metadata: authors: 0: author: Anderson,James E.
1: author: Borchert,Ingo
2: author: Mattoo,Aaditya
3: author: Yotov,Yoto Valentinov
count: World
docna: 0: docna: Dark costs, missing data : shedding some
            light on services trade
docty: Policy Research Working Paper
subtopic: International Trade and Trade Rules,Trade and Services,Transport Services,Insurance & Risk Mitigation,Construction Industry,Common Carriers Industry,Food & Beverage Industry,Pulp & Paper Industry,Textiles, Apparel & Leather Industry,Business Cycles and Stabilization Policies,General Manufacturing,Plastics & Rubber Industry
teratopic: Macroeconomics and Economic Growth,Industry,Finance and Financial Sector Development,International Economics and Trade,Transport
abstracts: cdata!: A structural gravity model is used to
            estimate barriers to services trade across many sectors,
            countries, and time. Since the disaggregated output data
            needed to infer border barriers flexibly are often missing
            for services, this paper derives a novel methodology for
            projecting output data. The empirical implementation sheds
            light on the role of institutions, geography, size, and
            digital infrastructure as determinants of border barriers.
            The paper finds that border barriers have generally fallen
            over time, but there are differences across sectors and
            countries. Notably, border effects for the smallest
            economies have remained stable, giving rise to a divergent
            pattern across countries.
repnme: repnme: Dark costs, missing data : shedding some
            light on services trade
display_title: Dark costs, missing data : shedding
            some light on services trade
listing_relative_url: /research/2015/10/25226393/dark-costs-missing-data-shedding-some-light-services-trade
topicv3: Manufacturing Sectors m1326521 1281,Transport m1326661 135,Trade m1326924 698,Trade in Services m1326928 780,Insurance Services m1505057 3836
publishtoextweb_dt: 2015-10-29T00:00:00Z
historic_topic: Macroeconomics and Economic Growth,Industry,Finance and Financial Sector Development,International Economics and Trade,Transport
no_of_pages: 65
author_keys: 0: author_key: 797593
1: author_key: 1002939
2: author_key: 429183
3: author_key: 1187776
model_extractions: WPS7465 Policy Research Working Paper 7465 Dark Costs, Missing Data Shedding Some Light on Services Trade _James E. Anderson Ingo Borchert Aaditya Mattoo Yoto V. Yotov_ Development Research Group Trade and International Integration Team October 2015
Policy Research Working Paper 7465

# **Abstract**

A structural gravity model is used to estimate barriers to services trade across many sectors, countries, and time. Since the disaggregated output data needed to infer border barriers flexibly are often missing for services, this paper derives a novel methodology for projecting output data. The empirical implementation sheds light on the role of institutions, geography, size, and digital infrastructure as determinants of border barriers. The paper finds that border barriers have generally fallen over time, but there are differences across sectors and countries. Notably, border effects for the smallest economies have remained stable, giving rise to a divergent pattern across countries.

This paper is a product of the Trade and International Integration Team, Development Research Group. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The authors may be contacted at james.anderson@bc.edu, I.Borchert@sussex.ac.uk, amattoo@worldbank.org, and yotov@drexel.edu.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# **Dark Costs, Missing Data: Shedding Some Light on Services Trade**<sup>_∗_</sup>

James E. Anderson<sup>_†_</sup> Ingo Borchert<sup>_‡_</sup> Aaditya Mattoo<sup>_§_</sup> Boston College and NBER University of Sussex World Bank Yoto V. Yotov<sup>_¶_</sup> Drexel University

## **JEL Classification Codes:** F13, F14, F16

**Keywords:** Gravity, Services Trade, Trade Costs in Services, Home Bias, Border Effects.

> _∗_ We would like to thank seminar participants at LSE’s CEP International Economics seminar, University of Sussex, Scottish Institute for Research in Economics (SIRE) at Edinburgh, and the 3rd IMF/WB/WTO Joint Trade Workshop at Washington DC. All remaining errors are our own. Research for this paper has been supported in part by the governments of Norway, Sweden, and the United Kingdom through the Multidonor Trust Fund for Trade and Development, and by the UK Department for International Development (DFID). The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent, or any of the aforementioned individuals or institutions.

> _†_ Department of Economics, Boston College, Chestnut Hill, MA 02467, USA. Phone: 617-552-3691. E- mail: james.anderson@bc.edu

> _‡_ Department of Economics, School of Business, Management and Economics, University of Sussex, Brighton, BN1 9SL, United Kingdom, Phone: +44-1273-678731, E-mail: I.Borchert@sussex.ac.uk

> _§_ Development Economics Research Group (DECTI), World Bank Group, 1818 H Street, N.W., Washington, DC 20433, USA. E-mail: amattoo@worldbank.org

> _¶_ School of Economics, LeBow College of Business, Drexel University, Economic Research Institute, Bulgarian Academy of Sciences, CESifo Research Network, Gerri C. LeBow Hall 1020, Market Street, Philadelphia, PA 19104, USA. Email: yotov@drexel.edu
# **1 Introduction**

Given the economic importance of services trade, surprisingly little is known about trade costs in services. Transparent border measures like tariffs are less important in services than relatively opaque regulations that affect trade, for example, in professional and financial services. In addition, transport costs do not take the form of well-defined freight rates but hard-to-measure forms such as the costs of electronically delivering business services. The absence of explicit measures of either protection or transport costs suggests that an analytical model of trade flows can help reveal information about barriers to services trade.

We use the structural gravity model and a newly constructed data set on production and trade in services to provide much new information about inferred services trade barriers. The paper makes three principal contributions. First, we estimate a rich pattern of border barriers at an unprecedented level of detail, varying by country, sector and over time. Such elaborate estimates of border barriers are predicated on the availability of services output data at a correspondingly disaggregated level. Second, since such services output data are not typically available outside the developed country realm, we develop a projection method that can, in principle, generate the required information, thereby facilitating the estimation of trade costs in services when key underlying data are missing or suspect. Third, the structural gravity theory employed for this procedure also helps us decompose border barriers. The empirical results are of interest in their own right as they shed light on the role of domestic institutions, geography, size, and digital infrastructure as determinants of border barriers and international trade of services.

We start by estimating a gravity model, described in Section 2, for 12 service sectors and 28 countries. For that purpose, we construct of a database combining information on services trade and production, respectively, covering the period 2000 to 2007. The broad sectoral and geographical coverage as well as the inclusion of intra-national trade flows sets this data set apart from previous gravity estimations.<sup>1</sup> The data are described in Section 3. The

> 1The gravity model has previously been used to explain the pattern of services trade. For instance, to

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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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heterogeneity across sectors has actually increased. Across countries, larger economies in our sample have enjoyed a fall in border barriers whereas smaller and less developed economies have suffered an increase in services borders barriers. Thus globalization effects (in this sense) are convergent within a set of larger economies and divergent between the smallest countries and the rest. These findings, as well as patterns of convergence and divergence in individual sectors, are described in Section 4.3. To the best of our knowledge, these phenomena have not been documented in the literature before.

Widespread data deficiencies in services prevent comparable estimation of border barriers— and potentially other trade cost measures—for a wider set of countries. Hence, our second principal contribution is to derive and implement a novel procedure to recover missing output data based on the strong performance of structural gravity in combination with recently uncovered properties of the PPML estimator. The theory underpinning this method is introduced in Section 5.1.

A key step in this procedure is the analysis of determinants of border barriers, estimated earlier as gravity model fixed effects. Structural gravity theory suggests that border barriers consist of three principal components: country-specific internal trade costs, country-specific border barriers, and an average (across countries) border effect. Empirically, we project border barriers onto observable country characteristics by employing suitable proxies for each of the three constituent elements. The econometric results of that regression, which we call ‘border estimation,’ are a successful first attempt at separating cross-national variation in internal trade costs from variation in pure border-crossing costs. The coefficient estimates appear to be intuitive with expected signs, reasonable magnitudes, and a solid model fit. For instance, we find that internal distance lowers inferred border barriers as it raises internal trade costs. Conversely, business-friendly domestic regulations that lower internal trade costs result in higher inferred border barriers. We also find evidence for the positive effect on pure border-crossing costs of advanced digital infrastructure, which facilitates services trade and thus is associated with lower border barriers.

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These results offer new insights on factors determining the size of border effects, some of which are potentially amenable to policy reform and, therefore, unveil channels that may translate unilateral policy intervention at the national level into changes in the volume of international services trade. In terms of the projection method, however, we exploit in particular the good model fit ( _R_<sup>2</sup> = 0 _._ 86) for satisfactory out-of-sample predictions of border estimates. Indeed, the ability to consistently predict border effects is a necessary and sufficient condition for successfully recovering potentially missing output data. This analysis is presented in Section 5.2.

The availability of disaggregated output information in our data set enables us to conduct various benchmarking exercises to evaluate the novel procedure’s accuracy. We conclude that the projection method works well, and we are able to characterize in detail the accuracy of predictions across countries and sectors (Section 5.4). The procedure’s good performance in a situation in which no production data are available at all is particularly appealing since this is going to be the norm if trade costs were to be estimated for economies beyond the developed country realm. While the current analysis focuses on services trade, our methods can be applied similarly to goods trade with potentially large payoffs. We leave such extensions for future work.

# **2 Structural Gravity Model**

We start with a brief review of the structural gravity model. Assuming product differentiation by place of origin Armington (1969) and globally common CES preferences, Anderson (1979) develops a gravity theory of trade. Anderson and van Wincoop (2003, 2004) refine the gravity model to derive the following sectoral gravity system that applies to trade in any 4
goods or services sector:<sup>3</sup> Let _Xij_<sup>_k_denotethevalueofshipmentsatdestinationpricesfromorigin</sup><sup>_i_todestination</sup><sup>_j_in</sup> services class _k_ . _Ej_<sup>_k_istheexpenditureonservices</sup><sup>_k_atdestination</sup><sup>_j_fromallorigins.</sup><sup>_Y_</sup> _i_<sup>_k_</sup> denotes the sales of services _k_ at destination prices from _i_ to all destinations, while _Y_<sup>_k_</sup> is the total output of services _k_ at delivered prices. _t_<sup>_k_</sup> _ij_<sup>_≥_1 denotes the variable trade cost factor on</sup> shipments of _k_ from _i_ to _j_ . _σk_ is the trade elasticity of substitution across origin countries _i_ in services class _k_ . Π<sup>_k_</sup> _i_<sup>and</sup><sup>_P k_</sup> _j_<sup>are theoretical constructs that capture general equilibrium trade</sup> cost effects. Anderson and van Wincoop (2003) refer to these terms as outward multilateral resistance (OMR) and inward multilateral resistance (IMR), respectively. Anderson and Yotov (2010a) refine the interpretation of the multilateral resistances as sellers’ and buyers’ incidence of all trade costs. The outward multilateral resistance Π<sup>_k_</sup> _i_<sup>consistentlyaggregates</sup> the incidence of trade costs on the producers of services _k_ in origin _i_ as if they shipped to a unified world market. The inward multilateral resistance _Pj_<sup>_k_consistentlyaggregatesthe</sup> incidence of trade costs on the consumers of services _k_ in destination _j_ as if they consumed from a world market.

The structural gravity system (1)-(3) translates into a simple econometric specification. Following now standard practice, we assume that bilateral trade data follow a Poisson distribution (see Santos Silva and Tenreyro, 2006, 2011) with its conditional mean taking the

> 3The demand-side gravity theory that we present here has alternative theoretical foundations on the supply side, e.g. Eaton and Kortum (2002). Anderson (2011) and Costinot and Rodriguez-Clare (2014) review the literature on the theoretical foundations and extensions of gravity.

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exponential form: where _Z_<sup>_k_</sup> is a vector of trade cost and activity/size variables, and _β_<sup>_k_</sup> is the vector of corresponding trade elasticities with respect to the various components of _Z_<sup>_k_</sup> . Specification (4) leads directly to an estimable equation of the form Here, _χ_<sup>_k_</sup> denotes a constant term; _x_<sup>_k_</sup> _i_<sup>isanexporterfixedeffectforcountry</sup><sup>_i_,</sup><sup>_mk_</sup> _j_<sup>isan</sup> importer fixed effect for destination _j_ , and _τij_<sup>_k≤_1isatradecostfactorrepresentingthe</sup> effect of gravity forces that reduce bilateral trade between _i_ and _j_ in sector _k_ , _Xij_<sup>_k_.</sup><sup>_εk_</sup> _ij_<sup>isan</sup> error term explained below. An important issue is whether sufficient data are available to distinguish between internal and external trade, i.e. within and between countries. When such data are available, which is the case in this study, it is possible to include and identify _τii_<sup>_k_, the intra-country trade cost for each sector</sup><sup>_k_.Its relationship to</sup><sup>_τ k_</sup> _ij_<sup>_,i_=</sup><sup>_j_is a component</sup> reflecting the relative cost of crossing a border. An important contribution of our work is that we construct a multi-dimensional (country-sector-year) database of such relative border cost estimates and we study their determinants.

The final step in obtaining an econometric gravity specification is to model the unobservable bilateral trade frictions _τij_<sup>_k_fromequation(5).Followingthevastgravityliterature</sup> for goods trade, the volume effect of bilateral trade costs _τij_<sup>_k≡tk_</sup> _ij_ 1 _−σ_ for services are approximated by a set of observables: Here, ln _DISTij,m_ is the logarithm of bilateral distance between trading partners _i_ and _j_ .

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Following Eaton and Kortum (2002), we decompose the distance effects into 2 intervals based on the median distance in our sample (about 2,551 km) in order to allow for nonlinear effects of distance on services trade. _CNTGij_ captures the presence of a contiguous border between partners _i_ and _j_ . _LANGij_ and _CLNYij_ account for common language and colonial ties, respectively. Finally, _SMCTRYij_ is an indicator variable equal to 1 for _i_ = _j_ and zero otherwise. _SMCTRYij_ has the advantage of being an exogenous variable that picks up all the relevant forces that discriminate between internal and international trade. We will define the _SMCTRY_ variable in two alternative ways. First, we will restrict _SMCTRY_ to a common effect across countries and years for each sector, in which case _β_ 6<sup>_k_isidentified</sup> off variation over time and across countries. Second, we use a very flexible specification in which we allow for country-year-sector specific _SMCTRY_ effects _βit,_<sup>_k_</sup> 6<sup>.Theadvantageof</sup> this approach is that it delivers a rich database of border estimates that will enable us to study their determinants.

In order to obtain econometrically sound gravity estimates for each service category in our sample, we adopt the latest developments in the empirical gravity literature. In particular, first, we account for the unobservable multilateral resistance terms with directional (source and destination), country-specific, time-varying dummy variables.<sup>4</sup> These country fixed effects also control for output and expenditures, as is apparent from equations (9) and (10). Second, our choice of estimation technique is the Poisson pseudo-maximum-likelihood (PPML) estimator which, as shown in Santos Silva and Tenreyro (2006, 2011), successfully addresses the prominent issues of heteroskedasticity and zeroes in bilateral trade flows. Importantly, the PPML estimator is perfectly consistent with the structural gravity model of Anderson and van Wincoop (2003), which serves as a theoretical foundation for our analysis. Finally, in order to address the critique from Cheng and Wall (2005) that the dependent variable in gravity estimations with fixed effects cannot fully adjust in a single year’s time,

> 4Anderson and van Wincoop (2003) use custom programming to account for the multilateral resistances in a static setting. Feenstra (2004) advocates the directional, country-specific fixed effects approach in a cross-section setting. Olivero and Yotov (2012) demonstrate that the MR terms should be accounted for with exporter-time and importer-time fixed effects in a dynamic gravity setting.

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we use panel data with 2-year intervals to obtain our most preferred gravity estimates.<sup>5</sup>

# **3 Data Description**

For our analyses, we construct a novel integrated data set of services trade and production data at the sectoral level for 28 countries and 12 services sectors over the period 2000-2007.<sup>6</sup> The limiting factor in our data is the availability of sectoral services production statistics. Table 1 lists the range of services sectors covered and the complete data set is available upon request. We briefly discuss each data component; more detailed information is contained in Appendix A.

The primary source of data on cross-border services trade flows are the “OECD Statistics on International Trade in Services: Volume II - Detailed Tables by Partner Country” (Complete Edition as obtained from OECD.Stat, henceforth “TiSP”). The database provides information on international trade in services by partner country for 32 reporting OECD countries plus the Russian Federation and Hong Kong SAR, China, which is in the top twenty service exporters in the world. In addition to the partner dimension, TiSP trade data are also broken down by type of service according to the Extended Balance of Payments Services (EBOPS) classification, i.e. standard components according to the fifth edition of the IMF’s Balance of Payments Manual. The level of sectoral detail reported varies across countries.

We focus on export flows as a more reliable measure of trade flows due to stronger reporting incentives for the exporting firms. Using TiSP’s import entries as mirror export

> 5This is consistent with the three-year intervals used in Trefler (2004), who also criticizes trade estimations pooled over consecutive years. Cheng and Wall (2005) and Baier and Bergstrand (2007) use 5-year intervals, while Eichengreen and Irwin (1996) use 5- and 10-year intervals in gravity estimations. Finally, Olivero and Yotov (2012) experiment with various intervals to check the robustness of their dynamic gravity results. They find that the yearly estimates indeed produce suspicious gravity parameters. We chose 2-year intervals due to the short time-coverage of our data.

> 6The 28 countries with trade and production data are: Australia, Austria, Belgium, Canada, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Ireland, Italy, Japan, Latvia, Lithuania, Luxembourg, Netherlands, Poland, Portugal, Slovakia, Slovenia, Spain, the Republic of Korea, Sweden, United Kingdom, United States. Trade information is available for another eight countries.

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flows allows us to recover additional export flows, thereby increasing the number of nonzero observations substantially.<sup>7</sup> We also use mirroring to recover services trade flows of two additional countries (Latvia and Lithuania) for which disaggregated output information exists in EUKLEMS but which do not report cross-border trade flows as part of OECD’s TiSP data set. Additional checks ensure that trade flows are consistent across different levels of the Even though the majority of OECD countries already accounts for a large share of global cross-border service trade<sup>8</sup> , we attempt to maximize coverage of global trade flows by augmenting the OECD TiSP data with information from the “United Nations International Trade in Services Database” as published by the United Nations Department of Economic and Social Affairs, Statistics Division. Since OECD’s TiSP constitutes our preferred data source, UN data serve to augment the data set only in instance when the corresponding OECD observation is missing.<sup>9</sup> An additional 120,000 observations can be gained by updating OECD data with UN data, which underscore the usefulness of drawing on both data sets.

Annual production data for services sectors are obtained from the “EU KLEMS Growth and Productivity Accounts: November 2009 Release” as updated in March 2011. The EU KLEMS Database provides for one of the most detailed sectoral breakdowns available. Coverage comprises mostly of OECD members which corresponds closely to the source for crossborder services trade. The raw data consist of “gross output at current basic prices” in millions of local currency units. We use data covering 2000-2007 as EU KLEMS series currently extend only up to 2007. As noted above, availability of services production data predetermines the dimensions of our sample to 28 countries, 12 sectors, and 8 years over the period 2000-2007, even though the gravity model estimations in section 4 use trade data for

> 7For within-OECD trade, the original export flow is always retained even if a matching mirror flow would be found to exist.

> 8In 2007, the 28 OECD members accounted for 74 percent of world exports and 69 percent of world imports.

> 9This implies that mirror OECD flows take precedence over original UN exports even if an exact match exists, and no mirroring is performed on UN data.

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an additional eight countries.<sup>10</sup> Production data is reported according to the NACE Rev.1 classification. In order to estimate the gravity model, NACE output data need to be concorded to the trade classification for services, which was done on the basis of the “Correspondence between ISIC Categories for Foreign Affiliates (ICFA) and Extended Balance of Payments Services Classification (EBOPS)” as published in Annex IV of the UN’s Manual on Statistics of International Trade in Services, with some modifications. Table 1 displays the 12 sectors that could successfully be concorded. Internal trade and expenditure are calculated from production data in the usual way, ie. a country’s internal trade for any given sector is obtained by subtracting sectoral exports from gross output. A country’s sectoral expenditure data is backed out as the sum of imports from all origin countries including itself or, equivalently, gross output less exports plus imports from abroad.

Standard gravity variables such as distance, common language, contiguity and colonial ties are taken from CEPII’s _Distances_ Database (see Mayer and Zignago, 2006; Head and Mayer, 2000). An important advantage of that source is its provision of population-weighted distances, which can be used to calculate consistently both bilateral distances as well as internal distances. We use the former in the gravity estimations of international services trade and the latter in our study of the determinants of borders.

# **4 Gravity Estimation and Border Effects**

This section offers partial equilibrium estimates and a discussion of the effects of standard trade cost variables (e.g. distance, common language, contiguity, etc.) on services trade for each of the sectors in our sample. An important contribution of our work is the treatment and analysis of international borders in services trade. Initially, we estimate the effects of international borders on services trade with an indicator variable that takes a value of

> 10These countries are Chile, Hong Kong SAR, China, Israel, Mexico, Norway, New Zealand, the Russian Federation and Turkey.

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one for trade flows within the same country (“ _SMCTRY_ ”) and zero otherwise, to capture the difference between internal and international trade. This approach is not new to the literature.<sup>11</sup> However, we make several contributions and extensions to this literature.

Unlike existing studies that focus on specific countries and obtain single border estimates at a given point of time, our estimates are multi-dimensional. First of all, we obtain countryspecific border estimates for all countries in our sample. This is an important departure from the existing trade literature that treats countries as point masses, an assumption that our estimates reveal is clearly rejected by the data. Second, we obtain time-varying border effects which enables us to study patterns over time. Our estimates reveal that, by and large, border barriers in services trade have fallen over time. Thus, we contribute to the literature by demonstrating that the effects of globalization are actually present and strong in gravity estimations of services trade. Combining country and time variation enables us to draw inferences about the differential effects of globalization. Third, we obtain border effects at the sectoral level. Our estimates reveal wide but intuitive variation across the service categories in our sample with potentially important policy implications. Finally, we are the first to analyze the determinants of international trade border effects. Our analysis focuses on services trade but our methods could be applied similarly to goods trade with potential for large payoffs. We leave such extensions for future work.

In order to emphasize the advantages of our methods, first we obtain and report results from a baseline model in which the _SMCTRY_ coefficient for each sector is restricted to be the same across all countries and years. This specification is consistent with the current treatment of domestic trade costs in the literature as equal (and equal to zero) for each country, i.e. treating countries as point masses. In Section 4.3 we present and discuss results from our preferred and more flexible specification, in which _SMCTRY_ coefficients are allowed to vary across countries and over time. These results reveal that proper account of

> 11See for example McCallum (1995); Anderson and van Wincoop (2003); Hillberry and Hummels (2003); Millimet and Osang (2007); Mayer and Head (2002); Anderson and Yotov (2010a,b); Coughlin and Novy (2013); Nitsch and Wolf (2013).

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internal trade costs has significant quantitative implications for the effects of the standard variables used to proxy for trade costs in empirical gravity models.

# **4.1 Gravity Estimates for Services Trade**

We start with a specification of the gravity model that imposes the standard assumption of equal internal trade costs.<sup>12</sup> Table 2 reports gravity estimates for each service category in our sample<sup>13</sup> which, as discussed above, are obtained with 2-year lagged panel data, the PPML estimator, and time-varying, directional, country-specific fixed effects from the following econometric model: Here _SMCTRYij_ is the Kronecker delta, _β_ 6<sup>_k_isthecommon(acrosscountriesandovertime)</sup> _SMCTRY_ coefficient, _ηi,t_<sup>_k_denotesthesetoftime-varyingexporterdummies,whichcontrol</sup> for outward multilateral resistances and countries’ output shares in sector _k_ , and _θj,t_<sup>_k_denote</sup> time-varying importer dummies that account for inward multilateral resistances and expenditure shares n sector _k_ , respectively. The relationships between the gravity fixed effects from specification (7) and those from equation (5) are _x_<sup>_k_</sup> _i,t_<sup>=exp[</sup><sup>_η_</sup> _i,t_<sup>_k_]and</sup><sup>_mk_</sup> _j,t_<sup>=exp[</sup><sup>_θ_</sup> _j,t_<sup>_k_],</sup> respectively. Standard errors are clustered by country pair.<sup>14</sup> Overall, we find that the disaggregated gravity model works well with services data. Estimated coefficients on standard trade cost variables in Table 2 almost always exhibit expected signs and reasonable magnitudes. We discuss the effects of standard gravity variables in greater detail below when _SMCTRY_ coefficients are allowed to vary across countries,

> 12Since the gravity model can only ever identify relative trade costs, our specification is equivalent to imposing the constraint of internal trade costs being equal and equal to zero.

> 13In Table 2 trade in ‘research and development’ services (RSRCH) is listed as a separate sector even though the EBOPS taxonomy treats it as a part of ‘miscellaneous business services’ (BUSIN). We think, though, that the results for both categories are of distinct economic interest. Our empirical results offer evidence for heterogeneous trade cost estimates in these two categories.

> 14Comparison between estimates obtained with and without clustering reveal that the clustered standard errors are a bit larger. This suggests positive intra-cluster correlations, as expected.

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sectors and time as this constitutes our preferred econometric specification. For now, the results in Table 2 reveal that, all else equal, international borders reduce services trade substantially. Ten of the twelve possible estimates on _SMCTRY_ are positive and six of them are large and highly significant. The border effects in services vary widely across sectors. This motivates our preferred specification that allows for _country-year_ -specific estimates of the border effects _βit_<sup>_k_foreachsectorinoursampleaccordingto:</sup>

# **4.2 Results on Standard Gravity Variables and Services Trade**

Estimates of the effects of standard gravity variables on services trade are reported in Table 3. We note first of all that the effects that we capture in Table 3 and the corresponding numbers in Table 2 are qualitatively similar. At the same time, there are also differences in terms of statistical significance and economic magnitude which underscore the importance of a flexible specification of border barriers. The price of this flexibility is that the associated coefficients are ‘estimated’ with zero degrees of freedom. Yet an auxiliary regression finds meaningful patterns in the flexible fixed effects estimates.

Distance is a significant impediment to trade in services, though its effect varies widely across sectors and depends on the distance interval. In many sectors such as Transportation, Travel, Communication, Construction, Merchanting and Audiovisual services, distance effects are large and highly significant only over short intervals. It appears intuitive that Travel services exhibit the largest distance effect. In Financial and Computer services, respectively, we obtain insignificant short-distance effects but negative and significant (though small) effects over long distances. Finally, distance does not exert any trade-impeding effect in Insurance services, Operational Leasing, Business services, and Research and Development.

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The highly non-linear effects of distance on services trade and the insignificant estimates that we obtain for one third of the sectors in our sample reveal important differences between the effects of distance for goods and for services trade and point to the need for further research.

We estimate positive and significant contiguity coefficients for only five out of twelve service categories. The rationale for significant effects in Transportation, Travel, and Communication services is straightforward; the explanation in the case of Operational Leasing is less obvious but could be related to the particular spatial location of lessors and lessees, respectively. In general, the role of contiguity in promoting cross-border services trade does not appear to be strong. This is in sharp contrast to the estimated effects of common borders on manufacturing trade (see e.g. Anderson and Yotov, 2010b).

As expected, sharing a common official language facilitates bilateral services trade. The largest effects are found in Insurance, Audiovisual and R&D services, which we attribute to the need for precise communication in these sectors. Business, Financial, and Merchanting services encompass a host of presumably coordination-/communication-intensive ‘business process outsourcing’ services, thus it is intuitive that the coefficients are of similar magnitude as the one in Communications.<sup>15</sup> Overall, language appears to exert a stronger effect on services trade than on manufacturing goods trade (Anderson and Yotov, 2010b), which is consistent with the higher requirement for personal interaction and communication in most services.

In contrast, colonial ties do not generally have much explanatory power for services trade. We conjecture that this is due to services trade being a relatively recent phenomenon, which is consistent with the results from Anderson and Yotov (2010b, 2011) who find the effects of colonial ties on manufacturing trade to have waned during the 1990s. The strongly negative and significant effects of colonial ties in Business and Research services, respectively, may reflect the fact that such services are increasingly being exchanged between highly 15The absence of a language effect e.g. in categories such as Computer services could point to the need for an alternative construction of language-related variables that go beyond common official language, see Melitz and Toubal (2014).

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industrialized economies that never had colonial relationships with each other. From a sampling perspective, it is probably also true that an indicator variable for colonial ties does not belong in the set of gravity covariates for a sample of OECD countries.

In sum, the estimates from this section reveal that the structural gravity model performs quite well with services data. Many of the standard gravity covariates are significant and their estimates make good economic sense. At the same time, we document important differences in the effects of standard gravity covariates between goods and services trade. Our benchmark results point to avenues for further research in modeling trade costs in services, which we leave for future work. Instead, we now focus attention on estimated border

# **4.3 Results on International Border in Services Trade**

Equation (8) delivers a multi-dimensional data set of sector-country-time estimates of the border effects in services trade. Due to the large number of _SMCTRY_ estimates, we first display the overall distribution of border effects across countries, sectors and years. Then we characterize border effects separately along each of the three dimensions of our new database (and their interactions whenever possible).

Figure 1 shows the full distribution of _SMCTRY_ estimates across all 12 sectors, 28 countries and 4 years. Our data enabled us to estimate 1,231 (out of 1,344 possible) border effects. The median coefficient estimate is 5.35, which points to substantial border effects in services trade. To get a sense of the magnitude of the border barriers, note that the median border effect (exp _{_ 5 _._ 35 _} −_ 1) _×_ 100 = 20 _,_ 961, which suggests that the border enormously deflects international trade in services. We attribute the large estimates of border effects in services trade to the fact that consumption of services is highly localized.

Figure 1 also reveals that there exist some negative _SMCTRY_ estimates, suggesting that internal trade is smaller than international trade. The negative estimates are concentrated 15
primarily in Travel services<sup>16</sup> and/or are obtained for large developed countries such as Germany and the United States. Thus the distribution of SMCTRY estimates for Travel services is shown separately in light gray in Figure 1. The largest border estimates in Figure 1 are for smaller and less developed economies such as Slovakia, Estonia, and Lithuania, and are concentrated in sectors such as Finance services, Insurance services and Research and Development services. Next we focus on the distribution of _SMCTRY_ estimates across sectors and across countries.

Figure 2 depicts the variation of the average (across countries) estimates of the _SMCTRY_ coefficients by sector. Border effects in services vary widely across sectors, which we believe owes much to the high concentration of some service categories in certain developed parts of the world. The largest border effects are observed in Finance services, Insurance services, and Research and Development services, respectively. The large estimates for Finance and Insurance services correspond to the fact that an overwhelming share of banking and insurance services are produced and consumed domestically. Our findings for Finance services are consistent with the results from Jensen and Lori Kletzer (2005) about the tradability of services based on sectors’ geographic concentration within the United States. For instance, banking activities exhibit very low geographic concentration, suggesting low tradability due to the need for face-to-face interaction. It is also interesting to see that the Research and Development sector has a noticeably higher average _SMCTRY_ coefficient than miscellaneous Business services (in terms of the EBOPS classification the former is part of the latter, see Note 13 above). Here, disentangling both sectors brings to the fore how business process outsourcing and related developments have lowered revealed border effects whereas R&D is still predominantly produced locally (possibly within the confines of the firm). At the other extreme, consistent with our priors, by far the lowest border barriers exist in the Travel, Transportation, and Communications sectors, respectively.

Figure 3 depicts the distribution across sectors of _SMCTRY_ estimates by country. The

> 16To a lesser extent also in Transportation services.

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figure suggests that, on average, the border barriers in services trade are appreciably higher for smaller and less developed economies than for large industrialized countries. Slovakia, Estonia, Lithuania, Latvia and Slovenia exhibit the sample’s largest average _SMCTRY_ coefficients, whereas the coefficients associated with Great Britain, Holland, Canada, Germany, and Austria are the smallest in the sample. The United States is the only country that exhibits negative average border effects. The inverse relationship between openness to international trade in services and country size is confirmed in Figure 4 in which average border estimates per country are plotted against real GDP. The negative relationship between the two variables is clear and the correlation index _ρ_ = _−._ 76 is large and statistically significant. The result that richer/more developed countries face lower barriers in services trade is consistent with, and complements, the findings of Waugh (2010) who shows that less developed countries face larger aggregate trade costs. Next, we extend Waugh’s analysis by studying the evolution of services borders over time.

Table 4 shows the evolution of average (across countries) _SMCTRY_ estimates over time for each sector. The main finding is that services borders have fallen significantly during the period of investigation (2000-2006) in all sectors and without exception. Our interpretation of the magnitude of the decrease in border barriers is that it reflects the effects of globalization on sectoral services trade. Our estimates also reveal that sectors with higher initial borders were subject to smaller effects of globalization, while the opposite is true for the sectors with lower initial borders. The correlation between the initial level of the border and decrease (in absolute value) is a remarkable -0.88. Thus, the order of sectors in terms of estimated border barriers is, in general, fairly stable over the period considered here, but the gap between the sectors with high and low borders has widened. This finding has potentially important policy implications.

We view the variation of the effects of globalization on services borders across sectors as intuitive. For instance, we find that sectors that experienced the largest decrease in borders include Travel services (120% decrease), Transportation services (61% decrease), and 17
Communication services (36% decrease). Anecdotal evidence suggests that these are exactly the sectors where the effects of improved communications and technology should be the strongest. On the opposite side of the spectrum we find sectors such as Audiovisual services (4% decrease) and Operational Leasing services (7% decrease). Interestingly, Insurance services (8% decrease) and Finance services (12% decrease) are also on the lower end of the distribution, suggesting that these categories have not been affected by globalization as much as other sectors in our sample. The highly localized consumption of financial and insurance services is a possible explanation for these results. Finally, we note that Research and Development services (12% decrease) is another category that is not very much affected by globalization.

Table 5 depicts the evolution of average (across sectors) _SMCTRY_ estimates over time for each country. The average change across all countries in our sample is a decrease of 14%; however, the fall is not across-the-board and the effects vary widely across countries. Border barriers in services trade have decreased for about two-thirds of the countries in our sample and they have increased for the rest of the countries.<sup>17</sup> Based on the change in the border effects, we classify the countries in our sample in four groups. The first group includes countries that experienced a significant fall in services borders. These countries are relatively richer and include most of the more developed European economies (e.g. Great Britain, Belgium, Holland, and Denmark, among others), some smaller European countries that have developed relatively fast (e.g. Poland and Hungary), and the Republic of Korea.

The second group of countries also experience decrease in services borders but the change is significantly smaller in magnitude. This group consists of relatively less developed economies including some European countries that are behind the European economic powers (e.g. Sweden, Spain and Portugal), some economies that were in transition (e.g. Slovenia and Slovakia), and Canada and Japan. The third group includes countries that actually suffered an increase in the borders for services trade. These countries include struggling

> 17We remind the reader that we measure _relative_ border barriers, so increase means relative to the average which itself is decreasing.

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and less developed economies such as Greece, Estonia, Latvia, and Lithuania. Finally, we put Germany and the United States in a separate group because these are two developed economies for which we observe an increase in the borders to services trade, however, these are also the two countries with the lowest borders in the initial and in the final year of our sample.

In order to check whether the effects of globalization are indeed related to country size and economic development, we split the countries in our sample into quintiles according to real GDP and we plot the evolution of the corresponding SMCTRY estimates in Figure 5. As before, motivated by the fact that Germany and the US are the only large developed economies that experience a small increase in the SMCTRY estimates over time and are also the two countries with the smallest borders to start with, we put those two countries in a separate group. Figure 5 captures several interesting features. First, as established before, smaller countries face higher borders in services trade. Second, it reveals that the border estimates for the countries in the lowest quintile have remained stable (or increased a bit) over the period of investigation. Third, we observe a decrease over time for the border estimates for the countries in the four upper quartiles in our sample. Our interpretation of this result as a reflection of globalization forces contributes to the extensive literature concerned with the “missing globalization” puzzle.<sup>18</sup> Specifically, we demonstrate that, in the case of services, globalization is an active force that is captured by the gravity model of trade.

Fourth, the decrease in the border effects on services trade has been faster for the countries in the second and third lowest quintiles as compared to the larger countries which, as noted before, face lower border barriers to begin with. This points to a convergence story among

> 18Coe _et al._ (2002) coin the term “missing globalization” and Disdier and Head (2008) provide a survey of the robust evidence for stable gravity estimates of distance over time. Our findings are in accordance with the results for goods trade from Yotov (2012) and Bergstrand _et al._ (2015). Yotov (2012) uses manufacturing goods data and demonstrates that the “distance puzzle” is resolved once the effects of international distance are measured properly relative to the corresponding effects of internal distance. Bergstrand _et al._ (2015) generalize this result to resolve the “missing globalization puzzle” with both sectoral goods data as well as with aggregate data.

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the countries in four upper quartiles. In contrast, over the period of inspection border effects for the smallest economies (first quintile) remained stable. Altogether this implies divergence between the smallest countries and the rest of the countries in our sample. Thus, in addition to complementing the finding from Waugh (2010) that less developed countries face larger resistance in the case of services trade as compared to richer countries, we also find that the group of smallest economies has not been reached by globalization forces. To the best of our knowledge, the phenomenon of divergence in border barriers has not been documented before. Finally, it is worth noting that the _SMCTRY_ estimates for the first and the second quintiles in our sample have increased between 2000 and 2002, while the estimates for the rest of the countries during this period have been stable. A possible explanation for these results is the recession in the early 2000s which may have raised protectionism and slowed down globalization forces, perhaps more so in poorer economies.

In order to further explore the convergence or divergence effects of globalization, we construct figures that capture the evolution of border effects across small and large countries, in terms of relative output shares in world supply, for each sector in our sample. Based on individual sectoral figures, we identify three groups of sectors. The first group includes sectors for which we observe convergence between the small and the large countries in our sample. The categories in this group include Transportation services, Travel services, and Merchandize services. Figure 6 illustrates for the case of Transportation services. The second group includes sectors in which the border barriers fell but in a way that rendered the gap between large and small countries largely stable. Here, we find sectors such as Construction services, Communication services, and Business and Professional services. Figure 7 illustrates for the case of Construction services. Finally, the third group includes sectors where there has been divergence in the effects of borders between small and large countries. This group includes Financial services, Insurance services, Operational Leasing, Research and Development services, and Audiovisual services. Figure 8 illustrates using Research and Development services.

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The descriptive analysis of border effects in services trade that we offer in this section can be summarized as follows. First we find that, for the most part, border barriers in services trade are large and significant. Second, we obtain heterogeneous border estimates across sectors that vary in an intuitive way. Third, our country-specific estimates reveal that smaller and less developed countries face larger resistance to international services trade. Fourth, we find that border effects in services trade have fallen over the period of investigation for all sectors in our sample. Finally, our estimates reveal that the more developed countries in our sample have enjoyed a fall in the borders in services trade, while smaller and less developed economies have from an increase in services border barriers.

# **5 Recovering Missing Output Information**

This section derives and empirically implements a procedure for recovering output information. Sectoral output data or, equivalently, internal trade flows observed in addition to border-crossing trade flows, are a necessary precondition for estimating border barriers as defined in the trade cost function (equation 6).<sup>19</sup> Whenever such statistical information for services sectors is not available at the desired level of disaggregation, this methodology can provide a way forward in instances in which trade costs could otherwise not be estimated. The fact that for the 28 OECD countries in our sample output information is available from the EUKLEMS database (cf. Section 3) allows us to assess the accuracy of our procedure.

> 19That information is generally required for making full use of structural gravity, eg. estimating general equilibrium trade costs indices, which we do not further pursue in this paper.

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# **5.1 Structural Gravity with Missing Data**

Following on from Section 2, equation (4) admits a structural interpretation of the exporter and importer fixed effects, respectively, for each sector: As defined before, _Yi_<sup>_k_</sup> denotes sectoral output (total sales at end user prices) and _Ej_<sup>_k_de-</sup> notes total sectoral expenditure, while Π<sup>_k_</sup> _i_<sup>and</sup><sup>_P k_</sup> _j_<sup>denoteoutwardandinwardmultilateral</sup> resistances for class _k_ . In practice, the fixed effects are estimated relative to a base country so, for example, _m_<sup>_k_</sup> 0<sup>and</sup><sup>_xk_</sup> 0<sup>arenotestimated,allowingforastandardconstantterm</sup><sup>_χk_.20</sup> For the base country, we assume that _Y_ 0<sup>_k_is observed, from which</sup><sup>_E_</sup> 0<sup>_k_is inferred as ‘apparent</sup> consumption’ deducting exports and adding imports to _Y_ 0<sup>_k_.Anormalizationofthesetof</sup> _P_<sup>_k_</sup> ’s and Π<sup>_k_</sup> ’s is required in any case, so it is natural to choose _P_ 0<sup>_k_=1(seeAndersonand</sup> Yotov, 2010a).<sup>21</sup> Limited data on sectoral output constitutes an important problem, for unfettered use of the structural gravity model requires the full set of output and trade data for all countries. An important contribution of this study is therefore to show how the gravity model can be used to project output information. Our methodology imposes the theoretical identity between the estimated importer and exporter country fixed effects with their structural gravity expressions in order to recover the required information. Fally (2015) shows that the fixed effects estimated with PPML are exactly consistent with the theoretical values from

> 20Structural gravity in theory has a scaling term equal to the inverse of worldwide sales times the mean measurement error in the bilateral trade data, data that are notoriously rife with measurement error. The practice in (5) combines the importer 0 and exporter 0 fixed effects with the worldwide scaling effect. Regression cannot identify both terms because the full set of fixed effects regressors are perfectly collinear when the constant vector is also included. (Perfect collinearity also arises if _x_<sup>_k_</sup> 0<sup>or</sup><sup>_mk_</sup> 0<sup>isattemptedtobe</sup> estimated.)

> 21This normalisation implies _mk_ 0<sup>=</sup><sup>_E_</sup> 0<sup>_k_whilst</sup><sup>_xk_</sup> 0<sup>isidentifiedfrom</sup><sup>_xk_</sup> 0 = _Y_ 0<sup>_k/χk_�</sup> _j_<sup>_τ k_</sup> 0 _j_<sup>_mk_</sup> _j_<sup>.</sup> Then (Π<sup>_k_</sup> 0<sup>)</sup><sup>_σk−_1=1</sup><sup>_/χk_�</sup> _j_<sup>_τ k_</sup> 0 _j_<sup>_mk_</sup> _j_<sup>completestheidentificationofmultilateralresistancesfromobservedandin-</sup> ferred variables.

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(9)-(10). Specifically, the importer fixed effect is equal to the product of regional expenditure and the power transform of inward multilateral resistance, whereas the exporter fixed effect is equal to the product of regional output and the power transform of outward multilateral resistance. Combining equations (5), (9) and (10) thus implies: The MR system from structural gravity is: Substitute (11) into (12) and (13) to obtain: System (14)-(15) yields fitted values for output and expenditures, respectively. World output � _Y_<sup>_k_</sup> = _χ_<sup>_k_�</sup> _i>_ 0<sup>_x_</sup> _i_<sup>_k_</sup> � _j_<sup>_τ k_</sup> _ij_<sup>_mk_</sup> _j_<sup>+</sup><sup>_Y_</sup> 0<sup>_k_isobtainedbysummingoverallcountries</sup><sup>_i ∈I_inequation</sup> (14).

Notice that there is no problem at a theoretical level if some output in a particular sector and year were zero. The corresponding market clearing equation is dropped from the system, all demands _Xij_<sup>_k_for goods by destinations</sup><sup>_j_from origin</sup><sup>_i_in</sup><sup>_k_are equal to zero, and outward</sup> multilateral resistance Π<sup>_k_</sup> _i_<sup>isnotdefined.Understandingthatwehave</sup><sup>_Y_</sup> _i_<sup>_k_=0inequation</sup> (9), all the steps from equations (11)-(15) remain valid, and we can understand that where Π<sup>_k_</sup> _i_<sup>appearsin(11)wemayaswellsetΠ</sup><sup>_k_</sup> _i_<sup>=0becausetheequationforseller</sup><sup>_i_insector</sup><sup>_k_</sup> does not hold due to there being no trade. However, the procedure for recovering output 23
described in this section is all about our suspicion that there is some trade and output data even though it is not observed. In this case, rather than dropping the exporter-year fixed effect of _i_ in sector _k_ and setting _Y_<sup>ˆ</sup> _i_<sup>_k_= 0,weexploitthepanelstructureandtheproperties</sup> of the PPML estimator to generate consistent estimates of output.

Taking the very strong stand that structural gravity generates the true data, these generated activity variables _{Y_<sup>�</sup> _i_<sup>_k,E_�</sup> _j_<sup>_k}_areperfectlyconsistentwiththetheory.Theirexpected</sup> value (asymptotically) is the true value. In reality, both the fitted values _Y_<sup>�</sup> _i_<sup>_k_andtheob-</sup> served values ( _Yi_<sup>_k_)</sup><sup>_∗_aremeasuredwitherror,andthemeasurementerroroftheobserved</sup> values might contaminate the estimates of the _τij_<sup>_k_’ssuchthatthefittedvaluesof(14)and</sup> (15) are not asymptotically unbiased.<sup>22</sup> The primary challenge to implementing the system of equations (14)-(15) lies in the fact that, by definition, one crucial component ( _β_<sup>ˆ</sup> _it,_<sup>_k_</sup> 6<sup>)ofthetradecostfunction</sup><sup>_τ k_</sup> _ij_<sup>cannot</sup> be estimated when output is missing or suspect. To see this, recall that the indicator for internal trade is the only variable that carries direct information on output. Thus we now turn to the issue of estimating border effects in the next section, in which we capitalize on the newly-created multi-dimensional database of border estimates from Section 4.3 to study their determinants.

# **5.2 On the Determinants of Border in Services Trade**

The wide variability across border estimates in each dimension (across countries, sectors, and time) sets the stage for meaningful econometric analysis. The contributions of this section are twofold. First, the empirical results from ‘border estimations’ add to our understanding

> 22Considering the potentially most problematic contamination issue is somewhat reassuring. The internal trade flows are typically generated as a residual ( _Xii_<sup>_k_)</sup><sup>_∗_=(</sup><sup>_Y_</sup> _i_<sup>_k_)</sup><sup>_∗−_�</sup> _j_ = _i_<sup>(</sup><sup>_X_</sup> _ij_<sup>_k_)</sup><sup>_∗_.Theeconometricmodel</sup> assumes that the observed bilateral trade flow value is related to the true value by ( _Xij_<sup>_k_)</sup><sup>_∗_=</sup><sup>_X_</sup> _ij_<sup>_kεk_</sup> _ij_<sup>where</sup><sup>_εk_</sup> _ij_ is a random error term. The gravity estimation would apply this assumption to all trade flows, internal and international. When would this assumption be met? Generating ( _Xii_<sup>_k_)</sup><sup>_∗_= (</sup><sup>_Y_</sup> _i_<sup>_k_)</sup><sup>_∗−_�</sup> _j_ = _i_<sup>(</sup><sup>_X_</sup> _ij_<sup>_k_)</sup><sup>_∗_isconsistent</sup> with ( _Xii_<sup>_k_)</sup><sup>_∗_=</sup><sup>_X_</sup> _ii_<sup>_kεk_</sup> _ii_<sup>ifandonlyif(</sup><sup>_Y_</sup> _i_<sup>_k_)</sup><sup>_∗_= �</sup> _j_<sup>_X_</sup> _ij_<sup>_kεk_</sup> _ij_<sup>;thatis,thereisnoadditionalsourceofmeasurement</sup> error in the output variables. This is a plausible assumption because statistical practice would normally include such consistency checks. But it is not guaranteed.

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of the forces behind the wedge between internal and border-crossing trade. This is an interesting question in itself because, as we demonstrated earlier, border effects in services trade are substantial while, at the same time, services now represent a larger share of GDP in the developed world compared to goods. Second, as discussed in the theoretical section, the ability to consistently predict border effects is a _necessary and sufficient_ condition for successfully recovering missing output data.

The dummy variable nature of _SMCTRYij_ implies that the coefficient _β_<sup>ˆ</sup> _it,_<sup>_k_</sup> 6<sup>is interpreted</sup> as a _relative_ border The middle expression captures the fact that for each sector the _SMCTRY_ estimates _β_<sup>ˆ</sup> _it,_<sup>_k_</sup> 6 account for, and consist of, three components that include _country-specific internal trade costs_ , _t_<sup>_k_</sup> _ii,t_<sup>, and</sup><sup>_country-specificborderbarriers_,</sup><sup>_bk_</sup> _it_<sup>, which push in opposite directions and are</sup> identified relative to the third component, which is _an average border_<sup> ̄</sup> _b_<sup>_k_</sup> _t_<sup>.Thetermsonthe</sup> right-hand side express the fitted value of the relative border cost as a deviation of observed internal trade from the importer and exporter fixed effects.

Our goal in this section is to find empirical proxies for the components of internal trade costs and border barriers that comprise _βit,_<sup>_k_</sup> 6<sup>.However, before we do so, we find it instructive</sup> to rearrange the preceding equation to transform it into the following estimating equation: Equation (17) represents a gravity model for internal trade and holds as an equality by construction. This is confirmed in column (1) of Table 6, where we regress the logarithm of internal trade on three covariates including the collection of border estimates _β_<sup>ˆ</sup> _it,_<sup>_k_</sup> 6<sup>, exporter-</sup> time fixed effects _η_ ˆ _i,t_<sup>_k_andimporter-timefixedeffects</sup><sup>_θ_ˆ</sup> _i,t_<sup>_k_,respectively.</sup> As expected, the coefficient estimates on each of these variables is equal to unity. The perfect model fit merely 25
reflects the fact that the _SMCTRY_ coefficients embody all information about internal trade in gravity estimations when total output is known.

The idea in subsequent specifications (columns 2 and 3) is then to replace the _SMCTRY_ coefficient—as if it were unobservable—with observable country characteristics and gauge the explanatory power thereof. Equation (18) defines the empirical specification for decomposing the international border effect _β_<sup>ˆ</sup> _it,_<sup>_k_</sup> 6<sup>:</sup> Guided by the structural interpretation of _SMCTRY_ estimates from equation (16), we partition covariates into three groups. First, we chose the variables in vector _Wi_ under the assumption that they primarily affect internal trade costs _tii,t_ . These variables include internal distance, the domestic distribution/concentration of economic activity, an institutional index from the Worldwide Governance Indicators (WGI) as it relates to ‘policies and regulations that permit and promote private sector development’ (Kaufmann _et al._ , 2010), and—at the cost of losing some observations—the OECD’s Product Market Regulation (PMR) index (Koske _et al._ , 2014). Guided by specification (17) we define ( _γ_ 1 _−_ 1) and ( _γ_ 2 _−_ 1) as size elasticities giving the effect on relative cross-border trade costs of variation in _ηi,t_<sup>_k_and</sup> _θi,t_<sup>_k_respectively.Thestructuralinterpretationofthesefixedeffectsisofeffectivedemand</sup> size _E_<sup>_k_andeffectivesupplysize</sup><sup>_Yk_respectively.Noticethatthesizeis</sup> _i,t_<sup>(</sup><sup>_P k_</sup> _i,t_<sup>)</sup><sup>_σk−_1</sup> _i,t_<sup>(Π</sup><sup>_k_</sup> _i,t_<sup>)</sup><sup>_σk−_1</sup> defined at the sector level for each country _i_ , anticipating heterogeneity across sectors for given countries.

The variables in the second group ( _Zi,t_ ) are chosen based on the assumption that they predominantly affect the size of the border barrier _bi,t_ . The vector of variables includes economic size (current GDP in PPP terms and population), the ‘Rule of Law’ index taken from the Worldwide Governance Indicators, the number of procedures it takes to enforce contracts (from the World Development Indicators), and measures of digital infrastructure 26
assumed to facilitate cross-border services trade (the number of secure Internet servers, fixedline teledensity, and the number of mobile subscriptions per 100 inhabitants, all taken from the WDI). Finally, we include sector and year fixed effects ( _ν_<sup>_k_</sup> and _μt_ , respectively) in order to capture the fact that the border estimates are identified relative to an average border<sup> ̄</sup> _bt_ . The change in the overall fit of the model when we move from the perfect-fit specification of column (1) in Table 6 to the specification described by equation (18) will be informative about how well these proxies do in terms of explaining the variability of border effects and in predicting internal trade.

Our main findings are presented in column (2) of Table 6. With 86% of variation explained the model fit is fairly high.<sup>23</sup> Hence, the observable characteristics do well in controlling for unobservable internal trade costs ( _tii_ ) and border barriers ( _bi_ ). In terms of predicted signs, factors that increase internal trade costs ( _Wi_ variables) will lead to lower internal trade, so we expect a negative relationship. Factors that increase the border barrier ( _Zi,t_ variables) would, _ceteris paribus_ , be associated with higher internal trade so we expect a positive coefficient.

The set of explanatory variables fits these priors very well; for instance, internal distance raises trade costs and thus comes in negative whereas business-friendly regulations lower trade costs and therefore exhibit a positive coefficient. Good digital infrastructure, in turn, reduces the deflective force of border barriers and leads to lower internal trade, thus coefficients of these variables generally exhibit a negative sign.

In column (3) we also consider the OECD’s Product Market Regulation (PMR) indicator, which has been widely used and enables us to account for the effects on trade flows of domestic regulatory barriers in service sectors. Consistent with expectations, we find that higher PMR values are associated with lower internal trade. Indeed, the negative coefficient on the PMR indicator is driven by the PMR subindex that captures (i) more complex regulatory procedures, (ii) administrative burdens and (iii) barriers in network sectors, all of which are relevant for internal trade costs. As such, we think that these results offer important

> 23The majority of explanatory power is in fact due to observable country characteristics, as sector and year fixed effects alone explain only 28.7% of the variation in log internal trade.

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insights. They are reported in separate models, though, as PMR inclusion comes at the cost of losing some observations.<sup>24</sup> The pooled regression is convenient for a quick insight into performance, but there is good reason to suspect that much heterogeneity obtains across sectors. Table 7 confirms this suspicion, but the main insights remain the same: negative size elasticities that are large in absolute value, not significantly different for exporter or importer size, negative distance elasticities, positive GDP per capita elasticities, large negative effects of the rule of law, etc.<sup>25</sup> One sector that performs relatively poorly is Travel, with a positive distance elasticity and notably poorer goodness of fit (at an adjusted _R_<sup>2</sup> of 0.736, low in the context of the other sectors).<sup>26</sup> Overall, we view our analysis of the determinants of international borders in services trade as a successful first attempt to study this matter. The estimates appear to be intuitive with expected signs, reasonable magnitudes and a remarkable model fit. Importantly, none of the regressors employed in our specifications relies on sectoral production data. The high _R_<sup>2</sup> = 0 _._ 86 in the main specification (column 2) is an encouraging and essential precondition for satisfactory out-of-sample predictions of border estimates, which in turn are crucial for the success of our methods to recover missing output. In the following section, we capitalize on the ability to predict internal trade and on the strong performance of the structural gravity model to test our new methods for recovering missing output data. 24The PMR indicators for the period under consideration are not available for Estonia, Lithuania, Latvia and Slovenia. PMR indices are only available at some discrete points in time; we take the 2003 values and exploit the variation in regulatory stringency across countries.

> 25Output projections of similar accuracy can be based on a more parsimonious model of national characteristics featuring only area, GDP, population and a governance index.

> 26The positive distance elasticity could reflect some idiosyncratic features of travel services. For instance, it is not implausible that the substitution elasticity for domestic travel is substantially lower (below unity) than for international trips as many domestic trips rather resemble “necessities.” We have experimented with including ‘receipts from international tourism’ as an additional control variable in the travel sector regression, the effect of which is positive and highly significant and renders the distance elasticity insignificant. This finding is consistent with two (not mutually exclusive) effects: it could either reflect mis-measurement in the sense that a good deal of internal travel might actually originate from international customers which, however, would be recorded in our setting as internal trade. There might also be a relative price effect at work such that a country’s relative attractiveness as a tourist destination (as evidenced by large receipts) is observationally equivalent to a high barrier of going abroad for domestic residents. A larger share of residents in such countries would thus vacation at home, thereby giving rise to the positive correlation.

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# **5.3 Econometric Approach**

We use equation (18) as an empirical strategy for predicting internal trade and, in combination with observed international trade, to reconstruct output based on fitted values of _X_<sup>ˆ</sup> _ii,t_<sup>_k_.</sup> In so doing we focus on the ‘worst’ case when no disaggregated production information is available at all for a given country and sector. Output predictions are then generated in four steps: (i) obtain a full set of country-sector-year specific _SMCTRY_ coefficients from estimating a gravity model; (ii) one particular country’s internal trade flow is discarded (and so is the associated _SMCTRY_ coefficient) as if no output were available in this case; then use equation (18) to project the remaining internal trade flows onto observables as in the previous Section 5.2; (iii) predict out-of-sample so as to recover unobserved internal trade based on the particular country’s observable characteristics; (iv) repeat steps (ii)-(iii) for each country and for each sector in our sample, collecting fitted values in each case. As a last step, we combine estimated internal trade with a country’s total exports to obtain total output (or with total imports to obtain total expenditure, respectively) and evaluate these predictions against their true values.

# **5.4 Results on Predicted Output**

We start by juxtaposing the overall distribution of actual log output (across all countries, sectors and years) and its estimated equivalent (Figure 9). Reassuringly, the kernel density estimates of the two distributions are fairly close, even though the novel procedure exhibits a slight tendency to overpredict output, and the representation in logs tends to de-emphasize large values. Therefore, we go on to evaluate the accuracy of our method in greater detail (i) by comparing the procedure’s predictions to ones arising from a na ̈ıve benchmark, and (ii) by expressing imputed output as a percentage deviation from its true value. The former provides a sense to what extent the novel imputations outperform an agnostic benchmark, obtained directly as the simple average of output across those countries retained for fitting the auxiliary regression. The latter set of results then quantifies how closely the predictions come 29
to their true values. Both exercises are based upon 1,215 output prediction that obtain from running out-of-sample estimations for each sector and country (each combination containing four years), as set out in section 5.2.

Upon computing the absolute deviation from a perfect prediction for both our procedure and the agnostic benchmark, respectively, we find that in 963 cases out of 1,215 countrysector-year estimates of output, equivalent to 79.3%, our method delivers more accurate predictions. The binary count measure comparison can be broken down by sector (Figure 10) and by country (Figure 11). Clearly, the accuracy of predictions is more varied in the country dimension. Nonetheless, it is reassuring to see structural gravity based imputations outperform an agnostic benchmark in nearly 80% of cases.<sup>27</sup> We proceed to characterize the percentage deviation of predicted to actual output, again by sector (Table 8) and by country (Table 10). By construction, 100% corresponds to a perfect prediction. Across all countries, sectors and years, median predicted output equals 108.9% of actual output. The interquartile range (columns 4-5) is also reasonably tight considering that all production information has been dropped before making these imputations. That said, it is true that the distribution of predictions is skewed upward as a result of a few very large numbers that obtain when the base on which the percentage deviation is calculated (actual output) is a small number. Thus the mean prediction (148%) exceeds the median prediction.

The disaggregation of results indicates that the consistency of predictions as well as their dispersion is fairly homogeneous across different services sectors, while there exists appreciably more variation across countries. Hence, the prediction accuracy is mostly affected by outliers for individual countries in certain sectors. We suspect that such mis-predictions occur when a country’s international services trade is minuscule relative to its internal trade, which leads to very large estimated border effects that in turn produce outlier predictions. Indeed, when partitioning the sample of predictions according to countries’ supply shares 27If the agnostic benchmark is taken to be _median_ output, the share of better predictions is still 65.4%.

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in a given sector, we find that predictions tend to be worse, and exhibit a larger variance, when supply shares are low (Table 9). It is also true, as conjectured, that predictions are less accurate when a smaller share of production is exported abroad (ie. the share of internal trade is high).<sup>28</sup> We conclude from this benchmarking exercise that the novel procedure of recovering missing output data based on structural gravity restrictions delivers reasonable results. Output figures thus estimated are robust to the specification of the auxiliary regression. The procedure’s good performance in a situation in which no production data at all is available is particularly appealing because outside OECD countries, almost no measures but projected measures exist. At the same time, it is clear that the precision of the estimated quantities depends on how much actual output information is available for estimating equation (18). Thus we conduct a sensitivity check to illustrate how output predictions depend on the relative share of inferred to actual information, which demonstrates two regularities: first, median inferred output (as a percentage deviation from its true value) is stable as it is consistently estimated even as less information is used to predict it. Second, the confidence interval widens as the auxiliary regression is based upon less and less countries. The pattern of loss in accuracy is qualitatively similar across countries, and does also not vary across years. The results of this robustness exercise are obviously noisy due to small sample size in combination with influential data; however, they do support the notion that the method proposed in section 5.2 is not particularly sensitive to either the amount of data available or individual countries used for out-of-sample prediction. More details and figures are offered in Appendix B.

28A full break-down by sector and country (as in Tables 8 or 10) for either type of partitioning is available upon request.

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# **6 Conclusion**

Structural gravity is applied to model barriers to services trade across many sectors, countries and time based on development of an integrated data set for services production and trade. Border barriers are flexibly inferred relative to internal costs. An important regularity is that relative border barriers are declining in the size of sectoral activity. The cause of this external scale economy merits further investigation. We also find that border barriers have generally fallen over time but also identify differences across services sectors and countries; in particular, border effects for the smallest economies have remained stable, giving rise to a divergent pattern across countries.

The good fit and intuitive interpretation of the results encouraged development of a projection model whereby services production and trade data can be generated believably. A crucial step in this procedure decomposes border barriers according to their structural components, and the empirical estimation of the resultant model sheds light on the role of institutions, geography, size and digital infrastructure as determinants of border barriers. The success of the projection method suggests that it could be usefully applied to analyze developing countries’ services trade. More generally, beyond services trade, for which the missing data problem is especially severe, our projection method may be useful when other trade or production data quality is suspect.

The full general equilibrium effect of border barriers in services trade includes their effect on multilateral resistances (see Agnosteva _et al._ , 2014). We leave this extension for future work. Such general equilibrium analyses may also combine goods and services trade, for which the methods and results developed in this paper would be useful.

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