Consider the following log-log model: ln(qi) = 0.57 + 0.76 ln(pi) + ui, where qi

Question

Consider the following log-log model:

ln(qi) = 0.57 + 0.76 ln(pi) + ui,
where qi indicates per-capita sales of cigarettes in district i, while pi denotes the average

price of cigarettes.

(a) Interpret the slope, i.e., the number 0.76.

(b) Suppose that some states implemented a law that restricts smoking in public

places. How would you test the effectiveness of such law?

(c) Suppose the dataset includes the price of alcohol in different districts, pAi . Con- sider the model:

ln(qi)=0 +1ln(pi)+2ln(pAi )+ui.

What is the expected sign of 2? Why? Provide an interpretation. Hint: cross- elasticity. How would you test the hypothesis that an increase in the price of alcohol decreases has a negative effect on the demand for cigarettes? Hint: use confidence intervals.

Explanation / Answer

Consider the following log-log model:

ln(qi) = 0.57 + 0.76 ln(pi) + ui,
where qi indicates per-capita sales of cigarettes in district i, while pi denotes the average

price of cigarettes.

(a) Interpret the slope, i.e., the number 0.76.

A one percent increase in the average price of cigarettes leads to a 0.76% increase in per-capita sales of cigaretts. This result is not intuitive because demand elasticies are usually negative. According to these estimates smoking is a giffen good.

(b) Suppose that some states implemented a law that restricts smoking in public

places. How would you test the effectiveness of such law?

First we should consider a dummy variable Di such that Di=1 if district i implemented the law and Di=0 otherwise. Then we can estimate the following model.

ln (qi) = B0 + B1 ln(pi) + B2Di + ui

To test the effectiveness of such law we can perform a simple t-test for H0 : B2 = 0.

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