# Calculation methods

## Annual average growth rate

The annual average growth rate is, unless otherwise specified, computed as the coefficient b in the exponential trend function y = aebt where t stands for time and y is the object of measurement. This method takes all observations in the analysed period into account. Therefore, the growth rate reflects trends that are less influenced by exceptional values.

On the Total and urban population page, annual population growth is expressed by the annual exponential rate of growth, defined as:

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

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

where i designates the economy and t the year.

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

where UVIexports,i,t is the unit value index of exports and UVIimports,i,t is the unit value 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 Xi,j is the value of exports of product i from economy j and n is the number of economies.

## 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 VIi,t is the value index of exports (imports), given by

xi,t is the value of exports (imports), UVIi,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, table 1) is calculated by dividing the export value index by the corresponding import unit value index and scaling up by 100:

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

## Lorenz curve

The Lorenz curve on 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 yi 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 + ... + pn

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

with y = y1 + y2 + ... + yn