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University of Groningen Faculty of Economics and Business MSc. International Economics and Business
Master thesis
THE HOME BIAS IN TRADE AND THE CASE OF THE
EUROPEAN UNION
Joost van den Beukel 2204924 Supervised by Prof. Dr. Bart Los
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Abstract
The effect of national borders on bilateral trade flows is large and influenced by many factors. This article focusses on the case of the European Union and one of the explanations provided in the literature; intermediate input trade. Lower costs to coordinate the production process resulted in internationally fragmented supply chains making the explanation less powerful. Theoretically consistent estimates are provided for both intermediate input trade and final goods trade. To provide the estimates a Poisson Pseudo Maximum Likelihood estimator is used. The results show that the estimates differ between intermediate input trade and final goods trade, supporting the hypothesis that stages are not clustered anymore.
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TABLE OF CONTENTS
1. INTRODUCTION 5
2. LITERATURE REVIEW 7
2.1 Estimates of the border effect 7
2.2 Explaining the border effect 8
2.3 Hypothesis 10
3. MODEL 12
3.1 The traditional gravity equation 12
3.2 The modified gravity equation 14
4. METHODOLOGY 18
4.1 Challenge 1: the multilateral resistance term 18
4.2 Challenge 2: zeroes in the trade flows 18
4.3 Challenge 3: trade costs 19
4.4 Challenge 4: heteroscedasticity of trade data 20
4.5 Specifications 20
5. DATA 22
6. RESULTS 25
6.1 Summary statistics 25
6.2 Results for the whole dataset 26
6.3 Results for intermediate input trade 28
6.4 Results for final goods trade 31
6.5 Intermediate input trade and final goods trade compared 32
7. CONCLUSION 34
8. REFERENCES 36
9. APPENDIX 38
9.1 Appendix A Distance matrix 38
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LIST OF TABLES
Table 1: a two-region example of an input output table 22
Table 2: summary statistics 25
Table 3: OLS and PPML estimates for the whole dataset 27
Table 4: OLS and PPML estimates for intermediate input trade 30
Table 5: OLS and PPML estimates for trade in final goods 31
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I. INTRODUCTION
To cross a national border as a tourist provides challenges in all kind of ways. Examples of these challenges are language barriers, a different currency or the requirement of a visa. When these challenges become more difficult, fewer tourists might be willing to cross the border from one country to another. Just as tourists, firms face challenges when one wants to move abroad or export its goods or services in a different country. Examples of challenges for firms are tariffs, quotas and non-tariff barriers such as product specific requirements. When these constraints become too big, firms might not be willing to move abroad or export their products. These examples make it interesting to examine the effect of national borders on trade flows between countries or regions. An interesting case is the European Union as many initiatives have been taken to further integrate member states. In fact, in 1958 the Association of European Border Regions (AEBR) was initiated to deal with the effect of national borders. The association receives funding from the European Union and specific policies have been established aimed at integrating border regions.
Quantifying the extent to which markets are fragmented provides interesting insights. Here we follow Head and Mayer (2000) who define a market as fragmented ‘when national borders influence the pattern of commercial transactions’ (Head and Mayer, 2000, p. 284). In this article markets are defined as NUTSII regions in the European Union. Research concerning the effect of national borders on bilateral trade flows commenced with an influential paper by McCallum (1995). In his article McCallum estimated a gravity equation to empirically show the effect of the U.S. – Canadian border on regional trade. His results show that Canadian provinces trade about 22 times more with other Canadian provinces than with U.S. states of similar size and distance. The gravity equation explains bilateral trade flows by the size of the two regions and the distance between them. Size has a positive effect on trade flows whereas distance has a negative effect. The home bias in trade refers to the excess intra-country trade that is estimated using a gravity equation. Obstfeld and Rogoff (2000) consider this to be one of the six major puzzles in international macroeconomics.
In the years that followed after McCallum’s (1995) paper articles first focused on providing estimates of the border effect for different time frames and regions1. From estimating the border effect the literature moved on to providing an explanation for the excess intra-country trade. One explanation focusses on the role of intermediate inputs in bilateral trade flows (Wolf, 1997; Chen, 2004; Hillberry and Hummels, 2008; Yi, 2010). The explanation boils down to two arguments. The first argument argues that firms from the same sector cluster in order to benefit from positive externalities such as increased productivity (Wolf, 1997; Henderson, 1974). When a production process is characterized by multiple stages then a large share of intermediate input trade takes place over a short distance which increases the effect of borders (Wolf, 1997; Hillberry and Hummels, 2008). The second argument argues that firms locate close to each other to decrease trade costs (Chen, 2004; Yi, 2010). When an intermediate good crosses a border multiple times, then trade costs are
1 For example, Helliwell and Verdier (2001) estimated the border effect of trade between Canadian provinces
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incurred each time the good crosses the border. By locating proximate to one another the good is traded within a country which lowers trade costs and increases intra-national trade.
The second part of this article will focus on this explanation and will argue that trade in intermediate inputs might not be an explanation for the home bias in trade anymore. The reasoning is based on the effects of the first and second unbundling (Baldwin, 2006). Basically, the first unbundling decreased transportation costs where economies of scale made it profitable to cluster the production process. The complexity of the production process required all stages to be clustered. The second unbundling changed this as the ICT revolution decreased communication costs. Now, it became possible to coordinate the different stages at distance where wage differences made this profitable. As a result, the importance of trade in intermediate inputs increased during the past decades as supply chains internationalised rapidly (Yi, 2003).
To sum up, this article will address two research questions. First, what is the effect of national borders on regional trade in the European Union? Second, is trade in intermediate inputs still an explanation for the home bias in trade? The value added of this article is threefold. First, up to date and detailed estimates for the effect of national borders on regional trade are provided. An unpublished database from the World Input Output Database (WIOD) is used to provide estimations for the year 2007 (Thissen, Lankhuizen and Los, in preparation). The database contains regional trade data at NUTSII level for the European Union, disaggregated at fourteen different industries. Second, this paper will provide theoretically consistent estimates of the border effect for trade in intermediate inputs and final goods. Baldwin and Taglioni (2014) show that the gravity equation as modelled by Anderson and van Wincoop (2003) is misspecified when trade in intermediate inputs is a large share of bilateral trade flows. Baldwin and Taglioni (2014) derive a modified model for the gravity equation where trade in intermediate inputs is modelled. The effect of this modification leads to different proxies for the variables representing the exporting and importing region. The database used provides the opportunity to construct the theoretically consistent proxies. Third, the results of this article show that the border effect for trade in intermediate inputs is not larger than the border effect for final goods. In fact, the border effect for trade in intermediate inputs is smaller by a magnitude of 0,53.
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2. LITARATURE REVIEW
This section will provide a discussion of the literature related to border effects and is structured into three parts. The first part will provide a discussion of the literature related to the first research question; what is the effect of national borders on regional trade in the European Union? The second part is focused on the second research question; can intermediate input trade be an explanation for the home bias in trade? Part three will discuss the hypotheses related to the research questions.
2.1 estimates of the border effect
The home bias literature commenced with an influential paper by McCallum (1995) who estimated the border effect for trade between Canadian provinces and U.S. states in 1988. Using a gravity equation and controlling for distance and size of the regions, a widely accepted method used in the home bias literature, he estimated that Canadian provinces trade 22 times more with themselves then with U.S. states of similar size and distance. Nitsch (2000) was the first to provide estimations of the border effect in the EU estimating a home bias of ten over the period 1979-1990. Besides including distance and size, Nitsch (2000) included a variable controlling for the location of country relative to other countries. This variable captures the effect of a country being located far away from other countries and close to only a few (e.g. Zealand and Australia). It is expected that countries like New-Zealand and Australia trade more with each other than two countries located near many other countries. Although the remoteness measure captures this effect to some extent, Anderson and van Wincoop (2003) show that it is theoretically inconsistent and does not capture the total effect. The implication is that the estimates by Nitsch (2000) are biased. A more extensive discussion on the remoteness of a country is provided in the section concerning the model.
Chen (2004) provides estimates for 78 different industries covering seven2 European countries in 1996. When the data is pooled Chen (2004) estimates a home bias of 6 whereas the industry specific estimates range from -1,14 to 19,17. Chen (2004) added an arbitrarily small constant to the dependent variable (ln(Xij,k + 1)) and estimated the specification using a Tobit procedure. This method was chosen to deal with the zeroes in the dataset which are excluded when estimating the specification using ordinary least squares. Although this method is one way to deal with the zeroes in the dependent variable, it is not preferred and is a problem further discussed in the section concerning the methodology.
Combes, Lafourcade and Mayer (2005) consider the effect of regional borders on inter-regional trade in France for the year 1993. Their results show a border effect of 6,3 whereas the border effects decreases by a factor of three when including the effect of social and business networks in the specification.
One of the challenges in the border effects literature is the measurement of intra-national trade flows due to the unavailability of data. Helble (2007) develops a method to more precisely gauge intra-national trade flows for France and Germany. Data on inter-regional trade flows are combined with inter-inter-regional transportation statistics to provide new proxies for intra-national trade. Using the same estimation method as Chen (2004), Helble
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(2007) estimates France to trade eight times more with itself than with fourteen other EU countries in the year 2002. For Germany the most recent available data was for the year 2004, where the estimates indicate a home bias of three.
In comparison to the above discussed articles, this research contributes to the existing literature in several ways. A first contribution is based on the availability of the data. A cross-sectional dataset covering all EU regions at NUTSII level, disaggregated at fourteen different industries for the year 2007 is available. The border effect will be estimated for smaller geographical units and a more recent year providing up to date estimates of the border effect in the European Union. A second contribution is methodological. To deal with the zeroes in the dataset Chen (2004) and Helble (2007) add a small constant to the dependent variable and make use of a Tobit procedure. This method is at odds with theory and therefore not preferable. When the dependent variable contains a large amount of zeroes, as Chen (2004) and Helble (2007) experience, the preferred method of estimation is a Poisson Pseudo Maximum Likelihood (PPML) estimator (Santos Silva and Tenreyro, 2006). This article will make use of the PPML estimator and will therefore use the full dataset when estimating the border effects.
2.2 explaining the border effect
The large effect of national borders on bilateral trade flows led to the development of a large stream in the literature focusing on an explanation. Head and Mayer (2009) make progress by improving the measurement of one specific variable; the internal distance. Others focused on social and business linkages (Lafourcade et al., 2005) or the absence of information (Rauch, 2001) in explaining the border effect. This article focusses on the role intermediate inputs play in the effect of national borders. It is not argued that the home bias is solely explained by intermediate inputs as multiple explanations might possibly explain the home bias in trade.
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spatial externalities of clustering, this would lead firms to cluster meaning intermediate input trade is localized and explaining a part of the home bias in trade.
A second article exploring the role of spatial clustering of intermediate input suppliers and final goods producers is Chen (2004). The data used covers bilateral trade flows for seven countries in the European Union in the year 1996. A standard gravity equation including size, distance, adjacency and the multilateral resistance term is used to estimate the border effect. Chen (2004) argues that firms cluster as a response to the incurred trade costs which causes trade between intermediate inputs suppliers and final goods producers to be localized. To test this hypothesis, an interaction term is included where the home dummy variable (taking the value of one for intra-national trade and zero otherwise) is interacted with a ‘geographic concentration’ index (Ellison and Glaeser, 1997). The index measures to what extent an industry is bound to a specific location (e.g. wine producers are bound to specific regions where they grow best). If an industry is not bound to a specific region, it is expected that firms cluster to decrease trade costs. The results confirm her hypothesis that firms cluster to decrease trade costs.
Hillberry and Hummels (2008) provide an explanation for the reduction of trade flows as a result of geographic frictions. The authors have access to an unpublished but rich dataset on trade statistics within the U.S. Specifically, per shipment information is available on value, industry classification, establishment, zip codes of origin and destination and actual shipping distance. First, the authors show that total trade flows decrease over distance mainly due to the number of unique goods traded (the extensive margin) and the number of unique firms trading. The average value per shipment remains fairly constant over distance (the intensive margin). The question the authors ask themselves is why trade is localized to a large extent? The authors argue that a possible explanation could be related to the industrial demand of a region. Specifically, their hypothesis states that regions specialize which make their industrial demand to vary with their specialization. Consider the following example to clarify their hypothesis. Limburg, a region in the Netherlands, produces intermediate goods; specifically, they produce the engines for Honda Civics. Any other region would only have demand for their output if it produces Honda Civics. To decrease trade costs, firms producing Honda Civics locate near Limburg. This implies that regions far away from Limburg do not have an industrial demand for the goods produced in Limburg but the regions nearby do.
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Chen (2004) makes use of a specification based on the Anderson and van Wincoop (2003) model. In this model the production of goods is assumed to be a one stage production process. Although this assumption is not taken too literally, it does have an influence on the estimated border effect. Yi (2010) develops a two-stage production model to explain the home bias in trade. He estimates the border effect using his two-stage production model and compares it to a one-stage Eaton and Kortum (2002) model. The findings show that the multistage model can explain two-fifth of the U.S. – Canada border effect, whereas the one-stage model can only explain one-sixth of the border effect. Yi (2010) explain two magnification effects that are related to the effect of trade barriers on trade flows when the production process involves multiple stages in different countries, implying (intermediate) goods to cross the border multiple times. His model incorporates these effects giving the model a stronger explanatory power. The first effect arises as goods cross the border multiple times meaning trade costs are incurred multiple times. Consider a simple hypothetical example. The Netherlands produces multiple intermediate inputs for the production of a car. These intermediate inputs are then exported to Germany where the car is assembled. Then, the car exported back to the Netherlands and sold to final consumers. Each time the (intermediate) goods crosses the border trade costs are incurred, meaning in this example the intermediate inputs produced in the Netherlands incur trade costs twice. The second effect arises as trade costs are incurred over the whole product, while the value added of the exporting country might be small. This makes the effective trade cost, which is the trade costs divided by the value added part of the total cost, larger. Both effects cause international trade to be smaller and intra-national trade to be larger, explaining the larger explanatory power of the model developed by Yi (2010).
In providing an explanation of the border effect the novelty of this study is twofold. First, this article makes use of two different theoretical foundations of the gravity equations; one where trade in goods is based on a consumer expenditure equation (Anderson and van Wincoop, 2003) and one where trade in intermediate inputs is incorporated (Baldwin and Taglioni, 2014). The difference between both models boils down to the definitions of the variables representing the size of a region or country. Where in the Anderson and van Wincoop (2003) model the mass variable is best proxied by GDP, in the Baldwin and Taglioni (2014) model this is gross use for the importing region and gross sales for the exporting region. So, this article provides theoretically consistent estimates of the home bias in trade differentiating between final goods trade and intermediate input trade. Second, estimates are provided for a more recent time period; 2007. This implies that the effects of the second unbundling (Baldwin, 2006) might have altered to what extent trade in intermediate inputs can explain the home bias in trade. This is further discussed in the next paragraph concerning the hypotheses.
2.3 Hypotheses
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by multiple stages then clusters of sectors lead to a high level of trade in intermediate goods over a short distance. This, in turn, increases the effect of national or regional borders on trade. The second line of reasoning is based on the effect of trade costs on the firms decision where to locate (Chen, 2004; Yi, 2010). As above, consider the production of a good to be characterized by multiple stages. If the different parts are produced in different countries, then each time the intermediate good crosses a border trade costs are incurred. To decrease the amount of trade costs incurred firms locate close to each other. So, the behavioural response of firms to trade costs increases the effect of national borders on trade.
This article will argue that a third factor, costs incurred to coordinate the production process at distance, altered the effect of trade in intermediate inputs on the home bias in trade. This argument is based on work by Baldwin (2006) who showed that the world experienced globalisation in two ways: a first unbundling and a second unbundling. The first unbundling, starting at the end of the 19th century, decreased costs of transportation via the steam revolution. Railroads could now transport goods at low costs over a long distance, making it profitable to cluster the production process and benefit from economies of scale. The complexity of the production process required firms to cluster all stages together to decrease coordination costs. However, since the mid-1980s globalization was characterized by the ICT revolution, referred to as the second unbundling by Baldwin (2006). The ICT revolution decreased the costs of communication making it possible to coordinate the different stages of the production over a long distance. Due to wage differences between industrialized and non-industrialized countries it became profitable to produce parts of the production process at distance. Where before the second unbundling competition was based on sectors (e.g. German cars versus French cars), after the second unbundling international competition took place at a lower level of aggregation; stages (e.g. Germany could now use French car parts to produce their cars and vice versa). So, the production of a certain good consists of multiple intermediate inputs produced in multiple countries. Yi (2003) shows how vertical specialization can explain a large share of the rise in world trade. In his model vertical specialization refers to a production process characterized by multiple, sequential stages which are performed in multiple countries (Hummels, Ishii and Yi, 2001).
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3. MODEL
The first gravity equation was developed by Tinbergen (1962) who related bilateral trade flows to the size of the two trading countries and the distance between them. The mass variable in the specification is positively related to bilateral trade flows whereas distance is negatively related to trade flows. A large extent of the bilateral trade flows could be explained by the gravity equation but one of the main critiques was that the specification lacked a theoretical foundation. Anderson (1979) was the first to develop a theoretical microfoundation for the gravity equation using a CES preference structure and product differentiation by country of origin. Further theoretical developments were made by Bergstrand (1985; 1989; 1990) and Deadorff (1998) in the years that followed. Current articles make use of the theoretical foundation developed by Anderson and van Wincoop (2003), a model which has been widely applied in the gravity literature. The main contribution of their paper consisted of the theoretical development of the multilateral resistance term. This model will be the first model discussed as it is widely used in the gravity literature and it provides the theoretical foundation for the gravity equation based on a consumer expenditure model.
To properly estimate the gravity equation when intermediate input trade plays an important role, Baldwin and Taglioni (2014) show that a modification needs to be made to the Anderson and van Wincoop (2003) model. Their model is based on the model developed by Krugman and Venables (1996) and is the second model discussed in this section. This model is the theoretical foundation to estimate the gravity equation when intermediate input trade is important.
3.1 The traditional gravity equation
The discussion of the traditional model is based on the papers from Anderson and van Wincoop (2003) and Baldwin and Taglioni (2006; 2014). The aim of this section is to derive a gravity equation which can be estimated with the available data. The starting point is the expenditure share identity:
podxod ≡ shareodEd (1)
where pod denotes the price paid by consumers in destination region d for goods produced in origin region o, xod refers to the quantity of a particular good produced in origin region o bought by consumers in destination region d. Ed refers to the total expenditure on all tradeable goods (including goods produced in region d itself) of consumers in region d, shareod refers to the share of the total expenditure (Ed) consumers in region d spend on a particular good in region o. The expenditure share identity is the bilateral trade flow from region o to region d for one specific variety. To develop the bilateral trade flow for all varieties, relative prices need to be introduced. Therefore, a constant elasticity of substitution (CES) demand structure is introduced and it is assumed all goods are traded. Now, the total bilateral trade flow of a particular good from region o to region d is represented as:
vod ≡ ( 𝑝𝑜𝑑
𝑃𝑑) 1-σ
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where Pd refers to the CES price index for consumers in region d. This implies 𝑝𝑜𝑑
𝑃𝑑 is the real price faced by consumers in destination region d who buy goods from region o. The elasticity of substitution is represented by σ where it is assumed all varieties are symmetric. Without the assumption of symmetric varieties one needs to include a variety index to account for the asymmetry of goods produced. This would complicate the model and is not necessary to derive the gravity equation. In principal equation (2) could be estimated if the availability of data would not be a problem. However, prices for which goods are traded are not available which means one has to solve this problem.
A next step would be to specify the price for which goods are traded, pod. The price is determined by the production costs of a particular good in region o, the trade costs and a mark-up:
pod = μodpoτod (3)
where μod represents the mark-up, po is the cost of producing a particular good in region o, τod are the bilateral trade costs. It is assumed producers face a Dixit-Stiglitz monopolistic competition meaning the mark-up is equal to one as μod is equal to all destinations3. This assumption simplifies further derivation of the model.
Next, the bilateral trade flows of each variety are aggregated to derive the total bilateral trade flow from region o to region d:
Vod = no(poτod)1-σ 𝐸𝑑 𝑃𝑑⁄ 1-σ (4)
where no refers to the number of varieties produced by nation o. The total bilateral trade flow from region o to region d is thus determined by multiplying the bilateral trade flow for a single variety with the number of varieties produced in region o. Like identity (2), if data availability would not have been a limitation, this equation could be estimated. However, the unavailability of data to estimate equation (4) means one has to overcome this problem.
To eliminate the price po in the model it is assumed markets clear which means total production of region o equals total sales of region o. Total sales are represented by Vod, then markets clear when
Yo = nopo1-σ ∑𝑑=1𝑅 ( τod1-σ 𝐸𝑑 𝑃𝑑⁄ 1-σ ) (5)
where Yo represents total production of region o. The right hand side variables were derived in equation (4) and the summation included refers to the summation of total sales of region o to all regions including itself. In equation (5) nopo1-σ are the variables of interest, thus solving equation (5) for these variables leads to
nopo1-σ = Yo / Ω o, where Ωo ≡ ∑𝑖=1𝑅 (τoi1-σ 𝐸𝑖⁄𝑃𝑖1-σ ) (6)
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where the term Ω refers to the market potential of region o. The final step to derive the gravity equation is to substitute equation (6) into equation (4):
Vod = τod1-σ Yo Ed 1 Ω𝑜⁄ 1 𝑃𝑑⁄ 1-σ (7)
Equation (7) is the traditional gravity equation which can be estimated with the data available. The equation includes trade costs which are represented by τod1-σ, demand potential represented by Ed, and supply potential represented by Yo. Furthermore, the gravity equation includes the multilateral resistance term developed by Anderson and van Wincoop (2003). The multilateral resistance term, 1 Ω𝑜⁄ 1 𝑃𝑑⁄ 1-σ , consists of three parts, namely the bilateral trade barrier between region o and d, region o’s resistance to trade with all regions, and region d’s resistance to trade with all regions. This can at best be explained by a simple example. Consider the bilateral trade flows between Australia and New-Zealand and the bilateral trade flows between the Netherlands and Germany. Both pairs of countries are located relatively close to each other which increases bilateral trade flows. The main difference between both pairs of countries is their position relative to all other countries. Australia and New-Zealand are located close to each other but are located far away from many other countries. This increases bilateral trade flows between both countries and decreases bilateral trade flows between other countries. On the contrary, the Netherlands and Germany are located close to each other and they are located close to many other countries. This decreases bilateral trade flows between both countries and increases bilateral trade flows between other countries nearby. So, the position relative to all other countries has an influence on the total bilateral trade flows. By not including the multilateral resistance term one has a specification with omitted variables.
To finalise the first part of this section, in equation (7) trade costs can be proxied by the bilateral distance, Yo is region o’s supply potential and can be proxied by its GDP, Ed is region d’s demand potential and can be proxied by its GDP. The multilateral resistance term can be accounted for by including origin and destination fixed effects.
3.2 The modified gravity equation
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First, a discussion of the utility function for consumers:
V = I / Pc; Pc ≡ pA1-α (P)α ; P ≡ (∫𝑖∈𝐺 i𝑝1-σ di)1/(1-σ) (8)
In equation (8) I refers to the income of a typical consumer and Pc refers to the consumer price index. The consumer price index consists of two parts: a price index for goods from sector A, pA, and a price index for goods from sector M, P. The share of income spend on goods from sector M is denoted by α, meaning that 1-α is the share of income spend on goods from sector A. P is a CES price index for all varieties available from sector M, G refers to the total of available varieties for consumers. The notation pi refers to the price paid by consumers for a variety i. Next, the cost function for firms is introduced:
C[w, P, x] = (F + axx)w1-αPα (9)
To produce a good in sector M the use of labour L and intermediate inputs M are required. The share of intermediate inputs in the production of goods in sector M is represented by α, a Cobb-Douglas cost share for the use of intermediate inputs. This implies 1-α is the share of labour required in the production of goods in sector M. In the cost function ax and F are costs parameters, total output is represented by x and w is the wage.
The next step is to specify the price paid by customers when the good is traded from origin region o to destination region d:
pod = τodwo1-αPoα (10)
As in the derivation of the traditional gravity model a Dixit-Stiglitz monopolistic competition is assumed meaning that the mark-up μod is equal to one, it therefore does not show up in equation (10). Similar to equation (3), τod represent the trade costs. The main difference compared to equation (3) in the traditional model (pod = μodpoτod) boils down to the price of a good produced in region o. In the traditional model the use of intermediate inputs is not modelled, the price po is the cost of production when using labour. Equation (10) explicitly incorporates the use of both labour, represented by wages wo, and intermediate inputs from sector M, represented by Po. Po is the price index for goods from sector M produced in region o. The following step is to derive an equation similar to equation (4) in the traditional model (Vod = no(poτod)1-σ 𝐸𝑑 𝑃𝑑⁄ 1-σ ), which is the total bilateral trade flow from region o to region d:
Vod = no(poτod)1-σ 𝐸𝑑⁄𝑃𝑑1-σ ; Ed ≡ α(Id + ndCd) (11)
where no is the number of different varieties produced, Id represents the income of consumers in nation d and Cd refers to the cost of producing a variety in nation d.
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and Taglioni (2014) the total expenditure of region d on tradable goods consists of two parts: consumer goods and intermediate inputs. The expenditure of consumers on final goods is represented by Id, the consumer income. The expenditure of firms on intermediates is represented by the cost function, Cd. In equation (11) α refers to the share of total expenditure on all goods (both from sector A and sector M) which is spend on goods from sector M. This means that the specification of nation d’s expenditure is the first important difference between both models.
As with the traditional model, equation (11) could be estimated if the availability of data would not have been a problem. However, the availability of data on the number of goods traded and the price for which goods are traded is limited. To cope with this problem it is assumed markets clear implying demand equals supply:
noCo = nopo1-σ ∑ 𝜏𝑑 od1-σ Pd1-σ Ed ; Co ≡ C[wo, Po, xo] (12)
where the cost function Co has been introduced in equation (9). Equation (12) is similar to equation (5): Yo = nopo1-σ ∑𝑑=1𝑅 ( τod1-σ 𝐸𝑑 𝑃𝑑⁄ 1-σ). Here, the second important difference between the traditional model and the model developed by Baldwin and Taglioni (2014) shows up. The difference boils down to the specification of the supply side of the equation. In the traditional model this is represented by Yo which is nation o’s total output. Yo equals its GDP when no intermediate inputs are imported as is the case in the traditional model. In the Baldwin and Taglioni (2014) model the supply side is modelled by the cost function as in equation (9): C[w, P, x] = (F + axx)w1-αPα. The cost function explicitly accounts for the use of intermediate inputs in the production process which makes GDP not the appropriate proxy for the supply side.
To derive the gravity equation where the use of intermediate inputs are modelled, equation (12) needs to be solved for the number of products traded and the price of the goods traded:
nopo1-σ = noCo / Ωo, where Ωo ≡ ∑𝑑 𝜏od1-σ Pd1-σ Ed (13)
where similar to the traditional model the term Ωo refers to the market potential of region o. The final step to derive the gravity equation where intermediate input trade is modelled requires one to plug equation (13) in equation (12):
Vod = τod1σ Ed Co 1 Ω𝑜⁄ 1 𝑃𝑑⁄ 1-σ (14)
where the expenditure term Ed is explicitly defined in equation (11) and supply term Co in equation (12). In the gravity equation the trade costs τod are proxied by the bilateral distance between both regions, and both mass variables, Ed for the importing region and Co for the exporting region, are proxied by their gross output. The multilateral resistance term, 1 Ω𝑜⁄ 1
𝑃𝑑 ⁄ 1-σ
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To sum up, this section discussed two theoretical models related to the gravity equation. The first model was the traditional model based on a consumer expenditure equation (Anderson and van Wincoop, 2003). The second model was a modification where intermediate input trade was explicitly modelled (Baldwin and Taglioni, 2014). The main difference between both models boils down to the definition of the demand and supply equations. In the traditional model solely the demand for consumers was modelled, in the model by Baldwin and Taglioni (2014) both consumer and firm demand is modelled. The theoretical difference between both models implies that the proxies for the mass variables in the specifications estimated differ. This will be further discussed in the next section.
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4. METHODOLOGY
The first part of this section will discuss four challenges and their solutions when estimating the gravity equation. The four challenges are the multilateral resistance term, the amount of zeroes in the trade data, how to proxy trade costs and how to deal with heteroscedasticity. The second part of this section will discuss the specifications of both theoretical models and the differences between the specifications.
4.1 challenge 1: the multilateral resistance term
The first challenge is related to the multilateral resistance term which is theoretically derived but unobservable. Not including the multilateral resistance term in the specification leads to the ‘Gold medal error’ mistakes as Baldwin and Taglioni (2006) name it. When not including the multilateral resistance term in the specification, the error term is correlated with one of the independent variables, namely τod. To make this point clear, recall the definitions of the two terms in the multilateral resistance term: Pd and Ωo. Focussing solely on the modified model (the same reasoning holds for the traditional model model), Pd is defined as P ≡ (∫𝑖∈𝐺 i𝑝1-σ
di)1/(1-σ), where pod = τodwo1-σPoα and Ωo is defined as Ωo ≡ ∑𝑑 𝜏od1-σ Pd1-σ Ed. In both definitions trade costs show up meaning that excluding the multilateral resistance term causes the error term to be correlated with τod leading to biased estimates. To solve this problem importer and exporter fixed effects are included, a solution suggested by Anderson and van Wincoop (2003) and introduced by Harrigan (1996). When one makes use of panel data exporter-time and importer-time fixed effects should be included (Olivero and Yotov, 2012). However, this article focusses solely on a single year of the database making the solution suggested for cross-sectional data sufficient.
4.2 challenge 2: zeroes in the trade flows
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Poisson regression it is not necessary to take the logarithm of the dependent variable. This article will therefore make use of the PPML estimator when estimating the specification. Furthermore, as robustness checks two other estimation methods considered by Santos Silva and Tenreyro (2006) are used. Both OLS and the Gamma Poisson Maximum Likelihood methods will be used to estimate the specifications.
4.3 challenge 3: trade costs
In both models trade costs are defined as “all costs incurred in getting a good to a final user other than the marginal cost of producing the good itself” (Anderson and van Wincoop, 2004, p. 691). Examples of trade costs are transportation costs, search costs and tariffs. Previous articles estimating the gravity equation proxied trade costs by using for example the bilateral distance between regions, whether the two countries had a common coloniser (Baldwin and Taglioni, 2014) or a common border (Baldwin and Taglioni, 2014; Chen, 2004). One of the goals of this article is to estimate two theoretical consistent gravity equations where the important difference is reflected in the measurement of the mass variables. Therefore, the distance from producer to customer is proxied, a solution widely used when estimating the home bias in trade. One can make a distinction between the external distance, which reflects the bilateral distance between two regions, and the internal distance, which reflects the trade costs for intra-regional trade.
Regarding the measurement of the distance between two regions or countries a majority of the articles makes use of the ‘great circle distance’ between two points. Data is widely available at country level and its simplicity makes it a widely accepted proxy for trade costs. One of the exceptions is Wolf (2000) who makes use of the minimum driving distance between two states in the US. Because a large share of intra-US trade is transported by road Wolf (2000) argues this measure appears preferable. Here, a similar method is used where the external distance is proxied by the distance by road between NUTSII regions in the European Union. Eurostat data show that in the EU over half (51%) of intra-EU trade is transported by road which makes this measure preferable.
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distribution of buyers and sellers have to be made. The first measure which will be used assumes each area consists of production hubs (Head and Mayer, 2000). Previous work by Wolf (1997) and Hillberry and Hummels (2008) shows that trade in intermediate inputs is clustered which provides an indication of the existence of production hubs. The formula used by Head and Mayer (2000) is the following:
0,38 * √ (area)
where the area is measured in square kilometres. As a robustness check, a second measurement will be used to provide an indication to what extent the results are sensitive to the measurement of the internal distance variable. This measure assumes buyers and sellers are uniformly distributed across the area (Nitsch, 2000). For the construction of the variable based on the assumption of Nitsch (2000) the following formula is used:
0,56 * √ (area)
where the area is measured in square kilometres.
4.4 challenge four: heteroscedasticity of trade data
One of the problems which arise when making use of trade data is heteroscedasticity. Santos Silva and Tenreyro (2006) show in their paper that when making use of ordinary least squares the estimates are biased and inconsistent. For example, in their estimations the authors show that when not dealing with heteroscedasticity the coefficient on the distance variable can be twice as large. In their paper the authors suggest the above mentioned Poisson Pseudo Maximum Likelihood (PPML) estimator which can deal with both the zeroes in the dataset and the heteroscedasticity. This makes the PPML estimator the preferred solution to deal with heteroscedasticity.
4.5 specifications
The first specification is based on the Anderson and van Wincoop (2003) model and is a log-linearization of equation (7) estimated using ordinary least squares. The logarithm is taken from the dependent variable to provide a better approximation of a normal distribution. The problem which arises with this method (dropping the zeroes out of the dataset) has been discussed above. The specification takes the following form:
ln Xij = αi + αj + β1Homeij + β2GDPi + β3GDPj + β4Dij + εij (15)
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region and GDPj for the importing region. Dij measures the bilateral distance between region i and region j where Dii measures the internal distance, εij depicts the error term. To estimate the Anderson and van Wincoop (2003) model using the PPML and GPML estimator one does not have to take the logarithm of the dependent variable which modifies the dependent variable in the above specification:
Xij = αi + αj + β1Homeij + β2GDPi + β3GDPj + β4Dij + εij (16)
where the variables included are the same as above and the difference is reflected in the dependent variable.
The third specification is based on the Baldwin and Taglioni (2014) model and is a log-linearization of equation (14) estimated using OLS:
ln Xij = αi + αj + β1Homeij + β2GOi + β3GOj + β4Dij + εij (17)
where Xij represents the bilateral trade flow from region i to region j in millions of Euros. Again, αi and αj are importer and exporter fixed effects and Homeij is a dummy variable taking the value of 1 for intra-country trade and zero otherwise. The difference between both theoretical models now shows up in the specification. GOi and GOj are gross output measures where GOi depicts the mass variable for the exporting region and GOj depicts the mass variable for the importing region. Dij depicts the distance between and within regions, εij is the error term. To estimate the Baldwin and Taglioni (2014) model using the PPML and GPML estimator the following specification is used:
Xij = αi + αj + β1Homeij + β2GOi + β3GOj + β4Dij + εij (18)
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5. DATA
This section will discuss the data sources used and any problems related to constructing the variables. To start, a brief explanation of an input output table for two regions is provided and shown in table 1. An input output table consists of several matrices and vectors. These are a matrix for intermediate input trade, matrix Z, a matrix with final demand, matrix F, a column vector x showing gross output (where x’ depicts the transpose) and a matrix W representing the use of primary inputs. In the table below region i and j in the most left column are the exporting regions, region i, j and region i final demand category k and l are the importing regions. Starting with matrix Z, element zij in the table below is the monetary value for intermediate input delivered from region i to region j. This means goods move from region i to region j, whereas the money flows from region j to region i. In matrix F element fj,ik depicts the monetary value for final demand from region j to region i, final demand category k. Goods move from region j to region i and money flows from region i to region j. Vector x represents gross output, meaning xi depicts the gross output for region i. Finally, in matrix W element wmi shows the use of primary input m in region i.
Table 1: a two-region example of an input output table Region i Region j Region i final
demand category k
Region i final demand category l
Total
Region i zii zij fi,ik fi,il xi
Region j zji zjj fj,ik fj,il xj
Primary inputs wmi wmj Primary inputs wni wnj
Total xi’ xj’
This article will make use of an input output table provided by the World Input Output Database (WIOD) project (Thissen, Lankhuizen and Los, in preparation). The provided input output table consists of regional trade data for the European Union, disaggregated at fourteen different industries. Furthermore, data is available for seventeen other countries or regions (‘rest of the world’) disaggregated at fourteen different industries. In the dataset four different uses of primary inputs are provided and five different final demand categories are included. Finally, the dataset covers a period of 2000-2010.
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resistance term in the model captures this effects meaning the estimates will not be biased because of this decision. To make this point more clear a simple example will be provided. Consider the regions Zuid-Holland in the Netherlands, Antwerp in Belgium and the country China. Before China joined the WTO high trade costs caused trade between Zuid-Holland and China to be low, trade between Antwerp and China to be low and trade between Zuid-Holland and Antwerp to be high. After China joined the WTO trade costs decreased for trade between Zuid-Holland and China and between Antwerp and China, trade costs between Zuid-Holland and Antwerp remained the same. This will lead to an increase in trade between Zuid-Holland – China and Antwerp – China. Furthermore, trade between Zuid-Holland and Antwerp will decrease. Lower trade costs with China reduce prices between China – Zuid-Holland and China – Antwerp, increasing the relative price between Zuid-Holland and Antwerp. This effect is captured by including the multilateral resistance term as formally explained in section three. A third not that should be made is the decision to take out the final demand category ‘inventory adjustment’. This category contains solely zeroes or negative values which could not be estimated using OLS or the PPML estimator. The negative values are for intra-regional trade, the zeroes are for inter-regional trade. Leaving out this final demand category has an effect on the estimation of the border effect for the whole dataset and for final demand only. It is expected that decision biases the results upwards. If one would trade more with itself then the border effect would increase, if one would trade less with itself the border effect would decrease.
The construction of GDP levels is based on the data available from the WIOD by summing the use of primary inputs per region. This variable is used to estimate the border effects on the whole dataset and on a subset of final goods trade only. For the gross output measures several variables have been constructed. The first variable consists of gross output per region for trade with the whole world, including both trade in intermediate inputs and trade in final goods. This variable is used for estimation of the border effect using the whole dataset. The second variable consists of gross output for trade in intermediate inputs per region for the whole world. The third variable is constructed using gross output for trade in intermediate inputs per region and industry while making use of intermediate input trade with the whole world. The second and third variables are used to estimate a subset containing only trade in intermediate inputs in the European Union.
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6. RESULTS
This section will start with a brief overview of the most relevant summary statistics. The second part will provide a discussion of the results obtained from the specifications estimated. Here, specific interest is in the coefficients on the mass variables as the measurement of the variables differs. The third part will provide a comparison of the results obtained for intermediate input trade and final goods trade focusing on the border effect and the distance coefficient.
6.1 summary statistics
Table 2 contains the summary statistics of the most relevant variable trade for all trade flows and only positive trade flows. Several notes should be made here. First, what can be seen from the first two rows is the large difference between the number of observations for all trade statistics and the statistics reported solely for positive trade values. The total number of zeroes in the dataset is 1.470.752, which is equal to 9,97% percent. This is much larger than previous datasets used to estimate the border effect. For example Chen (2004) made use of a dataset containing 5% of zeroes. As discussed in the methodology, the large amount of zeroes is one of the reasons which justify the use of the Poisson Pseudo Maximum Likelihood estimator.
Table 2: summary statistics
Variable Obs. Mean Std. Dev. Min. Max.
Intermediate input trade and final demand
Trade 14.756.238 1,437213 70,40572 0 88.077,9
Trade > 0 13.285.486 1,596317 74,19883 4,23e-21 88.077,9
Intermediate trade only
Trade 12.152.196 0,8426205 32,6272 0 46.951,62
Trade > 0 11.249.506 0,9102346 33,91008 4,23e-21 46.951,62
Final goods only
Trade 2.604.042 4,211876 152,0273 0 88.077,9
Trade > 0 2.035.980 5,387166 171,9144 1,94e-20 88.077,9
Notes: the table contains the number of observations for each variable (Obs.), the average value of the trade flow (Mean), the standard deviation (Std. Dev.) and the minimum and maximum value (Min. and Max.).
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17,65% when looking at the number of observations4. Therefore, it is more valuable to look at shares in monetary terms which are 51% for intermediate input trade and 49% for final demand trade. So, trade flows in the European Union between NUTSII regions disaggregated at fourteen different industries are characterized by 51% of trade being intermediate input trade and 49% of trade being final good trade. As shown in the section related to the model, the mass variable differs when trade in intermediate inputs is included. When one estimates a gravity equation using GDP as a proxy for the mass variables, Baldwin and Taglioni (2014) show that the estimate for the mass coefficients are lower when trade flows are characterized by a large share of intermediate input trade. Specifically, the authors show that this happens at a certain threshold; when bilateral trade flows are characterized by 50% (or more) of trade in intermediate inputs, the mass coefficient is significantly lower. Therefore, it is expected that the estimated mass coefficients for the whole dataset while using GDP as a proxy is lower than when the dataset is split and the appropriate proxy is used for either intermediate input trade or final goods trade.
6.2 results using the whole dataset
Table 3 on the next page presents the results estimating the gravity equation over the whole dataset. The first two columns present the results estimating specification 15 over the whole dataset using OLS. The difference between both columns is the measurement of the internal distance variable, where in the first column the Head distance measure is used and in the second column the Nitsch distance measure. The last two columns present the results when estimating the coefficients using the PPML estimator. As one can see from the number of observations included, the OLS procedure excludes all zeroes when estimating the specification. Furthermore, all estimates include origin and destination fixed effects. Table 3 shows results which are comparable to earlier work on border effects as all trade flows are estimated using GDP as a proxy for the mass variable.
All coefficients enter highly significant at the 1% level and with the expected signs; a positive effect for the size of a region on trade and a negative effect for the distance between both regions. Previous articles estimating the gravity equation estimate the mass variables to be close to unity (Santos Silva and Tenreyro, 2006; Wolf 2000 and Chen 2004 for the exporting region). The estimates of the mass variable in table 3 are of a different magnitude, where the coefficient for the exporting region when using OLS is almost half of unity (0,513 and 0,514). The results are however in line with work by Head and Mayer (2009) who estimate a coefficient of 0,53 for the exporting country and 0,89 for the importing country. There are two explanations why the coefficients are not close to unity. First, the mass variables are measured at regional level whereas bilateral trade flows are further disaggregated at fourteen industries. Chen (2004) estimated the gravity equation using trade data disaggregated at 78 different industries and specified the exporting mass variable at country and industry level. Her results show that the coefficient for the exporting region is just above one. This could imply that if the exporting and importing mass variables are
4 The number of rows equals 3486 (249 times 14) whereas the number of columns equals 4233 (249 times 14
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disaggregated at industry level, the estimates could be close to one. A second explanation is related to the composition of the bilateral trade flows. As mentioned, Baldwin and Taglioni (2014) show that as intermediate input trade becomes more important, the ability of GDP to proxy the size of the exporting and importing region decreases. As a result, the estimates of the mass variables are not close to unity but of a lower magnitude. With a dataset where almost 50% of bilateral trade is in intermediate inputs this could be a large part of the explanation.
Table 3: OLS and PPML estimates for the whole dataset
OLS OLS PPML PPML lnGDPo 0,513*** (0,013) 0,514*** (0,013) 0,800*** (0,078) 0,758*** (0,071) lnGDPd 0,809*** (0,032) 0,810*** (0,032) 0,695*** (0,053) 0,848*** (0,072) lnDistance Head -1,509*** (0,017) -1,686*** (0,030) lnDistance Nitsch -1,490*** (0,018) -1,728*** (0,059) Home 1,125*** (0,038) 1,221*** (0,039) 1,071*** (0,066) 1,686*** (0,081)
Fixed effects Yes Yes Yes Yes
R-squared 0,153 0,152 0,104 0,067
Observations 13.282.151 13.282.151 14.752.668 14.752.668
Border effect 3,08 3,39 2,92 5,40
Notes: estimates of the border effect for the whole dataset. OLS estimates have been estimated using the whole dataset. The PPML estimates have been constructed by making three subsets of the whole dataset (2 sets contain 5 industries of intermediate inputs and 1 final demand category, 1 set contains 4 industries of intermediate inputs and 1 final demand category). From the received estimates the average has been taking using a weight of 0,353 for the first two subsets and 0,294 for the third subset. Although this method is not preferable, with the computers at hand it was unfortunately not possible to make use of the PPML estimator for the whole dataset. In parentheses robust standard errors clustered by pair are shown for the OLS estimates, clustered standard by pair have are depicted for the PPML estimator. *, **, *** indicates significance at 10%, 5% and 1% level.
The estimated coefficients for the distance variable are larger than previous estimates5. Disdier and Head (2004) conduct a meta-analysis of the distance effect where 103 articles are considered. Their results show that the mean effect of distance is 0,90 where 90% of all estimates lie within the 0,28 - 1,55 range. A possible explanation is the measurement of the external distance variable. This article made use of the distance between regions by road. Hummels (2001) shows that the effect of distance on transport by road is larger, Disdier and Head (2004) find similar results supporting this hypothesis. A different explanation could be that other studies included variables such as adjacency (Chen, 2004; Head and Mayer, 2009) or common language (Santos Silva and Tenreyro, 2006; Baldwin and Taglioni, 2014). Where distance between two regions is a proxy for trade costs, by including other variables the
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magnitude of the distance coefficient might decrease as some part is captured by other coefficients. The effect of a different measurement of the internal distance variable is small on the distance coefficient. The difference is most pronounced reflected in the home coefficient.
To compute the actual border effect the antilog is taken from the coefficient estimated for the home dummy variable. When considering the preferred estimation method it can be seen that the results differ significantly between the different measures for internal distance. This result is in line with Head and Mayer (2009) who show that the border effect differs significantly with different measures for the internal distance. Furthermore, Head and Mayer (2009) estimate a border effect of 3,34 for EU countries over the period 1993-1995 while using the same Head distance measure. The authors made use of ordinary least squares which in this case results in a slightly lower border effect of 3,08. When considering the PPML estimator the border effect decreases further to a magnitude of 2,92. This result has two implications. First, the choice between different estimation techniques has an effect on the estimated border effect. With the dataset at hand the PPML estimator is the most preferred method to estimate the specification and it decreases the estimated effect. Second, the home bias in trade for the European Union has not been of such small magnitude. The most recent available results are estimates from Helble (2007) who estimated a border effect of 3 for Germany in 2004. Although this result seems promising, the estimates are biased and theoretically inconsistent.
To provide theoretically consistent estimates and to show how the coefficients differ for intermediate input trade and final good trade, subsets have been made to estimate the coefficients separately. The coefficients for the mass variables are of interest because both variables are measured differently for the two groups. Gross use for the importing region and gross sales for the exporting region should be better proxies than GDP when trade is characterized by intermediate inputs. On the other hand, when estimating the gravity equation using only final demand, GDP should do a better job. The other coefficients are of interest because previously they were misspecified due to above mentioned reason. Finally, the border effect is of interest to examine to what extent this differs between both groups.
6.3 results for intermediate input trade
Table 4 presents the results when estimating the gravity equation for intermediate input trade only. The different estimation techniques used are indicated in the header of each column. The results are presented in two groups; on the left hand side the results are presented for the Head internal distance measure, on the right hand side the results are presented for the Nitsch internal distance measure. The variables representing the mass variables are the following; lnGOo and lnGOd measure gross sales per exporting region o and gross use per importing region d. LnGOok measures gross sales per exporting region o and industry k, lnGOdk measures gross use per importing region d and industry k.
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intermediate input trade, but the difference is in line with other work on border effects when not making a subset. Head and Mayer (2009) estimate a coefficient of 0,89 and 0,53 for the exporting and importing country. When considering the difference between the two estimation techniques it can be seen that the difference is most pronounced between column 1 and 3. When using ordinary least squares the coefficient for the importing region is larger, when using the PPML estimator the coefficient for the exporting region is larger. There are two possible explanations for this result. First, the PPML estimator is able to deal with the zeroes in the dataset. Second, Santos Silva and Tenreyro (2006) show that when the coefficients between both estimation techniques differ, this might be due to heteroscedasticity. A White test shows that indeed the trade data is not homoscedastic implying this could be a possible explanation.
The distance coefficient is not much affected by the difference between the measurement of the exporting and importing region’s mass variables. Furthermore, both coefficients are slightly larger when estimated using the PPML estimator. In comparison to the results in table 3, where both intermediate input trade and final demand trade are included, the magnitude of the coefficients is lower for intermediate input trade. This finding is not in line with the findings by Baldwin and Taglioni (2014). Their results show that distance seems to be more important for trade in intermediate inputs. However, the results are in line with the hypothesis of this article. As communication costs dropped, it became possible to coordinate the production process at distance while remaining profitable. This might provide an explanation for the lower magnitude of the coefficient on distance.
The coefficients for the home dummy variables are all significant at the 1% level. Furthermore, when considering the PPML estimator the estimates have a smaller magnitude compared to the estimates using the PPML estimator for the whole dataset. However, the difference in magnitude is small (2,92 versus 2,75). It does suggest that trade in intermediate inputs might not be an explanation for the home bias in trade. A discussion of the difference between the border effects for trade in intermediate inputs and final demand will be done at the end of this section.
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Table 4: OLS and PPML estimates for intermediate input trade
OLS OLS PPML PPML OLS OLS PPML PPML
lnGOo 0,520*** (0,014) 1,064*** (0,141) 0,521*** (0,014) 0,769*** (0,102) lnGOok 1,162*** (0,003) 0,944*** (0,012) 1,162*** (0,003) 0,944*** (0,012) lnGOd 1,353*** (0,042) 0,700*** (0,080) 1,353*** (0,042) 0,781*** (0,062) lnGOdk 0,442*** (0,002) 0,463*** (0,023) 0,443*** (0,002) 0,463*** (0,023) lnDistance Head -1,534*** (0,017) -1,540*** (0,017) -1,580*** (0,031) -1,580*** (0,031) lnDistance Nitsch -1,518*** (0,018) -1,523*** (0,018) -1,610*** (0,055) -1,610*** (0,055) Home 1,074*** (0,039) 1,070*** (0,039) 1,013*** (0,066) 1,001*** (0,066) 1,166*** (0,040) 1,162*** (0,040) 1,569*** (0,076) 1,569*** (0,076)
Fixed effects Yes Yes Yes Yes Yes Yes Yes Yes
R-squared 0,170 0,269 0,136 0,387 0,168 0,267 0,095 0,281 Observations 10.501.784 10.501.784 12.149.256 12.145.770 10.501.784 10.501.784 12.149.256 12.145.770 Border effect 2,93 2,92 2,75 2,72 3,21 3,20 4,80 4,00 Industries included 14 out of 14 14 out of 14 2 subsets of 7 2 subsets of 7 14 out of 14 14 out of 14 2 subsets of 7 2 subsets of 7
Notes: estimates of the border effect for trade in intermediate inputs. To estimate the coefficients using OLS the whole dataset was used. Unfortunately, it was not possible to use the PPML estimator whith the whole dataset. Therefore, to estimate the coefficients using PPML the dataset was split in half; two sets of seven industries. The coefficients are the average of both results. The difference in the number of observations between both PPML methods is because lnGOok is gross sales per region and industry for
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6.4 results for trade in final goods
Table 5 presents the results when estimating the gravity equation using the Anderson and van Wincoop (2003) model for final goods trade only. The header of each column indicates the estimation technique used. The specification has been estimated twice with each estimation technique, the difference is reflected in the internal distance measure.
All coefficients show the expected signs and all coefficient are significant at a level of 1%. The coefficients on the mass variables are very similar in magnitude when considering OLS and the PPML estimator. Furthermore, the magnitudes of the estimates are similar to the results from Santos Silva and Tenreyro (2006). Their estimated coefficients using the PPML estimator are 0,773 and 0,741, respectively.
Table 5: OLS and PPML estimates for trade in final goods
OLS OLS PPML PPML lnGDPo 0,742*** (0,020) 0,744*** (0,020) 0,724*** (0,067) 0,805*** (0,481) lnGDPd 0,763*** (0,021) 0,764*** (0,021) 0,706*** (0,030) 0,791*** (0,055) lnDistance Head -1.424*** (0,020) -1,792*** (0,032) lnDistance Nitsch -1,386*** (0,020) -1,850*** (0,066) Home 0,945*** (0,020) 1,063*** (0,044) 1,208*** (0,069) 1,881*** (0,088)
Fixed effects Yes Yes Yes Yes
R-squared 0,121 0,12 0,176 0,119
Observations 2.035.478 2.035.478 2.603.412 2.603.412
Border effect 2,57 2,90 3,35 6,56
Notes: estimates of the border effect for trade in final goods. To estimate the results for the OLS and PPML method all final demand categories were used as one dataset. In parentheses robust standard errors clustered by pair are shown for the OLS estimates, clustered standard by pair have are depicted for the PPML estimator. *, **, *** indicates significance at 10%, 5% and 1% level.
