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Athreya, Kartik B.; Andrea Waddle,. "Implications of some alternatives to capital income taxation." Economic Quarterly. Federal Reserve Bank of Richmond. 2007. HighBeam Research. 22 Jul. 2018 <https://www.highbeam.com>.
Athreya, Kartik B.; Andrea Waddle,. "Implications of some alternatives to capital income taxation." Economic Quarterly. 2007. HighBeam Research. (July 22, 2018). https://www.highbeam.com/doc/1G1-164936625.html
Athreya, Kartik B.; Andrea Waddle,. "Implications of some alternatives to capital income taxation." Economic Quarterly. Federal Reserve Bank of Richmond. 2007. Retrieved July 22, 2018 from HighBeam Research: https://www.highbeam.com/doc/1G1-164936625.html
A general prescription of economic theory is that taxes on capital income are bad. That is, a robust feature of a large variety of models is that a positive tax on capital income cannot be part of a long-run optimum. This result suggests that it may be useful to search for alternatives to taxes on capital income. Several recent proposals advocate a move to fundamentally switch the tax base toward labor income or consumption and away from capital income. The main point of this article is to demonstrate that, as a quantitative matter, uninsurable idiosyncratic risk is important to consider when contemplating alternatives to capital income taxes. Additionally, we show that tax reforms may be viewed rather differently by households that differ in wealth and/or current labor productivity.
We are motivated to quantitatively evaluate the risk-sharing implications of taxes by the findings of two recent theoretical investigations. These are, respectively, Easley, Kiefer, and Possen (1993) and Aiyagari (1995). The work of Easley, Kiefer, and Possen (1993) develops a stylized two-period model where households face uninsurable idiosyncratic risks. Their findings suggest that, in general, when households face uninsurable risk in the returns to their human or physical capital, it is useful to tax the income from these factors and then rebate the proceeds via a lump-sum rebate. However, the framework employed in this study does not provide implications for the long-run steady state. Conversely, Aiyagari (1995) constructs an infinite-horizon economy in which households derive value from public expenditures and face uninsurable idiosyncratic endowment risks and borrowing constraints. In this case, the optimal long-run capital income tax rate is positive. Specifically, Aiyagari (1995) shows that the optimal capital stock implies an interest rate that equals the rate of time preference. However, labor income risks generate precautionary savings that force the rate of return on capital below this rate. Therefore, to ensure a steady state with an optimal capital stock, a social planner will need to discourage private-sector capital accumulation. A strictly positive long-run capital income tax rate is, therefore, sufficient to ensure optimality. (1)
The approach we take is to study several stylized tax reforms in a setting that allows the differential risk-sharing properties of alternative taxes to play a role in determining their desirability. We, therefore, choose to evaluate a model that combines features of Easley, Kiefer, and Possen (1993) with those of Aiyagari (1995), and is rich enough to map to observed tax policy. In terms of the experiments we perform, we study the tradeoffs involved with using either (i) labor income or (ii) consumption taxes to replace capital income taxes. Our work complements preceding work on tax reform by focusing attention solely on the differences that arise specifically from the exclusive use of either labor income taxes or consumption taxes. To our knowledge, the divergence in allocations emerging from the use of either labor or consumption taxes has not been investigated. (2) We study a model that confronts households with risks of empirically plausible magnitudes, and allows them to self-insure via wealth accumulation. Our work is most closely related to three infinite-horizon models of tax reform studied respectively by Imrohoroglu (1998), Floden and Linde (2001), and Domeij and Heathcote (2004). The environment that we study is a standard infinite-horizon, incomplete-markets model in the style of Aiyagari (1994), modified to accommodate fiscal policy. The remainder of the article is organized as follows. Section 1 describes the main model and discusses the computation of equilibrium. Section 2 explains the results and Section 3 discusses robustness and concludes the article.
1. MODEL
The key features of this model are that households face uninsurable and purely idiosyncratic risk, and have only a risk-free asset that they may accumulate. For tractability, we will focus throughout the article on stationary equilibria of this model in which prices and the distribution of households over wealth and income levels are time-invariant.
Households
The economy has a continuum of infinitely lived ex ante identical households indexed by their location i on the interval [0, 1]. The size of the population is normalized to unity, there is no aggregate uncertainty, and time is discrete. Preferences are additively separable across consumption in different periods, letting [beta] denote the time discount rate. Therefore, household i [member of] [0, 1] wishes to solve
[max.[{[c.sub.t.sup.i]}[member of][PI]([a.sub.0], [z.sub.0])]] [E.sub.[o]][[infinity].summation over (t=0)] [[beta].sup.t] u([c.sub.t.sup.i]), (1)
where {[c.sub.t.sup.i]} is a sequence of consumption, and [PI] ([a.sub.0], [z.sub.0]) is the set of feasible sequences given initial wealth [a.sub.0] and productivity [z.sub.0]. To present a flow budget constraint for the household, we proceed as follows.
Households face constant proportional taxes on labor income ([[tau].sup.l]), on capital income ([[tau].sup.k]), and on consumption ([[tau].sup.c]) (3) Households enter each period with asset holdings [a.sup.i] and face pre-tax returns on capital and labor of r and w, respectively. Each household is endowed with one unit of time, which it supplies inelastically, that is, [l.sup.i] = 1, and receives a lump-sum transfer b. It then receives an idiosyncratic (i.e., cross-sectionally independent) productivity shock [z.sup.i], which leaves it with income w[q.sup.i], where [q.sup.i] [equivalent to] [e.sup.z.sup.i]. Given the taxes on capital and labor income, the household comes into the period with gross-of-interest asset holdings (1 + r (1 - [[tau].sup.k])[a.sup.i]) and after-tax labor income (1 - [[tau].sup.l])w[q.sup.i]. The household's resources, denoted [y.sup.i], in a given period are then
[y.sup.i] = b + (1 - [[tau].sup.l])w[q.sup.i] + [1 + r(1 - [[tau].sup.k])][a.sup.i]. (2)
If we denote private current-period consumption and end-of-period wealth by [c.sup.i] and [a.sup.i'], respectively, the household's budget constraint is
(1 + [[tau].sup.c])[c.sup.i] [less than or equal to] [y.sup.i] - [a.sup.i']. (3)
The productivity shock evolves over time according to an AR(1) process
[z.sup.i'] = [rho][z.sup.i] + [[epsilon].sup.i], (4)
where [rho] determines the persistence of the shock and [[epsilon].sub.t.sup.i] is an i.i.d. normally distributed random variable with mean zero and variance [[sigma].sub.[epsilon].sup.2].
Stationary Recursive Household Problem
Given constant tax rates, constant government transfers, and constant prices, the household's problem is recursive in two state variables, a and z. Suppressing the household index i, we express the stationary recursive formulation of the household's problem as follows:
v(a, z) = max u(c) + E[v(a', z')|z], (5)
subject to (2), (3), and the no-borrowing constraint:
a' [greater than or equal to] 0 (6)
Given parameters ([tau], b, w, r), the solution to this problem yields a decision rule for savings as a function of current assets a and current productivity z:
a' = g(a, z|[tau], b, w, r). (7)
To reduce clutter, in what follows we denote optimal asset accumulation by the rule g(a, z) and optimal consumption by the rule c(a, z). As households receive idiosyncratic shocks to their productivity each period, they will accumulate and decumulate assets to smooth consumption. In turn, households will vary in wealth over time. The heterogeneity of households at a given time-t can be described by a distribution [[lambda].sub.t] (a, z) describing the fraction (measure) of households with current wealth and productivity (a, z). In general, the fraction of households with characteristics (a, z) may change over time. More specifically, let P (a, z, a', z') denote the transition function governing the evolution of distributions of households over the state space (a, z). P (a, z, a', z') should be interpreted as the probability that a household that is in state (a, z) today will move to state (a', z') tomorrow. It is a function of the household decision rule g(dot), and the Markov process for income z. …
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