On January 24, 2019 I have successfully defended my PhD at the Erasmus University Rotterdam. My dissertation is entitled “Of Machines and Men: Optimal Redistributive Policies under Technological Change“. If you are curious what it is all about, here is the introduction.


Robots are taking over jobs, self-driving taxis are roaming the streets, and artificial intelligence recommends what to buy and what to do. Hardly a day goes by without news about advances in some technology. Undoubtedly, technology is one of the main forces shaping the economy; but while economists agree that technological change drives economic growth, the process is not always smooth. As new technologies emerge, some jobs are being replaced while others are created. Moreover, some people can leverage technology and see their incomes rise, while others see their incomes stagnate or fall. Whether one assembles the parts of a car in a factory, or designs the car using the aid of computers may matter a great deal for whether one gains or loses from technology. Over the last decades, income inequality has gone up in most developed countries (Alvaredo et al., 2017) – and technological change is seen as one of the main drivers (see e.g. Van Reenen, 2011).

Rising inequality poses challenges for societies and governments which care about the distribution of incomes. There is an ongoing debate about how policy should respond to technology-driven inequality. Since skilled workers have benefited disproportionately from technological change, part of the debate centers around education policy. Already in the 1970s, Dutch Nobel Laureate Jan Tinbergen wrote about the ‘race between technological development and education’ (Tinbergen, 1975). Tinbergen argued in favor of raising enrolment into higher education to compress the distribution of wages by raising the supply of skilled workers. More recently, economists Goldin and Katz (2010) have also advocated for higher education subsidies – as well as for more progressive income taxes.

Another part of the debate focuses more directly on technology. Should we tax robots as they take over more and more jobs, as suggested – among others – by Bill Gates? Others who fear ‘technological unemployment’ have argued that societies should introduce a universal basic income. Technological change also plays a role in the concentration of income and wealth at the very top. For example, in 2017 six out of ten of the wealthiest US Americans had made their fortune in software technology.

Given the importance of technology-driven inequality, one might assume that economics – and in particular the field of public finance – would provide guidelines as to which redistributive policies to pursue. However, as it turns out, such advice is scarce. This thesis contributes to the body of research which studies optimal tax and education policy in light of technological change. In doing so, it provides guidance in how to address some of the distributive challenges brought about by technology. In other words, this thesis studies how governments should best respond to the distributional challenges which ‘machines’ bring upon ‘men’ (and women). To arrive at its conclusions, the thesis builds on work in public finance as well as on research about the impact of technology on the labor market.

Technological change and the labor market. Since the 1980s, income inequality has risen substantially in most developed countries (Alvaredo et al., 2017). A variety of factors is behind this development. Economies have become more open to globalization, the importance of unions has declined, and the financial sector has grown (OECD, 2011). However, if asked for the main reason behind rising inequality, many economists would mention technological change (see e.g. Van Reenen, 2011). The reason for this claim is the specific nature of growing income inequality. In particular, since the 1980s the wage gap between individuals with and without a college degree – the so-called skill-premium – increased in most developed countries. Over the same period, more and more people were attending college. To rationalize the rise in the relative price of skill in light of the increase in the relative supply of skill, economists have suggested that skill-demand must have outpaced skill-supply. Moreover, they have attributed the rising demand for skills to technological change (see Katz and Murphy, 1992; Acemoglu and Autor, 2011). This explanation has subsequently become known as skill-biased technical change (SBTC), but the idea can already been found in the writings of Tinbergen (1975).

The concept of SBTC has been formalized in the canonical model by Katz and Murphy (1992). In this model, low-skilled and high-skilled workers are imperfectly substitutable and technological change disproportionately raises the productivity of the high-skilled. Subsequently, economists have studied the role of different technologies as contributors to the rising skill-premium. For example, computer and information technology (ICT) has received a lot of attention (see e.g. DiNardo and Pischke, 1997; Autor et al., 2008, 1998). Almost two decades after the original paper by Katz and Murphy, Acemoglu and Autor (2011) argue that the canonical model of SBTC still does a good job in explaining major changes in the distribution of income since the 1980s. Chapters 2 and 3 of this thesis therefore use the canonical model as building block in modeling the labor market.

Acemoglu and Autor (2011) also discuss that for some other labor market phenomena, the canonical model is too stylized. In particular, it cannot generate the more recent pattern of labor market polarization (see e.g. Goos et al., 2014). Both employment and wages associated with incomes in the middle of the income distribution fell relative to employment and wages at the top and the bottom. This polarization of employment and wages is again partly attributed to technological change. However, the mechanism is different. Rather than complementing skilled workers, it is argued that technology substitutes for labor in routine tasks and complements labor in non-routine tasks. Importantly, routine tasks are often concentrated in occupations in the middle of the income distribution, rather than at the bottom. While a robot might be well-suited to perform the repetitive tasks of a factory worker earning a medium income, the less-earning hairdresser is unlikely to be replaced by a machine anytime soon. Again, the pattern of labor market polarization has been documented for many developed countries (see Goos et al., 2014). Robots fit the description of a technology which substitutes for routine labor and complements non-routine labor. Chapter 4 of this thesis which studies the ‘Optimal Taxation of Robots’ is therefore based on a model of labor market polarization. Empirical research confirms that those workers who lose most from the introduction of robots are concentrated in routine occupations (Acemoglu and Restrepo, 2017).

Having given an overview of the impact of technology on the labor market and the distribution of income, I now turn to the strand of economics which builds the second foundation for this thesis.

Public Finance. As a subfield of public economics, public finance is concerned with government policies, both on the revenue as well as on the expenditure side. Central to the study of such policies is their impact on the income distribution as well as on economic efficiency. For example, by taxing individuals’ incomes progressively, a policy maker can achieve a more equal distribution of incomes. However, taxes usually distort the decisions of individuals and firms, which leads to a loss of economic efficiency. The government thus redistributes with a ‘leaky bucket’. For example, taxing individuals’ labor income distorts incentives to work; and taxing machines makes firms want to substitute to other inputs.

The positive branch of public finance is concerned with the effect of actual government policies on the economy. In contrast, this thesis is written in the tradition of normative welfare economics. It builds on the seminal work of – among others – Pigou (1928), Musgrave (1959), Mirrlees (1971), Sheshinski (1972), Diamond and Mirrlees (1971), Atkinson and Stiglitz (1976), Diamond (1998), and Saez (2001). Normative welfare economics studies how governments wishing to maximize social welfare should design corrective and redistributive policies such as to balance the tradeoff between equity and efficiency. Social welfare is thereby defined as an aggregation over individual utilities. When maximizing social welfare, governments are restricted by budget constraints. Moreover, they usually have a restricted set of policy instruments at their disposal, which adds additional constraints.

For example, a government may be able to tax individuals’ incomes non-linearly, but may neither observe individual work effort nor ability, which rules out individualized lump-sum taxes. Marginal income taxes then distort incentives to supply labor. When designing the tax systems, such incentives need to be taken into account – which in this example gives rise to the Mirrlees (1971) model of optimal non-linear income taxation. Chapters 2 and 4 are both extensions of this model.

Chapter 2 studies how in an economy in which inequality is driven by SBTC, governments should optimally set nonlinear income taxes. Moreover, since income taxes are allowed to depend on an individual’s education, the chapter also addresses education policy. Chapter 4 introduces another instrument: a tax on robots. It asks what this tax on robots should be at the optimum, provided that the government can tax income non-linearly.

Suppose, in contrast, that the government can only tax income linearly, for example, because it cannot observe individual incomes, but only aggregate income. In this case, individuals do not have an incentive to pretend to be of lower ability – and maximization of social welfare is only subject to a budget constraint, as in Sheshinski (1972). Chapter 3 is an extension of this framework. It merges the model of linear income taxation with the canonical model of SBTC (Katz and Murphy, 1992; Acemoglu and Autor, 2011) to study how tax and education policy should optimally respond to SBTC. Having related my thesis to the the literature, I now give a more detailed discussion of the chapters.

The Chapters

Optimal Taxation of Income and Human Capital and Skill-Biased Technical Change. In Chapter 2 of this thesis, Bas Jacobs and I study how taxes on income and human capital should respond to SBTC. The chapter is motivated by the literature on SBTC (see e.g. Katz and Murphy, 1992; Acemoglu and Autor, 2011), as well as by the unresolved debate how to best respond to rising skill-premia driven by technical change. For example, Tinbergen (1975) has argued in favor of promoting higher education to compress wages and reduce inequality. Goldin and Katz (2010) also support stronger investment in education. In addition, they favor a more progressive income tax system.

In our model, individuals differ in their productivity and make two decisions: how much to work, and whether to enroll in higher education. Attending higher education is costly, so that only individuals who are sufficiently productive choose to invest in education. Wages are endogenous, and thus depend on the supply of low and high-skilled labor. The government maximizes social welfare by optimally setting non-linear income taxes, which may be conditioned on education. We interpret the difference in taxes paid by the marginally high-skilled and the marginally low-skilled as net tax on human capital.

We derive a number of results. First, for a given level of skill-bias, we find that marginal tax rates follow the Mirrlees (1971) formula, despite tax schedules being allowed to depend on education. The marginally low-skilled and marginally high-skilled individual face the same marginal tax rate. The optimal tax schedule can thus be implemented with a single non-linear tax schedule on labor earnings and an additional education subsidy (or tax).

Second, we show that in response to SBTC, marginal tax rates increase especially in the middle of the income distribution, around the income of the marginally high-skilled. Intuitively, SBTC raises income inequality in particular between skill-groups, and hence around the marginally high-skilled. To redistribute more from the high- to the low-skilled, marginal tax rates increase.

Third, we find that there are two reasons for which education is subsidized or taxed: first, education is subsidized to partly offset distortions from income taxation (see Bovenberg and Jacobs, 2005); second, education is taxed to redistribute from the high- to the low-skilled to reduce inequality. We show that on net, education is taxed.

Fourth, whether the net tax on education decreases or increases with SBTC is theoretically ambiguous. The reason is that while inequality increases due to SBTC, which calls for a higher net tax on education, income-tax distortions of education might increase as well, calling for a lower net tax on education.

Fifth, we find that the optimal tax system does not exploit general-equilibrium effects on the wage distribution for redistribution. Intuitively, any indirect redistribution which could be achieved by inducing wage compression can be achieved directly by the tax system. With education-specific taxes, the argument for subsidizing education in order to compress wages, as suggested by Tinbergen (1975), disappears.

Lastly, we simulate the impact of SBTC on optimal taxes numerically. To do so, we first calibrate our model to the US economy, using data from the Current Population Survey. Then, we compute optimal policy with and without skill-bias. We confirm that marginal tax rates increase under skill-bias in particular in the middle of the income distribution, whereas marginal tax rates fall towards the top. Overall, the tax system becomes more progressive. The net tax on education falls with skill-bias, hence education is subsidized more. We attribute the latter finding to income-tax distortions on education becoming more important, which overturns the push for higher net taxes on education due to increased inequality. Our results are in line with Goldin and Katz (2010) who argue that in response to SBTC income taxes should become more progressive, while education subsidies should be raised. However, education subsidies are not raised to compress the wage distribution, but in response to higher education-distortions of income taxation.

Optimal Linear Income Taxation and Education Subsidies with Skill-Biased Technical Change. In Chapter 3 of my thesis, Bas Jacobs and I again turn to the question how redistributive policy should respond to SBTC. The setup of the labor market follows that of Chapter 2. However, the government is now assumed to have access to a different set of tax instruments: a linear tax on labor income and a subsidy on education. This Chapter thus complements Chapter 2. In restricting the government to linear taxes, the Chapter is less realistic than Chapter 2. However, by assuming that income taxes may not be conditioned on education, it is a more realistic description of reality.

First, we find that for a given level of skill-bias, the optimal linear income tax trades off the benefits of income redistribution against labor-supply distortions and against distortions of enrolment in higher education. The total distributional benefits of income taxation consists of two components: direct distributional benefits, and indirect distributional losses. The direct distributional benefits arise from reductions in inequality due to income redistribution. However, by redistributing income, the government also lowers incentives to enrol in higher education. As the supply of high-skilled falls, the skill-premium rises. This wage decompression leads to distributional losses. The optimal education subsidy faces a similar tradeoff. For equity reasons, education should be taxed on a net basis, since the high-skilled earn more than the low-skilled. However, taxing education distorts enrolment in higher education downward, which has efficiency costs. Since the income tax also distorts enrolment in higher education downward, the education subsidy is used to alleviate education distortions (see also Bovenberg and Jacobs, 2005). Finally, like income taxation, the education subsidy has indirect effects on the wage distribution. By encouraging enrolment in higher education, and thereby increasing the relative supply of high-skilled workers, the skill-premium can be compressed.

Second, we study the impact of SBTC on optimal policy. This impact depends on changes in three determinants of optimal taxes and subsidies: direct distributional benefits, education distortions, and wage (de)compression effects. Analytically, the effect of SBTC on the three effects is ambiguous. We therefore calibrate our model to the US economy and simulate the impact of SBTC. We find that the income tax rate increases with SBTC from about 37% to 39%. Moreover, we find that education is subsidized on a net basis to exploit wage compression. Education is thus distorted upward. However, with SBTC, the subsidy rate falls from 60% to below 50%, whereas the net tax on education as a fraction of GDP increases. We attribute the increasing tax rate to rising distributional benefits. In addition, upward distortions of education becoming more severe, which also pushes towards higher taxes. In contrast, wage decompression effects also become more important with SBTC, which dampens the tax increase. The fall in the subsidy rate can be explained by rising distributional benefits of taxing education, as well as by rising upward distortions of education. These effects dominate over rising wage compression effects, which dampen the drop in the subsidy rate.

The wage (de)compression effects do not play a role in Chapter 2, since there, marginal tax rates could be conditioned on education. In the realistic case in which such conditioning is not possible, wage (de)compression effects become a central feature of the tax system. Most notably, while in Chapter 2 education is taxed on a net basis, we now find a net subsidy on education to be quantitatively optimal. Our findings that tax and education policy should exploit general-equilibrium effects on the wage distribution are in line with Tinbergen (1975), Dur and Teulings (2004), and Jacobs (2012).

Moreover, like in Chapter 2, the tax system becomes more progressive in response to SBTC, and the net tax on education declines. However, the subsidy rate falls, and the net tax as fraction of GDP increases. In contrast to Chapter 2, Chapter 3 does thus not find support for the argument to increase education subsidies in response to SBTC, as brought forward by Tinbergen (1975) and Goldin and Katz (2010). We attribute the different response of education subsidies across Chapters 2 and 3 to the presence (respectively, absence) of the skill-dependency of income taxes. Since real-world tax systems do not feature skill-dependent income taxes, our results suggest that education subsidies should decline with SBTC in response to increasing inequality.

Optimal Taxation of Robots. The final chapter of this thesis addresses the question whether and how robots should be taxed. The chapter is motivated by public concerns that automation replaces some jobs and raises inequality (see e.g. Ford, 2015; Brynjolfsson and McAfee, 2014; Frey et al., 2017) – and by a debate about the best policy response.

In the chapter, I study the optimal taxation of robots and labor income in a model in which robots substitute for routine labor and complement non-routine labor. I find that it is generally optimal to distort the use of robots. The robot tax is used to alleviate income-tax distortions of labor supply. Interestingly, robots may be either taxed or subsidized. In quantitative simulations for the US, I find a positive and sizable optimal robot tax for the short-run with fixed occupations. However, the welfare gains from introducing a robot tax are negligible. In the medium-run with occupational choice, the robot tax is reduced and approaches zero as the price of robots falls.

To reach these conclusions, I study a model in which individuals decide how much and in which occupations to work: manual non-routine, routine, or cognitive non-routine. I then characterize the optimal robot tax in the presence of an optimal non-linear income tax. The optimal robot tax exploits that robots affect wages in different occupations differentially. Specifically, a tax on robots increases relative demand for routine workers, which raises their wage relative to non-routine workers. Since routine workers mostly earn medium wages, the wage gap between cognitive non-routine workers – who earn higher wages – and routine workers is reduced. Such wage compression alleviates income-tax distortions of labor supply, since it makes it less tempting for cognitive workers to work less and earn the income of routine workers. As a result, the government can redistribute more, which raises welfare. However, at the same time the wage gap between routine workers and manual non-routine workers increases, which worsens income-tax distortions of labor supply, making the sign of the robot tax theoretically ambiguous. With continuous and overlapping wage distributions, and with occupational choice, a tax on robots has additional effects on wages, and thus on income-tax distortions on labor supply, which may dampen the effectiveness of the robot tax.

To study the optimal robot tax quantitatively, I calibrate the model to the US economy, using data on wages and occupational choice from the Current Population Survey. Moreover, to capture the effect of robots on the labor market, I build on evidence from Acemoglu and Restrepo (2017). I then compute optimal policy for two scenarios: in the short-run, occupations are fixed, whereas in the medium-run, individuals can change occupation in response to the introduction of a robot tax. The short-run tax on the stock of robots is 4%, while it is 0.4% in the medium-run. However, in both cases, the welfare gains from introducing a robot tax are negligible. I also study the effect of a drop in the price of robots. While in the short-run, the robot tax remains in the same order of magnitude, in the medium-run it approaches zero. The reason is that individuals move out of routine occupations, as robots become cheaper. A tax on robots can then not anymore achieve wage compression, and becomes obsolete. I conclude that in light of the negligible welfare gains, Chapter 4 does not provide strong support for a tax on robots.


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