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Information on the different types of average growth rates used by the world bank, including compound growth rates and least-squares growth rates. It also includes data on the average annual growth rates of various caribbean countries and their corresponding income groups. The document concludes with a discussion on the world bank's atlas method and the use of purchasing power parities for converting measures of income into a common currency.
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This is a measure of the size of an economy. The larger the GDP, the larger the size of the economy. Note that (a) GDP, despite its difficulties, is the closest we have come to measuring aggregate economic activity and (b) our best hope of understanding development or economic well being is to improve on, and supplement GDP with other measures.
Averages and Growth Rates^1
The World Bank uses a wide range of average numbers and growth rates for different purposes. An average is a single value within a range of data, used to represent all the values in the series. It is a measure of the central value or the central tendency. A growth rate can also be a measure of central tendency; for example, least squares growth rate of GDP over a period is a measure of trend.
We will first give a short description of the different types of averages and other measures of central tendency, give some hints for when or for what purpose it would be appropriate to use each of them, and show the relationship between them. Secondly, we will describe the different growth rates and their uses.
One-period growth rate
For the calculation of the growth rate for one period a simple percentage change methodology is appropriate.
The one period growth rate can be used on all kind of data (except for the case where the initial value is zero), to measure growth in economic indicators like GDP or CPI, and population growth, among others, from one period to the next.
Compounding or geometric average growth rate
(^1) These descriptions were extracted from the World Bank’s website to give you clear illustration of how different growth rates are actually calculated.
A compounding growth rate derives the average growth over a period. To compute the average
growth, the values at the start (0) and at the end (t) are the only values used. The compounding growth rate is a generalisation of the one-period growth rate, and computing a geometric average over the one-period growth rates will be identical to compute a compounding growth rate.
The formula for the one-period growth rate can be re-arranged:
Since:
It follows that:
where g is average percentage growth/change from period 0 to t.
The compound growth rate is used when averaging growth, interest and rate of return over discrete periods. Most economic phenomena are measured only at intervals (month, quarter or year) for which the compound growth model is appropriate.
Compound growth rates do not take into account intermediate values of the series, thus, is sometimes named end-point growth rates.
Annualised, or compounded sub-annual growth rates
When measuring growth in sub-annual time series; for example, quarterly GDP or monthly CPI,
there is always a choice of how to measure and present the growth. Growth can be presented:
(i) As the change from the same period the of previous year (4.98 to 4.99)
(ii) As the change from the previous period (3.99 to 4.99) or
(iii) As the change from the previous period (3.99 to 4.99) at annualised, or compounded rate of change.
The purpose of annualising the rates of change is to present period-to-period rates of change for different period lengths on the same scale, and thus to make it easier for the layman to interpret
An average growth rate estimated as a least-squares growth rate represents a trend, and it is not necessarily equal to any of the actual growth rates between any two periods.
Least squares growth rates are used in Bank publications when measuring trend-wise growth in economic variables such as GDP and GNP per capita. It should be noted that most national statistical offices use the compounding growth rate as an average growth rate, not the least squares growth rate.
These are used as indicators of well-being. The higher the GNI or GDP per capita, the better of are the citizens of a country.
Per Capita GDP for Caribbean Countries
Table 1 suggests that smallness alone may not be as significant in limiting economic growth and development as is commonly believed, and that other factors may be at play. For example, in 1970 Antigua and Barbuda, Grenada, Dominica, St. Kitts and Nevis, and St. Lucia had roughly similar real per capita GDP. By 2006 real per capita GDP in Antigua and St. Kitts and Nevis had increased between five-and six-fold to about $11,400 and $9,800, respectively; significantly higher than some of the “larger” countries including Belize, Guyana and Jamaica.
In Grenada, Dominica, St. Lucia and St. Vincent and the Grenadines per capita GDP in 2006 was less than half that in Antigua and St. Kitts, averaging about $4,600—about the same as Belize— and higher that Jamaica and Guyana.
Although these data are merely anecdotal, they do suggest that smallness alone cannot explain the differential levels of growth in per capita GDP observed over the past several decades within CARICOM. Why is it that some of the smaller countries in CARICOM have grown more rapidly in terms of per capita GDP than others?
Table 1: Per Capita GDP for Selected CARICOM Countries in US Dollars Country or Area 1970 1980 1985 1990 1995 2000 2005 2006 Antigua and Barbuda 400 1,523 2,980 6,324 7,263 8,665 10,481 11, Bahamas 2,982 6,920 9,405 12,406 12,231 16,506 18,155 18, Barbados 800 3,474 4,634 6,341 6,685 8,933 10,488 11, Belize 206 1,354 1,283 2,183 2,893 3,400 4,032 4, Dominica 248 809 1,376 2,430 3,190 3,961 4,427 4, Grenada 159 797 1,043 1,846 2,370 3,336 3,835 4, Guyana 378 777 613 542 841 970 1,117 1,
Jamaica 752 1,261 918 1,803 2,332 3,047 3,622 3, Saint Kitts and Nevis 293 1,109 1,857 3,910 5,336 7,149 8,724 9, Saint Lucia 235 1,147 1,761 3,022 3,782 4,627 5,473 5, Saint Vincent and the Grenadines
204 589 1,081 1,812 2,337 2,891 3,625 3,
Trinidad and Tobago 847 5,765 6,256 4,142 4,196 6,270 11,399 13, Source: UN Common Database: unstats.un.org/unsd/cdb/cdb_help/cdb_quick_start.asp
World Bank Classification of Countries
The World Bank’s main criterion for classifying economies is gross national income (GNI) per capita. Based on its GNI per capita, every economy is classified as low income, middle income
(subdivided into lower middle and upper middle), or high income. Other analytical groups based on geographic regions are also used.
The classifications are for all World Bank member countries (187) and all other economies with populations of more than 30,000 (215 total).
Geographic region: Classifications and data reported for geographic regions are for low-income and middle-income economies only. Low-income and middle-income economies are sometimes referred to as developing economies. The use of the term is convenient; it is not intended to imply that all economies in the group are experiencing similar development or that other economies have reached a preferred or final stage of development. Classification by income does not necessarily reflect development status.
Income group:
Economies are divided according to 2010 GNI per capita, calculated using the World Bank Atlas
method. The groups are:
Low income: $1,005 or less
Lower middle income: $1,006 - $3,
Upper middle income: $3,976 - $12,
High income: $12,276 or more.
World Bank Classification of Caribbean economies (November 2011)
Economy Income group Antigua and Barbuda Upper middle income Bahamas, The High income Barbados High income Belize Lower middle income Dominica Upper middle income
Purchasing Power Parities 3
An alternative approach to convert measures of income from national currencies into a common currency is by using conversion factors that reflect the purchasing power of currencies— Purchasing Power Parities ( PPP ).
PPP eliminates the inconsistencies inherent in exchange rate conversions, which are sometimes volatile and fail to reflect properly the differences in price levels between countries—particularly
with respect to non-traded items. (Devaluation of a country’s currency will reduce its GDP in US$ over night, but it does not make the citizens less well off unless they buy imported goods. The exchange rate is the price on foreign currency, and is relevant for actual transfers across the border, but it is not too relevant for the part of GDP that does not enter international trade).
The PPP rate is defined as the number of units of a country’s currency that is required to buy the same amount of goods and services in the country as one US$ would buy in the US. PPP as a rate of conversion ensures that money exchanged for a dollar buys the same volume of goods and services in every country. By equalising prices, PPP rates deliver a measure of relative GDP which is based on what constitutes “real” income, the volume of goods and services embodied in GDP. The method of using PPP is analogous to measuring GDP in different years at fixed base year prices.
As to actual PPP data, there are concerns related to coverage, continuity and timeliness of surveys, quality of results and aggregation procedures.
The World Bank does not use PPP converted data for administrative purposes. For setting the terms for lending at the World Bank, the atlas method is used to convert income from local currencies to a common currency (US$). However, the World Bank uses available PPP-based numbers for analytical and poverty reduction policy purposes, as demonstrated in recent editions of the World Development Report and the World Development Indicators.
PPP rates can be derived using several methods, each yielding different estimates. PPP rates are estimated on the basis of data from special price surveys. Price ratios of comparable items between countries are computed, and aggregated using corresponding weights based on GDP expenditure data. Several methods of aggregation exist, and there is no universal agreement as to which is superior - it depends on the purpose.
PPPs can be used either for binary comparisons, or for comparison of a group of countries. Binary comparisons between pairs of countries are obtained by computing the “ideal” index, the Fisher index. However, the Fisher index is not transitive, thus, other methods are (should be) used for multilateral comparisons. (Transitivity means that comparing country A with C directly should give the same result as comparing country A with B and C with B -- making the comparison of A and C indirectly.)
3These descriptions were extracted from the World Bank’s website to give you clear illustration of how this method is actually implemented.
The two most commonly used methods of aggregation in multilateral comparisons are (i) the Geary-Khamis and (ii) the Elteto, Koves and Szulc, which both produce transitive and base- country invariant results.
The Geary-Khamis method involves using observed price and expenditure data to obtain implicit quantity estimates, and evaluate these quantities at a single set of average “international prices” denominated in a common currency, like the “international dollar.” An “international dollar” has the same purchasing power as an US$ for total GDP in the US, but the purchasing power of the components are determined by the average international price structure, not the US price relatives.)
The Elteto, Koves and Szulc method involves a two-step process. First step is to get a set of binary Fisher indexes for all pairs of countries, and step two is to make these comparisons transitive by computing geometric means of all the direct and indirect indexes.
The results using the Geary-Khamis method will generally differ both in ranking and level compared to the results using the Elteto, Koves and Szulc method. The Geary-Khamis method has one advantage over the Elteto, Koves and Szulc method: it is additive. This means that components can be added to reach a total, making it possible to add expenditure at “international prices” to reach GDP at international prices. Thus, the use of the Geary-Khamis method makes it possible to put up an internally consistent set of national accounts data at “international prices”. However, the Geary-Khamis method tends to result in inflated quantity estimates for poorer countries.
Analysts use various debt ratios generated on the basis of debt statistics and macro-economic aggregates to assess the external situation of developing countries, and analyse their
In addition, it is common to look at the ratio between short term debt and total external debt.
Short term debt is usually made on less preferable terms, and a high ratio of short term debt to total debt can be sign of a weak economy. Typical ratios are:
Economic aggregates presented in World Debt Tables are prepared for the convenience of the user; their inclusion is not an endorsement of their value for economic analysis. Although debt indicators can give useful information about the developments in debt-servicing capacity, conclusion drawn from them will not be valid unless accompanied by careful economic evaluation. The macro-economic information provided is from standard sources, but it should be noticed that some series, especially for African countries, are incomplete.
First, we need to distinguish between poverty and inequality (or unequal income distribution). There are many economists who view poverty as essentially a matter of inequality. Such an approach is wrong, or misleading for two reasons. First, if one were to redistribute from the top to the middle of the income distribution, this would unequivocally make distribution more equal, but would have no impact at all on the incidence of poverty.
Secondly, if the level of income declines significantly in the economy in any given year, and inequality remained the same, the incidence of poverty would clearly rise.
The two points above mean that poverty and inequality in income distribution should not be made conceptually equivalent. But, a lack of conceptual equivalence does not mean an absence of association. Poverty, then, has its own conceptual identity.
Defining Poverty
In defining poverty we may distinguish between (i) absolute poverty and (ii) relative poverty.
Absolute poverty is based on a head-count measure, usually calculated in terms of income. In other words, we identify all those people who live beneath a certain level of income as poor. That gives us percentages of the total population - percentages which may be referred to as the incidence of poverty.
Clearly, when we make such calculations, we implicitly make two assumptions:
(i) It is possible, in principle, to identify and measure certain requirements that establish an absence of poverty: a so-called poverty line, drawn in income terms. Anyone who, because of insufficient income, is unable to meet those requirements—who falls beneath the poverty line—is deemed to be poor.
(ii) The numbers so deemed poor can be established, and expressed as a proportion of the total population, to arrive at the poverty ratio.
The question is: is it satisfactory to categorise anyone who falls beneath the poverty line as poor? The answer is no. Why? Because, among other things, the poverty line approach fails to take into consideration the extent of inequality among the poor.
The relative poverty concept suggests that poverty is about deprivation, and deprivation for a human being, must be a relative condition. Essentially, this approach to poverty begins with an identification of the style of living which is generally shared in each society and classifies all those who find it difficult to share in the customs, activities and diets comprising that style of living, as being poor. Generally, therefore, relative poverty is concerned with the notion of a tolerable level of living standard for any country.
In practice, most economists employ the notion of absolute poverty.
Measuring Poverty
A variety of methods, embodying a range of differing assumptions, are used in producing estimates of the incidence of poverty.
One approach is to draw a poverty line in terms of a particular level of family income, or family consumer expenditure per annum (or per month, per week, or per day). All families with income or consumer expenditure below that level are deemed to be living in poverty.
The question, then, arises of where, precisely, one draws the line: of what level of income or expenditure should be chosen as the cut-off point. One basis for such is nutritional adequacy, using calorie intake as the essential criterion. The next step is to identify what an acceptable minimum standard of diet is, in terms of calorie intake.
Should it be, for example, 2,000 calories per day, with allowances made for the differing needs of adults, children, males, females, different occupational groups, etc?
The next step is to determine what annual per capita consumer expenditure is necessary to achieve this and what proportion of the population are unable to afford this? The proportion of the population that is unable to afford this is referred to as the incidence of poverty.
Poverty: A ‘Gross Concept’
Using the absolute concept of poverty leads us to classify the population into two categories only: the rich and the poor. Is this sufficient? Clearly, a large number of economists proceed on the assumption that it is. What might be wrong with such an assumption?
Sen insists that poverty is too undiscriminating a concept to be a gross category. According to Sen, hidden in the gross percentage figure - that is, the percentage of the population below the poverty line - is the fact that the poor are different groups. In essence they are all poor, but for different reasons. That is extremely important. Why?
(c) Women and female children must be reached, whether through asset creation or
employment schemes, in conjunction with credit, in a way that minimises appropriation by males.
Note that these, along with other measures, cannot succeed in poverty alleviation if they are not pursued seriously: either in terms of funding or administrative input.
Unemployment and total employment in an economy are the broadest indicators of economic activity as reflected by the labor market. The International Labour Organization (ILO) defines the unemployed as members of the economically active population who are without work but available for and seeking work, including people who have lost their jobs and those who have voluntarily left work. Some unemployment is unavoidable in all economies. At any time some workers are temporarily unemployed—between jobs as employers look for the right workers and workers search for better jobs. Such unemployment, often called frictional unemployment, results from the normal operation of labor markets.
Unemployment refers to the share of the labor force without work but available for and seeking employment. Definitions of labor force and unemployment may differ by country (see about the data). Long-term unemployment refers to the number of people with continuous periods of unemployment extending for a year or longer, expressed as a percentage of the total unemployed. Unemployment by educational attainment shows the unemployed by level of educational attainment as a percentage of the total unemployed. The levels of educational attainment accord with the ISCED97 of the United Nations Educational, Cultural, and Scientific Organization.
HDI – A socio-economic measure
Focuses on three dimensions of human welfare:
As with any index, weights have to be used to construct the overall figure. Hence, the HDI is often computed as:
These weights are to some extent arbitrary. However, it is interesting to see that some countries;
for example, Pakistan, have relatively high GDP per capita but are much lower than this might suggest in the overall development index. This may suggest failures of government policy.
Indeed, the HDI can be calculated for groups and regions in a country:
The New Human Development Index
This new index was introduced by the United Nations Development Programme (UNDP) in November 2010. What is new in the New HDI?
Inequality is a property of the distribution in a population of some (presumably valued) resource such as income or wealth but also cattle, wives (in a polygynous society), and articles published by scholars in scientific journals. The distribution of such quantities is typically highly skewed, with a long tail to the right.
One can conceptualize inequality with the Lorenz curve. Take the example of income. Imagine that all income-receiving units (IRUs) are ranked by income from the smallest to the largest, and calculate the cumulative share of income accruing to each category of the populations from poorest to richest, as in the following table.
Data For Constructing Lorenz Curve
Income Group % of income Y X1 X 1 0.8 0.8 0.8 10. 2 1.4 2.2 2.2 20. 3 3.7 5.9 5.9 30. 4 8.1 14.0 14.0 40. 5 14.2 28.2 28.2 50. 6 12.7 40.9 40.9 60. 7 11.1 52.0 52.0 70. 8 16.4 68.4 68.4 80. 9 17.8 86.2 86.2 90. 10 13.8 100.0 100.0 100.
Y = cumulative % of income
X1 = cumulative % of households = cumulative % of income
X2 = cumulative % of households
The Lorenz curve
The Lorenz curve is the plot of the cumulative income share against the cumulative households share:
In the Lorenz curve the 45 degrees line represents a situation of perfect equality. Why?
In general, the closer the Lorenz curve is to the line of perfect equality, the less the inequality and the smaller the Gini coefficient.
Lorenz curve limitations:
Gini Coefficient
One common measure of inequality is the Gini coefficient. The Gini coefficient (G) or “Gini Index” or “Gini Ratio” is calculated from the Lorenz curve as the ratio:
G = Area A/(Area A + Area B)
Note that (Area A + Area B) is the area of a triangle, given by 100*100/2 = 5000.
Calculating The Gini Coefficient Income Group % of income Y X 1 0.8 0.8 10. 2 1.4 2.2 20. 3 3.7 5.9 30. 4 8.1 14.0 40. 5 14.2 28.2 50. 6 12.7 40.9 60. 7 11.1 52.0 70. 8 16.4 68.4 80. 9 17.8 86.2 90. 10 13.8 100.0 100.
a A + Area B 5000.
rea 1 4.
rea 2 15.
rea 3 40.
distribution and the uniform (perfect) distribution line; the denominator is the area under the uniform distribution line.
Gini coefficient limitations:
These limitations help to understand the problems caused by the improper use of equality measures. However, they do not render these measurements ineffective. If equality measures are computed in a well-documented and consistent way they can provide a good tool for quantitative comparisons.
Sen, Amartya: Development: Which Way Now? The Economic Journal, Vol. 93, December 1983, pp. 745-762.