����� ��� ∙����� ��� ∙����� ���� ���� (1) In equation (1), ��� stands for output of a firm _i_ in year _t_ and represents variable of value‐added as explained above with the caveats described; ��� denotes the capital stock of a firm and is calculated as the two period average of real fixed tangible capital for all four approaches while ��� designates the labor input of a firm, which is proxied by the number of employees as it is the only reliable proxy variable in Amadeus because other variables such wages are not available.<sup>11</sup> Furthermore, ��� is the unobserved total factor productivity and ��� is the random iid shock. As explained in the introduction of this section, we do not use OLS to estimate equation (1) as this estimation strategy suffers from simultaneity bias in its inputs. Instead, we use the various approaches of TFP from Ackerberg _et al_ . (2006; 2015), Olley and Pakes (1996) and Levinsohn and Petrin (2003). For the Ackerberg and Levinsohn and Petrin specifications, we use material inputs as a proxy for unobserved time‐varying productivity shocks. For the Olley and Pakes approach one needs investment instead, which is computed as the difference between capital stock of two subsequent years corrected for depreciation, i.e. ����� .

As previously stated, we also use a fourth TFP measure that has newly been developed in the economic literature which is put forward by Hsieh and Klenow (2009, 2014). For their TFP calculations, the authors follow a structural approach also using a Cobb‐Douglas estimate, but with commonly used labor shares so as to explicitly take into account policy distortions that would otherwise affect traditional TFP measures in their revenue as opposed to physical TFP. Hence, their TFPQ is estimated which is put in relative terms compared to each 2‐digit NACE classification sector code. As said, for this approach one needs to have common labor shares from one country which is most likely to serve as a reference point. We use Germany as it represents the EU’s most important economy across all its members. Labor market shares are defined as the wages and salaries for each 2‐digit NACE sector divided by each of their sectoral value‐added. Furthermore, we also take the EU as an average benchmark against which the TFPQ measure is made firm‐specific for each 2‐digit code. Although one could criticize this approach since we include multiple countries, the results obtained from employing the EU‐wide benchmark are much more meaningful. Besides, this approach is also justified on the grounds that actually the EU as a whole is by now a fairly integrated market.<sup>12</sup> Of note, all the appropriate proxy variables are first deflated and then put in Euros using constant exchange rate. Price data come from Eurostat’s National Accounts database and are mostly available at 2‐digit NACE industries. In case these data was missing we used either higher level of aggregation, or otherwise simple GDP deflators were used. For value‐added we used the value‐added in gross price index (i.e. implicit deflator) in constant prices with 2010 as reference year for all countries. For materials we used the deflator for intermediate consumption and finally for capital stock we used the consumption of fixed capital price index.

11 Note that subscripts for country and industry are supressed for now as they are estimated for each of them. Moreover, Amadeus does in fact report the firm’s total wage bill but has worse coverage than the number of employees as we use in this paper. In Amadeus there is no variable available that distinguishes employees by skill category.

12 Moreover, upon request we are also able to show that in fact normalization at country‐sector‐level as could be done with the relative TFPQ measure cannot capture the average effect from a regression if explanatory variables are also country‐sector‐year specific under the assumption of log‐normality and constant effect for all firms.

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