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

The central difficulty in estimating the parameters of equation [2] is [S.sub.i] is unobserved; location of purchase is not in the data. My solution to this problem is to parameterize the S function and then incorporate these parameters into equation [2]. Instead of a deterministic indicator function governing the decision to smuggle, the parameterization yields the probability, conditional on the observables, that individual i purchases cigarettes in a border locality. Specifically, I assume the probability an individual smuggles is decreasing in the cost of smuggling and increasing in the marginal gains from smuggling.

I model the smuggling cost of obtaining cigarettes in a lower-price locality as [delta]ln(D) - [phi], where D is the distance to the closest lower-price border state. The other cost parameter is [phi], which indexes the fixed cost individual i would incur by purchasing in the home state regardless of his location with respect to the lower-price border.

Note that I assume all smugglers make the same number of trips, which is akin to assuming smuggling costs are independent of the number of cigarettes purchased. Thus, conditional on the consumer's location, smuggling costs are fixed and vary only with the distance to a lower-price border. The data corroborate this assumption by strongly rejecting any correlation between distance and consumption absent any price difference across localities.

I assume the savings from purchasing in a lower-price jurisdiction is proportional to the difference in log home and log border state prices. Assuming the probability one smuggles can be approximated using a linear probability model, (18) the smuggling equation is

[4] P)[S.sub.i] = 1) = [phi] + [alpha](ln)([P.sub.h]) - ln([P.sub.b])) -[delta]ln([D.sub.i]) [equivalent to] [rho].

Using the law of iterated expectations, equation [2] becomes

[5] [[beta].sub.0] + [[beta].sub.1](ln([P.sub.h])(1 - P([S.sub.i] = 1)) + ln([P.sub.b])P([S.sub.i] = 1)) + [gamma] [X.sub.i] = [[beta].sub.0] + [[beta].sub.1] ln([P.sub.h]) - [[beta].sub.1] (ln([P.sub.h]) - ln([P.sub.b])) [rho] + [gamma] [X.sub.i].

Equation [5] represents a regression of log cigarette consumption on expected price given log distance, difference in log price, and [phi]. If p equals zero such that the consumer purchases at home with certainty, then only the home price matters. Conversely, if [rho] is one and the consumer smuggles with certainty, then only the border price matters.

In previous studies using consumption data, Lewit et al. (1981) and Lewit and Coate (1982) assume full smuggling in a 20-mile band, which implies [rho] = 1 if individuals live within 20 miles of the border and [rho] = 0 if they do not. Similarly, by using an average price within 25 miles for all consumers, Chaloupka (1991) implicitly sets [rho] = 1/2 for those within 25 miles of a border and assumes [rho] = 0 for the rest of the sample. My approach provides a less arbitrary and more reasonable account of casual smuggling than previous models as it allows

the probability of smuggling (i.e., the weights on home and border state prices) to vary over the entire population based on differences in smuggling incentives.

Substituting equation [4] into equation [5] yields the reduced form demand equation used throughout this study: (19)

[6] [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

One concern with the reduced form demand function given by equation [6] is the log distance measure. (20) This is a potential problem because one might expect the impact of distance on demand to go to zero as distance approaches infinity. The log distance term implies as distance becomes arbitrarily large, log demand decreases to negative infinity. While such a critique could be levied against any log-log model, it is important to note using log distance is a simplifying assumption, (21) and equation [6] represents a parametric approximation to the true demand function. To address this problem when calculating the home state price elasticities, I constrain the home state price elasticity to be weakly smaller in absolute value than the full price elasticity. In effect, this restricts cross-state purchases to be zero when the cross-border price differential is low and/or the consumer lives far from the border. (22)

As the model is constructed, the expectation is [delta], [phi], and [alpha] are all positive because the probability of smuggling should be decreasing in distance from a lower-price border, increasing in price difference, and increasing in the fixed cost parameter. It is natural to expect [[beta].sub.1] to be negative, which implies [[PI].sub.1], < 0, [[PI].sub.2] > 0, [[PI].sub.3] > 0, and [[PI].sub.4] < 0.

The expected signs of [[PI].sub.1] through [[PI].sub.4] illustrate the predictions of the model for the responsiveness of consumption to the home state price. Conditional on distance, an increase in the price difference should render consumption less sensitive to the home state price. Conversely, an increase in distance to a lower-price border should make demand more responsive to the home state price as the cost of obtaining a given amount of savings has risen.

ESTIMATION STRATEGY

I estimate demand functions on the intensive margin (Q = number of cigarettes smoked per day by smokers), extensive margin (Q = smoking participation rate), and full margin (Q = number of cigarettes smoked per day, including non-smokers). I employ state--MSA fixed effects in all regressions, so only within--MSA across-time variation in prices, distance, and price differences are used to identify the parameters of the demand function. It is important to use fixed effects in such regressions because individuals may differ across MSAs and across states in their preferences for smoking, conditional on price. For example, people might be less averse to smoking in a tobacco producing state such as Kentucky than in a high anti-smoking sentiment state like Massachusetts. The fact that Massachusetts is a high cigarette tax state and Kentucky is a low cigarette tax state is likely a function of these same preferences. Without fixed effects, demand regressions attribute some of the preference-related smoking differences across states or MSAs to price differences, causing an upwards omitted variables bias in the coefficient on price. (23)

Because I am interested in estimating demand functions, the price changes that occur in the data need to be independent of the unobservables in the quantity demanded equation, conditional on the observable variables included in the model. Keeler, Hu, Barnett, Manning, and Sung (1996) present evidence that such independence may not hold; they find cigarette producers price discriminate by state based on numerous demographic and state legal factors. If prices are a function of the demographic composition of the state and if these demographic factors play a role in preferences for cigarettes, price changes will be endogenous to cigarette demand. It is unlikely I will be able to control for all factors that jointly affect demand and price discrimination. Thus, using state average prices in the demand regressions is likely to lead to biased parameter estimates on the price variables. In order to account for this endogeneity, I instrument all price variables with tax variables. (24) Further, if price differences across MSAs in different states are correlated with distance between the MSAs, there will be measurement error in the price differences as I am using differences in average state prices. Instrumenting the price difference with the tax difference should overcome any biases associated with such measurement error. Note taxes are thus only a valid instrument for prices if state excise taxes are not set in response to the distance between MSAs across states or in response to differing home state price elasticities. (25)

While much of the data are collected at the individual level, the independent variables of interest vary at the state--MSA level. Thus, for each of the 12 tobacco supplements, I collapse the data into MSA--specific means using the non-response weights included in the survey data. This aggregation is justified by interpreting the consumer in the model presented in the fourth section as the representative or "average" consumer in a given MSA. (26) The aggregated data set contains 2,904 observations at the state--MSA level. I also weight all regressions by the number of observations that constitute each MSA mean and estimate heteroskedasticity--robust standard errors.

The demographic variables used in the regressions that follow are the state-MSA mean values of age, sex, weekly wage, marital status, race (with white as the excluded category), education (with no high school diploma as the omitted category), and labor force status (with not in the labor force as the omitted category). Means of all variables by year are presented in Table 5.

As Table 5 illustrates, there is a large decrease in the amount smoked by smokers and a modest decrease in the percentage of smokers over the time span of this analysis. These trends could be due to the price increases that occur over this period, but there are undoubtedly also secular trends stemming from aggregate changes in views and preferences with respect to smoking. Including a linear year trend in the demand models is thus appropriate. I present estimates both including and excluding the year trend for all specifications. (27)