Macroeconomic Implications of Tax Cuts for the Top Income Groups:

Macroeconomic Implications of Tax Cuts for the Top Income Groups: 1960-2010 Barış Kaymak Université de Montréal and CIREQ Markus Poschke McGill University and CIREQ Preliminary and Incomplete Please do NOT distribute. Abstract Over the last 40 years the US tax system went through striking changes that considerably reduced the progressivity of the system. This resulted in a dramatic reduction of effective tax rates on top income groups. This paper investigates the macroeconomic repercussions of this change in tax policy, particularly for the distributions of income, wealth, consumption and welfare. J.E.L. Codes: E32, J31, J41 Keywords: Tax Progressivity, Income Inequality, Wealth Inequality, Top 1% Department of Economics, Université de Montréal, C.P. 6128 succursale Centre-ville, Montréal, QC H3C 3J7, e-mail: baris.kaymak@umontreal.ca Department of Economics, Mcgill University 1

1 Introduction The progressivity of the US. tax system hit a record high during the mid-twentieth century, and has declined considerably since 1980s. The decline in the tax rates was most dramatic for the top income groups. The marginal tax rate on the top income tax bracket was close to 90% in 1960, compared to 35% in 2010 (Piketty and Saez, 2007). The average tax rate for the top 0.1% of the income distribution was 57% in 1960, compared to 34% in 2004 (Piketty and Saez, 2007). These changes in the tax policy have been accompanied by a rise in income inequality, leisure inequality (Aguiar and Hurst, 2007), consumption inequality (Aguiar and Bils, 2011), and wealth inequality (Wolff, 1998; Heathcote, Perri, and Violante, 2010). In this paper we ask the following question: To what extent is the decline in the progressivity of US. tax policy responsible for the inequality trends in the US? The prominent view of these trends is that the technological advances in the second half of the twentieth century accentuated the dispersion in productivity across workers, leading to higher income inequality. It is only expected that higher income inequality manifests itself in increased dispersion of consumption and wealth. Nonetheless, the timing of the trends suggests that the changes in the tax system may also have played a non-trivial role. The rise in income inequality began as early as the 1960s with increasingly dispersed wage incomes. Using data from tax returns, Piketty and Saez (2003) show that the share of the top 10% of the wage income distribution hit a minimum of 24% in 1954, and increased to 29% in 1983. Higher income inequality was not reflected in the wealth distribution in this period. Wealth inequality was essentially flat over this period. For instance, the share of the wealthiest 1% in total wealth was 33.5% in 1962, and 33.8% in 1983 (Wolff and Marley, 1989; Keister and Moller, 2000). In fact, Piketty and Saez (2003) argue that the concentration of capital income declined in the post WWII era. Beginning with the 1980s, the trend in income inequality picked up pace, and the wealth distribution started to became more concentrated. Between 1983 and 1995, the share of the wealthiest 1% in total wealth increased from 33.8% to 38.5% (Wolff and Marley, 1989; Keister and Moller, 2000). Kennickell (2009) shows that this trend continued through the 2000s. The wealth share of the top 10% of the wealth distribution, for instance, increased from 67.2% in 1989 to 71.5% in 2007. The post 1980s period also witnessed an increased correlation between wealth and income as top income groups made their way up the wealth distribution. In 2007, the top 1% of the income distribution held 2

26.2% of all wealth in US, up from 21.9% in 1989 (Kennickell, 2009). We argue that the highly progressive tax system could have been instrumental in maintaining stable wealth inequality prior to the 1980s. 1 With declining tax rates, especially for higher income groups, the impact of higher income inequality on wealth and consumption inequality was amplified. Furthermore, a less progressive tax system encourages labor supply and savings by higher income groups, thereby contributing to pretax inequality and adding further to the trends in inequality since the 1980s. Gauging the effects of declining tax progressivity in the US on wealth and pre-tax income inequality requires a quantitative analysis that incorporates technical change and a non-linear tax system. To this end, we employ a model of consumption, savings and bequests, and labor supply under incomplete markets building on Aiyagari (1994), Bewley (1986) and Huggett (1993). The demographic structure in the model closely follows the Castaneda, Diaz-Gimenez, and Rios-Rull (2003) implementation of these models. In particular, we combine dynastic and life-cycle elements of decision-making at the household level. Households in the model go through the life-cycle stages of work, where they are faced with an idiosyncratic income risk, and retirement, where they live off of their pension income and private wealth. Upon death, they are replaced by their off-spring. We assume that households are altruistic. This set-up allows us to capture the three basic motives to accumulate wealth that are crucial for replicating the US wealth distribution: a precautionary savings motive to insure against against life-cycle income risk, a consumption smoothing motive to save for retirement, and a bequest motive to endow estates. We explicitly introduce in this setting a tax-financed pay-as-you-go social security system, a progressive income tax system, estate taxation and corporate income taxation. The presence of a social security system helps account for the bottom-tail of the wealth distribution. The progressive income tax-system is crucial for translating the pre-tax earnings distribution to consumption and wealth inequality. Explicit modeling of estate and corporate income taxes are particularly essential in our context, because the two tax components account for much of the decline of the progressivity of the tax system in US (Piketty and Saez, 2007). We calibrate our model to replicate the earnings and wealth distribution in the 1960s, while matching the life-cycle and intergenerational transitions of income. We then intro- 1 We are not the first to propose that progressive taxation may have affected wealth inequality. Piketty and Saez (2003) suggest that the highly progressive tax system may have been responsible for limited accumulation of private wealth by top income groups in the decades after WWII. 3

duce two changes: rising cross-sectional dispersion of labor efficiency, and declining tax progressivity. In particular, households are exposed to personal income taxes of declining progressivity as well as lower estate and corporate taxes starting in the 1980s. Due to the complex nature of corporate and estate taxes, we do not use the statutory tax rates reported in the data. Instead, we estimate the effective tax rates at different income/estate levels using actual taxes paid by different income groups as reported by Piketty and Saez (2007). Having the two main competing sources of growing income and wealth inequality the changing skill premium and the changing tax system allows us to separately assess the role of each. With the complete, calibrated model, we simulate the evolution of income and wealth inequality from 1960 to 2005. We then assess the contribution of each component, by simulating counterfactual economies where either the tax system or technical change is kept constant. We conclude with a welfare analysis of the changes in the tax system. 2 Model The model is a standard model of consumption, savings and labor supply with uninsurable idiosyncratic income risk. It thus builds on Aiyagari (1994); Bewley (1986); Huggett (1993). We combine the standard model with a demographic structure that closely resembles Castaneda, Diaz-Gimenez, and Rios-Rull (2003), and a detailed, non-linear tax system. The economy consists of a continuum of heterogeneous consumers, a representative firm, and a government. Each model period corresponds to a year. Consumers form dynasties; each consumer is replaced by a descendant upon death. New entrants to the economy inherit an estate from their parents and start their working life. While working, they face a constant probability of retirement µ 0. Once retired, they still make consumption and savings choices, but cannot work anymore. Retirees die with a constant probability µ 1. Upon death, they are replaced by a descendant who inherits their estate. Let the proportion of retirees in the economy be M 1, and let R be one for retirees and zero for workers. At any point in time, a continuum of agents of measure 1 is alive, each endowed with individual-specific capital k and labor skill z. With these endowments, agents can generate a pre-tax income of y = zwh + rk, where w is the market wage per skill unit, 4

h [0, 1] is hours worked and r is the interest rate net of depreciation. Retirees do not work and receive a social security benefit ω(z), which depends on their pre-retirement labor skill. 2 Private income from labor and savings, corporate income and estates are subject to a detailed tax system, outlined below. The government uses tax revenue to finance an exogenous stream of expenditure G. Let the disposable income of an agent net of all types of income taxes be y d. This depends both on total income and on capital holdings, due to the different tax components. Agents can allocate their resources between consumption and investment in capital. This capital stock constitutes savings for an individual, and becomes the estate that is passed on to a descendant in case of death. To rule out negative bequests, agents cannot borrow. Let x denote an agent s beginning-of-period capital holdings, before paying potential estate taxes due on an inheritance, and k the capital holdings after paying any estate tax. Capital depreciates at a rate δ between periods. A worker s labor skill z follows a first-order Markov process F 0 (z z). A descendant enters the economy with her/his own labor skill, which is drawn from a cdf F 1 (z z). The distribution of skill upon labor market entry thus depends on parents pre-retirement skill. Agents value consumption, and they dislike work. They care about their welfare as well as about their offspring s, discounting future utility using a constant discount factor β (0, 1). The problem of an agent then is to choose labor hours, consumption and capital investment to maximize expected discounted utility of the entire dynasty. In doing so, agents take the wage rate, the interest rate and the aggregate distribution of agents over wealth and productivity, denoted by Γ, as given. Let Γ 0 be the distribution for workers, Γ 1 that for retirees, and let Γ = H(Γ) describe the evolution of the distribution over time. Also, let Γ 01 (x, z) denote the pre-estate tax capital distribution for entrants. The Bellman equation for a consumer s problem then is V(k, z, R; Γ) = { c 1 σ } max c,k 0, h [0,1] 1 σ θ h1+ɛ 1 + ɛ + βe[v(k, z, R ; Γ ) z] 2 In reality, the benefit depends on contributions during the working life. We choose a simpler formulation to keep the state space smaller. (1) 5

subject to c + x = y d (y) + ω(z, R) + k, k = x E(x, R, R ), h(k, z, 1; Γ) = 0 for all k, z, Γ, Γ = H(Γ), where the expectation is taken over retirement and survival risk and skill transition risk, for both survivors and entrants. 1 is an indicator function that takes on the value one if the argument is true, and zero otherwise. E(x, R, R ) denotes the estate tax liability, where x is the estate. The estate tax is zero except for entrants, i.e. unless R = 1 and R = 0. For retirees, the labor supply choice is fixed at zero. Only retirees receive social security benefits ω(z). The representative firm produces output Y using aggregate capital K and effective labor N. Its technology takes the Cobb-Douglas form F(K, N) = AK α N 1 α. Factor markets are competitive, and firms are profit maximizers. A competitive equilibrium of the model economy consists of a value function, V(k, z, R; Γ), policy functions for factor supplies, k (k, z, R; Γ) and h(k, z, R; Γ), a wage rate, w(γ), an interest rate r(γ), and an evolution function H(Γ) such that: 1. Given w(γ), r(γ) and H(Γ), V(k, z, R; Γ) solves the consumer s problem defined by (1) with the associated factor supplies k (k, z, R; Γ) and h(k, z, R; Γ). 2. Factor demands are given by the following inverse equations: r(γ) = αa(k/n) α 1 δ w(γ) = (1 α)a(k/n) 1 α 3. Markets clear: K = k (k, z, R; Γ)dΓ(k, z) and N = zh(k, z, R; Γ)dΓ(k, z). 4. H(Γ) is consistent with F 0 (z z), F 1 (z z), µ 0, µ 1 and the savings policy k (k, z, R; Γ). 6

5. The government budget is balanced: G + M 1 ω(z)dγ 1 (k, z) = [y y d (y)]dγ(k, z) + µ 1 M 1 E(x)dΓ 01 (x, z). A steady-state of the economy is a competitive equilibrium where the distribution of agents is stationary, i.e. Γ ss = H(Γ ss ). 2.1 The tax system The tax system consists of labor and capital income, corporate income, and estate taxes. Corporate income taxes are levied before households receive capital income. They are levied on agents capital income at a constant rate τ c. To reflect the fact that for most households, most of their net worth takes the form of real estate and thus is not subject to corporate income taxes, we assume that corporate income taxes only apply to capital income above a deductible d c. 3 Personal income taxes are modeled after the current U.S. income tax system, which can be approximated by a log-linear form for disposable income: 4 y d = λ(zwh + rk τ c max(rk d c, 0)) 1 τ. (2) The power parameter τ 1 controls the degree of progressivity of the tax system, while λ adjusts to meet the government s budget requirement. τ = 0 implies a proportional (or flat) tax system. When τ = 1, all income is pooled, and redistributed equally among agents. For values of τ between zero and one, the tax system is progressive. 5 See Guner, Kaygusuz, and Ventura (2014), Heathcote, Storesletten, and Violante (2014) and Bakis, Kaymak, and Poschke (2012) for evidence on the fit of this function. In the calibration section below, we document more in detail how λ and τ have evolved over time. One benefit of this formulation for the income tax system is that it also allows for negative taxes. Income transfers are, however, non-monotonic in income. When taxes are progressive, transfers are first increasing, and then decreasing in income. This feature of 3 Only about 20% of U.S. households hold stocks or mutual funds directly (Heaton and Lucas, 1996; Bover, 2010). We later calibrate d c, which is not an actual feature of the tax code, to match average corporate income tax rates paid across the income distribution. 4 Note that corporate income taxes, since they are levied before households actually receive that income, reduce the tax base for individual capital income taxes. 5 The average income tax rate is 1 λy τ, which increases in y if τ > 0. 7

this way of modeling income taxes allows addressing features of the real tax system like the earned income tax credit and welfare-to-work programs, which imply transfers that vary with income. The symmetric treatment of capital and labor income in (2) is in line with the U.S. tax code. Also note that retirees are still subject to non-linear capital income taxes. Finally, estates are subject to tax when they are transferred to the next generation. In the U.S. tax code, this consists in a linear tax τ e, which applies above a deductible d e. 6 Hence, E(x) = τ e max(x d e, 0). 3 Calibration 4 Results 5 Conclusion References Aguiar, Mark and Mark Bils. 2011. Has Consumption Inequality Mirrored Income Inequality? Mimeo. Aguiar, Mark and Erik Hurst. 2007. The Increase in Leisure Inequality. In Economic Well-being and Inequality. American Enterprise Institute. Aiyagari, Rao. 1994. Uninsured Idiosyncratic Risk and Aggregate Saving. Quarterly Journal of Economics 109 (3):659 684. Bakis, Ozan, Baris Kaymak, and Markus Poschke. 2012. On the Optimality of Progressive Income Redistribution. CIREQ Working Paper 10-2012. Bewley, T. 1986. Contributions to Mathematical Economics: In honor of Gerard Debreu, chap. Stationary Monetary Equilibrium with a Continuum of Independently Fluctuating Consumers. New York: North Holland, 79 102. 6 In fact, estate tax revenue actually levied suggests that due to exemptions, the de facto deductible is larger than the de jure one. We therefore calibrate the deductible to match the distribution of average estate tax rates paid across the income distribution. 8

Bover, Olympia. 2010. Wealth inequality and household structure: US vs. Spain. Review of Income and Wealth 56 (2):259 290. Castaneda, A., J. Diaz-Gimenez, and J. V. Rios-Rull. 2003. Accounting for the U.S. Earnings and Wealth Inequality,". Journal of Political Economy 111 (4):818 857. Guner, Nezih, Remzi Kaygusuz, and Gustavo Ventura. 2014. Income taxation of US households: Facts and parametric estimates. Review of Economic Dynamics in press. Heathcote, J., F. Perri, and G. Violante. 2010. Unequal we stand: An empirical analysis of economic inequality in the United States, 1967-2006. Review of Economic Dynamics 13 (1):15 51. Heathcote, Jonathan, Kjetil Storesletten, and Gianluca Violante. 2014. Optimal Tax Progressivity: An Analytical Framework. Federal Reserve Bank of Minneapolis Research Department Staff Report 496. Heaton, John and Deborah Lucas. 1996. Evaluating the Effects of Incomplete Markets on Risk Sharing and Asset Pricing. The Journal of Political Economy 104 (3):443 487. Huggett, M. 1993. The Risk-Free Rate in Heterogeneous-Agent Incomplete-Insurance Economies. Journal of Economic Dynamics and Control 17 (5-6):953 69. Keister, L. A. and S. Moller. 2000. Wealth Inequality in the United States. Annual Review of Sociology 26:63 81. Kennickell, A. B. 2009. Ponds and Streamns: Wealth and Income in the U.S., 1989-2007. Working Paper No: 2009-13. Piketty, Thomas and Emmanuel Saez. 2003. Income Inequality in the United States. Quarterly Journal of Economics 118 (1):1 39.. 2007. How Progressive is the U.S. Federal Tax System? A Historical and International Perspective. Journal of Economic Perspectives 21 (1):3 24. Wolff, E. N. and M. Marley. 1989. The Measurement of Saving, Investment, and Wealth, chap. Long-Term Trends in U.S. Wealth Inequality: Methodological Issues and Results. 15. University of Chicago Press, 765 844. 9

Wolff, Edward N. 1998. Recent Trends in the Size Distribution of Household Wealth. Journal of Economic Perspectives 12 (3):131 150. 10