## **Equation 10**

# **2.2. The Export Competitiveness Database**

The Export Competitiveness Database is the resulting database, containing a set of five indicators with information on export performance, measured as a relative change between period _t-1_ and period _t_ . In particular it contains indices of export growth, export market share change, changes in geographical and sectoral specialization (composition effects) and the export performance, i.e. changes in export market share growth once sectoral and geographical composition effects have been removed. The database contains information for trade in values, as well as in volume and unit value terms and all these terms are additive. Changes are computed relative to the same quarter in the previous year (year on year changes) and relative to the previous quarter (quarter on quarter changes). Year-on-year changes correct for seasonality and therefore these are chosen for describing the patterns and trends in Section 4. However, in some cases the user of the database may want to refer to the quarter-on-quarter changes. For this reason, the latter are also provided.

As a result, the database contains 18 time series for each of the 228 countries in the database. For benchmark purposes, the database also reports the evolution of world trade growth in values, volumes and unit values, against which individual country performances can be assessed.

Growth rates in the database are measured as log first differences (a.k.a. delta log). While expressing changes in the most common percentage growth rates would be much more intuitive, keeping them in this form allows an important advantage for the purpose of the paper. Namely, it allows adding up the various components of the export growth decomposition and to quickly grasp the proportionality of effects between indicators. To exemplify further, Table 1 reports the decomposition for the world region. Showing results in delta-logs allows immediately to see that the 3.2% growth in export market share between 2005 and 2013 is due to a 6.7% improvement due to push factors, but that about half of this effect has been offset by an unfavorable sectoral specialization (-3.7%). If we had used simple percentage growth rates we would have been unable to show how the various effects combine together. This difference is due to the fact that changes in natural logarithms (delta log) preserve the property of additivity, thus allowing to sum up percentage changes across components of the decomposition. This is not the case for the simple percentage export growth rates. While delta logs are only approximately equal to simple percentage growth rates, the discrepancies remain very small (0.02% in the just mentioned example of the market share change for East Asia and the Pacific).<sup>9</sup>

> 9 Log first differences are a good approximation of a percentage change. When used in conjunction with differencing, a logarithmic transformation converts absolute differences into relative (e.g. percentage) differences. Thus, the numbers reported in the tables represent an approximation of the percentage change in the variable from period to period (in our case relative to the same quarter of the previous year). Strictly speaking, the percentage change in a variable Y at period t is defined as (Y(t)-Y(t-1))/Y(t-1), which is approximately equal to LOG(Y(t)) - LOG(Y(t-1)). The approximation is almost exact if the percentage change is small. For example, a 5% percentage change in delta logs is equal to 4.88%, i.e. ln(1+5%)=0.0488. Related to the results in our database, the difference is very small for all countries reporting more than 10,000 elementary export flows. E.g. for Pakistan, which has about 10,000 elementary export flows, the average absolute difference between the conventional and the (weighted) mid-point growth rate was 0.05% (for an average growth rate of exports of -10% between 2008q4 and 2009q1. Discrepancies are a bit larger for

10