Calculation methods

by Sonia Blachier · June 9, 2021

Annual average growth rate

The annual average growth rate over multiple years is calculated in this handbook as least squares growth rate or as exponential growth rate.

The least squares growth rate is computed as the coefficient b when fitting the regression model ln (y_t+1) = a + bi for i ∈ {0, 1, 2, …, k}

with least squares, where k stands for the length of the time period (in years), t for the base year, and y represents the object of measurement. This method takes all observations in the analyzed period into account.

The exponential growth rate is calculated as

Throughout the handbook, the growth rates of monetary values are based on current prices, unless otherwise specified.

Trade openness index

The trade openness index (Trade indicators page, map 1) is calculated as the ratio of the arithmetic mean of merchandise exports (x) and imports (m) to GDPgross domestic product (y):

where i designates the economy and t the year.

Terms of trade index

The terms of trade index (Trade indicators page, figure 1, tables 1 and 2) with base year 2015 is calculated as follows:

where UVI_exports,i,t is the unit value index of exports and UVI_imports,i,t the unit value index of imports of economy i at time t.

Market concentration index of exports

The market concentration index of exports (Trade indicators page, figure 2) is calculated as a normalized Herfindahl-Hirschmann index:

where x_i,j is the value of exports of product i from economy j and n is the number of economies.

Product concentration index of exports

The product concentration index of exports (Trade indicators page, figure 3) is calculated as a normalized Herfindahl-Hirschmann index:

where x_i,j is the value of exports of product i from economy j and n is the number of product groups according to SITCStandard International Trade Classification, Revision 3, at the 3-digit level.

Volume index of exports (imports)

The volume index of exports (imports) (Trade indicators page, figure 3, tables 1 and 2) is calculated by dividing the export (import) value index by the corresponding unit value index and scaling up by 100:

where VI_i,t is the value index of exports (imports), given by

x_i,t is the value of exports (imports), UVI_i,t is the unit value index of exports (imports), i designates the economy and t the time period.

Purchasing power index of exports

The purchasing power index of exports (Trade indicators page, tables 1 and 2) is calculated by dividing the export value index by the corresponding import unit value index and scaling up by 100:

where VI_exports,i,t is the value index of exports (as defined above), UVI_imports,i,t is the unit value index of imports, i designates the economy and t the time period.

Lorenz curve

The Lorenz curve in the Gross domestic product page (figure 3) plots cumulative population shares ordered by GDP per capita, on the x-axis, against the cumulative shares of global GDP which they account for, on the y-axis. For the construction of the Lorenz curve, the n economies of the world are ordered with reference to their GDP per capita, so that

where y_i is GDP and pi the population of the economy at position i in this ranking, counted from below.

The cumulative population shares, measured on the x-axis, are calculated as

with p = p₁ + p₂ + … + p_n

The cumulative shares of global GDP, measured on the y-axis, are calculated as follows:

with y = y₁ + y₂ + … + y_n

UNCTAD Commodity Price Index

The UNCTAD Commodity Price Index, in the Prices page, is a fixed base-weight Laspeyres index with base year 2015=100. It is calculated as

where i is the identifier of the commodity group, q_i,2015 is the quantity in which products of commodity group i were exported by developing economies during the three years around the base year (from 2014 to 2016), and p_i,t is the price of a representative product, within commodity group i, in year t. For more details, see -—
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References

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