Sectoral trade freeness and agglomeration in the EU: an empirical test approach

Abstract

This paper studies the evolution of trade freeness and of the agglomeration of production, and their relationship at the sectoral level in a selected group of EU countries. Our main objectives are the search for stylized facts about their relationship and to check how our findings relate to the theoretical prediction about it in case of the home market effect. Our sectoral focus requires an original testing approach based on the combination of different bootstrap distributions. The results discussed show that a systematic relationship between trade freeness and agglomeration does not emerge at the sectoral level, this is true also for those sectors which support the home market effect hypothesis.

Appendices

Appendix A: Data, bootstrap and robustness

Throughout the paper we consider twenty-one sectors of activity classified according to ISIC rev.3/NACE 1.1, these sectors are as follows: -a- the aggregate for “Mining and Quarrying” (NACE: C, ISIC:10-14), -b- 18 subgroups of manufacture as partition of the “Total Manufacturing” aggregate (NACE: D, ISIC: 15-37; see Table 1 for the list of all the sectors), -c- the aggregate for “Electricity, Gas and Water Supply” (NACE: E, ISIC: 40-41), and -d- the aggregate for “Agriculture, Hunting and Forestry” (NACE: A, ISIC: 01-02). The countries comprised in the analysis are those in the EU-15 group: Austria, Belgium-Luxembourg, Denmark, Finland, France, Germany, Greece, Ireland, Italy, the Netherlands, Portugal, Spain, Sweden, and the United Kingdom. Data for Belgium and Luxembourg are recorded together for the so-called Belgium-Luxembourg Economic Union (BLEU). The time range is 1995–2006, whole-period figures are the average of all the yearly observations. We use values for four sequential subperiods defined as follows: period 1 values are the average of 1995–1997 yearly figures, period 2 of 1998–2000, period 3 of 2001–2003, and period 4 of 2004–2006.

1.1 Agglomeration analysis

To calculate the sectoral Theil Index we use employment figures (number of employees) at the Nuts-2 regional level; data are extracted from the Eurostat Regio database. We start with 207 Nuts-2 regions: Austria, 9 regions; Belgium, 10 regions; Germany, 38 regions; Denmark, 5 regions (5 deleted); Spain, 19 regions (8 deleted); Finland, 5 regions (1 deleted); France, 22 regions; Greece, 13 regions (1 deleted); Ireland, 2 regions; Italy, 21 regions; Luxembourg, 1 region (1 deleted); the Netherlands, 12 regions; Portugal, 5 regions; Sweden, 8 regions; and United Kingdom, 37 regions. Some regions were deleted in case of too many missing values. Employment data for sector 21 “Agriculture, Hunting and Forestry” were not available in the Eurostat Regio database, we, therefore, did not consider this sector for the agglomeration analysis.

1.2 Trade freeness

For the trade freeness indicator we use bilateral export among the EU-15 countries which constitute our sample, plus National Trade figures computed as “total production less total export.” All figures are in current US dollars. Bilateral export, total production, and total export are extracted from the OECD Stan database.

1.3 Production and demand shares for the HME

To test the HME we use sectoral-production and aggregate-demand country shares. Production shares are calculated using sectoral value-added figures, we use Domestic Absorption to account for demand. Domestic absorption is computed as “production less export plus import.” Value added, national production, export, and import in US dollars are extracted from the OECD Stan database.

1.4 The GINI coefficient as a robustness check for agglomeration

As written in the text, we have computed the GINI coefficient as a robustness check for the Agglomeration of Production. For this purpose, we calculate the GINI coefficient using all the available Nuts-2 regions and it ,therefore, accounts for geographic disparities across regions. The comparison with the Theil-Total index is straightforward. The ranking of the sectors is highly comparable, with 10 out of twenty sectors having the same ranking position as the one based on the Theil-Total Index. Furthermore, a similar bootstrap test based on the GINI coefficient rejects the null of “no significant variation” for 4 sectors. These are among the 6 sectors for which the bootstrap test for the Theil-Total Index (Table 3) rejects the same null.

On the contrary, a comparison with the Theil-Between is not straightforward because the GINI coefficient is not decomposable by groups. We have attempted it, however, by annulling within countries regional differences. This was done by replacing the regional observations with the within-country regional averages. By so doing, the GINI coefficient gets conceptually closer to the Theil-Between which is indeed calculated on the country means instead of the regional observations (Brulhart and Traeger 2005). Results show that in this way the between-agglomeration ranking of the sectors is close to the one based on the Theil-Between. We did not run any bootstrap test for this case because the artifact applied would bias too much the resampling. All results are available upon request.

1.5 Bootstrap-based test for the TFI variation

We test the hypothesis $\Delta \mathrm{TFI}_{p.p-1}^{k}\ne 0$ (where $\Delta \mathrm{TFI}_{p.p-1}^{k}=\mathrm{TFI}_{p}^{k}-\mathrm{TFI}_{p-1}^{k})$ by using bootstrap simulations to generate two distributions with $R$ observations each: one of $\mathrm{TFI}_{p}^{k}$ and one of $\mathrm{TFI}_{p-1}^{k}$ values. Each bootstrap runs $R=1000$ replications. The same procedure is executed $K$ times, one for each sector $k.$ The procedure is described here sequentially, we omit the superscript $k$ in what follows:

• 1. We start with two observed samples of $\mathrm{TFI}_{ij,p}$ values of size $N_{p}$ $\left( p=1,2\right)$; one for each period considered for the time difference.

• 2. The bootstrap generates $R$ samples $\left( r=1,...,R\right)$ of size $N_{p}\;\left( N_{p}^{r}\right)$ of bootstrap-generated $\mathrm{TFI}_{ij,p}$ values. This is done twice: once for $p$ and once for $p-1.$

• 3. For each sample $r,$ we calculate the average of the $N_{p}^{r}$ bootstrap-generated $\mathrm{TFI}_{ij,p}$ values:$\mathrm{TFI}_{p}^{r}$. So that we have two distributions (one for $p$ and one for $p-1$) of $R$ values $\mathrm{TFI}_{p}^{r}.$

• 4. We calculate the $R$ differences $\Delta \mathrm{TFI}_{p.p-1}^{r}=TFI_{p}^{r}-\mathrm{TFI}_{p-1}^{r}$, by so doing we have for each sector $k$ a distribution of $\Delta \mathrm{TFI}_{p.p-1}^{r}$($R$ observations).

• 5. The $\Delta \mathrm{TFI}_{p.p-1}^{r}$ distribution is used to generate standard errors to test the hypothesis $\Delta \mathrm{TFI}_{p.p-1}^{r}\ne 0$.

We check normality of the $\Delta \mathrm{TFI}_{p.p-1}^{r}$ distribution through the Shapiro-Francia Test (Shapiro and Francia 1972); normality is not rejected only in sectors 3, 7, 15. Given non-normality we resort to Bias-Corrected and Accelerated Confidence Intervals (BCA-CI) to define rejection areas. Sector 13 and 20 are not available for bootstrap simulation given the high number of missing values in the observed $N_{p}$ sample.

For a discussion of the different confidence intervals for hypothesis testing available in this context, see Diciccio and Romano (1988) . We refer the reader to Cameron and Trivedi (2005) chapter 11 for more information about the Bootstrap.

Appendix B: A percentiles-based test of the sign

The test of the sign discussed in Sect. 4.3 checks whether the portion $(J^{k})$ of positive bootstrap-generated values is statistically larger than half for deciding about the sign of the product of the contemporaneous variations $(Y^{k})$. In this context, the word statistically makes the difference. Indeed, if we were not looking for a statistically significant result, one might simply check what is the percentage of positive values in the bootstrap distribution $\left( Y_{r}^{k} \text { with }r=1,...,R\right) ,$ and conclude that $Y^{k}$ is positive if more than 50 % $Y_{r}^{k}$ values are positive. This reduces to observing the median of the distribution. The issue is that the median might be just one position away from zero. Then, a conclusion based only on the sign of the median could lead to a non-robust statement about the sign of $Y^{k}$. In the paper, the statistical significance of the conclusion is guaranteed through the use of the $Z_{1}^{k}$ statistic which has a normal distribution, and, therefore, parametric hypothesis testing is applied. We propose now an alternative way to decide about the sign of $Y^{k}$ which guarantees robustness at specific levels.

In the spirit of hypothesis testing based on Percentiles Confidence Intervals (Cameron and Trivedi 2005, Sect. 11.2.7), one may define buffers around the median which guarantee to decide about $H_{0}$ at a certain robustness level. We define these buffers $\gamma$ as follows: when $\gamma$ increases, the rejection area decreases; we get more restrictive on rejection of $H_{0}$. We opt for this definition because it guarantees that more evidence is required to opt for either sign of the statistic when larger buffers are used. We consider three standard levels: $\gamma =1~\%$, $\gamma =5~\%$, and $\gamma =10~\%$, and define, respectively, the rejection areas in the following Table 7.

Table 7 Rejection areas

The rationale behind the definition of the rejection areas for $H_{0}$ is that when at least $\left( 50+\gamma \right)$% $Y_{r}^{k}$ values are positive (negative), one can assume that $Y^{k}$ is positive (negative) at a robustness level equal to $\gamma \%$. On the contrary, if the portion of positive/negative is less than $\left( 50+\gamma \right) \%$, one concludes that the sign is not distinguishable because there is not enough evidence.³⁰

We run the two tests discussed in Sect. 4.3 using $\gamma =5~\%.$ The system of hypotheses is:

• 1. “$H_{0}:J^{k}=1/2$” against “$H_{1a}:J^{k}>1/2$”; rejection area for $45p>0$.

• 2. “$H_{0}:J^{k}=1/2$” against “$H_{1b}:J^{k}<1/2$”; rejection area for $55p<0$.

Results based on this approach are in the following Table 8, where are reported also the results based on the $Z_{1}^{k}$ statistic discussed in Sect. 4.3 for comparison. Except for sector 18/diff(P4-P3), rejection of the null hypothesis for the same alternative is exactly in the same cases as those selected by the $Z_{1}^{k}$ statistic $\left( \alpha =1~\%\right)$. This is a nice finding which supports the results discussed in the main body of the paper.

Table 8 Test of the sign, PC method