Transcript Optimal taxation - The Subjective Approach to Inequality

31 October 2011
Frank Cowell: EC426 Public Economics
MSc Public Economics
2011/12
http://darp.lse.ac.uk/ec426/
Commodity Taxation
Frank A. Cowell
Frank Cowell: EC426 Public Economics
Reusing what we know
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General results – what do we know?
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Derive “optimal” commodity tax rules
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using standard second-best techniques
a case for simplification?
Commodity tax rules on reform
Integration with income tax?
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On commodity taxation
On personal income tax
Issues of information
Modelling of incentives
For overview and introduction
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Salanié, B. (2003)
Kaplow (2008b), pp125-136
Frank Cowell: EC426 Public Economics
Overview...
An application of
standard
efficiency analysis
Commodity
Taxation
Optimal tax
rules
Commodity tax
reform
Commodity tax
and income tax
Frank Cowell: EC426 Public Economics
Commodity tax: approach
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Basic questions:
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Model role of the government as intervention in the price system
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Price “wedges” are used to raise the required revenue
Taxes expressed as either
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Can we set up a well-defined optimisation problem?
If so, what criteria should be applied to the problem?
Is there a case for taxing all commodities at the same rate?
If not, on which commodities should the tax burden fall more heavily?
An absolute addition to the producer price (a “specific tax” rate t)
A percentage increase in the price (an “ad valorem tax” rate t)
Proceed in stages
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Start with heuristic argument based on standard applied welfare
economics (Cf Coady and Drèze 2002)
Then Ramsey model
Then generalisations
Frank Cowell: EC426 Public Economics
A formal approach
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Ramsey (1927) formulated the model 80+ years ago!
Main question “should we have uniform commodity taxes?”
Objective is utility of representative person
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expressed in terms of extended price vector and non-labour income
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Max this s.t. budget constraint using specific taxes ti
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First-order conditions are:
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Use Roy’s identity in FOC:
Frank Cowell: EC426 Public Economics
Ramsey Rule
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Now use Slutsky equation:
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Hi is comp demand fn for i
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Substituting in FOC:
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This then implies:
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Ramsey rule: “reduce demand for every taxable good in same
proportion”
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Does not prescribe uniform tax rates
Does not give us an explicit formula for tax rate
Yields interpretable rules
Simple example (Corlett and Hague 1953)
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Two taxable consumer goods and (untaxable) labour
Tax more heavily the good that is complementary with the untaxed good
Frank Cowell: EC426 Public Economics
Atkinson-Stiglitz interpretation
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A&S (1972) define:
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Ramsey rule for ad valorem taxes:
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If  elastic labour supply (J0=0)
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and if Uik=0, ik, :
(“intuitive” result from DWL argument)
If inelastic labour supply (J0=)
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does this mean uniform taxation?
Frank Cowell: EC426 Public Economics
Uniform Taxation?
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The basis for a “common sense” guideline?
Consider budget constraint in Ramsey-type model if
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good 0 (labour) is untaxable
and the amount of labour is fixed at K
So budget constraint is
n
S qi[1+ti]xi
 wK
i=1
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qi is producer price of good i
ti is ad valorem tax on good i
Under uniform commodity taxation this becomes:
n
S qixi
 wK / [1+t]
i=1
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But this is equivalent to lump-sum taxation of labour!
Frank Cowell: EC426 Public Economics
Arguments for Uniform
Taxation?
Invention of new commodities
1.
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Substitutability may make it difficult to specify robust “boundaries”
between commodities.
But such boundaries are essential for differential tax rates.
“Fine-tuning” of tax rates may be infeasible.
Administration cost
2.
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Formal model of complexity?
Degree of disaggregation of the tax-collecting process
Minimisation of errors (Dhami and Al-Nowaihi 2006)
Perceived equity
3.
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Special taxes for “special” goods : OK
Higher taxes for “luxuries” : OK
But, “discriminatory” taxes elsewhere?
Frank Cowell: EC426 Public Economics
Heterogeneous consumers
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Broader social objectives need to be considered.
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Pattern of demand may vary with income
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distinguish between “luxury items” and conventional goods?
a basis for discriminatory taxation?
Approach by analogy with the Ramsey interpretation
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With representative consumer distributional equity is assumed away
Concentration on efficiency makes sense.
Instead of taking the utility of a representative consumer…
…use a specific Bergson-Samuelson welfare function W
Can impute inequality-averse values to W
(Atkinson and Stiglitz 1976, Kaplow 2008a)
Focus on marginal social utility of consumer j:
Frank Cowell: EC426 Public Economics
Optimal Commodity Taxation
with Heterogeneity
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Define averages across consumers:
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The many-person Ramsey rule:
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Proportion by which demand reduced is less where average
social valuation is large
depends on correlation between marginal social utility and
consumption of particular commodities.
could mean higher taxes on goods consumed primarily by
high-wage persons.
Frank Cowell: EC426 Public Economics
Indirect tax: summary
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Elementary micro-economics appears to give us a
powerful analytical tool
Using standard results get a neat characterisation of tax
structure in terms of elasticities
The approach can be generalised to many consumers
But assumes away some things that may be crucial in
actual tax design
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Determinants of commodity boundaries
Administrative costs
Is there a case for simplified taxation?
Can we use the analysis for guidance on tax reform?
Frank Cowell: EC426 Public Economics
Overview...
Use principle to
indicate beneficial
changes
Commodity
Taxation
Optimal tax
rules
Commodity tax
reform
Commodity tax
and income tax
Frank Cowell: EC426 Public Economics
Commodity tax reform: an
approach
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In evaluating a proposed tax reform, need to consider:
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Can fairly easily evaluate first two:
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Impact on tax revenues.
Effect on the welfare of each household.
Effect on social welfare
Use household expenditure surveys to estimate demand
Microsimulation model to determine tax effect
What about third point?
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impute social welfare weight to each household…
…then aggregate gains and losses of households
difficult: embodies normative value judgments
Frank Cowell: EC426 Public Economics
Tax reform problem (1)
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Simple approach to tax reform focuses just on welfare
improvement
This requires full comparability of households
Reform must be achievable within existing resources
So a favourable tax reform requires
 no decrease in tax revenues:
 no decrease in social welfare:
dR = Si MRi dti ≥ 0
dW ≥ 0
Obvious problem with this approach
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High informational requirements on individual welfare
Specification of social welfare function
Frank Cowell: EC426 Public Economics
Tax reform problem (2)
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To avoid imposing a specific structure on social
welfare…
… just try to find Pareto-improving tax reforms
Pareto improvement requires:
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achievable within existing resources
Pareto superiority of after-reform outcome
Translated this means
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non negative impact on tax revenues
must harm no one
benefit at least one person
Frank Cowell: EC426 Public Economics
Tax reform problem (3)
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To express a Pareto-improving reform
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Then acceptance of the reform requires:
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no decrease in tax revenues:
dR = Si MRi dti ≥ 0
must harm no one
dBj = Si MBij dti ≥ 0 for all j
Then improvement requires the above plus:
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MBij: the marginal benefit of household j from a change in
tax i
dBj: total change in benefit for household j
benefit at least one person: dBj >0 for some j
But these criteria are demanding:
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in practical applications…
…no solution satisfying the conditions
Frank Cowell: EC426 Public Economics
A refined approach
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Because of indecisiveness of Paretian approach, try a
modified criterion
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Base this on the “transfer principle” (Dalton 1920)
Assume a prior (welfare) ranking of households
A transfer is approved if
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Mayshar and Yitzhaki (1995, 1996 )
it distributes from the low ranking (rich)…
…to the high ranking (poor)
…without altering the ranking itself
Logic behind this:
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Similar to dominance criteria
Difficult to find first-order dominance?
Therefore worth looking at second-order dominance
Frank Cowell: EC426 Public Economics
Mayshar-Yitzhaki approach (1)
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Do not try to specify a specific SWF
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Do not try to find Pareto-improving tax reforms
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end up with no solution
Use consumption expenditure per adult-equivalent
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will be arbitrary by definition
generate an ordinal social ranking of households
“marginal social worth”?
who is more and who is less deserving of a marginal increase in their
income
Arrange households j = 1, 2, 3,…
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…in ascending order of marginal social worth
can then calculate cumulative benefit
Frank Cowell: EC426 Public Economics
Mayshar-Yitzhaki approach (2)
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Let di be the value of the increase in tax revenue
due to an increase in tax i
Define Cumulative Marginal Benefit function:
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CMBj(d) := dB1 + dB2 + … + dBj
conditioned on the vector of revenue changes d
Gives a practical method of checking tax reform
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use CMB-dominance criterion:
CMB1(d) = dB1 ≥ 0?
CMB2(d) = dB1 + dB2 ≥ 0?
…
…
…
CMBj(d) = dB1 + dB2 + … + dBj ≥ 0?
Frank Cowell: EC426 Public Economics
Mayshar-Yitzhaki criterion
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Gives simple principle for reform of commodity taxation
Accept the reform if and only if::
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Simple relationship between criteria:
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no decrease in tax revenues:
dR = Si di ≥ 0
dominance result holds: CMBj(d) ≥ 0 for all j
Pareto-improving criterion implies Dalton-improving
but not vice versa
Dalton-improving is more likely to result in a non-empty
solution set
Frank Cowell: EC426 Public Economics
Commodity tax reform
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The Dalton-improving tax reform appears an attractive approach
to the problem
Less demanding because it only requires:
 Identification of an ordinal social ranking of households
 The impact on tax revenues and on each household’s welfare
 Simple computation of effect of each tax instrument
Usually get a non-empty and a non-trivial solution set
After all non-trivial solutions have been obtained the alternative
tax reforms can be examined for their distributional impact
Frank Cowell: EC426 Public Economics
Overview...
An integrated
approach – do we
need commodity
taxes?
Commodity
Taxation
Optimal tax
rules
Commodity tax
reform
Commodity tax
and income tax
Frank Cowell: EC426 Public Economics
Nonlinear commodity taxation?
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Should consider the issue of proportional versus
nonlinear taxation of commodities.
“Nonlinear” includes affine functions
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The argument is whether each commodity should be
“repriced”
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like the so-called linear income tax function
perhaps not in a proportional fashion.
Similar argument is applied in other areas
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tariffs for output of state-owned industries
price support schemes
Frank Cowell: EC426 Public Economics
Informational considerations
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Main difference direct/indirect taxes is informational
base
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Informational requirements may preclude extensive
application of nonlinear commodity taxes
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use of smart cards? (Cowell 2008 )
ICC issues can arise with nonlinear pricing:
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similar to nonlinear pricing of consumer goods
can work for some goods and services
What if technology enhances informational base
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Direct tax authority can know details of personal resources.
Indirect tax authority can know structure of production and
transactions
Some groups may choose the “wrong contract”
Arises both in private and public sector
Difficulties disappear if you impose the regularity
conditions implied by linearity
Frank Cowell: EC426 Public Economics
Combined direct/indirect tax (1)
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Atkinson and Stiglitz (1976): optimal tax problem combining
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Consumer’s gross income is y = w[1x0]
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no lump- income sum component: I = 0
So budget constraint is Si=1n qi[1+ti]xi  y  T(y)
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Ramsey-type proportional commodity taxation
Mirrlees (1971)-type income taxation
qi is producer price of good i
ti is ad valorem tax on good i
T is income tax schedule
Chooses x0, x0,…, xn to maximise U(x0, x0,…, xn)
Government’s budget constraint is R  Si=1n qixiti + T(y)
Chooses t1,…,tn-1, T(.) to max SWF (function of individual utility)
FOCs yield tax rule
Frank Cowell: EC426 Public Economics
Combined direct/indirect tax (2)
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Use FOC rules to give general guidance on tax structure
Commodity taxes should be zero if
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But this holds also if income tax is not optimised
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(Kaplow 2006, Laroque 2005)
If preferences are not separable
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tastes are identical and
preferences are weakly separable in leisure and other goods
ti should be high if the MRSin increases strongly with leisure
extended also by Hellwig (2010)
Results robust when tastes are heterogeneous (Saez 2002)
a small tax on commodity i is desirable if high income earners have a
relatively higher taste for i …
 …or if consumption of i increases with leisure
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Frank Cowell: EC426 Public Economics
Conclusions
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Direct versus indirect
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Uniform commodity taxation
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Distinction between the two is essentially an issue of
information.
Big differences in terms of distributional effect.
No compelling case within the context of the model
There may be a case if you appeal to other factors
Do we need commodity taxes?
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depends on way incentives and information are modelled
also depends on structure of preferences
Frank Cowell: EC426 Public Economics
References (1)
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Atkinson, A. B. and Stiglitz, J. E. (1972) “The Structure of Indirect Taxation and
Economic Efficiency,” Journal of Public Economics, 6, 97-119
Atkinson, A. B. and Stiglitz, J. E. (1976) “The design of tax Structure: direct versus
Indirect Taxation,” Journal of Public Economics, 6, 55-75
*Coady, D. and Drèze, J. (2002) “Commodity taxation and social welfare: the
generalized Ramsey rule,” International Tax and Public Finance, 9, 295-316.
Corlett, W. J. and Hague, D. (1953) “Complementarity and the excess burden of
taxation,” Review of Economic Studies, 21, 21-30
Cowell, F. A. (2008) “Problems and Promise of Smart Cards in Taxation,” National
Tax Journal, 61, 865-882
Dalton, H. (1920) “Measurement of the inequality of incomes,” The Economic
Journal, 30, 348-361
Dhami, S. and Al-Nowaihi, A. (2006) “A simple model of optimal tax systems:
taxation, measurement and uncertainty,” Manchester School, 74, 645–669
Hellwig, M. F. (2010) “A generalization of the Atkinson-Stiglitz (1976) theorem on
the undesirability of nonuniform excise taxation,” Economics Letters, 108, 156-158
*Kaplow, L. (2006) “On the Undesirability of Commodity Taxation even when
Income Taxation is Not Optimal,” Journal of Public Economics, 90, 1235-1250
Frank Cowell: EC426 Public Economics
References (2)
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Kaplow, L. (2008a) “Optimal Policy With Heterogeneous Preferences,” National
Bureau of Economic Research, Working Paper 14170
Kaplow, L. (2008b) The Theory of Taxation and Public Economics, Princeton
University Press
Laroque, G.R. (2005) “Indirect taxation is superfluous under separability and taste
homogeneity: A simple proof,” Economics Letters, 87, 141–144
Mayshar, J. and Yitzhaki, S. (1995) “Dalton-improving indirect tax reform,” American
Economic Review, 95, 793-808
Mayshar, J. and Yitzhaki, S. (1996) “Dalton-improving tax reform: When households
differ in ability and needs,” Journal of Public Economics, 62, 399-412
Mirrlees, J. A. (1971) “An exploration in the theory of the optimal income tax,”
Review of Economic Studies, 38, 135-208
Ramsey F. P. (1927) “A contribution to the theory of taxation, The Economic Journal,
37, 47-61
Saez, E. (2002) “The desirability of commodity taxation under non-linear income
taxation and heterogeneous tastes,” Journal of Public Economics 83, 217–230
*Salanié, B. (2003), The Economics of Taxation, MIT Press, Chap 3