Lottery Purchases and Taxable Spending: Is There a Substitution Effect?

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1 Lottery Purchases and Taxable Spending: Is There a Substitution Effect? Kaitlin Regan April 2004 I would like to thank my advisor, Professor John Carter, for his guidance and support throughout the course of this study.

2 Introduction State legislatures have historically justified adoption of lottery programs as a means of supplementing general tax revenue. Many states designate the extra revenue specifically to funding education or other public services, and therefore may rely heavily on the success of the lottery. The purpose of this paper is to explore one aspect of the impact of lottery sales on total state revenue. It has been conjectured that lottery tickets are a substitute for other consumption goods. If this is the case, then an increase in lottery ticket sales will be accompanied by a decrease in sales of taxable consumption items. To the extent that this is true, any increase in total revenue to state government due to lottery sales may be partially offset by a decrease in sales tax revenue. It is possible, therefore, that the net addition to total state government revenue after the establishment of a lottery program is less than the amount of revenue generated through lottery sales. Thirty-seven states and the District of Columbia currently operate a lottery, and the level of participation in larger, multi-state lottery games has grown substantially over the past ten or fifteen years. Because lottery tax revenue has become a fundamental part of states budgets, it is important to determine the extent to which lottery revenue detracts from other tax revenue. Borg, Mason, and Shapiro (1993) (hereafter BMS) estimated the relationship between lottery sales and total sales tax revenue in nine individual states over the period from 1953 to The estimated coefficient on lottery revenue was negative and statistically significant in six of the nine states, suggesting that lottery tickets may be substitutes for taxable consumption items. This paper extends the original analysis by 1

3 employing updated data from twelve states spanning the period from 1980 to The twelve states included in the sample are Connecticut, Illinois, Maine, Maryland, Massachusetts, Michigan, New Jersey, New York, Ohio, Pennsylvania, Rhode Island, and Vermont. These were chosen because they all operated at least one lottery game throughout the entire time period. The data are combined into a panel, and a fixed effects pooled time series model is estimated. This paper also addresses the possibility that the model suffers from a simultaneous equations bias that would be caused by the inclusion of an endogenous independent variable. The simultaneity issue is discussed in more detail below. Methodology To get a better sense of what is at stake in this analysis, it is useful to consider a simple model in which total state revenue (Total Rev.) is a function of sales tax revenue (Sales) and lottery revenue (Lott). Sales tax revenue can also be expressed as a function of lottery revenue: Total Rev. = f( Sales(Lott), Lott) The impact of lottery revenue is expressed as the total derivative of total revenue with respect to lottery revenue: δtotal Re v. δf δsales δf = + δlott δsales δlott δlott 2

4 This statement reflects the assumption that lottery revenue impacts total revenue directly, in the form of the portion of total lottery revenue reserved for state governments, and it impacts total revenue indirectly, through sales tax revenue. If lotteries are in fact substitutes for taxable consumption items, then δsales/δlott is negative. Sales tax revenue should generally have a positive impact on total revenue, so that δf/δsales is positive. The above equation therefore states that if lotteries and taxable consumption items are substitutes for each other, then δtotal Re v. δf δsales δf = + δlott δsales δlott δlott δf < δlott This expression implies that the net impact of lottery revenue on total revenue is less than the direct impact of lottery revenue on total revenue if δf/δlott is negative. The empirical model employed in this study is a modification of one developed by BMS (1993), and attempts to capture the relationship between sales tax revenue and lottery revenue: lnsales it = β 0 + β 1 lnincome it + β 2 lnpopulation it + β 3 lntaxrate it + β 4 lnlott it + e it 3

5 The variables are defined as follows: Sales it = Total sales tax revenue to state i in year t. Income it = Per capita income in state i, year t. Population it = Population of state i, year t. Taxrate it = Sales tax rate in state i, year t. Lott it = Total lottery revenue in state i, year t. e it = Random disturbance term. The conventional double-log specification used here differs from the original model in three ways. In the first place, BMS (1993) suppressed the constant, constraining the intercept term to zero. Because the authors did not provide a reasonable explanation for suppressing the constant, the equation employed in this study includes a constant term. Secondly, because some states in their sample did not operate a lottery throughout the sample period, BMS (1993) employed lottery in linear, rather than logarithmic form. Because all of the states in the current study operated at least one lottery game throughout the sample period, it is possible to include lottery revenue as an independent variable in logarithmic form. Finally, BMS (1993) incorporated a price deflation term as an independent variable in the original model, presumably to adjust for inflation. All dollar-denominated dependent and independent variables in the current study are measured in nominal terms, so the coefficients would not change if the variables were deflated by some price deflation term. For this reason, the current model eliminates the price deflation term. 4

6 Simultaneity Before this equation is estimated, it is necessary to determine whether the lottery term is an endogenous variable. The model assumes that lottery revenue impacts sales tax revenue, but it is possible that sales tax revenue simultaneously impacts lottery revenue. If lottery tickets and taxable consumption items are substitutes, other taxable consumption expenditures will cause a decrease in lottery ticket expenditures. If this is the case, then the lottery term is negatively correlated with the random disturbance term, and ordinary least squares regression will yield a coefficient on lottery revenue that is biased downward (Hill, Griffiths, and Judge 2001, Stock and Watson 2003). It is thus possible that the negative sign on the coefficients in BMS (1993) is solely due to simultaneous equations bias. The Hausman test provides a method for testing the existence of simultaneity in the model. In order to perform the test, it is necessary to employ additional variables, or instruments, which explain lottery revenue and which are uncorrelated with the error term. Lottery revenue is estimated as a function of these instruments and all other independent variables in an auxiliary regression that generates a series of residuals. The dependent variable, sales tax revenue, is then regressed on all independent variables and the residuals from the auxiliary equation. If the coefficient on the residuals is significantly different from zero, the null hypothesis of no simultaneity is rejected (Hill, Griffiths, and Judge 2001). 5

7 Instruments for lottery revenue Numerous studies have been done in order to analyze the specific factors that influence the demand for lottery tickets. Ashley, Liu, and Chang (1999), for example, provide evidence that state lottery net revenue is best explained by the population, level of tourism, and level of pari-mutuel expenditures in the state. None of these variables meet the requirements for instruments of lottery revenue, however. In the first place, population must be ruled out, because it is already employed as an explanatory variable in the primary regression. Neither the tourism level nor pari-mutuel expenditures are desirable instruments, because both could be correlated with state sales tax revenue. Other studies have found evidence that state lottery sales are at least partially determined by the number of years the lottery has been in operation. This merits inclusion of a time variable on the right side of an equation in which lottery revenue is the dependent variable. The results from both Mikesell (1994) and Gulley and Scott (1993) support the conjecture that the time variable has a statistically significant impact on lottery sales. Mikesell (1994) proposes that lottery revenue over time tends to increase at a decreasing rate, so a squared time variable is also included as an instrument. For the purposes of this study, the time variable is calculated in terms of the number of years a given state has operated some form of lottery game. Because there is also good reason to believe that the number of different lottery games offered in a state affects total lottery revenue, this variable is also employed as an instrument. The time variables and the number of games variable are viable instruments for lottery revenue in this case, because none of them is directly correlated with sales tax revenue. 6

8 Empirical Results Table 1 contains definitions, sources, and descriptive statistics for the variables considered in this study. The results from three pooled time series estimations are summarized in Table 2. The first set of coefficients belongs to the auxiliary regression, in which lottery revenue is regressed on the other independent variables and the instruments for lottery revenue. The second set of coefficients complete the Hausman test, where sales tax revenue is the dependent variable and the residuals from the auxiliary regression are included on the right side of the equation. The third set of reported coefficients correspond to the estimation of the model as originally defined, where sales tax revenue is a function of per capita income, population, sales tax rate, and lottery revenue. Fixed effects estimation with pooled time series data requires estimation of separate intercept terms for each state in the sample to account for variations in the dependent variable that may be specific to an individual state. The intercepts are not reported, however, because their values have little bearing on the current analysis. The equations are estimated with first-order autoregressive errors to correct for serial correlation observed in preliminary regressions. 1 The results from the first estimation provide evidence that the chosen instruments for lottery revenue can reasonably explain variations in lottery revenue. The coefficients on all three instruments are statistically significant at the ten percent significance level, although the sign on the number of games is not as predicted. In the second regression, the coefficient on the residuals term is not significantly different from zero, meaning that the null hypothesis of no simultaneity cannot be rejected. 1 See Appendix for selected regression output, including fixed effects coefficients, as estimated with EViews

9 The primary equation can therefore be estimated without resort to instrumental variables methods. The R-square statistic for this regression is high, showing that the regression explains almost all of the variation in sales tax revenue. The coefficients on per capita income and the sales tax rate are both positive and statistically significant at the five percent significance level, but the coefficient on population is not significantly different from zero. These results are consistent with those observed by BMS (1993). This study, however, is primarily concerned with the impact of lottery revenue on sales tax revenue. Formally, the null hypothesis that the lottery coefficient is zero is tested against the alternative that it is negative. As shown, the estimated coefficient is small and positive, meaning that the null hypothesis cannot be rejected. This provides evidence that an increase in lottery sales is not associated with a decrease in taxable consumption expenditures, and that lottery tickets are not substitutes for taxable consumption items. Because the results of this study differ from those reported by BMS (1993), it is appropriate to investigate whether the equation is properly specified. Pooled time series estimation with panel data is essentially a restricted regression that requires the coefficients on all explanatory variables to be the same for all states in the sample. If the equation is estimated with the fixed effects method, then only the intercept term may vary from state to state. It is possible, however, that the assumption that the coefficients are equal for all states in the sample is erroneous, and that it is more appropriate to estimate the equation separately for each state. For this reason, state-level equations are also estimated, again with first order autoregressive errors to correct for serial correlation observed in most states. The 8

10 relationship between sales tax revenue and lottery revenue cannot be estimated for four states (Maryland, Massachusetts, New York, and Pennsylvania), because their sales tax rates remained constant over the entire time period. The Hausman test is also performed for the remaining eight states, and the hypothesis of no simultaneity can be rejected for two of these states, Connecticut and Vermont. The equation is therefore re-estimated for these states using Two-Stage Least Squares with the time variables and the number of games variable as instruments for lottery revenue. The results from the state-level auxiliary regressions and Hausman tests are not reported. The results from the state-level estimations are summarized in Table 3. The R- square statistics for these regressions are all above 0.98, suggesting that this model is reasonable for explaining variations in sales tax revenue to individual states. There is no evidence that lottery revenue negatively impacts sales tax revenue in any of the eight states for which the regression analysis is performed. The coefficient on lottery revenue is positive and statistically significant at the ten percent level against a two-sided alternative in two of the eight states for which the equation is estimated (New Jersey and Vermont). The coefficient on lottery revenue is not significantly different from zero in the remaining six states. These results are interesting, because they suggest that lottery revenue has a positive effect on sales tax revenue in at least two states. Conclusion The results observed in this study do not support the proposition that lottery purchases are substitutes for other taxable consumption expenditures. When the 9

11 relationship between sales tax revenue and lottery revenue is estimated with pooled data from twelve states, the coefficient on lottery revenue is not significantly different from zero. The results vary at the individual state level, but they suggest that lottery revenue has a statistically significant impact on sales tax revenue in no more than two of the eight states considered. These results do not, however, provide evidence that the negative coefficients found by BMS (1993) are due to simultaneity bias. In practice, it is not possible to test the actual BMS (1993) model with the original data, but the results from the Hausman tests performed on the current data do not suggest that the original model suffers from simultaneous equations bias. One surprising result found in this study is a positive, statistically significant coefficient on the lottery variable in two states, New Jersey and Vermont. This observation gives rise to the possibility that lottery tickets and taxable consumption items are complements in these states. It is plausible to envision a scenario in which lottery tickets are purchased in conjunction with other consumption items. An individual shopping at a grocery store, for example, may be inclined to purchase a lottery ticket at the cash register in addition to his or her groceries. In this scenario, the individual s participation in a lottery game does not detract from his or her taxable expenditures. While it is feasible that lottery tickets and other consumption items are complementary in some states, the current results are not conclusive, and the question warrants further empirical investigation. In summary, the results of this study do not provide evidence to support the conjecture that lottery purchases negatively impact sales tax revenue. While the real 10

12 effect of lottery revenue on sales tax revenue to specific states may depend on the tax structure of the state, none of the states considered in this study appear to be suffering from losses in sales tax revenue due to lottery purchases. 11

13 Table 1: Variable Definitions and Descriptive Statistics Variable Definition Mean (Source) (Std. Dev.) Sales Total sales tax revenue, in thousands of dollars. 2,611,905 (U.S. Census Bureau) (2,040,235) Income Per capita income, in dollars. 20, (U. S. Census Bureau) (6, ) Population Total state population, in thousands. 7, (U. S. Census Bureau) (5, ) Tax rate General sales tax rate (The Book of the States) (0.999) Lott Total lottery revenues, in thousands of dollars. 907,134.5 (U.S. Census Bureau) (798,724) Time Total number of years at least 1 lottery game has been in operation (Lottery Fast Facts) ( 6.575) Game Total number of Lotto games offered in the given year (Lottery Fast Facts) (1.149) Notes: Descriptive statistics are computed for panel data. 12

14 Table 2: Parameter Estimates for Pooled Time Series Equations with Fixed Effects lnlott lnsales lnsales lnincome ** 1.089** (1.114) (12.936) (14.988) lnpopulation (-0.344) (1.186) (0.929) lntaxrate ** 0.301** (-0.260) (4.091) (4.706) lnlott (0.855) (1.408) Time 0.163** (2.007) Timesq * (-1.850) Games * (-1.619) RESID (-0.316) AR(1) 0.836** 0.695** 0.703** (27.626) (14.895) (16.249) Number of Obs R-square Notes: Intercepts are not reported; t-statistics are in parentheses. *significant at α = 10% against a two-sided alternative. **significant at α = 5% against a two-sided alternative. 13

15 Table 3: Parameter Estimates for State-Level Equations CT IL ME MI NJ OH RI VT Intercept ** (0.643) (-0.101) (0.982) (-0.613) (0.501) (0.943) (-1.362) (1.547) lnincome 1.461** 0.922** 1.367** ** 1.268** 1.164* (4.267) (4.902) (1.450) (2.371) (4.125) (13.446) (2.048) lnpopulation (-0.713) (0.423) (-0.908) (0.621) (-0.464) (-0.851) (1.558) (-1.242) lntaxrate 0.933** ** 0.622** (4.647) (-1.137) (1.114) (0.858) (0.481) (-0.002) (-4.295) (2.390) lnlott ** * (-0.137) (1.636) (0.711) (0.090) (2.183) (-0.417) (-0.036) (2.315) AR(1) ** ** (1.018) (0.160) (0.644) (1.527) (0.698) (3.033) (-0.813) (0.681) Number of Obs R-square Notes: t-statistics are in parentheses. Results reported for CT and VT are from two-stage least squares regressions using Time, Timesq, and Games as instrumental variables. *significant at α = 10% against a two-sided alternative. **significant at α = 5% against a two-sided alternative. 14

16 REFERENCES Ashley, Terry, Yi Lui, and Semoon Chang. Estimating Net Lottery Revenues for States. Atlantic Economic Journal. June 1999, 27, pp Borg, Mary O., Paul M. Mason, and Stephen L. Shapiro. The Cross Effects of Lottery Taxes on Alternative State Tax Revenue. Public Finance Quarterly. April 1993, 21, pp Council of State Governments. The Book of the States. Lexington, KY: Council of State Governments, (multiple volumes). Gulley, O. David and Frank A. Scott, Jr. The Demand for Wagering on State- Operated Lotto Games. National Tax Journal. March 1993, 46, pp Hill, R. Carter, William E. Griffiths, and George G. Judge. Undergraduate Econometrics, Second Edition. New York: John Wiley & Sons, LaFleur, Teresa and Bruce LaFleur. Lottery Fast Facts. Maryland: TLF Publications, Inc., < LWLA03_ Ch04_NC_FastFacts.pdf > Mikesell, John L. State Lottery Sales and Economic Activity. National Tax Journal. March 1994, 47, pp Stock, James H. and Mark W. Watson. Introduction to Econometrics. Boston: Addison Wesley, United States Census Bureau. State Government Finances. < (Pre-1990 data provided by spreadsheet). 15

17 APPENDIX A: Selected Regression Output Table A1: Auxiliary Regression with Pooled Time Series Data Dependent Variable: LNLOTT? Method: Pooled Least Squares Date: 12/17/03 Time: 19:25 Sample: Included observations: 21 Excluded observations: 1 Number of cross-sections used: 12 Total panel (balanced) observations: 240 Convergence achieved after 8 iterations Variable Coefficient Std. Error t-statistic Prob. LNINC? LNPOP? LNTAX? TIME? TIMESQ? GAMES? AR(1) Fixed Effects _CT--C _IL--C _ME--C _MD--C _MA--C _MI--C _NJ--C _NY--C _OH--C _PA--C _RI--C _VT--C R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Sum squared resid Log likelihood F-statistic Durbin-Watson stat Prob(F-statistic)

18 Table A2: Hausman Test with Pooled Time Series Data Dependent Variable: LNSALES? Method: Pooled Least Squares Date: 12/17/03 Time: 19:27 Sample(adjusted): Included observations: 20 Excluded observations: 1 after adjusting endpoints Number of cross-sections used: 12 Total panel (balanced) observations: 228 Convergence achieved after 7 iterations Variable Coefficient Std. Error t-statistic Prob. LNINC? LNPOP? LNTAX? LNLOTT? RESID? AR(1) Fixed Effects _CT--C _IL--C _ME--C _MD--C _MA--C _MI--C _NJ--C _NY--C _OH--C _PA--C _RI--C _VT--C R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Sum squared resid Log likelihood F-statistic Durbin-Watson stat Prob(F-statistic)

19 Table A3: Primary Regression with Pooled Time Series Data Dependent Variable: LNSALES? Method: Pooled Least Squares Date: 12/17/03 Time: 19:20 Sample: Included observations: 21 Excluded observations: 1 Number of cross-sections used: 12 Total panel (balanced) observations: 240 Convergence achieved after 6 iterations Variable Coefficient Std. Error t-statistic Prob. LNINC? LNPOP? LNTAX? LNLOTT? AR(1) Fixed Effects _CT--C _IL--C _ME--C _MD--C _MA--C _MI--C _NJ--C _NY--C _OH--C _PA--C _RI--C _VT--C R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Sum squared resid Log likelihood F-statistic Durbin-Watson stat Prob(F-statistic)

20 APPENDIX B: Pooled Time Series Data State YEAR Sales Income Population Taxrate Lott CT , CT , CT , CT , CT , CT , CT , CT , CT , CT , CT , CT , CT , CT , CT , CT , CT , CT , CT , CT , CT , IL , IL , IL , IL , IL , IL , IL , IL , IL , IL , IL , IL , IL , IL , IL , IL , IL , IL , IL , IL , IL , ME , ME , ME , ME ,

21 ME , ME , ME , ME , ME , ME , ME , ME , ME , ME , ME , ME , ME , ME , ME , ME , ME , MD , MD , MD , MD , MD , MD , MD , MD , MD , MD , MD , MD , MD , MD , MD , MD , MD , MD , MD , MD , MD , MA , MA , MA , MA , MA , MA , MA , MA , MA , MA , MA ,

22 MA , MA , MA , MA , MA , MA , MA , MA , MA , MA , MI , MI , MI , MI , MI , MI , MI , MI , MI , MI , MI , MI , MI , MI , MI , MI , MI , MI , MI , MI , MI , NJ , NJ , NJ , NJ , NJ , NJ , NJ , NJ , NJ , NJ , NJ , NJ , NJ , NJ , NJ , NJ , NJ , NJ ,

23 NJ , NJ , NJ , NY , NY , NY , NY , NY , NY , NY , NY , NY , NY , NY , NY , NY , NY , NY , NY , NY , NY , NY , NY , NY , OH , OH , OH , OH , OH , OH , OH , OH , OH , OH , OH , OH , OH , OH , OH , OH , OH , OH , OH , OH , OH , PA , PA , PA , PA ,

24 PA , PA , PA , PA , PA , PA , PA , PA , PA , PA , PA , PA , PA , PA , PA , PA , PA , RI , RI , RI , RI , RI , RI , RI , RI , RI , RI , RI , RI , RI , RI , RI , RI , RI , RI , RI , RI , RI , VT , VT , VT , VT , VT , VT , VT , VT , VT , VT , VT ,

25 VT , VT , VT , VT , VT , VT , VT , VT , VT , VT ,

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