Question

You are trying to estimate the impact of cigarette taxes on smoking rates by comparing across European countries. You estimate the equation

log(smoke) =β +β log(VAT_cig) +u i01 i

where smokei are the number of smokers per 100,000 population in country i and V AT _cigi is the VAT on cigarettes in that country.

(a) Interpret the parameter β1.

You suspect that taxes on alcohol, VAT_alci, which are positively correlated with cigarette taxes, may be an important confound.

(b) Write the “true” model.

How would you expect the estimated coefficient βˆ1 to change if (c) Cigarettes and alcohol are substitute goods?

(d) Cigarettes and alcohol are complements?

Answer 1

a) if we change VAT_cigi by one percent, we’d expect smokers per thousand population to change by β1 percent.

b) VAT_alci is positively correlated with VAT_cigi. If we include both of them in the model problem of multicollinearity will arise.

So, we can have a model

log(smoke) =β +β log(VAT_alci) +u i01 i

c)  β1 coefficient will increase if alcohol is a substitute good. An increase in VAT on alcohol will cause people to shift on smoking.

β1 coefficient will decrease if alcohol is complementary good. An increase in VAT on alcohol will cause people to reduce smoking as well.