Thomas
Piketty,
Academic
year 2010-2011
Course Notes:
Measuring factor shares &
wealth-income ratios:
Illustration using French national
accounts
1. Basic Concepts
National income Y = GDP –
capital depreciation + net foreign factor income
(Net domestic product = Gross
domestic product – capital depreciation)
Decomposition by institutional
production sector:
National income Y = Yc + Yg
+ Yh + Yse (+ net foreign factor income)
Yc =
net income of corporate sector = YKc+YLc
(= corporate profits + corporate wages)
(financial
+ non-financial corporations) (sociétés
financières et non-financières)
Yg =
net income of govt sector YLg (= govt
sector wages) (=100% labor income)
(public
administration) (administrations publiques)
Yh = net
income of housing sector Yh (=YKh (=rental income) (=100% capital income)
(real & imputed
rental income) (excédent d’exploitation des ménages)
Yse =
net income of self-employment sector Yse =
YKse+YLse (=somewhat arbitrary)
(revenu mixte
des ménages)
Have
a look at raw tables from French National Accounts & check that you know
how to compute factor shares and wealth-income ratios:
[Tableau économique d'ensemble, TEE, France 1949-2009 (in excel format)]
[Tableau économique d'ensemble, TEE, France 2007 (in excel
format)] [(in pdf format)]
Note 1 : Detailed tables from French National accounts are
available on www.insee.fr.
International national accounts data is available on Eurostat
or Ocde web sites. The most detailed data, however,
is often solely available on each country’s national statistical institute web
site. E.g. for the U.S., look at Dept of Commerce web site for income accounts,
and at Federal Reserve web site for wealth/flow of funds accounts. For official
concepts and definitions used in national accounts, see ESA
1995 guidelines.
Note
2 : For detailed historical series on factor shares & wealth-income
ratios in
2. Sample
computations for year 2007
2.1. GDP vs National income
France
2007: GDP = 1 892.2 billions €
By definition, GDP = Gross Domestic Product = gross
value-added (PIB = Produit
intérieur brut =
valeur ajoutée
brute)
[more precisely, GDP = sum of gross value-added from
the various sectors (corporate sector, public sector, household sector) +
product taxes (VAT) ]
Capital depreciation (Consommation de capital fixe) = 252.2
billions € ( = typically 10-15% of GDP)
NDP = Net Domestic Product = GDP – Capital
depreciation (PIN = Produit
intérieur net = PIB – CCF) = 1 892.2 – 252.2 =
1 640.1 billions €
= net
value-added (valeur
ajoutée nette)
National income = Net National Product (NNP) = Net
Domestic Product + Net Foreign Income
France 2007:
Net foreign capital income = 161.8 – 164.4 = -2.6
billions €
Net foreign labor income =
9.6 – 1.4 = 8.2 billions €
Net foreign production taxes = -4.9 + 9.2 = 4.3
billions €
Net foreign income = -2.6 + 8.2 + 4.3 = 9.9 billions
France
2007: National income = 1640.1 + 9.9 = 1650.0 billions €
2.2. Capital
and labor shares α and 1-α in corporate
value-added (non-financial + financial corporations)
Corporate gross value-added = Wage bill (Rémunération des salariés)
+ Gross profits (Excédent
brut d’exploitation) + Product taxes
I.e. 1 035.1 (957.1 + 78.1) = 672.1 (622.8 + 49.3) + 322.5 (299.0 + 23.5)
+ 40.6 (51.6 + 5.7 -16.4 -0.4)
>>> Labor share =
672.1/(672.1+322.5) = 68%
Capital
share = 322.5/(672.1+322.5) = 32%
Corporate net value-added = Wage bill (Rémunération des salariés)
+ Net profits (Excédent
brut d’exploitation - CCF) + Product taxes
I.e. 878.0 (810.9 + 67.1) = 672.1 (622.8 + 49.3) + 165.3 (152.8 + 12.5)
+ 40.6 (51.6 + 5.7 -16.4 -0.4)
>>> Labor share =
672.1/(672.1+165.3) = 80%
Capital
share = 322.5/(672.1+165.3) = 20%
2.2. Capital
and labor shares α and 1-α in total
value-added (national economy)
Total gross value-added = Wage bill (Rémunération des salariés)
+ Gross profits (Excédent
brut d’exploitation + Revenu
mixte brut) + Product taxes
I.e. 1 892.2
= 976.3 + 661.5 (537.7 + 123.9) + 254.4 (289.7 - 35.3)
>>> Labor share =
976.3/(976.3+661.5) = 60%
Capital
share = 661.5/(976.3+661.5) = 40%
Total net value-added
= Wage bill (Rémunération
des salariés) + Net profits (Excédent brut d’exploitation
+ Revenu mixte brut - CCF)
+ Product taxes
I.e. 1 640.1
= 976.3 + 409.4 (302.0 + 107.4) + 254.4 (289.7 - 35.3)
>>>
Labor share = 976.3/(976.3+409.4) = 70% = 1-α
Capital share = 409.4/(976.3+409.4) =
30% = α
Be careful: to
simplify computations, here self-employment income (revenue mixte
net) was entirely attributed to the capital share; there are basically three
methods to compute the true capital share of self-employment income: (1) apply
the same capital share as in the corporate sector; (2) apply the same average labor income as in the corporate sector (ideally
controlling for skills: wage equation in employment survey); (3) apply the same
rate of return to capital stock as in the corporate sector; usually the three
methods deliver comparable results; in any case, this would result into a
lowering of the capital share α (from
about 30% to about 25%), and therefore of the average return rate computed
below (from about 4.8% to about 4%)
2.3. Capital/output ratio β
(national economy)
Net wealth (Valeur nette
du patrimoine) = 12 512.3 billions €
Net wealth / GDP = 12 512.3/1 892.2 = 6.6
Net wealth / NDP = 12 512.3/1 640.1 = 7.6
Net wealth excluding corporations = 12 512.3 –
713.4 – 1 558.5 = 10 240.4 billions €
(corporations have positive net wealth only to the
extent that Tobin’s q < 1)
Net wealth (exc. corp.)/National income =
10240.4/1650.0 = 6.2 = β
>>>
capital
share α = 30%
capital/output
ratio β = 6.2
average
capital return r = α/β = 4.8%
(pre-tax computations)
2.4. Capital/output ratio β
(household sector)
Net household wealth (Valeur nette du patrimoine) =
9 389.9 billions €
Gross household income (Solde des revenus primaires bruts) =
1 399.6 billions €
(1 399.6 = 984.5 + 290.9 (167.0+123.9) + 124.3
(161.6-27.3) >>> labor share = 984.5/1399.6
= 70%, capital share = 30%)
Net household income (Solde des revenus primaires nets) = 1 352.0 billions €
(1 352.0 = 984.5 + 243.2 (135.9+107.4) + 124.3
(161.6-27.3) >>> labor share = 984.5/1352.0
= 73%, capital share = 27%)
Total adult population 2007 (20-year-old and over) =
about 45 millions
Average wealth
per adult = 9 389.9 billions / 45 millions = 209 000 €
Average
income per adult = 1 352.2 billions / 45 millions = 30 000 €
Wealth/income
ratio = 9 389.9/1 352.0 = 209 000/30 000 = 6.9