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The Effect of Online Gaming on Commercial Casino Revenue

July 2011

Authors:

Washington State University

This study estimates the effect of the online gaming industry on the commercial casino gaming industry. The findings from this study suggest that during the pre-UIGEA period, online gaming was a moderate substitute good for brick and mortar gaming in the U.S. In an online gaming market characterized by loose regulation and relatively easy access, online gaming revenue is estimated to cannibalize commercial casino revenue at a rate of 27 to 30 cents on the dollar. This study also led to the discovery of a seemingly valid instrumental variable, internet user rates, which can be used to correct internet gaming coefficient estimates for potential bias in future studies.

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UNLV Gaming Research & Review Journal ♦ Volume 15 Issue 2

The Effect of Online Gaming on

Commercial Casino Revenue

Kahlil S. Philander

Abstract

This study estimates the effect of the online gaming industry on the commercial

casino gaming industry. The ndings from this study suggest that during the pre-UIGEA

period, online gaming was a moderate substitute good for brick and mortar gaming in

the U.S. During this early period in the online gaming market, which was characterized

by loose regulation and relatively easy access, online gaming revenue is estimated to

have cannibalized commercial casino revenue at a rate of 27 to 30 cents on the dollar. A

discussion of this nding’s relevance to the current gaming market and the related policy

considerations is provided. This study also led to the discovery of a seemingly valid

instrumental variable, internet user rates, which can be used to correct internet gaming

coefcient estimates for potential bias in future studies.

Keywords: internet gambling, online gaming, instrumental variable, ARIMA

Introduction

The adoption of online gaming in new jurisdictions tends to be touted by proponents

as a voluntary source of tax revenue (Legislative Analyst’s Ofce, 2010).

By regulating the industry, governments are thought to be able to increase

public revenues through an online gaming tax. These taxes are typically

levied on operators through a licensing fee and/or an excise tax applied to

gross gaming revenue.

To date, it has remained unclear what specic effect online gaming has

had on traditional brick and mortar (B&M) gaming. In particular, have

the two industries been gross-complements (an increase in the demand

for industry leads to an increase in the demand for the other), or have they

been gross-substitutes (an increase in the demand for one industry leads to

a decrease in the demand for the other). This paper seeks to measure the

nature of this relationship and the strength of the association.

Signicance

An understanding of the relationship between online gaming and brick and mortar

gaming is an important concept for both policy makers and private operators. For private

industries (or government-owned operators), the importance is clear. If the two industries

are substitutes, they should be concerned about cannibalizing their own sales; if the

industries are complements, they should explore how to leverage the benets across the

virtual and non-virtual gaming oor.

For policy makers, the distinction is more subtle. Among other considerations, policy

makers need to understand how the adoption of online gaming will affect the output and

tax revenue generated by existing B&M operations. For example, suppose that online

and B&M gaming are perfect substitutes and gross B&M revenue is taxed at 20%. The

introduction of online gaming at a 10% tax rate would actually lead to a decrease in tax

revenue – for every dollar in online gaming revenue, the government would receive $0.10,

but they would lose $0.20 from foregone B&M tax revenue. An argument similar to this

Kahlil S. Philander

University of Nevada

Las Vegas

Phone: (702) 722-

7342; Fax: (702) 895-2713;

Email: philande@unlv.

nevada.edu

If the two industries are

substitutes, they should be

concerned about cannibalizing

their own sales; if the industries

are complements, they should

explore how to leverage the

benets across the virtual and

non-virtual gaming ‡oor.

24 UNLV Gaming Research & Review Journal ♦ Volume 15 Issue 2

one has been posited regarding the effect of legal casino adoption on lottery revenue

(Walker, 2007a; Walker, 2007b). This argument of cross-industry tax effects is a specic

application of the more general argument from the seminal work of Ramsey (1927),

which provides a formal argument of the inter-relations between goods and excise taxes.

To date, there has been no published academic research that empirically estimates

the relationship between online and B&M gaming demand. As online gaming continues

to emerge as an area of interest for business research, understanding the nature of its

relationship with B&M gaming will be important for building theoretical and empirical

models.

Literature Review

Overview of Online Gaming in the United States

The rst recorded online casino to accept a wager was Intertops.com, based and

licensed in Antigua, which occurred in January 1996 (Business Wire, 2005). The online

gaming industry then grew to roughly 15 casinos by the end of 1996, 650 at the end of

1999, and 1,800 sites by the end of 2002 (Schwartz, 2006). The rst online poker room,

PlanetPoker, opened in 1998 and was quickly followed by many others (Williams &

Woods, 2007).

Online gaming continued to grow in the United States until October 2006, when the

Unlawful Internet Gambling Enforcement Act (UIGEA) was passed as an addition to the

Security and Accountability for Every Port Act of 2006. This measure effectively made

it illegal for any nancial transaction provider to transfer funds to online sites that take

bets on “outcomes of a contest, sports event or a game of chance” (Smith et al., 2007).1

2 Although this act did not make the specic act of betting illegal for the consumer, the

increased difculty of nancial transactions, and increasing uncertainty over the legality

of online gaming in the average consumer’s eyes, had a negative effect on online gaming

demand, and caused some foreign operators to exit the U.S. market (Rose, 2010). The

largest operator at the time, Party Gaming, was among the companies that left the U.S.

market. At the time, the U.S. online gaming industry was estimated to produce roughly 6

billion in revenue per year, while the commercial casino industry generated 32 billion in

revenue (Christiansen Capital Advisors, 2007; American Gaming Association, 2007).

Gaming Taxation Policy

The use of gaming regulation to generate tax revenue is often cited as a way to avoid

politically dubious tax increases while addressing budget shortfalls (Furlong, 1998;

Smith, 1999; Smith, 2000). Although the assumed electoral consequences of scal policy

changes have become the topic of recent debate (Alesina, Carloni, & Lecce, 2010), the

use of a Ramsey taxation framework, which applies excise taxes to generate a specic

amount of revenue (as opposed to using taxes to fund the nancing of a public good),

appears to be a reasonable assumption of general policy practices (Ramsey, 1927).

When cross-effects between goods’ demand are ignored, Ramsey (1927) suggests

that tax rates be inversely proportional to own-price elasticities of demand. However,

the introduction of cross-effects between goods complicates this axiom. Taxation on

a good must account for how distortions in demand for that good affect demand for

complementary and substitute goods. This concept has been noted by some gaming

researchers such as Smith (1999), “Empirical research on elasticity of gaming demand

has provided little practical guidance along these lines for taxation policy and design…

Estimating gambling demand elasticities is complicated by the extent to which different

gambling products are substitutes,” but policy applications and research into cross-

effects remain limited.

1 The SAFE Port Act had no direct relation to gaming, prior to the late addition of the UIGEA provisions. It

is an act designed to address maritime and cargo security.

2 The provisions outlined in the UIGEA did not come into full effect prior to June 1, 2010, though most

operators had already fully complied with the act, prior to that date.

UNLV Gaming Research & Review Journal ♦ Volume 15 Issue 2

between some industries, but none for online gaming. The relationships are all noted to be either

nil or substitutionary (as opposed to complementary).

Table 1

Relationships between Gaming Sectors – Maximum Reported Empirical Estimates3

Gaming Sector

From\To

Casino(1)

Gaming

Machines

Lottery

Betting

Services(2)

Casino

-27%

-20%

-32%

Gaming Machines

-27%

-20%

-32%

Lottery

-3%

(low-end)

-3%

(low-end)

Substitute

Magnitude

Unknown

-36%

Betting Services

Weak Substitute

-17%

Note: Reproduced from Swiss Institute of Comparative Law (2006)

(1) Results are largely from studies of U.S. venues where slot machines are by far the largest component of casino GGRs. The

effects of competition on casinos and gaming machines are assumed to be equal for this analysis.

(2) Assumes that these are predominantly horse and sports betting services.

In his early study of direct gaming demand elasticities, Suits (1979) estimates the

elasticity of demand for bookmaking services in Nevada, using data from the reduction of the

federal excise tax on bookmaking at the end of 1974. He generates an elastic range from -1.64 to

-2.17, indicating that the percent change in demand will be greater than the percentage change in

price. He also estimates elastic demand for betting at thoroughbred race tracks from a panel data

set of states offering horse racing,ranging from -1.59 to -2.14. Morgan and Vasche (1982) used

two multiple regression equations to measure the effect of real disposable income,

unemployment, and price of wagering (takeout rate) on pari-mutuel wagering demand. Wagering

demand was split into two variables, wagering per attendance and attendance per capita. The

authors estimate elasticity of pari-mutuel wagering with respect to price is -1.3. In his study of

3Empty Bingo related cells were removed

The Effect of Online Gaming on Commercial Casino Revenue

Estimates of Gaming Demand Responses

In terms of cross- effects within the gaming industry, Walker and Jackson (2008) use

a system of seemingly unrelated regression (probit) models to estimate the volume of

casino, dog racing, horse racing, and lottery gaming industries as a function of the other

industries’ volume, and other control variables. A statistically signicant relationship

is found with all cross-effects except for dog racing volumes and casino volumes, and

Indian casino square footage and dog racing volume. Casino gaming is noted to have a

negative relationship with lottery gaming, but a positive relationship with horse racing.

In their review of gaming services in the European Union, the Swiss Institute of

Comparative Law (2006) provides a summary table (reproduced in Table 1 below) of

the known relationships among gaming industries. The authors provide estimates of the

cross-elasticities between some industries, but none for online gaming. The relationships

are all noted to be either nil or substitutionary (as opposed to complementary).

Table 1

In his early study of direct gaming demand elasticities, Suits (1979) estimates the

elasticity of demand for bookmaking services in Nevada, using data from the reduction

of the federal excise tax on bookmaking at the end of 1974. He generates an elastic range

from -1.64 to -2.17, indicating that the percent change in demand will be greater than the

percentage change in price. He also estimates elastic demand for betting at thoroughbred

race tracks from a panel data set of states offering horse racing, ranging from -1.59 to

-2.14. Morgan and Vasche (1982) used two multiple regression equations to measure the

effect of real disposable income, unemployment, and price of wagering (takeout rate) on

pari-mutuel wagering demand. Wagering demand was split into two variables, wagering

per attendance and attendance per capita. The authors estimate elasticity of pari-mutuel

wagering with respect to price is -1.3. In his study of Illinois casinos, Landers (2008a;

2008b) estimates the price elasticity of casino gaming between -0.8 and -1.0. Landers

(2008a) also notes that estimates of price elasticities in prior literature vary between

-0.19 (lottery) and -2.81 (betting services). Thalheimer and Ali (2003) compute a log-log

model that allowed them to infer elasticities directly from the model coefcients. The

authors estimate an elastic (-1.5) price elasticity of demand in 1991, which decreased to

an inelastic value (-0.9) by 1998.

Methodology

Overview

This study estimates two time-series regression models to determine the effect

of online gaming revenue on brick and mortar gaming revenue. The model seeks to

estimate the relationship between real (ination adjusted) U.S. online gaming revenue

26 UNLV Gaming Research & Review Journal ♦ Volume 15 Issue 2

and real U.S. commercial casino consumer spending. In order to address potential bias

in coefcient estimate of online gaming revenue, an instrumental variable method, two-

stage least squares (2SLS), is used to estimate the model coefcients. An ARIMA model

is also computed to evaluate the robustness of the ndings.

Data

A large portion of online gaming activity takes place on foreign sites, which are

operating in countries with dubious regulation and reporting requirements. This makes

any analysis of the online gaming industry challenging, and dependent on market

estimates. In this study, data on the United States online gaming industry was made

available as a result of a trade dispute at the WTO between Antigua and the U.S.

(Christiansen Capital Advisors, 2007). The annual online gaming data covers the period

from 1999 to 2006, the year the UIGEA came into effect. The use of pre-UIGEA data

provides a revealing period to monitor the consumer behavior effects of online gaming,

since the lack of signicant regulation allowed operators and consumers to interact

with fewer market restrictions. Since not all online gaming operators are required to

le their revenue values with the government or another institution, the value provided

by Christiansen Capital Advisors (2007) are estimates, and not precise audited values.

Although the use of estimates may lead to inference issues, it should not bias the

parameter estimates. Data for 1998 was coded by applying the 1998 to 1999 World

estimates of online gaming by Christiansen Capital Advisors (2007) to the U.S. estimates

from 1999. For the period from 1988 to 1998, online gaming revenues were assumed

to be insignicant, and were coded as zero. The use of linearly approximated revenue

levels from 1995, when online gaming revenues were known to be zero (Business

Wire, 2005), and the last Christiansen Capital Advisors (2007) estimate in 1998, did

not signicantly alter the results. Therefore, the results appear to be robust to the minor

estimation errors in 1996 and 1997.

Total commercial gross gaming revenue for the United States was obtained from the

American Gaming Association (2010). The nominal values of B&M gaming revenue

and online gaming revenue were converted to real values, by applying the U.S. CPI-U

consumer price index (U.S. Department of Labor, Bureau of Labor Statistics, 2010).

Real U.S. gross domestic product was obtained from the International Monetary

Fund (2010). Commercial casino availability data was obtained from Walker (2007a)

and the American Gaming Association (2002, 2003, 2004, 2005, 2006, 2007). Summary

statistics for all estimation data is provided in Appendix B.

Omitted Data

The National Indian Gaming Commission (NIGC) was solicited for Indian gaming

revenues, however the NIGC was unable to provide data that predated 1998, and

therefore Indian gaming revenue was not included as an independent variable. Also

missing is a price variable. In empirical studies of the gaming industry, price is typically

operationalized as the house advantage for a given game (Eadington, 1999). Since

this study examines the U.S. gaming industries as a whole, it is not possible to include

price in the model, as there is no index of overall house advantage for the U.S. gaming

industry as a whole. The model design addresses potential bias from variable omission

through an instrumental variable estimation method. In their study of intrastate industry

relationships, Walker and Jackson (2008) previously estimate cross-industry effects

without a price variable.

Instrumental Variable Approach

In producing estimates of gaming revenue relationships using long-term time

series, the potential for omitted variable bias to enter the model error term becomes an

increasing concern, as there is no reliable proxy variable that can address the changes in

gamblers’ and society’s attitudes towards gaming over the 18 year period of this study.

UNLV Gaming Research & Review Journal ♦ Volume 15 Issue 2

The Effect of Online Gaming on Commercial Casino Revenue

If the model error term,

, contains omitted variables, such as attitudes towards gaming

or Indian gaming revenue, which are correlated with the independent variables, biased

coefcients may be estimated.3

In order to address the potentially endogenous online gaming variable, this study

uses an instrumental variable approach, two-stage least squares, to obtain a consistent

estimate of its effects. Instrumental variable estimation uses an exogenous variable that

is uncorrelated with the structural model error term, but correlated with the potentially

endogenous variable to obtain consistent coefcient estimates.4

Number of internet users per 100 people was used as an instrument for online

gaming revenue. The data was obtained from the International Telecommunication

Union (2010). The availability of no other potentially valid instruments inhibits the use

an overidentication test to measure whether internet user rates and the unexplained

variance in B&M gaming are correlated, but it seems intuitively unlikely that there

would be a statistically signicant relationship between these two variables. The non-

zero correlation assumption between internet user rates and online gaming revenue

seems intuitively plausible, as it may be the case that as the population of people with

access to the internet grows, so will the number of people gambling on the internet. This

assumption is tested in the results section.

Estimation Framework

The reduced form (rst stage) model that was estimated was specied as follows:

The structural model that was estimated was specied as follows:

3 As mentioned above, Indian gaming and price are also omitted variables of concern.

4 See, for example, Wooldridge (2010) for further discussion of instrumental variable methods.

The structural model that was estimated was specified as follows:



01 2 3 41

The inflation adjusted total commercial casino gross gaming revenue during

period (in billions of USD)

The estimate of inflation adjusted online

tt t t tt

BM OG GDP NCC BM

Where

ββ β β β ε

−

= +⋅ +⋅ +⋅ +⋅ +

= gaming revenue during period , from the first

stage regression (in billions of USD)

U.S. real gross domestic product during period (in billions of USD)

The number of U.S. states with legal

GDP t

NCC

= and operational commercial casinos in period t

The model error term

Results

First Stage Tests

As shown in Table 2, internet subscription rate is a statistically significant predictor of

online gaming revenue; t(11) =4.46, p=.001. The F-stat value for the instrumental variable was

F(1, 11) =19.92, greater than the threshold of 10 indicating a good instrument and satisfying the

( , )0

Cov IS OG ≠

condition (Sovey and Green, 2011).As expected, the prior years’ number of

internet users is positively correlated with current year internet gaming revenue

Table 2

Reduced Form Model Summary

Beta

Robust S.E.

t-stat

p-value

(Constant)

-2.635

3.067

2.77

0.018

LAG Internet Users Per 100

0.122

0.027

4.46

0.001

Real Gross Domestic Product

-0.001

<0.001

-2.57

0.026

Number of Commercial Casino

States

0.126

0.117

1.08

0.305

LAG Real B&M Revenue

-0.037

0.103

-0.36

0.722

structural model error term, but correlated with the potentially endogenous variable to obtain

consistent coefficient estimates.

Number of internet users per 100 people was used as an instrument for online gaming

revenue. The data was obtained from the International Telecommunication Union (2010). The

availability of no other potentially valid instruments inhibits the use an overidentification test to

measure whether internet user rates and the unexplained variance in B&M gaming are correlated,

but it seems intuitively unlikely that there would be a statistically significant relationship

between these two variables. The non-zero correlation assumption between internet user rates

and online gaming revenue seems intuitively plausible, as it may be the case that as the

population of people with access to the internet grows, so will the number of people gambling on

the internet. This assumption is tested in the results section.

Estimation Framework

The reduced form (first stage) model that was estimated was specified as follows:

01 12 3 41

The inflation adjusted online gaming revenue during period (in billions of USD)

Internet subscription rates per 100 people during period 1

t t t t tt

OG IS GDP NCC BM

Where

OG t

IS t

−−

−

=Π +Π ⋅ +Π ⋅ +Π ⋅ +Π ⋅ +

= −

U.S. real gross domestic product during period (in billions of USD)

The number of U.S. states with legal and operational commercial casinos in period t

The inflation adjusted total com

GDP t

NCC

−

=mercial casino gross gaming revenue during

period 1 (in billions of USD)

The model error term

−

See, for example, Wooldridge (2010) for further discussion of instrumental variable methods.

28 UNLV Gaming Research & Review Journal ♦ Volume 15 Issue 2

Results

First Stage Tests

As shown in Table 2, internet subscription rate is a statistically signicant predictor of

online gaming revenue; t(11) = 4.46, p=.001. The F-stat value for the instrumental variable

was F(1, 11) = 19.92, greater than the threshold of 10 indicating a good instrument and

satisfying the

( , )0

Cov IS OG �

condition (Sovey and Green, 2011). As expected,

the prior years’ number of internet users is positively correlated with current year internet

gaming revenue

Table 2

Two-Stage Least Squares Results

The general model ndings are provided in Table 3, below. The structural model,

which estimated the effect of online gaming on the commercial casino industry, appeared

to explain the variance in the dependent variable well, as the centered R2 value was

0.996, although the high adjusted R2 is also a function of the relatively small sample

size and the use of an autocorrelative term. An initial test for homoskedasticity indicated

non-constant variance F(4, 12) = 4399.43, p<0.001.5 Therefore, standard errors robust to

any arbitrary forms of heteroskedasticity were estimated using the robust procedure in

Stata (StataCorp LP, 2009). To address small sample issues in the parameter estimates,

a nite sample adjustment is used with the robust setting using the small procedure

in Stata (StataCorp LP, 2009). The test for autocorrelation failed to show a signicant

autocorrelative term, t = -2.21, p=0.052, therefore no corrections were made to compute

autocorrelation robust standard errors.6 The Shapiro-Wilks test failed to show a

signicant departure from normality, z = -1.612, p=0.947.

Table 3

Online gaming is found to be negatively related to commercial casino revenue,

indicating the two goods are substitutes. A one dollar increase in online gaming revenue is

estimated to coincide with a 28 cent reduction in commercial casino revenue. Real GDP

is positively related to commercial casino revenue, suggesting that it is a normal good.

Number of commercial casino states and the lagged value of gross commercial casino

revenue were positively related to the dependent variable. All control variables’ estimate

5 See the procedure outlined on page 535 of Wooldridge (2006).

6 See the procedure outlined on page 537 of Wooldridge (2006).

The structural model that was estimated was specified as follows:



01 2 3 41

The inflation adjusted total commercial casino gross gaming revenue during

period (in billions of USD)

The estimate of inflation adjusted online

tt t t tt

BM OG GDP NCC BM

Where

ββ β β β ε

−

= +⋅ +⋅ +⋅ +⋅ +

= gaming revenue during period , from the first

stage regression (in billions of USD)

U.S. real gross domestic product during period (in billions of USD)

The number of U.S. states with legal

GDP t

NCC

= and operational commercial casinos in period t

The model error term

Results

First Stage Tests

As shown in Table 2, internet subscription rate is a statistically significant predictor of

online gaming revenue; t(11) =4.46, p=.001. The F-stat value for the instrumental variable was

F(1, 11) =19.92, greater than the threshold of 10 indicating a good instrument and satisfying the

( , )0

Cov IS OG ≠

condition (Sovey and Green, 2011).As expected, the prior years’ number of

internet users is positively correlated with current year internet gaming revenue

Table 2

Reduced Form Model Summary

Beta

Robust S.E.

t-stat

p-value

(Constant)

-2.635

3.067

2.77

0.018

LAG Internet Users Per 100

0.122

0.027

4.46

0.001

Real Gross Domestic Product

-0.001

<0.001

-2.57

0.026

Number of Commercial Casino

States

0.126

0.117

1.08

0.305

LAG Real B&M Revenue

-0.037

0.103

-0.36

0.722

Two-Stage Least Squares Results

The general model findings are provided in Table 3, below. The structural model, which

estimated the effect of online gaming on the commercial casino industry, appeared to explain the

variance in the dependent variable well, as the centered R2value was 0.996, although the high

adjusted R2is also a function of the relatively small sample size and the use of an autocorrelative

term. An initial test for homoskedasticity indicated non-constant variance F(4, 12)=4399.43,

p<0.001.6Therefore, standard errors robust to any arbitrary forms of heteroskedasticity were

estimated using the robust procedure in Stata (StataCorp LP, 2009).To address small sample

issues in the parameter estimates, a finite sample adjustment is used with the robust setting using

the small procedure in Stata (StataCorp LP, 2009). The test for autocorrelation failed to show a

significant autocorrelative term,t = -2.21, p=0.052, therefore no corrections were made to

compute autocorrelation robust standard errors.7The Shapiro-Wilks test failed to show a

significant departure from normality, z = -1.612, p=0.947.

Table 3

Structural Model Summary

Beta

Robust S.E.

t-stat

p-value

(Constant)

-6.5331

1.1445

-5.71

<0.001

Real Online Gaming Revenue

-0.2767

0.1247

-2.22

0.049

Real Gross Domestic Product

0.0010

0.0002

5.41

<0.001

Number of Commercial Casino

States

0.4379

0.1080

4.05

0.002

LAG Real B&M Revenue

0.4775

0.1129

4.23

0.001

6See the procedure outlined on page 535 of Wooldridge (2006).

7See the procedure outlined on page 537 of Wooldridge (2006).

UNLV Gaming Research & Review Journal ♦ Volume 15 Issue 2

The Effect of Online Gaming on Commercial Casino Revenue

directions are in line with economic theory and are signicant at the 0.05 alpha level.

Income (GDP) Elasticities

As a robustness check, the GDP elasticity from the 2SLS model is compared to

estimates of income elasticities from prior literature. An income elasticity value measures

the percentage change in gaming revenue given a one percentage change in income.

Since observations of internet gaming revenue in early years of the data set were equal

to zero, elasticities in the model could not be interpreted directly from a log-log model

specication, but instead were computed indirectly from the linear model.7 The short-

run income elasticity computed was 0.74 and the long-run income elasticity was 1.41.

Nichols and Tosun (2007) estimated that state long-run income elasticities with respect

to casino gaming varied widely. The authors measured a range from 0.22 to 2.29, which

includes both the short-run and long-run estimates from this study. Landers’ (2008b)

study on the demand for casino gaming estimated income elasticities from 1.43 to 1.91,

much closer to the long-run elasticity than the short-run. This difference may be due

in part to the emergence and rapid growth of internet gaming during the period of this

study, as compared to the established casino period studied in Landers (2008b).

ARIMA Modeling

Although the instrumental variable approach addresses potential model endogeneity

in the online gaming revenue parameter estimates, it does not address concerns over

potential unit root issues in the data. That is, if the variables measured in the model

are non-stationary, the coefcient estimates may suffer from spurious correlation, and

therefore be biased. To evaluate whether the results from the two-stage model suffer from

this issue, this section includes an ARIMA modeling process to render the variables from

the 2SLS process stationary and control for unknown model parameters. ARIMA models

use autoregressive (AR), integrated (I), and moving average (MA) terms to predict the

dependent variable. In this study, variables are rst rendered stationary to satisfy the

integration term, and then an ARMA model is tted using the Bayesian Information

Criterion (BIC) selection method (Schwarz, 1979).8

Trend Stationary Tests

To test whether the variables used in this model are stationary processes, an

augmented Dickey-Fuller unit root test is conducted. Non-stationary variables are then

differenced and re-tested until a stationary process is revealed. Table 4 summarizes

the results of the unit root tests. A second difference of each model variable is noted to

produce series that satisfy the unit root test at the 0.05 alpha level. Therefore, second

differences of the variables are used in the ARIMA process.

Table 4

Augmented Dickey-Fuller Unit Root Test Statistics

7 For a proof of the elasticity formulas, see appendix A.

8 Due to the limited number of observations, only ARMA processes up to three are evaluated to minimize the

BIC.

Although the instrumental variable approach addresses potential model endogeneity in

the online gaming revenue parameter estimates, it does not address concerns over potential unit

root issues in the data. That is, if the variables measured in the model are non-stationary, the

coefficient estimates may suffer from spurious correlation, and therefore be biased. To evaluate

whether the results from the two-stage model suffer from this issue, this section includes an

ARIMA modeling process to render the variables from the 2SLS process stationary and control

for unknown model parameters. ARIMA models use autoregressive (AR), integrated (I), and

moving average (MA) terms to predict the dependent variable. In this study, variables are first

rendered stationary to satisfy the integration term, and then an ARMA model is fitted using the

Bayesian Information Criterion (BIC) selection method (Schwarz, 1979).9

Trend Stationary Tests

To test whether the variables used in this model are stationary processes, an augmented

Dickey-Fuller unit root test is conducted. Non-stationary variables are then differenced and re-

tested until a stationary process is revealed. Table 4 summarizes the results of the unit root tests.

A second difference of each model variable is noted to produce series that satisfy the unit root

test at the 0.05 alpha level. Therefore, second differences of the variables are used in the ARIMA

process.

Table 4

Augmented Dickey-Fuller Unit Root Test Statistics

Variable

Difference

p-value

First

Difference

p-value

Second

Difference

p-value

Brick & Mortar Revenue

-1.055

.733

-2.568

.100

-2.872

.049

Real Online Gaming

Revenue

0.712

.990

-2.046

.267

-4.615

<.001

Real Gross Domestic

Product

0.843

.992

-2.304

.171

-3.769

.003

9Due to the limited number of observations, only ARMA processes up to three are evaluated to minimize the BIC.

Number of Commercial

Casino States

-2.654

.082

-1.542

.513

-5.350

<.001

ARIMA Results

As mentioned, ARIMA processes integrated of order two, with up to three autoregressive

or moving average terms were estimated and the final model was selected using a BIC

minimization procedure. The final specification was an ARIMA (2, 2, 3) process with real online

gaming revenue and real gross domestic product as independent variables. Following the criteria

for model evaluation, the final model specification dropped the number of states with

commercial casinos variable.10

Table 5

Results are provided in Table 5.

ARIMA Model Output

Variable

Beta

Real Online Gaming Revenue

-0.2959**

(0.0305)

Real Gross Domestic Product

0.0018**

(0.0005)

AR (1)

0.2317

(0.3213)

AR (2)

-0.3541

(0.3058)

MA (1)

0.1037

(0.2172)

MA (2)

-0.1037

(0.2172)

MA (3)

-1.000**

(<0.001)

Heteroskedastically robust standard errors are provided in brackets

*denotes significant at the 0.05 level, **denotes significant at the 0.01 level

n=17, BIC=28.81, Wald Chi2(6) = 9.4x1011, p<0.001.

10 In some ARIMA model specifications, the maximum likelihood function could not be maximized with all

explanatory variables. In these cases, reduced form models were estimated.