The recent massive expansion of public debt around the world during the Great Recession raises the question how much debt a government can maximally service by raising the level of taxes. Or, to phrase this classic public finance question differently, how much additional tax revenue can the government generate by increasing income taxes? The idea that total tax revenues are a single-peaked function of the level of tax rates dates back to at least Arthur Laffer, and the plot of total tax revenues against the average tax has been known as the ‘Laffer curve’ ever since.
Deriving the Laffer curve for a specific economy (a country or collection of countries) is difficult on purely empirical grounds, since the time-series variation of the tax rate for a given country is typically small, and might not include tax rates close to the one maximising tax revenue. Therefore economists have typically relied on using models of the macroeconomy as laboratories in which the level of taxes can be varied in counterfactual experiments and the relationship between tax rates and tax revenues can be traced out, either analytically or with the use of computer simulations.
In a recent influential paper, Matthias Trabandt and Harald Uhlig (2011) numerically characterise Laffer curves for the US and the EU14. They find that the peak of the labour income tax Laffer curve in both regions is located between an average tax rate of 50% and 70%, depending on the country and the parameterisations of the model. They also find that the US can increase labour income tax revenues by 30%, and the EU14 only by 8%. According to their analysis, some of the European countries, such as Denmark and Sweden, find themselves very close to the top of their respective Laffer curves, and can increase their labour income tax revenues only by 1%.
The work of Trabandt and Uhlig (2011) is carried out in the context of the classical workhorse model in macroeconomics, the ‘representative agent’ model, where the economy consists of one representative household facing a flat labour income tax schedule, that is, the tax rate is independent of the level of income. However, in all OECD countries there is substantial heterogeneity across households in income, wealth, and other relevant economic characteristics. Furthermore, as we document below, all OECD countries have progressive tax schedules in which the average tax rate is higher for higher earners.
Our research (Holter et al. 2014) investigates how tax progressivity and household heterogeneity impacts the Laffer curve. We argue that a more progressive labour income tax schedule significantly reduces the maximal amount of tax revenues a government can raise and that certain (but not all) dimensions of household heterogeneity crucially affect the shape of the Laffer curve.
Measuring tax progressivity in OECD countries
To approximate the actual labour income tax system, we use a parsimonious functional form proposed by Benabou (2002). It has only two parameters, one of which (θ0) controls the tax level, while the other one (θ1) controls tax progressivity. We use the data from the OECD’s online tax calculator to estimate such tax functions for different types of households (single, married without children, with children), and obtain for each country a ‘progressivity index’, a weighted average value of the progressivity parameter (θ1), using the shares of household types in the US as the weights. Column 2 in Table 1 shows the values of this progressivity index, whereas column 3 normalises them so that it is equal to 1 for the US. The table shows that there is considerable cross-country variation in labour income progressivity, with countries such as Japan, Switzerland, Portugal, and the US appearing at the low end of the progressivity spectrum, while the Nordic countries, Ireland, and the Netherlands finding themselves at the high end of this spectrum.
Table 1. Tax progressivity in the OECD, 2000-07
Our model
The impact of tax progressivity is closely linked to the degree of household heterogeneity, since under progressive taxes heterogeneous workers will face different average and marginal tax rates. At the same time, the answer to our question is closely connected to the individual (and then properly aggregated) response of labour supply to taxes. The microeconometric literature, as surveyed e.g. by Keane (2011), has found that both the intensive and extensive margins of labour supply (the latter especially for women), life-cycle considerations, and human capital accumulation are important determinants of these individual responses. We therefore develop a life cycle model with uninsurable idiosyncratic wage risk and endogenous human capital accumulation, as well as labour supply decisions along the intensive and extensive margins. In the model, households make a consumption–savings choice and decide on whether or not to participate in the labour market (the extensive margin), how many hours to work conditional on participation (the intensive margin), and thus how much labour market experience to accumulate (which in turn partially determines future earnings capacities).
Why would we think that progressivity matters?
Why does the degree of tax progressivity matter for the government’s ability to generate labour income tax revenues in an economy characterised by idiosyncratic wage risk and other sources of household heterogeneity? There are several, potentially opposing effects of the degree of tax progressivity on the response of tax revenues to the level of taxes. Keeping hours worked constant, with higher tax progressivity the government collects more tax from high earners and less tax from low earners. However, changes in tax progressivity typically affects hours worked of both groups. First, increasing tax progressivity induces differential income and substitution effects on the workers in different parts of the earnings distribution. In addition, the presence of an extensive margin typically leads to higher labour supply elasticity for individuals with low potential wages that decide whether or not to participate in the labour market. A more progressive tax system with relatively low tax rates around the participation margin, where the labour supply elasticity is high, may in fact help to increase revenue if more of these agents decide to participate in the labour market.
Furthermore, in a life cycle model the presence of labour market risk will lead to higher labour supply elasticity for older agents due to a strong precautionary motive for younger agents (see Conesa et al. 2009). Because of more accumulated labour market experience, older agents have higher wages. Due to this effect a more progressive tax system may disproportionately reduce labour supply for high earners and lead to a reduction in tax revenue. Third, when agents undergo a meaningful life cycle, more progressive taxes will reduce the incentives for young agents to accumulate labour market experience and become high (and thus more highly taxed) earners. This effect will reduce tax revenues from agents at all ages as younger households will work less and older agents will have lower wages (in addition to working less). Finally, when human capital accumulation is modelled as years of labour market experience (learning by doing), as we do in our work, the life cycle human capital effect is counteracted by a greater short-term benefit (higher net wages in the short run) from accumulating human capital. Thus the question of how the degree of tax progressivity impacts the tax level–tax revenue relationship (i.e. the Laffer curve) is a complex and quantitative one.
What we find
We consider two alternative scenarios. According to the first, the government transfers the additional tax revenues as a lump-sum payment back to the households. According to the second, the government increases the stock of outstanding government debt and uses the additional tax revenues to pay the interest. The key difference between these thought experiments is that in the first, the lump-sum rebate induces a negative income effect on labour supply, whereas in the second experiment it doesn’t. The latter experiment also determines the maximally sustainable long run debt level in the economy.
Figure 1 plots Laffer curves for the US economy for varying degrees of progressivity under our first, lump-sum rebate scenario. The x-axis displays the average tax rate and total tax revenues (as % of the current US scenario). The green line represents the actual current US progressivity and the vertical line at 17% the current average US tax rate. Holding tax progressivity constant (that is, climbing along the green line), we see that the US is still relatively far from the peak of its Laffer curve – with the current progressivity of the tax system, tax revenues can be increased by about 56% if the average tax rate on labour income is raised from 17% today to about 58%.
Figure 1. The impact of tax progressivity on the Laffer curves (holding debt-to-GDP constant)
We also see from Figure 1 that the design of the tax system has a considerable impact on the Laffer curve – a key finding of our work. Under a flat tax system (the black line) the maximal revenue that could be raised is about 6% higher than its counterpart under current US progressivity. A tax schedule with current US progressivity in turn can raise 7% more revenue than a tax system that is twice as progressive, similar to the actual tax system in Denmark (which, according to our estimates, has the most progressive tax system among our OECD sample – see Table 1).
The left panel of Figure 2 shows the Laffer curves for the US economy under our second scenario, where extra tax revenues are used to service a larger government debt. Comparing Figure 2 to Figure 1 we observe that the peak of the Laffer curve is substantially higher when, instead of redistributing extra revenues to households, the government uses them to service additional government debt. Relative to the first scenario, the absence of a negative income effect on labour supply induces higher output and a larger tax base, despite the debt crowding-out of productive capital. The right panel of Figure 2 plots the maximum sustainable debt (as a fraction of benchmark US GDP) against the average tax rate for varying degrees of progressivity. For its current choice of progressivity (the green line), the US can sustain a debt burden of about 330% of its benchmark GDP, by increasing the average tax rate to about 42%. Thus, according to our findings the US is currently still nowhere close to its maximally sustainable debt levels, perhaps consistent with the fact that the risk premium on US debt in international bond markets is still quite low, although in recent years (after the time periods we use in the calibration) US debt has risen to 120% of GDP. From the right panel of Figure 2 we also observe that larger public debt can be sustained with a less progressive tax system. Converting to a flat tax system (the black line) increases the maximum sustainable debt to more than 350% of benchmark GDP, whereas adopting Danish tax progressivity lowers it to less than 250% of benchmark GDP.
Figure 2. Tax revenue and maximum sustainable debt level by tax level and progressivity
Summing up
Our work argues that the extent of tax progressivity is an important determinant of maximal tax revenues and maximally sustainable debt levels in economies characterised by household heterogeneity. This of course does not imply that progressive income taxation is an undesirable policy choice; it might be called for to provide social insurance or to aid in generating a socially more desirable after-tax income distribution. What our paper has tried to quantify are how the limits to the size of the government (measured alternatively by tax revenues or debt) depend on this choice.
References
Benabou, R (2002), “Tax and Education Policy in a Heterogeneous Agent Economy: What Levels of Redistribution Maximize Growth and Efficiency?”, Econometrica 70: 481–517.
Conesa, J C, S Kitao, and D Krueger (2009), “Taxing Capital? Not a Bad Idea After All!”, American Economic Review 99: 25–48.
Holter, H, D Krueger, and S Stepanchuk (2014), “How Does Tax Progressivity and Household Heterogeneity Affect Laffer Curves?”, CEPR Discussion Paper 10259.
Keane, M P (2011), “Labor Supply and Taxes: A Survey”, Journal of Economic Literature 49: 961–1045.
Trabandt, M and H Uhlig (2011), “The Laffer Curve Revisited”, Journal of Monetary Economics 58: 305–327.
