Identification strategy and estimation models

This Chapter adopts a gravity model approach to determine the effect of commercial diplomacy, proxied by diplomatic representation, on trade outcomes30. This approach follows Rose (2007) and the subsequent empirical literature as well as the empirical international trade literature in general.

Estimation of the basic log-linear model of the gravity model adopts the following functional form:

(4.1) Fij = f(Dij, Yi, Yj, Popi, Popj, Areaij, X)

30 _{As Section 3.3 outlines, the gravity model allows for the incorporation of multilateral resistance terms} to account for trade costs and factors that alleviate trade costs.

66 Where i denotes the exporter, j denotes the importer, Fij is the trade flow, Dij is the

geographical distance, Yi and Yj are GDPs, Popi and Popj stand for population sizes,

Area is the product of land areas of countries i and j, and X is a vector of dummy

variables.

Traditional estimation of the model above takes place using ordinary least squares (OLS). However, since Anderson and van Wincoop (2004) outlined the importance of multilateral resistance terms in the gravity equation, research has shifted to account for the structural nature of the gravity model by including fixed effects. In this regard, due to the violation of the strict exogeneity assumption with random effects (Olivero & Yotov, 2012), evidence overwhelmingly favours fixed over random effects (Egger, 2000). As such, empirical literature on the presence of diplomatic representation has focused on the inclusion of country and country-pair fixed effects to account for countries' heterogeneity. However, in the presence of endogeneity, only country-year and bilateral fixed effects will give consistent estimates of the variable(s) of interest (Baltagi, Egger, & Pfaffermayr, 2014; Bergstrand, Larch, & Yotov, 2015)31. Therefore, for this panel data study the use of country-pair specific time-invariant effects alone is inadequate. Time-varying fixed effects for the exporter and importer are critically important to capture any importer or exporter time-varying characteristics. These terms correct biases that would otherwise arise in panel datasets (Baier & Bergstrand, 2007; Baldwin & Taglioni, 2007; Bergstrand et al., 2015; Dutt et al., 2013; Gómez-Herrera, 2013).

The bilateral fixed effects control for time-invariant variables on the country-pair level, and thus capture the effects of commonly used gravity model variables that can no longer be estimated (Baldwin & Taglioni, 2007), such as geographic distance, land size, and dummy variables for common language and sharing a border (Baier & Bergstrand, 2007; Hayakawa et al., 2014; Yang & Martinez-Zarzoso, 2014). Moreover, the country-year fixed effects control for determinants that vary in the country-year (it and jt) dimensions, and therefore absorb the effects for GDP and population size as these variables vary in exactly those dimensions (Baier & Bergstrand, 2007; Bergstrand et al., 2015; Eicher & Henn, 2011a; Gómez-Herrera, 2013; Yang & Martinez-Zarzoso, 2014). Thus, the exclusion of these standard gravity

31 _{Most variables that could be considered as plausible instruments are at the same time determinants of} such policy instruments as well, as is shown by Kinne (2014) in the case of diplomatic representation.

67 model variables is necessary when using Baier and Bergstrand's (2007) set of fixed effects for identification purposes. This approach is common in the empirical literature that employs country-year and bilateral fixed effects32.

Accounting for country-year and bilateral fixed effects in a standard gravity model of international trade means that only variables that vary in the bilateral-time dimension remain. Besides the variable for commercial diplomacy, this is the case with standard gravity model dummy variables for whether a free trade agreement exists between two countries, and whether they share a common currency (Baldwin & Taglioni, 2007). Accounting for the inclusion of country-year and bilateral fixed effects, the gravity equation for the export- and import-promoting effects are as follows:

(4.2) ln(Fij,t,k) = β0 + β1Representationij,t + β2RTAij,t + β3Currencyij,t + uij + ui,t + uj,t

+ εij,t

(4.3) ln(Fij,t,k) = β0 + β1Representationji,t + β2RTAij,t + β3Currencyij,t + uij + ui,t + uj,t

+ εij,t

With Fij being the trade variable, t denoting year, and the u-terms denoting exporter-

year (uit), importer-year (ujt), and country-pair (uij) fixed effects. Representation is the

proxy for commercial diplomacy and denotes the presence of diplomatic representation of i in j in equation (4.2), and of j in i in equation (4.2). RTAij,t and

Currencyij,t are control variables for being members of a free trade agreement and

sharing a common currency, respectively. While the fixed effects account for multilateral resistance and unobserved bilateral heterogeneity, the inclusion of trade agreement and currency agreement membership as control variables is necessary to further reduce the potential for omitted variable bias, which may give upwards bias to the estimates for the effect of commercial diplomacy on trade.

In equations (4.2) and (4.3), the trade variable can be one of six types as denoted by k: total exports, total exports in homogeneous goods, total exports in reference priced goods, total exports in differentiated goods, the extensive margin, and the intensive margin. Information from Rauch (1999) is used to construct totals for homogeneous, reference priced, and differentiated goods. This information is available for seven of the ten broad industries in the SITC-classification and thus leads to some loss of data,

32 _{See e.g. Dutt et al. (2013), Bergstrand et al. (2015), Yang and Martinez-Zarzoso (2014), Eicher and} Henn (2011a, 2011b), Fugazza and Nicita (2013), Vijil (2014), Felbermayr and Toubal (2010), Head et al. (2010) and Melitz (2008).

68 though as Besedeš and Prusa (2006) note, this does not create a large bias when using annual data. To construct the extensive and intensive margins of trade this Chapter uses the margins as defined by Hummels and Klenow (2005), albeit with the adjustments made by Dutt et al. (2013). That is, whereas Hummels and Klenow (2005) calculate the margins for country-pairs relative to the rest of the world, Dutt et al.'s (2013) adjustment to calculate them relative to the world allows for a more intuitive interpretation of the margins. As such, with Gij _{being the set of goods exported by}

country i to country j, the index W representing the sum of all origin countries, X denoting exports (of good g), and dropping the subscript t, the extensive margin is: (4.4) Extensive margin (EMij) =

∑_{𝑔∈𝐺𝑖𝑗}𝑋_𝑊𝑗𝑔 ∑_{𝑔∈𝐺𝑊𝑗}𝑋_𝑊𝑗𝑔

This margin is a measure of the fraction of goods in which country i exports to country

j, weighting each product by its importance in world exports to j. The numerator

measures exports from the world to country j in the 4-digit products in which i exports to j. The denominator is all exports from the world to country j. Here, the extensive margin becomes the fraction of products that country i exports to country j if all products have equal importance to country j. The intensive margin is:

(4.5) Intensive margin (IMij) =

∑_{𝑔∈𝐺𝑖𝑗}𝑋_𝑖𝑗𝑔 ∑_{𝑔∈𝐺𝑖𝑗}𝑋_𝑊𝑗𝑔

This margin measures the overall market share country i has within the set of goods in which it exports to country j relative to world exports to country j in those goods. Both the extensive and intensive margins, defined as such, are bounded between 0 and 1. Thus, as the extensive margin increases, the relative importance of the goods that country i exports to country j (with respect to all goods the importing country receives) increases; a value of 1 indicates that the set of goods exported by country i exactly corresponds with all goods that the world exports to country j. As for the intensive margin, an increase from the lower to the upper boundary indicates that country i's market share in the set of goods that it exports to country j increases. Because these margins are consistent across countries and over time (Feenstra & Kee, 2008), they are accurate measures of export diversity, and export intensity.

The Representationij,t and Representationji,t variables denote whether diplomatic

presence exists or not, taking the value of one if it does and zero if it does not. Noting that exports from i to j can be stimulated by i's commercial diplomacy efforts in j, and

69 by j's commercial diplomacy efforts in i, equations (4.2) and (4.3) distinguish between the export- and import-promoting functions of diplomatic representation.

However, even with the set of fixed effects used above there may still be some simultaneity bias present in the equations that potentially renders the variable of interest to be biased upwards. Therefore, to strengthen identification this study follows Baier and Bergstrand (2007) and Hayakawa et al. (2014) by introducing the lagged effect of the commercial diplomacy proxy variable on current exports. This way, it also recognises that commercial diplomacy's main trade function is the collection of information through its networks and that it may take time for firms to respond to this information. Therefore, the following models serve as the main estimation equations: (4.6) ln(Fij,t,k) = β0 + β1Representationij,t-n + β2RTAij,t + β3Currencyij,t + uij + ui,t + uj,t

+ εij,t

(4.7) ln(Fij,t,k) = β0 + β1Representationji,t-n + β2RTAij,t + β3Currencyij,t + uij + ui,t + uj,t

+ εij,t

Here, the Representation variable is lagged by n years, where n is 1 to 4. The choice for an upper limit of four lag years is motivated by the five-yearly intervals in which the diplomatic representation data is available. In addition, estimations using a fifth lag year indicate that no significant effects of diplomatic representation remain. The diplomatic representation data is available in five year intervals; the time lagged estimations in equations (4.6) and (4.7) assume that within an interval (e.g. 1985 to 1989) there is no change to diplomatic representation – in a lagged estimation the effect of the diplomatic representation variable for 1985 is estimated on exports for 1986 to 198933.

The estimations to test Hypotheses H1a to H2b take place in two steps. The first step tests Hypotheses H1a and H2a which relate to commercial diplomacy working to increase trade in all types of goods and along both the extensive and intensive margins of trade. The second step is then to test Hypotheses H1b and H2b, which relate to the relative effectiveness of commercial diplomacy between the types of goods and between the margins of trade. This is accomplished by means of Wald-tests of the equality of coefficients.

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