Forecasting key strategic variables in the casino tourism industry.

Moss, Steven E. ; Barilla, Anthony G. ; Moss, Janet 等

ABSTRACT

We examine the issues of forecasting industry gross revenue models in the casino gaming industries of Nevada, Mississippi and Atlantic City. Industry gross revenues are used as benchmarks for casino performance, a major source of state tax collection, an important part of a state's tourism industry and an important point of consideration for states contemplating legalizing gambling. Our model divides the time-series forecasts into two separate components, seasonality and trend. The results show all three states have distinctly different monthly seasonal patterns. Trend forecasting models and the presence of interventions such as September 11 are also shown to vary by region. In Mississippi, September 11 had an insignificant effect on casino gaming revenues. The effects of the September 11 intervention vary by region in Nevada. Six of the eight regions within Nevada do not conform to the overall Nevada state model. Aggregating time series data between states or within Nevada will lead to more complex, less accurate forecasts. The results indicate that in most cases aggregated or pooled time-series data should not be used in estimating models centered on forecasting revenues for casino and gaming establishments.

INTRODUCTION

Forecasting revenues in the casino gaming industry runs into the intrinsic problem of dealing with aggregating multiple time-series data sets. Time series data from three of the largest gaming regions in the United States, Atlantic City, Mississippi and Nevada, will be used to compare seasonal estimation and trend estimation in forecasting models. Finally, similar tests will be conducted focusing on the aggregated and pooling of multiple time series data on a state and national level.

Since 1988, when only Nevada and New Jersey (Atlantic City) offered casino gambling, the casino industry experienced explosive growth and became a significant source of state and local tax revenues. As of 2000, thirty-three states allowed more than 600 casinos to operate legally ("Legalized gambling," 2000). Roehl (1994) suggested that growth in legalized gambling was fueled by state governments wanting to create employment opportunities (ex: Indiana, Louisiana, and Mississippi), capture additional tax revenues and tourism monies. These along with a changing attitude toward gambling facilitated the boom in the casino industry. Surveys show that 92% of Americans approved of casino entertainment, 62% find casino gambling acceptable for anyone, and approximately 52% had played a lottery within the past 12 months ("Report indicates," 1997; Cabot, 1996).

Prior to World War II, Atlantic City ("The World's Favorite Playground") was a popular entertainment choice. After World War II, its popularity began to decline. The deterioration was attributed to the availability of air travel during the 1950s, the economical and social problems that urban cities faced during the 1960s, and a westward migration of the population. Since Atlantic City's economy was dependent on tourism, the decision was made to legalize gambling in 1976.

In 1978, Atlantic City reported 700,000 yearly visitors. In the same year Resorts International, Atlantic City's first casino opened. Over the next ten years a dozen casinos were built, and by 1988 the number of yearly visitors increased to over 30 million. In 1990 one of Atlantic City's biggest gaming establishments, the 51-story Taj Mahal, opened. The Taj Mahal broke from the "traditional-style" casino, offering grand-style design items such as crystal chandeliers and Italian marble. The Taj Mahal also offers over 5,000 slot machines and over 200 table games. The new, bigger more upscale casino has become an Atlantic City norm, including three 5-Star Diamond hotels one of which is the Trump Plaza. The Mirage, Harrah's Entertainment Inc., and Hilton International, some of the largest companies in the casino industry, now market themselves more as entertainment and resort destinations than casinos (Ben-Amos, 1997). In December 2002, the historic Claridge Casino Hotel and Bally's Atlantic City merged creating the largest casino resort in Atlantic City.

Most of the capital needed to build a casino comes from high-yield public market and bank loans. Financing a casino project is a moneymaker for both lenders and underwriters (Darsa, 1997). During the casino building boom of the 1990s, more and more banks became willing to finance casinos and gaming companies. In 1993 only eight fiduciary institutions were actively involved in the casino and gaming business, by 1996 that number soared to 26 (Ben-Amos, 1997). Currently, the Trump Plaza, Trump's Castle and the Taj Mahal are the only casinos in Atlantic City not publicly owned. The casino and gaming industry accounts for almost 90% of Atlantic City's total revenue. In comparison, Las Vegas' gaming industry generates approximately 60% of their city's total revenue (Lucas, 1996).

Construction and remodeling projects in Atlantic City declined after the terrorist attacks of September 11, 2001. The downturn in Atlantic City's economy and the loss in revenues in New York since 9-11 has prompted the state of New York to consider legislation allowing gambling in six locations around the state. However, Atlantic City is expecting major growth since the opening of the Atlantic City Convention Center and a new connector expressway over to the Marina casinos (Turpin, 2002).

In 1990, legislation in Mississippi authorized gaming on its navigable waterways. In mid-1992 the first casino opened. While many categorize Mississippi casinos as a form of riverboat gambling (Roehl, 1994), the large facilities with their adjoining hotels, restaurants, and entertainment facilities generate most revenues today. Mississippi currently ranks as the third largest casino market in the United States. The 2003 Mississippi Gaming Commission updated a study from Meyer-Arendt, 1995 and estimated more than 50 million people have visited the state's casinos each year since 1995. Furthermore, of the more than 50 million people, who patronize Mississippi's casinos annually, approximately 65% come from Mississippi or adjoining states, and at least 80% come from the southeastern U.S. (Mississippi Gaming Commission, 2003).

Mississippi's gaming commission consistently regulates casino operations, facilitating time-series analysis (Russell, 1997). During the period of 1992 to 2003, Mississippi annual casino gaming revenues increased from $121 million to over $2.7 billion, and the number of casinos grew to approximately 30 (Mississippi Tax Commission, 2004). Casino space in Mississippi now exceeds 1.4 million square feet.

The gaming commission casino gross revenues report divides the state into two regions, the river region and the gulf coast region. The river region is predominately casinos around Tunica, Mississippi, with the majority of these casinos located close to Highway 61 just south of Memphis, Tennessee. The gulf coast region is centered in Biloxi, Mississippi.

Tunica's proximity to Memphis allows it to offer higher profile events, such as heavyweight boxing matches, which helps to attract more day-gamblers along with vacationers. Biloxi's location on the Gulf of Mexico allows the casinos to package the natural attractions of the gulf along with a large number of golf courses with gambling.

Gambling in the state of Nevada starts with Las Vegas. Las Vegas was founded as a city in 1905 and the first gambling licenses were issued in 1931. Corporations entered the casino business in the 1960's and since have acquired most of the casinos. This corporate involvement signaled a makeover in industry strategy ("The history," n.d.). In 2001 alone, more than 35 million people visited Las Vegas (Las Vegas Convention and Visitors Authority, 2002). Studies show that 86 percent of Las Vegas visitors gamble while there, each with an average gambling budget in excess of $600. Air travel is important to the health of the Las Vegas casino industry as 48% of the cities visitors arrive by air. The events of September 11, 2001 had a dramatic impact on the airline industry and also affected the gambling industries in Nevada (Moss, Ryan, and Parker, 2004). In the first twelve months following September 11, Las Vegas gaming revenues declined $298 million from the prior twelve months.

The state of Nevada reports casino gaming revenues in eleven geographic regions, with the Las Vegas Strip being the largest revenue generator. Due to the size of the Las Vegas Strip relative to the other casino regions in Nevada, it is easy to overlook areas such as South Lake Tahoe or the Boulder Strip. Nine of the eleven geographic reporting regions in Nevada are identifiable regions, such as the Las Vegas Strip, and two are catch-all categories for casinos that do not fall in the other nine regions. This paper analyzes the eight largest regions in Nevada as measured by casino gross revenues.

SEGMENTATION AND FORECASTING STRATEGIC VARIABLES

Strategic variables such as, market size, segmentation, and growth rate, are important parts of strategic planning models. Capon and Palij (1994) assert that proper market definition and selection of a firm's market segment will increase the model's ability to produce accurate forecasts of strategic variables. Capon and Palij further show that increased accuracy in long-term forecasts of key strategic variables results in increases in a firm's performance relative to its competitors.

Effective market segmentation occurs when quantifiable differences between segments are observed (Mo and Havitz, 1994). Diaz-Martin et.al., 2000 asserts the importance for firms, within the tourism industry, to find groups of customers with homogeneous characteristics. Moreover, Diaz-Martin et.al., 2000 used a Chow test to segment data based on customer expectations. By identifying these groups of customers a market segment can be defined and a more effective strategy can be developed. This study will analyze geographic destination regions where customers have homogeneous behavior in terms of season-visiting selection and market growth patterns.

Forecasts are also used in planning, employee scheduling and staffing (Preez and Witt, 2002), revenue projection studies for government agencies (state gaming and tax commissions), both national and regional tourism organizations, and by the individual casinos or suppliers of facilities (Sheldon and Var, 1985).

The ability to identify the existence or non-existence of seasonality or the appropriate seasonal patterns is essential to successful forecasting. Butler (1994) concludes that problems in staffing, obtaining capital, and capacity are attributed to seasonality. Butler further asserts that little research has been conducted on the topic of seasonality in tourism data. Regional differences also play a role in tourism seasonality. Both Hunsaker (2001) and Moss et. al (2004) used quarterly and monthly data when testing seasonality patterns in casino gaming revenues. Preez and Witt (2003) hypothesize that time series data can be aggregated across regions to increase sample size and to improve forecasting accuracy data. Reece (2001) noted that the regional and seasonal affects of Las Vegas and Atlantic City-Cape May change with the level of aggregation in the data. Moreover, when heterogeneous regions are aggregated or pooled results become misleading, forecasting accuracy diminishes, and the models have to be more complex.

By examining two separate time-series forecasting components for each casino gaming revenue series we test the degree of homogeneity amongst geographic regions. Seasonality and trend patterns help to determine to what degree data can be aggregated or pooled.

DATA

Monthly time-series casino gaming-revenue data from the Atlantic City, Mississippi and Nevada regions are analyzed in this research. In all three regions casino gaming-revenues represent the amount a casino wins from gaming operations and not the revenues from other sources such as restaurant or hotel operations. New Jersey's Casino Control Commission provided monthly casino gaming revenues from December 1996 through December 2003 (in 2003 the annual casino gaming revenue was $4.489 billion) for the 13 individual casinos operating in Atlantic City.

The Mississippi casino gaming revenue series is for all casinos (excluding Indian Gaming) operating in the state of Mississippi between August 1992 and December 2003 (in 2003 the annual casino gaming revenue was $2.705 billion). The data is divided between two geographic regions, the River Region and the Gulf Coast Region. Data was collected from the Mississippi State Tax Commission, Miscellaneous Tax Bureau and Casino Gross Gaming Revenues reports.

Nevada is the biggest revenue generator and has the most geographic gambling regions. The data, November 1996 through November 2003, for Nevada casino gaming revenue is available to the public and was collected from the State of Nevada, Gaming Control Board, Tax License Division, and Monthly Win and Percentage Fee Collection reports. Annual casino gaming revenue for Nevada was $9.634 billion as of November 2003. Table 1 lists the different geographic regions within Nevada used in this study.

METHODOLOGY

We use a general-to-specific methodology. This approach has three advantages in tourism forecasting. First, the model does not require extensive data mining, because the independent variables are time lags of the dependent variable with dummy variables representing important calendar events. Second, we avoid the multiple specification problems associated with specific-to-general models where time dependency becomes a problem. Third, we avoid spurious correlation problems (Song and Witt, 2003).

We analyze eleven time series which all exhibit trends (a non-stationary series) and seasonality. In the first part of the research we use an ANOVA model to estimate the seasonality effects for each series and then to compare seasonal patterns between geographic regions both intrastate and interstate. Seasonality is estimated with a ratio to centered moving methodology (Bowerman & O Connell, 1993; Moss et al., 2003).

In the second part of the research, we will use an autoregressive model for panel time series data to estimate trend patterns and interventions. Witt, Song, and Louvieris (2003) assert that VAR models yield unbiased and highly accurate two to three year forecasts, while Preez and Witt (2003) conclude that univariate ARIMA models produce the most accurate tourism forecasts.

We deseasonalize each panel series with the appropriate seasonal indices prior to VAR estimation. For series with the same seasonal patterns the raw seasonal indices are pooled into one set. Deseasonalizing the series prior to estimating the trend model maintains the full series length versus seasonal differencing and seasonal lags. In addition, this approach substantially reduces the model complexity (Moss, Ryan and Parker, 2004).

Using Doan's (1996) approach after each state's model is estimated we perform a Chow test using dummy variables designating sub-samples making it possible to test the stability across the individual panel series and to correct for heteroscedasticity. Because we have equal sample sizes, the Chow test for equality of linear regression models is well behaved when the linear regression models exhibit heteroscedasticity (Ghilagaber, 2004). Finally, because estimation models of the states may have similar structural forms, we use the Chow test to test for model equality between states.

RESULTS

Seasonal patterns for the geographical reporting areas within each state are estimated. The raw seasonal monthly indices are calculated with a ratio-to-moving average methodology (an index representing the percentage of yearly average attributed for each month within the year). A seasonal index below one indicates a lower than average month. If the seasonal indices for a region do not deviate significantly from one then there is no seasonality in the time series. The ANOVA model reveals if monthly deviations are significant and if the geographic reporting areas within the state interact with the monthly seasonal patterns. Table 2 represents the results of the only geographic region for Atlantic City.

The model shows that Atlantic City does exhibit a seasonal pattern as the seasonal indices are significantly different from one. Figure 1 depicts the seasonal patterns. Figure 1 shows Atlantic City's busiest months are July and August and the lowest revenue months are January, February, and December.

[FIGURE 1 OMITTED]

The results for the two Mississippi regions reveal a significant monthly seasonal pattern. Since the interaction term is insignificant we infer that Mississippi's two geographic regions are not significantly different from each other, see Table 3 and Figure 2. This makes it possible to deseasonalize the two Mississippi regions with one set of seasonal indices.

[FIGURE 2 OMITTED]

With eight geographic regions Nevada's model is more complex. The estimated model, shown in Table 4, supports the presence of a monthly seasonal pattern. Moreover, the interaction between Nevada's geographic regions is significant, thus there is an indication that seasonal patterns vary by geographic reporting area. Figure 3 shows South Lake Tahoe has the most extreme seasonal pattern within Nevada, with up to a 49% monthly deviation. All eight of the Nevada regions have months where the seasonal index significantly deviates from one, which indicates seasonality in all the time series. Since none of the eight Nevada geographic regions follow the same seasonal patterns aggregating or pooling the regions would result in inaccurate seasonal indices. By aggregating or pooling regions with dissimilar seasonal patterns, seasonal indices may offset one another resulting in an inadequate estimation of the true seasonal variation. Therefore, we deseasonalize each region individually.

[FIGURE 3 OMITTED]

Because the Nevada regions have inconsistent seasonal patterns, we use the Las Vegas Strip, Nevada's largest revenue reporting area, for the purpose of comparison with Atlantic City and Mississippi. Table 5 and Figure 4 show significantly different seasonal patterns between the three areas. Table 6 compares all 11 regions; Nevada's eight regions, Mississippi's two regions, and Atlantic City.

[FIGURE 4 OMITTED]

Part two of this research focuses on forecasting trend models for each of the geographic regions, both inter-and-intrastate. A first difference transformation is used prior to estimating the forecasting model because the deseasonalized series are all non-stationary. Table 7 reveals the resulting forecasting model for Atlantic City. The residuals of this model are verified to be white noise by observing the Ljung-Box Q-Statistics, auto-correlation function, and partial auto-correlation function. The model has an R2 (which in this case is for the trend portion of the transformed time series) of 45%. The R2 for the trend portion of the non-transformed time series is approximately 54%. An intervention variable for September 11, 2001 is found to be significant and negative in the Atlantic City forecasting model. The implication is that Atlantic City casino gaming revenues were negatively affected as a result of September 11.

Table 8 shows the estimated model (AR2) for Mississippi's two regions. The September 11, 2001 intervention variable was tested and found insignificant in Mississippi.

A Chow test is used to determine if there is a difference between the two Mississippi geographic reporting regions. Table 9 reveals the results of the Chow test, indicating no difference between Mississippi's two geographic reporting regions. Implying both regions conform to the overall estimated model, shown in Table 8, or pooling/aggregating is possible.

The eight regional Nevada series are also transformed with first differencing to obtain stationary series prior to estimation of the trend model. An additional problem arises within the Nevada series in the fact that the Las Vegas Strip gaming revenues are much greater than the other geographic regions in the state. To avoid scaling problems the eight first differenced series are standardized prior to estimation of the trend model. Table 10 displays the resulting model.

A complexity problem within the AR model occurs when a complex lag structure is needed to obtain a white noise residual series. Since each of the eight Nevada regions contribute to the model, the complexity arises from each individual region having its own and different lag structure. The Chow test shown in Table 11 reveals the different lag structures.

Table 11 also reveals significant and dramatic differences in trend equations between the eight geographic regions. We use a Chow test, for Nevada, in which dummy variables and interaction terms are tested one geographic region at a time. The number of lags required and the coefficients for the lag terms differ by geographic reporting area. The September 11, 2001 effect also differs within the geographic reporting areas. In Boulder, North Las Vegas and South Lake Tahoe the estimated negative effect of September 11 (as shown in the overall model) is reversed within the Chow test. For Downtown Las Vegas, Laughlin, and the Las Vegas Strip the estimated negative impact of September 11 is shown to have a greater negative impact than estimated in Nevada's overall model, shown in Table 10. Elko and Washoe are the only two regions that do not differ significantly from the overall forecasting model estimated for Nevada in either the impact of September 11 or autoregressive terms.

Finally, we use a Chow test to determine if the Mississippi series and the Atlantic City series can be combined to estimate a single model. Recall, since prior analysis indicated differences in forecasting models within the state, Nevada was excluded from this part of the analysis. The Chow test, shown in Table 12, indicates that the models for the two states are different. The difference arises from the impact of September 11 on the gaming revenues. In Mississippi, September 11 did not have a significant impact on casino gaming revenues, whereas, in Atlantic City, the impact was significant and negative. Other than September 11 both states gaming revenues follow a two lag auto-regressive model with no significant coefficient difference.

CONCLUSIONS

Industry gross revenues are forecasted for Nevada, Mississippi and Atlantic City's casino gaming industry. These revenues are a benchmark for individual casino performance and an important planning and strategic variable when dealing with capacity constraints. Casino gaming revenues are also important for state forecasts of potential tax revenues. For example, the casino gaming revenue tax accounts for as much as 10% of Mississippi's total tax collections. Trend and seasonal patterns are an important consideration for states considering legalizing casino gaming as a means of increasing tax collections. States use forecasts and past collection data from regions where existing casino gaming is already legal to estimate potential future tax collections.

This research divided time series forecasts into two components, seasonality and trend. We avoid the temptation of increasing sample size by pooling multiple time series data into a single panel model; even though it has been argued that the larger pooled samples may lead to more accurate forecasting models (Preez and Witt 2003). Our results show that, in general, multiple time series should not be aggregated or pooled when forecasting casino gaming revenues.

All three states are found to have distinctly different monthly seasonal patterns. The states with multiple geographic reporting regions, Mississippi and Nevada, had conflicting seasonality results. The two regions in Mississippi have no significant differences in seasonal patterns. Nevada's eight reporting regions, on the other hand, all follow different monthly seasonal patterns. These findings require that Nevada seasonality be addressed at the individual region level, while Mississippi and Atlantic City can be analyzed at the aggregate state level. If a panel was constructed combining the individual Nevada regions or the aggregate Nevada state data with Mississippi and Atlantic City erroneous seasonal patterns would result. For example, January in Atlantic City has a seasonal index of .9, whereas January on the Las Vegas Strip has a seasonal index of 1.15. Combining area specific seasonal indices would offset one another resulting in a forecast with a gross underestimation of seasonal fluctuations.

Trend forecasting models and the presence of interventions such as September 11 are also shown to vary by region. In Mississippi, September 11 had an insignificant effect on either regions casino gaming revenues. The effects of the September 11 intervention vary by region in Nevada. Six of the eight regions within Nevada do not conform to the overall Nevada state model. Aggregating time series data between states or within Nevada will lead to more complex, less accurate forecasts.

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Steven E. Moss, Georgia Southern University

Anthony G. Barilla, Georgia Southern University

Janet Moss, Georgia Southern University

Table 1: Nevada Revenue by Region

Nevada's Gaming Regions % Revenue by Region

Las Vegas Strip (LVS) 49.2%
Downtown Las Vegas (DLV) 7.5%
North Las Vegas (NLV) 2.3%
Washoe 11.7%
Laughlin (LL) 5.9%
Boulder Strip (BS) 6.4%
Elko 2.4%
South Lake Tahoe (SLT) 3.6%

Table 2: Atlantic City Seasonality

Source Sum of df Mean F Sig.
 Squares Square

Model 73.447 12 6.121 5072.752 .000
MONTH 73.447 12 6.121 5072.752 .000
Error 0.007 61 0.012
Total 73.521 73

Table 3: Mississippi Seasonality

Source Sum of df Mean F Sig.
 Squares Square

Model 234.773 24 9.782 2794.669 .000
Inter 0.031 11 0.003 0.803 .637
MONTH 0.719 11 0.065 18.663 .000
AREA 0.000 1 0.000 0.000 .997
Error 0.732 209 0.004
Total 235.505 233

Table 4: Nevada Seasonality

Source Sum of df Mean F Sig.
 Squares Square

Model 589.050 95 6.201 1819.186 .000
MONTH 1.057 11 0.096 28.182 .000
AREA 0.006 7 0.000 0.027 1.000
Inter 4.409 76 0.058 17.021 .000
Error 1.667 489 0.003
Total 590.717 584

Table 5: Comparison of Atlantic City, the Las Vegas Strip,
and Mississippi

Source Sum of df Mean F Sig.
 Squares Square

Model 272.351 36 7.565 4030.002 .000
MONTH 0.651 11 0.059 31.539 .000
AREA 0.003 2 0.001 0.076 .927
Inter 0.635 22 0.029 15.380 .000
Error 0.441 235 0.018
Total 272.792 271

Table 6
Seasonal Indices

Mon. AC MS BS Down Elko

1 0.90 * 0.99 1.06 * 1.08 * 0.96
2 0.91 * 0.99 0.97 0.97 0.91 *
3 1.01 1.07 * 1.09 * 1.11 * 1.09 *
4 0.98 1.00 1.01 1.01 1.00
5 1.05 * 1.01 1.00 1.03 0.99
6 1.02 0.99 0.97 0.93 * 1.00
7 1.16 * 1.14 * 1.02 0.96 1.05 *
8 1.17 * 1.04 * 0.94 * 0.97 1.02
9 1.01 0.97 0.95 * 0.98 1.10 *
10 0.98 0.97 * 1.04 1.06 * 1.06 *
11 0.95 * 0.94 * 0.95 * 0.94 * 0.91 *
12 0.87 * 0.92 * 0.99 0.95 * 0.88 *

Mon. LL LVS NLV SLT Washoe

1 1.12 * 1.15 * 1.08 * 0.86 * 0.87 *
2 1.05 * 0.93 * 1.00 0.80 * 0.82 *
3 1.19 * 1.01 1.12 * 0.92 * 1.01
4 1.04 0.95 * 0.99 0.83 * 0.99
5 1.01 1.04 1.01 0.96 1.09 *
6 0.92 * 0.90 * 0.95 * 1.03 1.04
7 0.94 * 0.98 0.99 1.49 * 1.11 *
8 0.91 * 1.03 0.97 1.33 * 1.12 *
9 0.94 * 0.98 0.92 * 1.11 * 1.09 *
10 1.02 1.01 1.00 0.96 1.06 *
11 0.98 0.98 0.98 0.79 * 0.93 *
12 0.87 * 1.03 0.97 0.93 * 0.89 *

* significant at the 5% level.

Table 7: Trend model for Atlantic City

Variable Coeff T-Stat Signif

Constant 1626342.284 1.067 0.286
AR lag 1 -0.823 -9.772 0.000
AR lag 2 -0.340 -3.433 0.001
911 -10218711.072 -6.425 0.000

Differencing = 1
Series = 1
R2 = 45%

Table 8: Trend model for Mississippi

Variable Coeff T-Stat Signif

Constant 1099993.717 3.475 0.001
AR lag 1 -0.693 -11.151 0.000
AR lag 2 -0.444 -6.409 0.000

Differencing = 1
Series = 2
R2 = 38%

Table 9: Mississippi Chow Test

Variable Coeff T-Stat Signif

Constant 1504258.357 3.031 0.002
AR lag 1 -0.745 -10.058 0.000
AR lag 2 -0.473 -5.072 0.000
Gulf Coast
GC -806859.726 -1.285 0.199
GC * AR lag 1 0.145 1.136 0.256
GC * AR lag 2 0.073 0.562 0.574

Chi-Squared(3) = 2.952 with Significance Level 0.399
Differencing = 1
R2 = 38%

Table 10: Trend model for Nevada

Variable Coeff T-Stat Signif

Constant 0.007 0.242 0.808
AR lag 1 -0.840 -21.059 0.000
AR lag 2 -0.654 -11.990 0.000
AR lag 3 -0.336 -6.133 0.000
AR lag 4 -0.260 -6.411 0.000
AR lag 9 0.091 2.942 0.003
911 -0.468 -2.320 0.020

Differencing = 1
Series standardized
Series = 8
R2 = 47%

Table 11: Chow Tests for Nevada

Variable Coeff T-Stat Signif

Boulder Strip R2 = 49%

BS -0.008 -0.131 0.895
BS * AR lag 1 -0.311 -2.929 0.003
BS * AR lag 2 -0.376 -2.354 0.019
BS * AR lag 3 -0.058 -0.359 0.719
BS * AR lag 4 -0.096 -0.834 0.405
BS * AR lag 9 0.285 3.528 0.000
BS * 911 0.743 2.743 0.006

Chi-Squared(7) = 71.677 with Significance Level 0.000

Down Town Las Vegas R2 = 48%

DTL -0.057 -0.690 0.490
DTL * AR lag 1 -0.077 -0.658 0.510
DTL * AR lag 2 -0.100 -0.688 0.492
DTL * AR lag 3 -0.287 -2.000 0.046
DTL * AR lag 4 -0.094 -0.789 0.431
DTL * AR lag 9 -0.285 -3.689 0.000
DTL * 911 -0.484 -1.846 0.065

Chi-Squared(7) = 26.567 with Significance Level 0.000

Elko 0.030 0.314 0.754
Elko * AR lag 1 0.147 1.160 0.246
Elko * AR lag 2 0.007 0.048 0.961
Elko * AR lag 3 -0.019 -0.106 0.915
Elko * AR lag 4 -0.004 -0.035 0.972
Elko * AR lag 9 -0.007 -0.067 0.946
Elko * 911 -0.240 -0.812 0.417

Chi-Squared(7) = 2.127 with Significance Level 0.952

Laughlin R2 = 48%

LL 0.028 0.293 0.769
LL * AR lag 1 0.249 2.146 0.032
LL * AR lag 2 0.018 0.135 0.893
LL * AR lag 3 -0.040 -0.328 0.743
LL * AR lag 4 -0.027 -0.235 0.814
LL * AR lag 9 0.102 1.169 0.242
LL * 911 0.878 -3.340 0.001

Chi-Squared(7) = 18.874 with Significance Level 0.009

Las Vegas Strip R2 = 48%

LVS -0.023 -0.244 0.807
LVS * AR lag 1 0.162 1.486 0.137
LVS * AR lag 2 0.268 1.620 0.105
LVS * AR lag 3 0.285 1.756 0.079
LVS * AR lag 4 0.232 2.030 0.042
LVS * AR lag 9 -0.202 -2.247 0.025
LVS * 911 -0.927 -3.215 0.001

Chi-Squared(7) = 38.498 with Significance Level 0.000

North Las Vegas R2 = 48%

NLV 0.006 0.073 0.942
NLV * AR lag 1 -0.166 -1.478 0.139
NLV * AR lag 2 -0.039 -0.217 0.828
NLV * AR lag 3 0.189 1.136 0.256
NLV * AR lag 4 0.190 1.393 0.163
NLV * AR lag 9 0.160 1.711 0.087
NLV * 911 0.897 2.687 0.007

Chi-Squared(7) = 18.135 with Significance Level 0.011

South Lake Tahoe R2 = 48%

SLT 0.026 0.312 0.755
SLT * AR lag 1 -0.061 -0.664 0.506
SLT * AR lag 2 0.050 0.326 0.744
SLT * AR lag 3 -0.249 -1.846 0.065
SLT * AR lag 4 -0.151 -1.453 0.146
SLT * AR lag 9 -0.130 -1.787 0.074
SLT * 911 1.030 4.986 0.000

Chi-Squared(7) = 51.062 with Significance Level 0.000

Washoe R2 = 47%
WAS 0.010 0.123 0.902
WAS * AR lag 1 0.007 0.056 0.955
WAS * AR lag 2 0.024 0.170 0.865
WAS * AR lag 3 0.037 0.216 0.829
WAS * AR lag 4 -0.043 -0.406 0.685
WAS * AR lag 9 0.080 1.103 0.270
WAS * 911 0.086 0.306 0.760

Chi-Squared(7) = 2.626 with Significance Level 0.917

Table 12: Chow test for Atlantic City/Mississippi.

Variable Coeff T-Stat Signif

Constant 935608.308 2.295 0.022
AR lag 1 -0.737 -10.352 0.000
AR lag 2 -0.472 -5.786 0.000
911 468690.366 0.471 0.638

Atlantic City

AC 690733.976 0.438 0.661
AC * AR lag 1 -0.086 -0.778 0.437
AC * AR lag 2 0.133 1.038 0.299
AC * 911 -10687401.438 -5.696 0.000

R2 = 44%
Differencing = 1
Series = 3
Chi-Squared(4) = 153.062 with Significance Level 0.000