Lecture 5

On the taxation of capital

April 11, 2013

Plan of the lecture

1. Taxes on firms and capital

2. Neutrality and the corporation taxes

3. Taxation of individual savings in a risky environment

Sources of tax revenue: France, 1995-2005

150 Taxation trends in the European Union

FRANCE

1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005

A. Structure of revenues as % of GDP Indirect taxes 16.0 16.6 16.5 16.4 16.4 15.8 15.4 15.4 15.3 15.5 15.8 VAT 7.4 7.7 7.7 7.6 7.7 7.3 7.2 7.1 7.1 7.2 7.4 Excise duties and consumption taxes 2.8 2.8 2.7 2.7 2.7 2.6 2.5 2.6 2.5 2.3 2.4 Other taxes on products (incl. import duties) 1.7 1.7 1.7 1.7 1.7 1.7 1.6 1.7 1.7 1.8 1.8 Other taxes on production 4.2 4.4 4.4 4.4 4.3 4.2 4.1 4.1 4.1 4.2 4.3

Direct taxes 8.4 9.0 9.7 11.8 12.5 12.5 12.6 11.8 11.4 11.6 11.9 Personal income 5.3 5.5 5.8 8.0 8.2 8.4 8.2 7.9 7.9 7.8 8.0 Corporate income 1.8 2.0 2.3 2.3 2.7 2.8 3.1 2.5 2.1 2.4 2.4 Other 1.4 1.5 1.6 1.5 1.6 1.3 1.4 1.3 1.3 1.4 1.5 Social Contributions 18.6 18.6 18.1 16.1 16.3 16.1 16.1 16.2 16.3 16.2 16.4 Employers´ 11.4 11.3 11.3 11.1 11.3 11.1 11.0 11.0 11.1 11.0 11.1 Employees´ 5.8 5.8 5.4 3.9 4.0 4.0 4.0 4.0 4.1 4.0 4.1 Self- and non-employed 1.4 1.5 1.4 1.0 1.0 1.0 1.1 1.1 1.1 1.1 1.1

B. Structure according to level of government as % of GDPCentral Government 17.7 18.6 18.8 18.7 19.4 18.6 18.1 17.5 17.1 18.2 17.8State government n.a. n.a. n.a. n.a. n.a. n.a. n.a. n.a. n.a. n.a. n.a.Local Government 4.5 4.7 4.7 4.7 4.6 4.3 4.1 4.1 4.2 4.5 4.8Social Sec. Funds 20.0 20.1 20.2 20.3 20.6 21.0 21.3 21.2 21.3 20.3 21.2EC Institutions 0.8 0.7 0.7 0.6 0.6 0.6 0.6 0.5 0.3 0.2 0.3

C. Structure according to economic function as % of GDPConsumption 12.1 12.4 12.3 12.1 12.1 11.6 11.3 11.3 11.1 11.2 11.4

Labour 23.0 23.1 23.1 23.0 23.5 23.2 23.1 22.9 23.1 22.9 23.3 Employed 21.8 22.0 22.0 22.1 22.5 22.3 22.2 22.1 22.3 22.1 22.5 Paid by employers 12.5 12.4 12.5 12.2 12.4 12.1 12.1 12.1 12.2 12.2 12.3 Paid by employees 9.3 9.5 9.5 9.9 10.2 10.1 10.1 10.0 10.0 9.9 10.2 Non-employed 1.1 1.1 1.1 0.9 0.9 0.9 0.9 0.8 0.8 0.8 0.9

Capital 8.0 8.7 9.0 9.2 9.6 9.6 9.8 9.1 8.7 9.1 9.4 Capital and business income 3.8 4.2 4.3 4.5 4.9 5.1 5.3 4.7 4.3 4.5 4.7 Income of corporations 1.8 2.0 2.3 2.3 2.7 2.8 3.1 2.5 2.1 2.4 2.4 Income of households 0.4 0.5 0.5 0.8 0.8 0.9 0.8 0.8 0.8 0.8 0.8 Income of self-employed (incl. sc) 1.5 1.7 1.5 1.3 1.4 1.5 1.5 1.4 1.4 1.4 1.4 Stocks (w ealth) of capital 4.3 4.5 4.6 4.7 4.7 4.5 4.5 4.4 4.4 4.5 4.7 Less: amounts assessed but unlikely to be collected 0.3 0.3 0.2 0.3 0.2 0.3 0.3 0.2 0.1 0.1 0.1

TOTAL 42.7 43.9 44.1 44.0 44.9 44.1 43.8 43.1 42.8 43.1 44.0

Of w hich environmental taxes 2.8 2.9 2.7 2.7 2.8 2.5 2.4 2.5 2.4 2.4 2.4 Energy 2.0 2.0 2.0 2.0 2.0 1.8 1.7 1.8 1.7 1.7 1.6 Transport 0.6 0.7 0.6 0.6 0.7 0.6 0.5 0.6 0.6 0.6 0.6 Pollution/Resources 0.2 0.2 0.1 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

D. Implicit tax ratesConsumption 21.5 22.1 22.2 22.0 22.1 20.9 20.3 20.3 20.0 20.2 20.2Labour employed 41.2 41.5 41.8 42.3 42.6 42.1 41.7 41.2 41.5 41.4 42.1Capital 31.2 34.4 35.2 35.2 38.0 37.5 38.0 36.7 35.4 36.9 38.9 Capital and business income 14.6 16.6 16.9 17.0 19.2 20.0 20.7 19.1 17.6 18.5 19.4 Corporations 21.0 25.5 25.9 24.6 29.4 30.0 33.7 29.8 24.1 26.8 29.1 Households 9.9 10.9 10.5 11.0 11.6 12.3 11.7 11.5 11.7 11.3 11.6p.m.:Real GDP ( % annual grow th rate) 2.2 1.1 2.2 3.5 3.2 4.0 1.9 1.0 1.1 2.3 1.2Output gap (potential) -1.3 -2.0 -1.7 -0.3 0.8 2.4 1.9 0.9 -0.1 0.0 -0.81) See ANNEX B for classification of taxes and ANNEX C for explanatory notes. n.a.: not applicableSource: Commission Services

Sources of tax revenue: UK, 2011-2012 forecasts

Source of revenue £ billions Percent.Income tax 152.9 27.2NIC 100.7 17.9VAT 100.3 17.8VAT refunds to public bodies 15.0 2.7Other indirect taxes 66.1 11.7Capital taxes

Capital gains tax 3.4 0.6Inheritance tax 2.7 0.5Stamp duty on land 5.8 1.0Stamp duty on shares 3.3 0.6

Company taxesCorporation tax 48.1 8.6Petroleum 2.0 0.4Business rates 25.5 4.5Bank levy 1.9 0.3

Council tax 26.1 4.6Other taxes 8.7 1.6National accounts taxes 562.4 100.0

How to assess a real life tax system?

Mirrlees Review, Tax by Design. Available on the IFS web site.

Optimal taxation model, when feasible.

Three rules of thumb.

1. Neutrality: treat similar activities in a similar way. Debt and equityfinance; owner occupied house and other assets; but pension savingsvs. other savings, individual vs. household.

2. Simplicity : lack of simplicity and neutrality invites tax avoidance.Game of cat and mouse played between the revenue authority andthe tax payers.

3. Stability.

II Neutrality of corporate taxes

Why tax companies?

Companies provide a convenient contractual arrangement that allowsgroups of individuals to own assets, while benefiting from limited liability.

We should not be interested in the welfare of companies.

Impact of the taxes on shareholders, customers, workers, suppliers.

Two reasons for taxing companies: convenience, difficulty to have the taxauthority ‘see through’ and incorporate profits to the shareholders’incomes before computing taxation (however this puts progressivity injeopardy).

Principle of neutrality

The form and structure of the corporate income tax should be consistentwith the form and structure of the personal income tax, and with policychoices for the taxation of savings.

Frontiers:

1. Owner-managers of small companies should not be tempted todisguise their labour income as capital income of any kind.

2. International issues.

3. Avoid double taxation: popular perception that corporate taxes haveno incidence on workers, which is probably wrong; debt vs. equity.

Suggestions of reform: cash-flow taxes, allowance for corporate equity(ACE), comprehensive business income tax (CBIT).

III Taxation of savings

In practice, in France, complicated and non transparent taxation ofsavings: privileged treatment of owner occupied housing, deferredtaxation of savings in pension funds, multiple financial channels (lifeinsurance, livret A, etc...).

Up to now the theoretical analysis has taken place in a staticenvironment.

However taxing labor today and planning to tax labor in the futureaffects the time profile of labor supply and savings. Also risk on futureproductivity seems a relevant feature that should be taken into account.

Society should be interested in lifetime welfare, and not in current incomeor consumption.

Insurance and intertemporal smoothing: a practicalviewpoint

Bovenberg and Sorensen (2004), Bovenberg, Hansen, and Sorensen(2008): a substantial fraction of lifetime social contributions of thetypical tax payer (75% in Danemark in 2002) is redistributed toher/himself during the life.

A dynamic setup

Suppose that the benevolent tax authority has a welfare objective basedon the per period expected life time utilities of the participants in theeconomy:

max ET∑t=1

βtu(Xt , `t , αt)

St + Xt = (1 + ρt)St−1 + wt`t

S0 given.

(α, β, w) are preference and productivity shocks.The risk free rate of interest is denoted ρt .

An optimal tax and benefit system would most probably involve somemutualization of risks.

Towards a dynamic integration of taxes and benefits?

Let Dt describe the nominal debt that the tax payer has contracted fromhis fellows citizens. This starts at zero at birth and may become negativeor positive over time. The quantity Dt can be updated as follows

Dt+1 = (1 + ρt)Dt + Bt ,

with the term Bt depending on circumstances:

I when a student borrows to finance his studies, Bt is equal to theamount he receives;

I a worker who pays taxes, as well as National Insurance Contributions,sees a fraction of her payments accounted for in a reduction of Bt ;

I an unemployed person receiving benefits sees fraction of his receiptsaccruing in Bt ;

I a retired person with a negative D may draw on her accumulatedcapital.

Then keep the simple shape of the income tax scheme, but let itsparameters (the brackets and rates) vary with the level of Dt , i.e. taxesare reduced for people who have contributed a lot in the past.

Possible applications: income tax smoothing or unemployment insurance(valuable if income becomes more variable); pensions (accumulated‘rights’ become a major determinant of the pension level). The devil is inthe details.

Department of Work and Pensions (2010) : Universal credit

Pros: allow more individual choice in the timing of work life, etc.. Thistype of development is made possible by the information society.

Cons: Can the government commit? The implementation of actualbenefits is very complicated.

A theoretical reason to discourage savings

Kocherlakota (2010), Dynamic public finance.Restrictive assumptions: infinitely lived agents.

Commitment: temptation of time inconsistency (inelasticity of thecurrent stock of capital).

Taxing savings in a riskless economy

Infinitely lived consumers with a known sequence of productivities wt .

Constant returns technology, with net marginal productivity of capital r .

Lessons from results seen up to now?

I Ramsey (if valid?): tax the goods more consumed by the rich; seemsto indicate one should tax savings.

I Chamley (1986)-Judd (1985): a small (constant) tax on capitalcumulates to ∞ over a long enough horizon; the price ofconsumption at t relative to consumption at t + T is multiplied by(

1 + r

1 + r(1− τ)

)T

.

I Atkinson-Stiglitz: under weak separability

U(X1, . . . ; L1, . . .) = u(v(X1, . . .), L1, . . .)

no taxation of savings at the optimum. Is weak separability realistic?

A stochastic economy

Finite number of infinitely lived consumers workers, h = 1, . . . ,H.

∞∑t=1

βt−1[u(X ht )− v(Lh

t )]

Each worker h faces a random sequence of earning abilities (wht ), which

are identically and independently distributed across agents.

There is a constant before tax exogenous interest rate r .

At date t, the worker is privately informed of wht , which may lead her to

update her beliefs on future wages. She chooses Lht given the tax

schedule.

Description of the economy: continued

Aggregate production at date t

Yt =H∑

h=1

Y ht .

Social welfare functionW (U1, . . . ,UH)

Aggregate savings St , public expenditure G . Feasibility requires

St = Yt + (1 + r)St−1 −H∑

h=1

X ht − G ,

together with the transversality condition

limt→∞

St

(1 + r)t≥ 0.

Initial condition: no savings at date 1.

Description of the economy: completed

As in Mirrlees’ model, the government is supposed to observe pre-taxincome, and not separately the wages and labor supply. In addition, wesuppose that the government observes consumption (or equivalentlysavings). It can raise taxes at will depending on his observations, i.e. atdate t on the sequence Y ht = (Y h

1 , . . . ,Yht ) and the sequence

X h,t−1 == (X h1 , . . . ,X

ht−1).

With commitment and no option for the tax payers to leave the country,the government decides of a family of functions ξ(Yt ; Y t−1,X t−1),t = 1, . . . ,∞. Finding the second best optimum is a difficult task!

Revelation principle: report of wages w t ; the mechanism specifiesfunction ξt(w t) and ηt(w t) so that the tax payers report the truth.

The inverse Euler equation

Let (X ∗,Y ∗) be the optimum, and consider a small deviation that leavesY unchanged at Y ∗, and changes only Xt and Xt+1.

To keep incentive constraints satisfied, we must control the utility levels:

u(Xt(w t)) = u(X ∗t (w t)) + du(w t),

u(Xt+1(w t+1)) = u(X ∗t+1(w t+1))− du(w t)

β.

The inverse Euler equation: continued

First order approximation yields

Xt − X ∗t = S∗t − St =du(w t)

u′(X ∗t ),

Xt+1 − X ∗t+1 = − 1

β

du(w t)

u′(X ∗t+1),

so that from the budget constraints

St+2 − S∗t+2 = −(1 + r)du(w t)

u′(X ∗t )+

1

β

du(w t)

u′(X ∗t+1).

Taking the expectation at date t, the first order condition is

β(1 + r)

u′(X ∗t )= Et

1

u′(X ∗t+1).

Taxing capital

By Jensen, the function x → 1/x being convex, for any positive randomvariable of positive variance X

1

EX< E

1

X.

Thereforeu′(X ∗t ) ≤ β(1 + r)Etu

′(X ∗t+1),

with strict inequality in case of positive variance.

If wt+1 is known for sure at date t, so is Xt+1, and the governmentshould let the agent save and borrow at the before tax interest rate r(separable preferences).

When wt+1 is random, compared with laissez faire present consumptionis encouraged, savings is discouraged at the second best optimum. Theexistence of savings make it more costly for the government to provideincentives to work.

From mechanism to taxes

Intertemporal wedge τt tax rate on savings at date t:

u′(X ∗t ) = (1− τt)β(1 + r)Etu′(X ∗t+1).

More precisely, at any state w t :

u′(ξt(w t)) = (1− τt(w t))β(1 + r)Etu′(ξt+1(w t+1)).

Problem: the tax system must now operate in two dimensions, laborsupply and savings. The above formula makes sure that savings is chosenas desired, once labor supply is optimal. Conversely the tax T (Y ) wouldimplement the desired labor supply, given optimal savings. They do notprevent joint deviations.

A supporting tax scheme

Kocherlakota (2005) makes the wealth tax paid at (t + 1) conditional onthe wage earned at (t + 1).

τt+1(w t+1) = 1− 1

u′(Xt+1(w t+1)) Et [1/u′((Xt+1(w t+1))]

Now the choices of the optimizing agents follow from the usual Eulerequation

u′(Xt) = β(1 + r)Et [(1− τt+1)u′(Xt+1)],

so that the inverse Euler equation holds!

Kocherlakota (2005) shows under further assumptions that it is possibleto design an income tax which together with the above wealth taximplements the optimum.

The optimal wealth tax is regressive!

By constructionEtτt+1 = 0.

It brings zero tax receipts in the aggregate.

It discourages savings by making it a more risky investment: its rate ispositive (resp. negative) when 1/u′(Xt+1) is smaller (larger) than itsexpected value at t. The agent is taxed at a higher rate when herconsumption is smaller.

Conclusion

Production efficiency: as much as possible, do not distort the use ofcapital in the productive sector.

Several potential motives to tax capital at the time when the returnsfrom capital are distributed: incentives as in the above model, equity ininheritance taxation, tagging if the more patient agents also are the moreproductive.

More transparency would be welcome in the profits of firms, so as toinclude them in the incomes of their owners for the purpose of taxation(in the UK, tax them at large rate 40%, allowing for deduction if theowner is subject to the lower rate or exempted).

References

Bovenberg, A. L., M. I. Hansen, and P. B. Sorensen (2008):“Individual savings accounts for social insurance: rationale andalternative designs,” International Tax and Public Finance, 15, 67–86.

Bovenberg, A. L., and P. B. Sorensen (2004): “Improving theequity-efficiency trade-off: mandatory savings accounts for socialinsurance,” International Tax and Public Finance, 11, 507–529.

Chamley, C. (1986): “Optimal taxation of capital income in generalequilibrium with infinite lives,” Econometrica, 54, 607–622.

Department of Work and Pensions (2010): “21st centurywelfare,” Discussion paper, UK government.

Judd, K. (1985): “Redistributive taxation in a simple perfect foresightmodel,” Journal of Public Economics, 28, 59–83.

Kocherlakota, N. (2005): “Zero expected wealth taxes: A Mirrleesapproach to dynamic optimal taxation,” Econometrica, 73, 1587–1621.

(2010): The New Dynamic Public Finance. Princeton UniversityPress.