How far to the border? The extent and impact of cross - border casual cigarette smuggling.

It is important to note distance does not appear as a separate right-hand side variable in equation [6]. This exclusion comes from the assumption that the distance to a lower-price jurisdiction impacts smuggling but not quantity demanded, conditional on the decision to smuggle. In other words, the model predicts distance does not belong in X. In the regressions that follow, I include log distance in X as an over-identification test of the exclusion restriction. (28)

RESULTS

Coefficient Estimates

Table 6 presents the results from the estimation of demand function [6]. Panels A-C contain estimates for the intensive, extensive, and full demand models, respectively. All three panels contain six columns of results; I control for year trends in only even numbered columns. Columns i and ii present estimates from the demand model ignoring all smuggling incentives and geographic variability. Such a model is similar to what other researchers have used when studying cigarette demand using micro data and is useful in understanding the impact of accounting for smuggling behavior. Columns iii-vi contain estimates from the demand model outlined in the previous sections, with the final two columns including Native American Reservations in the price difference and distance variables.

In the specifications that account for smuggling, the coefficient on log real home state price is negative and significant at either the five or ten percent level. As this coefficient also represents the full price elasticity, Table 6 illustrates, absent smuggling, that there is a consistent negative relationship between price and consumption on the intensive, extensive, and full margins.

The coefficient on the difference in log price, log distance interaction variable is a central parameter in this study because it describes how the responsiveness of demand to home state price changes varies with distance to a lower-price border. In all relevant columns of Table 6 (columns iii-vi), this coefficient is negative and is significant at the five percent level in all but the final two columns of Panel B. I estimate this coefficient to be around -0.2 in the intensive and extensive demand models and between -0.58 and -0.42 for the full model. Thus, the relationship between quantity demanded and the home state price is quite sensitive to the distance to the closest lower-price border. (29)

The coefficient on the difference in log price variable is positive in all specifications, but is often not significant at either the five or ten percent level. The estimates range from 0.69 to 1.06 on the intensive and extensive margins and 2.17 to 2.55 on the full margin. Finally, across all specifications in Table 6, the coefficient on the difference In log price squared varies in sign but is not statistically significant.

As discussed in the fifth section, the log distance variable does not appear in equation [6] as a separate explanatory variable. The inclusion of this coefficient provides an over-identification test that excluding distance from the demand model is appropriate. In all three panels, I find the coefficient on log distance to be small and not statistically significant at the five or ten percent level. (30) This is evidence that changes in distance do not affect consumption if the price difference is zero; conditional on the decision to smuggle, distance has no impact on quantity demanded.

Estimated Elasticities

The coefficient estimates shown in Table 6 yield insight into the relationship between cigarette consumption, cigarette prices, and distance. These effects can be summarized more simply by calculating the home state and full price elasticities, which give the percent change in cigarette consumption due to a one percent change in the home state price and in all prices, respectively. Both elasticities can be calculated from equation [6]:

[7] Home State Price Elasticity = [partial derivative]ln(Q)/[partial derivative]ln([P.sub.h])

= [[PI].sub.1] + [[PI].sub.2] + 2[[PI].sub.3](ln([P.sub.h]) - ln([P.sub.b])) + [[PI].sub.4]ln(D)

[8] [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Table 7 presents home state and full price elasticity estimates calculated from the coefficients in Table 6. All panels and columns correspond to the same specification from Table 6. In columns i and ii, where geographic variability and smuggling incentives are ignored, the home state and full price elasticities are identical by definition. Thus, only the former statistic is shown. Robust standard errors are in parentheses.

The home state price elasticities range from -0.03 to 0.08 on the intensive margin, -0.06 to -0.02 on the extensive margin and -0.11 to 0.06 for the full margin. In no specification are these elasticities differentiable from zero at the five or ten percent level. These numbers imply, on average, in the presence of cross-locality price differentials, home state price changes have a negligible effect on cigarette demand.

The home state price elasticities contrast markedly and statistically significantly with the full price elasticities, which range from -0.18 to -0.10 on the intensive margin, -0.30 to -0.23 on the extensive margin, and -0.53 to -0.44 on the full margin. These elasticities are larger in absolute value than the home state price elasticities, and the full margin elasticities are consistent with many of the elasticity estimates from the taxable sales literature. (31) When one adequately controls for cross-border purchases, it is possible for the full price elasticities calculated using micro data to mirror the estimates from the taxable sales literature.

A specific example is illustrative of the difference between the home state and full price elasticities. In the last column of Panel C, the home state price elasticity is 0.03 while the full price elasticity is -0.53. This gap suggests while smoking is unresponsive to changes in the home state price on average in the presence of casual smuggling, if smuggling were eradicated, home state cigarette price elasticities could reduce cigarette consumption. Due to the inelastic nature of the full price elasticity, cigarette taxes could serve as an effective revenue generating mechanism for states as well.

The elasticities in the first two columns range from -0.21 to -0.06 on the intensive and extensive margins and -0.44 to -0.33 on the full margin. They are generally consistent in magnitude and sign with other studies using individual consumption data with fixed effects (Farrelly et al., 2001; Farrelly and Bray, 1998; Coleman and Remler, 2004). In all three panels of Table 7, a comparison of the first two columns with the last four columns illustrates ignoring geographic variability causes one to overstate the home state price elasticity and understate the full price elasticity in absolute value, though the "naive" elasticity estimates are often quite close to, and are not statistically different from, the full price elasticities. (32) The implication of this finding is ignoring smuggling incentives when using micro-data will not produce large biases in estimates of the full price elasticity on average. This is an interesting result as there is no reason to believe, a priori, that the bias in the full price elasticity will be small. Further, omitting smuggling incentives from cigarette demand models will preclude one from estimating the home state price elasticity, which is arguably the more important parameter from a state tax policy perspective as it yields the actual effect of a tax increase on consumption in a given state rather than the potential effect absent smuggling.

Smoking Increases, Casual Smuggling Percentages, and Net Sales Effects

Because cross-state price differentials offer consumers access to lower-priced cigarettes, casual smuggling can increase cigarette consumption. I calculate smoking increases due to the effective price reduction from smuggling by comparing the predicted value from each regression to the predicted value from a counterfactual in which there is no casual smuggling. This counterfactual is constructed by setting the price difference equal to zero. More explicitly

[9] Percent Change in Q

E[Q | [P.sub.h] = [p.sub.h], [P.sub.b] = [p.sub.b]]] - E[Q | [P.sub.h] = [P.sub.b]]/ E[Q | [P.sub.h] = [p.sub.h], [P.sub.b] = [P.sub.b]].

Due to the functional form of the demand function, the preceding expression can be negative for those who live very far from the border. To correct for this problem, I set the percent change equal to zero if it is negative. Note this adjustment produces similar results to constraining the home state price elasticity to be weakly greater than the full price elasticity: those who live far from lower-price borders are assumed not to smuggle. The third row of each panel in Table 7 contains estimates of the percent increase in smoking due to smuggling. Cross-border purchases increase consumption between 1.2 and 2.5 percent on the intensive margin and between 4.0 and 8.2 percent for the full model. Further, the availability of cheaper cigarettes increases the smoking participation rate by 2.0 to 4.3 percent.

The demand model given by equation [6] also allows me to calculate the proportion of individuals who purchase cigarettes in border localities in a given MSA. I assume if everyone lived directly on the border, no one would purchase in the higher-price state. Comparing consumption for such individuals with consumption for those who do not live close to the border yields the percentage of consumers who smuggle:

[10] Smuggling Percentage =