Consumption smoothing and the measured regressivity of consumption taxes.
Athreya, Kartik B. ; Reilly, Devin
A maintained assumption of nearly all macroeconomic analysis is
that households prefer their consumption to remain smooth across time
and states of nature. Their ability to smooth consumption is affected by
a variety of constraints, including fiscal policy, and, in particular,
the choice of tax base. In practice, labor income and interest income on
savings have constituted the bulk of taxed activities. However, the
preceding forms of taxation create potentially important distortions.
Prescott (2004) shows that labor income taxes may be important in
depressing labor supply and average incomes to inefficient levels, while
Atkeson, Chari, and Kehoe (1999) show that it can never be optimal to
tax capital income in the steady state. In particular, capital income
taxes hinder the household's ability to smooth consumption
intertemporally by lowering the return on savings.
An alternative tax that avoids the hurdles to smoothing created by
capital income taxes is a tax on consumption. In general, however,
consumption taxes have been opposed on the basis that they are
"regressive" in the sense that, at any point in time, the
revenues may be disproportionately collected from households whose
incomes are lower than average. Households in the U.S. economy also face
substantial persistent and uninsurable idiosyncratic risks to their
income (see, e.g., Storesletten, Telmer, and Yaron [2004]). As a result,
many with currently low income will be those who have suffered an
adverse shock in the past. From this perspective, a tax system that
collects a substantial portion of its revenues from those who find
themselves with low income may seem undesirable.
Evaluating the burden of tax payments by income requires choosing a
definition of income by which to order households. Two candidates are
(i) income received in a given year and (ii) income realized over the
lifetime. For each of these definitions, one can compute the
regressivity of a given tax regime. The first measure of incidence,
which we term annual incidence, will compare the cumulative
contributions to tax collections of households collected at a point in
time, and then ranked by current (annual) income. The second, which we
refer to as lifetime incidence, will compare the cumulative
contributions to tax collections of households ranked by their realized
lifetime income.
Some have noted that the measured incidence of consumption taxes
depends on the notion of income being used. Notably, Metcalf (1997)
shows that while the annual incidence of consumption taxes appears
regressive, the lifetime incidence is roughly proportional. In
particular, when income is deterministic and has a "hump" at
middle age, relatively young households can expect income to grow, while
relatively old households can expect income to fall. Under the
presumption that households prefer smooth consumption, the young will
generally borrow, if allowed, while the old will run down assets to
finance consumption in retirement. This behavior implies that households
will consume large amounts relative to their income when young while the
reverse will hold when old. As a result, any cross-sectional assessment
of "who pays" a consumption tax will conclude that it is paid
disproportionately by the currently relatively poor. However, this
apparent regressivity is merely an artifact of households successfully
achieving smooth consumption.
The preceding intuition was derived in a purely deterministic
setting. However, the logic extends to the more general case where
income has both deterministic and stochastic components. In stochastic
settings, people in any cross-sectional data will differ even if they
share many characteristics such as age, gender, and education. However,
the nature of the shocks that lead a priori similar households to differ
matter for the assessment of the effects of tax policy. In particular,
given the variance of innovations to income faced by a household, its
ability to smooth consumption in the absence of complete insurance
markets depends crucially on the persistence of shocks. Loosely
speaking, the more that annual income "looks like" long-run
average income, the more informative annual incidence of consumption
taxes will be. When shocks are transitory, a current shock to
productivity will have less influence on the lifetime resources that a
household can expect over its remaining lifetime. As a result,
consumption levels will not need to be adjusted by much in order for the
lifetime budget constraint to be satisfied. In turn, unless the
household is near a constraint on borrowing, its consumption will not
respond to such shocks. By contrast, in an economy with highly
persistent labor income risk, a household who has just received a bad
shock may expect more of the same in the near and intermediate-term
future; thus, expected lifetime resources have to be revised downward,
possibly significantly (see, e.g., Deaton [1992]). Therefore,
satisfaction of the household's lifetime budget constraint will
require a commensurate reduction in current and future consumption.
Conversely, if a household receives a good realization of a persistent
shock, consumption is likely to jump up as lifetime expected resources
are revised upwards.
From a policymaker's perspective, the issue is this: the less
closely that consumption tracks income, the more effective we can say
that consumption smoothing is. However, annual incidence measures will
suggest regressivity. As a result, consumption taxes may appear
undesirable in precisely those instances in which households are
successful in managing the impact of income fluctuations on their
standard of living. The preceding is a relevant consideration: A
relatively large body of work has shown that households engage in
significant consumption smoothing over their lifetimes (see, e.g.,
Attanasio et al. [1999] and Gourinchas and Parker [2002]). In contrast
to annual incidence, lifetime incidence will not be distorted by the
effectiveness of household consumption smoothing.
Unfortunately for policymakers, recent work has debated the
persistence of income shocks (which are taken to represent productivity
shocks), with estimates that lie substantially away from each other. At
one end of the spectrum are the estimates of Storesletten, Telmer, and
Yaron (2004) who argue that aggregate cross-sectional evidence suggests
a unit-root component for shocks. At the other end of the spectrum are
the more recent estimates of Guvenen (2007), who has argued that shock
persistence is in fact far lower, and in an AR(1) setting, better
approximated by a persistence parameter of 0.8. Given this large range,
we present the implications of a switch to consumption taxes under a
variety of values for shock persistence and show that measured
regressivity does depend on the persistence of shocks.
In this article, we address two questions. First, how will a move
to pure consumption taxation matter for aggregate outcomes, and how do
the results depend on the persistence of shocks to productivity?
Specifically, under varying shock persistence, how do the levels and
variability of consumption, wealth, and labor supply respond to this tax
reform? Second, how regressive are consumption taxes? Do annual and
lifetime incidence measures of consumption taxes differ, and how do the
results depend on the persistence of productivity shocks? Specifically,
we utilize the Suits Index (Suits 1977), a standard measure of the
incidence of taxes, to determine how regressivity depends on (i) the
frequency at which income is measured and (ii) the stochastic structure
of idiosyncratic household productivity. We will then describe the
relationship of the Suits Index to direct cross-sectional measures of
inequality, in particular, the Gini Index and the coefficient of
variation.
Given our objectives, it is essential that we face the household
with a stochastic productivity process that accurately captures both the
true nature of household risk and the tools with which households smooth
consumption. Therefore, our model features a stochastic process for
productivity that contains a transitory component, a persistent
component, and a well-defined "hump-shaped" life-cycle profile
for average productivity. We equip households with the two tools thought
to be empirically most relevant for consumption smoothing:
self-insurance through asset accumulation, and flexible labor supply.
Our work is most closely related to Fullerton and Rogers (1991) and
Metcalf (1997), who study the dependence of measured regressivity on the
frequency of income measurement, though in stylized models that abstract
from uncertainty. Given the potential for uncertainty to alter
consumption smoothing, our article contributes to the literature by
allowing for stochastic shocks of varying persistence and flexible labor
supply. It is also related to Ventura (1999), Nishiyama and Smetters
(2005), Athreya and Waddle (2007), and Fuster, Imrohoroglu, and
Imrohoroglu (2008). Our work differs from prior work as it derives the
implications for tax incidence as a function of the stochastic
properties of income.
Our main findings are as follows. In terms of aggregates, we find
that a move to a consumption tax will increase savings taken into
retirement but will not alter either labor supply or consumption
variability substantially. The level of inequality does vary with the
persistence of productivity shocks, especially when using lifetime
measures of the relevant variables. With respect to regressivity, our
results show that the findings of Metcalf (1997) carry over to a
substantially richer setting: We show that regressivity is a measure
that is quantitatively sensitive to the frequency of income being used.
Our results obtain in spite of the fact that borrowing constraints bind
for most households early in life. While annual incidence shows
substantial regressivity, the lifetime incidence of a consumption tax is
proportional, irrespective of the persistence of income shocks. Perhaps
the central lesson of our article is that standard measures of the
incidence of consumption taxes can be rather misleading as a guide to
its implications for household consumption smoothing.
In what follows, Section 1 lays out some intuition for the role
played by consumption taxes. Section 2 presents the model and
equilibrium, Sections 3 and 4 present the parameterization and results,
and Section 5 concludes.
1. WHY MIGHT A SWITCH TO CONSUMPTION TAXES MATTER?
First, we provide some intuition for why a switch to consumption
taxation may indeed alter the optimization problem faced by agents.
Notice that in some very simple settings, tax systems that tax both
labor income and capital income are actually equivalent to systems in
which there is a pure consumption tax.
As a result, the move to a consumption tax from a regime of labor
and capital income taxes is not inherently a meaningful change, as it
may not change the household's underlying optimization problem.
Following Nishiyama and Smetters (2005), it is instructive to consider a
simple two-period model in which households enter with zero wealth
([a.sub.1] = 0), work only in the first period of life whereby they earn
a deterministic wage, [w.sub.1], pay a flat tax on labor income,
[[tau].sub.1], and save an amount, [a.sub.2]. In the second period,
households are taxed on their capital income at a flat rate,
[[tau].sub.k], and live off gross-of-interest (and net-of-capital income
tax) savings [a.sub.2] (1 + r(1 - [[tau].sub.k])) in the second period.
The per-period budget constraints are as follows. In the first period,
we have
[c.sub.1] + [a.sub.2] = [w.sub.1](1 - [[tau].sub.1]),
and in the second period we have
[c.sub.2] = (1 + r(1 - [[tau].sub.k]))[a.sub.2].
In the absence of borrowing constraints, the relevant constraint on
households is the single lifetime budget constraint:
[[c.sub.1]/(1 - [[tau].sub.l])] + [[c.sub.2]/(1 - [[tau].sub.l])(1
+ r (1 - [[tau].sub.k]))] = [w.sub.1].
Next, consider the same environment, but where labor and capital
income taxes have been replaced by consumption taxes alone. In this
case, the lifetime budget constraint is
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (1)
Inspecting (1) reveals that a regime in which consumption taxes in
period 1 are set at [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] generates
identical incentives and constraints for the household. In this case, a
system of flat capital and labor income taxes is equivalent to a system
of consumption taxes that very with age. The age-dependency of the
equivalent consumption tax regime is a direct result of nonzero capital
income taxation: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] if
[[tau].sub.k] = 0. Thus, whenever [[tau].sub.k] [not equal to] 0, it is
as if future consumption is being taxed at a rate different from current
consumption. In particular, a positive capital income tax implies that
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]: Future consumption
is more expensive than current consumption. (1)
More generally, in a longer (but still deterministic and
finite-lived) model, flat capital and labor income taxes are equivalent
to a regime in which there are (i) an age-dependent sequence of
consumption taxes, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],
and (ii) a lump-sum transfer, [[gamma].sub.0], to all households to
offset the difference in present values of labor income created by the
presence of capital income taxes. That is, the equivalent consumption
tax at any age j=1, 2, ..., J, is given by
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where we see again that if [[tau].sub.k] = 0, [MATHEMATICAL
EXPRESSION NOT REPRODUCIBLE IN ASCII]. Letting [[~.w].sub.j] denote income/productivity while the lump-sum transfer to households under a
consumption tax is given by
[[GAMMA].sub.0] = [summation over.sub.j=0][[[~.w].sub.j]/[(1 + r(1
- [[tau].sub.k])).sup.j]] - [summation over.sub.j=0][[[~.w].sub.j]/[(1 +
r).sup.j]].
Notice again that when [[tau].sub.k] = 0, there is no
age-dependence in the sequence of consumption taxes, nor is there any
transfer (i.e., [[gamma].sub.o] = 0).
Given these cases, we now turn to the aspects of our preferred
model that break the equivalence between consumption tax regimes and
those regimes that tax labor and capital income. First of all, like both
recent tax reform proposals and analyses, we will consider a move to a
regime of a flat consumption tax, implemented here as a flat sales tax on all household purchases. (2) These are among the most practical forms
of consumption taxes under consideration in policy discussions. Notably,
the inherent difficulties in implementing age-dependent taxes perhaps
account for the fact that they are not a feature of any major economy.
The absence of age-dependence then immediately rules out any equivalence
with income taxes. Second, the interest rate on savings in the model is
strictly positive. As a result, regardless of the size of capital
income, as long as it is positive, an age-dependent consumption tax will
be required to obtain equivalence. Third, we do not augment household
income with lump-sum transfers or taxes. Fourth, we do not allow
households to hold negative asset positions. As a result, young
households may find themselves unable to consume as much as they would
like. To the extent that consumption tracks household income,
consumption taxes will not look as regressive--even though the observed
fall in regressivity is an artifact of a binding constraint! Given all
these departures, it is likely that a switch to a flat consumption tax
regime generates meaningful changes in the economic environment within
which households operate.
2. MODEL
The economy is closely related to that in Ventura (1999), in that
it features a well-defined life-cycle path for labor productivity,
stochastic shocks, taxes, and elastic labor supply. There is a large
number of agents who consume and work for J periods and then retire. We
will focus on stationary settings where there is a time-invariant
measure of agents of each age j, and, moreover, that the
age-distribution is uniform.
During working life, households' productivity has a
deterministically evolving component, but is also subject to stochastic
shocks. In each period, households must choose labor effort,
consumption, and savings. After working life, households then enter
"retirement," which lasts for K periods. Households in
retirement are assumed to face no further labor market risk and,
therefore, solve a simple deterministic consumption-savings problem.
They face only the constraint that the optimal consumption path have a
present value equal to the present value of resources brought into
retirement, inclusive of transfers.
Preferences
Households value consumption and leisure. All households have
identical time-separable constant relative risk aversion (CRRA) utility
functions over an composite good defined by a Cobb-Douglas aggregate of
consumption and leisure, [c.sub.j] and [l.sub.j], respectively, at each
age-j during working life, and a "retirement felicity
function," [phi], that is defined on wealth, [x.sub.R], taken into
retirement.
Households discount future consumption of the composite good
exponentially using a time-invariant discount factor, [beta], and weight
total consumption expenditures, [c.sub.j], in each period by an
adjustment for the age-specific average household size, [ES.sub.j] (a
mnemonic for "equivalence scale"). Effective consumption is
then defined to be [[c.sub.j]/[ES.sub.j]]. The problem for the household
is to choose a vector sequence, [{[c.sub.j], [l.sub.j]}.sub.j=1.sup.J],
and retirement wealth, [x.sub.R], to maximize lifetime utility. The
absence of labor income in retirement implies that the value to a
household of entering retirement with a given level of wealth,
[x.sub.R], is the solution to the following problem. Let the maximal leisure available to households be denoted by [bar.l], and let
[PI]([x.sub.R]) be the feasible set of consumption sequences given that
a household enters retirement with resources [x.sub.R]:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)
The overall objective of the household can now be expressed as the
sum of the optimization problem applicable to working life and a
"continuation" value given by resources brought into
retirement. Let [PI]([[PSI].sub.0]) denote the space of all feasible
combinations ({[c.sub.j], [l.sub.j]}, [x.sub.R]) given initial state
[[PSI].sub.0]. The household optimization problem is
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)
Endowments
Households are endowed with one unit of time, which they can divide
between labor and leisure. Household income is determined as the product
of labor effort and labor productivity. Productivity in any given period
is the outcome of a process that has both deterministic and stochastic
components. We follow Storesletten, Telmer, and Yaron (2004) to
represent the logarithm of productivity (wages per effective unit of
labor), In [w.sub.j], of households as the sum of three components: an
age-specific mean of log productivity, [[mu].sub.j], persistent shocks,
[z.sub.j], and transitory shocks, [[eta].sub.j]. Therefore, we have
ln [w.sub.j] = [[mu].sub.j] + [z.sub.j] + [u.sub.j] (4)
with
[z.sub.j] = [rho][z.sub.j-1] + [[eta].sub.j], [rho] [less than or
equal to] 1, j [greater than or equal to] 2 (5)
[u.sub.j] ~ i.i.d N(0, [[sigma].sub.u.sup.2]), [[eta].sub.j] ~
i.i.d. N(0, [[sigma].sub.[eta].sup.2]), [u.sub.j], [[eta].sub.j] (6)
Households draw their first realization of the persistent shock
from a distribution with a conditional mean of zero, i.e., [z.sub.0].
The innovation to the persistent shock, [[eta].sub.1], is also
mean-zero, but has variance, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE
IN ASCII], that is drawn to help match the inequality of log labor
income among those entering the labor force. The variance of persistent
shocks drawn at all other ages differs from [MATHEMATICAL EXPRESSION NOT
REPRODUCIBLE IN ASCII] and is denoted [[sigma].sub.[eta].sup.2].
Market Arrangement
As is standard in models of exogenous uninsurable risks, households
of age-j can save and dissave by choosing a position in only a single
noncontingent bond, denoted [x.sub.j+1]. The economy is a small
open-economy setting, whereby savings earn an exogenous gross rate of
return (net of taxes). The household can also vary its labor supply,
both to respond to changes in labor productivity and to smooth
consumption of the composite good. For example, if financial resources
are low in the current period, a household with a given labor
productivity may choose to supply more labor than they would if they had
more financial wealth. This is because they would otherwise be forced
into a current period allocation that had low consumption and high
leisure, while their intertemporal smoothing motives dictate preventing
a fall in consumption. According to the experiment under study, labor
income, capital income from savings, and consumption may each be taxed
at (time-invariant) flat rates denoted by [[tau].sub.l], [[tau].sub.k]
and [[tau].sub.c], respectively. (3) Notice that in this model, given
the abstraction from multiple layers of production of the final
consumption good, the consumption tax will also be identical to a
value-added tax. Because we treat the economy as one that is open to
world trade and, furthermore, one in which the households under study do
not affect the total demand or supply of assets worldwide, the interest
rate on risk-free savings is assumed to be unaffected across tax
policies. Given elastic labor supply and the three taxes, the
generalized household budget constraint in each period is
[c.sub.j](1 + [[tau].sub.c]) + [x.sub.j+1] = [[~.w].sub.j](1 -
[l.sub.j])(1 - [[tau].sub.l]) + [x.sub.j](1 + r (1 - [[tau].sub.k])).
(7)
Optimal Household Decisions
Retirement
Age-J households value retirement savings via [phi]([x.sub.R]). The
consumption flow arising from a given level of savings is specified as
follows. Households aged J + 1 are guaranteed to have a minimal standard
of living given by a threshold, [[[tau].bar].sup.R], representing Social
Security and Medicare. Transfers during retirement are therefore not
means-tested and are given instead by a single lump-sum transfer,
[x.sub.[[tau].bar]], to all retiring households. Our approach follows
Huggett (1996). A household's wealth level at retirement is then
the sum of the household's personal savings, [x.sub.J+1], and the
baseline retirement benefit, [x.sub.[[tau].bar]]R,
[x.sub.R] = [x.sub.J + 1] [~.R] + [x.sub.[[tau].bar]]R. (8)
The amount [x.sub.[[tau].bar]]R is the wealth level that, when
annuitized at the gross after-tax interest rate [~.R] [equivalent to] (1
+ r (1 - [[tau].sub.k])), yields a flow of income each period equal to
the societal minimum retirement consumption floor, [[[tau].bar].sup.R].
That is, minimal retirement wealth, [x.sub.[[tau].bar]], solves
[K.summation over(k=1)] [[[[tau].bar].sup.R]/[([~.R]).sup.k] =
[x.sub. [[tau].bar]]R. (9)
To solve for indirect utility at retirement, define the budget
constraint for a retiree in period-k of retirement as follows:
(1 + [[tau].sub.c])[C.sub.k] + [x.sub.k+1] = [x.sub.k](1 + r(1 -
[[tau].sub.k])) + [[[tau].bar].sup.R]. (10)
Given the objective function during retirement (equation 2), the
optimal intertemporal allocation of consumption must satisfy the
following Euler equation:
[[[C.sub.t] + 1]/[C.sub.t]] = [(1/[beta][~.R]).sup.[1/[[theta](1 -
[alpha]) - 1]]]. (11)
Defining [gamma] = [(1/[beta][~.R]).sup.[1/[[theta](1 - [alpha]) -
1]]] we then see that (11) implies that consumption at any date-k of
retirement can be defined as:
[C.sub.k] = [[gamma].sup.k] [C.sub.0]. (12)
Given the preceding requirement on optimal consumption growth, we
use the budget constraint to pin down the level of the sequence of
retirement consumptions. First, we iterate on the per-period budget
constraint (equation 10) to obtain a single present value budget:
[[K.summation over (k=0)][[[c.sub.k](1 +
[[tau].sub.c])]/[[~.R].sub.k]] = [x.sub.R],
where [x.sub.R] is defined in (8).
As a result, we obtain
[c.sub.0] = [[x.sub.R]/[[summation].sub.k =
0.sup.K][[gamma].sup.k][(1 + [[tau].sub.c]/[[~.R].sup.k]]].
The remaining sequence is given by (12), which we denote as
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], which then yields
the indirect utility of retirement:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (13)
Working life
The solution of the household's problem during working life is
simplified by our use of Cobb-Douglas preferences. It is instructive to
display the manner in which the various taxes alter the optimal
allocation of consumption over time and the optimal mix of consumption
and leisure. First, within any given period, it is useful to think of a
household as first working full time and then "buying back"
consumption and leisure. Therefore, if a household works full time
(normalized to unity), has entered a period with savings [x.sub.j], and
plans to save [x.sub.j+1], its resources available to purchasing
consumption and leisure are pinned down. That is, consumption and
leisure purchases must satisfy
[c.sub.j](1 + [[tau].sub.c]) + [[~.w].sub.j][l.sub.j](1 -
[[tau].sub.l]) = [[~.w].sub.j](1 - [[tau].sub.l]) + [x.sub.j] (1 + r(1 -
[[tau].sub.k])) - [x.sub.j+1]. (14)
Letting [[LAMBDA].sub.j] [equivalent to][[~.w].sub.j](1 -
[[thu].sub.1] + [x.sub.j](1 + r(1 - [[tau].sub.k])) - [x.sub.j+1] denote
the total "resources" available for consumption and leisure,
we have from the infratemporal first-order conditions of the
household's problem that the optimal mix of expenditures on leisure
and consumption satisfies
[[l.sub.j]/[c.sub.j]] = [(1 - [theta])/[theta]][(1 +
[[tau].sub.c])/(1 - [[tau.sub.1])][[~.w].sub.j]. (15)
Notice that for any given realization of current productivity,
[[~.w].sub.j], and elasticity of substitution, [theta], the optimal mix
of leisure and consumption depends only on the ratio (1 +
[[tau].sub.c])/(1 - [[tau].sub.1]). That is, the levels of either tax
alone do not determine how households divide their resources between
leisure or consumption. The preceding expression, when substituted into
the household budget constraint, gives the optimal levels of consumption
and leisure, respectively, as a function of resources [[LAMBDA].sub.j]:
[c.sub.j] = [[[LAMBDA].sub.j][theta]/[1 + [[tau].sub.c]], and (16)
[l.sub.j] = [[[lambda].sub.j](1 - [theta])/(1 -
[[tau].sub.l])[[~.w].sub.j]] (17)
Given these rules for optimal consumption and leisure for any given
resources, the only remaining decision for the household is to choose
what resources to keep in the current period; this is simply done by
choosing the savings level [x.sub.j+1] optimally. Let U(*) denote the
within-period utility function. During working life, the intertemporal
first-order condition is given by
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (18)
Notice here that consumption and labor income taxes do not appear,
while the capital income tax does. This is the crux of the distortion to
private savings decisions induced by capital income taxes. Moreover, as
shown above, an equivalent system of consumption exists that implies
systematically increasing tax rates on consumption in the increasingly
distant future. This implies that capital income taxes lower the return
to saving and thereby encourage current consumption; when consumption
and leisure are complements, there is resultant reduction in work
effort.
Recursive Formulation
The household's problem can be represented recursively as
follows. At the beginning of each period, the household's options
are completely determined by its age-j, its wealth, [x.sub.j], its
current realized value of the persistent shock, [z.sub.j], and the
current realization of the transitory shock, [[eta].sub.j]. These items
are sufficient to determine the budget constraint faced by households in
the current period, and also to obtain the best forecast of next
period's realization of the persistent shock. (4)
Optimal household behavior requires that in each period, given
their state vector, the household chooses consumption, [c.sub.j], and
savings, [x.sub.j+1], to satisfy the following recursion:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (19)
subject to the budget constraint described in equation (7), and
where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] denotes the
expectation of the value of carrying savings,[ x.sub.j+1], into the
following period when the shocks tomorrow ([z.sub.j+1], [[eta].sub.j+1])
are drawn from the conditional joint distribution that reflects the
current realization of the persistent shock, [z.sub.j]. We focus on a
stationary equilibrium: Households optimize given prices, and the
distribution of the households over values of the state is stationary
(time-invariant).
3. PARAMETERIZATION
The model period is one calendar year. Households work for J = 44
periods, where j = 1 represents real-life age 21, and j = 44 is
retirement at age 65. Retirement lasts for K = 25 periods, so all agents
die at real-life age 90. Risk aversion and discounting are set at
[alpha] = 3 and [beta] = 0.96, respectively. The (gross) risk-free
interest rate on savings is [R.sup.f] = 1.01. Households are born with
zero financial wealth: [x.sub.1] = 0. Maximum leisure time, [bar.l], is
normalized to unity and the elasticity of labor supply, [theta], is set
to 0.5 to reflect that, on average, half of a household's
discretionary hours (16 hours per day) are spent working. Our benchmark
model features taxes on consumption, labor income, and capital income,
and we follow Fuster, Imrohoroglu, and Imrohoroglu (2008) to assign the
following values for these taxes: [[tau].sub.c] = 0.055, [[tau].sub.k] =
0.35, and [[tau].sub.l] =0.173. Under a switch to a pure consumption
tax, we ensure revenue-neutrality relative to our benchmark economy.
A brief summary of the stochastic process for productivity is the
following. We set [rho] = 0.99, [[sigma].sub.u.sup.2] = 0.063,
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] = 0.22, and
[[sigma].sub.[eta].sup.2] = 0.0275, as these values generate reasonable
income variability (given optimal labor supply) among the youngest
working-age households in the data, as well as the nearly linear
life-cycle growth of cross-sectional variance in log income documented
in Storesletten, Telmer, and Yaron (2004) and the total increase in
cross-sectional (log) income variance over the life cycle. The
parameters governing the income process also generate reasonable
wealth-to-income ratios over the life cycle (see, e.g., Athreya [2008]).
The mean of log productivity is given by the profile
[{[[mu].sub.j]}.sub.j=1.sup.J] and is based on the estimates of Hansen
(1993). We approximate the continuous state-space stochastic process for
income via a discrete state-space Markov chain using the method of
Tauchen (1986). Specifically, we use a 32-point discretization of the
persistent shock and a three-point discretization for the transitory
shock. We employ standard discrete-state space dynamic programming and
Monte Carlo simulation to solve for decisions and generate aggregate
outcomes, respectively. (5) The values of all policy-invariant
parameters are reported in Table 1.
Table 1 Parameter Values
Variable Value
[beta] (Discount Factor) 0.96
J (Working Life) 44
K (Retirement Length) 25
[R.sup.f] (Risk-Free Rate) 1.01
[x.sub.1] (Beginning of Life Assets) 0
[bar.l] (Maximum Leisure) 1
[theta] (Elasticity of Labor Supply) 0.5
4. CONSUMPTION TAX REFORM
We first report the model's implications for the aggregate
consequences of a move to pure consumption taxation for several
specifications of income persistence and risk aversion. Specifically, we
set [[tau].sub.l] = [[tau].sub.k] = 0 and set [[tau].sub.c] such that
the change is revenue-neutral. We provide measurements of consumption,
labor supply, and wealth distributions across tax regimes in each case.
We then turn to the issue of the measurement of the progressivity of
consumption taxes.
Consumption, Asset Accumulation, and Leisure
The means and coefficients of variation for the variables mentioned
above appear in Table 2, while Table 3 contains the Gini Coefficients
for annual income, lifetime income, annual consumption, lifetime
consumption, and wealth. The model does fairly well under relatively
high productivity shock persistence in reproducing estimates of observed
labor income and wealth inequality. Rodriguez et al. (2002), using the
1998 Survey of Consumer Finances, report a wealth Gini of 0.8 and an
annual income Gini of 0.55, very close to the model's predictions
under our benchmark model, which features high persistence. The model
also preserves the observed ordering of inequality seen in the data
(e.g., Rodriguez et al. 2002), where wealth is more unequal than income,
which in turn is more unequal than consumption. Therefore, the limited
insurance that households provide through saving and dissaving is
partially effective but nonetheless results in large wealth inequality.
Table 2 Aggregate Results
[rho] [alpha] [[tau].sub.l] [[tau].sub.k] [[tau].sub.c]
Case 1 0.99 3 0.173 0.35 0.055
Case 2 0.99 3 -- -- 0.338
Case 3 0.99 2 0.173 0.35 0.055
Case 4 0.99 2 -- -- 0.338
Case 5 0.8 3 0.173 0.35 0.055
Case 6 0.8 3 -- -- 0.35
Case 7 0.8 2 0.173 0.35 0.055
Case 8 0.8 2 -- -- 0.35
Case 9 0.5 3 0.173 0.35 0.055
Case 10 0.5 3 -- -- 0.35
Case 11 0.5 2 0.173 0.35 0.055
Case 12 0.5 2 -- -- 0.35
E(l) CV, l E(x) CV, x E(c)
Case 1 .503 0.188 1.958 2.114 0.606
Case 2 .503 0.188 2.351 2.012 0.580
Case 3 .503 0.194 1.650 2.344 0.605
Case 4 .502 0.195 1.948 2.238 0.579
Case 5 .528 0.265 1.984 1.449 0.579
Case 6 .527 0.268 2.616 1.363 0.547
Case 7 .525 0.265 1.659 1.653 0.578
Case 8 .524 0.269 2.219 1.543 0.545
Case 9 .538 0.282 1.994 1.254 0.578
Case 10 .538 0.284 2.635 1.191 0.545
Case 11 .535 0.283 1.670 1.448 0.577
Case 12 .535 0.286 2.238 1.366 0.544
CV, c E(c/ES). CV, c/ES. E (Lab. Inc) CV Lab. Inc
Case 1 1.088 0.530 1.062 0.908 1.396
Case 2 1.108 0.507 1.082 0.905 1.379
Case 3 1.082 0.530 1.057 0.910 1.410
Case 4 1.102 0.506 1.077 0.907 1.394
Case 5 0.890 0.507 0.864 0.885 1.395
Case 6 0.904 0.479 0.878 0.885 1.383
Case 7 0.899 0.506 0.874 0.885 1.400
Case 8 0.912 0.477 0.887 0.887 1.388
Case 9 0.864 0.506 0.834 0.889 1.448
Case 10 0.876 0.478 0.846 0.890 1.437
Case 11 0.875 0.505 0.846 0.890 1.453
Case 12 0.886 0.476 0.856 0.892 1.442
Table 3 Gini Coefficients
Annual Annual Wealth Lifetime Lifetime
Lab Cons. Lab Inc. Cons.
Inc.
[rho] = 0.99, 0.5342 0.4462 0.7574 0.4129 0.38
[alpha] = 3,
[[rho].sub.c] =
.055,
[[rho].sub.1] =
.173,
[[rho].sub.k] =
.35
[rho] = 0.99, 0.5319 0.4494 0.7483 0.4101 0.3834
[alpha] = 3,
[[tau].sub.c] =
.338,
[[tau].sub.1] =
0,
[[tau].sub.k] =
0
[rho] = 0.99, 0.5356 0.4464 0.7895 0.4129 0.3802
[alpha] = 2,
[[tau].sub.c] =
.055,
[[tau].sub.l] =
.173,
[[tau].sub.k] =
.35
[rho] = 0.99, 0.5332 0.4499 0.7806 0.41 0.3836
[alpha] = 2.
[[tau].sub.c] =
.338,
[[tau].sub.l] =
0,
[[tau].sub.k] =
0
[rho] = 0.8, 0.5487 0.3992 0.6599 0.219 0.1975
[alpha] = 3,
[[tau].sub.c] =
.055,
[[tau].sub.l] =
.173,
[[tau].sub.k] =
.35
[rho] = 0.8, 0.5483 0.3999 0.6438 0.217 0.1997
[alpha] = 3,
[[tau].sub.c].
= .35,
[[tau].sub.l] =
0,
[[tau].sub.k] =
0
[rho] = 0.8, 0.5477 0.4032 0.7073 0.2188 0.1982
[alpha] = 2,
[[tau].sub.c] =
.055,
[[tau].sub.l] =
.173,
[[tau].sub.k] =
.35
[rho] = 0.8, 0.5476 0.4032 0.6904 0.2169 0.2004
[alpha] = 2,
[[tau].sub.c].
= .35,
[[tau].sub.l] =
0,
[[tau].sub.k] =
0
[rho] = 0.5, 0.5591 0.3851 0.6145 0.1454 0.1271
[alpha] = 3,
[[tau].sub.c] =
.055,
[[tau].sub.l] =
.173,
[[tau].sub.k] =
.35
[rho] = 0.5, 0.5589 0.3854 0.6004 0.144 0.1287
[alpha] = 3,
[[tau].sub.c] =
.35,
[[tau].sub.l] =
0,
[[tau].sub.k] =
0
[rho] = 0.5, 0.5585 0.389 0.6683 0.1455 0.1276
[alpha] = 2,
[[tau].sub.c].
= .055,
[[tau].sub.l] =
.173,
[[tau].sub.k]=
.35
[rho] = 0.5, 0.5585 0.3886 0.6528 0.1441 0.1292
[alpha]= 2,
[[tau].sub.c] =
.35,
[[tau].sub.l] =
0,
[[tau].sub.K] =
0
Our first result is that the largest effects of a move to a
consumption tax occur in savings. This is due to the removal of the
intertemporal distortion created by the taxation of capital income, as
well as the need for additional savings in retirement to offset the
heavier tax burden faced by retirees who no longer escape taxation. The
magnitude of the increase in average savings is similar to other recent
work (see, e.g., Fuster, Imrohoroglu, and Imrohoroglu [2008], Table 3).
In the cases with lower persistence, when assets are more useful for
self-insurance, the increase in savings when switching to a pure
consumption tax is even larger. That is, a move to a consumption tax
regime under low income shock persistence induces a larger response in
aggregate savings than with higher persistence. This makes clear that
the size of the distortion created by a capital income tax depends on
the shock process faced by households. (6) Of course, the increased
savings means increased resources taken into retirement. However, under
a pure consumption tax regime, the ability of households to use these
resources to finance consumption will be altered. Figure 1 shows that
the removal of the intertemporal distortion in savings ultimately aids
substantially the ability of households to transfer resources into
retirement.
[FIGURE 1 OMITTED]
In contrast to outcomes under pure consumption taxes, the
persistence of shocks to productivity does not play an important role in
aggregate savings when income is taxed. The intuition here is that, with
capital income taxes in particular, arranging for consumption in the
distant future (e.g., at retirement) is more expensive than without a
capital income tax. As a result, even though lower persistence makes
self-insurance more effective, the distortion created by capital income
taxation makes future consumption expensive enough to make the net
increase in aggregate savings small.
With respect to wealth inequality, the coefficients of variation
and Gini Coefficients for wealth show that a move to a consumption tax
lowers wealth inequality and variability, irrespective of persistence
and risk aversion. This is an important observation for those concerned
with the long-run equity implications of consumption taxation. We also
see that, for a given tax regime, low persistence leads to low wealth
inequality. This occurs as lower persistence makes lengthy runs of good
or bad luck less likely. Conversely, lower risk aversion, by making
households more willing to allow for variation in their consumption,
creates a wealth distribution with a lower mean and higher coefficient
of variation for any given tax regime.
Turning next to effective consumption, we see that a move to a
consumption tax has a significant effect. In all economies under study,
our model predicts that a move to a pure consumption tax leads to about
a 6 percent drop in average effective consumption, while leaving the
coefficient of variation largely unchanged. Persistence matters for mean
effective consumption only at the highest value, [rho] = 0.99. However,
a move from the benchmark tax regime to pure consumption taxation does
not substantially affect the variability of consumption, as seen from
the coefficient of variations (c[upsilon]) shown in Table 2.
As a symptom of the effectiveness of self-insurance under
transitory income risk, we see that consumption inequality falls
substantially when the persistence drops below 0.99. This result does
not depend on tax regime or risk aversion. Looking at Table 3, we see
that the Gini Coefficients for consumption show a similar pattern of
inequality as the coefficients of variation. When measured at an annual
frequency, the consumption Gini decreases as persistence falls,
indicating that inequality is higher in states with more persistent
shocks regardless of tax regime or risk aversion. This result is
accentuated when consumption is reported as a lifetime measure.
Unlike its effects on wealth accumulation and effective
consumption, a move to consumption taxes has little impact on labor
supply. Moreover, this is robust as it occurs for all levels of risk
aversion and shock persistence that we consider. This is important, as
the elimination of labor income taxation might have been thought to
induce greater labor supply. However, recall equation (15), which shows
that the optimal mix of consumption and labor depends on the ratio [[1 +
[[tau].sub.c]]/[1 - [[tau].sub.l]]] A move to a pure consumption tax
increases both the numerator and the denominator, potentially undoing
much of the change created by a jump in the consumption tax. This
happens in the model on average. We see in Table 2 that, although
consumption falls, leisure remains more or less constant. We also see
that, regardless of tax regime and risk aversion, the mean and
coefficient of variation of leisure rise with lower persistence. With
higher persistence, each shock changes potential future earnings by more
than if shocks were transitory. This means that the only way to keep
consumption smooth over the life cycle is to work hard in both bad times
and good times, which makes leisure less volatile. The result that labor
supply does not move much with a consumption tax reform is somewhat
telling. Recent work has made clear that household labor supply can be
an important smoothing device (e.g., Pijoan-Mas [2006] and Blundell,
Pistaferri, and Preston [2008]). Yet, in our experiments, labor hours
and earnings respond very little in response to the elimination of
income taxes in favor of consumption taxes. The behavior of labor
supply, therefore, provides an additional source of evidence that
consumption taxes do not expose households to increased risk.
Given the relative invariance of labor supply across economies, the
induced stochastic process for labor income is also similar across
economies. For example, we see only a slight increase in inequality as
persistence decreases, which is reflected in the annual labor income
Gini Coefficient, as well as small changes in response to risk aversion.
With respect to persistence, our finding stems from the increased
volatility in labor supply in low persistence states, which leads to
more volatile income for agents. However, labor income inequality
depends heavily on whether it is measured annually or over the lifetime.
Given any combination of risk aversion and persistence, we see that
annual income inequality is substantially higher than lifetime income
inequality, as realized lifetime productivity will be much less volatile
than its annual counterpart. Moreover, as the persistence of income
grows, the level of annual income inequality decreases slightly, while
lifetime income inequality increases dramatically. This is because the
variance of realized productivity over the lifetime will be much larger
when shocks are persistent.
Measured Progressivity and its Relation to Consumption Smoothing
Having laid out the aggregate implications of a move to a
consumption tax, we now turn to the central questions of our article
regarding the measurement of the incidence of consumption taxes and the
relationship of these statistics to direct measures of consumption
smoothing. To measure the progressivity of a given tax regime for a
given economy, we use the Suits Index (Suits 1977). Let [S.sub.x]
represent the Suits index for a given tax regime and state, and
[T.sub.x](y) represent the cumulative tax burden for a given level of
accumulated household income, y, then:
[S.sub.x] = 1 - [integral][T.sub.x](y)dy.
A Suits index can therefore range between - 1 and 1. A positive
index implies a progressive tax, while a negative index implies
regressivity in the tax regime. An index of 0 is proportional. Table 4
reports the value of the Suits index across experiments and for three
reference variables: realized annual income, realized lifetime income,
and wealth. Our preferred "direct" measures of consumption
smoothing are the coefficient of variation of consumption and the Gini
Coefficient for consumption.
Table 4 Suits Indexes
By By By
Annual Lifetime Wealth
Income Income
[rho] = 0.99, [alpha] = 3, -0.02 0.00 -0.41
[[tau].sub.c] = .055, [[tau].sub.l]
= .173, [[tau].sub.k] = .35
[rho] = 0.99, [alpha] = 3, -0.12 -0.03 -0.42
[[tau].sub.c] = .338, [[tau].sub.l]
= .0, [[tau].sub.k] = 0
[rho] = 0.99, [alpha] = 2, -0.02 0.00 -0.47
[[tau].sub.c] = .055, [[tau].sub.l]
= .173, [[tau].sub.k] = .35
[rho] = 0.99, [alpha] = 2, -0.12 -0.03 -0.49
[[tau].sub.c] = .338, [[tau].sub.l]
= 0, [[tau].sub.k] = 0
[rho] = 0.8, [alpha] = 3, -0.04 0.00 -0.44
[[tau].sub.c] = .055, [[tau].sub.l]
= .173, [[tau].sub.k] = .35
[rho] = 0.8, [alpha] = 3, -0.19 -0.02 -0.44
[[tau].sub.c] = .35, [[tau].sub.l] =
0, [[tau].sub.k] = 0
[rho] = 0.8, [alpha] = 2, -0.04 0.00 -0.50
[[tau].sub.c] = .0.55, [[tau].sub.l]
= .173, [[tau].sub.k] = .35
[rho] = 0.8, [alpha] = 2, -0.19 -0.02 -0.51
[[tau].sub.c] = .35, [[tau].sub.l] =
0, [[tau].sub.k] = 0
[rho] = 0.5, [alpha] = 3, -0.05 0.00 -0.46
[[tau].sub.c] = .055, [[tau].sub.l]
= .173, [[tau].sub.k] = .35
[rho] = 0.5, [alpha] = 3, -0.22 -0.02 -0.46
[[tau].sub.c] = .35, [[tau].sub.l] =
0, [[tau].sub.k] = 0
[rho] = 0.5, [alpha] = 2, -0.05 0.00 -0.53
[[tau].sub.c] = .055, [[tau].sub.l]
= .173, [[tau].sub.k] = .35
[rho] = 0.5, [alpha] = 2, -0.22 -0.02 -0.53
[[tau].sub.c] = .35, [[tau].sub.l] =
0, [[tau].sub.k] = 0
The basic input to the Suits index is a function mapping the
relative contribution of households ranked by a given reference variable
to tax revenues. However, instead of plotting tax contributions by
accumulated percentages of households, as is the case with the Gini
index, which is based on a Lorenz curve, the Suits index relies on a
curve constructed by plotting the cumulative percentage of the reference
variable against the cumulative percent of total tax burden on the
vertical axis. A given point on the x-axis of the more familiar Lorenz
curve refers to a household whose realization of the reference variable
(e.g., income) lies above a given fraction of households. By contrast, a
given point on the x-axis of the Suits index function gives the
accumulated percentage of the reference variable. For example, a value
on the x-axis of 0.3 for a Lorenz curve of tax contributions by income
refers to a household whose income is above 30 percent of households. A
value on the x-axis of 0.3 under the Suits index refers to the entire
set of households whose collective contribution to total income is 30
percent. In particular, unless the reference variable is distributed
uniformly, these two measures will not coincide.
Our main finding is that the measured frequency of income is
important for the assessment of the progressivity of consumption taxes,
both in absolute terms and relative to that obtaining under income
taxes. By contrast, measured income frequency matters very little in the
assessment of progressivity under income taxes. This result is robust as
it survives across varying levels of income shock persistence as well as
risk aversion. Each row in Figure 2 displays the Suits function under
annual and lifetime measures of income for a given level of income shock
persistence. Risk aversion is held fixed at [alpha] = 3. Since
productivity is risky, income is a random variable. Therefore, we
measure income ex-post. In the case of lifetime income, we compute,
using our simulated income histories, realized lifetime labor incomes
for a large sample of households. As seen in Figure 2, the Suits
function for annual incidence lies significantly above the 45[degrees]
line for the consumption tax regime. However, the Suits function for
lifetime incidence is essentially proportional. This finding echoes the
earlier finding of Metcalf (1997) and suggests that the presence of
uninsurable productivity risk does not alter the implications for
regressivity of a consumption tax. The measurement of income also
affects the relative regressivity of consumption taxes versus income
taxes. Figure 2 shows that, under annual measures of income, the
consumption tax appears much more regressive when compared to a regime
with income taxes.
[FIGURE 2 OMITTED]
As mentioned at the outset, the more transitory is productivity
risk, the more labor earnings are likely to respond to a change in
productivity. This is because the ability of a household to generate
earnings over its remaining lifetime is relatively less affected when
shocks to its productivity are transitory. As a result, the household
smooths both consumption and its complement, leisure, quite effectively.
In turn, households often consume amounts that are large in relation to
their earned income when young and small relative to their earned income
when old. As seen in Figure 2, the lower is persistence, the more annual
incidence suggests that consumption taxes are regressive. Table 4
presents the numerical values of the Suits indexes.
When measured by annual income, a move to a consumption tax from
the benchmark tax system leads to more regressivity, and the measure of
regressivity increases as income persistence falls. This is because
transitory shocks are effectively smoothed via both asset accumulation
or decumulation and changes in labor supply. However, as the persistence
of productivity shocks rises, such smoothing becomes more difficult.
Table 2 shows that the variability of both consumption and effective
consumption rise systematically with persistence. Similarly, Table 3
shows that when computed either using lifetime or annual consumption,
the Gini Coefficient remains remarkably stable across tax regimes. As
with the coefficient of variation, the consumption Gini falls
substantially as persistence falls. The preceding makes clear that
measures of regressivity that are based on annual income may be
misleading for household well-being because they rise, while two
independent and direct measures of consumption smoothing indicate an
improvement in insurance. In sharp contrast, lifetime incidence measures
show little variation with shock persistence. It is also important to
note that we disallow borrowing in the model; more ability to issue debt
would further exaggerate the measured regressivity of consumption taxes.
Lastly, while not shown here for brevity, the results in Figure 2 are
nearly replicated when risk aversion is lowered below [alpha] = 3. While
we have focused on consumption, notice that in Table 1 the mean and
coefficient of variation in labor effort are very similar across tax
regimes for all the values of income persistence and risk aversion we
consider. Therefore, consumption taxes are unlikely to damage household
well-being along this dimension.
Taxes that fall disproportionately on households with low wealth
may also be seen as regressive. Therefore, we turn now to measures of
regressivity based on rankings of households by wealth. Wealth is a
"stock" variable and so there is no "frequency"
dimension to its measurement, but the issue of progressivity remains: Do
the relatively wealthy pay disproportionately more than those who have
fewer assets? As seen in Figure 3, the answer is no under either tax
regime. In fact, the Suits index for tax progressivity shown in Table 4
indicates that when measured by wealth, both income and consumption
taxes are quite regressive. The measured regressivity of taxes when the
Suits function is constructed using wealth does respond to changes in
risk aversion. As seen in both Figure 3 and Table 4, higher risk
aversion implies lower measured regressivity. This is an implication of
the increased precautionary savings motive under higher risk aversion,
which leads low-wealth households to increase their savings
disproportionately more than their high-wealth counterparts. Therefore,
any given quantile of wealth represents a larger number of households
under low risk aversion than under high risk aversion. As seen earlier
in Table 2, neither mean consumption nor mean income changes
substantially with risk aversion. Therefore, the contribution to total
tax revenues of the lower wealth quantiles will be greater under low
risk aversion. In addition to the preceding, comparing the columns
within each row of Figure 3 shows that risk aversion has essentially no
effect on the relative progressivity of income and consumption tax
regimes. In terms of the overall regressivity of consumption taxes
relative to current tax policy, the preceding results make clear that
consumption is not inherently more regressive, especially when a
lifetime perspective is taken.
[FIGURE 3 OMITTED]
5. CONCLUDING REMARKS
The smoother is consumption for a household, the more its tax
burden remains invariant to its income. Ironically, this implies that
when insurance and credit markets are most successful in delivering
intertemporally and intratemporally smooth consumption, tax incidence
using high frequency income measures (such as annual income) will, all
else equal, imply the greatest regressivity. In this article, we have
constructed and simulated a rich model of consumption, savings, and work
effort over the life cycle. We have argued that while annual incidence
suggests that consumption taxes are regressive, lifetime incidence
suggests proportionality. Moreover, for a given level of income shock
persistence, consumption taxes do not matter substantially for the
variability of consumption. Lastly, we show that lifetime incidence is
similar across tax regimes, labor productivity persistence, and risk
aversion levels.
REFERENCES
Athreya, Kartik. 2008. "Default, Insurance, and Debt Over the
Life-Cycle." Journal of Monetary Economics 55 (May): 752-74.
Athreya, Kartik, and Andrea L. Waddle. 2007. "Implications of
Some Alternatives to Capital Income Taxation." Federal Reserve Bank
of Richmond Economic Quarterly 93 (Winter): 31-55.
Atkeson, Andrew, V. V. Chari, Patrick J. Kehoe. 1999. "Taxing
Capital Income: A Bad Idea." Federal Reserve Bank of Minneapolis Quarterly Review 23 (Summer): 3-17.
Attanasio, Orazio, James Banks, Costas Meghir, and Guglielmo Weber.
1999. "Humps and Bumps in Lifetime Consumption." Journal of
Business and Economic Statistics 17: 22-35.
Blundell, Richard, Luigi Pistaferri, and Ian Preston. 2008.
"Consumption Inequality and Partial Insurance." Mimeo,
University College London.
Deaton, Angus. 1992. Understanding Consumption. New York: Oxford
University Press.
Erosa, Andres, and Martin Gervais. 2001. "Optimal Taxation in
Infinitely-Lived Agent and Overlapping Generations Models: A
Review." Federal Reserve Bank of Richmond Economic Quarterly 87
(Spring): 23-44.
Fullerton, Don, and Diane Lim Rogers. 1991. "Lifetime Versus
Annual Perspectives on Tax Incidence." National Tax Journal 44
(September): 277-87.
Fuster, Luisa, Ayse Imrohoroglu, and Selahattin Imrohoroglu. 2008.
"Altruism, Incomplete Markets, and Tax Reform." Journal of
Monetary Economics 55 (January): 65-90.
Gourinchas, Pierre-Olivier, and Jonathan A. Parker. 2002.
"Consumption Over the Life Cycle." Econometrica 70 (January):
47-89.
Guvenen, Fatih. 2007. "Learning Your Earning: Are Labor Income
Shocks Really Very Persistent?" American Economic Review 97 (June):
687-712.
Hansen, Gary D. 1993. "The Cyclical and Secular Behavior of
the Labour Input: Comparing Efficiency Units and Hours Worked."
Journal of Applied Econometrics 8: 71-80.
Huggett, Mark. 1996. "Wealth Distribution in Life-Cycle
Economies." Journal of Monetary Economics 38: 469-94.
Metcalf, Gilbert E. 1997. "The National Sales Tax: Who Bears
the Burden?" CATO Policy Analysis No. 289.
Nishiyama, Shinichi, and Kent Smetters. 2005. "Consumption
Taxes and Economic Efficiency with Idiosyncratic Wage Shocks."
Journal of Political Economy 113: 1,088-115.
Pijoan-Mas, Josep. 2006. "Precautionary Savings or Working
Longer Hours?" Review of Economic Dynamics 9 (April): 326-52.
Prescott, Edward C. 2004. "Why Do Americans Work So Much More
than Europeans?" Federal Reserve Bank of Minneapolis Quarterly
Review 28 (July): 2-13.
Rodriguez, Santiago Budria, Javier Diaz-Gimenez, Vincenzo Quadrini,
and Jose-Victor Rios-Rull. 2002. "Updated Facts on the U.S.
Distributions of Earnings, Income, and Wealth." Federal Reserve
Bank of Minneapolis Quarterly Review 26 (Summer): 2-35.
Storesletten, Kjetil, Christopher I. Telmer, and Amir Yaron. 2004.
"Consumption and Risk Sharing over the Life Cycle." Journal of
Monetary Economics 51 (April): 609-33.
Suits, Daniel B. 1977. "Measurement of Tax
Progressivity." American Economic Review 67 (September): 747-52.
Tauchen, George. 1986. "Finite State Markov Chain
Approximations to Univariate and Vector Autoregressions." Economic
Letters 20: 177-81.
Ventura, Gustavo. 1999. "Flat Tax Reform: A Quantitative
Exploration." Journal of Economic Dynamics and Control 23
(September): 1,425-58.
The views expressed in this article do not necessarily reflect
those of the Federal Reserve Bank of Richmond or the Federal Reserve
System. E-mail:
[email protected].
(1) It is for this reason that Erosa and Gervais (2001) emphasize
that wherever a consumption tax system would be optimally age-dependent,
but is unavailable for exogenous reasons, positive flat capital income
taxes can be used along with labor income taxes to acheive the same
outcome.
(2) Alternative regimes to implement consumption taxes include
making all savings fully tax-deductible, or imposing a value-added tax.
(3) An interesting extension for future work would be to allow for
more general, possibly progressive, tax schemes.
(4) Given that the tax rates are assumed to remain constant
throughout time, they do not need to be included in the "state
vector."
(5) All code is available from the authors on request.
(6) Changes in the persistence of the shock alter the unconditional variance of the shock. However, given that productivity is a log-normal
random variable, changes in the varriance affect the mean of the level
of productivity. When we lower the persistence of shocks, we therefore
increase the variance of the transitory component such that the mean
level of income always remains constant. Part of the effect on savings
seen is due to the higher variance of transitory shocks under lower
persistence.