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Abstract
The empirical literature on the elasticity of taxable income (ETI) sometimes questions whether estimated values are consistent with being on the revenue-increasing section of the Laffer curve, usually in the context of a single rate tax system or for top marginal rates. This paper obtains expressions for this ‘Laffer-maximum’ or revenue-maximising ETI which can be applied to any tax rate in a multi-rate system. For the New Zealand income tax system in 2010, it is found that a wide range of revenue-maximising ETI values can be expected across individual taxpayers, across tax brackets and in aggregate. The paper also simulates the effect of multi-rate tax reforms on these revenue-maximising ETIs.
Acknowledgements
We have benefited from discussions with Raj Chetty and comments by two referees.
Notes
1. The Laffer curve is sometimes defined in terms of the total revenue and an average tax rate. Here, it is discussed in terms of separate schedules which relate revenue to each marginal tax rate.
2. This is because the standard specification, starting from a quasi-linear utility function, gives rise to an expression for taxable income, , of the form
+
, where
is the taxable income in the absence of taxation and
is the tax rate. Hence, there is a constant elasticity,
, of
with respect to
, rather than
: see Creedy (2010).
3. For a simple tax system with only one marginal tax rate, the condition under which a rate increase leads to an increase in total revenue is easily expressed in terms of the aggregate ETI. An economy is on the ‘wrong’ side of the Laffer curve if the elasticity of taxable income with respect to the tax rate,, is less than
. Hence, as Goolsbee (1999) and Hall (1999) indicate, this translates into an elasticity of taxable income with respect to the net-of-tax rate,
, greater than
.
4. For reviews of empirical estimates, see Goolsbee (1999), Giertz (2007, 2009a, 2009b) and Saez, Slemrod, and Giertz (2012).
5. There is an interesting comparison here with Cournot’s (1838) pathbreaking discussion of demand curves. He showed that, for a producer of a good facing a falling demand curve, the total revenue initially increases and then decreases as the price rises, with the maximum revenue being at the point of unit elasticity. He argued that, although it would be extremely difficult to identify a precise value of the elasticity at any time, it is important to know whether the producer is on the rising or falling side of the revenue curve.
6. Some individuals may become incorporated, and thus pay tax at a reduced rate and apply a wide range of deductions, when marginal personal rates increase. The extent of such shifting can depend on the regulations and costs involved in incorporation. Hence, the ETI is itself subject to policy changes, rather than being a fundamental fixed parameter. Also the effects of rate increases may not be symmetrical with respect to subsequent reductions, as it is less likely that the process would be reversed.
7. In addition, this framework does not account for behavioural responses at the extensive margin.
8. The distinction between gross income and taxable income is ignored here; if there are endogenous, income-related deductions, the following analysis must be in terms of income after deductions have been made. In addition, general equilibrium effects are ignored here.
9. The standard assumption made is that there are no income effects; a change in a lower rate simply changes the amount of tax without leading to a change in taxable income. For a detailed treatment of all components of aggregate revenue changes, see Creedy and Gemmell (2013a).
10. See, for example, Creedy and Gemmell (2002, 2006).
11. Fullerton (2008) gives the familiar revenue maximising tax rate for a proportional tax system, in terms of the ETI, as . Using (Equation9
(9) ), and setting
and
for a proportional tax, rearrangement of (Equation9
(9) ) gives the revenue maximising tax rate,
, as
.
12. Equation (Equation5(5) ) can be used to calculate maximum ETIs consistent with any particular value of
. For example, revenue authorities may wish to target a particular revenue increase by raising one or more marginal tax rates. It is important to know for which taxpayers or income groups this is likely to involve taxable income and/or revenue reductions.
13. The value of 0.61 in 2010 fell to 0.492 in 2011 when the top tax rate was reduced to 0.33.
14. One caveat is that a change in may induce some taxpayers to reduce their incomes to zero (for example, by migrating or otherwise leaving the labour market).
15. For example, for a family with two children, an FTC payment of $149 per week plus IWTC of $60 per week (if one or more parents are working, at least part-time) would be received in 2011 when the household annual income is below $36,827. With the abatement of FTC and IWTC for incomes above this threshold level, some FTC continues to be received by households with incomes up to $74k, and up to $90k for IWTC. With three or more children, some IWTC continues to be received by households with incomes in excess of $100k. See http://www.ird.govt.nz/wff-tax-credits/.
16. In fact, following the reductions to all statutory tax rates in May 2010, the WfF abatement rate was raised in May 2011.
17. New Zealand Inland Revenue data, available at: http://www.ird.govt.nz/aboutir/external-stats/revenue-refunds/inc-dist-of-ind/. The data shown in the chart, in $100 bands, have been derived from the published Inland Revenue data where incomes are split into $1000 or $5000 bands up to $250,000. Hence, for example, between $47,000 and $48,000 the total taxable income is $1,887 million, that is, $188 million per $100 within this $1000 range.
18. Similar distributions for earlier years reveal spikes at $60k but not at $70k when the upper threshold (prior to 2008–2009) was set at $60k. A comparable, if more muted, pattern emerges when the lower threshold rose from $38k to $48k in 2008-09. The New Zealand system provides strong incentives, and legal opportunity, for the self-employed or small business owner to allocate up to $70k of earnings to an otherwise non-working or part-time working spouse where the primary earner’s income exceeds this amount.
19. See Creedy and Gemmell (2013b, p. 6) for details of the derivation.
20. The curves in are similar to that traced out by Giertz (2009b) for changes in the top tax rate in the United States. Giertz (2009b, p. 130) shows that different assumed empirical values for the ETI generate a decline in revenue from the top income tax bracket in response to a marginal tax rate increase, as the ETI rises from 0.2 to 1.0.
21. Such an exercise would also be complicated by the simultaneous effects of the global recession that arguably reduced New Zealand incomes over a sustained period from 2008, independently of the 2010 tax changes.
22. The full set of components of tax rate changes are explored analytically by Creedy and Gemmell (2013a).
23. As emphasised earlier, these simulations also take no account of the impact of the abatement of family tax credits which tend to lower aggregate ETI values.
24. It can be shown that is below the actual rate of 0.21 for ETI
1.9. The equivalent case for
requires much higher values of the ETI.