What Determines whether Preferential Liberalization of Barriers against Foreign Investors in Services Are Beneficial or Immizerising: Application to the Case of Kenya

Despite the fact that many modern preferential trade agreements include commitments to foreign investors in imperfectly competitive services sectors, the literature has not established conditions under which these agreements are beneficial or harmful. The authors fill that void by developing a model with monopolistic competition and foreign direct investment in services with Dixit-Stiglitz endogenous productivity effects from additional varieties. They specify a numerical model, with probability distributions of all parameters. The model is executed 30,000 times, and results are reported as probability of an outcome, based on the sample distribution. In order to ground the results in reality, the authors apply the model to Kenya. They show that preferential commitments in services could be immizerising. Losses are more likely the greater the share of initial rent capture on the services barriers in our home country and the more technologically advanced are the excluded regions relative to the partner region. JEL F12 F13 F14 F15 F23 F47 C68 L16

6 at least one-third Kenyan and one-third of the members of the Boards of Directors must be Kenyan (restraints that may allow Kenyans to capture rents on incumbent multinational enterprises operating in Kenya).

Professional Services
There are rather severe restrictions on the rights of foreigners to operate with a license in many of the professional services sectors, including legal, accounting, auditing and engineering services. Foreign professionals working in Kenya must typically do so in the office of a licensed Kenyan, providing rents to Kenyans.

III. Estimation of the Tariff Equivalence of the Regulatory Barriers
Estimates of the ad valorem equivalents of the regulatory barriers in services are key to the results. Our methodology builds on a series of studies supported by the Australian Productivity Commission, especially the papers by Warren (2000) in telecommunications, Kalirajan et al. (2000) in financial services, Kang (2000) in transportation services and  in engineering services. For each of these service sectors, the authors first developed a matrix to evaluate and score the regulatory environment in the sector they were studying. The regulatory regimes are evaluated on criteria such as ease of getting a license; measures that restrict a form of commercial presence; maximum ownership shares allowed for foreign investors; and whether senior executives are allowed to work in the country either permanently or temporarily. They collected data and assessed the regulatory regimes of many countries. Evaluations of each criterion were transformed into a quantitative score and weights were assigned to each criterion so that the regulatory regimes of each country were transformed a "restrictiveness index." They then regressed the price of services against their restrictiveness index and other relevant variables to determine the impact of the regulatory barriers on the price of services. 10 Through this regression, it is possible to obtain an ad valorem equivalence of the regulatory barriers in the countries of their sample.
Our methodology assumes that the international regression estimated by these authors applies to Kenya. To build on their regression estimates, it is necessary to score the identical matrix of regulatory 7 barriers. For this task, we first need to assess the regulatory environment in the services sectors in our model. This was based on a 54 page questionnaire of the regulatory regimes in key Kenyan business services sectors, namely, insurance, banking, fixed line and mobile telecommunications services and maritime transportation services and a separate questionnaire in engineering services. 11 We supplemented this questionnaire information based on a good set of studies on the services sectors that were presented at the conference on "Trade in Services" in Nairobi, Kenya on March 26-27, 2007 (attended by one of the authors) and World Bank reports, including World Bank (2007).
Based on the information obtained, Mircheva (2007) scored the regulatory regimes in fixed line and mobile telecommunications, banking, insurance and maritime transportation services sectors and produced a measure of the trade restrictiveness index for each sector. Mircheva then used her calculation of the restrictiveness indices for the various Kenyan services sectors in the regression for the corresponding services sector to obtain the price impact of the regulatory barriers. From the price impact estimate, she calculated the ad valorem equivalents of the discriminatory and non-discriminatory barriers in her services sectors. In the case of professional services, we used engineering services as a proxy for all professional services and the work was carried out by Josaphat Kweka. 12 The results of the estimation are presented in table 1.
The alternative to the methodology we have chosen is to estimate a gravity equation, as has been done in several studies, including Francois et al. (2005). An advantage of the gravity approach is that it allows the authors to estimate the ad valorem equivalents of barriers in services for many countries and sectors without having to collect data on the regulatory regimes. But the gravity model requires data on services flows which are typically only available on a cross-border basis; so it ignores barriers to foreign direct investment in services. The principal advantage of our approach over a gravity estimation procedure is that our estimates are specifically linked to the regulatory regime, including the important barriers against 11 We thank Ms. Sonal Sejpal of the Kenyan law firm of Anjarwalla & Khanna Advocates for leading the research work on the general effort. Nora Dihel led the survey in engineering services. 12 See appendix D, "Engineering Services in Kenya." Since the methodology requires the existence of a crosscountry regression estimate of the impact of barriers to foreign direct investment, and engineering services is the only professional service for which it exists, we must use engineering services as our proxy. 8 foreign direct investment. In our discussions in Kenya and elsewhere, policy-makers wanted to know the barriers that are in place that gave rise to the ad valorem equivalents. Being able to link the estimates to the regulatory regime gave credibility in the discussions with government policy-makers, and began the discussion of what are the most important reform issues.
Nonetheless, we acknowledge that our estimates are subject to a margin of error. As a result, when we conduct sensitivity analysis, we include in the sensitivity analysis estimates of the ad valorem equivalents of the barriers in our services sectors.

IV. Overview of the Model
A full algebraic description of the model may be found in appendix F. Here we provide a general description of the structure while focusing on the extensions to a model that can address preferential liberalization. The principal extension from earlier work of  is that we disaggregate the rest of the world region into three regions: (1) the European Union; (2) the union of the East African Customs Union and COMESA, which we call our African region; and (3) the Rest of the World. We retain the small open economy model framework, so only Kenya is modeled fully. There are 55 sectors in the model shown in table 1. The primary factors are skilled, semi-skilled and unskilled labor; mobile capital; sector-specific capital in imperfectly competitive sectors; and primary inputs imported by multinational service providers, reflecting specialized management expertise or technology of the firm.
Each firm type in each imperfectly competitive sector requires its own sector specific capital; this implies that there are decreasing returns to scale in the use of the mobile factors and industry marginal cost curves for firms of the same type slope up. This is explained algebraically in appendix G.
There are three categories of sectors in the model: (1) perfectly competitive goods and services sectors: (2) imperfectly competitive goods sectors; and (3) imperfectly competitive services sectors with foreign direct investment. The cost, production and pricing structures in the three categories differ widely.
In the imperfectly competitive sectors, this requires introducing different firm types with distinct cost structures for each region. 9

Perfectly competitive goods and services sectors
Regardless of sector, all firms minimize the cost of production. In the competitive goods and services sectors, goods or services are produced under constant returns to scale and where price equals marginal costs with zero profits. This includes all 20 of the agriculture sectors and 19 manufacturing or services sectors listed in table 1. In these sectors, products are differentiated by country of origin, i.e., we employ the Armington assumption. All firms (including imperfectly competitive firms) can sell on the domestic market or export. Firms optimize their output decision between exports and domestic sales based on relative prices and their constant elasticity of transformation function. Having chosen how much to allocate between exports and domestic sales, firms also optimize their output decision between exports to the three possible export regions, based on relative prices the three regions and their constant elasticity of transformation production function for shifting output between the regions.

Goods produced subject to increasing returns to scale
In all imperfectly competitive goods and services sectors, goods are differentiated at the firm level. Firms in each region are assumed to have identical cost structures, but the costs of firms differ across regions. So there are four firm types per sector in the model-one representative firm type for each region. We assume that the seven manufactured goods may be produced domestically or imported from firms in any region in the model. Firms in these industries set prices such that marginal cost (which does not vary with output) equals marginal revenue; and there is free entry, which drives profits to zero.
Foreigners produce the goods abroad at constant marginal cost but incur a fixed cost of exporting to Kenya. The cif import price of foreign goods is simply defined by the import price, and, by the zero profits assumption, in equilibrium the import price must cover fixed and marginal costs of foreign firms.
Firms set prices using the Chamberlinian large group monopolistic competition assumption within a Dixit-Stiglitz framework, which results in constant markups over marginal cost for both foreign firms and domestic firms. 10 Since we assume that consumers have a love of variety with a Dixit-Stiglitz demand structure for products in all imperfectly competitive sectors, to be consistent, we assume that foreign consumers also have a love of variety with the same demand structure. Then Kenyan firms in these sectors face a Dixit-Stiglitz demand structure in their export markets. Analogous to domestic pricing, we assume that Kenyan firms set prices on export markets based on the large group monopolistic competition assumption. It follows from these two assumptions that the elasticity of demand for Kenyan firms on their exports in imperfectly competitive markets is the Dixit-Stiglitz elasticity of substitution. 13 Alterative elasticities of export demand, including perfectly elastic demand, as in our perfectly competitive sectors, are inconsistent with the symmetric treatment of home and foreign markets in these products. Firms then set marginal revenue equal to marginal costs in each of the three export markets; then the export markets contribute to the quasi-rents of the firm and affect the entry and exit decisions of domestic firms.
For simplicity we assume that the composition of fixed and marginal cost is identical in all firms producing under increasing returns to scale (in both goods and services). This assumption in a Dixit-Stiglitz based Chamberlinian large-group model assures that output per firm for all firm types remains constant, i.e., the model does not produce rationalization gains or losses. 14 Changes in industry-level output occur through entry or exit of firms. The number of varieties (firms) affects the productivity of the use of imperfectly competitive goods based on the standard Dixit-Stiglitz formulation. The effective cost 13 This is an extension of , where it was assumed that export demand in imperfectly competitive sectors is perfectly elastic. 14 If we were to drop the large group monopolistic assumption and allow firms to take the reactions of their competitors into account in their price or quantity setting decisions, then increased competition from liberalization would decrease price-cost margins, increase output per firm and lead to welfare gains from rationalization. Such a model, however, would not necessarily lead to larger welfare estimates than our model with large group monopolistic pricing. Since output per firm increases, the economy would obtain fewer varieties from the liberalization of services and less of a gain from the Dixit-Stiglitz externality. That is, there is a welfare tradeoff between rationalization gains and the Dixit-Stiglitz variety externality. Markusen (2011) has developed a small illustrative CGE model with the Krugman style cost structure and Dixit-Stiglitz demand structure employed in this paper. He builds two models on this structure: one with Bertrand pricing among firms and a second model with large group monopolistic pricing. He shows that with Bertrand pricing there are substantial welfare gains from rationalization, as well as Dixit-Stiglitz variety gains. But, given his parameterization, the overall welfare gains are slightly less than in the monopolistic competition model due to the fact that there are fewer varieties obtained from the liberalization. 11 function for users of goods produced subject to increasing returns to scale declines in the total number of firms in the industry. 15

Service sectors that are produced under increasing returns to scale and imperfect competition
These nine sectors are telecommunications, banking and insurance services, various transportation services and professional business services. There is evidence that there are economies of scale in these sectors in some range of their output, even if the larger firms in some of the sectors operate under constant returns to scale. Then perfect competition is not possible, even though a large number of firms could exist. 16 Given that services cannot be stored, FDI to achieve a domestic presence (what is known as the proximity burden) has historically been crucial to the effective delivery of services. While technological change has progressively allowed more services to be supplied on a cross-border basis, to effectively compete in services "trade," it still is likely that it requires more of a domestic presence than trade in goods, which suggests that cross border services are not good substitutes for service providers who have a domestic presence. 17 Our model allows for both types of foreign service provision in these sectors. There are cross border services allowed in this sector and they are provided from abroad at constant costs-this is analogous to competitive provision of goods from abroad.
Crucial to the results, we allow multinational service firms to establish a presence in Kenya to compete with Kenyan firms directly. As in the goods sectors, services that are produced subject to increasing returns to scale are differentiated at the firm level. Firms in these industries set prices such that marginal cost (which is constant) equals marginal revenue; and there is free entry, which drives profits to zero. We assume firm level product differentiation and the same pricing rules as in the imperfectly competitive goods sectors. Thus, again there are no rationalization impacts. 15 Broda and Weinstein (2004) find that increased product variety contributes to a fall of 1.2 percent per year in the "true" import price index. 16 See Tarr (2012) for references and a brief discussion of econometric papers that estimate economies of scale in all of these sectors. 17 Data on the sales of foreign affiliates of U.S. firms suggests that sales through FDI are the most important channel for U.S. firms to sell services to foreigners (Francois and Hoekman, 2010, p.655). See Francois and Hoekman (2010), Francois (1990) and Markusen (1989) for elaboration of the proximity burden in services.
For domestic firms, costs are defined by the costs of primary factors and intermediate inputs.
When multinationals service providers decide to establish a presence in Kenya, they will import some of their technology or management expertise. That is, foreign direct investment generally entails importing specialized foreign inputs. Thus, the cost structure of multinationals differs from national only service providers. Multinationals incur costs related to both imported primary inputs and Kenyan primary factors, in addition to intermediate factor inputs. Foreign provision of services differs from foreign provision of goods, since the service providers use Kenyan primary inputs. Domestic service providers do not import the specialized primary factors available to the multinationals. Hence, domestic service firms incur primary factor costs related to Kenyan labor and capital only. These services are characterized by firmlevel product differentiation. For multinational firms, the barriers to foreign direct investment affect their profitability and entry. Reduction in the constraints on foreign direct investment will induce foreign entry 18 that will typically lead to productivity gains because when more varieties of service providers are available, buyers can obtain varieties that more closely fit their demands and needs (the Dixit-Stiglitz variety effect).
Evidence on the role of trade and FDI in increasing total factor productivity through technology transfer Grossman and Helpman (1991) have developed models of economic growth that have highlighted the role of trade and greater variety of intermediate goods as a vehicle for technological spillovers that allow less developed countries to close the technological gap with industrialized countries. 19 Winters et al. (2004, 84) summarize the empirical literature by concluding that "the recent empirical evidence seems to suggest that openness and trade liberalization have a strong influence on productivity and its rate of change." Beginning with the path-breaking work of Coe and Helpman (1995), a rich empirical literature now exists 18 The data in table 2 reveal that the Africa region has a zero market share in four of the business services sectors. Our model assumes that the market share of the Africa region will remain at zero in any counterfactual simulation. 19 Trade or services liberalization may increase productivity and growth indirectly through its positive impact on the development of institutions. It may also induce firms to move down their average cost curves, or import higher quality products or shift production to more efficient firms within an industry. Tybout and Westbrook (1995) find evidence of this latter type of rationalization for Mexican manufacturing firms. 13 that shows that important mechanisms for the transmission of knowledge and the increase in total factor productivity are the purchase of imported intermediate goods and inward foreign direct investment. Several papers, such as Coe, Helpman, and Hoffmaister (1997) and Keller (2000), show that for small developing countries, trading with large technologically advanced countries is crucial for TFP growth. Schiff et al. (2002) show that developing country trade with technologically advanced countries is very important in technology intensive sectors, but trade with developing countries can be important for productivity spillovers in less technologically complex products in which developing countries have comparative advantage. Regarding foreign direct investment, we have cited several papers above that show that FDI that leads to a diverse set of services suppliers improves total factor productivity. Although FDI in the same sector has ambiguous effects on productivity, several papers have found significant productivity spillovers from FDI in both upstream (supplying) industries (e.g., Javorcik, 2004;Blalock and Gertler, 2008;and Javorcik and Spatareanu, 2008) and downstream (using) industries (e.g., Wang, 2010;Jabbour and Mucchielli, 2007). A more detailed summary of this literature is provided in  Appendix E).
In our model, the parameter that reflects the ability of a region to increase total factor productivity through the transmission of new technologies is the elasticity of varieties with respect to the price. Based on Schiff et al (2002), we assign central values to this elasticity based on the region and the research and development intensity of the sector. The assigned central values for these parameters by sector and region are in table 2. We conduct extensive sensitivity analysis on this parameter, both piecemeal and systematic.

Social Accounting Matrix
The key data source for our study is the social accounting matrix taken from Kiringai,Thurlow and Wanjala (2006). Given our focus on services, we found it necessary to disaggregate the single 14 transportation sector into five sectors and the single financial services sector into insurance, and banking and other financial services. 20 A full listing of the sectors is provided in table 1. .

Trade Data by Regional Partner and Sector
To obtain the shares of imports and exports from the different regions of our model, we used trade data for 2007 obtained from WITS access to the COMTRADE database. The regions of our model are Kenya, the European Union, the East African Customs Union plus COMESA and the Rest of the World. We mapped two digit sectors from the COMTRADE database into the sectors of our model. 21

Tariff Data
We started with MFN tariff rates at the eight digit level taken from the website of the Kenyan government. These tariff rates were then aggregated to the sectors of our model, using simple averages.
At MFN rates, however, the implied tariff revenues were larger than reported collections. This is largely due to tariff preferences to regional partners and other preference items or tariff exemptions. In 2005, the ratio of total taxes on imports to the total value of imports was 8.4 percent. 22 Since zero tariffs apply on all imports from the East African Customs Union and from COMESA, we apply the MFN tariff rates only on the trade flows from outside of these African regions (EU and Rest of World in our model) and take a weighted average tariff rate of the MFN rates on the non-East African regions. The resulting weighted average tariff rate on non-East African imports still exceeds 8.4 percent. We then equi-proportionally reduced all the MFN tariffs in our model so that the estimated collected tariffs on imports from the EU and Rest of World divided by the total value of import is 8.4 percent. The resulting tariff rates (applied only to non-East African imports) are reported in Table 1.

Share of Market Captured by Multinational Service Providers
It was necessary to calculate the market share of multinational firms in the services sectors by region of the model. Take the banking sector as an example. We need to know the share of the market captured by Kenyan, EU, African and Rest of the World firms. This entailed acquiring a list of all banks 15 operating in Kenya along with their market share, and, when the bank is owned by multiple parties, allocating the ownership across the regions of our model. The database Bankscope was sufficient for this task in most cases, but websites of the banks had to be consulted to allocate ownership shares in several cases. The results, by region and sector, are presented in table 2. 23 Broda et al. (2006) estimated Dixit-Stiglitz product variety elasticities of substitution at the 3 digit level in 73 countries. Among the 73 countries, there were four in sub-Saharan Africa: the Central African Republic, Madagascar, Malawi and Mauritius. We judged that Madagascar was the country closest in characteristics to Kenya, so we took the values of the elasticities estimated for Madagascar as a proxy for the elasticities for Kenya. Of the 34 goods sectors in our model, seven are imperfectly competitive. These are the goods sectors in which the Dixit-Stiglitz elasticity of substitution is less than six. One exception was metals and machines, where production function estimates indicate this is an increasing returns to scale sector (see, for example, Tarr, 1984). The elasticity of substitution values are shown in table 4 and details are in appendix C.

VI. Results for Preferential Reduction of All Services Barriers-Central Elasticity Case
We execute several scenarios to assess the impacts of Kenya entering into a bilateral free trade agreement that includes services with the European Union, and similarly with the Africa region. In these scenarios we assume that Kenyan ad valorem equivalents of the barriers against foreign investors in services are reduced by fifty percent with respect to the region with which Kenya has an agreement. We assume that Kenya already offers tariff free access to goods originating from its African trade partners, so in the scenario where we evaluate the agreement with the Africa region we include only liberalization of discriminatory barriers against foreign investors in services. Insofar as combining preferential trade agreements could potentially reduce trade diversion inherent in separate agreements (see, e.g., Harrison et al. (2002;2004), we examine the impacts of the combination of free trade agreements with both the Africa region and the European Union. We compare these impacts with unilateral non-discriminatory liberalization. Finally, given our earlier result on the importance of reducing non-discriminatory barriers 16 against investors in services, we examine the impact of a fifty percent reduction of non-discriminatory barriers against service providers combined with unilateral liberalization of discriminatory barriers.
As discussed in , who captures the rents from the barriers is very important for the welfare results. Consequently, for each policy scenario, we execute two versions of the model with our central elasticities. In one case, we assume that Kenyans do not capture any rents from the barriers. In the second scenario, we assume that the discriminatory barriers generate rents that are captured by Kenyans. These results are presented in table 3. In our systematic sensitivity analysis, in each of the 30,000 scenarios, we allow the share of rents captured by Kenyans to vary stochastically between zero and one.

Aggregate Effects 24
We present results on the impacts on aggregate variables including welfare, the real exchange rate, aggregate exports and imports, the return to capital, skilled labor and unskilled labor and the percentage change in tariff revenue. In order to obtain an estimate of the adjustment costs, we estimate the percentage of each of our factors of production that have to change sectors.
Significant gains with the EU-deriving primarily from services liberalization. We estimate that the preferential arrangement with the EU that includes both goods and services would generate gains for Kenya of 0.7 percent of consumption with no initial rent capture and 0.5 percent of consumption if there is initial rent capture by Kenyans. The gains come primarily from the preferential liberalization of services, although the relative contribution is much larger with no initial rent capture. That is, the gains to Kenya from preferential liberalization of tariffs with the EU are invariant to the rent capture in services assumption at 0.2 percent of consumption. But, if there is initial rent capture, the gains to Kenya of preferential liberalization of services fall from 0.5 percent of consumption to 0.3 percent of consumption.
Small gains from preferential liberalization with the Africa region. In the case of preferential liberalization with the Africa region, the gains are smaller-0.3 percent of consumption in the case of no initial rent capture and 0.1 percent of consumption in the case of rent capture initially by Kenya. The agreement with the EU includes tariff reduction, while tariff free access in the Africa region is considered part of the status quo; so the appropriate scenario for comparison of the relative gains for Kenya is the scenario in the second column of the central results table, labeled "EU discriminatory services." With no initial rent capture, the gains for Kenya of an agreement with the EU are 60 percent greater than the gains from an agreement with the Africa region. With initial rent capture, gains of an agreement with the EU are three times greater than the gains from an agreement with the Africa region. We show in the sensitivity 24 Discussion of additional scenarios in the table may be found in Balistreri and Tarr (2011). 17 section that there is a possibility of losses from an agreement with the Africa region in the initial rent capture case.
Why are the gains larger for the agreement with the "northern" region? As we discussed above, trade with and FDI from large technologically advanced regions can be expected to lead to technology diffusion that increases total factor productivity. Although trade and FDI from small developing countries can contribute to technology diffusion, it has been estimated to do so to a significantly lesser extent, at least for research and development intensive sectors. The elasticity of the number of varieties (firms) with respect to price is the parameter in our model that captures that effect, and the values we have chosen are in table 2. 25 In Balistreri and Tarr (2011) we show that the number of varieties from the EU substantially increases as a result of preferential liberalization with the EU, while the estimated expansion of varieties from the Africa region is much more modest in response to preferential liberalization with respect to the African region. We show in the sensitivity analysis below that this elasticity of supply parameter is very important for the results: preferential agreements in services are more likely to be beneficial the higher the supply elasticities of the partner country's services suppliers and the lower the supply elasticities of the excluded countries services suppliers.

Non-discriminatory liberalization would result in a five-fold increase in the gains compared
with preferential liberalization with the EU. With non-discriminatory liberalization, Kenyans would be able to access goods and services from the least cost supplier in the world. This would eliminate all trade diversion losses, reduce any adverse terms of trade losses and result in the maximum number of new foreign varieties for productivity improvement from trade and FDI liberalization. Consequently, the gains are much larger in this case. Because the rest of the world has a much larger share of the goods market in Kenya than it enjoys in the services sectors, the gains from non-discriminatory liberalization come more from liberalization of goods than from services.
The largest gains come from reduction in the barriers that domestic as well as foreign firms face. Consistent with the work of Balistreri,  in a model with an aggregate rest of the world, we find that the largest gains for Kenya would come from liberalization of the nondiscriminatory barriers in services. That is, when we estimate the impact of a fifty percent reduction in the non-discriminatory services barriers on top of unilateral liberalization of all discriminatory services barriers, 25 The elasticity of supply corresponds to the share of the sector's costs that are due to a specific factor of production. In all of the imperfectly competitive sectors, we assume there are four specific factors: one for each region in the model. Then, as industry output expands, the price of the specific factor necessary for production of that variety increases, thereby increasing the cost of production of firms. Since the cost of production of firms increases as the industry supply increases, the industry marginal cost curve of each region will slope up in each of these sectors. And higher cost shares of the specific factor will lead to less elastic industry marginal cost curves in that sector.
18 the estimated gains are 10.3 percent of consumption with no rent capture or 7.0 percent of consumption with initial rent capture.

VII. Sensitivity Analysis
Given uncertainty of parameter values and the rent capture assumption, point estimates of the results may be viewed with skepticism. In this section we assess the impact of parameter values and key modeling assumptions on the results. In table 4, we show the "piecemeal sensitivity analysis," where we change the value of a single parameter while holding the values of all other parameters unchanged at our central elasticity values. This table also shows the impact of some key modeling assumptions.
In our "systematic sensitivity analysis," we execute 30,000 simulations. In each simulation, we allow the computer to randomly select the values of all parameters, subject to the specified probability distributions of the parameters. Through the systematic sensitivity analysis we will be able to assess how robust the results are and obtain confidence intervals of the results.

Rent capture assumption
In the row labeled θr, we retain the increasing returns to scale assumption in the selected goods and services sectors, but allow the initial rent capture share in the services sectors to be either zero (central value ) or 1 (upper value). We see that there is approximately a forty percent reduction in the welfare gain from a free trade agreement with the EU if rents are captured initially (from a welfare gain of 0.67 percent of consumption to 0.49 percent of consumption). In the case of an agreement with the African region, the gains fall even more dramatically, from a welfare gain of 0.29 percent of consumption to a gain of 0.05 percent of consumption in our central elasticity case.

Impact of Constant Returns to Scale-Possible Negative Welfare Effects
In the row labeled θr-CRTS model, we assume constant returns to scale in all sectors, which eliminates the Dixit-Stiglitz externality from additional varieties. We allow the initial rent capture share in the services sectors to be either zero (central value) or 1 (upper value). We see that without the Dixit-Stiglitz variety externality, the gains from an agreement with the EU fall dramatically. With no initial rent capture, the gains for the EU agreement would be .09 percent of consumption, and would fall to a negative value (-0.06 percent of consumption) with initial rent capture. In the case of an agreement with the Africa region, the gains are 0.14 percent of consumption with no initial rent capture and are negative (-0.06 percent of consumption) with initial rent capture.
In the row labeled IRTS by sector, the results show that the increasing returns to scale (IRTS) assumption is much more important in the services sectors than in the goods sectors. In the agreement with the Africa region, the gains are only slightly diminished if we assume CRTS in all goods sectors.
Since the agreement with the EU also involves tariff reduction against imports of EU goods, the IRTS 19 assumption in goods results in non-trivial additional gains from the Dixit-Stiglitz externality of additional varieties of goods.

Piecemeal Sensitivity Analysis of Parameters
Ad valorem equivalents (AVEs) of the barriers against services providers-magnification of gains or losses. In the three rows of table 4 that begin with the label AVE, we see that magnifying the AVEs, magnifies the welfare impacts, either gains or losses; but the key pattern of the results regarding the relatively greater welfare gains from the agreement with the EU is robust to the AVE values. In these scenarios, with lower (upper) values, we scale all the AVEs of services sectors listed in table 1 by 0.5 (1.5). We employ all central model parameters in the row labeled AVE. Then the gains from a free trade agreement with either region are approximately 1.5 times the central values with high AVEs and about one-half of the central values with low AVEs. In the row labeled AVE & θr =1, we allow for loss of domestic rents on services with preferential liberalization. The loss of domestic rents in Kenya reduces the estimated gains of all scenarios, but gains from the EU agreement are always larger. Finally, in the row labeled AVE, θr =1 & εAFR= low, we vary the AVEs, allow for loss of domestic rents from services liberalization, and also employ low values of the elasticities of supply from the Africa region. With low elasticities from the Africa region, Kenya will gain few varieties or technology from the preferential liberalization of services with the Africa region. We see that Kenya loses from its preferential liberalization of services with the Africa region independent of the AVEs of the services barriers. But the absolute value of the losses are greater, the greater are the AVEs. With higher AVEs, partner countries obtain a larger price advantage over excluded countries, so there is a larger decline in the demand for excluded countries services following preferential services liberalization. The greater decline in demand for excluded countries products leads to a greater loss of varieties from excluded countries. Since the elasticity of supply from the Africa region is low, there are few additional varieties from the partner region and the welfare loss is greater with higher AVEs.
Model Parameters. Four model parameters stand out as having a strong impact on the results.
The elasticity of substitution between firm varieties in imperfectly competitive services sectors, σ(qi, qj) has a very strong impact. At the low end of the elasticity range, the estimated gains are almost 10 per cent of consumption from a preferential agreement with the EU and five percent of consumption from an agreement with the Africa region. Following from the Le Chatelier principle, larger elasticities typically lead to larger welfare gains in response to welfare improving reforms, as the economy can adapt more readily. Unlike other elasticities, however, a lower value of σ(qi,qj) increases the welfare gains. This is because lower values of this elasticity imply that varieties are less close to each other, so additional varieties are worth more. Since the policy shocks in goods are much less, the same elasticity variation in goods has a much smaller impact, but its impact is nonetheless significant. The elasticity of substitution 20 between value-added and business services, σ(va, bs), also has a strong impact. The better firms are able to substitute business services for labor and capital, the more the economy will gain from the reforms that reduce the quality adjusted price of business services. Finally, for the agreement with the EU, there is a strong impact from changes in the value of εEU, the elasticity of multinational service firm supply with respect to the price of output. .Larger values of this parameter mean that tariff preferences that open opportunities for EU service firms to provide new varieties, will not be so quickly choked by the increased cost of the specific factor required for EU firm expansion. For the agreement with Africa, there is a strong impact of the parameter εAFR.

Impact of Partner and Excluded Country Elasticities of Multinational Service Firm
Supply-why it is more likely to obtain gains from large technologically advanced partners. In figures 1 and 2, we present the results of 300 additional simulation to assess the impact and interrelationship of the elasticities of firm supply from partner and excluded countries, with and without initial rent capture in Kenya. In figure 1, we examine the estimates for the welfare effects in Kenya of a fifty percent preferential reduction of barriers in services against African partners. On the vertical axis is the set of elasticities of firm supply of African partners with respect to price. We scale this set of elasticities from between one-half to twice their central values. On the horizontal axis we scale the central values of the elasticities of firm supply of all excluded countries from one-half of their central values to twice their central values. Excluded regions in this case are the EU and Rest of the World. In figure 2, we do analogous simulations, except that since the preferential liberalization is with the EU, the EU elasticities are on the vertical axis and we scale the elasticities of the African region and the Rest of the World on the horizontal axis. In the left hand side panel, we present results with no initial rent capture, but initial rent capture is shown on the right hand side panel.
Regarding preferential reduction of barriers with African partners, we see that, with initial rent capture, there is a significant range of elasticities that result in losses for Kenya. Without initial rent capture, however, there are gains for all these values.
We see from figures 1 and 2 that the gains to the home country increase the higher the elasticity of supply of firms in partner countries and the lower the elasticity of supply of firms in excluded countries, with the partner country elasticity being by far the more important. Preferential reduction of barriers, leads to an increase in firms (varieties) and productivity from partner countries; but it also leads to a loss of service providers (varieties) from all excluded regions and the home country, which results in a loss of productivity. The lost productivity from lost varieties from the regions excluded and the home country from the preferential liberalization in services is analogous to the trade diversion losses in perfect competition. When firm elasticities in partner countries are high, the after tax price increase for firms in 21 partner countries from preferential reduction of barriers induces a large increase in partner country varieties, boosting productivity, thereby making it more likely that the preferential liberalization is welfare enhancing. For excluded countries, the price decrease of partner countries shifts in demand for their products and lowers their price; but the lower price induces fewer lost varieties when firms in excluded countries have low elasticities (the excluded country impact is more significant in figure 2). In addition to the variety impacts in imperfect competition, the rent and terms of trade impacts (which are present in perfect competition) reinforce the argument that high elasticities of partners and low elasticities of excluded countries increase the likelihood of welfare gains from a preferential agreement in services.

Systematic Sensitivity Analysis
In the systematic sensitivity analysis, we execute the model 30,000 times and harvest the results for desired variables. In each individual simulation, we allow the computer to randomly select values of all the parameters in the model (the parameters in table 4), based on the specified probability density functions (pdfs) of the parameters. We assume uniform probability density functions, with upper and lower values of the pdfs given by the upper and lower values in the piecemeal sensitivity analysis table.
We include initial rent capture in the systematic sensitivity analysis, with the rent capture parameter allowed to take values between zero and one with a uniform pdf.
The sample distributions of the results for preferential reduction of barriers with African partners on welfare and output, respectively, are shown in figures 3 and 5. Figure 4 and appendix figure 7 are similar for the welfare and output impacts, respectively, of a preferential trade agreement with the EU.
For the Africa-Kenya FTA, we find that 1.9 percent of the 30,000 simulations yield a negative welfare result, which we interpret as a 1.9 percent probability that preferential liberalization with the Africa region will be immizerising. A 95 percent confidence interval for equivalent variation as a percent of consumption is: 0.008 to 0.417 around a sample mean of .203. 26 For a free trade agreement with the EU that includes services, there are no negative welfare results. A 95 percent confidence interval for equivalent variation as a percent of consumption is: 0.37 to 0.94 around a sample mean of 0.63. 27 To further establish the relative importance of technology transfer in the choice of partners in preferential trade arrangements, we executed a second systematic sensitivity analysis of 30,000 runs. In this alternative systematic sensitivity analysis, we choose uniform pdfs for εAFR, εEU and εROW with lower and upper bounds for εAFR of 1 and 3, for εEU of 5 and 15 and for εROW of 7.5 and 22.5. All other probability distributions for all other parameters are unchanged, i.e., are as in table 4. Our estimate of the median gains from a preferential agreement with the Africa region falls, and the chance of the agreement 26 90 percent and 99 percent confidence intervals are 0.033 to 0.384 and -0.029 to 0.479, respectively. 27 90 and 99 percent confidence intervals are 0.41 to .89 and 0.30 to 1.07, respectively. 22 yielding negative welfare results increases to 9.5 percent. Our piecemeal sensitivity analysis above suggests that the key change is the lower pdf for εAFR.
In figure 5, we show "box and whisker" diagrams for the sample distribution of the percentage change in output by sector for a preferential services agreement with African partners. (See appendix, Regarding the means of the distributions, the striking result is, where there are declines in sector output, the contractions are generally very moderate. This contrasts with our results (not shown) that there are somewhat larger output declines for the agreement with the European Union and much more substantial output declines for these sectors in the unilateral scenario. This follows from the less substantial increase in competition or drop in overall protection to any sector in a preferential trade arrangement with the African countries.
Regarding the sensitivity analysis at the sector level, for the Africa agreement we see that the confidence intervals are rather tight for most sectors. But they reveal a large range of uncertainty for five sectors (other manufactured food, coffee, mining, road services and maritime services) where 50 percent confidence intervals indicate the sectors will expand; but 95 percent confidence intervals contain negative values. We conclude the predicted output changes for these five sectors are not robust. With respect to the EU agreement, while the sign of the direction of change does not change within the 95 percent confidence interval, the confidence intervals of expected output change are large for other manufactured food, maritime transportation, coffee and mining (among the expanding sectors) and (on the negative side) sugarcane, other manufactures and metals and machines. We can have confidence in the sign of the direction of change, but not in the magnitude of the mean estimate for these sectors.

VIII. Conclusions
In this paper we have shown that under imperfect competition with foreign direct investment and the Dixit-Stiglitz variety externality, welfare losses from preferential reduction of services barriers are possible. We showed that the losses are more likely the more technologically advanced are the excluded regions relative to the partner region and the more the home country captures rents from the existing services barriers. Our systematic sensitivity analysis shows that the mean estimate of the gains to Kenya from preferential reduction of barriers in services with the Africa region is very small, and there is a 1.9 percent chance that it would lose from such an agreement. Estimated gains for the agreement with the European Union are two to three times larger and occur with probability one. We estimate that 23 multilateral liberalization dominates preferential liberalization, as it would yield gains five times greater than a preferential agreement with the European Union.

Regulatory barriers
Note: The following are also CRTS sectors of the model, but with zero benchmark distortions: forestry, water, electricity, construction, real estate, administration, health, education.  ***Food is the proxy for grain mlling and sugar, bakery and confectioners; machinery is used for metals and machines; for non-metallic products, we used plastics, rubber, mineral and wood products.

Market Shares in Services Sectors with FDI
**We evaluate transportation as a medium R&D sector since three sectrors dominate R&D expenditures of US multinationals operating abroad. These are transportation, chemiicals and computers and electronics. Moreover, about two-thirds of all R&D expenditur Elasticity of supply with respect to price by Kenyan trading partner region R&D expenditures divided by sales (times 1000) for the US*   σ(q i , q j ): Elasticity of substitution between firm varieties in imperfectly competitive sectors σ(va, bs): Elasticity of substitution between value-added and business services σ(D, M): Elasticity of substitution between domestic and imported varieties σ(L, K): Elasticity of substitution between primary factors of production in value added σ(A 1 ,…A n ): Elasticity of substitution in intermediate production between composite Armington aggregate goods σ(D, E): Elasticity of transformation (domestic output versus exports) ε TZA : Elasticity of national service firm supply with respect to price of output ε EU : Elasticity of EU service firm supply with respect to price of output ε AFR : Elasticity of AFR service firm supply with respect to price of output ε ROW : Elasticity of Rest of World service firm supply with respect to price of output θ r : Share of rents in services sectors captured by domestic agents IRTS by sector: in goods (services) only, business services (Dixit-Stiglitz goods) in table 1 are CRTS. AVE: ad valorem equivalents of regulatory barriers in services; ε AFR = low means ε AFR = 0.5 central values.. export demand: in the upper case, perfectly elastic export demand is assumed for all model sectors. θ m : Shares of value added in multinational firms due to specialized primary factor imports Source: Authors' estimates. Note: The boxes are limited vertically by the 25% and 75% quartiles. The bars in the box are the means. The vertical lines extend to the 2.5% and 97.5% percentiles.          ***Food is the proxy for grain mlling and sugar, bakery and confectioners; machinery is used for metals and machines; for non-metallic products, we used plastics, rubber, mineral and wood products.

Appendix G: A Note of the Relationship Between Sector Specific Capital and the Elasticity of Supply in Applied General Equilibrium Models of Imperfect Competition
**We evaluate transportation as a medium R&D sector since three sectrors dominate R&D expenditures of US multinationals operating abroad. These are transportation, chemiicals and computers and electronics. M oreover, about two-thirds of all R&D expenditures of foreign multinationals operatingi in the US was performed in the same three sectors. See "U.S. and International Research and Development: Funds and Technology Linkages," at 'http://www.nsf.gov/statistics/seind04/c4/c4s5.htm.      Source: Authors' estimates.   Non metallic products -0.7 53.8 -2.1 -5.5

Figure 4: Means, 50 and 95 Percent Confidence Intervals of the Sample Frequency Distributions of the Output Changes by Sector from Kenyan Preferential Reduction of Services Barriers Against African Partners-30, 000 simulations.
Note: The boxes are limited vertically by the 25% and 75% quartiles. The bars in the box are the means. The vertical lines extend to the 2.5% and 97.5% percentiles.

Figure 5: Means, 50 and 95 Percent Confidence Intervals of the Sample Distributions of the Labor Payment Changes by Sector from Kenyan Preferential Reduction of Services Barriers Against African Partners-30,000 simulations.
Note: The boxes are limited vertically by the 25% and 75% quartiles. The bars in the box are the means. The vertical lines extend to the 2.5% and 97.5% percentiles.

and 95 Percent Confidence Intervals of the Sample Distributions of the Output Changes by Sector from Kenyan Preferential Reduction of Services Barriers Against EU Partners-30,000 simulations.
Note: The boxes are limited vertically by the 25% and 75% quartiles. The bars in the box are the means. The vertical lines extend to the 2.5% and 97.5% percentiles.  We used Kenya as the reporter country for both exports and imports. Results for both exports and imports are reported in the subsequent three tables, by CRTS and IRTS goods in our model separately.

Tariff Rate Calculations
Tariff and Sales Tax Data. We started with MFN tariff rates at the eight digit level taken from the website of the Kenyan government: www.kra.go.ke/customs/customsdownloads.php. These tariff rates were then aggregated to the sectors of our model, using simple averages.
We obtained data on the total taxes on imports and the total value of imports and took the ratio to obtain the average value of import taxes in the Kenyan economy. In 2005, this was 8.4 percent. 1 That is, on average, Kenyan importers paid 8.4 percent of the value of imports on import taxes that did not apply to domestic production.
As we reported in Balestreri, , the MFN tariff rates, multiplied times the trade flows, exceed the collected tariff rates. That is, using MFN tariff rates for all trade, the weighted average tariff rate exceeds the collected tariff rate of 8.4 percent for the economy as a whole. Thus, they exaggerate the protection received by Kenyan industry and agriculture. This is due to tariff preferences to regional partners and due to other preference items or tariff exemptions. We assume that zero tariffs apply 73 on all imports from the East African Customs Union and from COMESA. 2 Thus, we apply the MFN tariff rates only on the trade flows from outside of these African regions (EU and Rest of World in our model) and take a weighted average tariff rate of the MFN rates on the non-East African regions. The resulting weighted average tariff rate on non-East African imports still exceeds 8.4 percent. We then equiproportionally reduced all the MFN tariffs in our model so that the estimated collected tariffs on imports from the EU and Rest of World divided by the total value of import is 8.4 percent.    The primary source of data was various publications of Paul Buddle Communications, including "Kenya-Telecoms Market Statistics and Forecasts," March 20, 2008. Table 10 contains mobile phone subscription statistics by company and Table 2 lists the number of fixed-line phone subscribers. We defined market share as the share of total subscribers, summing fixed-line and mobile subscribers. The results for market share by country (in percent) are as follows: Kenya, 26; EU, 49; EAC, 0; COMESA, 0; Rest of World, 25.

II. Bank Shares in Kenya. Bank Market Shares
The data source for bank market shares was Bankscope, an on-line data source for about 29,000 banks world-wide. 6 Through Bankscope, we obtained data on total assets by bank in Kenya, owners -shareholders of the bank and the percent of the bank owned by each owner-shareholder. Market share of each bank was defined based on the bank's assets as a share of total bank assets in the country. We divided the regions into the European Union, East African Customs Union, COMESA and Rest of the World. 7

Ownership Shares of Banks
Each bank's market share was then allocated among geographic regions according to the shares of ownership of the bank. We then summed across the banks to obtain total market shares by region. In many cases, however, the Bankscope data were inadequate to allocate ownership shares by region. In these cases, we investigated bank websites, to obtain the required ownership information. The results of our supplementary inquiries are listed below.
The results we get are that owners of the banking sector of Kenya are as follows, in percent: Kenya, 61.8.; EU, 28.7; EAC, 0; COMESA, 0.2; ROW, 9.3. Detailed results on the ownership of the banks are in the tables below.      The premium information came from the Insurance Industry Annual Report for 2007 of the Association of Kenya Insurers. 8 Table 9 of their report lists premium income by company and type of insurance. We define market share of a company by the company share of total market premia.
For ownership shares, we commissioned a survey from a specialist at the Association of Kenyan Insurers. 9 He provided the data on the ownership shares of the Kenyan companies. In the table below, we list the result of these calculations.

IV. Railroad Transportation
In the hope of improved performance, in November 2006, Kenya's (and Uganda's) railways were turned over to Rift Valley Railways, a consortium led by South Africa's Sheltam Trade Close. This consortium won the right to operate the railways for 25 years. They are a monopolist, so we infer 100 percent ownership to the Rest of the World. 10

V. Pipeline Transportation
The Kenya Pipeline Company operates 800 kilometers of pipeline within Kenya for the transport of refined oil products. The pipeline runs from the refinery at the port of Mombassa to the capital of Nairobi, and with its western extension to Eldoret and to Kisimu. This pipeline is operated by the Kenya Pipeline Company, a wholly owned entity of the Government of Kenya. 11 In addition, there is a 320 kilometer pipeline under construction to extend the pipeline from Eldoret to Kampala Uganda. It is a Public-Private Partnership with the Governments of Uganda and Kenya originally each holding 24.5 percent shares. The remaining 51 percent was to be held by a consortium. Tamoil East Africa, a company registered in Uganda, owns 70 percent of the remainder. Tamoil East Africa is a wholly owned subsidiary of Tamoil Holdings, the Libyan state owned oil firm. The remaining 30 percent in the private consortium is held by Habib Investments, an investment company belonging to Habib Kagimu, a Ugandan businessman. However, in 2008, the Government of Uganda agreed to take only half of its 24.5 percent share and sell the other half to the private sector consortium. Thus, the share of the pipeline extention to Kampala of Tamoil East Africa increased to 44.3 percent and of Habib Investments to 19.0 percent. 12 We assume that shares of the market are proportional to the kilometers of the pipeline, and allocate ownership shares accordingly. There are 1120 kilometers of pipeline. The finished pipeline is 60 percent of the total and the Kampala extension is 40 percent. The Kenyan government holds 100 percent ownership interest in 800 kilometers (or 60 percent of the total) and 24.5 ownership interest in the remaining 320 kilometers (or 9.8 of the total) for a total share of 69.8 percent. The Uganda ownership share is the sum of the share of the Government of Uganda and the share of Habib Investments, i.e., 12.5 percent (equals .4 * (12.25 + 19.0)). The results are as follows. Kenya, 69.8; Uganda, 12.5; Rest of World, 17.7.

Appendix C : Estimates of the Dixit-Stiglitz Elasticities of Substitution for Kenyan Imperfectly Competitive Goods
It was necessary for us to obtain estimates of the Dixit-Stiglitz product variety elasticities of substitution for the imperfectly competitive sectors in our model. Christian Broda, Joshua Greenfield and David Weinstein (2006) estimated Dixit-Stiglitz product variety elasticities of substitution at the 3 digit level in 73 countries. Among the 73 countries, there were four in sub-Saharan Africa: the Central African Republic, Madagascar, Malawi and Mauritius. We judged that Madagascar was the country closest in characteristics to Kenya, so we took the values of the elasticities estimated for Madagascar as a proxy for the elasticities for Kenya. There are reasons to use both export shares as well as import shares. A larger share of a subcategory in imports reflects more imports, and more likely there are more varieties of imports. So weighting by the import share of a subcategory is better than an unweighted measure. Domestic varieties are also important. Since we do not have production data for the subcategories, we use export shares as a proxy for domestic production by subcategory. Analogously, weighting subcategories by export shares is better than unweighted categories. Since both import shares and export shares are useful in the weighting, we take one half the shares of both exports and imports as the weights. The resulting elasticities are reported in

On-going operations
Activities reserved by law to the profession Score 1 The engineering profession has an exclusive right to perform the following services: design and planning, representation for obtaining permits (signature of designs), tender and contract administration, project management including monitoring of execution, planning and managing maintenance, survey sites, testing and certification and expert witness activities. There is no law prohibiting a foreign provider with a commercial presence in Kenya from providing these services. The engineering profession has a shared right to provide the following services: feasibility studies, environmental assessment, and construction cost management. There is no law prohibiting a foreign provider with a commercial presence in Kenya from providing these services. Apart from design and planning, which can be done elsewhere and sent to Kenya, a foreign provider supplying services (i.e., without commercial presence in Kenya) will need a work permit in order to provide these services.

Multidisciplinary practices Score 0
There are no restrictions on cooperation between engineering professionals and other professionals. The same applies to foreign suppliers.

Advertising, marketing and solicitation Score 1
Advertising and marketing by Kenyan professional engineers as well as foreign suppliers is prohibited.
Fee setting Score 0.5 Prices /fees in the engineering services applicable to the private sector and other institutions outside the government are not regulated. In the case of professional engineering services rendered to the government, prices/fees are determined the Ministry in charge of engineering services but as of 2010, this function will be performed by the Engineering Registration Board (ERB). The ERB will set the prices/fees to be paid for professional engineering services rendered to the government; the service providers will be expected to compete on the technical aspect only.

Licensing requirements on management Score 0
No restrictions.

Movement of people -Temporary Score 0
No restrictions.

Other restrictions (Addition categories) Score 0.33
Restrictions on hiring professionals: Investment Promotion Act 2004 (cap 172) section 13.1. The employment of foreign natural persons for the implementation of foreign investment shall be agreed upon by the contracting parties and approved by Government. Table F1 summarizes the equilibrium conditions and associated variables. The nonlinear system (of 1,364 equations and variables) is formulated in GAMS/MPSGE and solved using the PATH algorithm. We proceed with a description and algebraic representation of each of the conditions itemized in Table F1.

F.1 Dual representation of technologies and preferences
Technologies and preferences are represented in the Kenya model through value functions that embed the optimizing behavior of agents. Generally, any linearly-homogeneous transformation of inputs into outputs is fully characterized by a unit-cost (or expenditure) function. Setting the output price equal to optimized unit cost yields the equilibrium condition for the activity level of the transformation. That is, a competitive constant-returns activity will increase up to the point that marginal benefit (unit revenue) equals marginal cost. In the case of the Kenya model not all transformations are constant returns, so there are exceptions. In general, however, we will use the convention of setting unit revenues (left-hand side) equal to unit cost (right-hand side) and associating this equilibrium condition with a transformation activity level.
Agents in Kenya wishing to purchase a particular good or service g face an aggregate price PA g . In constructing the aggregate prices, we will rely on the following notation for the component prices: PD g Price of domestic output (∀g ∈ G), PM g r Price of cross-border imports from region r of Business Services and CRTS goods (∀g ∈ (I ∪ K)), P g r Dixit-Stiglitz price index on region-r varieties (∀g ∈ (I ∪ J)).
Assuming a Constant Elasticity of Substitution (CES) aggregation of the components we where σ g F ∀g ∈ (I ∪ J) is the Dixit-Stiglitz elasticity of substitution and σ k DM is the Armington elasticity of substitution on CRTS goods. The arguments of these functions are the component prices. The ϕ parameters are CES distribution parameters that indicate scale and weighting of the arguments. These are calibrated to the Kenyan social accounts such that the accounts are replicated in the benchmark equilibrium.
For the IRTS sectors we have the Dixit-Stiglitz price indexes. These are functions of the number of varieties, firm-level costs, and the optimal markup. Assuming each firm is small relative to the size of the market the demand elasticity for a firm's variety is σ g F and the optimal markup over marginal cost is given by 1/(1 − 1 σ g F ). Let marginal cost equal PMC g r ∀g ∈ (I ∪ J), which is the price of a composite input to the Dixit-Stiglitz firms associated with region-r, and let the number of varieties by region equal N g r ∀g ∈ (I ∪ J).
The price indexes for the Dixit-Stiglitz goods are thus given by In equilibrium, the number of varieties by region adjusts such that we have zero profits.
Denote the Dixit-Stiglitz composite activity level associated with equation (4) by Q g r ∀g ∈ (I ∪ J). Given the Dixit-Stiglitz aggregation of varieties each firm produces a quantity Q g r (N g r ) σ g F /(1−σ g F ) . Assuming that fixed and variable costs are satisfied using the same input technology, and a firm-level fixed cost of f g r (in composite input units), we have the zero profit condition The technologies for producing the composite inputs for use in the Dixit-Stiglitz sectors depend on the type of sector. For all of the sectors there is a sector-specific capital input from the respective source region. Let PZ g r ∀g ∈ (I ∪ J) be the price of this sector-specific capital input. Domestic firms (producing goods or services) use domestic inputs, so the unit cost function is given by , for r = D; where ϵ g r is the elasticity of substitution between the sector-specific capital input and other inputs, and the θ's are the CES distribution parameters. Imports of Dixit-Stiglitz goods embody the gross of tariff imported inputs: , for r ̸ = D.
FDI firms, on the other hand, use domestic inputs as well as a specialized imported service from the sources region. The price of the specialized imports equals the price of foreign exchange (denoted PFX) times one plus the tariff rate (denoted t imp ir ). The unit cost for FDI firms is thus given by the following: , for r ̸ = D. , (9) where t int gs is the tax in sector s on purchases of good g and t f s is the factor tax. The substitution elasticity between value added and the business services composite is given where the α, β, and γ are share and scale parameters determined in the calibration to the input-output accounts. In the privatization scenarios explored in the Kenya model the γ s f parameters can be manipulated to represent pure productivity increases. For example, if the productivity of skilled labor increased by 10% in sector s we would simply multiply γ s SK by 1.1 raised to the power α s SK .
For the CRTS sectors a constant elasticity of transformation (CET) activity splits domestic output (with a unit value PY k ) into goods destine for domestic versus the region-specific export markets. Let the export price (for goods destine for region r ̸ = D) be PX k r then the CET technology is given by where σ τ indicates the elasticity of transformation and the γ are the CET distribution parameters. In the case of IRTS sectors, we assume that domestic firms use domestic output to produce Dixit-Stiglitz varieties. Thus the CET technology collapses without export coefficients [γ g r = 0 ∀g ∈ (I ∪ J)]: PD g = PY g ∀g ∈ (I ∪ J).
For CRTS sectors the export commodity is traded for foreign exchange at a fixed rate.
Let PFX equal the price of foreign exchange, and with a choice of units such that all gross of tax unit export prices are one at the benchmark, we have the following specification for the CRTS export activities: where t exp g is the export tax. For the IRTS sectors, domestic firms export the firm-level good where foreign agents are assumed to behave according to Dixit-Stiglitz preferences that are the same as domestic agents. Domestic IRTS firms face an export demand elasticity for their variety of σ g F and thus price their exports using the optimal markup.
In aggregate the IRTS export activities by region are characterized by Cross-border imports are purchased at the price of foreign exchange times one plus the tariff rate, which sets up the arbitrage condition for each import activity; PM g r = (1 + t imp gr )PFX for r ̸ = D.
Final demand includes three categories: household demand, government demand, and investment. The representative agents for each household h are assumed to have identical Cobb-Douglas preferences over the aggregated goods and services. The preferences are specified via a unit expenditure function associated with an economy-wide utility index (U ). Let PC be the true-cost-of-living index indicated by the following unit expenditure function: where the µ are value shares. The government faces a Leontief price index, PG, for government purchases: Similarly the price of investment, PINV is a Leontief aggregation of commodity purchases: Equations (1) through (18) define all of the transformation technologies for the model.
Next we turn to a specification of the market clearance conditions for each price.

F.2 Market clearance conditions
For each good or service there is a market, and, for any non-zero equilibrium price, supply will equal demand. We will use the convention of equating supply, on the left-hand side, to demand, on the right-hand side. The unit-value functions presented above are quite useful in deriving the appropriate compensated demand functions, by the envelope theorem (Shephard's Lemma).
Supply of the composite goods and services, trading at PA g , is given by the activity level, A g , and demand is derived from each production or final demand activity that uses the good or service. The market clearance condition is given by where h gs (Y s , p) are the conditional input demands (as a function of output and the price vector. These are found by taking the partial derivative of the unit cost function for sector s with respect to the gross of tax price of input g. For inputs that are not business services input demands are proportional to output: h gs (Y s , p) = β s g Y s ∀g ∈ (J ∪ K).
The input demands for business services are, however, more complex: where P srv s is the composite price of business services inputs: P srv For the IRTS sectors we have market clearance for the Dixit-Stiglitz regional composites: and for domestic firms we include demand for the Dixit-Stiglitz exports The IRTS composite input (trading at PMC g r ) is supplied by an activity, denoted Z g r ∀g ∈ (I ∪ J), and is demanded by the firms: Z g r = f g r N g r + Q g r (N g r ) 1/(1−σ g F ) ∀g ∈ (I ∪ J).
To derive (23) recall that firm-level output is Q g r (N g r ) σ g F /(1−σ g F ) so the use of the input across all firms is Q g r (N g r ) 1/(1−σ g F ) plus the total input use on fixed costs, f g r N g r .
Market clearance for the domestic output of CRTS sectors depends on supply from the CET activity and demand from the Armington activity: For IRTS sectors, supply is simply given by the CET activity (as there are no export coefficients in the CET technology for IRTS sectors). Output is then demanded by either the domestic or FDI firms. The market clearance conditions are given by for the service sectors, and for the Dixit-Stiglitz goods sectors.
Market clearance for exports of CRTS output is given by the CET supply function and demand is given by the export activity level (export demand is perfectly elastic): Reconciling gross output with the CET activities, we have market clearance for the commodities that trade at PY g : Import supply is perfectly elastic and import demand is derived from the Armington activities or embodied in the foreign Dixit-Stiglitz firm's inputs. For r ̸ = D, we have the following: Factor markets clear, where factor supply is given by the exogenous endowments to households, denoted S f , and input demands are derived from the cost functions: where P va s is the composite value-added price: P va s = ∏ f γ s f [(1 + t f s )PF f ] α s f . In addition, we have the market for the specific factor used in the IRTS sectors. Denoting the regional endowments of the specific factors SF g r ∀g ∈ (I ∪ J), we have:

F.4 Auxiliary Condition
In addition to the three sets of standard conditions presented above, we need to close the model with an auxiliary condition such that the real size of the government is held fixed. To do this we need to determine the index which scales direct taxes on households.
Associated with the variable T is the following condition: