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Federal Reserve Bank of Chicago
Saving Europe?: The Unpleasant
Arithmetic of Fiscal Austerity in
Integrated Economies
Enrique G. Mendoza, Linda L. Tesar,
and Jing Zhang
October 2014
WP 2014-13
Saving Europe?:
The Unpleasant Arithmetic of Fiscal Austerity in Integrated
Economies
Enrique G. Mendoza
Department of Economics
University of Pennsylvania
Philadelphia, PA 19104
and NBER
Linda L. Tesar
Department of Economics
University of Michigan
Ann Arbor, MI 48109
and NBER
Jing Zhang
Research Department
Federal Reserve Bank of Chicago
Chicago, IL, 60604∗
October 6, 2014
Abstract
What are the macroeconomic effects of tax adjustments in response to large public debt
shocks in highly integrated economies? The answer from standard closed-economy models is
deceptive, because they underestimate the elasticity of capital tax revenues and ignore crosscountry spillovers of tax changes. Instead, we examine this issue using a two-country model that
matches the observed elasticity of the capital tax base by introducing endogenous capacity utilization and a partial depreciation allowance. Tax hikes have adverse effects on macro aggregates
and welfare, and trigger strong cross-country externalities. Quantitative analysis calibrated to
European data shows that unilateral capital tax increases cannot restore fiscal solvency, because
the dynamic Laffer curve peaks below the required revenue increase. Unilateral labor tax hikes
can do it, but have negative output and welfare effects at home and raise welfare and output
abroad. Large spillovers also imply that unilateral capital tax hikes are much less costly under
autarky than under free trade. Allowing for one-shot Nash tax competition, the model predicts
a “race to the bottom” in capital taxes and higher labor taxes. The cooperative equilibrium
is preferable, but capital (labor) taxes are still lower (higher) than initially. Moreover, autarky
can produce higher welfare than both Nash and Cooperative equilibria.
Keywords: European debt crisis, tax competition, capacity utilization, fiscal austerity
JEL: E61, E62, E66, F34, F42, F62
∗
We are grateful for the support of the SAFE center at Goethe University under a grant of its program on
“Austerity and Economic Growth: Concepts for Europe.” Tesar also gratefully acknowledges the Isle de France
di Marco Foundation and the Paris School of Economics for their support during the early phases of the project.
Christian Proebsting provided excellent research assistance. We are grateful to Philippe Bacchetta, Chris House,
Harald Uhlig, and seminar participants at USC, Bilkent University, Indiana University, McGill University and Ohio
State, and conference participants at the ECB’s Global Research Forum on International Macroeconomics and Finance
and the 2013 CIREQ-ENSAI Dynamic Macro Workshop for helpful comments and suggestions. The views expressed
herein are those of the authors and not necessarily those of the Federal Reserve Bank of Chicago or the Federal Reserve
System. E-mail addresses: Mendoza, egme@sas.upenn.edu, Tesar, ltesar@umich.edu, Zhang, jzhangzn@gmail.com.
1
Introduction
The world’s advanced economies face a severe public debt crisis. Even before the onset of the
Great Recession in 2008, countries in the eurozone exceeded the public debt ceiling of 60 percent
of GDP, a condition set by the Maastricht Treaty. The slowing of economic activity combined with
increased transfer payments, financial system bailouts, and fiscal stimulus programs resulted in a
ballooning of public debt, as illustrated in Figure 1. In the countries at the center of the European
debt crisis (Greece, Ireland, Italy, Spain, and Portugal, or GIIPS) gross public debt as a share of
GDP rose 30 percentage points between 2008-2011, to a staggering 105 percent of GDP by 2011.
The ten largest remaining eurozone members (EU10) also experienced large debt increases, albeit
not as large as in the GIIPS. Their debt levels increased by nearly 18 percentage points of GDP,
reaching a ratio of 0.79 in 2011, well in excess of the Maastricht condition. Debt ratios of this
magnitude and on such a global scale are rare, and over the previous century occurred in times of
major wars and during the Great Depression.1
The European debt crisis changed the nature of fiscal policy discussions in Europe. Until
recently, the dominant issue in tax policy discussions was the harmonization of national tax rates
and measures to limit tax competition (Sorensen, 2001; Kellerman and Kammer, 2009).2 Once the
debt crisis started, however, the focus shifted toward the implementation of country-specific fiscal
austerity programs to address fiscal imbalances and bring the debt under control. A number of
countries, including Portugal, Greece, Italy, Ireland and Spain, and to a lesser extent France and
the Netherlands, adopted austerity packages that feature both expenditure cuts and increases in
tax rates.
While much ink has been spilled in both the financial and academic press on the pros and cons
of austerity measures in response to the debt crisis, there has been surprisingly little discussion of
1
Japan, the United Kingdom and the United States have also seen their debts reach very high levels. Over the
entire history of public debt in the United States, the data constructed by Bohn (2007) show that the surge in U.S.
public debt during the Great Recession ranks below only the two World Wars, and is above the Civil War and the
Great Depression.
2
Since the 1970s, EU member states have worked to bring value-added taxes into alignment, to remove barriers to
capital and labor movements across borders and to form a common European trade policy. The European Commission
initiated steps to create a common playing field for corporate taxation (the Common Consolidated Corporate Tax
Base), though the policy has not yet been adopted by eurozone Member States.
1
the constraints imposed on fiscal policy by the fact the eurozone countries are highly integrated.
Estimates of the sustainability of public debt (Abiad and Ostry, 2005; Mendoza and Ostry, 2008),
fiscal space (Ostry, Ghosh, Habermeier, Chamon et al., 2010), and the scope for raising revenue
(Trabandt and Uhlig, 2009, 2012) tend to treat countries as isolated economic units, setting aside
the potential for significant erosion of tax bases across countries due to factor mobility, or for
spillover effects on the budgets and welfare of other member countries.3 Taking these effects into
consideration is critical because the implications of fiscal austerity for macroeconomic aggregates
and social welfare depend both on the particular fiscal policy that countries decide to follow as well
as on the degree of integration of capital and goods markets.
This paper develops an open-economy macroeconomic framework for studying the international
dimensions of fiscal adjustment and uses it to examine the positive and normative effects of tax
policies targeted to offset shocks to public debt.4 The model captures the classic dynamic efficiency
(or supply-side) effects of distortionary taxes on factor incomes and consumption, as well as the
international externalities of domestic tax adjustments that result from cross-country mobility of
goods and assets.
Our framework for analysis is similar to the Neoclassical model used in Mendoza and Tesar
(1998, 2005) to study the international implications of domestic tax reforms that produce dynamic
efficiency gains, and the setting proposed by Auray, Eyquem, and Gomme (2013) to study tax
policies in open economies. An important limitation of these studies, and of those based on a wider
class of quantitative Neoclassical and NeoKeynesian dynamic general equilibrium models used to
study tax policy, is that the capital tax revenue has a very low elasticity to changes in tax rates,
which runs contrary to empirical evidence (see Gruber and Rauh, 2007; Dwenger and Steiner, 2012).
As a result, these models tend to overestimate the ability of the government to raise tax revenue
in response to debt shocks.
3
Externalities of fiscal policy have been widely discussed in the theoretical literature on international tax competition, much of which has focused on the EU, and in broader EU policy studies on tax harmonization and capital
income tax competition (see, for example, the survey by Persson and Tabellini (1995), the books by Frenkel, Razin,
and Sadka (1991) and Turnovsky (1997), and the quantitative studies by Klein, Quadrini, and Rios-Rull (2005),
Sorensen (1999), Sorensen (2003) and Eggert (2000)).
4
In this paper we limit the analysis to changes in tax rates, leaving the analysis of adjustments in expenditure
policy to future work.
2
To address this limitation, we introduce endogenous capital utilization and a limited tax allowance for capital depreciation.5 The two mechanisms interact in an important way. First, endogenous utilization allows agents to make short-run adjustments in the use of installed capital,
and hence capital income, in response to capital tax changes. This weakens the capacity to raise
tax revenue from capital taxes but also makes capital taxes less distorting. Second, the limited
depreciation allowance widens the base of the capital tax, and makes capital taxes more distorting
by increasing the marginal cost of capital utilization.6 The two mechanisms together result in a
dynamic Laffer curve (i.e. a mapping of the present value of the primary fiscal balance as a function
of tax rates) with a standard bell shape and a realistic elasticity of capital tax revenue. In contrast,
without these mechanisms the dynamic Laffer curve for capital taxes is monotonically increasing
for a wide range of tax rates.
In the model, national tax policies induce cross-country externalities that are driven by three
transmission channels: (1) relative prices, because national tax changes alter the prices of financial
assets (including internationally traded assets and public debt instruments) as well as factor prices
at home and abroad; (2) the world distribution of wealth, because efficiency effects of national tax
changes affect the allocations of capital and net foreign assets across countries; and (3) the erosion
of tax revenues, because via the first two channels national tax policies affect the ability of foreign
governments to raise tax revenue.
We conduct a quantitative analysis calibrated to eurozone data to study the positive and normative effects of alternative tax strategies that countries could follow to restore fiscal solvency in
response to debt shocks. We feed the debt shocks observed in the eurozone since 2008 into the
model and compute the short- and long-run effects on equilibrium allocations, prices and welfare
that result from responding to those shocks with capital or labor taxes, assuming first that tax
changes are undertaken unilaterally and then allowing for strategic interaction. The quantitative
results produce important insights into the potential effects of fiscal austerity options facing Europe.
5
Ferraro (2010) examined Ramsey optimal tax policy in a closed-economy model with endogenous capital utilization and an optimal choice of the depreciation allowance. He found that setting the capital income tax rate and the
depreciation allowance equal is optimal.
6
In representative-agent models calibrated to macroeconomic aggregates, setting the allowance to less than 100
percent of depreciation is also consistent with the data, since the allowance can only be claimed on nonresidential
capital and mainly by businesses, rather than individuals.
3
The first step in the analysis of unilateral tax adjustments is to construct dynamic Laffer
curves in an experiment calibrated to an average European country. To plot these curves, the
present discounted value of the primary fiscal balance is computed with the sequences of equilibrium
allocations and prices obtained for a set of tax rates. Since we keep government outlays constant,
these curves inherit the standard bell shape of the Laffer curves of tax revenues for distortionary
taxes. Tax adjustment can restore fiscal solvency after the debt shock only if there is a tax rate that
can produce an increase in the present discounted value of the primary fiscal balance of the same
magnitude as the debt shock.7 This is done under relatively conservative assumptions, because the
model assumes that there is no adverse impact of tax increases on long-run growth, and that debt
is priced at a risk-free rate (i.e. there is no default risk).
Even under these highly favorable conditions, the model predicts that tax adjustments to restore
fiscal solvency in response to the observed debt shocks may not be feasible, have large negative
welfare effects, and yield large cross-country spillovers. These spillovers generate open-economy
dynamic Laffer curves that are shifted down and to the left of the closed-economy curves, and also
below closed-economy estimates of steady-state Laffer curves (e.g. Trabandt and Uhlig, 2010). For
capital tax rates, the shift is so large that its maximum lies below what is needed to restore fiscal
solvency after the debt shock. In contrast, labor tax hikes can restore fiscal solvency, but with
negative effects on home allocations and welfare, and improvements abroad.
The large spillovers obtained with the unilateral tax adjustments indicate that strategic incentives are strong. This leads us to examine Nash solutions to one-shot tax competition games in
which both regions adjust taxes strategically to offset their observed debt shocks. We first solve a
baseline scenario with symmetric countries (i.e. a common debt shock set to 22 percentage points
of GDP). The Nash game produces a race to the bottom in capital taxes from 0.20 to 0.09. Labor
taxes increase from 0.35 to 0.43. Welfare, using the standard measure of lifetime compensating
variations in consumption, declines relative to the pre-crisis equilibrium by 1.66 percent. Moreover,
in the absence of a cooperative solution or a redistribution of the debt burden (i.e. debt haircuts),
each country attains higher welfare by moving to autarky.
7
Hence, to conduct these experiments we solve for the equilibrium transitional dynamics and new steady state that
result from a given set of tax changes, and calculate the equilibrium present discounted value of primary balances.
4
When the model is calibrated to reflect the asymmetries between GIIPS and the EU10, three
key findings emerge. First, Nash competition induces both regions to lower capital income taxes
and to significantly raise labor taxes relative to pre-crisis rates. Welfare declines by 1.5 percent in
GIIPS and by 1.1 percent in the EU10. Second, cooperation mitigates the cost of fiscal adjustment,
but the losses remain sizable. Third, GIIPS prefers the autarky outcome, in which international
externalities do not play a role, to even the most favorable cooperative allocation that allocates
to it all of the benefits of coordination. This finding suggests that efforts to maintain trade and
financial integration in Europe must take into account the negative externalities working through
international markets as the countries adjust to the debt crisis.
The rest of the paper is organized as follows. Section 2 describes the model, examines the
optimality conditions of households and firms, and defines the competitive equilibrium. Section
3 calibrates the model to eurozone data from before the 2008 crisis. Section 4 discusses the results of the quantitative analysis, starting with the implications of unilateral tax adjustments and
the construction of dynamic Laffer curves, followed by the analysis of the solutions to Nash and
Cooperative tax competition games. Section 5 provides conclusions.
2
A Two-Country Model with Cross-Country Tax Externalities
We study the fiscal adjustment in response to debt shocks using a two-country dynamic general
equilibrium model. The model shares several of the features of the widely used two-country Neoclassical model with exogenous long-run balanced growth, except for two important differences:
endogenous capacity utilization of the installed capital stock, and a limited tax allowance for capital depreciation expenses. The model abstracts from stochastic elements, because the focus of the
analysis is on the transitional dynamics and long-run implications of fiscal adjustment, rather than
on business cycle effects.
The world consists of two countries or regions: home (H) and foreign (F ). The countries are
perfectly integrated in goods and asset markets. The latter are modeled as one-period discount
bonds, without loss of generality given the absence of uncertainty. Each country is inhabited by an
infinitely-lived representative household. A representative firm in each country produces a single
5
tradable good using capital and labor as inputs. Physical capital and labor are immobile factors, but
trade in bonds is sufficient for inducing international spillovers of national tax policies, affecting
the global distribution of wealth, the size of the global capital stock and its distribution across
countries. In addition to this wealth reallocation mechanism, national tax policies also trigger
global externalities via relative prices and fiscal revenue spillovers.
Following King, Plosser, and Rebelo (1988), growth is driven by labor-augmenting technological
change that occurs at an exogenous rate γ. Accordingly, all variables (except labor and leisure)
are rendered stationary by dividing by the level of this technological factor.8 In addition, the
stationarity-inducing transformation of the model requires discounting utility flows at the rate
β̃ = β(1 + γ)1−σ , where β is the standard subjective discount factor of time-separable preferences,
and adjusting the laws of motion of physical and financial assets so that date-t + 1 stocks grow by
the balanced-growth factor 1 + γ.
We present below the structure of preferences, technology and the government sector of the
home country. The same structure applies to the foreign country, and when relevant we distinguish
variables across the two countries using asterisks to identify the foreign country.
2.1
Households
The representative home-country household has standard preferences:
∞
X
β̃
t (ct (1
t=0
− lt )a )1−σ
, σ > 1, a > 0, and 0 < β̃ < 1.
1−σ
(1)
The period utility function is the standard CRRA function in terms of a CES composite good made
of consumption, ct , and leisure. Since we assume a unit time endowment, leisure is defined as 1 − lt ,
where lt is the supply of labor.
1
σ
is the intertemporal elasticity of substitution in consumption,
and a governs the intertemporal elasticity of labor supply for a given value of σ.
The household takes as given government-determined proportional tax rates on consumption,
labor income and capital income, denoted τC , τL , and τK , respectively, and lump-sum government
8
The assumption that growth is exogenous implies that tax policies do not affect long-run economic growth. This
is in line with the empirical and quantitative findings of Mendoza, Milesi-Ferretti, and Asea (1997).
6
transfer or entitlement payments, denoted by et . The household also takes as given the rental rates
of labor wt and capital services rt , and the prices of domestic government bonds and internationaltraded bonds, qtg and qt .
The household rents out capital and labor inputs to firms and makes the investment and capacity
utilization decisions. Hence, the household rents to firms effective units of capital for production
k̃ = mk, where k is the capital stock and m the rate of utilization. We follow the standard practice
from the literature on endogenous capacity utilization (e.g. Greenwood, Hercowitz, and Huffman,
1988) by modeling the cost of utilization as faster depreciation. The rate of depreciation of the
capital stock increases with m, according to a convex function δ(m) = χ0 mχ1 /χ1 , with χ1 > 1 and
χ0 > 0 so that 0 ≤ δ(m) ≤ 1.
The price of capital and the price of consumer goods differ because investment incurs quadratic
adjustment costs:
φ(kt+1 , kt , mt ) =
η
2
(1 + γ)kt+1 − (1 − δ(mt ))kt
−z
kt
2
kt ,
(2)
where the coefficient η determines the speed of adjustment of the capital stock, while z is equal to
the long-run investment-capital ratio so that at steady state the capital adjustment cost is zero.9
The household chooses intertemporal sequences of consumption, leisure, investment inclusive
of adjustment costs x, international bonds b, domestic government bonds d, and utilization to
maximize utility in (1) subject to a sequence of period budget constraints given by:
(1 + τc )ct + xt + (1 + γ)(qt bt+1 + qtg dt+1 ) = (1 − τL )wt lt + (1 − τK )rt mt kt + θτK δ̄kt + bt + dt + et , (3)
and the following law of motion for the capital stock:
xt = (1 + γ)kt+1 − (1 − δ(mt ))kt + φ(kt+1 , kt , mt ),
9
(4)
It is well known that open-economy models with frictionless goods and asset markets require some form of capital
adjustment costs in order to reduce the cyclical volatility of investment to observed levels, and to capture the fact
that financial and physical assets cannot be adjusted at the same speed.
7
for t = 0, ..., ∞, given the initial conditions k0 > 0, b0 , and d0 .
The left-hand-side of equation (3) measures household expenditures, which include purchases of
consumption goods inclusive of the indirect tax, investment inclusive of capital adjustment costs,
international bonds, and domestic government bonds. The right-hand side shows household aftertax income. This includes net-of-tax income from labor and effective capital services rented out to
firms, a capital tax allowance for a fraction θ of depreciation costs, payments on holdings of public
and international bonds, and lump-sum entitlement payments from the government, e.
The formulation of the depreciation allowance as θτK δ̄kt in the above budget constraint is
based on two assumptions about how the allowance is implemented in practice. First, depreciation
allowances are usually set in terms of fixed depreciation rates of the declared value of capital, instead
of the true physical depreciation rate that varies with utilization. To capture this fact, we assume
that the depreciation rate for the capital tax allowance is set in terms of a constant depreciation
rate δ̄. This differs from the actual physical depreciation rate δ(m). The second assumption is
that, in this representative-agent model, the depreciation allowance only applies to a fraction θ of
the capital stock. This reflects the fact that depreciation allowances generally apply to the capital
income of businesses, not individuals, and also do not apply to residential capital.10
Since the focus of the analysis is on studying the effects of tax adjustments to respond to debt
shocks in countries with a high degree of openness, as is the case in the European Union, we assume
that the two regions in the model have perfectly integrated goods and asset markets. The latter
implies that international bond payments are not taxed. Also in line with other features of tax
systems in industrial countries, including European countries, capital income is taxed according
to the residence principle, but countries are allowed to tax capital income at different tax rates.
These assumptions also imply that we must assume that physical capital is owned entirely by
domestic residents, in order to support a competitive equilibrium with different capital taxes (see
10
The standard assumption of a 100 percent depreciation allowance has two unrealistic implications. First, it
renders m independent of the capital income tax in the long run. Second, in the short run the capital tax affects
the utilization decision margin only to the extent that it reduces the marginal benefit of utilization when traded
off against the marginal cost due to changes in the marginal cost of investment. Alternatively, we could assume
that there is a full depreciation allowance but that there are costs other than depreciation associated with capital
utilization for which there is no tax allowance. These two formulations are isomorphic, but we opted for the partial
depreciation allowance to maintain the traditional setup of capacity utilization.
8
Mendoza and Tesar, 1998; Frenkel, Razin, and Sadka, 1991). Without this assumption, crosscountry arbitrage of returns across capital and bonds at common world prices implies equalization
of pre- and post-tax returns on capital, which therefore requires identical capital income taxes
across countries. Other forms of financial-market segmentation, such as trading costs or shortselling constraints, could be introduced for the same purpose, but would make the model less
tractable.11
We impose a standard no-Ponzi-game condition on households. This restriction, along with the
budget constraint in (2), implies that the present value of total household expenditures equals the
present value of after-tax income plus initial asset holdings.
2.2
Firms
Since the household makes the investment and capital utilization decisions, and rents out to firms
effective capital services k̃, the representative firm’s problem reduces to a static optimization problem. Firms hire labor and effective capital services to maximize profits, given by yt − wt lt − rt k̃t ,
taking factor rental rates as given. The production function is assumed to be Cobb-Douglas:
yt = F (k̃t , lt ) = k̃t1−α ltα
(5)
where α is labor’s share of income and 0 < α < 1. Firms behave competitively and thus choose k̃t
and lt so as to equate their marginal products with their corresponding rental rates:
(1 − α)k̃t−α ltα = rt ,
(6)
αk̃t ltα−1 = wt .
(7)
Because of the linear homogeneity of the production technology, these factor demand conditions
imply the standard result that the value of output equals total factor payments: yt = wt lt + rt k̃t .
11
The assumptions of immobile capital and residence-based taxation could be replaced with source-based taxation
and this would result in similar saving and investment optimality conditions that would support competitive equilibria
with different capital income tax rates across countries. While actual tax codes tend to be source-based, however,
most industrial countries have bilateral tax treaties that render tax systems largely residence-based (see Frenkel,
Razin, and Sadka, 1991).
9
2.3
Public Sector
Fiscal policy in this economy has three components. The first component is government outlays,
and is composed of pre-determined sequences of government purchases on goods and services, gt ,
and transfer/entitlement payments to households, et , for t = 0, ..., ∞. Government purchases are
unproductive in the sense that they do not enter in household utility or the production function.
Under this assumption, it would follow trivially that the optimal response to a debt shock should
include setting gt = 0. We rule out this possibility because it is unrealistic, and also because if
the model is modified to allow government purchases to provide utility or production benefits, cuts
in these purchases would be distortionary in a way analogous to the taxes we are considering.
Hence, in the quantitative experiments we assume that gt = ḡ, where ḡ is the steady state level of
government purchases that prevailed before the debt shocks. Entitlement payments are treated in
the same way (with ē denoting the steady state level of entitlements before the debt shocks). Note,
however, that since entitlements represent a form of lump-sum transfer payments, they are always
non-distortionary in this representative agent setup. Still, they do impose on the government the
need to raise distorting tax revenue, since we do not allow for lump sum taxation, and hence again
the (trivial) optimal policy of eliminating transfer payments in response to debt shocks is ruled out.
The second component of fiscal policy is the tax structure. This includes the set of time invariant
tax rates on consumption τC , labor income τL , capital income τK , and the depreciation allowance
limited to a fraction θ of depreciation expenses.
The third component is government debt, dt . We assume the government is committed to repay
its debt, and thus it must satisfy the following sequence of budget constraints for t = 0, ..., ∞:
dt − (1 + γ)qtg dt+1 = τC ct + τL wt lt + τK (rt mt − θδ̄)kt − (gt + et ).
(8)
The right-hand-side of this equation shows the primary fiscal balance (tax revenues net of total
government outlays). This primary balance is financed with the change in debt including debt
service in the left-hand-side of the constraint.
Since the government is committed to repay, public debt dynamics must satisfy a standard
10
no-Ponzi-game condition. This condition ensures that the present value of government revenues
net of expenditures equals the initial public debt d0 .12 This is not an innocuous assumption in the
analysis of fiscal adjustment in response to debt shocks, because it implies both that governments
are committed to repay and that sovereign debt markets are working smoothly at all times. The
findings of this paper show that even under these ideal conditions, there are large inefficiencies,
welfare effects, and cross-country externalities involved in tax adjustments to respond to debt
shocks.
Because we calibrate the model using fiscal data in shares of GDP, it is useful to write the
intertemporal government budget constrain also in shares of GDP. Defining the primary balance
as pbt ≡ τC ct + τL wt lt + τK (rt mt − θδ̄)kt − (gt + et ), the constraint in shares of GDP is:
∞
pb0 X
d0
=
+
y0
y0
t=1
"t−1
Y
#
υi
i=0
pbt
yt
!
,
(9)
where υi ≡ (1 + γ)ψi qig and ψi ≡ yi+1 /yi . In this expression, the stream of future primary balances
is discounted to account for long-run growth at rate γ, transitional growth ψi as the economy
converges to the long-run, and the equilibrium price of public debt qig . Since y0 is endogenous (i.e.
it responds to debt shocks and required tax adjustments), it is useful to rewrite the above solvency
condition so that the debt ratio in the left-hand-side is an exogenous initial condition. Multiplying
both sides of the above condition times ψ0 = (y0 /y−1 ) we obtain:
"
"t−1 #
!#
∞
Y
pb0 X
pbt
d0
= ψ0
+
υi
.
y−1
y0
yt
t=1
(10)
i=0
The exogenous debt shocks that are the focus of our quantitative analysis are defined as observed
changes in d0 /y−1 (the debt ratio at the end of t − 1, since d0 is chosen on that date). Hence, the
solvency condition (10) represents a constraint that the new regimes with altered tax policy in
12
Note that, as explained in Mendoza and Tesar (1998), public debt in this model is Ricardian in the sense that
the equilibrium dynamics of government debt can be equivalently characterized as a sequence of lump-sum transfers
between government and households (separate from the “explicit” entitlement payments et ), with these transfers set
equal to the primary fiscal balance. We use this to simplify the numerical solution of the model. Once we have the
equilibrium sequence of debt-equivalent transfers, the implied equilibrium dynamics for public debt follows from an
initial condition calibrated to actual debt data and the government budget constraint.
11
response to a debt shock must satisfy.13 The left-hand-side is an exogenous constant taken from
the data, and the right-hand-side is the present discounted value of the primary balance-GDP ratios
(where pbt , yt and υt are equilibrium outcomes), discounted taking into account exogenous long-run
growth, endogenous transitional growth, and endogenous debt prices.
Combining the government’s budget constraint with the household’s budget constraint and the
firm’s zero-profit condition, we obtain the economy-wide resource constraint for the home region:
F (mt kt , lt ) − ct − gt − xt = (1 + γ)qt bt+1 − bt .
2.4
(11)
Competitive Equilibrium
A competitive equilibrium for this two-region economy is a sequence of prices {rt , rt∗ , qt , qtg , qtg∗ , wt ,
∗ ,m
∗
∗
∗
∗
∗
∗
wt∗ } and allocations {kt+1 , kt+1
t+1 ,mt+1 ,bt+1 , bt+1 , xt , xt , lt , lt , ct , ct , dt+1 , dt+1 } for t = 0, ..., ∞
such that: (a) households in each region maximize utility subject to their corresponding budget
constraints and no-Ponzi game constraints, taking as given all fiscal policy variables as well as
pre-tax prices and factor rental rates, (b) firms maximize profits subject to the Cobb-Douglas
technology taking as given pre-tax factor rental rates, (c) the government budget constraints hold
for given tax rates and exogenous sequences of government purchases and entitlements, and (d) the
following market-clearing conditions hold in the global markets of goods and bonds:
ω (yt − ct − xt − gt ) + (1 − ω) (yt∗ − c∗t − x∗t − gt∗ ) = 0,
(12)
ωbt + (1 − ω)b∗t = 0,
(13)
where ω denotes the relative size of the two regions. This parameter will be calibrated to match
the relative output shares of the two regions before the debt shocks occur.
13
In detrended
levels
(which areratios relative to the state of labor augmenting technology), we would have
∞
t
P
Q
s
d0 = pb0 +
qi (1 + γ)t pbt .
t=1
i=1
12
2.5
Optimality Conditions, Tax Distortions and International Externalities
The optimality conditions of the household and firm problems provide useful intuition for characterizing the model’s tax distortions and their international externalities. Consider first the Euler
equations for capital (excluding adjustment costs for simplicity), international bonds and domestic
government bonds. These conditions imply that the following arbitrage conditions hold:
1
(1 + γ)u1 (ct , 1 − lt )
1
= (1 − τK )F1 (mt+1 kt+1 , lt+1 )mt+1 + 1 − δ(mt+1 ) + τK θδ̄ =
= g,
qt
qt
β̃u1 (ct+1 , 1 − lt+1 )
(14)
(1 + γ)u1 (c∗t , 1 − lt∗ )
1
1
∗
∗
∗
∗
∗
∗
∗
=
(1
−
τ
)F
(m
k
,
l
)m
+
1
−
δ(m
)
+
τ
θ
δ̄
=
=
. (15)
1
K
t+1
t+1
t+1
t+1
t+1
K
∗ )
qt
qtg∗
β̃u1 (c∗t+1 , 1 − lt+1
The assumption that the regions are fully integrated in financial markets implies that the households’ intertemporal marginal rates of substitution in consumption are equalized across regions,
and are also equal to the rate of return on international bonds. Since physical capital is not mobile
and capital income taxes are residence based, households in each region face their own region’s distortionary tax on capital income. As a result, arbitrage equalizes the after-tax returns on capital
across regions, but pre-tax returns differ. Hence, the capital stock and output differ across regions
due to differences in capital taxation. Arbitrage in asset markets also implies that the price of
external bonds and domestic public bonds are equalized. Hence, at equilibrium: qt = qtg = qtg∗ .
As shown in Mendoza and Tesar (1995), unilateral changes in the capital income tax result in
a permanent reallocation of physical capital, and ultimately a permanent shift in wealth, from the
high-tax to the low-tax region. Thus, even though physical capital is not mobile across countries
directly, perfect mobility of financial capital and arbitrage of asset returns induces international
mobility of physical capital. In the stationary state with balanced growth, however, the global
interest rate R (the inverse of the bond price, R ≡ 1/q) is a function of β, γ and σ:
R=
(1 + γ)σ
,
β
(16)
and thus is independent of tax rates. The interest rate does change along the transition path and
alters the paths of consumption, output and international asset holdings. In particular, in the tax
13
competition games we study later, each country has an incentive to behave strategically by tilting
the path of the world interest rate in its favor to attract more capital. When both countries attempt
such a strategy, the outcome is lower capital taxes but also lower welfare for both (which is the
standard race-to-the-bottom result of the tax competition literature).
Consider next the optimality condition for labor supply. This condition reflects the standard
distortionary effects of labor and consumption taxes:
1 − τL
u2 (ct , 1 − lt )
F2 (kt , lt )
=
u1 (ct , 1 − lt )
1 + τC
(17)
Taxes on labor and consumption together drive a wedge (1 − τW ) ≡ (1 − τL )/(1 + τC ) between
the leisure-consumption marginal rate of substitution and the pre-tax real wage (which is equal to
the marginal product of labor). Since government purchases are kept constant and the consumption
tax is constant over time and known with certainty, consumption taxation does not distort saving
plans, and hence labor and consumption taxes are equivalent: Any (τC , τL ) pair consistent with
the same τW yields identical allocations, prices and welfare. Since European consumption tax
harmonization agreements limit the scope of national adjustments in consumption taxes, however,
we assume that any adjustments to τW implemented to respond to a debt shock reflect changes in
τL , with τC constant at its pre-debt-shock rate.
The distortions of capital, labor and consumption taxes discussed in the previous paragraphs
are standard in a wide class of Neoclassical and New Keynesian DSGE models. These models,
however, generally underestimate the elasticities of both investment and capital income tax revenues
to changes in capital taxes, because the capital stock is pre-determined at the beginning of each
period, and changes gradually as it converges to its balanced-growth steady state. In contrast,
in this model the government’s ability to tax capital income is significantly hampered because
capital income taxes not only drive a wedge between intertemporal marginal rates of substitution
in consumption and rates of return on capital, they also distort capacity utilization decisions. In
particular, the optimal choice for capacity utilization implies:
F1 (mt kt , lt ) =
1 + Φt 0
δ (mt ),
1 − τK
14
(18)
where Φt = η
(1+γ)kt+1 −(1−δ(mt ))kt
kt
− z is the marginal adjustment cost of investment. The cap-
ital tax creates a wedge between the marginal benefit of utilization on the left-hand-side of this
condition, which is the after-tax marginal product of effective capital already installed, and the
marginal cost of utilization on the right-hand-side, which is the marginal change in the rate of
depreciation caused by changes in utilization.
It follows from the above expression that an increase in τk , everything else constant, reduces
the utilization rate. This follows from the concavity of the production function and the fact that
δ(mt ) is increasing and convex. Intuitively, a higher capital tax reduces the after-tax marginal
benefit of utilization, and thus reduces the rate of utilization. Note also that the magnitude of this
distortion depends on whether the capital stock is above, below or at its balanced-growth steady
state. This is because the sign of Φt depends on Tobin’s Q, which is given by Qt = 1 + Φt . If Qt
is greater than 1 (Φt > 0), the desired investment rate is higher than the steady-state investment
rate. In this case, Qt > 1 increases the marginal cost of utilization (because higher utilization
means faster depreciation, which makes it harder to attain the higher target capital stock). The
opposite happens when Q is less than 1 (Φt < 0). In this case, the faster depreciation at higher
utilization rates makes it easier to run down the capital stock to reach its lower target level. Thus,
an increase in τk induces a larger decline in the utilization rate when the desired investment rate
is higher than its long-run target (i.e. Φt > 0).
The interaction of endogenous utilization and the limited depreciation allowance plays an important role in our analysis. Endogenous utilization means that the government cannot treat the
existing (pre-determined) capital stock as an inelastic source of taxation at any given date, because
effective capital services rented for production decline with the capital tax even when the capital
stock is already installed. This weakens the revenue-generating capacity of capital taxation, but it
also makes capital taxes less distorting, since it gives agent’s an additional margin of adjustment
in response to capital tax hikes. On the other hand, the limited depreciation allowance widens
the base of the capital tax, but it also strengthens the distortionary effect of τk by reducing the
post-tax marginal return on capital (see eq. 14). We will show in the quantitative section that
the two mechanisms together result in a dynamic Laffer curve with the familiar bell shape and
15
consistent with empirical estimates of the capital tax base elasticity, while removing them results
in a Laffer curve that is nearly linearly increasing for a wide range of capital taxes.
The cross-country externalities that result from the tax distortions discussed in this subsection
can be summarized as resulting from three distinct transmission channels. First, relative prices,
because national tax changes alter the prices of financial assets (including internationally traded
assets and public debt instruments) as well as the rental prices of effective capital units and labor
in both regions. Second, the distribution of wealth across the regions, because efficiency effects
of tax changes by one region affect the allocations of capital and net foreign assets across regions
(even when physical capital is not directly mobile). Third, the erosion of tax revenues, because via
the first two channels the tax policies of one region affect the ability of the other region to raise tax
revenue. When one region responds to a debt shock by altering its tax rates, it generates external
effects that can harm or benefit the other region via these three channels.
3
Calibration and Pre-Crisis Initial Conditions
This section reviews macroeconomic data to characterize the pre-debt-crisis initial conditions and
discusses the calibration of the model. We use data from the 15 largest countries in the eurozone
(Cyprus and Malta are excluded). In the baseline calibration, we consider fully symmetric regions
calibrated to eurozone-wide aggregates, and we also construct an asymmetric scenario in which we
introduce region heterogeneity in the parameters in which it is empirically significant (public debt
ratios, fiscal policy parameters, trade balances and relative economic size).
3.1
Pre-crisis Initial Conditions in the eurozone
Table 1 shows key statistics for aggregate expenditures and fiscal variables as shares of GDP for
eleven eurozone countries. The last three columns show GDP-weighted averages for the GIIPS
region (Greece, Ireland, Italy, Portugal and Spain), the EU10 region (the remaining countries), and
the full 15-country sample, denoted “All EU.” The All EU values will be used as targets for the
baseline calibration, and the GIIPS and EU10 values will be used for the asymmetric calibration.
The GIIPS GDP was about half the size of the EU10 GDP in 2008, so the GIIPS share is about
16
one-third of the two regions’ aggregate output.
The first three rows of Table 1 show estimates of effective tax rates on consumption, labor
and capital calculated from revenue and national income accounts statistics using the methodology
introduced by Mendoza, Razin, and Tesar (1994) (MRT). These tax rates have been widely used
in a number of studies including Carey and Tchilinguirian (2000), Sorensen (2001) and recently by
Trabandt and Uhlig (2009, 2012). The MRT methodology uses the wedge between reported pre-tax
and post-tax macro estimates of consumption, labor income and capital income to estimate the
effective tax rate levied on each of the three tax bases. This methodology has two main advantages.
First, it provides a fairly simple approach to estimating effective tax rates at the macro level using
readily available data, despite the complexity of the various credits and deductions of national tax
codes. Second, these tax rates correspond directly to the tax rates in a wide class of representativeagent models with taxes on consumption and factor incomes, including the model proposed here.
The main drawback of the MRT tax rates is that they are average, not marginal, tax rates, but
because they are intended for use in representative-agent models, this disadvantage is less severe
than it would be in a model with heterogeneous agents. Moreover Mendoza, Razin, and Tesar (1994)
show that existing estimates of aggregate marginal tax rates have a high time-series correlation with
the MRT effective tax rates, and that both have similar cross-country rankings.
Following Trabandt and Uhlig (2009), we modify the MRT estimates of labor and capital taxes
by adding supplemental wages (i.e. employers’ contributions to social security and private pension
plans) to the tax base for personal income taxes. These data were not available at the time of the
MRT 1994 calculations and, because this adjustment affects the calculation of the personal income
tax rate, which is an initial step for the calculation of labor and capital income tax rates, it alters
the estimates of both. In general, this adjustment makes the labor tax base bigger and therefore
the labor tax rate smaller than the MRT original estimates.14
Table 1 shows that 2008 tax rates were not very different across EU10 and GIIPS. This reflects
the tax harmonization treaties and directives adopted by the European Union since the 1960s, as
14
Trabandt and Uhlig make a further adjustment to the MRT formulae by attributing some of the operating surplus
of corporations and non-incorporated private enterprises to labor, with the argument that this represents a return
to entrepreneurs rather than to capital. We do not make this modification because the data do not provide enough
information to determine what fraction of the operating surplus should be allocated to labor.
17
well as the effects of competition in corporate income taxation. Consumption and labor tax rates
are slightly higher in EU10 than in GIIPS (0.18 v. 0.14 for consumption and 0.36 v. 0.33 for labor),
and capital taxes are just a notch higher in GIIPS than in EU10 (0.21 v. 0.20).15 This relative
homogeneity of the pre-debt-crisis tax structures is worth noting, because it contrasts with the
sizable difference in the size of the debt shocks across GIIPS and EU10 documented below. Hence,
the quantitative experiments conducted in the next section using the asymmetric calibration focus
on tax adjustments in response to heterogeneous public debt shocks across countries starting from
relatively homogeneous tax systems.
With regard to aggregate expenditure ratios, the GIIPS region has higher consumption and
investment shares of GDP than EU10 by 4 and 3 percentage points respectively. Their government
expenditure shares (purchases of goods and services, excluding transfers) are about the same, at
one-fifth of GDP. These three expenditure ratios are fairly stable over time, so using 2008 values
or time-series averages for the calibration makes little difference. This is not true, however, for net
exports, which show an average of −0.1 percent for GIIPS over the 1995–2011 period but by 2008
had dropped to −3 percent. In the asymmetric calibration we use this value, and since the model
only has two regions, it imposes a 3 percent pre-crisis steady state trade surplus on the EU10. For
the baseline symmetric calibration, the All EU trade balance was negligible in 2008, so we set it
to zero in the pre-crisis steady state for simplicity. Examining the countries individually, GIIPS
countries tend to have trade deficits with the exception of Ireland, and in EU10 Germany and the
Netherlands have large trade surpluses that influence signficantly the GDP weighted average for
EU10. Note, however, that these trade balances include all external trade of the eurozone countries,
not just trade flows within the eurozone.
In terms of fiscal flows, Eurostat data on total tax revenues and government outlays (including
both expenditures and transfer payments) show that both revenues and outlays are slightly higher
in EU10 than GIIPS, by 3 and 2 percentage points respectively. The gap between revenues and
expenditures, however, is about the same in both regions.
15
In contrast, these tax structures differ sharply from those of non-European industrial countries (see Mendoza,
Razin, and Tesar, 1994; Mendoza, Milesi-Ferretti, and Asea, 1997, for detailed international comparisons of tax
systems across all OECD industrial countries).
18
The bottom panel of Table 1 reports government debt to GDP ratios and their change between
end–2007 (beginning of 2008) and end–2011. These changes are our estimate of the “debt shocks”
that each country and region experienced, and hence they are the key exogenous impulse used in
the quantitative experiments of the next Section. The debt ratios correspond to consolidated gross
debt of the general government as reported by Eurostat, which is the measure used to evaluate
compliance with the Maastricht Treaty. Under the Treaty, eurozone governments are to keep this
ratio below 60 percent of GDP. As the table shows, however, debt ratios between end–2007 and
2011 rose sharply. Only five countries were in compliance with the Maastricht limit, and all of the
large European economies in both EU10 and GIIPS had debt ratios significantly higher than 0.6.
The debt shock in EU10 amounts to an increase of 18 percentage points of GDP (reaching a 79
percent debt ratio by 2011), while in GIIPS the ratio increased by 30 percentage points, reaching a
105 percent debt ratio in 2011.16 For All EU, the debt shock measures 22 percentage points, with
the debt ratio rising from 66 to 88 percent.
3.2
Calibration
Table 2 lists the parameter values of the model’s baseline calibration, and the information from the
All EU column of Table 1 or the existing literature that was used to target them. The calibration
is designed to represent the balanced-growth steady state that prevailed before the debt shocks
occurred, using 2008 observations from the data as empirical proxies for the corresponding allocations (as explained earlier, investment and consumption shares for 2008 or time-series averages
since 1970 are not markedly different). The model is calibrated to a quarterly frequency, and the
calibration strategy proceeds as described in the paragraphs below.
The fiscal policy parameters include the tax rates, the share of government expenditures in
GDP, the public debt ratio and the limit on the depreciation allowance. The tax rates, government
expenditures share and debt ratio are calibrated to the values in the All EU column of Table 1:
τK = 0.2, τL = 0.35, τC = 0.16, g/y = 0.21 and d/y = 0.66. These labor and consumption
tax rates imply a consumption-leisure tax wedge of τW = 0.44. The limit on the depreciation
16
GDP fell during this interval, which contributed to the increase in the debt to GDP ratio, but the decline in
GDP is swamped by the large increase in debt, particularly in GIIPS.
19
allowance, θ, is set to capture the facts that tax allowances for depreciation costs apply only to
capital income taxation levied on businesses, not individuals, and do not apply to residential capital
(which is included in k). Hence, the value of θ is set as θ = (REVKcorp /REVK )(K N R /K), where
(REVKcorp /REVK ) is the ratio of revenue from corporate capital income taxes to total capital income
tax revenue, and (K N R /K) is the ratio of non-residential fixed capital to total fixed capital. Using
2007 data from OECD Revenue Statistics for revenues, and from the European Union’s EU KLEMS
database for capital stocks for the six countries with enough data coverage (Austria, Finland,
Germany, Italy, Netherlands and Spain), these ratios range from 0.39 to 0.48 for (REVKcorp /REVK )
and from 37 to 46 percent for (K N R /K). Weighting by GDP, the aggregate value of θ is 0.22.
Consider next the technology parameters. The labor share of income, α, is set to 0.61, following
Trabandt and Uhlig (2009). The quarterly rate of labor-augmenting technological change, γ, is
0.0022, which corresponds to the 0.9 percent annual average growth rate in real GDP per capita
observed in the Euro area between 2000 and 2011 based on Eurostat data. Since the countries are
symmetric in the baseline calibration, relative country size is set to ω = 0.50.
To calibrate the depreciation rate function, we start by normalizing the long-run capacity utilization rate to m̄ = 1. Given γ = 0.0022 and the investment- and capital-output ratios from the
data, we solve for the long-run depreciation rate from the steady-state law of motion of the capital
stock (x/y = (γ + δ(m̄))k/y). This yields δ(m̄) = 0.0164 per quarter.17 The value of χ0 follows
then from the optimality condition for utilization at steady state, using α = 0.61 and k/y = 2.97,
which yields χ0 = (1 − α)/(k/y) = 0.03. Given this, the value of χ1 follows from evaluating the
depreciation rate function at steady state, which implies χ0 m̄χ1 /χ1 = 0.0164. Solving for χ1 yields
χ1 = 1.58. The constant depreciation rate for claiming the depreciation tax allowance, δ̄, is set
equal to the steady state depreciation rate. Hence, δ̄ = δ(m̄) = 0.0164.
For preference parameters, we set σ = 2.0 which is the value commonly used in the Macro
literature. The exponent of leisure in utility, a = 2.675 is from Mendoza and Tesar (1998). This
value supports a labor allocation of 18.2 hours, which is in the range of the 1993-1996 averages of
17
Investment rates are from the OECD National Income Accounts and capital-output ratios are from the AMECO
database of the European Commission. The 2008 GDP-weighted average investment rate across the GIIPS and EU10
is x/y =0.222 (see also the last column of Table 1), and the 2007 average capital-output ratio is k/y =2.97 (which is
also the average over the 2000-2008 period).
20
hours worked per person aged 15 to 64 in France (17.5), Germany (19.3) and Italy (16.5) reported
by Prescott (2004).
The value of β follows from the steady-state Euler equation for capital accumulation, using the
values set above for the other parameters that appear in this equation:
y
γ
= 1 + (1 − τK ) (1 − α) − δ (m̄) + τK θδ̄.
k
β̃
This yields β̃ = 0.992, and then since β̃ = β(1 + γ)1−σ it follows that β = 0.9942. The values of
β, γ and σ pin down the steady-state gross real interest rate, R = β −1 (1 + γ)σ = 1.0102. This is
equivalent to a net annual real interest rate of about 4.2 percent.
Once the interest rate is determined, the economy’s resource constraint pins down the steadystate ratio of net foreign assets to GDP. Since the data indicates tb/y = 0 for the symmetric
baseline, b/y = (tb/y)/ (1 + γ)R−1 − 1 = 0. In addition, the steady-state government budget
constraint can be used to solve for the implied ratio of government entitlement payments to GDP
e/y = Rev/y − g/y − (d/y) 1 − (1 + γ)R−1 = 0.163.
Under this calibration approach, both b/y and e/y are necessarily obtained as residuals, given
that the values of all the terms in the right-hand-side of the equations that determine them have
already been set. Hence, they generally will not match their empirical counterparts. In particular,
for entitlement payments the model underestimates significantly the 2008 observed ratio of entitlement payments to GDP (0.163 in the model v. 0.26 in the data for All EU). Notice, however,
that when the model is used to evaluate tax policies to restore fiscal solvency in response to debt
shocks, the fact that entitlement payments are lower than in the data strengthens our results. We
find that restoring fiscal solvency implies non-trivial tax adjustments with sizable welfare costs
and cross-country spillovers, all of which would be even larger with higher government revenue
requirements due to higher entitlement payments.
The value of the investment-adjustment-cost parameter, η, cannot be set using steady-state
conditions, because at steady state adjustment costs wash out from the model by construction.
Hence, we set the value of this parameter so that the model is consistent with the mid-point of the
empirical estimates of the short-run elasticity of the capital tax base to changes in capital tax rates.
21
The range of empirical estimates is 0.1–0.5, so the target midpoint is 0.3.18 Under the baseline
symmetric calibration, the model matches this short-run elasticity when we set η = 2.0. This value
of η is also in line with estimates in House and Shapiro (2008) of the response of investment in
long-lived capital goods to relatively temporary changes in the cost of capital goods.19
An alternative calibration strategy would have been to set η directly to the 1–2.5 range indicated
by the estimates of House and Shapiro (2008), and calibrate χ1 , the curvature parameter in the
depreciation rate function, to match the capital tax base elasticity. This would require also a
different approach to calibrate χ0 and δ̄. The value of χ0 would be pinned down by the fact that,
given m̄ = 1, the functional form of δ(m) implies χ0 = χ1 δ(m̄), and the value of δ̄ would then be
solved for using the optimality condition for utilization evaluated at steady state. This calibration
strategy is about equivalent quantitatively to the one we followed, however, because under our
calibration strategy setting η to match the capital tax base elasticity we obtained a value of η well
inside the House-Shapiro range of empirical estimates of this parameter.
Table 3 reports the 2008 GDP ratios of key macro-aggregates in the data and the model’s
balanced-growth, steady-state allocations for the baseline symmetric calibration and for the GIIPSEU10 asymmetric calibration. As noted earlier, the latter captures the observed differences in the
size of the regions, in all their fiscal policy parameters and in their trade balances. The ratios
of the model and the data in the symmetric baseline are nearly identical by design, because the
ratios from the data were used as calibration targets (except the consumption-output ratio). The
small differences in data and model columns for the GIIPS-EU10 scenario suggest that even in the
asymmetric case the model does a good job at capturing the pre-debt-crisis conditions in these
regions as the initial balanced-growth stationary state.
18
Gruber and Rauh (2007) obtained a main estimate of 0.2 for the elasticity of the corporate tax base relative to
corporate taxes in the United States, and Dwenger and Steiner (2012) obtained around 0.5 for Germany. Moreover,
Grubler and Rauh also noted the following after surveying the much larger literature estimating the elasticity of
individual tax bases to individual tax rates: “The broad consensus from this literature is that the elasticity of taxable
income with respect to the tax rate is roughly 0.4. Moreover, the elasticity of actual income generation through
labor supply/savings, as opposed to reported income, is much lower. And most of the response of taxable income to
taxation appears to arise from higher income groups.”
19
They estimated the elasticity of substitution between capital and consumption goods to be in the range of 6 to
14. In models with the standard Hayashi setup of capital adjustment costs without utilization choice, this elasticity
is equal to 1/(ηδ). Hence, for the value of δ(m̄) = 0.0164 in our model, this would imply values of η in the range
between 1 and 2.5.
22
4
Quantitative Analysis
We now turn to quantitative experiments that illustrate the macroeconomic implications of changes
in capital and labor tax rates that could be undertaken to restore fiscal solvency (i.e. balance the
intertemporal government budget constraint) in response to shocks to the initial public debt ratio.
As explained earlier, since labor and consumption taxes are equivalent and consumption taxes are
unchanged at the pre-debt shock rates, adjustments in labor taxes correspond to adjustments in
the consumption-leisure tax wedge (τW ). We refer to the home region as H and the foreign region
as F. We conduct two sets of experiments. In the first set, we assume that H implements unilateral
increases in either capital or labor tax rates, and study the effects on equilibrium allocations
and prices as well as social welfare in the H and F regions, and compare also with the effects
obtained in similar experiments in which H implements tax adjustments as a closed economy.
In light of the significant externalities obtained with unilateral tax changes, the second set of
experiments examines tax adjustments that restore fiscal solvency as solutions of cooperative and
non-cooperative tax competition games between H and F.
The algorithms follow a first-order approximation approach to the model’s equilibrium conditions around the balanced-growth stationary state.20 Since the model consists of two regions
trading freely in goods and asset markets, however, standard perturbation methods widely used in
the Macro literature cannot be applied directly. In particular, trade in bonds implies that, when
the model’s pre-debt-crisis steady state is perturbed by the debt shocks and the tax changes aimed
at restoring fiscal solvency, the equilibrium transition paths of allocations and prices and the new
steady-state equilibrium need to be solved for simultaneously. This is because in models of this
class stationary equilibria depend on initial conditions and thus cannot be determined separately
from the solution of the models’ dynamics. For this reason, Mendoza and Tesar (1998) developed
a solution method that nests a perturbation routine for solving transitional dynamics within a
shooting algorithm. This method iterates on candidate values of the new long-run net foreign asset
20
Mendoza and Tesar (1998, 2005) use a similar method. In their exercise, the algorithm solved for competitive
equilibria and Nash and cooperative games in situations in which capital income taxes were removed and the present
value of the revenue is replaced with other taxes. In this paper we solve for changes in capital and labor taxes that
can restore fiscal solvency in response to changes in the initial public debt ratio.
23
positions to which the model converges after being perturbed by debt and tax changes, until the
candidate values match the positions the model converges to when simulated forward to its new
steady state starting from the calibrated pre-debt-crisis initial conditions (see Mendoza and Tesar,
1998, for details).
4.1
Unilateral Tax Increases and Dynamic Laffer Curves
The first step in the quantitative analysis is to examine how unilateral movements in capital and
labor taxes alter the borrowing ability of the government (i.e. increase the present value of the primary fiscal balance) in the symmetric baseline calibration. For this purpose, as mentioned earlier,
we construct “Dynamic Laffer Curves” that map values of τK or τL into the present discounted
value of the primary fiscal balance they support at equilibrium. For each value of the tax rates, the
sequence of total tax revenue varies as equilibrium allocations and prices vary, while government
purchases and entitlement payments are kept constant. In addition, the present value computation captures the effect of changes in the equilibrium sequence of interest rates, which reflect the
government’s borrowing costs. We express the result as a ratio of pre-debt-crisis output y−1 , so
that it corresponds to the term in the right-hand-side of the intertemporal government budget constraint (10), and in graphs we plot the result as a change relative to the pre-debt-crisis public debt
ratio. Hence, the values along the vertical axis of the dynamic Laffer curves show the change in
the initial debt ratio that particular values of τK or τL can support at equilibrium.21 These Laffer
curves cross the zero line at the calibrated tax rates of the pre-debt-crisis stationary equilibrium
by construction, and a given tax rate can restore fiscal solvency for a given debt shock only if at
that tax rate the dynamic Laffer curve returns a value at least as large as the debt shock.
Since the F region is affected by spillovers of the unilateral tax changes in H, there needs be an
adjustment in F so that its intertemporal government budget constraint continues to hold at the
same level (i.e. the same present discounted value of primary fiscal balances). For simplicity, we
refer to this adjustment as maintaining “revenue neutrality” in the F region. This can be done by
21
Since gt +et remains constant at the pre-crisis level and equilibrium interest rates display relatively small movements, these Laffer Curves display the same shape as standard dynamic Laffer curves that map taxes into the present
value of tax revenue, instead of the primary fiscal balance.
24
changing foreign transfers, taxes or government purchases. The difference is that, since government
purchases are unproductive and taxes are distorting, reducing tax rates in response to favorable
tax spillovers from the H region is more desirable than increasing transfer payments. Hence, since
we are also assuming that government purchases remain constant in both regions, we allow F to
maintain revenue neutrality by adjusting τL∗ .
Dynamic Laffer Curves for Capital Taxes
The solid line in Figure 2 shows the dynamic Laffer curve of the H region for changes in τK ,
together with the corresponding curve assuming H is in autarky (the closed-economy dotted line).
As explained above, at the pre-debt-crisis calibrated value of τK = 0.2, the Laffer curves intersects
the zero line, because the present value of the primary balance does not change relative to the
pre-debt-crisis equilibrium.
As shown in Table 1, the debt shock for the GDP-weighted average of the eurozone is equal to
an increase of 0.22 in the debt ratio. This is indicated as the “Debt Shock” line in Figure 2. Hence,
0.22 is the amount by which the present value of the primary fiscal balance as share of GDP needs
to increase to restore fiscal solvency in the baseline symmetric calibration. The Figure shows that
there is no value of τK that can restore fiscal solvency in the H region in the open economy. The
maximum point of the dyamic Laffer curve is attained with a tax rate of 0.31, with an associated
maximum value equal to an increase in the present value of the primary balance of 9 percentage
points of GDP, far short of the required 22. The dynamic Laffer curve under autarky is steeper
at the pre-debt-crisis tax rate, and it peaks at a higher tax rate of 40 percent, raising the present
value of the primary balance by more than the required 22. As it happens, the H region can restore
fiscal solvency in autarky at almost the same tax rate corresponding to the maximum point of the
open-economy Laffer curve.
The fact that H acting unilaterally can generate more revenue as it increases τK if the economy
is closed than open shows that evaluating “fiscal space,” or the capacity to raise revenue, without
taking into account international trade in goods and assets and cross-country tax externalities,
leads to substantial overestimation of the effectiveness of capital tax hikes as a tool to restore fiscal
solvency. It also suggests that, by focusing on unilateral capital tax austerity alone, countries that
25
have heavier outstanding debt burdens have non-trivial incentives to consider moving to autarky,
imposing capital controls and/or trade barriers, or repudiating their debt.
Table 4 summarizes the effects that result from an unilateral increase in τK to the maximum
point on the open-economy Laffer curve (31 percent). In this scenario, the implied adjustment in
the labor tax in F to maintain revenue neutrality in response to the positive externalities from
the capital tax hike in H, reduces τL∗ from 0.35 to 0.33. Since H’s capital tax rate increases by
11 percentage points, and this tax is highly distorting, H experiences a large welfare cost of 5.54
percent, while F obtains a welfare gain of 0.85 percent.22
Comparing the H region outcomes as an open economy (first two columns of Table 4) v. closed
economy (last two columns) under the same 31 percent capital tax rate, we find that H in autarky
experiences an increase in the present value of its primary balance of 22.2 percentage points, more
than twice as large as in the open-economy case. The welfare loss is nearly the same (5.53 percent),
but normalizing by the amount of revenue generated, H is much better off in autarky. Another way
to see this is to consider the value of τK for H as a closed economy that yields the same 9 extra
percentage points of present value of the primary balance that H attains as an open economy with
τK = 0.3. As Figure 2 shows, H under autarky can do this with a 23.5 percent tax rate, which
carries a much smaller welfare cost than the 5.54 percent loss as an open economy. This shows
again that if fiscal austerity focuses on capital taxes, H would be much better off under autarky,
and hence it has strong incentives to move in that direction.
The impact and long-run effects on key macro-aggregates in both regions are shown in the
bottom of Table 4. The corresponding transition paths as the economies move from the pre-crisis
steady state to the new steady state are illustrated in Figure 3. In the H region, the increase in τK
causes a steady drop in k over time to a level 20.5 percent below the pre-crisis level, while in the
F region k ∗ rises gradually to a level 3 percent higher than in the pre-crisis equilibrium. Capacity
utilization falls sharply initially at home. We show below that this drives the higher elasticity of
the base of capital income taxation. Initially, labor increases in H and falls in F, but this pattern
22
Welfare effects are computed as in Lucas (1987), in terms of a percent change in consumption constant across
all periods that equates lifetime utility under a given debt shock and tax policy change with that attained in the
pre-fiscal-crisis steady state. We report the overall effect, which includes transitional dynamics across the pre- and
post-crisis steady states, as well as a comparison across steady states exclusive of transitional dynamics.
26
reverses during the transition to steady state because of the lower (higher) capital stock in the H
(F) region in the new steady state. As a result of the lower capital and labor, output in H contracts
by 11 percent in the long-run, underscoring efficiency losses due to the capital tax increase and the
costs of the fiscal adjustment.
The H region increases its net foreign asset position (NFA) by running substantial trade surpluses (tb/y) in the early stages of transition, while F decreases its NFA position by running trade
deficits. Hence, H is saving to smooth out the cost of the efficiency losses, as output follows a
monotonically decreasing path. Still, utility levels are lower than when H implements the same
capital tax under autarky, because of the negative cross-country spillovers.
The transitional dynamics of fiscal variables are plotted in Figure 4. In the H region, tax
revenue from capital income increases almost immediately to a higher constant level when τk rises,
while the revenues from labor and consumption taxes decline both on impact and in the long
run. Labor and consumption tax rates are not changing, but both tax bases fall on impact and
then decline monotonically to their new, lower steady states. The primary fiscal balance and
total revenue both rise initially but then converge to about the same levels as in the pre-crisis
stationary equilibrium. For the primary balance, this pattern is implied by the pattern of the total
revenue, since government expenditures and entitlements are held constant. For total revenue, the
transitional increase indicates that the rise in capital tax revenue more than offsets the decline in
the revenue from the other taxes in the transition, while in the long-run they almost offset each
other exactly. This is possible because the change in τK to 0.31 is on the increasing side of the
Laffer curve (see Figure 2), and in fact it is the maximum point of the curve. Hence, this capital
tax hike does not reduce capital tax revenues. At higher tax rates the opposite occurs, and total
revenues converge to a steady state lower than the pre-crisis level (e.g. with τK = 0.45 total revenue
falls to a new steady state 7 percent below the pre-crisis level).
The public debt dynamics in the bottom-right panel of Figure 4 shows that on impact, government debt in the H region responds to the 31 percent tax rate by increasing 9 percentage
points, reflecting the extra initial debt that can be supported at the higher capital tax rate (recall
9 percentage points is also what Figure 2 shows for τK = 0.31). Since the primary fiscal balance
27
rises on impact and then declines monotonically, the debt ratio also falls monotonically during the
transition, and converges to a ratio that is actually about 3 percentage points below the pre-crisis
level. Hence, the debt shock is completely undone by the capital tax hike in the long-run. If H
implements the same tax hike under autarky, it generates significantly larger revenues and primary
balances, and hence the debt ratio increases more initially and converges to a higher steady state
of 10 percentage points above the pre-crisis level. This is again a reflection of the cross-country
externalities faced by H as an open economy, since equally-sized tax hikes produce significantly
higher revenues under autarky.
The cross-country externalities are also reflected in the fiscal dynamics of the F region shown
in Figure 4. Maintaining revenue neutrality (in present value) still allows both its revenue and
primary balance to fall initially, while in the long run both converge to very similar levels as in the
pre-crisis steady state. Removing the labor tax adjustment in F that maintains revenue neutrality,
the present value of its primary balance as a share of GDP would increase by 11.4 percentage points
relative to the pre-crisis ratio, and both its revenue and primary balances would be higher than in
the plots shown in Figure 4. The welfare gain, however, would be negligible instead of 0.85 percent
in lifetime consumption.
This 0.85 percent welfare gain that F obtains because of the positive externalities from the
unilateral capital tax hike in H is largely overlooked in current discussions of fiscal adjustment in
Europe. H can raise more revenue by increasing τK along the upward-sloping region of its dynamic
Laffer curve, but its ability to do so is significantly hampered by the adverse externality it faces due
to the erosion of its tax bases. In F, the same externality indirectly improves government finances,
or reduces the distortions associated with tax collection, and provides it with an unintended welfare
gain.
The Roles of Endogenous Utilization and Limited Tax Allowance
We stated earlier that a key feature of the model is that it introduces endogenous capital
utilization in order to capture the observed elasticity of the capital tax base to changes in capital
tax rates, in contrast with standard dynamic equilibrium models without utilization in which this
elasticity is unrealistically low. In addition, we noted that the interaction with a limited tax
28
allowance for depreciation was also critical for this purpose. To demonstrate these arguments, we
compare dynamic Laffer curves for capital taxes under the following three senarios (see Figure 5):
(A) a standard neoclassical case with exogenous utilization and a full depreciation allowance (using
θ = 1 and shown as a dotted line); (B) the same neoclassical model but a limited depreciation
allowance (using θ = 0.22, shown as a dashed line); (B) the baseline symmetric calibration of our
model with both endogenous utilization and a limited depreciation allowance (using again θ = 0.22,
shown as a solid line). All other parameter values are the same across all these cases.
In case (A), the dynamic Laffer curve is nearly-linearly increasing in the 0.2–0.45 domain of
capital tax rates plotted. Moreover, we verified that this Laffer curve continues to be increasing even
when we extend the capital tax rate to 0.9. This is similar to the results obtained by Trabandt and
Uhlig (2010)) in a closed-economy setting. They found that present-value Laffer curves of capital
tax revenue either become decreasing at very high tax rates (if the interest rate for discounting is
kept constant) or are actually non-decreasing (discounting with equilibrium interest rates). This
behavior of the capital tax Laffer curves follows from the fact that the capital stock is predetermined
at any given date, and has a low elasticity in the short run. This allows the government to raise
substantial revenue over the transition period when increasing the capital tax rate, since the capital
stock declines gradually, and this higher transitional tax revenue dominates the fall in steady-state
tax revenue, resulting in a non-decreasing dynamic Laffer curve.
Introducing the limited depreciation allowance without endogenizing the utilization choice (Case
B) has two effects. First, it increases the effective rate of taxation on capital income, and thus
weakens the incentive to accumulate capital and lowers the steady-state capital-output ratio and
tax bases. Second, it has a positive impact on revenue by widening the capital tax base. The latter
effect dominates the first when the capital tax rate is small (in the 0.2–0.33 range), resulting in
slightly higher dynamic Laffer curve values than in (A), while the opposite holds when the capital
tax rate is high (above 0.33), resulting in sharply lower dynamic Laffer curve values than in (A).
In case (C) the tax allowance is again limited but now capacity utilization is an endoegenous
choice. This introduces effects that operate via distortions on efficiency and the ability to raise
revenue. On the side of tax distortions, it is clear from equation (18) that endogenous utilization
29
adds to the efficiency costs of capital income taxation, by introducing a wedge between the marginal
cost and benefits of capital utilization. On the revenue side, endogenous utilization allows agents
to make adjustments in effective capital, and thus alters the level of taxable capital income (even
though the capital stock is predetermined). Hence, when utilization falls in response to increases in
capital tax rates, it also weakens the government’s ability to raise capital tax revenue. These effects
lead to a bell-shaped dynamic Laffer curve that has more curvature and is significantly below those
in scenarios (A) and (B). Thus, endogenous utilization makes capital taxes more distorting and
weakens significantly the revenue-generating capacity of capital taxes.23
The effects of endogenous utilization and limited depreciation allowance on dynamic Laffer
curves identified above have significant implications for the elasticity of the capital income tax
base with respect to the capital tax. In particular, the combination of endogenous utilization and
limited depreciation allowance is what allowed us to calibrate the model so as to obtain a short-run
elasticity consistent with empirical estimates. As documented earlier, the empirical literature finds
estimates of the short-run elasticity of the capital tax base in the 0.1–0.5 range. Table 5 reports
the model’s comparable elasticity estimates and the impact effects on output, labor and utilization,
again for scenarios (A), (B) and (C). The neoclassical model with or without limited depreciation
allowance (cases A and B) yields negative short-run elasticities (i.e. the capital tax base rises in the
short run in response to capital tax rate increases). The reason is that labor supply rises on impact
due to a negative income shock from the tax hike. Given that the capital stock is fixed, output
rises on impact, and thus taxable labor and capital income both rise, producing an elasticity of
the opposite sign than that found in the data. In contrast, the model with endogenous utilization
(case C), generates a decline in output on impact due to a substantial drop in the utilization rate,
despite the rise in labor supply. With the calibrated value of η = 0.2, which is also the same used in
cases (A) and (B), the model generates a short-run elasticity of 0.29, which is about the midpoint
of the range of empirical estimates.
It is worth noting also that with exogenous utilization it is not possible to obtain a capital tax
base elasticity in line with empirical evidence even by re-calibrating the value of η, unless η itself is
23
Note that removing the limited depreciation allowance from case (C) still results in a Laffer curve significantly
below those of cases (A) and (B). It is also flatter and increasing for a wider range of capital taxes than case (C).
30
set unrealistically low. The model-predicted short-run elasticity of the capital tax base is negative
for η > 1, and it becomes positive and higher than 0.1 only for η < 0.1. This is significantly below
the empirically relevant range of 1–2.5 documented in the calibration section. Moreover, at the
value of η = 2 obtained in our baseline calibration, the model without utilization choice yields a
capital tax base elasticity of −0.031.
Dynamic Laffer Curves of Labor Tax Rates
Figures 6, 7 and 8 and Table 6 show the results for unilateral changes in H’s labor tax rate
analogous to the capital tax rate changes we have examined. The results are more optimistic in
terms of the ability of H to raise revenue and restore fiscal solvency in response to the debt shock.
The open-economy Laffer curve for τL (Figure 6) is considerably steeper than for the capital tax
rate, and it peaks at a tax rate of 0.49 with an increase in the present value of the primary balance
as a share of GDP of about 0.51, well above the 0.22 needed to offset the debt shock. The labor
tax rate that H as an open economy needs to support the 0.88 debt ratio is therefore much lower,
at about 38 percent, and under autarky is just a little lower. This is because the open- and closedeconomy Laffer curves are much closer to each other than in the case of the capital tax experiment,
even though again the closed-economy curve is higher and shifted to the right. This suggests that
international spillovers of tax policies are weaker with labor than with capital taxes, as we confirm
below.
Table 6 compares steady-state results for an increase in the labor tax that raises H’s present
value of the primary fiscal balance by roughly the same magnitude as in the capital tax experiment
of Table 4 (i.e. 9 percentage points). This is done so as to make the results in the two Tables
comparable. The required increase in τL is only one percentage point, from 35 to 36 percent. This
yields much smaller declines in steady-state output, consumption, capital and the investment rate
than in the capital tax case. The welfare cost is also much smaller at 0.91 percent. Comparing H
as a closed v. open economy, the gap in the increase of the present value of the primary balance is
almost negligible in the labor tax case, in contrast with the wide gap obtained for the capital tax.
Taken together these findings are consistent with two familiar results from tax analysis in
representative-agent models, which emphasize the efficiency costs of tax distortions. First, the
31
capital tax rate is the most distorting tax. Second, in open-economy models, taxation of a mobile
factor (i.e. capital) yields less revenue at greater welfare loss than taxation of the immobile factor
(i.e. labor). This is in line with our results showing that the cross-country tax externalities are
strong for capital taxes but weak for labor taxes. With capital taxes, H as an open economy cannot
restore fiscal solvency after a debt shock of 22 percentage points, while under autarky it can do it
with a capital tax of about 31 percent at a welfare cost of 5.53 percent. In contrast, with labor
taxes, H can offset the same debt shock with about a 38 percent labor tax either as an open economy
or under autarky, with a much smaller welfare cost of 2.43 percent. On the other hand, our results
also indicate that it is plausible for cross-country tax externalities to be significant even for labor
taxes. Figure 6 indicates that for debt shocks larger than 40 percentage points and/or pre-debtshock labor taxes higher than 40 percent, the cross-country externalities would be nontrivial and
in the same direction as those observed in the capital tax analysis.
Asymmetric Regions: GIIPS, EU10
Up to this point, we have focused only on experiments that use the symmetric baseline calibration. Now we study the effects of heterogeneity in region size. Table 7 shows results for tax policy
adjustments for each country in the GIIPS acting unilaterally. In each scenario, we solve the model
resetting the parameter controlling the relative size of the two regions so that H has the size of the
corresponding GIIPS country relative to the eurozone (shown in the second column of the Table).
Intuitively, each country in GIIPS treated in this way becomes much smaller, and the effect of a
domestic tax change on international prices is correspondingly smaller. This in turn means that
the impact on domestic capital outflow is greater, and thus the ability to raise revenue weakens
considerably. This is reflected in the peaks of the Laffer curves listed in the last two columns of
Table 7, which show the maximum increase in the present discounted value of the primary balance
that each GIIPS country can obtain individually using capital or labor taxes.
The results in the Table also show that none of the GIIPS countries can restore fiscal solvency
with a capital income tax hike (i.e.the peaks of the Laffer curves are smaller than the debt shocks
shown in the third column), and one of the five countries (Ireland) cannot do it even with the labor
tax. Note also that Greece and Ireland experienced debt shocks that are much higher than the
32
GDP-weighted GIIPS regional average of 0.3.
4.2
Strategic Interaction in Tax Responses to Debt Shocks
The findings from the analysis of unilateral tax changes showed that capital tax changes produce
significant cross-country externalities, suggesting that there is scope for strategic interaction and
potential gains from coordination in considering tax responses to restore fiscal solvency in response
to debt shocks. In particular, when a region raises its capital tax, the externalities move against
that region and make the other region relatively more efficient. The burden of fiscal adjustment in
response to debt shocks is heavier (lighter) for the region with the higher (lower) taxes. But the
governments of both regions are aware of the externalities, and thus have an incentive to engage in
tax competition.
To analyze strategic interaction, we follow Mendoza and Tesar (2005) and examine the solutions
to one-shot cooperative and non-cooperative games. They focused on tax reform experiments in
which the present value of revenue had to remain constant, whereas here we consider games in
which each region uses capital and labor taxes to respond to their corresponding debt shocks.
These games are solved first using the symmetric baseline calibration in which both regions are
identical, then introducing elements of heterogeneity one at a time, and finally considering two fully
heterogeneous regions, one calibrated to GIIPS and the other to EU10, capturing their differences
in country size, pre-debt-shock fiscal policies and trade balances, and size of debt shocks.
The formal characterization of the strategy space and the games is as follows. The strategy
space is defined in terms of vectors of possible capital tax rates that the government of each region
∗ ) in this strategy space, we solve for
can choose. For each given pair of capital tax rates (τK , τK
the pair of labor tax rates (τL , τL∗ ) that allows each region to increase the present value of its
primary balance at the corresponding competitive equilibrium as needed to restore solvency after
the debt shocks — 22 percentage points for both regions in the symmetric benchmark case, and 30
for GIIPS and 18 for EU10 in the asymmetric case. The games are played once, but the payoffs
are dynamic, because they take into account the full transitional dynamics from the pre-crisis
competitive equilibrium to the new stationary equilibrium of under a particular set of capital and
33
labor taxes in both regions.
Each region chooses its capital tax rate so as to maximize the lifetime utility of its residents taking as given the other region’s taxes and subject to the constraints that: (i) the implied allocations
∗ , τ ∗ ), with unchanged consumption
and prices for a tax structure given by the pairs (τK , τL ), (τK
L
taxes, are a competitive equilibrium; and (ii) labor taxes in each region adjust so that intertemporal
government budget constraints support increases in the present value of the primary fiscal balances
equal to each region’s debt shock, as shown in equation (10).
The regions choose capital tax rates from values in discrete grids with M and N nodes for the
∗ = {τ ∗ , τ ∗ , ..., τ ∗ }.
home and foreign country respectively: TK = {τK1 , τK2 , ..., τKM } and TK
K1 K2
KN
Hence, the strategy space is the set of M × N capital tax rate pairs. For each pair, we compute prices and allocations that satisfy conditions (a) and (b) and the associated welfare payoffs.
∗ is denoted V (τ |τ ∗ ). The
The payoff function for the home’s strategic choice of τK given τK
K K
∗ |τ ). Given these definitions, H’s recorresponding foreign payoff function is denoted by V ∗ (τK
K
∗ ) = arg max
∗
action curve is defined by the mapping τK (τK
τK [V (τK |τK )] and the one for F is
∗ (τ ) = arg max ∗ [V ∗ (τ ∗ |τ )]. The Nash non-cooperative equilibrium is given by the tax rate
τK
K
τK
K K
N , τ N ∗ ) at which these reaction functions intersect. That is, τ N =τ (τ N ∗ ) and τ N ∗ =τ ∗ (τ N ).
pair (τK
K K
K
K
K
K K
C , τ C∗ ) such that: (1) it satisfies properties (i)
A cooperative equilibrium is defined as the pair (τK
K
and (ii), and (2) the pair maximizes the payoff of a utilitarian European-wide social planner given
∗ ) + (1 − λ)V ∗ (τ ∗ |τ ) for an arbitrary
by the weighted sum of the two regions’ payoffs λV (τK |τK
K K
weight λ subject to participation constraints that require each region to be at least as well off as
C |τ C∗ ) ≥ V (τ N |τ N ∗ ) and V ∗ (τ C∗ |τ C ) ≥ V ∗ (τ N ∗ |τ N ). There can
under the Nash equilibrium: V (τK
K
K
K
K
K K
K
be several cooperative equilibria supported by different λ0 s,and the set of all cooperative equilibria
determines the core of the players’ contract curve. Note that these cooperative equilibria are still
tax-distorted competitive equilibria, because cooperation internalizes the effects of the international
tax externalities but does not remove domestic tax distortions themselves.
∗ ) space and identifies the Nash and pre-crisis
Figure 9 shows the reaction functions in (τK , τK
equilibria in the game with symmetric regions. The “Nash” column in Table 8 shows the corresponding tax rates, welfare outcomes, and changes in the present value of primary balance. Both
34
reaction functions have a negative slope because of the positive externalities that one country experiences if the other chooses a higher tax rate. For instance, the higher the capital tax rate in F,
the lower the optimal capital tax choice in H, because it allows H to reduce tax distortions while
still maintaining fiscal solvency. Starting from identical tax rates on capital of 0.20 pre-crisis, Nash
competition results in the familiar “race to the bottom” in capital taxes, to 0.08. Labor taxes
increase from 0.35 to 0.44 and welfare declines relative to the pre-crisis equilibrium by 1.63 percent.
Note that the welfare effects from the outcome of tax competition in response to debt shocks
involve two opposing effects. The first is that countries must raise revenue in response to the debt
shock. The second is that by competing in tax rates the regions are effectively reforming their tax
systems relative to pre-crisis tax rates (countries are optimally choosing labor and capital taxes to
raise the required revenue at the lowest efficiency cost). In principle it could be possible for the
gains from the latter to outweigh the costs of the former, but in our experiments using debt shocks
of the observed magnitudes this does not happen.
Consider next the symmetric cooperative equilibrium solutions shown in Figure 9. Because of
symmetry, we focus on the cooperative outcome for equal country weights (see column Cooperative
in Table 8). In the cooperative equilibrium, the capital tax rate is higher than under Nash: 0.12
versus 0.08, and the labor tax rate is lower: 0.42 versus 0.44. Cooperation allows countries to
commit to higher capital taxes relative to Nash and avoid painful increases in labor taxes, which
reduces the welfare cost of tax austerity to respond to the debt shocks from 1.63 to 1.45 percent
(i.e. the welfare gain from cooperation is about 0.18).
While tax coordination helps prevents welfare-reducing strategic interaction, the welfare costs
of adjusting taxes to offset debt shocks are still quite large in both Nash and cooperative outcomes.
Relative to the pre-crisis tax rates, capital taxes are lower and labor taxes are higher in the Nash
equilibrium after the debt shocks for two reasons. First, capital tax rates are lower because governments wish to reduce the tax that is most distorting in terms of welfare cost per unit of revenue
(i.e. the capital tax). Second, in an open economy governments have the incentive to undercut
other countries’ tax rates in an effort to attract foreign capital and thereby increase the tax base.
Since both countries are attempting the same strategy, the outcome is lower capital tax rates and
35
higher labor tax rates than is optimal under cooperation.
To highlight the impact of the strategic reaction by the foreign country on the home country,
we conduct two additional experiments. One is the “Autarky” experiment, which shows the effects
of fiscal adjustments to meet the debt shock in a closed economy. Note that under symmetry,
the autarky outcome is identical to the cooperative outcome above by construction. Thus, the
closed economy model will underestimate the welfare loss from the debt shock. The other is the
“Unilateral” experiment, which corresponds to the unilateral Laffer curve experiment illustrated in
Figure 2. As in that Figure, we assume that only H experiences the debt shock, and the foreign
country adjusts its labor tax rate to maintain revenue neutrality but does not behave strategically.
H chooses both capital and labor tax rates lower than those in the Nash equilibrium. Consequently,
the welfare cost of the debt shock for the home country is smaller in the unilateral case than in
the Nash case: 0.67 versus 1.63. This outcome, however, is not sustainable once we relax the
assumption that the foreign country is a passive player and allow it to respond optimally.
The last column of Table 8 reports the Nash outcome implied by the neoclassical model with
exogenous utilization (θ = 0.22). Relative to the benchmark results in the Nash column, the neoclassical model underestimates the tax competition effect on capital taxation. When the adjustment
in capital is sluggish, the two countries can rely more heavily on capital taxation. As a consequence,
they also end up with a less efficient tax system and therefore experience larger welfare losses.
We next move to the asymmetric game in which we introduce the elements of heterogeneity
across the GIIPS and EU10 regions one by one. The results are reported in Table 9. Starting
with country size (the second column of Table 9), tax competition benefits small countries in two
ways. One is that by having a smaller impact on world prices, the small country can play off of
the large country without offsetting price adjustments. Second, the smaller country faces a bigger
supply of foreign capital from which the home country can steal by undercutting the capital tax
rate. Indeed, the benefit of being small leads to an approximate 0.26 relative welfare benefit for
the smaller H region relative to the bigger region. An initial trade surplus (negative NFA position)
is an advantage for EU10. The initial drop in interest rates along the transition path reduces the
cost of servicing external debt. This has a sizable welfare effect, with a relative gain for EU10 of
36
nearly 2.5 percent. Asymmetries in initial tax rates also matter in the Nash game. Having a higher
capital tax rate but lower labor and consumption taxes benefits GIIPS at the expense of the EU10
in the Nash game (the higher the capital tax rate initially, the more to gain from the race to the
bottom).24 Finally, facing a larger debt shock places GIIPS at a disadvantage in the Nash game.
The impact of the differential debt shock is large: the GIIPS region suffers a welfare loss of 3.5
percent while the EU10 suffers only 0.59 percent. The last column of Table 9 reports the outcome
of putting all of these differential factors altogether. GIIPS undercuts EU10 in capital tax rates:
0.07 versus 0.09, but given its larger debt shock, GIIPS still experiences a substantial welfare loss of
1.55 percent, and EU10 experiences a welfare loss of 1.13 percent, relative to their pre-crisis levels.
Table 10 reports Nash, cooperative and autarky outcomes for the fully asymmetric game. The
Nash column repeats the results from the final column of Table 9. The important message of Table
10 is the comparison of the Nash equilibrium with the cooperative equilibrium and the autarky exit
option. Two points are worth noting. First, both regions are hurt by tax competition and would
prefer cooperation to Nash. However, in the event cooperation fails, GIIPS prefers to exit while
EU10 prefers tax competition to exit. Even in the case where the lion’s share of the gains from
cooperation are allocated to GIIPS (case 1), GIIPS prefers the autarky outcome. This means that
the international externalities work against GIIPS and tend to favor EU10. Failure to take these
international externalities into account undermines the sustainability of the union.
4.3
Discussion on the Frisch Elasticity
Our benchmark analysis focuses on the case in which labor is immobile across countries. This
assumption tends to underestiamte the elasticity of labor supply to fiscal austerity due to the debt
shocks or income shocks. Given the complexity to directly model labor mobility across countries,
we experiments with different Frisch elasticities to examine implications of this assumption. Given
the specification of our preferences, the Frisch elasticity is given by
ζ=
24
σ
1 − n̄
,
n̄ σ − a(1 − σ)
The pre-debt-crisis consumption-leisure tax wedges are 0.46 for EU10 v. 0.41 for GIIPS.
37
(19)
where n̄ denotes the steady state level of labor supply. Our baseline calibration specifies n̄ = 0.183.
Together with a = 2.675 and σ = 2, the implied Frisch elasticity is ζ = 1.91, which is within the
range, though on the upper side, of 1 and 2, commonly used in the macroeconomic literature. The
empircal labor literature tends to provide very low estimates of the Frische elasticity, e.g. 0.15 by
MaCurdy (1981).25 We experiment with a lower a of 0.056, which implies a Frisch elasticity of
0.15, and a higher a of 7.5, which implies a Frisch elasticity of 2.63.
We first study capital-tax laffer curves under different Frisch elasticities as shown in Figure
11. When the Frisch elasticity is high, the dynamic laffer curve shift down relative to the baseline
calibration, i.e., the capacity of generating extra revenues is reduced with more elastic labor supply
for any given capital tax hike. The dynamics laffer curve peaks at around 5.7% in contrast to 9%
in our baseline. The opposite is true for a low Frisch elasticity. The dynamic laffer curve peaks
at 46% at a capital tax rate of 0.41. In fact, the government can generate the revenue needed to
substain the debt shock at a capital tax rate of 0.25. Clearly, the Frisch elasticity which directly
impacts labor supply has a subtantial impact on the capital tax laffer curve. If one approximates the
outcomes under higher Frisch elasticities to those with international labor mobility, this experiment
shows that fiscal austerity will be more challenging or unpleasant than our baseline estimates.
We next look at the macro-economic implications of different Frisch elasticities in Table 11. For
each Frisch elasticity, we increase the home capital tax rate to raise the peak revenue substainable
in the high Frisch case, while the foreign country lowers its labor tax rate to maintain revenue
neutrality. As shown in the first row, a higher Frisch elasticity requires a larger increase in the
home capital tax rate to raise the same amount of revenue. Moreover, the home welfare loss also
rises with the Frisch elasticity; the high Frisch case implies a 4.1% overall welfare loss, while the low
Frisch case only implies 0.45%. Also, the higher is the Frisch elasticity, the larger are the declines
in output, consumption, capital stocks, investment and utilization in the home country. In short,
using the capital tax rate to offset debt shocks becomes much harder in terms of raising revenue
and more concerning in terms of spillovers when labor supply is elastic. In the high Frisch case,
the tax hike needs to be 4 percentage points larger, and the welfare loss is above 100% larger for
25
See Keane and Rogerson (2012) for an excellent review of the literature on estimating Frisch parameters.
38
the home country, while the foreign country cuts its labor tax one extra percentage point and has
a welfare gain nearly 2 times larger than in the baseline case.
The cross-country spillover is much weaker under the low Frisch case, which induces a tiny cut
in the foreign labor tax. What is interesting is that the spillover effect of the home capital tax
increase on the overall welfare in the foreign country turns negative when the Frisch elasticity is
low. This implication is important for understanding the game results below. With inelastic labor
everywhere there is barely permanent relocation of capital when the capital tax changes in the
home country unilaterally (foreign output and capital in the new steady state change little).
Finally we examine the game outcomes under different Frisch elasticities, and the results are
reported in Table 12. When the Frisch is high, the Nash outcome features higher equilibrium capital
tax rates and larger welfare losses for both countries than in the baseline case. Moreover, GIIPS
has both the capital and labor taxes higher than in the baseline to substain the same debt shock,
because the labor tax revenue contributes less with elastic labor supply. GIIPS continues to find
the autarky attractive even comparing to the best scenario in the cooperative game.
Lower elasticity pushes the game results in the opposite direction, yielding a stronger race to
the bottom: the capital tax rate is −0.12 in GIIPS, and −0.14 in EU10. Capital is subsidized
substantially, and labor is taxed more, but not much more than in the baseline case, because again
with very inelastic labor a small increase in the labor tax goes a long way in terms of generating
revenue. The welfare effects are positive in both countries in the Nash outcome. Now it is the
EU10 that finds the autarky attrative than the best outcome under cooperation.
All in all, the experiments on the Frisch parameter illustrate that a higher labor elasticity as a
proxy for international labor mobility implies more challenges in using capital taxes and triggers
stronger cross-country externalities. We also found that effects of changes in capital tax rates
are very sensitive to labor supply elasticies. In particular, very low labor elasticities make capital
taxation more useful to generate revenue unilaterally, but in strategic interaction trigger stronger
race to the bottom because using the labor tax is more advantageous to compete. These results
flesh out clearly the differences between unilateral comparisons and game results. The unilateral
comparisons fix things in a way that brings out the size of spillovers and ability to raise revenue
39
for taxes set to meet a revenue target, while the games let taxes be chosen optimally to maximize
payoffs. This is why a low Frisch elasticity seems to deliver this paradoxical result that from the
unilateral side it looks like capital taxation has more ability to offset debt shocks and the spillovers
are gone, but it would be misleading to conclude that because of this the incentives for strategic
interaction are gone too. In fact to the opposite, in the games actually a low Frisch elasticity
strengthens the ability to compete by cutting capital taxes, and results in equilibria where capital
is subsidized and labor taxed at about the same rate as in the baseline case. The message again is
that it is very hard to offset debt shocks with capital taxes (i.e. competition drives them to capital
subsidies).
5
Conclusions
Public debt ratios surged between 2008 and 2011 in many industrial countries, raising serious
questions about fiscal solvency and the need for fiscal adjustment. In the eurozone in particular,
public debt increased by a GDP-weighted average of 30 percentage points in the GIIPS region
and in the EU10 by 18 percentage points. If, in the presence of these large debt shocks, defaults
are to be averted (i.e. fiscal solvency maintained) and the eurozone countries are to remain fully
integrated in goods and asset markets, three key questions arise. First, is tax-driven adjustment
feasible (i.e. can it yield increases in the present value of the primary fiscal balances that match
the higher debt ratios)? Second, how do different tax-adjustment policies using capital or labor
taxes differ in terms of revenue, macroeconomic dynamics, cross-country externalities, and welfare
costs? Third, what are the implications of strategic interaction, and the benefits of coordination,
in the tax-adjustment response to debt changes in economies that trade freely in goods and assets?
The workhorse Neoclassical model with exogenous long-run growth widely used for quantifying
the effects of tax policies in the literature is poorly suited to answer these questions, because it
underestimates the elasticity of the capital tax base to changes in capital taxes. This is due to
the fact that the capital stock is pre-determined at any given date, and adjusts slowly over the
long run, and also to the standard assumption of a 100-percent depreciation tax allowance. As a
result, models of this class tend to produce rosy estimates of the effectiveness of capital tax hikes
40
for raising tax revenues and underestimate the significance of cross-country externalities.
In contrast, in this paper we answer the above questions using a two-country, dynamic general
equilibrium model that deviates from the workhorse Neoclassical model in two key respects. First,
it allows for endogenous utilization of capital, which allows agents to adjust taxable capital income
much quicker in response to capital tax changes. Second, it introduces a limited depreciation tax
allowance, which is in line with the actual treatment in tax codes that apply this allowance to
taxes levied to business incomes, not capital income accruing to individuals (e.g. dividends, capital
gains), and do not apply it to residential capital. These two features of the model make capital
income taxes more distortionary than in the Neoclassical model, and also lower signficantly the
ability of the government to raise capital income tax revenues. As a result, a reasonable calibration
of the model features a short-run elasticity of the capital tax base around the midpoint of empirical
estimates.
We calibrate the model to data for eurozone countries and find striking results. Raising capital
taxes unilaterally is not a feasible strategy for restoring fiscal solvency in response to the observed
debt shocks. The dynamic Laffer curve that maps capital taxes into changes in the present value
of the primary fiscal balance peaks far below the required increment. Labor taxes can do it, but
in both cases the tax hikes entail large welfare costs. Moreover, capital tax adjustments induce
large cross-country externalities, which favor the countries with less pressure to raise capital taxes
(i.e.the EU10). In addition, in both scenarios GIIPS can offset the observed debt shocks at lower
tax rates and welfare costs under autarky, which in the model provides them with a strong incentive
to move in that direction or default on their debt obligations.
Non-cooperative Nash competition, which involves choosing the optimal pairs of capital and
labor taxes to restore fiscal solvency in response to the observed debt shocks, yields the well-known
race to the bottom in capital tax rates. When countries can adjust capital and labor taxes, the
tax structure shifts sharply toward lower capital and higher labor taxation. In representativeagent models of the class we study this induces efficiency gains, reducing the welfare cost of fiscal
adjustment. The race ends with small positive capital taxes and higher labor taxes relative to precrisis rates, but the former are too low and the latter too high because countries do not internalize
41
the international externalities of their tax policies. Cooperation internalizes these externalities,
and thus reduces the size of the cut in capital taxes and hike in labor taxes. This makes fiscal
adjustment slightly less costly, but even in this case the welfare cost of the tax adjustments that
restore fiscal solvency remains large.
The costs of adjusting to the large debt shocks are lower when regions or countries are assumed
to be able to choose the best mix of their own capital and labor taxes acting unilaterally and
assuming the other countries remain passive. These results are not sustainable, however, because
they negate the strong incentives for strategic interaction. Moreover, the costs of implementing the
best mix of capital and labor tax changes to restore fiscal solvency are lower under autarky than
those of the Nash and Cooperative games for the GIIPS region, but higher for the EU10 region.
Hence, the GIIPS region is left with an incentive to move away from full economic integration.
The analysis of this paper has clear implications for current policy. Despite the fact that
the European nations have closely integrated goods and financial markets, policy discussions have
proceeded largely without taking into account international ramifications of domestic tax policy
adjustments. Economists have pointed out a number of factors that could give highly-indebted
European countries incentives to exit the eurozone; a depreciation of the currency could produce
an export boom and reduce unit labor costs, removal of the Maastricht debt and deficit targets
could enable countries to adopt more expansive monetary and fiscal policies, and default on external
debt could relax (at least temporarily) the country’s budget constraint. This paper identified and
quantified another factor that can undermine incentives to remain in the eurozone significantly: the
fiscal externalities from tax austerity that work against the GIIPS region. These factors deserve
careful consideration in discussions of fiscal austerity and fiscal sustainability.
42
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45
Figure 1: Debt Shocks in the eurozone
1. 10
1.00
+0.3
0.90
0.80
0.70
0.60
EU 10
0.50
0.40
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 20 10 2011
46
Figure 2: Dynamic Laffer Curves for the Capital Tax Rate
Notes: Dynamic Laffer curves plot the equilibrium present value of total tax revenue net
of the equilibrium present value of government spending and transfers as a ratio of predebt-crisis output relative to the pre-debt-crisis public debt ratio when the capital tax rate
changes.
47
Figure 3: Macro Responses to a Capital Tax Rate Increase
Notes: In this experiment, the foreign labor tax rate is adjusted from 0.35 to 0.32 to reserve its revenue
neutrality. All variables are reported as percent changes from pre-crisis steady state except the lower panel,
which are in percentage point differences from pre-crisis steady state. The solid red lines and the dotted
black lines are for the home and foreign country, respectively, in the open economy. The dashed green lines
are for the home country in the closed economy.
48
Figure 4: Fiscal Responses to a Capital Tax Rate Increase
Notes: All variables are reported as changes from pre-crisis steady state levels. The solid red lines and the
dotted black lines are for the home and foreign country, respectively, in the open economy. The dashed
green lines are for the home country in the closed economy.
49
Figure 5: Comparisons of Dynamic Laffer Curves for the Capital Tax Rate
Notes: The dotted red line is for the neoclassical case with exogenous utilization and full
depreciation allowance; the dashed black line is for the neoclassical case with exogenous
utilization and partial depreciation allowance; the solid blue line is for the benchmark
calibration with endogenous utilization and partial depreciation allowance.
50
Figure 6: Dynamic Laffer Curves for the Labor Tax Rate
Notes: Dynamic Laffer curves plot the equilibrium present value of total tax revenue net
of the equilibrium present value of government spending and transfers as a ratio of predebt-crisis output relative to the pre-debt-crisis public debt ratio when the labor tax rate
changes.
51
Figure 7: Macro Responses to a Labor Tax Rate Increase
Notes: In this experiment, foreign labor tax rate is adjusted from 0.35 to 0.34 to reserve its revenue neutrality.
All variables are reported as percent changes from pre-crisis steady state except the lower panel, which are
in percentage point differences from pre-crisis steady state. The solid red lines and the dotted black lines
are for the home and foreign country, respectively, in the open economy. The dashed green lines are for the
home country in the closed economy.
52
Figure 8: Fiscal Responses to a Labor Tax Rate Increase
Notes: All variables are reported as changes from pre-crisis steady state levels. The solid red lines and the
dotted black lines are for the home and foreign country, respectively, in the open economy. The dashed
green lines are for the home country in the closed economy.
53
Figure 9: Capital Tax Reaction Functions: Symmetric Game
Figure 10: Capital Tax Reaction Functions: Asymmetric Game
54
Figure 11: Capital Tax Dynamic Laffer Curves: Different Frisch Elasticities
0.6
ΔPV(Primary Balance)/y0
0.5
Low Frisch
Baseline
High Frisch
0.4
0.3
0.2
0.1
0
−0.1
−0.2
0.2
0.25
0.3
0.35
Capital Tax Rate
0.4
0.45
Notes: The solid red line is for the baseline Frisch elasticity; the dashed black line is for
the high Frisch elasticity; the dotted blue line is for the low Frisch elasticity.
55
56
0.42
0.49
0.60
0.72
0.12
Rev/y
Total Exp/y
(b) Debt Shocks
d2007 /y2007
d2011 /y2011
∆d/y
0.84
0.98
0.14
0.43
0.50
0.52
0.24
0.23
0.01
0.17
0.37
0.27
BEL
0.35
0.49
0.14
0.42
0.49
0.52
0.22
0.22
0.04
0.24
0.37
0.21
FIN
0.64
0.86
0.22
0.41
0.53
0.57
0.22
0.23
−0.02
0.17
0.36
0.25
FRA
EU10
0.65
0.81
0.15
0.36
0.44
0.56
0.19
0.18
0.06
0.17
0.34
0.16
GER
0.45
0.65
0.20
0.38
0.46
0.45
0.20
0.26
0.08
0.20
0.36
0.19
NET
0.20
0.34
0.14
0.33
0.39
0.50
0.22
0.17
0.06
0.23
0.32
0.12
Other
1.07
1.71
0.63
0.31
0.51
0.72
0.24
0.18
−0.14
0.15
0.33
0.12
GRE
0.25
1.08
0.83
0.29
0.43
0.51
0.22
0.19
0.09
0.21
0.23
0.17
IRE
1.03
1.20
0.17
0.41
0.49
0.59
0.22
0.20
−0.01
0.13
0.38
0.25
ITA
GIIPS
MACROECONOMIC STANCE AS OF 2008
0.68
1.08
0.40
0.41
0.45
0.67
0.23
0.20
−0.10
0.18
0.23
0.20
POR
0.36
0.69
0.33
0.32
0.41
0.57
0.29
0.19
−0.06
0.12
0.29
0.17
SPA
0.62
0.79
0.18
0.39
0.48
0.55
0.21
0.21
0.03
0.18
0.36
0.20
0.75
1.05
0.30
0.36
0.46
0.59
0.24
0.20
−0.03
0.14
0.33
0.21
GIIPS
0.66
0.88
0.22
0.38
0.47
0.56
0.22
0.21
0.01
0.16
0.35
0.20
All EU
GDP-weighted ave.
EU10
Note: EU10 includes Austria, Belgium, Estonia, Finland, France, Germany, Luxembourg, the Netherlands, the Slovak Republic and Slovenia.
Source: OECD Revenue Statistics, OECD National income Accounts, and EuroStat. Tax rates are authors’ calculations based on Mendoza, Razin, and Tesar (1994). ”Total
Exp” is total non-interest government outlays.
0.53
0.23
0.19
0.06
c/y
x/y
g/y
tb/y
(a) Macro Aggregates
τC
0.19
τL
0.42
τK
0.16
AUT
Table 1:
57
Gov’t exp share in GDP
consumption tax
labor income tax
capital income tax
depreciation allowance limitation
OECD National Income Accounts
MRT modified
MRT modified
MRT modified
(REVKcorp /REVK )(K N R /K), OECD Revenue Statistics and EU KLEMS
(Trabandt and Uhlig, 2009)
real GDP p.c. growth of euro area (Eurostat 2000–2011)
Elasticity of capital tax base (Gruber and Rauh, 2007), (Dwenger and Steiner, 2012)
steady state normalization
capital law of motion, x/y = 0.222, k/y = 2.97 (OECD, AMECO)
optimality condition for utilization given δ(m̄), m̄
set to yield δ(m̄) = 0.0164
symmetric countries
steady state Euler equation for capital
standard DSGE value
¯l = 0.18 (Prescott, 2004)
corp
Note: The implied growth adjusted discount factor β̃ is 0.992, and the implied pre-crisis annual interest rate is 4.2%. REVK
/REVK is the ratio
N
R
of corporate tax revenue to total capital tax revenue. K
/K is the ratio of nonresidential fixed capital to total fixed capital.
g/y
τC
τL
τK
θ
0.21
0.16
0.35
0.20
0.22
0.61
0.0022
2
1
0.0164
0.03
1.58
0.50
Technology:
α
labor income share
γ
growth rate
η
capital adjustment cost
m̄
capacity utilization
δ(m̄) depreciation rate
χ0
δ(m) coefficient
χ1
δ(m) exponent
ω
country size
Fiscal Policy:
0.9942
2.000
2.675
Preferences:
β
discount factor
σ
risk aversion
a
labor supply elasticity
Table 2: PARAMETER VALUES
Table 3: BALANCED GROWTH ALLOCATIONS (GDP RATIOS) OF 2008
Symmetric Case
All EU
Asymmetric Case
GIIPS
EU10
c/y
x/y
g/y ∗
Data
0.56
0.22
0.21
Model
0.57
0.22
0.21
Data
0.59
0.24
0.20
Model
0.60
0.22
0.20
Data
0.55
0.20
0.21
Model
0.54
0.23
0.21
tb/y
Rev/y
d/y ∗
0.00
0.38
0.66
0.00
0.38
0.66
-0.03
0.36
0.75
-0.03
0.36
0.75
0.03
0.39
0.62
0.03
0.39
0.62
58
59
0.20
0.16
0.35
τK
τC
τL
−11.02
−7.77
−20.47
−2.86
−4.35
0.00
9.66
−9.46
−0.00
0.27
−11.43
y
c
k
Percentage point changes
tb/y
x/y
r
l
m
−1.60
−3.03
−0.00
−0.53
−2.39
Long-Run Effect
−6.16
−5.54
9.03
0.31
0.16
0.35
New
Impact Effect
Percentage changes
Welfare effects (percent)
steady-state only
overall
PV of fiscal deficit over
pre-crisis GDP as percentage
point change from original ss
Old
Tax rates
Home
−9.65
6.78
−0.00
−0.29
−1.64
−1.63
2.68
0.00
−0.19
0.85
0.00
0.20
0.16
0.33
New
1.38
0.00
−0.00
0.56
−0.00
3.05
1.66
3.05
Long-Run Effect
Foreign
Impact Effect
0.20
0.16
0.35
Old
Open Economy
(Foreign maintains revenue neutrality with labor tax)
−3.09
−0.00
−0.46
−14.22
−6.13
−3.27
0.00
Impact Effect
0.20
0.16
0.35
Old
−7.42
−5.53
22.21
0.31
0.16
0.35
New
−3.03
−0.00
−0.23
−2.39
−9.50
−8.11
−19.12
Long-Run Effect
Home
Closed Economy
Table 4: MACROECONOMIC EFFECTS OF AN INCREASE IN THE HOME CAPITAL TAX RATE
60
−0.05
−0.03
0.29
Elasticity
[0.1, 0.5]
0.08%
0.20%
−0.66%
y1
0.021
0.056
0.017
l1
−1.89
m1
Note: Elasticity is measured as the percentage decrease of capital tax base in the first year after a
1% increase in the capital tax rate is introducede. y1 and m1 provides the percent deviation from
the initial steady state on impact. l1 denotes the percentage points change from the initial steady
state.
Empirical estimate∗
Models
exog. utilization & θ = 1
exog. utilization & θ = 0.22
endog. utilization & θ = 0.22
Table 5: SHORT-RUN ELASTICITY OF CAPITAL TAX BASE
61
0.20
0.16
0.35
τK
τC
τL
−1.44
−1.80
−1.44
−0.94
−1.58
0.00
0.60
−0.43
−0.00
−0.22
−0.54
y
c
k
Percentage point changes
tb/y
x/y
r
l
m
−0.09
−0.00
−0.00
−0.26
0.00
Long-Run Effect
−0.95
−0.91
9.03
0.20
0.16
0.36
New
Impact Effect
Percentage changes
Welfare effects (percent)
steady-state only
overall
PV of fiscal deficit over
pre-crisis GDP as percentage
point change from original ss
Old
Tax rates
Home
−0.60
0.42
−0.00
−0.02
−0.10
−0.09
0.18
0.00
−0.00
0.06
0.00
0.20
0.16
0.35
New
0.09
0.00
−0.00
0.04
−0.00
0.21
0.12
0.21
Long-Run Effect
Foreign
Impact Effect
0.20
0.16
0.35
Old
Open Economy
(Foreign maintains revenue neutrality with labor tax)
−0.01
−0.00
−0.26
−0.69
−1.13
−1.52
0.00
Impact Effect
0.20
0.16
0.35
Old
−1.03
−0.92
9.85
0.20
0.16
0.36
New
−0.00
−0.00
−0.25
−0.00
−1.34
−1.82
−1.34
Long-Run Effect
Home
Closed Economy
Table 6: MACROECONOMIC EFFECTS OF AN INCREASE IN THE HOME LABOR TAX RATE
62
0.025
0.021
0.172
0.019
0.117
0.500
Greece
Ireland
Italy
Portugal
Spain
Symetric bench
Country Size
0.22
0.40
0.50
0.15
0.36
0.27
∆Debt/y2008
0.09
0.02
0.02
0.04
0.02
0.03
0.51
0.43
0.42
0.45
0.42
0.44
Peak Rev Increase/y2008 of
Capital Tax Net Laffer Curve Labor Tax Net Laffer Curve
Table 7: PEAK INCREASE IN PRESENT VALUE OF PRIMARY BALANCE IN INDIVIDUAL GIIPS COUNTRIES
Table 8: SYMMETRIC-COUNTRY GAME OUTCOMES
Pre-Crisis
Home
τK
τL
∆PV(Primary Balance)/Y
∆Welfare v. pre-crisis
Foreign
τK
τL
∆PV(Primary Balance)/Y
∆Welfare v. pre-crisis
Autarky
Unilateral
Cooperative
Nash
Neocl. Nash
0.202
0.347
0.121
0.416
0.222
−1.448
0.077
0.425
0.222
−0.674
0.121
0.416
0.222
−1.448
0.083
0.435
0.222
−1.627
0.138
0.417
0.222
−2.709
0.202
0.347
0.121
0.416
0.222
−1.448
0.202
0.358
0
−0.584
0.121
0.416
0.222
−1.448
0.083
0.435
0.222
−1.627
0.138
0.417
0.222
−2.709
Note: In the Nash game, the home and foreign countries both have the debt shock of 0.22. We assign equal weights for the
two countries in the cooperative equilibrium. For the unilateral experiment, the foreign country keeps its pre-crisis capital
tax rate and adjusts its labor tax rate to maintain revenue neutrality, while the home country chooses its capital and labor
tax rate which maximizes its welfare subject to the debt requirement. In the neoclassical experiment, capacity utilization is
exogenous and θ is set at 0.22.
Table 9: ASYMMETRIC-COUNTRY NASH GAME OUTCOMES
Symmetric
Bench
Size
NFA
τK
Asymmetric
τL
GIIPS
τK
τL
∆PV(Primary Balance)/Y
∆Welfare v. pre-crisis
0.083
0.435
0.222
−1.627
0.070
0.438
0.222
−1.438
0.109
0.445
0.222
−3.245
0.080
0.436
0.222
−1.261
0.064
0.417
0.222
−0.603
EU 10
τK
τL
∆PV(Primary Balance)/Y
∆Welfare v. pre-crisis
0.083
0.435
0.222
−1.627
0.096
0.431
0.222
−1.698
0.064
0.431
0.222
−0.703
0.080
0.435
0.222
−1.594
0.102
0.454
0.222
−2.985
τC
Debt
All
0.073
0.433
0.222
−1.015
0.099
0.452
0.300
−3.503
0.066
0.435
0.300
−1.549
0.094
0.439
0.222
−2.318
0.073
0.426
0.180
−0.589
0.088
0.436
0.180
−1.127
Note: In the first six asymmetric experiments, we incorporate only one cross-country difference each time. For the size experiment, we
set ω to match the relative size between GIIPS and EU10. For the NFA experiment, we set the GIIPS pre-crisis current account as a
share of GDP at the observed level of −3%. In each of the three asymmetric tax experiments, we allow the corresponding precrisis tax
rates to vary across the two countries as in the data. Under the “Debt” column, we feed in the observed debt shocks for each country.
Under the “All” column, we incorporate all the above cross-country differences.
63
Table 10: GIIPS-EU10 GAME OUTCOMES
Pre-Crisis
GIIPS
τK
τL
∆PV(Primary Balance)/Y
∆Welfare v. pre-crisis
EU10
τK
τL
∆PV(Primary Balance)/Y
∆Welfare v. pre-crisis
Cooperative
Case 1
Case 2
Nash
Autarky
Unilateral
0.210
0.330
0.095
0.415
0.300
−1.032
0.057
0.420
0.300
−0.410
0.095
0.417
0.300
−1.238
0.112
0.414
0.300
−1.546
0.066
0.435
0.300
−1.549
0.200
0.360
0.121
0.421
0.180
−1.197
0.200
0.420
0
−0.511
0.122
0.420
0.180
−1.120
0.110
0.423
0.180
−0.924
0.088
0.436
0.180
−1.127
0.31
0.23
Weights
Note: For the cooperative equilibrium, Case 1 reports the most favorable allocation to GIIPS within the core; Case
2 reports the results most favorable to EU10 within the core. ’Weights’ report the social weight that the planner
assigns to GIIPS to obtain Pareto improvements over the Nash outcome. The weight assigned to EU10 is ’1-Weights’.
For the unilateral experiment, the foreign country keeps its pre-crisis capital tax rate and adjusts its labor tax rate
to satisfy the revenue neutrality, while the home country chooses its capital and labor tax rate which maximizes its
welfare subject to the debt requirement.
64
65
−2.11
−1.88
−1.27
−4.02
−1.56
−2.74
0.00
−7.63
−0.55
−0.45
−0.51
−1.02
−0.28
−0.57
0.00
−2.24
0.77
−0.10
−1.01
−0.37
0.00
0.00
−0.02
−0.04
−1.31
−0.30
∆Welfaress
∆Welfare
∆y1
∆yss
∆c1
∆css
∆k1
∆kss
∆tb1 /y1
∆tbss /yss
∆x1 /y1
∆xss /yss
∆r1
∆rss
∆l1
∆lss
∆m1
∆mss
7.44
−1.28
−7.04
−2.24
0.00
0.00
0.11
−0.19
−7.90
−1.79
−1.83
−8.51
−3.24
−5.93
0.00
−15.61
−4.48
−4.10
5.66
28.50
−0.53
1.10
0.96
0.62
0.00
1.10
−3.29
0.49
2.32
0.00
0.00
0.00
−0.09
0.20
−0.56
0.00
−0.77
0.10
0.66
0.00
0.00
0.00
−0.01
0.02
−0.10
0.00
−0.04
0.31
0.00
34.13
−7.46
1.14
4.99
0.00
0.00
0.00
−0.10
0.23
−1.27
0.00
−1.30
3.06
2.45
2.10
0.00
3.06
0.24
1.01
0.00
33.16
Foreign Country
a = 2.675
a = 7.5
−0.05
0.02
0.13
−0.15
0.00
0.02
−0.16
−0.06
0.00
34.68
a = 0.056
Note: The statistics with subscript ss denote changes in the steady state levels; while the statistics with subscript 1 indicate changes at
the impact period. For welfare, output, consumption and capital stocks, the statistics are in terms of percentage changes from the precrisis
steady states, while for primary balances over GDP, trade balances over GDP, investment over output, interest rates, labor supply and
utilization, the statistics are in terms of percentage point changes from the steady states.
3.30
−0.52
−3.40
−1.11
0.00
0.00
0.05
−0.20
−3.89
−0.89
5.66
5.66
∆PV(Primary Bal)/GDP
24.32
21.60
Home Country
a = 2.675
a = 7.5
τK (τL ) for H (F)
a = 0.056
(Foreign maintains revenue neutrality with labor tax)
Table 11: MACROECONOMIC EFFECTS UNDER DIFFERENT FRISCH ELASTICITIES
66
0.20
0.35
0.20
0.35
−0.14
0.48
0.18
5.79
−0.12
0.45
0.30
6.94
0.056
0.09
0.44
0.18
−1.13
0.07
0.44
0.30
−1.55
2.675
Nash
0.11
0.44
0.18
−2.67
0.10
0.45
0.30
−4.28
7.5
2.675
Cooperative
7.5
[−0.19, −0.17]
[0.12, 0.11]
[0.16, 0.15]
[0.49, 0.50]
[0.42, 0.42]
[0.41, 0.41]
0.18
0.18
0.18
[5.79, 5.92] [−1.12, −0.92] [−2.57, −1.89]
[0.00, 0.13]
[0.01, 0.20]
[0.10, 0.77]
[−0.17, −0.20]
[0.10, 0.11]
[0.14, 0.17]
[0.48, 0.47]
[0.41, 0.42]
[0.41, 0.41]
0.30
0.30
0.30
[6.95, 7.19] [−1.55, −1.24] [−4.18, −2.87]
[0.01, 0.25]
[0.00, 0.31]
[0.09, 1.41]
0.056
Note: For the cooperative games, we report the range of the cooperative outcomes in the core.
τK
τL
∆PV(Fiscal Bal)/GDP
∆Welfare v. pre-crisis
∆Welfare v. Nash
EU10
τK
τL
∆PV(Prim Bal)/GDP
∆Welfare v. pre-crisis
∆Welfare v. Nash
GIIPS
Frisch a
Pre-crisis
(Foreign maintains revenue neutrality with labor tax)
Table 12: GAME OUTCOMES UNDER DIFFERENT FRISCH ELASTICITIES
−0.18
0.49
0.18
6.20
0.41
−0.18
0.48
0.30
6.47
−0.47
0.056
0.12
0.42
0.22
−1.20
−0.07
0.10
0.42
0.30
−1.03
0.52
2.675
Autarky
0.17
0.41
0.18
−2.72
−0.06
0.14
0.41
0.30
−2.53
1.74
7.5
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