A paper by Mandel, Alamar, and Glantz, recently published in Tobacco Control, purports to show that the implementation of a smoking prohibition in Delaware had no statistically significant effect on the gaming revenue from slot machine-like video lottery terminals (VLTs) located at Delaware racetracks.¹ A subsequently published correction by Glantz and Alamar corrects for a data coding error and for reported heteroskedasticity in the data, but reaches the same conclusion of no significant effect.²

I have carefully examined the data and methodologies used in those studies, and conclude that their finding is questionable. Using more general approaches to controlling for heteroskedasticity and seasonality in the data, I find that both total gaming revenues and revenues per VLT declined significantly after the implementation of the Delaware smoke-free law.

Table 1 reports the results of ordinary least squares (OLS) regressions that replicate the model estimated in the correction of Glantz and Alamar. The first regression uses inflation adjusted total revenues as the dependent variable; the second uses revenues per machine. The underlying data are publicly available from the Delaware Lottery.³ The focus of the analysis is on the variable P_law, a dummy variable representing the implementation of the smoke-free law. The coefficient on P_law is negative in both equations. In the case of total revenues, the estimate is significant.

The estimates for the average revenue equation in table 1 are virtually identical to those reported by Glantz and Alamar. Accordingly, it is unlikely that data discrepancies are relevant for distinguishing my findings from those of the original studies.

With regard to the estimates for the total revenues equation, Glantz and Alamar report that the residuals from an OLS regression display heteroskedasticity. I do not find evidence that this problem is significant: White’s test fails to reject the null hypothesis of homoskedasticity (p  =  0.13). Nevertheless, a visual inspection of the residuals does suggest the presence of some mild heteroskedasticity. The authors’ method of correcting for this potential problem, however, is suspect. Glantz and Alamar report estimates from a weighted least squares (WLS) regression, using the inverse of the number of video lottery machines as a weight.

In the presence of heteroskedasticity, coefficient estimates are inefficient, but unbiased. Yet in the WLS estimates reported by Glantz and Alamar, the point estimate for the P_law coefficient (−2.4) is considerably different from the OLS estimate in table 1. This alone should give one pause in accepting the WLS estimate. Moreover, the WLS estimation results in a substantial reduction in the R² of the regression.

The pattern of residuals suggests that the source of heteroskedasticity is most prominent in the data for 1996—the first year of the sample. Two of the three Delaware “racinos” opened at the beginning of 1996, while the third did not open until August. Consequently, there was a sharp increase in the number of VLTs in operation during that year. This accounts for the dramatic effect of the weighting scheme employed by Glantz and Alamar. If observations from 1996 are dropped from the sample, there is clearly no evidence of heteroskedasticity (p  =  0.25), and the coefficient estimates for both the OLS and WLS specifications are essentially the same: For P_law, the OLS estimate is −7.82 (p  =  0.012) and the WLS estimate is −7.81 (p  =  0.041).

A more parsimonious approach to controlling for heteroskedasticity is to employ methods for calculating a heteroskedasticity consistent covariance matrix. Using the approach of Newey and West,⁴ I found that the point estimate for the coefficient on P_law reported in table 1 has a corrected standard error of 2.121, implying a p value of 0.010.

Heteroskedasticity is not the only problem plaguing the residuals from the regressions reported in table 1. Significant serial correlation is also present. Table 2 reports estimates of regressions including an AR(1) specification for the residuals. Newey-West HAC consistent estimates are used to calculate standard errors, adjusting for any heteroskedasticity and higher order serial correlation that might be present. The AR coefficients are highly significant in both regressions. Moreover, the coefficients on P_law show a highly significant negative effect associated with the implementation of the smoke-free law.

Finally, seasonal effects were estimated in Mandel et al¹ using quarterly dummy variables. The authors report that “only winter was found to be significant, thus only the results with winter are reported”. However, the significance of a particular seasonal dummy variable depends on the specification being considered. It is generally invalid to discard specific seasonal dummy variables based on individual significance tests from a particular regression. And in fact, I find that additional seasonal effects are significant.

Table 3 shows the results of monthly model that includes a constant term plus dummy variables for winter, spring, and summer. The dataset used for these regressions has also been extended to include observations through December 2004.

The results reveal significant seasonal variation, clearly refuting the contention that only the seasonal effects of winter are relevant. More importantly, the regression results reported in table 3 confirm that the coefficients on the smoking ban dummy variables are negative and highly significant.

Similar results were obtained with a complete set of monthly dummy variables included in the regression. The coefficients on P_law were found to be –6.54 (p < 0.001) for total revenues (R²  =  0.846) and –1583 (p < 0.001) for average revenue per machine (R²  =  0.777).

Point estimates of the P_law coefficient suggest losses of approximately $6.5 million per month (in inflation adjusted 2004 dollars). This figure represents a revenue loss of nearly 13% compared to the year preceding the smoking ban.

The stated purpose of Mandel et al¹ was to refute the contention of the gaming industry that smoking bans pose a threat to their business: “These results reject the argument that smoke-free laws hurt revenues from gaming”. I find, however, that the smoke-free law in Delaware did affect revenue from gaming. This finding is statistically significant and quite robust. The public health benefits of smoke-free laws should be weighed against these (and other, similar) economic costs.