2.2 Panel data models  (Page 9/10)

Finally, if advertising only induces current smokers to increase the number of cigarettes they consume, then the total ban on advertising should cause a one-time reduction in cigarette consumption that will reduce the profits of cigarette companies. However, which of these three mechanisms (if any) is correct is an empirical question.

Six European countries adopted a complete ban on cigarette advertising in the period after 1970. It this project we use annual data on smoking consumption in 22 developed countries for the 27 years between 1964 and 1990 to test the effect of a complete smoking ban on cigarette demand (giving us 594 observations). Moreover, since we have no a priori reason to choose one model specification over another, we check the stability of the estimated impact of an advertising ban on cigarette demand under several alternative model specifications.

We estimate three types of specifications of the model — the linear model, the log-linear model, and the log-log model. In general whether one uses a variable or the logarithm of the variable is the main difference in these three specifications. The linear model does not transform either the dependent or the independent variables. A variation on the linear models allows the use of the square and product of some of the independent variables in order to take care of any non-linearity in the data. The log-linear model takes the same form as the linear model except that the dependent variable is the logarithm of variable under study. Finally, in the log-log model both the dependent and independent variables are, if possible, in logarithm form.

For example, for this problem the dependent variable in any of these specifications is either the per capita consumption of tobacco or the logarithm of the per capita consumption of tobacco. The dependent variables might include (1) the real price of tobacco in each country for each year, (2) a measure of the per capita income level of the country for each year, (3) the unemployment rate of the country for each year, (4) a measure of the age distribution of the population to measure smoking intensity by age, (5) a trend variable to account for the rising awareness of the health costs of smoking, (6) a dummy variable equal to one for years that a country has a complete ban on cigarette advertising, and (7) a set of 21 dummy variables identifying the country. Let T it be the measure of per capita cigarette consumption in country i for year t ; P it , the price of tobacco; I it , the measure of per capita income level; U it , country i ’s unemployment rate in year t ; A it , country i ’s age distribution in year t ; Year , a trend variable; B it , the dummy variable for the ban; and C i , the dummy variable for country i .

Examples of the three models are:

1. Linear: $T_{it}={\beta }_0+{\beta }_1{P}_{it}+{\beta }_2{I}_{it}+\beta U_{it}+{\beta }_4{A}_{it}+{\beta }_{5}Yea{r}_t+{\beta }_6{B}_{it}+{\epsilon }_{it}$
2. Log-Linear: $\ln \left(T_{it}\right)={\beta }_0+{\beta }_1{P}_{it}+{\beta }_2{I}_{it}+\beta U_{it}+{\beta }_4{A}_{it}+{\beta }_{5}Yea{r}_t+{\beta }_6{B}_{it}+{\epsilon }_{it}$
3. Log-Log: $\ln \left(T_{it}\right)={\beta }_0+{\beta }_1\ln \left(P_{it}\right)+{\beta }_2\ln \left(I_{it}\right)+\beta U_{it}+{\beta }_4{A}_{it}+{\beta }_{5}Yea{r}_t+{\beta }_6{B}_{it}+{\epsilon }_{it}$

In models (1) and (2) it is possible to include additional explanatory variables that are the square of some of the currently included explanatory variables. In all three models it is possible to include as explanatory variables the product of the ban dummy and any of the currently included explanatory variables. Finally, in equation (2) we cannot take the logarithm of the unemployment rate because the data we have report zero levels of unemployment.