Markups and export-pricing strategies

Abstract

We analyze empirically export-price strategies across export destinations using detailed firm-product data. Most recent studies using disaggregated data to investigate why firms charge different prices for the same product on different markets focus on the cost component of prices and neglect the markup component. In this paper, we concentrate on the markup component and examine how variations in firms’ export prices may reflect price discrimination by comparing the markup of firms with different pricing strategies. We make use of detailed firm-level data for exporting firms in the Swedish food sector consisting of both manufacturing and intermediary trading firms. The paper documents the export-price variations within the two sub-sectors and explores how different price strategies correlate with markups. The results offer new information beyond the fact that exporters tend to have a higher markup. In particular, we find that firms in the food-processing sector with a greater ability to discriminate across markets mark their products up even more. This result points to the importance of underlying firm decisions in order to explain differences in export premiums across firms. In addition, the results reveal that markups are a complex function of firm and destination characteristics, and that the relationship between markups and pricing strategies in the manufacturing sector is not necessarily observed in other sectors of the supply chain.

Appendices

Appendix 1

Table 7 Variables and definitions

Appendix 2

2.1 Estimating firm markups

The benchmark approach to estimate firms’ markups is the framework of De Loecker and Warzynski (2012), which relies on the condition of cost minimization in order to relate elasticity of output, input shares and markups. By using a robust definition of the markup as the ratio between the price and the marginal cost, they show that the markup for firm f at time t may be defined as follows:

$$ \mu_{ft} = \frac{{\theta_{ft}^{X} }}{{\alpha_{ft}^{X} }} $$

(A1)

where $\theta_{ft}^{X} = \frac{{\delta Q_{ft} X_{ft} }}{{\delta X_{ft} Q_{ft} }}$ is the output elasticity of the variable input $X_{ft}$ and $\alpha_{ft}^{X} = \frac{{P_{ft}^{X} X_{ft} }}{{P_{ft} Q_{ft} }}$ is the share of expenditures on input $X_{ft}$ in total sales.¹⁹ While the expenditure shares are directly obtained from the data, output elasticities have to be estimated. Note however that Q _ft has to be adjusted by dividing it with exp(ε), where ε is the error term from the first stage regression, in order to sweep away variation in sales due to factors unrelated to input demand changes. The approach of De Loecker and Warzynski (2012) builds on two steps. The first one is to estimate the output elasticity by estimating the production function in line with the proxy methods of Olley and Pakes (1996) and Levinsohn and Petrin (2003). Once consistent estimates of the output elasticities are obtained, the markup in (A1) can be computed.

We use the translog-value added production function as in De Loecker and Warzynski (2012) with labor as a variable input while the capital stock (based on firms’ balance sheets) is assumed to be a dynamic input. This production function is used in the first stage together with a proxy for the productivity shock captured by inverting the demand for material (raw material and intermediate goods). Hence the proxy for productivity is captured by the expenditure on material, the stock of capital and the export status of the firm (similar variables as in De Loecker and Warzynski). Using this proxy in the production function implies that we may compute the productivity term as the difference between the expected output from the first stage and the sum of all inputs (using the estimated coefficients from the first stage production function as weights). The innovation of the productivity (given the coefficients from the first stage production function) is recovered by regressing productivity on its lag and additional variables influencing the productivity (we use export status and the propensity to exit). The production function parameters are then estimated in a second stage by relying on the moments that the innovation of the productivity is uncorrelated with capital (since it is decided a period before) and the lagged number of workers (since labor reacts on productivity). This finalize the procedure of estimating the parameters of the production function, and hence we may calculate the output elasticity for labor used in order to derive markups at the firm level.

2.2 Robustness—Roeger’s approach

As a robustness check of our results, we employ the commonly used method proposed by Roeger (1995) to estimate markups.²⁰ This method stems from Hall (1988) who showed how the markup can be obtained from the primal Solow residual (calculated from the production function) when there is market power. This residual, however, contains a productivity term that may cause endogeneity problems when the markup is estimated. Roeger demonstrated how this problem can be taken care of by subtracting the dual Solow residual (calculated from the cost functions) from the primal residual and the method only requires nominal data on firm sales and values of input factors. Thus, to obtain markups using Roeger’s approach, the following regression is to be estimated for each sector:

$$ \Updelta Y_{ft} = \mu \Updelta X_{ft} + \varepsilon_{ft} $$

(A2)

where ΔY _ft = Δln(sales) − Δln(capital costs), ΔX _ft = α _Lft L _ft [Δln(wage costs) −Δln(capital costs)] + α _Mft M _ft [Δln(materical costs) −Δln(capital costs)], and α _Lft L _ft = labor costs share in output = (wage costs)/(sales) and α _Mft M _ft = material costs share in output = (material costs) / (sales). Finally, μ is the markup to be estimated.

In order to analyze how the effect of firms’ price variations are related to their markups, we interact the price variable with the input growth composite, ΔX, according to:

$$ \Updelta Y_{ft} = \mu_{ 1} \Updelta X_{ft} + \mu_{ 2} [\Updelta X_{ft} \times \, PriceStrat_{fpt} ] \, + \beta \, PriceStrat_{fpt} + \varepsilon_{ft} $$

(A3)

In (A3), μ ₂ reflects how the average markup changes with the variation in firm f’s export price of product p at time t, with PriceStrat _fpt denoting the firm’s price strategy for product p. Although we do not observe changes in sales and inputs at the product level, there will be several observations for multi-product firms. β denotes the direct effect of the price variable.

The results in Table 8 are similar to those based on the method by De Loecker and Warzynski. In the benchmark estimations, positive and significant markups are found in both sectors. The estimated industry markup, however, is smaller, which echoes the finding in De Loecker and Warzynski. Looking at the interaction terms, the markup varies positively with the price variable only in the food-processing industry while the correlation is negative for wholesale.

Table 8 Relationship between markup and local price strategies using Roeger’s method