Constant versus variable markups: Implications for the law of one price

•Constant markups correspond to log-linear trade regressions.•A special case of variable markups corresponds to lin-log trade regressions.•Marginal costs contribute most to the deviations from the Law of One Price.

This paper compares the implications of having constant versus variable markups on the Law of One Price (LOP) by decomposing the good-category level prices into marginal costs of production, markups, and trade costs. Using a trade model, it is shown that the case of constant markups corresponds to log-linear trade regressions, while the case of variable markups corresponds to lin-log trade regressions. Empirical results show that marginal costs of production contribute most to the deviations from LOP for both cases of constant and variable markups; the decomposition of marginal costs further shows that destination-specific quality measures play the biggest role.