The production functions finally contain 18 countries times 52 sectors, which provides us with a total of 936 cells.<sup>13</sup> Note that the production functions were estimated twice: first using the approach of proxy materials and then, second, with reported materials and value‐added. They are also estimated only with firms that consistently report values for at least four years so as to remain as much as possible in line with previous works. As a result, we have tried to the feasible extent possible to come up with a balanced panel data set for our TFP estimates. In all, based on the three unbiased sets of estimates plus the TFPQ measure, we obtain eight firm‐level country‐specific time‐varying logarithmic TFP specifications as residuals from equation (1). Table A7 in the annex provides summary statistics for the variables used in equation (1) production function while Table A8 and A9 show summary statistics for our TFP estimates.

# **2.3 Input‐Output Tables**

Country specific input‐output tables are also taken from Eurostat and are constant price matrices with 2010 as reference point which is the earliest year for which these tables are available.<sup>14</sup> Several types of input‐output tables are provided on their website, but we choose the one with the best sector‐country coverage, namely the “Use Tables at Purchasers’ Prices”. One big disadvantage with these matrices is that the Retail sector is not well recorded for many countries which do not report any inputs in this sector. This may be due to reasons related to misreporting or perhaps due to an unclear sector definition of retail activities as the entire distribution sector to which retail belongs is also made up of two other sub‐sectors, namely Wholesale trade and Trade and repair of motor vehicles. There are several solutions with this problem. One is that we use the whole distribution sector as representative (excluding Trade and repair of motor vehicles) from where each industry and services sector sources its inputs regarding retail services; or that we chose wholesale services only. Both approaches are imperfect and have their weaknesses, but we have checked both strategies and prefer the ones that includes both Wholesale trade and Retail trade.

Another issue that we are faced with is that some services policy indicators are more disaggregated than that the input‐output tables allow us to compute any input coefficients. In order to tease out any sub‐ sector coefficients from these tables, we use Eurostat’s production data which serve us with an indirect way of carving out any sub‐sectors within an aggregate service sector. Admittedly, this method is not a prefect substitute, but allows us nonetheless to be as consistent and detailed as possible.

Furthermore, as part of our robustness check we also use EU‐wide input‐output coefficients in which all 28 member economies are taken up, including a good coverage of the retail sector, in addition to input‐ output coefficients from one exogenous country only which is the US. The main reason for using these two non‐country specific input‐output tables for computing input sourcing coefficients stems from the fact that there seems to be debate in the economic literature about whether one should use the assumption of equal industry technologies across countries or not. Equal technology coefficients seem reasonable if one thinks that the country selection in the sample are reasonably similar in their economic structures and technology endowments. Practically, this might as well form a convenient assumption if a suspicion exists that input‐output tables at the country level are not very well measured for some

> 13 An overview of this matrix with the number of firms in each of these cells is available upon request.

> 14 Note that for Bulgaria we used 2011 as a reference year for reasons related to data availability.

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