Optimal Capital Income Taxes in an Infinite-lived Representative-agent Model with Progressive Tax Schedules Been-Lon Chen Academia Sinica Chih-Fang Lai * National Taiwan University February 2014 Abstract In an infinite-lived representative-agent model with linear capital and labor income taxes, the influential studies by Chamley (1986) and Judd (1985) showed that the optimal capital tax should be zero in the long run. Our paper shows that in the same model, if the capital income tax rate is sufficiently progressive, the optimal capital tax is positive in the long run. Our findings justify a system of graduated marginal income tax rates adopted in most of the developed countries since the second half of the 19 th century. Keywords: one-sector model, optimal capital income taxation, non-linear tax. JEL classification: E62; H21, H22, O41 Earlier versions have benefitted from discussions with Yili Chien, Jang-Ting Guo and Kevin Lansing. Corresponding address: Been-Lon Chen, the Institute of Economics, Academia Sinica, 128 Academia Road Section 2, Taipei 11529, TAIWAN. Phone: (886-2)27822791 ext. 309; Fax: (886-2)2785-3946; email: bchen@econ.sinica.edu.tw. *Department of Economics, National Taiwan University, 21 Hsu-Chow Road, Taipei 10055, TAIWAN; email: d96323001@ntu.edu.tw.
1 Introduction Capital income is taxed in the US and the tax rate is progressive. Corporate profits in the US are first taxed at a flat rate of 40% at a corporate level. Then, when these profits are distributed as dividends, the income is taxed again at progressive rates from 10% to 35% at the household level. In fact, most developed countries have adopted comprehensive income tax systems with graduated marginal tax rates that date back as early as the second half of the 19 th century. 1 With progressive income taxes in most of the developed countries, an important question in tax policy analysis is whether it is optimal to tax capital income. In an infinite-lived representative-agent model with only linear capital and labor income taxes, Chamley (1986) and Judd (1985) found that, in the long run, the optimal capital tax should be zero. 2 The purpose of our paper is to show that, in the same model, if there is an income tax system with progressive capital income taxes, a positive capital tax is optimal in the long run. Our result is not only in sharp contrast to the zero capital tax result of Chamley (1986) and Judd (1985), but also particularly lends support to a system of graduated marginal income tax rates adopted in most of the developed countries since the second half of the 19 th century. Our result is understood as follows. In the long run, the Ramsey planner chooses capital such that the time-preference rate equals the post-tax marginal product of capital, which includes post-tax returns to capital, plus gains in utility from increases in capital income tax revenues adjusted by the social shadow price of capital, minus losses in utility from decreases in post-tax returns to capital due to progressive tax rates adjusted by the social shadow price of capital. Moreover, in the long run the household chooses capital such that the time-preference rate equals the post-tax marginal product of capital from the household s perspective, which includes only post-tax returns to capital. For the Ramsey planner s choice to be consistent with the household s choice, gains in utility from increases in capital income tax revenues minus losses in utility from decreases in post-tax returns to capital due to progressive tax rates must be zero. In the case of linear capital income tax rates, there is no loss of utility from decreases in post-tax returns to capital arising from progressive tax rates and thus gains in utility from increases in capital income tax revenues must be zero, thereby implying a zero capital tax in the long run. Yet, in the case of progressive capital tax rates, there is a loss in utility due to decreases in post-tax returns to capital arising from progressive tax rates. In this case, under a zero capital tax rate, if the schedule of the capital income tax rate is sufficiently progressive, the gain in utility from increases in capital income tax 1 According to Saez (2013), the German states such as Prussia and Saxony introduced the modern income tax during the second half of the 19th century, Japan in 1887, the UK in 1909, the US in 1913 and France in 1914. 2 Several studies revisited the issue by relaxing key assumptions and proved the zero capital tax result to be robust. See Lucas (1990), Jones et al (1993, 1997), Chari et al. (1994), Chari and Kehoe (1999) and Atkeson et al. (1999). 1
revenues is smaller than the loss in utility due to decreases in post-tax returns to capital arising from progressive tax rates. Then, the post-tax marginal product of capital from the Ramsey planner s perspective is smaller than its counterpart from the household s perspective. As a result, the modified golden rule condition indicates that the level of capital chosen by the Ramsey planner is smaller than the level of capital chosen by the household and there is over-accumulation of capital from the social perspective. An increase in capital income tax rates enlarges the increase in income tax revenues and decreases the loss in utility due to decreases in post-tax returns to capital arising from progressive tax rates. Therefore, it is optimal to tax capital income. Our paper is valuable as it justifies a positive capital tax even if there are no inherent distortions in an economy. Existing infinite-lived representative-agent models relied on inherent distortions to obtain a positive flat capital tax. 3 To the best of our knowledge, the only exceptions are Lansing (1999), Chen and Lu (2013) and Lu and Chen (2013). First, Lansing (1999) studied the Judd (1985) model and found a long-run positive capital tax, but his result requires a logarithmic capitalists utility and a zero government debt issue. Next, in a two-sector model with physical and human capital, Chen and Lu (2013) showed that the long-run capital tax is positive, but their result involves a specific learning technology wherein agent s learning time and human capital are inseparable as it was in Lucas (1988) and Bond, Wang and Yip (1996), as opposed to the learning technology in Lucas (1990). Finally, in an infinite-lived representative-agent model, Lu and Chen (2013) also found a long-run positive capital tax, but their result is obtained under a fixed share of government expenditure in output as opposed to fixed government expenditure. Moreover, these three existing models all study linear capital and labor income taxes. Our model contributes to these existing studies in that it obtains a positive capital income tax rate without relying on any one assumption of a zero debt issue, a particular form of preferences and technologies, and a fixed share of government expenditure in output. 4 Our paper also add values to existing models that explored optimal progressive capital income taxes put forth by Saez (2013), Conesa et al. (2009) and Farhi et al. (2012). First, Saez (2013) analyzed optimal progressive capital income taxation in an infinite-horizon heterogeneous-agent model and found that progressive capital income taxation is more effective than linear taxation to redistribute wealth. Our model is important in that it yields a positive capital tax in the long run, but the Saez model 3 For infinite-lived representative-agent models that found positive optimal capital taxes based on inherent distortions, see Guo and Lansing (1999) and Chen (2007) which incorporated market imperfections and productive public capital, and Aiyagari (1995) and Chamley (2001) which considered credit constraints. 4 Another strand of the literature has used overlapping generations (OLG) models to study optimal capital income taxes. In the OLG model without bequests, when taxes are linear, capital taxes are in generally positive in the long-run, simply because capital accumulation is due uniquely to life-cycle savings for retirement. See Atkinson and Sandmo (1980), Garriga (2001) and Erosa and Gervais (2002). 2
retains the long-run vanishing capital tax result as in Chamley (1986) and Judd (1985). 5 Next, in an OLG model with linear capital and progressive labor income taxes wherein agents are heterogeneous in different initial endowment and abilities, Conesa et al. (2009) uncovered that the optimal capital tax is positive when there are borrowing constraints. Our model augments values to Conesa et al. (2009) in that it finds optimal progressive capital income taxes without assuming heterogeneous agents and borrowing constraints. Finally, in another OLG model with non-linear taxation of labor and capital income and political economy constraints, Farhi et al. (2012) discovered that it is optimal to tax a progressive capital income tax when policies are not committed, but the capital income tax is zero with a non-linear tax on labor income when policies are fully committed. Our model adds values to Farhi et al. (2012) in that we find a progressive capital income tax when policies are fully committed. Moreover, all these three papers introduce heterogeneous agents and there is a tension between equity and efficiency of capital accumulation. 6 Even though the efficiency of capital accumulation is the only tension in our model, we find that a positive progressive capital tax is optimal. Finally, we also study a quantitative version of our model that is calibrated to the system of progressive capital and labor income taxes in the US with initial average capital and labor income tax rates equal to those in the current tax code. We find that if the tax schedule is sufficiently progressive, the optimal capital tax rate is positive. In the baseline parameterization with a 30% average capital tax rate and a 20% average labor tax rate in the US during 1960-2007, our revenue-neutral factor income tax incidence exercises indicate that the optimal income tax features a slightly decreasing average capital income tax rate and a largely decreasing average labor income tax rate. Such a tax reform increases consumption, labor supply and capital accumulation and lead to a considerable welfare gain that is larger than those obtained in existing literature. By changing the degree of the tax progressivity, we find that the optimal capital tax rate is increasing in the degree of the tax progressivity. We organize this paper as follows. In Section 2, we set up a model with non-linear factor income tax schedules and analyze households optimizations. In Section 3, we study the optimal factor income tax incidence in the Ramsey second-best problem. Finally, concluding remarks are offered in Section 4. References 5 There are infinite-lived agent models that incorporated progressive income taxes but did not analyze optimal capital taxes. See Carroll and Young (2009) which studied non-degenerated long-run distribution of capital holdings in a heterogeneous-agent model. See also representative-agent models by Guo and Lansing (1998) which explored the effect of the tax progressivity on the dynamic stability and by Li and Sarte (2004) which analyzed the effect of the tax progressivity on long-run economic growth. 6 See also the heterogeneous-agent model by Benabou (2002) that constructed a model with human capital, instead of physical capital, and studied non-linear taxation of income and the heterogeneous-agent model by Farhi et al. (2012) that explored the related issue of non-linear estate taxation. 3
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