Income effects and the elasticity of taxable income^*

* An earlier version of this paper was presented at New Zealand Association of Economists Annual Conference, AUT, July 2016.

Abstract

This paper examines income effects in regression estimates of the elasticity of taxable income (ETI). One previous approach involves the proportional change in the average net-of-tax rate. It is shown that this specification can be derived from a direct utility function. Alternatively, income effects have been examined using the proportional change in virtual income. Estimation of the ETI must deal with endogeneity because observed marginal tax rates and taxable incomes are jointly determined. This paper suggests that where data are available to allow ‘no reform’ income dynamics to be estimated, they can be used to obtain the required counterfactual change in taxable income. This enables OLS to be used with an exogenous counterfactual ‘expected (marginal) tax rate’ proxy. The two specifications were estimated for New Zealand, and suggest that income effects are, at most, relatively small. They are statistically significant, and negative, only when using the change in virtual income. Importantly, the size of the ETI (which varies when income effects are present) is different depending on the specification used.

KEYWORDS:

• Elasticity of taxable income
• income effects

Acknowledgments

We are grateful to conference participants at the New Zealand Association of Economists Annual conference, AUT, (2016), and the University of Exeter (UK) Tax Administration Research Centre Annual Workshop (2016), for helpful comments. We also thank two referees and the editor of this journal for helpful comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. Bach, Corneo, and Steiner (2011) also follow a similar approach, but in the context of income splitting for couples. They refer to the revenue-maximising top marginal rate as the ‘optimal’ rate.

2. The rates and thresholds can allow for a complex set of transfers (welfare benefits). However, if concentration is on higher income brackets, it is not necessary to allow for benefits and associated abatement, or taper, rates, which apply mainly to lower income groups.

3. The effective tax rate structure is not necessarily proportional over lower ranges because of the existence of various means-tested income transfers.

4. When reform involves changes in several marginal tax rates, η_{R, 1 − τ} may be positive or negative depending on the tax bracket involved. For example, taxpayers in higher tax brackets, for whom inframarginal rates are changed, will be subject to a combination of more than one tax-reform-induced change in R.

5. In Bakos et al. (2008, p. 31), typographical errors mean that y(1 − τ) = y − τy + R appears as y(1 − π) = y − y + R , and in their following (unnumberbed) equation, is printed instead of .

6. In addition, there are income changes which would occur in the absence of tax changes. The challenge is thus to avoid attributing those exogenous income changes to the tax rate changes, such that various forms of lagged income (and age terms) are typically added to regressions.

7. Studies using this instrument include, for example, Moffitt and Wilhelm (1998), Auten and Carroll (1999), Goolsbee (1999), Sillamaa and Veall (2000), Aarbu and Thoresen (2001), Gruber and Saez (2002), Selèn (2002), Giertz (2004, 2007, 2010), Hansson (2004), Kopczuk (2005), Auten, Carroll, and Gee (2008), and Heim (2009). Carroll (1998) suggests creating an instrument based on income for several sample years, and the Auten et al. (2008) instrument is based on the tax rate evaluated at the average taxable income over a seven-year period. For New Zealand, Thomas (2012) also used income controls, such as taxable income in 1986, to deal with ‘reversion-to-the-mean’ effects.

8. This instrument has also been questioned by, for example, Gelber (2010), Blomquist and Selin (2010), Auten and Kawano (2012), Weber (2012), Holmlund and Soderstrom (2011), and Burns and Ziliak (2012). Alternative approaches typically involve using income data for years prior to the tax change (see, for example, Burns & Ziliak, 2012).

9. See Creedy (1985) for an early application. Creedy (1995) and Moffitt and Gottschalk (2011) provide reviews of some of this literature.

10. This autoregressive specification for relative incomes is consistent with a dynamic process involving regression towards the mean of φ, where  log y_{j, i} − μ_j = φ( log y_{j − 1, i} − μ_{j − 1}) + u_{i, j}, and first-order serial correlation of γ, where u_{i, j} = γu_{i, j − 1} + ϵ_{i, j}. Creedy (1985) shows that, α₂ = γ + φ and α₃ = −γφ, such that estimates of φ and γ may be obtained as φ = {α₂ + (α²₂ + 4α₃)^0.5}/2 and γ = {α₂ − (α²₂ + 4α₃)^0.5}/2. In principle, additional lags could be added but, in practice, previous studies have found only one or two lags to be sufficient to capture the dynamics of interest.

11. Recent literature has discussed how to deal with transitory shock components of actual incomes. For discussion, see Weber (2014), who is the first to examine in detail the implications of serial correlation in this transitory component for IV approaches to estimation.

12. One disadvantage of this constructed expected tax rate proxy is that it may suffer from measurement error, which would tend to bias ETI estimates downwards and reduce t-ratios. While we find somewhat smaller parameter estimates using OLS, compared to IV methods, we continue to find these parameter estimates statistically different from zero. Unfortunately, IV methods cannot resolve this issue since using the expected tax rate as an instrument in a first-stage regression (as in Cary et al., 2015) would mean the ‘exogenous’ expected tax rate instrument is measured with error (in addition to the inefficiency associated with instrumenting).

13. The lowest rate, applicable up to $16,000, remained at 15%, with the 33% rate applicable to incomes in the range $38,000–60,000.

14. Equivalent percentage changes in the net-of-tax rate, 1 − τ, are −1.0%, −2.9% and +9.4%.

15. See Claus et al. (2002, Figures 1 and 2). There is a possibility that some individuals experience marginal tax rate changes resulting from fiscal drag. But with low inflation, the vast majority of income changes over this period can reasonably be thought to reflect non-tax-related income movements.

16. Though subsequent substantive personal income tax changes did not occur until 2008, a three percentage point reduction in the corporate tax rate in 2006 may have generated responses by personal income taxpayers. Shifting between personal and corporate tax status is relatively easy in New Zealand.

17. The mean of logarithms of income in 2003, 2004 and 2005 are 10.311, 10.367 and 10.367, with standard deviation of logarithms of 0.9194, 0.9110 and 0.9651, respectively.

18. In regressions on (32(32) ), 2002 is treated as period t and 1999 (1998) as period t − 1 (t − 2).

19. The dummy was set equal to 1 if the individual received, either in addition to or instead of wage and salary income, any ‘other income’ in 1998, 1999 and 2002. Other income includes dividends, trust and estate income, partnership, rental income, business or other income, shareholder employee income, and overseas income.

20. Results were nevertheless also obtained using instrumental variable methods. However, these performed badly, producing no consistency and often with wrong signs suggesting that the loss of efficiency may be severe in this case. This is plausible given the known volatility in the New Zealand annual income data.

21. In Bakos et al. (2008, p. 31), typographical errors mean that y(1 − τ) = y − τy + R appears as y(1 − π) = y − y + R , and in their following (unnumberbed) equation, is printed instead of .