The Laffer curve – the hump-shaped relationship between tax rates and government revenue – is a popular relationship from modern economics, one that any student of economics knows. As taxes increase, government revenue first increases but then starts to decline as the reduction in taxable income eventually dominates higher taxes. Recently, Trabbant and Uhlig (2011) study the Laffer curve in the context of the one-sector growth model with a representative household. They find that while there is room for revenue gains in the US economy, several European economies are close to the top of the Laffer curve. However, taxes in most countries are progressive – marginal and average tax rates increase with income. As a result, not only average tax rates, but also who pays and how much, matter for total tax revenue.
In recent crises, calls for closing fiscal deficits have been combined with proposals to shift the tax burden and increase marginal tax rates on higher earners. The message is that additional tax revenue should come from those who earn higher incomes. As top earners account for a disproportionate share of tax revenues and face the highest marginal tax rates, such proposals lead to a natural tradeoff regarding tax revenue. On the one hand, increases in tax revenue are potentially non-trivial given the income generated by high-income households. On the other hand, the implementation of such proposals would increase marginal tax rates precisely where they are at their highest levels, and thus where the individual responses are expected to be larger. Therefore, revenue increases might not materialise.
In a recent paper (Guner et al. 2014), we study these tradeoffs and try to understand how much additional revenue can be raised by making income taxes more progressive.1 We develop an equilibrium life-cycle model with individual heterogeneity and endogenous labour supply. The model framework is by now standard in the macroeconomic and public-finance literature, and in different versions has been used to address a host of issues – see Heathcote et al. (2009) for a survey. Individual heterogeneity is driven by initial, permanent differences in labour productivity and uninsurable productivity shocks over the life cycle. There are different forms of taxation: a non-linear income tax, a flat-rate income tax, a flat-rate capital income tax, and payroll taxes. The first two taxes capture the corporate income tax and income taxes at the state and local level. The non-linear tax schedule is the prime focus of our analysis and aims to capture the salient features of the federal income tax in the US.
As in Benabou (2002), Heathcote et al. (2014) and others, we use a simple tax function to represent federal income taxes in the data.2 The average household’s total taxable income is related to the average tax rate for this household in a way that varies with two parameters: the level of average tax rates and the progressivity of the tax. The parameters are estimated on tax-return micro-data from the Internal Revenue Service for the year 2000 (Statistics of Income Public Use Tax File).
We discipline our model to account for aggregate and cross-sectional facts about the US economy. In particular, our model is consistent with the shares of labour income of top earners. The model also accounts well for the distribution of income taxes paid in the US at the federal level, which is critical for the analysis. Tax liabilities are heavily concentrated in the data – more so than the distributions of total income and labour income. In the data, the first quintile and top quintile of the distribution of income account for 0.3% and about 75% of total revenues, respectively, while the richest 1% accounts for about 23%. The model is consistent with this rather substantial degree of concentration – the bottom quintile accounts for 0.4% of tax liabilities, the top quintile accounts for nearly 78%, while the richest 1% accounts for about 25% of total revenues. Furthermore, the model economy implies an elasticity of taxable income for top earners of about 0.4 – a value in line with available empirical estimates (Saez et al. 2012).
In our baseline exercise we keep the ‘level’ parameter of the tax function at its benchmark value, and vary the parameter governing its curvature or progressivity, τ. For each τ, we compute a steady state in our economy and report on a host of variables. Figure 1 illustrates the effects on government revenues – federal and total – in relation to the benchmark economy. The figure clearly depicts a Laffer-like curve associated to changes in progressivity. Revenue from federal taxes is maximised when τ increases from its benchmark value (0.053) to 0.13. The associated increase in federal taxes is only about 8.4%, or about 0.9% of output in the initial steady state. At τ = 0.13, the increase in overall tax collections – including tax collections at the local and state level and from corporate income taxes – is much smaller: 1.6%. Figure 2 shows why. As τ increases there is a substantial decline in labour supply, the capital stock, and aggregate output across steady states. Aggregate output, for example, declines by almost 12% when τ = 0.13. Hence, the government collects taxes from a smaller economy and while revenue from federal taxes increases by more than 8%, the increase in total tax revenue is substantially lower. As a result, tax collections from all sources are maximised at a lower level of progressivity (at τ = 0.10), and the associated increase in total tax revenue is just 2.2%.
Figure 1. Federal income tax and total tax revenue
Figure 2. Labour supply, capital, and output
Magnitude of tax rates
How large are the required changes in average and marginal rates resulting from the revenue-maximising shifts in progressivity? Table 1 shows the (effective) average and marginal rates associated to τ = 0.13 and τ = 0.10 for households at the top 10%, 5% and 1%, respectively. As Table 1 shows, in the benchmark economy, average rates are about 15.7%, 17.4%, and 20.7% for richest 10%, 5% and 1% of households, respectively. The corresponding marginal rates amount to 20.2%, 21.7%, and 24.9%. At maximal revenue for federal income taxes (when τ = 0.13), average rates at the top levels are 24.1%, 27.5%, and 34.4%, and marginal rates amount to 33.9%, 36.9%, and 42.9%, respectively. In other words, for the richest 5% of households in our economy, revenue maximisation dictates an increase in average rates of nearly ten percentage points, and an increase in marginal rates of about fifteen percentage points. Hence, revenue-maximising tax rates are non-trivially larger than those in the benchmark economy. From this perspective, the concomitant large effects on aggregates are not surprising.
Table 1. Tax rates at the benchmark and higher levels of progressivity
The message from these findings is clear. There is not much available revenue from revenue-maximising shifts in the burden of taxation towards high earners – despite the substantial changes in tax rates across income levels – and that these changes have non-trivial implications for economic aggregates.
To conclude, it is important to reflect on the absence of features in our model that would make our conclusions even stronger. First, we have abstracted away from human capital decisions that would be negatively affected by increasing progressivity. Since investments in individual skills are not invariant to changes in tax progressivity, larger effects on output and effective labour supply – relative to a case with exogenous skills – are to be expected. Second, we have not modelled individual entrepreneurship decisions and their interplay with the tax system. Finally, we have not modelled a bequest motive, or considered a dynastic framework more broadly. In these circumstances, it is natural to conjecture that the sensitivity of asset accumulation decisions to changes in progressivity would be larger than in a life-cycle economy. Hence, even smaller effects on revenues would follow.
Badel, A and M Huggett (2014), “Taxing Top Earners: A Human Capital Perspective”, mimeo.
Bakis, O, B Kaymak, and M Poshke (2012), “On the Optimality of Progressive Income Redistribution”, CIREQ Working Paper 10-2012.
Benabou, R (2002), “Tax and Education Policy in a Heterogeneous-Agent Economy: What Levels of Redistribution Maximize Growth and Efficiency?”, Econometrica 70(2): 481–517.
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1 There is a growing literature that studies the aggregate revenue and welfare consequences of higher progressivity. See, among others, Conesa and Krueger (2006), Conesa et al. (2009), Erosa and Koreshkova (2007), Diamond and Saez (2011), Bakis et al. (2012), Heathcote et al. (2014), and Piketty et al. (2014). See also Badel and Huggett (2014) and Holter et al. (2014) for recent analyses closer to our work.
2 Consider a household with total taxable income of I (relative to the mean household income in the economy). The average tax rate for this household is given by t(I) = 1 - λI-τ. Two parameters, λ and τ, govern the level of average tax rates and the progressivity of the tax function, respectively. If τ then taxes are proportional and given by 1 - λ. If, on the other hand, τ> 0, taxes are progressive. In particular, higher values of τ imply higher degrees of progressivity. To set values for λ and τ, we use the estimates of effective tax rates for this tax function in Guner et al. (2014). From IRS data, we estimate the key parameter governing progressivity (τ) to equal 0.053.