ECONOMICS WORKING PAPER SERIES

 

MODELING TRADE IN SERVICES:
MULTIPLE MODES, BARRIERS TO TRADE, AND DATA LIMITATIONS

Andre Barbe

Arthur Chambers

Tamar Khachaturian

David Riker

 

Working Paper 2017-04-B

 

U.S. INTERNATIONAL TRADE COMMISSION

500 E Street SW

Washington, DC 20436

April 2017

The authors are grateful to Zeynep Akgul and Martha Lawless for helpful comments and suggestions.

Office of Economics working papers are the result of ongoing professional research of USITC Staff and are solely meant to represent the opinions and professional research of individual authors. These papers are not meant to represent in any way the views of the U.S. International Trade Commission or any of its individual Commissioners. Working papers are circulated to promote the active exchange of ideas between USITC Staff and recognized experts outside the USITC and to promote professional development of Office Staff by encouraging outside professional critique of staff research.

Modeling Trade in Services: Multiple Modes, Barriers to Trade, and Data Limitations

Andre Barbe, Arthur Chambers, Tamar Khachaturian and David Riker

 

Office of Economics Working Paper 2017-04-B

April 2017

 

ABSTRACT

We develop a model of trade in services that includes firm heterogeneity and multiple modes of delivery, including cross-border trade and foreign affiliate transactions. We then use the model to estimate the effect of a 50 percent reduction in the barriers faced by non-EU services providers in EU markets. We find that this liberalization would increase the value of cross-border imports into the EU and purchases from foreign affiliates in EU countries. This sales increase ranges from 21.7 to 27.3 percent, depending on the services category and EU country. However, the liberalization would only decrease the sales of domestic producers by 0.4 to 6.1 percent, and reduce overall prices of the services in EU countries by 0.1 to 1.2 percent.

 

Andre Barbe                                                                Tamar Khachaturian

Office of Economic, Research Division                     Office of Industries, Services Division

Andre.Barbe@usitc.gov                                             Tamar.Khachaturian@usitc.gov

 

 

Arthur.Chambers                                                        David Riker

Office of Industries, Services Division                       Office of Economics, Research Division

Arthur.Chambers@usitc.gov                                      David.Riker@usitc.gov

 

1         Introduction

In 2015, international trade in services reached 13 percent of world GDP.[1] Although the volume of services trade has grown significantly over the last decade, it is still impeded by natural barriers such as language and distance, and by policy barriers that restrict foreign entry, the movement of people, competition, or regulatory transparency.[2] However, it is difficult to quantify the impact of these barriers on trade flows, or the effect that liberalization would have.

Services trade barriers are difficult to assess for a number of reasons. For one, there is very limited disaggregated information on the value of services trade flows. In addition, the international provision of services occurs through multiple and inter-connected modes of delivery, which can be complementary or competing. Finally, barriers to trade in services are complex and difficult to measure and compare across countries. Our research captures some of these complexities of international trade in services and overcomes some of these data challenges.

To this end, we develop a model of trade in services that includes firm heterogeneity and multiple modes of delivery, including cross-border exports (CBE) and foreign affiliate sales (FAS). We calibrate the model to 2014 trade data for professional services in European markets. We then use the model to estimate how trade flows and market prices would change if barriers to non-EU providers of the services were significantly reduced. The economic effects that we estimate include changes in the revenues of foreign providers, their use of different modes of delivery, market prices, and domestic sales in the European country markets included in the sample.

This analysis applies the modeling framework developed in Khachaturian and Riker (2016). That study focused on cross-border imports and foreign affiliate sales of professional services in the U.S. market. In contrast, this paper focuses on foreign supply of services in certain EU countries. Additionally, we extend the modeling framework to address two different types of foreign suppliers, those from outside the EU and those from other EU countries. This is an important distinction, because we expect that there is much less potential for further liberalization of intra-EU trade and foreign affiliate sales of services.

The analysis is based on the theoretical model of trade and foreign direct investment in Helpman, Melitz, and Yeaple (2004). Their model includes three key features that make it well-suited for analyzing trade liberalization in services industries: heterogeneity in the productivity of service providers from each country, alternative modes of supply to foreign markets, and fixed costs that are barriers to each mode of supply.[3] There is a large empirical literature that generally supports the predictions of the Helpman, Melitz, and Yeaple model. We build upon this foundation by developing a partial equilibrium version of their model that reduces data requirements.

The rest of this paper is organized into four parts. Section 2 provides an overview of the professional services industries included in the modeling analysis. Section 3 describes the modeling framework. Section 4 uses the model to estimate the impact of EU liberalization on trade in services. Section 5 offers concluding remarks.

2         Background Information on Modes of Supply and Barriers to Trade in Professional Services

Our analysis focuses on trade in two categories of professional services: 1) architectural and engineering services and 2) legal and accounting services. These categories were chosen due to data availability in the Eurostat database. Trade in these services occurs either in the form of cross-border supply (primarily mode 1 trade) or in the form of sales by foreign-owned affiliates established in the country (mode 3 trade).[4]

At the same time, there is considerable evidence that there are discriminatory barriers to the foreign provision of architectural and engineering services and of legal and accounting services in European markets, as described below based on the OECD Services Trade Restrictiveness Index (STRI).[5] We expect that partial reduction of these barriers would have economically significant effects on both major modes of supply.

2.1       Architectural and Engineering Services

Architects and engineers provide services related to the construction and design of buildings and other infrastructure, as well as the design of industrial procedures and production processes. In European markets, these services are supplied through multiple modes of delivery.[6] Due to technological advances, cross-border supply (or mode 1 supply), and specifically the digital delivery of services (for example, supplying architectural designs or engineering plans abroad via e-mail) is a growing area of trade. Mode 1 supply is often complemented by trade in the form of “movement of persons” (or mode 4 trade), when architects and engineers travel to provide services in foreign markets. For example, architectural designs provided through cross-border delivery might also warrant the architect visiting the project site to implement and manage the project. Finally, mode 3 trade, the supply of architectural and engineering services through the establishment of a commercial presence (e.g., a foreign affiliate), is an alternative and possibly complementary mode of supply, allowing companies to provide services continuously throughout various phases of projects in host countries.

Table A1 provides summary statistics on cross-border trade and foreign affiliate transactions in architectural and engineering services. In 2014, the value of cross-border trade in architectural and engineering services, which includes services supplied through modes 1 and 4, varied widely by country. Imports of architectural and engineering services from outside the EU showed a similar trend, with imports surging in France (102.7 percent) and the Czech Republic (68.9 percent), while declining slightly in Austria (-10.0 percent) and Hungary (-3.8 percent).[7] Architectural and engineering services supplied by foreign affiliates from outside the EU operating in the European countries presented here (so-called “inbound foreign affiliate sales”) declined in several countries, including in Germany (-31.2 percent) and Austria (-16.2 percent) but experienced modest growth in others, such as France (9.7 percent) and the Netherlands (6.0 percent).[8] In 2014, the year of the data used in the model calibration, inbound foreign affiliate sales were the dominant mode of supply in 6 of the 9 countries examined here (Czech Republic, Hungary, Italy, Netherlands, Poland, and Sweden).[9]

Although policies related to the foreign provision of architectural and engineering services tend to be less restrictive than those related to other professional services, countries nevertheless maintain regulations related to the entry or operation of foreign or foreign-owned service providers that likely impede trade, including, most notably, discriminatory qualification and licensing requirements. The OECD STRI for architectural and engineering services categorizes trade restrictions into five groups: restrictions on foreign entry, restrictions to movement of people, barriers to competition, other discriminatory measures, and regulatory transparency.[10] In architectural and engineering services, the most prevalent barriers are restrictions to movement of people (this category affects either all modes of trade or specifically mode 4 trade) and restrictions on foreign entry (this category affects mode 3 trade). In the former category, quotas and labor market tests MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefmuyTjMCPf gaiuaajugybabaOpaaaG+apeGaa8hfGaaa@3C43@  for example, work permits that require proof that the vacancy could not be filled by a local employee or that the work by the foreign employee will benefit the local economy MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefmuyTjMCPf gaiuaajugybabaOpaaaG+apeGaa8hfGaaa@3C43@  are common and restrict or limit foreign architects and engineers from traveling to host countries on a temporary basis. Also in this category, restrictions on recognition of foreign qualifications (for example, local practice or examination requirements) and licensing (residency and in a few cases, nationality requirements) are prevalent and affect all modes of trade.[11] Restrictions that affect the entry of foreign firms include specific requirements on the composition of boards of directors or the management of engineering and architecture firms (such as residency), restrictions on acquiring land (which affects construction services directly and the architectural and engineering services indirectly), and in some cases foreign equity restrictions for non-locally licensed architects. The remaining restrictions affect the use of professional titles (e.g., titles of “architect” or “engineer”), prices, and advertising architectural services.

Table A2 presents the STRI scores for each country examined here, along with a brief summary of their most restrictive measures applied to the architectural and engineering services sectors. For example, Poland restricts the acquisition and use of land and real estate by foreigners, conditions employment and residency permits on either proving positive local impacts or that the vacancy could not be filled locally, and maintains that providers of architectural and engineering services must be members of national associations that, in turn, require EU citizenship. The STRI scores for both architecture and engineering services range from less than 0.2 (France, Germany, Netherlands, and Sweden) to above 0.4 (Poland), which suggests fewer or less intense restrictions on trade in these services among countries with larger architecture and engineering services markets.[12]

2.2       Legal and Accounting Services

International trade in legal services typically involves foreign lawyers providing legal services in their home country law, international law, or third country law while trade in accounting services typically involves foreign accountants or auditors providing accounting and auditing services (though many large accounting firms also provide consulting services). It is reported that supplying services via the establishment of a commercial presence (mode 3) and via the movement of people (mode 4) are the preferred modes of delivery in foreign markets.[13]

Again, table A1 provides summary statistics on cross-border trade and foreign affiliate transactions in legal and accounting services. In 2014, cross-border imports of legal and accounting services combined exceeded inbound foreign affiliate sales in 4 of the 6 countries examined (Austria, France, Greece, and Netherlands). However, inbound foreign affiliate sales grew quickly in several smaller economies in 2013 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefmuyTjMCPf gaiuaajugybabaOpaaaG+apeGaa83eGaaa@3C42@ 14, with FAS growth in Austria (50.0 percent), Czech Republic (33.2 percent), and Poland (105.8 percent) all exceeding growth in cross-border imports by a large margin.[14] The trend is not uniform though, as France, Germany and Greece all saw large declines in inbound foreign affiliate sales while their cross-border imports of legal and accounting services grew.[15]

Policies related to the foreign provision of legal services tend to be the most restrictive among professional services, while the provision of accounting services tends to be less heavily restricted.[16] The STRI scores for legal services and accounting services are categorized into the same five groups as architectural and engineering services. Also like architectural and engineering services, the most prevalent are restrictions to movement of people and restrictions on foreign entry. Notably, in the former category, nationality and/or residency requirements to practice law or provide accounting services, along with lack of recognition of foreign qualifications, are significant impediments and affect all modes of trade.[17] In this same category, quotas and labor market tests are also prevalent and restrict or limit foreign attorneys or accountants from traveling to host countries on a temporary basis. Other prevalent restrictions in this category include local qualifications for a majority of the board of directors/equity partners/managers and limits on commercial association between locally and non-locally licensed attorneys.[18] Restrictions in other categories relate to the fee structure services providers are allowed to charge and minimum capital requirements for the establishment of an affiliate.

Table A3 presents the STRI scores for each country examined here, along with a brief summary of their most restrictive measures as applied to the legal and accounting services sectors. In one case (Poland) where trade in legal services is classified as completely restricted, ownership is restricted to locally-licensed attorneys for both domestic and international law, and boards of directors and managers must also be locally licensed attorneys. Additionally, foreign providers must completely re-do their university degree, practice requirement and exam in Poland to qualify if their home country does not have a reciprocity agreement with Poland. Less restrictive countries, like Netherlands, may still have other restrictions such as limits on foreign equity or require managers and boards of directors to be licensed to practice law. The practice of host country law is usually regulated more heavily than international law. In the countries covered here, accounting services tends to have lower STRI scores (indicative of being less heavily regulated) than legal services, with fewer restrictions on foreign equity or licensing (though auditing services typically has more stringent requirements).

3         Modeling Framework

In this section, we derive an economic model of foreign affiliate sales and cross-border exports of services, based on a partial equilibrium version of the Helpman, Melitz, and Yeaple (2004) framework.[19] Then we derive formulas for calculating the impact of reducing the fixed costs of the different modes of trade in these services.

The model focuses on a single national market, the destination country, and a single category of services. Firms provide services that are differentiated from the services provided by other firms within their category, and they engage in monopolistic competition. The parameter ε MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqyTdugaaa@37B3@  is the constant elasticity of substitution among different varieties of services within the category.

3.1       Firm Costs

Labor is the only factor of production, following Helpman, Melitz, and Yeaple (2004). The wage in the destination market is w MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4Daaaa@3708@ , and the wage in exporting country c MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4yaaaa@36F4@  is w c MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4Da8aadaWgaaWcbaWdbiaadogaa8aabeaaaaa@384A@ . Providers of the services vary in their productivity. The unit labor requirement of each firm, a MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamyyaaaa@36F2@ , is drawn from a distribution with cumulative distribution function G( a ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4ramaabmaapaqaa8qacaWGHbaacaGLOaGaayzkaaaaaa@3966@ . As in Helpman, Melitz, and Yeaple (2004), we assume that the productivity of individual firms has a Pareto distribution with shape parameter k>ε1>0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4Aaiabg6da+iabew7aLjabgkHiTiaaigdacqGH+aGpcaaIWaaa aa@3D15@ . There are n MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOBaaaa@36FF@  firms headquartered in the destination country, and n c MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOBa8aadaWgaaWcbaWdbiaadogaa8aabeaaaaa@3841@  firms headquartered in country c MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4yaaaa@36F4@ .

Beyond the unit labor requirement, the model includes three additional costs of serving a national market. The first is a variable cost of cross-border exports from country c MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4yaaaa@36F4@  to the destination country, τ c MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqiXdq3damaaBaaaleaapeGaam4yaaWdaeqaaaaa@3913@ , that has an iceberg form. (It is an ad valorem trade cost that increases the marginal cost of supplying the destination country from country c MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4yaaaa@36F4@  by ( τ c 1 )×100 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape WaaeWaa8aabaWdbiabes8a09aadaWgaaWcbaWdbiaadogaa8aabeaa k8qacqGHsislcaaIXaaacaGLOaGaayzkaaGaey41aqRaaGymaiaaic dacaaIWaaaaa@40C3@  percent.) The second is a fixed cost of exporting from country c MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4yaaaa@36F4@  to the destination country, equal to f Xc MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOza8aadaWgaaWcbaWdbiaadIfacaWGJbaapaqabaaaaa@3916@ . The third is a fixed cost incurred when a firm from country c MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4yaaaa@36F4@  establishes a foreign affiliate in the destination country. Following Helpman, Melitz, and Yeaple (2004), we represent this third cost in terms of the incremental fixed cost of foreign affiliate sales relative to cross-border exports, equal to f Ac MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOza8aadaWgaaWcbaWdbiaadgeacaWGJbaapaqabaaaaa@38FF@ .[20] The model also includes fixed costs of producing in the destination country to supply the domestic market, equal to f D MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOza8aadaWgaaWcbaWdbiaadseaa8aabeaaaaa@381A@ .

3.2       Firm Profits

The next step in the derivation of the model is to examine the firm’s profitability from alternative modes of supplying the services to the destination country. Profits are the difference between revenue and costs of supply. For example, equation (1) represents the revenue from a domestic firm with unit labor requirement a MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamyyaaaa@36F2@  serving the destination country.

R D ( a )= β E P ε1 p ( a ) 1ε MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOua8aadaWgaaWcbaWdbiaadseaa8aabeaak8qadaqadaWdaeaa peGaamyyaaGaayjkaiaawMcaaiabg2da9iaabckacqaHYoGycaqGGc GaamyraiaadcfapaWaaWbaaSqabeaapeGaeqyTduMaeyOeI0IaaGym aaaakiaadchadaqadaWdaeaapeGaamyyaaGaayjkaiaawMcaa8aada ahaaWcbeqaa8qacaaIXaGaeyOeI0IaeqyTdugaaaaa@4BFD@      (1)

Following the notation in Helpman, Melitz, and Yeaple (2004), E MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamyraaaa@36D6@  represents aggregate expenditures on all commodities in the destination country, β MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqOSdigaaa@37AD@  is the constant expenditure share on the services category out of aggregate expenditures, P MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamiuaaaa@36E1@  is a CES price index for the services category in the destination country, and p( a ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamiCamaabmaapaqaa8qacaWGHbaacaGLOaGaayzkaaaaaa@398F@  is the producer price of a firm with unit labor requirement a MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamyyaaaa@36F2@ .[21] Equation (2) is the marginal cost of supplying the service in the destination country.

mc( a )=wa MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamyBaiaadogadaqadaWdaeaapeGaamyyaaGaayjkaiaawMcaaiab g2da9iaadEhacaWGHbaaaa@3D5C@      (2)

The assumptions of CES demand and monopolistic competition in the model imply that the producer price is set as a constant mark-up over marginal costs.

p( a )=( ε ε1 ) wa MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamiCamaabmaapaqaa8qacaWGHbaacaGLOaGaayzkaaGaeyypa0Za aeWaa8aabaWdbmaalaaapaqaa8qacqaH1oqza8aabaWdbiabew7aLj abgkHiTiaaigdaaaaacaGLOaGaayzkaaGaaeiOaiaadEhacaWGHbaa aa@4486@     (3)

Combining these elements, equation (4) represents the profits of the firm from serving its domestic market.

π D ( a )= 1 ε  β E P ε1 [ ( ε ε1 )a w ] 1ε f D MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqiWda3damaaBaaaleaapeGaamiraaWdaeqaaOWdbmaabmaapaqa a8qacaWGHbaacaGLOaGaayzkaaGaeyypa0ZaaSaaa8aabaWdbiaaig daa8aabaWdbiabew7aLbaacaqGGcGaeqOSdiMaaeiOaiaadweacaWG qbWdamaaCaaaleqabaWdbiabew7aLjabgkHiTiaaigdaaaGcdaWada WdaeaapeWaaeWaa8aabaWdbmaalaaapaqaa8qacqaH1oqza8aabaWd biabew7aLjabgkHiTiaaigdaaaaacaGLOaGaayzkaaGaamyyaiaabc kacaWG3baacaGLBbGaayzxaaWdamaaCaaaleqabaWdbiaaigdacqGH sislcqaH1oqzaaGccqGHsislcaWGMbWdamaaBaaaleaapeGaamiraa Wdaeqaaaaa@5B17@      (4)

By a similar derivation, equation (5) is the profits of a country c MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4yaaaa@36F4@  firm that exports its service across the border into the destination country.

π Xc ( a )= 1 ε  β E  P  ε1 [ ( ε ε1 )a  w c   τ c ] 1ε f Xc MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqiWda3damaaBaaaleaapeGaamiwaiaadogaa8aabeaak8qadaqa daWdaeaapeGaamyyaaGaayjkaiaawMcaaiabg2da9maalaaapaqaa8 qacaaIXaaapaqaa8qacqaH1oqzaaGaaeiOaiabek7aIjaabckacaWG fbGaaeiOaiaadcfapaWaaWbaaSqabeaapeGaaeiOaiabew7aLjabgk HiTiaaigdaaaGcdaWadaWdaeaapeWaaeWaa8aabaWdbmaalaaapaqa a8qacqaH1oqza8aabaWdbiabew7aLjabgkHiTiaaigdaaaaacaGLOa GaayzkaaGaamyyaiaabckacaWG3bWdamaaBaaaleaapeGaam4yaaWd aeqaaOWdbiaabckacqaHepaDpaWaaSbaaSqaa8qacaWGJbaapaqaba aak8qacaGLBbGaayzxaaWdamaaCaaaleqabaWdbiaaigdacqGHsisl cqaH1oqzaaGccqGHsislcaWGMbWdamaaBaaaleaapeGaamiwaiaado gaa8aabeaaaaa@64F5@      (5)

Equation (6) is the incremental profits of a country c MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4yaaaa@36F4@  firm that serves the market in the destination country through foreign affiliate sales rather than cross-border exports.

π Ac ( a )= 1 ε  β E  P  ε1 [ ( ε ε1 )a w ] 1ε (   f Xc + f Ac   ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqiWda3damaaBaaaleaapeGaamyqaiaadogaa8aabeaak8qadaqa daWdaeaapeGaamyyaaGaayjkaiaawMcaaiabg2da9maalaaapaqaa8 qacaaIXaaapaqaa8qacqaH1oqzaaGaaeiOaiabek7aIjaabckacaWG fbGaaeiOaiaadcfapaWaaWbaaSqabeaapeGaaeiOaiabew7aLjabgk HiTiaaigdaaaGcdaWadaWdaeaapeWaaeWaa8aabaWdbmaalaaapaqa a8qacqaH1oqza8aabaWdbiabew7aLjabgkHiTiaaigdaaaaacaGLOa GaayzkaaGaamyyaiaabckacaWG3baacaGLBbGaayzxaaWdamaaCaaa leqabaWdbiaaigdacqGHsislcqaH1oqzaaGccqGHsisldaqadaWdae aapeGaaeiOaiaadAgapaWaaSbaaSqaa8qacaWGybGaam4yaaWdaeqa aOWdbiabgUcaRiaadAgapaWaaSbaaSqaa8qacaWGbbGaam4yaaWdae qaaOWdbiaabckaaiaawIcacaGLPaaaaaa@6735@      (6)

 

3.3       Productivity Cutoffs for Different Modes of Supply

A firm’s most profitable mode of supply depends on the firm’s unit labor requirement. All domestic firms with unit labor requirements below a D MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamyya8aadaWgaaWcbaWdbiaadseaa8aabeaaaaa@3815@  sell in the destination country. The cutoff level for domestic sales is implicitly defined in equation (7).

π D ( a D )=0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqiWda3damaaBaaaleaapeGaamiraaWdaeqaaOWdbmaabmaapaqa a8qacaWGHbWdamaaBaaaleaapeGaamiraaWdaeqaaaGcpeGaayjkai aawMcaaiabg2da9iaaicdaaaa@3E91@      (7)

In addition, country c MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4yaaaa@36F4@  firms with unit labor requirements below a cutoff level a Xc MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamyya8aadaWgaaWcbaWdbiaadIfacaWGJbaapaqabaaaaa@3911@  also supply the destination market, either through cross-border exports or through foreign affiliate sales. Firms from country c MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4yaaaa@36F4@  with unit labor requirements below the even lower cutoff a Ac MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamyya8aadaWgaaWcbaWdbiaadgeacaWGJbaapaqabaaaaa@38FA@  serve the market by establishing a foreign affiliate in the destination country. Firms from country c MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4yaaaa@36F4@  with unit labor requirements below a cutoff level a Xc MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamyya8aadaWgaaWcbaWdbiaadIfacaWGJbaapaqabaaaaa@3911@  but above a Ac MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamyya8aadaWgaaWcbaWdbiaadgeacaWGJbaapaqabaaaaa@38FA@  serve the destination country through cross-border exports. These cutoff levels are implicitly defined by the condition for zero profits in cross-border exports (in equation (8)) and for zero incremental profits for foreign affiliate sales relative to cross-border exports (in equation (9)).

π Xc ( a Xc )=0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqiWda3damaaBaaaleaapeGaamiwaiaadogaa8aabeaak8qadaqa daWdaeaapeGaamyya8aadaWgaaWcbaWdbiaadIfacaWGJbaapaqaba aak8qacaGLOaGaayzkaaGaeyypa0JaaGimaaaa@4089@      (8)

π Ac ( a Ac ) π Xc ( a Xc )=0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqiWda3damaaBaaaleaapeGaamyqaiaadogaa8aabeaak8qadaqa daWdaeaapeGaamyya8aadaWgaaWcbaWdbiaadgeacaWGJbaapaqaba aak8qacaGLOaGaayzkaaGaeyOeI0IaeqiWda3damaaBaaaleaapeGa amiwaiaadogaa8aabeaak8qadaqadaWdaeaapeGaamyya8aadaWgaa WcbaWdbiaadIfacaWGJbaapaqabaaak8qacaGLOaGaayzkaaGaeyyp a0JaaGimaaaa@4A05@      (9)

Following Helpman, Melitz, and Yeaple (2004) and the related literature, we assume that a Xc MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamyya8aadaWgaaWcbaWdbiaadIfacaWGJbaapaqabaaaaa@3911@  is greater than a Ac MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamyya8aadaWgaaWcbaWdbiaadgeacaWGJbaapaqabaaaaa@38FA@ . The most productive firms establish foreign affiliates, while the least productive country c MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4yaaaa@36F4@  firms do not serve the destination country at all.

Equations (4) through (9) imply that the relative cutoff levels depend on the relative magnitude of the different types of costs.

h Xc a Xc a D = ( f Xc f D ) 1 1ε w w c   τ c MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamiAa8aadaWgaaWcbaWdbiaadIfacaWGJbaapaqabaGcpeGaeyyy IO7aaSaaa8aabaWdbiaadggapaWaaSbaaSqaa8qacaWGybGaam4yaa WdaeqaaaGcbaWdbiaadggapaWaaSbaaSqaa8qacaWGebaapaqabaaa aOWdbiabg2da9maabmaapaqaa8qadaWcaaWdaeaapeGaamOza8aada WgaaWcbaWdbiaadIfacaWGJbaapaqabaaakeaapeGaamOza8aadaWg aaWcbaWdbiaadseaa8aabeaaaaaak8qacaGLOaGaayzkaaWdamaaCa aaleqabaWdbmaalaaapaqaa8qacaaIXaaapaqaa8qacaaIXaGaeyOe I0IaeqyTdugaaaaakmaalaaapaqaa8qacaWG3baapaqaa8qacaWG3b WdamaaBaaaleaapeGaam4yaaWdaeqaaOWdbiaabckacqaHepaDpaWa aSbaaSqaa8qacaWGJbaapaqabaaaaaaa@550F@      (10)

h Ac a Ac a D = ( f Ac f D ) 1 1ε w  ( w 1ε ( w c   τ c ) 1ε ) 1 ε1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamiAa8aadaWgaaWcbaWdbiaadgeacaWGJbaapaqabaGcpeGaeyyy IO7aaSaaa8aabaWdbiaadggapaWaaSbaaSqaa8qacaWGbbGaam4yaa WdaeqaaaGcbaWdbiaadggapaWaaSbaaSqaa8qacaWGebaapaqabaaa aOWdbiabg2da9maabmaapaqaa8qadaWcaaWdaeaapeGaamOza8aada WgaaWcbaWdbiaadgeacaWGJbaapaqabaaakeaapeGaamOza8aadaWg aaWcbaWdbiaadseaa8aabeaaaaaak8qacaGLOaGaayzkaaWdamaaCa aaleqabaWdbmaalaaapaqaa8qacaaIXaaapaqaa8qacaaIXaGaeyOe I0IaeqyTdugaaaaakiaadEhacaqGGcWaaeWaa8aabaWdbiaadEhapa WaaWbaaSqabeaapeGaaGymaiabgkHiTiabew7aLbaakiabgkHiTmaa bmaapaqaa8qacaWG3bWdamaaBaaaleaapeGaam4yaaWdaeqaaOWdbi aabckacqaHepaDpaWaaSbaaSqaa8qacaWGJbaapaqabaaak8qacaGL OaGaayzkaaWdamaaCaaaleqabaWdbiaaigdacqGHsislcqaH1oqzaa aakiaawIcacaGLPaaapaWaaWbaaSqabeaapeWaaSaaa8aabaWdbiaa igdaa8aabaWdbiabew7aLjabgkHiTiaaigdaaaaaaaaa@66E0@      (11)

3.4       Supply by Mode and the Price Index

Equation (12) represents the equilibrium quantity of foreign affiliate sales of country c MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4yaaaa@36F4@  firms ( q Ac MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamyCa8aadaWgaaWcbaWdbiaadgeacaWGJbaapaqabaaaaa@390A@  ) associated with the cutoff unit labor requirements implicitly defined by equations (7), and equation (13) represents the equilibrium value of these foreign affiliate sales ( v Ac MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamODa8aadaWgaaWcbaWdbiaadgeacaWGJbaapaqabaaaaa@390F@  ).

q Ac = n c  β E  P  ε1 ( ( ε ε1 )w ) ε 0 a Ac a ε  dG( a ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamyCa8aadaWgaaWcbaWdbiaadgeacaWGJbaapaqabaGcpeGaeyyp a0JaamOBa8aadaWgaaWcbaWdbiaadogaa8aabeaak8qacaqGGcGaeq OSdiMaaeiOaiaadweacaqGGcGaamiua8aadaahaaWcbeqaa8qacaqG GcGaeqyTduMaeyOeI0IaaGymaaaakmaabmaapaqaa8qadaqadaWdae aapeWaaSaaa8aabaWdbiabew7aLbWdaeaapeGaeqyTduMaeyOeI0Ia aGymaaaaaiaawIcacaGLPaaacaWG3baacaGLOaGaayzkaaWdamaaCa aaleqabaWdbiabgkHiTiabew7aLbaakmaawahabeWcpaqaa8qacaaI Waaapaqaa8qacaWGHbWdamaaBaaameaapeGaamyqaiaadogaa8aabe aaa0qaa8qacqGHRiI8aaGccaWGHbWdamaaCaaaleqabaWdbiabgkHi Tiabew7aLbaakiaabckacaWGKbGaam4ramaabmaapaqaa8qacaWGHb aacaGLOaGaayzkaaaaaa@640C@      (12)

v Ac = n c  β E  P  ε1 ( ( ε ε1 )w ) 1ε 0 a Ac a 1ε  dG( a ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamODa8aadaWgaaWcbaWdbiaadgeacaWGJbaapaqabaGcpeGaeyyp a0JaamOBa8aadaWgaaWcbaWdbiaadogaa8aabeaak8qacaqGGcGaeq OSdiMaaeiOaiaadweacaqGGcGaamiua8aadaahaaWcbeqaa8qacaqG GcGaeqyTduMaeyOeI0IaaGymaaaakmaabmaapaqaa8qadaqadaWdae aapeWaaSaaa8aabaWdbiabew7aLbWdaeaapeGaeqyTduMaeyOeI0Ia aGymaaaaaiaawIcacaGLPaaacaWG3baacaGLOaGaayzkaaWdamaaCa aaleqabaWdbiaaigdacqGHsislcqaH1oqzaaGcdaGfWbqabSWdaeaa peGaaGimaaWdaeaapeGaamyya8aadaWgaaadbaWdbiaadgeacaWGJb aapaqabaaaneaapeGaey4kIipaaOGaamyya8aadaahaaWcbeqaa8qa caaIXaGaeyOeI0IaeqyTdugaaOGaaeiOaiaadsgacaWGhbWaaeWaa8 aabaWdbiaadggaaiaawIcacaGLPaaaaaa@6587@      (13)

Similarly, equations (14) and (15) represent the equilibrium values of cross-border exports of country c MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4yaaaa@36F4@  ( v Xc MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamODa8aadaWgaaWcbaWdbiaadIfacaWGJbaapaqabaaaaa@3926@  ) and domestic shipments in the destination country ( v D MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamODa8aadaWgaaWcbaWdbiaadseaa8aabeaaaaa@382A@  ).

v Xc = n c  β E  P  ε1 ( ( ε ε1 ) w c   τ c ) 1ε a Ac a Xc a 1ε  dG( a ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamODa8aadaWgaaWcbaWdbiaadIfacaWGJbaapaqabaGcpeGaeyyp a0JaamOBa8aadaWgaaWcbaWdbiaadogaa8aabeaak8qacaqGGcGaeq OSdiMaaeiOaiaadweacaqGGcGaamiua8aadaahaaWcbeqaa8qacaqG GcGaeqyTduMaeyOeI0IaaGymaaaakmaabmaapaqaa8qadaqadaWdae aapeWaaSaaa8aabaWdbiabew7aLbWdaeaapeGaeqyTduMaeyOeI0Ia aGymaaaaaiaawIcacaGLPaaacaWG3bWdamaaBaaaleaapeGaam4yaa WdaeqaaOWdbiaabckacqaHepaDpaWaaSbaaSqaa8qacaWGJbaapaqa baaak8qacaGLOaGaayzkaaWdamaaCaaaleqabaWdbiaaigdacqGHsi slcqaH1oqzaaGcdaGfWbqabSWdaeaapeGaamyya8aadaWgaaadbaWd biaadgeacaWGJbaapaqabaaaleaapeGaamyya8aadaWgaaadbaWdbi aadIfacaWGJbaapaqabaaaneaapeGaey4kIipaaOGaamyya8aadaah aaWcbeqaa8qacaaIXaGaeyOeI0IaeqyTdugaaOGaaeiOaiaadsgaca WGhbWaaeWaa8aabaWdbiaadggaaiaawIcacaGLPaaaaaa@6D86@      (14)

v D =n β E  P  ε1 ( ( ε ε1 )w ) 1ε 0 a D a 1ε  dG( a ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamODa8aadaWgaaWcbaWdbiaadseaa8aabeaak8qacqGH9aqpcaWG UbGaaeiOaiabek7aIjaabckacaWGfbGaaeiOaiaadcfapaWaaWbaaS qabeaapeGaaeiOaiabew7aLjabgkHiTiaaigdaaaGcdaqadaWdaeaa peWaaeWaa8aabaWdbmaalaaapaqaa8qacqaH1oqza8aabaWdbiabew 7aLjabgkHiTiaaigdaaaaacaGLOaGaayzkaaGaam4DaaGaayjkaiaa wMcaa8aadaahaaWcbeqaa8qacaaIXaGaeyOeI0IaeqyTdugaaOWaay bCaeqal8aabaWdbiaaicdaa8aabaWdbiaadggapaWaaSbaaWqaa8qa caWGebaapaqabaaaneaapeGaey4kIipaaOGaamyya8aadaahaaWcbe qaa8qacaaIXaGaeyOeI0IaeqyTdugaaOGaaeiOaiaadsgacaWGhbWa aeWaa8aabaWdbiaadggaaiaawIcacaGLPaaaaaa@6261@      (15)

Equation (16) is the CES price index for the category of services in the destination country.

P=( ε ε1 ) [ n  ( w ) 1ε 0 a D a 1ε  dG( a )+ c ( n c ( w c   τ c ) 1ε a Ac a Xc a 1ε  dG( a ) )+ c ( n c ( w ) 1ε 0 a Ac a 1ε  dG( a ) ) ] 1 1ε MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamiuaiabg2da9maabmaapaqaa8qadaWcaaWdaeaapeGaeqyTduga paqaa8qacqaH1oqzcqGHsislcaaIXaaaaaGaayjkaiaawMcaamaadm aapaqaa8qacaWGUbGaaeiOamaabmaapaqaa8qacaWG3baacaGLOaGa ayzkaaWdamaaCaaaleqabaWdbiaaigdacqGHsislcqaH1oqzaaGcda GfWbqabSWdaeaapeGaaGimaaWdaeaapeGaamyya8aadaWgaaadbaWd biaadseaa8aabeaaa0qaa8qacqGHRiI8aaGccaWGHbWdamaaCaaale qabaWdbiaaigdacqGHsislcqaH1oqzaaGccaqGGcGaamizaiaadEea daqadaWdaeaapeGaamyyaaGaayjkaiaawMcaaiabgUcaRmaawafabe Wcpaqaa8qacaWGJbaabeqdpaqaa8qacqGHris5aaGcdaqadaWdaeaa peGaamOBa8aadaWgaaWcbaWdbiaadogaa8aabeaak8qadaqadaWdae aapeGaam4Da8aadaWgaaWcbaWdbiaadogaa8aabeaak8qacaqGGcGa eqiXdq3damaaBaaaleaapeGaam4yaaWdaeqaaaGcpeGaayjkaiaawM caa8aadaahaaWcbeqaa8qacaaIXaGaeyOeI0IaeqyTdugaaOWaaybC aeqal8aabaWdbiaadggapaWaaSbaaWqaa8qacaWGbbGaam4yaaWdae qaaaWcbaWdbiaadggapaWaaSbaaWqaa8qacaWGybGaam4yaaWdaeqa aaqdbaWdbiabgUIiYdaakiaadggapaWaaWbaaSqabeaapeGaaGymai abgkHiTiabew7aLbaakiaabckacaWGKbGaam4ramaabmaapaqaa8qa caWGHbaacaGLOaGaayzkaaaacaGLOaGaayzkaaGaey4kaSYaaybuae qal8aabaWdbiaadogaaeqan8aabaWdbiabggHiLdaakmaabmaapaqa a8qacaWGUbWdamaaBaaaleaapeGaam4yaaWdaeqaaOWdbmaabmaapa qaa8qacaWG3baacaGLOaGaayzkaaWdamaaCaaaleqabaWdbiaaigda cqGHsislcqaH1oqzaaGcdaGfWbqabSWdaeaapeGaaGimaaWdaeaape Gaamyya8aadaWgaaadbaWdbiaadgeacaWGJbaapaqabaaaneaapeGa ey4kIipaaOGaamyya8aadaahaaWcbeqaa8qacaaIXaGaeyOeI0Iaeq yTdugaaOGaaeiOaiaadsgacaWGhbWaaeWaa8aabaWdbiaadggaaiaa wIcacaGLPaaaaiaawIcacaGLPaaaaiaawUfacaGLDbaapaWaaWbaaS qabeaapeWaaSaaa8aabaWdbiaaigdaa8aabaWdbiaaigdacqGHsisl cqaH1oqzaaaaaaaa@A30D@      (16)

Our assumption that the productivity of individual firms has a Pareto distribution with shape parameter k MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4Aaaaa@36FC@  allows us to rewrite equations (13) through (16) in terms of the cutoff levels a D MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamyya8aadaWgaaWcbaWdbiaadseaa8aabeaaaaa@3815@ , a Xc MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamyya8aadaWgaaWcbaWdbiaadIfacaWGJbaapaqabaaaaa@3911@ , and a Ac MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamyya8aadaWgaaWcbaWdbiaadgeacaWGJbaapaqabaaaaa@38FA@ .

v Ac = n c  β E  P  ε1 ( ( ε ε1 )w ) 1ε ( k k( ε1 ) ) ( a Ac ) k( ε1 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamODa8aadaWgaaWcbaWdbiaadgeacaWGJbaapaqabaGcpeGaeyyp a0JaamOBa8aadaWgaaWcbaWdbiaadogaa8aabeaak8qacaqGGcGaeq OSdiMaaeiOaiaadweacaqGGcGaamiua8aadaahaaWcbeqaa8qacaqG GcGaeqyTduMaeyOeI0IaaGymaaaakmaabmaapaqaa8qadaqadaWdae aapeWaaSaaa8aabaWdbiabew7aLbWdaeaapeGaeqyTduMaeyOeI0Ia aGymaaaaaiaawIcacaGLPaaacaWG3baacaGLOaGaayzkaaWdamaaCa aaleqabaWdbiaaigdacqGHsislcqaH1oqzaaGcdaqadaWdaeaapeWa aSaaa8aabaWdbiaadUgaa8aabaWdbiaadUgacqGHsisldaqadaWdae aapeGaeqyTduMaeyOeI0IaaGymaaGaayjkaiaawMcaaaaaaiaawIca caGLPaaadaqadaWdaeaapeGaamyya8aadaWgaaWcbaWdbiaadgeaca WGJbaapaqabaaak8qacaGLOaGaayzkaaWdamaaCaaaleqabaWdbiaa dUgacqGHsisldaqadaWdaeaapeGaeqyTduMaeyOeI0IaaGymaaGaay jkaiaawMcaaaaaaaa@6AAE@      (17)

v Xc = n c  β E  P  ε1 ( ( ε ε1 )  w c   τ c ) 1ε ( k k( ε1 ) )[ ( a Xc ) k( ε1 ) ( a Ac ) k( ε1 ) ] MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamODa8aadaWgaaWcbaWdbiaadIfacaWGJbaapaqabaGcpeGaeyyp a0JaamOBa8aadaWgaaWcbaWdbiaadogaa8aabeaak8qacaqGGcGaeq OSdiMaaeiOaiaadweacaqGGcGaamiua8aadaahaaWcbeqaa8qacaqG GcGaeqyTduMaeyOeI0IaaGymaaaakmaabmaapaqaa8qadaqadaWdae aapeWaaSaaa8aabaWdbiabew7aLbWdaeaapeGaeqyTduMaeyOeI0Ia aGymaaaaaiaawIcacaGLPaaacaqGGcGaam4Da8aadaWgaaWcbaWdbi aadogaa8aabeaak8qacaqGGcGaeqiXdq3damaaBaaaleaapeGaam4y aaWdaeqaaaGcpeGaayjkaiaawMcaa8aadaahaaWcbeqaa8qacaaIXa GaeyOeI0IaeqyTdugaaOWaaeWaa8aabaWdbmaalaaapaqaa8qacaWG Rbaapaqaa8qacaWGRbGaeyOeI0YaaeWaa8aabaWdbiabew7aLjabgk HiTiaaigdaaiaawIcacaGLPaaaaaaacaGLOaGaayzkaaWaamWaa8aa baWdbmaabmaapaqaa8qacaWGHbWdamaaBaaaleaapeGaamiwaiaado gaa8aabeaaaOWdbiaawIcacaGLPaaapaWaaWbaaSqabeaapeGaam4A aiabgkHiTmaabmaapaqaa8qacqaH1oqzcqGHsislcaaIXaaacaGLOa GaayzkaaaaaOGaeyOeI0YaaeWaa8aabaWdbiaadggapaWaaSbaaSqa a8qacaWGbbGaam4yaaWdaeqaaaGcpeGaayjkaiaawMcaa8aadaahaa Wcbeqaa8qacaWGRbGaeyOeI0YaaeWaa8aabaWdbiabew7aLjabgkHi TiaaigdaaiaawIcacaGLPaaaaaaakiaawUfacaGLDbaaaaa@8081@      (18)

v D =n β E  P  ε1 ( ( ε ε1 )w ) 1ε ( k k( ε1 ) ) ( a D ) k( ε1 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamODa8aadaWgaaWcbaWdbiaadseaa8aabeaak8qacqGH9aqpcaWG UbGaaeiOaiabek7aIjaabckacaWGfbGaaeiOaiaadcfapaWaaWbaaS qabeaapeGaaeiOaiabew7aLjabgkHiTiaaigdaaaGcdaqadaWdaeaa peWaaeWaa8aabaWdbmaalaaapaqaa8qacqaH1oqza8aabaWdbiabew 7aLjabgkHiTiaaigdaaaaacaGLOaGaayzkaaGaam4DaaGaayjkaiaa wMcaa8aadaahaaWcbeqaa8qacaaIXaGaeyOeI0IaeqyTdugaaOWaae Waa8aabaWdbmaalaaapaqaa8qacaWGRbaapaqaa8qacaWGRbGaeyOe I0YaaeWaa8aabaWdbiabew7aLjabgkHiTiaaigdaaiaawIcacaGLPa aaaaaacaGLOaGaayzkaaWaaeWaa8aabaWdbiaadggapaWaaSbaaSqa a8qacaWGebaapaqabaaak8qacaGLOaGaayzkaaWdamaaCaaaleqaba WdbiaadUgacqGHsisldaqadaWdaeaapeGaeqyTduMaeyOeI0IaaGym aaGaayjkaiaawMcaaaaaaaa@6788@      (19)

P=( ε ε1 ) ( k k( ε1 ) ) 1 1ε [ n  ( w ) 1ε ( a D ) k( ε1 ) + c ( n c ( w c   τ c ) 1ε ( ( a Xc ) k( ε1 ) ( a Ac ) k( ε1 ) ) )+ c ( n c ( w ) 1ε ( a Ac ) k( ε1 ) ) ] 1 1ε MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamiuaiabg2da9maabmaapaqaa8qadaWcaaWdaeaapeGaeqyTduga paqaa8qacqaH1oqzcqGHsislcaaIXaaaaaGaayjkaiaawMcaamaabm aapaqaa8qadaWcaaWdaeaapeGaam4AaaWdaeaapeGaam4AaiabgkHi Tmaabmaapaqaa8qacqaH1oqzcqGHsislcaaIXaaacaGLOaGaayzkaa aaaaGaayjkaiaawMcaa8aadaahaaWcbeqaa8qadaWcaaWdaeaapeGa aGymaaWdaeaapeGaaGymaiabgkHiTiabew7aLbaaaaGcdaWadaWdae aapeGaamOBaiaabckadaqadaWdaeaapeGaam4DaaGaayjkaiaawMca a8aadaahaaWcbeqaa8qacaaIXaGaeyOeI0IaeqyTdugaaOWaaeWaa8 aabaWdbiaadggapaWaaSbaaSqaa8qacaWGebaapaqabaaak8qacaGL OaGaayzkaaWdamaaCaaaleqabaWdbiaadUgacqGHsisldaqadaWdae aapeGaeqyTduMaeyOeI0IaaGymaaGaayjkaiaawMcaaaaakiabgUca RmaawafabeWcpaqaa8qacaWGJbaabeqdpaqaa8qacqGHris5aaGcda qadaWdaeaapeGaamOBa8aadaWgaaWcbaWdbiaadogaa8aabeaak8qa daqadaWdaeaapeGaam4Da8aadaWgaaWcbaWdbiaadogaa8aabeaak8 qacaqGGcGaeqiXdq3damaaBaaaleaapeGaam4yaaWdaeqaaaGcpeGa ayjkaiaawMcaa8aadaahaaWcbeqaa8qacaaIXaGaeyOeI0IaeqyTdu gaaOWaaeWaa8aabaWdbmaabmaapaqaa8qacaWGHbWdamaaBaaaleaa peGaamiwaiaadogaa8aabeaaaOWdbiaawIcacaGLPaaapaWaaWbaaS qabeaapeGaam4AaiabgkHiTmaabmaapaqaa8qacqaH1oqzcqGHsisl caaIXaaacaGLOaGaayzkaaaaaOGaeyOeI0YaaeWaa8aabaWdbiaadg gapaWaaSbaaSqaa8qacaWGbbGaam4yaaWdaeqaaaGcpeGaayjkaiaa wMcaa8aadaahaaWcbeqaa8qacaWGRbGaeyOeI0YaaeWaa8aabaWdbi abew7aLjabgkHiTiaaigdaaiaawIcacaGLPaaaaaaakiaawIcacaGL PaaaaiaawIcacaGLPaaacqGHRaWkdaGfqbqabSWdaeaapeGaam4yaa qab0WdaeaapeGaeyyeIuoaaOWaaeWaa8aabaWdbiaad6gapaWaaSba aSqaa8qacaWGJbaapaqabaGcpeWaaeWaa8aabaWdbiaadEhaaiaawI cacaGLPaaapaWaaWbaaSqabeaapeGaaGymaiabgkHiTiabew7aLbaa kmaabmaapaqaa8qacaWGHbWdamaaBaaaleaapeGaamyqaiaadogaa8 aabeaaaOWdbiaawIcacaGLPaaapaWaaWbaaSqabeaapeGaam4Aaiab gkHiTmaabmaapaqaa8qacqaH1oqzcqGHsislcaaIXaaacaGLOaGaay zkaaaaaaGccaGLOaGaayzkaaaacaGLBbGaayzxaaWdamaaCaaaleqa baWdbmaalaaapaqaa8qacaaIXaaapaqaa8qacaaIXaGaeyOeI0Iaeq yTdugaaaaaaaa@B018@      (20)

We can further rewrite equations (17) through (20) in terms of the relative cutoff levels, h Xc MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamiAa8aadaWgaaWcbaWdbiaadIfacaWGJbaapaqabaaaaa@3918@  and h Ac MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamiAa8aadaWgaaWcbaWdbiaadgeacaWGJbaapaqabaaaaa@3901@ , and a common term Z MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOwaaaa@36EB@ .

v Ac = n c  Z  ( h Ac ) k( ε1 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamODa8aadaWgaaWcbaWdbiaadgeacaWGJbaapaqabaGcpeGaeyyp a0JaamOBa8aadaWgaaWcbaWdbiaadogaa8aabeaak8qacaqGGcGaam OwaiaabckadaqadaWdaeaapeGaamiAa8aadaWgaaWcbaWdbiaadgea caWGJbaapaqabaaak8qacaGLOaGaayzkaaWdamaaCaaaleqabaWdbi aadUgacqGHsisldaqadaWdaeaapeGaeqyTduMaeyOeI0IaaGymaaGa ayjkaiaawMcaaaaaaaa@4B7A@      (21)

v Xc = n c  Z ( w c   τ c w ) 1ε ( ( h Xc ) k( ε1 ) ( h Ac ) k( ε1 ) ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamODa8aadaWgaaWcbaWdbiaadIfacaWGJbaapaqabaGcpeGaeyyp a0JaamOBa8aadaWgaaWcbaWdbiaadogaa8aabeaak8qacaqGGcGaam Owamaabmaapaqaa8qadaWcaaWdaeaapeGaam4Da8aadaWgaaWcbaWd biaadogaa8aabeaak8qacaqGGcGaeqiXdq3damaaBaaaleaapeGaam 4yaaWdaeqaaaGcbaWdbiaadEhaaaaacaGLOaGaayzkaaWdamaaCaaa leqabaWdbiaaigdacqGHsislcqaH1oqzaaGcdaqadaWdaeaapeWaae Waa8aabaWdbiaadIgapaWaaSbaaSqaa8qacaWGybGaam4yaaWdaeqa aaGcpeGaayjkaiaawMcaa8aadaahaaWcbeqaa8qacaWGRbGaeyOeI0 YaaeWaa8aabaWdbiabew7aLjabgkHiTiaaigdaaiaawIcacaGLPaaa aaGccqGHsisldaqadaWdaeaapeGaamiAa8aadaWgaaWcbaWdbiaadg eacaWGJbaapaqabaaak8qacaGLOaGaayzkaaWdamaaCaaaleqabaWd biaadUgacqGHsisldaqadaWdaeaapeGaeqyTduMaeyOeI0IaaGymaa GaayjkaiaawMcaaaaaaOGaayjkaiaawMcaaaaa@6619@      (22)

v D =n Z MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamODa8aadaWgaaWcbaWdbiaadseaa8aabeaak8qacqGH9aqpcaWG UbGaaiiOaiaadQfaaaa@3C40@      (23)

Z β E [ n + c ( n c ( w c   τ c w ) 1ε ( ( h Xc ) k( ε1 ) ( h Ac ) k( ε1 ) ) )+ c ( n c ( h Ac ) k( ε1 ) ) ] 1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOwaiabggMi6kaabckacqaHYoGycaqGGcGaamyramaadmaapaqa a8qacaWGUbGaaeiOaiabgUcaRmaawafabeWcpaqaa8qacaWGJbaabe qdpaqaa8qacqGHris5aaGcdaqadaWdaeaapeGaamOBa8aadaWgaaWc baWdbiaadogaa8aabeaak8qadaqadaWdaeaapeWaaSaaa8aabaWdbi aadEhapaWaaSbaaSqaa8qacaWGJbaapaqabaGcpeGaaeiOaiabes8a 09aadaWgaaWcbaWdbiaadogaa8aabeaaaOqaa8qacaWG3baaaaGaay jkaiaawMcaa8aadaahaaWcbeqaa8qacaaIXaGaeyOeI0IaeqyTduga aOWaaeWaa8aabaWdbmaabmaapaqaa8qacaWGObWdamaaBaaaleaape Gaamiwaiaadogaa8aabeaaaOWdbiaawIcacaGLPaaapaWaaWbaaSqa beaapeGaam4AaiabgkHiTmaabmaapaqaa8qacqaH1oqzcqGHsislca aIXaaacaGLOaGaayzkaaaaaOGaeyOeI0YaaeWaa8aabaWdbiaadIga paWaaSbaaSqaa8qacaWGbbGaam4yaaWdaeqaaaGcpeGaayjkaiaawM caa8aadaahaaWcbeqaa8qacaWGRbGaeyOeI0YaaeWaa8aabaWdbiab ew7aLjabgkHiTiaaigdaaiaawIcacaGLPaaaaaaakiaawIcacaGLPa aaaiaawIcacaGLPaaacqGHRaWkdaGfqbqabSWdaeaapeGaam4yaaqa b0WdaeaapeGaeyyeIuoaaOWaaeWaa8aabaWdbiaad6gapaWaaSbaaS qaa8qacaWGJbaapaqabaGcpeWaaeWaa8aabaWdbiaadIgapaWaaSba aSqaa8qacaWGbbGaam4yaaWdaeqaaaGcpeGaayjkaiaawMcaa8aada ahaaWcbeqaa8qacaWGRbGaeyOeI0YaaeWaa8aabaWdbiabew7aLjab gkHiTiaaigdaaiaawIcacaGLPaaaaaaakiaawIcacaGLPaaaaiaawU facaGLDbaapaWaaWbaaSqabeaapeGaeyOeI0IaaGymaaaaaaa@874B@      (24)

3.5       Effect of Changes in Fixed Costs on Each Mode of Supply

Next, we calculate the impact of reducing the two types of fixed costs of trade on foreign affiliate sales, cross-border exports, and domestic sales in the destination country by totally differentiating equations (10), (11), (21), (22), (23), and (24), while holding aggregate expenditure levels, wages, variable trade costs, and the number of potential firm in each country fixed.[22] Equations (25) through (30) are the resulting equations in percentage changes. The notation v ^ dv v MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GabmODa8aagaqca8qacqGHHjIUdaWcaaWdaeaapeGaamizaiaadAha a8aabaWdbiaadAhaaaaaaa@3C2C@  represents the proportional, or percentage, change in variable v MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamODaaaa@3707@ .

v ^ Ac = Z ^ +( k( ε1 ) )  h ^ Ac MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GabmODa8aagaqcamaaBaaaleaapeGaamyqaiaadogaa8aabeaak8qa cqGH9aqpceWGAbWdayaajaWdbiabgUcaRmaabmaapaqaa8qacaWGRb GaeyOeI0YaaeWaa8aabaWdbiabew7aLjabgkHiTiaaigdaaiaawIca caGLPaaaaiaawIcacaGLPaaacaqGGcGabmiAa8aagaqcamaaBaaale aapeGaamyqaiaadogaa8aabeaaaaa@48D3@      (25)

v ^ Xc = Z ^ +( 1+( m Ac m Xc ) ( w c  τ w ) ε1 )( k( ε1 ) ) h ^ Xc ( m Ac m Xc ) ( w c  τ w ) ε1 ( k( ε1 ) ) h ^ Ac MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GabmODa8aagaqcamaaBaaaleaapeGaamiwaiaadogaa8aabeaak8qa cqGH9aqpceWGAbWdayaajaWdbiabgUcaRmaabmaapaqaa8qacaaIXa Gaey4kaSYaaeWaa8aabaWdbmaalaaapaqaa8qacaWGTbWdamaaBaaa leaapeGaamyqaiaadogaa8aabeaaaOqaa8qacaWGTbWdamaaBaaale aapeGaamiwaiaadogaa8aabeaaaaaak8qacaGLOaGaayzkaaWaaeWa a8aabaWdbmaalaaapaqaa8qacaWG3bWdamaaBaaaleaapeGaam4yaa WdaeqaaOWdbiaabckacqaHepaDa8aabaWdbiaadEhaaaaacaGLOaGa ayzkaaWdamaaCaaaleqabaWdbiabew7aLjabgkHiTiaaigdaaaaaki aawIcacaGLPaaadaqadaWdaeaapeGaam4AaiabgkHiTmaabmaapaqa a8qacqaH1oqzcqGHsislcaaIXaaacaGLOaGaayzkaaaacaGLOaGaay zkaaGabmiAa8aagaqcamaaBaaaleaapeGaamiwaiaadogaa8aabeaa k8qacqGHsisldaqadaWdaeaapeWaaSaaa8aabaWdbiaad2gapaWaaS baaSqaa8qacaWGbbGaam4yaaWdaeqaaaGcbaWdbiaad2gapaWaaSba aSqaa8qacaWGybGaam4yaaWdaeqaaaaaaOWdbiaawIcacaGLPaaada qadaWdaeaapeWaaSaaa8aabaWdbiaadEhapaWaaSbaaSqaa8qacaWG JbaapaqabaGcpeGaaeiOaiabes8a0bWdaeaapeGaam4DaaaaaiaawI cacaGLPaaapaWaaWbaaSqabeaapeGaeqyTduMaeyOeI0IaaGymaaaa kmaabmaapaqaa8qacaWGRbGaeyOeI0YaaeWaa8aabaWdbiabew7aLj abgkHiTiaaigdaaiaawIcacaGLPaaaaiaawIcacaGLPaaaceWGObWd ayaajaWaaSbaaSqaa8qacaWGbbGaam4yaaWdaeqaaaaa@7F85@      (26)

v ^ D = Z ^ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GabmODa8aagaqcamaaBaaaleaapeGaamiraaWdaeqaaOWdbiabg2da 9iqadQfapaGbaKaaaaa@3A58@     (27)

Z ^ =( k( ε1 ) )( c m Ac h ^ Ac c m Xc ( 1+( m Ac m Xc ) ( w c  τ w ) ε1 ) h ^ Xc + c m Xc ( m Ac m Xc ) ( w c  τ w ) ε1 h ^ Ac ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GabmOwa8aagaqca8qacqGH9aqpdaqadaWdaeaapeGaam4AaiabgkHi Tmaabmaapaqaa8qacqaH1oqzcqGHsislcaaIXaaacaGLOaGaayzkaa aacaGLOaGaayzkaaWaaeWaa8aabaWdbiabgkHiTmaawafabeWcpaqa a8qacaWGJbaabeqdpaqaa8qacqGHris5aaGccaWGTbWdamaaBaaale aapeGaamyqaiaadogaa8aabeaak8qaceWGObWdayaajaWaaSbaaSqa a8qacaWGbbGaam4yaaWdaeqaaOWdbiabgkHiTmaawafabeWcpaqaa8 qacaWGJbaabeqdpaqaa8qacqGHris5aaGccaWGTbWdamaaBaaaleaa peGaamiwaiaadogaa8aabeaak8qadaqadaWdaeaapeGaaGymaiabgU caRmaabmaapaqaa8qadaWcaaWdaeaapeGaamyBa8aadaWgaaWcbaWd biaadgeacaWGJbaapaqabaaakeaapeGaamyBa8aadaWgaaWcbaWdbi aadIfacaWGJbaapaqabaaaaaGcpeGaayjkaiaawMcaamaabmaapaqa a8qadaWcaaWdaeaapeGaam4Da8aadaWgaaWcbaWdbiaadogaa8aabe aak8qacaqGGcGaeqiXdqhapaqaa8qacaWG3baaaaGaayjkaiaawMca a8aadaahaaWcbeqaa8qacqaH1oqzcqGHsislcaaIXaaaaaGccaGLOa GaayzkaaGabmiAa8aagaqcamaaBaaaleaapeGaamiwaiaadogaa8aa beaak8qacqGHRaWkdaGfqbqabSWdaeaapeGaam4yaaqab0Wdaeaape GaeyyeIuoaaOGaamyBa8aadaWgaaWcbaWdbiaadIfacaWGJbaapaqa baGcpeWaaeWaa8aabaWdbmaalaaapaqaa8qacaWGTbWdamaaBaaale aapeGaamyqaiaadogaa8aabeaaaOqaa8qacaWGTbWdamaaBaaaleaa peGaamiwaiaadogaa8aabeaaaaaak8qacaGLOaGaayzkaaWaaeWaa8 aabaWdbmaalaaapaqaa8qacaWG3bWdamaaBaaaleaapeGaam4yaaWd aeqaaOWdbiaabckacqaHepaDa8aabaWdbiaadEhaaaaacaGLOaGaay zkaaWdamaaCaaaleqabaWdbiabew7aLjabgkHiTiaaigdaaaGcceWG ObWdayaajaWaaSbaaSqaa8qacaWGbbGaam4yaaWdaeqaaaGcpeGaay jkaiaawMcaaaaa@8D0E@      (28)

h ^ Ac =( 1 1ε ) f ^ Ac MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GabmiAa8aagaqcamaaBaaaleaapeGaamyqaiaadogaa8aabeaak8qa cqGH9aqpdaqadaWdaeaapeWaaSaaa8aabaWdbiaaigdaa8aabaWdbi aaigdacqGHsislcqaH1oqzaaaacaGLOaGaayzkaaGabmOza8aagaqc amaaBaaaleaapeGaamyqaiaadogaa8aabeaaaaa@4334@      (29)

h ^ Xc =( 1 1ε ) f ^ Xc MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GabmiAa8aagaqcamaaBaaaleaapeGaamiwaiaadogaa8aabeaak8qa cqGH9aqpdaqadaWdaeaapeWaaSaaa8aabaWdbiaaigdaa8aabaWdbi aaigdacqGHsislcqaH1oqzaaaacaGLOaGaayzkaaGabmOza8aagaqc amaaBaaaleaapeGaamiwaiaadogaa8aabeaaaaa@4362@      (30)

The variables m Ac MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamyBa8aadaWgaaWcbaWdbiaadgeacaWGJbaapaqabaaaaa@3906@  and m Xc MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamyBa8aadaWgaaWcbaWdbiaadIfacaWGJbaapaqabaaaaa@391D@  are the shares of sales by affiliates of companies from country c MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4yaaaa@36F4@  in the destination country and cross-border exports from country c MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4yaaaa@36F4@  in the destination country, respectively, as a fraction of total consumption of the service in the destination country.

Equations (31) through (34) reduce the number of equations by substitution for h ^ Ac MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GabmiAa8aagaqcamaaBaaaleaapeGaamyqaiaadogaa8aabeaaaaa@3911@  and h ^ Xc MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GabmiAa8aagaqcamaaBaaaleaapeGaamiwaiaadogaa8aabeaaaaa@3928@ .

v ^ Ac = Z ^ +( k( ε1 ) 1ε ) f ^ Ac MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GabmODa8aagaqcamaaBaaaleaapeGaamyqaiaadogaa8aabeaak8qa cqGH9aqpceWGAbWdayaajaWdbiabgUcaRmaabmaapaqaa8qadaWcaa WdaeaapeGaam4AaiabgkHiTmaabmaapaqaa8qacqaH1oqzcqGHsisl caaIXaaacaGLOaGaayzkaaaapaqaa8qacaaIXaGaeyOeI0IaeqyTdu gaaaGaayjkaiaawMcaaiqadAgapaGbaKaadaWgaaWcbaWdbiaadgea caWGJbaapaqabaaaaa@4B4B@      (31)

v ^ Xc = Z ^ +( 1+( m Ac m Xc ) ( w c  τ w ) ε1 )( k( ε1 ) 1ε ) f ^ Xc ( m Ac m Xc ) ( w c  τ w ) ε1 ( k( ε1 ) 1ε ) f ^ Ac MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GabmODa8aagaqcamaaBaaaleaapeGaamiwaiaadogaa8aabeaak8qa cqGH9aqpceWGAbWdayaajaWdbiabgUcaRmaabmaapaqaa8qacaaIXa Gaey4kaSYaaeWaa8aabaWdbmaalaaapaqaa8qacaWGTbWdamaaBaaa leaapeGaamyqaiaadogaa8aabeaaaOqaa8qacaWGTbWdamaaBaaale aapeGaamiwaiaadogaa8aabeaaaaaak8qacaGLOaGaayzkaaWaaeWa a8aabaWdbmaalaaapaqaa8qacaWG3bWdamaaBaaaleaapeGaam4yaa WdaeqaaOWdbiaabckacqaHepaDa8aabaWdbiaadEhaaaaacaGLOaGa ayzkaaWdamaaCaaaleqabaWdbiabew7aLjabgkHiTiaaigdaaaaaki aawIcacaGLPaaadaqadaWdaeaapeWaaSaaa8aabaWdbiaadUgacqGH sisldaqadaWdaeaapeGaeqyTduMaeyOeI0IaaGymaaGaayjkaiaawM caaaWdaeaapeGaaGymaiabgkHiTiabew7aLbaaaiaawIcacaGLPaaa ceWGMbWdayaajaWaaSbaaSqaa8qacaWGybGaam4yaaWdaeqaaOWdbi abgkHiTmaabmaapaqaa8qadaWcaaWdaeaapeGaamyBa8aadaWgaaWc baWdbiaadgeacaWGJbaapaqabaaakeaapeGaamyBa8aadaWgaaWcba WdbiaadIfacaWGJbaapaqabaaaaaGcpeGaayjkaiaawMcaamaabmaa paqaa8qadaWcaaWdaeaapeGaam4Da8aadaWgaaWcbaWdbiaadogaa8 aabeaak8qacaqGGcGaeqiXdqhapaqaa8qacaWG3baaaaGaayjkaiaa wMcaa8aadaahaaWcbeqaa8qacqaH1oqzcqGHsislcaaIXaaaaOWaae Waa8aabaWdbmaalaaapaqaa8qacaWGRbGaeyOeI0YaaeWaa8aabaWd biabew7aLjabgkHiTiaaigdaaiaawIcacaGLPaaaa8aabaWdbiaaig dacqGHsislcqaH1oqzaaaacaGLOaGaayzkaaGabmOza8aagaqcamaa BaaaleaapeGaamyqaiaadogaa8aabeaaaaa@86BB@      (32)

v ^ D = Z ^ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GabmODa8aagaqcamaaBaaaleaapeGaamiraaWdaeqaaOWdbiabg2da 9iqadQfapaGbaKaaaaa@3A58@     (33)

Z ^ =( k( ε1 ) 1ε )( c m Ac f ^ Ac c m Xc ( 1+( m Ac m Xc ) ( w c  τ w ) ε1 ) f ^ Xc + c m Xc ( m Ac m Xc ) ( w c  τ w ) ε1 f ^ Ac ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GabmOwa8aagaqca8qacqGH9aqpdaqadaWdaeaapeWaaSaaa8aabaWd biaadUgacqGHsisldaqadaWdaeaapeGaeqyTduMaeyOeI0IaaGymaa GaayjkaiaawMcaaaWdaeaapeGaaGymaiabgkHiTiabew7aLbaaaiaa wIcacaGLPaaadaqadaWdaeaapeGaeyOeI0Yaaybuaeqal8aabaWdbi aadogaaeqan8aabaWdbiabggHiLdaakiaad2gapaWaaSbaaSqaa8qa caWGbbGaam4yaaWdaeqaaOWdbiqadAgapaGbaKaadaWgaaWcbaWdbi aadgeacaWGJbaapaqabaGcpeGaeyOeI0Yaaybuaeqal8aabaWdbiaa dogaaeqan8aabaWdbiabggHiLdaakiaad2gapaWaaSbaaSqaa8qaca WGybGaam4yaaWdaeqaaOWdbmaabmaapaqaa8qacaaIXaGaey4kaSYa aeWaa8aabaWdbmaalaaapaqaa8qacaWGTbWdamaaBaaaleaapeGaam yqaiaadogaa8aabeaaaOqaa8qacaWGTbWdamaaBaaaleaapeGaamiw aiaadogaa8aabeaaaaaak8qacaGLOaGaayzkaaWaaeWaa8aabaWdbm aalaaapaqaa8qacaWG3bWdamaaBaaaleaapeGaam4yaaWdaeqaaOWd biaabckacqaHepaDa8aabaWdbiaadEhaaaaacaGLOaGaayzkaaWdam aaCaaaleqabaWdbiabew7aLjabgkHiTiaaigdaaaaakiaawIcacaGL PaaaceWGMbWdayaajaWaaSbaaSqaa8qacaWGybGaam4yaaWdaeqaaO WdbiabgUcaRmaawafabeWcpaqaa8qacaWGJbaabeqdpaqaa8qacqGH ris5aaGccaWGTbWdamaaBaaaleaapeGaamiwaiaadogaa8aabeaak8 qadaqadaWdaeaapeWaaSaaa8aabaWdbiaad2gapaWaaSbaaSqaa8qa caWGbbGaam4yaaWdaeqaaaGcbaWdbiaad2gapaWaaSbaaSqaa8qaca WGybGaam4yaaWdaeqaaaaaaOWdbiaawIcacaGLPaaadaqadaWdaeaa peWaaSaaa8aabaWdbiaadEhapaWaaSbaaSqaa8qacaWGJbaapaqaba GcpeGaaeiOaiabes8a0bWdaeaapeGaam4DaaaaaiaawIcacaGLPaaa paWaaWbaaSqabeaapeGaeqyTduMaeyOeI0IaaGymaaaakiqadAgapa GbaKaadaWgaaWcbaWdbiaadgeacaWGJbaapaqabaaak8qacaGLOaGa ayzkaaaaaa@90A5@      (34)

3.6       Effect of Changes in Fixed Costs on the Price Index

Next, we calculate the percentage change in the price index in the destination country. We totally differentiate equations (7), (8), (9), and (20), while holding aggregate expenditure levels, wages, variable trade costs, and the number of potential firm in each country fixed. Equations (35) through (38) are the resulting equations in percentage changes.

a ^ D = P ^ +( 1 1ε ) f ^ D MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gabmyya8aagaqcamaaBaaaleaapeGaamiraaWdaeqaaOWdbiabg2da 9iqadcfapaGbaKaapeGaey4kaSYaaeWaa8aabaWdbmaalaaapaqaa8 qacaaIXaaapaqaa8qacaaIXaGaeyOeI0IaeqyTdugaaaGaayjkaiaa wMcaaiqadAgapaGbaKaadaWgaaWcbaWdbiaadseaa8aabeaaaaa@4349@     (35)

a ^ Xc = P ^ +( 1 1ε ) f ^ Xc MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gabmyya8aagaqcamaaBaaaleaapeGaamiwaiaadogaa8aabeaak8qa cqGH9aqpceWGqbWdayaajaWdbiabgUcaRmaabmaapaqaa8qadaWcaa WdaeaapeGaaGymaaWdaeaapeGaaGymaiabgkHiTiabew7aLbaaaiaa wIcacaGLPaaaceWGMbWdayaajaWaaSbaaSqaa8qacaWGybGaam4yaa Wdaeqaaaaa@4541@     (36)

a ^ Ac = P ^ +( 1 1ε ) f ^ Ac MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gabmyya8aagaqcamaaBaaaleaapeGaamyqaiaadogaa8aabeaak8qa cqGH9aqpceWGqbWdayaajaWdbiabgUcaRmaabmaapaqaa8qadaWcaa WdaeaapeGaaGymaaWdaeaapeGaaGymaiabgkHiTiabew7aLbaaaiaa wIcacaGLPaaaceWGMbWdayaajaWaaSbaaSqaa8qacaWGbbGaam4yaa Wdaeqaaaaa@4513@     (37)

P ^ =( k( ε1 ) 1ε )( ( 1 c m Xc c m Ac ) a ^ D + c m Ac a ^ Ac + c m Xc ( 1+( m Ac m Xc ) ( w c  τ w ) ε1 ) a ^ Xc c m Xc ( m Ac m Xc ) ( w c  τ w ) ε1 a ^ Ac ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gabmiua8aagaqca8qacqGH9aqpdaqadaWdaeaapeWaaSaaa8aabaWd biaadUgacqGHsisldaqadaWdaeaapeGaeqyTduMaeyOeI0IaaGymaa GaayjkaiaawMcaaaWdaeaapeGaaGymaiabgkHiTiabew7aLbaaaiaa wIcacaGLPaaadaqadaWdaeaapeWaaeWaa8aabaWdbiaaigdacqGHsi sldaGfqbqabSWdaeaapeGaam4yaaqab0WdaeaapeGaeyyeIuoaaOGa amyBa8aadaWgaaWcbaWdbiaadIfacaWGJbaapaqabaGcpeGaeyOeI0 Yaaybuaeqal8aabaWdbiaadogaaeqan8aabaWdbiabggHiLdaakiaa d2gapaWaaSbaaSqaa8qacaWGbbGaam4yaaWdaeqaaaGcpeGaayjkai aawMcaaiqadggapaGbaKaadaWgaaWcbaWdbiaadseaa8aabeaak8qa cqGHRaWkdaGfqbqabSWdaeaapeGaam4yaaqab0WdaeaapeGaeyyeIu oaaOGaamyBa8aadaWgaaWcbaWdbiaadgeacaWGJbaapaqabaGcpeGa bmyya8aagaqcamaaBaaaleaapeGaamyqaiaadogaa8aabeaak8qacq GHRaWkdaGfqbqabSWdaeaapeGaam4yaaqab0WdaeaapeGaeyyeIuoa aOGaamyBa8aadaWgaaWcbaWdbiaadIfacaWGJbaapaqabaGcpeWaae Waa8aabaWdbiaaigdacqGHRaWkdaqadaWdaeaapeWaaSaaa8aabaWd biaad2gapaWaaSbaaSqaa8qacaWGbbGaam4yaaWdaeqaaaGcbaWdbi aad2gapaWaaSbaaSqaa8qacaWGybGaam4yaaWdaeqaaaaaaOWdbiaa wIcacaGLPaaadaqadaWdaeaapeWaaSaaa8aabaWdbiaadEhapaWaaS baaSqaa8qacaWGJbaapaqabaGcpeGaaeiOaiabes8a0bWdaeaapeGa am4DaaaaaiaawIcacaGLPaaapaWaaWbaaSqabeaapeGaeqyTduMaey OeI0IaaGymaaaaaOGaayjkaiaawMcaaiqadggapaGbaKaadaWgaaWc baWdbiaadIfacaWGJbaapaqabaGcpeGaeyOeI0Yaaybuaeqal8aaba Wdbiaadogaaeqan8aabaWdbiabggHiLdaakiaad2gapaWaaSbaaSqa a8qacaWGybGaam4yaaWdaeqaaOWdbmaabmaapaqaa8qadaWcaaWdae aapeGaamyBa8aadaWgaaWcbaWdbiaadgeacaWGJbaapaqabaaakeaa peGaamyBa8aadaWgaaWcbaWdbiaadIfacaWGJbaapaqabaaaaaGcpe GaayjkaiaawMcaamaabmaapaqaa8qadaWcaaWdaeaapeGaam4Da8aa daWgaaWcbaWdbiaadogaa8aabeaak8qacaqGGcGaeqiXdqhapaqaa8 qacaWG3baaaaGaayjkaiaawMcaa8aadaahaaWcbeqaa8qacqaH1oqz cqGHsislcaaIXaaaaOGabmyya8aagaqcamaaBaaaleaapeGaamyqai aadogaa8aabeaaaOWdbiaawIcacaGLPaaaaaa@A3E6@      (38)

Finally, we use equations (35) through (38) to solve for the percentage change in the price index in the destination market resulting from the reductions in f Ac MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOza8aadaWgaaWcbaWdbiaadgeacaWGJbaapaqabaaaaa@38FF@  and f Xc MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOza8aadaWgaaWcbaWdbiaadIfacaWGJbaapaqabaaaaa@3916@ . Equation (39) is the reduced-form expression for the price change.

P ^ =( k( ε1 ) k ( 1ε ) )( c m Ac f ^ Ac + c m Xc ( 1+( m Ac m Xc ) ( w c  τ w ) ε1 ) f ^ Xc c m Xc ( m Ac m Xc ) ( w c  τ w ) ε1 f ^ Ac ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gabmiua8aagaqca8qacqGH9aqpdaqadaWdaeaapeWaaSaaa8aabaWd biaadUgacqGHsisldaqadaWdaeaapeGaeqyTduMaeyOeI0IaaGymaa GaayjkaiaawMcaaaWdaeaapeGaam4AaiaabckadaqadaWdaeaapeGa aGymaiabgkHiTiabew7aLbGaayjkaiaawMcaaaaaaiaawIcacaGLPa aadaqadaWdaeaapeWaaybuaeqal8aabaWdbiaadogaaeqan8aabaWd biabggHiLdaakiaad2gapaWaaSbaaSqaa8qacaWGbbGaam4yaaWdae qaaOWdbiqadAgapaGbaKaadaWgaaWcbaWdbiaadgeacaWGJbaapaqa baGcpeGaey4kaSYaaybuaeqal8aabaWdbiaadogaaeqan8aabaWdbi abggHiLdaakiaad2gapaWaaSbaaSqaa8qacaWGybGaam4yaaWdaeqa aOWdbmaabmaapaqaa8qacaaIXaGaey4kaSYaaeWaa8aabaWdbmaala aapaqaa8qacaWGTbWdamaaBaaaleaapeGaamyqaiaadogaa8aabeaa aOqaa8qacaWGTbWdamaaBaaaleaapeGaamiwaiaadogaa8aabeaaaa aak8qacaGLOaGaayzkaaWaaeWaa8aabaWdbmaalaaapaqaa8qacaWG 3bWdamaaBaaaleaapeGaam4yaaWdaeqaaOWdbiaabckacqaHepaDa8 aabaWdbiaadEhaaaaacaGLOaGaayzkaaWdamaaCaaaleqabaWdbiab ew7aLjabgkHiTiaaigdaaaaakiaawIcacaGLPaaaceWGMbWdayaaja WaaSbaaSqaa8qacaWGybGaam4yaaWdaeqaaOWdbiabgkHiTmaawafa beWcpaqaa8qacaWGJbaabeqdpaqaa8qacqGHris5aaGccaWGTbWdam aaBaaaleaapeGaamiwaiaadogaa8aabeaak8qadaqadaWdaeaapeWa aSaaa8aabaWdbiaad2gapaWaaSbaaSqaa8qacaWGbbGaam4yaaWdae qaaaGcbaWdbiaad2gapaWaaSbaaSqaa8qacaWGybGaam4yaaWdaeqa aaaaaOWdbiaawIcacaGLPaaadaqadaWdaeaapeWaaSaaa8aabaWdbi aadEhapaWaaSbaaSqaa8qacaWGJbaapaqabaGcpeGaaeiOaiabes8a 0bWdaeaapeGaam4DaaaaaiaawIcacaGLPaaapaWaaWbaaSqabeaape GaeqyTduMaeyOeI0IaaGymaaaakiqadAgapaGbaKaadaWgaaWcbaWd biaadgeacaWGJbaapaqabaaak8qacaGLOaGaayzkaaaaaa@9369@      (39)

4         Application of the Model: Estimating the Effects of EU Trade Liberalization

4.1       Description of the Liberalization

As an application of this modeling framework, we estimate the impacts of a hypothetical liberalization of EU policy that reduces barriers to the two modes of trade in services. In this policy experiment, we reduce the fixed costs of supplying the EU countries from a non-EU country by 50 percent, for both cross-border exports and foreign affiliate sales.[23] On the other hand, we assume that there is no change in the fixed costs of supplying the EU destination country from other EU countries, since intra-EU trade flows are already liberalized. Specifically, we assume that f ^ Xc = f ^ Ac =0.50 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GabmOza8aagaqcamaaBaaaleaapeGaamiwaiaadogaa8aabeaak8qa cqGH9aqpceWGMbWdayaajaWaaSbaaSqaa8qacaWGbbGaam4yaaWdae qaaOWdbiabg2da9iabgkHiTiaaicdacaGGUaGaaGynaiaaicdaaaa@423B@  if source country c MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4yaaaa@36F4@  is outside of the EU and f ^ Xc = f ^ Ac =0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GabmOza8aagaqcamaaBaaaleaapeGaamiwaiaadogaa8aabeaak8qa cqGH9aqpceWGMbWdayaajaWaaSbaaSqaa8qacaWGbbGaam4yaaWdae qaaOWdbiabg2da9iaaicdaaaa@3F23@  if c MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4yaaaa@36F4@  is within the EU.

In this policy scenario, the percentage changes in cross-border exports and foreign affiliates reduce to equation (40) for non-EU countries, equation (41) for other EU countries, and equation (42) for domestic supply in the EU destination countries.

For non-EU countries:     v ^ Ac = v ^ Xc =k  P ^ +( k( ε1 ) 1ε ) f ^ Ac MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GabmODa8aagaqcamaaBaaaleaapeGaamyqaiaadogaa8aabeaak8qa cqGH9aqpceWG2bWdayaajaWaaSbaaSqaa8qacaWGybGaam4yaaWdae qaaOWdbiabg2da9iaadUgacaGGGcGabmiua8aagaqca8qacqGHRaWk daqadaWdaeaapeWaaSaaa8aabaWdbiaadUgacqGHsisldaqadaWdae aapeGaeqyTduMaeyOeI0IaaGymaaGaayjkaiaawMcaaaWdaeaapeGa aGymaiabgkHiTiabew7aLbaaaiaawIcacaGLPaaaceWGMbWdayaaja WaaSbaaSqaa8qacaWGbbGaam4yaaWdaeqaaaaa@519F@           (40)

For other EU countries:     v ^ Ac = v ^ Xc =k  P ^ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GabmODa8aagaqcamaaBaaaleaapeGaamyqaiaadogaa8aabeaak8qa cqGH9aqpceWG2bWdayaajaWaaSbaaSqaa8qacaWGybGaam4yaaWdae qaaOWdbiabg2da9iaadUgacaGGGcGabmiua8aagaqcaaaa@4191@           (41)

For domestic suppliers:     v ^ D =k  P ^ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GabmODa8aagaqcamaaBaaaleaapeGaamiraaWdaeqaaOWdbiabg2da 9iaadUgacaGGGcGabmiua8aagaqcaaaa@3C62@           (42)

4.2       Data Sources and Challenges

The data used in this model consist of inbound foreign affiliate sales, cross-border imports and exports, and total revenue for two industries (accounting/legal services and architecture/engineering services) for a sample of European countries, sourced from two Eurostat databases.[24] Cross-border trade and total revenue data are available separately for accounting services, legal services, architecture services, and engineering services; however, data on inbound foreign affiliate sales is only available as two combined categories: legal/accounting services and architecture/engineering services. Therefore it is necessary to aggregate cross-border trade and revenue data to make the industry groupings comparable across data sources. Data on inbound foreign affiliate sales is available only as recently as 2014, which necessitates using that year for other data sources as well. Cross-border trade and foreign affiliate sales are calculated as the value of trade between the country represented in the model (France, Hungary, etc.) and all countries outside the EU, because the policy scenario assumes the same reduction in fixed costs for all non-EU sources.

Despite the modest data requirements of this model, the Eurostat database was missing key pieces of data for architectural/engineering and legal/accounting services for several large European economies (such as the UK), and for this reason they are not include in our analysis. We attempted to supplement the Eurostat data with official data from various national statistical offices; however, the requirement to subtract intra-EU trade proved difficult as bilateral services trade data were not available in sufficient detail at the sectoral level from these sources. If more detailed data sources can be found, particularly for foreign affiliate sales, this model can be applied to more sectors and countries. Since it is not a general equilibrium model, missing data for one country or sector also does not preclude the model from being applied to other destination countries or sectors.

4.3       Effects of the Liberalization

The liberalization reduces the fixed costs of exporting to the EU destination country from non-EU source countries, while keeping domestic and intra-EU trade costs unchanged. As a result, it lowers average prices in the destination country. In terms of sources of supply, the liberalization increases the cross-border exports (CBE) and foreign affiliate sales (FAS) of non-EU countries into the EU, at the expense of domestic and intra-EU supply. However, the reduction in EU-sourced sales is small, due to the small initial shares of the markets supplied by non-EU sources.

4.3.1        Effects on Prices and Sales

Table 1 presents the estimated effects of the liberalization on the overall price index for legal and accounting services in each destination country. The table also shows the effect of the liberalization on the values of supply, by each mode, in each destination country. Table 2 does the same for architecture and engineering services.

These tables illustrate four main themes. First, the impact of liberalization on the destination country’s price index is small. Second, several types of supply change by the same percentage. Third, sales from EU-sources fall by relatively small percentages. Fourth, sales from non-EU sources increase consistently across modes, destination countries, and services categories, by around 25 percent.

Table 1: Effect of the Liberalization on the Price and Sales of Legal and Accounting Services

Percentage Changes

Destination
Country

Price Index

Domestic Sales or CBE or FAS from EU

CBE or FAS
from non-EU

Czech Republic

-0.3

-1.7

26.0

Greece

-0.1

-0.4

27.3

France

-0.1

-0.6

27.1

Hungary

-0.7

-3.7

24.1

Austria

-0.1

-0.5

27.3

Poland

-0.3

-1.4

26.4

Netherlands

-0.5

-2.6

25.1

 

 

Table 2: Effect of the Liberalization on the Price and Sales of Architecture and Engineering Services

Percentage Changes

Destination
Country

Price Index

Domestic Sales or CBE
or FAS from EU

CBE or FAS
from non-EU

Czech Republic

-0.5

-2.6

25.2

Germany

-0.5

-2.8

24.9

France

-0.8

-4.2

23.6

Italy

-0.5

-2.6

25.2

Hungary

-0.5

-2.3

25.4

Netherlands

-1.2

-6.1

21.7

Austria

-0.5

-2.5

25.2

Poland

-0.4

-2.2

25.6

Sweden

-0.5

-2.6

25.1

 

The small drop in price indices can be understood by examining equation (39). The overall price index can be thought of as a weighted average of the costs of supply of each mode from each source country. So the impact of the liberalization on a country’s overall price index depends on the market shares of the suppliers who are receiving reductions in their trade costs. The larger the market share of non-EU sources in a destination country, the more the destination price falls after the liberalization. However, the market share of non-EU sources is relatively small in all destination countries and services categories (see Tables 3 to 6). As a result, the liberalization only reduces the destination country price indices by 0.1 to 1.2 percent.

The sales of several modes of supply all change by the same percentage. This occurs because, for each mode of supply, all that matters for the sales of that mode is its price relative to the overall price index (see equations 41 and 42). Within each destination country, domestic sales and EU-sourced CBE and FAS each have the same change in costs (zero) and also face the same drop in the price index. As a result, they all have the same percentage change in sales. Similarly, non-EU sourced CBE and FAS face the same reduction in costs (50 percent) and the same change in the price index. As a result, equation (40) shows that both of these modes display the same percentage increase in sales.

The drop in sales from other EU sources in Tables 1 and 2 can be understood by examining equation (41). As was previously discussed, the change in sales of each mode depends on the change in the price index and the change in that mode’s costs. But costs do not change for other EU sources. As result, the percentage change in EU-sourced CBE and FAS is also equal to k MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4Aaaaa@36FC@  times the percentage change in the price index. As the drop in EU-sourced sales is driven by the drop in the price index, the largest drops in EU-sourced sales occur in countries and services categories with the largest drops in prices. And these are the countries and categories where non-EU sourced suppliers have larger market shares. Likewise for domestic sales in equation (42), the percentage change in domestic sales is equal to k MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4Aaaaa@36FC@  times the fall in prices.[25]

The story behind the change in CBE and FAS from non-EU sources is more complex. Their percentage increase in sales is defined by equation (40). The right hand side of these equations has two terms. The first is a price term that is the same as the percentage changes in sales of the other modes. It is determined by the market share of non-EU sources in the destination country, and is relatively small. The second term is determined by the change in the fixed costs of trade for the particular mode of supply. The second term is large relative to the change in the overall price index. For the particular parameter values used in the model, the second term is equal to 27.8 percent, for all of the non-EU sources, so the second term dominates the first. As a result, all countries show similar percentage increases in the value of non-EU sourced FAS and CBE, ranging from 21.7 to 27.3.

4.3.2       Effects on the Market Share of Different Modes of Supply

The following tables present the market share of each mode of supply in each destination country, before and after the liberalization. Table 3 and Table 4 are for legal and accounting services before and after, while Table 5 and Table 6 are for architecture and engineering services before and after.

The most striking result is how little the market shares change in response to the liberalization. This occurs because, according to tables 1 and 2, there is only a small percentage change in the shares of modes with the largest initial market shares (those from EU-sources). However, the modes with large percentage changes (those from non-EU sources) have small initial market shares. As a result, the market shares of the different modes of supply look very similar both before and after the liberalization.


 

Table 3: Market Share of each Mode of Supply in Legal and Accounting Services, before the Liberalization

Market Share (percent)

Destination Country

Cross Border from non-EU

Cross Border from EU

FAS from
non-EU

FAS from
EU

Domestic Sales

Czech Republic

2.1

7.2

4.2

8.4

78.2

Greece

1.5

8.1

0.0

3.7

86.8

France

2.1

4.6

0.1

1.5

91.7

Hungary

1.3

5.0

12.0

23.6

58.1

Austria

1.6

6.5

0.0

2.5

89.4

Poland

1.3

5.3

3.6

11.8

78.1

Netherlands

7.6

7.9

1.8

2.9

79.8

 

Table 4: Market Share of each Mode of Supply in Legal and Accounting Services, after the Liberalization

Market Share (percent)

Destination Country

Cross Border from non-EU

Cross Border from EU

FAS from
non-EU

FAS from
 EU

Domestic Sales

Czech Republic

2.6

7.0

5.3

8.2

76.8

Greece

1.8

8.0

0.0

3.7

86.4

France

2.7

4.6

0.1

1.4

91.2

Hungary

1.6

4.8

14.9

22.8

55.9

Austria

2.1

6.5

0.0

2.5

88.9

Poland

1.6

5.2

4.6

11.6

77.0

Netherlands

9.5

7.7

2.2

2.8

77.8

 


 

Table 5: Market Share of each Mode of Supply in Architecture and Engineering Services, before the Liberalization

Market Share (percent)

Destination Country

Cross Border from non-EU

Cross Border from EU

FAS from
non-EU

FAS from
EU

Domestic Sales

Czech Republic

2.6

6.8

6.7

13.1

70.8

Germany

5.3

9.3

4.9

9.3

71.3

France

10.2

9.2

4.8

7.0

68.8

Italy

4.4

7.9

4.8

11.7

71.2

Hungary

2.0

11.7

6.4

10.9

69.0

Netherlands

8.3

6.2

13.6

11.1

60.8

Austria

7.2

18.8

1.9

5.0

67.2

Poland

3.4

11.3

4.4

9.2

71.7

Sweden

1.4

3.1

8.1

13.8

73.7

 

Table 6: Market Share of each Mode of Supply in Architecture and Engineering Services, after the Liberalization

Market Share (percent)

Destination Country

Cross Border from non-EU

Cross Border from EU

FAS from
non-EU

FAS from
EU

Domestic Sales

Czech Republic

3.2

6.6

8.4

12.8

69.0

Germany

6.6

9.0

6.1

9.0

69.3

France

12.6

8.9

5.9

6.7

65.9

Italy

5.5

7.7

6.1

11.4

69.4

Hungary

2.5

11.4

8.1

10.6

67.4

Netherlands

10.1

5.8

16.6

10.4

57.1

Austria

9.0

18.3

2.4

4.9

65.5

Poland

4.2

11.1

5.6

9.0

70.2

Sweden

3.2

6.6

8.4

12.8

69.0

 

5         Conclusions

The model provides a practical tool for trade policy analysis for services industries where data are limited and the economics of multi-mode supply can be complex. The estimates indicate that 50 percent reductions in the fixed costs of the two modes of trade in these professional services would have large effects on the value of cross-border exports into the EU countries and on foreign affiliate purchases in these countries, but would have only small effects on the sales of domestic producers and on overall prices of the services in the EU markets.

This model quantifies the economic impact of hypothetical reductions in the fixed costs of trade, but the model does not provide a method for estimating the magnitude of cost reductions associated with specific policy changes. To provide an illustration of how the model works, we have assumed 50 percent reductions in one or both of the types of fixed costs. The relevant magnitudes of the cost reductions associated with policy changes are critical inputs into the analysis and therefore a very important area for future research.

Finally, there may be even larger potential gains from liberalizing markets for services in developing countries, so the challenge for future research will be collecting reliable data on markets shares in these markets in order to extend the analysis.

6         References

Di Giovanni, Julian, Andrei A. Levchenko, and Romain Rancière (2011): “Power Laws in Firm Size and Openness to Trade: Measurement and Implications.” Journal of International Economics 85: 42-52.

European Commission. “European Semester Thematic Factsheet: Regulation of Professional Services,” November 15, 2016 (accessed April 24, 2017). https://ec.europa.eu/info/sites/info/files/european-semester_thematic-factsheet_regulation-professional-services_en.pdf.

Eurostat. “International Trade in Services Database (since 2010) (BPM6)” (accessed April 12, 2017). https://ec.europa.eu/eurostat/web/international-trade-in-services/data/database.

Eurostat. ““Foreign Control of Enterprises by Economic Activity and a Selection of Controlling Countries” (accessed April 12, 2017). https://ec.europa.eu/eurostat/web/products-datasets/-/fats_g1a_08.

Grosso, Geloso M., et al. (2014): "Services Trade Restrictiveness Index (STRI): Construction, Architecture and Engineering Services." OECD Trade Policy Papers, No. 170, OECD Publishing, Paris.

Helpman, Elhanan, Marc J. Melitz, and Stephen R. Yeaple (2004): “Export Versus FDI with Heterogeneous Firms.” American Economic Review 94(1): 300-316.

Khachaturian, Tamar and David Riker (2016): “A Multi-Mode Partial Equilibrium Model of Trade in Professional Services” U.S. International Trade Commission, Office of Economics Working Paper 2016-11-A.

Organisation for Economic Co-operation and Development (OECD). “Services Trade Restrictiveness Index Regulatory Database” (accessed April 12, 2017). https://qdd.oecd.org/subject.aspx?Subject=063bee63-475f-427c-8b50-c19bffa7392d.

Riker, David (2015): “The Impact of Restrictions on Mode 3 International Supply of Services.” Journal of International and Global Economic Studies 8(1): 1-20.

World Bank (2017): “Trade in services (% of GDP).” Accessed April 11, 2017, https://data.worldbank.org/indicator/BG.GSR.NFSV.GD.ZS.

Zhai, Fan (2008): “Armington Meets Melitz: Introducing Firm Heterogeneity in a Global CGE Model of Trade.” Journal of Economic Integration 23(3): 575-604.


 

Appendix

Table A1: Trade in Certain Professional Services by Country in 2014 (million euros)

 

Country

Category of Services

Cross-Border Exports

Cross-Border Imports

Inbound FAS

Revenue

Austria

Architectural and Engineering

1,311.0

457.0

122.2

7,227.2

Austria

Legal and Accounting

130

89

1.8

5,502.3

Czech Republic

Architectural and Engineering

337.4

120.1

317.8

4,932.9

Czech Republic

Legal and Accounting

100.1

55.1

110.8

2,691.5

France

Architectural and Engineering

8,759.0

5,097.0

2,378.8

53,502.3

France

Legal and Accounting

731

814

17.8

38,253.1

Germany

Architectural and Engineering

5,945.0

3,660.0

3,359.4

71,401.8

Greece

Legal and Accounting

24.3

25.2

0.1

1,741.9

Hungary

Architectural and Engineering

72.0

45.0

143.1

2,252.9

Hungary

Legal and Accounting

91.5

25.1

228.2

1,972.4

Italy

Architectural and Engineering

1,046.0

860.2

948.4

19,782.2

Netherlands

Architectural and Engineering

2,623.8

1,170.0

1,927.7

15,603.4

Netherlands

Legal and Accounting

1699.3

1118.6

262.3

15,327.7

Poland

Architectural and Engineering

398.2

171.4

223.8

5,246.8

Poland

Legal and Accounting

356.1

62.2

179.7

5,294.5

Sweden

Architectural and Engineering

1,004.5

180.8

1,072.7

14,069.0

Note: Cross-border exports, cross-border imports, and inbound foreign affiliate sales exclude all intra-EU trade.

Source: Eurostat, International Trade in Services Database (accessed April 12, 2017); Eurostat, Foreign Control of Enterprises by Economic Activity and a Selection of Controlling Countries (accessed April 12, 2017).

 

Table A2: Architecture and Engineering Services Restrictions by Country

Country and Score

Restrictions on Foreign Entry

Restrictions on Movement of People

Other

Austria Architecture (0.301) Engineering (0.304 )

Acquisition and use of land and real estate by foreigners ; equity restrictions applying to non-locally licensed individuals or firms

Labor market tests; limitations on stay

Minimum capital requirements

Czech Republic Architecture (0.273) Engineering (0.258)

Equity restrictions applying to non-locally licensed individuals or firms

Residency requirements for board of directors; licensing requirements for board of directors; labor market tests; limitations on stay; local exam and practice requirements

Minimum capital requirements

France Architecture (0.197) Engineering (0.144)

Equity restrictions applying to non-locally licensed individuals or firms

Licensing requirements for board of directors; labor market tests; limitations on stay;

Minimum capital requirements

Germany Architecture (0.197) Engineering
(0.204)

Equity restrictions applying to non-locally licensed individuals or firms; foreign investment screening

Licensing requirements for managers; labor market tests; limitations on stay

Minimum capital requirements; fee setting

Hungary Architecture
(0.271) Engineering
(0.269)

Acquisition and use of land and real estate by foreigners

Labor market tests; (intra-company transfers, contractual/independent service suppliers); limitations on stay; nationality or citizenship requirements for license to practice

Minimum capital requirements

Italy Architecture
(0.236) Engineering (0.160)

Equity restrictions applying to non-locally licensed individuals or firms; acquisition and use of land and real estate by foreigners; licensing requirement for managers;

Labor market tests; quotas (independent suppliers); limits on stay; permanent residency/domicile required for practice; local exam requirements

 

Netherlands Architecture
(0.170) Engineering (0.171)

 

Labor market tests; limitations on stay

 

Poland Architecture
(0.439) Engineering
(0.432)

Acquisition and use of land and real estate by foreigners

Labor market tests for contractual/independent services suppliers; limitations on stay; nationality or citizenship requirements for license to practice

Minimum capital requirements

Sweden Architecture (0.197) Engineering
(0.198 )

Residency for management/board of directors/key foreign personnel

Labor market tests; limitations on stay

Minimum capital requirements

Source: OECD Services Trade Restrictiveness Index Simulator (accessed April 12, 2017). https://sim.oecd.org/default.ashx.

Note: Most restrictive policies in the "Foreign Entry" and "Movement of People" categories are listed (i.e. excluding those which may be scored greater than 0 but are subsumed by a binding restriction).The average STRI score in legal services for the countries presented here is 0.510, while the average STRI for accounting services is 0.288.



Table A3: Legal and Accounting Services Restrictions by Country

Country and Score

Restrictions on Foreign Entry

Restrictions on Movement of People

Other

Austria Accounting (0.342)

Legal (0.417)

Foreign equity restrictions for domestic law and auditing firms, joint stock companies for domestic law prohibited; acquisition and use of land and real estate by foreigners is restricted; commercial presence required for auditing firms

Residency requirements for board of directors of auditing firms; licensing requirements for managers of law and accounting firms; labor market tests; limitations on stay; nationality and residency requirements for licensing for practice of domestic law

Minimum capital requirements; restrictions on advertising for domestic law

Czech Republic Accounting (0.233)

Legal (0.311)

Restrictions on ownership by non-locally licensed attorneys (both domestic and international) and auditors; certain restrictions on commercial association for legal services; commercial presence required to provide certain cross-border legal services

Licensing requirements for boards of directors of law firms (both domestic and international) and auditing firms; labor market tests for legal and accounting; limitations on stay; residency/domicile requirements for licensing for legal services; local examination requirements for legal services

Fee setting for legal services; minimum capital requirements

France Accounting (0.483)

Legal (0.593)

Equity restrictions applying to not licensed individuals or firms for legal and accounting; certain restrictions on commercial association for legal services; commercial presence required to provide certain cross-border legal services

Licensing requirements for managers and boards of directors of both law and accounting firms; labor market tests; limitations on stay; no recognition of foreign qualifications

 

Greece Accounting (0.274)

Legal (0.492)

Equity restrictions applying to not licensed individuals or firms (domestic law and auditing); certain restrictions on commercial association for legal services; screening requirements; acquisition and use of land and real estate by foreigners is restricted

Nationality and licensing requirements for managers and board of directors; labor market tests for legal and accounting; limitations on stay; nationality/domicile requirements for licensing in domestic law

Minimum capital requirements; restrictions on advertising

Netherlands Accounting (0.164)

Legal (0.244)

 Equity restrictions applying to not licensed individuals or firms (domestic law and auditing); commercial presence required to provide certain cross-border legal services

Licensing requirements for managers and board of directors; labor market tests for legal and accounting; limitations on stay; domicile required to practice domestic law; other restrictions to movement of people; local examination requirement in legal and accounting (but not auditing); practice requirement in legal and accounting (but not auditing); lack of temporary licensing

 

Poland Accounting (0.234)

Legal (1.000)

Restrictions on ownership by non-locally licensed attorneys (both domestic and international); legal form; certain restrictions on commercial association; board of directors and managers must be licensed lawyers; establishment requirements for host country law; acquisition and use of land and real estate by foreigners is restricted (both legal and accounting)

Labor markets tests (legal and accounting); limitations on stay (legal and accounting); domicile requirements for host country law; recognition of foreign qualifications based on reciprocity (international law, auditing) and/or education/practice in Poland (domestic law); lack of temporary licensing;

Advertising restrictions (legal and accounting); minimum capital requirements (legal and accounting)

Source: OECD Services Trade Restrictiveness Index Simulator (accessed April 12, 2017). https://sim.oecd.org/default.ashx.

Note: Most restrictive policies in the "Foreign Entry" and "Movement of People" categories are listed (i.e. excluding those which may be scored greater than 0 but are subsumed by a binding restriction).The average STRI score in architecture services for the countries presented here is 0.249, while the average STRI for engineering services is 0.233.



[1] World Bank (2017).

[2] Grosso et al. (2014), 24-25.

[3] Helpman, Melitz, and Yeaple did not originally apply their model to services industries. Their empirical analysis only includes manufacturing industries. Riker (2015) applies the Helpman, Melitz, and Yeaple framework to services industries, but his data are not disaggregated by category of service.

[4] The WTO’s General Agreement Trade in Services (GATS) defines four modes of services delivery. Mode 1 pertains to cross-border trade, which occurs when an individual or firm in one country provides a service to a consumer in another country, often through electronic delivery (e.g., a U.S. architect emailing designs to a foreign client). Mode 2 pertains to consumption abroad, or when an individual from one country travels to another country to consume a service (e.g., a student from the United States studying at a UK. university). Mode 3 pertains to commercial presence, or when a company headquartered in one country opens a branch, office, or subsidiary in another country in order to provide services to residents of that country (e.g., a U.S. accounting firm providing auditing services to German consumers through a subsidiary located in Germany). Finally, mode 4 pertains to the movement of natural persons, or when an individual from one country travels to another country to supply services on a short term basis (e.g., a U.S. engineer traveling to France to provide services for a construction project located in that country). In general, cross-border trade in services occurs via modes 1, 2, and 4, whereas affiliate transactions occur via mode 3.

[5] The OECD STRI reflects policies in place in 2016.

[6] Unless otherwise noted, this paragraph is based on Grosso et al., (2014), 10-12.

[7] Eurostat, International Trade in Services Database (accessed April 12, 2017). Data for 2013 and 2014 are the most widely available years for the countries presented here. Eurostat data on cross-border trade roughly corresponds to modes 1, 2 and 4 (cross-border supply, consumption abroad, and the presence of natural persons) while Eurostat data on foreign affiliate transactions roughly corresponds to mode 3 (commercial presence) in the GATS modes of supply framework for services trade. See Koncz et al., (2006), 39-40.

[8] Eurostat, Foreign Control of Enterprises by Economic Activity and a Selection of Controlling Countries (accessed April 12, 2017).

[9] Eurostat, Foreign Control of Enterprises by Economic Activity and a Selection of Controlling Countries (accessed April 12, 2017).

[10] The following paragraph is based on Grosso et al. (2014), 24-25.

[11] Temporary licensing systems are often available and some countries recognize foreign degrees with some additional local criteria.

[12] OECD, Services Trade Restrictiveness Index, 2016.

[13] As indicated above, part of mode 4 is captured in the data on cross-border trade.

[14] Eurostat, International Trade in Services Database (accessed April 12, 2017).

[15] Eurostat, Foreign Control of Enterprises by Economic Activity and a Selection of Controlling Countries (accessed April 12, 2017).

[16] The following paragraph is based on Grosso et al. (2014), 9-10 and OECD (2016), 2.

[17] Some countries have implemented limited-licensing schemes which circumvent the necessity to be licensed in the host country and allow foreign attorneys to practice in their qualified areas of law (typically known as foreign legal consultants). Temporary practice rules adopted by some jurisdictions are considered an additional avenue for foreign attorneys to be able to practice law. Similar schemes also exist in certain countries for accounts and auditors, usually requiring reciprocal recognition of qualifications. See European Commission, “Regulation of Professional Services,” November 15, 2016, 8, for information on various EU countries’ recognition rates of professional qualifications.

[18] Restrictions on commercial association can impede the ability of foreign firms to partner with or employ local lawyers or accountants as an avenue to provide certain services (such as host country law or auditing services) to their clients, without the need to requalify in local markets.

[19] For the purposes of the model, cross-border exports refer to all trade that does not involve setting up a foreign affiliate.

[20] This is the cost of establishing foreign affiliate production, in excess of the cost of gaining market access.

[21] The HMY framework assumes that there are constant expenditure shares, corresponding to Cobb-Douglas preferences across categories of services.

[22] The following equations for the changes in the economic variables do not show all of the steps of the derivation. The technical appendix provides more details of the derivation.

[23] Since the fixed costs of trade include natural barriers as well as policy barriers, a 50 percent reduction in the fixed costs of trade would require a more than 50 percent reduction in the costs associated with policy barriers.

[24] Cross-border trade data is sourced from Eurostat, “International Trade in Services Database (since 2010) (BPM6),” while data on inbound foreign affiliate sales and total revenue comes from Eurostat, “Foreign Control of Enterprises by Economic Activity and a Selection of Controlling Countries (from 2008 onwards).” Total revenue is obtained by setting the controlling country parameter to “all countries” for each industry, while inbound foreign affiliate sales data is obtained by setting the controlling country parameter for each industry to “Extra-EU-28.” Data on cross-border exports and imports also exclude intra-EU trade by setting the partner country parameter to “Extra-EU-28.”

[25] It may seem counter-intuitive that domestic sales fall whenever the price index falls. However, note that the change in the price index is not the exogenous shock or root cause.  is not an exogenous change in price, it is a change in the price index caused by a change in the fixed costs of CBE and FAS, modes that are substitutes for domestic sales in the model.