Economic integration and similarity in trade structures

Luca De Benedictis; Lucia Tajoli

doi:10.1007/s10663-006-9024-x

Empirica

April 2007, Volume 34, Issue 2, pp 117–137 | Cite as

Economic integration and similarity in trade structures

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Luca De BenedictisEmail author
Lucia Tajoli

Original Paper

First Online: 03 March 2007

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Abstract

In this paper, we look at the similarity of the trade structures toward the EU market between four CEECs and the EU15. We evaluate the appropriateness of different indices to compare export flows—correlation indices and distance metrics—opting for the use of the Bray-Curtis semi-metric. We examine both how the export composition of a country has changed over time and how the export composition has changed with respect to the EU15 export composition. Finally, we test if the dynamics of sectoral distribution of the CEECs’ exports is related to the role acquired by processed trade in the 1990s. We give evidence that processed trade is crucial in explaining changes in the overall structure of exports of transition countries, and that greater economic integration in terms of trade flows and processing trade does not always lead to greater export similarity.

Keywords

EU CEECs Transition Similarity Nonparametrics

JEL Classification

F3 F42

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Notes

Acknowledgements

We wish to thank Salvatore Baldone, Giuseppe Celi, Alan Deardorff, Kener Kandogan, Stefano Manzocchi, Henry Thompson and the participants to the 6th SAET Conference in Rhodes, ETSG Conference in Madrid, and CNR Workshop in Florence and an anonymous referee for valuable comments and suggestions. Financial support from the EU 5th Framework Program, Project FLOWENLA, No HPSE-CT2001-00064 and from MIUR, PRIN-PIE 2003 and DDA-RN 2005 is gratefully acknowledged.

Appendix

The Appendix contains three different sections. The first one contains the description of the sectors included in the analysis. The second one contains a detailed report of the time-trend regressions described in Fig. 1. The third one analytically replicates the dynamics of the EU-similarity for the Hungarian case, in order to identify the cause of different prediction rising from the use of the correlation index or the Bray-Curtis distance metric.

Appendix 1: data sources and sectors

The source of all the data presented in the tables and in the analysis of this paper is the Eurostat database Comext “Intra-EU and extra-EU trade”, reporting annual trade data classified according to the Combined Nomenclature of the European Communities. The abbreviated definition of the 97 two-digit sectors of the Combined Nomenclature is reported in Table 3.

Table 3

Sectors

Products
Animals	Raw minerals	Silk	Nickel
Meat	Ores	Wool	Aluminium
Fish	Fuels	Cotton	Lead
Dairies	Inorganic chem.	Textile fibres	Zinc
Other animal prods.	Organic chem.	Filaments	Tin
Plants	Pharmaceuticals	Staple fibres	Other metals
Vegetables	Fertilizers	Special yarns	Cutlery and tools
Fruit	Dyes	Carpets	Other metal articles
Coffee and spices	Cosmetics	Tapestries	Machinery
Cereals	Soaps	Coated fabrics	Electrical machin.
Flours	Glues	Knitted fabrics	Railway
Seeds	Explosives	Knitted apparel	Autovehicles
Resins	Photog. Products	Apparel	Aircraft
Other vegetal prods.	Other chem.	Other textiles	Ships
Fats and oils	Plastics	Footwear	Precision tools
Meat preparations	Rubber	Hats	Clocks
Sugar	Leather	Umbrellas	Musical articles
Cocoa	Leather goods	Feather articles	Arms
Cereal preparations	Furs	Cement	Furniture
Veget. preparations	Wood	Ceramics	Toys
Other edibles	Cork	Glass	Other manuf.
Beverages	Wickerwork	Jewellery	Art pieces
Resid. food ind.	Cellulose	Iron	Others
Tobacco	Paper	Iron articles
	Printing	Copper

Appendix 2: time trend regressions

In this Appendix, we report the values of the CEECs exports towards the EU for 1989 and 2001 (Table 4). In Fig. 1, those values were normalized so that the values for 1992 equal 1.

In Tables 5 and 6 we report the regression statistics for the time trends pictured in Fig. 1.

Table 4

Value of CEECs’ exports to the EU (million euro)

	1989	1992	2001
Poland
Total exports	3863.41	7080.60	26623.57
Processing trade	572.67	1279.34	1121.73
Final exports	3290.74	5801.26	25501.84
Hungary
Total exports	2588.28	3987.85	24825.31
Processing trade	562.38	858.75	1080.37
Final exports	2025.90	3129.10	23744.94
Romania
Total exports	2547.59	1403.86	9376.50
Processing trade	474.96	407.80	1329.68
Final exports	2072.63	996.06	8046.82
Bulgaria
Total exports	530.43	905.38	3506.32
Processing trade	65.26	111.39	482.68
Final exports	465.18	793.99	3023.65

Table 5

Total Exports regressions on a time trend

	Estimate	SE	t Value	Pr (> \|t\|)	Adjusted-R ²
Poland
Time trend	0.2489	0.0204	12.21	0.0000	0.925
Hungary
Time trend	0.4607	0.0482	9.57	0.0000	0.883
Romania
Time trend	0.4189	0.0596	7.03	0.0000	0.801
Bulgaria
Time trend	0.2612	0.0189	13.81	0.0000	0.940

Table 6

Final Exports regressions on a time trend

	Estimate	SE	t Value	Pr (> \|t\|)	Adjusted-R ²
Poland
Time trend	0.2412	0.0241	9.99	0.0000	0.891
Hungary
Time trend	0.4454	0.0502	8.87	0.0000	0.866
Romania
Time trend	0.3468	0.0598	5.80	0.0001	0.731
Bulgaria
Time trend	0.2218	0.0182	12.18	0.0000	0.924

Appendix 3: r _xy vs. d _xy

Let’s mimic the characteristics of the sectoral distribution in Hungary and in the EU cases assuming that, existing n different sectors, ${i\in[1,n]}$, one of these sectors—machinery—becomes progressively relevant in the case of Hungary and remains stable in the case of the EU. We call x _j the Hungarian export share of that sector, and y _j the export share of the same sector in the European case, so that ${x\equiv[x_1, \ldots, x_j, \dots, x_n]}$ and ${y\equiv[y_1, \ldots, y_j, \dots, y_n]}$ .

Since the data under scrutiny are export shares, then

$$ \sum_i x_{i} \equiv \sum_i y_{i} \equiv 1 $$

(3)

and

$$ \frac{\sum_i x_{i}}{n} \equiv \frac{\sum_i y_{i}}{n} \equiv \frac{1}{n} $$

The distribution is therefore characterized by a constant mean, regardless the changes in sectoral shares.

Let’s focus the analysis on the changing sector x _j alone, shadowing the dynamic of the other n−1 sectors, so that the changes in the sectoral distribution of the x _i only depend on the variations of x _j. In the case of the EU, the sectoral distribution remains unchanged. Imposing symmetry on the n−1 residual sectors, ²¹ the linear correlation index expressed in Eq. 1 can be written as follows

$$ r_{xy}=\frac{\sigma_{xy}}{\sigma_{x} \sigma_{y}}=\frac{\left(x_j- \frac{1}{n}\right) \left(y_j- \frac{1}{n}\right)+ (n-1)\left(\frac{1-x_j}{n-1}- \frac{1}{n}\right)\left(\frac{1-y_j}{n-1}- \frac{1}{n}\right)}{\sigma_x \sigma_y} $$

(4)

where

$$ \sigma_{x}=\sqrt{\left(x_j- \frac{1}{n}\right)^2+ (n-1)\left(\frac{1-x_j}{n-1}- \frac{1}{n}\right)^2} $$

and

$$ \sigma_{y}=\sqrt{\left(y_j- \frac{1}{n}\right)^2+ (n-1)\left(\frac{1-y_j}{n-1}- \frac{1}{n}\right)^2}. $$

The sign of r _xy depends on x _j according to the following rule:

$$ r_{xy} \left\{ \begin{array}{lll} < 0 & \quad \hbox{if}& x_j < \frac{1}{n}\\ =0 & \quad \hbox{if}& x_j=\frac{1}{n}\\ > 0 & \quad \hbox{if}& x_j > \frac{1}{n} \end{array} \right. $$

and the sign of the partial derivative of r _xy w.r.t. x _j is

$$ \frac{\partial{r_{xy}}}{\partial{x_j}}=\frac{\left(y_j- \frac{1-y_j}{n-1}\right)}{\sigma_x \sigma_y}- \frac{r_{xy}}{\sigma_x} \;{\sigma^\prime_x} \left\{ \begin{array}{lll} < 0 & \quad \hbox{if}& y_j < \frac{1+(1-n)(r_{xy} \sigma_y \sigma^\prime_x)}{n}\\ > 0 & \quad \hbox{if}& y_j > \frac{1+(1-n)(r_{xy} \sigma_y \sigma^\prime_x)}{n} \end{array} \right. $$

where σ _x ^′ is the partial derivative of σ_x w.r.t. x _j.

In the present symmetric case, since the dynamic of the n−1 residual sectors is perfectly collinear, r _xy will always take the values −1 or +1. In general, when n is sufficiently large and x _j is relevant as well, r _xy is positive and increases (decreases) as x _j becomes larger depending on y _j being sufficiently large (small).

In fact, the values in the Hungarian EU-similarity were n = 97, y _j = 0.15 and x _j was growing from a 10% to a 30% value between 1989 and 2001. It is now clear why r _xy was steadily growing during the period.

On the other hand, the Bray-Curtis metric expressed in Eq. 2 can be rewritten as

$$ d^{bc}_{xy} = \frac{1}{2} \left(|y_j-x_j|+ |x_j-y_j|\right). $$

(5)

given our assumptions on x _j and y _j and taking into account Eq. 3.

The sign of d _xy ^bc is always positive while the sign of the partial derivative of d _xy ^bc w.r.t. x _j is

$$ \frac{\partial{d_{xy}^{bc}}}{\partial{x_j}}=-\frac{1}{2} \frac{\left|y_j-x_j\right|} {y_j-x_j}+ \frac{1}{2} \frac{\left|x_j-y_j\right|}{x_j-y_j} \left\{ \begin{array}{lll} < 0 & \quad\hbox{if}& x_j < y_j \\ \hbox{undefined} & \quad\hbox{if}& x_j = y_j \\ > 0 & \quad\hbox{if}& x_j > y_j \end{array} \right. $$

The shape of d _xy ^bc only depends on the value of y _j and it decreases as x _j tends to y _j from the left, it has a kink when x _j = y _j, and increases for values of x _j > y _j.

This explains why in the Hungarian EU-similarity the distance metric was decreasing until when x _j reached the same value of y _j and suddenly it changed its slope. r _xy and d _xy ^bc go in the same direction only for values of x _j < y _j, the concordance is broken when x _j becames greater than y _j.

In the choice between the correlation index and the Bray-Curtis metric, two general aspects run against the former. On the one hand, r _xy is heavily dependent on the mean and the standard deviation of the distribution of x _i and y _i that in case of pronounced skewness are distorted estimates of the location and the spread of the distribution. On the other hand, the mean value is fixed regardless of changes in the sectoral composition of export shares and it is sensitive to the number of sectors considered in the data aggregation.

The ${d_{xy}^{bc}}$ semi-metric has instead the advantage of not increasing in n, of being invariant to proportional sub-classifications of the n sectors considered (Sun and Ng 2000), it is not subject to the double-zeros paradox (Legendre and Legendre 1998), it lessen the effect of the largest differences since difference in high sectoral export shares contribute the same as difference between small sectoral export shares, and is appropriate in presence of skewed distributions.

Finally, since d _xy ^bc catches changes in the sign of x _j−y _j while r _xy reacts minimally to those changes, the former has to be preferred to the latter, when the sign of x _j−y _j is of interest. In other cases the two are monotone. d _xy ^bc should be therefore preferred to r _xy in general.

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Authors and Affiliations

Luca De Benedictis
- 1
Email author
Lucia Tajoli
- 2

1.DIEFUniversity of MacerataMacerataItaly
2.Dipartimento di Ingegneria GestionalePolitecnico di MilanoMilanoItaly

Economic integration and similarity in trade structures

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Acknowledgements

References

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