Moreover, we also use the Hsieh and Klenow (2009, 2014) way of estimating TFP which is relatively new and follows a different structure. More precisely, in their methodology the authors follow a structural approach using a Cobb‐Douglas estimate 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.

We estimate all four approaches and use them in our regression output discussion. In order to do so one needs to estimate sector‐specific production functions. These production functions are sector‐specific because industries differ in production technology. The main idea of estimating these production function is that through this way, unobserved firm productivity shocks can be approximated by a non‐ parametric function of observable firm characteristics. Since we are dealing with multiple countries in our data set, we estimate these production functions for each 2‐digit services and manufacturing sectors by country, although in some cases we regroup some countries due to their insufficient numbers. They are Germany with Austria, the Benelux, Sweden with Denmark, Estonia with Latvia, and finally UK with Ireland. The reason for choosing these groupings is that we think that each pair are fairly like‐minded in their economic structures. Regarding sector division, in total we have 57 different sectors, which is considerably more than in previous studies, because the high number of firm observations in each sector allows us to go ahead with this selection although some industries are also regrouped together. The industry groupings together with an overview of firm observations can be seen in Table A4 in the Annex.<sup>9</sup> Table A5 reports a similar overview by country.

To start estimating production functions we need firm‐level data on value‐added. Normally value‐added at the firm is defined as sales minus the value of inputs, which includes materials, services and energy. In the Amadeus data set, unfortunately only operating net revenue and material costs are reported, which we hence use to compute value‐added. Moreover, materials are not reported either for any firm in Cyprus, Denmark, UK, Greece, Ireland, Lithuania and Malta. Since this forms a substantial number of countries, we proxy material inputs for these countries. The way we choose to do so is based on Basu _et al_ . (2009) in which the authors compute materials as operational revenue minus operational profits and wages taking into account depreciation. Since this is of course a less precise measure of material inputs, we therefore check whether a strong correlation exists between both measures: the direct and proxied approach for all countries that report both types of methods. Table A6 report the regressions as correlations of the indirect measure on materials reported directly for these countries. The result shows that correlations are very strong with a high R2. Once we use this proxied method, the number of firms increases by 11 percent.<sup>10</sup> The production functions themselves are estimated using the standard approach of Cobb‐Douglas in logarithmic form, as shown in the following equation:

> 9 An interesting minor detail is that the frequency share of firm observations between services and goods closely follows their value‐added composition in GDP which in 2014 for goods was 24.3 percent, while for services this figure was 74 percent according to the World Development Indicators.

> 10 Note, however, that Malta only has 39 observations and are not included in the final data set. Furthermore, in Amadeus firms from Greece, Cyprus and Lithuania have neither reported nor proxied materials, and are therefore excluded from any further analysis in this paper.

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