Level and growth rate of per capita GDP

• Gross domestic product (GDP) is a measure of economic activity: value of all goods and services produced and sold in the market less the value of goods or services used in their creation

• Level of per capita GDP (expressed in Purchasing Parity Standards)

• Change of per capita GDP (before and after the 2008 crisis)

• In terms of level and rate of change of GDP the performance across EU countries (and regions) is remarkably different

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Purchasing Parity Standard (PPS)• In order to compare the GDP per capita of different

countries in a given year the basic figures are expressed in PPS, i.e. a common currency that eliminates the differences in price levels between countries

• These figures are intended for cross-country comparisons rather than for temporal analyses (in that case GDP at constant prices is needed) because, over time, the level of prices may change differently between countries

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• “The use of PPS series rather than the euro-based series tends to have a levelling effect, as those regions with very high GDP per inhabitant in euro terms also tend to have relatively high price levels (for example, the cost of living in central Paris or London is generally higher than the cost of living in rural areas of France or the United Kingdom).”

• “Calculations for GDP per inhabitant that are based on PPS series instead of euro series can result in considerable differences when ranking regions. For example, in 2009, the Swedish region of Ostra Mellansverige was recorded as having a GDP per inhabitant of EUR 26.600, ranking above the Italian region of Marche, with EUR 25.600. However, in PPS terms, Marche, at 24.600 PPS per inhabitant, was above of Ostra Mellansverige, at 23.800 PPS.”

Eurostat Regional Yearbook 2012 (page 28)

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Decomposition of per capita GDP

Population

Employment*

Employment

GPD

Population

GPD

Population

PopulationAge Working *

PopulationAge Working

Employment*

Employment

GPD

Labour Productivity (per person employed)* Employment Rate*Working age population share

Working Age Population: 15-64 (International standard and Eurostat definition) (Europe 2020: 20-64)

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Population

PopulationAge Working *

PopulationAge Working

Employment

*Employment

Worked Hours Total*

Worked Hours Total

GPD

*

Decomposition of per capita GDP

Labour Productivity (per hour worked)*Hours per worker*Employment Rate*Working age population share

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2012 (OECD data)GDP per head of population,

USD

GDP per hour worked, current

prices, USD

Hours worked per head of population

Austria 43848 53.7 817Belgium 40068 61.8 648

Czech Republic 26706 31.0 862Denmark 42176 59.5 708Estonia 23625 27.8 850Finland 38282 49.0 782France 36249 59.5 609

Germany 41231 58.3 708Greece 25309 34.5 734Hungary 22011 28.3 779Ireland 43579 71.2 612

Italy 33117 46.7 709Netherlands 43146 60.2 717

Poland 22167 28.1 790Portugal 25275 34.0 744

Slovak Republic 25323 34.7 730Slovenia 27493 39.2 702

Spain 32081 50.0 642Sweden 43176 54.7 789

United Kingdom 37446 48.5 772United States 51689 64.1 806

Euro area 36205 52.9 684

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GDP at constant prices• The calculation of the annual growth rate of GDP

volume is intended to allow comparisons of the dynamics of economic development both over time and between economies of different sizes

• For measuring the growth rate of GDP in terms of volumes, the GDP at current prices are valued in the prices of the previous year; then, the computed volume changes are imposed on the level of a reference year; this is called a chain-linked series

• Accordingly, price movements will not inflate the growth rate

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GDP growth rates• Annual rate of change:

(GDPt1-GDPt0)/GDPt0 =%∆GDP which can also be expressed as difference of natural logarithms

∆lnGDP= lnGDPt1- lnGDPt0

• The difference between two annual observations of the natural logarithm of a variable [ln(zt1) - ln(zt0)] corresponds, with a minimal margin of error, to the percentage rate of change of the same variable over the same tame interval: [ln(zt1) - ln(zt0)] (zt1-zt0)/zt0

Percentage rate of change and log difference

• Given a variable z, we take the natural log of it ln(z) and, then, differentiate (compute the first derivative)

• dln(z)/dz= 1/z• Thus, the differential (or infinitesimal variation) of the

natural log of a variable is equal to its percentage infinitesimal variation:

• dln(z)=dz/z • Considering time variations and assuming ln(z)

dln(z), i.e. relative small variations of natural logs, we can write

ln(z) z/z, which is precisely (zt1-zt0)/zt0 11

Decomposition of growth rates

• If z = x*y, (e.g. GDP per capita= GDP per employee times employees over population)

• dln(z)= dln(x*y)= dln(x)+dln(y)  

• dz/z=dx/x + dy/y z/z x/x + y/y  (zt1-zt0)/zt0 [(xt1-xt0)/xt0]+ [(yt1-yt0)/zt0]

• %∆(GDP/Population) = %∆(GDP/Employment) + %∆(Empl/Pop) or

• ∆ln(GDP/Population) = ∆ln(GDP/Employment) + ∆ln(Empl/Pop)

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Annual average rate of changeAnnual rate of change in a given period: more informative than the total variation between the initial and the final year – Mean of the annual rates of changes (or mean of

the annual log differences)

– Compound annual growth rate: requires only data for the initial (t1) and final year (tn):

[(GDPtn/GDPt1)1/(n-1) - 1]*100

– Linear regression of the natural log of GDP at constant prices on time (uses all the annual data; it is suitable when the period of time considered is sufficiently long)

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  1996 1997 1998 1999 2000

Average 1995-2000

EU (15 countries)

GDP 1.7 2.7 2.9 3.0 3.8 2.8

Employment 0.6 1.1 1.8 1.9 2.2 1.5

Labour productivity 1.1 1.6 1.1 1.1 1.6 1.3

GDP, employment and productivity: percentage change on previous year

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R&D intensity (total expenditures on GDP)

Annual average growth (compound)

  2012 2020 target 2012-2020Finland 3.55 4.00 1.50Germany 2.98 3.00 0.08Austria 2.84 3.76 3.57Slovenia 2.80 3.00 0.87France 2.29 3.00 3.43EU28 2.07 3.00 4.75Spain 1.30 2.00 5.53Hungary 1.30 1.80 4.15Italy 1.27 1.53 2.36Poland 0.90 1.70 8.27Romania 0.49 2.00 19.22

Compound annual growth rate= [(Rdint20/Rdint12)1/8 -1]x100