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\no Federal Reserve Bank of Minneapolis\par
\no Research Department Staff Report 534
\medskip
\smallskip
\no Revised December 2016\par
\bigskip
\bigskip
\no{\twelvepoint\bf An Aggregate Model for Policy Analysis with Demographic Change${}^*$}
\bigskip
\bigskip
\no{\smcaps Ellen R.~McGrattan}\nobreak\par
\no{University of Minnesota}\nobreak\par
\no{and Federal Reserve Bank of Minneapolis}
\bigskip
\smallskip
\no{\smcaps Edward C.~Prescott}\nobreak\par
\no{Arizona State University}\nobreak\par
\no{and Federal Reserve Bank of Minneapolis}
\vskip 2.25truein
{
\baselineskip=12pt
\noindent {ABSTRACT\ \hrulefill}
\vskip 5pt
\noindent
Many countries are facing challenging fiscal financing issues as their
populations age and the number of workers per retiree falls. Policymakers need
transparent and robust analyses of alternative policies to deal with the
demographic changes. In this paper, we propose a simple framework that can easily be
matched to aggregate data from the national accounts. We demonstrate
the usefulness of our framework by comparing quantitative results for our
aggregate model with those of a related model that includes
within-age-cohort heterogeneity through productivity differences.
When we assess proposals to switch
from the current tax and transfer system in the United States to a mandatory
saving-for-retirement system with no payroll taxation,
we find that the aggregate predictions for the two models are close.
\vskip 8pt
\noindent Keywords: retirement, taxation, Social Security, Medicare\nobreak\par
\vskip 3pt
\noindent JEL classification: H55, I13, E13
\vskip 8pt
\hrule
\bigskip
{
\baselineskip 11pt
\no${}^*$ {\eightpoint
All supplemental materials are available at
users.econ.umn.edu/$\sim$erm.
The views expressed herein are those of the authors and not
necessarily those of the Federal Reserve Bank of Minneapolis or the
Federal Reserve System.}
}
}
}
\newpage
\footline={\hss\tenrm\folio\hss}
\pageno=1
\section{Introduction}
Many countries are facing challenging fiscal financing issues as their
populations age and the number of workers per retiree falls.
In this paper, we propose a simple overlapping generations model with people
differing only in age. The model can easily be
matched to aggregate data from the national accounts and used to analyze
alternative policies when there is demographic change. We demonstrate
the usefulness of this aggregate model by comparing its quantitative predictions for
U.S.~data with those of a related model analyzed
in our earlier work in which we allowed for within-age-cohort heterogeneity.
(See McGrattan and Prescott (2016).)
When we assess an often-discussed proposal to switch
from the current tax and transfer system in the United States to a mandatory
saving-for-retirement system with no payroll taxation,
we find that the aggregate predictions for the two models are close.
The aggregate predictions we report are the welfare gains of switching policy
regimes and the resultant changes in national account statistics.
If the current system is continued,
taxes must be increased because the number of retirees in the United States
is projected to grow, and their retirement consumption must be somehow financed.
If the system is reformed, payroll
taxes and the associated transfers for Social Security and Medicare
are to be phased out, and
individuals have to save for their own retirement consumption.\note{%
Of course, in practice, saving would be mandatory; otherwise,
individuals would want to opt out and apply for transfer programs targeted to
the poor.} Regardless of whether current policy is continued or reformed,
we assume that spending on all other government transfer programs and purchases of goods and services
remain at their current level as a share of gross national product (GNP).
As in McGrattan and Prescott (2016), we restrict attention to reforms that are
by design welfare improving for all individuals. To ensure
that no one is made worse off, we broaden the tax base and lower marginal tax rates,
at least temporarily, during the transition to the new system.
We report results for both a temporary and a permanent change in the workers' tax schedules.
We verify in the aggregate model with only one productivity type that there is a welfare
gain for all age cohorts, and we show that the
gains are close in magnitude to the population-weighted average
gains in McGrattan and Prescott's (2016) benchmark model that has more
than one productivity type.
We then compare the models' aggregate predictions for statistics in the national
accounts and flow of funds, along with factor inputs and prices.
Like McGrattan and Prescott (2016), we find that reforming Social Security and
Medicare would have a large impact on aggregate statistics.
For example, McGrattan and Prescott (2016) predicted that GNP would be
4.5 percentage points below the current trend if current policy
is continued and 11.4 percentage points above trend if policy is reformed
and workers' tax schedules are changed only temporarily
during the transition. For the aggregate model with one productivity type,
we predict that GNP would be 6.3 percentage points below the current trend if
current policy is continued and 10.4 percentage points above trend if policy is reformed.
Taking differences, the predictions are 15.9 percentage points versus 16.7, respectively.
If tax schedules are permanently changed, the differences in GNP predictions
are 20.6 percentage points
for McGrattan and Prescott (2016) and
19.5 percentage points for the aggregate model proposed here.
Moreover, we find similarly close predictions for consumption, investment,
factor inputs and incomes, the interest rate, tax revenues, and household
net worth.
In Section 2, we present the model economy.
In Section 3, we discuss the parameter estimates and policy experiments.
Section 4 compares predictions of the models with
and without heterogeneity in productivity levels.
Section 5 concludes.
\section{The Model Economy}
The framework we use is a relatively standard overlapping generations model.
The only nonstandard feature that we introduce is the inclusion of multiple business
sectors to account for the fact that U.S.~Schedule C corporations are subject
to the corporate income tax, while pass-through businesses (for example,
sole proprietorships, partnerships, and Schedule S corporations) are not.
Allowing for differences in these businesses helps us match
total incomes and tax revenues.
We consider two versions of the model: the {\it homogeneous within-cohort} version assumes people differ
only in age, and the {\it heterogeneous within-cohort} version assumes people
differ both in age and in their level of productivity.
We are interested in comparing results
for these two versions of the model to see the impact that within-cohort heterogeneity
has on {\it aggregate} predictions.
\subsection{The Population}
We use $h\in \{1,2,\ldots, H\}$ to index the year since entering the workforce,
and we refer to this
as {\it age}.
We use $j\in\{1,2,\ldots,J\}$ to index the productivity level of the household members.
The measure of age $h$ households with productivity level $j$ at date $t$
is denoted $n^{h,j}_t$, and these parameters define the population dynamics.
The measure of people arriving as working-age households
with productivity level $j$ at date $t$ is $n^{1,j}_t$, and
we assume
$$ n^{1,j}_{t+1} = (1+\eta_t) n^{1,j}_t,
\EQN pop$$
with $\sum_j n^{1,j}_0=1$, where $\eta_t$
is the growth rate of households entering the workforce.
The probability of an age $h0$.
\subsection{The Households' Problem}
In each period, households choose consumption $c$ and labor input $\ell$ to maximize utility, and
they take as given their own level of assets $a$ and the law of motion for the aggregate states,
$s'=F(s)$. The states in $s$ are the distribution of assets in the economy,
the level of government debt, and the aggregate stocks of tangible and
intangible capital.
The value function of a household of age $h$
with productivity level $j$ satisfies
$$v_h(a,s,j) = \max_{a',c,\ell\geq 0} \{ u(c,\ell)+\beta \sigma^h_t v_{h+1}(a',s',j)\}
\EQN value
$$
subject to
$$\EQNalign{
& (1+\tau_{ct}) c + a'\sigma^h_t = (1+i_t) a + y_t - T^h_t(y_t)\EQN budget\cr
& y_t = w_t \ell \epsilon^j\EQN y\cr
& s' = F(s), \EQN s\cr
}
$$
where a prime indicates the next period value of a variable,
$\tau_{ct}$ is the tax on consumption,
$i_t$ is the after-tax interest rate,
$w_t$ is the before-tax wage rate,
$\epsilon^j$ is the productivity of an individual of type $j$,
$T^h_t(y_t)$ is the net tax function,
and $v_{H+1}=0$.
Households with $h>H_R$ are retired and have $\ell=0$.
The net tax schedule for retirees ($h>H_R$) is $T_t^j(y)=T_t^r(0)$ and is equal to the
(negative) transfers to retirees since they have no labor income.
The net tax schedule for workers ($h\leq H_R$) is $T_t^h(y)=T_t^w(y)$
and is equal to their total taxes on labor income less any transfers.
Savings are in the form of an annuity that makes payments to members of
a cohort in their retirement years conditional on them being alive.
Effectively, the return on savings depends
on the survival probability as well as the interest rate.\note{%
See McGrattan and Prescott (2016), who show that policy predictions
are robust across many variations of this basic framework.}
In solving the dynamic program in \Ep{value}, households take the aggregate state $s$ and
its evolution as given. Variables that define the aggregate state
are time $t$, the distribution of household assets, the aggregate capital
stocks used by the firms in production, and the government's fiscal policy variables.
We turn next to a discussion of the firms' problem and government policy.
\subsection{The Firms' Problem}
There are two sectors indexed by $i$, and competitive firms in each of these sectors
use inputs of capital and labor
to produce output with the following technologies:
$$ Y_{it} = K_{iTt}^{\theta_{iT}} K_{iIt}^{\theta_{iI}} (\Omega_t L_{it})^{1-\theta_{iT}-\theta_{iI}},
\EQN bigY
$$
where $i=1,2$. The inputs to production are tangible capital $K_{iTt}$, intangible capital $K_{iIt}$,
and labor $L_{it}$, and outputs in both sectors grow with labor-augmenting technical change at the rate
$\gamma$:
$$\Omega_{t+1} = (1+\gamma) \Omega_t.
\EQN omega$$
Firms in the first sector are subject to the corporate income tax and produce intermediate
good $Y_{1t}$; the empirical analogue of these firms are Schedule C corporations, sole proprietorships,
and partnerships.
Firms in the second sector are not subject to the corporate income tax and produce
intermediate good $Y_{2t}$; the empirical analogue of these firms are
pass-through entities like Schedule S corporations.
The aggregate production function of the composite final good is
$$ Y_t = Y_{1t}^{\theta_1} Y_{2t}^{\theta_2},
\EQN aggY $$
where $\theta_1+\theta_2=1$.
Capital stocks depreciate at a constant rate, so
$$\EQNalign{
K_{iT,t+1} &= (1-\delta_{iT})K_{iTt} + X_{iTt} \EQN tang\cr
K_{iI,t+1} &= (1-\delta_{iI})K_{iIt} + X_{iIt} \EQN intang\cr
}
$$
for $i=1,2,$ where $X_{iTt}$ and $X_{iIt}$ denote tangible and intangible investments in
sector $i$, respectively. Depreciation rates
are denoted as $\delta$ and are indexed by sector and capital type.
With competitive firms, factors of production---labor and
both types of capital---in equilibrium are paid their marginal products, which
are therefore the same in both sectors.
The accounting profits of Schedule C corporations are given by
$$\Pi_{1t} = p_{1t}Y_{1t}-w_t L_{1t}-X_{1It}-\delta_{1T} K_{1Tt},
\EQN prof$$
where $p_{1t}$ is
the price of the intermediate good relative to the final good.
Accounting profits are equal to sales less compensation, intangible
investment, and tangible depreciation. Notice that intangible investments
are fully expensed, while tangible investments are capitalized.
Distributions to the corporations' owners are given by
$$ D_{1t} = (1-\tau^\pi_{1t})\Pi_{1t}-K_{1T,t+1}+K_{1Tt},
\EQN dist1$$
where $\tau^\pi_{1t}$ is the corporate income tax levied
on Schedule C profits. These distributions are the after-tax
profits after subtracting retained earnings, $K_{1T,t+1}-K_{1Tt}$.
Other businesses are pass-through entities, so their distributions are
equal to their profits, which in this case is given by
$$ D_{2t} = \Pi_{2t} = p_{2t}Y_{2t}-w_t L_{2t}-X_{2It}-\delta_{2T} K_{2Tt},
\EQN dist2$$
where $p_{2t}$ is the price of the intermediate good relative to the final good.
These payouts are equal to sales less compensation, intangible investment,
and tangible depreciation.
Firms in both sectors maximize the present expected value of after-tax dividends
which are paid to the owners of all capital, namely, the households.
The relevant equilibrium price sequences for the households are
interest rates $\{i_t\}$ and wage rates $\{w_t\}$.
The term $i_ta_t$ in \Ep{budget}
is the combined after-tax dividend income to the households, which is intermediated
costlessly. If after-tax
returns on all assets are equated, it must be the case that the after-tax
interest rate $i_t$ paid to households is equal to the returns of both
types of capital in both sectors.
\subsection{The Government's Fiscal Policy}
The law of motion of government debt is given by
$$ B_{t+1} = B_t + i_t B_t + G_t - \sum_{h,j} n^{h,j}_t T^h_t(w_t\ell^{h,j}_t\epsilon^j)
- \tau^c_t C_t - \tau^\pi_{1t}\Pi_{1t}-\tau^d_{1t}D_{1t}-\tau^d_{2t} D_{2t}.
\EQN debt$$
Thus, next period's debt $B_{t+1}$ is this period's debt $B_t$
plus interest on this period's debt $i_tB_t$,
plus public consumption $G_t$,
minus tax revenues net of transfers. As noted earlier, households pay taxes on labor
and consumption and receive after-tax earnings on their capital income.
The taxes levied on capital income are taxes on Schedule C corporate profits and distributions
at rates $\tau_{1t}^\pi$ and $\tau_{1t}^d$, respectively, and taxes on distributions of
other business income at rate $\tau_{2t}^d$.
\subsection{Market Clearing}
The market for goods must clear in equilibrium, and this implies
$$
Y_t= C_t+X_{Tt}+X_{It}+G_t,
\EQN resource
$$
where $X_{Tt}=\sum_i X_{iTt}$ and $X_{It}=\sum_i X_{iIt}$.
Aggregate labor supply is denoted by $L_t$, and assuming the labor
market clears, it must be the case that
$$L_t=\sum_{h,j} n_t^{h,j}\ell_t^{h,j}\epsilon^j.
\EQN labor $$
Finally, assuming that capital markets clear, it must be the
case that the household policy functions $\{a'=f_h(s,k)\}_h$
imply the aggregate law of motion $s'=F(s)$, where
$F$ is taken as given by the private agents.
Next, we parameterize the model and work with two versions:
one that has within-cohort heterogeneity ($J=4$) as
in McGrattan and Prescott (2016) and another with one productivity
level $J=1$ and $\epsilon^j=1$ for all workers.
The $J=4$ specification is the heterogeneous within-cohort version of the model,
and the $J=1$ specification is the homogeneous within-cohort version.\note{%
McGrattan and Prescott (2016) also report results for the case with $J=7$,
but the main findings are unchanged.} We also refer to the
latter as our aggregate model since there is a representative agent in each cohort.
\section{Parameters and Policies}
In McGrattan and Prescott (2016), we describe in great detail the U.S.~data
that are used to parameterize the heterogeneous within-cohort model.\note{%
The main sources of the data are the
Board of Governors (1945--2015), U.S.~Congress (2012),
U.S.~Department of Commerce (2007), U.S.~Department of Commerce (1929--2015),
U.S.~Department of Labor (1962--2015), and U.S.~Department of Treasury (1962--2015).}
Here, we summarize their parameter choices and the choices we make here for the nested
homogeneous within-cohort model.
\subsection{Parameters}
Table 1 reports parameters calibrated to generate a balanced growth path
that is consistent with U.S.~aggregate statistics averaged over
the period 2000--2010.
More specifically, the model predicts
the same national account and fixed asset statistics as reported
by the Bureau of Economic Analysis (BEA), regardless of the choice of $J$.
(See Tables 1 and 2 in McGrattan and Prescott (2016) for full details.)
The first set of parameters listed in Table 1 are demographic
parameters: growth in population and years of working life.
We set the growth rate of the population equal to 1 percent and the work
life to 45 years.
In addition, we chose survival probabilities $\sigma^h_t$ to match the life
tables in Bell and Miller (2005).
These choices for population growth, working life, and survival probabilities
imply that the models' ratio of workers to retirees is 3.93, which is equal
to the ratio of people over age 15 in the 2005 CPS March Supplement
not receiving Social Security and Medicare benefits
to those who are receiving these benefits.
The second set of parameters listed in Table 1 are preference parameters.
The utility function is logarithmic, that is, $u(c,\ell) = \log c + \alpha \log (1-\ell).$
We set $\alpha$ equal to 1.185 to get the same predicted fraction of
time to work, roughly 28 percent, for the model that we observe in the data.
The discount factor $\beta$ is set equal to 0.987, and this choice along
with the choice of utility guarantees that 58.5 percent
of income goes to labor, which is the U.S.~share of compensation of employees plus 70 percent
of proprietors' income. The remaining income is paid to capital owners.
The next parameters in Table 1 are technology parameters: the growth rate,
capital shares, and depreciation rates.
Growth in labor-augmenting technology is set equal to 2 percent,
which is roughly trend growth in the United States.
The share parameter $\theta_1$ is the relative share of income to
Schedule C corporations and is set equal to 50 percent to be consistent
with IRS data on corporate receipts and deductions (because we do not
have detailed national account data that split corporate income shares for Schedule
C and Schedule S). The remaining shares and the depreciation rates are
chosen to be consistent with investments and capital stocks reported by the
BEA and the flow of funds. To attribute shares of investments and stocks to Schedule C
and all other businesses, we use information on depreciable assets from the IRS.
For the tangible stocks, this implies the following values:
$\theta_{1T}=0.182$, $\theta_{2T}=0.502$, $\delta_{1T}=0.050$, and $\delta_{2T}=0.015$.
In the case of intangible stocks, we cannot uniquely
identify all capital shares and depreciation rates. We somewhat arbitrarily assume that
two-thirds of the intangible capital is in Schedule C corporations and
one-third in other businesses, and we set the depreciation rates on
intangible capital equal to that of tangible capital in Schedule C corporations.
We also set the depreciation rates on intangible capital equal
to the tangible capital in Schedule C corporations.\note{%
See McGrattan and Prescott (2016) for an extensive sensitivity analysis.}
These choices imply that
$\theta_{1I}=0.190$, $\theta_{2I}=0.095$, $\delta_{1I}=0.050$, and $\delta_{2I}=0.050$.
The last set of parameters in Table 1 are policy parameters that remain fixed
during the numerical experiments, namely, spending and
debt shares and capital tax rates.
The level of government consumption $\phi_{Gt}$ in all $t$ is set equal
to 0.044 times GNP, which is the average share of U.S.~military expenditures over
the period 2000--2010.\note{%
The remainder is included with transfers, since it is substitutable with
private consumption.}
The debt to GNP share $\phi_{Bt}$ in all $t$
is set equal to 0.533, which is the average U.S.~ratio for 2000--2010.
Capital tax rates are assumed to be the same for all asset
holders, since most household financial assets are held in accounts managed
by fiduciaries. There are three rates: the tax on Schedule C profits, $\tau^\pi_1$,
the tax on Schedule C distributions, $\tau^d_1$, and the tax on distributions
of all other businesses, $\tau^d_2$. The statutory corporate income tax rate,
which is assessed on Schedule C profits, is 40 percent with federal and state
taxes combined. Not all firms pay this rate, so we use instead an estimate of
the ratio of total revenue to total Schedule C profits. This ratio is 33 percent.
The tax rate on Schedule C distributions is 14.4 percent, which is the
average marginal rate computed by the TAXSIM model described in
Feenberg and Coutts (1993) times the fraction of equity in taxed accounts.
The tax rate on all other businesses is set equal to 38.2 percent, which is
Barro and Redlick's (2011) estimate of the income-weighted average marginal
tax rate on wagelike income for federal, state, and FICA taxation during the period
2000--2010.
To parameterize the initial net tax schedules $T^h_0(\cdot)$, we use distributions
of adjusted gross incomes (AGIs), wages, taxes, and transfers from the 2005
Current Population Survey (CPS),
along with BEA totals (allowing us to scale up any categories in which the
CPS total is less than the BEA total). (See McGrattan and Prescott (2016, Tables
4 and 5) for complete details on the data used in the estimation.)
The tax data are available for tax filers who typically file on behalf of themselves and other
family members. Thus, when organizing the data, we first assign individuals
in the CPS to families, and we compute a family AGI. Families are defined to be
a group of people living in the same household that are either related or unmarried
partners and their relatives, and family AGI is the total AGI summed across AGIs for all tax
filers in the family. Individuals in the family that are at least 15 years old
are assigned an equal share of the family AGI, and this assignment determines
their income brackets when we parameterize the net tax functions, $T^h_0(\cdot)$.
First, consider the net tax schedule for workers. We model it as
a piecewise function found by linearizing
$T^w(y)$ on each AGI income interval $[{\underline y}_i,\bar y_i]$,
$i=1,\ldots, I$, as follows:
$$\EQNalign{
T^w(y) & = T_i(y) -\Psi^w_i\cr
& \simeq T'_i(\bar y)y -\{ [T_i'(\bar y)-T_i(\bar y)/\bar y] \bar y+\Psi^w_i\}\cr
& \equiv \beta_i y + \alpha_i,
\EQN tax function\cr
}
$$
where $\bar y$ is the midpoint in $[{\underline y}_i,\bar y_i]$ and $\Psi^w_i$
is a constant transfer to workers with labor income in this bracket.
The $\beta_i y$ term is the {\it marginal component} of the net tax
schedule, since it depends on income $y$,
and the intercept $\alpha_i$ is the {\it nonmarginal component} of the net
tax schedule, since it is the same for all income earners in the $i$th
income bracket.
The marginal tax rates, $T_i'(\bar y)$ in \Ep{tax function},
based on U.S.~data are shown in
panel A of Figure 1. Twelve rates are plotted and correspond to the twelve family
AGI brackets in our sample.
(The eleventh and twelfth rates are so close as to be indistinguishable.)
These rates are income-weighted average marginal tax rates,
adjusted for employer-sponsored pensions.
For the adjustment, we assume that the pension benefits increase with an
additional hour of work and, therefore, lower the effective marginal tax rates.
We compute the change in the benefits relative to the change in per capita compensation
and subtract the result from the rates.
We then fit a smooth curve through the adjusted rates, and the result
is plotted in Figure 1A.
Figure 1B shows the data underlying the nonmarginal components
($\alpha_i$) of the net tax schedule in \Ep{tax function}
for each of the twelve family AGI bins in our sample. Estimates are in
per capita terms. The first two categories
are government spending on nondefense spending and
transfers other than Social Security and Medicare.
The third category is employer contributions that
we categorize as nonmarginal. For example, if the family
receives a fringe benefit $f$, which is
deducted from total wages, then the
budget set includes a term equal to $f$ times their marginal tax rate (and,
therefore, we use the value of benefits multiplied by the relevant tax
rates). The main benefit in this category is employer contributions for insurance.
The fourth category is the residual category, namely,
$[T_i'(\bar y)-T_i(\bar y)/\bar y] \bar y$ in \Ep{tax function}.
This is constructed as the sum of the differences
between the marginal and average
tax rates from federal and state income filings and the employee's
part of FICA, multiplied by the amount of taxed labor income---wages
and salaries plus 70 percent of proprietors' income.
The estimates in Figure 1 are the underlying data for the tax schedule
in Table 2. The tax rates in panel A of Figure 1 are
the slopes, and the transfers in panel B are needed to estimate the intercepts.
To smooth out the function, we regress the
expenditures in panel B on the midpoints
of the intervals $[{\underline y}_i,\bar y_i]$ and use the linear
approximation for the nonmarginal components of the net tax schedule (that is,
the $\alpha_i$ intercept terms).
The outcome is shown under the heading
``Current Policy'' in Table 2.
All families in the model face this same
net tax schedule, regardless of their productivity type.
For retirees, we estimate transfers $T_0^r(\cdot)$ using
data for Social Security and Medicare and their share of all
other government spending.\note{%
In the United States, individuals can claim Social Security benefits while
still in the labor force. When parameterizing the model, we split our sample
into two: households receiving benefits and those that are not, regardless
of their hours. In most cases, Social Security recipients are supplying
little if any labor.}
The total varies little across family AGI groups,
and therefore we assume it is the same for all income
groups in our model.\note{%
Benefits increase with income, but higher incomes pay taxes on these benefits.
See Steurle and Quakenbush (2013) for estimates of
lifetime benefits of different groups. Also, we work with families
and assume that benefits are attributed to all members over the age of 15.}
Over the period 2000--2010, the expenditures are \$32,526 in 2004 dollars per retiree
and, in the aggregate, a little over 10 percent of GNP.
One more tax rate must be specified, namely, the tax rate on consumption $\tau_{ct}$.
This tax rate is set residually to impose balance on the
government budget. The rate is 6.5 percent in our baseline parameterization.
For the heterogeneous within-cohort model ($J>1$),
we also need to parameterize the productivity levels.
The baseline parameterization has $J=4$ types of families, which
we call {\it low, medium, high,} and {\it top 1 percent}.
The productivity level
$\epsilon^j$ for the low types is chosen so
that the share of
their labor income in the model is 8 percent and matches the share of labor income
for U.S.~families in AGI brackets covering
\$0 to \$15,000 in 2004 dollars.
Thirty-eight percent of the population over 15 years old is included
with this group.
We set the values of $\epsilon^j$ for the medium, high, and top 1 percent
types in a similar way, matching labor income shares
in the model to that of U.S.~families in AGI brackets \$15,000 to \$40,000,
\$40,000 to \$200,000, and over \$200,000, respectively.
These groups have population shares equal to
40, 21, and 1 percent, respectively, and labor income shares of
38, 47, and 7 percent, respectively. (See McGrattan and Prescott (2016).)
To generate these values in our model, we need
to set $\epsilon^j$ equal to 0.33, 0.98, 2.05, and
6.25 for the four productivity types.
When we simulate the model using the parameters in Tables 1 and 2,
our national account and fixed asset statistics match up exactly
with the U.S.~aggregates averaged over the period 2000--2010.
In the case that $J>1$, we also find that the distribution of labor income
for the baseline model is the same as the U.S.~2005 CPS sample.
In both, the Gini index is 0.49.
\subsection{Policies}
To evaluate the usefulness of the homogeneous within-cohort model, we
conduct an often-discussed policy reform, comparing the
continuation of the current U.S.~policy---taxing workers
to finance retiree consumption---with a switch
to a new policy in which individuals save for their own retirement.
We compute aggregate statistics during and after the transition,
as well as the welfare consequences for all current and
future families.
The policy experiments are conducted in the two versions of the model
discussed earlier:
the first assumes that productivity levels differ across four family
types ($J=4$), and the second assumes productivity levels are the same for
all families ($J=1$).
In all simulations considered, a demographic transition takes place, with
the number of workers per retiree falling from 3.93 to 2.40.
To generate the decline in the ratio, we assume that the population
growth rate falls linearly from 1 percent to 0 percent over the first
45 years of the transition and the working life is shortened by 2 years.
\subsubsection{Continue U.S.~Policy}
The continuation policy we consider assumes that transfers for
Social Security and Medicare rise at the same rate as
the retiree population. According to annual reports
summarized in U.S.~Social Security Administration (2013),
this is a conservative estimate for the growth rate of
these transfers. The rise in retiree transfers necessitates
increased taxation. Here, we hold the ratio of debt to
GNP and defense spending to GNP fixed and raise the consumption tax
rate to make up the necessary financing.
The net tax schedules for workers and retirees also remain
unchanged, but revenues change in response to
the demographic transition because economic decisions change.
The initial state is summarized by the
level of government debt and the distribution of
household asset holdings consistent with U.S.~current policy.
\subsubsection{Policy Reform}
We compare a continuation of the current U.S.~policy to
a saving-for-retirement regime, with FICA taxes and transfers to
retirees phased out.
Following McGrattan and Prescott (2016), we also change the
tax schedules for workers during the transition period in order to produce
a Pareto-improving transition. Two changes in these schedules are made.
First, we suspend
deductibility of certain employer benefits. Second, we partially flatten
the net tax schedule of workers.
Along the transition, we assume that net taxes and transfers are computed with
a linear combination of the initial tax schedules, $T^h_0(\cdot)$, and the
final tax schedules, $T^h_\infty(\cdot)$. The rate of change
of retiree transfers is equal to the rate
of change of the fraction retired.
More specifically, let $r_t$
be the fraction of the population that is retired in year $t$, and let $\mu_t$
be the ratio of new retirees in period $t$ relative to new retirees
on the final balanced growth path,
that is, $\mu_t=$ ($r_t-r_1$)/($r_\infty-r_1$), which starts at 0
and rises to 1 over time.
We assume that transfers for Medicare and Social Security
paid to retirees fall at the same rate as $-\mu_t$.
The rate of change of workers' net tax functions is assumed to be faster.
If tax rates are lowered at the
same rate that old-age transfers fall,
the current retirees are indifferent between a continuation of
current policy and a shift to the new system because their benefits
are not affected. But workers are worse off; they face higher
tax rates on their labor income when young but receive lower
transfers by the time they reach retirement age.
If payroll taxes are lowered more quickly than Social Security
and Medicare transfers, then current workers can
immediately take advantage of lower taxes on their
labor income. Specifically, we
let $\xi_t={\rm tanh}(1.5-.1t)$, which is a smoothly declining
function with range [$-1$,1], and we assume that the workers'
net tax schedule at time $t$ is given by
$T^w_t(y)=1/2(T^w_0(y)+T^w_\infty(y))+1/2(T^w_0(y) -T^w_\infty(y))
\xi_t$,
which falls at a rate that is a little more than twice as fast
as the phaseout of the transfers.
When the reform is complete, the payroll tax rates are zero.
This means that the slopes $\{T_{it}'(\bar y)\}$ in future
years at all income intervals, $[{\underline y}_i,\bar y_i]$, are lower.
It also means that the residual in \Ep{tax function} is lower.
In other words, we have a new piecewise linear
net tax schedule for the economy on the final balanced growth path,
with new values for $\{\alpha_i,\beta_i\}$ on AGI intervals
$i=1,\ldots, I$.
We report this new schedule in the columns
under the heading ``No FICA'' in Table 2.
When the FICA taxes are eliminated, so too are the retiree
transfers associated with Social Security and Medicare.
The final retiree transfers in this case are equal
to $T^r_\infty=-$13,344, which is an estimate of per capita
expenditures that, when aggregated, provides the roughly 19
percent of adjusted GNP of resources needed to maintain current spending levels
for public goods and transfers (other than Medicare and Social
Security).
When we phase out the deductibility of employer contributions,
we effectively lower a component of $\alpha_i$ in \Ep{tax function}, namely,
the nonmarginal employer benefits shown in Figure 1B.
The eventual net tax schedule for workers is reported in Table 2
under the column heading ``Suspend Deductibility.''
This broadening of the labor income tax base provides a source
of revenue for financing the transition in addition to consumption taxes.
In addition, when we change the net tax schedule for workers
by lowering marginal rates on labor income, we can accomplish
our goal of constructing a Pareto-improving policy reform.
If the marginal rates are lowered permanently, then the new
tax schedule is that shown in the last two columns of Table 2
under the heading ``Lower Marginal Rates.''
If it is temporary, we assume a reversal in policy and set the
final net tax schedule to be the same as the ``No FICA'' case in Table 2.
For this case,
the deductibility of employer benefits
is reintroduced and the (non-FICA) marginal tax rates are restored to their
earlier levels (found by subtracting the FICA taxes
from the total tax rates).
The reversion occurs at the midpoint of the transition, roughly
50 years after the changes begin.
The time series we use for phasing out FICA taxes and transfers
generate a Pareto-improving transition by design, but not uniquely.
We experimented with variations on the time path of workers' net
tax schedule and found others that generated Pareto improvements.
The one we report is particularly simple and easy to interpret
because the nonmarginal components ($\alpha_i$) are roughly constant
across AGI brackets, at \$13,344 per person in 2004 dollars,
since the residual category $T_i'(\bar y)\bar y-T_i(\bar y)$
is reduced when we lower marginal rates, holding fixed
average rates. If we aggregate the spending per person,
we find an amount equal to all transfers
(other than Social Security and Medicare) and nondefense spending
recorded in the national accounts.
In other words, we continue funding
general public service, public order and
safety, transportation and other economic affairs, housing and community services,
health, recreation and culture, education, income security,
unemployment insurance, veterans' benefits, workers' compensation,
public assistance, employment and training,
and all other transfers to persons unrelated to
Social Security or Medicare.
\section{Results}
In this section, we report model predictions for welfare and aggregate statistics,
comparing the economy if we continue with current policy or switch to a saving-for-retirement
system without payroll taxation or transfers to the elderly.
\subsection{Welfare}
Figure 2 reproduces the main findings in McGrattan and
Prescott (2016) in the case that $J=4$. In panel A of Figure 2,
we show the welfare gains of
gradually eliminating FICA taxes and old-age transfers,
while temporarily changing the workers' net tax functions to suspend deductibility of
employer benefits and lower marginal rates.
The welfare measure that we use
is remaining lifetime consumption
equivalents of cohorts by age at the time of the policy
change and lifetime consumption equivalents of future cohorts.
The figure shows the main result: this reform is Pareto-improving for
all ages and productivity levels. The gains are slight but positive
for cohorts alive at the time of the policy change and over 16 percent
for all but the least productive in the future.
Figure 2B shows the gains in the case that workers' tax
functions are changed permanently. The gains for
those alive at the time of the policy change are nearly the same
by design, while gains for future cohorts are increasing in level
of productivity. The gains for the least productive are
roughly 10 percent gains, while the gains for the most productive are
more than twice as large.
Figure 3 compares the weighted averages from Figure 2 with the
results of the homogeneous within-cohort model that has only one productivity type ($J=1$),
with weights equal to population shares.
As before, there are two cases: one with the workers' net
tax functions changed temporarily and another with the net tax functions
changed permanently. Here, we verify that the aggregate
model shows a Pareto improvement for all age cohorts.
The figures also show that the averages of McGrattan
and Prescott's (2016) heterogeneous-agent model are indistinguishable
from the homogeneous-agent model gains for the cohorts alive at the time
of the policy change. For future cohorts, there are some differences
when the tax functions are changed only temporarily (shown in panel A). For example,
on the new balanced growth path, the welfare gains are predicted
to be 14 percent, which overstates the weighted average of 11 percent for the
model with $J=4$.
However, in the case of a permanent change, both models predict
a 12 percent gain for cohorts born after the transition is complete.
\subsection{Aggregate Data}
In Table 3, we report changes in aggregate
statistics between the initial and final balanced growth
path. (Time series for the full transition are reported
in a separate appendix.) Columns (1) and (4) show
the results if we continue U.S.~policy, and these results are
the same regardless of whether we change the workers' net
tax functions temporarily or permanently when reforming policy.
Columns (2) and (5) show the results if we switch to a
saving-for-retirement system, with workers' net tax functions changed
temporarily (panel A) or permanently (panel B).
We report predictions for GNP, consumption, investments, factor
inputs, factor prices, tax revenues, and household net worth.
The results for the two versions of the model are remarkably
close and confirm the main finding in McGrattan and Prescott (2016),
who found large differences in economic activity
between staying with current policy and switching to
the new saving-for-retirement policy.
Consider first a continuation of current U.S.~policy.
If we compare GNP on the new balanced growth
path with GNP on the original balanced growth path, we
find a decline of $-4.5$ percent for the McGrattan and
Prescott (2016) benchmark model with heterogeneous agents (and $J=4$).
In the homogeneous-agent model, which assumes all individuals have
the same productivity level (that is, $J=1$), the prediction is slightly
lower at $-6.3$ percent. In fact, for all aggregate
statistics, we find the predictions are biased downward
by roughly 1 to 2 percentage points, with the exception
of the interest rate, which is the same for both models.
But the aggregate bias is small in comparison to the overall economic impact
of financing the retirement of the U.S.~aging population.
For example, both models predict that a continuation of policy leads
to sizable declines in tangible and intangible investments:
over 20 percent for tangibles and over 15 percent
for intangibles. Both predict large declines in factor incomes,
factor inputs, and total tax revenues.
Both predict a rise in the wage rate.
In fact, the direction
of change is the same for all variables.
Next, consider results for the reform with net tax functions of the
workers changed only temporarily, which are in columns (2) and
(5) of Table 3, panel A. The McGrattan and
Prescott (2016) benchmark model with heterogeneous agents (column 2)
predicts that GNP would rise 11.4 percent above the old
balanced growth path following the reform.
The model with homogeneous agents (column 5)
predicts a 10.4 percent rise. If we compare
GNP following a continuation of policy and GNP following a reform,
we also find similar results for the comparison: in the case of
heterogeneous agents, the difference in GNPs between the two future
regimes is 15.9 percentage points, and in
the case of homogeneous agents, the difference is 16.7 percentage
points. In other words, we find huge differences for both models.
Furthermore, if we rank the policies across {\it all} of the aggregate
variables, we find sizable differences in favor of reform, and
the differences are roughly
the same magnitudes for the heterogeneous and homogeneous-agent
models. Especially noteworthy is the difference in household
net worth, which is about 27 percent for both models.
The main findings are unchanged for the policy experiments
with workers' tax functions changed permanently. The results in
this case are shown in panel B of Table 3.
The difference in GNPs between the two future regimes is
20.6 percentage points in the heterogeneous-agents case
and 19.5 percentage points in the homogeneous-agents case, and
the difference in household net worth between the two future
regimes is 27.9 percentage points in the heterogeneous-agents case
and 25.7 percentage points in the homogeneous-agents case.
Furthermore, a comparison of the differences in all other variables
shows that gains to reform are sizable and that the model predictions
are remarkably close.
\section{Conclusions}
In this paper, we proposed a simple overlapping generations framework for analyzing
the aggregate impact of
fiscal policies in economies undergoing demographic change.
The proposed framework does not introduce any within-cohort heterogeneity,
but generates aggregate predictions in line with our
earlier work that does (McGrattan and Prescott, 2016). Our hope is that its simplicity
can be exploited by policymakers who need timely analysis.
\newpage
\noindent{\twelvepoint{\bf References}}
\vskip 5pt
{
\baselineskip=14pt
\parskip = 5pt
\parindent= -.25truein
\leftskip = .25truein
Barro, Robert J., and Charles J.~Redlick,
``Macroeconomic Effects from Government Purchases and Taxes,''
{\it Quarterly Journal of Economics}, 126 (2011), 51--102.
Bell, Felicitie C., and Michael L. Miller,
``Life Tables for the United States Social Security Area 1900-2100: Actuarial Study No. 120,''
Social Security Administration Publication No. 11-11536, 2005.
Board of Governors,
{\it Flow of Funds Accounts of the United States},
Statistical Release Z.1
(Washington, DC: Board of Governors of the Federal Reserve System, 1945--2015).
Feenberg, Daniel, and Elisabeth Coutts,
``An Introduction to the TAXSIM Model,''
{\it Journal of Policy Analysis and Management}, 12 (1993), 189--194.
McGrattan, Ellen R., and Edward C. Prescott,
``On Financing Retirement with an Aging Population,''
{\it Quantitative Economics}, 2016, forthcoming.
Steurle, C.~Eugene, and Caleb Quakenbush,
``Social Security and Medicare Taxes and Benefits over a Lifetime: 2013 Update,''
Urban Institute, 2013
(http://www.urban.org).
U.S.~Congress, Congressional Budget Office,
``Effective Marginal Tax Rates for Low- and Moderate-Income Workers''
(Washington, DC: U.S.~Government Printing Office, 2012).
U.S.~Department of Commerce, Bureau of Economic Analysis,
``Comparison of BEA Estimates of Personal Income and IRS
Estimates of Adjusted Gross Income: New Estimates for 2005
and Revised Estimates for 2004,''
{\it Survey of Current Business}
(Washington, DC: U.S.~Government Printing Office, 2007).
U.S.~Department of Commerce, Bureau of Economic Analysis,
``National Income and Product Accounts of the United States,''
{\it Survey of Current Business}
(Washington, DC: U.S.~Government Printing Office, 1929--2015).
U.S.~Department of Labor, Bureau of Labor Statistics,
``Current Population Survey, March Supplement''
(Washington, DC: U.S.~Government Printing Office, 1962--2015).
U.S.~Department of the Treasury, Internal Revenue Service,
``Statistics of Income''
(Washington, DC: U.S.~Government Printing Office, 1918--2015).
U.S.~Social Security Administration,
``Status of the Social Security and Medicare Programs:
A Summary of the 2013 Annual Reports,''
Social Security and Medicare Board of Trustees, 2013
(http://www.socialsecurity.gov).
}
\newpage
\vfill\eject
\centerline{\smcaps Table 1 }
\vskip -5pt
\centerline{\smcaps Parameters of the Economy Calibrated to U.S.~Aggregate Data}
\medskip
\centerline{\vbox{\tabskip=0pt\offinterlineskip
\def\tablerule{\noalign{\hrule}}
\halign to400pt{\tabskip=1em plus2em
#&#\hfil&
#&\hfil#&
#\tabskip=0pt\cr
\tablerule
\noalign{\vskip 2pt}
\tablerule
\noalign{\bigskip}
\strut&\hskip -.3truein {\smcaps Demographic parameters} && &\cr
\noalign{\bigskip}
\strut&\hskip -.1truein Growth rate of population ($\eta$) && 1\%&\cr
\noalign{\vskip 3pt}
\strut&\hskip -.1truein Work life in years && 45&\cr
\noalign{\bigskip}
\strut&\hskip -.3truein {\smcaps Preference parameters} && &\cr
\noalign{\bigskip}
\strut&\hskip -.1truein Disutility of leisure ($\alpha$) && 1.185&\cr
\noalign{\vskip 3pt}
\strut&\hskip -.1truein Discount factor ($\beta$) && 0.987&\cr
\noalign{\bigskip}
\strut&\hskip -.3truein {\smcaps Technology parameters} && &\cr
\noalign{\bigskip}
\strut&\hskip -.1truein Growth rate of technology ($\gamma$) && 2\%&\cr
\noalign{\vskip 3pt}
\strut&\hskip -.1truein Income share, Schedule C corporations ($\theta_1$)
&& 0.500&\cr
\noalign{\vskip 5pt}
\strut&\hskip -.1truein Capital shares && &\cr
\noalign{\vskip 5pt}
\strut&\hskip .1truein Tangible capital, Schedule C ($\theta_{1T}$) && 0.182&\cr
\noalign{\vskip 3pt}
\strut&\hskip .1truein Intangible capital, Schedule C ($\theta_{1I}$) && 0.190&\cr
\noalign{\vskip 3pt}
\strut&\hskip .1truein Tangible capital, other business ($\theta_{2T}$) && 0.502&\cr
\noalign{\vskip 3pt}
\strut&\hskip .1truein Intangible capital, other business ($\theta_{2I}$) && 0.095&\cr
\noalign{\vskip 5pt}
\strut&\hskip -.1truein Depreciation rates && &\cr
\noalign{\vskip 5pt}
\strut&\hskip .1truein Tangible capital, Schedule C ($\delta_{1T}$) && 0.050&\cr
\noalign{\vskip 3pt}
\strut&\hskip .1truein Intangible capital, Schedule C ($\delta_{1I}$) && 0.050&\cr
\noalign{\vskip 3pt}
\strut&\hskip .1truein Tangible capital, other business ($\delta_{2T}$) && 0.015&\cr
\noalign{\vskip 3pt}
\strut&\hskip .1truein Intangible capital, other business ($\delta_{2I}$) && 0.050&\cr
\noalign{\bigskip}
\strut&\hskip -.3truein {\smcaps Spending and debt shares } && &\cr
\noalign{\bigskip}
\strut&\hskip -.1truein Defense spending ($\phi_G$) && 0.044&\cr
\noalign{\vskip 3pt}
\strut&\hskip -.1truein Government debt ($\phi_B$) && 0.533&\cr
\noalign{\bigskip}
\strut&\hskip -.3truein {\smcaps Capital tax rates } && &\cr
\noalign{\bigskip}
\strut&\hskip -.1truein Profits, Schedule C corporations ($\tau^\pi_1$) && 0.330&\cr
\noalign{\vskip 3pt}
\strut&\hskip -.1truein Distributions, Schedule C corporations ($\tau^d_1$) && 0.144&\cr
\noalign{\vskip 3pt}
\strut&\hskip -.1truein Distributions, other business ($\tau^d_2$) && 0.382&\cr
\noalign{\vskip 3pt}
\noalign{\bigskip}
\tablerule
\noalign{\vskip 2pt}
\tablerule}}}
\newpage
\centerline{\smcaps Table 2 }
\vskip -5pt
\centerline{\smcaps Current and Future
Labor Income Net Tax Schedules, $T_\infty^w(y)=\alpha_i+\beta_i y$}
\medskip
\centerline{\vbox{\tabskip=0pt\offinterlineskip
\def\tablerule{\noalign{\hrule}}
\halign to400pt{\tabskip=.5em plus1em
#&#\hfil&
#&\hfil#&
#&\hfil#&
#&\hfil#&
#&\hfil#&
#&\hfil#&
#&\hfil#&
#&\hfil#&
#&\hfil#&
#\tabskip=0pt\cr
\noalign{\medskip}
\tablerule
\noalign{\vskip 2pt}
\tablerule
\noalign{\smallskip}
\strut& && \multispan{3}\hidewidth \hidewidth&&
\multispan{3}\hidewidth \hidewidth&&
\multispan{7}\hidewidth Additionally:\hidewidth&\cr
\noalign{\vskip -5pt}
\strut& && && && && &&\multispan{8}\hrulefill\cr
\strut& && \multispan{3}\hidewidth \hidewidth&&
\multispan{3}\hidewidth \hidewidth&&
\multispan{3}\hidewidth Suspend \hidewidth&&
\multispan{3}\hidewidth Lower \hidewidth&\cr
\strut& && \multispan{3}\hidewidth Current Policy \hidewidth&&
\multispan{3}\hidewidth No FICA\hidewidth&&
\multispan{3}\hidewidth Deductibility\hidewidth&&
\multispan{3}\hidewidth Marginal Rates\hidewidth&\cr
\noalign{\vskip -5pt}
\strut& Earnings & \multispan{17}\hrulefill\cr
\strut& Over: && \omit\hidewidth $\alpha_i$\hidewidth&&
\omit\hidewidth $\beta_i$\hidewidth&&
\omit\hidewidth $\alpha_i$\hidewidth&&
\omit\hidewidth $\beta_i$\hidewidth&&
\omit\hidewidth $\alpha_i$\hidewidth&&
\omit\hidewidth $\beta_i$\hidewidth&&
\omit\hidewidth $\alpha_i$ \hidewidth&&
\omit\hidewidth $\beta_i$ \hidewidth&\cr
\noalign{\vskip -5pt}
\strut& \multispan{18}\hrulefill\cr
\noalign{\vskip -5pt}
\noalign{\medskip}
\strut& 0&& $-$11,762&& 0.059&& $-$11,401&& $-$0.066&& $-$11,376&& $-$0.066&& $-$13,344&& 0.000&\cr
\noalign{\vskip 5pt}
\strut& 5,132&& $-$12,819&& 0.246&& $-$12,619&& 0.056&& $-$12,268&& 0.056&& $-$13,344&& 0.044&\cr
\noalign{\vskip 5pt}
\strut& 11,664&& $-$13,518&& 0.264&& $-$13,427&& 0.123&& $-$12,752&& 0.123&& $-$13,344&& 0.088&\cr
\noalign{\vskip 5pt}
\strut& 17,418&& $-$14,365&& 0.293&& $-$14,403&& 0.160&& $-$13,302&& 0.160&& $-$13,344&& 0.132&\cr
\noalign{\vskip 5pt}
\strut& 23,718&& $-$15,211&& 0.316&& $-$15,379&& 0.175&& $-$13,836&& 0.175&& $-$13,344&& 0.176&\cr
\noalign{\vskip 5pt}
\strut& 29,692&& $-$15,971&& 0.332&& $-$16,255&& 0.187&& $-$14,353&& 0.187&& $-$13,344&& 0.220&\cr
\noalign{\vskip 5pt}
\strut& 36,351&& $-$17,000&& 0.349&& $-$17,447&& 0.192&& $-$15,245&& 0.192&& $-$13,344&& 0.230&\cr
\noalign{\vskip 5pt}
\strut& 45,274&& $-$18,503&& 0.367&& $-$19,182&& 0.242&& $-$16,505&& 0.242&& $-$13,344&& 0.240&\cr
\noalign{\vskip 5pt}
\strut& 58,274&& $-$20,359&& 0.382&& $-$21,325&& 0.275&& $-$17,189&& 0.275&& $-$13,344&& 0.250&\cr
\noalign{\vskip 5pt}
\strut& 74,560&& $-$22,880&& 0.396&& $-$24,236&& 0.301&& $-$19,382&& 0.301&& $-$13,344&& 0.260&\cr
\noalign{\vskip 5pt}
\strut& 106,007&& $-$28,810&& 0.409&& $-$31,083&& 0.332&& $-$25,571&& 0.332&& $-$13,344&& 0.270&\cr
\noalign{\vskip 5pt}
\strut& 191,264&& $-$45,792&& 0.409&& $-$50,690&& 0.372&& $-$43,894&& 0.372&& $-$13,344&& 0.290&\cr
\noalign{\vskip 5pt}
\tablerule
\noalign{\vskip 2pt}
\tablerule}}}
\item{} {\eightpoint {\it Note:} Earnings and net tax function intercepts are reported in 2004 dollars. }
\newpage
\centerline{\smcaps Table 3 }
\vskip -5pt
\centerline{\smcaps Changes in Balanced Growth Aggregate Statistics}
\medskip
\centerline{\vbox{\tabskip=0pt\offinterlineskip
\def\tablerule{\noalign{\hrule}}
\halign to400pt{\tabskip=1em plus2em
#&#\hfil&
#&\hfil#&
#&\hfil#&
#&\hfil#&\vrule
#&\hfil#&
#&\hfil#&
#&\hfil#&#\tabskip=0pt\cr
\tablerule
\noalign{\vskip 2pt}
\tablerule
\strut& && && && && && && &\cr
\noalign{\vskip -7pt}
\strut& &&\multispan{5}\hidewidth Heterogeneous within Cohort\hidewidth&&
\multispan{5}\hidewidth Homogeneous within Cohort\hidewidth&\cr
\strut& && && && && && && &\cr
\noalign{\vskip -15pt}
\strut& &\multispan{13}\hrulefill\cr
\strut& && && && && && && &\cr
\noalign{\vskip -10pt}
\strut& &&\hidewidth Continue\hidewidth &&\hidewidth Reform\hidewidth &&\hidewidth Difference\hidewidth
&&\hidewidth Continue\hidewidth &&\hidewidth Reform\hidewidth &&\hidewidth Difference\hidewidth&\cr
\strut& &&\hidewidth (1)\hidewidth &&\hidewidth (2)\hidewidth &&\hidewidth (2)$-$(1)\hidewidth
&&\hidewidth (4)\hidewidth &&\hidewidth (5)\hidewidth &&\hidewidth (5)$-$(4)\hidewidth&\cr
\noalign{\vskip -10pt}
\strut& && && && && && && &\cr
\tablerule
\noalign{\vskip 5pt}
\strut& \multispan{12}\hidewidth \smcaps \ \ \ A. Workers' Net Tax Functions Changed Temporarily during Reform\hidewidth&\cr
\noalign{\vskip 5pt}
\strut& GNP && $-$4.5&& 11.4&& 15.9&& $-$6.3&& 10.4&& 16.7&\cr
\strut& && && && && && && &\cr
\noalign{\vskip -10pt}
\strut& Consumption && $-$0.2&& 13.5&& 13.7&& $-$2.1&& 13.7&& 15.7&\cr
\strut& && && && && && && &\cr
\noalign{\vskip -10pt}
\strut& Tangible investment &&$-$20.6&& 3.0&& 23.6&& $-$21.9&& 1.1&& 23.0&\cr
\strut& && && && && && && &\cr
\noalign{\vskip -10pt}
\strut& Intangible investment &&$-$15.6&& 5.8&& 21.4&& $-$16.6&& 4.5&& 21.0&\cr
\strut& && && && && && && &\cr
\noalign{\vskip -10pt}
\strut& Labor income && $-$5.8&& 10.8&& 16.6&& $-$7.4&& 9.6&& 17.1&\cr
\strut& && && && && && && &\cr
\noalign{\vskip -10pt}
\strut& Capital income &&$-$24.2&&$-$15.5&& 8.7&& $-$26.0&&$-$16.1&& 10.0&\cr
\strut& && && && && && && &\cr
\noalign{\vskip -10pt}
\strut& Tangible capital && $-$2.4&& 27.3&& 29.6&& $-$3.9&& 24.9&& 28.8&\cr
\strut& && && && && && && &\cr
\noalign{\vskip -10pt}
\strut& Intangible capital && $-$4.3&& 20.0&& 24.3&& $-$5.4&& 18.5&& 23.9&\cr
\strut& && && && && && && &\cr
\noalign{\vskip -10pt}
\strut& Labor input && $-$9.8&& $-$1.8&& 8.0&& $-$10.5&& $-$1.3&& 9.2&\cr
\strut& && && && && && && &\cr
\noalign{\vskip -10pt}
\strut& Wage rate && 4.4&& 12.8&& 8.4&& 3.4&& 11.1&& 7.7&\cr
\strut& && && && && && && &\cr
\noalign{\vskip -10pt}
\strut& Interest rate, level (\%)&& 4.3&& 3.8&& $-$0.5&& 4.3&& 3.8&& $-$0.5&\cr
\strut& && && && && && && &\cr
\noalign{\vskip -10pt}
\strut& Tax revenues && 7.3&&$-$10.2&&$-$17.5&& 6.4&& $-$9.8&&$-$16.1&\cr
\strut& && && && && && && &\cr
\noalign{\vskip -10pt}
\strut& Household net worth && $-$3.0&& 24.4&& 27.4&& $-$4.5&& 22.3&& 26.8&\cr
\noalign{\medskip}
\strut& \multispan{12} \hidewidth \smcaps \ \ \ B. Workers' Net Tax Functions Changed Permanently during Reform\hidewidth&\cr
\noalign{\vskip 5pt}
\strut& GNP && $-$4.5&& 16.1&& 20.6&& $-$6.3&& 13.2&& 19.5&\cr
\strut& && && && && && && &\cr
\noalign{\vskip -10pt}
\strut& Consumption && $-$0.2&& 19.5&& 19.7&& $-$2.1&& 17.6&& 19.7&\cr
\strut& && && && && && && &\cr
\noalign{\vskip -10pt}
\strut& Tangible investment &&$-$20.6&& 3.0&& 23.6&&$-$21.9&& $-$0.2&& 21.7&\cr
\strut& && && && && && && &\cr
\noalign{\vskip -10pt}
\strut& Intangible investment &&$-$15.6&& 7.2&& 22.9&&$-$16.6&& 0.2&& 21.2&\cr
\strut& && && && && && && &\cr
\noalign{\vskip -10pt}
\strut& Labor income && $-$5.8&& 15.1&& 20.9&& $-$7.4&& 12.0&& 19.5&\cr
\strut& && && && && && && &\cr
\noalign{\vskip -10pt}
\strut& Capital income &&$-$24.2&&$-$10.3&& 13.9&&$-$26.0&&$-$12.4&& 13.6&\cr
\strut& && && && && && && &\cr
\noalign{\vskip -10pt}
\strut& Tangible capital && $-$2.4&& 27.0&& 29.3&& $-$3.9&& 23.1&& 27.0&\cr
\strut& && && && && && && &\cr
\noalign{\vskip -10pt}
\strut& Intangible capital && $-$4.3&& 21.6&& 25.9&& $-$5.4&& 18.6&& 24.0&\cr
\strut& && && && && && && &\cr
\noalign{\vskip -10pt}
\strut& Labor input && $-$9.8&& 5.2&& 15.0&&$-$10.5&& 4.1&& 14.7&\cr
\strut& && && && && && && &\cr
\noalign{\vskip -10pt}
\strut& Wage rate && 4.4&& 9.4&& 5.0&& 3.4&& 7.6&& 4.2&\cr
\strut& && && && && && && &\cr
\noalign{\vskip -10pt}
\strut& Interest rate, level (\%) && 4.3&& 4.0&& $-$0.3&& 4.3&& 4.0&& $-$0.3&\cr
\strut& && && && && && && &\cr
\noalign{\vskip -10pt}
\strut& Tax revenues && 7.3&&$-$29.1&&$-$36.4&& 6.4&&$-$29.8&&$-$36.2&\cr
\strut& && && && && && && &\cr
\noalign{\vskip -10pt}
\strut& Household net worth && $-$3.0&& 24.9&& 27.9&& $-$4.5&& 21.2&& 25.7&\cr
\noalign{\vskip 2pt}
\tablerule
\noalign{\vskip 2pt}
\tablerule}}}
{
\baselineskip = 12pt
\item{} {\eightpoint {\it Note:} Statistics are percentage changes between the final and initial balanced growth paths,
with the exception of the interest rate, which is the level on the final growth path.}
}
\newpage
\centerline{\ }
\vskip -40pt
\centerline{\smcaps Figure 1}
\vskip -5pt
\centerline{\smcaps Marginal and Nonmarginal Components of the Net Tax
Function}
\vskip -5pt
\bigskip
\centerline{ A. Marginal tax rates on labor income }
\def\epsfsize#1#2{.40#1}
\centerline{\epsffile{./figures/fig1A.eps}}
\bigskip
\centerline{ B. Nonmarginal components that affect worker budget sets}
\def\epsfsize#1#2{.40#1}
\centerline{\epsffile{./figures/fig1B.eps}}
\newpage
\centerline{\ }
\vskip -45pt
\centerline{\smcaps Figure 2}
\vskip -5pt
\centerline{\smcaps Percentage Welfare Gains by Age Cohort and Productivity Type}
\vskip -7pt
\centerline{\smcaps Heterogeneous-Agents Model }
\bigskip
\centerline{ A. $T^w(y)$ Changed Temporarily }
\def\epsfsize#1#2{.40#1}
\centerline{\epsffile{./figures/fig2A.eps}}
\bigskip
\centerline{ B. $T^w(y)$ Changed Permanently}
\def\epsfsize#1#2{.40#1}
\centerline{\epsffile{./figures/fig2B.eps}}
\newpage
\centerline{\ }
\vskip -45pt
\centerline{\smcaps Figure 3}
\vskip -5pt
\centerline{\smcaps Percentage Welfare Gains by Age Cohort}
\vskip -7pt
\centerline{\smcaps Homogeneous-Agents Model and Heterogeneous-Agents Model Average}
\bigskip
\centerline{ A. $T^w(y)$ Changed Temporarily }
\def\epsfsize#1#2{.40#1}
\centerline{\epsffile{./figures/fig3A.eps}}
\bigskip
\centerline{ B. $T^w(y)$ Changed Permanently}
\def\epsfsize#1#2{.40#1}
\centerline{\epsffile{./figures/fig3B.eps}}
\bye