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.
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.
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
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 for 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 UNCTAD (2018).
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 Gt 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 ut and vt are independently distributed according to distributions N(0,W) and N(0,Q), respectively.
The nowcast for the target variable at time t is obtained by extracting the corresponding element from vector Gt above, once B and the latent factor ht 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 (Cantú, 2018).