatility | −0.538 | −0.688 | −0.438 | −1.089 | −1.01 | −0.937 |
−0.71 | −0.91 | −0.47 | −1.40 | −1.32 | −1.25 | |
California Lottery | −0.034 | −0.037 | −0.039 | −0.057 ** | −0.059 ** | −0.062 ** |
Dummy Var. | −1.52 | −1.59 | −1.64 | −2.06 | −2.15 | −2.24 |
Economic and Racing Industry Variables | ||||||
Price | −0.622 | −0.672 | −0.590 | −2.111 | −2.139 | −2.170 |
−1.22 | −1.21 | −1.03 | −1.14 | −1.15 | −1.01 | |
Income | 1.116 ** | 1.104 ** | 1.007 ** | 1.632 | 1.742 | 1.779 |
2.29 | 2.22 | 2.03 | 1.59 | 1.63 | 1.48 | |
Purse per Race | 0.535 *** | 0.535 *** | 0.520 *** | 1.092 ** | 1.112 ** | 1.169 ** |
8.25 | 7.84 | 7.37 | 2.49 | 2.51 | 2.27 | |
Number of Races | −0.359 ** | −0.358 ** | −0.349 * | 0.143 | 0.132 | 0.152 |
−2.07 | −2.05 | −1.90 | 0.29 | 0.26 | 0.27 | |
Off Track Wager | 1.859 *** | 1.905 *** | 1.873 ** | 2.264 | 2.322 | 2.639 |
2.77 | 2.74 | 2.50 | 1.42 | 1.43 | 1.36 | |
Relative Comp. Index | −0.008 | −0.008 | −0.008 | −0.185 ** | −0.188 ** | −0.207 ** |
RCI | −0.42 | −0.41 | −0.37 | −2.44 | −2.46 | −2.27 |
Model Diagnostics | ||||||
Adj. R | 0.69 | 0.69 | 0.68 | 0.47 | 0.47 | 0.46 |
Fit | 0.68 | 0.68 | 0.68 | 0.50 | 0.50 | 0.49 |
Serial Correlation (p-value) | 0.50 | 0.43 | 0.32 | 0.21 | 0.22 | 0.26 |
Normality (p-value) | 0.17 | 0.05 | 0.05 | 0.49 | 0.57 | 0.46 |
Log-Likelihood | 95 | 95 | 94 | 79 | 79 | 79 |
AIC | −170 | −169 | −168 | −139 | −139 | −137 |
BIC | −146 | −146 | −144 | −115 | −115 | −113 |
Num. of Iterations | 16 | 16 | 19 | 21 | 21 | 23 |
Explanatory Variables | California | Del Mar | Santa Anita | ||
---|---|---|---|---|---|
S&P | CRSP | Schiller | S&P | S&P | |
Financial Market Outcomes and Lottery | |||||
Tail Impact | 0.477 *** | 0.509 *** | 0.497 *** | 0.155 *** | 0.177 *** |
3.19 | 3.41 | 3.31 | 7.98 | 14.71 | |
Bond-Spread | 6.015 *** | 6.130 *** | 4.861 * | 1.470 | 4.634 * |
3.19 | 3.03 | 1.97 | 0.83 | 1.89 | |
Excess Returns | −0.129 * | −0.122 * | −0.081 | −0.058 | −0.014 |
−1.92 | −1.84 | −1.10 | −1.36 | −0.29 | |
Market Volatility | −1.490 ** | −1.414 ** | −1.351 * | 0.316 | −0.734 |
−2.58 | −2.38 | −1.93 | 0.70 | −1.35 | |
California Lottery | −0.052 ** | −0.055 ** | −0.060 ** | −0.019 | −0.020 |
Dummy Var. | −2.22 | −2.33 | −2.28 | −1.34 | −0.89 |
Economic and Racing Industry Variables | |||||
Price | −2.072 * | −2.150 * | −2.045 * | −0.217 | −0.410 |
−1.85 | −1.90 | −1.67 | −1.12 | −0.60 | |
Income | 2.280 *** | 2.404 *** | 2.398 *** | 0.210 | 0.750 |
3.13 | 3.16 | 2.77 | 1.09 | 1.52 | |
Purse per Race | 0.423 ** | 0.398 ** | 0.360 * | 0.154 ** | 0.363 ** |
2.25 | 2.12 | 1.70 | 2.34 | 2.22 | |
Number of Races | −0.556 *** | −0.551 *** | −0.612 *** | −0.114 | 0.340 ** |
−5.28 | −5.16 | −4.98 | −1.21 | 2.16 | |
Off Track Wager | 1.985 * | 2.072 | 2.106 | 0.854 * | 0.084 |
1.67 | 1.66 | 1.46 | 1.96 | 0.35 | |
Relative Comp. Index | −0.101 ** | −0.108 ** | −0.115 ** | 0.042 | −0.081 |
RCI | −2.55 | −2.59 | −2.58 | 1.13 | −1.40 |
Model Diagnostics | |||||
Adj. R | 0.77 | 0.77 | 0.75 | 0.84 | 0.80 |
Fit | 0.78 | 0.78 | 0.76 | 0.84 | 0.81 |
Serial Correlation (p-value) | 0.44 | 0.35 | 0.21 | 0.80 | 0.37 |
Normality (p-value) | 0.10 | 0.11 | 0.06 | 0.73 | 0.24 |
Log-Likelihood | 102 | 102 | 100 | 123 | 119 |
AIC | −183 | −183 | −178 | −223 | −215 |
BIC | −157 | −157 | −151 | −197 | −189 |
Num. of Iterations | 21 | 24 | 33 | 23 | 16 |
Explanatory Variables | Simple | Improved | ||||
---|---|---|---|---|---|---|
S&P | CRSP | Schiller | S&P | CRSP | Schiller | |
Financial Market Outcomes and Lottery | ||||||
Tail Impact | 0.444 *** | 0.470 *** | 0.443 *** | |||
2.95 | 3.20 | 3.10 | ||||
Bond-Spread | 22.748 *** | 25.492 *** | 30.416 *** | 17.438 ** | 19.775 ** | 23.819 ** |
3.02 | 3.40 | 3.10 | 2.06 | 2.36 | 2.10 | |
Excess Returns | −0.323 | −0.286 | −0.236 | −0.282 | −0.310 | −0.223 |
−1.65 | −1.50 | −1.09 | −1.30 | −1.46 | −0.90 | |
Market Volatility | −4.334 ** | −4.451 *** | −5.669 *** | −3.412 * | −3.636 ** | −4.482 * |
−2.51 | −2.65 | −2.83 | −1.84 | −2.02 | −1.89 | |
California Lottery | −0.174 *** | −0.193 *** | −0.258 *** | −0.147 ** | −0.159 ** | −0.223 ** |
Dummy Var. | −2.65 | −2.81 | −3.23 | −2.15 | −2.30 | −2.30 |
Economic and Racing Industry Variables | ||||||
Price | −3.405 *** | −3.556 *** | −3.892 *** | −2.952 ** | −3.122 ** | −3.478 ** |
−3.39 | −3.69 | −3.46 | −2.40 | −2.60 | −2.48 | |
Income | 3.284 *** | 3.381 *** | 3.662 *** | 3.000 *** | 3.217 *** | 3.444 *** |
4.58 | 4.33 | 4.33 | 2.94 | 3.11 | 2.81 | |
Purse per Race | 0.996 *** | 0.991 *** | 0.874 *** | 0.478 ** | 0.443 ** | 0.356 |
4.50 | 4.51 | 3.59 | 2.17 | 2.18 | 1.59 | |
Number of Races | −0.970 *** | −1.016 *** | −1.241 *** | −0.821 *** | −0.846 *** | −1.056 *** |
−7.28 | −7.68 | −6.13 | −4.93 | −5.10 | −4.33 | |
Off Track Wager | 2.607 ** | 2.651 ** | 3.072 * | 2.396 * | 2.446 * | 2.888 |
2.19 | 2.20 | 1.74 | 1.81 | 1.87 | 1.51 | |
Relative Comp. Index | −0.138 *** | −0.144 *** | −0.161 *** | −0.137 *** | −0.144 *** | −0.165 *** |
RCI | −4.48 | −4.69 | −4.14 | −3.30 | −3.57 | −3.29 |
Model Diagnostics | ||||||
Adj. R | 0.74 | 0.74 | 0.74 | 0.77 | 0.78 | 0.77 |
Fit | 0.75 | 0.75 | 0.75 | 0.79 | 0.79 | 0.78 |
Serial Correlation (p-value) | 0.59 | 0.53 | 0.52 | 0.33 | 0.24 | 0.25 |
Normality (p-value) | 0.16 | 0.10 | 0.04 | 0.18 | 0.15 | 0.07 |
Log-Likelihood | 98 | 98 | 97 | 104 | 104 | 103 |
AIC | −176 | −175 | −174 | −185 | −187 | −184 |
BIC | −152 | −151 | −150 | −159 | −160 | −158 |
Num. of Iterations | 14 | 14 | 14 | 15 | 14 | 16 |
Static | Simple | Improved | |||||||
---|---|---|---|---|---|---|---|---|---|
% Change | Mean | St. Dev. | Min | Max | Mean | St. Dev. | Min | Max | |
Price | −0.68 | −1.10 *** | 0.46 | −1.92 | −0.25 | −0.96 ** | 0.40 | −1.66 | −0.22 |
Income | 0.88 ** | 1.18 *** | 0.50 | 0.27 | 2.07 | 1.06 *** | 0.44 | 0.25 | 1.83 |
PRC | 0.54 *** | 0.25 *** | 0.11 | 0.06 | 0.43 | 0.20 ** | 0.08 | 0.05 | 0.34 |
No. of Races | −0.55 *** | −0.25 *** | 0.11 | −0.44 | −0.06 | −0.26 *** | 0.11 | −0.45 | −0.06 |
Off-Track | 0.49 *** | 1.35 ** | 0.30 | 0.53 | 1.77 | 1.16 ** | 0.26 | 0.47 | 1.52 |
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Ramezani, C.A.; Ahern, J.J. How Do Financial Market Outcomes Affect Gambling? J. Risk Financial Manag. 2023, 16, 294. https://doi.org/10.3390/jrfm16060294
Ramezani CA, Ahern JJ. How Do Financial Market Outcomes Affect Gambling? Journal of Risk and Financial Management. 2023; 16(6):294. https://doi.org/10.3390/jrfm16060294
Chicago/Turabian StyleRamezani, Cyrus A., and James J. Ahern. 2023. "How Do Financial Market Outcomes Affect Gambling?" Journal of Risk and Financial Management 16, no. 6: 294. https://doi.org/10.3390/jrfm16060294