2 Approaches to Estimation

In using regression methods, a constant elasticity specification is ubiquitous in the literature, whereby the logarithm of taxable income is expressed as a linear function of the logarithm of the net-of-tax rate. Fixed effects are generally eliminated by taking first-differences, so the form of equation to be estimated has the change in the logarithm of taxable income related to the change in the logarithm of the net-of-tax rate (these log-changes also providing approximations to the proportional changes), along with other available exogenous variables such as age. The approach therefore requires information about taxable income of a sample of individuals in at least two years (before and after a tax structure change), and the regression is cross-sectional.[4] A measure of initial or lagged income is often added as a regressor, to capture any tendency for proportional income changes to depend on income levels. All the observed change in income is attributed to the tax change and the exogenous variables included in the regression.

The reduced-form specification faces the well known problem that, with a nonlinear income tax function reflecting marginal rate progression, the change in the net-of-tax rate is itself endogenous. To overcome this problem numerous of authors have used an instrumental variable approach in which the instrument is, for each individual, the marginal net-of-tax rate which would be faced in the second period if there were no change in income.[5] The first stage involves a regression of the change in the actual log-net-of-tax rate on the change in the log-net-of-tax rate that would apply with no change in income, and other exogenous variables. This is used to obtain 'predicted' values of the log-change in the net of tax rate. The latter is then used in the second stage regression (with the change in the logarithm of income as dependent variable) instead of the actual change. Hence, the most commonly adopted 'standard instrument' involves using the tax rate that would apply post-reform to the taxpayer's pre-reform income. Where comparisons involve a number of years, annual incomes are often adjusted for inflation.[6] Alternatively, in determining the individual's reform-only change in marginal tax rates, some studies have adopted a common intermediate income between pre- and post-reform levels.[7]

As is well-known, following Feldstein (1995) relatively large estimates for the ETI (he found values between 1 and 3 for the 1986 and 1993 US tax reforms), subsequent studies have tended to find lower values in the 0.2-0.6 range. However, recent reviews by Giertz (2009) and Saez et al. (2012) have suggested that even the more rigorous recent studies, including those employing a variety of income controls, obtain a wide range of statistically significant ETI estimates. Results from five studies: Goolsbee (1999), Kopczuk (2005), Auten et al. (2008), Giertz (2009) and Saez et al. (2012), covering all major US tax reforms since 1924-25, are reported in Appendix A.

Even where small positive and plausible ETI estimates are reported, they generally form part of a suite of results that include a much wider range of values, including 'wrongly' signed estimates. Partly in response to the varied findings, Giertz (2010) concludes that 'it is incredibly difficult to isolate responses to changes in tax rates from income changes due to a myriad of other complex factors. While flexible income controls are intended to control for both mean reversion and divergence within the income distribution, it is impossible to conclude that these problems are adequately mitigated'. It is thus important to develop improved methods based on new instruments.