A contribution to a multidimensional analysis of trade competition

2.1 Sectoral shares similarity

The KSI is one of the most widely used indexes of structural similarity (Palan, 2010) and is therefore taken as the starting point for this study. The KSI compares the share of each sector in two export structures. i and h are the exporting countries and m (m = 1, 2, …, M) represents the destination market. Finally, j is a sectoral index (j = 1, 2, …, J). The index is expressed as follows:

(1)

The weights of sector j in the export structure of i and h to m are expressed, respectively, as v_jim and v_jhm. Additionally, v_jim = x_jim/x_im, where x_jim are the exports of sector j from i to m and x_im are the total exports from i to m. The same definitions apply to v_jhm. K_ihm ranges between 0 (perfect similarity between the two export structures) and 2 (maximum dissimilarity).

This index has two counter-intuitive characteristics. First, the admissible range does not provide an immediate quantitative message regarding the level of structural similarity. Second, despite being a measure of structural similarity, it increases with structural dissimilarity. In order to overcome these two problems, we consider as our baseline index a modified version of the KSI, expressed as:

(2)

The most common value for β is 0.5. We assume this value for β throughout. Therefore, E_ihm ranges between 0 and 1. In this perspective, the level of structural similarity is maximum (i.e., E_ihm = 1) when the weights of each sector are equal in the exports of countries i and h to market m.

2.2 Inter-sectoral similarity

The traditional approach to measure structural similarity (i.e., KSI or its adaptations) does not consider the degree of dissimilarity between sectors. With the aim of adjusting E_ihm in order to capture this dimension, we propose a generalised version of the procedure suggested by Crespo and Simões (2012). To that end, making use of the different levels of sectoral disaggregation that comprise a specific statistical nomenclature, we calculate the weighted average of the structural similarity indexes obtained at different levels of sectoral disaggregation (g = 1, 2, …, G; in which G is the most disaggregated level),1 with the weight of each level given by α^g:

(3)

with . is calculated as in Equation 2 for each level g. The main difference between the index proposed in Crespo and Simões (2012) and the measure that we suggest in this paper is the fact that Crespo and Simões (2012) assume equal weights for all levels of sectoral disaggregation (i.e., a simple average) while we generalise that measure by allowing the weights to be defined according to the objectives of each study.

This procedure allows us to take into account that some sectors are more similar in terms of their characteristics and production requirements. In comparison with E_ihm, S_ihm allows that distinct sectors at a higher level of sectoral disaggregation are classified as more similar if, when lower levels of disaggregation are considered, they belong to the same sector than when that does not occur.

The weights assigned to each level of disaggregation depend, as stated above, on the importance that the researcher wants to give to this dimension of structural similarity. Greater importance to this dimension implies more weight to less disaggregated levels of sectoral analysis. Of course, we should bear in mind that this option corresponds to assume a concept of trade competition based, in a higher proportion, on the level of potential competition instead of present competition, as explained in the Introduction.2

2.3 Intra-sectoral similarity

Several studies have reported an increasing specialisation by quality ranges at the international level, suggesting that besides inter-sectoral differences between the specialisation patterns of the countries, there are important intra-sectoral differences (Fontagné et al., 2008; Kaitila, 2010; Vandenbussche et al., 2013). In order to incorporate this aspect in the evaluation of the degree of structural similarity, it is necessary to measure the quality of the goods, which, by definition, is a complex task. When we consider trade data, the use of unit export values as a quality proxy is the usual procedure to overcome this problem (Stiglitz, 1987).

To incorporate intra-sectoral similarity in the structural similarity index, we evaluate the difference, for each sector, between the quality level of the exports from the two countries under consideration. To that end, we calculate the index O_ihm as follows:

(4)

with

(5)

and

(6)

For sector j, UV(x_jim) and UV(x_jhm) are the unit values of the exports from i and h to m, respectively.

O_ihm works as an adjustment factor that reduces the level of structural similarity between i and h according to the average degree of intra-sectoral dissimilarity. In its turn, the degree of intra-sectoral similarity is calculated considering a weighted average of the differences, in each sector, in terms of quality ranges. The weights—expressed by ɛ_jihm—are the average share of j in the exports from i and h to m.

Therefore, the indicator capturing sectoral shares similarity and intra-sectoral similarity is obtained as:

(7)

When the unit export values of i and h to m are exactly the same, Z_jihm = 1. If this is the case for all products, O_ihm = 1 and, therefore, A_ihm = E_ihm. A greater difference in the unit export values implies a greater penalisation on E_ihm, indicating a lower degree of structural similarity between i and h.

2.4 Structural similarity—an overall index

In the above subsections, we discussed indexes of structural similarity that include three dimensions—sectoral shares similarity, inter-sectoral similarity and intra-sectoral similarity. Now, in order to obtain an overall measure of structural similarity, we construct an index that simultaneously includes all these dimensions:

(8)

C_ihm is calculated in same way as S_ihm (Equation 3) but now incorporating the adjustment suggested in the previous subsection in order to consider the intra-sectoral similarity. This adjustment is introduced only at the most disaggregated level of sectoral analysis because we need such level of detail to allow the assumption of prices as quality proxy. An important consequence of this aspect is however the fact that the importance given to intra-sectoral similarity depends on the weight given to the most disaggregated level of sectoral analysis (α^G). Therefore, the value of α^G should be high enough to account for intra-sectoral similarity and low enough to capture inter-sectoral similarity. The concrete values are of course a subjective decision of the researcher but, in our opinion, α^G should range between 0.5 and 0.9.3

The index C_ihm takes its maximum value (i.e., C_ihm = 1) when the exports of i and h to market m are equal in terms of the three dimensions of structural similarity considered.

2.5 Total exports overlap

All the indexes discussed until now are (partial or overall) measures of structural similarity. In this subsection, we argue that the competition between two countries in a given market depends not only on the level of structural similarity but also on the value of total exports and, more specifically, on the degree of overlap between these two flows. A simple example illustrates the point. Let us consider three countries—A, B and C—and assume that the weights of all sectors are equal in the three countries, the only difference being the overall value of their exports, which is similar between A and B but very different between these countries and C. Although E_ihm indicates a similar level of structural similarity between all pairs of countries (in this case, maximum similarity), these situations are distinct and express different levels of trade competition.

This question was introduced by Jenkins (2008) by referring that structural similarity indexes capture only the composition of the exports of the two countries under comparison and that this procedure implies obtaining a single value for a pair of countries. According to Jenkins (2008, p. 1355), “no index which implies that Honduras is as much a competitive threat to China's export markets as China is for Honduran exports is credible.” To overcome this limitation, Jenkins (2008) introduces two new indicators: the static and the dynamic index of competitive threat. These indexes reflect the proportion of total exports of a country concentrated in products in which the other country is globally competitive.

Following a different perspective, we incorporate the overlap between total exports by adjusting the structural similarity indicator. Obviously, accounting for this dimension implies obtaining not a single value per pair of countries but instead a value for each of the two countries under comparison. We start by proposing an adjustment to E_ihm in order to take into account the level of total exports overlap between the two countries under analysis, which, in its simplest form, is expressed as:

(9)

where

(10)

In this version, the impact of the degree of trade overlap is fully captured in our index. We may however consider a generalised version of in which the adjustment of the structural similarity index depends on the importance given to this dimension. In this case, we have:4

(11)

The influence of the total exports overlap decreases as the parameter λ increases (λ ≥ 1), with B_ihm converging to E_ihm.

In this case, trade competition is maximum when both the weights of each sector and total exports are equal in the two countries. In all the cases in which x_im ≠ x_hm, we will have a trade competition index assuming different values for the countries under analysis (B_ihm for country i and B_ihm for country h; hereinafter we will designate these indexes as country-specific indexes and B_ihm as country-pair-specific index). This is an important characteristic of this dimension. In the following steps of our methodological approach, when we combine this dimension with other dimensions we will also obtain different values for countries i and h. In order to obtain B_ihm and B_ihm, we start from E_ihm and assume the following reasoning: (i) for the larger exporter, we calculate E_ihm − (E_ihm − B_ihm), being therefore the trade competition index equal to B_ihm; (ii) for the smaller exporter, the index corresponds to E_ihm + (E_ihm − B_ihm), introducing this way a penalisation factor that adds to the measure of structural similarity in order to obtain an index of trade competition. In formal terms, we have:

(12)

and

(13)

B_ihm and B_ihm range between 0 and 2.

If we wish to take into account all the dimensions of structural similarity—sectoral shares similarity, inter-sectoral similarity and intra-sectoral similarity—and the degree of total exports overlap, we can obtain a new index of trade competition:

(14)

where:

(15)

Since varies by country, we can also obtain indicators U_ihm for each country. U_ihm and U_ihm are calculated using the same logic of U_ihm:

(16)

and

(17)

4.1 Sectoral shares similarity

We will start with the L_ih based on E_ihm which is the index most frequently used in the literature to analyse structural similarity and which, for this reason, will provide a benchmark to measure the impact of the remaining dimensions of trade competition. To compute this index, we consider data at the most disaggregated level (HS6).

The results in Table 2 allow us to retain some important conclusions. First, a significant degree of heterogeneity is detected. In fact, considering the evidence for 2015, the values for the 15 country pairs range between 0.09 (GR-HU) and 0.426 (DE-FR).

Table 2. Trade competition indexes (sectoral shares similarity and inter-sectoral similarity)

TCI ihm	E ihm			S ihm (1)			S ihm (2)			S ihm (3)
	2007	2011	2015	2007	2011	2015	2007	2011	2015	2007	2011	2015
	0.444	0.435	0.426	0.460	0.448	0.439	0.488	0.475	0.466	0.533	0.515	0.506
				(1.035)	(1.032)	(1.032)	(1.100)	(1.093)	(1.094)	(1.199)	(1.186)	(1.189)
	0.387	0.356	0.388	0.401	0.370	0.402	0.431	0.397	0.428	0.475	0.438	0.468
				(1.039)	(1.039)	(1.035)	(1.114)	(1.115)	(1.102)	(1.228)	(1.231)	(1.205)
	0.129	0.118	0.127	0.139	0.128	0.136	0.160	0.148	0.156	0.191	0.177	0.185
				(1.079)	(1.081)	(1.074)	(1.241)	(1.247)	(1.230)	(1.481)	(1.495)	(1.459)
	0.248	0.264	0.309	0.266	0.280	0.326	0.301	0.314	0.360	0.354	0.363	0.410
				(1.069)	(1.061)	(1.054)	(1.213)	(1.186)	(1.165)	(1.426)	(1.372)	(1.329)
	0.344	0.312	0.321	0.360	0.326	0.336	0.392	0.356	0.366	0.440	0.401	0.411
				(1.046)	(1.047)	(1.047)	(1.139)	(1.143)	(1.140)	(1.277)	(1.286)	(1.280)
	0.360	0.331	0.335	0.376	0.345	0.350	0.407	0.374	0.379	0.454	0.417	0.422
				(1.044)	(1.045)	(1.044)	(1.130)	(1.131)	(1.129)	(1.260)	(1.261)	(1.258)
	0.154	0.146	0.141	0.165	0.157	0.151	0.188	0.178	0.172	0.221	0.211	0.202
				(1.070)	(1.072)	(1.070)	(1.216)	(1.220)	(1.217)	(1.432)	(1.441)	(1.434)
	0.226	0.223	0.241	0.240	0.237	0.256	0.269	0.266	0.285	0.312	0.300	0.330
				(1.063)	(1.066)	(1.062)	(1.192)	(1.195)	(1.185)	(1.383)	(1.346)	(1.369)
	0.282	0.264	0.248	0.299	0.278	0.264	0.332	0.307	0.296	0.382	0.351	0.343
				(1.060)	(1.056)	(1.064)	(1.177)	(1.165)	(1.191)	(1.353)	(1.331)	(1.381)
	0.128	0.127	0.124	0.139	0.137	0.133	0.161	0.156	0.152	0.195	0.185	0.180
				(1.086)	(1.075)	(1.073)	(1.265)	(1.228)	(1.226)	(1.530)	(1.456)	(1.451)
	0.188	0.183	0.207	0.203	0.197)	0.222	0.234	0.225	0.251	0.279	0.268	0.294
				(1.078)	(1.077)	(1.069)	(1.241)	(1.233)	(1.208)	(1.483)	(1.467)	(1.416)
	0.277	0.221	0.256	0.295	0.234	0.273	0.329	0.260	0.306	0.380	0.299	0.356
				(1.062)	(1.058)	(1.066)	(1.186)	(1.176)	(1.196)	(1.371)	(1.353)	(1.392)
	0.095	0.088	0.090	0.104	0.097	0.099	0.123	0.115	0.118	0.151	0.143	0.147
				(1.095)	(1.101)	(1.106)	(1.294)	(1.309)	(1.320)	(1.588)	(1.619)	(1.640)
	0.113	0.117	0.105	0.123	0.127	0.115	0.143	0.147	0.135	0.173	0.177	0.166
				(1.086)	(1.084)	(1.096)	(1.266)	(1.254)	(1.290)	(1.532)	(1.508)	(1.581)
	0.153	0.161	0.176	0.171	0.177	0.192	0.207	0.211	0.224	0.260	0.261	0.272
				(1.116)	(1.103)	(1.089)	(1.350)	(1.313)	(1.272)	(1.699)	(1.626)	(1.545)

• E_ihm is the structural similarity index between exporting countries i and h for market m (accounting for similarity in sectoral weights); S_ihm is a trade competition index between exporting countries i and h for market m that accounts for sectoral weights similarity and inter-sectoral similarity; the methodological options for S_ihm indicators are as follows: for S_ihm⁽¹⁾, we have (α₁, α₂, α₃) = (0.025; 0.075; 0.9); S_ihm⁽²⁾—(α₁, α₂, α₃) = (0.1; 0.15; 0.75); and S_ihm⁽³⁾—(α₁, α₂, α₃) = (0.2; 0.3; 0.5); is an overall trade competition index for the country pair i and h. In this table, we have four different for each country pair (i.e., , , and ); numbers between parentheses are the ratios . Bold is used for the country pair having the highest value of the ratio and italics for the pair with the minimum value.

Second, DE-FR and DE-GB are the pairs that show the highest overall level of structural similarity, with values for of 0.426 and 0.388, respectively. Other pairs that also reveal high levels of structural similarity are FR-GB (0.335) and DE-SE (0.321). Adding to this last result, we can verify that all the values of above 0.2 concern country pairs including at least one of the three largest European economies (Germany, France and the United Kingdom). Fourth, the pair that presents the lowest level of structural similarity (GR-HU) reveals an interesting characteristic: there are eight destination markets for which E_GR,HU,m = 0. This contrasts with the average number of E_ihm = 0 for all pairs which is 0.67. In our sample, Greece is the country that exports the smallest number of products to the 123 destination markets considered. Using the HS6 digit level, Greece exports on average 455 products (out of the 6,280 possible). This number compares with an average of 2,575 for Germany, 2,034 for France, 1,835 for the United Kingdom, 1,067 for Sweden and 677 for Hungary. This evidence means therefore that Greece and Hungary are exporting a small number of different products. Fifth, it is possible to say that the central message emerging from the data for 2015 is also valid for the two other years under analysis.

4.2 Inter-sectoral similarity

The incorporation of inter-sectoral similarity requires assigning weights to the different levels of sectoral disaggregation (HS2, HS4 and HS6). To minimise the subjectivity in this process, we test three alternative sets of values for these weights (α₁, α₂ and α₃) gradually increasing the importance attributed to less disaggregated levels (HS2 and HS4).6 Each of these alternatives leads to a different S_ihm indicator (S_ihm⁽¹⁾, S_ihm⁽²⁾ and S_ihm⁽³⁾) and consequently to a different L_ih.

The results shown in Table 2 support two main conclusions. First, in comparison with the evidence drawn from , there is an increase in the level of trade competition for all pairs of countries. This is of course an implication of the adjustment introduced by the consideration of the inter-sectoral dimension. In the extreme case, when α₃ = 1 we obtain . The consideration of other levels of sectoral disaggregation obviously leads to an increase in the level of structural similarity. When lower values are assigned to α₃, the impact of the inter-sectoral similarity is more pronounced and therefore the differential of vis-à-vis increases. Second, this increase is more pronounced for the pairs with the lowest values of , namely GR-HU, GR-SE and HU-SE. Taken as example, the highest increase occurs in the case GR-HU in which is 10.6% higher than . This result can be compared with increases of 3.2% for the pair DE-FR and 3.5% for DE-GB.

In the Appendix (Table A2), we present some complementary evidence. For each pair, the destination markets were ranked according to their average weight in total exports from the smallest to the largest value and then divided into ten groups (the number of destination markets for each pair is 123 and, except for the first three groups—less relevant markets—which include 13 countries each, the other seven groups have 12 countries each).

For all the 15 pairs considered, the 24 most important markets (groups 9 and 10) absorb more than 75% of total exports. For each group, we selected a set of indicators (E_ihm, S_ihm⁽²⁾, A_ihm, B_ihm⁽²⁾, U_ihm⁽⁵⁾) and present their average values ( respectively).

In Table A2, we present, for each group of destination markets, the ratios between the average values of TCI_ihm indexes and the average values of E_ihm. From this evidence, we obtain a deeper understanding about the causes of the increase of the indicators (in comparison with ). It is possible to conclude that, for the majority of the country pairs, the impact of introducing the inter-sectoral dimension is stronger in the first groups of countries, that is, in the case of the less important destination markets. For example, in the case of the pair GR-HU (which registers the highest increase of indicators vis-à-vis ), the evidence shows that the impact is more pronounced in groups 1–4. This occurs because: (i) since is a very small number, small increases in absolute terms give rise to considerable changes in relative terms; (ii) using the HS6 nomenclature, these countries are exporting different (although relatively similar) products. This means that there is a high likelihood that these products belong to the same category when we use the HS4 or HS2 nomenclatures. As an example, let us consider the case of group 2. The ratio between and is 4.856. The destination markets that are most responsible for this increase are Costa Rica, Ivory Coast, Venezuela, Tanzania and Ecuador. The case of this last country is illustrative of what occurs with the less important markets. Using the HS6 nomenclature, Greece and Hungary export 39 and 88 products, respectively, for this market but only three products are the same (E_GR,HU,m = 0.00001). However, using HS2, exports become concentrated in some categories such as sector 39 “Plastics and Articles Thereof,” sector 84 “Nuclear Reactors, Boilers, Machinery and Mechanical Appliances, Parts Thereof” and sector 90 “Optical, Photographic, Cinematographic, Measuring, Checking, Medical or Surgical Instruments and Apparatus; Parts and Accessories.” As a consequence, S_GR,HU,m⁽²⁾ = 0.017 which means that S_GR,HU,m⁽²⁾/E_GR,HU,m = 1,700.

4.3 Intra-sectoral similarity

Table 3 contains the results for L_ih based on A_ihm—accounting for sectoral shares similarity and intra-sectoral similarity—and C_ihm—also including inter-sectoral similarity.

Table 3. Trade competition indexes (sectoral shares similarity, inter-sectoral similarity and intra-sectoral similarity)

TCI ihm	A ihm			C ihm (1)			C ihm (2)			C ihm (3)
	2007	2011	2015	2007	2011	2015	2007	2011	2015	2007	2011	2015
	0.203	0.272	0.262	0.242	0.302	0.292	0.307	0.353	0.343	0.412	0.434	0.424
	(0.457)	(0.626)	(0.615)	(0.546)	(0.695)	(0.685)	(0.692)	(0.813)	(0.805)	(0.928)	(0.999)	(0.996)
	0.215	0.201	0.212	0.247	0.230	0.243	0.302	0.281	0.296	0.389	0.361	0.380
	(0.557)	(0.564)	(0.545)	(0.640)	(0.647)	(0.625)	(0.782)	(0.788)	(0.762)	(1.007)	(1.012)	(0.978)
	0.055	0.050	0.051	0.072	0.066	0.068	0.104	0.096	0.099	0.154	0.142	0.147
	(0.424)	(0.419)	(0.404)	(0.561)	(0.558)	(0.538)	(0.809)	(0.812)	(0.783)	(1.193)	(1.204)	(1.161)
	0.128	0.141	0.164	0.157	0.169	0.196	0.211	0.221	0.251	0.294	0.301	0.338
	(0.513)	(0.534)	(0.532)	(0.631)	(0.641)	(0.633)	(0.848)	(0.836)	(0.814)	(1.182)	(1.139)	(1.095)
	0.192	0.173	0.178	0.223	0.202	0.208	0.277	0.252	0.259	0.363	0.331	0.339
	(0.557)	(0.555)	(0.556)	(0.647)	(0.647)	(0.647)	(0.806)	(0.809)	(0.807)	(1.056)	(1.063)	(1.058)
	0.143	0.170	0.167	0.181	0.201	0.199	0.244	0.254	0.252	0.345	0.337	0.338
	(0.397)	(0.515)	(0.498)	(0.502)	(0.609)	(0.592)	(0.678)	(0.767)	(0.752)	(0.959)	(1.019)	(1.007)
	0.054	0.068	0.060	0.075	0.086	0.078	0.112	0.120	0.111	0.171	0.172	0.162
	(0.349)	(0.466)	(0.428)	(0.484)	(0.591)	(0.556)	(0.727)	(0.820)	(0.788)	(1.106)	(1.174)	(1.148)
	0.071	0.112	0.116	0.101	0.138	0.144	0.153	0.184	0.192	0.235	0.248	0.268
	(0.314)	(0.502)	(0.483)	(0.446)	(0.619)	(0.597)	(0.677)	(0.825)	(0.797)	(1.040)	(1.115)	(1.111)
	0.108	0.130	0.118	0.142	0.158	0.147	0.201	0.207	0.198	0.295	0.284	0.278
	(0.383)	(0.491)	(0.475)	(0.505)	(0.598)	(0.592)	(0.714)	(0.784)	(0.797)	(1.045)	(1.076)	(1.118)
	0.046	0.051	0.045	0.065	0.069	0.062	0.100	0.099	0.093	0.154	0.147	0.140
	(0.358)	(0.404)	(0.365)	(0.508)	(0.538)	(0.501)	(0.783)	(0.781)	(0.749)	(1.208)	(1.158)	(1.134)
	0.078	0.078	0.086	0.103	0.102	0.112	0.151	0.147	0.159	0.224	0.216	0.233
	(0.412)	(0.426)	(0.414)	(0.548)	(0.560)	(0.542)	(0.800)	(0.803)	(0.769)	(1.188)	(1.180)	(1.123)
	0.126	0.101	0.112	0.159	0.126	0.143	0.216	0.170	0.198	0.305	0.239	0.284
	(0.456)	(0.456)	(0.438)	(0.572)	(0.569)	(0.561)	(0.778)	(0.769)	(0.775)	(1.099)	(1.081)	(1.111)
	0.033	0.035	0.035	0.048	0.049	0.050	0.076	0.076	0.078	0.120	0.116	0.120
	(0.343)	(0.400)	(0.395)	(0.503)	(0.561)	(0.561)	(0.801)	(0.859)	(0.867)	(1.259)	(1.319)	(1.338)
	0.036	0.047	0.037	0.053	0.064	0.054	0.085	0.094	0.084	0.134	0.142	0.132
	(0.318)	(0.401)	(0.352)	(0.472)	(0.545)	(0.512)	(0.755)	(0.804)	(0.804)	(1.191)	(1.208)	(1.256)
	0.058	0.065	0.068	0.085	0.091	0.095	0.135	0.139	0.143	0.213	0.213	0.218
	(0.378)	(0.403)	(0.389)	(0.556)	(0.566)	(0.539)	(0.883)	(0.865)	(0.814)	(1.388)	(1.327)	(1.239)

• A_ihm is a trade competition index between exporting countries i and h for market m that accounts for sectoral weights similarity and intra-sectoral similarity; C_ihm is a trade competition index between exporting countries i and h for market m that accounts for sectoral weights similarity, inter-sectoral similarity and intra-sectoral similarity; the methodological options for the C_ihm indicators are as follows: for C_ihm⁽¹⁾, we have (α₁, α_2, α₂) = (0.025; 0.075; 0.9); C_ihm⁽²⁾—(α₁, α_2, α₂) = (0.1; 0.15; 0.75); and C_ihm⁽³⁾—(α₁, α_2, α₂) = (0.2; 0.3; 0.5); is an overall trade competition index for the country pair i and h. In this table, we have four different for each country pair (i.e., , , and ); numbers between parentheses are the ratios . Bold is used for the country pair having the highest value of the ratio and italics for the pair with the minimum value.

Let us consider, once again, 2015 as reference year. A first important finding is that there is a strong similarity in the quality ranges of the products exported by the following country pairs: DE-FR ( = 0.615), DE-SE ( = 0.556), DE-GB ( = 0.545) and DE-HU ( = 0.532). While the results for the first three pairs are expected, the fourth is less obvious. However, this evidence should be understood in a historical context where Hungary has been showing a strong improvement in terms of quality of exports. This evolution is not new. Crespo and Fontoura (2007) conclude that, in 2003, Hungary is one of the Central and Eastern European Countries where the weight of the higher categories in terms of quality ranges is the highest. Moreover, this study concludes that, in the case of Estonia, Slovakia and Hungary, “exports of a higher quality correspond to sectors with a higher weight on trade” (Crespo and Fontoura, 2007, pp. 625–626). This idea also helps to explain the evidence obtained in our analysis. In fact, in the present case, we can say that Germany and Hungary, despite some differences in terms of sectoral shares, have some important sectors in which the unit values of exports are similar, conducing to high values for Z_jihm. This occurs, for example, in the following sectors: sector 84 “Nuclear Reactors, Boilers, Machinery and Mechanical Appliances; Parts Thereof,” sector 85 “Electrical Machinery and Equipment and Parts Thereof; Sound Recorders and Reproducers; Television Image and Sound Recorders and Reproducers, Parts and Accessories of such Articles” and sector 87 “Vehicles; Other than Railway or Tramway Rolling Stock, and Parts and Accessories Thereof.”

On the other extreme, showing higher levels of dissimilarity in terms of quality ranges exported (with ratios between and below 0.4), we can identify the pairs GR-SE, GB-GR, HU-SE and GR-HU. Despite some obvious differences in quantitative terms, the key ideas emerging from remain valid for all the years considered.

Complementing this result with the evidence from Table A2, we see that the difference (in relative terms) between and is smaller for the pair DE-FR than for the other pairs and that this higher similarity is found for all ten groups of countries with the exception of groups 3 and 4.

Turning now to L_ih based on C_ihm, what occurs in this case is a consequence of what we concluded from the pieces we have gathered until this moment. When we consider , the conclusions are very similar to those derived from , which is not surprising because in this specific case α₃ is 0.9 and therefore the inter-sectoral dimension has a small impact on the overall measure of structural similarity. When lower values for α₃ are considered, which occurs with and even more with , the impact of the several dimensions changes. For example, in this last case, the conclusions obtained from reveal the high influence of the inter-sectoral dimension. In all the cases, however, the ranking of the country pairs does not change significantly in terms of their degree of structural similarity, allowing to retain some of the key ideas presented above, namely the high level of structural similarity registered among the largest European economies.

4.4 Total exports overlap

The indexes attend simultaneously to sectoral shares similarity and total exports overlap (Table 4). We use three alternative values for the parameter λ involved in these indexes. With λ = 1 (full incorporation of the total exports overlap dimension), from it is possible to conclude that, in all years under analysis, there is a less pronounced decrease in the index for the pair FR-GB ( = 0.335 drops to  = 0.190, in 2015)7 due to the fact that these countries have the most similar global dimension (in terms of total exports).

Table 4. Trade competition indexes (structural similarity and total exports overlap)

TCI ihm	B ihm (2)			U ihm (2)			U ihm (5)			U ihm (8)
	2007	2011	2015	2007	2011	2015	2007	2011	2015	2007	2011	2015
	0.330	0.317	0.307	0.179	0.221	0.212	0.227	0.258	0.248	0.304	0.316	0.306
	(0.742)	(0.728)	(0.722)	(0.403)	(0.509)	(0.498)	(0.511)	(0.593)	(0.583)	(0.685)	(0.726)	(0.718)
	0.261	0.241	0.263	0.167	0.156	0.165	0.204	0.190	0.201	0.263	0.244	0.258
	(0.675)	(0.677)	(0.677)	(0.432)	(0.438)	(0.424)	(0.528)	(0.534)	(0.516)	(0.680)	(0.685)	(0.663)
	0.073	0.068	0.071	0.041	0.038	0.038	0.059	0.054	0.055	0.086	0.080	0.081
	(0.568)	(0.572)	(0.557)	(0.319)	(0.318)	(0.299)	(0.456)	(0.460)	(0.432)	(0.669)	(0.679)	(0.639)
	0.157	0.164	0.193	0.101	0.106	0.124	0.134	0.138	0.158	0.185	0.186	0.211
	(0.633)	(0.622)	(0.624)	(0.407)	(0.402)	(0.401)	(0.540)	(0.521)	(0.511)	(0.746)	(0.704)	(0.682)
	0.212	0.193	0.196	0.138	0.126	0.128	0.171	0.157	0.158	0.223	0.204	0.206
	(0.617)	(0.620)	(0.612)	(0.402)	(0.405)	(0.399)	(0.498)	(0.503)	(0.494)	(0.649)	(0.656)	(0.643)
	0.281	0.259	0.263	0.141	0.158	0.156	0.191	0.199	0.198	0.269	0.264	0.265
	(0.779)	(0.785)	(0.783)	(0.392)	(0.477)	(0.464)	(0.530)	(0.602)	(0.589)	(0.748)	(0.799)	(0.789)
	0.086	0.084	0.080	0.041	0.051	0.044	0.062	0.069	0.062	0.094	0.098	0.091
	(0.557)	(0.574)	(0.564)	(0.267)	(0.346)	(0.314)	(0.401)	(0.473)	(0.443)	(0.610)	(0.670)	(0.642)
	0.148	0.148	0.161	0.066	0.091	0.096	0.100	0.120	0.128	0.152	0.167	0.177
	(0.655)	(0.663)	(0.666)	(0.293)	(0.408)	(0.399)	(0.442)	(0.541)	(0.530)	(0.675)	(0.748)	(0.735)
	0.179	0.168	0.156	0.090	0.100	0.092	0.127	0.131	0.124	0.186	0.180	0.174
	(0.634)	(0.636)	(0.627)	(0.320)	(0.379)	(0.370)	(0.452)	(0.498)	(0.498)	(0.660)	(0.684)	(0.699)
	0.075	0.077	0.073	0.038	0.042	0.037	0.058	0.060	0.055	0.089	0.087	0.082
	(0.585)	(0.602)	(0.593)	(0.298)	(0.327)	(0.298)	(0.455)	(0.467)	(0.441)	(0.699)	(0.686)	(0.665)
	0.126	0.121	0.138	0.070	0.068	0.076	0.101	0.097	0.106	0.148	0.141	0.154
	(0.669)	(0.663)	(0.668)	(0.370)	(0.374)	(0.365)	(0.534)	(0.531)	(0.512)	(0.788)	(0.773)	(0.743)
	0.185	0.146	0.164	0.106	0.083	0.092	0.144	0.113	0.127	0.204	0.158	0.181
	(0.666)	(0.661)	(0.640)	(0.382)	(0.377)	(0.360)	(0.520)	(0.510)	(0.495)	(0.735)	(0.717)	(0.708)
	0.060	0.054	0.056	0.030	0.031	0.032	0.048	0.047	0.049	0.076	0.072	0.076
	(0.629)	(0.618)	(0.628)	(0.317)	(0.348)	(0.354)	(0.505)	(0.532)	(0.547)	(0.794)	(0.816)	(0.845)
	0.065	0.070	0.064	0.031	0.039	0.033	0.049	0.057	0.052	0.078	0.085	0.081
	(0.577)	(0.597)	(0.610)	(0.273)	(0.332)	(0.316)	(0.437)	(0.487)	(0.495)	(0.693)	(0.727)	(0.772)
	0.111	0.115	0.125	0.062	0.066	0.067	0.098	0.099	0.101	0.153	0.152	0.153
	(0.722)	(0.719)	(0.708)	(0.403)	(0.409)	(0.380)	(0.638)	(0.619)	(0.572)	(1.000)	(0.944)	(0.868)

• B_ihm is a trade competition index between exporting countries i and h for market m that accounts for sectoral weights similarity and total exports overlap; U_ihm is a trade competition index between exporting countries i and h for market m that accounts for sectoral weights similarity, inter-sectoral similarity, intra-sectoral similarity and total exports overlap; the methodological option for B_ihm⁽²⁾ is λ = 2; the methodological options for the U_ihm indicators are as follows: for U_ihm⁽²⁾, we have (α₁, α_2, α₂, λ) = (0.025; 0.075; 0.9; 2); U_ihm⁽⁵⁾—(α₁, α_2, α₂, λ) = (0.1; 0.15; 0.75; 2); and U_ihm⁽⁸⁾—(α₁, α_2, α₂, λ) = (0.2; 0.3; 0.5; 2); is an overall trade competition index for the country pair i and h. In this table, we have four different for each country pair (i.e., , , and ); numbers between parentheses are the ratios . Bold is used for the country pair having the highest value of the ratio and italics for the pair with the minimum value.

In the case of and , the indicators suffer a lower decrease when compared with the impact on . Nevertheless, the qualitative impact is similar in what concerns the ranking of the most penalised country pairs. Considering once again the evidence presented in Table A2, we can see that, with the exception of groups 4 and 5, it is for the pair FR-GB that we find a narrower gap between and ⁽²⁾.

Regarding , the overall trade competition indexes capturing simultaneously the three dimensions of structural similarity and total exports overlap, we calculate nine alternatives resulting from varying the values given to α₁, α₂, α₃ and λ. In Table 4, we present three of these alternatives which are developed assuming λ = 2 and three alternative sets of parameters for α₁, α₂, and α₃: U_ihm⁽²⁾ is based on (α₁, α₂, α₃) = (0.025, 0.075, 0.9); U_ihm⁽⁵⁾—(α₁, α₂, α₃) = (0.1, 0.15, 0.75); and U_ihm⁽⁸⁾—(α₁, α₂, α₃) = (0.2, 0.3, 0.5). The remaining alternatives are presented in the Appendix (Table A3).

From the results presented in Table 4, we conclude that, with the exception of in 2007, the three country pairs comparing the largest European economies reveal the highest values in all the measures considered, that is, for all years and combination of parameters, despite some obvious quantitative differences. This evidence arises from a combination of effects: (i) less accentuated difference in terms of total exports; (ii) the highest similarity in terms of sectoral shares; and (iii) similarity in the quality ranges exported.

4.5 An analysis by exporting country

Finally, Table 5 contains evidence concerning the idea introduced in subsection 2.5 that to measure competition for one pair of countries, instead of only one index we should have a different value for each of the countries under consideration. For this analysis, we have selected some and indicators with different values for the parameters.

Table 5. Trade competition indexes—an analysis by exporting country (2015)

Pairs	TCI ihm  = B ihm (2)	TCI ihm  = U ihm (2)	TCI ihm  = U ihm (5)	TCI ihm  = U ihm (8)
DE,FR	= 0.307	= 0.212	= 0.248	= 0.306
	= 0.314	= 0.216	= 0.253	= 0.312
	= 0.537	= 0.368	= 0.433	= 0.536
DE,GB	= 0.263	= 0.165	= 0.201	= 0.258
	= 0.274	= 0.171	= 0.208	= 0.267
	= 0.503	= 0.315	= 0.384	= 0.492
DE,GR	= 0.071	= 0.038	= 0.055	= 0.081
	= 0.077	= 0.041	= 0.059	= 0.087
	= 0.176	= 0.095	= 0.139	= 0.207
DE,HU	= 0.193	= 0.124	= 0.158	= 0.211
	= 0.203	= 0.131	= 0.166	= 0.222
	= 0.415	= 0.260	= 0.336	= 0.455
DE,SE	= 0.196	= 0.128	= 0.158	= 0.206
	= 0.205	= 0.134	= 0.166	= 0.215
	= 0.437	= 0.281	= 0.352	= 0.464
FR,GB	= 0.263	= 0.156	= 0.198	= 0.265
	= 0.321	= 0.189	= 0.240	= 0.322
	= 0.350	= 0.208	= 0.264	= 0.353
FR,GR	= 0.080	= 0.044	= 0.062	= 0.091
	= 0.094	= 0.052	= 0.073	= 0.105
	= 0.188	= 0.105	= 0.150	= 0.219
FR,HU	= 0.161	= 0.096	= 0.128	= 0.177
	= 0.175	= 0.104	= 0.139	= 0.192
	= 0.307	= 0.183	= 0.246	= 0.343
FR,SE	= 0.156	= 0.092	= 0.124	= 0.174
	= 0.189	= 0.113	= 0.151	= 0.210
	= 0.308	= 0.181	= 0.245	= 0.346
GB,GR	= 0.073	= 0.037	= 0.055	= 0.082
	= 0.083	= 0.042	= 0.061	= 0.092
	= 0.165	= 0.083	= 0.124	= 0.189
GB,HU	= 0.138	= 0.076	= 0.106	= 0.154
	= 0.163	= 0.089	= 0.125	= 0.182
	= 0.251	= 0.136	= 0.194	= 0.284
GB,SE	= 0.164	= 0.092	= 0.127	= 0.181
	= 0.199	= 0.112	= 0.153	= 0.218
	= 0.312	= 0.174	= 0.243	= 0.351
GR,HU	= 0.056	= 0.032	0.049	= 0.076
	= 0.115	= 0.065	= 0.100	= 0.153
	= 0.065	= 0.036	= 0.056	= 0.087
GR,SE	= 0.064	= 0.033	= 0.052	= 0.081
	= 0.129	= 0.065	= 0.104	= 0.164
	= 0.080	= 0.042	= 0.065	= 0.090
HU,SE	= 0.125	= 0.067	= 0.101	= 0.153
	= 0.183	= 0.099	= 0.151	= 0.231
	= 0.169	= 0.091	= 0.136	= 0.206

• The methodological options concerning the TCI_ihm indicators are explained in Table 4; and are the trade competition indexes for countries i and h, respectively.

There are interesting results to highlight from Table 5. First, the evidence obtained with emphasises the fact that the smaller country may suffer an important increase in its country-specific index. This makes clear that the larger countries are stronger competitors than we can infer from the analysis of the baseline index (). The results provided in the first column of Table 5 allow us to conclude that Greece is the country that suffers the strongest competition from the three larger European economies. In fact, when we compare the with (i = DE, GB, FR), it is possible to see very high increases in the country-specific index for Greece. The ratios between the country-specific index and the baseline index are 2.48 for the pair DE-GR, 2.35 for the pair FR-GR and 2.26 for the pair GB-GR. Second, other pairs with a very significant impact for the smaller country include DE-SE (with a ratio of 2.23) and DE-HU (with a ratio of 2.15). Third, the gap between and the correspondent is small for all the countries h considered (France, the United Kingdom, Greece, Hungary and Sweden). For example, with data for 2015, the gap between and is very small ( = 0.307;  = 0.314). The same occurs, in qualitative terms, for the remaining countries. In fact, the increases registered by the indexes for Germany are always inferior to 10%. This result arises because German exports are higher than the values presented by France in 95 markets, the United Kingdom in 106 markets, Greece in 120 markets, Hungary in 122 markets and Sweden in 121 markets. Fourth, the other pair presenting a gap of similar magnitude between and the indicator for the larger exporter is FR-HU ( = 0.175, with an increase of 8.7%). Fifth, FR-GB and HU-SE reveal the smallest gap between and ( and (). These are the two pairs with closest values of total exports (x_FR/x_GB = 1.11 and x_SE/x_HU = 1.41). However, France exports more than the United Kingdom to 81 markets while Sweden exports more than Hungary for 95 markets. Finally, the findings for the indicators are, in general terms, similar to those using the indicators.