Background: Increasing tobacco taxes to increase price is a proven tobacco control measure. This article investigates how smokers respond to tax and price increases in their choice of discount brand cigarettes versus premium brands.

Objective: To estimate how increase in the tax rate can affect smokers’ choice of discount brands versus premium brands.

Methods: Using data from International Tobacco Control surveys in Canada and the USA, a logit model was constructed to estimate the probability of choosing discount brand cigarettes in response to its price changes relative to premium brands, controlling for individual-specific demographic and socioeconomic characteristics and regional effects. The self-reported price of an individual smoker is used in a random-effects regression model to impute price and to construct the price ratio for discount and premium brands for each smoker, which is used in the logit model.

Findings: An increase in the ratio of price of discount brand cigarettes to the price of premium brands by 0.1 is associated with a decrease in the probability of choosing discount brands by 0.08 in Canada. No significant effect is observed in case of the USA.

Conclusions: The results of the model explain two phenomena: (1) the widened price differential between premium and discount brand cigarettes contributed to the increased share of discount brand cigarettes in Canada in contrast to a relatively steady share in the USA during 2002–2005 and (2) increasing the price ratio of discount brands to premium brands—which occurs with an increase in specific excise tax—may lead to upward shifting from discount to premium brands rather than to downward shifting. These results underscore the significance of studying the effectiveness of tax increases in reducing overall tobacco consumption, particularly for specific excise taxes.