Abstract
This paper shows how income changes in response to changes in marginal income tax rates (MTRs) translate into tax revenue changes for the familiar multi-step income tax function used in many countries. Previous literature has focused on the relatively straightforward case of a proportional income tax or the top MTR only. The paper examines revenue responses at both the individual and aggregate levels, and it is shown that for individual MTRs within a multi-rate regime, simple expressions for tax revenue responsiveness can be derived that nevertheless capture the various behavioural and structural responses to income tax reforms involving changes to multiple rates and thresholds. Illustrations are provided using changes to the New Zealand income tax structure in the 2010 budget. This reduced all marginal tax rates while leaving income thresholds unchanged.
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Notes
It avoids the considerable complexities of attempting to combine the varied behavioural adjustments into a structural model, as well as providing (under certain assumptions) a convenient method of measuring the marginal excess burden arising from tax changes. However, its use crucially depends on an assumed absence of income effects. The elasticity can be influenced by policy changes concerning, for example, regulations regarding income shifting and the timing of income receipts and tax payments. The seminal paper is Feldstein (1995), with important evidence for the US by Auten and Carroll (1995, 1999) and Auten et al. (2008). Giertz (2007) and Saez et al. (2012) provide comprehensive reviews of evidence, while Creedy (2010) provides an introduction to the underlying analytics.
Saez et al. (2012) examined changes in total tax revenue obtained from the top marginal rate in the course of deriving the aggregate excess burden. Following Saez, the two components were also discussed by, for example, Giertz (2009). The simple proportional income tax case is discussed by Goolsbee (1999) and Hall (1999). Blomquist and Simula (2010) consider the welfare effects of an equal percentage point change in the marginal tax rate at all income levels, and compare results with a linearised budget constraint.
Blundell (2011) argues that hours and employment responses are unlikely to be the most prevalent reactions to top income tax rate changes; hence taxable income response estimates are potentially more relevant. An alternative approach is to use behavioural micro-simulation models that incorporate an elasticity of taxable income; see, for example, Elmendorf et al. (2008) for an application. However, such models are rarely available to individual researchers and the approach in this paper offers a simple analytical and practical method to decompose revenue responses to tax rate changes.
See the survey in Creedy and Gemmell (2002). The revenue elasticity is also used in discussions of local measures of tax progressivity.
Following Feldstein (1999), Saez et al. (2012), Brewer et al. (2010) and Blundell (2011) also use the elasticity of taxable income (ETI) concept to derive and discuss simple analytical results, in terms of the ETI, for the deadweight losses associated with top marginal tax rates. Creedy (2010) provides a comparable analysis for the multi-step income tax considered here.
For discussion of the empirical importance of income-related deductions in personal income tax regimes in OECD countries, see Caminada and Goudswaard (1996) and Wagstaff and van Doorslaer (2001). For the US, Feldstein (1999, p. 675) estimated that total income tax deductions in 1993 amounted to about 60 % of estimated taxable income.
The restriction to exogenous income changes is easily handled when considering individual elasticity values, but of course the nature of the overall distribution of income, which is needed to obtain aggregate values, may well be influenced by the incentive effects of the consequent tax changes.
Saez et al. (2012, p. 7) do not discuss the separate role of the revenue elasticity in this context. Discussion of the rate and base effects is often discussed in the context of a simple proportional tax structure, with constant average and marginal rate, t, where the revenue elasticity is everywhere unity. Thus, if \(\bar{y}\) is arithmetic mean income, \(\frac{dT}{dt}=\bar{y}+\frac{td\bar{y}}{dt}\) and in terms of elasticities, \(\eta_{T,t}=1+\eta_{\bar{y},t}\).
The constant revenue line in Fig. 1 is similar to that obtained by Fullerton (1982, p. 9), concentrating on labour supply responses to tax increases. Fullerton drew a downward sloping convex curve with the labour supply elasticity on the vertical axis and the tax rate on the horizontal axis. For tax revenue to increase when the tax rate increases, the supply elasticity must be sufficiently small, that is, the combination of tax rate and elasticity must lie to the south west of his curve. In simulations, Fullerton (1982, p. 13) held the revenue elasticity, η T,y , constant as the tax rate was varied (by increasing average and marginal rates by the same percentage).
The revenue elasticity properties of this function are examined in more detail in Creedy and Gemmell (2002).
The partial individual elasticity, \(\eta_{T,\tau _{j}}^{\prime }\), for j<k (that is, for changes in marginal tax rates below the tax bracket in which the individual falls) is also obtained as \(\eta_{T,\tau _{j}}^{\prime }=\frac{\tau_{j} ( a_{j+1}-a_{j} ) }{T ( y ) }=\frac{T_{j} ( y ) }{T ( y ) }\), where T j (y) is tax paid at the rate, τ j , and T(y) is total tax paid by the individual. Across all tax brackets \(\sum_{j=1}^{k}\eta_{T,\tau _{j}}^{\prime }=1\).
This analysis assume that both s and t do not change in response to changes in τ k .
It is assumed that all individuals face the same income thresholds, so that endogenous allowances are not considered here.
For the US, Saez et al. (2012) find values for \(( \frac{\bar{y}_{K}-a_{K}}{\bar{y}_{K}} ) \) around 1.5; that is, \(( \frac{\bar{y}_{K}}{\bar{y}_{K}-a_{K}} ) \simeq 0.67\).
The table is obtained from unpublished Inland Revenue Department data covering 3,304,210 individuals.
References
Auten, G., & Carroll, R. (1995). Behavior of the affluent and the 1986 tax reform act. In Proceedings of the 87th annual conference on taxation of the national tax association, Columbus, Ohio (pp. 70–76).
Auten, G., & Carroll, R. (1999). The effect of income taxes on household behavior. Review of Economics and Statistics, 81, 681–693.
Auten, G., Carroll, R., & Gee, G. (2008). The 2001 and 2003 tax rate reductions: an overview and estimate of the taxable income response. National Tax Journal, 61, 345–364.
Blomquist, S., & Simula, L. (2010). Marginal deadweight loss when the income tax is nonlinear. CESifo Working Paper no. 3053.
Blundell, R. (2011). Empirical evidence and tax policy design: lessons from the Mirrlees Review. Canadian Journal of Economics, 44, 1106–1137.
Brewer, M., Saez, E., & Shephard, A. (2010). Optimal household labor income tax and transfer programs. In J. Mirrlees et al. (Eds.), Dimensions of tax design: the Mirrlees Review. Oxford: Oxford University Press. For Institute for Fiscal Studies.
Caminada, K., & Goudswaard, K. (1996). Progression and revenue effects of income tax reform. International Tax and Public Finance, 3, 57–66.
Claus, I., Creedy, J., & Teng, J. (2012). The elasticity of taxable income in New Zealand. Fiscal Studies, 33, 287–303.
Creedy, J. (2010). The elasticity of taxable income: an introduction and some basic analytics. Public Finance and Management, 10, 556–589.
Creedy, J., & Gemmell, N. (2002). The built-in flexibility of income and consumption taxes. Journal of Economic Surveys, 14, 509–532.
Elmendorf, D. W., Furman, J., Gale, W. G., & Harris, B. H. (2008). Distributional effects of the 2001 and 2003 tax cuts: how do financing and behavioral responses matter? National Tax Journal, 61, 365–380.
Feldstein, M. (1995). The effect of marginal tax rates on taxable income: a panel study of the 1986 Tax Reform Act. Journal of Political Economy, 103, 551–572.
Feldstein, M. (1999). Tax avoidance and the dead weight loss of the income tax. Review of Economics and Statistics, 81, 674–680.
Fullerton, D. (1982). On the possibility of an inverse relationship between tax rates and government revenues. Journal of Public Economics, 19, 3–22.
Giertz, S. H. (2007). The elasticity of taxable income over the 1980s and 1990s. National Tax Journal, LX, 743–768.
Giertz, S. H. (2009). The elasticity of taxable income: influences on economic efficiency and tax revenues, and implications for tax policy. In A. D. Viard (Ed.), Tax policy lessons from the 2000s (pp. 101–136). Washington: AEI Press.
Goolsbee, A. (1999). Evidence on the high-income Laffer curve for six decades of tax reform. Brookings Papers on Economic Activity, 1999, 1–47.
Hall, R. E. (1999). Comments and discussion. Brookings Papers on Economic Activity, 1999, 48–51.
Saez, E. (2004). Reported incomes and marginal tax rates, 1960–2000: evidence and policy implications. In J. Poterba (Ed.), Tax policy and the economy (pp. 117–173). Cambridge: MIT Press.
Saez, E., Slemrod, J. B., & Giertz, S. H. (2012). The elasticity of taxable income with respect to marginal tax rates: a critical review. Journal of Economic Literature, 50, 3–50.
Wagstaff, A., & van Doorslaer, E. (2001). What makes the personal income tax progressive? A comparative analysis for fifteen OECD countries. International Tax and Public Finance, 3, 299–316.
Acknowledgements
The authors are, respectively, the Truby Williams Professor of Economics at Melbourne University, and Professor of Public Finance, Victoria University of Wellington. The research was supported by the New Zealand Royal Society through their Cross Departmental Research Pool scheme. We have benefited from very helpful comments on a previous version by two anonymous referees, the editor of this journal, and by Matt Benge, Steve Cantwell, Raj Chetty, Andrew Coleman, and Chris Heady. The work began in an attempt to answer a question raised by Antoine Bozio.
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Creedy, J., Gemmell, N. Measuring revenue responses to tax rate changes in multi-rate income tax systems: behavioural and structural factors. Int Tax Public Finance 20, 974–991 (2013). https://doi.org/10.1007/s10797-012-9255-7
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DOI: https://doi.org/10.1007/s10797-012-9255-7