The demand for cigarette smuggling.

Saba, Richard P. ; Beard, T. Randolph ; Ekelund, Robert B., Jr. 等

INTRODUCTION

An enduring issue in economic analysis involves accounting for the behavior of agents when illegal or quasi-legal activity is rewarded. Smuggling, retrading under regulations or restrictions, bribery, and bootlegging are all aspects of the general phenomenon. Common contemporary forms of such activity are the smuggling of prohibited substances such as drugs or medicines, prohibited arms or weapons, or highly taxed commodities between countries.(1) But smuggling or bootlegging of highly taxed or otherwise regulated legal commodities such as alcohol, cigarettes, or gasoline also takes place within countries. In the United States, such illegal activity, both "casual" and "organized", may have significant effects on state tax revenues. It may also alter the expected consumption effects of specific tax changes. In a competitive environment, the existence of different tax structures between states may mean that a given state's tax enactments will not have their desired revenue or consumption effects.

This paper offers a new econometric methodology for estimating the economic effect of "border crossing" between U.S. states. Our technique, in contrast to previous models of cross-border effects, allows accommodation of the dichotomy between variations in state-level sales due to state-specific characteristics such as prices, tastes, incomes and other demographic factors, the presence of organized smuggling, tourism, and so on, and demand variations due to casual border crossing. Beginning with a simple theoretical model of a representative consumer's border-crossing decision, we develop a nonlinear econometric model which produces estimates of the representative consumer's demand in each state. It allows estimation of the degree and direction of sales to border-crossing consumers for each state and facilitates explicit testing of the statistical significance of border crossing in explaining variations in cigarette sales between jurisdictions. The data set is comprised of state-level cigarette sales for the forty-eight contiguous states and the District of Columbia over the period 1960 to 1986. We obtain strong evidence that border crossing is a significant factor in explaining cigarette sales differentials and we identify states which have important border-crossing sales. Further, we note the consequences of border crossing for demand elasticity estimation and tax policy: in general, the evidence indicates that the ability of states to raise revenue via cigarette taxation is more constrained than conventional analysis suggests.

The paper is divided into five sections. Section II discusses bootlegging and previous literature on cigarette demands and smuggling. Section III presents our theoretical and empirical models, while section IV discusses the data and our statistical results. Section V concludes the paper and examines some of the policy implications of our findings.

II. THE ECONOMIC LITERATURE ON SMUGGLING

Smuggling, bootlegging or "arbitrage" takes place when full prices (net of all costs) differ for legal or illegal goods between specific economic units. When net returns to smuggling or bootlegging - all production and consumption opportunity costs being considered - are positive, arbitrage will occur in an organized and/or casual fashion. A primary (though not an exclusive) reason for smuggling has been the often-significant divergence between full prices in different locales caused by differences in tax treatment.

A variety of models starting with Wales [1968], have been employed to analyze problems related to smuggling and bootlegging. Jensen, Thursby, and Thursby [1988], and Bhagwati and Hansen [1973]) study "Camouflaging" systems - the mixture of legal and illegal sales - from the firm's perspective with contrasting welfare results. Smith [1976] integrates illegal markets into the traditional theory of taxation but explicitly ignores casual smuggling. Earlier studies considering cross-border effects have not specified a theoretical foundation and, in this respect, our approach is fundamentally different.

To estimate border demands earlier studies typically weight tax or price differences by populations along contiguous borders (e.g., Advisory Commission on Intergovernmental Relations [1985]). Analyses by Baltagi and Levin [1986], and Manchester [1973]) account for cross-border sales by including the lowest border-state prices, and find bootlegging sales to be significant but of a small magnitude. In a recent model, Thursby, Jensen, and Thursby [1991] differentiate between organized and casual smuggling of cigarettes by applying an interesting sales estimation technique to time-series data for twenty-nine states. Their results show that, while organized smuggling significantly affected sales in North Carolina, casual border crossing is statistically unimportant. To accommodate cross-border effects in their model, however, Thursby et al. [p. 807] use a rough measure of the motivation for casual smuggling - the average retail price in neighboring states. Hence, while a number of previous studies attempt to control for casual smuggling, the specifications selected are not ideal.(2)

III. A MODEL OF CROSS-BORDER EFFECTS

Our analysis begins with a simple utility-theoretic model of the "representative consumer's" border-crossing decision. Faced with a cigarette price differential, taste for cigarettes, level of income, and cost of travel, we determine the "critical distance" at which the consumer is indifferent between purchasing at home or in a lower-priced bordering jurisdiction. This critical distance allows us to construct feasible border-crossing regions which, when combined with population and geographic information, facilitates simultaneous nonlinear estimation of both cigarette sales and the extent of casual border crossing. Hence, our approach significantly differs from previous studies by deriving the econometric specification from a microanalytic foundation. Further, our model permits an intuitive, direct test of the statistical significance of border crossing in explaining state sales variations.

A Simple Formulation of Cross-Border Effects

We formulate the model by assuming that the objective of a "representative" consumer in state i is to maximize her utility, which is derived from the consumption of cigarettes and a composite good with a price of $1 per unit in all states.(3) Formally, let

[p.sub.i] = real price of cigarettes per pack in the homestate i

[p.sub.j] = real price of cigarettes per pack in state j which borders state i

y = the consumer's real income

z = demographic characteristics of the consumer

[x.sup.*](p,y,z) = the consumer's ordinary demand for cigarettes for relevant price p

c = the consumer's real cost of travel per roundtrip mile, assumed to be independent of quantities purchased

[m.sub.ij] = the (one way) distance the consumer must travel to reach state j

In the absence of significant income effects, consumer's surplus provides us with an attractive approximation to the benefits consumers receive from exploiting price differentials between adjacent jurisdictions. In particular, suppose that border state j offers a price [p.sub.j] [less than] [p.sub.i]. Then the additional gross benefit the consumer receives from purchasing at the lower price is approximately s([p.sub.i], [p.sub.j]), given by

(1) s([p.sub.i], [p.sub.j]) = [integral of] [x.sup.*](r, y, z)dr between limits [p.sub.i] and [p.sub.j].

Travel to state j, however, implies a roundtrip cost of c [center dot] [m.sub.ij], resulting in a net benefit (loss) of s([p.sub.i], [p.sub.j]) - c [center dot] [m.sub.ij]. Hence, the "critical distance" [Mathematical Expression Omitted] at which the representative consumer is just indifferent between traveling to state j with its lower price or remaining in state i and incurring no travel costs is approximately

(2) [Mathematical Expression Omitted].

It is easy to see that [Mathematical Expression Omitted] is increasing in [p.sub.i], decreasing in [p.sub.j], increasing in factors that increase ordinary demand [x.sup.*], and decreasing in the travel cost parameter c.

The Econometric Model

Previous studies of cigarette sales have identified a number of special circumstances important in explaining variations in cigarette sales across states and through time. First, there is some evidence that professional smuggling activities ("camouflaging") may affect sales in North Carolina.(4) This professional smuggling is to be distinguished from the casual border crossing in which we are primarily interested. Second, the demographic characteristics of some states' populations differ widely, suggesting the presence of potentially important taste variations between jurisdictions that may affect sales. Third, the levels of tourism and transient visitation vary significantly among states. Finally, the passage of time itself has corresponded with a secular decline in cigarette usage as the perceived health consequences of smoking have become more widely disseminated and as various legal sanctions restricting smoking have become widespread.

An important complication in estimating the extent and direction of border-crossing activity in the U.S. arises from the geographic dimension of the problem and the related issue of consumer "double counting." First, states typically border a number of other states and, to the extent that two or more of these border states have lower prices, some consumers in a higher-priced "home state" may travel to one lower-priced border state, while others travel to another. Further, not all border states will be "low-price" states, and sales in the home state may also reflect border crossing into it. Therefore, one expects sales in most states to reflect both departures of home state consumers to cheaper border states, and the arrival of out-of-state consumers for whom the destination state is cheaper. Additionally, since consumers presumably differ in, for example, their tastes for smoking, consumers who enter a state from a higher-priced border area bring their demand characteristics and unique tastes with them. All of these complications should be accounted for in the econometric specification.

The issue of "double counting" of consumers arises when a state has two or more lower-priced border states that are "close together." Suppose, for example, that a consumer in state i lives close to two cheaper border states. Such a consumer will then decide which, if either, of the border states to visit based on price differentials, travel costs, and the distances involved. If [Mathematical Expression Omitted] and [Mathematical Expression Omitted] are the "critical distances" to cheaper border states 1 and 2, respectively, then any consumer who lives closer to state 1 than [Mathematical Expression Omitted], and closer to state 2 than [Mathematical Expression Omitted], will select one or the other state depending on which yields the highest utility. Regardless of how one assumes consumers are distributed within states, the relevant geographic areas from which border crossing may occur can overlap.

To formulate the model in a tractable way, a set of simplifying assumptions which reduce the complexities imposed by geography are necessary. We assume the following:

1. State populations are uniformly distributed.(5)

2. Border lengths between states are "linearized" by calculating straight-line distances from northern to southern (or eastern to western) points of contact "as the crow flies."

3. States which meet at a "point" are assumed to have a linear border of one mile.

Utilizing these assumptions, the relevant border-crossing areas (and, by implication, the percentage of the state population which border crosses) can be calculated simply as the percentage of the state's total area (times the state's population) within the relevant "border-crossing region," as represented by the ratio [Mathematical Expression Omitted], where [Mathematical Expression Omitted] is the critical distance for a consumer to travel from state i to the cheaper border state j, [b.sub.ij] is the linearized border between i and j, and [A.sub.i] is the total area of state i. Hence, the border-crossing region is represented as a rectangle with side lengths [Mathematical Expression Omitted] and [b.sub.ij]. "Double counting" occurs when these rectangles "overlap" although, as will be seen, the degree of double counting that actually occurs can be shown to be trivial in practical application.

Utilizing the assumptions given above and equation (2), total cigarette sales in the state i at time t can be given by

(3) [Mathematical Expression Omitted]

where

[Sales.sub.it] = total sales (in packs) in state i in year t

j = border state index; no state has more than eight border states

[[Theta].sub.ijt] = indicator variable; equal to 1 if border state j "exists" and has a lower price than home state i in year t; [[Theta].sub.ijt] = 0 otherwise

[Mathematical Expression Omitted] = "critical distance" of travel for a consumer in state i to cheaper border state j in year t

[b.sub.ij] = "linearized" border (in miles) between states i and j

[A.sub.i] = area (in square miles) of state i

[Pop.sub.it] = population of state i in year t

[Mathematical Expression Omitted] = Marshallian demand for cigarettes of a representative consumer from state i in year t

[[Theta].sub.jit] = indicator variable; equal to 1 if border state i "exists" and has a higher price than state j in year t; [[Theta].sub.jit] = 0 otherwise

[Mathematical Expression Omitted] = "critical distance" of travel for a consumer from the more expensive border state j to state i in year t

[A.sub.j] = area (in square miles) of border state j

[Mathematical Expression Omitted] = Marshallian demand for cigarettes of a representative consumer from state j in year t

Equation (3) explains sales in state i in year t as the sum of sales to that percentage of residents of state i who do not border cross to a cheaper state, plus sales to out-of-state consumers who cross into state i due to higher prices in their home states. By suitably indexing the expression for [m.sup.*] given in equation (2) and substituting into equation (3), we obtain a nonlinear regression model which can be estimated by nonlinear least squares techniques.

Specification of the model also requires that one assume a functional form for the Marshallian demand curves of each state's "representative consumer." Because of the model's high degree of inherent complexity, and the requirement that representative consumers be allowed to differ between states to account for sales differences arising from population heterogeneity, professional smuggling (in the case of North Carolina), tourism and other factors, we adopt the linear form given by (4):(6)

[Mathematical Expression Omitted]

where

[Mathematical Expression Omitted] = cigarette packs per year demanded by a representative consumer in state i in year t

[[Alpha].sub.io] = demand intercept for state i

[p.sub.it] = relevant real price per pack of cigarettes in year t

T = time trend variable

[z.sub.it] = demographic variables for state i in year t

[[Alpha].sub.1], [[Alpha].sub.2], [[Beta].sub.r] = coefficients

The demographic variables used in our estimation are (1) average real per capita income by state per year, (2) the percentage of black residents per state per year, (3) the percentage of each state's residents under eighteen years of age each year,(7) (4) the percentage of each state's residents identified as subscribing to "Fundamentalist" Christian religious doctrines by year,(8) and (5) a measure of each state's relative tourism dependence calculated yearly as the ratio of each state's hotels or lodging places per capita to the nation's corresponding ratio in each year, the result being reduced by 1 so that a state having a mean hotels per capita ratio (in a given year) has a tourism dependence score of zero (for that year).(9) Further, the representative demands are allowed to vary by demand intercept coefficients corresponding to the nine census regions for the forty-eight contiguous states, and a dummy variable representing North Carolina, the latter as a control for the professional smuggling alleged to occur from that jurisdiction. Additionally, as tourists would appear to be unlikely candidates for border crossing, the relative tourism dependence variable is mean scaled (set equal to zero) in border-crossing demands, but is allowed to affect home-state demands in the normal fashion.(10)

Our specification is completed by our treatment of the critical "real cost of travel per (roundtrip) mile" variable c. Since it is quite difficult to obtain a reasonable measure of this value, and since the magnitude of this cost is likely to significantly affect the estimated results, we exploit the nonlinearity of the regression equation (3) by assuming that this cost c is unknown and represent it as c = 1/F, where F is a parameter to be estimated. This procedure has three significant advantages. First, the estimation results will not exhibit bias due to incorrect assumptions about the (real) costs of travel. Second, and most importantly, the overidentifying restriction F = 0 implies no border crossing (by implying effectively infinite travel costs), and is a testable hypothesis. Consequently, the statistical significance of border crossing can be directly evaluated, and such a test has a natural interpretation. Finally, if one assumed any hypothetical travel cost value, then the estimated value of F can be interpreted as the percentage of representative consumers living in the relevant border-crossing region defined by (2) who actually border cross. This can be incorporated in the estimation by redefining c as c = V/F, where V is the estimated travel cost and F is interpreted as a border-crossing participation rate. Hence, while one cannot determine whether a given flow of border crossers represents all potential crossers from a small area, or only some fraction of potential crossers from a larger area, selection of a travel cost V constitutes an uninformative normalization.

We note finally that the estimable form given by (3), which utilizes total sales per state as the dependent variable, is almost certain to exhibit heteroskedastic errors since sales can vary by orders of magnitude between large and small states. To correct for this phenomenon, we divide both sides of (3) by state i's population in year t, thus converting the model for estimation purposes to one that explains "sales per capita" instead of total sales. The model we finally estimate is

(5) [Mathematical Expression Omitted]

where [Mathematical Expression Omitted]. F (and F is defined as above.)(11)

IV. DATA AND STATISTICAL RESULTS

Data for our analysis came from several sources. Information on average state prices per pack and total annual state sales for the lower forty-eight states and the District of Columbia for the years 1960-1986 was compiled from The Tax Burden on Tobacco Historical Compilation 1988, while a time series of state populations and per capita income, state areas and other geographical and demographic information was obtained from the U.S. Statistical Abstract, City County Data Books, and the Costat II tapes. Religion data were obtained from Churches and Church Membership in the United States: An Enumeration and Analysis by Counties, States and Regions. All financial variables were converted to real 1983 dollars.

After determining that (5) was an identified model given our sample price differentials, we estimated (5) as a nonlinear least squares estimation problem using the SAS NLREG procedure and DUD subroutine.

Table I gives estimated parameter values, asymptotic t scores, and some summary statistics for our estimation.(12) (Parameter names are relabelled for ease of presentation.) We note first that all model variables are significant at the 1 percent level, including the price variable which some previous studies that failed to account for border crossing found to be insignificant. The results suggest that a 1[cent] increase in average real cigarette pack prices is associated with a consumption decrease of about 1.3 packs per year for a typical representative consumer. Further, the estimates suggest that cigarettes are a normal good, such that a $1000 increase in average real income results in increased consumption amounting to about seven packs a year for a typical consumer. Additionally, the passage of time has effected a secular decline in cigarette consumption averaging about 2.6 packs per year between 1960 and 1986.

Our other demographic variables also exhibit significant and intuitively plausible effects. A 10 percent increase in the percentage of black consumers increases average consumer cigarette usage by about 4.6 packs per year, a significant effect. Further, high proportions of under age eighteen consumers and a high representation of consumers labelled "Fundamentalist" Christians both significantly reduce representative consumer purchases. We note also that large relative levels of tourist accommodations, a proxy for tourist presence, significantly increase [TABULAR DATA FOR TABLE I OMITTED] cigarette sales, and that North Carolina exhibits statistically higher representative consumer sales even when border crossing is controlled for, confirmation of the findings of Thursby et al. [1991] that suggest the importance of organized smuggling in this jurisdiction.

Most important for our purposes, the border-crossing parameter F is highly significant (t = 11.58) and of the "correct" sign. Hence, the estimation results provide strong evidence of the importance of border-crossing activities for explaining sales variations even when demographic characteristics and price variations are controlled for.

The empirical magnitude of border crossing is estimated by calculating, for each jurisdiction, the percentages of total sales attributable to border-crossing consumers and, in similar fashion, the percentage of each jurisdiction's endowment of representative consumers who leave for cheaper bordering states. Table II presents the results of this exercise for the years 1973 and 1986. States losing at least 2 percent of their consumers to cheaper bordering jurisdictions in our sample mid-point year 1973 include Connecticut (2.4 percent), D.C. (8.4 percent), Kansas (5.7 percent), Nebraska (4.6 percent), New Mexico (6.2 percent), Utah (5.3 percent) and Wyoming (4.7 percent), while Kentucky, Maryland, New Hampshire, Rhode Island and Vermont all "imported" between 2 and 9 percent of their total sales from their neighbors. Somewhat surprising is the estimate of just six-tenths of 1 percent of total sales to border crossers in North Carolina, a result that may reflect the low-tax policies of North Carolina's neighboring states (such as Kentucky) in 1973.

The figures for 1986, the final sample year, illustrate both some major changes in tax treatments and several enduring differentials in relative tax burdens as reflected in prices. Jurisdictions losing non-trivial percentages of their customers to lower-priced neighbors include Delaware (1.5 percent), D.C. (51.0 percent) and Massachusetts (1.0 percent). The very high figure for the District of Columbia reflects the extreme ease of border crossing combined with the high taxes levied there on cigarettes throughout the 1980s. States importing at least 2 percent of their sales in 1986 are New Hampshire (4.5 percent), Rhode Island (3.6 percent) and Vermont (2.4 percent), all of which border relatively populous, more highly taxed jurisdictions such as Massachusetts or Connecticut.

Although our results suggest that, for most states, border crossing flows are small, the existence of some areas with extensive border crossing suggests that the ability of border crossing to affect demand elasticities and cigarette tax revenues may be significant. To address those issues and examine the importance of border crossing for estimation of the revenue effects of cigarette tax policy changes, we estimated a restricted version of our model given in equation (5) by imposing the condition F = 0 (i.e., no border-crossing effects), dubbed the "naive model," and calculated the price elasticities of total demand for all jurisdictions using actual 1973 and 1986 prices and sales and parameter values from both the "naive" and unrestricted model. Table III presents the "naive" estimation results, while Table IV presents the elasticity estimates.

We note first that in all cases the naive elasticities are less than the unrestricted elasticities, the difference often amounting to a factor of two or more.(13) Further, while naive estimation typically suggests inelastic responses, price elasticities greater than unity emerge in the majority of cases when border crossing is included. These elasticities exceed by a wide margin those found [TABULAR DATA FOR TABLE II OMITTED] [TABULAR DATA FOR TABLE III OMITTED] in most studies of cigarette demands. Further, the jurisdictions exhibiting the greatest elasticities are often those in which the magnitude of border crossing is seen to be greatest: the District of Columbia, estimated to lose 51 percent of its consumers to neighboring jurisdictions in 1986, exhibits a very high sales price elasticity of -9.87 for that year, although one is reluctant to place excessive emphasis on such a result for so atypical a jurisdiction. Similar though less sharply drawn effects are seen for Rhode Island and Vermont. These results suggest that, for some jurisdictions, the ability of cigarette taxes to raise additional revenues may fall far short of what simple analysis might imply.

[TABULAR DATA FOR TABLE IV OMITTED]

V. CONCLUSION

This study uses a formal microanalytic foundation adaptable to econometric estimation in order to investigate the impact of border crossing on product demands within and between jurisdictions (our particular application being to cigarette sales among the lower forty-eight states for the period 1960 to 1986). Our model permits both an estimate of the actual extent of casual bootlegging, and a test of the significance of border crossing in explaining variations in state sales. Our findings suggest the following conclusions.

(1) Border crossing is a significant determinant of cigarettes sales in at least some states.

(2) While the extent of border-crossing activity is typically small (less than 1 percent of total sales), several jurisdictions enjoyed large inflows of buyers, while several others exported thousands of consumers to less costly adjacent jurisdictions.

(3) Cross-border effects typically result in large increases in estimated price elasticities over those elasticities implied by naive analysis.

(4) Prices are significant determinants of sales.

(5) Cigarettes are a normal good.

(6) Black consumers, those over eighteen years of age, and those not identifying with "Fundamentalist" Christian traditions buy more cigarettes.

(7) Relatively high levels of tourism result in increased sales.

(8) Sales in North Carolina are especially high, possibly reflecting professional camouflaging operations in that state.

A number of important policy conclusions are suggested by our model. In terms of cigarettes, the empirical results indicate that, for some states, price elasticity could be much higher than policymakers may believe because of border crossing. In addition to creating a large excess burden due to out-of-state smuggling, tax revenues (from increases in a state's cigarette excise tax) may rise far less than anticipated. Naively instituted state policies, at the very least, will clearly have the effect of exporting taxpayers.

Finally, it should be emphasized that the model developed herein is perfectly general as regards "jurisdiction" and "product." Generally, any cheaply transported product is a candidate for smuggling when taxes (excise or other) or any other factors create significant price differentials between political jurisdictions. In this light, cigarette price differences created by different tax impositions within states are only one example of the motivation to smuggle. The recent and ongoing border-crossing "crisis" between Canada and the northern-most states of the United States, only partially generated by huge cigarette price differentials, is a case in point. Given the availability of appropriate data, the Canada-U.S. smuggling "crisis" or the effects of any cross-border differentials may be analyzed using the general methodology introduced here.

1. In 1991, for example, Singapore invoked the "three-quarter tank rule" whereby cab drivers crossing to Malaysia (with dramatically lower gasoline taxes) were required to have three-quarters of a tank of gas. The measure is a crude attempt to raise the cost of smuggling.

2. Other studies of cigarette and alcohol demands have emphasized the addictive and/or social aspects of consumption. See Saffer and Grossman [1987], Coate and Grossman [1988], Lewitt, Coate, and Grossman [1981], and Chaloupka [1991] for some interesting results.

3. It is important for interpretation that the "representative consumer" concept be kept in mind. For example, a "representative consumer" smokes one-third of the time, etc.

4. See Thursby et al. [1991] for a discussion of this issue.

5. Unfortunately, the representation of state population distributions using more complicated "frequency gradients" leads to discontinuities in border-crossing flows as parameters change, and therefore represents a very difficult estimation problem. These discontinuities can be made unimportant by making the population gradient finer, although this can lead to unsolvably large problems in the absence of enormous computing power. As a practical matter, several state-specific simulations of border-crossing demands suggest that the assumption of uniformity is not destructive in general.

6. The simple linear form of (4) is not required by our theoretical framework and is adopted for ease of estimation only. The inclusion of additional variables and/or a structure similar to Chaloupka [1991] is also possible, although the extreme nonlinearity of the model imposes great burdens in estimation when the number of parameters becomes "excessive." Seber and Wild [1989] offer valuable guidance.

7. Estimation utilizing the percentages of consumers over sixty-five years of age produces results consistent with these reported here.

8. We are indebted to Professor Melissa Waters for providing us with the religion data and suggesting the "Fundamentalist Christian" classification we use. This classification includes several Baptist denominations, Mormons, and numerous smaller churches.

9. Letting [h.sub.t] be the average number of lodging places per capita among jurisdictions in year t, and hit state i's lodging places per capita in year t, our variable is ([h.sub.it]/[h.sub.t]) - 1. This form was adopted so that changes over time in the average sizes of lodging places are controlled for, and so that the mean measure of tourism is equal to zero in any given year. Direct use of the variable [h.sub.it], however, produces highly consistent results.

10. This restriction is unimportant for the results obtained.

11. This formulation clearly requires that prices be "exogenous," a framework consistent with the assumption that cigarettes are competitively supplied at prices approximating long-run average costs. In particular, we require that prices be stochastically independent of the disturbances in the sales equation.

12. Sales data for North Carolina for the period 1960-1968, and sales data for Colorado for the period 1960-1984, are unavailable. However, the data include all other variables necessary for estimation, so that Colorado and North Carolina border-crossing demands can be incorporated every year, and no inconsistency or missing values arise at any time. Rather, all that occurs is deletion of these sales observations dependent variables for these states for these years.

13. This condition is not imposed by the functional form of (5) since border-crossing representative consumers may have less elastic demands than home-state buyers.

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