# Calculation methods

## 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*the unit value index of imports of economy

_{imports,i,t}*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*is the unit value index of exports (imports),

_{i,t}*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*is the unit value index of imports,

_{imports,i,t}*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

*p*=

*p*

_{1}+

*p*

_{2}+ … +

*p*

_{n}

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

*y*=

*y*

_{1}+

*y*

_{2}+ … +

*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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