Baltagi, Griffin and Xiong (2000) estimate a dynamic demand model for cigarettes based on panel data from 46 American states over 30 years 1963-1992. The estimated equation is
ln Cit = a + в і ln Ci, t-i + 3p ln Pi, t + вз ln Ya + /34 ln Pun + uu (12.69)
where the subscript i denotes the ith state (i = 1,…, 46), and the subscript t denotes the tth year (t = 1,…,30). Cit is real per capita sales of cigarettes by persons of smoking age (14
years and older). This is measured in packs of cigarettes per head. Pit is the average retail price of a pack of cigarettes measured in real terms. Yit is real per capita disposable income. Puit denotes the minimum real price of cigarettes in any neighboring state. This last variable is a proxy for the casual smuggling effect across state borders. It acts as a substitute price attracting consumers from high-tax states like Massachusetts to cross over to New Hampshire where the tax is low. The disturbance term is specified as a two-way error component model:
Uit = Vi + t + Vit i = 1,…, 46 t = 1,…,30 (12.70)
where vi denotes a state-specific effect, and t denotes a year-specific effect. The time-period effects (the t) are assumed fixed parameters to be estimated as coefficients of time dummies for each year in the sample. This can be justified given the numerous policy interventions as well as health warnings and Surgeon General’s reports. For example:
(1) the imposition of warning labels by the Federal Trade Commission effective January 1965;
(2) the application of the Fairness Doctrine Act to cigarette advertising in June 1967, which subsidized antismoking messages from 1968 to 1970;
(3) the Congressional ban on broadcast advertising of cigarettes effective January 1971.
The vi are state-specific effects which can represent any state-specific characteristic including the following:
(1) States with Indian reservations like Montana, New Mexico and Arizona are among the biggest losers in tax revenues from non-Indians purchasing tax-exempt cigarettes from the reservations.
(2) Florida, Texas, Washington and Georgia are among the biggest losers of revenues due to the purchasing of cigarettes from tax-exempt military bases in these states.
(3) Utah, which has a high percentage of Mormon population (a religion which forbids smoking), has a per capita sales of cigarettes in 1988 of 55 packs, a little less than half the national average of 113 packs.
(4) Nevada, which is a highly touristic state, has a per capita sales of cigarettes of 142 packs in 1988, 29 more packs than the national average.
These state-specific effects may be assumed fixed, in which case one includes state dummy variables in equation (12.69). The resulting estimator is the Within estimator reported in Table 12.8. Comparing these estimates with OLS without state or time dummies, one can see that the coefficient of lagged consumption drops from 0.97 to 0.83 and the price elasticity goes up in absolute value from —0.09 to —0.30. The income elasticity switches sign from negative to positive going from —0.03 to 0.10.
The OLS and Within estimators do not take into account the endogeneity of the lagged dependent variable, and therefore 2SLS and Within-2SLS are performed. The instruments used are one lag on price, neighboring price and income. These give lower estimates of lagged consumption and higher own price elasticities in absolute value. The Arellano and Bond (1991) two-step estimator yields an estimate of lagged consumption of 0.70 and a price elasticity of —0.40, both of which are significant. Sargan’s test for over-identification yields an observed value of 32.3. This is asymptotically distributed as and is not significant. This was obtained using the Stata command (xtaboud2,twostep) with the collapse option to reduce the number of moment conditions used for estimation.
Table 12.8 Dynamic Demand for Cigarettes: 1963-92*
* Numbers in parentheses are t-statistics.
Source: Some of the results in this Table are reported in Baltagi, Griffin and Xiong (2000).