results offer benchmark gravity estimates for sectoral cross-border services trade, alongside a detailed set of border effects.<sup>2</sup> Gravity works well with sectoral services data: most estimates are significant with expected signs and reasonable magnitudes. We document important differences in estimated coefficients of standard gravity variables between goods and services and across services sectors, respectively. For example, we obtain highly non-linear effects of distance on services trade with strong negative effects for short distances and insignificant effects for long distances. In addition, our estimates reveal that contiguity and colonial ties— traditionally strong predictors for goods trade—have more nuanced effects, with the effect of contiguity depending strongly on the particular sector and colonial ties being generally insignificant. In contrast, language effects are much stronger for services trade than for goods trade. We also demonstrate empirically that accounting properly for internal trade costs is important for proper estimation of international trade costs. These results are presented in Section 4.2.

A key output of this analysis is a multi-dimensional set of relative border barrier estimates by sector, country and year for cross-border services trade. Border barriers in services trade are large, significant, and vary widely. (i) Across countries, our estimates reveal that economic size reduces border barriers in services trade. (ii) Across sectors, border barriers vary in an intuitive way. (iii) Over time, border barriers in services trade have fallen, even though the decrease varies considerably across sectors and across countries. Border barriers have fallen in all sectors but more so in sectors with lower initial borders. Thus, border barrier estimate the determinants of services trade compared to those of goods trade (Kimura and Lee, 2006; Lejour and de Paiva Verheijden, 2004; Tharakan _et al._ , 2005), to estimate the time trend in distance effects (Head _et al._ , 2008) or the effect of Internet penetration in partner countries on US services imports (Freund and Weinhold, 2004). Miroudot _et al._ (2012) provide evidence linking lower international trade costs with higher productivity in services sectors.

> 2Following the General Agreement on Trade in Services (GATS), it has become customary to take a broad view of trade in services to include not just cross-border trade but also international transactions through foreign investment or the movement of people. This paper, however, focuses only on trade costs associated with cross-border services trade and travel (i.e. people travelling abroad as consumers of services) because these are the only international transactions covered in trade statistics available for a significant number of countries. The focus on cross-border services trade, driven by data availability, also implies that we are abstracting from any potential correlation of cross-border trade with the ease of trading a particular service via other modes, in particular via establishing commercial presence abroad. On the interdependence of modes see eg. Christen and Francois (2010). Our estimates of trade barriers should be interpreted accordingly.

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