THE THEORY OF OPTIMAL TAXATION:NEW DEVELOPMENTS AND

POLICY RELEVANCE

Peter Birch SørensenUniversity of Copenhagen,

EPRU and CESifo

Invited Plenary Lecture20th Scientific Meeting of SIEP, Pavia, September 2008

PRELIMINARIES

The optimal tax revolution: theorists versus practitioners

An irrelevant objection to optimal tax theory: The straw man of the ’benevolent dictator’

Optimalindirect taxation

INDIRECT TAXATION: THE UNIFORM-TAX CONTROVERSY

Suppose a certain amount of revenue has to be raised from indirect taxation. The issue then arises:

Should indirect taxes be differentiated?Optimal tax theory: Generally Yes!Practitioners: No!

(Note: Uniform indirect taxation is equivalent to having no indirect taxation at all)

RAMSEY TAXATION

The optimal indirect tax system causes an equi-proportionate reduction in the compensated demands for all commodities

The Corlett-Hague rule

Impose relatively high tax rates on commoditiesthat are complements to (less substitutable for)leisure

NB: Implementing the optimal tax system requiresknowledge of compensated own-price and cross-price elasticities

THE CASE FOR UNIFORM TAXATION

Separable preferences (all commodities equally substitutable for leisure)

Uniform taxation easier to administer and less susceptible to fraud

Ramsey taxation requires frequent tax rate changes due to changes in tastes and technology

Differentiated taxation invites lobbyism

A MODEL WITH HOUSEHOLD PRODUCTION(Kleven, Richter and Sørensen, OEP, 2000)

Consumers get utility from goods, services andleisure

All goods are bought in the market; services canbe produced in the home or can be delivered fromthe market

Time can be spent on home production, marketproduction or leisure

The government levies taxes on commodities andon labor income

OPTIMAL TAXATION WITHHOUSEHOLD PRODUCTION

• The optimal tax system causes an equi-proportionate reduction in the compensated demands for all market-produced goods and services

• If home production is large, it may be optimal to tax consumer services at a relatively low rate even if they are complements to leisure

• If all goods and services are equally substitutable for leisure (so that uniform taxation would be optimal in the absence of home production), it is certainly optimal to tax consumer services at a low rate

OPTIMAL TAXATION WITHHOUSEHOLD PRODUCTION

• Taxes should distort the pattern of market activity as little as possible

• A high tax on complements to leisure may not be an efficient way of stimulating labour supply to the market if such a tax encourages substition of home production for market production

• Untaxed home production tends to reduce market production of services relative to the production of other goods (since household production mainly takes the form of services)

• Hence there is a presumption in favour of a lenient tax treatment of certain services

AN ALTERNATIVE FRAMEWORK: BECKER

• Consumers get utility from consumption ’activities’

• Consumption activities (’household production’) require inputs of commodities and time

• Consumers spend time on consumption activities and on work in the market

• The government must raise a certain amount of revenue from commodity taxes and cannot directly tax time spent on consumption activities

THE INVERSE FACTOR SHARE RULEKleven (JPubE 2004)

1

jj j

j j j j

WnRt ,

P a Wn

Implication: The larger the time input required for consumption, the higher is the optimal tax rate

● The inverse factor share rule preserves the first-best allocation (in the absence of ’pure’ leisure)

● Implementing the inverse factor share rule only requires data on consumption and time allocation

PRELIMINARY CONCLUSIONSON INDIRECT TAXATION

There are still strong administrative and politicaleconomy arguments for maintaining a high degreeof uniformity in indirect taxation,

but recent contributions to optimal tax theory have

made it easier to identify the

● commodities that are candidates for special tax treatment

● parameters that determine the optimal indirect tax structure

Optimal taxationof capital income

SHOULD CAPITAL INCOME BE TAXED?ANSWERS FROM OPTIMAL TAX THEORY

• Standard infinite horizon Ramsey model: No!

• Overlapping generations model: Generally ’Yes’, except if preferences are separable in leisure and consumption

SHOULD THE CAPITAL INCOME TAXBE UNIFORM?

Suppose a given amount of revenue must be raised from taxes on capital. The question then arises:

Should capital income taxes be ’neutral’, i.e. uniform across different investments?

(Most) economists: Yes!Politicians: No!Optimal tax theory: It depends!

THE CASE FOR’NEUTRAL’ CAPITAL INCOME TAXATION

● Production Efficiency Theorem: Avoid production distortions when all pure profits can be taxed away and all household transactions with firms can be taxed

● We don’t have the information needed to implement optimal differential capital taxation, and even if we had, the welfare gain from moving from neutral to optimal capital taxation would be small (Auerbach (1989))

● Non-neutral capital income taxation creates administrative problems and invites lobbyism

A SIMPLE MODEL OF CAPITAL TAXATION IN THE OPEN ECONOMY

● Two perfectly competitive production sectors

● Three production factors: capital, labor and a fixed factor (e.g. land)

● Output prices and the required return on capital given from the world market (small open economy with perfect capital mobility)

● Labor is immobile across borders but perfectly mobile between the two domestic sectors

● Fixed total supplies of capital and labor

THE OPTIMAL TAX PROBLEM

Maximize national income

subject to the constraint that

a certain amount of revenue has to be raisedfrom taxes on capital (which may be differentiated across sectors)

OPTIMAL RESIDENCE-BASED TAXATION

If the residence principle can be enforced, it is optimal to levy a uniform capital income tax on all domestic and foreign investment

Thus neutral capital taxation is desirable whenforeign source income can be taxed

but

the residence principle is hard to enforce

OPTIMAL SOURCE-BASED TAXATION (Sørensen, ITAX (2007))

1 2 1 2

1 1 2 2

t t t t

Ramsey rule for capital taxation :

At the margin, the optimal tax policy causesan equiproportionate reduction of investmentin all sectors

THE COBB-DOUGLAS CASE

• With Cobb-Douglas production functions the elasticities of capital demand depend solely on the income shares of labor, capital and land and on the share of total employment in each sector

• The optimal relative capital income tax rate is higher the higher the income share of rents and the higher the labor income share

Implication: The more capital-intensive sector should carry a lower relative tax rate, since capital demand is more sensitive to taxation in this sector

AN INVERSE ELASTICITY RULE FOR SOURCE-BASED CAPITAL TAXATION

In the special case where only capital is mobileacross sectors (specialized labor), capital demand in a sector will depend only on thecapital tax rate imposed on that sector(zero cross-price elasticities)

In that case the optimal capital income tax rateon a sector is proportional to the inverse of theelasticity of sectoral capital demand withrespect to the sectoral tax rate

OPTIMAL TAXATION AND CAPITAL FLIGHT

• The elasticity of capital demand stems mainlyfrom international capital mobility

• A high elasticity of capital demand means thata higher tax rate will induce a relatively largecapital export

• The Ramsey rule for source-based capitaltaxation is therefore consistent with a concernto avoid too much capital flight (and the desireto impose relatively low tax rates on particularly’mobile’ activities)

CAN OPTIMAL DIFFERENTIAL CAPITALTAXATION BE IMPLEMENTED?

● If production functions do not deviate too much from the Cobb-Douglas form, the elasticities of capital demand may be deduced from observable variables (income shares and employment shares)

● Even if the Cobb-Douglas assumption is a bad approximation, the elasticity of capital demand is likely to be lower, the lower the relative importance of capital in production

Optimal taxationof labour income

MAKING MIRRLEES OPERATIONAL

● Mirrlees (1971) made a fundamental contribution to the theory of optimal taxation, but for many years the theory remained difficult to apply

● Building on Piketty (1997) and Diamond (1998), Saez (2001, 2002) derived explicit optimal tax formulas in terms of labour supply elasticities and observed properties of the (wage) income distribution

(key simplification: zero income effects)

A MODEL OF LABOUR SUPPLY(Saez, QJE, 2002)

● Workers allocate themselves across J different occupations involving different levels of effort and income

● By adjusting their effort, workers can move one step up or down on this income ladder (intensive labour supply response)

● Workers can decide to participate or to stay outside the labour market. As net earnings in an occupation increases, more workers move from non-employment into this occupation (extensive labour supply response)

THE OPTIMAL TAX SCHEDULEIN THE SAEZ MODEL

marginal tax rate at income level

'participation tax rate' at income level

fraction of workers at income level

= social value of one euro dist

1 11 1

i

j

i

j

Jj ji

j jj ii i i j

m i

t j

h i

g

tmh g

m h t

0

ributed to

individuals at income level 1

= intensive labour supply elasticity

extensive labour supply elasticity

J

j ji

i

j

j h g

RESULTS FROM THE SAEZ MODEL

● With zero participation elasticities, the guaranteed minimum income and the marginal tax rate on low-income earners are both high

● If participation elasticities are high, net transfers to the working poor exceed transfers to the non-working poor and the marginal tax rate on low earnings is negative (rationale for US type Earned Income Tax Credit)

Interesting application of the Saez formula: By solving for gj one can derive the distributional weights that would make the actual observed tax schedule optimal (Bourgignon and Spadaro (2005))

CONCLUSIONS

● The administrative and political economy case for uniform and neutral taxation remains strong, so deviations from uniformity and neutrality should be accepted only when there is a strong efficiency case for doing so

● Recent developments in optimal tax theory have made it easier to identify the (few) commodities/sectors where deviations from uniformity and neutrality may be warranted

● Deviations from uniformity and neutrality occur anyway; insisting that they must be defensible on optimal tax grounds may provide a bulwark against ’illegitimate’ non-neutralities

CONCLUSIONS

● When the income elasticity of labour supply is (close to) zero, the optimal tax schedule for labour income becomes a relatively simple function of distributional weights and a few observable variables

● This optimal tax formula can be ”turned on its head” and used to derive the distributional weights that would make the existing tax policy optimal. This in turn may help to inform policy-making: Is this really the distributional pattern that policy makers want?