coefficients (Table 5). Our data on institutions originally vary with increasing values indicating better institutions, but are rescaled so that increasing values represent worse domestic institutions along with our regulatory variables that have a similar functional scale.<sup>22</sup> Hence, our main motivation for reversing these values is because such a transformed scale would be consistent with our regulatory variable and which could facilitate the ease of interpretation of the results. For instance, if a negative and significant sign is found on the interaction term, it would mean that higher levels of regulations in services are particularly harmful in countries which have weak domestic institutions.

Results in Table 4 show that none of the institutional interaction terms have a significant sign when entered separately. This is quite the opposite however when we look at the other three specifications presented in Table A14, including our second preferred TFP measure from Hsieh and Klenow. They all show that regulatory barriers in institutionally weak countries have an additional negative impact on economic performance. This significant effect is for the overall regulatory index, entry barriers as well as conduct regulations when entered separately. The differential effect using the FDI indicator does not come out significant in any of its individual entries. However, when putting the services linkages together, the only significant effect as part of the interactive effect of institutions using Ackerberg is for FDI restrictions as shown in Table 4. It means that, FDI restrictions are particularly harmful in EU countries with relatively weaker domestic institutions, which would confirm previous work by Beverelli _et al_ . (2015). Yet, as a second very strong result is that also entry barriers are showing to have a significant differential effect for countries with weak institutions in all other three TFP specifications (presented in Table A14) when entering separately as well as together in columns (6), (12) and (18). Throughout all three performance measures, this differential negative impact in institutionally weak countries is quite substantial as the coefficient sizes are large.

Again, we repeat our results by using common input‐output coefficients from the EU‐wide input‐output matrix (see Tables 5 and A15). The interaction effects obtain a lot of explanatory power in the sense that entry regulations come out strongly significant for all TFP specifications, this time also for our preferred Ackerberg measure. However, this significance drops when entered with the entire range of institutional interactions. In Table 5, columns (4) and (6) also show that the FDI restrictions remains a robust indicator for negative performance in countries that exhibit a lower level of domestic institutions. In all other TFP methods presented in Table A15, the differential effect of having weak institutions repeats the outcomes as obtained in Tables 4 and A14. Throughout these results, therefore, entry regulation in combination with the role of institutions have strong predictions for explaining the performance of TFP in downstream industries. Note again that the coefficient sizes are particularly large so that this negative interaction effect is very harmful in countries which institutionally are lagging behind.

Summarizing our results, it turns out that on the whole institutions matter for benefitting from lowering regulatory restrictions in services. Countries that are institutionally weak appear to have significantly lower levels of economic performance in the process of deregulation.

> 22 The original indicators from rule of law, level of corruption and regulatory quality vary from ‐2.5 to + 2.5 with increasing levels signifying stronger institutions. In our case, we first rescale this index with +2.5 so that our measure varies from 0‐5 and then reverse all indicators. Next, we perform a factor component analysis so as to retrieve the main variation among these three variable indicators since they are all highly correlated with each other. The reason for doing so is that the recent literature has used all three indicators as a proxy for the role of institutions. A principle or factor component analysis transforms these variables into one meaningful proxy.

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