A set of ad valorem [...]]]> I thought I might try a few posts on academic economics. The issues are things that interest me rather than being new theories.  This post is motivated by my (partial) reading of the book by Kaplow (2008) on tax theory.  Comments welcome.

A set of ad valorem excise taxes (t₁,t₂,…t_n) which minimises the sum of their  inefficiency costs subject to raising government revenue R  is given by the inverse elasticities rule

t_i = k(ε_di^-1 + ε_si^-1) for i =1,…n

where k is a (constant) Lagrange multiplier associated with the government’s budget.  This is the Ramsey rule (after Ramsey, 1927). Since elasticities of demand and supply clearly vary across commodities implementing this rule involves setting non-uniform excises across commodities.  If ε_si → 0 (so suppliers are price takers) then the standard result, that the size of an excise is inversely proportional to the price elasticity of demand, obtains. See Salanié (2003, p. 63-64).

The Ramsey rule requires high excises on goods in inelastic demand. It assumes (i) consumers are identical, (ii) demands are not interdependent, (iii) there is no income tax which can be optimised when excises are being optimised, (iv) that the government’s objective is to raise a fixed amount of revenue that minimises the aggregated efficiency costs, and, (v) that income effects can be ignored.

Diamond and Mirrlees (1971) extend this analysis to a production economy under the limiting assumption that the economy displays constant returns to scale. This is important since inputs such as fuels are used both as consumer goods and as productive inputs. The key result is that the production sector should not be distorted by excise taxes.  There is therefore an a priori case against taxes on intermediate goods which are produced by some firms and used as inputs by others. 

Diamond (1975) showed that accounting for heterogeneous individuals the Ramsey rule needs to be modified to reflect both efficiency (lower tax rates on elastically-demanded goods) and distributional objectives (goods purchased by wealthy individuals) should be taxed more. Thus both price and the income elasticities of demand are important.  

That non-uniform excise taxes are optimal here is shown by Corlett and Hague (1953-54) to stem from the fact that leisure cannot be taxed. As a second-best approximation, given this inability, the optimal Ramsey rule entails levying heavier taxes on goods and services that are complementary with leisure (e.g. yachts and sports cars) rather than goods complementary to labour (e.g. urban transportation). The intuition is that a uniform excise is equivalent to a proportional tax on labour which discourages effort. This distortion can be countered by discouraging leisure which occurs if goods complementary with leisure are taxed.  

Modern tax theory (Kaplow, 2009) suggests that, to an approximation, redistribution should be confined to income taxes and transfer programs whereas other government policies, such as excise taxes, should be assessed solely on efficiency grounds.  Distributional concerns are not relevant since these can and should be addressed via income taxes.

In addition, as Atkinson and Stiglitz (1976) show, provided there is weak labour separability in the utility function – so the labour/leisure choice is independent of purchasing decisions – and provided an optimal income tax can be selected as well as optimal excises – uniform excises are preferable on all goods and services irrespective of price (or income) elasticities.  Since uniform excises amount to an increased tax on incomes this suggests that income taxes can pursue both efficiency and redistributive goals – excises are redundant and can be set at a uniform level of zero.

Kaplow suggests the need to integrate income tax determination with excise modelling and does so by considering ‘distribution-neutral’ (and ‘revenue-neutral’) reform packages whereby income taxes are adjusted to offset the effects of any policy change under consideration such as an excise or externality tax change.  Then there are no distributional impacts of the policy change. Moreover, with weak labour separability there will also be no effects on labour supply so that the standard tradeoffs in the optimal income tax literature – between efficiency and distribution – can be set to one side.

With some qualifications this greatly simplifies the economic analysis of various issues since first-best policy prescriptions can now be used.  Pollution and congestion externalities can be addressed by setting Pigouvian taxes equal to marginal social costs, public sector pricing can be set at marginal cost and so on. 

Moreover in this setting, with the assumption of weak labour separability, the Atkinson-Stiglitz result on the inefficiency of differential taxes can be generalised to arbitrary rather than optimal income taxes.  Furthermore, any measure which eliminates proportionately excise differentials across commodities will also produce an efficiency gain (Kaplow, 2008, p. 133-134).

An immediate implication is that luxury good taxes as well as exemptions from tax liability for necessity goods are inefficient.

Clearly a crucial issue is whether or not leisure is weakly-separable in the utilities of consumers.  There is much empirical evidence on such issues.  Browning and Meghir (1991) reject the hypothesis.  Other evidence is cited in Salanié (2003, p. 117-119).

These are powerful results that limit the case for excise taxes. Of course these arguments do not detract from the use of specifically high taxes to address externalities or indeed goods with specific harmful effects that are not external. They do however reduce the theoretical case for using excises as revenue-gathering policies.

Real world issues such as administrative costs of taxes and risks of evasion are also important issues determining choice of taxes.  Income taxes have high collection costs and evasion is relatively easy compared to excises or the GST. Indeed a uniform GST without exemptions satisfies the Atkinson-Stiglitz prescription.

References

A. Atkinson and J. Stiglitz, ‘The Design of Tax Structure: Direct Versus Indirect Taxation’, Journal of Public Economics, 6, 1976, 55-75.

M. Browning & C. Meghir, ‘The Effects of Male and Female Labour Supply on Commodity Demands’, Econometrica, 59. 1991, 925-951.

W.J. Corlett & D.C. Hague, ‘Complementarity and the Excess Burden of Taxation’, Review of Economic Studies, 21, 1953-54, 21-30.

P. Diamond, ‘A Many-Person Ramsey Rule’, Journal of Public Economics, 4, 1975, 335-342.

P. Diamond & J. Mirrlees, ‘Optimal Taxation and Public Production, I: Production Efficiency’, American Economic Review, 61, 1971, 8-27.

P. Diamond & J. Mirrlees, ‘Optimal Taxation and Public Production, II: Tax Rules’, American Economic Review, 61, 1971, 261-278.

L. Kaplow, The Theory of Taxation and Public Economics, Princeton University Press, Princeton, 2008.

F. Ramsey, ‘A Contribution to the Theory of Taxation’, Economic Journal, 37, 1927, 47-61.

B. Salanié, The Economics of Taxation, MIT Press, Cambridge, 2003.