From State and Local Government Review, (1997) Vol. 29, pp.34-42.

Lotteries for Education:

Windfall or Hoax?

Donald E. Miller

Patrick A. Pierce

Saint Mary's College


This study was supported by a grant to both authors from the Center for Academic Innovation at Saint Mary's College. The authors wish to acknowledge the assistance of Erin O'Neill and Beth Urban in data collection and data entry, respectively. We also benefitted from comments by Joe Stewart.

During the 1980s and into the '90s, the nation witnessed a flurry of lottery adoptions. As declining rates of federal fund transfers and increasing numbers of tax revolts (Sears and Citrin 1982) squeezed states' budgets, state legislatures looked for relatively painless ways to raise revenue. Lotteries proved particularly attractive methods of producing revenue to state legislators and governors because they are a voluntary form of taxation. Individuals pay the tax because they want to pay the tax.

However, state policy makers often attempted to make the lottery even more palatable to voters by devoting the funds to a particular purpose. For instance, in Indiana, the lottery's proceeds go to a "Build Indiana" fund to repair the state's transportation infrastructure. The most popular purpose for lottery funds has been education. Historically, states have played a major role in funding schools; such funding is consistent with tradition and therefore more acceptable. Further, state funding can partially counter the regressive and politically unpopular nature of the source of local funds--the property tax.

However, the politics of lottery adoption may be less than perfectly related to the policy outcome. Policy studies are replete with examples of how proposed policies are modified in the policy process and implementation (Pressman and Wildavsky 1984). As increasing revenues are raised through state lotteries, what are the budgetary consequences? The present study examines the impact of one kind of lottery adoption--education--on state spending.

Public School Financing

Elementary and secondary education has traditionally been a local function. Local school districts provided most of the administration, policy making, and funding of schools. However, beginning in the 1960s, state and national influence on schools and school funding became increasingly important. In the 1960s, the federal government responded to the pressing needs of poorer school districts and the perception that education served national purposes by passing the Elementary and Secondary Education Act (1965). Because of this and related legislation, the federal share of elementary and secondary education expenditures rose from 4.4 per cent in 1960 to 8.0 per cent in 1968 (Council of State Governments 1973, 302).

The 1970s witnessed the growth of the school finance reform movement, which sought to equalize educational spending and decrease reliance on the regressive property tax (Fuhrman 1982; Serrano v. Priest 1971). Regressive refers to the fact that in order to net the same income for a school in a poor district, property would need to be taxed at a higher rate. The mechanisms to accomplish these objectives varied across the states, but the general result was to increase the state share of education funding. Hence, during the 1970s, many states' share of school funding grew to majority status (Burrup and Brimley 1982).

The end of the 1970s brought a flurry of tax and spending limitation proposals. The most celebrated of the successful attempts were California's Proposition 13 and Massachusetts' Proposition 2 ½ (Sears and Citrin 1982; Baratz and Moskowitz 1978; Tompkins 1981; Tvedt 1981). Although some writers have concluded that these and other limitations did not necessarily produce the dramatic effects claimed by proponents and opponents (Williams 1982), the political impact of tax and spending limitations (and the threat thereof) is indisputable. School finance problems were exacerbated in the 1980s by reduced federal grants-in-aid. Thus, increased fiscal pressure was placed on state governments. As property taxes were limited or cut on the local level and federal aid was reduced, the burden on states was significant.

Lotteries--A Possible Solution

The federal cutbacks in education of the '80s and the perception that taxpayers were in revolt placed state policy makers in a quandary. States needed to increase revenue to replace declining federal dollars. However, traditional taxpayer resistance to tax increases and new taxes was perceived to be heightened in the face of media coverage of the national spirit of tax revolt.(1) In this context, lotteries were obviously politically and fiscally attractive.

Lotteries are a form of voluntary taxation, i.e., individuals pay the tax only if they so wish. Hence, opposition to lotteries as taxation was minimal and tied to cultural and moral concerns about gambling and its potential addictiveness. When the object of the lottery was to fund education, even these forces failed to block the adoption of state lotteries (Pierce and Miller 1995).

We know a great deal about the politics of lottery adoption (Berry and Berry 1992; Winn and Whicker 1989-90; Filer, Moak, and Uze 1988; Pierce and Miller 1995). Some observers in the press, as well as some politicians, have questioned the effectiveness of lotteries on state school finance but this view has never been investigated systematically. As for democratic rule and representation, voters should expect a lottery funding education to increase the level of funding for education beyond the status quo. Therefore, we can profitably examine the short- and long-term impacts of education lotteries on the level of state spending on education. When voters and policy makers endorse a lottery for education, does education really benefit?


The cases in our data set represent the 50 states over the time period 1966-1990, and the dependent variable (real education spending per capita) is ratio-level. We first look only at those states that have adopted an education lottery during the time period. We are interested in the short-term and long-term effects of lottery adoption. In statistical terms, these issues are addressed through interrupted time series analysis (McDowell et al. 1980). Lewis-Beck (1979) offers an interesting approach to modeling the short-term and long-term factors involved in such a time series. The lottery is an interruption in the time series, disturbing existing trends (in this case, the level of education spending). Change in education expenditures may then be seen as responding to short- and long-term changes associated with the interruption. The three variables affecting education expenditures are an annual counter for years from 1966 to 1990, a dummy variable scored 0 for observations before the lottery was in effect and 1 for observations after the lottery was in effect, and an annual counter for years scored 0 before the lottery and 1, 2, 3, ... for observations after the lottery began producing revenue. We expect that the coefficient for the first variable (the annual counter) will be positive and significant, indicating the long-term trend toward greater educational expenditures in all states. The short-term effect of the lottery will be indicated by the coefficient for the second variable and the long-term effect of the lottery will be measured by the coefficient for the third variable. Both of these coefficients (short-term and long-term change) are, of course, expected to be positive. We should note that passage of the lottery does not immediately result in the operation of the lottery. Thus, we use the date when the lottery began producing revenue as the interruption of the time series.

The key problem in using time serial data concerns the nature of the error terms, i.e., autocorrelation. Error terms are probably strongly correlated over time, violating an important assumption of Ordinary Least Squares (OLS) regression. As a result, the variance of the error terms is seriously underestimated and the significance of the coefficients is overestimated. To remedy the problem of autocorrelation, the data are transformed by taking into account the correlation of the error terms. In the present case, a first-order autoregressive function will be assumed (with good cause, see Lewis-Beck 1979) and the Cochrane-Orcutt procedure is used to transform the data when the Durbin-Watson statistic indicates the need. (Ostrom 1978; Lewis-Beck 1979; Kmenta 1986).

To oversimplify, (the Cochrane-Orcutt technique) first estimates the correlation of the error terms...; accordingly, it corrects each observation, subtracting an amount determined by the autocorrelation estimate. These steps are repeated until the estimates converge. (Lewis-Beck 1979, 1136)

An additional problem of time series data is sampling error, producing biased estimates. In this case, particular kinds of states are more likely to adopt an education lottery, and those characteristics may affect the budgetary consequences of the lottery. Sampling error can operate across time as well as space; changes in spending may be the result of forces operating across all states at a particular time rather than the result of the lottery. Therefore, in the second stage of the analysis, we will also employ pooled time series regression (Stimson 1985). The dimensions of the pooled time series are 50 states and 25 points in time (years). As Stimson notes,

Pooling data gathered across both units and time points can be an extraordinarily robust research design, allowing the study of causal dynamics across multiple cases, where the potential cause may even appear at different times in different cases. (1985)

Another happy consequence of pooling the cross-sectional units is to reduce the likelihood that autocorrelation will be severe (Stimson 1985). The greater the degree of cross-sectional dominance (in this case, 50 states > 25 years), the smaller the number of cases that may be serially dependent, i.e., related to the previous case. Hence, the pooled analysis can probably dispense with transforming the variables to eliminate autocorrelation. Furthermore, the resulting coefficients will be far more easily interpreted (Smith 1995).

This model may still be inadequate, however. The OLS assumption of homoskedasticity is typically violated in pooled time series regression. As Stimson (1985) notes, differences in the "size" of the units will usually produce systematic differences in the residuals, thus heteroskedasticity. For example, the errors for California and New York are likely to be greater than those for New Hampshire and North Dakota. The straightforward remedy for this problem is to employ unit intercepts for the cross-sectional units to account for the differences between the states.(2) This is commonly called Least Squares with Dummy Variables (LSDV) (Stimson 1985; Smith 1995; Kmenta 1986).

Smith (1995) notes that comparative analyses of state politics should be concerned with cross-sectional differences, but our focus is on the dynamic impact of education lotteries. Hence, we want to address changes across time rather than across space. LSDV allows us to accomplish that goal by controlling for the cross-sectional variation in educational spending. Its failure to deal with the meaning of these cross-sectional differences is irrelevant to our purposes.

The use of LSDV also justifies testing a "naive" model of the impact of education lotteries on education spending. That is, our model does not contain specific factors accounting for cross-sectional differences in education spending, e.g., interest group strength or state liberalism. The impact of these variables is controlled by dummy variables for the states, thus capturing the effects of all these explanatory factors. We might also note that the dummy variables effectively account for additional factors that might be excluded regardless of the sophistication of the model.

Finally, we may want to consider the perspective of policy makers on the relationship between the lottery and education spending. All lotteries are not created equal; the revenue generated by the lottery may vary considerably over time and across states. Budgetary politics require policy makers to attend to the extent of available revenue. The simple existence of a lottery does not necessarily affect the budget from this perspective. State policy makers will consider the level of revenue generated by the lottery. Higher levels of revenue should enable the state to increase education spending, whereas lower levels may cause some degree of stagnation in spending. To test this possibility, a simpler model is sufficient. Here, only two variables need be included with the dummy variables: an annual counter for years from 1966 to 1990, and annual net lottery revenue (also in real (1987) per capita dollars). Again, the counter taps the general increase in educational expenditures over time. The coefficient for the second variable (lottery revenue) will therefore indicate the extent to which lottery revenue further boosted (or changed) educational spending.


Our first look at the impact of education lotteries on state spending for education is on the level of individual states that have adopted such a lottery. Between 1965 and 1990, 12 states enacted a lottery for education: California, Florida, Idaho, Illinois, Michigan, Missouri, Montana, New Hampshire, New Jersey, New York, Ohio, and West Virginia. Using the counter index, the after lottery index, and the lottery indicator dummy variables to model state education spending, the estimated coefficients are displayed in Table 1. New Hampshire is excluded from the table because it possessed a lottery over the entire time period. As a result, it has no "pre-lottery" history to compare to its "post-lottery" educational spending.




The results in Table 1 display remarkable diversity. For all states except Illinois and Ohio which had a sufficiently large Durbin-Watson statistic, the Cochrane-Orcutt procedure was used. The counter variable indicates the rate of change in educational spending per capita over the 1966-1990 period and is negative as often as it is positive. However, these trends are rarely statistically significant. For the two states where the coefficients can be readily interpreted, Illinois and Ohio, the trends are highly significant with spending increasing 39 dollars and 23 dollars annually, respectively. The results for the short-term impact of the lottery are even less impressive. None of the coefficients even approaches statistical or substantive significance. The long-term impact of the lottery is again varied. In Illinois and Ohio, the rate of educational spending drops significantly once a lottery is in place, 40 dollars and 9 dollars, respectively. However, Michigan's lottery which showed no significant short term gain seemed to spur a significantly positive change in educational spending (t value = 2.167). Also worth noting are the low R-squares for almost all of the states. The exceptions are Illinois, New Jersey, and Ohio where the model fits well.

A more robust analysis of the impact of education lotteries on state educational spending "pools" the cross-sectional units over the time period (Stimson 1985). Pooled time series regression increases the degrees of freedom in our analyses and allows for more dynamic analysis of the data (Stimson 1985). Also, using pooled time series regression limits the problem of sampling error affecting parameter estimates (compared with our examination of the states analyzed individually above) (Stimson 1985). In other words, pooled time series regression effectively provides a comparative analysis by including states that have and have not adopted education lotteries. For example, we cannot really know that the significant long-term increase in the rate of educational spending following lottery adoption in Michigan can be attributed to the lottery or to some other characteristic of the state, unless we examine other states including those which have not adopted an education lottery (or any other form of lottery) simultaneously in a pooled analysis.(3)




The state dummy variables are of minimal interest to the present study, but the estimated coefficients show the existence of significant cross-sectional variation. States with particularly large and significant unit intercepts include Alaska (b = 957.0) and New Hampshire (b = -410.5). As the intercept (547.5) is the estimate of the likely amount of spending in 1965, one can appreciate the substantive significance of that cross-sectional variation.

The focus of this study, however, is to examine the impact of lottery adoption on education spending. The highly significant coefficient for the counter variable indicates that states generally increased education spending prior to adoption of a lottery by about 12 dollars annually per capita. In the first year of the lottery's operation, a state could be expected to raise education spending by 50 dollars per capita. However, the long-term impact of a lottery is not nearly so felicitous. After a lottery is put into effect, the rate of change in education spending drops by about 6 dollars annually, i.e., spending now increases at only 6 dollars annually.

A final point to be made concerns our use of a "naive" model that accounts for cross-sectional variation only through state dummy variables. We noted above (p. 7) that LSDV should remedy this potential problem, but we can provide empirical support for this theoretical argument. Comparing the results in Table 2 (all states) to those in Table 3 (only those states with an education lottery) will enable us to empirically evaluate the adequacy of using state dummy variables to account for the cross-sectional variation. If states with education lotteries had unmeasured characteristics (not captured by the dummy variables) differing from other states that affected education spending, the results in Tables 2 and 3 would be markedly different.




In fact, the coefficients in Tables 2 and 3 are remarkably similar, suggesting that LSDV has effectively solved this problem. The estimated short- and long-term impacts of the lottery in Tables 2 and 3 are quite similar. The intercept is the only exception to this rule; 547 for the total sample and 390 for states with education lotteries. However, this was expected since the mean per capita expenditure is significantly higher (t = 10.22) in states that did not adopt an educational lottery. ($581 as opposed to $469 in states with an education lottery).

However, these patterns of short- and long-term change may be the result of the varying levels of revenue available to the states over time from the lottery. To investigate this question, educational spending was regressed on lottery revenue and a counter variable. The results are displayed below in Table 4.




Lottery revenue seems to depress educational spending, but not reliably so. For each dollar per capita of lottery revenue, one could expect educational spending (real per capita) to decline 28 dollars but the standard error is over 42 dollars. Nonetheless, the failure of lotteries to increase spending is incontrovertible and is not the result of differences in generated revenue.

There may be one remaining problem with the results reported in Table 4. Non-linear relationships are common with economic and fiscal variables. Indeed, the results in Table 2 suggest that the initial burst of revenue has a sizeable effect on education spending, that tails off in later years. If the relationship is non-linear, correlation and regression coefficients will underestimate the strength of the relationship. We performed the necessary exponential transformation of lottery revenue to test this hypothesis of curvilinearity. The results, not displayed here, were again not statistically significant for lottery revenue (and the model fit no better than the purely linear one). However, the sign of the coefficient for lottery revenue was once again negative, indicating the possibility that lottery revenue reduced educational spending.


The popularity of lotteries and legalized gambling is based in part on their claim to painlessly provide additional revenue to needed state functions. The most popular purpose to which these revenues have been devoted is education. However, we have demonstrated that these are false promises for education. States are likely to decrease their growth of spending for education upon operating a lottery designated for that purpose. Furthermore, the decrease in the rate of growth is a long-term function of lottery adoption that occurs regardless of revenue generated by the lottery.

A more detailed look at the impact of education lotteries on educational spending reveals perhaps an even more perverse portrait. Immediately upon beginning the lottery, a state is likely to increase its educational spending. Furthermore, this increase is the nontrivial amount of nearly 50 dollars per capita, which is almost 10 percent of the mean value for educational spending over this time period ($555). Citizens (if attentive) would then infer that the lottery was a tremendous boon to education. Policy makers in good conscience could credit the lottery with enabling them to increase spending in education. However, both would be wrong. In the years following the initial use of the lottery, the rate of growth in educational spending declines. We should emphasize that spending does not decrease; rather, its rate of increase is cut in half. That is, spending increases at the rate of 6 dollars annually per capita rather than 12 dollars per capita.

A major contribution provided by the present use of pooled time series analysis is to demonstrate that these changes are not the result of sampling error. Regardless of the state or the time at which its lottery operated, educational spending declined once a state put a lottery into operation. Hence, the pattern of a declining rate of spending is not simply an artifact of state fiscal problems in the 1980s. The present analysis indicates that states without lotteries maintained and increased their educational spending more than states with lotteries. This conclusion is made possible only by pooling the time series of all the states.


Further research is needed to explore how states have changed their fiscal policy as they accrue lottery revenue. In the area of education, it seems clear that the revenue is not used to increase spending. But where does the revenue go? An important initial observation concerns the amount of revenue generated by the lottery. In almost every state, lottery revenue constitutes a very small percentage of total revenue. In such situations, economists refer to the funds as replacing general revenue. That is, an amount from the general revenue equal to that of the lottery revenue is replaced by the lottery.

Following the trail, one can consider the further fiscal consequences. If general revenue is "saved" by the use of the lottery, how are those savings used? A number of consequences are possible. These funds might be: 1) shifted to other functions and purposes; 2) used to finance a tax cut; or 3) used to balance the budget and leave a sizeable surplus. In the fiscal climate facing states in the 1980s and '90s, we believe that the first alternative is unlikely generally. There might be cases in which a consensus has developed in a state concerning the need to repair a deteriorating infrastructure or the need to increase funding for law enforcement. However, these will be isolated cases.

State legislators and particularly governors should find the second and third alternatives especially attractive. Tax cuts are always popular, at least in the short term. As for the third alternative, governors with ambitions for higher political office can hardly fail to recognize the value of running on the record of assembling a surplus without raising taxes. And indeed, there is some evidence that lottery revenue is used in these ways (Pierce and Miller 1996; Jones and Amalfitano 1994).

To conclude, lottery revenue is unlikely to materially increase funding for education--and perhaps any other purpose. However, such revenue has political returns for governors that are significant. Hence, citizens should recognize that the claims that lotteries will improve education funding are likely to be as misleading as the odds of their winning those lotteries are meager.

However, this pattern may vary by the purpose of the lottery. Even if the pattern does hold, increased spending is not the only appeal used by policy makers to support lottery adoption. Another matter to explore is how increased levels of voluntary taxation have affected tax collections by the state. Lotteries could be used to affect either spending or taxes, both, or neither. All of these possibilities should be of concern to citizens, policy makers, and policy scholars, and therefore deserve further study.

Table 1

State-Level Analysis of the Impact of Education Lottery Adoption

With t values in parenthesis

Intercept Counter Short-term impact Long-term impact Adj. R2 D-W









-.108 2.26









.007 2.34









-.099 2.93









.848 1.71









.168 1.26









-.023 2.62









-.029 2.39
New Jersey









.879 2.13
New York









-.069 2.22









.974 1.52
West Virginia









-.139 2.92

n = 25

* Cochrane-Orcutt procedure not needed

Table 2


Pooled Time Series Results for State Educational Spending:

The Impact of Lottery Operation

Independent variable Estimated coefficient Standard error t-statistic
COUNTER 11.97 .400 30.937
SHORT-TERM CHANGE 49.67 16.40 3.022
LONG-TERM CHANGE -5.59 1.40 -4.054
Intercept 547.49 18.80 29.131

n = 1250

Adjusted R2 = .846

Note: Coefficients for the state dummy variables are omitted for the sake of clarity.

Table 3

Pooled Time Series Results for Educational Spending of States with Education Dedicated Lotteries: The Impact of Educational Lottery Operations

Independent variable Estimated coefficient Standard error t-statistic
COUNTER 11.84 .725 16.33
SHORT-TERM CHANGE 50.77 10.99 4.62
LONG-TERM CHANGE -5.362 1.021 -5.25
Intercept 390.74 13.56 28.82

n = 300

Adjusted R2 = .826

Note: Coefficients for the state dummy variables are omitted for the sake of clarity.

Table 4


Pooled Time Series Results for State Educational Spending:

The Impact of Lottery Revenue

Independent variable Estimated coefficient Standard error t-statistic
LOTTERY REVENUE -0.2807 0.4254 -0.6597
COUNTER 11.83 .380 31.0566
Intercept 549.35 18.89 29.0750

n = 300

Adjusted R2 = .844

Note: Coefficients for the state dummy variables are omitted for the sake of clarity.


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1. 1. The argument that these tax revolts were not national in nature does not gainsay the fact that state policy makers perceived a nationwide increase in resistance to taxes.

2. 2. The number of dummy variables (N - 1 = 49) is not trivial, but still manageable.

3. 3. As expected, pooling the time series data results in eliminating the serious autocorrelation seen in the individual state time series. The Durbin-Watson statistic is 1.799, sufficiently insignificant that we may dispense with the transformation of our variables. Again, by avoiding transforming the variables, we can produce estimated coefficients that are more easily interpreted (Smith 1995).