In this appendix we motivate and discuss the empirical models and results used to produce the casual and commercial smuggling estimates presented in the main text under "A New Estimate of Interstate Cigarette Smuggling Rates" (see Page 12). The results of this study build upon the existing literature, which provides considerable support for the presence of substantial tax-induced smuggling, both casual and commercial. For instance, Lovenheim (2007) estimates that 13 percent to 25 percent of U.S. consumers engage in casual smuggling while Thursby and Thursby (2000) find that commercial smuggling accounted for nearly 7.3 percent of total sales in the United States in 1990.

Such estimates have usually been generated from representative consumer demand models in which variables such as price, tourism, income, race and religious affiliations, among other demographic variables, are used to characterize demand. The researchers then include tax or price differentials, American Indian and military populations and distance to North Carolina (as the primary source of commercial smuggling) among other variables to measure the impacts of casual and commercial smuggling.

The empirical model employed herein differs from the general representative consumer demand models of the existing literature. We do not contend that our method is superior to those proposed before us; rather, our model should be viewed as a complementary method of measuring cigarette smuggling. Furthermore, given that our results are consistent with the findings of the existing literature, the finding of substantial levels of tax-induced smuggling is robust. The primary difference between our model and those generally used in the literature is that we do not estimate a standard demand model. Rather, we first estimate state-level sales as a function of in-state consumption. As will be described in further detail below, the resulting unexplained portion of state sales can then be attributed primarily to smuggling practices, assuming measurement error is relatively small. As such, we use the residual (unexplained sales) from the aforementioned regression as the dependent variable in a second regression which includes tax differentials and other common variables to explain the level of casual and commercial smuggling.

Per-adult tax-paid cigarette sales (hereafter per-adult sales) can be defined as the sum of in-state consumption and net smuggling, as presented in Equation 1:

PCSalesit = Consit + NetSmugit

where PCSales is per-adult cigarette sales, Cons represents the in-state per-adult consumption, NetSmug is the per-adult number of packs of cigarettes exported to residents of other states minus the number of packs imported by residents of the home state from other states or other jurisdictions (including Indian reservations and military bases), and i and t indicate state and year.

Our first-stage regression equates to a naïve version of Equation 1 in that we do not control for any smuggling. Instead, we include only in-state consumption on the right-hand-side of the equation. If the smuggling of cigarettes is not prominent, then sales within the state will be approximately equal to in-state consumption. As such, the R-square from such a regression would be fairly close to one.[*] However, if smuggling is a prominent feature of the cigarette market, such a naïve model will fail to explain a much larger percentage of the variation in per-adult sales, resulting in large residuals (in magnitude).

The sign and magnitude of the residuals from the estimation of the naïve model are of particular interest to us. Specifically, for low-tax states, the naïve model will systematically under-predict actual sales (positive residual), as consumers from other states travel across state-lines to purchase cigarettes in the lower-tax state. Thus, actual sales in the low-tax state will exceed the amount indicated by in-state consumer demand. Similarly, the model will systematically over-predict actual sales for high-tax states (negative residual), as in-state residents choose to purchase cigarettes in nearby lower-tax states, from Indian reservations or military bases, or from illegal markets.

In order to estimate our naïve model of per-adult tax-paid cigarette sales, in-state per-adult consumption must first be characterized. We define in-state per-adult consumption by Equation 2:

Consit = Smokeit * Intensityit * Rit

where Smoke is the smoking prevalence in the state (the percent of the adult population in the state who are smokers), Intensity is the average number of packs consumed during a year by smokers in the state, and R is a parameter between zero and one allowing for the under-reporting of smoking prevalence.[†]

Data on smoking prevalence is available from the Centers for Disease Control and Prevention (CDC) through its Behavioral Risk Factor Surveillance System (BRFSS). Unfortunately, data regarding smoking intensity is not readily available. Computing smoking intensity for the U.S. as a whole (based on observed consumption and smoking prevalence for the U.S.), the average smoker consumed 377.5 packs per year in 1995, and this volume has declined by nearly eight packs per year through 2006, as displayed in Figure 1.[‡] Given this close-to-linear trend in smoking intensity and the lack of data for this variable, we make some simplifying assumptions. Specifically, we assume that smoking intensity does not vary across states and that it trends linearly through time. Some evidence exists suggesting an under-reporting of cigarette consumption in survey data, such as the BRFSS.[§] However, this issue more readily plagues estimates of smoking intensity (i.e., cigarette consumption per day) than it does estimates of smoking prevalence. As such, we assume that under-reporting of smoking prevalence is not a major concern for our study and that any changes in the rate of under-reporting varies identically across all states and follows a linear trend. With these assumptions in mind, Equation 2 becomes

Consit = Smokeit * f(Trendt)

where f(Trendt) represents the above-described linear function of smoking intensity and under-reporting.

Figure 1

Figure 1 - click to enlarge

The empirical specification of our naïve model, then, sets per-adult sales as a function of smoking prevalence and a time trend. We estimate this model using state-level data for the U.S. contiguous states (excluding North Carolina) for the time period 1990-2006. North Carolina is excluded from our sample as it is modeled as the primary source of commercially smuggled cigarettes, which will be described in greater detail below.[¶]

Descriptive statistics and sources for all variables used in this study can be found in Table 1. Table 2 presents the maximum likelihood estimates of our naïve model. Columns 1 and 2 present the linear specification of the model, while the preferred log-linear specification is presented in Columns 3 and 4.[**] Both specifications control for groupwise heteroskedasticity to allow for non-constant variance across the states.[††] Both smoking prevalence and the time trend are of the expected sign and significance level. Per the results presented in the final two columns of Table 2, a 1 percentage point increase in the smoking prevalence rate results in a 5.3 percent increase in per-adult sales in the state. Furthermore, per-adult sales are shown to decrease by an average of 1.8 percent per year, which we attribute to the decline in smoking prevalence over time.

Table 1: Descriptive Statistics and Sources of Data

Table 1: Descriptive Statistics and Sources of Data - click to enlarge

[1] Tax Burden on Tobacco, 2007
[2] Behavioral Risk Factor Surveillance System Survey Data (BRFSS), various years
[3] U.S. Census Bureau, Intercensal County Population Estimates
[4] Computed
Note: All prices are represented in constant year 2000 dollars.

Table 2: Maximum Likelihood Estimation: State Per Adult Cigarette Sales, 1990 - 2006

Table 2: Maximum Likelihood Estimation: State Per Adult Cigarette Sales, 1990 - 2006 - click to enlarge

Notes: Statistical significance of 1%, 5% and 10% are represented by ***, **, and *, respectively.
Results are corrected for groupwise heteroskedasticity via the HREG command within NLOGIT 3.0.

As mentioned above, it is not the coefficient estimates from the naïve model that interest us; rather, it is the residuals from this naïve model that are of particular importance. Figure 2 presents a scatter plot of per-adult sales and smoking prevalence for the 47 states in our sample for the year 2006. The exponential trend-line is purely for explanation purposes and does not represent our actual estimation of the naïve model. Two observations, in particular, have been identified and labeled in the scatter plot: Delaware and New Mexico. 

The residual for Delaware is nearly 114 packs; that is, per-adult sales in Delaware are 114 packs more than is predicted by the naïve model. New Mexico, on the other hand, observes a residual of over 28 packs; that is, per-adult sales in New Mexico are 28 packs less than predicted by the model. Casual observation of the tax-differentials with the bordering states can help explain these residuals. In 2006, Delaware's cigarette tax was 55 cents while the average tax of the states bordering Delaware was over 148 cents, a difference of over 93 cents per pack. As such, we should expect many residents of surrounding states to travel into Delaware to purchase their cigarettes at a lower price. The New Mexico experience should be the opposite of Delaware's because its cigarette tax is, on average, 24 cents higher than the taxes in bordering states. The observed residuals for the other states can also generally be explained by border tax differential.[‡‡]

We now turn our attention to a more formal analysis of smuggling through the examination of the residuals from the naïve model. We attribute most of the variation of the residual from the naïve model to the occurrence of the two types of smuggling: casual and commercial (organized). Casual smuggling can take the form of cross-border shopping between states, cross-border shopping to and/or from Canada and Mexico, and the purchase of un-taxed cigarettes on military bases and Indian reservations by non-military personnel and non-tribal members.

To account for tax-induced cross-border shopping across state lines we include the weighted average tax differential (home tax rate - average border tax rate) between the home state and the bordering states.[§§] Similar to the weighting method employed by Coats (1995), the weights are based on county border populations. However, large tax differentials probably will not cause significant cross-border shopping if only a few people live along the borders. As such, we include the population living on either side of the border divided by the home state's total population (percent border population). This percentage can take on a value greater than one when the border population in surrounding states is sufficiently large, thus causing the border population to exceed the home state's total population. Finally, we include an interaction term between the average tax differential and percent border population.

To capture the impact of the presence of Indian reservations, we include the tax rates of the states in which Indian reservations are present. This is effectively the tax differential between the home state and the tribal land, as no taxes are generally applied to cigarettes sold on Indian lands.[***] Ideally, we would also like to include for the states bordering either Canada or Mexico the tax differential with the Canadian province(s) and Mexican state(s). Unfortunately, accurate data on such tax rates, particularly for Mexico, were not available. As such, we simply include the home state tax rate for those states bordering either Canada or Mexico.

As described by Thursby and Thursby (2000), commercial smuggling primarily occurs "over-the-road" or by "diversion." Diversion involves the manipulation of accounting records, reporting only a portion of their sales. In effect, firms divert the unreported portion, on which no taxes were paid, to the illegal sector. As this type of smuggling involves manipulating the accounting records, regular auditing can reduce such occurrences. Over-the-road smuggling occurs when bulk cigarettes are purchased legally in low-tax states and then shipped to higher-tax states. Counterfeit stamps are then placed on the cigarette packs, which are

Figure 2:

Figure 2 - click to enlarge

then often sold in legal markets. Distributors in the low-tax states are often paid to not place the home-state's stamp on the cigarettes; however, such payment is not necessary in North Carolina (as of 1994) or in South Carolina (as of 1996) as both states repealed the use of the state stamp. Such actions effectively promote commercial smuggling by reducing professional smugglers' transaction costs.

Our empirical model controls for only over-the-road smuggling, as has been common in the literature with the exception of Thursby and Thursby (2000). North Carolina has generally been modeled as the primary source of commercially smuggled cigarettes and we will follow the same convention. The tax differential between the home state and North Carolina is, therefore, included as our measure of commercial smuggling. We estimated additional specifications in which we added distance from North Carolina and an interaction term between the tax differential and distance variables, but they were both statistically insignificant and performed poorly. As such, we eliminated them from the final model. This is consistent with much of the previous literature as transportation costs account for a very small portion (less than one percent) of the total value of cigarettes, suggesting that such costs should exert a negligible impact on smuggling.[†††]

The OLS estimation results in which we regress the residuals from the log-linear naïve model against the above described tax differential and population variables is presented in Columns 3 and 4 of Table 3.[‡‡‡] The estimates corresponding to the linear naïve model are presented for robustness purposes only and can be found in Columns 1 and 2 of Table 3. It is important to understand what the dependent variable represents when interpreting these results. Recall that the residual is the actual per-adult sales minus the predicted sales from the naïve model. A positive residual, then, indicates that the naïve model under-predicted actual sales; that is, in-state consumption is less than sales in the state, suggesting the smuggling of cigarettes out of the state by non-residents. A negative residual suggests that the naïve model over-predicted sales and therefore indicates that residents of the state chose to buy significant quantities of cigarettes from outside the state.

Table 3: Unexplained Per Capita Sales from Naïve Model, 1990 - 2006

Table 3: Unexplained Per Capita Sales from Naïve Model, 1990 - 2006 - click to enlarge

Notes: Statistical significance of 1%, 5%, and 10% are represented by ***, **, and *, respectively.

All independent variables included in the model are statistically significant with the sole exception of the Canadian border variable. An increase in the tax differential with North Carolina (our measure of commercial smuggling) is shown to reduce the residual, indicating an increase in commercial smuggling of cigarettes from North Carolina. States along the Mexican border, and particularly those with higher tax rates, also experience increased smuggling of cigarettes into the state from Mexico.

The same can be said of Indian reservations; of those states with at least one Indian reservation, those with higher taxes experience increased smuggling from the reservations. The implications from the model concerning casual smuggling across state borders are not as clear, as the coefficient of average tax rate differential is positive while the interaction term is negative. However, given the mean percent border population of 1.305, the impact of a 1-cent increase in the average tax differential is clearly negative (-0.148), suggesting that the larger the home tax rate relative to the average bordering tax rate, the greater the smuggling into the state from the lower-tax neighboring states.

Given the above estimation results, we compute the percentage of cigarette pre-smuggling sales in each state for several types of smuggling: casual smuggling across state boundaries and from Indian reservations, casual smuggling across international borders (Canada and Mexico) and commercial smuggling from North Carolina. Pre-smuggling sales is the estimated quantity of cigarettes that would have been sold in the state had no smuggling occurred (effectively, in-state consumption alone). Mathematically, it equates to observed sales minus estimated smuggling. For states that are estimated to be importers of smuggled cigarettes, estimated smuggling takes on negative values and pre-smuggling sales will exceed observed sales. For net exporters of smuggled cigarettes, pre-smuggling sales will be less than observed.

Table 4 presents our state-level average estimates of the percent of sales that are smuggled (by smuggling component and in total) over our entire sample period 1990-2006 (this table is reprinted from the earlier section titled "A New Estimate of Interstate Cigarette Smuggling Rates"). Those states for which percent smuggled is negative are net importers of smuggled cigarettes. The imports of smuggled cigarettes exceed 20 percent of sales in only four states: Arizona, California, New York and Washington, with California topping out at nearly 25 percent of sales. Only Delaware's and Virginia's exports of smuggled cigarettes exceed 20 percent of total sales, although New Hampshire is close with over 17 percent smuggled.[§§§] Delaware is interesting, as its exports are nearly 30 percent of sales.

Table 4: Estimated Tax-Induced Smuggling as a Percent of Sales:
1990-2006 Annual Averages

Table 4: Estimated Tax-Induced Smuggling as a Percent of Sales: 1990-2006 Annual Averages - click to enlarge

Notes: Estimates computed based on the regression results presented in columns 3 and 4 of Table 3. The sum of commercial, casual and Canada/Mexico smuggling does not equal the total presented in the final column due to the non-linear nature of the model.

Delaware raised taxes twice during the sample period: a 10-cent increase in 1991 to 24 cents per pack, and a 31-cent increase in 2003 to 55 cents per pack. The average tax rate of the neighboring states increased from 18.6 cents per pack in 1990 to over 148 cents per pack in 2006. This rapidly increasing tax differential (in magnitude) has led to significant cross-border shopping, as residents of New Jersey, Pennsylvania and Maryland all seek to avoid their own states' high cigarette taxes.

Given our particular interest in the states of Michigan, New Jersey and California, additional discussion of the results in regards to these three states is warranted. As mentioned above, California is estimated to be the top importer of cigarettes. Much of the imported cigarettes are smuggled in from Mexico, accounting for about 10 percent of sales. Commercial smuggling accounts for another 7.4 percent while casual smuggling amounts to nearly
6 percent of sales.

Michigan and New Jersey, as high-tax states, are also net importers of smuggled cigarettes at nearly 16 percent and 12.3 percent of sales, respectively. Casual smuggling across state lines and from Indian reservations accounts for a roughly 6 percent reduction in sales in Michigan while commercial smuggling reduces sales by another 11.6 percent. Michigan is estimated to export roughly 1.2 percent of its sales to Canada, though. The smuggling of cigarettes into New Jersey amounts to 12.3 percent of sales with the primary source of imports being commercially smuggled cigarettes.

 Casual smuggling does not appear to be significant in New Jersey on average over the sampling period as the border tax rate differential was relatively close to zero (and positive in some years while negative in others) until recent years. More specifically, New Jersey's tax rate was lower than the average of its neighbors for seven of the 17 years in our sample. However, New Jersey began aggressively raising its cigarette tax in 2003, and the rate now exceeds its neighbors' average by over a dollar per pack.

Table 5 presents the estimated total change in cigarette sales in our three states of interest in response to specified changes in the 2006 tax rates. The estimated sales responses are due solely to changes in smuggling behavior, not to price-induced changes in the quantity demanded. The 2006 tax rates on cigarettes in California, Michigan, and New Jersey were 87, 200, and 240 cents per pack, respectively.

We compute the percent change in the total quantity of cigarettes smuggled in response to an increase or decrease in the 2006 rate by either 25 or 50 cents. Consider a 50-cent increase in each state's tax (one at a time), holding constant all other tax rates in the U.S. Such an increase represents a 57.5 percent increase in the state tax and is estimated to cause a 25.3 percent decline in sales due to the increase in smuggling. The same 50-cent change in Michigan's tax (a 25 percent

increase) is shown to reduce sales by 10.5 percent due to smuggling. Finally,
a 50-cent tax increase in New Jersey (a 20.8 percent increase) results in an estimated 18.8 percent decline in sales.

Table 5: Change in Sales Due to Selected Changes in Tax Rates for Selected States

Table 5: Change in Sales Due to Selected Changes in Tax Rates for Selected States - click to enlarge

The above sales responses can be used to compute the tax elasticity due to smuggling activity. The results suggest a tax elasticity of -0.44 for California, -0.42 for Michigan and -0.90 for New Jersey. The estimates for California and Michigan compare favorably to those computed by Lovenheim (2007), who estimated the home state price elasticity of -0.46 for California and -0.22 for Michigan. However, Lovenheim's estimate of New Jersey's home state price elasticity is a positive 0.38. Not only is our estimate negative, as would be expected, but it is nearly 2.5 times as large in magnitude. One reason for the large differences in our results for New Jersey relative to Lovenheim's may revolve around our use of more recent data covering the large tax increases experienced in New Jersey beginning in 2003. As such, one could argue that our results may be more reliable for policy recommendation purposes if for no other reason than our sample is more representative of current tax rates.


[*] Furthermore, the estimated intercept and slope coefficients should be insignificant from zero and one, respectively.

[†] We would like to thank a referee for suggesting the inclusion of under-reporting in our model.

[‡] 1995 - 2006 is used as the sample period for this statistic rather than our full 1990 - 2006 sample period because aggregated U.S. statistics prior to 1995 are not available on the BRFSS web page.

[§] See, for example, Warner (1978).

[¶] The estimation results and the implications of this study are largely unchanged if Kentucky and Virginia (also prominent tobacco states) are excluded from the sample as sources of commercially smuggled cigarettes.

[**] OLS estimation produces similar estimates to the ML estimates presented here, however, ML estimation is preferred due to its robustness to distributional assumptions regarding the error term.

[††] Allowing for groupwise heteroskedasticity may minimize any bias due to the assumption of constant smoking intensity and under-reporting across the states.

[‡‡] Delaware and New Mexico were chosen for this discussion for no other reason than that the corresponding residuals are the largest and smallest (respectively) of all states in 2006.

[§§] All monetary values are represented in constant year 2000 dollars.

[***] With that said, many states, Michigan being one of them, have reached agreements with at least some tribes where the tribes have agreed to collect the state tax on sales of cigarettes to non-tribal members.

[†††] See Thursby and Thursby (2000) and Thursby et.al. (1991).

[‡‡‡] We also estimated a model of Equation 1 directly which includes smoking prevalence, a time trend, and all our smuggling variables included in the second stage of our model.  This specification  is more similar to those of the existing literature.  The results are similar to those of our preferred estimation strategy presented in this paper and are available from the authors upon request.

[§§§] These findings are relatively consistent with those of Lovenheim (2008), as he estimates the percent change in net sales due to smuggling in Delaware, New Hampshire and Virginia to be 52.3 percent, 104.2 percent and 65.4 percent respectively.  While the percentages differ, these three states are all in the top five exporters of smuggled cigarettes based on his estimates.