Thomas Piketty, Paris School of Economics

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)

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:

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 France, see Piketty 2010 & Data Appendix Part 1  Data Appendix Part 2 (see Appendix A)

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

>>> France 2007 :

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%)

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