Dynamic Scoring: Alternative Financing Schemes

Abstract

Neoclassical growth models predict that reductions in capital or labor tax rates are expansionary when lump-sum transfers are used to balance the government budget. This paper explores the consequences of bond-financed tax reductions that bring forth a range of possible offsetting policies, including future government consumption, capital tax rates, or labor tax rates. Through the resulting intertemporal distortions, current tax cuts can be contractionary. The paper also finds that more aggressive responses of offsetting policies to debt engender less debt accumulation and less costly tax cuts.

Full text

DYNAMIC SCORING: ALTERNATIVE FINANCING SCHEMES
ERIC M. LEEPER AND SHU-CHUN SUSAN YANG
Abstract. Neoclassical growth models predict that reductions in capital or la-
bor tax rates are expansionary when lump-sum transfers are used to balance the
government budget. This paper explores the consequences of bond-financed tax
reductions that bring forth a range of possible offsetting policies, including future
government consumption, capital tax rates, or labor tax rates. Through the result-
ing intertemporal distortions, current tax cuts can be contractionary. The paper
also finds that more aggressive responses of offsetting policies to debt engender less
debt accumulation and less costly tax cuts.
1. Introduction
Can tax cuts pay for themselves? If not, to what extent do tax cuts expand the
tax base to offset revenue losses? These questions are under active consideration by
U.S. fiscal authorities who are studying dynamic scoring to assess the budgetary cost
of tax changes. Dynamic scoring computes the revenue effects of a tax proposal using
macroeconomic models in which tax changes can affect aggregate income and feedback
to revenues through the tax base.1Recent academic research employs calibrated
neoclassical growth models to bring modern quantitative analysis to bear on the
questions in fully general equilibrium environments [Mankiw and Weinzierl (2006)
and Trabandt and Uhlig (2006)].
This paper pursues two themes that are important for dynamic scoring but are
abstracted from in existing academic work. First, how do the fiscal costs of tax
cuts vary with alternative assumptions about financing methods: reducing transfers
or purchases, raising other taxes, or increasing borrowing? Second, if tax cuts are
financed through borrowing, how do the costs vary with the aggressiveness of the
Date : December 19, 2006. Indiana University and NBER, eleeper@indiana.edu; Joint Committee
on Taxation, U.S. Congress, susan.yang@mail.house.gov. We are grateful to anonymous referees
and the editor for helpful suggestions. This material is based upon work supported by the National
Science Foundation under Grant No. SES-0452599. The views expressed in this paper are strictly
those of the authors and should not be attributed to the Joint Committee on Taxation or any
Member of Congress.
1See Auerbach (2005) for a useful overview and Furman (2006) for a review of recent dynamic
analyses performed by government agencies.

DYNAMIC SCORING: ALTERNATIVE FINANCING SCHEMES 2
offsetting fiscal reaction to debt growth? The first theme figures prominently in prac-
tical analyses by fiscal agencies [Congressional Budget Office (2005), Joint Committee
on Taxation (2005), U.S. Department of Treasury (2006)], but tend to be handled
in stark ways in academic studies. The second theme is implicit in fiscal agencies’
studies in which debt accumulation is tracked, but overlooked in academic work.
Mankiw and Weinzierl (2006) examine dynamic scoring in a neoclassical growth
model, assuming that contemporaneous lump-sum transfers adjust to balance the
budget. A version of the model calibrated to U.S. data suggests that permanent
reductions in capital (labor) tax rates can expand the tax base enough to offset
53 percent (17 percent) of the revenue loss. As the authors themselves point out,
however, their analysis does not address several factors that are potentially impor-
tant for dynamic scoring, including the possibility that financing schemes may dis-
tort economic behavior. Trabandt and Uhlig (2006) consider a distorting financing
method—reductions in government consumption—but assume that government debt
evolves exogenously; hence, their paper does not study the consequences of perma-
nent or transitory changes in the state of government indebtedness induced by tax
changes.
We analyze a conventional neoclassical growth model that is a discrete-time version
of Mankiw and Weinzierl’s model. Government issues debt to finance a tax cut, and
has access to lump-sum and distorting financing schemes to maintain fiscal solvency.
To the extent that a reduction in one fiscal distortion is replaced by a change in some
other distortion, or combination of distortions, the results derived from lump-sum fi-
nancing are likely to change. Specifically, we consider permanent reductions in capital
or labor tax rates. Fiscal sustainability is ensured by one of three instruments: (1)
lower government transfer-output ratios, (2) lower government consumption-output
ratios, or (3) increases in other tax rates. The budgetary cost of tax cuts is measured
by changes in tax revenues net of interest payments on outstanding debt.2
The paper studies how permanent cuts in capital and labor tax rates affect the
economy, both in long-run steady states and along the transition path to a new steady
state. Two conclusions emerge. First, the expansionary effects of a tax cut depend
crucially on the choice of which fiscal instrument adjusts and on the magnitude of the
adjustment in response to a deteriorating budget. The stronger is the response, the
less debt accumulates, and the more favorable are the expansionary effects of a tax
cut. Second, government indebtedness matters for the budgetary cost of a tax cut
especially in the long(er) run: a more aggressive response to a deteriorating budget
2In contrast to Mankiw and Weinzierl, we do not compute revenue feedback measures, which are
defined as the proportion of revenue losses offset by an expanded tax base. When a cut in one tax
rate is offset by an increase in another tax rate, there is no change in the static score—the change
in revenue holding the tax base fixed—and revenue feedback is undefined. In addition, when a tax
cut is debt-financed, interest payments should be factored into computing the budgetary impact.

DYNAMIC SCORING: ALTERNATIVE FINANCING SCHEMES 3
yields a smaller debt-output ratio and makes a tax cut less costly. This result holds
even when the fiscal adjustment is non-distorting.
2. Budget Solvency and Tax Cuts
Neoclassical growth models, such as Baxter and King (1993), take the long-run
growth rate of the economy as exogenous and impose the restriction that a debt-
financed tax cut inevitably involves some offsetting policies to ensure budget solvency.
Offsetting policies, however, may be unnecessary when long-run growth rates are
endogenous. King and Rebelo (1990) find that lower income tax rates produce higher
long-run economic growth. Ireland (1994) further demonstrates that when the long-
run growth rate after a tax cut outpaces the growth rate of government debt, the
expansionary effects of a debt-financed tax cut can pay off debt without any further
fiscal adjustments. Subsequent studies by Bruce and Turnovsky (1999) and Novales
and Ruiz (2002), however, find that tax cuts can improve the long-run budget only
when the elasticity of intertemporal substitution of consumption is implausibly high.
Although some doubt remains about whether a deficit-financed tax cut can actually
be self-financing, this paper focuses on circumstances in which tax cuts induce current
or future fiscal adjustments that maintain a sustainable budget.
In the U.S. economy, state governments quickly initiate offsetting policies because
many state constitutions require balancing the budget within a couple of years. No
analogous statutory requirement constrains federal behavior, and offsetting policy ac-
tions can take much longer to be implemented. For example, when the debt-output
ratio rose rapidly in the early and mid-1980s (partly due to the large tax cuts in the
Economic Recovery Act of 1981), the Gramm-Rudman-Hollings balanced-budget law
was enacted in 1985 to reduce deficits. In addition, the Omnibus Budget Reconcil-
iation Acts of 1990 and 1993, which increased individual and corporate income tax
rates, were passed to reduce government debt. A rapidly rising debt-GDP ratio since
2001 again has spurred calls for cutting federal deficits [Greenspan (2005a,b)].
Aside from anecdotal examples, some econometric evidence finds that policy makers
systematically take corrective measures in response to rising debt levels. Using long-
term U.S. data from 1916 to 1995, Bohn (1998) concludes that the primary surplus
responds positively to the debt-GDP ratio and makes the debt ratio mean-reverting,
after controlling for war-time spending and for cyclical fluctuations. Davig and Leeper
(2006) estimate a regime-switching rule for tax policy over the post-war period in the
U.S. and find that policy swings between periods when taxes are unresponsive to debt
and periods when they respond aggressively. Davig (2005) uses a Markov-switching
model to test the global sustainability of U.S. post-war policy; he finds that threats to
long-run sustainability posed by expanding periods of discounted debt are mitigated
by the expectation of returning to a regime where debt is repaid. This evidence

DYNAMIC SCORING: ALTERNATIVE FINANCING SCHEMES 4
underscores the empirical relevance of considering postponed offsetting policies to
ensure budget solvency following a tax cut.
Throughout the analysis, we maintain the assumption that private agents are en-
dowed with all the information needed to form rational expectations. Agents antic-
ipate future offsetting policies during periods of expanding debt. Budget solvency
in the model means that the intertemporal government budget constraint is satis-
fied both ex ante and ex post. While the debt-output ratio after a tax cut can be
permanently higher, debt cannot permanently grow faster than the economy.
3. The Model
The model economy consists of a government, a representative competitive house-
hold, and a representative competitive firm.
3.1. The private sector. The household chooses consumption, Ct, capital, Kt,
hours worked, Lt, and one-period government bonds, Bt,to maximize expected utility,
given by
E0
∞

t=0
βtC1−γ
t−1
1−γ+χ(1 −Lt)1−θ−1
1−θ,
subject to the budget constraint
Ct+Kt+Bt=1−τK
trtKt−1+1−τL
tWtLt+(1−δ)Kt−1+Bt−1Rt−1+Tt,
taking all prices and policies as given. Etis the mathematical expectation conditional
on the household’s information set at t.βis the discount factor (0 <β<1). γand
θare the inverses of elasticities of intertemporal substitution of consumption and
leisure (γ>0andθ≥0). τK
tand τL
tare proportional tax rates levied on capital and
labor income. Ttis lump-sum transfers if positive (taxes if negative). δis the capital
depreciation rate (0 ≤δ≤1). Wtis the real wage and rtis the capital rental rate.
A representative firm rents capital and labor from the household to maximize profit
AKα
t−1htLt1−α−WtLt−rtKt−1,
where Ais total factor productivity (A>0), his the constant growth rate of labor
augmenting technology (h≥1),andαis the share of capital in output (0 <α<1).
The firm takes prices parametrically.
Total goods produced each period are Yt=AKα
t−1(htLt)1−α.

DYNAMIC SCORING: ALTERNATIVE FINANCING SCHEMES 5
3.2. The government. This paper is a positive analysis of the budgetary conse-
quences of tax cuts which are financed in various ways. To study the implications
of alternative financing schemes, we posit the simplest possible rules for policy in-
struments that are consistent with fiscal solvency. Fiscal instruments are chosen as
a function of the state of government indebtedness, as measured by the debt-output
ratio. The rules adopted here are abstractions designed to capture the practice of
offsetting policy: when the fiscal budget deteriorates and debt rises, explicit fiscal
actions are taken to improve the budget situation.
The fiscal rules are:
ln τK
t
τK=qKln sB
t−1
sB,q
K≥0(1)
ln τL
t
τL=qLln sB
t−1
sB,q
L≥0(2)
ln sT
t
sT=qTln sB
t−1
sB,q
T≤0(3)
and
ln sG
t
sG=qGln sB
t−1
sB,q
G≤0(4)
where sB
t≡Bt
Yt,sT
t≡Tt
Yt,sG
t≡Gt
Ytand variables without time subscripts denote steady
state values. The rules build in a one-year delay for the response of an offsetting
policy.3
We refe r to th e q’s in rules (1)-(4) as the “fiscal adjustment parameters.” Sign re-
strictions on qK,q
L,q
T,and qGare straightforward. When the debt-output ratio rises
above its initial steady-state level, one of the future distorting tax rates is raised, the
government consumption-output is reduced, or the transfers-output ratio is lowered
to maintain fiscal solvency. To isolate the impacts of each financing instrument, one
of the q’s is nonzero in each experiment. For example, if the transfers-output ratio
is adjusted, qT<0, qG=qK=qL= 0. The magnitudes of the q’s characterize how
strongly the offsetting policy reacts to debt.
Policy choices must satisfy rules (1)-(4) and the government’s budget constraint at
each date:
Bt=Gt+Rt−1Bt−1−τL
tWtLt−τK
trtKt−1+Tt,(5)
where for simplicity we assume all government debt is one-period and indexed for
inflation.
3Longer delays can be easily handled. We only present results under one-year delay; the results
under five-year delay are very similar.

DYNAMIC SCORING: ALTERNATIVE FINANCING SCHEMES 6
Any equilibrium must satisfy both the first-order conditions for the household and
the firm and the transversality conditions for debt and capital accumulation. For
debt, this condition is EtlimT→∞ βt+Tu(ct+T)Bt+T
ht+T= 0, which essentially ensures
that in any optimum the household does not overaccumulate government liabilities.
Writing the government’s flow budget constraint, (5), in terms of shares of output,
iterating forward, and imposing transversality yields the government’s intertemporal
budget constraint:
Bt
Yt
=sB
t=
∞

j=1
dt,t+j(1 −α)τL
t+j+ατK
t+1 −sG
t+j−sT
t+j.(6)
dt,t+jis the growth-adjusted stochastic discount factor given by dt,t+j≡
j−1

i=0
R−1
t+i
Yt+i+1
Yt+i.
In equilibrium, (6) determines the value of government debt. It also imposes re-
strictions on dynamic interactions between current debt and expected future policies.
A debt-financed tax cut that raises Bt/Ytrequires some combination of fiscal variables
and/or discount factors in the future to be expected to adjust. Of course, there are
many expected sequences of fiscal policies that satisfy (6). The policy rules (1)-(4)
serve to specify one of many paths of fiscal variables. Feasibility is ensured by the
judicious choice of response magnitude parameters—the q’s in the rules.4Note that,
as written, (6) holds in realizations. Taking expectations at treveals that the value
of debt at tdepends on the expected present values of future fiscal instruments.
3.3. The solution method. Following King, Plosser, and Rebelo (2002), the model,
which has a deterministic growth trend h, is scaled by the factor of ht.This creates
a new discount factor, β∗≡βh1−γ,such that the steady state of the economy has
constant output growth and constant consumption-output, investment-output, and
debt-output ratios. An analytical solution is not available; the equilibrium conditions
are log-linearized around the steady state growth path and analyzed in terms of
percentage deviations from that growth path. The model is solved using Sims’s
(2001) algorithm.5
3.4. The equilibrium. A competitive rational expectations equilibrium is defined
as the agent’s decisions, {Ct,L
t,K
t,B
t}∞
t=0, the firm’s decisions, {Lt,K
t}∞
t=0, prices,
{rt,W
t}∞
t=0, and policy variables, {Bt,G
t,τL
t,τK
t,T
t}, such that, given initial levels
of capital and debt, K−1and B−1,the optimality conditions for agents’ and firms’
4At the end of the paper, we consider another set of policy rules.
5We examine permanent tax cuts. The use of log-linearization may raise concerns about the
quality of the first-order approximation when the equilibrium is away from the original steady state.
Such concerns are alleviated by the facts that the equilibrium system for the model is nearly log-
linear and that the size of tax cuts considered here is fairly small (a reduction of 1 percent of tax
rates from their original steady state levels).

DYNAMIC SCORING: ALTERNATIVE FINANCING SCHEMES 7
problems are satisfied in each period; the goods, capital, labor, and bond markets
clear; the transversality conditions for capital and debt hold; the government budget
constraint and the policy rules (equations (1)-(4)) are satisfied. The analysis focuses
on the ranges of the fiscal adjustment parameters—the q’s—that are consistent with
the existence of a rational expectations equilibrium.
3.5. Model calibration. The model is calibrated at an annual frequency. Table 1
reports the benchmark values of parameters and steady state values of variables before
a permanent tax rate change. The choices of the values for structural parameters
are comparable to those in similar models with distorting capital and labor income
taxation [Braun (1994), McGrattan (1994), Jones (2002), and Yang (2005)]. The
model implies that in the original steady state, the fraction of time spent working
is 0.20, the consumption-output ratio is 0.63, and the investment-output ratio is
0.17. The debt-output ratio in the steady state before a tax cut is 0.376, roughly
corresponding to the ratio of federal debt held by the public to GDP in 2005 [Table
78, Economic Report of the President (2006)].
Benchmark settings of the q’s are presented in the left column of table 2. These
values are chosen so that after a permanent 1 percent reduction in the capital or
labor tax rate, the economy evolves to a new steady state in which the debt-output
ratio is 0.442, the postwar average for the ratio of privately held federal debt to GDP
[1947-2005, Table 78, Economic Report of the President (2006)].6
4. Dynamic Impacts of Permanent Tax Rate Cuts
This section reports the dynamic impacts of permanent reductions in capital and
labor tax rates and shows how those impacts change when the financing schemes vary
among permanently higher lump-sum transfers, a lower government consumption-
output ratio, and increases in other proportional tax rates.
4.1. Tax-rate cuts financed by lump-sum transfers. To show that the govern-
ment financing rule is an important determinant of the effects of permanent tax cuts,
first we examine the consequences of tax rate cuts financed by lump-sum transfers.
The policy rule for the transfer-output share, (3), is operative, so debt-financed deficits
reduce expected future transfers. Fiscal adjustment parameters are qT=−0.341 for
a capital tax cut and qT=−0.371 for a labor tax cut (table 2). Figure 1 reports the
responses to a capital tax rate cut (solid lines), and to a permanent cut in the labor
tax rate (dashed-dotted lines).
Both tax cuts have strong expansionary effects on output (the tax base), with higher
investment and hours worked along the transition path. In the short run, substitution
6Section 5.1 reports the sensitivity of outcomes to variations in the strength of fiscal responses.

DYNAMIC SCORING: ALTERNATIVE FINANCING SCHEMES 8
effects created by lower tax rates entice agents to invest more and work harder, raising
output. As the economy converges to the new steady state, wealth effects from higher
disposable income begin to dominate, raising consumption and leisure; investment and
hours worked subside somewhat, but remain above their original steady state levels.
Although Mankiw and Weinzierl (2006) finance the tax-rate reductions with con-
temporaneous lump-sum transfer cuts, rather than debt, Ricardian equivalence en-
sures the two exercises produce identical effects on C,K,L,Y, and the prices. The
qualitative patterns for permanent capital or labor tax cuts are the same in this model
as in Mankiw and Weinzierl’s model. The tax base expands along the transition path
and in the new steady state for either tax cut (figure 1). Revenues from capital and
labor income taxes are permanently lower (bottom right panel) and the shortfall is
absorbed by permanently lower lump-sum transfers (bottom left panel). Our model
implies 95 percent (47 percent) of the revenue losses associated with a capital (labor)
tax rate cut are offset by an expanded tax base in the long run when transfers finance
the deficits.7
When the government has access to a non-distorting tax instrument, lower tax
rates appear to be expansionary and tax cuts are self-financing to a large degree.
4.2. Alternative financing schemes. We turn now to the transitional dynamics
following a permanent reduction in capital (or labor) tax rates, when the tax cuts
are financed initially by government debt and eventually by permanent reductions
in government consumption or permanent increases in labor (or capital) tax rates.
Figure 2 plots the dynamic responses of macroeconomic and budgetary variables to a
permanent, unexpected 1 percent cut in the capital tax rate. Dashed-dotted lines are
the impacts with qG=−0.119 and qT=qK=qL= 0; solid lines are the impacts with
qL=0.149 and qG=qT=qK= 0; for reference, we repeat part of the responses from
figure 1, which are dashed lines obtained when qT=−0.341 and qG=qK=qL=0.
8
When the capital tax rate is permanently cut, it increases the expected rate of
return to investment. Regardless of which policy rule is used, agents sacrifice con-
sumption in order to invest more in the first few years; consumption initially falls
7Differences in revenue feedback between our result and Mankiw and Weinizerl’s mainly stem
from model calibrations. Changing three aspects of our calibration helps to reconcile the differences:
(1) reducing the original steady state capital tax rate from 0.35 to 0.25; (2) increasing the steady
state time share spent working from 20 to 34 percent; (3) reducing the intertemporal elasticity of
substitution from 1 to 0.5. Under this alternative calibration, our model implies 67 percent and 25
percent of revenue loss for a capital and labor tax cut is offset by an expanded tax base under lump-
sum transfer financing. Reducing the steady state capital tax rate plays the most important role
in moving our results towards Mankiw and Weinzierl’s. The average U.S. capital tax rate between
1947 and 2004 is about 0.39, according to Jones’ (2002) method.
8We do not allow a tax rate to adjust in response to its own shock so that the tax rate being
shocked can be permanently held at 1 percent below its original steady state level.

DYNAMIC SCORING: ALTERNATIVE FINANCING SCHEMES 9
below the level in the original steady state path. Lower consumption raises the mar-
ginal utility of consumption, raising the benefit of working and the supply of labor.
Higher labor and higher capital stock produce more output.
On the government financing side, the capital tax rate cut drives up the government
debt-output ratio. When lump-sum transfers fall with debt, the tax reduction has its
largest positive effects on investment, hours, and output (dashed lines). This outcome
is not surprising, as a distorting source of tax revenues is replaced by a non-distorting
source.
Alternative financing schemes, however, involve changing some other distortion,
with important implications for the impacts of tax changes. Reductions in the gov-
ernment consumption-output ratio (dotted-dashed lines) raise wealth as the govern-
ment absorbs a smaller share of output. Wealthier households consume more leisure,
reducing hours worked both along the transition path and in the new steady state.
In the long run, the reduction in the government consumption ratio crowds in private
consumption, raising consumption above its original steady state level. Ultimately, a
higher after-tax return on investment raises the steady state capital stock and output,
though by less than when lump-sum transfers adjust to clear the government budget.
When the labor income tax rate (solid lines) rises to compensate for the lower
capital tax rate, the permanently lower after-tax return to labor reduces hours worked
in the new steady state. After rising initially, output declines to about 0.2 percent
below its original steady state level. This negative outcome on the long-run tax base
is strikingly different from the case when lump-sum transfers are used to respond
to higher debt. Permanently higher investment, coupled with a fixed government
consumption-output ratio, implies that consumption is lower in the new steady state.
Total revenues derived from capital and labor income taxes are permanently lower
when government consumption or lump-sum transfers adjust, while revenues rise when
labor tax rates adjust. Because permanently higher revenues after a capital tax cut
arise from higher future labor tax rates, it would be misleading to infer that capital
tax cuts per se generate permanently higher revenues.
To measure the budgetary cost of a tax cut, we also compute revenues net of
interest payment (net revenues) to service debt. Regardless of which policy rule is
used, interest payments rise and net revenues fall steadily as the debt-output ratio
gradually climbs to a permanent higher level (bottom panels of the figure). Although
a capital tax cut financed by a labor tax rate increase generates more revenues, net
revenues still fall as the increased tax revenues are insufficient to compensate for the
additional interest payment due to the debt-financed tax cut.
Analogous, but different, patterns of results emerge when a permanent labor tax
rate reduction is financed by three alternative schemes. Figure 3 reports responses to

DYNAMIC SCORING: ALTERNATIVE FINANCING SCHEMES 10
a 1 percent labor tax rate cut. Dashed-dotted lines are the impacts with qG=−0.130
and qT=qK=qL= 0; solid lines give the responses when capital taxes adjust with
qK=0.206 and qT=qG=qL= 0; dashed lines reports effects under qT=−0.371
and qG=qK=qL=0.
Once again, the tax impacts on investment, hours worked, and output are largest
when lump-sum transfers respond to debt to satisfy the government budget constraint.
Permanently lower labor tax rates raise the return to labor and increase equilibrium
hours and output for the first few years. The deficit-financed tax cut raises debt as a
share of output.
When future government consumption is reduced in response to the rising debt, the
positive wealth effect offsets the substitution effect induced by a higher after-tax real
wage and, within 18 years of the tax cut, hours worked fall as the economy converges
to a new steady state with lower employment and output. As before, the reduced
steady state government share crowds in private consumption.
If higher debt raises expected capital taxes, the long-run negative output effects are
still more pronounced; output falls about 1 percent below the original steady state
level in the new steady state. Lower expected returns to investment sharply reduce
investment, output, and consumption.9After an initial increase, hours worked rapidly
fall below their original steady state level. When capital taxes are expected to adjust
to balance the budget, a permanent cut in labor taxes produces only an ephemeral
expansionary effect; in the long run, the tax base falls.
Like a capital tax cut, net revenues fall under all financing schemes for a debt-
financed labor tax cut. The differences in net revenues are quite small among the
three financing schemes despite some differences in revenues and the interest rate.
As the three financing schemes yield nearly identical paths for the debt-output ratio,
it is clear that government indebtedness plays an important role in determining the
budgetary cost of a tax cut.
Mankiw and Weinizerl show that the elasticity of intertemporal substitution of
leisure plays an important role in determining revenue feedback numbers. We con-
sidered two alternative settings for this parameter—θ=2andθ= 5—implying the
smaller elasticities of 0.5 and 0.2. While the responses of key macroeconomic vari-
ables to either tax rate shock vary somewhat, the qualitative patterns are the same
as those under the benchmark values. Importantly, the paper’s message—that the
ultimate source of fiscal financing matters to conclusions about dynamic scoring—is
unaltered by different assumptions about labor elasticity.
Fiscal adjustments operating through different financing instruments (government
consumption or one of the two distorting income taxes) can generate permanent
9Similar results appear in Gordon and Leeper’s (2005) study of countercyclical fiscal policies.

DYNAMIC SCORING: ALTERNATIVE FINANCING SCHEMES 11
changes in important macroeconomic variables. In particular, the expansionary effects
of a tax cut can be reversed in the longer run. Moreover, even if a tax cut raises the
tax base and total revenues, it may reduce revenues net of interest payments on the
debt. This result is an outgrowth of the permanent increase in the debt-output ratio
induced by the permanent tax cuts.
5. Changes in Government Indebtedness and the Impacts of Tax Cuts
The above analysis focuses on the consequences of which fiscal instrument adjusts
to maintain budget solvency. In this section, we focus on how changes in government
indebtedness affect the expansionary effects and the budgetary costs of tax cuts.
5.1. Transition dynamics under two long-run debt-output ratios. Figure 4
compares the tax base, net revenues, and debt-output ratios under two sets of settings
of the fiscal adjustment parameters for a permanent 1 percent reduction in the capital
tax rate.10 The offsetting policy used to maintain fiscal solvency is labeled at the
bottom of each column. The first set of q’s yields a long-run debt-output ratio of
0.442, as in the earlier analysis. The second set of q’s are selected such that the long-
run debt-output ratio rises to 1 (the approximate upper bound for the ratio of federal
debt to GDP in postwar U.S. data). Values of the q’s are presented in table 2. Notice
that higher long-run debt-output ratios are associated with smaller magnitudes of
fiscal adjustment parameters.
Several observations emerge from the figure. First, less debt is accumulated along
a transition path and in the final steady state when the response magnitude of a
fiscal adjustment parameter is relatively large (dotted-dashed lines). Second, more
positive expansionary or less contractionary effects are associated with a smaller long-
run debt-output ratio (except, of course, when transfers adjust). For example, when
government consumption adjusts in response to a capital tax rate cut, the tax base
in the new steady state falls only slightly when qG=−0.119. With qG=−0.086,
in contrast, the tax cut produces stronger negative effects on the tax base (column 2
of figure 4). When labor taxes adjust in response to a capital tax rate cut (column
3), although the long-run expansionary effect is negative under both qL’s examined,
the larger the qL,the smaller the reduction in the tax base. Finally, tax cuts are
less expensive (net revenues fall less) when they are associated with smaller long-run
debt-output ratios. This holds even when lump-sum transfers adjust (column 1 of
the figure).
5.2. Steady state analysis. Figures 4 suggests that how aggressively fiscal instru-
ments adjust after a permanent tax cut, with the inevitable consequences for debt
10A very similar picture emerges when labor taxes are permanently reduced.

DYNAMIC SCORING: ALTERNATIVE FINANCING SCHEMES 12
accumulation, matters for the fiscal costs of the tax reductions. We probe this phe-
nomenon more deeply by turning to a steady state analysis in which the debt-output
ratio is permitted to vary continuously from 0.376—its 2005 level—to 1.0—near its
postwar peak.
A change in the steady state is triggered by a permanent 1 percent reduction in
either the capital or the labor tax rate. Associated with the new tax rate are steady
state values of endogenous variables, indexed by the new steady state value of the
debt-output ratio. Let Δxdenote the change in xacross the two steady states. The
government budget constraint in the two steady states implies a restriction among
policy variables across steady states of the form
(h−β−1)ΔsB=ΔsG+ΔsT−(1 −α)ΔτL−αΔτK,(7)
where in one set of experiments ΔτK=.01 and in the other set ΔτL=.01. It is
straightforward to use (7) to compute the adjustment required in other instruments
as a function of the posited change in debt, ΔsB.
Given the steady state values of policy variables, (sT,s
G,τK,τL), equilibrium con-
sumption, capital, and labor satisfy the following system of nonlinear equations:11
1=βh−γα1−τKAkα−1L1−α+1−δ,(8)
χ(1 −L)−θ=c−γ1−τL(1 −α)AkαL−α,(9)
and
c+(h−1+δ)k=(1−sg)AkαL1−α,(10)
where variables in lower cases are those scaled by the growth factor ht.
Figure 5 summarizes the relationship between the debt-output ratio and various
budgetary variables for three distorting fiscal adjustments under the benchmark pa-
rameter values in table 1. The x-axis in each of the nine plots has debt-output ratios
in the new steady state varying from 0.376 to 1. The offsetting policy used is labeled
on the top of each column. The first row of the figure reports magnitudes of fiscal
instruments in levels in the new steady state. The second and last rows plot percent
changes in the tax base and net revenues relative to their levels in a steady state
without a tax cut. Solid lines are the effects of a capital tax cut, and the dotted-
dashed lines are the effects of a labor tax cut. The vertical gray lines correspond to
the debt-output ratio 0.442, as analyzed in section 4.
11Analytical results for a steady state are obtainable but do not lend themselves to intuitive
interpretations for our analysis. Mankiw and Weinzierl (2006) derive an analytical expression to
calculate revenue feedback in a model with simpler fiscal policies.

DYNAMIC SCORING: ALTERNATIVE FINANCING SCHEMES 13
The message is clear: across the three distorting financing schemes, a higher debt-
output ratio is associated with (1) larger required fiscal adjustments, (2) less favorable
expansionary effects, and (3) more costly tax cuts. Since a higher debt-output ratio
means that a larger share of government resources is devoted to debt service, either
government consumption or transfers have to be permanently lower, or one of the
two tax rates has to be permanently higher to sustain a higher debt-output ratio. As
analyzed in section 4, reductions in government consumption or increases in a capital
or labor tax rate have contractionary effects, offsetting the impacts of the tax rate
cuts; with larger fiscal adjustments, contractionary effects are more likely. Finally,
if the tax base falls, declines in net revenues are exacerbated by the higher interest
payments associated with higher long-run debt-output ratios.
Combining the analyses of transition paths and steady states, we find that the
systematic relationship between the response magnitude of fiscal adjustments to debt
and long-run expansionary outcomes have important policy implications. While tax
policy can be expansionary, debt management policy also matters. A relatively small
response in the short run when the budget starts to deteriorate can be more costly
in the long run.
6. Sensitivity Analysis
Transitional dynamics have been analyzed under simple assumptions about policy
rules. These rules serve as a tool for tracking the transition path and quantifying
the aggressiveness of fiscal adjustments to debt. The qualitative conclusions obtained
under these rules about the relationships among the aggressiveness of debt manage-
ment policy, government indebtedness, and the expansionary effects and budget cost
of a tax cut, however, are not sensitive to the particular policy rule, as long as the
rule delivers a sustainable budget.
We check the sensitivity of the transitional dynamics to the specification of policy
rules by considering a different set of rules, similar to the ones adopted in Trabandt
and Uhlig (2006). In their setup, debt accumulates at the exogenously given long-run
growth rate of the economy, h. One of the fiscal instruments adjusts endogenously to
ensure the budget constraint is satisfied each period.12 Figures 6 and 7 contain the
transitional dynamics and the steady state after a 1 percent permanent reduction in
capital and labor tax rates under the parameters in table 1.
With a constant debt growth rule, while the debt-output ratio can deviate from
the pre-tax cut level each period, the magnitude of the deviation is small because
relatively strong fiscal adjustment is triggered at the time of a permanent tax cut. As
12Trabandt and Uhlig (2006) only consider the rule where government consumption adjusts to
balance the budget.

DYNAMIC SCORING: ALTERNATIVE FINANCING SCHEMES 14
a result, the expansionary effects of either tax cut are more favorable and the fiscal
cost of the tax cuts are smaller, compared to the delayed fiscal adjustments examined
in section 4.
For example, under a delayed labor tax rate adjustment, the tax base eventually
falls below the original steady state level for a capital tax rate cut (figure 2) but
stays positive under the constant debt growth rule (figure 6). Because the debt rule
keeps the debt-output ratio much smaller throughout the horizon, the labor tax rate
rises only slightly to maintain budget solvency. Unlike the case of the delayed fiscal
adjustments, the expansionary effects from the permanent capital tax rate cut are
never outweighed by the contractionary effects of the increase in the labor tax rate.
Similar comparative results are found for the labor tax rate cut. When the capital tax
rate adjusts, the tax base falls 0.3 percent below the path without a tax cut (figure
7), much smaller than the same experiment under the earlier policy rule—1 percent
(figure 3).
When debt grows exogenously, it cannot change with either tax cut. However,
interest payments rise in most cases because of the higher interest rate, except for
the labor tax rate cut under capital tax adjustments (the bottom left panel in figure
3). As the capital tax rate rises to balance the budget, agents substitute away from
capital into bonds; the interest rate must fall to clear the bond market.
Comparing net revenues in figures 2 and 6, we see that the fiscal costs of same-sized
capital tax rate cuts can be substantially different: when government pursues a more
aggressive debt management policy by making debt growth exogenous, the tax cut is
much less costly. In the case of a capital tax rate cut financed by higher labor tax
rates, net revenues are even slightly above the path without a tax cut in the long run.
This is because there are few additional interest payments to offset the revenue gains
from the higher labor tax rates.
The results obtained under the constant debt growth rule further highlight our
previous conclusion under the earlier policy rule: when debt is well managed, a tax
cut is more likely to be expansionary, making it less costly both along a transition
path and in the long run.
7. Concluding Remarks
Dynamic scoring is a complex business. This paper has maintained the assump-
tion that the true model of the economy, including parameter values, is known with
certainty. Despite that heroic assumption, the model predicts a wide range of expan-
sionary effects and revenue consequences from permanent cuts in tax rates. Those

DYNAMIC SCORING: ALTERNATIVE FINANCING SCHEMES 15
consequences depend of two critical aspects of fiscal behavior: which fiscal instru-
ments agents expect will adjust to any revenue shortfalls and the extent to which
shortfalls are financed with new debt issuances.
Previous work has made simplifying assumptions about these two aspects of fiscal
policy to conclude that permanent tax cuts may, to a large extent, be self-financing.
This paper points out, in contrast, that the range of possible dynamic scoring results
mirrors the broad range of financing options actually available to policymakers.
As long as fiscal authorities are not committed—or cannot commit—to specific
financing schemes, the response of private agents to tax cuts will be conditioned on
expectations of the full range of possible schemes. The analysis in this paper argues
that a complete assessment of the revenue costs of tax changes produces a matrix of
predicted consequences. Rows of the matrix represent the offsetting fiscal instruments
and columns represent alternative changes in steady state debt levels. Analyses that
include the two dimensions of the matrix can help inform policy choices.

DYNAMIC SCORING: ALTERNATIVE FINANCING SCHEMES 16
References
Auerbach, A. J. (2005): “Dynamic Scoring: An Introduction to the Issues,” Man-
uscript, University of California, Berkeley.
Baxter, M., and R. G. King (1993): “Fiscal Policy in General Equilibrium,”
American Economic Review, 86, 1154–1174.
Bohn, H. (1998): “The Behavior of U.S. Public Debt and Deficits,” Quarterly Jour-
nal of Economics, 113(3), 949–963.
Braun, R. A. (1994): “Tax Disturbances and Real Economic Activity in the Postwar
United States,” Journal of Monetary Economics, 33(June), 441–462.
Bruce, N., and S. J. Turnovsky (1999): “Budget Balance, Welfare, and the
Growth Rate: ‘Dynamic Scoring’ of the Long-Run Government Budget,” Journal
of Money, Credit and Banking, 31(2), 162–186.
Congressional Budget Office (2005): “Analyzing the Economic and Budgetary
Effects of a 10 Percent Cut in Income Tax Rates,” CBO, Washington, D.C., De-
cember 1.
Davig, T. (2005): “Periodically Expanding Discounted Debt: A Threat to Fiscal
Policy Sustainability?,” Journal of Applied Econometrics, 20(7), 829–840.
Davig, T., and E. M. Leeper (2006): “Fluctuating Macro Policies and the Fiscal
Theory,” in NBER Macroeconomics Annual 2006, forthcoming, ed. by D. Acemoglu,
K. Rogoff, and M. Woodford. MIT Press, Cambridge.
Economic Report of the President (2006):. United States Government Print-
ing Office, Washington, D.C.
Furman, J. (2006): “A Short Guide to Dynamic Scoring,” Center for Budget and
Policy Priorities, August 24.
Gordon, D. B., and E. M. Leeper (2005): “Are Countercyclical Fiscal Policies
Counterproductive?,” NBER Working Paper No. 11869.
Greenspan, A. (2005a): “Remarks by Chairman Alan Greespan, Globalization, at
the Council on Foreign Relations,” accessed on 3/24/2005.
(2005b): “Testimony of Chairman Alan Greenspan, Future of the Social
Security Program and Economics of Retirement, before the Special Committee on
Aging, U.S. Senate,” accessed on 3/24/2005.
Ireland,P.N.(1994): “Supply-side Economics and Endogenous Growth,” Journal
of Monetary Economics, 33, 559–571.
Joint Committee on Taxation (2005): “Macroeconomic Analysis of Various
Proposals to Provide $500 Billion in Tax Relief,” JCT, U.S. Congress, Washington,
D.C., (JCX-4-05), March 1.
Jones, J. B. (2002): “Has Fiscal Policy Helped Stabilize the Postwar U.S. Econ-
omy?,” Journal of Monetary Economics, 49(May), 709–746.
King,R.G.,C.I.Plosser,and S. T. Rebelo (2002): “Production, Growth
and Business Cycles: Technical Appendix,” Computational Economics, 20(1-2),
87–116.

DYNAMIC SCORING: ALTERNATIVE FINANCING SCHEMES 17
King, R. G., and S. Rebelo (1990): “Public Policy and Economic Growth: Devel-
oping Neoclassical Implications,” Journal of Political Economy, 98(5), S126–S150.
Mankiw,N.G.,and M. Weinzierl (2006): “Dynamic Scoring: A Back-of-the-
Envelope Guide,” Journal of Public Economics, forthcoming.
McGrattan, E. R. (1994): “The Macroeconomic Effects of Distortionary Taxa-
tion,” Journal of Monetary Economics, 33(3), 573–601.
Novales, A., and J. Ruiz (2002): “Dynamic Laffer Curves,” Journal of Economic
Dynamics and Control, 27(2), 181–206.
Sims, C. A. (2001): “Solving Linear Rational Expectations Models,” Journal of
Computational Economics, 20(1-2), 1–20.
Trabandt, M., and H. Uhlig (2006): “How Far Are We From the Slippery Slope?
The Laffer Curve Revisited,” SFB 649 Discussion Paper 2006-023, Humboldt Uni-
versity.
U.S. Department o f Tr easury (2006): A Dynamic Analysis of Permanent Ex-
tension of the President’s Tax Relief. Office of Tax Analysis, Washington, D.C.,
July 25.
Yang, S.-C. S. (2005): “Quantifying Tax Effects Under Policy Foresight,” Journal
of Monetary Economics, 52(8), 1557–1568.

DYNAMIC SCORING: ALTERNATIVE FINANCING SCHEMES 18
parameter value parameter value parameter value
α0.36 δ0.1 sT0.07
β0.96 h1.02 τK0.35
γ1χ3τL0.25
θ1sG0.2 sB0.376
Tabl e 1 . Benchmark parameter settings.
long-run sB0.442 (benchmark) 1
tax shock ΔτK=−1% ΔτL=−1% ΔτK=−1% ΔτL=−1%
qG-0.119 -0.130 -0.086 -0.088
qT-0.341 -0.371 -0.246 -0.251
qL0.149 - - 0.108 - -
qK- - 0.206 - - 0.140
Tabl e 2 . Fiscal adjustment parameters under various policy rules.
The q’s are chosen to allow the debt-output ratio to rise from an initial
level of 0.376 to a new long-run level of 0.442 (second column) or 1.0
(third column).

DYNAMIC SCORING: ALTERNATIVE FINANCING SCHEMES 19
0 10 20 40 60 80 100
−0.5
0
0.5 Consumption
0 10 20 40 60 80 100
0
1
2Investment
0 10 20 40 60 80 100
0
0.2
0.4 Hours
0 10 20 40 60 80 100
0
0.5
1Output/Tax Base
0 10 20 40 60 80 100
−10
−5
0
5Lump−Sum Transfers
0 10 20 40 60 80 100
−0.4
−0.2
0Tax Revenues
Capital tax cut
Labor tax cut
Figure 1. Lump-sum Financing. Impulse responses to a perma-
nent 1% capital or labor tax rate reduction when lump-sum transfers
adjust to balance the budget (in percent). The surprise tax cut occurs
at period 0. Responses are plotted over a 100-year horizon when the
economy has approximately reached its new steady state path.

DYNAMIC SCORING: ALTERNATIVE FINANCING SCHEMES 20
0 10 20 40 60 80 100
−0.5
0
0.5 Consumption
0 10 20 40 60 80 100
0
1
2Investment
0 10 20 40 60 80 100
−0.5
0
0.5 Hours
0 10 20 40 60 80 100
−0.5
0
0.5 Output/Tax Base
0 10 20 40 60 80 100
0
10
20 Debt/Output
0 10 20 40 60 80 100
−1
0
1Tax Revenues
0 10 20 40 60 80 100
0
10
20 Interest Payments
0 10 20 40 60 80 100
−2
−1
0Net Revenues
sGsT
τL
Figure 2. Capital Taxes: Alternative Financing Schemes. Re-
sponses to a permanent 1% capital tax rate reduction (in percent).
The surprise tax cut occurs at period 0. Responses are plotted over a
100-year horizon when the economy has approximately reached its new
steady state path. Government consumption adjusts: dotted-dashed
line; labor tax rates adjust: solid line; lump-sum transfers adjust:
dashed line.

DYNAMIC SCORING: ALTERNATIVE FINANCING SCHEMES 21
0 10 20 40 60 80 100
−1
0
1Consumption
0 10 20 40 60 80 100
−5
0
5Investment
0 10 20 40 60 80 100
−0.5
0
0.5 Hours
0 10 20 40 60 80 100
−2
0
2Output/Tax Base
0 10 20 40 60 80 100
0
10
20 Debt/Output
0 10 20 40 60 80 100
−1
−0.5
0Tax Revenues
0 10 20 40 60 80 100
0
10
20 Interest Payments
0 10 20 40 60 80 100
−2
−1
0Net Revenues
sG
sT
τK
Figure 3. Labor Taxes: Alternative Financing Schemes. Re-
sponses to a permanent 1% labor tax rate reduction. The surprise tax
cut occurs at period 0. Responses are plotted over a 100-year hori-
zon when the economy has approximately reached its new steady state
path. Government consumption adjusts: dotted-dashed line; capital
tax rates adjust: solid line; lump-sum transfers adjust: dashed line.

DYNAMIC SCORING: ALTERNATIVE FINANCING SCHEMES 22
0 500 1000
0
0.5
1Tax Base
0 500 1000
−2
−1
0
1Tax Base
0 500 1000
−4
−2
0
2Tax Base
0 500 1000
−10
−5
0Net Revenues
0 500 1000
−10
−5
0Net Revenues
0 500 1000
−10
−5
0Net Revenues
0 500 1000
0
50
100 Debt/Output
sT Adjusts
0 500 1000
0
50
100
150 Debt/Output
sG Adjusts
0 500 1000
0
50
100 Debt/Output
τL Adjusts
Figure 4. Government Indebtedness and Fiscal Adjustments:
Permanent 1% Capital Tax Rate Reduction. Responses plotted
over a 1000-year horizon. Solid line allows long-run debt-output ratio
to rise to 1.0; dotted-dashed line allows ratio to rise to 0.442. First
column—transfers adjust: dotted-dashed (qT=−.341),solid (qT=
−.246).Second column—government consumption adjusts: dotted-
dashed (qG=−.119), solid (qG=−.086).Third column—labor taxes
adjust: dotted-dashed (qL=.149), solid (qL=.108).

DYNAMIC SCORING: ALTERNATIVE FINANCING SCHEMES 23
0.5 1
0.175
0.18
0.185
0.19
0.195
Govt. Consumption/Output
Debt/Output 0.5 1
0.26
0.28
Labor Tax Rate
Debt/Output 0.5 1
0.36
0.38
0.4
0.42
Capital Tax Rate
Debt/Output
0.5 1
−3
−2
−1
0
Tax Base
Debt/Output
%
0.5 1
−4
−2
0
Tax Base
%
Debt/Output 0.5 1
−8
−6
−4
−2
Tax Base
%
Debt/Output
0.5 1
−15
−10
−5
Net Revenues
Debt/Output
%
0.5 1
−8
−6
−4
−2
0Net Revenues
Debt/Output
%
0.5 1
−12
−10
−8
−6
−4
−2
Net Revenues
Debt/Output
%
sB=.442
Figure 5. Steady State Analysis. Solid lines–a permanent 1% cap-
ital tax rate cut; dotted-dashed lines–a permanent 1% labor tax rate
cut. First column–government consumption adjusts; second column–
labor tax rate adjusts; third column–capital tax rate adjusts. Fiscal
instruments are in levels; tax base and net revenues are percent changes
relative to pre-tax cut steady state levels.

DYNAMIC SCORING: ALTERNATIVE FINANCING SCHEMES 24
0 10 20 30 40
−0.5
0
0.5 Consumption
0 10 20 30 40
0
1
2Investment
0 10 20 30 40
−0.5
0
0.5 Hours
0 10 20 30 40
0
0.5 Output/Tax Base
0 10 20 30 40
−0.4
−0.2
0Debt/Output
0 10 20 30 40
−0.5
0
0.5 Tax Revenues
0 10 20 30 40
0
1
2Interest Payments
0 10 20 30 40
−1
0
1Net Revenues
sGsT
τL
Figure 6. Exogenous debt growth rule. Responses to a perma-
nent 1% capital tax rate reduction (in percent). The surprise tax cut
occurs at period 0. Reponses plotted over a 40-year horizon. Gov-
ernment consumption adjusts in dotted-dashed lines; labor tax rates
adjust in solid lines; lump-sum transfers adjust in dashed lines.

DYNAMIC SCORING: ALTERNATIVE FINANCING SCHEMES 25
0 10 20 30 40
−0.5
0
0.5 Consumption
0 10 20 30 40
−2
0
2Investment
0 10 20 30 40
−0.5
0
0.5 Hours
0 10 20 30 40
−0.5
0
0.5 Output/Tax Base
0 10 20 30 40
−0.5
0
0.5 Debt/Output
0 10 20 30 40
−1
−0.5
0Tax Revenues
0 10 20 30 40
−2
0
2Interest Payments
0 10 20 30 40
−1
0
1Net Revenues
sGsT
τK
Figure 7. Exogenous debt growth rule. Responses to a perma-
nent 1% labor tax rate reduction (in percent). The surprise tax cut
occurs at period 0. Reponses plotted over a 40-year horizon. Gov-
ernment consumption adjusts in dotted-dashed lines; capital tax rates
adjust in solid lines; lump-sum transfers adjust in dashed lines.