4.2 Incorporating Income Dynamics

A partial solution to deal with potential biases was suggested by Saez et al. (2012, p. 27-8) , whereby, 'in situations with mean reversion, it is useful to include episodes of both increases and decreases in tax rates for identification, as mean reversion creates biases in opposite directions in the case of tax increases versus tax decreases'. Saez et al. (2012, p. 28) also find that 'panel regression estimates of taxable income responses are sensitive to the choice of instrument for the marginal tax rate', such that 'standard methods do not control adequately for mean reversion'. Indeed, as argued further below, these standard methods cannot capture more general features of income dynamics, and hence their ability to separate 'tax reform only' from 'non-tax induced' changes in income is questionable, especially given the potential for various, reform-specific, biases described above.

The key problem with the standard instrument is that it represents the simplest approximation of income dynamics, namely no change in (real) reported incomes in the absence of tax reform. The alternative approach proposed here involves modelling taxpayers' income dynamics using annual income data that, by construction, are unaffected by tax reform.

The method captures any exogenous regression to the mean and serial correlation in relative income changes over a number of years during which there are no tax changes, to yield predicted values of future incomes, given current and past income levels. This yields a conditional probability distribution of income for each future year and taxpayer. Using this information allows construction of two possible marginal tax rate instruments. First, the mean income from the conditional income distribution, given initial income for each taxpayer, for any post-reform year, j, E(y_j), can be obtained (individual subscripts are suppressed). For this expected mean income, the associated tax rate is obtained from the post-reform tax code. This instrument is labelled τ_E(y)^*.

Alternatively, the complete probability distribution of incomes for year j for each taxpayer can be used in conjunction with the post-reform tax code to obtain the set of tax rates associated with each income level. Using the full conditional income distribution to weight each tax rate appropriately yields an 'expected marginal tax rate' after reform which more fully incorporates information on income dynamics. This expected tax rate instrument is labelled τ_E(τ)^*.

In terms of Figure 1, a probability distribution of income, centred for example on y₂, potentially includes a wide dispersion of incomes with associated tax rates t_k and t_k-1, as well as t_k+1 and any other higher or lower rates. Hence, whereas the set of 'expected income' based tax rates, τ_E(y)^*, includes only the discrete set of rates specified in the tax schedule, 'expected tax rates', τ_E(τ)^*, can take a wide range of values, reflecting the income-weighting of each discrete rate.