Participation in global value chains (GVCs) and markups: firm evidence from six European countries

Abstract

We examine the relationship between firms’ participation in global value chains (GVCs) and price markups. Utilizing data from 14,316 firms across six European nations sourced from AMADEUS data linked to the EFIGE project, we observe significant diversity among countries and industries regarding firm-specific, time-varying markups. After mitigating sample selection bias through coarsened exact matching (CEM), we discover that firms involved in exporting produced-to-order goods and importing service and material inputs have a markup premium 3 and 4% higher than non-trading firms. Our findings remain robust to alternative definitions of GVC participation, different data matching techniques (propensity score matching), and different markup estimates. These results contribute to the limited but increasingly crucial literature on markup disparities, offering valuable insights for crafting industrial policies.

Appendix

1.1 A. Alternative estimations of the production function

The paper uses four approaches to estimate output elasticities and obtain markup estimates. The baseline approach is a Cobb–Douglas value-added production function following Wooldridge (2009), as described in Section 2.3. Alternatively, we estimate a value-added production function using the Ackerberg et al. (2015) method (ACF, henceforth). Third, we estimate a gross-output Cobb–Douglas production function using Wooldridge (2009). Fourth, we estimate a value-added translog production function.

1.1.1 A1. The ACF method

The main argument of the ACF method is that the labor coefficient in Eq. (4) cannot be identified in the Olley and Pakes (1996) and Levinsohn and Petrin (2003) methods. Ackerberg et al. (2015) propose a two-stage method, by which equation in the main text can be written as

$${y}_{it}= {{\beta }_{l}l}_{it}+{{\beta }_{k}k}_{it}+{h}_{t}\left({k}_{it}, {m}_{it}{,z}_{it}\right)+{\varepsilon }_{it}=\varphi ({l}_{it}, {k}_{it}, {m}_{it}{,z}_{it})+{\varepsilon }_{it}$$

(a.1)

Equation (a.1) is estimated via ordinary least squares and is used to separate the expected output ${\widehat{\varphi }}_{it}$ from the residuals. Additionally, assuming the same Markov process for productivity as described by equation (5) and considering that ${\omega }_{it}={h}_{t}\left({k}_{it}, {{l}_{it}, m}_{it}{,z}_{it}\right)$ and ${\varphi }_{t}\left({k}_{it}, {{l}_{it}, m}_{it}{,z}_{it}\right)$, we can project ${\omega }_{it}$ on its lag such to get the second equation to estimate.

$${\widehat{\varphi }}_{it}-{{\beta }_{l}l}_{it}-{{\beta }_{k}k}_{it}={{\rho ({\widehat{\varphi }}_{it-1}-\beta }_{l}l}_{it-1}+{{\beta }_{k}k}_{it-1})+{\xi }_{it}$$

(a.2)

In short, in the ACF method, all the coefficients are estimated in the second stage using valid moment conditions and where ${\widehat{\varphi }}_{it-1}$ is replaced by its estimate from the first stage. Once, the estimated ${\beta }_{l}$ is retrieved,²¹ the markup is then estimated as described in Section 3.2.

Table A.1 ACF vs. Wooldridge markups

Table A.1 compares markups of the ACF and the baseline Wooldridge method. Average and medium markup estimates using the ACF method are relatively larger, as well as more skewed. Comparing the ACF with the Wooldridge markup estimates, the latter are more in line with previous findings. Nevertheless, our main findings are robust to using the ACF markups (see Table A.1).

1.1.2 A2. The gross output production function

As in De Loecker et al. (2020), we assume for robustness the following gross-output production function:

$${q}_{it}={{\beta }_{l}l}_{it}+{{\beta }_{k}k}_{it}{+{{\beta }_{m}m}_{it}+\omega }_{it}+{\varepsilon }_{it}$$

(a.3)

where ${q}_{it}$ is the logarithm of gross output and ${m}_{it}$ is the logarithm of intermediate input in Wooldridge setup; the output elasticity with respect to labor equals to ${\widehat{\theta }}_{it}^{l}=\frac{\partial {q}_{it}}{\partial {l}_{it}}={\widehat{\beta }}_{l}$, which is obtained using the Wooldrige (2009) method. The markup is obtained as ${\widehat{\mu }}_{it}=\frac{{\widehat{\beta }}_{l}}{{S}_{it}^{l}}{\text{exp}}(-{\widehat{\varepsilon }}_{it})$, where ${\widehat{\varepsilon }}_{it}$ is the estimated residual from the first stage regression and ${s}_{it}^{l}$ is the labor expenditure share over gross output, which is observed in the data.

1.1.3 A3. The translog production function

Finally, an estimation of a translog value-added specification is added for robustness since it allows for a firm-specific output elasticity. Equation (2) of the main text is then replaced by

$${y}_{it}={{\beta }_{l}l}_{it}+{{\beta }_{k}k}_{it}+{{\beta }_{ll}l}_{it}^{2}+{{\beta }_{kk}k}_{it}^{2}+{{{\beta }_{lk}{l}_{it}k}_{it}+\omega }_{it}+{\varepsilon }_{it}$$

(a.4)

This equation is estimated using the ACF method,²² as described above. In this setup, the output elasticity with respect to labor equals to ${\widehat{\theta }}_{it}^{l}=\frac{\partial ln{Y}_{it}}{\partial {lnL}_{it}}=\widehat{{\beta }_{l}}+{{\widehat{\beta }}_{lk}k}_{it}+{{2\widehat{\beta }}_{ll}l}_{it}$.

Figure A.1 shows the distribution of markups for different setups. Markups below unit, meaning that prices are below marginal costs, make economic sense in the short term. The baseline markups, which are derived from a value-added Cobb–Douglas production function using the Wooldridge (2009) method, have a relatively narrow distribution, with most markups falling within a possible range of values (WRDG_CDVA). In the Cobb–Douglas gross output specification (WRDG_CDGO), the range of markup values is wider, and markups below one are more common, as are very high markups.²³ Markup estimates from a value-added Cobb–Douglas production function using the ACF method (ACF_CDVA and ACF_TRVA) sow larger markups than in the other setups. Despite these differences, our main findings are robust to using markups from different setups.

Fig. A.1

Density graphs of markups. WRDG_CDVA stands for markups estimated from a value-added Cobb–Douglas production function using the Wooldridge (2009) method. ACF_CDVA stands for markups estimated from a value-added Cobb–Douglas production function using the Ackerberg et al. (2015) method. WRDG_CDGO stands for markups estimated from a gross-output Cobb–Douglas production function using the Wooldridge (2009) method. ACF_TRVA is for markups estimated from a value-added translog production function using the Ackerberg et al. (2015) method.

Table A.2 Summary statistics of variables for the production function