# 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.

## 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 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

_{1}+ p

_{2}+ … + p

_{n}

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

_{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, qi,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 pi,t is the price of a representative product, within commodity group i, in year t. For more details, see -—

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## Nowcasts

The nowcasts of world merchandise exports and world services exports represent real-time evaluations of these variables based on a large set of relevant and timely indicators. They are based on dynamic factor models which capture common latent trends in these data through their cross correlations. In their state-space representation, the models can be written as:

where *G _{t}* is a combination of the reference and indicator series, ht is the time-varying factor,

*B*is a matrix of factor loadings,

*D*defines the time structure of the respective factor, and the error terms

*u*and

_{t}*v*are independently distributed according to distributions N(0,W) and N(0,Q), respectively. The nowcast for the target variable at time

_{t}*t*is obtained by extracting the corresponding element from vector

*G*above, once

_{t}*B*and the latent factor

*h*have been estimated through maximum likelihood. This model is adapted to accommodate variables of different frequencies and unbalanced datasets. It should be noted that the nowcast figures cannot be considered as official data, as they are the result of an estimation. For more details on the methodology, see -—

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## References

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