Constant versus Variable Markups: Implications for the Law of One Price
One sentence summary: The case of constant markups corresponds to log-linear trade regressions, while a special case of variable markups corresponds to lin-log trade regressions; marginal costs of production contribute most to the deviations from the Law of One Price.
The corresponding paper by Hakan Yilmazkuday has been accepted for publication at International Review of Economics and Finance.
Abstract
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.
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.
Non-technical Summary
The workhorse empirical models of international trade based on constant markups (e.g., log linear gravity studies) have been criticized by the international finance literature that they cannot match the data on international price differences, especially when exporters price discriminate across importers. Accordingly, one of the most successful strategies in the international finance literature has been to nest constant elasticity of substitution (CES) models to have variable markups (i.e., markups changing with the quantity sold) such that the so-called "Penn effect", according to which the price level is higher in richer countries, can be explained. Nevertheless, when it comes to measuring the effects of constant versus variable markups on international price dispersion, the existing studies have mostly focused on calibrating complicated models. Therefore, there is a lack of an easy-to-implement estimation strategy in the literature on this subject.
This paper introduces such an estimation strategy considering the trade implications of having constant versus variable markups by using constant relative risk aversion (CRRA) versus constant absolute risk aversion (CARA) consumer utility functions, respectively. The functional form of the importer-country utility function further determines the price elasticity of demand and the elasticity of substitution (across products imported from different countries) through utility maximization. When each source country maximizes its profits using a pricing-to-market strategy, it is shown that CRRA preferences corresponds to CES and thus constant markups, while CARA preferences corresponds to non-CES and thus variable markups.
The key innovation is that, when trade implications are estimated to obtain elasticity measures (and thus implied markups), having cases of constant versus variable markups is reduced to using quantities in logs versus levels on the left hand side of the estimated equations, where the right hand sides are exactly the same; i.e., constant markups correspond to log-linear regressions (as in CES-based gravity studies), while variable markups correspond to lin-log regressions.
Using the NBER-UN data on quantity traded and unit prices covering bilateral trade between 171 countries for 749 good categories, we estimate trade patterns implied by the model (i.e., log-linear and lin-log trade regressions) to obtain estimates of (constant and variable) markups after controlling for source-specific quality measures and distance effects (including time-to-trade). After estimating markups by trade equations, we estimate price equations implied by the model to decompose destination prices into marginal costs of production, markups, and trade costs. While marginal costs of production are further decomposed into source-specific input costs, source-specific quality and destination-specific quality measures, trade costs are further decomposed into freight costs and border costs.
The decomposition of destination prices is further used to calculate the source of deviations from the Law of One Price (LOP) across destination countries for the cases of constant and variable markups at the good-category level. The results under the case of constant (variable) markups imply that, on average across goods, marginal costs of production has the lion's share with a contribution of about 92% (97%) to the mean of deviations from LOP, while trade costs contribute only about 8% (2%). The contribution of markups is almost none on average across goods in both cases, although, in the case of variable markups, they can contribute up to 10% of the deviations from LOP for certain goods.
The results are very similar when the variance of deviations from LOP for the average good is considered: marginal costs of production contribute about 96% (98%) and trade costs contribute about 5% (2%) when constant (variable) markups are considered.
Since marginal costs of production explain the lion's share of the deviations from LOP, their decomposition into source-specific input costs, source-specific quality and destination-specific quality measures is of further interest. The corresponding results support the former set of studies by showing that destination-specific quality measures contribute most to marginal costs of production, followed by source-specific quality measures and source-specific input costs, for both cases of constant and variable markups, and for both the mean and the variance of deviations from LOP.