Do capital income tax cuts trickle down?

INTRODUCTION

Capital income tax reductions are often used to stimulate economic activity during business downturns or to promote economic growth. In general, lowering capital income tax rates improves the after-tax rate of return of investment and facilitates capital accumulation. A higher capital stock, in turn, raises the marginal product of labor and the real wage. Consequently, it is often argued that capital income tax reductions have trickle-down effects because labor also benefits from a higher income.

Can capital income tax cuts improve both capital owners' and non-owners' welfare? While the trickle-down effect seems plausible, the underlying analysis ignores fiscal adjustments due to the revenue loss resulting from a tax cut. I analyze the distributional effects of capital income taxes within a dynamic macroeconomic model. In particular, I focus on how capital and non-capital owners are affected by a capital income tax cut under various offsetting policies necessary to maintain government budget solvency. Such an analysis is especially relevant to policy makers facing a deteriorating budget.

The distributional effects of taxes have long been an important subject in public finance and tax policy. Since the first general equilibrium model to study corporate tax incidence by Harberger (1962), a voluminous literature has enhanced our understanding of the economic incidence of various types of taxes. (1) However, conventional distributional studies do not concern government indebtedness. They focus on comparing tax reform options, which collect the same amount of revenues and are revenue neutral relative to the simulated current-law tax system (for example, Fullerton and Rogers (1993), Altig et al. (2001), Jorgenson and Yun (2001), and Nishiyama and Smetters (2005)). Even if debt is present in a model, the analysis does not address the distributional issue in a fiscal environment where the present value of government liability changes. (2)

I use a neoclassical growth model commonly adopted for studying fiscal policy in modern macroeconomics. Typical neoclassical growth models have a single representative agent who owns the entire capital stock. In this model, heterogeneity of capital ownership derives from two types of agents: savers and non-savers, as introduced in Campbell and Mankiw (1989). Savers are conventional forward-looking agents who work, save, consume, and own the entire capital stock; they are the capital owners in the model. Non-savers, being liquidity constrained, work and consume all of their disposable income; they are the non-capital owners in the model. (3)

Additional differences between savers and non-savers are introduced. In reality, people with higher income are more likely to save. (4) I assume that a representative saver in the model earns more income than a representative non-saver because of higher labor productivity and capital income. Under a progressive income tax system, savers are subject to a higher average labor income tax rate than non-savers.

Three financing instruments are considered to satisfy an intertemporal budget constraint. Government can respond to rising debt resulting from a permanent capital tax cut by reducing: 1) government consumption, which provides public services; 2) government investment, which forms public capital; or 3) transfer payments.

The model is deterministic. The economy begins with a steady state under the initial fiscal policy. The government announces and implements a permanent ten percent reduction in the capital income tax rate, and the economy evolves to a new steady state. The government is fully credible and able to commit to its policy. The distributional analysis is based on the utility derived under a high and a low capital income tax rate over an infinite horizon.

I find that whether or not the trickledown effect emerges depends on how the government manages its debt to maintain a sustainable budget. When transfers to non-capital owners are reduced, their welfare decreases through lower consumption and higher hours worked as a result of reduced disposable income. Moreover, when government decreases its productive investment, the marginal productivity of private inputs falls, which has a negative impact on all agents' income. As a result, the overall welfare of both types of agents decreases despite a permanent reduction in the capital income tax rate.

Finally, I illustrate the well-known fallacy that using tax liability as a proxy to measure tax burden can lead to false conclusions. Higher tax liability can result from higher tax rates and/or more economic activities. I show examples where people who pay more taxes can be better off relative to the situation without the tax cut, and vice versa.

THE MODEL

The economy has two types of infinitely lived agents: savers and non-savers, competitive firms, and a government. Both the population and the total amount of time an agent is endowed with are normalized to one.

The Setup

Savers

With predetermined capital and government debt, a representative saver chooses consumption ([C.sup.S.sub.t]), capital ([K.sup.S.sub.t]), labor ([L.sup.S.sub.t]), and government bonds ([B.sup.S.sub.t]) to maximize the expected utility over consumption and leisure (1 - [L.sup.S.sub.t])

[1] [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],

subject to the budget constraint

[2] [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

The superscripts s and n indicate variables associated with savers and non-savers. [beta] is the discount factor (0 < [beta] < 1). [[??].sup.S.sub.t] is a composite of consumption goods, consisting of consumption financed by private spendings ([C.sup.S.sub.t], referred as private consumption) and public services financed by government consumption ([G.sub.t]). [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], and [[tau].sup.K.sub.t] are tax rates on private consumption, savers' labor income, and capital income. [B.sup.S.sub.t] is government debt issued at t, which pays [R.sub.t] [B.sup.S.sub.t] at t + 1. [r.sub.t] is the rental rate of capital. [[delta].sup.T] is the capital depreciation rate for tax purposes, and [delta] is the economic depreciation rate of capital (0 [less than or equal to] [[delta].sup.T], [delta] [less than or equal to] 1). The elasticity of intertemporal substitution of consumption is 1/[gamma], and the elasticity of intertemporal substitution of leisure for savers is 1/[[theta].sup.S] ([gamma] > 0 and [[theta].sup.S] [greater than or equal to] 0). [x.sup.S] is savers' preference weight on leisure.

To capture the income differential between average savers and non-savers in reality, the model assumes that savers have a higher productivity than non-savers. The weight of labor efficient units for savers is v. [W.sub.t] is the wage rate per labor efficiency unit. A saver who supplies [L.sup.S.sub.t] units of time earns [W.sub.t] v [L.sup.S.sub.t].

Government consumption, [G.sub.t], is used to provide an equal amount of public services per capita. Following Barro (1981), the contemporaneous level of public services and private consumption are substitutes in utility terms: each unit of public service delivers a fraction [sigma] of the utility derived from consuming a unit of private consumption (0 [less than or equal to] [sigma] [less than or equal to] 1). Assume that the ratio of the number of savers to the total population is h. Then, the composite consumption that enters the utility function is [[??].sup.S.sub.t] [equivalent to] [C.sup.S.sub.t] + [sigma]h [G.sub.t]. (5) When [sigma] = 0, the model has the usual assumption that government consumption is wasteful.

Non-savers

A representative non-saver solves a static optimization problem to maximize utility each period:

[3] [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],

subject to the budget constraint

[4] [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],

where non-savers' composite of consumption goods is defined as [[??].sup.S.sub.t] [equivalent to] [C.sup.n.sub.t] + [sigma] (1 - h)[G.sub.t] and [T.sub.t] is government transfers. Transfers only target non-savers because they earn relatively low income. The model assumes different labor elasticities for savers and non-savers. See the appendix for the rationale.

Note that non-savers solve an intratemporal problem. As they have no vehicle to carry wealth to next period, the optimal choice is to consume all of their disposable income each period. Their labor decisions are affected by the marginal disunity from labor and the labor income tax rate. (6)

Firms

A representative firm rents capital from savers and rents labor from both types of agents to produce output [Y.sub.t] according to the Cobb-Douglas production function:

[5] [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],

where 0 < [alpha] < 1, [K.sub.t-1] and [K.sup.G.sub.t-1] are the private and public capital for production during period t, and [L.sub.t] = v [L.sup.S.sub.t] + (1 - v [L.sup.n.sub.t] is the weighted aggregate labor inputs in efficiency units. Private and public capital evolves according to [K.sub.t] =[I.sub.t] + (1 - [delta])[K.sub.t-1] and [K.sup.G.sub.t] = [I.sup.G.sub.t] + (1 - [delta]) [K.sup.G.sub.t-1], where [I.sub.t] and [I.sup.G.sub.t] are private and public investment. The elasticity of output with respect to public capital is [[alpha].sub.G] (0 [less than or equal to] [[alpha].sub.G] < 1). If public capital is unproductive, [[alpha].sub.G] = 0. The firm solves the profit-maximization problem:

[6] [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (7)

Government