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Although Table 2.2 roughly described the crime changes before and after the repeal according to offense types and the days of the week, the raw daily average numbers in that table were unlikely to accurately describe the repeal effects because of potential confounding factors. For precise estimation, the DD and DDD models were introduced. Table 2.3 reports the results, respectively, for the two DD models and the one DDD model that were specified in the previous section, in terms of an average marginal effect. For the space limitation, the marginal effects of the other variables than the DD and DDD interactions were not reported here.38

The first row denotes the estimation results of the first DD model, which had the two differences of Sunday vs. non-Sunday and pre- vs. post-repeal for the treatment group only. For this first DD model, the coefficients for total crime and misdemeanor were statistically significant at the two-tailed 1% level. The average marginal effect for total crimes was 0.057, which implies the repeal was statistically significantly associated with a 0.057 unit increase in expected Sunday total-crime incidents for a 1/8 mile radius area per Sunday, holding all other values equal. The average marginal effect for

misdemeanors was 0.016, implying that the repeal was associated with a 0.016 unit increase in expected misdemeanor incidents for a 1/8 mile radius area per Sunday. Meanwhile, the average marginal effects for violent and property crimes were 0.012 and 0.027, respectively, but they were not statistically significant.

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The results of the second DD model, which had the two differences of treatment vs. control and pre- vs. post-repeal for incidents occurring on Sundays only, are reported in the second row. This second DD model had similar results as those of the first DD model. For total crime, the repeal was statistically significantly associated with a 0.041 unit increase in expected total crime incidents at the two-tailed 0.1% level, holding all other values equal. Misdemeanor incidents increased after the repeal, having the average marginal effect of 0.020. Also, the average marginal effects for violent and property crime incidents were not statistically significant.

The DDD model results, which are of main interest, are reported in the third row in Table 2.3. The DDD estimates in general resemble those in the above two DD models. The average marginal effects for violent and property crimes were also statistically insignificant. For total crime and misdemeanor, the average marginal effects remained statistically significant at the two-tailed 1% level. The average marginal effect for total crime was 0.053, being almost the same to that of the first DD model. Given that a year typically has 52 weeks and Sundays, one Sunday-open W&S store's 1/8 mile radius area is expected to experience additional 2.76 total crime incidents a year due to the repeal. The absolute value of 2.76 per se is small, although the value only represents the tiny geographical area of a 1/8 mile radius. Misdemeanor incidents had the average marginal effect of 0.017, and it corresponds to additional 0.88 misdemeanor incidents a year due to the repeal.

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Table 2-3. Poisson Regression Average Marginal Effects in the DD and DDD Models

Note: The unit of observation is the average daily number of relevant crime incidents occurring within one W&S store's 1/8 mile radius. The difference name "Sun" stands for the difference between crime incidents on Sunday and those on non-Sundays; "Treat" stands for the difference between the treatment and control groups; and "Post" stands for the difference between the pre-repeal and post-repeal periods. Models 1 and 2 are estimated from the DD specifications, while Model 3 is estimated from the DDD specification. Coefficients in cells are average marginal effects of predicted number of relevant crime incidents, coming from unique Poisson regressions. The robust standard errors are provided in parentheses. The entire coefficients in the models are available on request.For the statistical significance, *: p<0.05, **: p<0.01; ***: p<0.001.

2.4.3. The Geographical Displacement/Attraction Effect39

Although Table 2.3 consistently suggested statistically significant increases in total crime and misdemeanor incidents occurring within the 1/8 mile radius areas of the treatment group stores on Sunday after the repeal, it did not address a policy-relevant question of whether an increase in alcohol availability produces a net increase in crime in

39 _{In addition to this geographical displacement, the inter-temporal displacement effect is also} investigated. In addition, the triple interaction terms for Saturdays and Mondays are included in the Sunday DDD model for this investigation. In general, no inter-temporal displacement effect on Saturdays and Mondays is detected at all. The full results for the inter-temporal displacement are available upon request.

Total Crime Violent Crime Property Crime Misdemeanor

(1) α1in DD Model 1 (Diff: Sun/Post) (N= 30,678) 0.057** (0.018) 0.012 (0.007) 0.027 (0.016) 0.016** (0.005) (2) β1 in DD Model 2 (Diff: Treat/Post) (N= 21,900) 0.041** (0.016) 0.008 (0.009) 0.020 (0.013) 0.020*** (0.005) (3) γ1 in DDD Model 3 (Diff: Sun/Treat/Post) (N= 158,503) 0.053** (0.019) 0.013 (0.009) 0.026 (0.016) 0.017** (0.005)