# 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 exp(*b*)-1 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.

## Volume index of exports (imports)

The volume index of exports (imports) (Trade indicators page, figure 1) 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.

## Market concentration index of exports

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

where *x _{i,j}* is the value of exports of product

*j*from economy

*i*, and

*m*is the number of economies.

## Product concentration index of exports

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

where *x _{i,j}* is the value of exports of product

*j*from economy

*i*, and

*n*is the number of product groups.

## Lorenz curve

The Lorenz curve in the Gross domestic product page (figure 3) plots cumulative population shares ordered by GDPgross domestic product per capita, on the x-axis, against the cumulative shares of global GDPgross domestic product 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 GDPgross domestic product per capita, so that

where *y _{i}* is GDPgross domestic product and

*p*the population of the economy at position

_{i}*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 GDPgross domestic product, measured on the y-axis, are calculated as follows:

*y*=

*y*

_{1}+

*y*

_{2}+ … +

*y*

_{n}

## UNCTAD Commodity Price Index

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

where *j* is the identifier of the commodity group, *m* is the number of considered groups, *q _{j,2015}* is the quantity in which products of commodity group

*j*were exported by developing economies during the three years around the base year (from 2014 to 2016), and

*p*is the price of a representative product, within commodity group

_{j,t}*j*, in year

*t*. For the calculation of the subindices of the UCPIUNCTAD Commodity Price Index, the same formula is applied to a subset of commodity groups. For more details, see -—

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## References

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