Assessing the impact of Atlantic City casinos on Nevada gaming revenues.

The commencement of casino gaming activities in Atlantic City, New Jersey, during 1978 marked the end of Nevada's virtual monopoly of casino-style gambling.(1) In the 14 years hence, apparently no quantitative studies have been undertaken to discern how Nevada gaming has been impacted by this

event. Most experts downplay the significance of the Atlantic City market due to its distance from Nevada |e.g., Cargill and Morus, 1988~. Yet, Thompson |1985~ suggests that the effective market for casino gambling is national in scope and is linked to vacation and recreation time. The legislatively commissioned study Fiscal Agenda for Nevada |Ebel, 1990~ surmises that Atlantic City did not significantly affect the Nevada gaming industry before 1980 and proposes that since then, "the evidence seems to indicate that the legalization of casino gambling in Atlantic City has had a measurable negative impact on the Las Vegas visitor industry." Unfortunately, the study presents no rigorous analysis of the magnitude of this impact on Nevada gaming revenues.

Nevada's gaming industry plays a prominent role in the economic organization of the state.(2) It has been suggested that 60 percent of Nevada employment is in some way tied to the gaming industry |Cargill and Morus, 1988~. Direct taxes on gaming activity alone account for over 40 percent of the state's general revenue. But Nevada's gaming industry faces an uncertain future because legalized games of chance have enjoyed a recent widespread level of public acceptance |Eadington, 1991~. Thirty-two states now permit some type of lottery--riverboat casinos have just begun operating along the Mississippi River, and localized gambling is legal in Colorado and South Dakota. Nevertheless, in terms of casino-type gaming, the only major foreign (i.e., external) market is Atlantic City.

It is widely accepted that most state economies are affected to some degree by general business conditions |Sherwood-Call, 1988~; although, until Cargill's paper in 1979, many experts believed Nevada was an exception. The case for dependencies among regional economies has been recognized and embraced in numerous studies |LeSage, 1990~, however, such approaches have typically exploited propinquity through the construction of adjacent-state and gravity variables. Atlantic City is nearly 2,500 miles from Nevada.

The purpose of this paper is to quantify the impact of the Atlantic City casino gaming activity on Nevada gross taxable gaming revenues by using a dynamic unobserved components time series model. The approach is an extension of the study by Shonkwiler |1992~ which documented the flexibility and power of using a structural time series model in the forecasting of Nevada gaming revenues. Structural time series models have the ability to represent local linear (stochastic) trends and stochastic seasonality. These models appear to have particular relevance when regional time series data are nonstationary as recognized by LeSage |1990~. The local linear or stochastic trend model applied in the earlier study is augmented with exogenous variables to explicitly account for the effects of changing consumer incomes, Atlantic City play, and the California lottery. To motivate the analysis, some historical perspective of the Nevada gaming economy is provided. Then, the structural time series model is developed and applied to quarterly data.

I. Background

Consider the quarterly deflated Nevada gross taxable gaming revenues data presented in Figure I for the period 1969:1 through 1991:2.(3) These data exhibit seasonal variation and a strong upward trend. Since undeflated or nominal gross taxable gaming revenues represent the money actually spent (lost) by casino players, the deflated series can be considered a quantity index of the demand for gaming.(4) This index experienced strong growth during the 1970s, stalled during the inflation and subsequent recession of the early 1980s, and then continued growing the remainder of the 1980s. These features are better captured in Figure II, which illustrates year-over-year percentage rates of growth.

The horizontal lines in Figure II represent the average rates of growth of real gaming revenues. For the period 1970:1 through 1979:4, the average real growth rate was 8.02 percent, and for the period 1983:1 through 1991:2, the average real growth rate was 4.77 percent.(5) A t-test that the mean growth rates in both periods are equal yields a test statistic of 3.23 with 72 degrees of freedom.(6) Clearly this hypothesis can be rejected at any customary level of significance. Although the latter period was marked by the operation of nine or more Atlantic City casinos, it would be naive to ascribe the lower growth rate to this factor alone. A number of socioeconomic factors could account for slower growth in the demand for gaming; yet if these factors were operating at the national level, they should likely impact Atlantic City activity in a similar manner. However, over the same 1983:1 through 1991:2 period, year-over-year growth in real casino play averaged 10.9 percent in Atlantic City.(7)

TABLE 1

Las Vegas Visitors by Region

Period                 East   Midwest   South   West

                          (Thousands of Visitors)

1975-76 average        1090     1752     1041   5066
1978-80 average        1348     2393     1239   5815
1985-87 average         757     2287     1730   9821

                       East   Midwest   South   West

                            (Percentage Change)

1978-80 vs. 1975-76    23.7     36.6     19.0   14.8
1985-87 vs. 1978-80   -43.8     -4.4     39.6   68.9

Source: Adapted from Table 6.2 in R. D. Ebel, ed. |1990~, A
Fiscal Agenda for Nevada.

Alternatively, consider Table 1 which presents average numbers of Las Vegas visitors by region for three disjoined periods. Particular attention should be focused on the differences in regional rates of growth. Between the first and second periods, the east and midwest display higher rates of growth than the south and the west, but this relationship changes when comparing the 1985-87 period to the 1978-80 period. In fact, average visitor levels from the east and midwest actually decline in the face of an almost 69 percent increase of western visitors, and note this occurs despite a much higher base level.

Issues of proximity could be used to explain the higher levels of western visitors, but this does not resolve the disparities in growth rates. The observed patterns of rates of change are consistent with the notion that Atlantic City siphoned off Las Vegas visitors with its pull being greatest on locations nearby and diminishing over distance. The fact that visitors from the south still showed strong gains relative to the east and midwest can be explained by the fact that several southern states (notably Texas) are closer to Las Vegas than to Atlantic City and also some regional biases against the northeast still exist in the south.

If it were assumed that without the advent of gaming in Atlantic City eastern and midwestern visitor growth rates would have matched those of the south (which are still 43 percent less than those of the west), Las Vegas would have seen about 15 percent more visitors during the 1985-87 period. Further, if it were assumed that the other regions' growth rates would have matched that of the west, about 25 percent more visitors would have arrived. Whether Las Vegas's gross taxable gaming revenues would have expanded proportionately is merely speculation.(8) Nevertheless, these observations on regional visitor levels and gaming growth rates establish a prima facie case that Atlantic City gaming may have impacted Nevada gross taxable gaming revenues.

II. Modeling Considerations

A formal quantitative approach is required in order to infer the magnitude of the impact of Atlantic City casino gaming on Nevada taxable gaming revenues. A major impediment to performing such an analysis pertains to measuring the Atlantic City gamblers who, in the absence of casinos there, would have traveled to Nevada. Of course these gamblers are not directly observed, and their potential losses in Nevada cannot be gauged either. Thus, efforts are focused on constructing a variable to account for gambling expenditures foregone in Nevada due to the operation of Atlantic City casinos. It is hypothesized that this unobserved or latent variable is related to the level of Atlantic City gaming activity.

To measure gaming activity or intensity in Atlantic City, the sum of the deflated drop and handle is used. Again, the author argues that this deflated value has the interpretation of a quantity index. In this case, it may be considered as the demand for wagering in Atlantic City casinos. Whether the amount of play in Atlantic City displaces some Nevada gambling expenditures must be determined empirically. A dynamic unobserved components model is used because the competitive force of Atlantic City is not directly observed. Rather, it is indicated by the magnitude of the amount of wagering occurring there.

The basic model is given by the three equation system:

|Y.sub.t~ = ||Mu~.sub.t~ + |X.sub.t~ |Alpha~ + ||Epsilon~.sub.t~, (1)

|Mathematical Expression Omitted~

and ||Beta~.sub.t~ = ||Beta~.sub.t-i~ = ||Epsilon~.sub.t~. (3)

Expression (1) is termed the measurement equation with |y.sub.t~ in this case representing the |t.sup.th~ observation on deflated quarterly Nevada taxable gaming revenues. The unobserved component, ||Mu~.sub.t~, represents the level of the series |y.sub.t~, and |X.sub.t~ is a row vector of K exogenous variables which are weighted by the estimable parameters in the K element column vector |Alpha~. The structural error |Epsilon~, is assumed drawn from a white noise process.

The evolution of the unobserved component or state, ||Mu~.sub.t~, is given by equation (2). This state equation also contains exogenous variables, |Z.sub.t~, that typically enter in first difference form |Harvey, 1989, p. 410~, as indicated by the use of the difference operator, |Delta~. The vector |Gamma~ contains the estimable parameters which weight corresponding elements in |Delta~|Z.sub.t~. Note that the level equation depends on a growth rate, ||Beta~.sub.t-1~, and may be corrupted by the white noise process, ||Eta~.sub.t~, which is assumed to be independent of the ||Epsilon~.sub.t~, process. The third equation indicates that the growth rate also is an unobserved component that evolves according to a random walk.

The reduced form associated with the basic model in equations (1-3) can be obtained by successive differencing of the measurement equation (1) and substitution of terms. This yields:

|Delta~|y.sub.t~ = |Delta~||Mu~.sub.t~ + |Delta~|X.sub.t~ |Alpha~ + |Delta~||Epsilon~.sub.t~ = |Delta~|X.sub.t~ |Alpha~ + ||Beta~.sub.t-1~ + |Delta~|Z.sub.t~ |Gamma~ + |Delta~||Epsilon~.sub.t~ + ||Eta~.sub.t~, (4)

||Delta~.sup.2~ |y.sub.t~ = ||Delta~.sub.2~|X.sub.2~ |Alpha~ + |Delta~||Beta~.sub.t-1~ + ||Delta~.sup.2~|Z.sup.t~ |Gamma~ + ||Delta~.sup.2~ ||Epsilon~.sub.t~ + |Delta~||Eta~.sub.t~

= ||Delta~.sup.2~|X.sub.t~ |Alpha~ + ||Delta~.sup.2~|Z.sub.t~ |Gamma~ + ||Delta~.sup.2~||Epsilon~.sub.t~ + |Delta~||Eta~.sub.t~ + ||Xi~.sub.t-1~, and (5)

||Delta~.sub.2~ ||Epsilon~.sub.t~ + |Delta~ ||Eta~.sub.t~ + ||Xi~.sub.t-1~ = ||Epsilon~.sub.t~ - 2 ||Epsilon~.sub.t-1~ + ||Epsilon~.sub.t-2~ + ||Eta~.sub.t~ - ||Eta~.sub.t-1~ + ||Xi~.sub.t-1~.

Thus, the reduced form has the stochastic structure of a restricted ARIMA (0, 2, 2). If |Mathematical Expression Omitted~, then the reduced form is doubly integrated

||Delta~.sup.2~ |Y.sub.t~ = ||Delta~.sup.2~ |X.sub.t~ |Alpha~ + ||Delta~.sup.2~ |Z.sup.t~ |Gamma~ + ||Xi~.sup.t-1~, (6)

and the parameters may be estimated by standard regression methods using the second differences of the data. If |Mathematical Expression Omitted~, then the system may be represented as

|Delta~ |Y.sub.t~ = |Delta~ |X.sup.t~ |Alpha~ + |Delta~ |Z.sub.t~ |Gamma~ + ||Beta~.sub.0~t + |Delta~||Epsilon~.sub.t~ + ||Eta~.sub.t~, (7)

which suggests that the level is stochastic but not the growth rate. Finally, if |Mathematical Expression Omitted~, then the reduced form is simply

|Y.sub.t~ = |X.sub.t~ |Alpha~ + |Z.sub.t~ |Gamma~ + ||Beta~.sub.0~t + ||Epsilon~.sub.t~. (8)

Although the stochastic specification of the structural model depends on only three parameters (and the initial conditions ||Mu~.sub.0~ and ||Beta~.sub.0~), it nests a number of important specifications. Of particular value is that the model provides a means for testing whether a series is trend stationary |Mathematical Expression Omitted~ or difference stationary |Mathematical Expression Omitted~. Nelson and Kang |1981~ point out that regressing a difference stationary series against time will result in the incorrect inference that time is a statistically significant variable. Furthermore, regressions on the levels of difference stationary variables that are not co-integrated |Engle and Granger, 1987~ can result in a host of asymptotic divergences involving both parameters and test statistics |Durlauf and Phillips, 1988; Stock and Watson, 1988~. The inherent feature of the basic structural model is that it provides a local approximation to a linear trend by allowing the level and slope to change slowly over time according to a random walk mechanism |Harvey, 1989~.

Seasonality may be introduced in the basic structural model by constructing quarterly dummy (binary) variables and respecifying (1) as:

|y.sub.t~ = ||Mu~.sub.t~ + |X.sub.t~ |Alpha~ + ||Delta~.sub.1~ |d.sub.1t~ + ||Delta~.sub.2~ |d.sub.2t~ + ||Delta~.sub.3~ |d.sub.3t~ + ||Epsilon~.sub.t~. (9)

where |d.sub.it~ are the dummy variables and ||Delta~.sub.i~ are the associated parameters. A characteristic of this specification is the assumption that the seasonal patterns are constant over the sample. However, this is an empirical question that can be addressed using the approach of Harvey and Todd |1983~. Following their development, a process is presumed to generate the quarterly seasonal components according to:

|Mathematical Expression Omitted~

where ||Omega~.sub.t~ is independently and identically distributed with mean zero and variance is |Mathematical Expression Omitted~. This formulation allows the seasonal components to evolve over time by a mechanism that insures the sum of the seasonal components over any four consecutive quarters to have an expected value of zero |Harvey and Todd, 1983~. If |Mathematical Expression Omitted~, then the seasonal components are considered non-stochastic and a specification similar to (9) may be used.

III. The Empirical Model

As mentioned, the series to be modeled is the Nevada quarterly deflated gross taxable revenue series. Ninety observations span the period 1969:1 through 1991:2. Work by Cargill |1979~ has suggested that gaming revenues are affected by the business cycle so real disposable income (RDI) enters the measurement equation as an exogenous variable. Furthermore, Cargill has advocated that the California lottery, which came on line in the fourth quarter of 1985, has impacted Nevada gaming.(9) To capture this influence, total quarterly California lottery expenditures deflated by the personal disposable income price deflator are represented by the exogenous variable CAL in the measurement equation.

In the state equation, a variable (AC) representing wagering activity in Atlantic City is specified. It is constructed as the average deflated drop and handle over the preceding four quarters. Because wagering activity in the current quarter is not used to construct AC, issues surrounding the potential for simultaneous equations bias are avoided. However, the resulting series displays a rather smooth trend and seasonal variations are lost. To rectify this, seasonal variation was reintroduced by weighting a given observation of AC by a corresponding seasonal factor.(10) In this manner, the unique seasonal characteristics of the AC series are maintained.

The empirical dynamic unobserved components model then is

|Mathematical Expression Omitted~

Estimation of the unknown variances and parameters in (11) is accomplished using maximum likelihood under the assumption that the white noise processes are drawn from independent normal distributions. Initial results suggested that |Mathematical Expression Omitted~ and |Mathematical Expression Omitted~ were not significantly different than zero. A likelihood ratio test of this hypothesis yielded a test statistic of 1.36, which is distributed as a chi-square with two degrees of freedom. Accepting this hypothesis means that (11) can be cast in the simpler form

|y.sub.t~ = ||Mu~.sub.t~ + ||Alpha~.sub.1~ |RDI.sub.t~ + ||Alpha~.sub.2~ |CAL.sub.t~ + ||Alpha~.sub.3~ |d.sub.2t~ + ||Alpha~.sub.4~ |d.sub.4t~ + ||Alpha~.sub.5~ |d.sub.5t~ + ||Epsilon~.sub.t~

||Mu~.sub.t~ = ||Mu~.sub.t-1~ + ||Beta~.sub.0~ + ||Gamma~.sub.1~ |Delta~ |AC.sub.t~ + ||Eta~.sub.t~. (12)

The |d.sub.it~ variables account for constant seasonal variation in the quarterly Nevada gaming revenues series. They are constructed in such a manner that the implied seasonal adjustment for the first quarter is |-|Alpha~.sub.3~|-|Alpha~.sub.4~|-|Alpha~.sub.5~.

Estimation results for the model represented by (12) are reported in Table 2. The statistical significance of |Mathematical Expression Omitted~ can be interpreted as meaning that the quarterly gross taxable gaming revenue series is difference stationary (follows a random walk). Model assessment is aided by the inclusion of a standard squared coefficient of determination as well as |Mathematical Expression Omitted~ which measures the reduction in variance the model provides relative to the variance of the series |y.sub.t~ - |Y.sub.t-4~. The measure |Mathematical Expression Omitted~ (1) accounts for the level of first order autocorrelation of the estimated innovations (residuals) and the Box-Ljung statistic is a test that the innovation series is white noise. It is distributed as chi-square with 10 degrees of freedom.

The three exogenous variables RDI, CAL, and |Delta~AC all enter the model with the expected signs, and the magnitudes of the t-values on the estimated coefficients suggest they are estimated with good precision. To assess the impacts of these exogenous variables, the reduced form expression derived from (12) can be used.(11) The impact of

|y.sub.t~ = ||Mu~.sub.1~ |RDI.sub.t~ + ||Alpha~.sub.2~ |CAL.sub.t~ + ||Beta~.sub.0~t + ||Gamma~.sub.1~ |AC.sub.t~ + ||Eta~.sub.1~ / |Delta~ + ||Epsilon~.sub.t~ (13)

each of the conditioning variables given a one unit change in the variable is, ceteris paribus, its associated coefficient. While such an interpretation is proper in a static, single-period context, it may not hold in a dynamic, multiple-period context. With this TABULAR DATA OMITTED caveat in mind, Figures III and IV show how Atlantic City casino gambling and the California lottery have impacted Nevada gross taxable revenues.(12)

Figure III traces out the estimated reduction in Nevada gross taxable gaming revenues due to Atlantic City competition. As suggested by the Ebel study, prior to 1980 Atlantic City had little impact. But with a number of casino openings in the early 1980s, the competitive pressure of Atlantic City mounted rapidly. This is more easily seen in Figure IV which depicts this estimated revenue reduction as a percentage of observed Nevada gross taxable revenues. By 1985, the impact of Atlantic City reached an apparently stable level of reducing Nevada gaming revenues by about 10 to 12 percent. Also, the impacts are seasonal. They are least severe in the first quarter and peak in the third quarter. This would be consistent with the relative attraction of Atlantic City in the winter months versus the summer months.

Also included in Figure IV are the impacts of the California lottery expressed as a percentage reduction in observed Nevada gross taxable gaming revenues. Note that the lottery's impact was strongest in its first quarter of operation when it was estimated to have accounted to about a 5 1/2 percent reduction in gaming revenues. Since its inception, it is estimated that the lottery has averaged just under a 3 percent reduction.

This result is about 1 percentage point less than that estimated by Cargill and Raffiee |1990~ who used only a dummy variable to capture the lottery's effect.

Table 3 is provided to summarize the magnitudes of the estimated impacts of Atlantic City and the California lottery on a fiscal year basis. Several matters need to be disclosed to temper the credence given to the numbers reported therein. First, the numbers are derived from parameter estimates that have associated standard errors. Both these measures are themselves conditioned by the empirical specification chosen. Further, the model which represents Nevada gaming revenues is dynamic and contains a unit root. This means that the effect of a shock (disturbance) does not die out over time. Hence, there is no clear assurance that if the California lottery or Atlantic City casino gambling had not arisen that Nevada gross taxable gaming revenues would have attained levels reflecting the addition of the estimated revenue reductions. Nevertheless, the estimates presented in Table 3 represent one scenario which is based on an apparently robust econometric model.

With the above caveats in mind, the implications for Nevada's gaming revenue tax collections can be assessed. Using an effective tax rate of 6 percent leads to the finding that in fiscal 1990-91, Nevada may have foregone about $46 million in gaming tax collections due to the operations of Atlantic City casinos and the California lottery. Of course, this is a direct impact that ignores the taxes on ancillary goods and services that any additional gambling activity would have generated.(13) And unlike many other types of activities, the consequences for employment and possibly wages and salaries are immediate.

IV. Conclusions

This study has provided evidence that interregional events may affect state economies. While this is not a particularly novel finding, of specific interest is that interregional effects are not necessarily proportional to distance nor spread contiguously. Atlantic City casino gambling has had a significant negative influence on the growth of Nevada's gambling industry accompanied by a reduction in state gaming tax collections. This relationship was elicited even though real Nevada gaming revenues were undergoing continued growth. The methodology used was able to discern the impact of Atlantic City in part because the possibility of a unit root in the data was accounted for and the resulting dynamic specification was determined as a feature of the data.

TABLE 3

Expected Reductions in Nevada Gross Taxable Gaming Revenues by
Fiscal Years

(Amounts in millions of dollars)

Fiscal Year      Due to            Due to            Total
              Atlantic City   California Lottery

78-79             16.9                                16.9
79-80             55.4                                55.4
80-81            115.2                               115.2
81-82            186.0                               186.0
82-83            259.0                               259.0
83-84            328.0                               328.0
84-85            374.3                               374.3
85-86            410.5              92.5             503.0
86-87            446.3              73.3             519.6
87-88            496.1             110.8             606.9
88-89            562.2             138.1             700.3
89-90            607.7             130.3             738.0
90-91            662.3             112.7             775.0

Total           4519.9             657.7            5177.6

1 Eadington |1982~ compares and contrasts Atlantic City gaming characteristics to those of Nevada.

2 For a detailed overview of the growth and importance of gaming and tourism for Nevada, see the book edited by Ebel |1990~.

3 The data are deflated by the personal disposable income price deflator. Beginning the gaming revenue series with 1969 data coincides with the birth of corporate casinos in Nevada |Eadington and Hattori, 1978~.

4 The fact that gross taxable gaming revenues are adjusted for unrepaid credit play further supports this interpretation.

5 The three-year period of the early 1980s is omitted from both regimes, even though Atlantic City was in operation, because it could be argued that macroeconomic events distorted gaming during this period.

6 The test was performed under the maintained hypothesis that the variance of the growth rates in the first period was twice the variance of growth rates in the second period.

7 Real play is defined as the drop plus handle deflated by the disposable income price deflator. Thus, it is a measure of wagering intensity or demand. The drop represents the amount of money either directly wagered or exchanged for chips at table games (craps, blackjack, roulette, baccarat). The handle represents the amount of money put into slot machines.

8 Over this period, Las Vegas's gaming revenues comprised about two-thirds of the state total.

9 About 50 percent of the visitors to Nevada are from California. The instant-win lottery type games may compete with slot machine play and the jackpot games may compete with keno. Clotfelter and Cook |1990~ discuss the relationships between lotteries and other types of gambling.

10 The seasonal weights corresponding to each quarter are I: .88; II: 1.04; III: 1.14; and IV: .95.

11 The seasonal dummy variables have been suppressed.

12 These data have all been converted to nominal or current dollar values.

13 There is a 10 percent tax on casino food, beverages, and entertainment as well as a 6 percent sales tax on most retail goods and some services.

REFERENCES

Cargill, T. F. "Is the Nevada Economy Recession Proof?" Nevada Review of Business and Economics, 1979, pp. 3-15.

Cargill, T. F.; Morus, S.A. "A Vector Autoregression Model of the Nevada Economy," Economic Review, Federal Reserve Bank of San Francisco, 1988, pp. 21-32.

Cargill, T. F.; Raffiee, K. "The Nevada VAR Model: Update and General Observations," Nevada Review of Business and Economics, 1990, pp. 2-9.

Clotfelter, C. T.; Cook, P. J. "On the Economics of State Lotteries," Journal of Economic Perspectives, 4, 4, 1990, pp. 105-19.

Durlauf, S. N.; Phillips, P. C. B. "Trends Versus Random Walks in Time Series Analysis," Econometrica, 56, 1988, pp. 1333-54.

Eadington, W. R. "Regulatory Objectives and the Expansion of Casino Gambling," Nevada Review of Business and Economics, Fall 1982, pp. 4-13.

-----. "Public Policy Considerations and Challenges and the Spread of Commercial Gambling," Newsletter of the Institute for the Study of Gambling and Commercial Gaming, 3, 6, April 1991, p. 9.

Eadington, W. R.; Hattori, J. S. "A Legislative History of Gambling in Nevada," Nevada Review of Business and Economics, 1978, pp. 13-7.

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Engle, R. F.; Granger, C. W. J. "Co-Integration and Error Correction: Representation, Estimation, and Testing," Econometrica, 55, 1987, pp. 251-76.

Harvey, A. C. Forecasting, Structural Time Series Models, and the Kalman Filter, New York: Cambridge University Press, 1989.

Harvey, A. C.; Todd, P. H. J. "Forecasting Economic Time Series with Structural and Box-Jenkins Models: A Case Study," Journal of Business and Economic Statistics, 4, 1983, pp. 299-309.

LeSage, J. P. "Forecasting Metropolitan Employment Using an Export-Base Error-Correction Model," Journal of Regional Science, 30, 1990, pp. 307-23.

Nelson, C. R.; Kang, H. "Spurious Periodicity in Inappropriately Detrended Time Series," Econometrica, 49, 1981, pp. 741-51.

Sherwood-Call, C. "Exploring the Relationships Between National and Regional Economic Fluctuations," Economic Review, Federal Reserve Bank of San Francisco, 1988, pp. 15-25.

Shonkwiler, J. S. "A Structural Time Series Model of Nevada Gross Taxable Gaming Revenues," Review of Regional Studies, 22, 1992, pp. 239-49.

Stock, J. H.; Watson, M. W. "Variable Trends in Economic Series," Journal of Economic Perspectives, 2, 1988, pp. 147-74.

Thompson, W. N. "Patterns of Public Response to Lottery, Horserace, and Casino Gambling Issues," Nevada Review of Business and Economics, 1985, pp. 12-22.