the terms and refer to the set of fixed effects by exporter and importer, respectively. Finally, o is the residual term. Sectoral fixed effects are not applied in the model, since the analysis oo oo δδ γγ considers the sum of trade following the different digital services groupings, as outlined in Annex εε Table A2. Both equations show that the model is estimated using data for a single year, which therefore presents a cross-country section. Panel regressions are also performed for robustness check later on. The study takes the year 2015 given that this year is the latest year available for the dependent variable.

Note that the model is estimated with PPML with fixed effects as recommended by Santos Silva and Tenreyro (2006). By doing so, Fally (2015) shows that the estimated fixed effects correspond exactly to the terms required by the structural model. Furthermore, regressions are estimated with robust standard error clustered by country-pair. The dependent variable, D o , denoting digital services trade, is also bilateral and includes all directions of trade. That means that, in accordance with the recent literature, it also includes DD internal trade, which is equal to the domestic production that is both produced and consumed in a given country. The reason for doing so is that otherwise the estimated fixed effects would not relate to the output and expenditure terms set out by the gravity theory of trade. Yet, not all datasets provide this domestic trade. The best available source is the gross trade data from the OECD TiVA data. The advantage of this source is that it contains harmonized trade and production data, so selftrade is simply calculated as production less total world exports. Using the most recent version of the TiVA dataset, the analysis covers services trade and production data for 64 exporters and importers for the year 2015, the latest year available.<sup>21</sup> Finally, both equation (1) and (2) also include the term C ∗intlo . This vector refers to several control variables included in the baseline model and as part of the robustness checks below. Most importantly, this term includes the data model each country follows by itself, regardless of its trading partner. The reason to control for this trait is that it may not be by coincidence that countries choose to apply a particular data model. Indeed, this choice may be driven by the extent to which a country trades digital services with partner countries to begin with. As such, by not including these controls, this relationship would suffer from reversed causality or would be influenced by the fact that precisely a partner country shares the same data model.

These control variables need to be interacted with a dummy indicator that reflects whether a country-pair are dissimilar or not, called “intl”. This aims to cover for trade costs affecting international flows and not domestic flows (i.e. internal trade). The use of this measure also follows the recent gravity literature such as the one developed in Yotov (2012). In particular, Yotov _et al._ (2016) states that the inclusion of this dummy leads to the theoretically consistent identification of the effects of bilateral trade policies as shown in Dai _et al_ . (2014). Also, this interaction term can be 21 See footnote 10 that explains the decision to select TiVA instead of other services trade sources. The choice is mainly driven by both data availability and consistency between the services trade databases. Compared to the ITPD-E database, which is extensive in the coverage of developing countries, the following points matter for this choice. First, the TiVA data separates the various digital services sectors of interest. The ITPD-E dataset instead takes the various sub-sectors of the digital economy together. Second, many developing countries included in the ITPD-E database show few observations after aggregating into sector groupings in line with Annex Table A3. This points out to the fact that the ITPD-E data is not in a “squared” or balanced format, missing many observations in services, which in TiVA are present (even though they may be estimated). Hence, even though the limited number of developing countries in TiVA does not match the total number of countries with an identified data model, this database is still considered a preferred option. Nonetheless, data from the ITPD-E database is used for a robustness check and find largely similar results.

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