Frank C

owell:

Frank C

owell: E

conomics

Econom

ics Public E

conomics

Public E

conomics

MSc Public Economics 2008/9

http://darp.lse.ac.uk/ec426

Wealth TaxationWealth Taxation

16 February 2009

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Some preliminary questions

Why wealth taxation?Why wealth taxation? Revenue raising?Revenue raising? Efficiency?Efficiency? Equity?Equity?

What are wealth taxes?What are wealth taxes? taxing personal wealth…taxing personal wealth… ……and the transmission of wealthand the transmission of wealth

What is wealth?What is wealth? compositioncomposition distributiondistribution

What is the appropriate way of modelling impact of What is the appropriate way of modelling impact of wealth tax?wealth tax?

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Overview...Wealth taxation

Wealth distribution

Wealth trends

Long-run models

Wealth Distribution and Taxation

Why wealth taxation? Types of tax

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Why wealth taxation?

Consider the motives behind the introduction of any form of Consider the motives behind the introduction of any form of taxtax

Revenue raisingRevenue raising Funding public goods?Funding public goods?

Efficiency considerationsEfficiency considerations Allocative efficiencyAllocative efficiency Minimisation of distortionMinimisation of distortion Administrative simplicityAdministrative simplicity

Equity considerationsEquity considerations Short-run inequality Short-run inequality Long-run inequalityLong-run inequality

How do these considerations apply here?How do these considerations apply here?

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Estate, inheritance and gift taxes international comparison

Taxes as percent of total tax revenueTaxes as percent of total tax revenue Source Source Cremer and Cremer and PestieauPestieau (2003) (2003) from OECD Revenue Statistics (2000) from OECD Revenue Statistics (2000)

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Efficiency and equity considerations

Efficiency case for or against wealth taxes is unclearEfficiency case for or against wealth taxes is unclear ((Cremer and Cremer and PestieauPestieau 2003 2003))

Equity case for wealth taxes is more promisingEquity case for wealth taxes is more promising But needs careful empirical analysisBut needs careful empirical analysis Who owns what?Who owns what?

Direct impact of wealth taxes on redistribution likely to be smallDirect impact of wealth taxes on redistribution likely to be small small revenue raised…small revenue raised… ……less than 1% of receipts?less than 1% of receipts? not much taken from rich to give to poornot much taken from rich to give to poor

But what of long run? But what of long run? taxes may influence savings behaviour and bequest behaviourtaxes may influence savings behaviour and bequest behaviour these influence wealth accumulation and inequalitythese influence wealth accumulation and inequality

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Annual wealth tax: examples

France. France. solidarity tax on wealth solidarity tax on wealth

Sweden. Sweden. 2003 out of a 1,314 billion kronor "general government" revenue, 2003 out of a 1,314 billion kronor "general government" revenue,

3.818 billion kronor of "wealth tax" was collected. 3.818 billion kronor of "wealth tax" was collected. tax rate is 1.5% the net worth exceeding 1,500,000 kronor (single tax rate is 1.5% the net worth exceeding 1,500,000 kronor (single

person, estate of deceased personperson, estate of deceased person

Switzerland. Switzerland. Progressive wealth tax with a maximum of around 1% Progressive wealth tax with a maximum of around 1% exact amount varies between cantons.exact amount varies between cantons.

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Inheritance tax: examples Inheritance tax: Inheritance tax:

The Republic of Ireland (where it is a tax on beneficiaries). The Republic of Ireland (where it is a tax on beneficiaries). The United Kingdom: see Inheritance tax (United Kingdom). The United Kingdom: see Inheritance tax (United Kingdom). Some states of the US: Nebraska, New Jersey, Pennsylvania ,Tennessee Some states of the US: Nebraska, New Jersey, Pennsylvania ,Tennessee

Estate tax: Estate tax: The United States:The United States: Some states of the US: Missouri, Virginia, Washington ,West Virginia, Some states of the US: Missouri, Virginia, Washington ,West Virginia,

Wisconsin, WyomingWisconsin, Wyoming Estate duty (death duty)Estate duty (death duty)

Hong Kong. Hong Kong. Bermuda Bermuda

Without inheritance taxes Without inheritance taxes AustraliaAustralia British Virgin IslandsBritish Virgin Islands Vanuatu Vanuatu Some states of the US:: New Mexico, South Dakota , South Carolina, Utah Some states of the US:: New Mexico, South Dakota , South Carolina, Utah

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Overview...Wealth taxation

Wealth distribution

Wealth trends

Long-run models

Wealth Distribution and Taxation

Definitions, composition and inequality

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Wealth: the facts

Wealth in UKWealth in UK conceptsconcepts compositioncomposition age profileage profile inequality – comparison with incomeinequality – comparison with income shape of distributionshape of distribution

UK in contextUK in context comparisons with other UK datacomparisons with other UK data ……with other countrieswith other countries

How change over time?How change over time? next sectionnext section

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Wealth concepts in the UK British Household Panel SurveyBritish Household Panel Survey

fairly comprehensivefairly comprehensive suffers from standard participation / attrition problemssuffers from standard participation / attrition problems

Wealth and assets surveyWealth and assets survey still at experimental stagestill at experimental stage

HMRC Identified personal wealthHMRC Identified personal wealth emerges directly from the estate multiplier methodemerges directly from the estate multiplier method it is clearly biased (missing wealth, missing persons)it is clearly biased (missing wealth, missing persons) differs from balance-sheet concept of wealthdiffers from balance-sheet concept of wealth

HMRC Series C: marketable wealth onlyHMRC Series C: marketable wealth only valuation issues addressedvaluation issues addressed excluded population correctedexcluded population corrected

HMRC Series D: includes a valuation of pension rightsHMRC Series D: includes a valuation of pension rights unfortunately no longer regularly publishedunfortunately no longer regularly published

HMRC Series E: includes a valuation of state pension rightsHMRC Series E: includes a valuation of state pension rights unfortunately no longer regularly publishedunfortunately no longer regularly published

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HMRC “Identified wealth” 1999n

et c

apit

al v

alu

e of

es

tate

Sec

uri

ties

Cas

h

Loa

ns,

mor

tgag

es

etc

Pol

icie

s of

in

sura

nce

Res

iden

tial

b

uild

ings

Oth

er B

uild

ings

an

d L

and

Oth

er a

sset

s

Net

as

% g

ross

Mor

tgag

es

Oth

er d

ebts

0 - £50,000 5.6% 17.6% 5.5% 22.9% 39.8% 0.5% 8.2% 70.8% 1.7% 27.5%

£50000 - £100,000 5.2% 15.1% 4.6% 19.2% 49.8% 0.1% 5.9% 86.2% 1.5% 12.3%

£100000 - £150,000 6.2% 16.4% 4.0% 20.0% 46.9% 0.2% 6.3% 90.3% 1.0% 8.7%

£150000 - £200,000 10.5% 14.9% 4.9% 18.4% 41.8% 0.6% 8.8% 91.4% 2.1% 6.5%

£200000 - £500,000 16.2% 15.2% 1.7% 16.7% 37.8% 2.8% 9.6% 94.2% 2.4% 3.4%

£500000 - £1000,000 28.2% 13.9% 1.9% 11.3% 26.2% 5.9% 12.6% 96.4% 1.2% 2.3%

£1,000,000 and over 36.0% 12.5% 1.5% 5.0% 18.1% 3.9% 23.1% 96.2% 0.5% 3.2%

Residential buildings about 40% of net worth, except for £500,000+

Debts concentrated amongst those with less than £100,000

Securities concentrated amongst the richSource: HMRC statistics table 13.2Source: HMRC statistics table 13.2

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HMRC “Identified wealth” 2003

Residential buildings about 50% of net worth, except for £500,000+

Debts concentrated amongst those with less than £100,000

Securities concentrated amongst the rich

net

capi

tal v

alue

of

esta

te

Secu

riti

es

Cas

h

Loa

ns, m

ortg

ages

et

c

Pol

icie

s of

in

sura

nce

Res

iden

tial

bu

ildin

gs

Oth

er B

uild

ings

an

d L

and

Oth

er a

sset

s

Net

as

% g

ross

Mor

tgag

es

Oth

er d

ebts

0 - £50,000 4.6% 22.7% 5.6% 8.9% 47.6% 0.1% 10.5% 61.0% 5.7% 33.4%

£50000 - £100,000 4.5% 16.2% 3.0% 14.6% 55.0% 0.0% 6.8% 83.3% 4.1% 12.6%

£100000 - £150,000 3.9% 14.0% 2.4% 18.6% 55.2% 0.1% 5.8% 84.4% 4.3% 11.3%

£150000 - £200,000 4.5% 14.4% 0.7% 12.1% 59.4% 1.6% 7.5% 89.0% 4.9% 6.1%

£200000 - £500,000 8.5% 12.8% 0.9% 12.6% 54.7% 1.5% 9.0% 89.7% 6.5% 3.8%

£500000 - £1000,000 17.6% 11.2% 1.6% 7.6% 42.5% 5.3% 14.1% 93.8% 3.9% 2.3%

£1,000,000 and over 23.8% 10.8% 1.9% 5.0% 28.1% 8.1% 22.4% 94.2% 2.9% 3.0%

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Proportion of wealth in residential buildings. UK 1999

0%

10%

20%

30%

40%

50%

60%age 18-44

age 45-64

aged 65 and over

All ages

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Proportion of wealth in residential buildings. UK 2003

0%

10%

20%

30%

40%

50%

60%

70%

0 - £50,000 £50,000 - £100,000 - £150,000 - £200,000 - £500,000 - £1,000,000 -

age 18-44

age 45-64

aged 65 and over

All ages

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Proportion of wealth in securities. UK 1999

0%

10%

20%

30%

40%

50%

60%age 18-44

age 45-64

aged 65 and over

All ages

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Proportion of wealth in securities. UK 2003

0%

5%

10%

15%

20%

25%

30%

35%age 18-44

age 45-64

aged 65 and over

All ages

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Wealth distribution by age. UK 1999

Quantile points of top...

£0£100,000

£200,000£300,000

£400,000£500,000£600,000

£700,000£800,000

£900,000£1,000,000

age 18-44 age 45-64 aged 65 and over

40%30%20%10%5%1%

Quantiles fan out and stay fanned out

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Wealth distribution by age. UK 2003

Quantile points of top...

£0

£200,000

£400,000

£600,000

£800,000

£1,000,000

£1,200,000

age 18-44 age 45-64 aged 65 and over

40%30%20%10%5%1%

Quantiles fan out, but not so much

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Identified Wealth UK 1999

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Identified Wealth UK 2003

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Income and Wealth: Lorenz

0

10

20

30

40

50

60

70

80

90

100

0 10 20 30 40 50 60 70 80 90 100

Proportion of population

Pro

po

rtio

n o

f In

co

me

IdentifiedWealth 1999

Income BeforeTax 1998/9

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0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Proportion of population

Pro

por

tion

of

wea

lth

Identified Wealth Gini=0.58

Series C Gini=0.67

Series D Gini=0.59

Series E Gini=0.49

UK wealth, 1994: Lorenz

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UK: BHPS (LWS) and HMRC

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

0.00 0.20 0.40 0.60 0.80 1.00

UK BHPS 2000 NW1

UK HMRC 2000 Series C

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Household portfolio composition – LWS

Wealth components Canada Finland Germany Italy Sweden

United

Kingdom

US

PSID

US

SCF

1999 1998 2002 2002 2002 2000 2001 2001

Non-financial assets 78 84 87 85 72 83 67 62

Principal residence 64 64 64 68 61 74 52 45

Real estates 13 20 23 17 11 9 14 17

Financial assets 22 16 13 15 28 17 33 38

Deposit accounts 9 10 n.a. 8 11 9 10 10

Bonds 1 0 n.a. 3 2 n.a. n.a. 4

Stocks 7 6 n.a. 1 6 n.a. 23 15

Mutual funds 5 1 n.a. 3 9 n.a. n.a. 9

Total assets 100 100 100 100 100 100 100 100

Total debt 26 16 18 4 35 21 22 21

Home secured 22 11 15 2 n.a. 18 n.a. 18

Total net worth 74 84 82 96 65 79 78 79

Source: Sierminska et al (2006); see also Source: Sierminska et al (2006); see also Davies et al (2006) Davies et al (2006)

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LWS series ordered by Ginic of v Gini

ITALY 2004 NW1 1.387 0.565

ITALY 2002 NW1 1.477 0.573

FINLAND 1998 NW1 1.453 0.588

CYPRUS 2002 NW1 3.993 0.635

FINLAND 1994 NW1 1.419 0.648

UK BHPS 2000 NW1 1.705 0.689

CANADA 1999 NW1 2.396 0.755

GERMANY 2002 NW1 2.550 0.758

SWEDEN 2002 NW1 5.969 0.849

US SCF 2001 NW1 5.062 0.911

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Measurement tool for wealth distributions Choose an arbitrary base level wealth Choose an arbitrary base level wealth bb Calculate a conditional mean and normalise:Calculate a conditional mean and normalise:

““average” average” E E ((x | xx | x bb)) “ “base”base” b b

Advantages:Advantages: easy interpretationeasy interpretation focuses on upper tailfocuses on upper tail

Disadvantage: Disadvantage: depends not only on distribution but also on the arbitrary depends not only on distribution but also on the arbitrary bb

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Functional form for wealth distribution

0 1 2 3 4 5

f(x)

= 1.5

= 2.0

The Pareto Distribution

FF((xx) = 1 ) = 1 −− [ [ xx / / xx ] ]

ff((xx))xxxx captures “weight” of the tailcaptures “weight” of the tail xx “locates” the distribution “locates” the distribution average average = = base base −− 1 1

Higher (less inequality)

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-7

-6

-5

-4

-3

-2

-1

08 9 10 11 12 13 14 15

log Wealth

log(

1−F

)

Pareto diagram: application

UK: Identified Personal Wealth 2003Inland Revenue Statistics 2006 Table 13.1

log (1−F) = −1.7618 log W + 19.761

Plot log wealth against log( 1 – F)

Data points

Top 7 points

Fit straight line

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Wealth distribution: Summary Patchy information: internally and internationally Patchy information: internally and internationally Observable part conforms to a standard patternObservable part conforms to a standard pattern

Pareto distributionPareto distribution A good fitA good fit A convenient modelA convenient model

Wealth much more unequal than incomeWealth much more unequal than income A rational explanation for this?A rational explanation for this? Important policy consequences?Important policy consequences?

Distinctive patterns of wealth holdingDistinctive patterns of wealth holding By age By age By position in the distributionBy position in the distribution

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Overview...Wealth taxation

Wealth distribution

Wealth trends

Long-run models

Wealth Distribution and Taxation

Rising inequality or stability?

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Trends in wealth inequality Useful to look at Useful to look at trendstrends in distribution in distribution

what effect of wealth taxation in the past?what effect of wealth taxation in the past? equalisation?equalisation? is there a trend toward stability…?is there a trend toward stability…? …….or divergence?.or divergence?

For historical and recent wealth trends in USFor historical and recent wealth trends in US Kopczuk and Saez, (2004)Kopczuk and Saez, (2004) Substantial time coverage: Substantial time coverage: From early 20From early 20thth century century

For historical wealth trends in UKFor historical wealth trends in UK Atkinson et al. (1989)Atkinson et al. (1989) Similar time coverage…Similar time coverage… But incomplete seriesBut incomplete series

Recent picture from Inland Revenue dataRecent picture from Inland Revenue data

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Distribution of wealth US 1916-2000

Wealth owned by various groups

05

1015202530354045

1915

1925

1935

1945

1955

1965

1975

1985

1995

2005

perc

ent

top 2%

top 1%

top 0.5%

top 0.25%

top 0.1%

top 0.05%

top 0.01%

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Distribution of marketable wealth UK 1976-2002 (Series C)

Wealth owned by various groups

0102030405060708090

100

1976

1978

1980

1982

1984

1986

1988

1990

1992

1994

1996

1998

2000

2002

perc

ent

top 50%

top 25%

top 10%

top 5%

top 2%

top 1%

Gini Coefficient

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Pareto’s : USA and UK

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

3

1900

1910

1920

1930

1940

1950

1960

1970

1980

1990

2000

US income

UK income

US wealth

England & Wales wealth

UK wealth (1)

UK wealth (2)

• Sources: see Cowell (2009) Chapter 4 Sources: see Cowell (2009) Chapter 4

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Wealth trends

US and UK: Substantial wealth inequalityUS and UK: Substantial wealth inequality UK Inequality falls in early 20UK Inequality falls in early 20thth century century

roughly from first world warroughly from first world war substantive rises in income tax and estate dutysubstantive rises in income tax and estate duty

Reductions in inequality continue through mid-centuryReductions in inequality continue through mid-century US inequality falls from time of great depressionUS inequality falls from time of great depression

Largely attributable to stock pricesLargely attributable to stock prices Large concentration of corporate stock in wealth of very richLarge concentration of corporate stock in wealth of very rich

But US inequality also carried on falling through to 70sBut US inequality also carried on falling through to 70s This despite recovery in stock pricesThis despite recovery in stock prices Antitrust legislation?Antitrust legislation? Development of estate taxDevelopment of estate tax

Distribution remarkably stable over time in recent yearsDistribution remarkably stable over time in recent years appropriate to use an equilibrium-distribution approach?appropriate to use an equilibrium-distribution approach?

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Overview...Wealth taxation

Wealth distribution

Wealth trends

Long-run models

Wealth Distribution and Taxation

Fairy tales?

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A way forward Direct impact of wealth taxes on redistribution will be smallDirect impact of wealth taxes on redistribution will be small But wealth taxes may work by influencing long-run But wealth taxes may work by influencing long-run

distribution of resources.distribution of resources. requires careful modellingrequires careful modelling small taxes can have powerful effects on the equilibrium small taxes can have powerful effects on the equilibrium ((KaplowKaplow

2000) 2000)

Develop a story of what happens to wealth distribution in the Develop a story of what happens to wealth distribution in the long run (long run (PikettyPiketty 2000 2000):):

Characterise each generation as a fixed time unitCharacterise each generation as a fixed time unit Set up intergenerational budget constraintSet up intergenerational budget constraint Model dynastic tastes or habitsModel dynastic tastes or habits Model exogenous resource flowModel exogenous resource flow Specify family formation mechanismSpecify family formation mechanism

Examine three illustrative modelsExamine three illustrative models can be used to illustrate role of tax in long-run distributioncan be used to illustrate role of tax in long-run distribution

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Outline of model (1)

Common practice to combine in a neoclassical modelCommon practice to combine in a neoclassical model ((Becker and Tomes 1979))

Preferences and behaviourPreferences and behaviour Cobb-Douglas preferences (simplified savings behaviour)Cobb-Douglas preferences (simplified savings behaviour) utility maximisation by parental generationutility maximisation by parental generation look one generation aheadlook one generation ahead

Simplified family characteristicsSimplified family characteristics exogenous attributesexogenous attributes no “marriage story”no “marriage story” no “fertility story”no “fertility story”

Resources and marketsResources and markets ““perfect” marketsperfect” markets exogenous (labour) earnings and initial endowmentsexogenous (labour) earnings and initial endowments

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CCn n + + BBnn+1+1 /[1+ /[1+rrnn] ] WWnn

½½k Wk Wnn+1+1 = = ss[1+[1+rrnn] ] WWnn ++ s E s Enn+1+1

WWnn ++ E Enn+1+1 /[1+ /[1+rrnn] ]

WWnn+1+1 = = [1+[1+rrnn] ] WWnn ++ E Enn+1+1

½½k Wk Wnn+1+1 = = BBnn+1 +1

Ratio of kids to parentsRatio of kids to parents

Illustrative model (1)

Earnings of generation n+1Earnings of generation n+1

Generation n’s consumptionGeneration n’s consumption

Planned bequestPlanned bequest Total wealth of generation nTotal wealth of generation n

Generational budget constraint Wealth accumulation equation Prospective resources Proportionate savings rate s Equation for wealth accumulation

Stochastic “earnings” will give a simple Markov chain.Stochastic “earnings” will give a simple Markov chain. given sensible parameter values will get convergence (regression to mean)given sensible parameter values will get convergence (regression to mean) Initial wealth inequalities will be damped awayInitial wealth inequalities will be damped away

In the long run wealth inequality is going to be determined just by In the long run wealth inequality is going to be determined just by EE..

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Simulation approach It is common to put some variant of is this into a It is common to put some variant of is this into a

simulation model.simulation model. But is it based on optimisation – and of what sortBut is it based on optimisation – and of what sort??

Type of utility function s crucialType of utility function s crucial What motive for bequests…?What motive for bequests…? ……see e.g. see e.g. GokhaleGokhale et al. (2001) et al. (2001) who come to strong conclusions who come to strong conclusions

based solely on “accidental bequests”.based solely on “accidental bequests”. What characteristics of the simulation model?What characteristics of the simulation model?

representative agentrepresentative agent size and length of the runsize and length of the run criteria for evaluationcriteria for evaluation

Type of solution?Type of solution? convergence to equilibrium?convergence to equilibrium? an equilibrium distribution?an equilibrium distribution?

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Illustrative model (2)

An intergenerational perspective An intergenerational perspective based on based on ChampernowneChampernowne-Cowell (1998)-Cowell (1998) common elements with recent literaturecommon elements with recent literature

Use a simplified model focuses on the role of consumptionUse a simplified model focuses on the role of consumption naïve savings behaviournaïve savings behaviour but family features are absentbut family features are absent

A model of single person-dynasties.A model of single person-dynasties. each individual ( “Mutt”) leaves all his terminal wealth to just one each individual ( “Mutt”) leaves all his terminal wealth to just one

descendant.descendant. Mutt inherits Mutt inherits TT years after attaining adulthood and dies years after attaining adulthood and dies TT years after that. years after that.

Wealth left in excess of Wealth left in excess of WW**attracts inheritance tax at rate attracts inheritance tax at rate .. During the earnings span Mutts get the same earnings, During the earnings span Mutts get the same earnings, EE**.. Mutts consume:Mutts consume:

CC** if they have positive wealth if they have positive wealth otherwise otherwise EE** . .

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A Mutt's Life

age

earn

ings

0-T T

E*

t

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Generations of Mutts

0-T Tn =0

0-T Tn =1

0-T Tn =2

0-T Tn =3

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Consumption in the model

income

con

sum

pti

on

y(t)

c(t)

C*

E*

c(t)=C* if W(t)>0 =E* if W(t)=0

E*

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Bequest and inheritance

bequest

inh

erit

ance

Bn

W(0)

W*

W*

W(0) =min {Bn , [1Bn + W* }

1

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Wealth over the Lifetime Given savings rule and inherited wealth Given savings rule and inherited wealth WW(0) we get(0) we get ^ ^ ^ ^ WW((tt) = max { ) = max { WW(0) e(0) ertrt BB [e [ertrt 1], 0}, 1], 0}, B B := [:= [CC* * EE*]/*]/rr ^̂ So wealth rises/declines according as So wealth rises/declines according as WW(0) (0) BB Evaluating at end of life (Evaluating at end of life (t = Tt = T) and substituting for ) and substituting for WW(0):(0): ^ ^ BBnn+1+1 = max { = max { min {Bn ,[1Bn + W* } e erTrT BB [e [erTrT 1], 0}1], 0}

Change in bequest Change in bequest BBnn+1+1 = = BBnn+1+1 − − BBnn as a function of as a function of BBnn Get three possible regimesGet three possible regimes

1.1. where where BBn n > > W*

2.2. where where W((tt) = 0) = 03.3. intermediate between 1 and 2intermediate between 1 and 2

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Bequest Dynamics

Bn falling Bn fallingBn rising

Bn10050 150 200 250 300

Bn

StableStableStableStable

UnstableUnstable

oW*B̂

-40

-30

-20

-10

10

20

30

40

0

The phase diagram Paths to riches Paths to ruin Find equilibria (B = 0) Now cut tax…

Plot B against B

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Wealth distribution amongst the wealthy

0

0.0025

0.005

0.0075

0.01

0.0125

0.015

0.0175

0.02

0.0225

150 160 170 180 190 200 210 220

f(W)

W

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Wealth distribution. All Mutts

0

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0.005

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0 50 100 150 200 250

f(W)

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Illustrative model (3) Focus on family formation (Champernowne-Cowell 1998) Focus on family formation (Champernowne-Cowell 1998)

each generation is a discrete uniteach generation is a discrete unit pairs always consist of people with equal wealthpairs always consist of people with equal wealth no-one benefits from more than one bequestno-one benefits from more than one bequest bequest is divided equally amongst the bequest is divided equally amongst the kk kids ( kids (kk given) given)

Model applies to upper wealth levels Model applies to upper wealth levels above some specified wealth above some specified wealth level level WW**

For any For any W>WW>W**, the proportion of testators with , the proportion of testators with kk kids is kids is ppkk, , independent of independent of WW ppkk ≥ 0 ≥ 0 k k ppkk = 1 = 1 k k kpkpkk = 2 = 2 two examples:two examples:

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Equilibrium concept

Let Fn be the wealth distribution in generation n.

So Fn(W) is the proportion of the population in generation n with wealth W

Let Fn+1 be the wealth distribution in generation n+1

We have equilibrium if Fn = Fn+1 = F

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Work out equilibrium condition Take a person with wealth W in a family where the parents had k kids

if parental wealth was W' per head bequest must have been 2[1−]W' so each kid would get 2[1−]W'/k therefore W' = kW/ 2[1−]

Given that there are pk such families we get

Fn+1(W) = k ½k pk Fn(kW/ 2[1−])

Equilibrium requires

F(W) = k ½k pk F(kW/ 2[1−])

The only functional form that permits a solution for all values of W is Paretian.

F(W) = 1−AW

So the equilibrium condition is then:

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Tax and Equilibrium Wealth Distribution

case (i) case (ii) Narrow spread Wider spread of Family Size of Family Size (%) Gini Gini 2 1.22 0.410 - - 5 1.55 0.323 1.42 0.35210 2.11 0.237 1.90 0.26315 2.73 0.183 2.44 0.20520 3.43 0.146 3.07 0.16325 4.28 0.117 3.86 0.130

Higher tax produces lower long-run inequalityIf tax is too low – no long-run equilibrium Quite low tax rates produce values similar to actual economies.

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Equilibrium Distribution: Model 3

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

200 250 300 350 400 450 500 550 600 650 700 750 800

Wealth

freq

uenc

y

=2.113 (Narrow family spread)

=1.9002 (Wide family spread)

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Summary

Dynastic model produces a bifurcationDynastic model produces a bifurcation Convergence to equilibrium distributionConvergence to equilibrium distribution Inequality within and between groups Inequality within and between groups Source of inequality lies in savings behaviourSource of inequality lies in savings behaviour

Role of uncertainty captured in savings behaviourRole of uncertainty captured in savings behaviour Family structure affects long-run equilibriumFamily structure affects long-run equilibrium

spread out families reduce effectiveness of taxation spread out families reduce effectiveness of taxation

Tweaking the models would modify this a littleTweaking the models would modify this a little Variation in income Variation in income Out-of-class marriageOut-of-class marriage ((Champernowne-Cowell 1998Champernowne-Cowell 1998))

Potentially major role for taxationPotentially major role for taxation

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References (1) Atkinson, A. B., Gordon, J. P. F. and Harrison, A. J. (1989)Atkinson, A. B., Gordon, J. P. F. and Harrison, A. J. (1989) “Trends in “Trends in

the shares of top wealth-holders in Britain 1923-1981,” the shares of top wealth-holders in Britain 1923-1981,” Oxford Bulletin Oxford Bulletin of Economics and Statisticsof Economics and Statistics, , 5151, 315-332., 315-332.

Becker, G. S. and Tomes, N. (1979) “An equilibrium theory of the Becker, G. S. and Tomes, N. (1979) “An equilibrium theory of the distribution of income and intergenerational mobilitydistribution of income and intergenerational mobility,” ,” Journal of Journal of Political EconomyPolitical Economy, , 8787, 1153-1189 , 1153-1189

Cowell, F.A. (2009) Cowell, F.A. (2009) Measuring InequalityMeasuring Inequality, Oxford University Press, Oxford University Press Cremer, H. and Cremer, H. and PestieauPestieau, P. (2003), P. (2003) “ “Wealth Transfer Taxation: A Wealth Transfer Taxation: A

Survey,” CESifo Working Paper No. 106Survey,” CESifo Working Paper No. 106 ChampernowneChampernowne, D. G. and Cowell, F. A. (1998), D. G. and Cowell, F. A. (1998) Economic Inequality Economic Inequality

and Income Distributionand Income Distribution, Cambridge University Press, Cambridge, , Cambridge University Press, Cambridge, Chapter 10.Chapter 10.

Davies, J.B., Davies, J.B., SandstromSandstrom, S., , S., ShorrocksShorrocks, A.F. and Wolff, E.N. (2006), A.F. and Wolff, E.N. (2006) “The World Distribution of Household Wealth,” WIDER“The World Distribution of Household Wealth,” WIDER

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References (2)

GokhaleGokhale, J. and , J. and KotlikoffKotlikoff, L. J. and , L. J. and SeftonSefton, J. and , J. and WealeWeale, M. (2001), M. (2001) “Simulating the Transmission of Wealth Inequality Via Bequests“Simulating the Transmission of Wealth Inequality Via Bequests,” ,” Journal Journal of Public Economicsof Public Economics, , 7979, 93-128, 93-128

Kaplow, L. (2000) Kaplow, L. (2000) “A framework for assessing estate and gift taxation,” “A framework for assessing estate and gift taxation,” NBER Working Paper 7775NBER Working Paper 7775

Kopczuk, W. and Saez, E. (2004) “Top Wealth Shares in the United States, Kopczuk, W. and Saez, E. (2004) “Top Wealth Shares in the United States, 1916-2000: Evidence from Estate Tax Returns,” NBER Working Paper 1916-2000: Evidence from Estate Tax Returns,” NBER Working Paper 1039910399

Piketty, T. (2000) “Theories of persistent inequalities,” in Atkinson, A. B. Piketty, T. (2000) “Theories of persistent inequalities,” in Atkinson, A. B. and Bourguignon, F. (eds) and Bourguignon, F. (eds) Handbook of Income DistributionHandbook of Income Distribution, North Holland, , North Holland, Amsterdam, pp 429-476Amsterdam, pp 429-476

Sierminska, E., Brandolini, A. and Smeeding, T. M. (2006) “Comparing Sierminska, E., Brandolini, A. and Smeeding, T. M. (2006) “Comparing Wealth Distribution Across Rich Countries: First Results from the Wealth Distribution Across Rich Countries: First Results from the Luxembourg Wealth Study, Luxembourg Wealth Study Working Paper 1Luxembourg Wealth Study, Luxembourg Wealth Study Working Paper 1